K4- 


The  Publishers  and  the  Authors  will  be  grateful  to 
any  of  the  readers  of  this  volume  who  will  kindly  call 
their  attention  to  any  errors  of  omission  or  of  commis- 
sion that  they  may  find  therein.  It  is  intended  to  make 
oui*  publications  standard  works  of  study  and  reference, 
and,  to  that  end,  the  greatest  accuracy  is  sought.  It 
rarely  happens  that  the  early  editions  of  works  of  any 
size  are  free  from  errors;  but  it  is  the  endeavor  of  the 
Publishers  to  have  them  removed  immediately  upon  being 
discovered,  and  it  is  therefore  desired  that  the  Authors 
may  be  aided  in  their  task  of  revision,  from  time  to  time, 
by  the  kindly  criticism  of  their  readers. 

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432  4TH  AVENUE. 


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WILLIAM  KENT,  M.E.,  Sc.D., 

Consulting  Engineer. 
Member  Amer.  Soc'y  Mechl.  Engrs.  and  Amer.  Inst.  Mining  Engrs. 


NINTH  EDITION,  THOROUGHLY  REVISED 

WITH  THE  ASSISTANCE   OF 

ROBERT  THURSTON  KENT,  M.  E., 

Consulting  Engineer. 
Junior  American  Society  of  Mechanical  Engineers. 

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LONDON:  CHAPMAN  &  HALL,  LIMITED 

1916 


COPYRIGHT,  1895,  1902,  1910,  1915, 

BY 

WILLIAM  KENT. 


Eighth  Edition  entered  at  Stationers'  Hall. 


Composition  and  Electrotyping  by  the  STANHOPE  PRESS,  Boston,  Mass.,  and 

the  PUBLISHERS  PRINTING  COMPANY,  New  York. 
Printing  and  Binding  by  BRAUNWORTH  &  COMPANY,  Brooklyn,  N.  Y. 


PREFACE  TO  THE  NINTH  EDITION. 

NOVEMBER,  1915. 

SINCE  the  eighth  edition  was  published,  five  years  ago,  there  have 
been  notable  advances  in  many  branches  of  engineering,  rendering 
obsolete  portions  of  the  book  which  at  that  time  were  in  accord  with 
practice.  In  addition,  many  engineering  standards  have  been  changed 
during  the  five-year  period,  necessitating  a  thorough  revision  of  many 
sections  of  the  work.  The  absolutely  necessary  revisions  to  bring  the 
book  up  to  date  -have  involved  changes  in  over  400  pages  of  the  eighth 
edition,  and  the  addition  of  over  150  pages  of  new  matter.  The 
treatment  of  many  subjects  in  the  earlier  edition  has  been  condensed 
into  smaller  space  to  enable  the  insertion  of  the  new  matter  without 
increasing  the  size  of  the  book  to  unwieldy  proportions.  Extensive 
revisions  have  been  made  in  the  subjects  of  materials,  mechanics, 
fans  and  blowers,  heating  and  ventilation,  fuel,  steam-boilers  and 
engines,  and  steam-turbines.  The  chapter  on  machine-shop  practice 
has  been  rewritten  and  doubled  in  size,  and  now  covers  many  subjects 
which  were  omitted  in  earlier  editions.  The  new  matter  includes 
many  data  on  planing,  milling,  drilling  and  grinding,  together  with 
an  elaborate  treatment  of  the  subject  of  machine-tool  driving.  The 
subject  of  electrical  engineering  has  been  completely  rewritten  and 
brought  into  agreement  with  present  practice.  Of  the  new  tables 
added  the  following  are  considered  of  special  importance.  Square 
roots  of  fifth  powers;  Four-place  logarithms;  Standard  sizes  of  welded 
steel  pipe;  Standard  pipe  flanges;  Properties  of  wire  rope;  Fire  brick 
and  other  refractories;  Properties  of  structural  sections  and  columns; 
Chemical  standards  for  iron  castings;  Flow  of  air,  water  and  steam; 
Analyses  and  heating  values  of  coals;  Rankine  efficiency;  Cooling 
towers;  Properties  of  ammonia;  -Power  required  for  driving  machine 
tools  of  all  types,  both  singly  and  in  groups;  Electric  resistance  and 
conductivity  of  wires;  Street  railway  installation;  Electric  lamp  char- 
acteristics; Illuminating  data. 

NOTE  TO  SECOND  PRINTING  OF  THE  NINTH 
EDITION. 

In  line  with  the  policy  of  keeping  the  book  up  to  date  and  elimi- 
nating all  obsolete  matter,  the  section  on  hydraulic  turbines  has  been 
completely  rewritten  for  the  second  printing  of  the  ninth  edition. 
The  presentation  of  the  theory  has  been  improved,  new  design  con- 
stants have  been  given,  and  the  tables  of  capacity,  etc.,  represent  the 
performance  of  the  most  recent  types  of  turbines. 

MARCH,  1917. 

iii 


40223,3 


IV  PREFACE. 


ABSTRACT  FROM  PREFACE  TO  THE 
FIRST  EDITION,  1895. 

MORE  than  twenty  years  ago  the  author  began  to  follow  the  advice 
given  by  Nystrom:  "  Every  engineer  should  make  his  own  pocket-book, 
as  he  proceeds  in  study  and  practice,  to  suit  his  particular  business." 
The  manuscript  pocket-book  thus  begun,  however,  soon  gave  place  to 
more  modern  means  for  disposing  of  the  accumulation  of  engineering 
facts  and  figures,  viz.,  the  index  rerum,  the  scrap-book,  the  collection  of 
indexed  envelopes,  portfolios  and  boxes,  the  card  catalogue,  etc.  Four 
years  ago,  at  the  request  of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to  mechanical 
engineering,  and  of  condensing,  digesting,  and  arranging  it  in  form  for 
publication.  In  addition  to  this,  a  careful  examination  was  made  of  the 
transactions  of  engineering  societies,  and  of  the  most  important  recent 
works  on  mechanical  engineering,  in  order  to  fill  gaps  that  might  be  left 
in  the  original  collection,  and  insure  that  no  important  facts  had  been 
overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  preparation  of  the 
Pocket-book  that  will,  it  is  believed,  cause  it  to  differ  from  other  works 
of  its  class.  In  the  first  place  it  was  considered  that  the  field  of  mechani- 
cal engineering  was  so  great,  and  the  literature  of  the  subject  so  vast,  that 
as  little  space  as  possible  should  be  given  to  subjects  which  especially 
belong  to  civil  engineering.  While  the  mechanical  engineer  must  con- 
tinually deal  with  problems  which  belong  properly  to  civil  engineering, 
this  latter  branch  is  so  well  covered  by  Traut wine's  "  Civil  Engineer's 
Pocket-book  "  that  any  attempt  to  treat  it  exhaustively  would  not  only 
fill  no  "  long-felt  want,"  but  would  occupy  space  which  should  be  given 
to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has  been  that  he 
would  not  assume  the  position  of  an  "  authority  "  in  giving  rules  and 
formulae  for  designing,  but  only  that  of  compiler,  giving  not  only  the 
name  of  the  originator  of  the  rule,  where  it  was  known,  but  also  the  volume 
and  page  from  which  it  was  taken,  so  that  its  derivation  may  be  traced 
when  desired.  When  different  formulas  for  the  same  problem  have  been 
found  they  have  been  given  in  contrast,  and  in  many  cases  examples 
have  been  calculated  by  each  to  show  the  difference  between  them.  In 
some  cases  these  differences  are  quite  remarkable,  as  will  be  seen  under 
Safety-valves  and  Crank-pins.  Occasionally  the  study  of  these  differences 
has  led  to  the  author's  devising  a  new  formula,  in  which  case  the  deriva- 
tion of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data  of  experiments 
from  recent  periodical  literature,  and  numerous  references  to  other  data 
are  given.  In  this  respect  the  present  work  will  be  found  to  differ  from 
other  Pocket-books. 

The  author  desires  to  express  his  obligation  to  the  many  persons  who 
huve  assisted  him  in  the  preparation  of  the  work,  to  manufacturers  who 


PREFACE.  V 

have  furnished  their  catalogues  and  given  permission  for  the  use  of  their 
tables,  and  to  many  engineers  who  have  contributed  original  data  and 
tables.  The  names  of  these  persons  are  mentioned  in  their  proper  places 
in  the  text,  and  in  all  cases  it  has  been  endeavored  to  give  credit  to  whom 
credit  is  due. 

WILLIAM  KENT. 


PREFACE  TO  THE  EIGHTH  EDITION. 

SEPTEMBER,  1910. 

DURING  the  first  ten  years  following  the  issue  of  the  first  edition  of  this 
book,  in  1895,  the  attempt  was  made  to  keep  it  up  to  date  by  the  method 
of  cutting  out  pages  and  paragraphs,  inserting  new  ones  in  their  places,  by 
inserting  new  pages  lettered  a,  b,  c,  etc.,  and  by  putting  some  new  matter 
in  an  appendix.  In  this  way  the  book  passed  to  its  7th  edition  in  October, 
1904.  After  50,000  copies  had  been  printed  it  was  found  that  the  electro- 
typed  plates  were  beginning  to  wear  out,  so  that  extensive  resetting  of  type 
would  soon  be  necessary.  The  advances  in  engineering  practice  also  had 
been  so  great  that  it  was  evident  that  many  chapters  required  to  be  entirely 
rewritten.  It  was  therefore  determined  to  make  a  thorough  revision  of  the 
book,  and  to  reset  the  type  throughout.  This  has  now  been  accomplished 
after  four  years  of  hard  labor.  The  size  of  the  book  has  increased  over  300 
pages,  in  spite  of  all  efforts  to  save  space  by  condensation  and  elision  of 
much  of  the  old  matter  and  by  resetting  many  of  the  tables  and  formulae 
in  shorter  form.  A  new  style  of  type  for  the  tables  has  been  designed  for 
the  book,  which  is  believed  to  be  much  more  easily  read  than  the  old. 

The  thanks  of  the  author  are  due  to  many  manufacturers  who  ha^re  fur- 
nished new  tables  of  materials  and  machines,  and  to  many  engineers  who 
have  made  valuable  contributions  and  helpful  suggestions.  He  is  especially 
indebted  to  his  son,  Robert  Thurston  Kent,  M.E.,  who  has  done  the  work 
of  revising  manufacturers'  tables  of  materials  and  has  done  practically  all 
of  the  revising  of  the  subjects  of  Compressed  Air,  Fans  and  Blowers,  Hoist- 
ing  and  Conveying,  and  Machine  Shop. 


CONTENTS. 

(For  Alphabetical  Index  see  page  1479.) 

MATHEMATICS. 

Arithmetic. 

PAGE 

Arithmetical  and  Algebraical  Signs 1 

Greatest  Common  Divisor 2 

Least  Common  Multiple 

Fractions 

Decimals 

Table.     Decimal  Equivalents  of  Fractions  of  One  Inch 3 

Table.     Products  of  Fractions  expressed  in  Decimals 

Compound  or  Denominate  Numbers 5 

Reduction  Descending  and  Ascending 5 

Decimals  of  a  Foot  Equivalent  to  Fractions  of  an  Inch 5 

Ratio  and  Proportion 6 

Involution,  or  Powers  of  Numbers 7 

Table.     First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.     First  Forty  Powers  of  2 8 

Evolution.     Square  Root 8 

Cube  Root 9 

Alligation 9 

Permutation 10 

Combination 10 

Arithmetical  Progression 10 

Geometrical  Progression 11 

Percentage,  Profit  and  Loss,  Efficiency 12 

Interest 12 

Discount 13 

Compound  Interest 

Compound  Interest  Table,  3,  4,  5,  and  6  per  cent 

Equation  of  Payments >, 

Partial  Payments 14 

Annuities 15 

Tables  of  Amount,  Present  Values,  etc.,  of  Annuities 15 

Weights  and  Measures. 

Long  Measure 17 

Old  Land  Measure 17 

Nautical  Measure 17 

Square  Measure 

Solid  or  Cubic  Measure 

Liquid  Measure 

The  Miners'  Inch 

Apothecaries'  Fluid  Measure 

Dry  Measure i ~ 19 

Shipping  Measure 

Avoirdupois  Weight 19 

Troy  Weight 19 

Apothecaries'  Weight 20 

To  Weigh  Correctly  on  an  Incorrect  Balance 20 

Circular  Measure 20 

Measure  of  Time 20 

vii 


Vlll  CONTENTS. 

PAGE 

Board  and  Timber  Measure 20 

Table.     Contents  in  Feet  of  Joists,  Scantlings,  and  Timber.  ...  21 

French  or  Metric  Measures 21 

British  and  French  Equivalents 22 

Metric  Conversion  Tables 23 

Compound  Units 

of  Pressure  and  Weight 27 

of  Water,  Weight  and  Bulk 27 

of  Air,  Weight  and  Volume 27 

of  Work,  Power,  and  Duty .  27 

of  Velocity 4 27 

Wire  and  Sheet  Metal  Gages 28 

Circular-mil  Wire  Gage 29,  30 

U.  S.  Standard  Wire  and  Sheet  Gage  (1893) 29,  32 

Twist-drill  and  Steel-wire  Gages 31 

Decimal  Gage 32 

Algebra. 

Addition,  Multiplication,  etc 33 

Powers  of  Numbers 

Parentheses,  Division 

Simple  Equations  and  Problems 

Equations  containing  two  or  more  Unknown  Quantities 

Elimination 

Quadratic  Equations 

Theory  of  Exponents 

Binominal  Theorem 

Geometrical  Problems  of  Construction 

of  Straight  Lines 37 

^f  Angles 38 

of  Circles 39 

of  Triangles 

of  Squares  and  Polygons 

of  the  Ellipse 45 

of  the  Parabola 

of  the  Hyperbola 

of  the  Cycloid 50 

of  the  Tractrix  or  Schiele  Anti-friction  Curve 50 

of  the  Spiral 51 

of  Rings  inside  a  Circle '51 

of  Arc  of  a  Large  Circle 51 

of  the  Catenary 52 

of  the  Involute 52 

of  plotting  Angles 

Geometrical  Propositions 53 

Degree  of  a  Railway  Curve 54 

Mensuration,  Plane  Surfaces. 

Quadrilateral,  Parallelogram,  etc 54 

Trapezium  and  Trapezoid 54 

Triangles 54 

Polygons.     Table  of  Polygons 55 

Irregular  Figures 56 

Properties  of  the  Circle 57 

Values  of  TT  and  its  Multiples,  etc 57 

Relations  of  arc,  chord,  etc 58 

Relations  of  circle  to  inscribed  square,  etc 59 

Formulse  for  a  Circular  Curve 59 

Sectors  and  Segments 60 

Circular  Ring 60 

The  Ellipse 60 

The  Helix 61 

The  Spiral 61 

Surfaces  and  Volumes  of  Similar  Solids 61 


CONTENTS.  ix 

Mensuration,  Solid  Bodies.  PAGE 

Prism 62 

Pyramid 62 

Wedge 62 

Rectangular  Prismoid 62 

Cylinder 62 

Cone 62 

Sphere 62 

Spherical  Triangle 63 

Spherical  Polygon 63 

The  Prismoid 63 

The  Prismoidal  Formula 63 

Polyedron 63 

Spherical  Zone 64 

Spherical  Segment 64 

Spheroid  or  Ellipsoid 64 

Cylindrical  Ring ; 64 

Solids  of  Revolution 64 

Spindles 64 

Frustum  of  a  Spheroid 64 

Parabolic  Conoid 65 

Volume  of  a  Cask 65 

'Irregular  Solids 65 

Plane  Trigonometry. 

Solution  of  Plane  Triangles 66 

Sine,  Tangent,  Secant,  etc ...'..' 66 

Signs  of  the  Trigonometric  Functions 67 

Trigonometrical  Formulae 68 

Solution  of  Plane  Right-angled  Triangles 69 

Solution  of  Oblique-angled  Triangles 69 

Analytical  Geometry. 

Ordinates  and  Abscissas 70 

Equations  of  a  Straight  Line,  Intersections,  etc 70 

Equations  of  the  Circle 71 

Equations  of  the  Ellipse 71 

Equations  of  the  Parabola 72 

Equations  of  the  Hyperbola 72 

Logarithmic  Curves 73 

Differential  Calculus. 

Definitions 73 

Differentials  of  Algebraic  Functions 74 

Formulae  for  Differentiating 74 

Partial  Differentials 75 

Integrals 75 

Formulae  for  Integration 75 

Integration  between  Limits 76 

Quadrature  of  a  Plane  Surface 76 

Quadrature  of  Surfaces  of  Revolution 77 

Cubature  of  Volumes  of  Revolution ' 77 

Second,  Third,  etc.,  Differentials 77 

Maclaurin's  and  Taylor's  Theorems 78 

Maxima  arid  Minima 78 

Differential  of  an  Exponential  Function 79 

Logarithms 79 

Differential  Forms  which  have  Known  Integrals 80 

Exponential  Functions .  . 80 

Circular  Functions 81 

The  Cycloid 81 

Integral  Calculus 82 


X  CONTENTS. 

The  Slide  Bule. 

Examples  solved  by  the  Slide  Rule .  .  . 82 

Logarithmic  Ruled  Paper. 

Plotting  on  Logarithmic  Paper 84 

Mathematical  Tables. 

Formula  for  Interpolation 86 

Reciprocals  of  Numbers  1  to  2000 

Squares,  Cubes,  Square  Roots  and  Cube  Roots  from  0.1  to  1600 

Squares  and  Cubes  of  Decimals 108 

Fifth  Roots  and  Fifth  Powers 109 

Square  Roots  of  Fifth  Powers  of  Pipe  Sizes 

Circumferences  and  Areas  of  Circles Ill 

Circumferences  of  Circles  in  Feet  and  Inches  from  1  inch  to  32 

feet  11  inches  in  diameter 

Areas  of  the  Segments  of  a  Circle 

Lengths  of  Circular  Arcs,  Degrees  Given 

Lengths  of  Circular  Arcs,  Height  of  Arc  Given 

Circles  and  Squares  of  Equal  Area 125 

Number  of  Circles  Inscribed  within  a  Large  Circle 125 

Spheres 126 

Square  Feet  in  Plates  3  to  32  feet  long  and  1  inch  wide 128 

Gallons  in  a  Number  of  Cubic  Feet 

Cubic  Feet  in  a  Number  of  Gallons 130 

Contents  of  Pipes  and  Cylinders,  Cubic  Feet  and  Gallons 

Cylindrical  Vessels,  Tanks,  Cisterns,  etc 132 

Capacities  of  Rectangular  Tanks  in  Gallons 

Number  of  Barrels  in  Cylindrical  Cisterns  and  Tanks 

Logarithms 135 

Table  of  Logarithms 

Hyperbolic  Logarithms 

Four-place  Logarithms  of  Numbers  from  1  to  1000 167 

Natural  Trigonometric  Functions 169 

Logarithmic  Trigonometric  Functions 172 

MATERIALS. 

Chemical  Elements 173 

Specific  Gravity  and  Weight  of  Materials 173 

The  Hydrometer : 175 

Metals,  Properties  of 

Aluminum 177 

Antimony 177 

Bismuth 178 

Cadmium 178 

Copper 178 

Gold 178 

Iridium 178 

Iron 178 

Lead 178 

Magnesium 179 

Manganese 179 

Mercury : 179 

Nickel 179 

Platinum 179 

Silver 179 

Tin 179 

Zinc 179 

Miscellaneous  Materials. 

Order  of  Malleability,  etc.,  of  Metals 180 

Measures  and  Weights  of  Various  Materials 180 


CONTENTS.  XI 

PAGE 

Formulae  and  Table  for  Weight  of  Rods,  Plates,  etc 181 

Commercial  Sizes  of  Iron  and  Steel  Bars 182 

Weights  of  Iron  and  Steel  Sheets 183 

of  Iron  Bars 184 

of  Round  Steel  Bars 185 

of  Fillets 185 

of  Round,  Square,  and  Hexagon  Steel 186 

of  Plate  Iron 187 

of  Flat  Rolled  Iron 188 

of  Steel  Blooms 190 

of  Roofing  Materials 191-196 

Snow  and  Wind  Loads  on  Roofs 191 

Roof  Construction 191 

Specifications  for  Tin  and  Terne  Plates 194 

Corrugated  Sheets 194 

Weights  and  Thickness  of  Cast-iron  Pipe 196-199 

Weights  of  Cast-iron  Pipe  Columns 200 

Weight  of  Open-end  Cast-iron  Cylinders 200 

Standard  Sizes  of  Welded  Pipe 201-205 

Weight  and  Bursting  Strength  of  Welded  Pipe 205 

Tubular  Electric  Line  Poles 206 

Protective  Coatings  for  Pipes 206 

Valves  and  Fittings 206-217 

Standard  Pipe  Flanges 208-212 

Forged  Steel  Flanges 211 

Standard  Hose  Couplings 218 

Wooden  Stave  Pipe.  .  .• 218 

Riveted  Hydraulic  Pipe 219 

Riveted  Iron  Pipes 220 

Spiral  Riveted  Pipe 220 

Weight  of  Steel  for  Riveted  Pipe 221 

Bent  and  Coiled  Pipes 221 

Flexibility  of  Pipe  Bends 221 

Shelby  Cold-drawn  Steel  Tubing 222 

Seamless  Brass  and  Copper  Tubes 224,  225 

Aluminum  Tubing 226 

Lead  and  Tin-lined  Lead  Pipe 226 

Iron  Pipe  Lined  with  Tin,  Lead,  Brass,  and  Copper 227 

Weight  of  Sheet  and  Bar  Brass 228 

of  Sheet  Zinc 228 

of  Copper  and  Brass  Wire  and  Plates 229 

of  Aluminum  Sheets,  Bars,  and  Plates 230 

of  Copper  Rods 230 

Screw-threads,  U.  S.  Standard 231 

Whitworth  Screw-threads 232 

Limit-gages  for  Screw-threads .  .  .  .  : 232 

Automobile  Screws  and  Nuts 233 

International  Screw-thread 233 

Acme  Screw-thread 234 

Machine  Screws,  A.  S.  M.  E.  Standard 234 

Standard  Taps 235 

Wood  Screws 236 

Machine  Screw  Heads 237 

Set  Screws  and  Cap  Screws 238 

Weights  of  Rivets 238,  239 

Shearing  Value  of  Rivets.  Bearing  Value  of  Riveted  Plates 240 

Length  of  Rivets  for  Various  Grips 241 

Lag  Screws 241 

Weight  of  Bolts  with  Square  Heads  and  Nuts 242 

Washers .242,  243 

Hanger  Bolts 243 

Turnbuckles 243 

Track  Bolts 244 

Cut  Nails 244 

Material  Required  per  Mile  of  Railroad  Track 245 

Wire  Nails 246 

Spikes.  .,,,,,,,*,, 248 


Xii  CONTENTS. 

PAGE 

Wires  of  Different  Metals 248 

Steel  Wire,  Size,  Strength,  etc 249 

Piano  Wire 250 

Telegraph  Wire 250-252 

Plow-steel  Wire 250,  258 

Galvanized  Iron  Wire 250 

Copper  Wire,  Bare  and  Insulated 251,  252 

Notes  on  Wire  Rope 253 

Wire  Rope  Tables 255-262 

Varieties  and  Uses  of  Wire  Rope 256 

Splicing  of  Wire  Ropes 263 

Chains  and  Chain  Cables 264 

Sizes  of  Fire  Brick 266 

Refractoriness  of  American  Fire-brick 268 

Slag  Bricks  and  Slag  Blocks 268 

Magnesia  Bricks 269 

Fire  Clay  Analysis 269 

Zirconia 270 

Asbestos 270 

Standard  Cross-sections  of  Materials,  for  Draftsmen 271 

Strength  of  Materials. 

Stress  and  Strain 272 

Elastic  Limit 273 

Yield  Point 273 

Modulus  of  Elasticity 274 

Resilience 274 

Elastic  Limit  and  Ultimate  Stress 275 

Repeated  Stresses 275 

Repeated  Shocks 276 

Stresses  due  to  Sudden  Shocks 278 

Tensile  Strength 278 

Measurement  of  Elongation 279 

Shapes  of  Test  Specimens 280 

Increasing  Tensile  Strength  of  Bars  by  Twisting 280 

Compressive  Strength 281 

Columns,  Pillars,  or  Struts 283 

Hodgkinson's  Formula.     Euler's  Formula 

Gordon's  Formula.     Rankine's  Formula 

Wrought-iron  Columns 2S5 

Built  Columns 285-286 

The  Straight-line  Formula 285 

Comparison  of  Column  Formulae 286 

Tests  of  Large  Built  Steel  Columns 287 

Working  Strains  in  Bridge  Members 287 

Strength  of  Cast-iron  Columns 

Safe  Load  on  Cast-iron  Columns 291 

Strength  of  Brackets  on  Cast-iron  Columns 292 

Moment  of  Inertia 293 

Radius  of  Gyration 293 

Elements  of  Usual  Sections 

Eccentric  Loading  of  Columns 296 

Transverse  Strength 297 

Formulae  for  Flexure  of  Beams 297 

Safe  Loads  on  Steel  Beams 298,  309 

Beams  9f  Uniform  Strength 301 

Dimensions  and  Weights  of  Structural  Steel  Sections 302 

Allowable  Tension  in  Steel  Bars 305 

Properties  of  Rolled  Structural  Shapes 305 

"  Steel  I-Beams , 307 

"  Steel  Wrought  Plates 308 

"  Corrugated  Plates 310 

Spacing  of  Steel  I-Beams 311 

Properties  of  Steel  Channels 312 

"  T  Shapes 313 


CONTENTS.  .  Xlll 

PAGE 

Properties  of  Angles 316 

"  Z-bars 317 

Rivet  Spacing  for  Structural  Work 321 

Dimensions  and  Safe  Load  on  Built  Steel  Columns 323-330 

Bethlehem  Girder  and  I-beams  and  H-columns 331 

Torsional  Strength 334 

Elastic  Resistance  to  Torsion 334 

Combined  Stresses 335 

Stress  due  toTemperature 335 

Strength  of  Flat  Plates 336 

Thickness  of  Flat  Cast-iron  Plates 336 

Strength  of  Unstayed  Flat  Surfaces 337 

Unbraced  Heads  of  Boilers 337 

Strength  of  Stayed  Surfaces 338 

Stresses  in  Steel  Plating  under  Water  Pressure 338 

Spherical  Shells  and  Domed  Heads 339 

Thick  Hollow  Cylinders  under  Tension 339 

Thin  Cylinders  under  Tension 340 

Carrying  Capacity  of  Steel  Rollers  and  Balls 340 

Resistance  of  Hollow  Cylinders  to  Collapse 341,  343 

Formula  for  Corrugated  Furnaces 342 

Hollow  Copper  Balls 345 

Holding.  Power  of  Nails,  Spikes,  Bolts,  and  Screws 346 

Cut  versus  Wire  Nails 347 

Strength  of  Bolts 347 

Initial  Strain  on  Bolts 347 

Strength  of  Chains 348 

Stand  Pipes  and  their  Design 349 

Riveted  Steel  Water-pipes 351 

Kirkaldy's  Tests  of  Materials 352-358 

Cast  Iron 352 

Iron  Castings 352 

Iron  Bars,  Forgings,  etc 352--. 

Steel  Rails  and  Tires 353 

Spring  Steel,  Steel  Axles,  Shafts 354 

Riveted  Joints,  Welds 355 

Copper,  Brass,  Bronze,  etc 356 

Wire-rope 356 

Wire 357 

Ropes,  Hemp,  and  Cotton . .  357 

Belting,  Canvas 357 

Stones 357 

Brick,  Cement,  Wood 358 

Tensile  Strength  of  Wire 358 

Watertown  Testing-machine  Tests 359 

Riveted  Joints 359 

Wrought-iron  Bars,  Compression  Tests 359 

Steel  Eye-bars 360 

Wrought-iron  Columns 360 

Cold  Drawn  Steel 361 

Tests  of  Steel  Angles x .  .  362 

Shearing  Strength 362 

Relation  of  Shearing  to  Tensile  Strength 362 

Strength  of  Iron  and  Steel  Pipe 363 

Threading  Tests  of  Pipe 363 

Old  Tubes  used  as  Columns 363 

Methods  of  Testing  Hardness  of  Metals 364 

Holding  Power  of  Boiler-tubes 364 

Strength  of  Glass 365 

Strength  of  Ice 366 

Strength  of  Timber 366 

Expansion  of  Timber 367,  369 

Tests  of  American  Woods . 367 

Shearing  Strength  of  Woods 367 

Copper  at  High  Temperatures 368 

Drying  of  Wood 368 

Preservation  of  Timber « 368 


XIV  CONTENTS. 

PAGE 

Copper  Castings  of  High  Conductivity 368 

Tensile  Strength  of  Rolled  Zinc  Plates 369 

Strength  of  Brick,  Stone,  etc.  .  '. 369 

"  Lime  and  Cement  Mortar. 372 

"  Flagging .'.'.'  373 

Tests  of  Portland  Cement 373 

Moduli  of  Elasticity  of  Various  Materials 374 

Factors  of  Safety 374 

Properties  of  Cork 377 

Vulcanized  India-Rubber 378 

Specifications  for  Air  Hose 379 

Nickel 379 

Aliuninum,  Properties  and  Uses 380 

Alloys. 

Alloys  of  Copper  and  Tin,  Bronze 384 

Alloys  of  Copper  and  Zinc,  Brass 386 

Variation  in  Strength  of  Bronze 386 

Copper-tin-zinc  Alloys 387 

Liquation  or  Separation  of  Metals 388 

Alloys  used  in  Brass  Foundries 390 

Tobin  Bronze 392 

Qualities  of  Miscellaneous  Alloys 392 

Copper-zinc-iron  Alloys 393 

'  Alloys  of  Copper,  Tin,  and  Lead 394 

Phosphor  Bronze 394 

Alloys  for  Casting  under  Pressure 395 

Aluminum  Alloys 396 

Caution  as  to  Strength  of  Alloys 398 

Alloys  of  Aluminum,  Silicon,  and  Iron 398 

Tungsten-aluminum  Alloys 399 

The  Thermit  Process 400 

Aluminum-tin  Alloys 400 

Manganese  Alloys 401 

Manganese  Bronze 401 

German  Silver 402 

Monel  Metal 403 

Copper-nickel  Alloys 403 

Alloys  of  Bismuth .404 

Fusible  Alloys 404 

Bearing  Metal  Alloys 405 

Bearing  Metal  Practice,  1907 407 

White  Metal  for  Engine  Bearings 407 

Alloys  containing  Antimony 407 

White-metal  Alloys 407 

Babbitt  Metals 407,  408 

Type-metal 408 

Solders 409 

Ropes  and  Cables. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes 410 

Rope  for  Hoisting  or  Transmission 411 

Cordage,  Technical  Terms  of 411 

Splicing  of  Ropes 412 

Cargo  Hoisting 414 

Working  Loads  for  Manila  Rope  .  .                     414 

Knots 415 

Life  of  Hoisting  and  Transmission  Rope 415 

Efficiency  of  Rope  Tackles 415 

Springs. 

Laminated  Steel  Springs 417 

Helical  Steel  Springs 418 


CONTENTS.  XV 

PAGE 

Carrying  Capacity  of  Springs 419 

Elliptical  Springs 423 

Springs  to  Resist  Torsional  Force 423 

Phosphor-bronze  Springs 424 

Chromium-Vanadium  Spring  Steel 424 

Test  of  a  Vanadium  Steel  Spring 424 

Riveted  Joints. 

Fairbairn's  Experiments 424 

Loss  of  Strength  by  Punching 424 

Strength  of  Perforated  Plates 424 

Hand  versus  Hydraulic  Riveting 424 

Formulae  for  Pitch  of  Rivets 427,  434 

Proportions  of  Joints 427 

Efficiencies  of  Joints 428 

Diameter  of  Rivets 429 

Shearing  Resistance  of  Rivet  Iron  and  Steel 430 

Strength  of  Riveted  Joints 431 

Riveting  Pressures 435 

Tests  of  Soft  Steel  Rivets 435 

Iron  and  Steel. 

Classification  of  Iron  and  Steel 436 

Grading  of  Pig  Iron 437 

Manufacture  of  Cast  Iron 437 

Influence  of  Silicon  Sulphur,  Phos.  and  Mn  on  Cast  Iron 438 

Microscopic  Constituents • 439 

Analyses  of  Cast  Iron 439 

Specifications  for  Pig  Iron  and  Castings 441,  443 

Specifications  for  Cast-iron  Pipe 441 

Chemical  Standards  for  Castings 441 

Strength  of  Cast  Iron 444,  451 

Strength  in  Relation  to  Cross-section 446,  447 

"  Semi-steel " 446,  453 

Shrinkage  of  Cast  Iron 447 

White  Iron  Converted  into  Gray 448 

Mobility  of  Molecules  of  Cast  Iron 449 

Expansion  of  Iron  by  Heat 449,  465 

Permanent  Expansion  of  Cast  Iron  by  Heating 449 

Castings  from  Blast  Furnace  Metal 450 

Effect  of  Cupola  Melting 450 

Additions  of  Titanium,  etc.,  to  Cast  Iron 450,  451 

Mixture  of  Cast  Iron  with  Steel 453 

Bessemerized  Cast  Iron 453 

Bad  Cast  Iron «-. 453 

Malleable  Cast  Iron ! 454 

Design  of  Malleable  Castings 457 

Specifications  of  Malleable  Iron 457 

Strength  of  Malleable  Cast  Iron 458 

Wrought  Iron 459 

Chemistry  of  Wrought  Iron 460 

Electrolytic  Iron 460 

Influence  of  Rolling  on  Wrought  Iron 460 

Specifications  for  Wrought  Iron 461 

Stay-bolt  Iron 462 

Tenacity  of  Iron  at  High  Temperatures 463 

Effect  of  Cold  on  Strength  of  Iron 464 

Durability  of  Cast  Iron 465 

Corrosion  of  Iron  and  Steel 466 

Corrosion  of  Iron  and  Steel  Pipes 467 

Electrolytic  Theory,  and  Prevention  of  Corrosion 468 

Chrome  Paints,  Anti-corrosive 469 

Corrosion  Caused  by  Stray  Electric  Currents 470 

Electrolytic  Corrosion  due  to  Overstrain 470 


XVI  CONTENTS. 

PAGE 

Preservative  Coatings,  Paints,  etc 471 

Inoxydation  Processes,  Bower-Barff,  etc 472 

Aluminum  Coatings 473 

Galvanizing 473 

Sherardizing,  Galvanizing  by  Cementation 474 

Lead  Coatings 474 

Steel. 

Manufacture  of  Steel 475 

Crucible,  Bessemer,  and  Open  Hearth  Steel 475 

Relation  between  Chemical  and  Physical  Properties 476 

Electric  Conductivity 477 

"  Armco  Ingot  Iron  " 477 

Variation  in  Strength 477,  478 

Bending  Tests  of  Steel 478 

Effect  of  Heat  Treatment  and  of  Work 478 

Hardening  Soft  Steel 479 

Effect  of  Cold  Rolling 479 

Comparison  of  Full-sized  and  Small  Pieces 480 

Recalescence  of  Steel 480 

Critical  Point 480 

Metallography 480 

Burning,  Overheating,  and  Restoring  Steel 481 

Working  Steel  at  a  Blue  Heat 482 

Oil  Tempering  and  Annealing 482 

Brittleness  due  to  Long-continued  Heating 483 

Influence  of  Annealing  upon  Magnetic  Capacity 483 

Treatment  of  Structural  Steel 483 

May  Carbon  be  Burned  out  of  Steel? 485 

Effect  of  Nicking  a  Bar 485 

Dangerous  Low  Carbon  Steel 486 

Specific  Gravity 486 

Occasional  Failures 486 

Segregation  in  Ingots  and  Plates 487 

Endurance  of  Steel  under  Repeated  Stresses 487 

Welding  of  Steel 488 

The  Thermit  Welding  Process 488 

Oxy-acetylene  Welding  and  Cutting  of  Metals 488 

Hydraulic  Forging 488 

Fluid-compressed  .Steel 488 

Steel  Castings 489 

Crucible  Steel 490 

Effect  of  Heat  on  Gram 491 

Heating  and  Forging 491 

Tempering  Steel 493 

Kinds  of  Steel  used  for  Different  Purposes 494 

High-speed  Tool  Steel 

Manganese  Steel- 494 

Chrome  Steel 496 

Aluminum  Steel 496 

Tungsten  Steel 496 

Nickel  Steel 497 

Copper  Steel 499 

Nickel- Vanadium  Steel 499 

Static  and  Dynamic  Properties  of  Steel 500 

Strength  and  Fatigue  Resistance  of  Steels 501 

Chromium- Vanadium  Steel • 502 

Heat  Treatment  of  Alloy  Steels 502,  503 

Specifications  for  Steel 504-51 1 

High-strength  Steel  for  Shipbuilding 507 

Fire-box  Steel 508 

Steel  Rails 508 

MECHANICS. 

Matter,  Weight,  Mass 511 

Force,  Unit  of  Force 512 


CONTENTS.  XVli 

PAGE 

Local  Weight * 512 

Inertia 513 

Newton's  Laws  of  Motion 513 

Resolution  of  Forces 513 

Parallelogram  of  Forces 513 

Moment  of  a  Force .      .  514 

Statical  Moment,  Stability 515 

Stability  of  a  Dam 515 

Parallel  Forces 515 

Couples 515 

Equilibrium  of  Forces 516 

Center  of  Gravity 516 

Moment  of  Inertia 517 

Centers  of  Oscillation  and  Percussion 518 

Center  and  Radius  of  Gyration 518 

The  Pendulum 520 

Conical  Pendulum 520 

Centrifugal  Force 521 

Velocity,  Acceleration,  Falling  Bodies 521 

Value  of  g 522 

Angular  Velocity 522 

Height  due  to  Velocity 523 

Parallelogram  of  Velocities 522 

Velocity  due  to  Falling  a  Given  Height 524 

Fundamental  Equations  in  Dynamics 525 

Force  of  Acceleration 526 

Formulae  for  Accelerated  Motion 527 

Motion  on  Inclined  Planes '.- 527 

Momentum 527 

Work,  Energy,  Power 528 

Work  of  Acceleration 529 

Work  of  Accelerated  Rotation .  . 529 

Force  of  a  Blow 529 

Impact  of  Bodies 530 

Energy  of  Recoil  of  Guns 531 

Conservation  of  Energy.  .  . T 531 

Sources  of  Energy 531 

Perpetual  Motion 532 

Efficiency  of  a  Machine 532 

Animal-power,  Man-power 532 

Man-wheel,  Tread  Mills 533 

Work  of  a  Horse 533 

Horse-gin 534 

Resistance  of  Vehicles 534 


Elements  of  Mechanics. 

The  Lever.  .  535 

The  Bent  Lever 536 

The  Moving  Strut 536 

The  Toggle-joint 536 

The  Inclined  Plane 537 

The  Wedge 537 

The  Screw 537 

The  Cam 537 

Efficiency  of  a  Screw 538 

Efficiency  of  Screw  Bolts 538 

Pulleys  or  Blocks '. 539 

Differential  Pulley 539 

Wheel  and  Axle 539 

Toothed- wheel  Gearing 539 

Endless  Screw,  Worm  Gear 540 

Differential  Windlass 540 

Differential  Screw 540 

Efficiency  of  a  Differential  Screw 641 


XV1U  CONTENTS. 

Stresses  in  Framed  Structures. 

Cranes  and  Derricks 541 

Shear  Poles  and  Guys 542 

King  Post  Truss  or  Bridge 543 

Queen  Post  Truss 543 

Burr  Truss 544 

Pratt  or  Whipple  Truss 544 

Method  of  Moments 545 

Howe  Truss 546 

Warren  Girder 546 

Roof  Truss 547 

The  Economical  Angle 548 

HEAT. 

Thermometers  and  Pyrometers 549 

Centigrade  and  Fahrenheit  degrees  compared . 550 

Temperature  Conversion  Table 552 

Copper-ball  Pyrometer 553 

Thermo-electric  Pyrometer 554 

Temperatures  in  Furnaces 554 

Seger's  Fire-clay  Pyrometer 555 

Wiborgh  Air  Pyrometer 655 

Mesure  and  Nouel's  Pyrometer 556 

Uehling  and  Steinbart  Pyrometer 557 

Air- thermometer 557 

High  Temperatures  Judged  by  Color 558 

Boiling-points  of  Substances 559 

Melting-points 559 

Unit  of  Heat 560 

Mechanical  Equivalent  of  Heat 560 

Heat  of  Combustion 560 

Heat  Absorbed  by  Decomposition 561 

Specific  Heat 562 

Thermal  Capacity  of  Gases 564 

Expansion  by  Heat 565 

Absolute  Temperature,  Absolute  Zero 567 

Latent  Heat  of  Fusion §68 

Latent  Heat  of  Evaporation 568 

Total  Heat  of  Evaporation 569 

Evaporation  and  Drying 569 

Evaporation  from  Reservoirs • 569 

Evaporation  by  the  Multiple  System 570 

Resistance  to  Boiling *  . .  570 

Manufacture  of  Salt 570 

Solubility  of  Salt 571 

Salt  Contents  of  Brines 571 

Concentration  of  Sugar  Solutions 572 

Evaporating  by  Exhaust  Steam 572 

Drying  in  Vacuum 573 

Driers  and  Drying 574 

Design  of  Drying  Apparatus 576 

Humidity  Table 577 

Radiation  of  Heat 578 

Black-body  Radiation 579 

Conduction  and  Convection  of  Heat 579 

Rate  of  External  Conduction 580 

Heat  Conduction  of  Insulating  Materials 581 

Heat  Resistance,  Reciprocal  of  Heat  Conductivity 582 

Steam-pipe  Coverings 584 

Transmission  through  Plates 587 

Transmission  in  Condenser  Tubes 588 

Transmission  of  Heat  in  Feed-water  Heaters 590 

Transmission  through  Cast-iron  Plates 591 

Heating  Water  by  Steam  Coils 591 

Transmission  from  Air  or  Gases  to  Water 592 


CONTENTS.  XIX 

PAGE 

Transmission  from  Flame  to  Water 593 

Cooling  of  Air 594 

Transmission  from  Steam  or  Hot  Water  to  Air 595 

Thermodynamics 597 

Entropy 599 

Reversed  Carnot  Cycle,  Refrigeration .  .  , 600 

Principal  Equations  of  a  Perfect  Gas 600 

Construction  of  the  Curve  PV«  =  C 602 

Temperature-Entropy  Diagram  of  Water  and  Steam 602 

PHYSICAL  PROPERTIES   OF   GASES. 

Expansion  of  Gases 603 

Boyle  and  Marriotte's  Law 603 

Law  of  Charles,  Avogadro's  Law 604 

Saturation  Point  of  Vapors 604 

Law  of  Gaseous  Pressure 604 

Flow  of  Gases 605 

Absorption  by  Liquids 605 

Liquefaction  of  Gases,  Liquid  Air 605 

AIR. 

Properties  of  Air 606 

Barometric  Pressures 606 

Air-manometer 607 

Conversion  Table  for  Air  Pressures 607 

Pressure  at  Different  Altitudes 607,  609 

Leveling  by  the  Barometer  and  by  Boiling  Water 607 

To  find  Difference  in  Altitude 608 

Weight  of  Air  at  Different  Pressures  and  Temperatures 609 

Moisture  in  Atmosphere 609,  611 

Humidity  Table 610 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 610,  613 

Specific  Heat  of  Air 614 

Flow  of  Air. 

Flow  of  Air  through  Orifices 615 

Flow  of  Air  in  Pipes 617 

Tables  of  Flow  of  Air 622,  623 

Effects  of  Bends  in  Pipe 624 

Anemometer  Measurements 624 

Equalization  of  Pipes 625 

Wind. 

Force  of  the  Wind 626 

Wind  Pressure  in  Storms 627 

Windmills 627 

Capacity  of  Windmills 629 

Economy  of  Windmills 630 

Electric  Power  from  Windmills 632 

Compressed  Air. 

Heating  of  Air  by  Compression 632 

Loss  of  Energy  in  Compressed  Air 632 

Loss  due  to  Heating 633 

Work  of  Adiabatic  Compression  of  Air 634 

Compound  Air-compression 635 


XX  CONTENTS. 

PAGE 

Mean  Effective  Pressures 635,  636 

Horse-power  Required  for  Compression 637 

Compressed-air  Engines 638 

Mean  and  Terminal  Pressures 638 

Air-compression  at  Altitudes 639 

Popp  Compressed-air  System 639 

Small  Compressed-air  Motors 640 

Efficiency  of  Air-heating  Stoves 640 

Efficiency  of  Compressed-air  Transmission 640 

Efficiency  of  Compressed-air  Engines 640 

Air-compressors .- 641 

Tests  of  Air  compressors 643 

Steam  Required  to  Compress  100  Cu.  Ft.  of  Air. 644 

Requirements  of  Rock-drills 645 

Compressed  Air  for  Pumping  Plants 645 

Compressed  Air  for  Hoisting  Engines 646 

Practical  Results  with  Air  Transmission 647 

Effect  of  Intake  Temperature 647 

Compressed-air  Motors  with  Return  Circuit 648 

Intercoolers  for  Air-compressors 64.8 

Centrifugal  Air-compressors 648 

High-pressure  Centrifugal  Fans 649 

Test  of  a  Hydraulic  Air-compressor 650 

Mekarski  Compressed-air  Tramways 652 

Compressed  Air  Working  Pumps  in  Mines .  , 652 

Compressed  Air  for  Street  Railways 652 

Fans  and  Blowers. 

Centrifugal  Fans 653 

Best  Proportions  of  Fans 653 

Pressure  due  to  Velocity 653 

Blast  Area  or  Capacity  Area 655 

Pressure  Characteristics  of  Fans 655 

Quantity  of  Air  Delivered 655 

Efficiency  of  Fans  and  Positive  Blowers 657 

Tables  of  Centrifugal  Fans t 658-666 

Effect  of  Resistance  on  Capacity  of  Fans 664 

Sirocco  or  Multivane  Fans '664 

Methods  of  Testing  Fans 667 

Horse-power  of  a  Fan 668 

Pitot  Tube  Measurements 669 

Thomas  Electric  Air  and  Gas  Meter 669 

Flow  of  Air  through  an  Orifice 670 

Diameter  of  Blast-pipes 670 

Centrifugal  Ventilators  for  Mines 672 

Experiments  on  Mine  Ventilators 673 

Disk  Fans » 675 

Efficiency  of  Disk  Fans 676 

Positive  Rotary  Blowers 677 

Steam-jet  Blowers  and  Exhausters 679 

Blowing  Engines 680 

HEATING  AND  VENTILATION. 

Ventilation 681 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct 683 

Heating  and  Ventilating  of  Large  Buildings 684 

Comfortable  Temperatures  and  Humidities 685 

Carbon  Dioxide  Allowable  in  Factories 685 

Standards  of  Ventilation 686 

Air  Washing 687 

Contamination  of  Air 687 

Standards  for  Calculating  Heating  Problems 687 


CONTENTS.  XXI 

PAGE 

Heating  Value  of  Coal 687 

Heat  Transmission  through  Walls,  etc 688 

Allowance  for  Exposure  and  Leakage 689 

Heating  by  Hot-air  Furnaces .  690 

Carrying  Capacity  of  Air-pipes 691 

Volume  of  Air  at  Different  Temperatures 692 

Sizes  of  Pipes  Used  in  Furnace  Heating 692 

Furnace  Heating  with  Forced  Air  Supply 693 

Rated  Capacity  of  Boilers  for  House  Heating 693 

Capacity  of  Grate-surface 694 

Steam  Heating,  Rating  of  Boilers 694 

Testing  Cast-iron  Heating  Boilers 696 

Proportioning  House  Heating  Boilers 696 

Coefficient  of  Transmission  in  Direct  Radiation 697 

Heat  Transmitted  in  Indirect  Radiation 698 

Short  Rules  for  Computing  Radiating  Surface 698 

Carrying  Capacity  of  Steam  Pipes  in  Low  Pressure  .Heating ....  698 

Proportioning  Pipes  to  Radiating  Surface 700 

Sizes  of  Pipes  in  Steam  Heating  Plants 701 

Resistance  of  Fittings 701 

Removal  of  Air,  Vacuum  Systems 702 

Overhead  Steam-pipes 702 

Steam-consumption  in  Car-heating 702 

Heating  a  Greenhouse  by  Steam 702 

Heating  a  Greenhouse  by  Hot  Water 703 

Hot-water  Heating 703 

Velocity  of  Flow  in  Hot- water  Heating 703 

Sizes  of  Pipe  for  Hot- water  Heating 704 

Sizes  of  Flow  and  Return  Pipes 705 

Heating  by  Hot-water,  with  Forced  Circulation 707 

Corrosion  of  Pipe  in  Hot- water  Heating 708 

Blower  System  of  Heating  and  Ventilating 708 

Advantages  and  Disadvantages  of  the  Plenum  System 708 

Heat  Radiated  from  Coils  in  the  Blower  System 708 

Test  of  Cast-iron  Heaters  for  Hot-blast  Work 709 

Factory  Heating  by  the  Fan  System 710 

Artificial  Cooling  of  Air 710 

Capacities  of  Fans  for  Hot-blast  Heating 711 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 712 

Heating  a  Building  to  70°  F 712 

Heating  by  Electricity 713 

Mine- ventilation 714 

Friction  of  Air  in  Underground  Passages 714 

Equivalent  Orifices - 715 

WATER. 

Expansion  of  Water 716 

Weight  of  Water  at  Different  Temperatures. 716,  717 

Pressure  of  Water  due  to  its  Weight 718,  719 

Head  Corresponding  to  Pressures 718 

Buoyancy 719 

Boiling-point 719 

Freezing-point 719 

Sea-water 719 

Ice  and  Snow 720 

Specific  Heat  of  Water 720 

Compressibility  of  Water '. . .  720 

Impurities  of  Water 720 

Causes  of  Incrustation 721 

Means  for  Preventing  Incrustation 721 

Analyses  of  Boiler-scale 722 

Hardness  of  Water 723 

Purifying  Feed-water 723 

Softening  Hard  Water 724 


XX11  CONTENTS. 

Hydraulics.    Flow  of  Water.  PAGE 

Formulae  for  Discharge  through  Orifices  and  Weirs 726 

Flow  of  Water  from  Orifices 727 

Flow  in  Open  and  Closed  Channels 728 

General  Formulae  for  Flow .  .  .  : 728 

Chezy's  Formula 728 

Values  of  the  Coefficient  c 728,  732 

Table,  Fall  in_Feet  per  mile,  etc 729 

Values  of  \/r  for  Circular  Pipes 730 

Kutter's  Formula 730 

D'Arcy's  Formula 732 

Values  of  a  \/r  for  Chezy's  Formula 733 

Values  of  the  Coefficient  of  Friction 734 

Loss  of  Head 735 

Resistance  at  the  Inlet  of  a  pipe 735 

Exponential  Formulae,  Williams'  and  Hazen's  Tables 736 

Short  Formulas 737 

Flow  of  Water  in  a  20-inch  Pipe , 737 

Coefficients  for  Reducing  H.  and  W.  to  Chezy's  Formula 737 

Tables  of  Flow  of  Water  in  Circular  Pipes 738-743 

Flow  of  Water  in  Riveted  Pipes 743 

Long  Pipe  Lines 743 

Flow  of  Water  in  House-service  Pipes 744 

Friction  Loss  in  Clean  Cast-iron  Pipe 745 

Approximate  Hydraulic  Formulae 746 

Compound  Pipes,  and  Pipes  with  Branches 746 

Rifled  Pipes  for  Conveying  Oils 746 

Effect  of  Bend  and  Curves 747 

Loss  of  Pressure  Caused  by  Valves,  etc 747,  748 

Hydraulic  Grade-line 748 

Air-bound  Pipes 748 

Water  Hammer 749 

Vertical  Jets 749 

Water  Delivered  through  Meters 749 

Price  Charged  for  Water  in  Cities 749 

Fire  Streams 749 

Hydrant  Pressures  Required  with  Different  Lengths  and  Sizes  of 

Hose 750 

Pump  Inspection  Table 751 

Pipe  Sizes  for  Ordinary  Fire  Streams 752 

Friction  Losses  in  Hose 752 

Rated  Capacity  of  Steam  Fire-engines 752 

Flow  of  Water  through  Nozzles 753 

The  Siphon 754 

Velocity  of  Water  in  Open  Channels 755 

Mean  Surface  and  Bottom  Velocities 755 

Safe  Bottom  and  Mean  Velocities 755 

Resistance  of  Soil  to  Erosion 755 

Abrading  and  Transporting  Power  of  Water 755 

Frictional  Resistance  of  Surfaces  Moved  in  Water 756 

Grade  of  Sewers 757 

Measurement  of  Flowing  Water 757 

Piezometer 757 

Pitot  Tube  Gauge 

Maximum  and  Mean  Velocities  in  Pipes. 758 

The  Venturi  Meter 758 

Measurement  of  Discharge  by  Means  of  Nozzles 759 

The  Lea  V-notch  Recording  Meter 759 

Flow  through  Rectangular  Orifices 760 

Measurement  of  an  Open  Stream 760 

Miners'  Inch  Measurements 761 

Flow  of  Water  over  Weirs 762 

Francis's  Formica  for  Weirs 762 

Weir  Table 763 

Bazin's  Experiments 763 

The  Cippoleti,  or  Trapezoidal  Weir 764 

The  Triangular  Weir :...... 764 


CONTENTS.  xxiii 

WATER-POWER. 

Power  of  a  Fall  of  Water 765 

Horse-power  of  a  Running  Stream 765 

Current  Motors 765 

Bernouilli's  Theorem 765 

Maximum  Efficiency  of  a  Long  Conduit 766 

Mill-power .     766 

Value  of  Water-power 76(j 

Water  Wheels.    Hydraulic  Turbines. 

Theory  of  Turbines 768 

Determination  of  Dimensions  of  Turbine  Runners 769A 

Comparison  of  Formulae  for  Dimensions  of  Turbines 769A 

Comparison  of  American  High  Speed  Runners 770 

Type  Characteristics  of  Turbines 770 

Specific  Discharge 770B 

Use  of  Type  Characteristics  to  Determine  Size  and  Type  of 

Turbines 770B 

Classes  of  Radial  Inward  Flow  Turbines 771 

Estimating  Weight  of  Turbines 771A 

Selection  of  Turbines 771A 

Eifficiency  of  Turbine  wheels 771s 

Relation  of  Efficiency  and  Water  Consumption  to  Speed ......  772 

Tests  at  the  Philadelphia  Exposition 772 

Relation  of  Gare  Openings  to  Efficiency 773 

Tests  of  Turbine  Discharge  by  Salt  Solution 774' 

Efficiency  Tables  for  Turbines 776-777 

Draft  Tubes 778 

Recent  Turbine  Practice 778 

Some  Large  Turbines 779 

The  Fall-increaser  for  Turbines 780 

Tangential  or  Impulse  Water  Wheels.- 

The  Pelton  Water  Wheel 780 

Considerations  in  the  Choice  of  a  Tangential  Wheel 781 

Control  of  Tangential  Water  Wheels 781 

Efficiency  of  the  Doble  Nozzle 782 

Tests  of  a  12-inch  Doble  Motor 782 

Water-power  Plants  Operating  under  High  Pressures 782 

Amount  of  Water  Required  to  Develop  a  Given  Horse-Power .  783 

Formulae  for  Calculating  the  Power  of  Jet  Water  Wheels 784 

Tangential  Water-wheel  Table 787 

The  Power  of  Ocean  Waves. 

Energy  of  Deep  Sea  Waves 786 

Utilization  of  Tidal  Power 787 

PUMPS    AND    PUMPING    ENGINES. 

Theoretical  Capacity  of  a  Pump 788 

Depth  of  Suction 788 

The  Deane  Pump 7X9 

Sizes  of  Direct-acting  Pumps 789,  791 

Amount  of  Water  Raised  by  a  Single-acting  Lift-pump 790 

Proportioning  the  Steam-cylinder  of  a  Direct-acting  Pump 790 

Speed  of  Water  through  Pipes  and  Pump-passages 790 

Efficiency  of  Small  Pumps 790 

The  Worthington  Duplex  Pump 791 

Speed  of  Piston 791-792 

Speed  of  Water  through  Valves 792 

Underwriters'  Pumps,  Standard  Sizes 792 

Boiler-feed  Pumps 792 

Pump  Valves 793 

The  Worthington  High-duty  Pumping  PJngine 793 


CONTENTS. 

The  d'Auria  Pumping  Engine 793 

A  72,000,000-Gallon  Pumping  Engine 793 

The  Screw  Pumping  Engine 794 

Finance  of  Pumping  Engine  Economy 794 

Cost  of  Pumping  1000  Gallons  per  Minute 795 

Centrifugal  Pumps 796 

Design  of  a  Four-stage  Turbine  Pump 797 

Relation  of  Peripheral  Speed  to  Head 797 

Tests  of  De  Laval  Centrifugal  Pump 798 

A  High-duty  Centrifugal  Pump 801 

Rotary  Pumps 801 

Tests  of  Centrifugal  and  Rotary  Pumps 802 

Duty  Trials  of  Pumping  Engines 802 

Leakage  Tests  of  Pumps 803 

Notable  High-duty  Pump  Records 805 

Vacuum  Pumps 806 

The  Pulsometer 806 

The  Jet  Pump 807 

The  Injector 807 

Pumping  by  Compressed  Air 808 

Gas-engine  Pumps ;  The  Humphrey  Gas  Pump 808 

Air-lift  Pump 808 

Air-lifts  for  Deep  Oil-wells 809 

The  Hydraulic  Ram 810 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram 810 

Hydraulic  Pressure  Transmission. 

Energy  of  Water  under  Pressure 812 

Efficiency  of  Apparatus 812 

Hydraulic  Presses 813 

Hydraulic  Power  in  London 814 

Hydraulic  Riveting  Machines 814 

Hydraulic  Forging 814 

Hydraulic  Engine 815 

FUEL. 

Theory  of  Combustion 816 

Analyses  of  the  Gases  of  Combustion 817 

Temperature  of  the  Fire 818 

Classification  of  Solid  Fuels 818 

Classification  of  Coals 819 

Analyses  of  Coals 820 

Caking  and  Non-Caking  Coals 820 

Cannel  Coals 821 

Rhode  Island  Graphitic  Anthracite 821 

Analysis  and  Heating  Value  of  Coals 821-828 

Approximate  Heating  Values 822 

Lord  and  Haas's  Tests 823 

Sizes  of  Anthracite  Coal 823 

Space  occupied  by  Anthracite 823 

Bernice  Basin,  Pa.,  Coal 824 

Connellsville  Coal  and  Coke 824 

Bituminous  Coals  of  the  Western  States 824 

Analysis  of  Foreign  Coals 825 

Sampling  Coal  for  Analyses 825 

Relative  Value  of  Steam  Coals —  826 

Calorimetric  Tests  of  Coals 826 

Classified  Lists  of  Coals 828-830 

Purchase  of  Coal  Under  Specifications 830 

Weathering  of  Coal 830 

Pressed  Fuel 831 

Spontaneous  Combustion  of  Coal 832 

Coke 832 

Experiments  in  Coking 833 

Coal  Washing 833 


CONTENTS.  XXV 

PAGE 

Recovery  of  By-products  in  Coke  Manufacture 833 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke- 
ovens 834 

Products  of  the  Distillation  of  Coal 834 

Wood  as  Fuel 835 

Heating  Value  of  Wood 835 

Composition  of  Wood 835 

Charcoal 836 

Yield  of  Charcoal  from  a  Cord  of  Wood 836 

Consumption  of  Charcoal  in  Blast  Furnaces 837 

Absorption  of  Water  and  of  Gases  by  Charcoal 837 

Miscellaneous  Solid  Fuels 837 

Dust-fuel — Dust  Explosions 837 

Peat  or  Turf 838 

Sawdust  as  Fuel 838 

Wet  Tan-bark  as  Fuel 838 

Straw  as  Fuel 839 

Bagasse  as  Fuel  in  Sugar  Manufacture 839 

Liquid  Fuel. 

Products  of  Distillation  of  Petroleum 840 

Lima  Petroleum 840 

Value  of  Petroleum  as  Fuel 840 

Fuel  Oil  Burners 842 

Specifications  for  Purchase  of  Fuel  Oil 843 

Alcohol  as  Fuel 843 

Specific  Gravity  of  Ethyl  Alcohol 844 

Vapor  Pressures  of  Saturation  of  Alcohol  and  other  Liquids ....  844 

Fuel  Gas. 

Carbon  Gas 845 

Anthracite  Gas 845 

Bituminous  Gas 846 

Water  Gas 846 

Natural  Gas  in  Ohio  and  Indiana 847 

Natural  Gas  as  a  Fuel  for  Boilers 847 

Producer-gas  from  One  Ton  of  Coal 848 

Combustion  of  Producer-gas 849 

Proportions  of  Gas  Producers  and  Scrubbers 849 

Gas  Producer  Practice 851 

Capacity  of  Producers 851 

High  Temperature  Required  for  Production  of  CO 852 

The  Mond  Gas  Producer 852 

Relative  Efficiency  of  Different  Coals  in  Gas-engine  Tests 853 

Use  of  Steam  in  Producers  and  Boiler  Furnaces 854 

Gas  Analyses  by  Volume  and  by  Weight 854 

Gas  Fuel  for  Small  Furnaces 854 

Blast-furnace  Gas 855 

Acetylene  and  Calcium  Carbide. 

Acetylene 855 

Calcium  Carbide 856 

Acetylene  Generators  and  Burners 857 

The  Acetylene  Blowpipe 857 

Ignition  Temperature  of  Gases 858 

Illuminating  Gas. 

Coal-gas 858 

Water-gas 858 

Analyses  of  Water-gas  and  Coal-gas 860 

Calorific  Equivalents  of  Constituents 860 

Efficiency  of  a  Water-gas  Plant 861 

Space  Required  for  a  Water-gas  Plant 862 

Fuel- value  of  Illuminating  Gas 863 


XXVI  CONTENTS. 

PAGE 

Flow  of  Gas  in  Pipes. **»»,» 864-866 

Services  for  Lamps 864 

Factors  for  Reducing  Volumes  of  Gas 865 

STEAM. 

Temperature  and  Pressure 867 

Total  Heat 867 

Latent  Heat  of  Steam 867 

Specific  Heat  of  Saturated -Steam 867 

The  Mechanical  Equivalent  of  Heat 868 

Pressure  of  Saturated  Steam 868 

Volume  of  Saturated  Steam 868 

Specific  Heat  of  Superheated  Steam 869 

Specific  Density  of  Gaseous  Steam 870 

Table  of  the  Properties  of  Saturated  Steam 871-874 

Table  of  the  Properties  of  Superheated  Steam 874,  875 

Flow  of  Steam. 

Flow  of  Steam  through  a  Nozzle 876 

Napier's  Approximate  Rule 876 

Flow  of  Steam  in  Pipes 877 

Flow  of  Steam  in  Long  Pipes,  Ledoux's  Formula 877 

Table  of  Flow  of  Steam  in  Pipes 878 

Carrying  Capacity  of  Extra  Heavy  Steam  Pipes 879 

Resistance  to  Flow  by  Bends,  Valves,  etc 879 

Sizes  of  Steam-pipes  for  Stationary  Engines 879 

Sizes  of  Steam-pipes  for  Marine  Engines 880 

Proportioning  Pipes  for  Minimum  Loss  by  Radiation  and  Friction  880 

Available  Maximum  Efficiency  of  Expanded  Steam 881 

Steam-pipes. 

Bursting-tests  of  Copper  Steam-pipes 882 

Failure  of  a  Copper  Steam-pipe 882 

Wire-wound  Steam-pipes 882 

Materials  for  Pipes  and  Valves  for  Superheated  Steam 882 

Riveted  Steel  Steam-pipes 883 

Valves  in  Steam-pipes 883 

The  Steam  Loop 883 

Loss  from  an  Uncovered  Steam-pipe 884 

Condensation  in  an  Underground  Pipe  Line 884 

Steam  Receivers  in  Pipe  Lines 884 

Equation  of  Pipes 884 

Identification  of  Power  House  Piping  by  Colors 885 

THE   STEAM-BOILER. 

The  Horse-power  of  a  Steam-boiler 885 

Measures  for  Comparing  the  Duty  of  Boilers 886 

Unit  of  Evaporation 886 

Steam-boiler  Proportions 887 

Heating-surface 887 

Horse-power,  Builders'  Rating 888 

Grate-surface 888 

Areas  of  Flues 889 

Air-passages  Through  Grate-bars 889 

Performance  of  Boilers 889 

Conditions  which  Secure  Economy 890 

Air  Leakage  in  Boiler  Settings 891 

Efficiency  of  a  Boiler 891 

Autographic  CO2  Recorders 891 

Relation  of  Efficiency  to  Rate  of  Driving,  Air  Supply,  etc 893 

Effect  of  Quality  of  Coal  upon  Efficiency 895 

Effect  of  Imperfect  Combustions  and  Excess  Air  Supply 896 

Theoretical  Efficiency  with  Pittsburgh  Coal 896 


CONTENTS.  XXVII 

/ 

The  Straight  Line  Formula  for  Efficiency 896 

High  Rates  of  Evaporation 898 

Boilers  Using  Waste  Gases 898 

Maximum  Efficiencies  at  Different  Rates  of  Driving 898 

Rules  for  Conducting  Boiler  Tests 899 

Heat  Balance  in  Boiler  Tests 907 

Factors  of  Evaporation 908 

Strength  of  Steam-boilers. 

Rules  for  Construction 908 

Shell-plate  Formulae 913 

Efficiency  of  Riveted  Joints 914 

Loads  Allowed  on  Stays 916 

Holding  Power  of  Boiler  Tubes 916 

Safe-working  Pressures 918 

Boiler  Attachments,  Furnaces,  etc. 

Fusible  Plugs 2 918 

Steam  Domes 918 

Mechanical  Stokers 918 

The  Hawley  Down-draught  Furnace 919 

Under-feed  Stokers 919 

Smoke  Prevention 920 

Burning  Illinois  Coal  without  Smoke 921 

Conditions  of  Smoke  Prevention 922 

Forced  Combustion 923 

Fuel  Economizers 924 

Thermal  Storage 927 

Incrustation  and  Corrosion 927 

Boiler-scale  Compounds 929 

Removal  of  Hard  Scale 930 

Corrosion  in  Marine  Boilers 930 

Use  of  Zinc '. 931 

Effect  of  Deposit  on  Flues 931 

Dangerous  Boilers 932 

Safety-valves. 

Rules  for  Area  of  Safety-valves 932 

Spring-loaded  Safety-valves 933 

Safety  Valves  for  Locomotives 935 

The  Injector. 

Equation  of  the  Injector 936 

Performance  of  Injectors 937 

Boiler-feeding  Pumps 937 

Feed-water  Heaters. 

Percentage  of  Saving  Due  to  Use  of  Heaters 938 

Strains  Caused  by  Cold  Feed-water 939 

Calculation  of  Surface  of  Heaters  and^Condensers 939 

Open  vs.  Closed  Feed-water  Heaters 940 

Steam  Separators. 

Efficiency  of  Steam  Separators 941 

Determination  of  Moisture  in  Steam. 

Steam  Calorimeters 942 

Coil  Calorimeter 942 

Throttling  Calorimeters 943 

Separating  Calorimeters 943 


XXV111  CONTENTS. 

PAGE 

Identification  of  Dry  Steam 944 

Usual  Amount  of  Moisture  in  Steam 944 

Chimneys. 

Chimney  Draught  Theory 944 

Force  of  Intensity  of  Draught 945 

Rate  of  Combustion  Due  to  Height  of  Chimney 947 

High  Chimneys  not  Necessary 948 

Height  of  Chimneys  Required  for  Different  Fuels 948 

Protection  of  Chimney  from  Lightning 949 

Table  of  Size  of  Chimneys 950 

Velocity  of  Gas  in  Chimneys 951 

Size  of  Chimneys  for  Oil  Fuel 951 

Chimneys  with  Forced  Draught 952 

Largest  Chimney  in  the  World 952 

Some  Tall  Brick  Chimneys 953,  954 

Stability  of  Chimneys 954 

Steel  Chimneys 956 

Reinforced  Concrete  Chimneys 958 

Sheet-iron  Chimneys 958 

THE  STEAM  ENGINE. 

•  Expansion  of  Steam ; 959 

Mean  and  Terminal  Absolute  Pressures 960 

Calculation  of  Mean  Effective  Pressure 961 

Mechanical  Energy  of  Steam  Expanded  Adiabatically 963 

Measures  for  Comparing  the  Duty  of  Engines 963 

Efficiency,  Thermal  Units  per  Minute 964 

Real  Ratio  of  Expansion 965 

Effect  of  Compression 965 

Clearance  in  Low-  and  High-speed  Engines 966 

Cylinder-condensation 966 

Water-consumption  of  Automatic  Cut-off  Engines 967 

Experiments  on  Cylinder-condensation 967 

Indicator  Diagrams 968 

Errors  of  Indicators 969 

Pendulum  Indicator  Rig 969 

The  Manograph 969 

The  Lea  Continuous  Recorder 970 

Indicated  Horse-power 970 

Rules  for  Estimating  Horse-power 970 

Horse-power  Constants 971 

Table  of  Engine  Constants 972 

To  Draw  Clearance  on  Indicator-diagram 974 

To  Draw  Hyperbola  Curve  on  Indicator-diagram 974 

Theoretical  Water  Consumption 975 

Leakage  of  Steam 976 

Compound  Engines. 

Advantages  of  Compounding 976 

Woolf  and  Receiver  Types  of  Engines 977 

Combined  Diagrams > 979 

Proportions  of  Cylinders  in  Compound  Engines 980 

Receiver  Space 980 

Formula  for  Calculating  Work  of  Steam 981 

Calculation  of  Diameters  of  Cylinders 982 

Triple-expansion  Engines 983 

Proportions  of  Cylinders 983 

Formulae  for  Proportioning  Cylinders 983 

Types  of  Three-stage  Expansion  Engines 985 

Sequence  of  Cranks 986 

Velocity  of  Steam  through  Passages , 986 

A  Double-tandem  Triple-expansion  Engine 986 

Quadruple-expansion  Engines 986 


CONTENTS.  XXIX 
Steam-engine  Economy. 

JrALriU 

Economic  Performance  of  Steam-engines 987 

Feed- water  Consumption  of  Different  Types 987 

Sizes  and  Calculated  Performances  of  Vertical  High-speed  Engine  988 

The  Willans  Law,  Steam  Consumption  at  Different  Loads 991 

Relative  Economy  of  Engines  under  Variable  Loads 992 

Steam  Consumption  of  Various  Sizes 992 

Steam  Consumption  in  Small  Engines 993 

Steam  Consumption  at  Various  Speeds '993 

Capacity  and  Economy  of  Steam  Fire  Engines 993 

Economy  Tests  of  High-speed  Engines 994 

Limitation  of  Engine  Speed 995 

British  High-speed  Engines 995 

Advantage  of  High  Initial  and  Low-back  Pressure 996 

Comparison  of  Compound  and  Single-cylinder  Engines 997 

Two-cylinder  and  Three-cylinder  Engines 997 

Steam  Consumption  of  Engines  with  Superheated  Steam 998 

Steam  Consumption  of  Different  Types  of  Engine 999 

The  Lentz  Compound  Engine 999 

Efficiency  of  Non-condensing  Compound  Engines 1000 

Economy  of  Engines  under  Varying  Loads 1000 

Effect  of  Water  in  Steam  on  Efficiency 1001 

Influence  of  Vacuum  and  Superheat  on  Steam  Consumption. . . .  1001 

Practical  Application  of  Superheated  Steam 1002 

Performance  of  a  Quadruple  Engine 1003 

Influence  of  the  Steam-jacket 1004 

Best  Economy  of  the  Piston  Steam  Engine 1005 

Highest  Economy  of  Pumping-engines 1006 

Sulphur-dioxide  Addendum  to  Steam-engine 1007 

Standard  Dimensions  of  Direct-connected  Generator  Sets 1007 

Dimensions  of  Parts  of  Large  Engines 1007 

Large  Rolling-mill  Engines , 1008 

Counterbalancing  Engines 1008 

Preventing  Vibrations   of  Engines * 1008 

Foundations  Embedded  in  Air 1009 

Most  Economical  Point  of  Cut-off 1009 

Type  of  Engine  used  when  Exhaust-steam  is  used  for  Heating. .  1009 

Cost  of  Steam-power 1009 

Cost  of  Coal  for  Steam-power 1010 

Power-plant  Economics 1011 

Analysis  of  Operating  Costs  of  Power-plants 1013 

Economy  of  Combination  of  Gas  Engines  and  Turbines 1014 

Storing  Steam  Heat  in  Hot  Water 1014 

Utilizing  the  Sun's  Heat  as  a  Source  of  Power 1015 

Rules  for  Conducting  Steam-engine  Tests 1015 

Dimensions  of  Parts  of  Engines. 

Cylinder. 1021 

Clearance  of  Piston 1021 

Thickness  of  Cylinder 1021 

Cylinder  Heads 1022 

Cylinder-head  Bolts 1022 

The  Piston 1023 

Piston  Packing-rings 1023 

Fit  of  Piston-rod 1024 

Diameter  of  Piston-rods 1024 

Piston-rod  Guides 1024 

The  Connecting-rod 1025 

Connecting-rod  Ends 1026 

Tapered  Connecting-rods 1026 

The  Crank-pin 1027 

Crosshead-pin  or  Wrist-pin . 1029 

The  Crank-arm 1029 

The  Shaft,  Twisting  Resistance 1030 

*    iistance  to  Bending . . , X032 


XXX  CONTENTS. 

_  PAGE 

Equivalent  Twisting  Moment 1032 

Fly-wheel  Shafts 1033 

Length  of  Shaft-bearings 1034 

Crank-shafts  with  Center-crank  and  Double-crank  Arms 1036 

Crank-shaft  with  two  Cranks  Coupled  at  90° 1037 

Crank-shaft  with  three  Cranks  at  120° 1038 

Valve-stem  or  Valve-rod 1038 

The  Eccentric 1039 

The  Eccentric-rod 1039 

Reversing-gear 1039 

Current  Practice  in  Engine  Proportions,  1897 1039 

Current  Practice  in  Steam-engine  Design,  1909 1040 

Shafts  and  Bearings  of  Engines 1042 

Calculating  the  Dimensions  Of  Bearings 1042 

Engine-frames  or  Bed-plates 1044 

Fly-wheels. 

Weight  of  Fly-wheels 1044 

Weight  of  Fly-wheels  for  Alternating-current  Units 1047 

Centrifugal  Force  in  Fly-wheels 1047 

Diameters  for  Various  Speeds 1048 

Strains  in  the  Runs 1049 

Arms  of  Fly-wheels  and  Pulleys 1050 

Thickness  of  Rims 1050 

A  Wooden  Rim  Fly-wheel 1051 

Wire- wound  Fly-wheels 1052 

The  Slide-Valve. 

Definitions,  Lap,  Lead,  etc 1052 

Sweet's  Valve-diagram , 1054 

The  Zeuner  Valve-diagram 1054 

Port  Opening,  Lead,  and  Inside  Lead 1057 

Crank  Angles  for  Connecting-rods  of  Different  Lengths 1058 

Ratio  of  Lap  and  of  Port-opening  to  Valve- travel 1058 

Relative  Motions  of  Crosshead  and  Crank 1060 

Periods  of  Admission  or  Cut-off  for  Various  Laps  and  Travels. .  1060 

Piston- valves 1061 

Setting  the  Valves  of  an  Engine 1061 

To  put  an  Engine  on  its  Center 1061 

Link-motion 1062 

The  Walschaerts  Valve-gear 1064 

Governors. 

Pendulum  or  Fly-ball  Governors 1065 

To  Change  the  Speed  of  an  Engine 1066 

Fly-wheel  or  Shaft  Governors 1066 

The  Rites  Inertia  Governor 1066 

Calculation  of  Springs  for  Shaft-governors 1066 

Condensers,  Air-pumps,  Circulating-pumps,  etc.. 

The  Jet  Condenser 1068 

Quantity  of  Cooling  Water 1068 

Ejector  Condensers 1069 

The  Barometric  Condensers 1069 

The  Surface  Condenser 1069 

Coefficient  of  Heat  Transference  in  Condensers 

The  Power  Used  for  Condensing  Apparatus 

Vacuum,  Inches  of  Mercury  and  Absolute  Pressure 

Temperatures,  Pressures  and  Volumes  of  Saturated  Air 

Condenser  Tubes 1072 

Tube-plates 1073 

Spacing  of  Tubes 1073 

Air-pump 

Area  through  Valve-seats 1°73 


CONTENTS. 

PAGE 

Work  done  by  an  Air-pump 1074 

Most  Economical  Vacuum  for  Turbines 1075 

Circulating-pump 1075 

The  Leblanc  Condenser 1076 

Feed-pumps  for  Marine  Engines 1076 

An  Evaporative  Surface  Condenser 1076 

Continuous  Use  of  Condensing  Water 1076 

Increase  of  Power  by  Condensers 1077 

Advantage  of  High  Vacuum  in  Reciprocating  Engines 1078 

The  Choice  of  a  Condenser 1078 

Cooling  Towers 1079 

Calculation  of  Air  Supply  for  Cooling  Towers 1080 

Tests  of  a  Cooling  Tower  and  Condenser 1080 

Water  Evaporated  in  a  Cooling  Tower 1080 

Weight  of  Water  Vapor  mixed  with  One  Pound  of  Air -. . . .  1081 

Evaporators  and  Distillers 1082 

Rotary  Steam  Engines — Steam  Turbines. 

Rotary  Steam  Engines 1082 

Impulse  and  Reaction  Turbines 1082 

The  DeLaval  Turbine 1082 

The  Zolley  or  Rateau  Turbine 1083 

The  Parsons  Turbine 1083 

The  Westinghouse  Double-flow  Turbine 1083 

Mechanical  Theory  of  the  Steam  Turbine 1084 

Heat  Theory  of  the  Steam  Turbine 1084 

Velocity  of  Steam  in  Nozzles 1085 

Speed  of  the  Blades 1086 

Comparison  of  Impulse  and  Reaction  Turbines 1087 

Loss  due  to  Windage 1087 

Efficiency  of  the  Machine 1087 

Steam  Consumption  of  Turbines 1088 

Effect  of  Vacuum  on  Steam  Turbines 1088 

Tests  of  Turbines 1088 

Efficiency  of  the  Rankine  Cycle 1089 

Factors  for  Reduction  to  Equivalent  Efficiency 1090 

Effect  of  Pressure,  Vacuum  and  Superheat 1090 

Steam  and  Heat  Consumption  of  the  Ideal  Engine 1091 

Westinghouse  Turbines  at  74th  St.  Station,  New  York 1092 

A  Steam  Turbine  Guarantee 1092 

Efficiency  of  a  5000-K. W.  Steam  Turbine  Generator 1092 

Comparison  of  Large  Turbines  and  Reciprocating  Engines  .....  1092 

Steam  Consumption  of  Small  Steam  Turbines 1093 

Low-pressure  Steam  Turbines 1093 

Tests  of  a  15,000-K.W.  Steam-engine  Turbine  Unit 1095 

Reduction  Gear  for  Steam  Turbines 1095 

Hot-air  Engines. 

Hot-air  or  Caloric  Engines * 1095 

Test  of  a  Hot-air  Engine , 1095 

INTERNAL,    COMBUSTION    ENGINES. 

Four-cycle  and  Two-cycle  Gas-engines 1096 

Temperatures  and  Pressures  Developed 1096 

Calculation  of  the  Power  of  Gas-engines 1097 

Pressures  and  Temperatures  at  End  of  Compression 1098 

Pressures  and  Temperature  at  Release 1099 

after  Combustion 1099 

Mean  Effective  Pressures 1099 

Sizes  of  Large  Gas-engines 1100 

Engine  Constants  for  Gas-engines 1101 

Rated  Capacity  of  Automobile  Engines 1101 

Estimate  of  the  Horse-power  of  a  Gas-engine 1101 


XXX11  CONTENTS. 

PAGE 

Oil  and  Gasoline  Engines 1101 

The  Diesel  Oil  Engine 1102 

The  De  La  Vergne  Oil  Engine 1102 

Alcohol  Engines 1102 

Ignition 1102 

Timing 1103 

Governing 1103 

Gas  and  Oil  Engine  Troubles 1103 

Conditions  of  Maximum  Efficiency 1103 

Heat  Losses  in  the  Gas-engine 1104 

Economical  Performance  of  Gas-engines 1104 

Utilization  of  Waste  Heat  from  Gas-engines 1105 

Rules  for  Conducting  Tests  of  Gas  and  Oil  Engines 1105 

LOCOMOTIVES. 

Resistance  of  Trains 1108 

Resistance  of  Electric  Railway  Cars  and  Trains 1110 

Efficiency  of  the  Mechanism  of  a  Locomotive 1111 

Adhesion 1111 

Tractive  Force 1111 

Size  of  Locomotive  Cylinders 1112 

Horse-power  of  a  Locomotive 1113 

Size  of  Locomotive  Boilers 1113 

Wootten's  Locomotive 1114 

Grate-surface,  Smokestacks,  and  Exhaust-nozzles 1115 

Fire-brick  Arches 1115 

Economy  of  High  Pressures 1116 

Leading  American  Types 1116 

Classification  of  Locomotives 1116 

Steam  Distribution  for  High  Speed 1117 

Formulae  for  Curves . 1117 

Speed  of  Railway  Trains 1118 

Performance  of  a  High-speed  Locomotive 1118 

Fuel  Efficiency  of  American  Locomotives 1119 

Locomotive  Link-motion 1119 

Dimensions  of  Some  American  Locomotives 1120 

The  Mallet  Compound  Locomotive 1120 

Indicated  Water  Consumption 1122 

Indicator  Tests  of  a  Locomotive  at  High-speed 1122 

Locomotive  Testing  Apparatus 1123 

Weights  and  Prices  of  Locomotives 1124 

Waste  of  Fuel  in  Locomotives 1 125 

Advantages  of  Compounding 1 125 

Depreciation  of  Locomotives 1125 

Average  Train  Loads 1125 

Tractive  Force  of  Locomotives,  1893  and  1905 1125 

Superheating  in  Locomotives 1126 

Counterbalancing  Locomotives 

Narrow-gauge  Railways 1127 

Petroleum-burning  Locomotives 

Fireless  Locomotives :....-....  1127 

Self-propelled  Railway  Cars 

Compressed-air  Locomotives 1128 

Air  Locomotives  with  Compound  Cylinders 1129 

SHAFTING. 

Diameters  to  Resist  Torsional  Strain 1130 

Deflection  of  Shafting 1131 

Horse-power  Transmitted  by  Shafting 1132 

Flange  Couplings 1133 

Effect  of  Cold  Rolling 1133 

Hollow  Shafts. .                                                1133 

Sizes  of  Collars  for  Shafting 1133 

Table  for  Laying  Out  Shafting , , , , , , U34 


* 

CONTENTS.  XXxiii 

^ 

PULLETS.  PAGE 

Proportions  of  Pulleys 1135 

Convexity  of  Pulleys 1136 

Cone  or  Step  Pulleys 1 136 

Method  of  Determining  Diameter^  of  Cone  Pulleys 1136 

Speeds  of  Shafts  with  Cone  Pulleys 1137 

Speeds  in  Geometrical  Progression ,  1138 

BELTING. 

Theory  of  Belts  and  Bands 1138 

Centrifugal  Tension 1139 

Belting  Practice,  Formulae  for  Belting 1139 

Horse-power  of  a  Belt  one  inch  wide 1140 

A.  F.  Nagle's  Formula 1141 

Width  of  Belt  for  Given  Horse-power , . . .  1141 

Belt  Factors 1 142 

Taylor's  Rules  for  Belting 1143 

Earth's  Studies  on  Belting 1146 

Notes  on  Belting 1146 

Lacing  of  Belts 1147 

Setting  a  Belt  on  Quarter-twist 1147 

To  Find  the  Length  of  Belt 1148 

To  Find  the  Angle  of  the  Arc  of  Contact 1148 

To  Find  the  Length  of  Belt  when  Closely  Rolled 1148 

To  Find  the  Approximate  Weight  of  Belts 1148 

Relations  of  the  Size  and  Speeds  of  Driving  and  Driven  Pulleys.  1148 

Evils  of  Tight  Belts 1149 

Sag  of  Belts 1149 

Arrangement  of  Belts  and  Pulleys 1149 

Care  of  Belts 1150 

Strength  of  Belting (. .  1150 

Adhesion,  Independent  of  Diameter rv.  1151 

Endless  Belts 1151 

Belt  Data 1151 

U.  S.  Navy  Specifications  for  Leather  Belting 1151 

Belt  Dressings 1151 

Cement  for  Cloth  or  Leather 1152 

Rubber  Belting 1152 

Steel  Belts 1152 

Chain  Drives. 

Roller  Chain  and  Sprocket  Drives 1153 

Belting  versus  Chain  Drives 1155 

Data  used  in  Design  of  Chain  Drives 1156 

Comparison  of  Rope  and  Chain  Drives 1157 

GEARING. 

Pitch,  Pitch-circle,  etc 3157 

Diametral  and  Circular  Pitch 1158 

Diameter  of  Pitch-line  of  Wheels  from  10  to  100  Teeth 1159 

Chordal  Pitch 1159 

Proportions  of  Teeth 1 159 

Gears  with  Short  Teeth 1160 

Formulae  for  Dimensions  of  Teeth 1160 

Width  of  Teeth 1161 

Proportions  of  Gear-wheels 1161 

Rules  for  Calculating  the  Speed  of  Gears  and  Pulleys 1162 

Milling  Cutters  for  Interchangeable  Gears 1162 

Forms  of  the  Teeth. 

The  Cycloidal  Tooth 1162 

The  Involute  Tooth 1165 


XXXiV  CONTENTS, 

PAGE 

Approximation  by  Circular  Arcs -. 1166 

Stub  Gear  Teeth  for  Automobiles 1167 

Stepped  Gears 1168 

Twisted  Teeth 1168 

Spiral  Gears 1168 

Worm  Gearing 1168 

The  Hindley  Worm 1169 

Teeth  of  Bevel-wheels 1169 

Annular  and  Differential  Gearing 1169 

Efficiency  of  Gearing 1170 

Efficiency  of  Worm  Gearing 1171 

Efficiency  of  Automobile  Gears 1172 

Strength  of  Gear  Teeth. 

Various  Formulae  for  Strength 1172 

Comparison  of  Formulae 1 174 

Raw-hide  Pinions 1177 

Maximum  Speed  of  Gearing 1177 

A  Heavy  Machine-cut  Spur-gear 1 178 

Frictional  Gearing 1178 

Frictional  Grooved  Gearing 1178 

Power  Transmitted  by  Friction  Drives 1178 

Friction  Clutches 1179 

Coil  Friction  Clutches 1180 

HOISTING  AND   CONVEYING. 

Working  Strength  of  Blocks 1181 

Chain-blocks 1181 

Efficiency  of  Hoisting  Tackle 1182 

Proportions  of  Hooks 1182 

Heavy  Crane  Hooks 1183 

Strength  of  Hooks  and  Shackles 1184 

Power  of  Hoisting  Engines 1184 

Effect  of  Slack  Rope  on  Strain  in  Hoisting 1186 

Limit  of  Depth  for  Hoisting 1 186 

Large  Hoisting  Records \ 1186 

Safe  Loads  for  Ropes  and  Chains 1187 

Pneumatic  Hoisting 1 187 

Counterbalancing  of  Winding-engines 1188 

Cranes. 

Classification  of  Cranes 1189 

Position  of  the  Inclined  Brace  in  a  Jib  Crane 1190 

Electric  Overhead  Traveling  Cranes 1190 

Power  Required  to  Drive  Cranes 1191 

Dimensions,  Loads  and  Speeds  of  Electric  Cranes 1191 

Notable  Crane  Installations 1192 

A  150-ton  Pillar  Crane 1192 

Compressed-air  Traveling  Cranes 1192 

Electric  versus  Hydraulic  Cranes 

Power  Required  for  Traveling  Cranes  and  Hoists 1193 

Lifting  Magnets 1193 

Telpherage 1196 

'  Coal-handling  Machinery. 

Weight  of  Overhead  Bins 1196 

Supply-pipes  from  Bins 1196 

Types  of  Coal  Elevators 1196 

Combined  Elevators  and  Conveyors 1197 

Coal  Conveyors 1 197 

Horse-power  of  Conveyors 1 198 


CONTENTS.  XXXV 

PAGE 

Bucket,  Screw,  and  Belt  Conveyors 1198 

Weight  of  Chain  and  of  Flights 1199 

Capacity  of  Belt  Conveyors 1 199 

Belt  Conveyor  Construction 1200 

Horse-power  to  Drive  Belt  Conveyors 1200 

Relative  Wearing  Power  of  Conveyor  Belts * 1200 

Pneumatic  Conveying 1201 

Pneumatic  Postal  Transmission 1201 


, 


Wire-rope  Haulage. 

Self-acting  Inclined  Plane 1202 

Simple  Engine  Plane 1203 

Tail-rope  System 1203 

Endless  Rope  System 1203 

Wire-rope  Tramways 1204 

Stress  in  Hoisting-ropes  on  Inclined  Planes 1204 

An  Aerial  Tramway  21  miles  long .. . .  1205 

Suspension  Cableways  and  Cable  Hoists 1205 

Tension  Required  to  Prevent  Wire  Slipping  on  Drums 1206 

Formulae  for  Deflection  of  a  Wire  Cable 1207 

Taper  Ropes  of  Uniform  Tensile  Strength 1208 


WIRE-ROPE  TRANSMISSION. 


Working  Tension  of  Wire  Ropes 1208 

Sheaves  for  Wire-rope  Transmission 1208 

Breaking  Strength  of  Wire  Ropes. 1209 

Bending  Stresses  of  Wire  Ropes 1209 

Horse-power  Transmitted 1210 

Diameters  of  Minimum  Sheaves 1211 

Deflection  of  the  Rope 1211 

Limits  of  Span 1212 

Long-distance  Transmission 1212 

Inclined  Transmissions 1212 

Bending  Curvature  of  Wire  Ropes 1213 

ROPE-DRIVING. 

Formulae  for  Rope-driving 1214 

Horse-power  of  Transmission  at  Various  Speeds 1215 

Sag  of  the  Rope  between  Pulleys. 1216 

Tension  on  the  Slack  Part  of  the  Rope 12*16 

Miscellaneous  Notes  on  Rope-driving .  .  , 1217 

Data  of  Manila. Transmission  Rope 1218 

Cotton  Ropes 1218 

FRICTION  AND   LUBRICATION. 

Coefficient  of  Friction 1219 

Rolling  Friction '. 1219 

Friction  of  Solids < 1219 

Friction  of  Rest , 1219 

Laws  of  Unlubricated  Friction 1219 

Friction  of  Tires  Sliding  on  Rails 1219 

Coefficient  of  Rolling  Friction 1220 

Laws  of  Fluid  Friction .' 1220 

Angles  of  Repose  of  Building  Materials 1220 

Coefficient  of  Friction  of  Journals 1220 

Friction  of  Motion 1221 

Experiments  on  Friction  of  a  Journal 1221 

Coefficients  of  Friction  of  Journal  with  Oil  Bath 1221,  1223 

Coefficients  of  Friction  of  Motion  and  of  Rest 1222 

Value  of  Anti-friction  Metals . .  1223 

Cast-iron  for  Bearings 1223 


x — ^y  CONTENTS. 

PAGE 

Friction  of  Metal  under  Steam-pressure 1223 

Morin's  Laws  of  Friction 1223 

Laws  of  Friction  of  Well-lubricated  Journals 1225 

Allowable  Pressures  on  Bearing-surfaces 1226 

Oil-pressure  in  a  Bearing 1228 

Friction  of  Car-journal  Brasses 1228 

Experiments  on  Overheating  of  Bearings 1228 

Moment  of  Friction  and  Work  of  Friction 1229 

Tests  of  Large  Shaft  Bearings 1230 

Clearance  between  Journal  and  Bearing 1230 

Allowable  Pressures  on  Bearings 1230 

Bearing  Pressures  for  Heavy  Intermittent  Loads 1231 

Bearings  for  Very  High  Rotative  Speed 1231 

Bearing  Pressures  in  Shafts  of  Parsons  Turbine 1232 

Thrust  Bearings  in  Marine  Practice 1232 

Bearings  for  Locomotives 1232 

Bearings  of  Corliss  Engines 1232 

Temperature  of  Engine  Bearings 1232 

Pivot  Bearings 1232 

The  Schiele  Curve 1232 

Friction  of  a  Flat  Pivot-bearing 1233 

Mercury-bath  Pivot 1233 

Ball  Bearings,  Roller  Bearings,  etc 1233 

Friction  Rollers 1233 

Conical  Roller  Thrust  Bearings. 1234 

The  Hyatt  Roller  Bearing 1235 

Notes  on  Ball  Bearings 1235 

Saving  of  Power  by  Use  of  Ball  Bearings 1237 

Knife-edge  Bearings 1238 

Friction  of  Steam-engines 1238 

Distribution  of  the  Friction  of  Engines 1238 

Friction  Brakes  and  Friction  Clutches. 

Friction  Brakes 1239 

Friction  Clutches 1239 

Magnetic  and  Electric  Brakes 1240 

Design  of  Band  Brakes 1240 

Friction  of  Hydaulic  Plunger  Packing 1241 

Lubrication. 

Durability  of  Lubricants 1241 

§ualifications  of  Lubricants 1242 

xamination  of  Oils 1242 

Specifications  for  Petroleum  Lubricants 1243 

Penna.  R.  R.  Specifications 1244 

Grease  Lubricants 

Testing  Oil  for  Steam  Turbines 1244 

8uantity  of  Oil  to  Run  an  Engine 

ylinder  Lubrication 1245 

Soda  Mixture  for  Machine  Tools 

Water  as  a  Lubricant 124 

Acheson's  Deflocculated  Graphite 1246 

Solid  Lubricants 1246 

Graphite,  Soapstone,  Metaline 1246 

THE  FOUNDRY. 

Cupola  Practice 1247 

Melting  Capacity  of  Different  Cupolas 1248 

Charging  a  Cupola 1248 

Improvement  of  Cupola  Practice 

Charges  in  Stove  Foundries 1250 

Foundry  Blower  Practice 1250 


CONTENTS.  XXXV11 


PAGE 

Results  of  Increased  Driving 1252 

Power  Required  for  a  Cupola  Fan 1253 

Utilization  of  Cupola  Gases 1253 

Loss  of  Iron  in  Melting 1253 

Use  of  Softeners ; . .  1253 

Weakness  of  Large  Castings 1253 

Shrinkage  of  Castings 1254 

Growth  of  Cast  Iron  by  Heating 1254 

Hard  Iron  due  to  Excessive  Silicon 1254 

Ferro  Alloys  for  Foundry  Use 1255 

Dangerous  Ferro-silicon 1255 

Quality  of  Foundry  Coke 1255 

Castings  made  in  Permanent  Cast-iron  Molds 1255 

Weight  of  Castings  from  Weight  of  Pattern 1256 

Molding  Sand 1256 

Foundry  Ladles 1257 


: 


THE  MACHINE-SHOP. 


Speed  of  Cutting  Tools 1258 

Table  of  Cutting  Speeds 1258 

Spindle  Speeds  of  Lathes 1259 

Rule  for  Gearing  Lathes 1259 

Change-gears  for  Lathes 1260 

Quick  Change  Gears 1260 

Metric  Screw-threads 1261 

Cold  Chisels 1261 

Setting  the  Taper  in  a  Lathe 1261 

Lubricants  for  Lathe  Centers 1261 

Taylor's  Experiments  on  Tool  Steel 1261 

Proper  Shape  of  Lathe  Tool 1261 

Forging  and  Grinding  Tools 1263 

Best  Grinding  Wheel  for  Tools 1263  -~- 

Chatter « 1264 

Use  of  Water  on  Tool 1264 

Interval  between  Grindings 1264 

Effect  of  Feed  and  Depth  of  Cut  on  Speed 1264 

Best  High  Speed  Tool  Steel — Heat  Treatment 1265 

Table,  Cutting  Speeds  of  Taylor- White  Tools 1266 

Best  Method  of  Treating  Tools  in  Small  Shops 1268 

Quality  of  Different  Tool  Steels 1268 

Parting  and  Thread  Tools 1268 

Durability  of  Cutting  Tools 1268 

Economical  Cutting  Speeds 1268  -^ 

New  High  Speed  Steels,  1909 1269 

Stellite 1269 

Planer  Work 1270-1275 

Cutting  and  Return  Speeds  of  Planers 1270 

Power  Required  for  Planing 1270 

Time  Required  for  Planing 1271 

Standard  Planer  Tools 1271-1275 

Milling  Machine  Practice <, 1275-1284 

Forms  of  Milling  Cutters 1275 

Number  of  Teeth  in  Milling  Cutters 1276 

Keyways  in  Milling  Cutters 1277 

Power  Required  for  Milling 1278 

Modern  Milling  Practice,  1914 1279 

Milling  wiJi  or  against  the  Feed 1280 

Lubricant  for  Milling  Cutters •:.  . .  1281 


Typica 
High-s 


Jigh-speed  Milling 1282 

Limiting  Factors  of  Milling  Practice 1283 

Speeds  and  Feeds  for  Gear  Cutting 1284 

Drills  and  Drilling 1285-1290 

Forms  of  Drills 1285 

Drilling  Compounds 1286 


XXXV111  CONTENTS. 

1>AGE 

Twist  Drill  and  Steel  Wire  Gages ...;>...,.. 1286 

Power  Required  to  Drive  Drills 1286,  1287 

Feeds  and  Speeds  of  Drills 1288 

Extreme  Results  with  Drills ; 1289 

Experiments  on  Twist  Drills 1289 

Cutting  Speeds  for  Tapping  and  Threading 1290 

Sawing  Metals 1291 

Case-hardening,  Cementation,  Harvey izing 1291 

Change  of  Shape  due  to  Hardening  and  Tempering 1291 

Power  Required  for  Machine  Tools. 

Resistance  Overcome  in  Cutting  Metal :. .  1292 

Power  Required  to  Run  Lathes 1292-1295 

Sizes  of  Motors  for  Machine  Tools 1294-1298 

Horse-power  Constants  for  Cutting  Metals 1299 

Pulley  Diameters  for  Motors 1300 

Geared  Connections  for  Motors,  Table 1301 

Motor  Requirements  for  Planers 1302 

Tests  on  a  Motor-driven  Planer 1303 

Power  Required  for  Wood-working  Machinery 1303 

Power  Required  to  Drive  Shafting 1305 

Power  Required  to  Drive  Machines  in  Groups 1305 

Machine  Tool  Drives,  Speeds  and  Feeds 1307 

Geometrical  Progression  of  Speeds  and  Feeds 1307 

Methods  of  Driving  Machine  Tools 1307 

Abrasive  Processes. 

The  Cold  Saw 1309 

Reese's  Fusing-disk 1309 

Cutting  Stone  with  Wire 1309 

The  Sand-blast 1309 

Polishing  and  Buffing '. 1310 

Laps  and  Lapping 1310 

Emery-wheels 131 1-1317 

Artificial  Abrasives 1313 

Mounting  Grinding  Wheels,  Safety  Devices 1314 

Grinding  as  a  Substitute  for  Finish  Turning 1317 

Grindstones 1317 

Various  Tools  and  Processes. 

Taper  Bolts,  Pins,  Reamers,  etc 1318 

Morse  Tapers 1319 

Jarno  Taper 1319 

Tap  Drills 1320 

Taper  Pins 1321 

T-slots,  T-bolts  and  T-nuts 1321 

Punches  and  Dies,  Presses,  etc 1321 

Punch  and  Die  Clearances > . .  1321 

Kennedy's  Spiral  Punch 1322 

.  Sizes  of  Blanks  Used  in  the  Drawing  Press 1322 

Pressure  Obtained  by  the  Drop  Press 1322 

Flow  of  Metals 1323 

Fly-wheels  for  Presses,  Punches,  Shears,  etc. 1323 

Forcing,  Shrinking,  and  Running  Fits 1324 

Pressures  for  Mounting  Wheels  and  Crank  Pins 1324 

Fits  for  Machine  Parts 1325 

Running  Fits 1325 

Shop  Allowances  for  Electrical  Machinery 

Pressure  Required  for  Press  Fits 

Stresses  due  to  Force  and  Shrink  Fits 1326 

Force  Required  to  Start  Force  and  Shrink  Fits 1327 

Formulae  for  Flat  and  Square  Keys 1328 


CONTENTS.  XXXIX 

PAGE 

Keys  of  Various  Forms 1328-1331 

Depth  of  Key  Seats 1329 

Gib  Keys 1332 

Holding  Power  of  Keys  and  Set  Screws 1332 

DYNAMOMETERS. 

Traction  Dynamometers 1333 

The  Prony  Brake 1333 

The  Alden  Dynamometer 1334 

Capacity  of  Friction-brakes 1334 

Transmission  Dynamometers 1335 

ICE  MAKING  OR  REFRIGERATING-MACHINES. 

Operations  of  a  Refrigerating-Machine 1336 

Pressures,  etc.,  of  Available  Liquids 1337 

Properties  of  Sulphur  Dioxide  Gas 1338 

Properties  of  Ammonia 1339,  1340 

Solubility  of  Ammonia 1341 

Properties  of  Saturated  Vapors 1341 

Heat  Generated  by  Absorption  of  Ammonia 1341 

Cooling  Effect,  Compressor  Volume  and  Power  Required,  with 

Different  Cooling  Agents 1341 

Ratios  of  Condenser,  Mean  Effective,  and  Vaporizer  Pressures .  .  1342 

Properties  of  Brine  used  to  absorb  Refrigerating  Effect 1343 

Chloride-of-calcium  Solution 1343 

Ice-melting  Effect 1344 

Ether-machines 1344 

Air-machines 1344 

Carbon  Dioxide  Machines 1344 

Methyl  Chloride  Machines 1345 

Sulphur-dioxide  Machines 1345 

Machines  Using  Vapor  of  Water 1345 

Ammonia  Compression-machines 1345 

Dry,  Wet  and  Flooded  Systems 1345 

Ammonia  Absorption-machines 1346 

Relative  Performance  of  Compression  and  Absorption  Machines  1346 

Efficiency  of  a  Refrigerating-machine 1347 

Diagrams  of  Ammonia  Machine  Operation 1348 

Cylinder-heating 1349 

Volumetric  Efficiency 1349 

Pounds  of  Ammonia  per  Ton  of  Refrigeration 1350,  1351 

Mean  Effective  Pressure,  and  Horse-power 1350 

The  Voorhees  Multiple  Effect  Compressor 1350 

Size  and  Capacities  of  Ammonia  Machines ,  .  .  .  .  1352 

Piston  Speeds  and  Revolutions  per  Minute 1353 

Condensers  for  Refrigera  ting-machines 1353 

Cooling  Tower  Practice  in  Refrigerating  Plants 1354 

Test  Trials  of  Refrigerating-machines 1355 

Comparison  of  Actual  and  Theoretical  Capacity 1355 

Performance  of  Ammonia  Compression-machines 1 356 

Economy  of  Ammonia  Compression-machines 1357 

Form  of  Report  of  Test 1358 

Temperature  Range 1359 

Metering  the  Ammonia 1359 

Performance  of  Ice-making  Machines 1359 

Performance  of  a  75-ton  Refrigerating-machine 1361-1363 

Ammonia  Compression-machine,  Results  of  Tests '.  .  1364 

Performance  of  a  Single-acting  Ammonia  Compressor 1364 

Performance  of  Ammonia  Absorption-machine 1364 

Means  for  Applying  the  Cold 1365 

Artificial  Ice-manufacture , Ib66 

Test  of  the  New  York  Hygeia  Ice-making  Plant 1367 

An  Absorption  Evaporator  Ice-making  System 1367 

Ice-making  with  Exhaust  Steam 1367 


Xl  CONTENTS. 

PAGE 

Tons  of  Ice  per  Ton  of  Coal 1367 

Standard  Ice  Cans  or  Molds 1368 

Cubic  Feet  of  Insulated  Space  per  Ton  Refrigeration 1368 

MARINE  ENGINEERING. 

Rules  for  Measuring  and  Obtaining  Tonnage  of  Vessels 1368 

The  Displacement  of  a  Vessel 1369 

Coefficient  of  Fineness 1369 

Coefficient  of  Water-line 1369 

Resistance  of  Ships 1369 

Coefficient  of  Performance  of  Vessels 1370 

Defects  of  the  Common  Formula  for  Resistance 1370 

Rankine's  Formula 1370 

Empirical  Equations  for  Wetted  Surface 1371 

E.  R.  Mumford's  Method 1371 

Dr.  Kirk's  Method 1372 

To  find  the  I.H.P.  from  the  Wetted  Surface. 1372 

Relative  Horse-power  required  for  Different  Speeds  of  Vessels .  .  1373 

Resistance  per  Horse-power  for  Different  Speeds 1373 

Estimated  Displacement,  Horse-power,  etc.,  of  S team- vessels. .  .  1374 

Speed  of  Boats  with  Internal  Combustion  Engines 1374 

Data  of  Ships  of  Various  Types 1376 

Relation  of  Horse-power  to  Speed 1376 

The  Screw-propeller. 

Pitch  and  Size  of  Screw 1377 

Propeller  Coefficients 1378 

Efficiency  of  the  Propeller 1379 

Pitch-ratio  and  Slip  for  Screws  of  Standard  Form 1379 

Table  for  Calculating  Dimensions  of  Screws 1380 

Marine  Practice. 

Comparison  of  Marine  Engines,  1872,  1881,  1891,  1901 1380 

Turbines  and  Boilers  of  the  "  Lusitania" 1381 

Performance  of  the  "Lusitania,"  1908 1381 

Dimensions  and  Performance  of  Notable  Atlantic  Steamers.  . .  . 

Relative  Economy  of  Turbines  and  Reciprocating  Engines 1382 

Reciprocating  Engines  with  a  Low-pressure  Turbine 1383 

The  Paddle-wheel. 

Paddle-wheels  with  Radial  Floats 1383 

Feathering  Paddle-wheels 1383 

Efficiency  of  Paddle-wheels 1384 

Jet  Propulsion. 

Reaction  of  a  Jet 1384 

CONSTRUCTION  OF  BUILDINGS. 

Foundations. 

Bearing  Power  of  Soils 1385 

Bearing  Power  of  Piles 1386 

Safe  Strength  of  Brick  Piers 1386 

Thickness  of  Foundation  Walls 1386 

Masonry. 

Allowable  Pressures  on  Masonry 1386 

Crushing  Strength  of  Concrete 1386 

Reinforced  Concrete 1386 


CONTENTS.  Xll 

Beams  and  Girders.  PAGE 

Safe  Loads  on  Beams 1387 

Safe  Loads  on  Wooden  Beams 1387 

Maximum  Permissible  Stresses  in  Structural  Materials 1388 

Walls. 

Thickness  of  Walls  of  Buildings 1388 

Walls  of  Warehouses,  Stores,  Factories,  and  Stables 1388 

Floors,  Columns  and  Posts. 

Strength  of  Floors,  Roofs,  and  Supports 1389 

Columns  and  Posts 1389 

Fireproof  Buildings 1389 

Iron  and  Steel  Columns 1389 

Lintels,  Bearings,  and  Supports 1390 

Strains  on  Girders  and  Rivets 1390 

Maximum  Load  on  Floors 1390 

Strength  of  Floors 1391 

Maximum  Spans  for  1,  2  and  3  inch  Plank 1392 

Mill  C9lumns .  , 1393 

Safe  Distributed  Loads  on  Southern-pine  Beams 1393 

Approximate  Cost  of  Mill  Buildings 1394 

ELECTRICAL  ENGINEERING. 

C.  G.  S.  System  of  Physical  Measurement 1396 

Practical  Units  used  in  Electrical  Calculations 1396 

Relations  of  Various  Units 1397 

Units  of  the  Magnetic  Circuit 1398 

Equivalent  Electrical  and  Mechanical  Units 1399 

Permeability 1400 

logics  between  Flow  of  Water  and  Electricity 1400 

Electrical  Resistance. 

Laws  of  Electrical  Resistance 1400 

Electrical  Conductivity  of  Different  Metals  and  Alloys 1401 

Conductors  and  Insulators 1402 

Resistance  Varies  with  Temperature : 1402 

Annealing 1402 

Standard  of  Resistance  of  Copper  Wire 1402 

Wire  Table,  Standard  Annealed  Copper 1404 

Direct  Electric  Currents. 

Ohm's  Law 1406 

Series  and  Parallel  or  Multiple  Circuits 1406 

Resistance  of  Conductors  in  Series  and  Parallel 1407 

Internal  Resistance 1408 

Power  of  the  Circuit 1408 

Electrical,  Indicated,  and  Brake  Horse-power 1408 

Heat  Generated  by  a  Current 1408 

Heating  of  Conductors 1409 

Heating  of  Coils 1409 

Fusion  of  Wires 1409 

Allowable  Carrying  Capacity  of  Copper  Wires : .  1410 

Underwriters'  Insulation 1410 

Electric  Transmission,  Direct-Currents. 

Drop  of  Voltage  in  Wires  Carrying  Allowed  Currents 1410 

Section  of  Wire  Required  for  a  Given  Current 1410 

Weight  of  Copper  for  a  Given  Power 1411 


Xlii  CONTENTS. 

PAGE 

Short-circuiting 1411 

Economy  of  Electric  Transmission 1411 

Efficiency  of  Electric  Systems 1412 

Wire  Table  for  110,  220,  500,  1000,  and  2000  volt  Circuits 1413 

Resistances  of  Pure  Aluminum  Wire 1414 

Electric  Railways. 

Schedule  Speeds,  Miles  per  Hour 1414 

Train  Resistance 1415 

Rates  of  Acceleration 1415 

Safe  Maximum  Speed  on  Curves 1416 

Electric  Resistance  of  Rails  and  Bonds 1416 

Electric  Locomotives 1416 

Efficiencies  of  Distributing  Systems 1417 

Steam  Railroad  Electrifications 1418 

Electric  Welding. 

Arc  Welding 1419 

Data  of  Electric  Welding  in  Railway  Shops 1419 

Resistance  Welding 1419 

Cost  of  Welding 1420 

Electric  Heaters. 

Elementary  Form  of  Heater 1420 

Relative  Efficiency  of  Electric  and  Steam  Heating 1421 

Heat  Required  to  Warm  and  Ventilate  a  Room 1421 

Domestic  Heating 1421 

Electric  Furnaces. 

Arc  Furnaces  and  Resistance  Furnaces 1422 

Uses  of  Electric  Furnaces 1423 

Electric  Smelting  of  Pig-iron 1424 

Ferro-alloys 1424 

Non-ferrous  Metals 1424 

Electric  Batteries. 

Primary  Batteries 1425 

Description  of  Storage-batteries  or  Accumulators 1425 

Rules  for  Care  of  Storage-batteries 1426 

Efficiency  of  a  Storage  Cell 1427 

Uses  of  Storage-batteries '. 1427 

Edison  Alkaline  Battery 1428 

Electrolysis 1428 

Electro-chemical  Equivalents 1429 

The  Magnetic  Circuit. 

Lines  and  Loops  of  Force 1430 

Values  of  B  and  H 1431 

Tractive  or  Lifting  Force  of  a  Magnet 1431 

Determining  the  Polarity  of  Electro-magnets 

Determining  the  Direction  of  a  Current 1432 

Dynamo-electric  Machines. 

Rating  of  Generators  and  Motors 1432 

Temperature  Limitations  of  Capacity 143£ 

Methods  of  Determining  Temperatures 143 

Temperature  Limits  of  Hottest  Spot 

Moving  Force  of  a  Dynamo-electric  Machine 1435 


CONTENTS.  xliii 

PAGE 

Torque  of  an  Armature 1435 

Torque,  Horse-power  and  Revolutions 1436 

Electro-motive  Force  of  the  Armature  Circuit 1436 

Strength  of  the  Magnetic  Field 1436 

Direct-Current  Generators. 

Series-,  Shunt-  and  Compound- wound 1437 

Commutating  Pole  Machines 1438 

Parallel  Operation 1439 

Three- Wire  System 1439 

Alternating  Currents. 

Maximum,  Average  and  Effective  Values 1440 

Frequency 1440 

Inductance 1440 

Capacity 1440 

Power  Factor 1440 

Reactance,  Impedance,  Admittance 1441 

Skin  Effect 1442 

Ohm's  Law  Applied  to  Alternating  Current  Circuits 1442 

Impedance  Polygons 1442 

Self-inductance  of  Lines  and  Circuits 1446 

Capacity  of  Conductors 1446 

Single-phase  and  Polyphase  Currents t  1446 

Measurement  of  Power  in  Polyphase  Circuits 1447 

Alternating  Current  Generators. 

Synchronous  Generators 1448 

Rating 1448 

Efficiency 1448 

Regulation ; 1449 

Rating  of  a  Generator  Unit 1449 

Windings 1449 

Voltages 1450 

Parallel  Operation 1450 

Exciters 1450 

Transformers. 

Primary  and  Secondary 1451 

Voltage  Ratio 1451 

Rating 1451 

Efficiency 1451 

Connections 1452 

Auto  Transformers 1453 

Constant-Current  Transformers . , 1453 

Synchronous  Converters. 

Description 1453 

Effective  E.M.F.  between  Collector  Rings 1454 

Voltage  Regulation 1455 

Starting  Synchronous  Converters 1455 

Motor-Generators. 

Balancers 1456 

Boosters 1456 

Dynamotors 1457 

Frequency  Changers 1457 

Mercury  Arc  Rectifier 1457 


xliv  CONTENTS. 

Alternating'Current  Circuits. 

PAGfi 

Calculation  of  Alternating  Current  Circuits 1457 

Relative  Weight  of  Copper  Required  in  Different  Systems .....  1459 

Rule  for  Size  of  Wires  for  Three-phase  Transmission  Lines 1459 

Notes  on  High-tension  Transmission 1459 

Voltages  Advisable  for  Various  Line  Lengths 1460 

Line  Spacing 1460 

Size  of  Line  Conductors 1460 

A  135,000- volt  Three-phase  Transmission  System 1461 

Electric  Motors. 

Classification  of  Motors 1461 

Characteristics  of  Motors 1461 

Series  Motor 1461 

Speed  Control  of  Motors 1462 

Shunt  IMotor 1462 

Compound  Motor 1462 

Induction  Motor;  Squirrel-cage  Motor 1463 

Multi-speed  Induction  Motors 1463 

Synchronous  Motors 1463 

Single-phase  Series  Motor 1464 

Repulsion  Induction  Motor 1464 

Reversible  Repulsion  Motor 1464 

Variable-speed  Repulsion  Motor 1464 

Motor  Applications. 

Pumps 1464 

Fans 1465 

Air  Compressors 1465 

Hoists .  . 1465 

Machine  Tools 1466 

Motors  for  Machine  Tools 1467 

Illumination — Electric  and  Gas  Lighting. 

Illumination 1468 

Terms,  Units,  Definitions .... 1468 

Relative  Color  Values  of  Illuminants 1469 

Relation  of  Illumination  to  Vision •. . .  1469 

Types  of  Electric  Lamps 1470 

Street  Lighting 1470 

Illumination  by  Arc  Lamps  at  Different  Distances 1471 

Data  of  Some  Arc  Lamps 1471 

Relative  Efficiency  of  Illuminants 1472 

Characteristics  of  Tungsten  Lamps 1473 

Interior  Illumination 1473 

Quantity  of  Electricity  or  Gas  Required  for  Illuminating 1474 

Standard  Units;  Mazda  and  Welsbach 1475 

Cost  of  Electric  Lighting 1475 

Recent  Street  Lighting  Installations 1476 

Symbols  Used  in  Electric  Diagrams 1477 


NAMES  AND  ABBREVIATIONS  OF  PERIODICALS  AND 
TEXT -BOOKS  FREQUENTLY  REFERRED  TO  IN 
THIS  WORK. 


Am.  Mach.     American  Machinist. 

App.  Cyl.  Mech.     Appleton's  Cyclopaedia  of  Mechanics,  Vols.  I  and  II. 

Bull.  I.  &  S.  A.     Bulletin  of  the  American  Iron  and  Steel  Association. 

Burr's  Elasticity  and  Resistance  of  Materials. 

Clark,  R.  T.  D.  D.  K.  Clark's  Rules,  Tables,  and  Data  for  Mechanical 
Engineers. 

Clark,  S.  E.     D.  K.  Clark's  Treatise  on  the  Steam-Engine. 

Col.  Coll.  Qly.     Columbia  College  Quarterly. 

El.  Rev.     Electrical  Review. 

El.  World.     Electrical  World  and  Engineer. 

Engg.     Engineering  (London). 

Eng.  News.     Engineering  News. 

Eng.  Rec.     Engineering  Record. 

Engr.     The  Engineer  (London). 

Fairbairn's  Useful  Information  for  Engineers. 

Flynn's  Irrigation  Canals  and  Flow  of  Water. 

Indust.  Eng.     Industrial  Engineering. 

Jour.  A.  C.  I.  W.  Journal  of  American  Charcoal  Iron  Workers' 
Association. 

Jour.  Ass.  Eng.  Soc.  Journal  of  the  Association  of  Engineering 
Societies. 

Jour.  F.  I.     Journal  of  the  Franklin  Institute. 

Lanza's  Applied  Mechanics. 

Machy.     Machinery. 

Merriman's  Strength  of  Materials. 

Modern  Mechanism.  Supplementary  volume  of  Appleton's  Cyclo- 
paedia of  Mechanics. 

Peabody's  Thermodynamics. 

Proc.  A.  S.  H.  V.  E.  Proceedings.  Am.  Soc'y  of  Heating  and  Ventilat- 
ing Engineers. 

Proc.  A.  S.  T.  M.     Proceedings  Amer.  Soc'y  for  Testing  Materials. 

Proc.  Inst.  C.  E.     Proceedings  Institution  of  Civil  Engineers  (London). 

Proc.  Inst.  M.  E.  Proceedings  Institution  of  Mechanical  Engineers 
(London) . 

Proceedings  Engineers'  Club  of  Philadelphia. 

Rankine,  S.  E.     Rankine's  The  Steam  Engine  and  other  Prime  Movers. 

Rankine's  Machinery  and  Millwork. 

Rankine,  R.  T.  D.     Rankine's  Rules,  Tables,  and  Data. 

Reports  of  U.  S.  Iron  and  Steel  Test  Board. 

Reports  of  U.  S.  Testing  Machine  at  Watertown,  Massachusetts. 

Rontgen's  Thermodynamics. 

Seaton's  Manual  of  Marine  Engineering. 

Hamilton  Smith,  Jr.'s  Hydraulics. 

Stevens  Indicator. 

Thompson's  Dynamo-electric  Machinery. 

Thurston's  Manual  of  the  Steam  Engine.  « 

Thurston's  Materials  of  Engineering. 

Trans.  A.  I.  E.  E.  Transactions  American  Institute  of  Electrical 
Engineers. 

Trans.  A.  I.  M.  E.  Transactions  American  Institute  of  Mining 
Engineers. 

Trans.  A.  S.  C.  E.     Transactions  American  Society  of  Civil  Engineers. 

Trans.  A.  S.  M.  E.  Transactions  American  Society  of  Mechanical 
Engineers. 

Trautwine's  Civil  Engineer's  Pocket  Book. 

The  Locomotive  (Hartford,  Connecticut). 

Unwin's  Elements  of  Machine  Design. 

Weisbach's  Mechanics  of  Engineering, 

Wood's  Resistance  of  Materials. 

Wood's  Thermodynamics,   _, 


MATHEMATICS. 


Greek  Letter. 


a  Alpha 

j8  Beta 

y  Gamma 

8  Delta 

e  Epsilon 

C  Zeta 


Eta 

N     v 

Nu 

T 

T    Tan 

9  Theta 

H     £ 

Xi 

Y 

v   Upsilon 

Iota 

0      o 

Omicron 

$ 

<t>   Phi 

Kappa 
Lambda 

II       7T 
P        P 

Pi 

Kho 

X 

Y   Chi 
$   Psi 

Mu 

2     as 

Sigma 

O 

w   Omega 

Arithmetical  and  Algebraical  Signs  and  Abbreviations* 


+  plus  (addition). 
+  positive. 
—  minus  (subtraction). 
-  negative. 
±  plus  or  minus. 
T  minus  or  plus. 
=  equals. 
X  multiplied  by. 
ab  or  a.b  =  a  X  b. 
-5-  divided  by. 
/   divided  by. 

2  _«/6  _««.».     15-16  =  if  - 
0.2 -£;  0.002 -jJL. 

V  square  root. 
^  cube  root. 
M  4th  root. 

:  is  to,  ::  so  is,  :  to  (proportion). 
2  :  4  ::  3  :  6,  2  is  to  4  as  3  is  to  6. 
:  ratio;  divided  by. 
2  :  4,  ratio  of  2  to  4  =  2/4. 
.*.  therefore. 
>  greater  than. 
<  less  than. 
D  square. 
O  round. 

0  degrees,  arc  or  thermometer. 
'  minutes  or  feet. 
"  seconds  or  inches. 

"'  accents  to  distinguish  letters, 

as  a',  a",  a'". 
<*!•  «2,  03,  ab,  etc,  read  a  sub  1,  a  sub 

ft,  etc. 


on) 


-  parenthesis,  braclr^ts, 


braces,     vinculum ;     denoting 
that  the  numbers  enclosed  are 
to  be  taken  together;  as, 
(a  +  b)c  =  4  +  3  X  5  =  35, 

a2,  a3,  a  squared,  a  cubed. 

an,  a  raised  to  the  nth  power. 


109  =  10    to     the    9th     power  = 

1,000,000,000. 
sin  a  =  the  sine  of  a. 
sin"1  a  =  the  arc  whose  sine  is  a. 

sin  a-»  =    — ^ — 

sin  a 

log  =  logarithm. 

loge  or  hyp  log  =  hyperbolic  loga- 
rithm. 
%  per  cent. 
A  angle. 


,L  right  angle. 

JL  perpendicular  to. 

sin,  sine. 

cos,  cosine. 

tan,  tangent. 

sec,  secant. 

versin,  versed  sine. 

cot,  cotangent. 

cosec,  cosecant. 

covers,  co-versed  sine. 

In  Algebra,  the  first  letters  of 
the  alphabet,  a,  b,  c,  d,  etc.,  are 
generally  used  to  denote  known 
quantities,  and  the  last  letters, 
w,  x,  y,  z,  etc.,  unknown  quantities. 

Abbreviations    and    Symbols    com- 
monly used, 
d,  differential  (in  calculus). 

,  integral  (in  calculus). 


,  integral  between  limits  a  and  b. 


A,  delta,  difference. 

2,  sigma,  sign  of  summation. 

n,  pi,    ratio    of   circumference   of 

circle  to  diameter  =  3.14159. 
g,  acceleration   due  to  gravity  = 

32.16  ft.  per  second  per  second. 

Abbreviations    frequently    used    in 

this  Book. 

L.,  1.,  length  in  feet  and  inches. 
B.,  b.,  breadth  in  feet  and  inches. 
D.,  d.,  depth  or  diameter. 
H.,  h.,  height,  feet  and  inches. 
T.,  t.,  thickness  or  temperature. 
V.,  v.,  velocity. 
F.,  force,  or  factor  of  safety, 
f.,  coefficient  of  fricti9n. 
E.,  coefficient  of  elasticity. 
11.,  r.,  radius. 
W.,  w.,  weight. 
P.,  p.,  pressure  or  load. 
H.P.,  horse-power. 
I.H.P.,  indicated  horse-power. 
B.H.P.,  brake  horse-power, 
h.  p.,  high  pressure, 
i.  p.,  intermediate  pressure. 
I.  p.,  low  pressure. 
A.W.G.,     American    Wire    Gauge 

(Brown  &  Sharpe). 
B.W.G.,  Birmingham  Wire  Gauge. 
r.  p.  m.,  or  revs,  per  min..  revolu- 
tions per  minute. 
Q.  =*  quantity,  or  volume. 


ARITHMETIC. 


.    ARITHMETIC. 

The  user  of  this  book  is  supposed  to  have  had  a  training  in  arithmetic  as 
well  as  in  elementary  algebra.  Only  those  rules  are  given  here  which  are 
apt  to  be  easily  forgotten. 

GREATEST  COMMON  MEASURE,  OR  GREATEST 
COMMON  DIVISOR  OF  TWO  NUMBERS. 

Rule.  —  Divide  the  greater  number  by  the  less;  then  divide  the  divisor 
by  the  remainder,  and  so  on,  dividing  always  the  last  divisor  by  the  last 
remainder,  until  there  is  no  remainder,  and  the  last  divisor  is  the  greatest 
common  measure  required. 


LEAST  COMMON  MULTIPLE  OF  TWO  OR  MORE 
NUMBERS. 

Rule.  —  Divide  the  given  numbers  by  any  number  that  will  divide  the 
greatest  number  of  them  without  a  remainder,  and  set  the  quotients  with 
the  undivided  numbers  in  a  line  beneath. 

Divide  the  second  line  as  before,  and  so  on,  until  there  are  no  two  num- 
bers that  can  be  divided;  then  the  continued  product  of  the  divisors,  last 
quotients,  and  undivided  numbers  will  give  the  multiple  required. 

FRACTIONS. 

To  reduce  a  common  fraction  to  its  lowest  terms.  —  Divide  both 
terms  by  their  greatest  common  divisor:  39/52  =  3/4. 

To  change  an  improper  fraction  to  a  mixed  number.  —  Divide  the 
numerator  by  the  denominator;  the  quotient  is  the  whole  number,  and 
the  remainder  placed  over  the  denominator  is  the  fraction:  39/4  =  93/4. 

To  change  a  mixed  number  to  an  improper  fraction.  —  Multiply 
the  whole  number  by  the  denominator  of  the  fraction;  to  the  product  add 
the  numerator;  place  the  sum  over  the  denominator:  17/g  =  i5/8. 

To  express  a  whole  number  in  the  form  of  a  fraction  with  a  given 
denominator.  —  Multiply  the  whole  number  by  the  given  denominator, 
and  place  the  product  over  that  denominator:  13  =  39/3. 

To  reduce  a  compound  to  a  simple  fraction,  also  to  multiply 
fractions.  —  Multiply  the  numerators  together  for  a  new  numerator  and 
the  denominators  together  for  a  new  denominator: 

2.4       8      .       2^4       8 
3°f  3  =  9'  alS°    3X3  =  9' 

To  reduce  a  complex  to  a  simple  fraction.  —  The  numerator  and 
denominator  must  each  first  be  given  the  form  of  a  simple  fraction;  then 
multiply  the  numerator  of  the  upper  fraction  by  the  denominator  of  the 
lower  for  the  new  numerator,  and  the  denominator  of  the  upper  by  the 
numerator  of  the  lower  for  the  new  denominator: 

7/8    =  7/8  =  28  =  1 
l3/4        7/4        56        2* 

To  divide  fractions.  —  Reduce  both  to  the  form  of  simple  fractions, 
Invert  the  divisor,  and  proceed  as  in  multiplication: 

3  35       34       12       3 

4  +1V4  -5  +  4~  4X5~20-  5' 

Cancellation  of  fractions.  —  In  compound  or  multiplied  fractions, 
divide  any  numerator  and  any  denominator  by  any  number  which  will 
divide  them  both  without  remainder,  striking  out  the  numbers  thus 
divided  and  setting  down  the  quotients  in  their  stead. 

To  reduce  fractions  to  a  common  denominator.  —  Reduce  each 
fraction  to  the  form  of  a  simple  fraction;  then  multiply  each  numerator 


DECIMALS. 


fcy  all  the  denominators  except  its  own  for  the  new  numerator,  and  all 
the  denominators  together  for  the  common  denominator: 


— , 

42* 


14  f 
42* 


IS 
42* 


To  add  fractions.  —  Reduce  them  to  a  common  denominator,  then 
add  the  numerators  and  place  their  sum  over  the  common  denominator: 


21  +  14  4-  18 
42 


53 
43 


To  subtract  fractions.  —  Reduce  them  to  a  common  denominator, 
subtract  the  numerators  and  place  the  difference  over  the  common  denom- 
inator: 

1  _  3       7-6       J_ 

2  7  ~      14      "  14 


DECIMALS. 

To  add  decimals.  —  Set  down  the  figures  so  that  the  decimal  points 
are  one  above  the  other,  then  proceed  as  in  simple  addition:  18.75'  4-  0.012 
=  18.762. 

To  subtract  decimals.  —  Set  down  the  figures  so  that  the  decimal 
points  are  one  above  the  other,  then  proceed  as  in  simple  subtraction: 
18.75  -  0.012  =  18.738. 

To  multiply  decimals.  —  Multiply  as  in  multiplication  of  whole  num- 
bers, then  point  off  as  many  decimal  places  as  there  are  in  multiplier  and 
multiplicand  taken  together:  1.5  X  0.02  =  .030  =  0.03. 

To  divide  decimals. —  Divide  as  in  whole  numbers,  and  point  off  in 
the  quotient  as  many  decimal  places  as  those  in  the  dividend  exceed  those 
in  the  divisor.  Ciphers  must  be  added  to  the  dividend  to  make  its  decimal 
places  at  least  equal  those  in  the  divisor,  and  as  many  more  as  it  is  desired 
to  have  in  the  quotient:  1.5  -J-  0.25  =  6.  0.1  -i-  0.3  =  0.10000  -i-  0.3 
=  0.3333  +. 

Decimal  Equivalents  of  Fractions  of  One  Inch. 


1-64 

.015625 

17-64 

.265625 

33-64 

.515625 

49-64 

.765625 

1-32 

.03125 

9-32 

.28125 

17-32 

.53125 

25-32 

.78125 

3-64 

.046875 

19-64 

.296875 

35-64 

.546875 

51-64 

.796875 

1-16 

.0625 

5-16 

.3125 

9-16 

.5625 

13-16 

.8125 

5-64 

.078125 

21-64 

.328125 

37-64 

.578125 

53-64 

.828125 

3-32 

.09375 

11-32 

.34375 

19-32 

.59375 

27-32 

.84375 

7-64 

.109375 

23-64 

.359375 

39-64 

.609375 

55-64 

.859375 

1-8 

.125 

3-8 

.375 

5-8 

.625 

7-8 

.875 

9-64 

.140625 

25-64 

.390625 

41-64 

.640625 

57-64 

.890625 

5-32 

.15625 

13-32 

.40625 

21-32 

.65625 

29-32 

.90625 

11-64 

.171875 

27-64 

.421875 

43-64 

.671875 

59-64 

.921875 

3-16 

.1875 

7-16 

.4375 

11-16 

.6875 

15-16 

.9375 

13-64 

.203125 

29-64 

.453125 

45-64 

.703125 

61-64 

.953123 

7-32 

.21875 

15-32 

.46875 

23-32 

,71875 

31-32 

.96875 

15-64 

.234375 

31-64 

.484375 

47-64 

.734375 

63-64 

.984375 

1-4 

.25 

1-3 

.50 

3-4 

.75 

1 

1. 

To  convert  a  common  fraction  into  a  decimal.  —  Divide  the  nume- 
rator by  the  denominator,  adding  to  the  numerator  as  many  ciphers 
prefixed  by  a  decimal  point  as  are  necessary  to  give  the  number  of  decimal 
places  desired  in  the  result:  1/3  =  1.0000  •*•  3  =  0.3333  +. 

To  convert  a  decimal  into  a  common  fraction.  —  Set  down  the 
decimal  as  a  numerator,  and  place  as  the  denominator  1  with  as  many 
ciphers  annexed  as  there  are  decimal  places  in  the  numerator;  erase  the 


ARITHMETIC. 


S3.  $ 


$  2  8 

NO  <s  rx 
t>  00  CO 


i  §  5  3 

>q  t>*  r>»  cq 


in  T  en  —  Q 

eM  ON  NO  en  O 

\O  o  in  o  m 

m  NO  \o  !>•  t> 


t>»  \o  \o  NO  m  m 

rq  m  oo  —  T  i>» 

t>»  «—  m  o  -<r  GO 

•«r  »n  in  \o  NO  vo 

O  ON  oo  fN  >o  «n  in 
en  5r  ^T  S  in  S  2 

^  ^o  t>i  o*  o  R  SS  iS 
vo*—  \O'—  rNtsr-NC^ 
—  moofS>nON<SNO 
c<^  en  en  "^  ^t  ^.  "^  *f\ 

O  en  ir\  06  O  en  iin  oo  O 
o  —  fScn«nspr>.GOO 
moo.  —  •^•t>«OenvOO 

^  oo    —    ^-    06    '—    >n    GO    <s    »n 

—  oovOcnoooineNOrs 

ON  —    •^•rNOCNimcO'—    en 

"1 ;  ts    c^i    CM    en    en    en    en    ^    ^ 

O  —  «n  O^  ^  00  en  t>,  —  \O  O 
O'^-t>.O^r>'-^cO  —  in 
•^•NOoo  —  enmooor4inr>. 

~~.  ^~.  ".  ^  N.  ^  °i  ^  **!  ^  "i 

t>»     <N     t^     (S     00     en     OO     ^     O^     TO     «n 
fNrNNOvOininT-tenenenfN 

§    -.    -.    -.    -.    2    jq    cs    CM    cs    ^   Jn 

u^  —  F>  <n  o  v5  Fi  ON  in  ^  F>  ^  O 
eNQOenONinONO  —  rxenoo^O 
«Ot>«ONO(M'^-inrNOOO'—  enm 
o  O  o  —  —  —  — 4  —  —  cs  cs  cs  CM 

c\i  ^  \o  en  o  oo  in  <s  ON  so  en  *—  oo  «n 
inOoOO«Senint>,oooeN'<r«r>tN, 
enTmt>»ooONO^~eN'^'inNOt>»oo 
OOOOOO  —  —  —  —  •~^1™^^^ 

sO^en    —   ONi>»tnen'—    ONCOO^TP^O 

inen^—  O^NO^<SOoomen^-  ONt>«»n 
^-fNenen-*inNOt>»r>.ooONOO  —  c^ 
o  o  o  o  o  o  o  o  o  o  o  '-;«-;'-;  *~. 

ONOot^^om^fenmvN  —  oONcor%>ovn 
c^J5;^.iXOvcnr>.'-inoNenvOo^oocN 
OO  —  •—  •—  (SeNenenrn^^mininN£ 
OOOOOOOOOOOOOOOC3 


fMoom  —  r>enNN'- 

;j  ~^  «sj  en  en  "t  «r>  in  o.  <q  r>.  cq  cq  O; 


COMPOUND   NUMBERS. 


decimal  point  In  the  numerator,  and  reduce  the  fraction  thus  formed  to  Its 
lowest  terms: 


To  reduce  a  recurring  decimal  to  a  common  fraction.  —  Subtract 
the  decimal  figures  that  do  not  recur  from  the  whole  decimal  including 
one  set  of  recurring  figures;  set  down  the  remainder  as  the  numerator  of 
the  fraction,  and  as  many  nines  as  there  are  recurring  figures,  followed  by 
as  many  ciphers  as  there  are  non-recurring  figures,  in  the  denominator. 
Thus: 

0.79054054,  the  recurring  figures  being  054. 
Subtract    __  79 

7807  'i  117 

99900  "*  (redllced  to  its  l°west  terms)    —  * 


.COMPOUND    OR    DENOMINATE    NUMBERS. 

Reduction  descending. — To  reduce  a  compound  number  to  a  lower 
denomination.  Multiply  the  number  by  as  many  units  of  the  lower 
denomination  as  makes  one  of  the  higher. 


, 

fr 
ae 


3  yards  to  inches:  3  X  36  =  108  inches. 
0.04  square  feet  to  square  inches:  .04  X  144 


•  5.76  sq.  in. 


_  the  given  number  is  in  more  than  one  denomination  proceed  in  steps 
from  the  highest  denomination  to  the  next  lower,  and  so  on  to  the  lowest, 
adding  in  the  units  of  each  denomination  as  the  operation  proceeds. 

3  yds.  1  ft.  7  in.  to  inches:  3X3  =  9,4-1=10,  10  X  12  =  120, +7  =  127 in. 

Reduction  ascending.  —  To  express  a  number  of  a  lower  denomina- 
tion in  terras  of  a  higher,  divide  the  number  by  the  number  of  units  of 
the  lower  denomination  contained  in  one  of  the  next  higher;  the  quotient 
is  in  the  higher  denomination,  and  the  remainder,  if  any,  in  the  lower. 
127  inches  to  higher  denomination. 

127  -^  12  =  10  feet  +  7  inches;  10  feet  •*-  3  =  3  yards  4-  1  foot. 

Ans.  3  yds.  1  ft.  7  in. 

To  express  the  result  in  decimals  of  the  higher  denomination,  divide  the 
given  number  by  the  number  of  units  of  the  given  denomination  contained 
in  one  of  the  required  denomination,  carrying  the  result  to  as  many  places 
of  decimals  as  may  be  desired. 

127  inches  to  yards:     127  -^  36  •=  319/ae  =  3.5277  4-  yards. 

Decimals  of  a  Foot  Equivalent  to  Inches  and  Fractions 
of  an  Inch. 


Inches 

0 

H 

X 

H 

H 

ft 

X 

% 

0 

0 

.01042 

.02083 

.03125 

.04167 

.05208 

.06250 

.07292 

1 

.0833 

.0938 

.1042 

.1146 

.1250 

.1354 

.1458 

.1563 

2 

.1667 

.1771 

.1875 

.1979 

.2083 

.2188 

.2292 

.2396 

3 

.2500 

.2604 

.2708 

.2813 

.2917 

.3021 

.3125 

.3229 

4 

.3333 

.3438 

.3542 

.3646 

.3750 

.3854 

.3958 

.4063 

5 

.4167 

.4271 

.4375 

.4479 

.4583 

.4688 

.4792 

.4896 

.  6 

.5000 

.5104 

.5208 

.5313 

.5417 

.5521 

.5625 

.5729 

7 

.5833 

.5938 

.6042 

.6146 

.6250 

.6354 

.6458 

.6563 

8 

.6667 

.6771 

.6875 

.6979 

.7083 

.7188 

.7292 

.7396 

9 

.7500 

.7604 

.7708 

.7813 

.7917 

.8021 

.8125 

.8229 

10 

.8333 

.8438 

.8542 

.8646 

.8750 

.8854 

.8958 

.9063 

11 

.9167 

.9271 

.9375 

.9479 

.9583 

.9688 

.9792 

.9896 

ARITHMETIC. 


RATIO  AND  PROPORTION. 

Ratio  Is  the  relation  of  one  number  to  another,  as  obtained  by  dividing 
the  first  number  by  the  second.  Synonymous  with  quotient. 

Ratio  of  2  to  4,  or  2  :  4  =  2/4=  l/2. 
Ratio  of  4  to  2,  or  4  :  2  =  2. 

Proportion  is  the  equality  of  two  ratios.  Ratio  of  2  to  4  equals  ratio 
of  3  to  6,  2/4=3/6;  expressed  thus,  2  :  4  ::  3  :  6;  read,  2  is  to  4  as  3  is  to  6. 

The  first  and  fourth  terms  are  called  the  extremes  or  outer  terms,  the 
second  and  third  the  means  or  inner  terms. 

The  product  of  the  means  equals  the  product  of  the  extremes: 

2  :  4  :  :  3  :  6;     2  X  6  =  12;     3  X  4  =  12. 

Hence,  given  the  first  three  terms  to  find  the  fourth,  multiply  the 
second  and  third  terms  together  and  divide  by  the  first. 

2  :  4  : :  3  :  what  number?     Ans.    ~-^  =  6. 

Algebraic  expression  of  proportion.  — a  :  b  :  :  c  :  d;  r  =  -;  ad  *»5c; 

be  be    ,      ad,  ad 

from  which  a  =   -r  ;  d=  —  ;  6=  —  ;   c  =  -7-  • 
a  a  c  o 

From  the  above  equations  may  also  be  derived  the  following: 
6  :  a::d  :  c        a  +  b  :  a  :  :c  +  d  :  c'       a  +  b  :  a  —  b  :  :  c  +  d  ;  c  —  d 
a  :  c  : :  b  :  d        a  +  b  :  b  : :  c  +  d  :  d        an  :  b™  :  _:  cn  :  dn 
a-.b^cid        a  -b:b::c  -  d:d        ^  :   ty  :  :  ^/c  ^ 
a  —  b  :  a:  :c  —  d  :  c 

Mean  proportional  between  two  given  numbers,  1st  and  2d,  is  such 
a  number  that  the  ratio  which  the  first  bears  to  it  equals  the  ratio  which  it 
bears  to  the  second.  Thus,  2:4::4:8;4isa  mean  proportional  between 

2  and  8.     To  find  the  mean  proportional  between  two  numbers,  extract 
the  square  root  of  their  product. 

Mean  proportional  of  2  and  8  =  V2  X  8  =  4. 

Single  Rule  of  Three;  or,  finding  the  fourth  term  of  a  proportion 
when  three  terms  are  given.  —  Rule,  as  above,  when  the  terms  are  stated 
in  their  proper  order,  multiply  the  second  by  the  third  and  divide  by  the 
first.  The  difficulty  is  to  state  the  terms  in  their  proper  order.  The 
term  which  is  of  the  same  kind  as  the  required  or  fourth  term  is  made  the 
third;  the  first  and  second  must  be  like  each  other  in  kind  and  denomina- 
tion. To  determine  which  is  to  be  made  second  and  which  first  requires 
a  little  reasoning.  If  an  inspection  of  the  problem  shows  that  the  answer 
should  be  greater  than  the  third  term,  then  the  greater  of  the  other  two 
given  terms  should  be  made  the  second  term  —  otherwise  the  first.  Thus, 

3  men  remove  54  cubic  feet  of  rock  in  a  day;  how  many  men  will  remove 
in  the  same  time  10  cubic  yards?    The  answer  is  to  be  men  —  make  men 
third  term;  the  answer  is  to  be  more  than  three  men,  therefore  make  the 
greater  quantity,  10  cubic  yards,  the  second  term;  but  as  it  is  not  the  same 
denomination  as  the  other  term  it  must  be  reduced,  =  270  cubic  feet. 
The  proportion  is  then  stated: 

3  X  270 
54  :  270  : :  3  :  x  (the  required  number);  x  =  — ^ir~  =  15  men. 

O'x 

The  problem  is  more  complicated  if  we  increase  the  number  of  given 
terms.  Thus,  in  the  above  question,  substitute  for  the  words  "in  the 
same  time"  the  words  '*  in  3  days."  First  solve  it  as  above,  as  if  the  work 
were  to  be  done  in  the  same  time;  then  make  another  proportion,  stating 
it  thus:  If  15  men  do  it  in  the  same  time,  it  will  take  fewer  men  to  do  it  in 
3  days;  make  1  day  the  second  terra  and  3  days  the  first  term,  3:1:: 
15  men  :  5  men. 


POWERS    OF    NUMBERS. 


. 

FJ 


Compound  Proportion,  or  Double  Rule  of  Three.  —  By  this  rule 
are  solved  questions  like  the  one  just  given,  in  which  two  or  more  statings 
are  required  by  the  single  rule  of  three.  In  it,  as  in  the  single  rule,  there 
is  one  third  term,  which  is  of  the  same  kind  and  denomination  as  the 
fourth  or  required  term,  but  there  may  be  two  or  more  first  and  second 
terms.  Set  down  the  third  term,  take  each  pair  of  terms  of  the  same  kinc1 
separately,  and  arrange  them  as  first  and  second  by  the  same  reasoning  as 
is  adopted  in  the  single  rule  of  three,  making  the  greater  of  the  pair  the 
second  if  this  pair  considered  alone  should  require  the  answer  to  be»greater. 

Set  down  all  the  first  terms  one  under  the  other,  and  likewise  all  the 
second  terms.  Multiply  all  the  first  terms  together  and  all  the  second 
terms  together.  Multiply  the  product  of  all  the  second  terms  by  the  third 
term,  and  divide  this  product  by  the  product  of  all  the  first  terms. 
Example:  If  3  men  remove  4  cubic  yards  in  one  day,  working  12  hours  a 
day,  how  many  men  working  10  hours  a  day  will  remove  20  cubic  yards 
in  3  days? 

Yards  4        90 

: :  3  men  :  x  men . 

Products  120     240  : :  3  :  6  men.     Ans. 

To  abbreviate  by  cancellation,  any  one  of  the  first  terms  may  cancel 
either  the  third  or  any  of  the  second  terms;  thus,  3  in  first  cancels  3  in 
third,  making  it  1,  10  cancels  into  20  making  the  latter  2,  which  into  4 
makes  it  2,  which  into  12  makes  it  6.  and  the  figures  remaining  are  only 
1  :  6  : :  1  :  6. 


Yards 
Days 
Hours 

4 
3 
10 

20 
1 
12 

INVOLUTION,  OR  POWERS  OF  NUMBERS. 


Involution  is  the  continued  multiplication  of  a  number  by  itself  a  given 
number  of  times.  The  number  is  called  the  root,  or  first  power,  and  the 
products  are  called  powers.  The  second  power  is  called  the  square  and 
the  third  power  the  cube.  The  operation  may  be  indicated  without  being 
performed  by  writing  a  small  figure  called  the  index  or  exponent  to  the 
right  of  and  a  little  above  the  root;  thus,  33  =  cube  of  3,  =  27. 

To  multiply  two  or  more  powers  of  the  same  number,  add  their  expo- 
nents; thus,  22  X  23  =  25,  or  4  X  8  =  32  =  25. 

To  divide  two  powers  of  the  same  number,  subtract  their  exponents; 


thus,  23  -*•  22  =  2l  =  2;    22  -s-  24  =  2~2  =.£5 


The  exponent  may 


thus  be  negative.  23  -f-  23  =  2°  =  1,  whence  the  zero  power  of  any 
number  =  1.  The  first  power  of  a  number  is  the  number  itself.  The 
exponent  may  be  fractional,  as  2*,  2$,  which  means  that  the  root  is  to  be 
raised  to  a  power  whose  exponent  is  the  numerator  of  the  fraction,  and 
the  root  whose  sign  is  the  denominator  is  to  be  extracted  (see  Evolution). 
The  exponent  may  be  a  decimal,  as  2°'5,  21'5;  read,  two  to  the  five-tenths 
power,  two  to  the  one  and  five-tenths  power.  These  powers  are  solved  by 
means  of  Logarithms  (which  see). 

First  Nine  Powers  of  the  First  Nine  Numbers. 


^1 

b 

o 

^ 

4th 

5th 

6th 

7th 

8th 

9th 

J§ 

s§ 

en  § 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

PL. 

PH 

PH 

1 

, 

1 

1 

1 

1 

1 

1 

1 

2 

4 

8 

16 

32 

64 

128 

256 

512 

3 

9 

27 

81 

243 

729 

2187 

6561 

19683 

A 

16 

64 

256 

1024 

4096 

16384 

65536 

262144 

5 

25 

125 

625 

3125 

15625 

78125 

390625 

1953125 

6 

36 

216 

1296 

7776 

46656 

279936 

1679616 

10077696 

7 

49 

343 

2401 

16807 

1  1  7649 

823543 

5764801 

40353607 

8 

64 

512 

4096 

32768 

262144 

2097152 

16777216 

134217728 

9 

81 

729 

6561 

59049 

531441 

4782969 

43046721 

387420489 

ARITHMETIC, 


The  First  Forty  Powers  of  2. 


0 

I 

o 

Q 

J3 

o 

QJ 

1 

1 

J3 

i 

O 

1 

£ 

> 

^ 

PH 

*" 

ft 

> 

ft 

0 

, 

9 

512 

18 

262144 

27 

134217728 

36 

68719476736 

1 

2 

10 

1024 

19 

524288 

28 

268435456 

37 

137438953472 

2 

4 

11 

2048 

20 

1048576 

29 

536870912 

38 

274877906944 

3 

8 

12 

4096 

21 

2097152 

30 

1073741824 

39 

549755813888 

4 

16 

13 

8192 

22 

4194304 

31 

2147483648 

40 

1099511627776 

5 

32 

14 

16384 

23 

8388608 

32 

4294967296 

6 

64 

15 

32768 

24 

16777216 

33 

8589934592 

7 

128 

16 

65536 

25 

33554432 

34 

17179869184 

8 

256 

17 

131072 

26 

67108864 

35 

34359738368 

EVOLUTION. 

Evolution  is  the  finding  of  the  root  (or  extracting  the  root)  of  any 
number  the  power  of  which  is  given. 

The  sign  V  indicates  that  the  square  root  is  to  be  extracted:  ^  <\J  <^/ 
the  cube  root,  4th  root,  nth  root. 

A  fractional  exponent  with  1  for  the  numerator  of  the  fraction  is  also 
used  to  indicate  that  the  operation  of  extracting  the  root  is  to  be  per- 
formed; thus,  2*,  2*  =  <\/2,  -\/2. 

When  the  power  of  a  number  is  indicated,  the  involution  not  being  per- 
formed, the  extraction  of  any  root  of  that  power  may  also  be  indicated  by 
dividing  the  index  of  the  power  by  the  index  of  the  root,  indicating  the 
division  by  a  fraction.  Thus,  extract  the  square  root  of  the  6th  power 
of  2: 

*/2«  =  2*  =  2*  =  23  =  8. 

The  6th  power  of  2,  as  in  the  table  above,  is  64:  v'ei  =  8. 

Difficult  problems  in  evolution  are  performed  by  logarithms,  but  the 
square  root  and  the  cube  root  may  be  extracted  directly  according  to  the 
rules  given  below.  The  4th  root  is  the  square  root  of  the  square  root. 
The  6th  root  is  the  cube  root  of  the  square  root,  or  the  square  root  of  the 
cube  root;  the  9th  root  is  the  cube  root  of  the  cube  root;  etc. 

To  Extract  the  Square  Root.  —  Point  off  the  given  number  into 
periods  of  two  places  each,  beginning  with  units.  If  there  are  decimals, 
point  these  off  likewise,  beginning  at  the  decimal  point,  and  supplying 
as  many  ciphers  as  may  be  needed.  Find  the  greatest  number  whose 
square  is  less  than  the  first  left-hand  period,  and  place  it  as  the  first 
figure  in  the  quotient.  Subtract  its  square  from  the  left-hand  period, 
and  to  the  remainder  annex  the  two  figures  of  the  second  period  for 
a  dividend.  Double  the  first  figure  of  the  quotient  for  a  partial  divisor; 
find  how  many  times  the  latter  is  contained  in  the  dividend  exclusive 
of  the  right-hand  figure,  and  set  the  figure  representing  that  number  of 
times  as  the  second  figure  in  the  quotient,  and  annex  it  to  the  right  of 
the  partial  divisor,  forming  the  complete  divisor.  Multiply  this  divisor 
by  the  second  figure  in  the  quotient  and  Subtract  the  product  from  the 
dividend.  To  the  remainder  bring  down  the  next  period  and  proceed  as 
before,  in  each  case  doubling  the  figures  in  the  root  already  found  to  obtain 
the  trial  divisor.  Should  the  product  of  the  second  figure  in  the  root  by 
the  completed  divisor  be  greater  than  the  dividend,  erase  the  second 
figure  both  from  the  quotient  and  from  the  divisor,  and  substitute  the 
next  smaller  figure,  or  one  small  enough  to  make  the  product  of  the  second 
figure  by  the  divisor  less  than  or  equal  to  the  dividend. 


6QUA 
o  i  A  1  rcnofl 


CUBE   ROOT. 


SQUARE   ROOT. 

3.1415926536  U/77245  -f 
1 

27(214 
1189 

34712515 
(2429 

354218692 
7084 


CUBE    ROOT. 


35444  160865 
1141776 

55448511908936 
)1772425 


300  X  I2 
30  X  1 


1.881.365.963.6251 12345 
1 

=  300  881 
X2  =    60 
22=      4 

364  728 


300X122  =43200 

30  X  12     X  3    =   1080 

32  =          9 


44289 


I 

300  X  1232  =   4538700 

30  X  123   X  4    =        14760 

42=  16 


4553476 

300X12342        =456826800 

30X1234X5=        185100 

52=  25 


457011925 


20498963 


18213904 


2285059625 


2285059625 


To  extract  the  square  root  of  a  fraction,  extract  the  root  of  a  numerator 

/4~      2 
and  denominator  separately,    1/g  =  ~»  or  first  convert  the  fraction  into 

a  decimal,   *\|  =  V.4444  4-  =  0.6666  -K 

To  Extract  the  Cube  Root.  —  Point  off  the  number  into  periods  of  3 
figures  each,  beginning  at  the  right  hand,  or  unit's  place.  Point  off 
decimals  in  periods  of  3  figures  from  the  decimal  point.  Find  the  greatest 
cube  that  does  not  exceed  the  left-hand  period;  write  its  root  as  the  first 
figure  in  the  required  root.  Subtract  the  cube  from  the  left-hand  period, 
and  to  the  remainder  bring  down  the  next  period  for  a  dividend. 

Square  the  first  figure  of  the  root;  multiply  by  300,  and  divide  the 
product  into  the  dividend  for  a  trial  divisor;  write  the  quotient  after 
the  first  figure  of  the  root  as  a  trial  second  figure. 

Complete  the  divisor  by  adding  to  300  times  the  square  of  the  first 
figure,  30  times  the  product  of  the  first  by  the  second  figure,  and  the 
square  of  the  second  figure.  Multiply  this  divisor  by  the  second  figure; 
subtract  the  product  from  the  remainder.  (Should  the  product  be  greater 
than  the  remainder,  the  last  figure  of  the  root  and  the  complete  divisor 
are  too  large;  substitute  for  the  last  figure  the  next  smaller  number,  and 
correct  the  trial  divisor  accordingly.) 

To  the  remainder  bring  down  the  next  period,  and  proceed  as  before  to 
find  the  third  figure  of  the  root  —  that  is,  square  the  two  figures  of  the 
root  already  found;  multiply  by  300  for  a  trial  divisor,  etc. 

If  at  any  time  the  trial  divisor  is  greater  than  the  dividend,  bring  down 
another  period  of  3  figures,  and  place  0  in  the  root  and  proceed. 

The  cube  root  of  a  number  will  contain  as  many  figures  as  there  are 
periods  of  3  in  the  number. 

To  Extract  a  Higher  Root  than  the  Cube.  —  The  fourth  root  is  the 
square  root  of  the  square  root;  the  sixth  root  is  the  cube  root  of  the  square 
root  or  the  square  root  of  the  cube  root.  Other  roots  are  most  conve- 
niently found  by  the  use  of  logarithms. 

ALLIGATION. 

shows  the  value  of  a  mixture  of  different  ingredients  when  the  quantity 
and  value  of  each  are  known. 

Let  the  ingredients  be  a,  b,  c,  d,  etc.,  and  their  respective  values  per 
unit  w,  x,  y,  z,  etc. 


10  ARITHMETIC. 

A  «=  the  sum  of  the  quantities  =  a+b+c+dt  etc. 
P  =  mean  value  or  price  per  unit  of  A. 
AP  =  aw  +  bx  +  cy  +  dz,  etc. 
P  =  aw  +  bx  +  cy  +  dz 
A 

PERMUTATION 

shows  in  how  many  positions  any  number  of  things  may  be  arranged  in  a 
row;  thus,  the  letters  a,  b,  c  may  be  arranged  in  six  positions,  viz.  abc,  acb, 
cab,  cba,  bac,  bca. 

Rule.  —  Multiply  together  all  the  numbers  used  in  counting  the  things; 
thus,  permutations  of  1,  2,  and  3  =  1X2X3  =  6.  In  how  many 
positions  can  9  things  in  a  row  be  placed? 

1X2X3X4X5X6X7X8X9  =  362880. 

COMBINATION 

shows  how  many  arrangements  of  a  few  things  may  be  made  out  of  a 
greater  number.  Rule:  Set  down  that  figure  which  indicates  the  greater 
number,  and  after  it  a  series  of  figures  diminishing  by  1,  until  as  many  are 
set  down  as  the  number  of  the  few  things  to  be  taken  in  each  combination. 
Then  beginning  under  the  last  one,  set  down  said  number  of  few  things; 
then  going  backward  set  down  a  series  diminishing  by  1  until  arriving 
under  the  first  of  the  upper  numbers.  Multiply  together  all  the  upper 
numbers  to  form  one  product,  and  all  the  lower  numbers  to  form  another; 
divide  the  upper  product  by  the  lower  one. 

How  many  combinations  of  9  things  can  be  made,  taking  3  in  each  com- 
bination? 

9X8X7  _  504  _ 

1X2X3"     6 

ARITHMETICAL  PROGRESSION, 

in  a  series  of  numbers,  is  a  progressive  increase  or  decrease  in  each  succes- 
sive number  by  the  addition  or  subtraction  of  the  same  amount  at  each 
step,  as  1,  2,  3,  4,  5,  etc.,  or  15,  12,  9,  6,  etc.  The  numbers  are  called  terms, 
and  the  equal  increase  or  decrease  the  difference.  Examples  in  arithmeti- 
cal progression  may  be  solved  by  the  following  formulae: 

Let  a  =  first  term,  I  =  last  term,  d  =  common  difference,  n  =  number 

of  terms,  s  =  sum  of  the  terms; 

1  /  /         1    \2 

I  =  a  +  (n  —  l)d,  =  —  -  d  ±  y  2ds  -f  I  a  —  -  d\  9 

2s  s    ,    (n  —  I)d 

~  ~n  ~~  a>  =  ri        — 2 — 


X"*J*  2  2d 

2  2 


==id±  Id  4-ldV-- 


l-a 
d-^-l* 

P  -  a 


'  2s  -  I  —  a 

I  -  a    , 

~T~   *"  *• 

2s 
!  I  +  a '  2d 


2(s  -  an) 

n(n  -  1)  ' 
2(nl  -  s) 

n(n  -  1) 

d  —  2a  ±  V(2a  -  < 

*)2  +  8ds 

2d 

21  +  d  ±  ^(21  -f  d)! 

*  -  Sds 

GEOMETRICAL   PROGRESSION. 


GEOMETRICAL  PROGRESSION. 


11 


»ix  ci  series  of  numbers,  is  a  progressive  increase  or  decrease  in  each  suc- 
cessive number  by  the  same  multiplier  or  divisor  at  each  step,  as  1,  2,  4,  8, 
16,  etc.,  or  243,  81,  27,  9,  etc.  The  common  multiplier  is  called  the  ratio. 
Let  a  =  first  term,  I  =  last  term,  r  =  ratio  or  constant  multiplier,  n  = 
number  of  terms,  m  =  any  term,  as  1st,  2d,  etc.,  s  =  sum  of  the  terms: 


log  I  =  log  a  +  (n  -  1)  logr,  l(s  —  J)71""1  -  a(s  -  a)n~l  =  0, 

m  =  arm—1  log  m  =  log  a  +  (m  —  1)  log  r. 

n~^-n^/a^       _     lrn_l 


rl-a 


log?  -  log  a 

logr            h1' 
log  I  —  log  a 

~~  log  (s  —  a)  —  log  (s  -  I) 


log  [a  +  (r  -  l)s]  -  log  a  ( 

logr 
log?  —  log  [Ir  —  (r  —  l)s] 

logr 


Population  of  the  United  States. 

(A  problem  in  geometrical  progression.) 


Year. 

1860 
1870 
1880 
1890 
1900 
1910 
1920 


Population. 

31,443,321 
39,818,449* 
50,155,783 
62,622,250 
76,295,220 
91,972,267 
Est.  110,367,000 


Increase  in  10    Annual  Increase, 
Years,  per  cent.          per  cent. 


26.63 
25.96 
24.86 
21.834 
20.53 
Est.  20.0 


2.39 
2.33 
2.25 
1.994 
1.886 
Est.  1.840 


Estimated  Population  in  Each  Year  from  1880  to  1919. 
(Based  on  the  above  rates  of  increase,  in  even  thousands.) 


I860. 

50,156 

1890. 

62.622 

1900. 

76.295 

1910.. 

91.972 

1881. 

51,281 

1891. 

63.871 

1901  . 

77.734 

1911  .. 

93.665 

1882. 

52.433 

1892. 

65.145 

1902. 

79.201 

1912.. 

95.388 

1883. 

53.610 

1893. 

66444 

1903. 

80.695 

1913.. 

97,143 

1884. 

54.813 

1894. 

67.770 

1904. 

82.217 

1914.. 

98.930 

1885. 

56,043 

1895. 

69,122 

1905. 

83.768 

1915.. 

100.750 

1886. 

57.301 

1896. 

70.500 

1906. 

85.348 

1916.. 

102.604 

1887. 

58,588 

1897. 

71.906 

1907. 

86.958 

1917.. 

104.492 

1888. 

59.903 

1898. 

73.341 

1908. 

88.598 

1918.. 

106.414 

1889. 

61,247 

1899. 

74.803 

1909. 

90.269 

1919.. 

108.373 

*  Corrected  by  addition  of  1,260,078,  estimated  error  of  the  census  of 
1870,  Census  Bulletin  No.  16,  Dec,  13, 1890. 


12  ARITHMETIC. 

The  preceding  table  has  been  calculated  by  logarithms  as  follows: 
log  r  =  log  I  —  log  a  -5-  (n  —  1),  log  m  =  log  a  +  (m  -  1)  log  f 

Pop.  1900.  .  .76,295,220  log  =  7.8824988  =  log  I 

1890.  .  .62,622,250  log  =  7.7967285  =  log  a 

diff.  =     .0857703 

n  «=  11,  n  -  1  =  10;  diff.  -J-  10  =     .00857703          =  log  r, 
add  log  for  1890       7.7967285  •=  log  a 

log  for  1891  =  7.80530553  No.  =  63,871  . . 
add  again         .00857703 

log  for  1892       7.81388256  No.  =  65,145  . . . 

Compound  interest  is  a  form  of  geometrical  progression;  the  ratio 
being  1  plus  the  percentage. 


PERCENTAGE:  PROFIT  AND  LOSS:    PER  CENT 
OF  EFFICIENCY. 

Per  cent  means  "by  the  hundred."  A  profit  of  10  per  cent  means  a 
gain  of  $10  on  every  $100  expended.  If  a  thing  is  bought  for  $1  and  sold 
for  $2  the  profit  is  100  per  cent;  but  if  it  is  bought  for  $2  and  sold  for  $1 
the  loss  is  not  100  per  cent,  but  only  50  per  cent. 

Rule  for  percentage:  Per  cent  gain  or  loss  is  the  gain  or  loss  divided  by 
the  original  cost,  and  the  quotient  multiplied  by  100. 

Efficiency  is  defined  in  engineering  as  the  quotient  "output  divided  by 
input,"  that  is,  the  energy  utilized  divided  by  the  energy  expended.  The 
difference  between  the  input  and  the  output  is  the  loss  or  waste  of  energy. 
Expressed  as  a  fraction,  efficiency  is  nearly  always  less  than  unity.  Ex- 
pressed as  a  per  cent,  it  is  this  fraction  multiplied  by  100.  Thus  we  may 
say  that  a  motor  has  an  efficiency  of  0.9  or  of  90  per  cent. 

The  efficiency  of  a  boiler  is  the  ratio  of  the  heat  units  absorbed  by  the 
boiler  in  heating  water  and  making  steam  to  the  heating  value  of  the  coal 
burned.  The  saving  in  fuel  due  to  increasing  the  efficiency  of  a  boiler 
from  60  to  75%  is  not  25%,  but  only  20%.  The  rule  is:  Divide  the  gain 
in  efficiency  (15)  by  the  greater  figure  (75).  The  amount  of  fuel  used  is 
inversely  proportional  to  the  efficiency;  that  is,  60  Ibs.  of  fuel  with  75% 
efficiency  will  do  as  much  work  as  75  Ibs.  with  60%  efficiency.  The 
saving  of  fuel  is  15  lb*.  which  is  20%  of  75  Ibs. 


INTEREST  AND  DISCOUNT. 

Interest  is  money  paid  for  the  use  of  money  for  a  given  time;  tho 
factors  are: 

p,  the  sum  loaned,  or  the  principal; 

t,  the  time  in  years; 

r,  the  rate  of  interest ; 

i,  the  amount  of  interest  for  the  given  rate  and  time; 

a  =  p  +  i  =    the  amount  of  the  principal  with  interest 

at  the  end  of  the  time. 
Formulas: 

i  —  interest  =  principal  X  time  X  rate  per  cent  =  i  =  J-QQ  I 

a  —  amount  =  principal  +  interest  =  p  +  ^g  •' 
lOOi 


r  -rate- 


INTEREST  AND   DISCOUNT.  33 

If  the  rate  is  expressed  decimally,  —  thus,  6  per  cent  =  .06, —  the 
formulse  become 

Rules  for  finding  Interest.  —  Multiply  the  principal  by  the  rate  per 
annum  divided  by  100,  and  by  the  time  in  years  and  fractions  of  a  year. 

If  the  time  is  given  in  days,  interest  =  Principal  X  rate  X  no.  of  Jays  _ 

ooo  X  100 

In  banks  interest  is  sometimes  calculated  on  the  basis  of  360  days  to  a 
year,  or  12  months  of  30  days  each. 

Short  rules  for  interest  at  6  per  cent,  when  360  days  are  taken  as  1  year: 

Multiply  the  principal  by  number  of  days  and  divide  by  6000. 

Multiply  the  principal  by  number  of  months  and  divide  by  200. 

The  interest  of  1  dollar  for  one  month  is  £  cent. 

Interest  of  10O  Dollars  for  Different  Times  and  Rates. 

Time  3%         3%        4%         5%         6%         8%         10% 

lyear  $2.00      $3.00      $4.00      $5.00      $6.00       $8.00     $10.00 

1  month  .16|         .25          .33£         .41§        .50  .66|         .83$ 

lday=g|5year.0055i    .0083£    .0111$     .0138f     .0166§    .0222§      .02775 

is  year  .005479  .008219  .010959  .013699  .016438  .0219178  .0273973 


Discount  is  interest  deducted  for  payment  of  money  before  it  is  due. 

True  discount  is  the  difference  between  the  amount  of  a  debt  payable 
at  a  future  date  without  interest  and  its  present  worth.  The  present 
worth  is  that  sum  which  put  at  interest  at  the  legal  rate  will  amount  to 
the  debt  when  it  is  due. 

To  find  the  present  worth  of  an  amount  due  at  a  future  date,  divide  the 
amount  by  the  amount  of  $1  placed  at  interest  for  the  given  time.  The 
discount  equals  the  amount  minus  the  present  worth. 

What  discount  should  be  allowed  on  $103  paid  six  months  before  it  is 
due,  interest  being  6  per  cent  per  annum? 

— ?  =  $100  present  worth,  discount  =  3.00. 
1  +1  X  .06  X  ^ 

Bank  discount  is  the  amount  deducted  by  a  bank  as  interest  on  money 
loaned  on  promissory  notes.  It  is  interest  calculated  not  on  the  actual 
sum  loaned,  but  on  the  gross  amount  of  the  note,  from  which  the  discount 
is  deducted  in  advance.  It  is  also  calculated  on  the  basis  of  360  days 
in  the  year,  and  for  3  (in  some  banks  4)  days  more  than  the  time  specified 
in  the  note.  These  are  called  days  of  grace,  and  the  note  is  not  payable 
till  the  last  of  these  days.  In  some  States  days  of  grace  have  been 
abolished. 

What  discount  will  be  deducted  by  a  bank  in  discounting  a  note  for  $103 
payable  6  months  hence?  Six  months  =  182  days,  add  3  days  grace  =  185 


Compound  Interest.  —  In  compound  interest  the  interest  is  added  to 
the  principal  at  the  end  of  each  year,  (or  shorter  period  if  agreed  upon). 

Let  p  =  the  principal,  r  =  the  rate  expressed  decimally,  n  =  no.  of 
years,  and  a  the  amount: 


o  —  amount  —  p(l  +  r)n;  r  —  rate  =»   u  -  -  1. 
p  —  principal  =»    (l  £  .n  ;  no.  of  y.ears=-  n  = 


14 


ARITHMETIC. 


Compound  Interest  Table. 

(Value  of  one  dollar  at  compound  interest,  compounded  yearly,  at 
3,  4,  5,  and  6  per  cent,  from  1  to  50  years.) 


£ 

Per  cent 

t 

§ 
** 

Per  cent 

3 

4 

5 

6 

3 

4 

5 

6 

i 

.03 

.04 

.05 

.06 

16 

.6047 

1  .8730 

2.1829 

2.5403 

2 

.0609 

.0816 

.1025 

.1236 

17 

.6528 

1.9479 

2.2920 

2.6928 

3 

.0927 

.1249 

.1576 

.1910 

18 

.7024 

2.0258 

2.4066 

2.8543 

4 

.1255 

.1699 

.2155 

.2625 

19 

.7535 

2.1068 

2.5269 

3.0256 

5 

.1593 

.2166 

.2763 

.3382 

20 

.8061 

2.1911 

2.6533 

3.2071 

6 

.1941 

.2653 

.3401 

.4185 

21 

.8603 

2.2787 

2.7859 

3.3995 

7 

.2299 

.3159 

.4071 

.5036 

22 

.9161 

2.3699 

2.9252 

3.6035 

8 

.2668 

.3686 

.4774 

.5938 

23 

.9736 

2.4647 

3.0715 

3.8197 

9 

.3048 

.4233 

.5513 

.6895 

24 

2.0328 

2.5633 

3.2251 

4.0487 

10 

.3439 

.4802 

.6289 

.7908 

25 

2.0937 

2.6658 

3.3863 

4.2919 

11 

.3842 

.5394 

.7103 

1.8983 

30 

2.4272 

3.2433 

4.3219 

5.7435 

12 

.4258 

.6010 

.7958 

2.0122 

35 

2.8138 

3.9460 

5.5159 

7.6862 

13 

.4685 

.6651 

.8856 

2.1329 

40 

3.2620 

4.8009 

7.0398 

10.2858 

14 

1.5126 

.7317 

.9799 

2.2609 

45 

3.7815 

5.8410 

8.9847 

13.7648 

15 

1.5580 

.8009 

2.0789 

2.3965 

50 

4.3838 

7.1064 

11.4670 

18.4204 

At  compound  interest  at  3  per  cent  money  will  double  itself  in  23 1/2  years, 
at  4  per  cent  in  172/3  years,  at  5  per  cent  in  14.2  years,  and  at  6  per  cent  io 
11. 9  years. 

EQUATION  OF  PAYMENTS. 

By  equation  of  payments  we  find  the  equivalent  or  average  time  in 
which  one  payment  should  be  made  to  cancel  a  number  of  obligations  due 
at  different  dates;  also  the  number  of  days  upon  which  to  calculate  interest 
or  discount  upon  a  gross  sum  which  is  composed  of  several  smaller  sums 
payable  at  different  dates. 

Rule.  —  Multiply  each  item  by  the  time  of  its  maturity  in  days  from  a 
fixed  date,  taken  as  a  standard,  and  divide  the  sum  of  the  products  by 
the  sum  of  the  items:  the  result  is  the  average  time  in  days  from  the  stand- 
ard date. 

A  owes  B  $100  due  in  30  days,  $200  due  in  60  days,  and  $300  due  in  90 
days.  In  how  many  days  may  the  whole  be  paid  in  one  sum  of  $600? 

100X30+200X60+300X90  =  42,000;     42,000-^600  =  70  days,     ans. 

A  owes  B  $100,  $200,  and  $300,  which  amounts  are  overdue  respectively 
30,  60,  and  90  days.  If  he  now  pays  the  whole  amount,  $600,  how  many 
days'  interest  should  he  pay  on  that  sum?  Ans.  70  days. 


PARTIAL,  PAYMENTS. 

To  compute  interest  on  notes  and  bonds  when  partial  payments  have 
been  made. 

United  States  Rule.  —  Find  the  amount  of  the  principal  to  the  time 
of  the  first  payment,  and,  subtracting  the  payment  from  it,  find  the 
amount  of  the  remainder  as  a  new  principal  to  the  time  of  the  next  pay* 
meat. 


ANNUITIES. 


15 


If  the  payment  is  less  than  the  interest,  find  the  amount  of  the  principal 
to  the  time  when  the  sum  of  the  payments  equals  or  exceeds  the  interest 
due,  and  subtract  the  sum  of  the  payments  from  this  amount. 

Proceed  in  this  manner  till  the  time  of  settlement. 

Note.  —  The  principles  upon  which  the  preceding  rule  is  founded  are: 

1st.  That  payments  must  be  applied  first  to  discharge  accrued  interest, 
and  then  the  remainder,  if  any,  toward  the  discharge  of  the  principal. 

2d.   That  only  unpaid  principal  can  draw  interest. 

Mercantile  Method.  —  When  partial  payments  are  made  on  short 
notes  or  interest  accounts,  business  men  commonly  employ  the  following 
method: 

Find  the  amount  of  the  whole  debt  to  the  time  of  settlement ;  also  find 
the  amount  of  each  payment  from  the  time  it  was  made  to  the  time  of 
settlement.  Subtract  the  amount  of  payments  from  the  amount  of  the 
debt:  the  remainder  will  be  the  balance  due. 


ANNUITIES. 

An  Annuity  is  a  fixed  sum  of  money  paid  yearly,  or  at  other  equ^l  times 
agreed  upon.  The  values  of  annuities  are  calculated  by  the  principles  of 
compound  interest. 

1.  Let  i  denote  interest  on  $  1  for  a  year,  then  at  the  end  of  a  year  trier 
amount  will  be  1  +  i.     At  the  end  of  n  years  it  will  be  (1  -f  i)n. 

2.  The  sum  which  in  n  years  will  amount  to  1  is  or  (1  +  i)  —  nf 


or  the  present  value  of  1  due  in  n  years. 

3.  The  amount  of  an  annuity  of  1  in  any  number  of  years  n  is      '     : — —  • 

4.  The  present  value  of  an  annuity  of  1  for  any  number  of  years  n  is 


5.   The  annuity  which  1  will  purchase  for  any  number  of  years  n  la 

i 


6.   The  annuity  which  would  amount  to  1  in  n  years  is  • 


(1  +  i)n  -  , 
Amounts,  Present  Values,  etc.,  at  5%  Interest. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

Years 

CH-t)« 

(l-fzTn 

(l+i)n_i 

1-0+0-" 

i 

i 

I 

i 

1-0  +  0-n 

(1+t-)n_* 

1  . 

.05 

.952381 

1.00 

.952381 

1.05 

1.00 

2. 

.1025 

.907029  ' 

2.05 

1.859410 

.537805 

.487805 

3. 

.157625 

.863838 

3.1525 

2.723248 

.367209 

.317209 

4. 

.215506 

.822702 

4.310125 

3.545951 

.282012 

.232012 

5. 

.276282 

.783526 

5.525631 

4.329477 

.230975 

.180975 

6. 

.340096 

.746215 

6.801913 

5.075692 

.197017 

.147018 

7. 

.407100 

.710681 

8.142008 

5.786373 

.172820 

.122820 

8. 

.477455 

.676839 

9.549109 

6.463213 

.154722 

.104722 

9. 

.551328 

.644609 

1  1  .026564 

7.107822 

.  1  40690 

.090690 

10. 

.628895 

.613913 

12.577893 

7.721735 

.129505 

.079505 

16 


ARITHMETIC. 


J£  "fr  cq  IN.  en      Ov— 'i^iinNO*      o^  <N  IN.'  eN  od     inrsic^ixad     fN  od  NO  "T  en 
GO  — fNixTt-     —  QGOIN.VO     mm  T  T  en     tnencNCN—     — 


tNenOsenoO  vONOenrxhs  enaOaO(SGO  rj-fNinoOm  OrxtNenNO 

NONOeN— ;—  o^  GO  GO  NO  in  ONoeNNOin  oo^  —  NO  in  cqo^fn'<t;o 

NOmoo^in  o'eNoot>.Qo"  — '•^•O^TO  !>.' en  — '  od  O^*  en' O*  t>»  in  ^ 

SzrJTJ^^"  f^ocoi^O  NOin-tn-T  enenencN—  — w 


. 

o  rs  GO  —  O      ^  ts  [  "f  ao 
''  '' 


o  r>.  -< 

[  "f  ao  "1 
'' 


tn  in-^-i^Tr^  OO-^-oo—  c^G 

s  —  tr»  —  \q  >o\  oo  ts  o^  —  m  O  oq 

K-*   vOO^'o'in   csl  ad  >O  <n  •*  hs' 
- 


O*  •—  NO'  m*  —      fx  o^'  in  T  m      ix  —  in  o  NO" 
Tents  —  ~     — —     ^^  «nmT 


t^mO 

—  oo  O 

T-—  oor>» 


TencN  —  —      — —          ^  "^"^ 


p i  fx  —  T  NO     «n  T  -f  csj  o     f  O  m  r> ,  NO     o^  t>.  oq  CN  m     —  IN.  in  —  eN 


NO  m  o  en  vq  In  -^  -^r  f 
''        ' 


)  O      ^r  o  in  ix  NO      O^  r>  ;  oq  ?N  -T      o  «n  csi  r>.  oq 
'  '  '  '' 


co  ONOm^o  txTcntN.o  n-ooooom 

f»«O  in-«t-^-fNiO  •«roini>.Nq  C^.'O.***"^*** 

'in  •—  "m'o^'ooo*  •—  in'o^^'o  vom'ooooo' 

om  «n  —  ONOOI>»  t>  NO  m  m  m  T  ^  ^r  en  CN 


rn'inoONo'  rin-'oao 
o<vj^rcMn  m  —  ooooo 
•^rm«N  —  •—  •-  —  — 


. 

—     "»•  o  in  r>.  NOt  a^  NO  r>  —  r^ 

'oin—  r>.'"r—  '•&<* 

NOmm  T  T  T  en  cq 


V  in  —  —  '  t>C     en  in  —  o—     tntx  —  NO'CN     co'intNO 
OfN^om     m*-oONOO     txvONOinm     T  T  T  "t 


>•  *^  rsi     %o  O  in  o^  o 
O'  en  —  —      ^t"  O  NO'  en  « 

rT^cn     CSCN  —  — 


IH  o 


WEIGHTS   AND    MEASURES.  17 


TABLES  FOB  CALCULATING  SINKING-FUNDS  AND 
PRESENT  VALUES. 

Engineers  and  others  connected  with  municipal  work  and  industrial 
enterprises  often  find  it  necessary  to  calculate  payments  to  sinking-funds 
which  will  provide  a  sum  of  money  sufficient  to  pay  off  a  bond  issue  or 
other  debt  at  the  end  of  a  given  period,  or  to  determine  the  present  value 
of  certain  annual  charges.  The  accompanying  tables  were  computed  by 
Mr.  John  W.  Hill,  of  Cincinnati,  Eng'g  News,  Jan.  25,  1894. 

Table  I  (opposite  page)  shows  the  annual  sum  at  various  rates  of  interest 
required  to  net  $1000  in  from  2  to  50  years,  and  Table  II  shows  the  present 
value  at  various  rates  of  interest  of  an  annual  charge  of  $1000  for  from  5 
to  50  years,  at  five-year  intervals,  and  for  100  years. 

Table  II.  —  Capitalization  of  Annuity  of  $1000  for 
from  5  to  10O  Years. 


1 

Rate  of  IL  terest,  per  cent. 

5 
10 
15 
20 
25 

30 
35 
40 
45 
50 
100 

31/2 

3 

3V2 

4 

4V2 

5 

5V2 

6 

4,645.88 
8,752.17 
12,381.41 
15,589.215 
18,424.67 

20,930.59 
23,145.31 
25,103.53 
26,833.15 
28,362.48 
36,614.21 

4.579.60 
8,530.13 
11,937.80 

4,5  1  4.  92 
8,316.45 
11,517.23 

4,451.68 
8,110.74 
11,118.06 

4,389.91 
7,912.67 
10,739.42 

4,329.45 
7,721.73 
10,379.53 

4,268.09 
7,537.54 
10,037.48 

4,212.40 
7,360.19 
9,712.30 

14,877.27 
17,413.01 

19,600.21 

14,212.12 
16,481.28 

18,391.85 

13,590.21 
15,621.93 

17,291.86 

13,007.88 
14,828.12 

16,288.77 

12,462.13 
14,093.86 

15,372.36 

11,950.26 
13,413.82 

14,533.63 

11,469.96 
12,783.38 

13,764.85 

21,487.04 
23,114.36 
24,518.49 
25,729.58 
31,598.81 

20,000.43 
21,354.83 
22,495.23 
23,455.21 
27,655.36 

18,664.37 
19,792.65 
20,719.89 
21,482.08 
24,504.96 

17,460.89 
18,401.49 
19,156.24 
19,761.93 
21,949.21 

16,374.36 
17,159.01 
17,773.99 
18,255.86 
19,847.90 

15,390.48 
16,044.92 
16,547.65 
16,931.97 
18,095.83 

14,488.65 
15,046.31 
15,455.85 
15,761.87 
16,612.64 

WEIGHTS  AND  MEASURES. 

Long  Measure.  —  Measures  of  Length. 

12  inches  =  1  foot. 

3  feet  =  1  yard. 

1760  yards,  or  5280  feet  =  1  mile. 

Additional  measures  of  length  in  occasional  use:  1000  mils  =  1  inch; 
4  inches  =  1  hand;  9  inches  =  1  span;  2  1/2  feet  =  1  military  pace;  2  yards 
=  1  fathom;  5  1/2  yards,  or  161/2  feet  =  1  rod  (formerly  also  called  pole  or 
perch). 

Old  Land  Measure.  —  7.92  inches  =  1  link;  100  links,  or  66  feet,  or  4 
rods  =  1  chain;  10  chains,  or  220  yards  =  1  furlong;  8  furlongs,  or  80 
chains  =  1  mile;  10  square  chains  =  1  acre. 

Nautical  Measure. 

6080.26JeeU.or  1.15156  stat-  J  =1  nautical 

3  nautical  miles  =1  league. 

60  nautical  miles,  or  69.168  )  _ 
statute  miles  J  - 


/nt  thp  pmiatnr^ 
lat  tne  equator). 


360  degrees 


circumference  of  the  earth  at  the  equator. 


*  The  British  Admiralty  takes  the  round  figure  of  6080  ft.  which  is  the 
length  of  the  "  measured  mile"  used  in  trials  of  vessels.  The  value  varies 
from  6080.26  to  6088.44  ft.  according  to  different  measures  of  the  earth's 
diameter.  There  is  a  difference  of  opinion  among  writers  as  to  the  use 
of  the  word  "  knot"  to  mean  length  or  a  distance  —  some  holding  that 
it  should  be  used  only  to  denote  a  rate  of  speed.  The  length  between 
knots  on  the  log  line  is  1/120  of  a  nautical  mile,  or  50.7  ft.,  when  a  half- 
minute  glass  is  used;  so  that  a  speed  of  10  knots  is  equal  to  10  nautical 
miles  per  hour. 


18  ARITHMETIC. 

Square  Measure.  —  Measures  of  Surface. 

144  square  inches,  or  183.35  circular  )  _  ,  f     . 

inches  )or» 

9  square  feet  =  1  square  yard. 

30V4  square  yards,  or  2721/4  square  feet         ••=  1  square  rod. 
10  sq.  chains,  or  160  sq.  rods,  or  4840  sq.    )       , 

yards,  or  43560  sq.  feet 

640  acres  or  27,878,400  sq.  ft.  =1  square  mile. 

An  acre  equals  a  square  whose  side  is  208.71  feet. 
Circular  Inch;  Circular  Mil.  —  A  circular  inch  is  the  area  of  a  circle 

1  inch  m  diameter  =  0.7854  square  inch. 

1  square  inch  =  1.2732  circular  inches. 

A  circular  mil  is  the  area  of  a  circle  1  mil,  or  0.001  inch  in  diameter. 
10002  or  1,000,000  circular  mils  =-  1  circular  inch. 

1  square  inch  =  1,273,239  circular  mils. 

t   The  mil  and  circular  mil  are  used  in  electrical  calculations  involving 
tne  diameter  and  area  of  wires. 

Solid  or  Cubic  Measure.  —  Measures  of  Volume. 

1728  cubic  inches  =  1  cubic  foot. 
27  cubic  feet      =  1  cubic  yard. 

1  cord  of  wood  =  a  pile,  4X4X8  feet  =  128  cubic  feet. 
1  perch  of  masonry  =  161/2  X  11/2  X  1  foot   =  243/4  cubic  feet. 

Liquid  Measure. 

4  pills      =  1  pint. 
2  pints     =  1  quart. 
4  nnart«    —  i  p-niirm  J  U.  S.  231  cubic  inches. 

-  1  gallon  jEng  277.274  cubic  inches. 

Old  Liquid  Measures.  —  31 1/2  gallons  =  1  barrel;  42  gallons  =  1  tierce; 

2  barrels,  or  63  gallons  =  1  hogshead;  84  gallons,  or  2  tierces  =  1  pun- 
cheon; 2  hogsheads,  or  126  gallons  =  1  pipe  or  butt;  2  pipes,  or  3  pun- 
cheons =  1  tun. 

A  gallon  of  water  at  62°  F.  weighs  8.33531b.  (air  free,  weighed  in  vacuo). 

The  U.  S.  gallon  contains  231  cubic  inches;  7.4805  gallons  =  1  cubic 
foot.  A  cylinder  7  in.  diam.  and  6  in.  high  contains  1  gallon,  very  nearly, 
or  230.9  cubic  inches.  The  British  Imperial  gallon  contains  277.274  cubic 
inches  =  1.20032  U.  S.  gallon,  or  10  ibs.  of  water  at  62°  F. 

The  gallon  is  a  very  troublesome  unit  for  engineers.  Much  labor  might 
be  saved  if  it  were  abandoned  and  the  cubic  fo9t  used  instead.  The 
capacity  of  a  tank  or  reservoir  should.be  stated  in  cubic  feet,  and  the 
delivery  of  a  pump  in  cubic  feet  per  second  or  in  millions  of  cubic  feet  in 
24  hours.  One  cubic  foot  per  second  =  86,400  cu.  ft.  in  24  hours.  One 
million  cu.  ft.  per  24  hours  =  11.5741  cu.  ft.  per  sec. 

The  Miner's  Inch.  —  (Western  U.  S.  for  measuring  flow  of  a  stream 
of  water.)  An  act  of  the  California  legislature,  May  23,  1901,  makes  the 
standard  miner's  inch  1.5  cu.  ft.  per  minute,  measured  through  any  aper- 
ture or  orifice. 

The  term  Miner's  Inch  is  more  or  less  indefinite,  for  the  reason  that  Cali- 
fornia water  companies  do  not  all  use  the  same  head  above  the  centre  of 
the  aperture,  and  the  inch  varies  from  1.36  to  1.73  cu.  ft.  per  min.,  but 
the  most  common  measurement  is  through  an  aperture  2  ins.  high  and 
whatever  length  is  required,  and  through  a  plank  11/4  ins.  thick.  The 
lower  edge  of  the  aperture  should  be  2  ins.  above  the  bottom  of  the  meas- 
uring-box, and  the  plank  5  ins.  high  above  the  aperture,  thus  making  a  6-in. 
head  above  the  centre  of  the  stream.  Each  square  inch  of  this  opening 
represents  a  miner's  inch,  which  is  equal  to  a  flow  of  1 1/2  cu.  ft.  per  min. 

Apothecaries'  Fluid  Measure. 

60  minims  =  1  fluid  drachm.  8  drachms  =  1  fluid  ounce. 

In  the  U.  S.  a  fluid  ounce  is  the  128th  part  of  a  U.  S.  gallon,  or  1.805 
cu.  ins.  It  contains  456.3  grains  of  water  at  39°  F.  In  Great  Britain 
the  fluid  ounce  is  1.732  cu.  ins.  and  contains  1  ounce  avoirdupois,  or  437.5 
grains  of  water  at  62°  F. 


WEIGHTS   AND   MEASURES.  19 

Dry  Measure,  U.  S. 

2  pints  =  1  quart.        8  quarts  =  1  peck.  4  pecks  =  1  bushel. 

The  standard  U.  S.  bushel  is  the  Winchester  bushel,  which  is,  in 
cylinder  form,  18  1/2  inches  diameter  and  8  inches  deep,  and  contains 
2150.42  cubic  inches. 

A  struck  bushel  contains  2150.42  cubic  inches  =  1.2445  cu.  ft.;  1 
cubic  foot  =  0.80356  struck  bushel.  A  heaped  bushel  is  a  cylinder  18 1/2 
inches  diameter  and  8  inches  deep,  with  a  heaped  cone  not  less  than 
6  inches  high.  It  is  equal  to  1 V*  struck  bushels.  (When  applied  to 
apples  and  pears  the  bushel  should  be  heaped  so  as  to  contain  2737.715 
cu.  in.  =  1.2731  struck  bushels. — Decision  of  U.  S.  Court  of  Customs 
Appeals,  1912.) 

The  British  Imperial  bushel  =  8  imperial  gallons  or  2218.192  cu.  in.  = 
1.2837  cu.  ft.  The  British  quarter  =  8  imperial  bushels. 

Capacity  of  a  cylinder  in  U.  S.  gallons  =  square  of  diameter,  in  inches 
X  height  in  inches  X  .0034.  (Accurate  within  1  part  in  100,000.) 

Capacity  of  a  cylinder  in  U.  S.  bushels  =  square  of  diameter  in  inches 
X  height  in  inches  X  0.0003652. 

Shipping  Measure. 

Register  Ton.— For  register  tonnage  or  for  measurement  of  the  entire 
ternal  capacity  of  a  vessel: 

100  cubic  feet  =  1  register  ton. 

This  number  is  arbitrarily  assumed  to  facilitate  computation. 
Shipping  Ton. — For  the  measurement  of  cargo: 

40  cubic  feet  =  1  U.  S.  shipping  ton  =  32.143  U.  S.  bushels. 

42  cubic  feet  =  1  .British  shipping  ton  =  32.719  imperial  bushels. 

Carpenter's  Rule. — Weight  a  vessel  will  carry  =  length  of  keel  X 
breadth  at  main  beam  X  depth  of  hold  in  feet  -h  95  (the  cubic  feet 
allowed  for  a  ton).  The  result  will  be  the  tonnage.  For  a  double- 
decker  instead  of  the  depth  of  the  hold  take  half  the  breadth  of  the 


Measures  of  Weight.— Avoirdupois  or  Commercial 
Weight. 

16  drachms,  or  437.5  grains  =  1  ounce,  oz. 
16  ounces,  or  7000  grains  =  1  pound,  Ib. 
28  pounds  =  1  quarter,  qr. 

4  quarters  =  1  hundredweight,  cwt.  =  112  Ib. 

20  hundredweight  =  1  ton  of  2240  Ib.,  gross  or  long  ton. 

2000  pounds  =  1  net,  or  short  ton. 

2204.6  pounds  =  1  metric  ton. 

1  stone  =  14  pounds;  1  quintal  =  100  pounds. 

The  drachm,  quarter,  hundredweight,  stone,  and  quintal  are  now 
seldom  used  in  the  United  States. 

Troy  Weight 

24  grains  =  1  pennyweight,  dwt. 

20  pennyweights  =  1  ounce,  oz.  =  480  grains. 

12  ounces  =  1  pound,  Ib.  =  5760  grains. 

Troy  weight  is  used  for  weighting  gold  and  silver.  The  grain  is  the 
same  in  Avoirdupois.  Troy,  and  Apothecaries'  weights.  A  carat,  for 
weighing  diamonds  =  3.086  grains  =  0.200  gramme.  (International 
Standard,  1913.) 

Apothecaries'  Weight. 

20  grains      =  1  scruple,  3 

3  scruples  —  1  drachm,  3  -      60  grains. 

8  drachms  »  1  ounce,  5  —    480  grains. 

12  ounces     «  1  pound,  Ib.  «  5760  grains. 


20  ARITHMETIC. 

To  determine  whether  a  balance  has  unequal  arms.  —  After  weigh- 
ing an  article  and  obtaining  equilibrium,  transpose  the  article  and  the 
weights.  If  the  balance  is  true,  it  will  remain  in  equilibrium;  if  untrue, 
the  pan  suspended  from  the  longer  arm  will  descend. 

To  weigh  correctly  on  an  incorrect  balance.  —  First,  by  substitu- 
tion. Put  the  article  to  be  weighed  in  one  pan  of  the  balance  and  counter- 
poise it  by  any  convenient  heavy  articles  placed  on  the  other  pan. 
Remove  the  article  to  be  weighed  and  substitute  for  it  standard  weights 
until  equipoise  is  again  established.  The  amount  of  these  weights  is  the 
weight  of  the  article. 

Second,  by  transposition.  Determine  the  apparent  weight  of  the 
article  as  usual,  then  its  apparent  weight  after  transposing  the  article  and 
the  weights.  If  the  difference  is  small,  add  half  the  difference  to  the 
smaller  of  the  apparent  weights  to  obtain  the  true  weight.  If  the  differ- 
ence is  2  per  cent  the  error  of  *  his  method  is  1  part  in  10,000.  For  larger 
differences,  or  to  obtain  a  perfectly  accurate  result,  multiply  the  two 
apparent  weights  together  and  extract  the  square  root  of  the  product. 

Circular  Measure. 

60  seconds,  *  =  1  minute,  '. 
60  minutes, '  =  1  degree,  °. 
90  degrees       =  1  quadrant. 
380  =  circumference. 

Arc  of  angle  of  57.3°,  or  360°  •*•  6.2832  =  1  radian  —  the  arc  whose  length 
is  equal  to  the  radius. 

Time. 

60  seconds  =  1  minute. 
60  minutes  =  1  hour. 
24  hours       =  1  day. 

7  days        =  1  week. 
365  days,  5  hours,  48  minutes,  48  seconds  «»  1  year. 

By  the  Gregorian  Calendar  every  year  whose  number  is  divisible  by  4 
is  a  leap  year,  and  contains  366  days,  the  other  years  containing  365  days, 
except  that  the  centesimal  years  are  leap  years  only  when  the  number  of 
the  year  is  divisible  by  400. 

The  comparative  values  of  mean  solar  and  sidereal  time  are  shown  by 
the  following  relations  according  to  Bessel: 

365.24222  mean  solar  days  =  366.24222  sidereal  days,  whence 
1  mean  solar  day  =  1.00273791  sidereal  days; 

1  sidereal  day  =  0.99726957  mean  solar  day; 
24  hours  mean  solar  time  =  24*  3    56«.555  sidereal  time; 
24  hours  sidereal  time  =  23*  56*n  4«.091  mean  solar  time, 

whence  1  mean  solar  day  is  3»  55«.91  longer  than  a  sidereal  day,  reckoned 
in  mean  solar  time. 

BOARD  AND  TIMBER  MEASURE. 

Board  Measure. 

In  board  measure  boards  are  assumed  to  be  one  inch  in  thickness.  To 
obtain  the  number  of  feet  board  measure  (B.  M.)  of  a  board  or  stick  of 
square  timber,  multiply  together  the  length  in  feet,  the  breadth  in  feet, 
and  the  thickness  in  inches. 

To  compute  the  measure  or  surface  in  square  feet.  —  When  all 
dimensions  are  in  feet,  multiply  the  length  by  the  breadth,  and  the  prod- 
uct will  give  the  surface  required. 

When  either  of  the  dimensions  are  in  inches,  multiply  as  above  and 
divide  the  product  by  12. 

When  all  dimensions  are  in  inches,  multiply  as  before  and  divide  product 
by  144. 

Timber  Measure. 

To  compute  the  volume  of  round  timber.  —  When  all  dimensions 
are  in  feet,  multiply  the  length  by  one  quarter  of  the  product  of  the  mean 


WEIGHTS   AND   MEASURES. 


21 


girth  and  diameter,  and  the  product  will  give  the  measurement  in  cubic 
feet.  When  length  is  given  in  feet,  and  girth  and  diameter  in  inches 
divide  the  product  by  144;  when  all  the  dimensions  are  in  inches,  divide 
by  1728. 

To  compute  the  volume  of  square  timber.  —  When  all  dimensions 
are  in  feet,  multiply  together  the  length,  breadth,  and  depth;  the  product 
will  be  the  volume  in  cubic  feet.  When  one  dimension  is  given  in  inches, 
divide  by  12;  when  two  dimensions  are  in  inches,  divide  by  144:  when  all 
three  dimensions  are  in  inches,  divide  by  1728. 

Contents  in  Feet  of  Joists,  Scantling,  and  Timber, 

Length  in  Feet. 


Size. 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

Feet  Board  Measure. 


2X4 

8 

9 

11 

12 

13 

15 

16 

17 

19 

20 

2X6 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

2X8 

16 

19 

21 

24 

27 

29 

32 

35 

37 

40 

2  X  10 

20 

23 

27 

30 

33 

37 

40 

43 

47 

50 

2  X  12 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

2  X  14 

28 

33 

37 

42 

47 

51 

56 

61 

65 

70 

3X8 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

3  X  10 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

3  X  12 

36 

42 

48 

54 

60 

66 

72 

78 

84 

90 

3  X  14 

42 

49 

56 

63 

70 

77 

64 

91 

98 

105 

4X4 

16 

19 

21 

24 

27 

29 

32 

35 

37 

40 

4X6 

24 

28 

32 

36 

40 

44 

43 

52 

56 

60 

4X8 

32 

37 

43 

43 

53 

59 

64 

69 

75 

80 

4  X  10 

40 

47 

53 

60 

67 

73 

80 

87 

93 

100 

4  X  12 

48 

56 

64 

72 

80 

83 

96 

104 

112 

120 

4  X  14 

56 

65 

75 

84 

93 

103 

112 

121 

131 

140 

6X6 

36 

42 

43 

54 

60 

66 

72 

78 

84 

90 

6X8 

48 

56 

64 

72 

80 

83 

96 

104 

112 

120 

6  X  10 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

6  X  12 

72 

84 

96 

108 

120 

132 

144 

156 

168 

180 

6X  14 

84 

98 

112 

126 

140 

154 

168 

182 

196 

210 

8X8 

64 

75 

85 

96 

107 

117 

128 

139 

149 

160 

8  X  10 

80 

93 

107 

120 

133 

147 

160 

173 

187 

200 

8  X  12 

96 

112 

128 

144 

160 

176 

192 

208 

224 

240 

8  X  14 

112 

131 

149 

168 

187 

205 

224 

243 

261 

280 

10  X  10 

100 

117 

133 

150 

167 

183 

200 

217 

233 

250 

10  X  12 

120 

140 

160 

180 

200 

220 

240 

260 

2ttO 

300 

10  X  14 

140 

163 

187 

210 

233 

257 

280 

303 

327 

350 

12  X  12 

144 

168 

192 

216 

240 

264 

288 

312 

336 

360 

12  X  14 

168 

196 

224 

252 

280 

308 

336 

364 

392 

420 

14  X  14 

196 

229 

261 

294 

327 

359 

392 

425 

457 

490 

FRENCH  OB  METRIC  MEASURES. 

The  metric  unit  of  length  is  the  metre  =  39.37  inches. 

The  metric  unit  of  weight  is  the  gram  =  15.432  grains. 

1  he  following  prefixes  are  used  for  subdivisions  and  multiples:  Milli  = 
Viooq,  Centi  =  Vioo,  Deci  =  1/10,  Deca  =  10,  Hecto  =  100,  Kilo  =  1000. 
«i.yna  =  10,000. 


22  ARITHMETIC. 

FRENCH  AND  BRITISH  (AND  AMERICAN) 
EQUIVALENT  MEASURES. 

Measures  of  Length. 

FRENCH.  BRITISH  and  U.  S. 

1  metre  =  39.37  inches,  or  3.28083  feet,  or  1.09361  yards. 

0.3048  metre  =  1  foot. 

1  centimetre    =  0.3937  inch. 
2.54  centimetres  =  1  inch. 

1  millimetre    =  0.03937  inch,  or  1  /25  inch,  nearly. 
25.4  millimetres  =  1  inch. 

1  kilometre      =  1093. Gl  yards,  or  0.62137  mile. 

Of  Surface 

FRENCH  BRITISH  and  U.  S. 

1  omiarp  mptrp  -  j  10.7639  square  feet. 

~  1     1.196  square  yards. 

0.836  square  metre  =  1  square  yard. 

0.0929  square  metre  =  1  square  foot. 

1  square  centimetre          =  0. 15500  square  inch. 
6.452  square  centimetres        =  1  square  inch. 

1  square  millimetre  =  0.00155  sq.  in.  =  1973.5  circ.  mils. 

645.2  square  millimetres         =  1  square  inch. 

1  centiare  =  1  sq.  metre  =  10.764  square  feet. 

1  are  =  1  sq.  decametre  =  1076.41 

1  hectare  =  100  ares         =  107641  =  2.4711  acres. 

1  sq.  kilometre  =  0.386109  sq.  miles  =  247.11 

1  sq.  myriametre  =  38.6109 

Of  Volume 

FRENCH.  BRITISH  and  U.  S. 

i  miVnV  rnpfro  J  35.314  cubic  feet, 

1  cubic  metre  =  -j     13QS  cubic  yards 

0.7645  cubic  metre  =  1  cubic  yard. 

0.02832  cubic  metre  =  1  cubic  foot. 

1  oiibio  rlpHmptrP     -  i  61.0234  cubic  inches. 
1     0.035314  cubic  foot. 
28.32  cubic  decimetres    =  1  cubic  foot. 

1  cubic  centimetre    =  0.061  cubic  inch. 
16.387  cubic  centimetres  =  1  cubic  inch. 
1  cubic  centimetre  =  1  millilitre  =    0.061  cubic  inch. 
1  decilitre  =6.102      " 

1  litre  =  1  cubic  decimetre  =  61.0234    '  =  1.05671 

quarts,  U.  S. 

1  hectolitre  or  decistere  =  3.5314  cubic  feet   =  2.8375  bu.,  U.  S. 

1  stere,  kilolitre,  or  cubic  metre  =  1.308  cubic  yards  =  28.37  bu., 

Of  Capacity 

FRENCH.  BRITISH  and  U.  S. 

f  6 1.0234  cubic  inches. 
oiil'gaUoi?  (American), 
2.202  pounds  of  water  at  62°  F. 
28.317  litres  =  1  cubic  foot. 

4.543  litres  =  1  gallon  (British). 

3.785  litres  =  1  gallon  (American). 

Of  Weight. 

FRENCH.  BRITISH  and  U.  S. 

1  gramme  =  15,432  grains. 

0.0648  gramme  =  1  grain. 

1  kilogramme  =  2.204622  pounds. 

0.4536  kilogramme  =  1  pound. 

1  tonne  or  metric  ton  I  =  j  0.9842  ton  of  2240  pounds. 
1000  kilogrammes  f  =  j  22G4. 6  pounds. 

1.016  metric  tons  «    1  ton  of  2240  pounds. 


WEIGHTS  AND  MEASURES. 


23 


Mr.  O.  H.  Titmann,  in  Bulletin  No.  9  of  the  U.  S.  Coast  and  Geodetic 
Survey,  discusses  the  work  of  various  authorities  who  have  compared  the 
yard  and  the  metre,  and  by  referring  all  the  observations  to  a  common 
standard  has  succeeded  in  reconciling  the  discrepancies  within  very 
narrow  limits.  The  following  are  his  results  for  the  number  of  inches  in  a 
metre  according  to  the  comparisons  of  the  authorities  named:  1817. 
Hassler,  39.36994  in.  1818.  Kater,  39.36990  in.  1835.  Baily,  39.36973 
in.  1866.  Clarke,  39.36970  in.  1885.  Comstock,  39.36984  in.  The  mean 
of  these  is  39.36982  in. 

The  value  of  the  metre  is  now  denned  in  the  U.  S.  laws  as  39.37  inches. 

French  and  British  Equivalents  of  Compound  Units. 

FRENCH.  BRITISH. 

gramme  per  square  millimetre  =        1.422  Ibs.  per  sq.  in. 

kilogramme  per  square     '  =  1422.32 

centimetre  =      14.223  " 

.0335  kg.  per  sq.  cm.  =  1  atmosphere  =      14.7       "      "     "     " 

0.070308  kilogramme  per  square  centimetre  =        1  Ib.  per  square  inch. 

kilogrammetre  =        7.2330  foot-pounds. 

gramme  per  litre  =  0.062428  Ib.  per  cu.  ft.  =  58.349  grains  per  U.  S  gal. 

of  water  at  62°  F. 
1  grain  per  U.  S.  gallon=l  part  in  58,349        =  1.7138   parts   per    100,000 

—  0.017138  grammes  per  litre. 

METRIC  CONVERSION  TABLES. 

The  following  tables,  with  the  subjoined  memoranda,  were  published 
in  1890  by  the  United  States  Coast  and  Geodetic  Survey,  office  of  standard 
weights  and  measures,  T.  C.  Mendenhall,  Superintendent. 


- 


Tables  for  Converting  TJ.  S.  Weights  and  Measures  — 
Customary  to  Metric. 

LINEAR. 


Inches  to  Milli- 
metres. 

Feet  to  Metres. 

Yards  to  Metres. 

Miles  to  Kilo- 
metres. 

2  = 

3  = 
4  = 
5  = 

25.4001 
50.8001 
76.2002 
101.6002 
127.0003 

0.304801 
0.609601 
0.914402 
1.219202 
1.524003 

0.914402 
1  .828804 
2.743205 
3.657607' 
4.572009 

1.60935 
3.21869 
4.82804 
6.43739 
8.04674 

8  = 

152.4003 
177.8004 
203.2004 
228.6005 

1.828804 
2.133604 
2.438405 
2:743205 

5.486411 
6.400813 
7.315215 
8.229616 

9.65608 
11.26543 
12.87478 
14.48412 

SQUARE. 


Square  Inches  to 
Square  Centi- 
metres. 

Square  Feet  to 
Square  Deci- 
metres. 

Square  Yards  to 
Square  Metres. 

Acres  to 
Hectares. 

K 

1  = 

6.452 

9.290 

0.836 

04047 

2  = 

12.903 

18.581 

1.672 

0.8094 

3  = 

19.355 

27.871 

2.508 

1.2141 

A    

25.807 

37.161 

3.344 

1.6187 

5  = 

32.258 

46.452 

4.181 

2.0234 

6  = 

38.710 

55.742 

5.017 

2.4281 

7  = 

45.161 

65.032 

5.853 

2.8328 

8  = 

51.613 

74.323 

6.689 

3.2375 

9  = 

58.065 

83.613 

7.525 

3.6422 

ARITHMETIC. 


CUBIC. 


Cubic  Inches  to 
Cubic  Centi- 
metres. 

Cubic  Feet  to 
•Cubic  Metres. 

Cubic  Yards  to 
Cubic  Metres. 

Bushels  to 
Hectolitres. 

Ui-UUJ  Si- 
ll II  II  II  11 

16.387 
32.774 
49.161 
65.549 
81.936 

0.02832 
0.05663 
0.08495 
0.11327 
0.14158 

0.765 
1.529 
2.294 
3.058 
3.823 

0.35242 
0.70485 
1.05727 
1  .40969 
1.76211 

6  = 

8  = 

98.323 
114.710 
131.097 
147.484 

0.16990 
0.19822 
0.22654 
0.25485 

4.587 
5.352 
6.116 
6.881 

2.11454 
2.46696 
2.81938 
3.17181 

CAPACITY. 


Fluid  Dracnms 
to  Millilitres  or 
Cubic  Centi- 
metres. 

Fluid  Ounces  to 
Millilitres  . 

Quarts  to  Litres. 

Gallons  to 
Litres. 

1  = 

2  = 
3  = 
4  = 
5  = 

6  = 

8  = 
9  = 

3.70 
7.39 
11.09 
14.79 
18.48 

22.18 
25.88 
29.57 
33.28 

29.57 
59.15 
88.72 
118.30 
147.87 

177.44 
207.02 
236.59 
266.16 

0.94636 
1  .89272 
2.83908 
3.78544 
4.73180 

5.67816 
6.62452 
7.57088 
8.51724 

3.78544 
7.57088 
11.35632 
15.14176 
18.92720 

22.71264 
26.49808 
30.28352 
34.06896 

WEIGHT. 


Grains  to  Milli- 
grammes. 

Avoirdupois 
Ounces  to 
Grammes. 

Avoirdupois 
Pounds  to  Kilo- 
grammes. 

Troy  Ounces  to 
Grammes. 

1  =» 

2  

4  = 
5  = 

6  = 

8-= 
9- 

64.7989 
129.5978 
194.3968 
259.1957 
323.9946 

388.7935 
453.5924 
518.3914 
583.1903 

28.3495 
56.6991 
85.0486 
113.3981 
141.7476 

170.0972 
198.4467 
226.7962 
255.1457 

0.45359 
0.90719 
1  .36078 
1.81437 
2.26796 

2.72156 
3.17515 
3.62874 
4.08233 

31.10348 
62.20696 
93.31044 
124.41392 
155.51740 

186.62089 
217.72437 
248.82785 
279.93133 

1  chain   =    20.11 69  metres. 
1  square  mile   =   259  hectares. 
1  fathom  =    1 .829  metres. 
1  nautical  mile  =    1853.27  metres. 
1  foot  =   0.304801  metre. 
1  avoir,  pound   =   453.5924277  gram. 
15432.35639  grains    =    1  kilogramme. 


METRIC   CONVERSION   TABLES. 


25 


Tables  for  Converting  U.  S.  Weights  and  Measures — 
Metric  to  Customary. 

LINEAR. 


Metres  to 
Inches. 

Metres  to 
Feet. 

Metres  to 
Yards. 

Kilometres  to 
Miles. 

1  = 

2  = 

4  = 
5  = 

39.3700 
78.7400 
118.1100 
157.4800 
196.8500 

3.28083 
6.56167 
9.84250 
13.12333 
16.40417 

1.093611 
2.187222 
3.280833 
4.374444 
5.468056 

0.62137 
1  .24274 
1.86411 
2.48548 
3.10685 

1: 

236.2200 
275.5900 
314.9600 
354.3300 

19.68500 
22.96583 
26.24667 
29.52750 

6.561667 
7.655278 
8.748889 
9.842500 

3.72822 
4.34959 
4.97096 
5.59233 

SQUARE. 


Square  Centi- 
metres to 
Square  Inches. 

Square  Metres 
to  Square  Feet. 

Square  Metres 
to  Square  Yards. 

Hectares  to 
Acres. 

1  = 

0.1550 

10.764 

1.196 

2.471 

2  = 

0.3100 

21.528 

2.392 

4.942 

3  = 

0.4650 

32.292 

3.588 

7.413 

4  = 

0.6200 

43.055 

4.784 

9.884 

5  = 

0.7750 

53.819 

5.980 

12.355 

6  = 

0.9300 

64.583 

7.176 

14826 

7  = 

1.0850 

75.347 

8.372 

17.297 

8  = 

1.2400 

86.111 

9.563 

19.768 

9  = 

1.3950 

96.874 

10.764 

22.239 

CUBIC. 


Cubic  Centi- 
metres to  Cubic 
Inches. 

Cubic  Deci- 
metres to  Cubic 
Inches. 

Cubic  Metres  to 
Cubic  Feet. 

Cubic  Metres  to 
Cubic  Yards. 

1  = 

0.0610 

61.023 

35.314 

1.308 

2  - 

0.1220 

122.047 

70.629 

2.616 

3  = 

0.1831 

183.070 

105.943 

3.924 

4  = 

0.2441 

244.093 

141.258 

5.232 

5  = 

0.3051 

305.117 

176.572 

6.540 

6  = 

0.3661 

366.140 

211.887 

7.848 

•j  

0.4272 

427.163 

247.201 

9.156 

8  = 

0.4882 

488.187 

282.516 

10.464 

9  = 

0.5492 

549.210 

317.830 

11.771 

CAPACITY. 


Milhlitres  or 
Cubic  Centi- 
metres toFluid 

Centimetres 
to  Fluid 
Ounces. 

Litres  to 
Quarts. 

Dekalitres 
to 
Gallons. 

Hektolitres 
to 
Bushels. 

Drachms. 

1  = 

0.27 

0.338 

1.0567 

2.6417 

2.8375 

2  = 

0.54 

0.676 

2.1134 

5.2834 

5.6750 

3  = 

0.81 

1.014 

3.1700 

7.9251 

8.5125 

4  = 

1.08 

1.352 

4.2267 

10.5668 

11.3500 

5  = 

1.35 

1.691 

5.2834 

13.2085 

14.1875 

6  = 

1.62 

2.029 

6.3401 

15.8502 

17.0250 

j  

1.89 

2.363 

7.3968 

18.4919 

.  19.8625 

8  = 

2.16 

2.706 

8.4534 

21.1336 

22.7000 

9  = 

2.43 

3.043 

9.5101 

23.7753 

25.5375 

26 


ARITHMETIC. 
WEIGHT. 


Milligrammes 
to  Grains. 

Kilogrammes 
to  Grains. 

Hectogrammes 
(  1  00  grammes) 
to  Ounces  Av. 

Kilogrammes 
to  Pounds 
Avoirdupois. 

1  = 

2  = 
3  = 
4  = 
5  = 

0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

15432.36 
30864.71 
46297.07 
61729.43 
77161.78 

3.5274 
7.0548 
10.5822 
14.1096 
17.6370 

2.20462 
4.40924 
6.61386 
8.81849 
11.02311 

6  = 

•j  

8  = 
9  = 

0.09259 
0.10803 
0.12346 
0.13839 

92594.14 
108026.49 
123458.85 
138891.21 

21.1644 
24.6918 
28.2192 
31.7466 

13.22773 
15.43235 
17.63697 
19.84159 

Quintals  to 
Pounds  Av. 

Milliers  or  Tonnes  to 
Pounds  Av. 

Grammes  to  Ounces. 
Troy. 

1  =, 

220.46 

2204.6 

0.03215 

2  = 

440.92 

4409.2 

0.06430 

3  = 

661.38 

6613.8 

0.09645 

4  = 

881.84 

8818.4 

0.12860 

5  - 

1102.30 

11023.0 

0.16075 

6  = 

1322.76 

13227.6 

0.19290 

7  - 

1543.22 

15432.2 

0  22505 

8== 

1763.68 

17636.8 

0.25721 

9  = 

1984.14 

19841.4 

0.28936 

The  British  Avoirdupois  pound  was  derived  from  the  British  standard 
Troy  pound  of  1758  by  direct  comparison,  and  it  contains  7000  grains  Troy. 

The  grain  Troy  is  therefore  the  same  as  the  grain  Avoirdupois,  and  the 
pound  Avoirdupois  in  use  in  the  United  States  is  equal  to  the  British 
pound  Avoirdupois. 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an 
International  Bureau  of  Weights  and  Measures  has  been  established  near 
Paris. 

The  International  Standard  Metre  is  derived  from  the  Metre  des 
Archives,  and  its  length  is  defined  by  the  distance  between  two  lines  at  0° 
Centigrade,  on  a  platinum-iridium  bar  deposited  at  the  International 
Bureau. 

The  International  Standard  Kilogramme  is  a  mass  of  platinum-indium 
deposited  at  the  same  place,  and  its  weight  in  vacua  is  the  same  as  that  of 
the  Kilogramme  des  Archives. 

Copies  of  these  international  standard  weights  and  measures  are 
deposited  in  the  office  of  the  United  States  Bureau  of  Standards. 

The  litre  is  equal  to  a  cubic  decimetre  of  water,  and  it  is  measured  by 
the  quantity  of  distilled  water  which,  at  its  maximum  density,  will 
counterpoise  the  standard  kilogramme  in  a  vacuum;  the  volume  of  such 
a  quantity  of  water  being,  as  nearly  as  has  been  ascertained,  equal  to  a 
cubic  decimetre. 

The  metric  system  was  legalized  in  the  United  States  in  1866.  Many 
attempts  were  made  during  the  50  years  following  to  have  the  U.  S. 
Congress  pass  laws  to  make  the  metric  system  the  legal  standard,  but  they 
have  all  failed.  Similar  attempts  in  Great  Britain  have  also  failed.  For 
arguments  for  and  against  the  metric  system  see  the  report  of  a  committee 
of  the  American  Society  of  Mechanical  Engineers,  1903,  Vol.  24. 


WEIGHTS    AND   MEASURES.  27 

COMPOUND  UNITS. 

Measures  of  Pressure  and  Weight. 

One  pound  force  (or  pressure)  =  the  force  exerted  by  gravity  on  1  Ib. 
of  matter  at  a  place  where  the  acceleration  due  to  gravity  is  32.1740 
feet-per-second  per  second;  that  is  (very  nearly)  the  force  of  gravity  on 
1  Ib.  of  matter  at  latitude  45°  at  the  sea  level. 


1  Ib.  per  square  inch 


144  Ib.  per  square  foot. 

2.0355  in.  of  mercury  at  32°  P. 
2.0416   "     "          "          "62°F. 
2.309  ft.  of  water  at  62°  F. 
27.71  ins.    "        "       "62°  F. 


j     0.1276  in.  of  mercury  at  62°  F. 
1  ounce  per  sq.  in.  1.732  in.  of  water  at  62°  F. 


2116.3  Ib.  per  square  foot. 
I  33.947  ft.  of  water  at  62°  F. 


;i4.71b.  per  sqJn.)  -  j  ™%i>21in,  ofm^curfat  32' F, 


760  millimetres  of  mercury  at  32°  F. 
i    0.03609  Ib.  or  .5774  oz.  per  sq.  in. 
1  inch  of  water  at  62°  F.  =  •<    5.196  Ib.  per  square  foot. 

0.0735  in.  of  mercury  at  62°  F. 


1  foot  of  water  at  62°  F.  -          ™  »   P 


_j 

H 


0.491  Ib.  or  7.86  oz.  per  sq.  in. 

1  inch  of  mercury  at  62°  F.       =  -{    1.134  ft.  of  water  at  62°  F. 

(  13.61  in.  of  water  at  62°  F. 


Weight  of  One  Cubic  Foot  of  Pure  Water. 

At  32°  F.  (freezing-point) 62.418  Ib. 

"   39.1°  F.  (maximum  density) 62.425    ' 

"   62°  F.  (standard  temperature)  in  vacuo 62.355    " 

"    212°  F.  (boiling-point,  under  1  atmosphere) 59.76 

American  gallon  =  231       cubic  ins.  of  water  at  62°  F.   =  8.3356  Ib. 
British  "       =  277.274  "  "       "      "        "        =  10  Ib. 

Weight  of  1  cu.  ft.  of  air-free  distilled  water  at  62°,  weighed  in  air  at 
62°  with  brass  weights  of  8. 4  density  =  62.287  Ib.  =  8.3267  Ib.  per  U.  S. 
gallon. 

Weight  and  Volume  of  Air. 

1  cubic  ft.  of  air  at  32°  F.  and  atmospheric  pressure  weighs  0.080728  Ib. 
i  tt.  «„  v.~'~i~4-    f    •„    +.  ooo  ™         i  0.0005606  Ib.  per  sq.  in. 

.  in  height  of  air  at  3.  \  0.015534  inches  of  water  at  62°  F. 

For  air  at  any  other  temperature  T°  Fahr.  multiply  by  492  -=-  (460  +  T). 
1  Ib.  pressure  per  sq.  ft.  =       12.387  ft.  of  air  at  32°  F. 

1    "  "    sq.  in.  =  1784.          "    "    "     " 

1  inch  of  water  at  62°  F.          =      64.37      "    "    "     " 
For  air  at  any  other  temperature  multiply  by  (460  +  T)  -~  492. 

At  any  fixed  temperature  the  weight  of  a  given  volume  is  proportional 
to  the  absolute  pressure. 

Measures  of  Work,  Power,  and  Duty. 

Unit  of  work. — One  foot-pound,  i.e.,  a  pressure  of  one  pound  exerted 
through  a  space  of  one  foot. 

Horse-power. — The  rate  of  work.  Unit  of  horse-power  =  33,000 
f t.-lb.  per  minute,  or  550  ft.-lb.  per  second  =  1 ,980,000  ft.-lb.  per  hour. 

Heat  unit.  =  heat  required  to  raise  1  Ib.  of  water  1°  F.  (see  page  560). 

00    (")(")() 

Horse-power  expressed  in  heat-units  =       '      ~  =  42.442  heat-units  per 

minute  =  0.7074  heat-unit  per  second  =  2546.5  heat  units  per  hour. 
1  Ib.  of  fuel  per  H.P.  per  hour  =  1,980,000  ft.-lb.  per  Ib.  of  fuel. 
1,000,000  ft.-lb.  per  Ib.  of  fuel  =  1.98  Ib.  of  fuel  per  H.P.  per  hour. 

5280       ^2 
Velocity. — Feet  per  second  =  %QQQ  =  Is  x  miles  Per  hour. 

tons  per  mile  =  2240  =  14  lb<  per  yarci  (sin£le  rail)  • 


28 


ARITHMETIC. 


WIRE  AND  SHEET-METAL  GAUGES  COMPARED. 


•8^ 

<jj  §3 
*§  § 

So® 

Irl 

.po 

S  *  5s 

•gi° 

ing's  and 
iburn  & 
:'s  Gauge. 

» 

—  «  ajo 

-  O  o 
J§  a)-22 

yt'G  nj 
%«% 

!"2  § 
^B°  . 

<gl|i 

Ui 
l«£a- 

;s  o>  c^05 
«  <*§  cS 

9 

|a 

S  c8 

go 

g-2  ^ 
oc  £ 

Sg£ 

|2& 

•§"§  ® 

||| 

J-li 

pill 

3  ™  c8 

*e£i 
p  £s 

1° 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

0000000 

.49 

.500 

.6666 

.5 

7/o 

000000 

.46 

464 

.625 

.469 

6,0 

00000 

.43 

.432 

.5883 

.438 

5/o 

0000 

.454 

.46 

.393 

.4 

.406 

000 

.425 

.40964 

.362 

.372 

.500 

.375 

3/2 

00 

.38 

.3648 

.331 

.348 

.4452 

344 

2/n 

0 

.34 

.32486 

.307 

.324 

.3964 

.313 

0 

.3 

.2893 

.283 

227 

.3 

.3532 

.281 

1 

2 

.284 

.25763 

.263 

.219 

.276 

.3147 

266 

2 

3 

.259 

.22942 

.244 

.212 

.252 

.2804 

.25 

3 

4 

.238 

J20431 

.225 

.207 

.232 

.250 

.234 

4 

5 

.22 

.18194 

.207 

.204 

.212 

.2225 

,219 

5 

6 

.203 

.16202 

.192 

.201 

.192 

.1981 

.203 

6 

7 

.18 

.14428 

.177 

.199 

.176 

.1764 

.188 

7 

6 

.165 

.12849 

.162 

.197 

.16 

.1570 

.172 

8 

9 

.148 

.11443 

.148 

.194 

.144 

.1398 

.156 

9 

10 

.134 

.10189 

.135 

.191 

.128 

.1250 

.141 

10 

11 

.12 

.09074 

.12 

.188 

.116 

.1113 

.125 

11 

12 

.109 

.08081 

.105 

.185 

.104 

.0991 

.109 

12 

13 

.095 

.07196 

.092 

.182 

.092 

.0882 

.094 

13 

14 

.033 

.06403 

,08 

.180 

.08 

.0785 

078 

14 

15 

.072 

.05707 

.072 

.178 

.072 

.0699 

.07 

15 

16 

.065 

.05082 

.063 

.175 

.064 

.0625 

.0625 

16 

17 

.058 

.04526 

.054 

.172 

.056 

.0556 

.0563 

17 

18 

.049 

.0403 

.047 

.168 

.048 

.0495 

.05 

18 

19 

.042 

.03589 

.041 

164 

.04 

.0440 

.0433 

19 

20 

.035 

.03196 

.035 

.161 

.036 

.0392 

.0375 

20 

21 

.032 

.02846 

.032 

.157 

.032 

.0349 

.0344 

21 

22 

.028 

.02535 

.028 

.155 

.028 

.03125 

.0313 

22 

23 

.025 

.02257 

.025 

.153 

.024 

.02782 

0281 

23 

24 

.022 

.0201 

.023 

.151 

.022 

.02476 

.025 

24 

25 

.02 

.0179 

.02 

.148 

.02 

.02204 

.0219 

25 

26 

.018 

.01594 

.018 

.146 

.018 

.01961 

.0188 

26 

27 

.016 

.01419 

.017 

.143  •  .0164 

.01745 

.0172 

27 

28 

.014 

.01264 

.016 

.139  .0148 

.015625 

.0156 

28 

29 

.013 

.01126 

.015 

.134  .0136 

.0139 

.0141 

29 

30 

.012 

.01002 

.014 

.127  .0124 

.0123 

.0125 

30 

31 

.01 

.00893 

.013 

.120 

.0116 

.0110 

.0109 

31 

32 

.009 

.00795 

.013 

.115 

.0108 

.0098 

.0101 

32 

33 

.008 

.00708 

.011 

.112 

.01 

.0037 

.0094 

33 

34 

.007 

,0063 

.01 

.110 

.0092 

.0077 

.0086 

34 

35 

.005 

.00561 

.0095 

.103 

.0084 

.0069 

.0078 

35 

36 

.004 

.005 

.009 

.106 

.0076 

.0061 

.007 

36 

37 

.00445 

.0085 

.103 

.0068 

.0054 

.0066 

37 

38 

.00396 

.008 

.101 

.006 

.0048 

.0063 

38 

39 

.00353 

.0075 

.099 

.0052 

.0043 

39 

40 

.00314 

.007 

.097 

.0048 

.00386 

40 

41 

.095 

.0044 

.00343 

41 

42 

.092 

.004 

.00306 

42 

43 

.088 

.0036 

.00272 

43 

44 

.085 

.0032 

.00242 

44 

45 

.081 

.0028 

.00215 

45 

46 

.079 

.0024 

.00192 

46 

47 

.077 

.002 

.00170 

47 

•   48 

.075 

.0016 

.00152 

48 

49 

.072 

.0012 

.00135 

49 

50 

.065 

.001 

.00120 

50 

WIRE   AND   SHEET  METAL   GAUGES ,  29 


THE  EDISON  OB  CIRCULAR  MIL  WIRE  GAUGE. 

(For  table  of  copper  wires  by  this  gauge,  giving  weights,  electrical 
resistances,  etc.,  see  Copper  Wire.) 

Mr.  C.  J.  Field  (Stevens  Indicator,  July,  1887)  thus  describes  the  origin 
of  the  Edison  gauge: 

The  Edison  company  experienced  inconvenience  and  loss  by  not  having 
a  wide  enough  range  nor  sufficient  number  of  sizes  in  the  existing  gauges. 
This  was  felt  more  particularly  in  the  central-station  work  in  making 
electrical  determinations  for  the  street  system.  They  were  compelled  to 
make  use  of  two  of  the  existing  gauges  at  least,  thereby  introducing  a 
complication  that  was  liable  to  lead  to  mistakes  by  the  contractors  and 
linemen. 

In  the  incandescent  system  an  even  distribution  throughout  the  entire 
system  and  a  uniform  pressure  at  the  point  of  delivery  are  obtained  by 
calculating  for  a  given  maximum  percentage  of  loss  from  the  potential  as 
delivered  from  the  dynamo.  In  carrying  this  out,  on  account  of  lack  of 
regular  sizes,  it  was  often  necessary  to  use  larger  sizes  than  the  occasion 
demanded,  and  even  to  assume  new  sizes  for  large  underground  conductors. 
The  engineering  department  of  the  Edison  company,  knowing  the  require- 
ments, have  designed  a  gauge  that  has  the  widest  range  obtainable  and 
a  large  number  of  sizes  which  increase  in  a  regular  and  uniform  manner. 
The  basis  of  the  graduation  is  the  sectional  area,  and  the  number  of  the 
wire  corresponds.  A  wire  of  100,000  circular  mils  area  is  No.  100;  a  wire 
of  one  half  the  size  will  be  No.  50;  twice  the  size  No.  200. 

In  the  older  gauges,  as  the  number  increased  the  size  decreased.  With 
this  gauge,  however,  the  number  increases  with  the  wire,  and  the  number 
multiplied  by  1000  will  give  the  circular  mils. 

The  weight  per  mil-foot,  0.00000302705  pounds,  agrees  with  a  specific 
gravity  of  8.889,  which  is  the  latest  figure  given  for  copper.  The  ampere 
capacity  which  is  given  was  deduced  from  experiments  made  in  the  com- 
pany's laboratory,  and  is  based  on  a  rise  of  temperature  of  50°  F.  in  the 
wire. 

In  1893  Mr.  Field  writes,  concerning  gauges  in  use  by  electrical  engineers: 

The  B.  and  S.  gauge  seems  to  be  in  general  use  for  the  smaller  sizes,  up 
to  100,000  c.m.,  and  in  some  cases  a  little  larger.  From  between  one  and 
two  hundred  thousand  circular  mils  upwards,  the  Edison  gauge  or  its 
equivalent  is  practically  in  use,  and  there  is  a  general  tendency  to  desig- 
nate all  sizes  above  this  in  circular  mils,  specifying  a  wire  as  200,000, 
400,000,  500,000,  or  1,000,000  C.M. 

In  the  electrical  business  there  is  a  large  use  of  copper  wire  and  rod  and 
other  materials  of  these  large  sizes,  and  in  ordering  them,  speaking  of 
them,  specifying,  and  in  every  other  use,  the  general  method  is  to  simply 
specify  the  circular  milage.  I  think  it  is  going  to  be  the  only  system  in 
the  future  for  the  designation  of  wires,  and  the  attaining  of  it  means 
practically  the  adoption  of  the  Edison  gauge  or  the  method  and  basis  of 
this  gauge  as  the  correct  one  for  wire  sizes. 

THE  U.  S.  STANDARD  GAUGE  FOR  SHEET  AND 
PLATE  IRON  AND  STEEL,   1893. 

There  is  in  this  country  no  uniform  or  standard  gauge,  and  the  same 
numbers  in  different  gauges  represent  different  thicknesses  of  sheets  or 
plates.  This  has  given  rise  to  much  misunderstanding  and  friction 
between  employers  and  workmen  and  mistakes  and  fraud  between  dealers 
and  consumers. 

An  Act  of  Congress  in  1893  established  the  Standard  Gauge  for  sheet 
Iron  and  steel  which  is  given  on  the  next  page.  It  is  based  on  the  fact  that 
a  cubic  foot  of  iron  weighs  480  pounds. 

A  sheet  of  iron  1  foot  square  and  1  inch  thick  weighs  40  pounds,  or  640 
ounces,  and  1  ounce  in  weight  should  be  1/640  inch  thick.  The  scale  has 
been  arranged  so  that  each  descriptive  number  represents  a  certain 
number  of  ounces  in  weight  and  an  equal  number  of  640ths  of  an  inch  in 
thickness. 

The  law  enacts  that  on  and  after  July  1,  1893,  the  new  gauge  shall  be 
used  in  determining  duties  and  taxes  levied  on  sheet  and  plate  iron  and 
(Continued  on  page  32.} 


30 


ARITHMETIC. 


Edison,  or  Circular  Mil  Gauge  for  Electrical  Wires. 


Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter in 
Mils. 

Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter in 

Mils. 

Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter in 
Mils. 

3 

3,000 

54.78 

70 

70,000 

264.58 

190 

190,000 

435.89 

5 

5,000 

70.72 

75 

75,000 

273.87 

200 

200,000 

447.22 

8 

8,000 

89.45 

80 

80,000 

282.85 

220 

220,000 

469.05 

12 

12,000 

109.55 

85 

85,000 

291.55 

240 

240,000 

489.90 

15 

15,000 

122.48 

90 

90,000 

300.00 

260 

260,000 

509.91 

20 

20,000 

141.43 

95 

95,000 

308.23 

280 

280,000 

529.16 

25 

25,000 

158.12 

100 

100,000 

316.23 

300 

300,000 

547.73 

30 

30,000 

173.21 

110 

110,000 

331.67 

320 

320,000 

565.69 

35 

35,000 

187.09 

120 

120,000 

346.42 

340 

340,000 

583.10 

40 

40,000 

200.00 

130 

130,000 

360.56 

360 

360,000 

600.00 

45 

45,000 

212.14 

140 

140,000 

374.17 

50 

50,000 

223.61 

150 

150,000 

387.30 

55 

55,000 

234.53 

160 

160,000 

400.00 

60 

60,000 

244.95 

170 

170,000 

412.32 

65 

65,000 

254.96 

180 

180,000 

424.27 

Twist  Drill  and  Steel  Wire  Gauge. 

(Manufacturers  Standard) 


No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

1 

0.2280 

14 

0.1820 

27 

0.1440 

40 

0.0980 

53 

0.0595 

67 

0.0320 

2 

.2210 

15 

.1800 

28 

.1405 

41 

.0960 

54 

.0550 

68 

.0310 

.2130 

16 

.1770 

29 

.1360 

42 

.0935 

55 

.0520 

69 

.0292 

4 

.2090 

17 

.1730 

30 

.1285 

43 

.0890 

56 

.0465 

70 

.0280 

5 

.2055 

18 

.1695 

31 

.1200 

44 

.0860 

57 

.0430 

71 

.0260 

6 

.2040 

19 

.1660 

32 

.1160 

45 

.0820 

58 

.0420 

72 

.0250 

7 

.2010 

20 

.1610 

33 

.1130 

46 

.0810 

59 

.0410 

73 

.0240 

8 

.1990 

21 

.1590 

34 

.1110 

47 

.0785 

60 

.0400 

74 

.0225 

9 

.1960 

22 

.1570 

35 

.1100 

48 

.0760 

61 

.0390 

75 

.0210 

10 

.1935 

23 

.1540 

36 

.1065 

49 

.0730 

62 

.0380 

76 

.0200 

11 

.1910 

24 

.1520 

37 

.1040 

50 

.0700 

63 

.0370 

77 

.0180 

12 

.1890 

25 

.1495 

38 

.1015 

51 

.0670 

64 

.0360 

78 

.0160 

13 

.1850 

26 

.1470 

39 

.0995 

52 

.0635 

65 

.0350 

79 

.0145 

66 

.0330 

80 

.0135 

Stubs'  Steel  Wire  Gauge. 

(For  Nos.  1  to  50  see  table  on  page  31.) 


No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

z 

inch. 
.413 

P 

inch. 
.323 

F 

inch. 
.257 

51 

inch. 
.066 

61 

inch. 
.038 

71 

inch. 
.026 

Y 

.404 

O 

.316 

Fi 

.250 

52 

.063 

62 

.037 

72 

.024 

X 

.397 

N 

.302 

D 

.246 

53 

.058 

63 

.036 

73 

.023 

w 

.386 

M 

.295 

0 

.242 

54 

.055 

64 

.035 

74 

.022 

V 

.377 

T, 

.290 

B 

.238 

55 

.050 

65 

.033 

75 

.020 

TT 

.368 

K 

.281 

A 

.234 

56 

.045 

66 

.032 

76 

.018 

T 

.358 

,T 

.277 

1 

(See 

57 

.042 

67 

.031 

77 

.016 

8 

.348 

T 

.272 

to 

{page 

58 

.041 

68 

.030 

78 

.015 

fi 

.339 

H 

.266 

50 

(29 

59 

.040 

69 

.029 

79 

.014 

Q 

.332 

G 

.261 

60 

.039 

70 

.027 

80 

.013 

The  Stubs'  Steel  Wire  Gauge  is  used  in  measuring  drawn  steel  wire  or 
drill  rods  of  Stubs'  make,  and  is  also  used  by  many  makers  of  American 
drill  rods. 


WIRE   AND   SHEET   METAL   GAUGES. 


31 


U.  S.  STANDARD  GAUGE  FOR  SHEET  AND  PLATE 
IRON  AND   STEEL,  1893. 


Number  of 
Gauge. 

Approximate 
Thickness  in 
Fractions  of 
an  Inch. 

**    9 
8  «-a  *  . 

HIP 

fr* 

Approximate 
Thickness 
in 

Millimeters. 

Weight  per 
Square  Foot 
in  Ounces 
Avoirdupois. 

Weight  per 
Square  Foot 
in  Pounds 
Avoirdupois. 

fit 

^§5 

|§S 

^£.2 

Weight  per 
Square  Meter 
in  Kilograms. 

1  Weight  per  Sq.  1 
M  eter  in  Founds! 
Avoirdupois.  | 

0000000 

1-2 

0.5 

12.7 

320 

20. 

9.072 

97.65 

215.28 

000000 

15-32 

0.46875 

1  1  .90625 

300 

18.75 

8.505 

91.55 

201.82 

00000 

7-16 

0.4375 

11.1125 

280 

17.50 

7.938 

85.44 

188.37 

0000 

13-32 

0.40625 

10.31875 

260 

16.25 

7.371 

79.33 

174.91 

000 

3-8 

0.375 

9.525 

240 

15. 

6.804 

73.24 

161.46 

00 

11-32 

0.34375 

8.73125 

220 

13.75 

6.237 

67.13 

148.00 

0 

5-16 

0.3125 

7.9375 

200 

12.50 

5.67 

61.03 

134.55 

1 

9-32 

0.28125 

7.14375 

180 

11.25 

5.103 

54.93 

121.09 

2 

17-64 

0.265625 

6.746875 

170 

10.625 

4.819 

51.88 

114.37 

3 

1-4 

0.25 

6.35 

160 

10. 

4.536 

48.82 

107,64 

4 

15-64 

0.234375 

5.953125 

150 

9.375 

4.252 

45.77 

100.91 

5 

7-32 

0.21875 

5.55625 

140 

8.75 

3.969 

42.72 

94.18 

6 

13-64 

0.203125 

5.159375 

130 

8.125 

3.685 

39.67 

87.45 

7 

3-16 

0.1875 

4.7625 

120 

7.5 

3.402 

36.62 

80.72 

.       8 

11-64 

0.171875 

4.365625 

110 

6.875 

3.118 

33.57 

74.00 

9 

5-32 

0.15625 

3.96875 

100 

6.25 

2.835 

30.52 

67.27 

10 

9-64 

0.140625 

3.571875 

90 

5.625 

2.552 

27.46 

60.55 

11 

1-8 

0.125 

3.175 

80 

5. 

2.268 

24.41 

53.82 

12 

7-64 

0.109375 

2.778125 

70 

4.375 

.984 

21.36 

47.09 

13 

3-32 

0.09375 

2.38125 

60 

3.75 

.701 

18.31 

40.36 

14 

5-64 

0.078125 

1  .984375 

50 

3.125 

.417 

15.26 

33.64 

15 

9-128 

0.0/03125 

1  .7859375 

45 

2.8125 

.276 

13.73 

30.27 

16 

1-16 

0.0625 

1.5875 

40 

2.5 

.134 

12.21 

26.91 

17 

9-160 

0.05625 

1  .42875 

36 

2.25 

.021 

10.99 

24.22 

18 

1-20 

0.05 

1.27 

32 

2. 

0.9072 

9.765 

21.53 

19 

7-160 

0.04375 

1.11125 

28 

.75 

0.7938 

8.544 

18.84 

20 

3-80 

0.0375 

0.9525 

24 

.50 

0.6804 

7.324 

16.15 

21 

1  1-320 

0.034375 

0.873125 

22 

.375 

0.6237 

6.713 

14.80 

22 

1-32 

0.03125 

0.793750 

20 

.25 

0.567 

6.103 

13.46 

23 

9-320 

0.028125 

0.714375 

18 

.125 

0.5103 

5.49 

12.11 

24 

1-40 

0.025 

0.635 

16 

1. 

0.4536 

4.882 

10.76 

25 

7-320 

0.021875 

0.555625 

14 

0.875 

0.3969 

4.272 

9.42 

26 

3-160 

0.01875 

0.47625 

12 

0.75 

0.3402 

3.662 

8.07 

27 

1  1-640 

0.0171875 

0.4365625 

11 

0.6875 

0.3119 

3.357 

7.40 

28 

1-64 

0.015625 

0.396875 

10 

0.625 

0.2835 

3.052 

6.73 

29 

9-640 

0.0140625 

0.3571875 

9 

0.5625 

0.2551 

7746 

6.05 

30 

1-80 

0.0125 

0.3175 

8 

0.5 

0.2268 

2.441 

5.38 

31 

7-640 

0.0109375 

0.2778125 

7 

0.4375 

0.1984 

2.136 

4.71 

32 

13-1280 

0.01015625 

0.25796875 

'  <     61/2 

0.40625 

0.1843 

1.983 

4.37 

(33 

3-320 

0.009375 

0.238125 

6 

0.375 

0.1701 

1.831 

4.04 

34 

11-1280 

0.00859375 

0.21828125 

51/2 

0.34375 

0.1559 

1.678 

3.70 

35 

5-640 

0.0078125 

0.1984375 

5 

0.3125 

0.1417 

1.526 

3.36 

36 

9-1280 

0.00703125 

0.17859375 

4V2 

0.28125 

0.1276 

1.373 

3.03 

37 

17-2560 

0.00664062 

0.16867187 

41/4 

0.26562 

0.1205 

1.297 

2.87 

38 

1-160 

0.00625 

0.15875 

0.25 

0.1134 

1.221 

2.69 

- 


32 


THE   DECIMAL   GAUGE. 


(continued  from  page  29)  steel;  and  that  in  its  application  a  variation  of 
2 1/2  per  cent  either  way  may  be  allowed. 

The  Decimal  Gauge.  —  The  legalization  of  the  standard  sheet- 
metal  gauge  of  1893  and  its  adoption  by  some  manufacturers  of 
sheet  iron  have  only  added  to  the  existing  confusion  of  gauges.  A  joint 
committee  of  the  American  Society  of  Mechanical  Engineers  and  the 
American  Railway  Master  Mechanics'  Association  in  1895  agreed  to 
recommend  the  use  of  the  decimal  gauge,  that  is,  a  gauge  whose  number 
for  each  thickness  is  the  number  of  thousandths  of  an  inch  in  that  thick- 
ness, and  also  to  recommend  "  the  abandonment  and  disuse  of  the  various 
other  gauges  now  in  use,  as  tending  to  confusion  and  error."  A  notched 
gauge  of  oval  form,  shown  in  the  cut  below,  has  come  into  use  as  a  standard 
form  of  the  decimal  gauge. 

In  1904  The  Westinghouse  Electric  &  Mfg.  Co.  abandoned  the  use  of 
gauge  numbers  in  referring  to  wire,  sheet  metal,  etc. 

Weight  of  Sheet  Iron  and  Steel.    Thickness  by  Decimal  Gauge. 


§ 

i 

Weight  per 
Square  Foot 

6 

§ 

m 

Weight  per 
Square  Foot 

3 

.2  • 

J* 

in  Pounds. 

!> 

'§  ' 

"£ 

in  Pounds. 

• 

"OBO 

• 

09 

t>o 

1 

• 

0 

£  d 

JO  ^ 

o. 

O 

E  £ 

-£  -tJ 

"O 

•a 

fehfl 

i 

o^. 

®  ft-^ 

'd 

^  £ 

iS 

o  ~ 

&   4)     • 

00   ft,*^ 

.3 

X  * 

M 

*O 

"i-    ^» 

.5 

o 

X 

$5 

"*"__  r* 

Q 

I 

ft 

0  ft 
M 

135 

02 

Q 

P 

2 
1 

'a)^  3 

£ 

0.002 

1/500 

0.05 

0.08 

0.082 

0.060 

1/16- 

1.52 

2.40 

2.448 

0.004 

1/250 

0.10 

0.16 

0.163 

0.065 

13/200 

1.65 

2.60 

2.652 

0.006 

3/500 

0.15 

0.24 

0.245 

0.070 

7/100 

1.78 

2.80 

2.856 

0.008 

Vl25 

0.20 

0.32 

0.326 

0.075 

3/40 

1.90 

3.00 

3.060 

0.010 

1/100 

0.25 

0.40 

0.408 

0.080 

2/25 

2.03 

3.20 

3.264 

0.012 

3/250 

0.30 

0.48 

0.490 

0.085 

17/200 

2.16 

3.40 

3.468 

0.014 

7/500 

0.36 

0.56 

0.571 

0.090 

9/100 

2.28 

3.60 

3.672 

0.016 

1/64  + 

0.41 

0.64 

0.653 

0.095 

19/200 

2.41 

3.80 

3.876 

0.018 

9/500 

0.46 

0.72 

0.734 

0.100 

1/10 

2.54 

4.00 

4.080 

0.020 

1/50 

0.51 

0.80 

0.816 

0.110 

H/100 

2.79 

4.40 

4.488 

0.022 

H/500 

0.56 

0.88 

0.898 

0.125 

1/8 

3.18 

5.00 

5.100 

0.025 

1/40 

0.64 

.00 

.020 

0.135 

27/200 

3.43 

5.40 

5.508 

0.028 

7/250 

0.71 

.12 

.142 

0.150 

3/20 

3.81 

6.00 

6.120 

0.032 

1/32  + 

0.81 

.28 

.306 

0.165 

33/200 

4.19 

6.60 

6.732 

0.036 

9/250 

0.91 

.44 

.469 

0.180 

9/50 

4.57 

7.20 

7.344 

0.040 

1/25 

1.02 

.60 

.632 

0.200 

1/5 

5.08 

8.00 

8.160 

0.045 

9/200 

1.14 

.80 

.836 

0.220 

n/50 

5.59 

8.80 

8.976 

0.050 

1/20 

1.27 

2.00 

2.040 

0.240 

6.10 

9.60 

9.792 

0.055 

11/200 

1.40 

2.20 

2.244 

0.250 

i/f 

6.35 

10.00 

10.20C 

ALGEBRA.  33 


ALGEBRA. 

Addition.  —  Add  a,  b,  and  —  c.     Ans.  a  4  b  —  c. 
Add   2a  and    -  3a.     Ans.    -  a.     Add   2ab,  -  Sab,  -  c,    -  3c.     Ans, 
-  ab  -  4c.     Add  a2  and  2a.     Ans.  a2  -f  2a. 
Subtraction.  —  Subtract  a  from  b.     Ans.  &  —  a.     Subtract  —  a  from 

—  6.     Ans.   —  b  +  a. 

Subtract  b  +  c  from  a.  Ans.  a  —  6  —  c.  Subtract  3a26  —  9c  from 
4a26  -f  c.  Ans.  a26  +  lOc.  RULE:  Change  the  signs  of  the  subtrahend 
and  proceed  as  in  addition. 

Multiplication.  —  Multiply  a  by  b.  Ans.  ab.  Multiply  ab  by  a  +  b. 
Ans.  a26  +  ab2. 

Multiply  a  4-  b  by  a  4  6.    Ans.  (a  4-6)  (a46)=a24-2a&+62. 

Multiply  —  a  by  —  b.  Ans.  ab.  Multiply  —a  by  b.  Ans.  —  a&. 
Like  signs  give  plus,  unlike  signs  minus. 

Powers  of  numbers.  —  The  product  of  two  or  more  powers  of  any 
number  is  the  number  with  an  exponent  equal  to  the  sum  of  the  powers: 
a2  x  a3  =  a5;  a262  X  ab  =  a363;  -  7ab  X  2ac  =  -  14ft26c. 

To  multiply  a  polynomial  by  a  monomial,  multiply  each  term  of  the 
polynomial  by  the  monomial  and  add  the  partial  products:  (6a  —  36) 
X  3c  =  I8ac  -  96c. 

To  multiply  two  polynomials,  multiply  each  term  of  one  factor  by  each 
term  of  the  other  and  add  the  partial  products:  (5a  —  66)  X  (3a  —  46) 
=  15a2  -  38a6  4-  2462. 

The  square  of  the  sum  of  two  numbers  =  sum  of  their  squares  +  twice 
their  product. 

The  square  of  the  difference  of  two  numbers  =  the  sum  of  their  squares 

—  twice  their  product. 

The  product  of  the  sum  and  difference  of  two  numbers  =  the  difference 
of  their  squares: 

(a  4-  6)2  =  a2  4-  2a6  4-  62;  (a  -  6)2  =  a2  -  2a6  4-  &2; 
(a  4-  6)  X  (a  -  6)  =  a2  -  62. 

The  square  of  half  the  sums  of  two  quantities  is  equal  to  their  product 
plus  the  square  of  half  their  difference:  (^^Y  =  ab  +  (^-bY- 

The  square  of  the  sum  of  two  quantities  is  equal  to  four  times  their 
products,  plus  the  square  of  their  difference:  (a  +  6)2  =  4a6  4-  (a  —  6)2. 

The  sum  of  the  squares  of  two  quantities  equals  twice  their  product, 
plus  the  square  of  their  difference:  a2  +  62  =  2a6  4-  (a  —  6)2. 

The  square  of  a  trinomial  ==  square  of  each  term  4  twice  the  product 
of  each  term  by  each  of  the  terms  that  follow  it:  (a  +  6  4  c)2  =  a2  4  62 
4  c2  4-  2a6  4-  2ac  +  2bc;  (a  —  b  -  c)?  =  -a2  +  62  +  c*  -  2a6-  2ac  +  2bc. 

The  square  of  (any  number  4-  1/2)  =  square  of  the  number  +  the  number 
+  1/4;  =  the  number  X  (the  number  4-  1)  4- 1/4:  (a+  i/2)2  =  a2  4-  a  4-  1/4, 
=  a  (a  +  1)  4- 1/4-  (4l/2)2  =  42  +  4  4- 1/4=4  X  5  +  1/4  =  201/4. 

The  product  of  any  number  4-  1/2  by  any  other  number  +  1/2  =  product 
of  the  numbers  4-  half  their  sum  4- 1/4.  (a  +  i/2)  X  (6  4-  1/2)  =  ab  +  1/2(0  46) 
4  1/4.  4l/2  X  6V2  =  4X64-  i/2(4  4-  6)  4-  V4  =  24  4-  5  4-  1/4  =  29V4. 

Square,  cube,  4th  power,  etc.,  of  a  binomial  a  4-  6. 

(a  4  6)2  =  a2  4-  2a6  4-  62;  (a  4-  6)3  =  a3  4-  3a26  +  3a62  4-  6« 
(a  4-  6)4  =  a4  4-  4a36  4-  6a262  4-  4a63  4-  64. 

In  each  case  the  number  of  terms  is  one  greater  than  the  exponent  of 
the  power  to  which  the  binomial  is  raised. 

2.  In  the  first  term  the  exponent  of  a  is  the  same  as  the  exponent  of  the 
power  to  which  the  binomial  is  raised,  and  it  decreases  by  1  in  each  suc- 
ceeding term. 

3.  6  appears  in  the  second  term  with  the  exponent  1,  and  its  exponent 
increases  by  1  in  each  succeeding  term. 

4.  The  coefficient  of  the  first  term  is  1. 

5.  The  coefficient  of  the  second  term  is  the  exponent  of  the  power  to 
which  the  binomial  is  raised. 


34  ALGEBRA. 


6.  The  coefficient  of  each  succeeding  term  is  found  from  the  next  pre- 
ceding term  by  multiplying  its  coefficient  by  the  exponent  of  a,  and 
dividing  the  product  by  a  number  greater  by  1  than  the  exponent  of  b. 
(See  Binomial  Theorem,  below.) 

Parentheses.  —  When  a  parenthesis  is  preceded  by  a  plus  sign  it  may 
be  removed  without  changing  the  yalue  of  the  expression:  a  +  b  +  (a  + 
b)  =  2a  +  2b.  When  a  parenthesis  is  preceded  by  a  minus  sign  it  may 
be  removed  if  we  change  the  signs  of  all  the  terms  within  the  parenthesis: 
1  —  (a  —  b  —  c)  =  1  —  a  +  b  +  c.  When  a  parenthesis  is  within  a 
parenthesis  remove  the  inner  one  first:  a  —  [6  —  {c  —  (d  —  e)}]  =  a  —  [ft  — 
{c  —  d  +  ej]=  a  -  [b  -  c  +  d  -  e]  =  a  -  b  +  c  —  d  +  e. 

A  multiplication  sign,  X,  has  the  effect  of  a  parenthesis,  in  that  the 
operation  indicated  by  it  must  be  performed  before  the  operations  of 
addition  or  subtraction,  a  4-  b  X  a  +  b  =  a  +  ab  +  b;  while  (a  -f-  6) 
X  (a  +  6)  =  a2  +  2ab  +  62,  and  (a  +  b)  X  a  +  b  =  a2  +  ab  +  b. 

The  absence  of  any  sign  between  two  parentheses,  or  between  a  quan- 
tity and  a  parenthesis,  indicates  that  the  parenthesis  is  to  be  multiplied  by 
the  quantity  or  parenthesis:  a(a  +  b  +  c)  =  a2  +  ab  +  ac. 

Division.  — The  quotient  is  positive  when  the  dividend  and  divisor 
have  like  signs,  and  negative  when  they  have  unlike  signs:  abc  -*-  b  =  ac; 
abc  •*•  —  6  =  —  ac. 

To  divide  a  monomial  by  a  monomial,  write  the  dividend  over  the 
divisor  with  a  line  between  them.  If  the  expressions  have  common  factors, 
remove  the  common  factors: 

azbx       ax     a4  a3       1 

azbx  -*•  aby  =  -r —  =  —  ;  —,  =  a;  -7  =  -^  =  a~~2. 
aby         y      a3         'a6      a2 

To  divide  a  polynomial  by  a  monomial,  divide  each  term  of  the  poly- 
nomial by  the  monomial:  (Sab  —  12ac)  -5-  4a  =  26  —  3c. 

To  divide  a  polynomial  by  a  polynomial,  arrange  both  dividend  and 
divisor  in  the  order  of  the  ascending  or  descending  powers  of  some  common 
letter,  and  keep  this  arrangement  throughout  the  operation. 

Divide  the  first  term  of  the  dividend  by  the  first  term  of  the  divisor,  and 
write  the  result  as  the  first  term  of  the  quotient. 

Multiply  all  the  terms  of  the  divisor  by  the  first  term  of  the  quotient 
and  subtract  the  product  from  the  dividend.  If  there  be  a  remainder, 
consider  it  as  a  new  dividend  and  proceed  as  before:  (a2  —  b2)  -*•  (a  +  b). 

a2  -  62    I  a  +  b. 
a2  +  ab  I  a  —  b. 

-  ab  -~~&~ 

-  ab  -  ft2. 


The  difference  of  two  equal  odd  powers  of  any  two  numbers  is  divisible 
by  their  difference  but  not  by  their  sum: 


The  difference  of  two  equal  even  powers  of  two  numbers  is  divisible  by 
their  difference  and  also  by  their  sum:  (a2  —  b2)  -5-  (a  —  6)  =  a  -4-  6. 

The  sum  of  two  equal  even  powers  of  two  numbers  is  not  divisible  by 
either  the  difference  or  the  sum  of  the  numbers;  but  when  the  exponent 
of  each  of  the  two  equal  powers  is  composed  of  an  odd  and  an  even  factor, 
the  sum  of  the  given  power  is  divisible  by  the  sum  of  the  powers  expressed 
by  the  even  factor.  Thus  x6  +  y6  is  not  divisible  by  x  -f  y  or  by  x  —  y, 
but  is  divisible  by  x2  +  if. 

Simple  equations.  —  An  equation  is  a  statement  of  equality  between 
two  expressions;  as,  a  +  b  =  c  +  d. 

A  simple  equation,  or  equation  of  the  first  degree,  is  one  which  contains 
only  the  first  power  of  the  unknown  quantity.  If  equal  changes  be  made 
(by  addition,  subtraction,  multiplication,  or  division)  in  both  sides  of  an 
equation,  the  results  will  be  equal. 

Any  term  may  be  changed  from  one  side  of  an  equation  to  another, 
provided  its  sign  be  changed:  a+b  =  c+d\a^c+d  —  b.  To  solve 


ALGEBRA.  35 

an  equation  having  one  unknown  quantity,  transpose  all  the  terms  involv- 
ing the  unknown  quantity  to  one  side  of  the  equation,  and- all  the  other 
terms  to  the  other  side;  combine  like  terms,  and  divide  both  sides  by  the 
coefficient  of  the  unknown  quantity. 

Solve  Sx  -  29  -  26  -  3x.     Sx  +  3x  =  29  4-  26;  llx  =  55;  x  =  5,  ans. 

Simple  algebraic  problems  containing  one  unknown  quantity  are  solved 
by  making  x  =  the  unknown  quantity,  and  stating  the  conditions  of  the 
problem  in  the  form  of  an  algebraic  equation,  and  then  solving  the  equa- 
tion. What  two  numbers  are  those  whose  sum  is  48  and  difference  14? 
Let  x  =  the  smaller  number,  re  4-  14  the  greater,  x  +  x  +  14  =  48. 
2x  =  34,  x  =  17;  x  -I-  14  =  31,  ans. 

Find  a  number  whose  treble  exceeds  50  as  much  as  its  double  falls  short 
of  40.  Lets  =  the  number.  3x  -  50  =  40  -  2x;  5x  «  90;  a;  =  18,  ans. 
Proving,  54  -  50  =  40  -  36. 

Equations  containing  two  unknown  quantities.  —  If  one  equation 
contains  two  unknown  quantities,  x  and  y,  an  indefinite  number  of  pairs 
of  values  of  x  and  y  may  be  found  that  will  satisfy  the  equation,  but  if  a 
second  equation  be  given  only  one  pair  of  values  can  be  found  that  will 
satisfy  both  equations.  Simultaneous  equations,  or  those  that  may  be 
satisfied  by  the  same  values  of  the  unknown  quantities,  are  solved  by 
combining  the  equations  so  as  to  obtain  a  single  equation  containing  only 
one  unknown  quantity.  This  process  is  called  elimination. 

Elimination  by  addition  or  subtraction.  —  Multiply  the  equation  by 
such  numbers  as  will  make  the  coefficients  of  one  of  the  unknown  quanti- 
ties equal  in  the  resulting  equation.  Add  or  subtract  the  resulting  equa- 
tions according  as  they  have  unlike  or  like  signs. 

M 

Substituting  value  of  ?/  in  first  equation,  2x  4-  3  =  7;  x  =  2. 

Elimination  by  substitution.  —  From  one  of  the  equations  obtain  the 
value  of  one  of  the  unknown  quantities  in  terms  of  the  other.  Substi- 
tute for  this  unknown  quantity  its  value  in  the  other  equation  and  reduce 
the  resulting  equations. 


4  3y  ^  7.        Multiply  by  2:  .    _„ 

-  by  =  3.       Subtract :  4a?  —  5y  —  3    l\y  -  11 ;  y  =>  1« 


c^irr^  f  2.r  +  3y  =  8.     (1).       From  (1)  we  find  x 
bolvel3z  +7y  =  7.     (2). 

Substitute  this  value  in  (2):  3  (8  ~  3?/)  4-7^  =  7;  = 


whence  y  =  -  2.     Substitute  this  value  in  (1):  2x  —  6  =  8;  x  =  7. 

Elimination  by  comparison.  —  From  each  equation  obtain  the  value  of 
one  of  the  unknown  quantities  in  terms  of  the  9ther.  Form  an  equation 
from  these  equal  values,  and  reduce  this  equation. 

Solve  2x  —  9y  =  11.    (1)    and  3x  -  4y  =  7.     (2).     From  (1)  we  find 


From  (2)  we  find  x 


Equating  these  values  of  x, ll  t  9^  =  7  ~t  4y ;  IQy  -  -  19;  y  =  -  1. 

»j  O 

Substitute  this  value  of  y  in  (1):  2x  4-9  =  11;  x  =  1. 

If  three  simultaneous  equations  are  given  containing  three  unknown 
quantities,  one  of  the  unknown  quantities  must  be  eliminated  between  two 
pairs  of  the  equations;  then  a  second  between  the  two  resulting  equations. 

Quadratic  equations.  —  A  quadratic  equation  contains  the  square  of 
the  unknown  quantity,  but  no  higher  power.  A  pure  quadratic  contains 
the  square  only;  an  affected  quadratic  both  the  square  and  the  first  power. 

To  solve  a  pure  quadratic,  collect  the  unknown  quantities  on  one  side, 

id  the  known  quantities  on  the  other;  divide  by  the  coefficient  of  the 

iknown  quantity  and  extract  the  square  root  of  each  side  of  the  resulting 

[nation. 

Solve  3z2  -  15  =  0.     3z*  =  15;  x*  =  5;  x  =  >/5. 

A  root  like  x/5,  which  is  indicated,  but  which  can  be  found  only  approxi- 
'  Ay.  is  called  a  surd. 


36  ALGEBRA. 

Solve  3a*  +  15  -  0.     3z?=  -  15;  a*  =  -  5;  x  =  v. 

The  square  root  of  —  5  cannot  be  found  even  approximately,  fo/  tha 
square  of  any  number  positive  or  negative  is  positive;  therefore  a  root 
which  is  indicated,  but  cannot  be  found  even  approximately,  is  called 
imaginary. 

To  solve  an  affected  quadratic,  1.  Convert  the  equation  into  the  form 
a*x2  ±  2abx  =  c,  multiplying  or  dividing  the  equation  if  necessary,  so  as 
to  make  the  coefficient  of  x2  a  square  number. 

2.  Complete  the  square  of  the  first  member  of  the  equation,  so  as  to 
convert  it  to  the  form  of  a2x2  ±  2abx  +  b2,  which  is  the  square  of  the 
binomial  ax  ±  &,  as  follows:  add  to  each  side  of  the  equation  the  square  of 
the  quotient  obtained  by  dividing  the  second  term  by  twice  the  square 
root  of  the  first  term. 

3.  Extract  the  square  root  of  each  side  of  the  resulting  equation. 
Solve  3.*2  -  4.r  =  32.     To  make  the  coefficient  of  x2  a  square  number, 

multiply  by  3  :  9x2  -  I2x  =  96;  I2x  +  (2  X  3x)  =  2;  22  =  4. 

Complete  the  square:  9x2  —  I2x  +  4  =  100.  Extract  the  root: 
3x  —  2  =•  ±10,  whence  x  =  4  or  —  22/3.  The  square  root  of  100  is 
either  +  10  or  —  10,  since  the  square  of  —  10  as  well  as  +  102  =  100. 

Every  affected  quadratic  may  be  reduced  to  the  form  ax*+bx+c=-Q. 

The  solution  of  this  equation  is  x  =  --  -  — 

Problems  involving  quadratic  equations  have  apparently  two  solutions, 
as  a  quadratic  has  two  roots.  Sometimes  both  will  be  true  solutions,  but 
generally  one  only  will  be  a  solution  and  the  other  be  inconsistent  with  the 
conditions  of  the  problem. 

The  sum  of  the  squares  of  two  consecutive  positive  numbers  is  481. 
Find  the  numbers. 

Let  x  =.  one  number,  x+1  the  other.  z2  +  (x  -f  I)2  =  481.  2x*  -f 
2x  +  1  =  481. 

x2  +  x  =  240.  Completing  the  square,  x2  +x  -f  0.25  =  240.25. 
Extracting  the  root  we  obtain  x  +  0.5  =  ±  15.5;  x  =  15  or  -  16.  The 
negative  root  —  16  is  inconsistent  with  the  conditions  of  the  problem. 

Quadratic  equations  containing  two  unknown  quantities  require 
different  methods  for  their  solution,  according  to  the  form  of  the  equations. 
For  these  methods  reference  must  be  made  to  works  on  algebra. 

Theory  of  exponents.  —  %a  when  n  is  a  positive  integer  is  one  of  n 


equal  factors  of  a.      \o™  means  a  is  to  be  raised  to  the  with  power  and  the 
nth  root  extracted. 


tnat  the  nth  root  of  a  is  to  be  taken  and  the  result 
raised  to  the  with  power. 

«\/a™  =  (  \l~a\m  =  an.  When  the  exponent  is  a  fraction,  the  numera- 

tor indicates  a  power,  and  the  denominator  a  root.     a6/2  =  v/a6  =  a3; 
a3/2  =  Va3  =  a1-  s. 

To  extract  the  root  of  a  quantity  raised  to  an  indicated  power,  divide 
the  exponent  by  the  index  of  the  required  root;  as, 


Subtracting  1  from  the  exponent  of  a  is  equivalent  to  dividing  by  a: 
02-i=  a'  =o;  a'-i  =  a«  -  ^-  1;  a°-i  =  a~>  ~  i;  a-»-i=a-2=l. 

A  number  with  a  negative  exponent  denotes  the  reciprocal  of  the  num- 
ber with  the  corresponding  positive  exponent. 

A  factor  under  the  radical  sign  whose  root  can  be  taken  may,  by  having 
the  root  taken,  be  removed  from  under  the  radical  sign: 


GEOMETRICAL   PROBLEMS. 


37 


A  factor  outside  the  radical  sign  may  be  raised  to  the  corresponding 
power  and  placed  under  it: 


Binomial  Theorem. 

sion  of  the  form  x  +  a 


-  To  obtain  any  power,  as  the  nth,  of  an  expres- 


•x*  + 


etc.  *~*  i-2-3- 

The  following  laws  hold  for  any  term  in  the  expansion  of  (a  4-  x)n. 

The  exponent  of  x  is  less  by  one  than  the  number  of  terms. 

The  exponent  of  a  is  n  minus  the  exponent  of  x. 

The  last  factor  of  the  numerator  is  greater  by  one  than  the  exponent  of  a. 

The  last  factor  of  the  denominator  is  the  same  as  the  exponent  of  x. 

In  the  rth  term  the  exponent  of  x  will  be  r  —  1. 

The  exponent  of  a  will  be  n  —  (r  —  1),  or  n  —  r  4-  1. 

The  last  factor  of  the  numerator  will  be  n  —  r  4-  2. 

The  last  factor  of  the  denominator  will  be  =  r  —  1. 

Hence  the  rth  term  =  "(»  -  D(»  -  2)  .      («  -  r+ 2)  ^ 

l.^.O....^?*  —    1^ 


GEOMETRICAL  PROBLEMS. 


1.  To  bisect  a  straight  line,  or 
an  arc  of  a  circle  (Fig.  1).  —  From 
the  ends  A,  B,  as  centres,  describe 
arcs  intersecting  at  C  and  D,  and 
draw  a  line  through  C  and  D  which 
will  bisect  the  line  at  E  or  the  arc 
at  F. 

2.  To  draw  a  perpendicular  to 
a  straight  line,  or  a  radial  line  to 
a     circular     arc.  —  Same     as     in 
Problem  1.     C  D  is  perpendicular  to 
the  line  A  B,  and  also  radial  to  the 
arc. 

3.  To  draw  a  perpendicular  to 
a  straight  line  from  a  given  point 
in  that  line  (Fig.  2).  —  With  any 
radius,  from  the  given  point  A  in  the 
line  B  C,  cut  the  line  at  B  and  C. 
With  a  longer  radius  describe  arcs 
from  B  and  C,  cutting  each  other  at 
D,  and  draw  the  perpendicular  D  A. 

4.  From  the  end  A  of  a  given 
line  A  D  to  erect  a  perpendicular 
AE  (Fig.  3).  —  From  any  centre  F, 
above  A  D,  describe  a  circle  passing 
through  the  given  point  A ,  and  cut- 
ting the  given  line  at  D.     Draw  D  F 
and  produce  it  to  cut  the  circle  at  Et 
and  draw  the  perpendicular  A  E. 

Second  Method  (Fig.  4).  —  From 
the  given  point  A  set  off  a  distance 
A  E  equal  to  .three  parts,  by  any 
scale;  and  on  the  centres  A  and  E, 
with  radii  of  four  and  five  parts 
respectively,  describe  arcs  intersect- 
ing at  C,  Draw  the  perpendicular 
A  C. 

NOTE.  —  This  method  is  most 
useful  on  very  large  scales,  where 
straight  edges  are  inapplicable.  Any 
multiples  of  the  numbers  3,  4,  5  may 
be  taken  with  the  same  effect,  as  6,  & 
10,  or  9,  12.  15. 


38 


GEOMETRICAL   PROBLEMS. 


5.  To  draw  a  perpendicular  to 
a  straight  line  from  any  point 
without  it  (Fig.  5).  —  From  the 
point  A,  with  a  sufficient  radius  cut 
the  given  line  at  F  and  G,  and  from 
these  points  describe  arcs  cutting  at 
E.  Draw  the  perpendicular  A  E. 


6.  To  draw  a  straight  line 
parallel  to  a  given  line,  at  a  given 
distance  apart  (Fig.  6).  —  From 
the  centres  A,  B,  in  the  given  line, 
with  the  given  distance  as  radius, 
describe  arcs  (7,  D,  and  draw  the 
parallel  lines  C  D  touching  the  arcs. 


7.  To  divide  a  straight  line  into 
a  number  of  equal  parts  (Fig.  7). 
—  To  divide  the  line  A  B  into,  say, 
five  parts,  draw  the  line  A  C  at  an 
angle  from  A ;  set  off  five  equal  parts; 
draw  B5  and  draw  parallels  to  it 
from  the  other  points  of  division  in 
A  C.  These  parallels  divide  A  B  as 
required. 

NOTE.  —  By  a  similar  process  a 
line  may  be  divided  into  a  number 
of  unequal  parts;  setting  off  divisions 
on  A  C,  proportional  by  a  scale  to  the 
required  divisions,  and  drawing 
parallels  cutting  A  B.  The  triangles 
All,  A 22,  A33,  etc.,  are  similar 
triangles. 


8.   Upon  a  straight  line  to  draw 
an  angle  equal  to  a  given  angle 

(Fig.  8).  —  Let  A  be  the  given  angle 
and  F  G  the  line.  From  the  point  A 
with  any  radius  describe  the  arc  D  E. 
From  F  with  the  same  radius 
describe  I  H.  Set  off  the  arc  I H 
equal  to  D  E,  and  draw  F  H.  The 
angle  F  is  equal  to  A,  as  required. 


9.   To  draw  angles  of  60°  and 

80°  (Fig.  9).  —  From  F,  with  any 
radius  F  /,  describe  an  arc  /  H ;  and 
from  /,  with  the  same  radius,  cut 
the  arc  at  H  and  draw  F  H  to  form 
the  required  angle  I  F  H.  Draw  the 
perpendicular  H  K  to  the  base  line  to 
form  the  angle  of  30°  F  H  K. 


10.   To   draw  an  angle   of  45° 

(Fig.  10).  —  Set  off  the  distance  F  /; 
draw  the  perpendicular  /  H  equal  to 
/  Ft  and  join  H  " 


\. 


FIG.  9. 


F. 


Fto  form  the  angle  at 
The  angle  at  H  is  "also  45°. 


FIG.  10. 


GEOMETRICAL   PROBLEMS. 


39 


FIG.  11. 


Fia.  15. 


11.  To  bisect  an  angle  (Fig.  11). 
—  Let  ACB  be  the  angle;  with  C  as 
a  centre  draw  an  arc  cutting  the 
sides  at  A,  B.     From  A  and  B  as 
centres,   describe  arcs  cutting  each 
other  at  Z>.     Draw  C  D,  dividing  the 
angle  into  two  equal  parts. 

12.  Through  two  given  points 
to  describe  an  arc  of  a  circle  with 
a  given  radius   (Fig.  12).  —  From 
the  ppints  A  and  B  as  centres,  with 
the  given  radius,  describe  arcs  cut- 
ting at  C;  and  from  C  with  the  same 
radius  describe  an  arc  A  B. 

13.  To  find  the  centre  of  a  circle 
or  of  an  arc  of  a  circle  (Fig.  13).  — 
Select  three  points,  A,  B,  C,  in  the 
circumference,  well  apart;  with  the 
same  radius  describe  arcs  from  these 
three  points,  cutting  each  other,  and 
draw    the    two    lines,     D  E,     FG, 
through     their     intersections.     The 
point  O,  where  they  cut,  is  the  centre 
of  the  circle  or  arc. 

To  describe  a  circle  passing 
through  three  given  points.  — 
Let  A,  B,  C  be  the  given  points,  and 
proceed  as  in  last  problem  to  find  the 
centre  O,  from  which  the  circle  may 
be  described. 


14.  To  describe  an  arc  of  a 
circle  passing  through  three 
given  points  when  the  centre  is 
not  available  (Fig.  14).  —  From 
the  extreme  points  A,  B,  as 
centres,  describe  arcs  AH,  B  G. 
Through  the  third  point  C  draw 
A  E:  B  F,  cutting  the  arcs. 
Divide  A  F  and  B  E  into  any 
number  of  equal  parts,  and  set 
off  a  series  of  equal  parts  of  the 
same  length  on  the  upper  por- 
tions of  the  arcs  beyond  the 
points  E  F.  Draw  straight 
lines,  B  L,  BM,  etc.,  to  the 
divisions  in  A  F,  and  A  I,  A  K, 
etc.,  to  the  divisions  in  EG. 
The  successive  intersections  N, 
O,  etc.,  of  these  lines  are  points 
in  the  circle  required  between  the 
given  points  A  and  C,  which  may 
be  drawn  in;  similarly  the  remain- 
ing part  of  the  curve  BC  may 
be  described.  (See  also  Problem 
54.) 


15.  To  draw  a  tangent  to  a 
circle  from  a  given  point  in  the 
circumference  (Fig.  15). —  Through 
the  given  point  A,  draw  the  radial 
line  A  C,  and  a  perpendicular  to  it, 
FGt  which  is  "the  tangent  required. 


40 


GEOMETRICAL  PROBLEMS. 


16.  To    draw    tangents    to    a 
circle  from  a  point  without  it  (Fig. 
16).  —  From    A,    with    the    radius 
A  C,    describe   an    arc    BCD,    and 
from  C,  with  a  radius  equal  to  the 
diameter  of  the  circle,  cut  the  arc  at 
BD.      Join   BC,   CD,   cutting   the 
circle  at  E  F,  and  draw  A  E,  AF, 
the  tangents. 

NOTE.  —  When  a  tangent  is 
already  drawn,  the  exact  point  of 
contact  may  be  found  by  drawing  a 
perpendicular  to  it  from  the  centre. 

17.  Between  two  inclined  lines 
to  draw  a  series  of  circles  touching 
these    lines    and    touching    each 
other  (Fig.  17).  —  Bisect  the  inclina- 
tion of  the  given  lines  A  B,  C  D,  by 
the  line  N  O.    From  a  point  P  in  this 
line  draw  the  perpendicular  P  B  to  the 
line  A  B,  and  on  P  describe  the  circle 
B  D,  touching  the  lines  and  cutting 
the  centre  line  at  E.     From  E  draw 
E  F  perpendicular  to  the  centre  line, 
cutting    A  B    at    F,    and    from    F 
describe  an  arc  E  G,  cutting  A  B  at 
G.     Draw     GH    parallel     to     B  P, 
giving   H,   the  centre  of  the  next 
circle,    to    be    described    with    the 
radius  HE,  and  so  on  for  the  next 
circle  IN. 

Inversely,  the  largest  circle  may 
be  described  first,  and  the  smaller 
ones  in  succession.  This  problem  is 
of  frequent  use  in  scroll-work. 

18.  Between  two  inclined  lines 
to  draw  a  circular  segment  tan- 
gent   to    the    lines    and    passing 
through  a  point  F  on  the  line  FC 
which   bisects    the   angle   of   the 
lines  (Fig.  18).  — Through  F  draw 
DA    at  right  angles  to  FC;  bisect 
the  angles  A  and  Z),  as  in  Problem 
11,  by  lines  cutting  at  C,  and  from 
C  with  radius  C  F  draw  the  arc  H  F  G 
required. 

19.  To  draw  a  circular  arc  that 
will  be  tangent  to  two  given  lines 
AB  and  C  D  inclined  to  one  another, 
one  tangential  point  E  being  given 

(Fig.  19).  —  Draw  the  centre  line 
GF.  From  E  draw  E  F  at  right 
angles  to  A  B ;  then  F  is  the  centre 
of  the  circle  required. 

20.  To  describe  a  circular  arc 
Joining  two  circles,  and  touching 
one  of  them  at  a  given  point  (Fig. 
20).  —  To  join  the  circles  A  B,  FG, 
by  an  arc  touching  one  of  them  at 
F,  draw  the  radius  E  F,  and  produce 
it  both  ways.     Set  off  F  H  equal  to 
the  radius  A  C  of  the  other  circle; 
join  CH  and  bisect  it  with  the  per- 
pendicular   L  I,    cutting  E  F  at   I. 
On  the  centre  7,   with   radius  IF, 
describe  the  arc  FA  as  required. 


GEOMETRICAL   PROBLEMS. 


FIG.  22. 
E 


FIG.  23. 


FIG.  24. 


FIG.  25. 


FIG.  26. 


21.  To  draw  a  circle  with  a 
given  radius  R  that  will  be  tan- 
gent to  two  given  circles  A  and  B 

(Fig.  21).  —  From  centre  of  circle 
A  with  radius  equal  R  plus  radius 
of  A,  and  from  centre  of  B  with 
radius  equal  to  R  +  radius  of  B, 
draw  two  arcs  cutting  each  other  in 
C,  which  will  be  the  centre  of  the 
circle  required. 


22.   To  construct  an  equilateral 
triangle,    the    sides    being    given 

(Fig.  22).  —  On  the  ends  of  one  side, 
A,  B,  with  A  B  as  radius,  describe 
arcs  cutting  at  C,  and  draw  A  C,  C  B. 


23.  To  construct  a  triangle  of 
unequal  sides  (Fig.  23).  —  On 
either  end  of  the  base  A  D,  with  the 
side  B  as  radius,  describe  an  arc; 
and  with  the  side  C  as  radius,  on  the 
other  end  of  the  base  as  a  centre,  cut 
the  arc  at  E.  Join  A  E,  D  E. 


24.  To  construct  a  square  on™ 
given  straight  line  A  B  (Fig.  24). 
—  With  A  B  as  radius  and  A  and  B 
as  centres,  draw  arcs  A  D  and  B  C, 
intersecting  at  E.  Bisect  E  B  at 
F.  With  E  as  centre  and  E  F  as 
radius,  cut  the  arcs  A  D  and  B  C 
in  D  and  C.  Join  A  C,  C  Dt  and 
D  B  to  form  the  square. 


25.   To    construct    a    rectangle 
with  given  base  E  F  and  height  EH 

(Fig.  25).  —  On  the  base  E  F  draw 
the  perpendiculars  E  //,  F  O  equal 
to  the  height,  and  join  G  H. 


26.  To  describe  a  circle  about 
a  triangle  (Fig.  26).  —  Bisect  two 
sides  A  B,  A  C  of  the  triangle  at 
E  F,   and   from  these  points  draw 
perpendiculars    cutting    at    K.     On 
the  centre  K,  with  the  radius  K  A, 
draw  the  circle  ABC. 

27.  To   inscribe  a   circle  in  a 
triangle  (Fig.  27).— Bisect  two  of 
the  angles  A,  C,  of  the  triangle  by 


42 


GEOMETRICAL    PROBLEMS. 


lines  cutting  at  D;  from  D  draw  a 
perpendicular  D  E  to  any  side,  and 
with  D  E  as  radius  describe  a  circle. 
When  the  triangle  is  equilateral, 
draw  a  perpendicular  from  one  of  the 
angles  to  the  opposite  side,  and  from 
the  side  set  off  one  third  of  the 
perpendicular. 

28.  To  describe  a  circle  about 
a  square,  and  to  inscribe  a  square 
in  a  circle  (Fig.  28).  —  To  describe 
the  circle,  draw  the  diagonals  A  B, 
C  D  of  the  square,  cutting  at  E.     On 
the  centre  E,  with  the  radius  A  E, 
describe  the  circle. 

To  inscribe  the  square.  —  Draw 
the  two  diameters,  A  B,C  D,  at  right 
angles,  and  join  the  points  A,  B, 
C  D,  to  form  the  square. 

NOTE.  —  In  the  same  way  a  circle 
may  be  described  about  a  rectangle. 

29.  To   inscribe   a   circle   in  a 
square  (Fig.  29).  —  To  inscribe  the 
circle,  draw  the  diagonals  A  B,  C  D 
of  the  square,  cutting  at  E;  draw  the 
perpendicular  E  F  to  one  side,  and 
with  the  radius  E  F  describe  the 
circle. 


FIG.  28. 
A      G  C 


30.  To  describe  a  square  about 
a  circle  (Fig.  30).  —  Draw  two 
diameters  A  B,  C  D  at  right  angles. 
With  the  radius  of  the  circle  and 
A,  B,  C  and  D  as  centres,  draw  the 
four  half  circles  which  cross  one 
another  in  the  corners  of  the  square. 


31.  To  inscribe  a  pentagon  in 
a  circle  (Fig.  31).  —  Draw  diam- 
eters A  C,  B  D  at  right  angles,  cut- 
ting at  o.  Bisect  A  o  at  E,  and  from 
E,  with  radius  E  B,  cut  A  C  at  F; 
from  B,  with  radius  B  F,  cut  the 
circumference  at  G,  H,  and  with  the 
same  radius  step  round  the  circle  to 
/  and  K\  join  the  points  so  found  to 
form  the  pentagon. 


32.  To  construct  a  pentagon 
on  a  given  line  A  B  (Fig.  32).— 
From  B  erect  a  perpendicular  B  C 
half  the  length  of  A  B ;  join  A  C  and 
prolong  it  to  D,  making  C  D  =  B  C. 
Then  B  D  is  the  radius  of  the  circle 
circumscribing  the  pentagon.  From 
A  and  B  as  centres,  with  B  D  as 
radius,  draw  arcs  cutting  each  other 
in  O,  which  is  the  centre  of  the  circle. 


FIG.  32. 


GEOMETRICAL    PROBLEMS. 


43 


FIG.  34. 


33.  To    construct    a    hexagon 
upon  a   given   straight  line   (Fig. 

33).  —  From  A  and  B,  the  ends  of 
the  given  line,  with  radius  A  B, 
describe  arcs  cutting  at  g;  from  gt 
with  the  radius  g  A,  describe  a  circle; 
with  the  same  radius  set  off  the  arcs 
A  G,  G  F,  and  B  D,  D  E.  Join  the 
points  so  found  to  form  the  hexagon. 
The  side  of  a  hexagon  =  radius  of  its 
circumscribed  circle. 

34.  To  inscribe  a  hexagon  in  a 
circle    (Fig.    34).  —  Draw   a   diam- 
eter  ACS.     From   A    and  B  as 
centres,  with  the  radius  of  the  circle 
A  C,  cut  the  circumference,  at  D,  E, 
F,  G,  and  draw  A  D,  D  E,  etc.,  to 
form  the  hexagon.     The  radius  of 
the  circle  is  equal  to  the  side  of  the 
hexagon;  therefore  the  points  D,  Et 
etc.,  may  also  be  found  by  stepping 
the  radius  six  times  round  the  circle. 
The  angle  between  the  diameter  and 
the  sides  of  a  hexagon  and  also  the 
exterior  angle  between  a  side  and  an 
adjacent  side  prolonged  is  60  degrees; 
therefore  a  hexagon    may    conven- 
iently be  drawn  by  the  use  of  a  60- 
degree  triangle. 

35.  To     describe     a     hexagon 
about  a  circle  (Fig.  35).  —  Draw  a 
diameter  A  D  B,  and  with  the  radius 
A  D,  on  the  centre  A,  cut  the  circum- 
ference at  C;  join  A  C,  and  bisect  it 
with  the  radius  D  E ;  through  E  draw 
FG,  parallel  to  A  C,  cutting  the  diam- 
eter at  F,  and  with  the  radius  D  F 
describe    the    circumscribing    circle 
F  H.     Within  this  circle  describe  a 
hexagon  by  the  preceding  problem. 
A  more  convenient  method  is  by  use 
of  a  60-degree  triangle.     Four  of  the 
sides  make  angles  of  60  degrees  with 
the  diameter,  and  the  other  two  are 
parallel  to  the  diameter. 

36.  To  describe  an  octagon  on 
a  given  straight  line  (Fig.  36).  — 
Produce   the  given  line  'A  B  both 
ways,  and  draw  perpendiculars  A  E. 
BF;  bisect  the  external  angles^,  and 
B  by  the  lines  A  H,  B  C,  which  make 
equal  to  A  B.     Draw  C  D  and  H  G 
parallel  to  A  E,  and  equal  to  A  B; 
from   the   centres   G,    D,    with   the 
radius  A  B,  cut  the  perpendiculars  at 
E,  F,  and  draw  E  F  to  complete  the 
octagon. 

37.  To   convert  a   sqaare   into 
an  octagon  (Fig.  37).  —  Draw  the 
diagonals  of  the  square  cutting  at  e; 
from  the  corners  A,  B,  C,  D,  with 
A  e  as  radius,  describe  arcs  cutting 
the  sides  at  gn,  fk,  hm,  and  ol,  and 
join  the  points  so  found  to  form  the 
octagon.     Adjacent  sides  of  an  octa- 
gon make  an  angle  of  135  degrees. 


GEOMETRICAL  PROBLEMS. 


38.  To  inscribe  an  octagon  in 
a  circle  (Fig.  38).  —  Draw  two 
diameters,  A  C,  B  D  at  right  angles; 
bisect  the  arcs  A  B,  B  C,  etc.,  at  e  f, 
etc.,  and  join  A  e,  €  B,  etc.,  to  form 
the  octagon, 


39.  To  describe  an  octagon 
about  a  circle  (Fig.  39).  —  P -scribe 
a  square  about  the  given  circle  A  B; 
draw  perpendiculars  h  k,  etc.,  to  the 
diagonals,  touching  the  circle  to 
form  the  octagon. 


40.  To  describe  a  polygon  of 
any  number  of  sides  upon  a  given 
straight  line  (Fig.  40).  —  Produce 
the  given  .line  A  B,  and  on  A,  with  the 
radius  A  B,  describe  a  semicircle; 
divide  the  semi-circumference  into 
as  many  equal  parts  as  there  are  to 
be  sides  in  the  polygon  —  say,  in 
this  example,  five  sides.  Draw  lines 
from  A  through  the  divisional  points 
D,  b,  and  c,  omitting  one  point  a; 
and  on  the  centres  B,  D,  with  the 
radius  A  B,  cut  A  b  at  E  and  A  c  at  F. 
Draw  D  E,  E  Ft  F  B  to  complete  the 
polygon. 


41.  To  inscribe  a  circle  within 
a  polygon  (Figs.  41,  42).  —  When 
the  polygon  has  an  even  number  of 
sides  (Fig.  41),  bisect  two  opposite 
sides  at  A  and  B;  draw  A  B,  and 
bisect  it  at  C  by  a  diagonal  D  E,  and 
with  the  radius  C  A  describe  the 
circle. 

When  the  number  of  sides  is  odd 
(Fig.  42),  bisect  two  of  the  sides  at  A 
and  B,  and  draw  lines  A  E,  B  D  to  the 
opposite  angles,  intersecting  at  C; 
from  <7,  with  the  radius  C  A,  describe 
the  circle. 


42.  To  describe  a  circle  without 
a  polygon   (Figs.   41,   42).  —  Find 
the  centre  C  as  before,  and  with  the 
radius  C  D  describe  the  circle. 

43.  To   inscribe   a   polygon   of 
any  number  of  sides  within  a  circle 

(Fig.  43).  —Draw  the  diameter  A  B 
and  through  the  centre  E  draw  the 


H  D  G 

FIG.  39. 


Fio.  42. 


GEOMETRICAL   PROBLEMS. 


45 


perpendicular  E  C,  cutting  the  circle 
at  F.  Divide  E  F  into  four  equal 
parts,  and  set  off  three  parts  equal 
to  those  from  F  to  C.  Divide  the 
diameter  A  B  into  as  many  equal 
parts  as  the  polygon  is  to  have  sides; 
and  from  C  draw  C  D,  through  the 
second  point  of  division,  cutting  the 
circle  at  D.  Then  A  D  is  equal  to  one 
side  of  the  polygon,  and  by  stepping 
round  the  circumference  with  the 
length  A  D  the  polygon  may  be  com- 
pleted. 


Table  of  Polygonal  Angles. 


Number 
of  Sides. 

Angle 
at  Centre. 

Number 
of  Sides. 

Angle 
at  Centre. 

Number 
of  Sides. 

Angle 
at  Centre. 

No. 

4 
5 
6 

8 

Degrees. 
120 
90 
72 
60 

g* 

No. 
9 
10 
11 
12 
13 
14 

Degrees. 
40 
36 

gw 
i£ 

No. 
15 
16 
17 
18 
19 
20 

Degrees. 
22l/2 

iH 

19 
18 

In  this  table  the  angle  at  the  centre  is  found  by  dividing  360  degrees,  the 
number  of  degrees  in  a  circle,  by  the  number  of  sides  in  the  polygon;  and 
by  setting  off  round  the  centre  of  the  circle  a  succession  of  angles  by  means 
of  the  protractor,  equal  to  the  angle  in  the  table  due  to  a  given  number  of 
sides,  the  radii  so  drawn  will  divide  the  circumference  into  the  same  num- 
ber of  parts. 

44.  To  describe  an  ellipse  when 
the  length  and  breadth  are  given 
(Fig.  44). — A  B,  transverse  axis; 
C  Z>,  conjugate  axis;  F  G,  foci.  The 
sum  of  the  distances  from  C  to  F 
and  G,  also  the  sum  of  the  distances 
from  F  and  G  to  any  other  point  in 
the  curve,  is  equal  to  the  transverse 
axis.  From  the  centre  C,  with  A  E 
as  radius,  cut  the  axis  A  B  at  F  and 
G,  the  foci;  fix  a  couple  of  pins  into 
the  axis  at  F  and  G,  and  loop  on  a 
thread  or  cord  upon  them  equal  in 
length  to  the  axis  A  B,  so  as  when 
stretched  to  reach  to  the  extremity 
C  of  the  conjugate  axis,  as  shown  in 
dot-lining.  Place  a  pencil  inside  the 
cord  as  at  //,  and  guiding  the  pencil 
in  this  way,  keeping  the  cord  equally 
in  tension,  carry  the  pencil  round  the 
pins  F,  G,  and  so  describe  the 
ellipse. 

NOTE.  —  This  method  is  employed 
in  setting  off  elliptical  garden-plots, 
walks,  etc. 

2d  Method  (Fig.  45).  —  Along  the 
straight  edge  of  a  slip  of  stiff  paper 
mark  off  a  distance  a  c  equal  to  A  C, 
half  the  transverse  axis;  and  from 
the  same  point  a  distance  a  b  equal 
to  C  G,  half  the  conjugate  axis. 


FIG.  44. 


GEOMETRICAL  PROBLEMS. 


Place  the  slip  so  as  to  bring  the  point  b  on  the  line  A  B  of  the  transverse 
axis,  and  the  ppint  c  on  the  line  D  E;  and  set  off  on  the  drawing  the  posi- 
tion of  the  point  a.  Shifting  the  slip  so  that  the  point  b  travels  on  the 
transverse  axis,  and  thexpoint  c  on  the  conjugate  axis,  any  number  of 
points  in  the  curve  may  be  found,  through  which  the  curve  may  be 
traced. 

3d  Method  (Fig.  46).  —  The  action 
of  the  preceding  method  may  be 
embodied  so  as  to  afford  the  means 
of  describing  a  large  curve  contin- 
uously by  means  of  a  bar  m  k,  with 
steel  points  m,  I,  k,  riveted  into  brass 
slides  adjusted  to  the  length  of  the 
semi-axis  and  fixed  with  set-screws. 
A  rectangular  cross  E  G,  with  guiding- 
slots  is  placed,  coinciding  with  the 
two  axes  of  the  ellipse  A  C  and  B  H. 
B7  sliding  the  points  k,  I  in  the  slots, 
and  carrying  round  the  point  m,  the 
curve  may  be  continuously  described. 
A  pen  or  pencil  may  be  fixed  at  m. 

4th  Method  (Fig.  47).  —  Bisect  the 
transverse  axis  at  C,  and  through  C  * 
draw  the  perpendicular  D  E,  making 
C  D  and  C  E  each  equal  to  half  the 
conjugate  axis.  From  D  or  E,  with 
the  radius  AC,  cut  the  transverse 
axis  at  F,  Ff,  for  the  foci.  Divide 
A  C  into  a  number  of  parts  at  the 
points  1,  2,  3,  etc.  With  the  radius 
Al  on.  F  and  F'  as  centres,  describe 
arcs,  and  with  the  radius  B  1  on  the 
same  centres  cut  these  arcs  as  shown. 
Repeat  the  operation  for  the  other 
divisions  of  the  transverse  axis.  The 
series  of  intersections  thus  made  are 
points  in  the  curve,  through  which 
the  curve  may  be  traced. 

5th  Method  (Fig.  48).  —  On  the 
two  axes  A  B,  D  E  as  diameters,  on 
centre  C,  describe  circles;  from  a 
number  of  points  a,  b,  etc.,  in  the 
circumference  A  F  B,  draw  radii  cut- 
ting the  inner  circle  at  a',  6',  etc. 
From  a,  b,  etc.,  draw  perpendiculars 
to  AB;  and  from  a',  b't  etc.,  draw 
parallels  to  A  B,  cutting  the  respec- 
tive perpendiculars  at  n,  o,  etc.  The 
intersections  are  points  in  the  curve, 
through  which  the  curve  may  be 
traced. 

6to  Method  (Fig.  49).  —  When  the 
transverse  and  conjugate  diameters 
are  given,  A  B,  CD,  draw  the  tangent 
EF  parallel  to  A  B.  Produce  CD, 
and  on  the  centre  G  with  the  radius 
of  half  A  B,  describe  a  semicircle 
H  D  K;  from  the  centre  G  draw  any 
number  of  straight  lines  to  the  points 
E,  r,  etc.,  in  the  line  E  Ft  cutting  the 
circumference  at  /,  m,  n,  etc.;  from 
the  centre  O  of  the  ellipse  draw 
straight  lines  to  the  points  E,  r,  etc.; 
and  from  the  points  I,  m,  n,  etc., 
draw  parallels  to  G  C,  cutting  the 
tines  O  E,  O  rt  etc.,  at  Lt  Mt  3v,  etc.  Fio.  49. 


GEOMETRICAL    PROBLEMS. 


47 


These  are  points  in  the  circumference  of  the  ellipse,  and  the  curve  may  be 
traced  through  them.  Points  in  the  other  half  of  the  ellipse  are  formed 
by  extending  the  intersecting  lines  as  indicated  in  the  figure. 

45.  To  describe  an  ellipse 
approximately  by  means  of  cir- 
cular arcs.  —  First.  —  With  arcs 
of  two  radii  (Fig.  50).  —  Find  the 
difference  of  the  semi-axes,  and  set 
it  off  from  the  centre  O  to  a  and  c  on 
O  A  and  O  C;  draw  ac,  and  set  off 
half  a  c  to  d;  draw  d  i  parallel  to  a  c; 
set  off  O  e  equal  to  O  d;  join  e  i,  and 
draw  the  parallels  e  m,  d  m.  From 
m,  with  radius  m  C,  describe  an  arc 
through  C;  and  from  i  describe  an 
arc  through  D ;  from  d  and  e  describe 
arcs  through  A  and  B.  The  four 
arcs  form  the  ellipse  approximately. 
NOTE.  —  This  method  does  not 
apply  satisfactorily  when  the  con- 
jugate axis  is  less  than  two  thirds  of 
the  transverse  axis. 

2d  Method  (by  Carl  G.  Barth,  Fig. 
51).  —  In  Fig.  51  a  b  is  the  major  and 
c  d  the  minor  axis  of  the  ellipse  to  be 
approximated.  Lay  off  b  e  equal  to 
the  semi-minor  axis  c  O,  and  use  a  e 
as  radius  for  the  arc  at  each  extrem- 
ity of  the  minor  axis.  Bisect  e  o  at  / 
and  lay  off  eg  equal  toef,  and  use  gb 
as  radius  for  the  arc  at  each  extrem- 
ity of  the  major  axis. 

method  is  not  considered  applicable  for  cases  in  which  the  minor 
less  than  two  thirds  of  the  major. 

3d  Method:  With  arcs  of  three  radii 
(Fig.  52).  —  On  the  transverse  axis 
A  B  draw  the  rectangle  B  G  on  the 
height  O  C;  to  the  diagonal  A  C 
draw  the  perpendicular  G  H  D;  set 
off  O  K  equal  to  O  C,  and  describe  & 
semicircle  on  A  K,  and  produce  O  C 
to  L;  set  off  O  M  equal  to  C  L,  and 
from  D  describe  an  arc  with  radius 
D  M]  from  A,  with  radius  O  L,  cut 
A  B  at  N;  from  H,  with  radius  HN, 
cut  arc  a  b  at  a.  Thus  the  five 
centres  D,  a,  b,  H,  Hf  are  found, 
from  which  the  arcs  are  described  to 
form  the  ellipse. 

This  process  works  well  for  nearly 
all  proportions  of  ellipses.  It  is  used 
in  striking  out  vaults  and  stone 
bridges. 

4th  Method  (by  F.  R.  Honey, 
Figs.  53  and  54).  —  Three 
radii  are  employed.  With 
the  shortest  radius  describe 
the  two  arcs  which  pass 
through  the  vertices  of  the 
major  axis,  with  the  longest 
the  two  arcs  which  pass 

through  the  vertices  of  the 

minor  axis,  and  with  the  third 
radius  the  four  arcs  which 
connect  the  former. 


The 
axis  is 


b        Jid 

FIG.  53. 


48 


GEOMETRICAL   PROBLEMS. 


A  simple  method  of  determining  the  radii  of  curvature  is  illustrated  in 
Fig.  53.  Draw  the  straight  lines  a  f  and  a  c,  forming  any  angle  at  a.  With 
a  as  a  centre,  and  with  radii  a  b  and  a  c,  respectively,  equal  to  the  semi- 
minor  and  semi-major  axes,  draw  the  arcs  b  e  and  c  d.  Join  e  d,  and 
through  b  and  c  respectively  draw  b  g  and  c  f  parallel  to  e  d,  intersecting 
a  c  at  g,  and  a  /  at  /;  a  f  is  the  radius  of  curvature  at  the  vertex  of 
the  minor  axis;  and  a  g  the  radius  of  curvature  at  the  vertex  of  the 
major  axis. 

Lay  off  d  h  (Fig.  53)  equal  to  one  eighth  of  6  d.  Join  e  h,  and  draw  c  k 
and  b  I  parallel  to  e  h.  Take  a  k  for  the  longest  radius  ( =  R),  a  I  for  the 
shortest  radius  (=  r),  and  the  arithmetical  mean,  or  one  half  the  sum  of 
the  semi-axes,  for  the  third  radius  (=  p),  and  employ  these  radii  for  the 
eight-centred  oval  as  follows: 

Let  a  Sander/  (Fig.  54) 
be  the  major  and  minor 
axes.  Lay  off  a  e  equal 
to  r,  and  a  f  equal  to  p; 
also  lay  off  c  g  equal  to  R, 
and  c  h  equal  to  p'.  With 
g  as  a  centre  and  gfi  as  a 
radius,  draw  the  arc  h  k; 
with  the  centre  e  and 
radius  e  f  draw  the  arc  /  k,  a 
intersecting  h  k  at  k. 
Draw  the  line  g  k  and 


produce   it,    making   g   I 
equal   to    R.     Draw   k   e 


and  produce  it,  making 
k  m  equal  to  p.  With  the 
centre  g  and  radius  g  c 
(=  R)  draw  the  arc  c  I; 
with  the  centre  k  and 
radius  kl  (=  p)  draw  the 
arc  I  m,  and  with  the 
centre  e  and  radius  e  m 
(=  r)  draw  the  arc  m  a. 

The  remainder  of  the  work  is  symmetrical  with  respect  «,o  the 
axes. 

46.  The  Parabola.  —  A  parabola  (D  A  C,  Fig.  55)  is  a  curve  such 
that  every  point  in  the  curve  is  equally  distant  from  the  directrix  K  L 
and  the  focus  F.  The  focus  lies  in  the  axis 

A  B  drawn  from  the  vertex  or  head  of  the       K  P  \ 

curve  A,  so  as  to  divide  the  figure  into  two 
equal  parts.  The  vertex  A  is  equidistant 
from  the  directrix  and  the  focus,  or  A  e  =  A  F. 
Any  line  parallel  to  the  axis  is  a  diameter. 
A  straight  line,  as  E  G  or  DC,  drawn  across 
the  figure  at  right  angles  to  the  axis  is  a 
double  ordinate,  and  either  half  of  it  is  an 
ordinp.te.  The  ordinate  to  the  axis  E  F  G, 
drawn  through  the  focus,  is  called  the  para- 
meter of  the  axis.  A  segment  of  the  axis, 
reckoned  from  the  vertex,  is  an  abscissa  of 
the  axis,  and  it  is  an  abscissa  of  the  ordinate 
drawn  from  the  base  of  the  abscissa.  Thus, 
A  B  is  an  abscissa  of  the  ordinate  B  C. 


E 
«/ 

A 

L 

/^ 

\^\ 

F 

\ 

n/ 

O 

\ 

o 

\ 

\ 

T 

o 

D                  B 

b 

^-a      C 

FIG.  55. 


Abscissae  of  a  parabola  are  as  the  squares  of  their  ordinates. 


To  describe  a  parabola  when  an  abscissa  and  its  ordinate  are  given 

(Fig.  55).  —  Bisect  the  given  ordinate  B  C  at  a,  draw  A  a,  and  then  a  b 
perpendicular  to  it,  meeting  the  axis  at  6.  Set  off  A  e,  A  F,  each  equal  to 
B  b;  and  draw  K  e  L  perpendicular  to  the  axis.  Then  K  L  is  the  directrix 
and  F  is  the  focus.  Through  F  and  any  number  of  points,  o,  o,  etc.,  in  the 
axis,  draw  double  ordinates,  n  o  n,  etc.,  and  from  the  centre  F,  with  the 
radii  F  et  o  e,  etc.,  cut  the  respective  ordinates  at  E,  G,  n,  n,  etc..  The 
curve  may  be  traced  through  these  points  as  shown. 

2d  Method:  By  means  of  a  square  and  a  cord  (Fig.  56).  —  Place  a 


GEOMETRICAL   PROBLEMS. 


49 


FIG.  56. 


/ 

{ 

y 

7 

* 

9 

^ 

'j_ 

'i 

)  d  cbaBabad 

FIG.  57. 

straight-edge  to  the  directrix  E  N, 
and  apply  to  it  a  square  LEG. 
Fasten  to  the  end  G  one  end  of  a 
thread  or  cord  equal  in  length  to  the 
edge  E  (7,  and  attach  the  other  end 
to  the  focus  F;  slide  the  square  along 
the  straight-edge,  holding  the  cord 
taut  against  the  edge  of  the  square 
by  a  pencil  D,  by  which  the  curve  is 
described. 

3d  Method:  When  the  height  and 
the  base  are  given  (Fig.  57).  —  Let 
A  B  be  the  given  axis,  and  C  D  a 
double  ordinate  or  base;  to  describe 
a  parabola  of  which  the  vertex  is  at 
A.  Through  A  draw  E  F  parallel  to 
C  D,  and  through  C  and  D  draw  C  E 
and  D  F  parallel  to  the  axis.  Divide 
B  C  arid  B  D  into  any  number  of 
equal  parts,  say  five,  at  a,  6,  etc.,  and 
divide  C  E  and  D  F  into  the  same 
number  of  parts.  Through  the 
points  a,  b,  c,  d  in  the  base  CD  on 
each  side  of  the  axis  draw  perpen- 
diculars, and  through  a,  b,  c,  d  in  C  E 
and  D  F  draw  lines  to  the  vertex  A , 
cutting  the  perpendiculars  at  e,  /,  g,  h. 
These  are  points  in  the  parabola,  and 
the  curve  CAD  may  be  traced  as 
shown,  passing  through  them. 
47.  The  Hyperbola  (Fig.  58).  —  A  hyperbola  is  a.  plane  curve,  such 
that  the  difference  of  the  distances  from  any  point  of  it  to  two  fixed  points 

is  equal  to  a  given  distance.  The 
fixed  points  are  called  the  foci. 

To  construct  a  hyperbola.  — 
Let  F/  and  F  be  the  foci,  and  Fe  F 
the  distance  Between  them.  Take  a 
ruler  longer  than  the  distance  F1  F, 
and  fasten  one  of  its  extremities  vj 
the  focus  F' .  At  the  other  extrem 
ity,  H,  attach  a  thread  of  such  a 
length  that  the  length  of  the  ruler 
shall  exceed  the  length  of  the  thread 
by  a  given  distance  A  B.  Attach 
the  other  extremity  of  the  thread  at 
the  focus  F. 

Press  a  pencil,  P,  against  the  ruler, 
and  keep  the  thread  constantly  tense, 
while  the  ruler  is  turned  around  F'  as 
a  centre.  The  point  of  the  pencil 
will  describe  one  branch  of  the  curve. 
2d  Method:  By  points  (Fig.  59).  — 
From  the  focus  F'  lay  off  a  distance 
F'  N  equal  to  the  transverse  axis,  or 
distance  between  the  two  branches  of 
the  curve,  and  take  any  other  dis- 
tance, as  F'  II,  greater  than  F'  N. 

With  F'  as  a  centre  and  F'  H  as  a 
radius  describe  the  arc  of  a  circle. 

hen  with  F  as  a  centre  and  N  H  as  a  radius  describe  an  arc  intersecting 
he  arc  before  described  at  p  and  q.     These  will  be  points  of  the  hyper- 
oia,  for  F'  q  —  F  q  is  equal  to  the  transverse  axis  A  B. 
If,  with  F  as  a  centre  and  F'  H  as  a  radius,  an  arc  be  described,  and  a 
second  arc  be  described  with  F'  as  a  centre  and  N  H  as  a  radius,  two  points 
in  the  other  branch  of  the  curve  will  be  determined.     Hence,  by  changing 
the  centres,  each  pair  of  radii  will  determine  two  points  in  each  branch. 
The  Equilateral  Hyperbola.  —  The  transverse  axis  of  a  hyperbola  is 


FIG.  58. 


\P/ 


FIG.  59. 


50 


GEOMETRICAL   PROBLEMS. 


the  distance,  on  a  line  joining  the  foci,  between  the  two  branches  of  the 
curve.  The  conjugate  axis  is  a  line  perpendicular  to  the  transverse  axis, 
drawn  from  its  centre,  and  of  such  a  length  that  the  diagonal  of  the  rect- 
angle of  the  transverse  and  conjugate  axes  is  equal  to  the  distance  between 
the  foci.  The  diagonals  of  this  rectangle,  indefinitely  prolonged,  are  the 
asymptotes  of  the  hyperbola,  lines  which  the  curve  continually  approaches, 
but  touches  only  at  an  infinite  distance.  If  these  asymptotes  are  perpen- 
dicular to  each  other,  the  hyperbola  is  called  a  rectangular  or  equilateral 
hyperbola.  It  is  a  property  of  this  hyperbola  that  if  the  asymptotes  are 
taken  as  axes  of  a  rectangular  system  of  coordinates  (see  Analytical  Geom- 
etry), the  product  of  the  abscissa  and  ordinate  of  any  point  in  the  curve  is 
equal  to  the  product  of  the  abscissa  and  ordinate  of  any  other  point ;  or,  if 
p  is  the  ordinate  of  any  point  and  v  its  abscissa,  and  p\,  and  vi  are  the 
ordinate  and  abscissa  of  any  other  point,  pv  =  p\v\\  or  pv  =  a  constant. 

48.  The  Cycloid  (Fig. 

60).  —If  a  circle  A  a  be  6  f 

rolled  along  a  straight 
line  A  6,  any  point  of  the 
circumference  as  A  will 
describe  a  curve,  which  is 
called  a  cycloid.  The 
circle  is  called  the  gene- 
rating circle,  and  A  the 
generating  point. 

To  draw  a  cycloid.  — 
Divide  the  circumference 
of  the  generating  circle 

into  an  even  number  of  equal  parts,  as  A  1, 12,  etc.,  and  set  off  these  dis- 
tances on  the  base.  Through  the  points  1,  2,  3,  etc.,  on  the  circle 
draw  horizontal  lines,  and  on  them 
set  off  distances  la  =  A 1 ,  2b  =  A  2,  3c  = 
A3,  etc.  The  points  A ,  a,  ft,  c,  etc., 
will  be  points  in  the  cycloid,  through 
which  draw  the  curve. 

49.  The  Epicycloid  (Fig.  61)  is 
generated  by  a  point  D  in  one  circle 
D  C  rolling  upon  the  circumference  of 
another  circle  A  C  B,  instead  of  on  a 
flat  surface  or  line;  the  former  being 
the  generating  circle,  and  the  latter 
the  fundamental  circle.   The  generat- 
ing circle  is  shown  in  four  positions, 
in    which    the   generating    point   is 
successively  marked  D,  D',  D",  D'". 
A  D'"  B  is  the  epicycloid. 


FIG.  61. 


50.  The  Hypocycloid  (Fig.  62) 
is  generated  by  a  point  in  the  gener- 
ating circle  rolling  on  the  inside  of 
the  fundamental  circle. 

When    the    generating    circle  = 
Tadius  of  the  other  circle,  the  hypo- 
cycloid  becomes  a  straight  line. 


51.  The  Tractrix  or  Schiele's 
anti-friction  curve  (Fig.  63).  —  R 
is  the  radius  of  the  shaft,  C,  1,  2,  etc., 
ihe  axis.  From  O  set  off  on  R  a 
rmall  distance,  oa;  with  radius  A  and 
centre  a  cut  the  axis  at  1,  join  a  1, 
and  set  off  a  like  small  distance  a  b; 
from  b  with  radius  R  cut  axis  at  2, 
join  b  2,  and  so  on,  thus  finding 
points  o,  a,  b,  c,  d,  etc.,  through  which 
the  curve  is  to  be  drawn. 


GEOMETRICAL   PROBLEMS. 


51 


52.  The  Spiral.  —  The  spiral  is  a  curve  described  by  a  point  which 
moves  along  a  straight  line  according  to  any  given  law,  the  line  at  the  same 
time  having  a  uniform  angular  motion.  The  line  is  called  the  radius  vector. 

If  the  radius  vector  increases  directly 
as  the  measuring  angle,  the  spires, 
or  parts  described  in  each  revolution, 
thus  gradually  increasing  their  dis- 
tance from  each  other,  the  curve  is 
known  as  the  spiral  of  Archimedes 


FIG.  64. 


his  curve  is  commonly  used  for 
cams.  To  describe  it  draw  the 
radius  vector  in  several  different 
directions  around  the  centre,  with 
equal  angles  between  them;  set  off 


the  distances  1,  2,  3,  4,  etc.,  corresponding  to  the  scale  upon  which  the 

curve  is  drawn,  as  shown  in  Fig.  64. 

In  the  common  spiral  (Fig.  64)  the 
pitch  is  uniform;  that  is,  the  spires 
are  equidistant.  Such  a  spiral  is 
made  by  rolling  up  a  belt  of  uniform 
thickness. 

To  construct  a  spiral  with  four 
centres  (Fig.  65).— Given  the 
pitch  of  the  spiral,  construct  a  square 
about  the  centre,  with  the  sum  of 
the  four  sides  equal  to  the  pitch. 
Prolong  the  sides  in  one  direction  as 
shown;  the  corners  are  the  centres  for 
each  arc  of  the  external^  angles, 
forming  a  quadrant  of  a  spire. 


FIG.  65. 


53.  To  find  the  diameter  of  a  circle  into  which  a  certain  number  of 
rings  will  fit  on  its  inside  (Fig.  66).  —  For  instance,  what  is  the  diameter 
of  a  circle  into  which  twelve  i/2-inch  rings  will  fit,  as  per  sketch?  Assume 
that  we  have  found  the  diameter  of  the  required  circle,  and  have  drawn 

the  rings  inside  of  it.  Join  the 
centres  of  the  rings  by  straight  lines, 
as  shown:  we  then  obtain  a  regular 
polygon  with  12  sides,  each  side 
being  equal  to  the  diameter  of  a 

fiven  ring.  We  have  now  to  find 
he  diameter  of  a  circle  circum- 
scribed about  this  polygon,  and  add 
the  diameter  of  one  ring  to  it;  the 
sum  will  be  the  diameter  of  the  circle 
into  which  the  rings  will  fit. 
Through  the  centres  A  and  D  of  two 
adjacent  rings  draw  the  radii  C  A 

R\(  \^  }  __       _,'    /  }/  and  CD;  since  the  polygon  has  twelve 

X-NC^^JT   S  sides  the  angle  A  C  D  =  30°  and 

N^^===^K^  AC  B  =  15°.     One  half  of  the  side 

^^^S^^^  A  D  is  equal  to  A  B.     We  now  give 

§7  the  following  proportion:  The  sine 

FIG.  66.  of  the  angle  A  C  B  is  to  A  B  as  1  is  to 

the  required  radius.     From  this  we 


. 

_  t  the  following  rule:  Divide  A  B  by  the  sine  of  the  angle  A  C  B\  the 
quotient  will  be  the  radius  of  the  circumscribed  circle;  add  to  the  corre- 
sponding diameter  the  diameter  of  one  ring;  the  sum  will  be  the  required 
diameter  F  G. 

54.  To  describe  an  arc  of  a  circle  which  is  too  large  to  be  drawn 
by  a  beam  compass,  by  means  of  points  in  the  arc,  radius  being  given. 
— Suppose  the  radius  is  20  feet  and  it  is  desired  to  obtain  five  points  in  an 
arc  whose  half  chord  is  4  feet.  Draw  a  line  equal  to  the  half  chord,  full 


uAvuiais  ui>  yuiiua  i,  2,  o,  uuu  •*  icci  iiuui   me  mat  pcipciiuicuiai.      ciuu 

Talues  of  y  in  the  formula  of  the  circle,  x*  *  j/a  »  R\  by  substituting  for 


52 


GEOMETRICAL  PROBLEMS. 


x  the  values  0,  1,  2,  3,  and  4,  etc.,  and  for  R2  the  square  of  the  radius,  or 
400.     The  values  will  be  y  =  ^R2  ~  x2  =  V400,  ^399,  V396,  V391, 

V384;  =  20,         19.975,     19.90,       19.774,       19.596. 
Subtract  the  smallest, 

or   19.596,   leaving  0.404,   0.379,        0.304,       0.178,         0  feet. 

Lay  off  these  distances  on  the  five  perpendiculars,  as  ordinates  from  the 
half  chord,  and  the  positions  of  five  points  on  the  arc  will  be  found. 
Through  these  the  curve  may  be 
drawn.  (See  also  Problem  14.) 

55.  The  Catenary  is  the  curve 
assumed  by  a  perfectly  flexible  cord 
when  its  ends  are  fastened  at  two 
points,  the  weight  of  a  unit  length 
being  constant. 

The  equation  of  the  catenary  is 

/  x       _?\ 
y=^(ea-}-e   a),  in  which  e  is  the 

base  of  the  Napierian  system  of  log- 
arithms. 

To  plot  the  catenary.  —  Let  o 
(Fig.  67)  be  the  origin  of  coordinates. 
Assigning  to  a  any  value  as  3,  the 
equation  becomes 


( 


To   find  the  lowest  point  of   the 
curve. 

Puts  =  0;   /.  y  =  - 


Then  put        x  =  \\  .'.  f—gl 

Put  z  =  2;  .'.  1/=|( 


H^  (1.396  +0.717)  =3.17. 
)  =  ?  (1.948  +0.513)  =3.69. 


Put  x  =  3,  4,  5,  etc.,  etc.,  and  find  the  corresponding  values  of  y.     For 
each  value  of  y  we  obtain  two  symmetrical  points,  as  for  example  p  and,  pr. 
In  this  way,  by  making  a  successively  equal  to  2,  3,  4,  5,  6,  7,  and  8,  the 
curves  of  Fig.  67  were  plotted. 

In  each  case  the  distance  from  the  origin  to 
the  lowest  point  of  the  curve  is  equal  to  a;  for 
putting  x  =  o,  the  general  equation  reduces  to 

For  values  of  a  —  6,  7,  and  8  the  catenary 
closely  approaches  the  parabola.  For  deriva- 
tion of  the  equation  of  the  catenary  see  Bow- 
ser's Analytic  Mechanics. 

56.  The  Involute  is  a  name  given  to  the 
curve  which  is  formed  by  the  end  of  a  string 
which  is  unwound  from  a  cylinder  and  kept 
taut;  consequently  the  string  as  it  is  unwound 
will  always  lie  in  the  direction  of  a  tangent 
to  the  cylinder.  To  describe  the  involute  of 
any  given  circle,  Fig.  68,  take  any  point  A  on 
its  circumference,  draw  a  diameter  A  B,  and 
from  B  draw  B  b  perpendicular  to  A  B.  Make 
B  b  equal  in  length  to  half  the  circumference 
of  the  circle.  Divide  B  b  nnd  the  semi-circum- 
ference into  the  same  number  of  equal  parts, 
say  six.  From  each  point  of  division  1,  2, 
3,  etc.,  on  the  circumference  draw  lines  to  the  centre  C  of  the  circle. 
Then  draw  lai  perpendicular  to  (71;  2  a^  perpendicular  to  (72;  and 
80  on.  Make  \a\  equal  to  b  6t;  2  dz  equal  to  b  62;  3  «a  equal  to  b  b&;  and 
so  on.  Join  the  points  A,  alt  ctz,  03,  etc.,  by  a  curve;  this  curve  will  be 
t&e  required  involute. 


FIG.  68. 


GEOMETRICAL   PROPOSITIONS.  53 


57.   Method  of  plotting  angles  without  using  a  protractor.  —  The 

radius  of  a  circle  whose  circumference  is  360  is  57.3  (more  accurately 
57.296).  Striking  a  semicircle  with  a  radius  57.3  by  any  scale,  spacers 
set  to  10  by  the  same  scale  will  divide  the  arc  into  18  spaces  of  10°  each 
and  intermediates  can  bo  measured  indirectly  at  the  rate  of  1  by  scale  for 
each  1°,  or  interpolated  by  eye  according  to  the  degree  of  accuracy  required 
The  following  table  shows  the  chords  to  the  above-mentioned  radius,  for 
every  10  degrees  from  0°  up  to  110°.  By  means  of  one  of  these  a  10° 
point  is  fixed  upon  the  paper  next  less  than  the  required  angle,  and  the 
remainder  is  laid  oft  at  the  rate  of  1  by  scale  for  each  degree. 

Angle.                Chord.  Angle.  Chord.  Angle.  Chord. 

1° 0.999      40° 39.192        80° 73658 

10° 9.988      50° 48.429  90°..,  81029 

20° 19.899      60° 57.296      100° '.  87>82 

30° 29.658      70° 65.727      110° 93.869 


GEOMETRICAL  PROPOSITIONS. 

In  a  right-angled  triangle  the  square  on  the  hypothenuse  is  equal  to  the 
sum  of  the  squares  on  the  other  two  sides. 

If  a  triangle  is  equilateral,  it  is  equiangular,  and  vice  versa. 

If  a  straight  line  from  the  vertex  of  an  isosceles  triangle  bisects  the  base, 
It  bisects  the  vertical  angle  and  is  perpendicular  to  the  base. 

If  one  side  of  a  triangle  is  produced,  the  exterior  angle  is  equal  to  the 
sum  of  the  two  interior  and  opposite  angles. 

If  two  triangles  are  mutually  equiangular,  they  are  similar  and  their 
corresponding  sides  are  proportional. 

If  the  sides  of  a  polygon  are  produced  in  the  same  order,  the  sum  of  the 
exterior  angles  equals  four  right  angles.  (Not  true  if  the  polygon  has 
re-entering  angles.) 

In  a  quadrilateral,  the  sum  of  the  interior  angles  equals  four  right 
angles. 

In  a  parallelogram,  the  opposite  sides  are  equal;  the  opposite  angles  are 
equal;  it  is  bisected  by  its  diagonal,  and  its  diagonals  bisect  each  other. 

If  three  points  are  not  in  the  same  straight  line,  a  circle  may  be  passed 
through  them. 

If  two  arcs  are  intercepted  on  the  same  circle,  they  are  proportional  to 
the  corresponding  angles  at  the  centre. 

If  two  arcs  are  similar,  they  are  proportional  to  their  radii. 

The  areas  of  two  circles  are  proportional  to  the  squares  of  their  radii. 

If  a  radius  is  perpendicular  to  a  chord,  it  bisects  the  chord  and  it  bisects 
the  arc  subtended  by  the  chord. 

A  straight  line  tangent  to  a  circle  meets  it  in  only  one  point,  and  it  13 
perpendicular  to  the  radius  drawn  to  that  point. 

If  from  a  point  without  a  circle  tangents  are  drawn  to  touch  the  circle, 
there  are  but  two;  they  are  equal,  and  they  make  equal  angles  with  the 
chord  joining  the  tangent  points. 

If  two  lines  are  parallel  chords  or  a  tangent  ,and  parallel  chord,  they 
intercept  equal  arcs  of  a  circle. 

If  an  angle  at  the  circumference  of  a  circle,  between  two  chords,  is  sub- 
tended by  the  same  arc  as  an  angle  at  the  centre,  between  two  radii,  tho 
angle  at  the  circumference  is  equal  to  half  the  angle  at  the  centre. 

If  a  triangle  is  inscribed  in  a  semicircle,  it  is  right-angled. 

If  two  chords  intersect  each  other  in  a  circle,  the  rectangle  of  the  seg- 
ments of  the  one  equals  the  rectangle  of  the  segments  of  the  other. 

And  if  one  chord  is  a  diameter  and  the  other  perpendicular  to  it,  the 
rectangle  of  the  segments  of  the  diameter  is  equal  to  the  square  on 
half  the  other  chord,  and  the  half  chord  is  a  mean  proportional  between 
the  segments  of  the  diameter. 

If  an  angle  is  formed  by  a  tangent  and  chord,  it  is  measured  by  one  half 
of  the  arc  intercepted  by  the  chord;  that  is,  it  is  equal  to  half  the  angle  at 
the  centre  subtended  by  the  chord. 


54  MENSURATION  —  PLANE   SURFACES. 


a  Railway  Curve.  —  This  last  proposition  is  useful  in  staking 
out  railway  curves.  A  curve  is  designated  as  one  of  so  many  degrees,  and 
the  degree  is  the  angle  at  the  centre  subtended  by  a  chord  of  100  ft.  To 
lay  out  a  curve  of  n  degrees  the  transit  is  set  at  its  beginning  or  "  point  of 
curve,"  pointed  in  the  direction  of  the  tangent,  and  turned  through  i/2?i 
degrees;  a  point  100  ft.  distant  in  the  line  of  sight  will  be  a  point  in  the 
curve.  The  transit  is  then  swung  1/2  n  degrees  further  and  a  100  ft.  chord 
is  measured  from  the  point  already  found  t9  a  point  in  the  new  line  of 
sight,  which  is  a  second  point  or  "  station  "  in  the  curve. 

The  radius  of  a  1°  curve  is  5729.65  ft.,  and  the  radius  of  a  curve  of  any 
degree  is  5729.65  ft.  divided  by  the  number  of  degrees. 

Some  authors  use  the  angle  subtended  by  an  arc  (instead  of  chord)  of 
100  ft.  in  defining  the  degree  of  a  curve.  For  a  statement  of  the  relative 
advantages  of  the  two  definitions,  see  Eng.  News,  Feb.  16,  1911. 

MENSURATION. 

PLANE  SURFACES. 

Quadrilateral*  —  A  four-sided  figure. 

Parallelogram.  —  A  quadrilateral  with  opposite  sides  parallel. 

Varieties.  —  Square:  four  sides  equal,  all  angles  right  angles.  Rect- 
angle: opposite  sides  equal,  all  angles  right  angles.  Rhombus:  four  sides 
equal,  opposite  angles  equal,  angles  not  right  angles.  Rhomboid:  opposite 
sides  equal,  opposite  angles  equal,  angles  not  right  angles. 

Trapezium.  —  A  quadrilateral  with  unequal  sides. 

Trapezoid.  —  A  quadrilateral  with  only  one  pair  of  opposite  sides 
parallel.  _ 

Diagonal  of  a  square  =  ^2  X  side2  =  1.4142  X  side.  _ 

Diag.  of  a  rectangle  =  v  sum  of  squares  of  two  adjacent  sides. 

Area  of  any  parallelogram  =  base  X  altitude. 

Area  of  rhombus  or  rhomboid  =  product  of  two  adjacent  sides  X  sine 
of  angle  included  between  them. 

Area  of  a  trapezoid  =  product  of  half  the  sum  of  the  two  parallel  sidea 
by  the  perpendicular  distance  between  them. 

To  find  the  area  of  any  quadrilateral  figure.  —  Divide  the  quad- 
rilateral into  two  triangles;  the  sum  of  the  areas  of  the  triangles  is  the 
area. 

Or,  multiply  half  the  product  of  the  two  diagonals  by  the  sine  of  the 
angle  at  their  intersection. 

To  find  the  area  of  a  quadrilateral  which  may  be  inscribed  in  a 
circle.  —  From  half  the  sum  of  the  four  sides  subtract  each  side  severally; 
multiply  the  four  remainders  together;  the  square  root  of  the  product  is 
the  area. 

Triangle.  —  A  three-sided  plane  figure. 

Varieties.  —  Right-angled,  having  one  right  angle;  obtuse-angled,  hav- 
ing one  obtuse  angle;  isosceles,  having  two  equal  angles  and  two  equal 
sides;  equilateral,  having  three  equal  sides  and  equal  angles. 

The  sum  of  the  three  angles  of  every  triangle  =  180°. 

The  sum  of  the  two  acute  angles  of  a  right-angled  triangle  =  90°. 

Hypothenuse  of  a  right-angled  triangle,  the  side  opposite  the  right 
angle,  =  Vsum  of  the  squares  of  the  other  two  sides.  If  a  and  6  are  the 
two  sides  and  c  the  hypothenuse,  c2=a2  +  &2;  a  =  Vc2-&2=V(c+&)(/-&). 

If  the  two  sides  are  equal,  side  =  hyp  -9-  1.4142;  or  hyp  X.7071. 

To  find  the  area  of  a  triangle  : 

RULE  1.   Multiply  the  base  by  half  the  altitude. 

RULE  2.  Multiply  half  the  product  of  two  sides  by  the  sine  of  the 
included  angle. 

RULE  3.  From  half  the  sum  of  the  three  sides  subtract  each  side 
severally;  multiply  together  the  half  sum  and  the  three  remainders,  and 
extract  the  square  root  of  the  product. 

The  area  of  an  equilateral  triangle  is  equal  to  one  fourth  _the  square  of 

one  of  its  sides  multiplied  by  the  square  root  of  3,  =»  a  .     ,  a  being  tht 
tide;  or  a8  X  0,433013, 


MENSURATION. 


55 


Area  of  a  triangle  given,  to  find  base:  Base  =  twice  area  •*•  perpendicular 
height. 

Area  of  a  triangle  given,  to  find  height:  Height  =  twice  area  -s-  base. 

Two  sides  and  base  given,  to  find  perpendicular  height  (in  a  triangle  in 
which  both  of  the  angles  at  the  base  are  acute). 

RULE.  —  As  the  base  is  to  the  sum  of  the  sides,  so  is  the  difference  of  the 
sides  to  the  difference  of  the  divisions  of  the  base  made  bv  drawing  the 
perpendicular.  Half  this  difference  being  added  to  or  subtracted  from 
half  the  base  will  give  the  two  divisions  there9f.  As  each  side  and  its 
opposite  division  of  the  base  constitutes  a  right-angled  triangle.,  the 
perpendicular  is  ascertained  by  the  rule:  Perpendicular  =  Vhyp2  —  base2* 

Areas  of  similar  figures  are  to  each  other  as  the  squares  of  their 
respective  linear  dimensions.  If  the  area  of  an  equilateral  triangle  of 
side  =  1  is  0.433013  and  its  height  0.86603,  what  is  the  area  of  a  similai 
triangle  whose  height  =  1?  0.866032  :  I2  ::  0.433013  :  0.57735,  Ans. 

Polygon.  —  A  plane  figure  having  three  or  more  sides.  Regular  or 
irregular,  according  as  the  sides  or  angles  are  equal  or  unequal.  Polygons 
are  named  from  the  number  of  their  sides  and  angles. 

To  find  the  area  of  an  irregular  polygon.  —  Draw  diagonals  dividing 
the  polygon  into  triangles,  and  find  the  sum  of  the  areas  of  these  triangles. 

To  find  the  area  of  a  regular  polygon: 

RULE.  —  Multiply  the  length  of  a  side  by  the  perpendicular  distance  to 
the  centre;  multiply  the  product  by  the  number  of  sides,  and  divide  it  by 
2.  Or,  multiply  half  the  perimeter  by  the  perpendicular  let  fall  from  the 
centre  on  one  of  the  sides. 

The  perpendicular  from  the  centre  is  equal  to  half  of  one  of  the  sides  of 
the  polygon  multiplied  by  the  cotangent  of  the  angle  subtended  by  the 
half  side. 

The  angle  at  the  centre  =  360°  divided  by  the  number  of  sides. 


Table  of  Regular  Polygons^ 


«H 

Radius  of  Cir- 

II 

cumscribed 

12  • 

c3  o 

t 

d 

ft 

Circle. 

^Q1"1 

^  d 

2 

1 

1 

iH 

£ 

~ 

K3 
t 

1.1 

2  ® 

C-TJ 

si 

i;' 

1 

"d 

6 

S  $ 

m 

1- 

w 

*o 

02 

J 

i—  i  II 

i"1 

°« 

S^^j 

"S 

0)^9 

^  a 

o 

g 

OQ 

o£ 

II 

11 

"S'S  2 

o 

^  S 

& 

i 

1 

1 

•   £ 

1 

J'3 

1 

r 

3 

Triangle 

0.4330 

0.5773 

2.000 

0.5773 

0.2887 

1.732 

120° 

60° 

4 

Square 

1.0000 

1.0000 

.414 

0.7071 

0.5000 

1.4142 

90 

90 

5 

Pentagon 

1  .  7205 

0.7265 

.236 

0.8506 

0.6882 

1  .  1  756 

72 

108 

6 

Hexagon 

2.5981 

0.8660 

.155 

1  .  0000 

0.866 

1  .  0000 

60 

120 

7 

Heptagon 

3.6339 

0.7572 

.11 

1  .  1  524 

1  .  0383 

0.8677 

51  26' 

1284-7 

8 

Octagon 

4.8284 

0.8284 

.082 

1  .  3066 

.2071 

0.7653 

45 

135 

9 

Nonagon 

6.1818 

0.7688 

.064 

1  4619 

.3737 

0.684 

40 

140 

10 
11 

Decagon 
Undecagon 

7.6942 
9.3656 

0.8123 
0.7744 

.051 
.042 

1.618 
1  .  7747 

.5388 
.7028 

0.618 
0.5634 

36 
3243' 

144 
1473-11 

12 

Dodecagon 

11.1962 

0.8038 

.035 

1.9319 

.866 

0.5176 

30 

150 

*  Short  diameter,  even  number  of  sides,  =  diam.  of  inscribed  circle: 
short  diam.,  odd  number  of  sides,  =  rad.  of  inscribed  circle  +  rad.  ol 
circumscribed  circle. 


56 


AREA   OF   IRREGULAR  FIGURES. 


To  find  the  area  of  a  regular  polygon,  when  the  length  of  a  side 
only  is  given: 

RULE.— Multiply  the  square  of  the  side  by  the  figure  for  "area,  side  — 
1,"  opposite  to  the  name  of  the  polygon  in  the  table. 

Length  of  a  side  of  a  regular  polygon  inscribed  in  a  circle  =  diam. 
X  sin  (180°  •*-  no.  of  sides). 


No.  of  sides  sin  (180° /n)          No.  sin  (180° /n) 


0.86603 
.70711 
.58778 
.50000 
.43388 
.38268 


9  0.34202 

10  .30902 

11  .28173 

12  .25882 

13  .23931 

14  .22252 


No.  sin  (180°/n) 

15  0.20791 

16  .19509 

17  .18375 

18  .17365 

19  .16458 

20  .15643 


To  find  the  area  of  an  irregular 
i^gure  (Fig.  69).  —  Draw  ordinates 
f, cross  its  breadth  at  equal  distances 
apart,  the  first  and  the  last  ordinate 
each  being  one  half  space  from  the 
ends  of  the  figure.  Find  the  average 
breadth  by  adding  together  the 
lengths  of  these  lines  included  be- 
tween the  boundaries  of  the  figure, 
and  divide  by  the  number  of  the  lines 
added;  multiply  this  mean  breadth 
by  the  length.  The  greater  the  num- 
ber of  lines  the  nearer  the  approxi- 
mation. 


\l*  3  4  $ 


£ 


FIG.  69. 


In  a  figure  of  very  irregular  outline,  as  an  indicator-diagram  from  a 
high-speed  steam-engine,  mean  lines  may  be  substituted  for  the  actual 
lines  of  the  figure,  being  so  traced  as  to  intersect  the  undulations,  so  that 
the  total  area  of  the  spaces  cut  off  may  be  compensated  by  that  of  the 
extra  spaces  inclosed. 

2d  Method:  THE  TRAPEZOIDAL  RULE.  —  Divide  the  figure  into  any 
sufficient  number  of  equal  parts;  add  half  the  sum  of  the  two  end  ordinates 
to  the  sum  of  all  the  other  ordinates;  divide  by  the  number  of  spaces 
(that  is,  one  less  than  the  number  of  ordinates)  to  obtain  the  mean 
ordinate,  and  multiply  this  by  the  length  to  obtain  the  area. 

3d  Method:  SIMPSON'S  RULE.  —  Divide  the  length  of  the  figure  into  any 
even  number  of  equal  parts,  at  the  common  distance  D  apart,  and  draw 
ordinates  through  the  points  of  division  to  touch  the  boundary  lines 
Add  together  the  first  and  last  ordinates  and  call  the  sum  A ;  add  together 
the  even  ordinates  and  call  the  sum  J5;  add  together  the  odd  ordinates, 
except  the  first  and  last,  and  call  the  sum  C.  Then, 


area  of  the  figure  = 


A+4B+2C 


XD. 


4/fe  Method:  DURAND'S  RULE.  —  Add  together  */io  the  sum  of  the  first 
and  last  ordinates,  1  Vio  the  sum  of  the  second  and  the  next  to  the  last 
(or  the  penultimates),  and  the  sum  of  all  the  intermediate  ordinates. 
Multiply  the  sum  thus  gained  by  the  common  distance  between  the  ordi- 
nates to  obtain  the  area,  or  divide  this  sum  by  the  number  of  spaces  to 
f  btain  the  mean  ordinate. 

Prof.  Durand  describes  the  method  of  obtaining  his  rule  in  Engineering 
News,  Jan.  18,  1894.  He  claims  that  it  is  more  accurate  than  Simpson's 
rule,  and  practically  as  simple  as  the  trapezoidal  rule.  He  thus  describes 
its  application  for  approximate  integration  of  differential  equations.  Any 
definite  integral  may  be  represented  graphically  by  an  area.  Thus,  let 

Q  =  fu  dx 


be  an  integral  in  which  u  is  some  function  of  x,  either  known  or  admitting 
of  computation  or  measurement.  Any  curve  plotted  with  x  as  abscissa 
and  u  as  ordinate  will  then  represent  the  variation  of  u  with  x,  and  tht 


MENSURATION. 


57 


area  between  such  curve  and  the  axis  X  will  represent  the  integral  in 
question,  no  matter  how  simple  or  complex  may  be  the  real  nature  of  the 
function  u. 

Substituting  in  the  rule  as  above  given  the  word  "  volume"  for  "  area" 
and  the  W9rd  "section"  for  "  ordinate,"  it  becomes  applicable  to  the 
determination  of  volumes  from  equidistant  sections  as  well  as  of  areas 
from  equidistant  ordinates. 

Having  approximately  obtained  an  area  by  the  trapezoidal  rule,  the 
area  by  Durand's  rule  may  be  found  by  adding  algebraically  to  the  sum  of 
the  ordinates  used  in  the  trapezoidal  rule  (that  is,  half  the  sum  of  the  end 
ordinates  -f  sum  of  the  other  ordinates)  1/10  of  (sum  of  penultimates 
—  sum  of  first  and  last)  and  multiplying  by  the  common  distance  between 
the  ordinates. 

5ih  Method.  —  Draw  the  figure  on  cross-section  paper.  Count  the 
number  of  squares  that  are  entirely  included  within  the  boundary;  then 
estimate  the  fractional  parts  of.  squares  that  are  cut  by  the  boundary,  add 
together  these  fractions,  and  add  the  sum  to  the  number  of  whole  squares. 
The  result  is  the  area  in  units  of  the  dimensions  of  the  squares.  The  finer 
the  ruling  of  the  cross-section  paper  the  more  accurate  the  result. 

6th  Method.  —  Use  a  planimeter. 

7th  Method.  —  With  a  chemical  balance,  sensitive  to  one  milligram, 
draw  the  figure  on  paper  of  uniform  thickness  and  cut  it  out  carefully; 
weigh  the  piece  cut  out,  and  compare  its  weight  with  the  weight  per 
square  inch  of  the  paper  as  tested  by  weighing  a  piece  of  rectangular  shape. 


THE  CIRCLE. 


Circumference  =  diameter  X  3.  1416,  nearly;  more  accurately,  3.14159265359. 

99  "^^^ 

Approximations,         =  3.143;  =  3.1415929. 


The  ratio  of  circum.  to  diam.  is  represented  by  the  symbol 
Area  =  0.7854   X  square  of  the  diameter. 


(called  Pi). 


Multiples  of  »r. 

1*  =  3.14159265359 
In  =  6.28318530718 
37r  =  9.42477796077 
4*  =  12.56637061436 
5x  =  15.70796326795 
6^  =  18.84955592154 
In  =  21.99114857513 
8;:  =  25.13274122872 
9*  =  28.27433388231 


7T/4 


Multiples  of|- 

=  0.7853982 
X  2  =  1.5707963 
X  3  =  2.356194r 
X  4  =  3.1415927 
X  5  =  3.9269908 
X  6  =  4.7123890 
X  7  =  5.4977871 
X  8  =  6.2831853 
X  9  =  7.0685835 


Ratio  of  diam.  to  circumference  =  reciprocal  of  «  =  0.3183099. 

1/7^=0.101321 
VK=  1.772453 
V7/7  =0.564189 
vV/4  =0.886226 
LogTr    =0.497 14987 
Log  ir/4_=  1.895090 
Log  vV  =0.248575 
Log  vV/4=  1.947545 


iprocal  of  »/4  =  1.27324. 

10/7r=     3.18310 

Multiples  of  I/TT. 

12/x=     3.81972 

I/TT  =  0.31831 

x/2  =      1.570796 

2/7T  =  0.63662 

7T/3  =      1.047197 

3/?r  =  0.95493 

7T/6  =     0.523599 

4/7r=  1.27324 

7T/12  =     0.261799 

5/7T  =  1.59155 

ir/64  =      0.049087 

6/7r=  1.90986 

Tr/360  =      0.0087266 

7/7r=  2.22817 

360/7r=  114.5915 

8/7T  =  2.54648 

*•*  =      9.86960 

9/7T  =  2.86479 

1-^-4*-=  0.0795775 

Diam.  in  ins.  =  13.5405  Varea  in  sq.  ft. 

Area  in  sq.  ft.  =  (diam  in  inches)2  X  .0054542. 

D  =  diameter,     R  =  radius,     C  =  circumference, 


;  area. 


58 


THE   CIRCLE. 


.  =      ;  =  .0795802  ;=        - 


R  =  •- 


0.31831(7; 


0.159155C; 


;  =  2  4/-;  =  1. 

V    * 


12838 


~  ;  =  0.564189 


Areas  of  circles  are  to  each  other  as  the  squares  of  their  diameters. 
To  find  the  length  of  an  arc  of  a  circle: 

RULE  1.  As  360  is  to  the  number  of  degrees  in  the  arc,  so  is  the  circum- 
ference of  the  circle  to  the  length  of  the  arc. 

RULE  2.  Multiply  the  diameter  of  the  circle  by  the  number  of  degrees 
in  the  arc,  and  this  product  by  0.0087266. 


Relations  of  Arc,  Chord,  Chord  of  Half  the  Arc,  etc. 

Let  R  =  radius,  D  =  diameter,  L  =  length  of  arc, 
C  =  chord  of  the  arc,  c  =  chord  of  half  the  arc, 
V  =  rise,  or  height  of  the  arc, 

9/>  V  1  0  F 


Length  of  the  arc  =  L 


-  (very  nearly),  = 


+  2c'  nearly» 


4F2X 


15CS+33FS 
Chord  of  the  arc  C,  =  2  >/c2  -  F2;  = 


..  nearly. 


-  (D  -  2F)2;  =  8c  -  3L 
=  2  \/(D  -  F)  X  F. 
Chord  of  half  the  arc,  c  =  i/2  v/<72+  4F2;  =  VD  x  F;  =  (3L  -f  C)  •*•  8. 
Diameter  of  the  circle,  D  =       ;=   V4  C24-  F^; 


Rise  of  the  arc,  F  =  ^  ;  =  1/2  (D  -  ' 

(or  if  F  is  greater  than  radius     1/2  (I>  +  ' 


-  <72)  ; 


Half  the  chord  of  the  arc  is  a  mean  proportional  between  the  rise  and 
the  diameter  minus  the  rise:  1/2  C  =  V'F  X  (  £  -  F). 

Length  of  the  Chord  subtending  an  angle  at  the  centre  =  twice  the 
sine  of  half  the  angle.  (See  Table  of  Sines.) 

Ordinates  to  Circular  Arcs.  —  C  =  chord,  F  =  height  of  the  arc,  or 
middle  ordinate,  x  =  abscissa,  or  distance  measured  on  the  chord  from  its 
central  point,  y  =  ordinate,  or  distance  from  the  arc  to  the  chord  at  the 
point  x,  V  =  R  -  ^R2  -  1/4C'2;  y  =  ^R2  -  x2  -  (R  -  F). 


Length  of  a  Circular  Arc.  —  Huyghens's  Approximation. 

Length  of  the  arc,  L  =  (8c  —  C)  •*•  3.  Professor  Williamson  shows 
that  when  the  arc  subtends  an  angle  of  30°,  the  radius  being  100,000  feet 
(nearly  19  miles),  the  error  by  this  formula  is  about  two  inches,  or  1/600000 
part  of  the  radius.  When  the  length  of  the  arc  is  equal  to  the  radius,  i.e., 
when  it  subtends  an  angle  of  57°.  3,  the  error  is  less  than  1/7680  part  of  the 
radius.  Therefore,  if  the  radius  is  100,000  feet,  the  error  is  less  than 
100000/7680  =  13  feet.  The  error  increases  rapidly  with  the  increase  of 
the  angle  subtended.  For  an  arc  of  120°  the  error  is  1  part  in  400;  for  an 
arc  of  180°  the  error  is  1.18%, 


MENSURATION. 


59 


In  the  measurement  of  an  arc  which  is  described  with  a  short  radius  the 
error  is  so  small  that  it  may  be  neglected.  Describing  an  arc  with  a  radius 
of  12  inches  subtending  an  angle  of  30°,  the  error  is  1/50000  of  an  inch. 

To  measure  an  arc  when  it  subtends  a  large  angle,  bisect  it  and  measure 
each  half  as  before — in  this  case  making  B  =•  length  of  the  chord  of  half  the 
arc,  and  b = length  of  the  chord  of  one  fourth  the  arc;  then  L  =  (166  -  25)  -*-  3. 

Formulas  for  a  Circular  Curve. 

J.  C.  Locke,  Eng.  News,  March  16,  1908. 
c 


u 


;-  =  ^2R  (R-  V(R  +&)(#_  6) 
=  2\Sm  (2R  —  m),  =  2R  sin  1/27, 
=  2 17  cos  1/2  7. 

e  =  R  exsec  1/27,  =»  R  tan  l/27  tan  1/47, 
=  T  tan  1/4  7. 


7i)sin7l  =  a  cot  1/2  7. 


2a 


2m  ' 


-  c)  (2R  -  c)),  =  2R  sin  1/47. 
Y  =  R  vers  i/27, 


JK  sin  1/2  /  tan  1/4  /,  =  1/2  c  tan  1/4  /. 


-£if 


+6)  (fi  - 


(sin  1/2  7)2,  =  R  vers  7, 


R  sin  7  tan  1/27,  =  &  tan  1/27,  =••  T  sin  7. 
=  #tani/27.  r      L^ 


I  =  ±L  x  57.295780°. 

I  —  c 


=  IR  X  0.01745329, 


Area  of  Segment  =  —  --  • 


2  sin  7 


X  57.295780°. 


1Z& 
2  * 


Relation  of  the  Circle  to  its  Equal,  Inscribed,  and  Circum- 
scribed Squares. 


Diameter  of  circle  X 

Circumference  of  circle  X 
Circumference  of  circle  X 
Diameter  of  circle  X 

Circumference  of  circle  X 
Area  of  circle  X  0.90031  -f- 
Area  of  circle  X 
Area  of  circle  X 
Side  of  square  X 
X 

"       X 
X 

Perimeter  of  square  X 
Square  inches  X 


0.88623  ) 
0.28209  J 
1.1284 
0.7071    ) 
0.22508}     = 
liameter) 


diameter 
1.2732 
0.63662 
1.4142 
4.4428 
1.1284 
3.5449 
0.88623 
1.2.732 


side  of  equal  square, 
perimeter  of  equal  square. 

side  of  inscribed  square. 

=  area  of  circumscribed  square. 
=  area  of  inscribed  square. 
=  diam.  of  circumscribed  circle. 
=  circum. 

=»  diam.  of  equal  circle. 
«=  circum.        ^         ^ 

=  circular  inches. 


GO  MENSURATION. 

Sectors  and  Segments.  —  To  find  the  area  of  a  sector  of  a  circle. 

RULE  1.   Multiply  the  arc  of  the  sector  by  half  its  radius. 

RULE  2.  As  360  is  to  the  number  of  degrees  in  the  arc,  so  is  the  area  of 
the  circle  to  the  area  of  the  sector. 

RULE  3.  Multiply  the  number  of  degrees  in  the  arc  by  the  square  of  the 
radius  and  by  0.008727. 

To  find  the  area  of  a  segment  of  a  circle:  Find  the  area  of  the  sector 
which  has  the  same  arc,  and  also  the  area  of  the  triangle  formed  by  the 
chord  of  the  segment  and  the  radii  of  the  sector. 

Then  take  the  sum  of  these  areas,  if  the  segment  is  greater  than  a  semi- 
circle, but  take  their  difference  if  it  is  less.  (See  Table  of  Segments.) 

Another  Method:  Ar^a  of  segment  =  V2.R2  (arc  —  sin  A),  in  which  A  is 
the  central  angle,  R  the  radius,  and  arc  the  length  of  arc  to  radius  1  . 

To  find  the  area  of  a  segment  of  a  circle  when  its  chord  and  height  only 
are  given.  First  find  radius,  as  follows: 


radius  -  1  [sq^e  °f™^  ChOrd  +  height  ]  . 

2.  Find  the  angle  subtended  by  the  arc,  as  follows:    half  chord  •*• 
radius  =  sine  of  half  the  angle.     Take  the  corresponding  angle  from  a 
table  of  sines,  and  double  it  to  get  the  angle  of  the  arc. 

3.  Find  area  of  the  sector  of  which  the  segment  is  a  part: 

area  of  sector  =  area  of  circle  X  degrees  of  arc  -*•  360. 

4.  Subtract  area  of  triangle  under  the  segment: 

Area  of  triangle  =  half  chord  X  (radius  —  height  of  segment).     . 

The  remainder  is  the  area  of  the  segment. 

When  the  chord,  arc,  and  diameter  are  given,  to  find  the  area.  From 
the  length  of  the  arc  subtract  the  length  of  the  chord.  Multiply  the 
remainder  by  the  radius  or  one-half  diameter;  to  the  product  add  the 
chord  multiplied  by  the  height,  and  divide  the  sum  by  2. 

Given  diameter,  d,'and  height  of  segment,  h. 


When  h  is  from  0  to  1/4  c?,  area      =  feVl.766(/fe  -  fe2; 

1/2  d,  area  =  h\/Q.Ol7d2  +  \.ldh  -  h2 


(approx.).     Greatest  error  0.23%,  when  h  =  i/4rf. 

To  find  the  chord:  From  the  diameter  subtract  the  height;  multiply 
the  remainder  by  four  times  the  height  and  extract  the  square  root. 

When  the  chords  of  the  arc  and  of  half  the  arc  and  the  rise  are  given: 
To  the  chord  of  the  arc  add  four  thirds  of  the  chord  of  half  the  arc;  mul- 
tiply the  sum  by  the  rise  and  the  product  by  0.40426  (approximate). 

Circular  Ring.  —  To  find  the  area  of  a  ring  included  between  the  cir- 
cumferences of  two  concentric  circles:  Take  the  difference  between  the.  areas 
of  the  two  circles;  or,  subtract  the  square  of  the  less  radius  from  the  square 
of  the  greater,  and  multiply  their  difference  by  3.14159. 

The  area  of  the  greater  circle  is  equal  to  nR*; 
and  the  area  of  the  smaller,  ~r2. 

Their  difference,  or  the  area  of  the  ring,  is  n(R*  -  r2). 
The  Ellipse.  —  Area  of  an  ellipse  =  product  of  its  semi-axes  X3.14159 

=  product  of  its  axes  X  0.785398. 

The  Ellipse.  —  Circumference  (approximate)  =  3.1416   y  -  -  —  ,   D 

and  d  being  the  two  axes. 

Trautwine  gives  the  following  as  more  accurate:  When  the  longer  axis 
D  is  not  more  than  five  times  the  length  of  the  shorter  axis,  dt 


Circumference  -  3.1416 


MENSURATION.  61 

"When  D  is  more  than  5d,  the  divisor  8.8  is  to  be  replaced  by  the  fallowings 

ForD/d  =  6     789        10     12    14      16      18       20     30      40        50 
Divisor    =  9   9.2   9.3   9.35  9.4  9.5  9.6  9.68   9.75   9.8   9.92   9.98       10 


in  which  A  =          -  —  Ingenieurs  Taschenbuch,  1896.    (a  and  6,  semi-axes.) 


Carl  G.  Earth  (Machinery,  Sept.,  1900)  gives  as  a  very  close  approxi- 
mation to  this  formula 


Area  of  a  segment,  of  an  ellipse  the  base  of  which  is  parallel  to  one  of 
the  axes  of  the  ellipse.  Divide  the  height  of  the  segment  by  the  axis  of 
which  it  is  part,  and  find  the  area  of  a  circular  segment,  in  a  table  9f  circu- 
lar segments,  of  which  the  height  is  equal  to  the  quotient;  multiply  the 
area  thus  found  by  the  product  of  the  two  axes  of  the  ellipse. 

Cycloid.  —  A  curve  generated  by  the  rolling  of  a  circle  on  a  plane. 

Length  of  a  cycloidal  curve  =  4  X  diameter  of  the  generating  circle. 
Length  of  the  base  =  circumference  of  the  generating  circle. 
Area  of  a  cycloid  =  3  X  area  of  generating  circle. 

Helix  (Screw).  —  A  line  generated  by  the  progressive  rotation  cf  a 
point  around  an  axis  and  equidistant  from  its  center. 

Length  of  a  helix.  —  To  the  square  of  the  circumference  described  by  the 
generating  point  add  the  square  of  the  distance  advanced  in  one  revolution, 
and  take  the  square  root  of  their  sum  multiplied  by  the  number  of  revolu- 
tions of  the  generating  point.  Or, 


«  length,  n  being  number  of  revolutions. 

Spirals.  —  Lines  generated  by  the  progressive  rotation  of  a  point 
around  a  fixed  axis,  with  a  constantly  increasing  distance  from  the  axis. 

A  plane  spiral  is  made  when  the  point  rotates  in  one  plane. 

A  conical  spiral  is  made  when  the  point  rotates  around  an  axis  at  a 
progressing  distance  from  its  center,  and  advancing  in  the  direction  of  the 
axis,  as  around  a  cone. 

Length  of  a  plane  spiral  line.  —  When  the  distance  between  the  coils  is 
uniform. 

RULE.  —  Add  together  the  greater  and  less  diameters;  divide  their  sum 
by  2;  multiply  the  quotient  by  3.1416,  and  again  by  the  number  of  revo- 
lutions. Or,  take  the  mean  of  the  length  of  the  greater  and  less  circum- 
ferences and  multiply  it  by  the  number  of  revolutions.  Or, 

length  =  im(R  +r),  R  and  r  being  the  outer  and  inner  radii.    To  find  n, 

let  t  =  thickness  of  coil  or  band,  s  =  space  between  the  coils,  n  =    .  . — •• 

i  ~r  s 

Length  of  a  conical  spiral  line.  —  Add  together  the  greater  and  less 
diameters;  divide  their  sum  by  2  and  multiply  the  quotient  by  3.1416. 
To  the  square  of  the  product  of  this  circumference  and  the  number  of 
revolutions  of  the  spiral  add  the  square  of  the  height  of  its  axis  and  take 
the  square  root  of  the  sum. 


Or,  length 


SOLID  BODIES. 

Surfaces  and  Volumes  of  Similar  Solids.  —  The  surfaces  of  two 
similar  solids  are  to  each  other  as  the  squares  of  their  linear  dimensions; 
the  volumes  are  as  the  cubes  of  their  linear  dimensions.  If  L  =  the  side 


62  MENSURATION. 

of  a  cube  or  other  solid,  and  /  the  side  of  a  similar  body  of  different  size, 
S,  s,  the  surfaces  and  V,  v,  the  volumes  respectively,  S  :  s  ::  L2 :  /*; 
V  :  v  ::  L3  :  J«. 

The  Prism.  —  To  find  the  surface  of  a  right  prism:  Multiply  the  perim- 
eter of  the  base  by  the  altitude  for  the  convex  surface.  To  this  add  the 
areas  of  the  two  ends  when  the  entire  surface  is  required. 

Volume  of  a  prism  =  area  of  its  base  X  its  altitude. 

The  pyramid.  —  Convex  surface  of  a  regular  pyramid  =  perimeter  of 
its  base  X  half  the  slant  height.  To  this  add  area  of  the  base  if  the  whole 
surface  is  required. 

Volume  of  a  pyramid  =  area  of  base  X  one  third  of  the  altitude. 

To  find  the  surface  of  a  frustum  of  a  regular  pyramid:  Multiply  half  the 
slant  height  by  the  sum  of  the  perimeters  of  the'  two  bases  for  the  convex 
surface.  To  this  add  the  areas  of  the  two  bases  when  the  entire  surface  is 
required . 

To  find  the  volume  of  a  frustum  of  a  pyramid:  Add  together  the  areas  of 
the  two  bases  and  a  mean  proportional  between  them,"  and  multiply  the 
sum  by  one  third  of  the  altitude.  (Mean  proportional  between  two 
numbers  =  square  root  of  their  product.) 

Wedge.  —  A  wedge  is  a  solid  bounded  by  five  planes,  viz.:  a  rectangular 
base,  two  trapezoids,  or  two  rectangles,  meeting  in  an  edge,  and  two 
triangular  ends.  The  altitude  is  the  perpendicular  drawn  from  any  point 
in  the  edge  to  the  plane  of  the  base. 

To  find  the  volume  of  a  wedge:  Add  the  length  of  the  edge  to  twice  the 
length  of  the  base,  and  multiply  the  sum  by  one  sixth  of  the  product  of 
the  height  of  the  wedge  and  the  breadth  of  the  base. 

Rectangular  prismoid.  —  A  rectangular  prisrnoid  is  a  solid  bounded 
by  six  planes,  of  which  the  two  bases  are  rectangles,  having  their  corre- 
sponding sides  parallel,  and  the  four  upright  sides  of  the  solid  are  trape- 
zoids. 

To  find  the  volume  of  a  rectangular  prismoid:  Add  together  the  areas  of 
the  two  bases  and  four  times  the  area  of  a  parallel  section  equally  distant 
from  the  bases,  and  multiply  the  sum  by  one  sixth  of  the  altitude. 

Cylinder.  —  Convex  surface  of  a  cylinder  =  perimeter  of  base  X 
altitude.  To  this  add  the  areas  of  the  two  ends  when  the  entire  surface  is 
required. 

Volume  of  a  cylinder  —  area  of  base  X  altitude. 

Cone.  —  Convex  surface  of  a  cone  =  circumference  of  base  X  half  the 
slant  height.  To  this  add  the  area  of  the  base  when  the  entire  surface  is 
required. 

Volume  of  a  cone  =  area  of  base  X  one  third  of  the  altitude. 

To  find  the  surface  of  a  frustum  of  a  cone:  Multiply  half  the  side  by  the 
sum  of  the  circumferences  of  the  two  bases  for  the  convex  surface;  to  this 
add  the  areas  of  the  two  bases  when  the  entire  surface  is  required. 

To  find  the  volume  of  a  frustu?n  of  a  cone:  Add  together  the  areas  of 
the  two  bases  and  a  mean  proDortional  between  them,  and  multiply 
the  sum  by  one  third  of  the  altitude.  Or,  Vol.  =  0.261Sa(624-  c2  +  be); 
a  =  altitude;  b  and  c,  diams.  of  the  two  bases. 

Sphere.  —  To  find  the  surface  of  a  sphere:  Multiply  the  diameter  by  the 
circumference  of  a  great  circle;  or,  multiply  the  square  of  the  diameter  by 
3.14159. 

Surface  of  sphere  —  4  x  area   of  its  great  circle. 
*'  *'        **        =i  convex  surface  of  its  circumscribing  cylinder. 

Surfaces  of  spheres  are  to  each  other  as  the  squares  of  their  diameters. 
To  find  the  volume  of  a  sphere:  Multiply  the  surface  by  one  third  of  the 
radius;  or,  multiply  the  cube  of  the  diameter  by  ;r/6;  that  is,  by  0.5236, 
Value  of  7T/6  to' 10  decimal  places  =  0.5235987756. 
The  volume  of  a  sphere  =  2/3  the  volume  of  its  circumscribing  cylinder. 
Volumes  of  spheres  are  to  each  other  as  the  cubes  of  their  diameters. 


MENSURATION.  63 


Spherical  triangle.  —  To  find  the  area  of  a  spherical  triangle:  Compute 
the  surface  of  the  quadrantal  triangle,  or  one  eighth  of  the  surface  of 
the  sphere.  From  the  sum  of  the  three  angles  subtract  two  right  angles; 
divide  the  remainder  by  90,  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

Spherical  polygon.  —  To  find  the  area  of-a  spherical  polygon:  Compute 
the  surface  of  the  quadrantal  triangle.  From  the  sum  of  all  the  angles 
subtract  the  product  of  two  right  angles  by  the  number  of  sides  less  two; 
divide  the  remainder  by  90  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

The  prismoid.  —  The  prismoid  is  a  solid  having  parallel  end  areas,  and 
may  be  composed  of  any  combination  of  prisms,  cylinders,  wedges,  pyra- 
mids, or  cones  or  frustums  of  the  same,  whose  bases  and  apices  lie  in  the 
end  areas. 

Inasmuch  as  cylinders  and  cones  are  but  special  forms  of  prisms  and 
pyramids,  and  warped,  surface  solids  may  be  divided  into  elementary 
forms  of  them,  and  since  frustums  may  also  be  subdivided  into  the  elemen- 
tary forms,  it  is  sufficient  to  say  that  all  prismoids  may  be  decomposed 
into  prisms,  wedges,  and  pyramids.  If  a  formula  can  be  found  which  is 
equally  applicable  to  all  of  these  forms,  then  it  will  apply  to  any  combi- 
nation of  them.  {Such  a  formula  is  called 


The  Prismoictal  Formula. 

Let  A  =   area  of  the  base  of  a  prism,,  wedge,  or  pyramid: 
Ai,  Azt  Am  =  the  two  end  and  the  middle  areas  of  a  prismoid,  or  of  any  ol 
its  elementary  solids;  h  =  altitude  of  the  prismoid  or  elementary  solid? 
V  =  its  volume; 


For  a  prism,  Ai,  Am  and  A*  are  equal,  =  A;  V  =  ^  X  SA  =  hA. 

Fora  wedge  with  parallel  ends,  42  =  0,  Am=--  \  Xi;V=|(4i+2A:)=-  —  • 

For  a  cone  or  pyramid,  Az  =  0,  Am  =  -  AI;  V  =  -  (A\  +  A\)  =  -^-- 

The  prismoidal  formula  is  a  rigid  formula  for  all  prismoids.  The  only 
approximation  involved  in  its  use  is  in  the  assumption  that  the  given  solid 
may  be  generated  by  a  right  line  moving  over  the  boundaries  of  the  end 
areas. 

The  area  of  the  middle  section  is  never  the  mean  of  the  two  end  areas  if 
the  prismoid  contains  any  pyramids  or  cones  among  its  elementary  forms. 
When  the  three  sections  are  similar  in  form  the  dimensions  of  the  middle 
area  are  always  the  means  of  the  corresponding  end  dimensions.  This 
fact  often  enables  the  dimensions,  and  hence  the  area  of  the  middle  section, 
to  be  computed  from  the  end  areas. 

Polyedrons.  —  A  polyedron  is  a  solid  bounded  by  plane  polygons.  A 
regular  polyedron  is  one  whose  sides  are  all  equal  regular  polygons. 

To  find  the  surface  of  a  regular  polyedron.  —  Multiply  the  area  of  one  of 
the  faces  by  the  number  of  faces;  9r,  multiply  the  square  of  one  of  the 
edges  by  the  surface  of  a  similar  solid  whose  edge  is  unity. 


A  TABLE  OP  THE'  REGULAR  POLYEDRONS  WHOSE  EDGES  ARE  UNITY. 

Names.                                  No*,  of  Faces.          Surface.  Volume. 

Tetraedron 4  1.7320508  0.1178513 

Hexaedron 6  6.0000000  1.0000000 

Octaedron 8  3.4641016  0.4714045 

Dodecaedron 12  20.6457288  7.6631189 

Icosaedroa 20  8.6602540  2.1816950 


g4  MENSURATION. 

To  find  the  volume  of  a  regular  polyedron.  —  Multiply  the  surface 
by  one  third  of  the  perpendicular  let  fall  from  the  centre  on  one  of  the 
faces;  or,  multiply  the  cube  of  one  of  the  edges  by  the  solidity  of  a  similar 
polyedron  whose  edge  is  unity. 

Solid  of  revolution.  —  The  volume  of  any  solid  of  revolution  is  equal 
to  the  product  of  the  area  of  its  generating  surface  by  the  length  of  the 
path  of  the  centre  of  gravity  of  that  surface. 

The  convex  surface  of  any  solid  of  revolution  is  equal  to  the  product  of 
the  perimeter  of  its  generating  surface  by  the  length  of  path  of  its  centre 
of  gravity. 

Cylindrical  ring.  —  Let  d  =  outer  diameter;  d'  =  inner  diameter; 
1/2  (d  -  d')  =  thickness  =  t;  1/4* I2  =  sectional  area;  1/2 (d  +d')  =  mean 
diameter  =  M;  m  =  circumference  of  section;  IT  M  =  mean  circum- 
ference of  ring;  surface  =  n  t  X  n  M;  =  1/4  ^  (d2  -  d/2);  =  9.86965  t  M ; 
=  2.46741  (d2  -  d/2);  volume  =  1/4  *  tz  M  n\  =  2.467241  .2  M. 

Spherical  zone.  —  Surface  of  a  spherical  zone,  or  segment  of  a  sphere 
=  its  altitude  X  the  circumference  of  a  great  circle  of  the  sphere.  A 
great  circle  is  one  v/hose  plane  passes  through  the  centre  of  the  sphere. 

Volume  of  a  zone  of  a  sphere.  —  To  the  sum  of  the  squares  of  the  radii 
of  the  ends  add  one  third  of  the  square  of  the  height;  multiply  the  sum 
by  the  height  and  by  1.5708. 

Spherical  segment.  —  Volume  of  a  spherical  segment  with  one  base.  — 
Multiply  half  the  height  of  the  segment  by  the  area  of  the  base,  and  the 
cube  of  the  height  by  0.5236  and  add  the  two  products.  Or,  from  three 
times  the  diameter  of  the  sphere  subtract  twice  the  height  of  the  segment; 
multiply  the  difference  by  the  square  of  the  height  and  by  0.5236.  Or,  to 
three  times  the  square  of  the  radius  of  the  base  of  the  segment  add  the 
square  of  its  height,  and  multiply  the  sum  by  the  height  and  by  0.5236. 

Spheroid  or  ellipsoid.  —  When  the  revolution  of  the  generating  sur- 
face of  the  spheroid  is  about  the  transverse  diameter  the  spheroid  is 
prolate,  and  when  about  the  conjugate  it  is  oblate. 

Convex  surface  of  a  segment  of  a  spheroid.  —  Square  the  diameters  of  the 
spheroid,  and  take  the  square  root  of  half  their  sum;  then,  as  the  diameter 
from  which  the  segment  is  cut  is  to  this  root  so  is  the  height  of  the  segment 
to  the  proportionate  height  of  the  segment  to  the  mean  diameter.  Multiply 
the  product  of  the  other  diameter  and  3. 1416  by  the  proportionate  height. 

Convex  surface  of  a  frustum  or  zone  of  a  spheroid.  —  Proceed  as  by 
previous  rule  for  the  surface  of  a  segment,  and  obtain  the  proportionate 
height  of  the  frustum.  Multiply  the  product  of  the  diameter  parallel  to 
the  base  of  the  frustum  and  3.1416  by  the  proportionate  height  of  the 
frustum. 

Volume  of  a  spheroid  is  equal  to  the  product  of  the  square  of  the  revol  v- 
ing  axis  by  the  fixed  axis  and  by  0.5236.  The  volume  of  a  spheroid  is  two 
thirds  of  that  of  the  circumscribing  cylinder. 

Volume  of  a  segment  of  a  spheroid.  —  1.  When  the  base  is  parallel  to  the 
revolving  axis,  multiply  the  difference  between  three  times  the  fixed  axis 
and  twice  the  height  of  the  segment,  by  the  square  of  the  height  and  by 
0.5236.  Multiply  the  product  by  the  square  of  the  revolving  axis,  and 
divide  by  the  square  of  the  fixed  axis. 

2.  When  the  base  is  perpendicular  to  the  revolving  axis,  multiply  the 
difference  between  three  times  the  revolving  axis  and  twice  the  height  of 
the  segment  by  the  square  of  the  height  and  by  0.5236.  Multiply  the 
product  by  the  length  of  the  fixed  axis,  and  divide  by  the  length  of  the 
revolving  axis. 

Volume  of  the  middle  frustum  of  a  spheroid.  —  1.  When  the  ends  are 
circular,  or  parallel  to  the  revolving  axis:  To  twice  the  square  of  the  middle 
diameter  add  the  square  of  the  diameter  of  one  end;  multiply  the  sum  by 
the  length  of  the  frustum  and  by  0.2618. 

2.  When  the  ends  are  elliptical,  or  perpendicular  to  the  revolving  axis: 
To  twice  the  product  of  the  transverse  and  conjugate  diameters  of  the 
middle  section  add  the  product  of  the  transverse  and  conjugate  diameters 
of  one  end;  multiply  the  sum  by  the  length  of  the  frustum  and  by  0.2618. 

Spindles.  —  Figures  generated  by  the  revolution  of  a  plane  area, 
bounded  by  a  ctirve  other  than  a  circle,  when  th  j  curve  is  revolved  about 
a  chord  perpendicular  to  its  axis,  or  about  its  double  ordinate.  They  are 
designated  by  the  name  of  the  arc  or  curve  from  which  they  are  generated, 
as  Circular,  Elliptic,  Parabolic,  etc.,  etc. 


MENSURATION.  65 

Convex  surface  of  a  circular  spindle,  zone,  or  segment  of  it.  —  Rule:  Mul- 
tiply the  length  by  the  radius  of  the  revolving  arc;  multiply  this  arc  by  the 
central  distance,  or  distance  between  the  centre  of  the  spindle  and  centre 
of  the  revolving  arc;  subtract  this  product  from  the  former,  double  the 
remainder,  and  multiply  it  by  3.1416. 

Volume  of  a  circular  spindle.  —  Multiply  the  central  distance  by  half 
the  area  of  the  revolving  segment;  subtract  the  product  from  one  third  of 
the  cube  of  half  the  length,  and  multiply  the  remainder  by  12.5664. 

Volume  of  fruslum  or  zone  of  a  circular  spindle.  —  From  the  square  of 
half  the  length  of  the  whole  spindle  take  one  third  of  the  square  of  half  the 
length  of  the  frustum,  and  multiply  the  remainder  by  the  said  half  length 
of  the  frustum;  multiply  the  central  distance  by  the  revolving  area  which 
generates  the  frustum;  subtract  this  product  from  the  former,  and  multi- 
ply the  remainder  by  6.2832. 

Volume  of  a  segment  of  a  circular  spindle.  —  Subtract  the  length  of  the 
segment  from  the  half  length  of  the  spindle;  double  the  remainder  and 
ascertain  the  volume  of  a  middle  frustum  of  this  length;  subtract  the 
result  from  the  volume  of  the  whole  spindle  and  halve  the  remainder. 


this  product  by  8. 

Parabolic  conoid.  —  Volume  of  a  parabolic  conoid  (generated  by  the 
revolution  of  a  parabola  on  its  axis).  —  Multiply  the  area  of  the  base  by 
half  the  height. 

Or  multiply  the  square  of  the  diameter  of  the  base  by  the  height  and  by 

Volume  of  a  fruslum  of  a  parabolic  conoid.  —  Multiply  half  the  sum  of 
xne  areas  of  the  two  ends  by  the  height. 

Volume  of  a  -parabolic  spindle  (generated  by  the  revolution  of  a  parabola 
on  its  base).  —  Multiply  the  square  of  the  middle  diameter  by  the  length 
and  by  0.4189.  The  volume  of  a  parabolic  spindle  is  to  that  of  a  cylinder 
of  the  same  height  and  diameter  as  8  to  15. 

Volume  of  the  middle  frustum  of  a  parabolic  spindle.  —  Add  together 
8  times  the  square  of  the  maximum  diameter,  3  times  the  square  of  the 
end  diameter,  and  4  times  the  product  of  the  diameters.  Multiply  the 
sum  by  the  length  of  the  frustum  and  by  0.05236.  This  rule  is  applicable 
for  calculating  the  content  of  casks  of  parabolic  form. 

Casks.  —  To  find  the  volume  of  a  cask  of  any  form.  —  Add  together  39 
times  the  square  of  the  bung  diameter,  25  times  the  square  of  the  head 
diameter,  and  26  times  the  product  of  the  diameters.  Multiply  the  sum 
by  the  length,  and  divide  by  31,773  for  the  content  in  Imperial  gallons,  or 
by  26,470  for  U.  S.  gallons. 

This  rule  was  framed  by  Dr.  Hutton,  on  the  supposition  that  the  middle 
third  of  the  length  of  the  cask  was  a  frustum  of  a  parabolic  spindle,  and 
each  outer  third  was  a  frustum  of  a  cone. 

To  find  the  ullage  of  a  cask,  the  quantity  of  liquor  in  it  when  it  is  not  full. 
1.  For  a  lying  cask:  Divide  the  number  of  wet  or  dry  inches  by  the  bung 
diameter  in  inches.  If  the  quotient  is  less  than  0.5,  deduct  from  it  one 
fourth  part  of  what  it  wants  of  0.5.  If  it  exceeds  0.5,  add  to  it  one  fourth 
part  of  the  excess  above  0.5.  Multiply  the  remainder  or  the  sum  by  the 
whole  content  of  the  cask.  The  product  is  the  quantity  of  liquor  in  the 
cask,  in  gallons,  when  the  dividend  is  wet  inches;  or  the  empty  space,  if 
dry  inches. 

2.  For  a  standing  cask:  Divide  the  number  of  wet  or  dry  inches  by  the 
length  of  the  cask.  If  the  quotient  exceeds  0.5,  add  to  it  one  tenth  of  its 
excess  above  0.5;  if  less  than  0.5,  subtract  from  it  one  tenth  of  what  it 
wants  of  0.5.  Multiply  the  sum  or  the  remainder  by  the  whole  content  of 
the  cask.  The  product  is  the  quantity  of  liquor  in  the  cask,  when  the 
dividend  is  wet  inches;  or  the  empty  space,  if  dry  inches. 

Volume  of  cask  (approximate)  U.  S.  gallons  =  square  of  mean  diam. 
X  length  in  inches  X  0.0034.  Mean  diameter  =  half  the  sum  of  the 
bung  and  head  diameters. 

Volume  of  an  irregular  solid.  —  Suppose  it  divided  into  parts,  resem- 
bling prisms  or  other  bodies  measurable  by  preceding  rules.  Find  the  con- 
lent  of  each  part;  the  sum  of  the  contents  is  the  cubic  contents  of  the  solid. 


66  PLANE   TRIGONOMETRY. 


The  content  of  a  small  part  is  found  nearly  by  multiplying  half  the  sum 
of  the  areas  of  each  end  by  the  perpendicular  distance  between  them. 

The  contents  of  small  irregular  solids  may  sometimes  be  found  by  im- 
mersing them  under  water  in  a  prismatic  or  cylindrical  vessel,  and  observ- 
ing the  amount  by  which  the  level  of  the  water  descends  when  the  solid  is 
withdrawn.  The  sectional  area  of  the  vessel  being  multiplied  by  the 
descent  of  the  level  gives  the  cubic  contents. 

Or,  weigh  the  solid  in  air  and  in  water;  the  difference  is  the  weight  of 
water  it  displaces.  Divide  the  weight  in  pounds  by  62.4  to  obtain  volume 
in  cubic  feet,  or  multiply  it  by  27.7  to  obtain  the  volume  in  cubic  inches. 

When  the  solid  is  very  large  and  a  great  degree  of  accuracy  is  not 
requisite,  measure  its  length,  breadth,  and  depth  in  several  different 
places,  and  take  the  mean  of  the  measurement  for  each  dimension,  and 
multiply  the  three  means  together. 

When  the  surface  of  the  solid  is  very  extensive  it  is  better  to  divide  it 
into  triangles,  to  find  the  area  of  each  triangle,  and  to  multiply  it  by  the 
mean  depth  of  the  triangle  for  the  contents  of  each  triangular  portion;  the 
contents  of  the  triangular  sections  are  to  be  added  together. 

The  mean  depth  of  a  triangular  section  is  obtained  by  measuring  the 
depth  at  each  angle,  adding  together  the  three  measurements,  and  taking 
one  third  of  the  sum. 


PLANE  TRIGONOMETRY. 

Trigonometrical  Functions. 

Every  triangle  has  six  parts  —  three  angles  and  three  sides.  When  any 
three  of  these  parts  are  given,  provided  one  of  them  is  a  side,  the  other 
parts  may  be  determined.  By  the  solution  of  a  triangle  is  meant  the 
determination  of  the  unknown  parts  of  a  triangle  when  certain  parts  are 
given. 

The  complement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
angle  or  arc  from  90°. 

In  general,  if  we  represent  any  arc  by  A,  its  complement  is  90°  -  A. 
Hence  the  complement  of  an  arc  that  exceeds  90°  is  negative. 

The  supplement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
angle  or  arc  from  180°.  If  A  is  an  arc  its  supplement  is  180°  —  A.  The 
supplement  of  an  arc  that  exceeds  180°  is  negative. 

The  sum  of  the  three  angles  of  a  triangle  is  equal  to  ISO0.  Either  angle  is 
the  supplement  of  the  other  two.  In  a  right-angled  triangle,  the  right 
angle  being  equal  to  90°,  each  of  the  acute  angles  is  the  complement  of 
the  other. 

In  all  right-angled  triangles  having  the  same  acute  angle,  the  sides  have  to 
each  other  the  same  ratio.  These  ratios  have  received  special  names,  as 
follows: 

If  A  is  one  of  the  acute  angles,  a  the  opposite  side,  b  the  adjacent  side, 
and  c  the  hypothenuse. 

The  sine  of  the  angle  A  is  the  quotient  of  the  opposite  side  divided  by  the 

hypothenuse.     Sin  A  == -• 

The  tangent  of  the  angle  A  is  the  quotient  of  the  opposite  side  divided  by 
the  adjacent  side.  Tan  A  =  j-- 

The  secant  of  the  angle  A  is  the  quotient  of  the  hypothenuse  divided  by  the 
adjacent  side.  Sec  A  =  -r  • 

The  cosine  (cos),  cotangent  (cot),  and  cosecant  (coscc)  of  an  angle 
are  respectively  the  sine,  tangent,  and  secant  of  the  complement  of  that 
angle.  The  terms  sine,  cosine,  etc.,  are  called  trigonometrical  functions. 

In  a  circle  whose  radius  is  unity,  the  sine  of  an  arc,  or  of  the  angle  at  the 
centre  measured  by  that  arc,  is  the  perpendicular  let  fall  from  one  extremity  of 
the  arc  upon  the  diameter  passing  through  the  other  extremity. 

The  tangent  of  an  arc  is  the  line  which  touches  the  circle  at  one  extremity 


PLANE   TRIGONOMETRY. 


67 


of  the  arc,  and  is  limited  by  the  diameter  (produced)  passing  through  the  other 
extremity. 

The  secant  of  an  arc  is  that  part  of  the  produced  diameter  which  is  inter" 
cepted  between  the  centre  and  the  tangent. 

The  versed  sine  of  an  arc  is  that  part  of  the  diameter  intercepted  between 
the  extremity  of  the  arc  and  the  foot  of  the  sine. 

In  a  circle  whose  radius  is  not  unity,  the  trigonometric  functions  of  an 
arc  will  be  equal  to  the  lines  here  denned,  divided  by  the  radius  of  the 
circle. 

it  1C  A  (Fig.  71)  is  an  angle  in  the  first  quadrant,  and  CF  =  radius, 


The  sine  of  the  angle  = 


FG 
Rad 


Cos  = 


Tan 


I A 

''  Had  ' 

Cosec  = 


Secant 

CL 
Rad  ' 


CT 

Rad  ' 

Versin  = 


CG 

Rad 

Cot  = 

GA 

''  Rad  * 


= 

Rad* 
PL 
Rad* 


FIG. 


If  radius  is  1,  then  Rad  in  the  denominator  is 
omitted,  and  sine  =  F  G,  etc. 

The  sine  of  an  arc  =  half  the  chord  of  twice  the 
arc. 

The  sine  of  the  supplement  of  the  arc  is  the 
same  as  that  of  the  arc  itself.     Sine  of  arc  B  D  F 
=  F  G  =  sin  arc  F  A. 
The  tangent  of  the  supplement  is  equal  to  the  tangent  of  the  arc,  but 
with  a  contrary  sign.     Tan  BDF  =  —  BM. 

The  secant  of  the  supplement  is  equal  to  the  secant  of  the  arc,  but  with 
a  contrary  sign.  Sec  BDF  =  —  CM. 

Signs  of  the  functions  in  the  four  quadrants.  —  If  we  divide  a 
circle  into  four  quadrants  by  a  vertical  and  a  horizontal  diameter,  the 
upper  right-hand  quadrant  is  called  the  first,  the  upper  left  the  second, 
the  lower  left  the  third,  and  the  lower  right  the  fourth.  The  signs  of  the 
functions  in  the  four  quadrants  are  as  follows: 

First  quad.  Second  quad.  Third  quad.  Fourth  quad. 
Sine  and  cosecant,  +  +  —  — 

Cosine  and  secant,  -4-  —  —  + 

Tangent  and  cotangent,    4-  —  +  — 

The  values  of  the  functions  are  as  follows  for  the  angles  specified: 


Angle  

o 

30 

45 

60 

QO 

120 

135 

150 

180 

970 

S60 

Sine  

0 

1 
2 

1 

V2 

v/3 
2 

1 

T~ 

1 

1 
2 

0 

-1 

0 

X/o 

I 

1 

1 

1 

\/^~ 

Cosine  

1 

~2 

V~2 

2* 

U 

2" 

2~ 

-1 

0 

1 

Tangent  

0 

J_ 

1 

Vs 

00 

-V3~ 

-1 

1 

0 

GO 

0 

Cotangent  .... 

00 

vf 

1 

I 

0 

J_ 

-1 

-\/3~3 

oo 

0 

\/3 

x/3 

Secant  

1 

2 

X/2 

2 

oo 

-2 

_x/2~ 

2 

-1 

00 

1 

Cosecant  

oc 

2 

\/2 

2 

v/3 

1 

2 

v? 

2 

oo 

-1 

to 

Versed  sine  ... 

d 

2-\/3 

\/2  i 

1 
2 

1 

3 

2 

V/J-f-l 

2+Va 

2 

1 

0 

2 

V2 

V2 

2 

68  PLANE  TRIGONOMETRY. 


TRIGONOMETRICAL,  FORMULAE. 

The  following  relations  are  deduced  from  the  properties  of  similai 
triangles  (Radius  =  1): 

cos  A  :  sin  A  : :  1  :  tan  A,  whence  tan  A  — r ; 

cos  A 

sin  A  :  cos  A  : :  1  :  cot  A.        "  cotan  A  =  —. — 7  ; 

sin  A 

cos  Ail         nl  i  sec  A,        "        sec  A 


cos  A' 

sin  A  1 1          : :  1  :  cosec  A,    "    cosec  A  —  -: — 7- ; 

sin  A 

tan  A  1 1  .       1 1 1  i  cot  A         ••      tan  A  =      1 


cot  A 

The  sum  of  the  square  of  the  sine  of  an  arc  and  the  square  of  its  cosine 
equals  unity.     Sin2  A  4-  cos2  A  =  1. 

Also,  1  4-  tan2  A  =  sec2  A;     I  +  cot2  A  =  cosec2  A. 

Functions  of  the  sum  and  difference  of  two  angles : 

Let  the  two  angles  be  denoted  by  A  and  B,  their  sum  A  4-  B  =*  C,  and 
their  difference  A  -  B  by  D. 

sin   (A  +  B)  =  sin  A  cos  B  4-  cos  A  sin  B; (1) 

cos  (A  +  B)  =  cos  A  cos  B  —  sin  A  sin  B; (2) 

sin  (A  —.  B)  =  sin  A  cos  B  —  cos  A  sin  B; (3) 

cos  (A  —  B)  =  cos  A  cos  B  +  sin  A  sin  B (4) 

From  these  four  formulae  by  addition  and  subtraction  we  obtain 

sin  (A  +  B)  +  sin  (A  -  B)  =  2  sin  A  cos  B;  .    .    .    .  (5 

sin  (A  +  B)  —  sin  (A  —  B)  =±  2  cos  A  sin  B;  .    .    .    .  (6 

cos  (A  +  B)  +  cos  (A  —  B)  =  2  cos  A  cos  5;  .    .    .    .  (7 

cos  (A  —  B)  —  cos  (A  4-  B)  =  2  sin  A  sin  5 (8 

If  we  put  A  +  B  =  C,  and  A  —  B  =  Z>,  then  A  =  1/2  (C  4-  D)  and  5  = 
v   and  we  have 

sin  (7  +  sin  D  =  2  sin  1/2(C  4-  D)  cos  i/2«?  -  D);  .  (9) 

sin  C  -  sin  D  =  2  cos  1/2  (C  4-  D)  sin  1/2  (C7  -  Z>);  .  .  (10) 

cos  C  +  cos  Z>=  20031/2(0  4-  D)  cos  i/2 ((7  -  D);  .  .  (11) 

cos  D  -  cos  C  =  2  sin  1/2  (C  4-  Z>)  sin  V2  (C  -  Z>).  .  .  (12) 

Equation  (9)  may  be  enunciated  thus:  The  sum  of  the  sines  of  any  two 
angles  is  equal  to  twice  the  sine  of  half  the  sum  of  the  angles  multiplied  by 
the  cosine  9f  half  their  difference.  These  formulae  enable  us  to  transform 
a  sum  or  difference  into  a  product. 

The  sum  of  the  sines  of  two  angles  is  to  their  difference  as  the  tangent  of 
half  the  sum  of  those  angles  is  to  the  tangent  of  half  their  difference. 

sin  A  4-  sin  B  =  2  sin  V2(A  4-  B)  cos  V2(A  -B)        tan  V2  (A  4-  B} 
sin  A  -  sin  B       2  cos  i/2  (A  +  B)  sin  i/2  (A  -  B)  **"  tan  i/2  (A  -  B)' 

The  sum  of  the  cosines  of  two  angles  is  to  their  difference  as  the  cotan- 
gent.of  half  the  sum  of  those  angles  is  to  the  tangent  of  half  their  difference. 

cos  A  4-  cos  B  =  2  cos  l/2(A  4-  B}  cos  V2(A  -B)  =   cot  l/2(A4-£)[      (     . 
cos  B  -  cos  A       2  sin  1/2  (A  4-  B)  sin  1/2  (A  -  B)      tan  i/2  (A  -  B) ' 

The  sine  of  the  sum  of  two  angles  is  to  the  sine  of  their  difference  as  the 
sum  of  the  tangents  of  those  angles  is  to  the  difference  of  the  tangents. 


sin  (A  4-  B)  ^  tan  A  +  tan  B . 
sin  (A  -  £)       tan  A  -  tan  B ' 


(15) 


PLANE   TRK 
MnU+A)              !            jj. 

3ONOMET 

tan  (A-f 
tan  (A  — 
cot   (A  + 
cot  (A  — 

cos  2  A 
cot  2A 

cos  1/2  A 
cot  1/2  A 

BY.                              69 

£.      tan  A  -f  tan  3  . 

cos  A  cos  5 

sin  (A  —  5) 

P         tan  A  -  tan  B  . 

cosAcosl?"  ^                        •*' 
cos  (A  4-  B)                     itanJB- 

••       1  +  tan  A  tan  ,6  * 

cos  A  cos  5 
cos  (A  —  J5)      t 

cot  B  +  cot  A  ' 

cos  A  cos  5 
Functions  of  twice  an  angle: 

sin'  2  A  =  2  sin  A  cos  A; 
tin  01           2  tan  A 

cot  B  —  cot  A 

«=  cos2  A  —  sin2  A  ; 
cot2  A  -  1 

~  1  -  tan2  A  * 
Functions  of  half  an  angle: 

2  cot  A 

.  /  1  —  cos  A 

•    J  1  +  cos  A. 

cm  1/2  A-  -J.  y         2         ; 

!a*-L     V           2 
\/l  4-  cos  A 

tin  I/*  1         f    i/1    ~  C°S  A    - 

»    1  4-  cos  A    ' 

V  i  —  cos  A 

For  tables  of  Trigonometric  Functions,  see  Mathematical  Tables. 


Solution  of  Plane  Right-angled  Triangles. 


Let  A  and  B  be  the  two  acute  angles  and  C  the  right  angle,  and  a,  6,  and 
c  the  sides  opposite  these  angles,  respectively,  then  we  have 

d  " 

1.   sin  A  =  cos  B  =  ~  ;      3.   tan  A 


2.   cos  A  =  sin  £ 


4.   cot  A  =  tan  B 


1.  In  any  plane  right-angled  triangle  the  sine  of  either  of  the  acute 
angles  is  equal  to  the  quotient  of  the  opposite  leg  divided  by  the  hypothe- 
nuse. 

2.  The  cosine  of  either  of  the  acute  angles  is  equal  to  the  quotient  of 
the  adjacent  leg  divided  by  the  hypothenuse. 

3.  The  tangent  of  either  of  the  acute  angles  is  equal  to  the  quotient  of 
the  opposite  leg  divided  by  .the  adjacent  leg. 

4.  The  cotangent  of  either  of  the  acute  angles  is  equal  to  the  quotient 
of  the  adjacent  Teg  divided  by  the  opposite  leg. 

5.  The  square  of  the  hypothenuse  equals  the  sum  of  the  squares  of  the 
other  two  sides. 


Solution  of  Oblique-angled  Triangles. 

The  following  propositions  are  proved  in  works  on  plane  trigonometry. 
In  any  plane  triangle  — • 

Theorem  1.  The  sines  of  the  angles  are  proportional  to  the  opposite 
sides. 

Theorem  2.  The' sum  of  any  two  sides  is  to  their  difference  as  the  tan- 
gent of  half  the  sum  of  the  opposite  angles  is  to  the  tangent  of  half  their 
difference. 

Theorem  3.  If  from  any  angle  of  a  triangle  a  perpendicular  be  drawn  to 
the  opposite  side  or  base,  the  whole  base  will  be  to  the  sum  of  the  other 
two  sides  as  the  difference  of  those  two  sides  is  to  the  difference  of  the 
segments  of  the  base. 

CASE  I.  Given  two  angles  and  a  side,  to  find  the  third  angle  and  the 
other  two  sides.  1.  The  third  angle  —  180°  —  sum  of  the  two  angles. 
2.  The  sides  may  be  found  by  tlie  following  proportion; 


70  ANALYTICAL  GEOMETRY. 

The  sine  of  the  angle  opposite  the  given  side  is  to  the  sine  of  the  angle 
opposite  the  required  side  as  the  given  side  is  to  the  required  side. 

CASE  II.  Given  two  sides  and  an  angle  opposite  one  of  them,  to  find 
the  third  side  and  the  remaining  angles. 

The  side  opposite  the  given  angle  is  to  the  side  opposite  the  required 
angle  as  the  sine  of  the  given  angle  is  to  the  sine  of  the  required  angle. 

The  third  angle  is  found  by  subtracting  the  sum  of  the  other  two  from 
180°,  and  the  third  side  is  found  as  in  Case  I. 

CASE  III.  Given  two  sides  and  the  included  angle,  to  find  the  third 
side  and  the  remaining  angles. 

The  sum  of  the  required  angles  is  found  by  subtracting  the  given  angle 
from  180°.  The  difference  of  the  required  angles  is  then  found  by  Theorem 
II.  Half  the  difference  added  to  half  the  sum  gives  the  greater  angle,  and 
half  the  difference  subtracted  from  half  the  sum  gives  the  less  angle.  The 
third  side  is  then  found  by  Theorem  I. 

Another  method: 

Given  the  sides  c,  6,  and  the  included  angle  A,  to  find  the  remaining  side 
a  and  the  remaining  angles  B  and  C. 

From  either  of  the  unknown  angles,  as  B,  draw  a  perpendicular  Be  to 
the  opposite  side. 

Then 

Ae  =  c  cos  A,     Be  =  c  sin  A,    eC  =  b  —  Ac     Be  •*•  eC  =  tan  C. 

Or,  in  other  words,  solve  Be,  Ae  and  BeC  as  right-angled  triangles. 

CASE  IV.    Given  the  three  sides,  to  find  the  angles. 

Let  fall  a  perpendicular  upon  the  longest  side  from  the  opposite  angle, 
dividing  the  given  triangle  into  two  right-angled  triangles.  The  two  seg- 
ments of  the  base  may  be  found  by  Theorem  III.  There  will  then  be 
given  the  hypothenuse  and  one  side  of  a  right-angled  triangle  to  find  the 
angles. 

For  areas  of  triangles,  see  Mensuration. 


ANALYTICAL  GEOMETRY. 

Analytical  geometry  is  that  branch  of  Mathematics  which  has  for  its 
object  the  determination  of  the  forms  and  magnitudes  of  geometrical 
magnitudes  by  means  of  analysis. 

Ordinates  and  abscissas.  —  In  analytical  geometry  two  intersecting 
lines  YY',  XX'  are  used  as  coordinate  axes, 
XX'  being  the  axis  of  abscissas  or  axis  of  X, 
and  YY'  the  axis  of  ordinates  or  axis  of  Y. 

A,  the  intersection,  is  called  the  origin  of  co-  /:; 7 

ordinates.     The  distance  of   any   point   P  /u         / 

from  the  axis  of  Y  measured  parallel  to  the  / 

axis  of  X  is  called  the  abscissa  of  the  point, 
as  AD  or  CP,  Fig.  72.     Its  distance  from  the 


f 

V' 


axis  of  X,  measured  parallel  to  the  axis  of 

Y,  is  called  the  ordinate,   as  AC  or  PD. 

The  abscissa  and  ordinate  taken  together 

are  called  the  coordinates  of  the  point  P. 

The  angle  of  intersection  is  usually  taken  as  Y 

a  right  angle,  in  which  case  the  axes  of  X  pIG    72 

and  Y  are  called  rectangular  coordinates. 

The  abscissa  of  a  point  is  designated  by  the  letter  x  and  the  ordinate 
oy  y. 

The  equations  of  a  point  are  the  equations  which  express  the  distances 
of  the  point  from  the  axis.  Thus  x  =  a,  y  =  b  are  the  equations  of  the 
point  P. 

Equations  referred  to  rectangular  coordinates.  —  The  equation  of 
a  line  expresses  the  relation  which  exists  between  the  coordinates  of  every 
point  of  the  line. 

Equation  of  a  straight  line,  y  =  ax  ±  b,  in  which  a  is  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  -Y,  and  b  the  distance  above  A  in 
which  the  line  cuts  the  axis  of  Y. 

Every  equation  of  the  first  degree  between  two  variables  is  the  equation 


ANALYTICAL    GEOMETRY.  71 

of  a  straight  line,  as  Ay  4-  Bx  f  C  »  0,  which  can  be  reduced  to  the  form 
y  =  o#  ±  6. 

Equation  of  the  distance  between  two  points: 

D  =  vV'  -  z')2  +  (y"  -  I/O2, 

in  which  x'y',  x"y"  are  the  coordinates  of  the  two  points. 
Equation  of  a  line  passing  through  a  given  point: 

y  -  y'  =  a(x  -  x'), 

in  which  x'y'  are  the  coordinates  of  the  given  point,  a,  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  x,  being  undetermined,  since  any 
number  of  lines  may  be  drawn  through  a  given  point. 
Equation  of  a  line  passing  through  two  given  points: 


Equation  of  a  line  parallel  to  a  given  line  and  through  a  given  point: 

y  —  y'  =  a(x  —  x'}. 
Equation  of  an  angle  V  included  between  two  given  lines: 

a'  —  a 


in  which  a  and  a'  are  the  tangents  of  the  angles  the  lines  make  with  the 
axis  of  abscissas. 

If  the  lines  are  at  right  angles  to  each  other  tang  V  =  oo,  and 

1  +  a'a  =  0. 

Equations  of  an  intersection  of  two  lines,    whose  equations  are 
y  =  ax   f  b,         and    y  =  a'x  +•  &', 
b  -  b'  ab'  -  a'b 

x  -  ~  ^r-rf*   and   y  =  T^5T 

Equation  of  a  perpendicular  from  a  given  point  to  a  given  line: 

y  -  y'  =  -  -  (x*  -  x'). 
Equation  of  the  length  of  the  perpendicular  Pi 


The  circle.  —  Equation  of  a  circle,  the  origin  of  coordinates  being  at 
the  centre,  and  radius  -=  A': 

x2  -f  2/2  =  R*. 
II  the  origin  is  at  the  left  extremity  of  the  diameter,  on  the  axis  of  X: 

y2  =  2Rx  -  x2. 

If  the  origin  is  at  any  point,  and  the  coordinates  of  the  centre  are  x'y' 
(x  -  z')2  +  (y  -  2/')2  =  #2. 

Equation  of  a  tangent  to  a  circle,  the  coordinates  of  the  point  of  tan- 
gency  being  x"y"  and  the  origin  at  the  centre, 

yy"  +  xx"  =  R2. 

The  ellipse.  —  Equation  of  an  ellipse,  referred  to  rectangular  coordi- 
nates with  axis  at  the  centre: 

AW  +  £2x2  =  A*B\ 
in  which  4  is  half  tUe  transverse  axis  and  £  qajf  the  conjugate  **fs. 


72  ANALYTICAL    GEOMETRY. 

Equation  of  the  ellipse  wiien  the  origin  is  at  the  vertex  of  the  transverse 
axis; 

B2 
y*  =  ~j(2Ax  -  *'). 

The  eccentricity  of  an  ellipse  is  the  distance  from  the  centre  to  either 
focus,  divided  by  the  semi-transverse  axis,  or 


The  parameter  of  an  ellipse  is  the  double  ordinate  passing  through  the 
focus.  It  is  a  third  proportional  to  the  transverse  axis  and  its  conjugate, 
or 

2»2 

2  A  :  2B  ::  2B  :  parameter;  or  parameter  =  -^— 

Any  ordinate  of  a  circle  circumscribing  an  ellipse  is  to  the  corresponding 
ordinate  of  the  ellipse  as  the  semi  -trans  verse  axis  to  the  semi-conjugate. 
Any  ordinate  of  a  circle  inscribed  in  an  ellipse  is  to  the  corresponding 
ordinate  of  the  ellipse  as  the  semi  -conjugate  axis  to  the  semi-transverse. 

Equation  of  the  tangent  to  an  ellipse,  origin  of  axes  at  the  centre: 

A*yy"  +  Bzxx"  =  A*B*. 

y"x"  being  the  coordinates  of  the  point  of  tangency. 

Equation  of  the  normal,  passing  through  the  point  of  tangency,  and 
perpendicular  to  the  tangent: 

»-v-s5?<*-*">- 

The  normal  bisects  the  angle  of  the  two  lines  drawn  from  the  point  of 
tangency  to  the  foci. 

The  lines  drawn  from  the  foci  make  equal  angles  with  the  tangent. 

The  parabola.  —  Equation  of  the  parabola  referred  to  rectangular 
coordinates,  the  origin  being  at  the  vertex  of  its  axis,  y2  =  2px,  in  which 
2p  is  the  parameter  or  double  ordinate  through  the  focus. 

The  parameter  is  a  third  proportional  to  any  abscissa  and  its  correspond- 
ing ordinate,  or 

x  :  y  ::  y  :  2p. 

Equation  of  the  tangent: 

yy"  =  p(x 


y"x"  being  coordinates  of  the  point  of  tangency. 
Equation  of  the  normal: 

y  -  y"  -  -  ~(x  -  x"). 

The  sub-normal,  or  projection  of  the  normal  on  the  axis,  is  constant,  and 
equal  to  half  the  parameter. 

The  tangent  at  any  point  makes  equal  angles  with  the  axis  and  with  the 
line  drawn  from  the  pDint  of  tangency  to  the  focus. 

The  hyperbola.  —  Equation  of  the  hyperbola  referred  to  rectangular 
coordinates,  origin  at  the  centre: 


in  which  A  is  the  semi-transverse  axis  and  B  the  semi-conjugate  axis. 
Equation  when  the  origin  is  at  the  right  vertex  of  the  transverse  axis: 


Conjugate  and  equilateral  hyperbolas.  —  If  on  the  conjugate  axis 


DIFFERENTIAL   CALCULUS.  73 

as  a  transverse,  and  a  focal  distance  equal  to  ^A2  + Bz,  we  construct 
the  two  branches  of  a  hyperbola,  the  two  hyperbolas  thus  constructed  are 
called  conjugate  hyperbolas.  If  the  transverse  and  conjugate  axes  are 
equal,  the  hyperbolas  are  called  equilateral,  in  which  case  y*-x2=  -A* 
when  A  is  the  transverse  axis,  and  x2  -  ?/2  =  —  B2  when  B  is  the  trans- 

The  parameter  of  the  transverse  axis  is  a  third  proportional  to  the  trans- 
rerse  axis  and  its  conjugate. 

2 A  :  2B  ::  2J5  :  parameter. 

The  tangent  to  a  hyperbola  bisects  the  angle  of  the  two  lines  drawn  from 
the  point  of  tangency  to  the  foci. 

The  asymptotes  of  a  hyperbola  are  the  diagonals  of  the  rectangle 
described  on  the  axes,  indefinitely  produced  in  both  directions. 

The  asymptotes  continually  approach  the  hyperbola,  and  become 
tangent  to  it  "at  an  infinite  distance  from  the  centre. 

Equilateral  hyperbola.  —  In  an  equilateral  hyperbola  the  asymptotes 
make  equal  angles  with  the  transverse  axis,  and  are  at  right  angles  to  each 
other.  With  the  asymptotes  as  axes,  and  P  =  ordinate,  V  —  abscissa, 
py  =  a  constant.  This  equation  is  that  of  the  expansion  of  a  perfect 
gas,  in  which  P  =  absolute  pressure,  V  =  volume. 

Curveof  Expansion  of  Gases.  —  PV™  =  a  constant,  or  Pi  Vin=PzVzn, 
in  which  Fi  and  ¥2  are  the  volumes  at  the  pressures  Pi  and  Pz.  When 
these  are  given,  the  exponent  n  may  be  found  from  the  formula 


. 

1 


log  Pi  -  log  Pz 

log  Vz  —  log  Vi 


Conic  sections,  —  Every  equation  of  the  second  degree  between  two 
variables  will  represent  either  a  circle,  an  ellipse,  a  parabola  or  a  hyperbola. 
These  curves  are  those  which  are  obtained  by  intersecting  the  surface  of  a 
cone  by  planes,  and  for  this  reason  they  are  called  conic  sections. 

Logarithmic  curve,  —  A  logarithmic  curve  is  one  in  which  one  of  the 
coordinates  of  any  point  is  the  logarithm  of  the  other. 

The  coordinate  axis  to  which  the  lines  denoting  the  logarithms  are 
parallel  is  called  the  axis  of  logarithms,  and  the  other  the  axis  of  numbers. 
If  y  is  the  axis  of  logarithms  and  x  the  axis  of  numbers,  the  equation  of  the 
curve  is  y  =  log  x. 

If  the  base  of  a  system  of  logarithms  is  a,  we  have  ay  =  x,  in  which  y  is 
the  logarithm  of  x. 

Each  system  of  logarithms  will  give  a  different  logarithmic  curve.  If 
y  ^  o,  x  =  1.  Hence  every  logarithmic  curve  will  intersect  the  axis  of 
numbers  at  a  distance  from  the  origin  equal  to  1. 


DIFFERENTIAL  CALCULUS. 

The  differential  of  a  variable  quantity  is  the  difference  between  any  two 
of  its  consecutive  values;  hence  it  is  indefinitely  small.  It  is  expressed  by 
writing  d  before  the  quantity,  as  dx,  which  is  read  differential  of  x. 

The  term  ^  is  called  the  differential  coefficient  of  y  regarded  as  a  func- 
tion of  x.  It  is  also  called  the  first  derived  function  or  the  derivative. 

The  differential  of  a  function  is  equal  .to  its  differential  coefficient  mul- 
tiplied by  the  differential  of  the  independent  variable;  thus,  -^dx  =  dy. 

The  limit  of  a  variable  quantity  is  that  value  to  which  it  continually 
approaches,  so  as  at  last  to  differ  from  it  by  less  than  any  assignable 
quantity^ 

The  differential  coefficient  is  the  limit  of  the  ratio  of  the  increment  of 
the  independent  variable  to  the  increment  of  the  function. 

The  differential  of  a  constant  quantity  is  equal  to  0. 

The  differential  of  a  product  of  a  constant  by  a  variable  is  equal  to  the 
constant  multiplied  by  the  differential  of  the  variable. 

If  u  =  Av,     du  =  A  dv* 


74  DIFFERENTIAL  CALCULUS. 

In  any  curve  whose  equation  is  y  =  /(#),  the  differential  coefficient 
•5T-  =  tan  a;  hence,  the  rate  of  increase  of  the  function,  or  the  ascension  of 

the  curve  at  any  point,  is  equal  to  the  tangent  of  the  angle  which  the 
tangent  line  makes  with  the  axis  of  abscissas. 

All  the  operations  of  the  Differential  Calculus  comprise  but  two  objects: 

1.  To  find  the  rate  of  change  in  a  function  when  it  passes  from  one  state 
of  value  to  another,  consecutive  with  it. 

2.  To  find  the  actual  change  in  the  function:  The  rate  of  change  is  the 
differential  coefficient,  and  the  actual  change  the  differential. 

Differentials  of  algebraic  functions.  —  The  differential  of  the  sum 
or  difference  of  any  number  of  functions,  dependent  on  the  same  variable, 
is  equal  to  the  sum  or  difference  of  their  differentials  taken  separately: 

If    u  =  y  4-  z  —  w,    du  —  dy  +  dz  —  dw. 

The  differential  of  a  product  of  two  functions  dependent  on  the  same 
variable  is  equal  to  the  sum  of  the  products  of  each  by  the  differential  of 
the  other: 

_      74.     fj       d(uv)   _  du_       dv 
uv  u         v 

The  differential  of  the  product  of  any  number  ol  functions  is  equal  to 
the  sum  of  the  products  which  arise  by  multiplying  the  differential  of  each 
function  by  the  product  of  all  the  others: 

d(uts)  —  tsdu  +  usdt  +  utds. 

The  differential  of  a  fraction  equals  the  denominator  into  the  diffeiential 
of  the  numerator  minus  the  numerator  into  the  differential  of  the  denom- 
inator, divided  by  the  square  of  the  denominator: 

_      (tL\  —  v^u~  u  dv 

If  the  denominator  is  constant,  dv  =  0,  and  dt  —  — 5-  =  —  • 

v  v 

If  the  numerator  is  constant,  du  =  0,  and  dt  = -$• 

The  differential  of  the  square  root  of  a  quantity  is  equal  to  the  differen- 
tial of  the  quantity  divided  by  twice  the  square  root  of  the  quantity: 


If     v  =  it1/2'     or     v  - 


2V  u 


2 


The  differential  of  any  power  of  a  function  is  equal  to  the  exponent  multi- 
plied by  the  function  raised  to  a  powerless  one,  multiplied  by  the  differen- 
tial of  the  function,  d(un)  =  nun~ldu. 

Formulas  for  differentiating  algebraic  functions. 

1.  d  (a)  =  0. 

2.  d  (ax)  =  a  dx. 

3.  d  (x  +  y)  =  dx  +  dy. 

4.  d  (x  —  y)  =  dx  —  dy. 

5.  d  (xy)  =  x  dy  +  y  dx. 

To  find  the  differential  of  the  form  u  =  (a  +  bxn)m: 
Multiply  the  exponent  of  the  parenthesis  into  the  exponent  of  the  vari- 
able within  the  parenthesis,  into  the  coefficient  of  the  variable,  into  the 


DIFFERENTIAL   CALCULUS.  75 

binomial  raised  to  a  power  less  1 ,  into  the  variable  within  the  parenthesis 
raised  to  a  power  less  1,  into  the  differential  of  the  variable. 

du  =  d(a  +  bxn)m  =  mnb(a  +  bxn)m~l  xn~l  dx. 

To  find  the  rate  of  change  for  a  given  value  of  the  variable: 
Find  the  differential  coefficient,  and  substitute  the  value  of  the  variable 
in  the  second  member  of  the  equation. 

EXAMPLE.  —  If  x  is  the  side  of  a  cube  and  u  its  volume,  u  =  x3,  -r-  =  3x2. 

Hence  the  rate  of  change  in  the  volume  is  three  times  the  square  of  the 
edge.  If  the  edge  is  denoted  by  1,  the  rate  of  change  is  3. 

Application.  The  coefficient  of  expansion  by  heat  of  the  volume  of  a 
body  is  three  times  the  linear  coefficient  of  expansion.  Thus  if  the  side 
of  a  cube  expands  0.001  inch,  its  volume  expands  0.003  cubic  inch.  1.0013 
=  1.003003001. 

A  partial  differential  coefficient  is  the  differential  coefficient  of  a 
function  of  two  or  more  variables  under  the  supposition  that  only  one 
of  them  has  changed  its  value. 

A  partial  differential  is  the  differential  of  a  function  of  two  or  more 
variables  under  the  supposition  that  only  one  of  them  has  changed  its 
value. 

The  total  differential  of  a  function  of  any  number  of  variables  is  equal 
to  the  sum  of  the  partial  differentials. 

If  u  =  f  (xy),  the  partial  differentials  are  -r-  dx,  ~rdy. 

' 

Integrals.  —  An  integral  is  a  functional  'expression  derived  from  a 
differential.  Integration  is  the  operation  of  finding  the  primitive  func- 
tion from  the  differential  function.  It  is  indicated  by  the  sign/i  which  is 

read  "the  integral  of."  Thus  fix  dx  =  z2;  read,  the  integral  of  2xdx 
equals  x2. 

To  integrate  an  expression  of  the  form  mxm~1dx  or  xmdx,  add  1  to  the 
exponent  of  the  variable,  and  divide  by  the  new  exponent  and  by  the 

differential  of  the  variable:  JZx^dx  =  a:3.     (Applicable  in  all  cases  except 

when   m  =  —  1.     For  Jx      dx  see  formula  2,  page  81.) 

The  integral  of  the  product  of  a  constant  by  the  differential  of  a  vari- 
*)le  is  equal  to  the  constant  multiplied  by  the  integral  of  the  differential: 


If  u  -=  x*  +  y3  -  z,  du  =  -     dx  +       dy  +       dz;  =  2xdx  +  3y*  dy  -  dz. 


fax™  dx  =  a   f 


xmdx  =  a 


m  +  1* 


The  integral  of   the  algebraic  sum  of   any  number  of  differentials  is 
equal  to  the  algebraic  sum  of  their  integrals: 


du  =  2axzdx  —  bydy—  z2  dz;  (  du=  - 


Since  the  differential  of  a  constant  is  0,  a  constant  connected  with  a 
variable  by  the  sign  +  or  —  disappears  in  the  differentiation;  thus 
d(a  -4-  xm)  =  dxm  =  mxm~l  dx.  Hence  in  integrating  a  differential 
expression  we  must  annex  to  the  integral  obtained  a  constant  represented 
by  C  to  compensate  for  the  term  which  may  have  been  lost  in  differen- 
tiation. Thus  if  we  have  dy  =  adx^fdy  =»  afdx.  Integrating, 

y  =  ax  ±  C. 


76  DIFFERENTIAL   CALCULUS. 

The  constant  C,  which  is  added  to  the  first  integral,  must  have  such  a 
value  as  to  render  the  functional  equation  true  for  every  possible  value 
that  may  be  attributed  to  the  variable.  Hence,  after  having  found  the 
first  integral  equation  and  added  the  constant  C,  if  we  then  make 
the  variable  equal  to  zero,  the  value  which  the  function  assumes  will  be 
the  true  value  of  C. 

An  indefinite  integral  is  the  first  integral  obtained  before  the  value  of 
the  constant  C  is  determined. 

A  particular  integral  is  the  integral  after  the  value  of  C  has  been  found. 

A  definite  integral  is  the  integral  corresponding  to  a  given  value  of  the 
'-ariable. 

Integration  between  limits.  —  Having  found  the  indefinite  integral 
and  the  particular  integral,  the  next  step  is  to  find  the  definite  integral 
and  then  the  definite  integral  between  given  limits  of  the  variable. 

The  integral  of  a  function,  taken  between  two  limits,  indicated  by  given 
values  of  x,  is  equal  to  the  difference  of  the  definite  integrals  correspond- 
ing to  those  limits.  The  expression 


X 


X" 

dy 


is  read:  Integral  of  the  differential  of  y,  taken  between  the  limits  xf  and 
x"\  the  least  limit,  or  the  limit  corresponding  to  the  subtractive  integral, 
being  placed  below. 

Integrate  du  •—  9xz  dx  between  the  limits  x  =  1  and  x  =  3,  u  being  equal 

to  81  when  x  =  0.     /du  =  /Qxz  dx  =  3x3  -f  C;  C  =  81  when  x  =  0,  then 

=  3 

du  =  3(3)3  +  8i>  minus  3(1)3  +  »i  =  73. 


Integration  of  particular  forms. 

To  integrate  a  differential  of  the  form  du  =  (a  +  bxn)mxn    l  dx. 

1.  If  there  is  a  constant  factor,  place  it  without  the  sign  of  the  integral, 
and  omit  the  power  of  the  variable  without  the  parenthesis  and  the  differ- 
ential ; 

2.  Augment   the  exponent  of   the  parenthesis  by  1,  and  then  divide 
this  quantity,  with  the  exponent  so  increased,  by  the  exponent  of  the 
parenthesis,  into  the  exponent  of  the  variable  within  the  parenthesis, 
into  the  coefficient  of  the  variable.     Whence 


(wH-Dnd 

The  differential  of  an  arc  is  the  hypothenuse  of  a  right-angle  triangle  of 
which  the  base  is  dx  and  the  perpendicular  dy. 

If  2  is  an  arc,  dz  =  ^dxz  +  dyz    z  =J  ^dx2  +  dy*. 

Quadrature  of  a  plane  figure. 

The  differential  of  the  area  of  a  plane  surface  is  equal  to  the  ordmate  int^ 
the  differential  of  the  abscissa. 

ds  =  y  dx. 

To  apply  the  principle  enunciated  in  the  last  equation,  in  finding  the  area 
of  any  particular  plane  surface: 

Find  the  value  of  y  in  terms  of  x,  from  the  equation  of  the  bounding  line; 
substitute  this  value  in  the  differential  equation,  and  then  integrate 
between  the  required  limits  of  x. 

Area  of  the  parabola.  —  Find  the  area  of  any  portion  of  the  com- 
mon parabola  whose  equation  is 

yz  =  2px;     whence  y  = 


DIFFERENTIAL   CALCULUS.  77 

Substituting  this  value  of  y  in  the  differential  equation  ds  =  y  dx  gives 


If  we  estimate  the  area  from  the  principal  vertex,  x  =  0,  y  =  0,  and 

o 
C  =  0;  and  denoting  the  particular  integral  by  s7,  s'  =  ^  zi/. 

o 

That  is,  the  area  of  any  portion  of  the  parabola,  estimated  from  the 
vertex,  is  equal  to  2/3  of  the  rectangle  of  the  abscissa  and  ordinate  of  the 
extreme  point.  The  curve  is  therefore  quadrable. 

Quadrature  of  surfaces  of  revolution.  —  The  differential  of  a  surface 
of  revolution  is  equal  to  the  circumference  of  a  circle  perpendicular  to  the 
axis  into  the  differential  of  the  arc  of  the  meridian  curve. 


•  ds  = 

in  which  y  is  the  radius  of  a  circle  of  the  bounding  surface  in  a  i 
pendicular  to  the  axis  of  revolution,  and  r  is  the  abscissa,  or  distance  of 
the  plane  from  the  origin  of  coordinate  axes. 

Therefore,  to  find  the  volume  of  any  surface  of  revolution: 

Find  the  value  of  y  and  dy  from  the  equation  of  the  meridian  curve  in 
terms  of  x  and  dx,  then  substitute  these  values  in  the  differential  equation, 
and  integrate  between  the  proper  limits  of  x. 

By  application  of  this  rule  we  may  find: 

The  curved  surface  of  a  cylinder  equals  the  product  of  the  circum- 
ference of  the  base  into  the  altitude. 

The  convex  surface  of  a  cone  equals  the  product  of  the  circumference  of 
the  base  into  half  the  slant  height. 

The  surface  of  a  sphere  is  equal  to  the  area  of  four  great  circles,  or  equal 
to  the  curved  surface  of  the  circumscribing  cylinder. 

Cubature  of  volumes  of  revolution.  —  A  volume  of  revolution  is  a 
volume  generated  by  the  revolution  of  a  plane  figure  about  a  fixed  line 
called  the  axis. 

If  we  denote  the  volume  by  V,  dV  =  xy2  dx. 

The  area  of  a  circle  described  by  any  ordinate  y  is  ny2;  hence  the  differ- 
ential of  a  volume  of  revolution  is  equal  t9  the  area  of  a  circle  perpendicular 
to  the  axis  into  the  differential  of  the  axis. 

The  differential  of  a  volume  generated  by  the  revolution  of  a  plane 
figure  about  the  axis  of  Y  is  nx2  dy. 

To  find  the  value  of  V  for  any  given  volume  of  revolution  : 

Find  the  value  of  y2  in  terms  of  x  from  the  equation  of  the  meridian 
curve,  substitute  this  value  in  the  differential  equation,  and  then  integrate 
between  the  required  limits  of  x. 

By  application  of  this  rule  we  may  find: 

The  volume  of  a  cylinder  is  equal  to  the  area  of  the  base  multiplied 
by  the  altitude. 

The  volume  of  a  cone  is  equal  to  the  area  of  the  base  into  one  third  the 
altitude. 

The  volume  of  a  prolate  spheroid  and  of  an  oblate  spheroid  (formed  by 
the  revolution  of  an  ellipse  around  its  transverse  and  its  conjugate  axis 
respectively)  are  each  equal  to  two  thirds  of  the  circumscribing  cylinder. 

If  the  axes  are  equal,  the  spheroid  becomes  a  sphere  and  its  volume  = 

-  nRz  X  D  =  -  7rZ>3;  R  being  radius  and  D  diameter. 
o  o 

The  volume  of  a  paraboloid  is  equal  to  half  the  cylinder  having  the  same 
base  and  altitude. 

The  volume  of  a  pyramid  equals  the  area  of  the  base  multiplied  by  one 
third  the  altitude. 

Second,  third,  etc.,  differentials.  —  The  differential  coefficient  being 
a  function  of  the  independent  variable,  it  may  be  differentiated,  and  we 
thus  obtain  the  second  differential  coefficient; 


78  DIFFERENTIAL  CALCULUS 

^\  =-  ——•      Dividing  by  dxt  we  have  for  the  second  differential 


coefficient  -r-^,  which  is  read  :  second  differential  of  u  divided  by  the  square 
of  the  differential  of  x  (or  dx  squared). 

The  third  differential  coefficient   ^  is  read:  third  differential  of  u 

divided  by  dx  cubed. 

The  differentials  of  the  different  orders  are  obtained  by  multiplying 
the  differential  coefficient  by  the  corresponding  powers  of  dx;  thus 

^   dx3  =  third  differential  of  u. 
dx3 

Sign  of  the  first  differential  coefficient.  —  If  we  have  a  curve 
Artiose  equation  is  y  =  fx,  referred  to  rectangular  coordinates,  the  curve 

will  recede  from  the  axis  of  X  when   -~  is  positive,  and  approach  the 

axis  when  it  is  negative,  when  the  curve  lies  within  the  first  angle  of  the 
coordinate  axes.  For  all  angles  and  every  relation  of  y  and  x  the  curve 
will  recede  from  the  axis  of  X  when  the  ordinate  and  first  differential 
coefficient  have  the  same  sign,  and  approach  it  .when  they  have  different 
signs.  If  the  tangent  of  the  curve  becomes  parallel  to  the  axis  of  X  at  any 

point  ~-  =  0.    If  the  tangent  becomes  perpendicular  to  the  axis  of  X  at 

any  point  ^|  =  oo.  t 

Sign  of  the  second  differential  coefficient.  —  The  second  differential 
coefficient  has  the  same  sign  as  the  ordinate  when  the  curve  is  convex 
toward  the  axis  of  abscissa  and  a  contrary  sign  when  it  is  concave. 

Maclaurin's  Theorem.  —  For  developing  into  a  series  any  function 
of  a  single  variable  as  u  =  A  +  Bx  +  Cxz  +  Dx3  +  Ex*,  etc.,  in  which 
A,  B,  C,  etc.,  are  independent  of  x: 


In  applying  the  formula,  omit  the  expressions  x  «=  0,  although  the 
coefficients  are  always  found  under  this  hypothesis. 
EXAMPLES: 

(a  +  x)m  =  am  +  mam~l  x  + 


.  -  i  -  4  + 


a  +  x       a       a2       a3       a4  an  +  1 

Taylor's  Theorem.  —  For  developing  into  a  series  any  function  of  the 
sum  or  difference  of  two  independent  variables,  as  u'  «=  j(x  ±  y): 


in  which  u  is  what  u'  becomes  when  y  —  0,  ~  is  what  •—•  becomes  when 

y  —  0,  etc. 

Maxima  and  minima.  —  To  find  the  maximum  or  minimum  value 
of  a  function  of  a  single  variable: 

1.  Find  the  first  differential  coefficient  of  the  function,  place  it  equal 
to  0,  and  determine  the  roots  of  the  equation. 

2.  Find  the  second  differential  coefficient,  and  substitute  each  real  root, 


DIFFERENTIAL  CALCULUS.  79 

In  succession,  for  the  variable  in  the  second  member  of  the  equation. 
Each  root  which  gives  a  negative  result  will  correspond  to  a  maximum 
value  of  the  function,  and  each  which  gives  a  positive  result  will  corre- 
spond to  a  minimum  value. 

EXAMPLE.  —  To  find  the  value  of  x  which  will  render  the  function  y  a 
maximum  or  minimum  in  the  equation  of  the  circle,  y2  +  x2  =  R2; 

f|  -  -  y;  making  -  jj  ~  0  gives  x  -  0. 

The  second  differential  coefficient  is:  ~  =  -  x  +3 y*  • 

When  x  —  0,  y  —  R;  hence    -^  =  -  ^»  which  being  negative,  y  is  a 

maximum  for  R  positive. 

In  applying  the  rule  to  practical  examples  we  first  find  an  expression  for 
the  function  which  is  to  be  made  a  maximum  or  minimum. 

2.  If  in  such  expression  a  constant  quantity  is  found  as  a  factor,  it  may 
be  omitted  in  the  operation;  for  the  product  will  be  a  maximum  or  a  mini- 
mum when  the  variable  factor  is  a  maximum  or  a  minimum. 

3.  Any  value  9f  the  independent  variable  which  renders  a  function  a 
maximum  or  a  minimum  will  render  any  power  or  root  of  that  function  a 
maximum  or  minimum;  hence  we  may  square  both  members  of  an  equa- 
tion to  free  it  of  radicals  before  differentiating. 

By  these  rules  we  may  find : 

The  maximum  rectangle  which  can  be  inscribed  in  a  triangle  is  one 
whose  altitude  is  half  the  altitude  of  the  triangle. 

The  altitude  of  the  maximum  cylinder  which  can  be  inscribed  in  a  cone 
is  one  third  the  altitude  of  the  cone. 

'The  surface  of  a  cylindrical  vessel  of  a  given  volume,  open  at  the  top, 
is  a  minimum  when  the  altitude  equals  half  the  diameter. 

The  altitude  of  a  cylinder  inscribed  in  a  sphere  when  its  convex  surface  is 
a  maximum  is  r  v^2.  r  =  radius. 

The  altitude  of  a  cylinder  inscribed  in  a  sphere  when  the  volume  is  a 
maximum  is  2r  •*•  Vs. 

Maxima  and  Minima  without  the  Calculus.  —  In  the  equation 
y  =  a :  4-  bx  +  ex2,  in  which  a,  &,  and  c  are  constants,  either  positive  or 
negative,  if  c  be  positive  y  is  a  minimum  when  x  =  —  b  -*-  2c;  if  c  be 
negative  y  is  a  maximum  when  x  =  —  b  •*•  2c.  In  the  equation  y  =  a  + 
bx  +c/x,  y  is  a,  minimum  when  bx  =  c/x. 

APPLICATION.  — The  cost  of  electrical  transmission  is  made  up  (1)  of 
fixed  charges,  such  as  superintendence,  repairs,  cost  of  poles,  etc.,  which 
may  be  represented  by  a;  (2)  of  interest  on  cost  of  the  wire,  which  varies 
with  the  sectional  area,  and  may  be  represented  by  bx;  and  (3)  of  cost  of 
the  energy  wasted  in  transmission,  which  varies  inversely  with  the  area 
of  the  wire,  or  c/x.  The  total  cost,  y  =  a  4-  bx  +  c/x,  is  a  minimum 
when  item  2  =  item  3,  or  bx  =  c/x. 

Differential  of  an  exponential  function. 

If  u  =  ax    .     .     . (1) 

then  du  =  dax  =  axkdx (2) 

in  which  k  is  a  constant  dependent  on  a. 

The  relation  bet  ween  a  and  k  is  o*  =  e;  whence  a  =  e*  ....  (3) 
in  which  e  =  2.7182818  .  .  .  the  base  of  the  Naperian  system  of  loga- 
rithms. 

Logarithms.  —  The  logarithms  in  the  Naperian  system  are  denoted  by 
I,  Nap.  log  or  hyperbolic  log,  hyp.  log,  or  loge  ;  and  in  the  common  system 
Iways  by  log. 

fc  —  Nap.  logo;  log  a     =  k  log  e (4) 


80  DIFFERENTIAL  CALCULUS. 

The  common  logarithm  of  e,  =  log  2.7182818  .  .  .  «*  0.4342945  .  .  .  ; 
Is  called  the  modulus  of  the  common  system,  and  is  denoted  by  Af. 
Hence,  if  we  have  the  Naperian  logarithm  of  a  number  we  can  find  the 
common  logarithm  of  the  same  number  by  multiplying  by  the  modulus. 
Reciprocally,  Nap.  log  =  com.  log  X  2.3025851. 

If  in  equation  (4)  we  make  a  =  10,  we  have 


1  =  k  log  e,  or  ?  =  log  e  =  M  . 


That  is,  the  modulus  of  the  common  system  is  equal  to  1,  divided  by  the 
Naperian  logarithm  of  the  common  base. 
From  equation  (2)  we  have 

du       dax 
—  *—  •-  kdx. 
u        ax 

If  we  make  a  =  10,  the  base  of  the  common  system,  x  =  log  u,  and 

j  /i  j        du  „    1       du  ^  f 

d  (log  u)  -  dx  =  ~  X  £  -  -  X  M. 

That  is,  the  differential  of  a  common  logarithm  of  a  quantity  is  equal  to 
the  differential  of  the  quantity  divided  by  the  quantity,  into  the  modulus. 
If  we  make  a  =  e,  the  base  of  the  Naperian  system,  x  becomes  the  Nape- 
rian logarithm  of  u,  and  k  becomes  1  (see  equation  (3));  hence  M  =  1, 
and 

du          du 

d  (Nap.  log  u)  =  dx  —  —  -  ;   =  —  • 
ax  u 

That  is,  the  differential  of  a  Naperian  logarithm  of  a  quantity  is  equal  to 
the  differential  of  the  quantity  divided  by  the  quantity;  and  in  the 
Naperian  system  the  modulus  is  1. 

Since  k  is  the  Naperian  logarithm  of  a,  du  =  ax  I  a  dx.  That  is,  the 
differential  of  a  function  of  the  form  ax  is  equal  to  the  function,  into  the 
Naperian  logarithm  of  the  base  .a,  into  the  differential  of  the  exponent. 

If  we  have  a  differential  in  a  fractional  form,  in  which  the  numerator  is 
the  differential  of  the  denominator,  the  integral  is  the  Naperian  logarithm 
of  the  denominator.  Integrals  of  fractional  differentials  of  other  forms 
are  given  below: 

Differential  forms  which  have  known  integrals;  exponential 
functions.  (I  =  Nap.  log.) 


+  C; 


4. 

6.  I  •  ,    "^         -  l(x  ±  a  +  Vx*~±  2ax)  +  C; 


CALCULUS. 


81. 


7. 


8. 


9. 


10. 


2a  cte 


-j 


f  —  |«^ 

J  x\/a*  +  x* 


2a<ta        =  l  la  -  Va2  -  x~A  +  C; 
a2  -  a:2         \  a  +  ^a2  -  z2/ 

r  *~2^    =_z  fi  +  vi  +  o«s«\  [  c 

x  -{-  x  »  * 


Circular  functions.  —  Let  z  denote  an  arc  in  the  first  quadrant,  y  its 
sine,  x  its  cosine,  y  its  versed  sine,  and  t  its  tangent;  and  the  following  nota- 
tion be  employed  to  designate  an  arc  by  any  one  of  its  functions,  viz., 

sin"1  y  denotes  an  arc  of  which  y  is  the  sine, 
cos"1^  "  "  "  "  "  x  is  the  cosine, 
tan"^  "  "  "  "  "  Ms  the  tangent, 

(read  "arc  whose  sine  is  ?/,"  etc.),  —  we  have  the  following  differential 
forms  which  have  known  integrals  (r  =  radius): 


|  cos  zdz        •=  sin  z+  C\ 
I  —  sin  z  dz    •=  cos  z  +  C\ 


sin  z  dz  =  versin  z  +  (7; 


The  cycloid.  —  If  a  circle  be  rolled  along  a  straight  line,  any  point  of 
the  circumference,  as  P,  will  describe  a  curve  which  is  called  a  cycloid. 
The  circle  is  called  the  generating  circle,  and  P  the  generating  point. 


SLIDE 


The  transcendental  equation  of  the  cycloid  is 


x  =  versin  ~i v 

and  the  differential  equation  is  dx  = 


The  area  of  the  cycloid  is  equal  to  three  times  the 
area  of  the  generating  circle. 

The  surface  described  by  the  arc  of  a  cycloid  when 
revolved  about  its  base  is  equal  to  64  thirds  of  the 
generating  circle. 

The  volume  of  the  solid  generated  by  revolving 
a  cycloid  about  its  base  is  equal  to  five  eighths  of  the 
circumscribing  cylinder. 

Integral  calculus.  —  In  the  integral  calculus  we 
have  to  return  from  the  differential  to  the  function 
from  which  it  was  derived.  A  number  of  differential 
expressions  are  given  above,  each  of  which  has  a 
known  integral  corresponding  to  it,  which,  being 
differentiated,  will  produce  the  given  differential. 

In  all  classes  of  functions  any  differential  expression 
may  be  integrated  when  it  is  reduced  to  one  of  the 
known  forms;  and  the  operations  of  the  integral  cal- 
culus consist  mainly  in  making  such  transformations 
of  given  differential  expressions  as  shall  reduce  them 
to  equivalent  ones  whose  integrals  are  known. 

For  methods  of  making  these  transformations 
reference  must  be  made  to  the  text-books  on  differen- 
tial and  integral  calculus. 


THE  SLIDE  RULE. 

The  slide  rule  is  based  on  the  principles  that  the 
addition  of  logarithms  multiplies  the  numbers  which 
they  represent,  and  subtracting  logarithms  divides 
the  numbers.  By  its  use  the  operations  of  multiplica- 
tion, division,  the  finding  of  powers  and  the  extraction 
of  roots,  may  be  performed  rapidly  and  with  an  ap- 
proximation to  accuracy  which  is  sufficient  for  many 
purposes.  With  a  good  10-inch  Mannheim  rule  the 
results  obtained  are  usually  accurate  to  1/4  of  1  per 
cent.  Much  greater  accuracy  is  obtained  with  cylin- 
drical rules  like  the  Thacher. 

The  rule  (see  Fig.  73)  consists  of  a  fixed  and  a 
sliding  part  both  of  which  are  ruled  with  logarithmic 
scales;  that  is,  with  consecutive  divisions  spaced  not 
equally,  as  in  an  ordinary  scale,  but  in  proportion 
to  the  logarithms  of  a  series  of  numbers  from  1  to 
10.  By  moving  the  slide  to  the  right  or  left  the  loga- 
rithms are  added  or  subtracted,  and  multiplication 
or  division  of  the  numbers  thereby  effected.  The 
scales  on  the  fixed  part  of  the  rule  are  known  as  the 
A  and  D  scales,  and  those  on  the  slide  as  the  B  and 
C  scales.  A  and  B  are  the  upper  and  C  and  D 
are  the  lower  scales.  The  A  and  B  scales  are  each 
divided  into  two,  left  hand  and  right  hand,  each 
being  a  reproduction,  one  half  the  size,  of  the  C  and 
D  scales.  A  "runner,"  which  consists  of  a  framed 
glass  plate  with  a  fine  vertical  line  on  it,  is  used  to 
facilitate  some  of  the  operations.  The  numbering  on 
each  scale  begins  with  the  figure  1,  which  is  called 


FIG.  73. 


THE  SLIDE  RULE.  83 

the  "index"  of  the  scale.  In  using  the  scale  the  figures  1,  2,  3,  etc.,  are 
to  be  taken  either  as  representing  these  numbers,  or  as  10,  20,  30,  etc., 
100,  200,  300,  etc.,  0.1,  0.2,  0.3,  etc.,  that  is,  the  numbers  multiplied  or 
divided  by  10,  100,  etc.,  as  may  be  most  convenient  for  the  solution  of  a 
given  problem. 

The  following  examples  will  give  an  idea  of  the  method  of  using  the 
glide  rule,, 

Proportion.  —  Set  the  first  term  of  a  proportion  on  the  C  scale  opposite 
the  second  term  on  the  D  scale,  then  opposite  the  third  term  on  the  C 
scale  read  the  fourth  term  on  the  D  scale. 

EXAMPLE,  —  Find  the  fourth  term  in  the  proportion  12  :  21  ::  30  :  x. 
Move  the  slide  to  the  right  until  12  on  C  coincides  with  21  on  Z),  then 
opposite  30  on  C  read  x  on  D  =  52.5.  The  A  and  B  scales  may  be  used 
instead  of  C  and  D. 

Multiplication.  —  Set  the  index  or  figure  1  of  the  C  scale  to  one  of  the 
factors  on  ZX 

EXAMPLE.  —  25  X  3.  Move  the  slide  to  the  right  until  the  left  index 
of  C  coincides  with  25  on  the  D  scale.  Under  3  on  the  C  scale  will  be 
found  the  product  on  the  Z)  scale,  =  75. 

Division,  —  Place  the  divisor  on  C  opposite  the  dividend  on  D,  and  the 
quotient  will  be  found  on  D  under  the  index  of  C. 

EXAMPLE.  —  750  •*-  25.  Move  the  slide  to  the  right  until  25  on  C  coin- 
cides with  750  on  D.  Under  the  left  index  of  C  is  found  the  quotient  on 
D,  =  30. 

Combined  Multiplication  and  Division.  —  Arrange  the  factors  to  be 
multiplied  and  divided  in  the  form  of  a  fraction  with  one  more  factor  in 
the  numerator  than  in  the  denominator,  supplying  the  factor  1  if  necessary. 
Then  perform  alternate  division  and  multiplication,  using  the  runner  to 
Indicate  the  several  partial  results. 

4X5X8 
EXAMPLE^  —  —  3  ..  g     =  8.9  nearly.     Set   3  on  C  over  4  on  D,  set 

O  X   O 

runner  to  5  on  C,  then  set  6  on  C  under  the  runner,  and  read  under  8  on 
C  the  result  8*9  -  on  D. 

Involution  and  Evolution.  —  The  numbers  on  scales  A  and  B  are  the 
squares  of  their  coinciding  numbers  on  the  scales  C  and  D,  and  also  the 
numbers  on  scales  C  and  D  are  the  square  roots  of  their  coinciding  num- 
bers on  scales  A  and  B. 

EXAMPLE,  —  42  =  16.  Set  the  runner  over  4  on  scale  D  and  read  16 
on  A.__ 

^16  =  4.     Set  the  runner  over  16  on  A  and  read  4  on  D. 

In  extracting  square  roots,  if  the  number  of  digits  is  odd,  take  the  num- 
ber on  the  left-hand  scale  of  A ;  if  the  number  of  digits  is  even,  take  the 
number  on  the  right-hand  scale  of  A. 

To  cube  a  number  perform  the  operations  of  squaring  and  multiplica- 
tion. 

EXAMPLEO  —  2s  =  8.  Set  the  index  of  C  over  2  on  D,  and  above  2 
on  B  read  the  result  8  on  A0 

Extraction  of  the  Cube  Root.  —  Set  the  runner  over  the  number  on  A, 
then  move  the  slide  until  there  is  found  under  the  runner  on  B,  the  same 
number  which  is  found  under  the  index  of  C  on  D;  this  number  is  the 
cube  root  desired. 

EXAMPLE  —  ^8=2.  Set  the  runner  over  8  on  A,  move  the  slide 
along  until  the  same  number  appears  under  the  runner  on  B  and  under 
the  index  of  C  on  D;  this  will  be  the  number  2. 

Trigonometrical  Computations.  —  On  the  under  side  of  the  slide  (which 
is  reversible)  are  placed  three  scales,  a  scale  of  natural  sines  marked  St 
a  scale  of  natural  tangents  marked  T,  and  between  these  a  scale  of  equal 
parts.  To  use  these  scales,  reverse  the  slide,  bringing  its  under  side  to 
the  top.  Coinciding  with  an  angle  on  S  its  sine  will  be  found  on  At  and 
coinciding  with  an  angle  on  T  will  be  found  the  tangent  on  D.  Sines  and 
tangents  can  be  multiplied  or  divided  like  numbers. 


84  LOGARITHMIC   RULED    PAPER* 

LOGARITHMIC  RULED  PAPER. 

W.  F.  Durand   (Eng.  News,  Sept.  28,  1893.) 

As  plotted  on  ordinary  cross-section  paper  the  lines  which  express 
relations  between  two  variables  are  usually  curved,  and  must  be  plotted 
point  by  point  from  a  table  previously  computed.  It  is  only  where  the 
exponents  involved  in  the  relationship  are  unity  that  the  line  becomes 
straight  and  may  be  drawn  immediately  on  the  determination  of  two  of 
its  points.  It  is  the  peculiar  property  of  logarithmic  section  paper  that 
for  all  relationships  which  involve  multiplication,  division,  raising  to 
powers,  or  extraction  of  roots,  the  lines  representing  them  are  straight. 
Any  such  relationship  may  be  represented  by  an  equation  of  the  form: 
y  =  Bxn.  Taking  logarithms  we  have:  log  y  =  log  B  4-  n  log  x. 

Logarithmic  section  paper  is  a  short  and  ready  means  of  plotting  such 
logarithmic  equations.  The  scales  on  each  side  are  logarithmic  instead 
of  uniform,  as  in  ordinary  cross-section  paper.  The  numbers  and  divi- 
sions marked  are  placed  at  such  points  that  their  distances  from  the  origin 
are  proportional  to  the  logarithms  of  such  numbers  instead  of  to  the 
numbers  themselves.  If  we  take  any  point,  as  3,  for  example,  on  such  a 
scale,  the  real  distance  we  are  dealing  with  is  log  3  to  some  particular 
base,  and  not  3  itself.  The  number  at  the  origin  9f  such  a  scale  is  always 
1  and  not  0,  because  1  is  the  number  whose  logarithm  is  0.  This  1  may, 
however,  represent  a  unit  of  any  order,  so  that  quantities  of  any  size 
whatever  may  be  dealt  with. 

If  we  have  a  series  of  values  of  x  and  of  Bx  ,  and  plot  on  logarithmic 
section  paper  x  horizontally  and  Bxn  vertically,  the  actual  distances 
Involved  will  be  log  x  and  log  (Bxn),  or  log  B  +  n  log  x.  But  these  dis- 
tances will  give  a  straight  line  as  the  locus.  Hence  all  relationships 
expressible  in  this  form  are  represented  on  logarithmic  section  paper  by 
straight  lines.  It  follows  that  the  entire  locus  may  be  determined  from 
any  two  points;  that  is,  from  any  two  values  of  Bxn\  or,  again,  by  any  one 
point  and  the  angle  of  inclination;  that  is,  by  one  value  of  Bxn  and  the 
value  of  ft,  remembering  that  n  is  the  tangent  of  the  angle  of  inclination 
to  the  horizontal. 

A  single  square  plotted  on  each  edge  with  a  logarithmic  scale  from  1 
fco  10  may  be  made  to  serve  for  any  number  whatever  from  0  to  oo.  Thus 
to  express  graphically  the  locus  of  the  equation:  y  =  rrs/2.  Let  Fig.  74 
denote  a  square  cross-sectioned  with  logarithmic  scales,  as  described. 
Suppose  that  there  were  joined  to  it  and  to  each  other  on  the  right  and 
above,  an  indefinite  series  of  such  squares  similarly  divided.  Then,  con- 
sidering, in  passing  from  one  square  to  an  adjacent  one  to  the  right  or 
above,  that  the  unit  becomes  of  next  higher  order,  such  a  series  of  squares 
would,  with  the  proper  variation  of  the  unit,  represent  all  values  of  either 
x  or  y  between  0  and  oo, 

Suppose  the  original  square  divided  on  the  horizontal  edge  into  3  parts, 
and  on  the  vertical  edge  into  2  parts,  the  points  of  division  being  at  A, 
B,  D,  F,  G,  I.  Then  lines  joining  these  points,  as  shown,  will  be  at  an 
inclination  to  the  horizontal  whose  tangent  is  3/2.  Now,  beginning  at  0, 
OF  will  give  the  value  of  a^/2  for  values  of  x  from  1  to  that  denoted  by  HF, 
or  OB,  or  about  4.6.  For  greater  values  of  x  the  line  would  run  into  the 
adjacent  square  above,  but  the  location  of  this  line,  if  continued,  would 
be  exactly  similar  to  that  of  BD  in  the  square  before  us.  Therefore  the 
line  BD  will  give  values  of  :r3/2  for  x  between  B  and  C,  or  4.6  and  10,  the 
corresponding  values  of  y  being  of  the  order  of  tens,  and  ranging  from  10 
to  31.3.  For  larger  values  of  x  the  unit  of  x  is  of  the  higher  order,  and 
we  run  into  an  adjacent  square  to  the  right  without  change  of  unit  for  y. 
In  this  square  we  should  traverse  a  line  similar  to  IG.  Therefore,  by  a 
proper  choice  of  units  we  may  make  use  of  IG  for  the  determination  of 
values  of  £3/2  where  x  lies  between  10  and  the  value  at  G,  or  about  21.5. 
We  should  then  run  into  an  adjacent  square  above,  requiring  the  unit  on 
y  to  be  of  the  next  higher  order,  and  traverse  a  line  similar  to  AEt  which 


takes  us  finall 


LOGARITHMIC   RULED  PAPER. 


85 


takes  us  finally  to  the  opposite  corner  and  completes  the  cycle.  Follow- 
ing this,  the  same  series  of  lines  would  result  for  numbers  of  succeeding 
orders. 

The  value  of  x3/2  for  any  value  of  x  between  1  and  oo  may  thus  be  read 
from  one  or  another  of  these  lines,  and  likewise  for  any  value  between 
0  and  1.  The  location  of  the  decimal  point  is  readily  found  by  a  little 
attention  to  the  numbers  involved.  The  limiting  values  of  x  for  any 
given  line  may  be  marked  on  it,  thus  enabling  a  proper  choice  to  be  readily 
made.  Thus,  in  Fig.  74  we  mark  OF  as  0  -  4.6,  BD  as  4.6  -  10,  1G  as 


O      p 


10  —  21.5,  and  A E  as  21.5  —  100.  If  values  of  x  less  than  1  are  to  be 
dealt  with,  AE  will  serve  for  values  of  x  between  1  and  0.215,  IG  for 
values  between  0.215  and  0.1,  BD  for  values  between  0.1  and  0.046,  and 
OF  for  values  between  0.046  and  0.001. 

The  principles  involved  in  this  case  may  be  readily  extended  to  any 
other,  and  in  general  if  the  exponent  be  represented  by  m/n,  the  complete 
set  of  lines  may  be  drawn  by  dividing  one  side  of  the  square  into  m  and 
the  other  into  n  parts,  and  joining  the  points  of  division  as  in  Fig.  74.  In 
all  there  will  be  (m  -f  n  —  1)  lines,  and  opposite  t9  any  point  on  X  there 
will  be  n  lines  corresponding  to  the  n  different  beginnings  of  the  nth  root 


86  MATHEMATICAL  TABLES. 

of  the  mth  power,  while  opposite  to  any  point  on  Y  will  be  m  lines  corre- 
sponding to  the  different  beginnings  of  the  mth  root  of  the  nth  power. 
Where  the  complete  number  of  lines  would  be  quite  large,  it  is  usually 
unnecessary  to  draw  them  all,  and  the  number  may  be  limited  to  those 
necessary  to  cover  the  needed  range  in  the  values  of  x. 

If,  instead  of  the  equation  y  =  xnt  we  have  a  constant  term  as  a  multi- 
plier, giving  an  equation  in  the  more  general  form  y  =  Bxn,  or  Bx  m/n, 
there  will  be  the  same  number  of  lines  and  at  the  same  inclination,  but 
all  shifted  vertically  through  a  distance  equal  to  log  B.  If,  therefore, 
we  start  on  the  axis  of  Y  at  the  point  B,  we  may  draw  in  the  same  series 
of  lines  and  in  a  similar  manner.  In  this  way  PQ  represents  the  locus 
giving  the  values  of  the  areas  of  circles  in  terms  of  their  diameters,  being 
the  locus  of  the  equation  A  =  1/4  »  d2  or  y  =  1/4"'  £2- 

If  in  any  case  we  have  x  in  the  denominator  such  that  the  equation  is 
in  the  form  y  =  B/xn,  this  is  equal  to  y  =  Bx~n.  and  the  same  general 
rules  hold.  The  lines  in  such  case  slant  downward  to  the  right  instead  of 
upward.  Logarithmic  ruled  paper,  with  directions  for  the  use,  may  be 
obtained  from  Keuffel  &  Esser  Co.,  127  Fulton  St.,  New  York. 


MATHEMATICAL  TABLES. 

Formula  for  Interpolation. 

(n-1)  (n-2)   ^    ,    (n-1)  (n-2)  (n-3) 
—  -      --    -      —  ^     —         - 


(n  — 


— 


ai  =  the  first  term  of  the  series;  n,  number  of  the  required  term;  an,  the 
required  term;  di,  dz,  d3,  first  terms  of  successive  orders  of  differences 
between  ai,  a2,  a3,  a4,  successive  terms. 

EXAMPLE.  —  Required  the  log  of  40.7,  logs  of  40,  41  ,  42,  43  being  given  as 
below. 

Terms  alt  a2,  as,  a4(:     1.6021     1.6128     1.6232     1.6335 

1st  differences:  0.0107     0.0104     0.0103 
2d  -  0.0003  -  0.0001 

3d  +  0.0002 

For  log.  40,  n  =  1;  log  41,  n=  2;  for  log  40.7,  n  —  1.7;  n  —  1  =  0.7:  n  —  2 
=  -  0.3;  n  -  3  =-  1.3. 


an  =1.6021+0.7  (0.0107)  +(0.7)(-0.3K-0.0003)  +(0.7)(-0.3)(-  1.3)(0.0002!| 
=  1.6021  4-  0.00749  +  0.000031  4-  0.000009  =  1.6096  +. 


RECIPROCALS   OF  NUMBERS. 


RECIPROCALS  OF  NUMBERS. 


87 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

1 

1.00000000 

64 

01562500 

127 

•00787402 

190 

.00526316 

253 

.00395257 

2 

.50000000 

5 

01538461 

8 

•00781250 

1 

.C0523560 

4 

.00393701 

3 

.33333333 

6 

01515151 

9 

•00775194 

2 

.00520833 

5 

.00392157 

4 

.25000000 

7 

01492537 

130 

00769231 

3 

.00518135 

6 

.00390625 

5 

.20000000 

8 

01470588 

1 

00763359 

4 

.00515464 

7 

.00389105 

6 

.16666667 

9 

01449275 

2 

00757576 

5 

.00512820 

8 

.0038/597 

7 

.14285714 

70 

01428571 

3 

•00751880 

6 

.00510204 

9 

.00386100 

8 

.12500COO 

1 

•01408451 

4 

•00746269 

7 

.00507614 

260 

.00384615 

9 

11111111 

2 

•01388889 

5 

00740741 

8 

.00505051 

1 

.00383142 

10 

'.10000000 

3 

•01369863 

6 

•00735294 

9 

.00502513 

2 

.00381679 

11 

.09090909 

4 

•01351351 

7 

-00729927 

200 

.00500000 

3 

.00380228 

12 

.08333333 

5 

•01333333 

8 

-00724638 

1 

.00497512 

4 

.00378786 

13 

.07692308 

6 

01315789 

9 

-00719424 

2 

.00495049 

5 

.00377358 

14 

.07142857 

7 

•01298701 

140 

•00714286 

3 

.0049261  1 

6 

.00375940 

15 

.06666667 

8 

•01282051 

1 

•00709220 

4 

.004901% 

7 

.00374532 

16 

.06250000 

9 

•01265823 

2 

•00704225 

5 

.00487805 

8 

.00373134 

17 

.05882353 

80 

•01250000 

3 

-00699301 

6 

.00485437 

9 

.00371747 

18 

.05555556 

1 

•01234568 

4 

•00694444 

7 

.00483092 

270 

.00370370 

19 

.05263158 

2 

01219512 

5 

.00689655 

8 

.00480769 

1 

.00369004 

20 

.05000000 

3 

•01204819 

6 

.00684931 

9 

.00478469 

2 

.00367647 

.04761905 

4 

•01190476 

7 

.00680272 

210 

.00476190 

3 

.00366300 

^ 

.04545455 

£ 

01176471 

8 

.00675676 

11 

.00473934 

4 

.00364%3 

2 

.04347826 

e 

•01  162791 

9 

-00671141 

12 

.00471698 

5 

.00363636 

4 

.04166667 

7 

•01149425 

150 

-00666667 

13 

.00469484 

6 

.00362319 

c 

.04000000 

8 

•01136364 

1 

.00662252 

14 

.00467290 

7 

.00361011 

6 

.03846154 

9 

01  123595 

2 

.00657895 

15 

.00465116 

8 

.00359712 

T 

.03703704 

90 

•01111111 

3 

.00653595 

16 

.00462963 

9 

.00358423 

8 

.03571429 

1 

01098901 

4 

.00649351 

17 

.00460829 

280 

.00357143 

g 

.03448276 

2 

010S6956 

5 

.00645161 

18 

.00458716 

1 

.00355872 

30 

.03333333 

3 

•01075269 

6 

.00641026 

19 

.00456621 

2 

.00354610 

.03225806 

4 

•01063830 

7 

.00636943 

220 

.00454545 

3 

.00353357 

j 

.03125000 

c 

01052632 

8 

.0063291  1 

| 

.00452489 

4 

.00352113 

• 

.03030303 

6 

•01041667 

9 

.00628931 

2 

.00450450 

5 

.00350877 

4 

.02941176 

7 

•01030928 

160 

.00625000 

3 

.00448430 

6 

.0034%50 

« 

.02857143 

8 

•01020408 

1 

.00621118 

4 

.00446429 

7 

.00348432 

6 

.027/7778 

9 

•01010101 

2 

.00617284 

5 

.00444444 

8 

.00347222 

j 

.02702703 

100 

•01000000 

3 

.00613497 

6 

.00442478 

9 

.00346021 

8 

.02631579 

1 

•00990099 

4 

.00609756 

7 

.00440529 

290 

.00344828 

g 

.02564103 

2 

•00980392 

5 

.00606061 

8 

.004385% 

1 

.00343643 

40 

.02500000 

2 

•00970874 

6 

.00602410 

9 

.00436681 

2 

.00342466 

| 

.02439024 

A 

•00%  1538 

7 

.00598802 

230 

.00434783 

3 

.00341297 

'4 

.02380952 

c 

•00952381 

8 

.00595238 

1 

.00432900 

4 

.00340136 

\ 

.02325581 

t 

•009433% 

9 

00591716 

2 

.00431034 

5 

.00338983 

t 

.02272727 

7 

.00934579 

170 

.00588235 

3 

.00429184 

6 

.00337838 

i 

02222222 

8 

-00925926 

1 

.00584795 

4 

.00427350 

7 

.00336700 

6 

.02173913 

9 

.00917431 

2 

.00581395 

5 

.00425532 

8 

.00335570 

7 

.02127660 

110 

.00909091 

3 

.00578035 

6 

.00423729 

9 

00334448 

8 

.02083333 

11 

.00900901 

4 

.00574713 

7 

.00421941 

300 

.00333333 

c 

.02040816 

12 

.00892857 

5 

.00571429 

8 

.00420168 

.00332226 

50 

.02000000 

13 

.00884956 

6 

.00568182 

9 

.00418410 

2 

.00331126 

1 

.01960784 

14 

.00877193 

7 

.00564972 

240 

.00416667 

3 

.00330033 

j 

.01923077 

15 

.00869565 

8 

.00561798 

1 

.00414938 

4 

.00328947 

- 

.01886792 

16 

.00862069 

9 

.00558659 

2 

.00413223 

5 

.00327869 

/ 

.01851852 

17 

.00854701 

180 

.00555556 

3 

.00411523 

6 

.00326797 

c 

.01818182 

18 

.00847458 

1 

.00552486 

4 

.00409836 

7 

.00325733 

( 

.01785714 

19 

.00840336 

2 

.00549451 

5 

.00408163 

8 

.00324675 

7 

.01754386 

120 

.00833333 

3 

.00546448 

6 

.00406504 

9 

.00323625 

8 

.01724138 

1 

.00826446 

4 

.00543478 

7 

.00404858 

310 

.00322581 

9 

.01694915 

2 

.00819672 

5 

.00540540 

8 

.00403226 

11 

.00321543 

60 

.01666667 

3 

.00813008 

6 

.00537634 

9 

.00401606 

12 

.00320513 

1 

.01639344 

4 

.00806452 

7 

.00534759 

250 

.00400000 

-13 

.00319489 

2 

.01612903 

5 

.00800000 

8 

.00531914 

1 

.00398406 

14 

.00318471 

3 

.01587302 

6 

.00793651 

9 

.00529100 

Z 

.00396825 

15 

.00317460 

88 


MATHEMATICAL  TABLES. 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

~  316 

.00316456 

381 

.00262467 

446 

.00224215 

511 

.00195695 

576 

.00173611 

17 

.00315457 

2 

.00261780 

7 

.00223714 

12 

.00195312 

7 

.00173310 

18 

.00314465 

3 

.00261097 

8 

.00223214 

13 

.00194932 

8 

.00173010 

19 

.00313480 

4 

.00260417 

9 

.00222717 

14 

.00194552 

9 

.00172712 

320 

.00312500 

5 

.00259740 

450 

.00222222 

15 

.00194175 

580 

.00172414 

1 

.00311526 

6 

.00259067 

1 

.00221729 

16 

.00193798 

1 

.00172117 

2 

.00310559 

7 

.00258398 

2 

.00221239 

17 

.00193424 

2 

.00171821 

3 

.00309597 

8 

.00257732 

3 

.00220751 

18 

.00193050 

3 

.00171527 

4 

.00308642 

9 

.00257069 

4 

.00220264 

19 

.00192678 

4 

.00171233 

5 

.00307692 

390 

.00256410 

5 

.00219780 

520 

.00192308 

5 

.00170940 

6 

.00306748 

1 

.00255754 

6 

.00219298 

1 

00191939 

6 

.00170648 

7 

.00305810 

2 

.00255102 

7 

.00218818 

2 

.00191571 

7 

.00170358 

8 

.00304878 

3 

.00254453 

8 

.00218341 

3 

.00191205 

8 

.00170068 

9 

.00303951 

4 

.00253807 

9 

.00217865 

4 

00190840 

9 

.00169779 

330 

.00303030 

5 

.00253165 

460 

.00217391 

5 

.00190476 

590 

.00169491 

1 

.00302115 

6 

.00252525 

1 

.00216920 

6 

.00190114 

1 

.00169205 

2 

.00301205 

7 

.00251889 

2 

.00216450 

7 

.00189753 

2 

.00168919 

3 

.00300300 

8 

.00251256 

3 

.00215983 

8 

.00189394 

3 

.00168634 

4 

.00299401 

9 

.00250627 

4 

.00215517 

9 

.00189036 

4 

.00168350 

5 

.00298507 

400 

.00250000 

5 

.00215054 

530 

.00188679 

5 

.00168067 

6 

.00297619 

1 

.00249377 

6 

.00214592 

1 

.00188324 

6 

.00167785 

7 

.00296736 

2 

.00248756 

7 

.00214133 

2 

.00187970 

7 

.00167504 

8 

.00295858 

3 

.00248139 

8 

.00213675 

3 

.00187617 

8 

.00167224 

9 

.00294985 

4 

.00247525 

9 

.00213220 

4 

.00187266 

9 

.00166945 

340 

.00294118 

5 

.00246914 

470 

.00212766 

5 

.00186916 

600 

.00166667 

1 

.00293255 

6 

.00246305 

1 

.00212314 

6 

.00186567 

1 

00166389 

2 

.00292398 

7 

.00245700 

2 

.00211864 

7 

.00186220 

2 

.00166113 

3 

.00291545 

8 

.00245098 

3 

.00211416 

8 

.00185874 

3 

.00165837 

4 

.00290698 

9 

.00244499 

4 

.00210970 

9 

.00185528 

4 

.00165563 

5 

.00289855 

410 

.00243902 

5 

.00210526 

540 

.00185185 

5 

.00165289 

6 

.00289017 

11 

.00243309 

6 

.00210084 

1 

.00184843 

6 

00165016 

7 

.00288184 

12 

.00242718 

7 

.00209644 

2 

.00184502 

7 

.00164745 

8 

.00287356 

13 

.00242131 

8 

.00209205 

3 

.00184162 

8 

.00164474 

9 

.00286533 

14 

.00241546 

9 

.00208768 

4 

.00183823 

9 

.00164204 

350 

,00285714 

15 

.00240964 

480 

.00208333 

5 

.00183486 

610 

.00163934 

1 

.00284900 

16 

.00240385 

1 

.00207900 

6 

00183150 

11 

00163666 

2 

.00284091 

17 

.00239808 

2 

.00207469 

7 

.00182815 

12 

.00163399 

3 

.00283286 

18 

.00239234 

3 

.00207039 

8 

.00182482 

13 

00163132 

4 

.00282486 

19 

.00238663 

4 

.00206612 

9 

00182149 

14 

.00162866 

5 

.00281690 

420 

.00238095 

5 

.00206186 

550 

.00181818 

15 

.00162602 

6 

.00280899 

1 

.00237530 

6 

.00205761 

1 

00181488 

16 

00162338 

7 

.00280112 

2 

.00236967 

7 

.00205339 

2 

.00181159 

17 

.00162075 

8 

.00279330 

3 

.00236407 

8 

.00204918 

3 

.00180832 

18 

00161812 

9 

.00278551 

4 

.00235849 

9 

.00204499 

4 

00180505 

19 

.00161551 

360 

.00277778 

5 

.00235294 

490 

.00204082 

5 

.00180180 

620 

00161290 

1 

.00277008 

6 

.00234742 

1 

.00203666 

6 

00179856 

1 

.00161031 

2 

.00276243 

7 

.00234192 

2 

.00203252 

7 

.00179533 

2 

00160772 

3 

.00275482 

8 

.00233645 

3  .00202840 

8 

00179211 

.  3 

00160514 

4 

.00274725 

9 

.00233100 

4 

.00202429 

9 

.00178891 

4 

.00160256 

5 

.00273973 

430 

.00232558 

5 

.00202020 

560 

.00178571 

5 

00160000 

6 

.00273224 

1 

.00232019 

6 

.00201613 

1 

.00178253 

6 

.00159744 

7 

.00272480 

2 

.00231481 

7 

.00201207 

2 

.00177936 

7 

00159490 

8 

.00271739 

3 

.00230947 

8 

.00200803 

3 

.00177620 

8 

.00159236 

9 

.00271003 

4 

.00230415 

9 

.00200401 

4 

.00177305 

9 

00158982 

370 

.00270270 

5 

.00229885 

500 

.00200000 

5 

.00176991 

630 

.00158730 

1 

.00269542 

6 

.00229358 

1 

.00199601 

6 

.00176678 

1 

00158479 

2 

.00268817 

7 

.00228833 

2 

.00199203 

7 

00176367 

2 

.00158228 

^ 

.00268096 

8 

.00228310 

3 

.00198807 

8 

.00176056 

3 

00157978 

4 

.00267380 

9 

.00227790 

4 

.00198413 

9 

.00175747 

4 

.00157729 

e 

.00266667 

440 

.00227273 

5 

.00198020 

570 

.00175439 

5 

00157480 

t 

.00265957 

1 

.00226757 

6 

.00197628 

1 

00175131 

6 

.00157233 

7 

.00265252 

2 

.00226244 

7 

.00197239 

2 

.00174825 

7 

.00156986 

8 

.00264550 

3 

.00225734 

8 

.00196850 

3 

.00174520 

8 

.00156740 

9 

.00263852 

4 

.00225225 

9 

.00196464 

.00174216 

9 

.00156494 

380 

.00263158 

5 

.00224719 

510 

.00196078 

5 

.00173913 

640 

.00156250 

RECIPROCALS   OF  NUMBERS. 


89 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipnx 
cal. 

641 

.001560% 

706 

.00141643 

771 

.00129702 

836 

.00119617 

901 

.001  10988 

2 

.00155763 

7 

00141443 

2 

.00129534 

7 

.001  19474 

2 

.001  10865 

3 

.00155521 

8 

00141243 

3 

.00129366 

8 

.00119332 

3 

.00110742 

4 

.00155279 

9 

.00141044 

4 

.00129199 

9 

.00119189 

4 

.00110619 

5 

.00155039 

710 

00140345 

5 

.00129032 

840 

.00119048 

5 

.00110497 

6 

.00154799 

11 

.00140647 

6 

.00128866 

1 

.001  18906 

6 

.001  10375 

7 

.00154559 

12 

.00140449 

7 

.00128700 

2 

.001  18765 

7 

.00110254 

8 

.00154321 

13 

.00140252 

8 

.00128535 

3 

.001  18624 

8 

.00110132 

9 

.00154033 

14 

.00140056 

9 

.00128370 

4 

.00118483 

9 

.00110011 

650 

.00153846 

15 

.00139860 

780 

.00128205 

5 

.001  18343 

910 

.00109890 

1 

.00153610 

16 

.00139665 

1 

.00128041 

6 

.001  18203 

11 

.00109769 

2 

.00153374 

17 

.00139470 

2 

.00127877 

7 

.00118064 

12 

.00109649 

3 

.00153140 

18 

.00139276 

3 

.00127714 

8 

.00117924 

13 

.00109529 

4 

.00152905 

19 

.00139032 

4 

.00127551 

9 

.00117786 

14 

.00109409 

5 

.00152672 

720 

.00138889 

5 

.00127388 

850 

.00117647 

15 

.00109290 

6 

.00152439 

1 

.00138696 

6 

.00127226 

1 

.00117509 

16 

.00109170 

7 

.00152207 

2 

.00138504 

7 

.00127065 

2 

.00117371 

17 

.00109051 

8 

.00151975 

3 

.00138313 

8 

.00126904 

3 

.00117233 

18 

.00108932 

9 

.00151745 

4 

.00138121 

9 

.00126743 

4 

.001170% 

19 

00108814 

660 

.00151515 

5 

00137931 

790 

.00126582 

5 

.001  16959 

920 

.00108696 

.00151236 

6 

.00137741 

1 

.00126422 

6 

.001  16822 

1 

.00108578 

2 

.00151057 

7 

.00137552 

2 

.00126263 

7 

.001  16686 

2 

.00108460 

3 

.00150330 

8 

.00137363 

3 

.00126103 

8 

.00116550 

3 

.00108342 

4 

.00150602 

9 

.00137174 

4 

.00125945 

9 

.00116414 

4 

.00108225 

5 

.00150376 

730 

00136936 

5 

.00125786 

860 

.00116279 

5 

.00108108 

6 

.00150150 

1 

.00136799 

6 

.00125628 

1 

.00116144 

6 

.00107991 

7 

.00149925 

2 

00136612 

7 

.00125470 

2 

.00116009 

7 

.00107875 

8 

.00149701 

3 

.00136426 

8 

.00125313 

3 

.00115875 

8 

.00107759 

9 

.00149477 

4 

00136240 

9 

.00125156 

4 

.00115741 

9 

.00107.643 

670 

.00149254 

5 

.00136054 

800 

.00125000 

5 

.00115607 

930 

.00107527 

1 

.00149031 

6 

00135870 

1 

.00124844 

6 

.00115473 

1 

.00107411 

2 

.00148809 

7 

.00135685 

2 

.00124688 

7 

.00115340 

2 

.00107296 

4 

.00148588 

8 

00135501 

3 

.00124533 

8 

.00115207 

3 

.00107181 

4 

.00148368 

9 

.00135318 

4 

.00124378 

9 

.00115075 

4 

.00107066 

j 

.00148148 

740 

00135135 

5 

.00124224 

870 

.001  14942 

5 

.00106952 

( 

.00147929 

1 

.00134953 

6 

.00124069 

1 

.00114811 

6 

.00106838 

7 

.00147710 

2 

00134771 

7 

.00123916 

2 

.00114679 

7 

.00106724 

8 

.00147493 

3 

.00134589 

8 

.00123762 

3 

.00114547 

8 

.00106610 

9 

.00147275 

4 

.00134409 

9 

.00123609 

4 

.00114416 

9 

.00106496 

680 

.00147059 

c 

.00134228 

810 

.00123457 

5 

.00114286 

940 

.00106383 

1 

.00146843 

6 

00134048 

11 

.00123305 

6 

.00114155 

1 

.00]  06270 

2 

.00146628 

7 

.00133869 

12 

.00123153 

7 

.00114025 

2 

.00106157 

3 

.00146413 

8 

00133690 

13 

.00123001 

8 

.00113895 

3 

00106044 

z 

.00146199 

9 

.00133511 

14 

.00122850 

9 

.00113766 

4 

.00105932 

c 

.00145985 

750 

00133333 

15 

.00122699 

880 

.00113636 

5 

00105820 

( 

.00145773 

1 

.00133156 

16 

.00122549 

1 

.00113507 

6 

00105708 

j 

.00145560 

2 

00132979 

17 

.00122399 

2 

.00113379 

7 

00105597 

8 

.00145349 

.00132802* 

18 

.00122249 

3 

.00113250 

8 

.00105485 

9 

.00145137 

4 

00132626 

19 

.00122100 

4 

.00113122 

9 

00105374 

690 

.00144927 

c 

.00132450 

820 

.00121951 

5 

.001  12994 

950 

.00105263 

J 

.00144718 

6 

00132275 

] 

.00121803 

6 

.00  H  2867 

1 

.00105152 

4 

.00144509 

7 

.00132100 

2 

.00121654 

7 

.00112740 

2 

.00105042 

2 

.00144300 

8 

.00131926 

3 

.00121507 

8 

.00112613 

3 

.00104932 

4 

.00144092 

9 

.00131752 

4 

.00121359 

9 

.001  12486 

4 

.00104822 

c 

.00143885 

760 

.00131579 

5 

.00121212 

890 

.001  12360 

5 

.00104712 

6 

.00143678 

1 

.00131406 

6 

.00121065 

1 

.00112233 

6 

00104602 

7 

.00143472 

2 

.00131234 

7 

.00120919 

2 

.00112108 

7 

.00104493 

8 

.00143266 

3 

.00131062 

8 

.00120773 

3 

.001  1  1982 

8 

00104384 

9 

.00143061 

4 

.00130890 

9 

.00120627 

4 

00111857 

9 

.00104275 

700 

.00142857 

5 

.00130719 

830 

.00120482 

5 

.00111732 

960 

.00104167 

1 

.00142653 

6 

.00130548 

1 

.00120337 

6 

.00111607 

1 

.00104058 

2 

.00142450 

7 

00130378 

2 

.00120192 

7 

.001  1  1483 

2 

.00103950 

3 

.00142247 

8 

.00130208 

3 

.00120048 

8 

.00111359 

3 

.00103842 

4 

.00142045 

9 

.00130039 

4 

.00119904 

9 

.00111235 

4 

.00103734 

3 

.00141844 

770 

.00129870 

5 

.001  19760 

900 

.00111111 

5 

.00103627 

00 


MATHEMATICAL  TABLES. 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 

No. 

Recipro- 
cal. 

.000815661 

966 

.00103520 

1031 

.000969932 

10% 

.000912409 

1161 

.000861326 

1226 

7 

.00103413 

2 

.000968992 

7 

.000911577 

2 

.000860585 

7 

.0008149% 

8 

.00103306 

3 

.000968054 

8 

.000910747 

3 

.000859845 

8 

.000814332 

9 

.00103199 

4 

.000967118 

9 

.000909918 

4 

.000859106 

9 

.000813670 

970 

.00103093 

5 

.000966184 

1100 

.000909091 

5 

.000858369 

1230 

.000813008 

I 

.00102987 

6 

.000965251 

1 

.000908265 

6 

.000857633 

1 

.000812348 

2 

.00102881 

7 

.000964320 

2 

000907441 

7 

.000856898 

2 

.000811688 

3 

.00102775 

8 

.000963391 

3 

.000906618 

8 

.000856164 

3 

.000811030 

4 

.00102669 

9 

.000962464 

4 

.000905797 

9 

.000855432 

4 

.000810373 

5 

.00102564 

1040 

000%  1538 

5 

.000904977 

1170 

.000854701 

5 

.000809717 

6 

.00102459 

1 

.000960615 

6 

.000904159 

1 

.000853971 

6 

.000809061 

7 

.00102354 

2 

.000959693 

7 

.000903342 

2 

.000853242 

7 

.000808407 

8 

.00102250 

3 

.000958774 

8 

.000902527 

3 

.000852515 

8 

.000807754 

9 

.00102145 

4 

.000957854 

9 

.000901713 

4 

.000851789 

9 

.000807102 

980 

.00102041 

5 

.000956938 

1110 

.000900901 

5 

.000851064 

1240 

.000806452 

1 

.00101937 

6 

.000956023 

1  1 

.000900090 

6 

.000850340 

1 

.000805802 

2 

.00101833 

7 

.000955110 

12 

.000899281 

7 

.00084%  18 

2 

.000805153 

3 

.00101729 

8 

.000954198 

13 

.000898473 

8 

.0008488% 

3 

.000804505 

4 

.00101626 

9 

.000953289 

14 

.000897666 

9 

.000848176 

4 

.000803858 

5 

.00101523 

1050 

.000952381 

15 

0008%861 

1180 

.000847457 

5 

.000803213 

6 

.00101420 

1 

.000951475 

16 

.0008%057 

1 

.000846740 

6 

.000802568 

7 

.00101317 

2 

.000950570 

17 

.000895255 

2 

.000846024 

7 

.000801925 

8 

.00101215 

3 

.000949668 

18 

.000894454 

3 

000845308 

8 

.000801282 

9 

.00101112 

4 

.000948767 

191.000893655 

4 

.000844595 

9 

.000800640 

990 

.00101010 

5 

.000947867 

1120 

000892857 

5 

.000843882 

1250 

.000800000 

1 

.00100908 

6 

.000946970 

1 

.000892061 

6 

.000843170 

1 

.000799360 

2 

.00100806 

7 

.000946074 

2 

.000891266 

7 

.000842460 

2 

.000798722 

3 

.00100705 

8 

.000945180 

3 

.000890472 

8 

.000841751 

3 

.000798085 

4 

.00100604 

9 

.000944287 

4 

.00088%80 

9 

.000841043 

4 

.000797448 

5 

.00100502 

1060 

.0009433% 

5 

.000888889 

1190 

.000840336 

5 

.0007%813 

6 

.00100402 

1 

.000942507 

6 

.000888099 

1 

00083%31 

6 

.0007%  178 

7 

.00100301 

2 

.000941620 

7 

.000887311 

2 

.000838926 

7 

.000795545 

8 

.00100200 

3 

.000940734 

8 

.000886525 

3 

.000838222 

8 

.000794913 

9 

.00100100 

4 

.000939850 

9 

.000885740 

4 

.000837521 

9 

.000794281 

1000 

.00100000 

5 

.000938%7 

1130 

.000884956 

5 

.000836820 

1260 

.000793651 

1 

.000999001 

6 

000938086 

1 

.000884173 

6 

.000836120 

1 

.000793021 

2 

.000998004 

7 

.000937207 

2 

.000883392 

7 

.000835422 

2 

.000792393 

3 

.000997009 

8 

.000936330 

3 

.000882612 

8 

.000834724 

3 

.000791766 

4 

.000996016 

9 

.000935454 

4 

.000881834 

9 

.000834028 

4 

000791139 

5 

.000995025 

1070 

.000934579 

5 

.000881057 

1200 

.000833333 

5 

.000790514 

6. 

.000994036 

1 

.000933707 

6 

000880282 

] 

000832639 

6 

.000789889 

7 

.000993049 

2 

.000932836 

7 

.000879508 

2 

.000831947 

7 

.000789266 

8 

.000992063 

3 

.00093  1%6 

8 

.000878735 

3 

.000831255 

8 

.000788643 

9 

.000991080 

4 

000931099 

9 

.000877%3 

4 

.000830565 

9 

000788022 

1010 

.000990099 

5 

.000930233 

1140 

.000877193 

5 

.000829875 

1270 

.000787402 

11 

.000989120 

6 

.000929368 

1 

000876424 

6 

000829187 

1  000786782 

12 

.000988142 

7 

.000928505 

2 

.000875657 

7 

.000828500 

21.000786163 

13 

.000987167 

8 

.000927644 

3 

.000874891 

8 

.000827815 

3|.000785546 

14 

.000986193 

9 

000926784 

4 

.000874126 

9 

.000827130 

4 

000784929 

15 

.000985222 

1080 

.000925926 

5 

.000873362 

1210 

.000826446 

5 

000784314 

16 

.000984252 

1 

000925069 

6 

000872600 

11  .000825764 

6 

.UUU/tf>699 

17 

.000983284 

2 

.000924214 

7 

.000871840 

12  .000825082 

7 

.000783085 

18 

.000982318 

3 

.000923361 

8 

.000871080 

13  000824402 

8 

000782473 

19 

.000981354 

4 

.000922509 

9 

.000870322 

14 

000823723 

9 

.000781861 

1020 

.000980392 

5 

.000921659 

1150 

.000869565 

15 

.000823045 

1280 

000781250 

1 

.000979432 

6 

000920810 

1 

000868810 

161.000822368 

1 

.000780640 

2 

.000978474 

7 

.0009  19%3 

2 

.000868056 

17 

.000821693 

2 

.000780031 

3 

.000977517 

8 

.000919118 

3 

.000867303 

18 

.000821018 

3 

.000779423 

4 

.000976562 

9 

.000918274 

4 

.000866551 

19 

.000820344 

4 

.000778816 

5 

.000975610 

1090 

.000917431 

5 

.000865801 

1220 

.0008  1%72 

5 

.000778210 

6 

.000974659 

1 

.000916590 

6 

.000865052 

1 

.000819001 

6 

.000777605 

7 

.000973710 

2 

.00091575 

7 

.000864304 

2 

.000818331 

7 

.000777001 

8 

.000972763 

3 

.000914913 

8 

.000863558 

3 

.000817661 

8 

.000776397 

9 

.000971817 

4 

.00091407: 

9 

.000862813 

4 

000816993 

9 

.000775795 

1030 

.000970874 

5 

.000913242 

1160 

.000862069 

5 

.000816326 

1290 

.000775194 

RECIPROCALS   OP  NUMBERS. 


91 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 

No. 

Recipro- 

No. 

Recipro* 
cal. 

1291 

.000774593 

1356 

.000737463 

1421 

.000703730 

i486 

.000672948 

1551 

.000644745 

2 

.000773994 

7 

.000736920 

2 

.000703235 

7 

.000672495 

2 

.000644330 

3 

.000773395 

8 

.000736377 

3 

.000702741 

8 

.000672043 

? 

.000643915 

4 

.000772797 

9 

.000735835 

4 

.000702247 

g 

.000671592 

t 

.000643501 

5 

.000772201 

1360 

.000735294 

5 

.000701754 

1490 

.000671141 

c 

.000643087 

6 

.000771605 

1 

.000734754 

6 

.000701262 

1 

.000670691 

\ 

.000642673 

7 

.000771010 

2 

.000734214 

7 

.000700771 

2 

.000670241 

7 

.000642261 

8 

.000770416 

3 

.000733676 

8 

.000700280 

3 

.000669792 

8 

.000641848 

9 

.000769823 

4 

.000733138 

9 

.000699790 

4 

.000669344 

9 

.000641437 

1300 

.000769231 

5 

.000732601 

1430 

.000699301 

5 

.0006688% 

1560 

.000641026 

1 

.000768639 

6 

.000732064 

1 

.000698812 

6 

.000668449 

.000640615 

2 

.000768049 

7 

.000731529 

2 

.000698324 

7 

.000668003 

2 

.000640205 

3 

.000767459 

8 

.000730994 

3 

.000697837 

8 

.000667557 

g 

.000639795 

4 

.000766871 

9 

.000730460 

4 

.000697350 

9 

.000667111 

^ 

.000639386 

5 

.000766283 

1370 

.000729927 

5 

.000696864 

1500 

.000666667 

• 

.000638978 

6 

.000765697 

1 

.000729395 

6 

000696379 

1 

.000666223 

t 

.000638570 

7 

.000765111 

2 

.000728863 

7 

000695894 

2 

.000665779 

7 

.000638162 

8 

.000764526 

3 

.000728332 

8 

000695410 

3 

.000665336 

8 

.000637755 

9 

.000763942 

4 

.000727802 

9 

000694927 

4 

.000664894 

9 

.000637349 

1310 

.000763359 

5 

.000727273 

1440 

000694444 

5 

.000664452 

1570 

.000636943 

11 

.000762776 

6 

.000726744 

1 

000693962 

6 

.000664011 

1 

.000636537 

12 

.000762195 

7 

.000726216 

2 

000693481 

7 

.000663570 

2 

.000636132 

13 

.000761615 

8 

.000725689 

3 

000693001 

8 

.000663130 

3 

.000635728 

14 

.000761035 

9 

.000725163 

4 

000692521 

9 

.000662691 

4 

.000635324 

15 

.000760456 

1380 

.000724638 

5 

000692041 

1510 

000662252 

5 

.000634921 

16 

.000759878 

1 

.000724113 

6 

000691563 

11 

000661813 

6 

.000634518 

17 

.000759301 

2 

.000723589 

7 

000691085 

12 

000661376 

7 

.000634115 

18 

.000758725 

3 

.000723066 

8 

000690608 

13 

000660939 

8 

.000633714 

19 

.000758150 

4 

.000722543 

9 

000690131 

14 

000660502 

9 

.000633312 

1320 

.000757576 

5 

.000722022 

1450 

000689655 

15 

000660066 

580 

.000632911 

.000757002 

6 

.000721501 

1 

000689180 

16 

00065%31 

.000632511 

2 

.000756430 

7 

.000720980 

2 

000688705 

17 

0006591% 

2 

.000632111 

3 

.000755858 

8 

.000720461 

3 

000688231 

18 

000658761 

3 

000631712 

4 

.000755287 

9 

.000719942 

4 

000687758 

19 

000658328 

4 

.000631313 

5 

.000754717 

1390 

.000719424 

5 

000687285 

1520 

000657895 

5 

000630915 

6 

.000754148 

1 

.000718907 

6 

000686813 

1 

000657462 

6 

000630517 

7 

.000753579 

2 

.000718391 

7 

000686341 

2 

000657030 

7 

C00630I20 

8 

.000753012 

3 

.000717875 

8 

000685871 

3 

000656598 

8 

000629723 

9 

.000752445 

4 

.000717360 

9l  000685401 

4 

000656168 

9 

000629327 

1330 

.000751880 

5 

.000716846 

1460 

.000684932 

5 

000655738 

590 

000628931 

1 

.000751315 

6 

000716332 

1 

000684463 

6 

000655308 

1 

000628536 

2 

.000750750 

7 

.000715820 

2 

.000683994 

7 

000654879 

2 

000628141 

3 

.000750187 

8 

000715308 

3 

.000683527 

8 

000654450 

3 

000627746 

4 

.000749625 

9 

.0007147% 

4 

.000683060 

9 

000654022 

4 

000627353 

5 

.000749064 

1400 

.000714286 

5 

000682594 

1530 

000653595 

5 

000626959 

6 

.000748503 

1 

.000713776 

6 

.000682128 

1 

000653168 

6 

000626566 

7 

.000747943 

2 

.000713267 

7 

.000681663 

2 

000652742 

7 

000626174 

8 

.000747384 

3 

.000712758 

8 

.000681199 

3 

000652316 

8 

000625782 

9 

.000746826 

4 

.000712251 

9 

.000680735 

4 

000651890 

9 

000625391 

1340 

.000746269 

5 

.000711744 

1470 

.000680272 

5 

000651466 

600 

000625000 

1 

.000745712 

6 

.000711238 

1 

.000679810 

6 

000651042 

2 

000624219 

2 

.000745156 

7 

.000710732 

2 

.000679348 

7 

000650618 

4 

000623441 

3 

.000744602 

8 

.000710227 

3 

000678887 

8 

000650195 

6 

000622665 

4 

.000744048 

9 

.000709723 

4 

.000678426 

9 

000649773 

8 

000621890 

5 

.000743494 

1410 

.000709220 

5 

000677966 

1540 

000649351 

610 

000621  1  18 

6 

.000742942 

11 

.000708717 

6 

.000677507 

1 

000648929 

12 

000620347 

7 

.000742390 

12 

.000708215 

7 

.000677048 

2 

000648508 

14 

000619578 

8 

.000741840 

13 

.000707714 

8 

.000676590 

3 

000648088 

16 

000618812 

9 

.000741290 

14 

.000707214 

9 

.000676132 

4 

000647668 

18 

000618047 

1350 

.000740741 

15 

.000706714 

1480 

.000675676 

5 

000647249 

620 

000617284 

1 

.000740192 

16 

.000706215 

1 

.000675219 

6 

000646830 

2 

000616523 

2 

.000739645 

17 

.000705716 

2 

.000674764 

7 

000646412 

A 

000615763 

3 

.000739098 

18 

.000705219 

3 

.000674309 

8 

000645995 

6 

000615006 

4 

.000738552 

19  000704722 

4 

.000673854 

9 

000645578 

8 

000614250 

5 

.000738007 

1  420  1.  000704225 

5 

.000673401 

1550 

.000645161 

630 

000613497 

MATHEMATICAL  TABLES. 


No. 
"1632 

Recipro- 
cal* 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

.000612745 

1706 

.000586166 

1780 

.000561798 

1854 

.000539374 

1928 

.000518672 

4 

.00061  1995 

8 

.000585480 

2 

000561167 

6 

.000538793 

1930 

.000518135 

6 

.00061  1247 

1710 

.000584795 

4 

.000560538 

8 

.000538213 

2 

.000517599 

8 

.000610500 

12 

.0005841  12 

6 

.000559910 

1860 

.000537634 

4 

.000517063 

1640 

.000609756 

14 

.000583430 

8 

000559284 

2 

.000537057 

6 

.000516528 

2 

.000609013 

16 

.000582750 

1790 

.000558659 

4 

.000536480 

8 

.0005159% 

4 

.000608272 

18 

000582072 

2 

.000558035 

6 

.000535905 

1940 

.000515464 

6 

.000607533 

1720 

.000581395 

4 

.000557413 

8 

.000535332 

2 

.000514933 

8 

.0006067% 

2 

.000580720 

6 

.000556793 

1870 

.000534759 

4 

.000514403 

1650 

.000506061 

4 

.000580046 

8 

.000556174 

2 

.000534188 

6 

.000513874 

2 

.000605327 

6 

.000579374 

1800 

.000555556 

4 

.000533618 

8 

.000513347 

4 

.000604595 

8 

.000578704 

'2 

000554939 

6 

000533049 

1950 

.000512820 

6 

.000503865 

1730 

.000578035 

4 

.000554324 

8 

.000532481 

2 

.000512295 

8 

.000603136 

2 

.000577367 

6 

.000553710 

1880 

.000531915 

4 

.000511770 

1660 

.000602110 

4 

.000576701 

8 

.000553097 

2 

.000531350 

6 

.000511247 

2 

.000601585 

6 

.000576037 

1810 

.000552486 

4 

.000530785 

8 

.000510725 

4 

.000500962 

8 

.000575374 

12 

.000551876 

6 

.000530222 

1960 

.000510204 

6 

.000600240 

1740 

000574713 

14 

.000551268 

8 

000529661 

2 

.000509684 

8 

.000599520 

2 

.000574053 

16 

.000550661 

1890 

.000529100 

4 

.000509165 

1670 

.000598802 

4 

.000573394 

18 

.000550055 

2 

.000528541 

6 

.000508647 

2 

.000598086 

6 

.000572737 

1820 

.000549451 

4 

.000527983 

8 

.000508130 

4 

.000597371 

8 

.000572082 

2 

.000548848 

6 

.000527426 

197C 

.000507614 

6 

.000596658 

1750 

.000571429 

4 

.000548246 

8 

.000526870 

2 

.000507099 

8 

.000595947 

2 

.000570776 

6 

.000547645 

1900 

.000526316 

4 

.000506585 

1680 

.000595238 

4 

.000570125 

8 

.000547046 

2 

.000525762 

6 

.000506073 

2 

000594530 

6 

000569476 

1830 

000546448 

4 

000525210 

8 

.000505561 

4 

.000593824 

8 

.000568828 

2 

.000545851 

6 

.000524659 

1980 

.000505051 

6 

.000593120 

1760 

.000568182 

4 

.000545256 

8 

.000524109 

2 

.000504541 

8 

.000592417 

2 

.000567537 

6 

.000544662 

1910 

.000523560 

4 

.000504032 

1690 

.000591716 

4 

.000566893 

8 

.000544069 

12 

.000523012 

6 

.000503524 

2 

.000591017 

6 

.000566251 

1840 

000543478 

14 

.000522466 

8 

.000503018 

4 

.000590319 

8 

.00056561  1 

2 

.000542888 

16 

.000521920 

1990 

.000502513 

6 

.000589622 

1770 

.000564972 

4 

.000542299 

18 

.000521376 

2 

.000502008 

8 

.000588928 

2 

.000564334 

6 

.000541711 

1920 

.000520833 

4 

.000501504 

1700 

.000588235 

4 

.000563698 

8 

.000541125 

2 

.000520291 

6 

.000501002 

2 

.000587544 

6 

.000563063 

1850 

.000540540 

4 

.000519750 

8 

.000500501 

4 

.000586854 

8 

.000562430 

2 

.000539957 

6 

.000519211 

2000 

.000500000 

Use  of  reciprocals.  —  Reciprocals  may  be  conveniently  used  to  facili- 
tate computations  in  long  division.  Instead  of  dividing  as  usual,  multiply 
the  dividend  by  the  reciprocal  of  the  divisor.  The  method  is  especially 
useful  when  many  different  dividends  are  required  to  be  divided  by  the 
same  divisor.  In  this  case  find  the  reciprocal  of  the  divisor,  and  make  a 
small  table  of  its  multiples  up  to  9  times,  and  use  this  as  a  multiplication- 
table  instead  of  actually  performing  the  multiplication  in  each  case. 

EXAMPLE.  —  9871  and  several  other  numbers  are  to  be  divided  by  1638. 
The  reciprocal  of  1638  is  .000610500. 
Multiples  of  the 


reciprocal: 


1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 


.0006105 
.0012210 
.0018315 
.0024420 
.0030525 
.0036630 
.0042735 
.0048840 
.0054945 
.0061050 


The  table  of  multiples  is  made  by  continuous  addi- 
tion of  6105.     The  tenth  line  is  written  to  check  the 
accuracy  of  the  addition,  but  it  is  not  afterwards  used. 
Operation. • 

Dividend         9871 

Take  from  table  1 0006105 

7 0.042735 

8 00.48840 

9 005.4945 


Quotient 6.0262455 

Correct  quotient  by  direct  division 6.0262515 

The  result  will  generally  be  correct  to  as  many  figures  as  there  are  signi- 
ficant figures  in  the  reciprocal,  less  one,  and  the  error  of  the  next  figure  will 
in  general  not  exceed  one.  In  the  above  example  the  reciprocal  has  six 
significant  figures,  610500,  and  the  result  is  correct  to  five  places  of  figures. 


SQUARES,   CUBES,   SQUARE  AND   CUBE  ROOTS.       03 


SQUARES,  CUBES,  SQUARE  BOOTS  AND  CUBE  ROOTS  OF 
NUMBERS  FROM  0.1  TO   1600. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

0  1 

.01 

.001 

.3162 

.4642 

3.1 

9.61 

29.791 

.761 

1.458' 

.15 

.0225 

.0034 

.3873 

.5313 

.2 

10.24 

32.768 

.789 

1.474 

.2 

.04 

.008 

.4472 

.5848 

.3 

10.89 

35.937 

.817 

1.489 

.25 

.0625 

.0156 

.500 

.6300 

.4 

11.56 

39.304 

.844 

1.504 

.3 

.09 

.027 

.5477 

.6694 

.5 

12.25 

42.875 

.871 

1.518 

.35 

.1225 

.0429 

.5916 

.7047 

.6 

12.96 

46.656 

.897 

1.533 

.4 

16 

.064 

.6325 

.7368 

.7 

13.69 

50.653 

.924 

1.547 

.45 

.2025 

.0911 

.6708 

.7663 

.8 

14.44 

54.872 

.949 

1.560 

.5 

.25 

.125 

.7071 

.7937 

.9 

15.21 

59.319 

.975 

1.574 

.55 

.3025 

.1664 

.7416 

.8193 

4. 

16. 

64. 

2. 

1.5874 

.6 

.36 

.  .216 

.7746 

.8434 

.1 

16.81 

68.921 

2.025 

1.601 

.65 

.4225 

.2746 

.8062 

.8662 

.2 

17.64 

74.088 

2.049 

1.613 

.7 

.49 

.343 

.8367 

.8879 

.3 

18.49 

79.507 

2.074 

1.626 

.75 

.5625 

.4219 

.8660 

.9086 

.4 

19.36 

85..184 

2.098 

1.639 

.8 

.64 

.512 

.8944 

.9283 

.5 

20.25 

91.125 

2.121 

1.651 

.85 

.7225 

.6141 

.9219 

.9473 

.6 

21.16 

97.336 

2.145 

1.663 

.9 

.81 

.729 

.9487 

.9655 

.7 

22.09 

103.823 

2.168 

1.675 

.95 

.9025 

.8574 

.9747 

.9830 

.8 

23.04 

110.592 

2.191 

1.687 

1. 

1. 

.9 

24.01 

1  1  7.649 

2.214 

1.698 

1.05 

'.1025 

J58 

!025 

1.016 

5. 

25. 

125. 

2.2361 

1.7100 

j 

.21 

.331 

.049 

1.032 

.1 

26.01 

132.651 

2.258 

1.721 

J5 

.3225 

.521 

.072 

1.048 

.2 

27.04 

140.608 

2.280 

1.732 

.2 

.44 

728 

.095 

1.063 

.3 

28.09 

148.877 

2.302 

1.744 

.25 

•  .5625 

.953 

.118 

1.077 

.4 

29.16 

157.464 

2.324 

1.754 

.3 

.69 

2.197 

.140 

1.091 

.5 

30.25 

166.375 

2.345 

1.765 

.35 

.8225 

2.460 

.162 

1.105 

.6 

31.36 

175.616 

2.366 

1.776 

.4 

.96 

2.744 

.183 

1.119 

.7 

32.49 

185.193 

2.387 

1.786 

.45 

2.1025 

3.049 

.204 

1.132 

.8 

33.64 

195.112 

2.408 

1.797 

.5 

2.25 

3.375 

.2247 

1.1447 

.9 

34.81 

205.379 

2.429 

1.807 

.55 

2.4025 

3.724 

.245 

1.157 

6. 

36. 

216. 

2.4495 

1.8171 

.6 

2.56 

4.096 

.265 

1.170 

.1 

37.21 

226.981 

2.470 

1.827 

.65 

2.7225 

4.492 

.285 

K182 

.2 

38.44 

238.328 

2.490 

1.837 

.7 

2.89 

4.913 

.304 

1.193 

.3 

39.69 

250.047 

2.510 

1.847 

.75 

3.0625 

5.359 

.323 

1.205 

.4 

40.96 

262.144 

2.530 

1.857 

.8 

3.24 

5.832 

.342 

1.216 

.5 

42.25 

274.625 

2.550 

1.866 

1.85 

3.4225 

6.332 

.360 

1.228 

.6 

43.56 

287.496 

2.569 

1.876 

1.9 

3.61 

6.859 

.378 

1.239 

.7 

44.89 

300.763 

2.588 

1.885 

1.95 

3.8025 

7.415 

.396 

1.249 

.8 

46.24 

314.432 

2.608 

1.895 

2. 

4. 

8. 

.4142 

1  .2599 

.9 

47.61 

328.509 

2.627 

1.904 

.1 

4.41 

9.261 

.449 

1.281 

7. 

49. 

343*. 

2.6458 

1.9129 

.2 

4.84 

10.648 

.483 

1.301 

j 

50.41 

357.911 

2.665 

1.922 

.3 

5.29 

12.167 

.517 

1.320 

\2 

51.84 

373.248 

2.683 

1.931 

.4 

5.76 

13.824 

.549 

1.339 

.3 

53.29 

389.017 

2.702 

1.940 

.5 

6.25 

15.625 

.581 

1.357 

.4 

54.76 

405.224 

2.720 

1.949 

.6 

6.76 

17.576 

.612 

1.375 

.5 

56.25 

421.875 

2.739 

1.957 

.7 

7.29 

19.683 

.643 

1.392 

.6 

57.76 

438.976 

2.757 

1.966 

.8 

7.84 

21.952 

.673 

1.409 

.7 

59.29 

456.533 

2.775 

1.975 

.9 

8.41 

24.389 

.703 

1.426 

.8 

60.84 

474.552 

2.793 

1.983 

3. 

• 

9. 

27. 

.7321 

1  .4422 

.9 

62.41 

493.039 

2.811 

1.992 

94 


MATHEMATICAL  TABLES. 


No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root, 

sT~ 

64. 

512. 

2.8284 

2. 

45 

2025 

91123 

6.7082 

3.5569 

65.61 

531.441 

2.846 

2.008 

46 

2116 

97336 

6.7823 

3.5830 

\2 

67.24 

551.368 

2.864 

2.017 

47 

2209 

103823 

6.8557 

3.6088 

.3 

68.89 

571.787 

2.881 

2.025 

48 

2304 

110592 

6.9282 

3.6342 

.4 

70.56 

592.704 

2.898 

2.033 

49 

2401 

1  1  7649 

7. 

3.6593 

.5 

72.25 

614.125 

2.915 

2.041 

50 

2500 

125000 

7.0711 

3.6840 

.6 

73.96 

636.056 

2.933 

2.049 

51 

2601 

132651 

7.1414 

3.7084 

.7 

75.69 

658.503 

2.950 

2.057 

52 

2704 

140608 

7.2111 

3.7325 

.8 

77.44 

681.472 

2.966 

2.065 

53 

2809 

148877 

7.2801 

3.7563 

.9 

79.21 

704.969 

2.983 

2.072 

54 

2916 

]  57  464 

7.3485 

3.7798 

9. 

81. 

729. 

3. 

2.0801 

55 

3025 

166375 

7.4162 

3.8030 

.1 

82.81 

753.571 

3.017 

2.088 

56 

3136 

175616 

7.4833 

3.8259 

.2 

84.64 

778.688 

3.033 

2.095 

57 

3249 

185193 

7.5498 

3.8485 

.3 

86.49 

804.357 

3.050 

2.103 

58 

3364 

195112 

7.6158 

3.8709 

.4 

88.36 

830.584 

3.066 

2.110 

59 

3481 

205379 

7.6811 

3.8930 

.5 

90.25 

857.375 

3.082 

2.118 

60 

3600 

216000 

7.7460 

3.9149 

.6 

92.16 

884.736 

3.098 

2.125 

61 

3721 

226981 

7.8102 

3.9365 

.7 

94.09 

912.673 

3.114 

2.133 

62 

3844 

238328 

7.8740 

3.9579 

.8 

96.04 

941.192 

3.130 

2.140 

63 

3969 

250047 

7.9373 

3.9791 

.9 

98.01 

970.299 

3.146 

2.147 

64 

4096 

262144 

8. 

4. 

10 

100 

1000 

3.1623 

2.1544 

65 

4225 

274625 

8.0623 

4.0207 

11 

121 

1331 

3.3166 

2.2240 

66 

4356 

287496 

8.1240 

4.0412 

12 

144 

1728 

3.4641 

2.2894 

67 

4489 

300763 

8.1854 

4.0615 

13 

169 

2197 

3.6056 

2.3513 

68 

4624 

314432 

8.2462 

4.0817 

14 

196 

2744 

3.7417 

2.4101 

69 

4761 

328509 

8.3066 

4.1016 

15 

225 

3375 

3.8730 

2.4662 

70 

4900 

343000 

8.3666 

4.1213 

16 

256 

4096 

4. 

2.5198 

71 

5041 

357911 

8.4261 

4.1408 

17 

289 

4913 

4.1231 

2.5713 

72 

5184 

373248 

8.4853 

4.1602 

18 

324 

5832 

4.2426 

2.6207 

73 

5329 

389017 

8.5440 

4.1793 

19 

361 

6859 

4.3589 

2.6684 

74 

5476 

405224 

8.6023 

4.1983 

20 

400 

8000 

4.4721 

2.7144 

75 

5625 

421875 

8.6603 

4.2172 

21 

441 

9261 

4.5826 

2.7589 

76 

5776 

438976 

8.7178 

4.2358 

22 

484 

10648 

4.6904 

2.8020 

77 

5929 

456533 

8.7750 

4.2543 

23 

529 

12167 

4.7958 

2.8439 

78 

6084 

474552 

8.8318 

4.2727 

24 

576 

13824 

4.8990 

2.8845 

79 

6241 

493039 

8.8882 

4.2908 

25 

625 

15625 

5. 

2.9240 

80 

6400 

5.12000 

8.9443 

4.3089 

26 

676 

17576 

5.0990 

2.9625 

81 

6561 

531441 

9. 

4.3267 

27 

729 

19683 

5.1962 

3. 

82 

6724 

551368 

9.0554 

4.3445 

28 

784 

21952 

5.2915 

3.0366 

83 

6889 

571787 

9.1104 

4.3621 

29 

841 

24389 

5.3852 

3.0723 

84 

7056 

592704 

9.1652 

4.3795 

30 

900 

27000 

5.4772 

3.1072 

85 

7225 

614125 

9.2195 

4.3968 

31 

961 

29791 

5.5678 

3.1414 

86 

7396 

636056 

9.2736 

4.4140 

32 

024 

32768 

5.6569 

3.1748 

87 

7569 

658503 

9.3276 

4.4310 

33 

089 

35937 

5.74^6 

3.2075 

88 

7744 

681472 

9.3808 

4.4480 

34 

156 

39304' 

5.8310 

3.2396 

89 

7921 

704969 

9.4340 

4.4647 

35 

225 

42875 

5.9161 

3.2711 

90 

8100 

729000 

9.4868 

4.4814 

36 

296 

46656 

6. 

3.3019 

91 

8281 

753571 

9.5394 

4.4979 

37 

369 

50653 

6.0828 

3.3322 

92 

8464 

778688 

9.5917 

4.5144 

38 

444 

54872 

6.1644 

3.3620 

93 

8649 

804357 

9.6437 

4.5307 

39 

521 

59319 

6.2450 

3.3912 

94 

8836 

830584 

9.6954 

4.5468 

40 

600 

64000 

6.3246 

3.4200 

95 

9025 

857375 

9.7468 

4.5629 

41 

681 

68921 

64031 

3.4482 

96 

9216 

884736 

9.7980 

4.5789 

42 

764 

74088 

6.4807 

3.4760 

97 

9409 

912673 

98489 

4.5947 

43 

849 

79507 

6.5574 

3.5034 

98 

9604 

941  192 

9.8995 

4.6104 

44 

936 

85184 

6.6332 

3.5303 

99 

9801 

970299j 

9.9499 

4.6261 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.   95 


No. 

Sq. 

Cube 

Sq. 

Root. 

Cube 
Root. 

No. 

Square. 

Cube.. 

Sq. 
Root. 

Cube 
Root. 

Too" 

10000 

1000000 

10. 

4.6416 

155 

24025 

3723875 

12.4499 

5.3717 

101 

10201 

1030301 

10.0499 

4.6570 

156 

24336 

3796416 

12.4900 

5.3832 

102 

10404 

1061208 

10.0995 

4.6723 

157 

24649 

3869893 

12.5300 

5.3947 

103 

10609 

1092727 

10.1489 

4.6875 

158 

24964 

3944312 

12.5698 

5  4061 

104 

10816 

1124864 

10.1980 

4.7027 

159 

25281 

4019679 

12.6095 

5.4175 

105 

11025 

1157625 

10.2470 

4.7177 

160 

25600 

4096000 

12.6491 

5.4288 

106 

11236 

1191016 

10.2956 

4.7326 

161 

25921 

4173281 

12.6886 

5.4401 

107 

11449 

1225043 

10.3441 

4.7475 

162 

26244 

425  1  528 

12.7279 

5.4514 

10S 

11664 

1259712 

10.3923 

4.7622 

163 

26569 

4330747 

12.7671 

5.^26 

109 

11881 

1295029 

10.4403 

4.7769 

164 

26896 

4410944 

12.8062 

5.W37 

110 

12100 

1331000 

10.4881 

4.7914 

165 

27225 

4492125 

12.8452 

5.4848 

1  1  1 

12321 

1367631 

10.5357 

4.8059 

166 

27556 

4574296 

12.8841 

5.4959 

112 

12544 

1404928 

10.5830 

4.8203 

167 

27889 

4657463 

12.9228 

5.5069 

113 

12769 

1442897 

10.6301 

4.8346 

168 

28224 

4741632 

12.9615 

5.5178 

114 

12996 

1481544 

10.6771 

4.8488 

169 

28561 

4826809 

13.0000 

5.5288 

115 

13225 

1  520875 

10.7238 

4.8629 

170 

28900 

4913000 

13.0384 

5.5397 

116 

13456 

1560896 

10.7703 

4.8770 

171 

29241 

5000211 

13.0767 

5.5505 

117 

13689 

1601613 

10.8167 

4.8910 

172 

29584 

5088448 

13.1149 

5.5613 

118 

13924 

1643032 

10.8628 

4.9049 

173 

29929 

5177717 

13.1529 

5.5721 

119 

14161 

1685159 

10.9087 

4.9187 

174 

30276 

5268024 

13.1909 

5.5828 

120 

14400 

1728000 

10.9545 

4.9324 

175 

30625 

5359375 

13.2288 

5.5934 

121 

14641 

1771561 

1  1  .0000 

4.9461 

176 

30976 

5451776 

13.2665 

5.6041 

122 

14884 

1815848 

1  1  .0454 

4.9597 

177 

31329 

5545233 

13.3041 

5.6147 

123 

15129 

1860867 

1  1  .0905 

4.9732 

178 

31684 

5639752 

13.3417 

5.6252 

124 

15376 

1906624 

11.1355 

4.9866 

179 

32041 

5735339 

13.3791 

5.6357 

125 

15625 

1953125 

11.1803 

5.0000 

180 

32400 

5832000 

13.4164 

5.6462 

126 

15876 

2000376 

11.2250 

5.0133 

181 

32761 

5929741 

13.4536 

5.6567 

127 

16129 

2048383 

1  1  .2694 

5.0265 

182 

33124 

6028568 

13.4907 

5.6671 

12S 

16384 

2097152 

11.313" 

5.0397 

183 

33489 

6128487 

13.5277 

5.6774 

129 

16641 

2146689 

11.3578 

5.0528 

184 

33856 

6229504 

13.5647 

5.6873 

130 

16900 

2197000 

11.4018 

5.0658 

185 

34225 

6331625 

13.6015 

5.6980 

131 

17161 

2248091 

11.4455 

5.0788 

186 

34596 

6434856 

13.6382 

5.7083 

132 

17424 

2299963 

11.4891 

5.0916 

187 

34969 

6539203 

13.6748 

5.7185 

133 

17689 

2352637 

11.5326 

5.1045 

188 

35344 

6644672 

13.7113 

5.7287 

134 

17956 

2406104 

11.5758 

5.1172 

189 

35721 

6751269 

13.7477 

5.7388 

135 

18225 

2460375 

11.6190 

5.1299 

190 

36100 

6859000 

13.7840 

5.7489 

136 

18496 

2515456 

11.6619 

5.1426 

191 

36481 

6967871 

13.8203 

5.7590 

137 

18769 

2571353 

11.7047 

5.1551 

192 

36864 

7077888 

13.8564 

5.7690 

138 

19044 

2628072 

11.7473 

5.1676 

193 

37249 

7189057 

13.8924 

5.7790 

139 

19321 

2685619 

11.7898 

5.1801 

194 

37636 

7301384 

13.9284 

5.7890 

140 

19600 

2744000 

11.8322 

5.1925 

195 

38025 

7414875 

13.9642 

5.7989 

141 

19331 

2803221 

11.8743 

5.2048 

196 

38416 

7529536 

14.0000 

5.8088 

142 

20164 

2863288 

11.9164 

5.2171 

1.97 

38809 

7645373 

14.0357 

5.8186 

143 

20449 

2924207 

1  1  .9583 

'5.2293 

198 

39204 

7762392 

14.0712 

5.8285 

144 

20736 

2985984 

12.0000 

5.2415 

199 

39601 

7880599 

14.1067 

5.8383 

145 

21025 

3048625 

120416 

5.2536 

200 

40000 

8000000 

14.1421 

5.8480 

146 

21316 

3112136 

12.0830 

5.2656 

201 

40401 

8120601 

14.1774 

5.8578 

147 

21609 

3176523 

12.1244 

5.2776 

202 

40804 

8242408 

14.2127 

5.8675 

148 

21904 

3241792 

12  1655 

5.2896 

203 

41209 

8365427 

14.2478 

5.8771 

149 

22201 

3307949 

12.2066 

5.3015 

204 

41616 

8489664 

14.2829 

5.8868 

150 

22500 

3375000 

12.2474 

5.3133 

205 

42025 

8615125 

14.3178 

5.8964 

151 

22801 

344295  1 

12.2882 

5.3251 

206 

42436 

8741816 

14.3527 

5.9059 

152 

23104 

3511808 

12.3288 

5.3368 

207 

42849 

8869743 

14.3875 

5.9155 

153 

23409 

3581577 

12.3693 

5.3485 

208 

43264 

8998912 

14.4222 

5.9250 

154  23716 

3652264 

12.4097 

5.3601 

209 

43681 

9129329 

14.4568 

5.9345 

96 


MATHEMATICAL  TABLES. 


No. 

Sq. 

Cube. 

Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

2H)" 

44100 

9261000 

14.4914 

5.9439 

265 

70225 

18609625 

16.2788 

6.4232 

211 

44521 

939393  1 

14.5258 

5.9533 

266 

70756 

18821096 

16.3095 

6.4312 

212 

44944 

9528128 

14.5602 

5.9627 

267 

71289 

19034163 

16.3401 

6.4393 

213 

45369 

9663597 

14.5945 

5.9721 

268 

71824 

19248832 

16.3707 

6.4473 

214 

45796 

9800344 

14.6287 

5.9814 

269 

72361 

19465109 

16.4012 

6.4553 

215 

46225 

9938375 

14.6629 

5.9907 

270 

72900 

19683000 

16.4317 

6.4633 

216 

46656 

10077696 

14.6969 

6.0000 

271 

73441 

19902511 

16.4621 

6.4713_ 

217 

47089 

1  02  1  83  1  3 

14.7309 

6.0092 

272 

73984 

20123648 

16.4924 

6.4792 

21S 

47524 

10360232 

14.7648 

6.0185 

273 

74529 

20346417 

16.5227 

6.4872 

1 

47961 

10503459 

14.7986 

6.0277 

274 

75076 

20570824 

16.5529 

6.4951 

220 

48400 

10648000 

14.8324 

6.0368 

275 

75625 

20796875 

16.5831 

6.5030 

221 

48841 

10793861 

14.8661 

6.0459 

276 

76176 

21024576 

16.6132 

6.5108 

222 

49284 

1  094  1  048 

14.8997 

6.0550 

277 

76729 

21253933 

16.6433 

6.5187 

223 

49729 

11089567 

14.9332 

6.0641 

278 

77284 

21484952 

16.6733 

6.5265 

224 

50176 

11239424 

14.9666 

6.0732 

279 

77841 

21717639 

16.7033 

6.5343 

225 

50625 

11390625 

15.0000 

6.0822 

280 

78400 

21952000 

16.7332 

6.5421 

226 

51076 

11543176 

15.0333 

6.0912 

281 

78961 

22188041 

16.7631 

6.5499 

227 

51529 

11697083 

15.0665 

6.1002 

282 

79524 

22425768 

16.7929 

6.5577 

228 

51984 

11852352 

15.0997 

6.1091 

283 

80089 

22665187 

16.8226 

6.5654 

229 

52441 

12008989 

15.1327 

6.1180 

284 

80656 

22906304 

16.8523 

6.5731 

230 

52900 

12167000 

15.1658 

6.1269 

285 

81225 

23149125 

16.8819 

6.5808 

231 

53361 

12326391 

15.1987 

6.1358 

286 

81796 

23393656 

16.9115 

6.5885 

232 

53824 

12487168 

15.2315 

6.  1  446 

287 

82369 

23639903 

16.9411 

6.5962 

233 

54289 

12649337 

15.2643 

6.1534 

288 

82944 

23887872 

16.9706 

6.6039 

234 

54756 

12812904 

15.2971 

6.1622 

289 

83521 

24137569 

17.0000 

6.6115 

235 

55225 

12977875 

15.3297 

6.1710 

290 

84100 

24389000 

17.0294 

6.6191 

236 

55696 

13144256 

15.3623 

6.1797 

291 

84681 

24642171 

17.0587 

6.6267 

237 

56169 

13312053 

153948 

6.1885 

292 

85264 

24897088 

17.0880 

6.6343 

238 

56644 

13481272 

15.4272 

6.1972 

293 

85849 

25153757 

17.1172 

6.6419 

239 

57121 

13651919 

15.4596 

6.2058 

294 

86436 

25412184 

17.1464 

6.6494 

240 

57600 

13824000 

15.4919 

6.2145 

295 

87025 

25672375 

17.1756 

6.6569 

241 

58081 

13997521 

15.5242 

6.223  1 

296 

87616 

25934336 

17.2047 

6.6644 

242 

58564 

14172488 

15.5563 

6.2317 

297 

88209 

26198073 

17.2337 

6.6719 

243 

59049 

14348907 

15.5885 

6.2403 

298 

88804 

26463592 

17.2627 

6.6794 

244 

59536 

14526784 

15.6205 

6.2488 

299 

89401 

26730899 

17.2916 

6.6869 

245 

60025 

14706125 

15.6525 

6.2573 

300 

90000 

27000000 

17.3205 

6.6943 

246 

60516 

14886936 

15.6844 

6.2658 

301 

90601 

27270901 

17.3494 

6.7018 

247 

61009 

1  5069223 

15.7162 

6.2743 

302 

91204 

27543608 

17.3781 

6.7092 

248 

61504 

15252992 

15.7480 

6.2828 

303 

91809 

27818127 

17.4069 

6.7166 

249 

62001 

15438249 

15.7797 

6.2912 

304 

92416 

28094464 

17.4356 

6.7240 

250 

62500 

1  5625000 

15.8114 

6.2996 

305 

93025 

28372625 

1  7.4642 

6.7313 

251 

63001 

15813251 

15.8430 

6.3080 

306 

93636 

28652616 

17.4929 

6.7387 

252 

63504 

16003008 

15.8745 

6.3164 

307 

94249 

28934443 

17.5214 

6.7460 

253 

64009 

16194277 

15.9060 

6.3247 

308 

•  94864 

29218112 

17.5499 

6.7533 

254 

64516 

16387064 

15.9374 

6.3330 

309 

95481 

29503629 

17.5784 

6.7606 

255 

65025 

16581375 

15.9687 

6.3413 

310 

96100 

29791000 

1  7.6068 

6.7679 

256 

65536 

16777216 

16.0000 

6.3496 

311 

96721 

3008023  1 

17.6352 

6.7752 

257 

66049 

16974593 

16.0312 

6,3579 

312 

97344 

30371328 

17.6635 

6.7824 

258 

66564 

17173512 

16.0624 

6.3661 

313 

97969 

30664297 

17.6918 

6.7897 

259 

67081 

17373979 

16.0935 

6.3743 

314 

98596 

30959144 

17.7200 

6.7969 

260 

67600 

17576000 

16.1245 

6.3825 

315 

99225 

31255875 

17.7482 

6.8041 

261 

68121 

17779581 

16.1555 

63907 

316 

99856 

31554496 

17.7764 

6.8113 

262 

68644 

1  7984728 

16.1864 

6.3988 

317 

100489 

31855013 

17.8045 

6.8185 

263 

69169 

18191447 

16.2173 

6.4070 

318 

101124 

32157432 

17.8326 

6.8256 

264 

69696 

18399744  16.2481 

6.4151 

319 

101761 

32461759 

17.8606 

6.8328 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.   97 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

320 

102400 

32768000 

17.8885 

6.8399 

375 

1  40625 

52734375 

19.3649 

7.2112 

321 

103041 

33076161 

17.9165 

6.8470 

376 

141376 

53157376 

19.3907 

7.2177 

322 

1  03684 

33386248 

17.9444 

6.8541 

377 

142129 

53582633 

19.4165 

7.2240 

323 

104329 

33698267 

17.9722 

6.8612 

378 

1  42884 

54010152 

1  9.4422 

7.2304 

324 

104976 

34012224 

18.0000 

6.8683 

379 

143641 

54439939 

19.4679 

7.2368 

325 

105625 

34328125 

18.0278 

6.8753 

380 

1  44400 

54872000 

1  9.4936 

7.2432 

326 

106276 

34645976 

18.0555 

6.8824 

381 

145161 

55306341 

19.5192 

72495 

327 

106929 

34965783 

18.0831 

6.8894 

382 

145924 

55742968 

19.5448 

7.2558 

328 

107584 

35287552 

18.1108 

6.8964 

383 

1  46689 

56181887 

19.5704 

7.2622 

329 

108241 

35611289 

18.1384 

6.9034 

384 

147456 

56623104 

19.5959 

7.2685 

330 

108900 

35937000 

18.1659 

6.9104 

385 

148225 

57066625 

19.6214 

7.2748 

331 

109561 

36264691 

18.1934 

6.9174 

386 

1  48996 

57512456 

19.6469 

7.2811 

332 

110224 

36594368 

18.2209 

6.9244 

387 

149769 

57960603 

19.6723 

7.2874 

333 

110889 

36926037 

18.2483 

6.9313 

388 

150544 

58411072 

19.6977 

7.2936 

334 

111556 

37259704 

18.2757 

6.9382 

389 

151321 

58863869 

19.7231 

7.2999 

335 

112225 

37595375 

18.3030 

6.9451 

390 

152100 

59319000 

19.7484 

7.306! 

336 

1  1  2896 

37933056 

18.3303 

6.9521 

391 

152881 

59776471 

19.7737 

7.3124 

337 

113569 

38272753 

183576 

6.9589 

392 

153664 

60236288 

19.7990 

7.3186 

338 

114244 

38614472 

18.3848 

6.9658 

393 

1  54449 

60698457 

1  9.8242 

7.3248 

339 

114921 

38958219 

18.4120 

6.9727 

394 

155236 

61162984 

1  9.8494 

7.3310 

340 

1  1  5600 

39304000 

18.4391 

6.9795 

395 

156025 

61629875 

19.8746 

7.3372 

341 

116281 

39651821 

18.4662 

6.9864 

396 

156816 

62099136 

1  9.8997 

7.3434 

342 

116964 

40001688 

18.4932 

6.9932 

397 

157609 

62570773 

19.9249 

7.3496 

343 

1  1  7649 

40353607 

18.521)3 

7.0000 

398 

1  58404 

63044792 

19.9499 

7.35*8 

344 

118336 

40707584 

18.5472 

7.0068 

399 

159201 

63521199 

19.9750 

7.361$ 

345 

119025 

41063625 

18.5742 

7.0136 

400 

1  60000 

64000000 

20.0000 

7.3681 

346 

119716 

41421736 

18.6011  7.0203 

401 

160801 

64481201 

20.0250 

7.3742 

347 

120409 

41781923 

18.62797.0271 

402 

161604 

64964808 

20.0499 

7.3803 

348 

121104 

42144192 

18.6548 

7.0338 

403 

162409 

65450827 

20.0749 

7.3864 

349 

121801 

42508549 

18.6815 

7.0406 

404 

163216 

65939264 

20.0998 

7.3925 

350 

122500 

42875000 

18.7083 

7.0473 

405 

164025 

66430125 

20.1246 

7.3986 

351 

123201 

43243551 

18.7350 

7.0540 

406 

164836 

66923416 

20.1494 

7.4047 

352 

123904 

43614208 

18.7617 

7.0607 

407 

165649 

67419143 

20.1742 

7.4108 

353 

124609 

43986977 

18.7883 

7.0674 

408 

166464 

67917312 

20.1990 

7.4169 

354 

125316 

44361864 

18.8149 

7.0740 

409 

167281 

68417929 

20.2237 

7.4229 

355 

126025 

44738875 

18.8414 

7.0807 

410 

168100 

68921  COO 

202485 

7.4290 

356 

126736 

45118016 

18.8680 

7.0873 

411 

168921 

69426531 

20.2731 

7.4350 

357 

127449 

45499293 

18.8944 

7.0940 

412 

1  697  44 

69934528 

20.2978 

7.4410 

358 

128164 

45882712 

18.9209 

7.1006 

413 

170569 

70444997 

20.3224 

7.4470 

359 

128881 

46268279 

18.9473 

7.1072 

414 

171396 

70957944 

20.3470 

7.4530 

360 

129600 

46656000 

189737 

7.1138 

415 

172225 

71473375 

20.3715 

7.4590 

361 

130321 

47045881 

19.0000 

7.1204 

416 

173056 

71991296 

20.3961 

7.4650 

362 

131044 

47437928 

19.0263 

7.1269 

417 

1  73889 

72511713 

20.4206 

7.4710 

363 

131769 

47832147 

19.0526 

7.1335 

418 

1  74724 

73034632 

20.4450 

7.4770 

364 

132496 

48228544 

19.0788 

7.1400 

419 

175561 

73560059 

20.4695 

7.4829 

365 

133225 

48627125 

19.1050 

7.1466 

420 

1  76400 

74088000 

20.4939 

74889 

366 

133956 

49027896 

19.1311 

7.1531 

421 

177241 

74618461 

20.5183 

7.4948 

367 

134689 

49430863 

19.1572 

7.1596 

422 

1  78084 

75151448 

20.5426 

7.5007 

368 

135424 

49836032 

19.1833 

7.1661 

423 

1  78929 

75686967 

20.5670 

7.5067 

369 

136161 

50243409 

19.2094 

7.1726 

424 

179776 

76225024 

20.5913 

7.5126 

370 

1  36900 

50653000 

19.2354 

7.1791 

425 

180625 

76765625 

20.6155 

7.5185 

371 

137641 

51064811 

19.2614 

7.1855 

426 

18M76 

77308776 

20  6398 

7  5244 

372 

138384 

51478848 

19.2873 

7.1920 

427 

182329 

77854483 

20.6640 

7  5302 

373 

374 

139129 
139876 

51895117  19313217  1984 
52313624  19.3391  '7.2048 

428 
429 

183184 
184041 

78402752 
78953589 

20.6882 
20.7123 

7.5361 
7.5420 

'98 


MATHEMATICAL  TABLES. 


No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

430 
431 
432 
433 
434 

184900 
185761 
186624 
187489 
188356 

79507000 
80062991 
80621568 
81182737 
81746504 

20.7364 
20.7605 
20.7846 
20.8087 
20.8327 

7.5478 
7.5537 
7.5595 
7.5654 
7.5712 

485 
486 
487 
488 
489 

235225 
236196 
237169 
238144 
239121 

114084125 
114791256 
115501303 
116214272 
116930169 

22.0227 
22.0454 
22.0681 
22.0907 
22.1133 

7.8568 
7.8622 
7.8676 
7.8730 
7.8784 

435 
436 
437 
438 
439 

189225 
190096 
1  90969 
191844 
192721 

82312875 
82881856 
83453453 
84027672 
846045  1  9 

20.8567 
20.8806 
20.9045 
20.9284 
20.9523 

7.5770 

7.5828 
7.5886 
7.5944 
76001 

490 
491 
492 
493 
494 

240100 
241081 
242064 
243049 
244036 

1  1  7649000 
118370771 
119095488 
119823157 
120553784 

22.1359 
22.1585 
22.1811 
22.2036 
22.2261 

7.8837 
7.8891 
7.8944 
7.8998 
7.9051 

440 
441 
442 
443 
444 

193600 
194481 
195364 
196249 
197136 

85184000 
85766121 
86350888 
86938307 
87528384 

20.9762 
21.0000 
21.0238 
21.0476 
21.0713 

7.6059 
7.6117 
7.6174 
7.6232 
7.6289 

495 
496 
497 
498 
499 

245025 
246016 
247009 
248004 
249001 

121287375 
122023936 
122763473 
123505992 
124251499 

22.2486 
22.2711 
22.2935 
22.3159 
22.3383 

7.9105 
7.9158 
7.9211 
7.9264 
7.9317 

445 
446 
447 
448 
449 

198025 
198916 
199809 
200704 
201601 

88121125 
88716536 
893  1  4623 
89915392 
90518849 

21  0950 
21.1187 
21.1424 
21.1660 
21.1896 

7.6346 
7.6403 
7.6460 
7.6517 
7.6574 

500 
501 
502 
503 
504 

250000 
251001 
252004 
253009 
254016 

125000000 
125751501 
1  26506008 
127263527 
128024064 

22.3607 
22.3830 
22.4054 
22.4277 
22.4499 

7.9370 
7.9423 
7.9476 
7.9528 
7.9581 

450 
451 
452 
453 
454 

202500 
203401 
204304 
205209 
206116 

91125000 
91733851 
92345408 
92959677 
93576664 

21.2132 
21.2368 
21.2603 
21.2838 
21.3073 

7.6631 
7.6688 
7.6744 
7.6800 
7.6857 

505 
506 
507 
508 
509 

255025 
256036 
257049 
258064 
259081 

128787625 
129554216 
130323843 
131096512 
131872229 

22.4722 
22.4944 
22.5167 
22.5389 
22.5610 

7.9634 
7.9686 
79739 
7.9791 
7.9843 

455 
456 
457 
458 
459 

207025 
207936 
208849 
209764 
210681 

94196375 
94818816 
95443993 
96071912 
96702579 

21.3307 
21.3542 
21.3776 
21.4009 
21.4243 

7.6914 
7.6970 
7.7026 
7.7082 
7.7138 

510 
511 
512 
513 
514 

260100 
261121 
262144 
263169 
264196 

132651000 
133432831 
134217728 
135005697 
135796744 

22.5832 
22.6053 
22.6274 
22.6495 
22.6716 

7.9896 
7.9948 
8.0000 
8.0052 
8.0104 

460 
461 
462 
463 
464 

211600 
212521 
213444 
214369 
215296 

97336000 

97972181 
98611128 
99252847 
99897344 

21.4476 
21.4709 
21.4942 
21.5174 
21.5407 

7.7194 
7.7250 
7.7306 
7.7362 
7.7418 

515 
516 
517 
518 
519 

265225 
266256 
267289 
268324 
269361 

136590875 
137388096 
138188413 
138991832 
139798359 

22  6936 
22.7156 
22.7376 
22.7596 
22.7816 

8.0156 
8.0208 
8.0260 
8.0311 
8.0363 

465 
466 
467 
468 
469 

216225 
217156 
218089 
219024 
219961 

100544625 
101194696 
101847563 
102503232 
103161709 

21.5639 
21.5870 
21.6102 
21.6333 
21.6564 

7.7473 
7.7529 
7.7584 
7.7639 
7.7695 

520 
521 
522 
523 
524 

270400 
271441 
272484 
273529 
274576 

140608000 
141420761 
142236648 
143055667 
143877824 

22.8035 
22.8254 
22.8473 
22.8692 
22.8910 

8.0415 
8.0466 
8.0517 
8.0569 
8.0620 

470 
471 
472 
473 
474 

220900 
221841 
222784 
223729 
224676 

103823000 
104487111 
105154048 
105823817 
106496424 

21.6795 
21.7025 
21.7256 
21.7486 
21.7715 

7.7750 
7.7805 
7.7860 
7.7915 
7.7970 

525 
526 
527 

528 
529 

275625 
276676 
277729 

278784 
279841 

144703125 
145531576 
146363183 
147197952 
148035889 

22.9129 
22.9347 
22.9565 
22.9783 
23.0000 

8.0671 
8.0723 
8.0774 
8.0825 
8.0876 

475 
476 
477 
478 
479 

225625 
226576 
227529 
228484 
22944  1 

107171875 
107850176 
108531333 
109215352 
109902239 

21.7945 
21.8174 
21  8403 
21.8632 
21.8861 

7.8025 
7.8079 
7.8134 
7.8188 
7.8243 

530 
531 
532 
533 
534 

280900 
281961 
283024 
284089 
285156 

148877000 
149721291 
1  50568768 
151419437 
152273304 

23.0217 
23.0434 
23.0651 
23  0868 
23.1084 

80927 
8.0978 
8.1028 
8.1079 
8.1130 

480 
481 
482 
483 
484 

230400 
231361 
232324 
233289 
234256 

110592000 
111284641 
111980168 
112678587 
1  13379904 

21.9089 
21.9317 
21.9545 
21.9773 
22.0000 

7.8297 
7.8352 
7.8406 
7.8460 
7.8514 

535 
536 
537 
538 
539 

286225 
287296 
288369 
289444 
290521 

153130375 
1  53990656 
154854153 
155720S72 
156590819 

23.1301 
23.1517 
23.1733 
23.1948 
23.2164 

8.1180 
8.123! 
8.128! 
8.1332 
8.1332 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.   99 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

540 
541 
542 
543 
544 

291600 
292681 
293764 
294849 
295936 

157464000 
158340421 
159220088 
160103007 
160989184 

23.2379 
23.2594 
23.2809 
23.3024 
23.3238 

8.1433 
8.1483 
8.1533 
8.1583 
8.1633 

595 

596 
597 
598 
599 

354025 
355216 
356409 
357604 
358801 

210644875 
211708736 
212776173 
213847192 
214921799 

24.3926 
24.4131 
24.4336 
24.4540 
24.4745 

8.4108 
8.4155 
8.4202 
8.4249 
8.4296 

545 

546 
547 
548 
549 

297025 
298116 
299209 
300304 
301401 

161878625 
162771336 
163667323 
164566592 
165469149 

23.3452 
23.3666 
23.3880 
23.4094 
23.4307 

8.1683 
8.1733 
8.1783 
8.1833 
8.1882 

600 
601 
602 
603 
604 

360000 
361201 
362404 
363609 
364816 

216000000 
217081801 
218167208 
219256227 
220348864 

24.4949 
24.5153 
24.5357 
24.5561 
24.5764 

8.4343 
8.4390 
8.4437 
8.4484 
8.4530 

550 
551 
552 
553 
554 

302500 
303601 
304704 
305809 
306916 

166375000 
167284151 
168196608 
169112377 
170031464 

23.4521 
23.4734 
23.4947 
23.5160 
23.5372 

8.1932 
8.1982 
8.2031 
8.2081 
8.2130 

605 
606 
607 
608 
609 

366025 
367236 
36S449 
369664 
370881 

221445125 
222545016 
223648543 
224755712 
225866529 

24.5967 
24.6171 
24.6374 
24.6577 
24.6779 

8.4577 
8.4623 
8.4670 
8.4716 
8.4763 

555 

556 
557 

558 
559 

308025 
309136 
310249 
311364 
312481 

170953875 
171879616 
1  72808693 
173741112 
174676879 

23.5584 
23.5797 
23.6008 
23.6220 
23.6432 

8.2180 
8.2229 
8.2278 
8.2327 
8.2377 

610 
611 
612 
613 
614 

372100 
373321 
374544 
375769 
376996 

226981000 
228099131 
229220928 
230346397 
231475544 

24.6982 
24.7184 
24.7386 
24.7588 
24.7790 

8.4809 
8.4856 
8.4902 
8.4948 
8.4994 

560 
561 
562 
563 
564 

313600 
314721 
315844 
316969 
318096 

175616000 
176558481 
177504328 
178453547 
179406144 

23.6643 
23.6854 
23.7065 
23.7276 
23.7487 

8.2426 
8.2475 
8.2524 
8.2573 
8.2621 

615 
616 
617 
618 
619 

378225 
379456 
380689 
381924 
383161 

232608375 
233744896 
234885113 
236029032 
237176659 

24.7992 
24.8193 
24.8395 
24.8596 
24.8797 

8.5040 
8.5C86 
8.5132 
8.5178 
8.5224 

565 
566 
567 
568 
569 

319225 
320356 
321489 
322624 
323761 

180362125 
181321496 
182284263 
183250432 
184220009 

23.7697 
23.7908 
23.8118 
23.8328 
23.8537 

8.2670 
8.2719 
8.2768 
8.2816 
8.2865 

620 
621 
622 
623 
624 

384400 
385641 
386884 
388129 
389376 

238328000 
239483061 
240641848 
241804367 
242970624 

24.8998 
24.9199 
24.9399 
24.9600 
24.9800 

8.5270 
8.5316 
8.5362 
8.5408 
8.5453 

570 
571 
572 
573 
574 

324900 
326041 
327184 
328329 
329476 

185193000 
186169411 
187149248 
188132517 
189119224 

23.8747 
23.8956 
23.9165 
23.9374 
23.9583 

8.2913 
8.2962 
8.3010 
8.3059 
8.3107 

625 
626 
627 
628 
629 

390625 
391876 
393129 
394384 
395641 

244140625 
245314376 
246491883 
247673152 
248858189 

25.0000 
25.0200 
25.0400 
25.0599 
25.0799 

8.5499 
8.5544 
85590 
8.5635 
8.5681 

575 
576 
577 
578 
579 

330625 
331776 
332929 
334084 
335241 

190109375 
191102976 
192100033 
193100552 
194104539 

23.9792 
24.0000 
24.0208 
24.0416 
24.0624 

8.3155 
8.3203 
8.3251 
8.3300 
8.3348 

630 
631 
632 
633 
634 

396900 
398161 
399424 
400689 
401956 

250047000 
251239591 
252435968 
253636137 
254840104 

25.0998 
25.1197 
25.1396 
25.1595 
25.1794 

8.5726 
8.5772 
8.5817 
8.5862 
8.5907 

580 
581 
582 
583 
584 

336400 
337561 
338724 
339889 
341056 

195112000 
196122941 
197137368 
198155287 
199176704 

24.0832 
24.1039 
24.1247 
24.1454 
24.1661 

8.3396 
8.3443 
8.3491 
8.3539 
8.3587 

635 
636 
637 
638 
639 

403225 
404496 
405769 
407044 
408321 

256047875 
257259456 
258474853 
259694072 
260917119 

25.1992 
25.2190 
25.2389 
25.2587 
25.2784 

8.5952 
8.5997 
8.6043 
8.6088 
8.6132 

585 
586 
587 
588 
589 

342225 
343396 
344569 
345744 
34692  1 

200201625 
201230056 
202262003 
203297472 
204336469 

24.1868 
24.2074 
24.2281 
24.2487 
24.2693 

8.3634 
8.3682 
8.3730 
8.3777 
8.3825 

640 
641 
642 
643 
644 

409600 
410881 
412164 
413449 
414736 

262144000 
263374721 
264609288 
265847707 
267089984 

25.2982 
25.3180 
25.3377 
25.3574 
25.3772 

8.6177 
8.6222 
8.6267 
8.6312 
8.6357 

590 
591 
592 
593 
594 

348100 
349281 
350464 
351649 
352836 

205379000 
206425071 
207474688 
208527857 
209584584 

24.2899 
24.3105 
24.3311 
24.3516 
24.3721 

8.3872 
8.3919 
8.3967 
8.4014 
8.4061 

645 
646 
647 
648 
649 

416025 
417316 
4  1  8609 
419904 
421201 

268336125 
269586136 
27084002.3 
272097792 
273359449 

25.3969 
25.416 
25.436 
25.4558 
25.475 

8.6401 
8.6446 
8.6490 
8.6535 
8.6579 

100 


MATHEMATICAL  TABLES. 


No. 

650 
651 
652 
653 
654 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

705 
706 
707 
708 
709 

Square 

Cube* 

Sq. 
Root. 

Cube 
Root. 

422500 
42380! 
425104 
426409 
427716 

274625000 
275894451 
277167808 
278445077 
279726264 

25.4951 
25.5147 
25.5343 
25.5539 
25.5734 

6.6624 
8.6668 
8.6713 
8.6757 
8.6801 

497625 
498436 
499849 
501264 
502681 

350402625 
351895816 
353393243 
354894912 
356400829 

26.5518 
26.5707 
26.5895 
26.6083 
26.6271 

8.9001 
8.9043 
8.9085 
8.9127 
8.9169 

655 
656 
657 
658 
659 

429025 
430336 
431649 
432964 
434281 

281011375 
282300416 
283593393 
284890312 
286191179 

25.5930 
25.6125 
25.6320 
25.6515 
25.6710 

8.6845 
8.6890 
8.6934 
8.6978 
8.7022 

710 
711 
712 
713 
714 

504100 
505521 
506944 
508369 
509796 

35791  100C 
359425431 
360944128 
362467097 
363994344 

26.6458 
26.6646 
26.6833 
26.7021 
26.7208 

8.9211 
8.9253 
8.9295 
8.9337 
8.9378 

660 
661 
662 
663 
664 

435600 
43692  1 
438244 
439569 
440896 

287496000 
288804781 
290117528 
291434247 
292754944 

25.6905 
25.7099 
25.7294 
25.7488 
25.7682 

8.7066 
8.7110 
8.7154 
8.7198 
8.7241 

715 
716 
717 
718 
719 

511225 
512656 
5  1  4089 
515524 
516961 

365525875 
367061696 
368601813 
370146232 
371694959 

26.7395 
26.7582 
26.7769 
26.7955 
26.8142 

8.9420 
8.9462 
8.9503 
8.9545 
8.9587 

665 
566 
667 
663 
669 

442225 
443556 
444889 
446224 
447561 

294079625 
295408296 
296740963 
298077632 
299418309 

25.7876 
25.8070 
25.8263 
25.8457 
25.8650 

8.7285 
87329 

8.7373 
8.7<16 
8.7460 

720 

721 
722 
723 
724 

518400 
519841 
521284 
522729 
524176 

373248000 
374805361 
376367048 
377933067 
379503424 

26.8328 
26.8514 
26.8701 
26.8887 
26.9072 

8.9628 
8.9670 
8.9711 
8.9752 
8.9794 

670 
671 
672 
673 
674 

448900 
450241 
451584 
452929 
454276 

300763000 
302111711 
303464448 
304821217 
306182024 

25.8844 
25.9037 
25.9230 
25.9422 
25.9615 

8.7503 
8.7547 
8.7590 
8.7634 
8.7677 

725 
726 
727 
728 
729 

525625 
527076 
528529 
529984 
531441 

381078125 
382657176 
384240583 
385828352 
387420489 

26.9258 
26.9444 
26.9629 
26.9815 
27.0000 

8.9835 
8.9876 
8.9918 
8.9959 
9.0000 

675 
676 
677 
673 
679 

455625 
456976 
458329 
459684 
461041 

307546875 
308915776 
310288733 
311665752 
313046839 

25.9808 
26.0000 
26.0192 
26.0384 
26.0576 

8.7721 
8.7764 
8.7807 
8.7850 
8.7893 

730 
731 

732 
733 
734 

532900 
534361 
535824 
537289 
538756 

389017000 
390617891 
392223168 
393832837 
395446904 

27.0185 
27.0370 
27.0555 
27.0740 
27.0924 

9.0041 
9.0082 
9.0123 
9.0164 
9.0205 

680 
681 
682 
683 
684 

462400 
463761 
465124 
466489 
467856 

314432000 
315821241 
317214568 
318611987 
320013504 

26.0768 
26.0960 
26.1151 
26.1343 
26.1534 

8.7937 
8.7980 
8.8023 
8.8066 
8.8109 

735 

736 
737 
738 
739 

540225 
541696 
543169 
5  4464  4 
546121 

397065375 
398688256 
400315553 
401947272 
403583419 

27.1109 
27.1293 
27.1477 
27.1662 
27.1846 

9.0246 
9.0287 
9.0328 
9.0369 
9.0410 

685 
686 
687 
688 
689 

469225 
470596 
471969 
473344 
474721 

321419125 
322828856 
324242703 
325660672 
327082769 

26.1725 
26.1916 
26.2107 
26.2298 
26.2488 

8.8152 
8.8194 
8.8237 
8.8280 
8.8323 

740 
741 
742 
743 
744 

54760C 
54908  1 
550564 
552049 
553536 

405224000 
406869021 
408518488 
410172407 

411830784 

27.2029 
27.2213 
27.2397 
27.2580 
27.2764 

9.0450 
90491 
9.0532 
9.0572 
9.0613 

690 
691 
692 
693 
694 

476100 
477481 
478864 
480249 
481636 

328509000 
329939371 
331373888 
332812557 
334255384 

26.2679 
26.2869 
26.3059 
26.3249 
26.3439 

8.8366 
8.8408 
8.8451 
8.8493 
8.8536 

745 

746 
747 
748 
749 

555025 
556516 
558009 
559504 
561001 

413493625 
415160936 
416832723 
418508992 
420189749 

27.2947 
273130 
27.3313 
27.3496 
27.3679 

9.0654 
9.0694 
9.0735 
9.0775 
9.0816 

695 
696 
697 
698 
699 

483025 
484416 
485809 
487204 
488601 

335702375 
337153536 
338608873 
340068392 
341532099 

26.3629 
26.3818 
26.4008 
26.4197 
26.4386 

8.8578 
8.8621 
8.8663 
8.8706 
8.8748 

750 
751 
752 
753 

754 

562500 
564001 
565504 
567009 
568516 

421875000 
423564751 
425259008 
426957777 
428661061 

27.3861 
27.4044 
27.4226 
27.4408 
27.4591 

9.0856 
90896 
9.0937 
9.0977 
9.1017 

700 
701 
702 
703 
704 

490000 
491401 
492804 
494209 
495616 

343000000 
344472101 
345948408 
347428927 
348913664 

26.4575 
26.4764 
26.4953 
26.5141 
26.5330 

88790 
8.8833 
8.8875 
8.8917 
8.8959 

755 
756 
757 
758 
759 

570025 
571536 
573049 
574564 
576081 

430368875 
432081216 
433798093 
435519512 
437245479 

27.4773 
27.4955 
27.5136 
27.5318 
27.5500 

9  1057 
9.1098 
9.1138 
9  1178 
9.1219 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.       101 


No 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

760 

577600 

438976000 

27.5681 

9.1258 

~8l5 

664225 

541343375 

28.5482 

9.3408 

76 

57912 

440711081 

27.5862 

9.1298 

816 

665856 

543338496 

28.5657 

9.3447 

762 

580644 

442450728 

27.6043 

9.1338 

81 

667489 

545338513 

28.5832 

9.3485 

763 

532  1  69 

444194947 

27.6225 

9.1378 

818 

66912 

547343432 

28.6007 

9.3523 

764 

583696 

445943744 

27.6405 

9.1418 

819 

67076 

549353259 

28.6182 

9.3561 

765 

585225 

447697125 

27.6586 

9.1458 

820 

672400 

55136800C 

28.6356 

9.3599 

766 

586756 

449455096 

27.6767 

9.  1  498 

82 

67404 

55338766 

28.6531 

9.3637 

767 

588289 

451217663 

27.6948 

9.1537 

822 

67568 

55541224S 

28.6705 

9.3675 

768 

589824 

452984832 

27.7128 

9.1577 

823 

67732 

55744176 

28.6880 

9.3713 

769 

591361 

454756609 

27.7308 

9.1617 

824 

678976 

559476224 

28.7054 

9.3751 

770 

592900 

456533000 

27.7489 

9.1657 

825 

68062 

561515625 

28.7228 

9.3789 

771 

594441 

458314011 

27.7669 

9.1696 

826 

682276 

563559976 

28.7402 

9.3827 

772 

595984 

460099648 

27.7849 

9.1736 

827 

683929 

565609283 

28.7576 

9.3865 

773 

597529 

461889917 

27.8029 

9.1775 

828 

685584 

567663552 

28.7750 

9.3902 

774 

599076 

463684824 

27.8209 

9.1815 

829 

68724 

569722789 

28.7924 

9.3940 

775 

600625 

465434375 

27.8388 

9.1855 

830 

688900 

571787000 

28.8097 

9.3978 

776 

602176 

467288576 

27.8568 

9.1894 

83 

69056 

57385619 

28.8271 

9.4016 

777 

603729 

469097433 

27.8747 

9.^33 

832 

692224 

575930368 

28.8444 

9.4053 

778 

605284 

470910952 

27.8927 

9.1973 

833 

693889 

578009537 

28.8617 

9.4091 

779 

606341 

472729139 

27.9106 

9.2012 

834 

695556 

580093704 

28.8791 

9.4129 

780 

603400 

474552000 

27.9285 

9.2052 

835 

697225 

582182875 

28.8964 

9.4166 

781 

609961 

476379541 

27.9464 

9.2091 

836 

698896 

584277056 

28.9131 

9.4204 

782 

611524 

478211768 

27.9643 

9.2130 

837 

700569 

586376253 

28.9310 

9.4241 

783 

6(3089 

430048687 

27.9821 

9.2170 

838 

702244 

588480472 

28.9482 

9.4279 

784 

614656 

431890304 

28.0000 

9.2209 

839 

703921 

590589719 

28.9655 

9.4316 

785 

616225 

483736625 

28.0179 

9.2248 

840 

705600 

592704000 

28.9828 

9.4354 

786 

617796 

485587656 

28.0357 

9.2287 

841 

707281 

594823321 

29.0000 

9.4391 

787 

619369 

487443403 

28.0535 

9.2326 

842 

708964 

596947688 

29.0172 

9.4429 

788 

620944 

489303872 

28.0713 

9.2365 

843 

710649 

599077107 

29.0345 

9.4466 

789 

622521 

491169069 

28.0891 

9.2404 

844 

712336 

601211584 

29.0517 

9.4503 

790 

624100 

493039000 

28.1069 

9.2443 

845 

714025 

603351125 

29.0689 

9.4541 

791 

625631 

494913671 

28.1247 

9.2482 

846 

715716 

605495736 

29.0861 

9.4578 

792 

627264 

496793088 

28.1425 

9.2521 

847 

717409 

607645423 

29.1033 

9.4615 

793 

623349 

498677257 

28.1603 

9.2560 

848 

719104 

609800192 

29.1204 

9.4652 

794 

630436 

500566184 

28.1780 

9.2599 

849 

720801 

611960049 

29.1376 

9.4690 

795 

632025 

502459875 

28.1957 

9.2638 

850 

722500 

614125000 

29.1548 

9.4727 

796 

633616 

504358336 

28.2135 

9.2677 

851 

724201 

616295051 

29.1719 

9.4764 

797 

635209 

506261573 

28.23129.2716 

852 

725904 

618470208 

29.  1  890 

9.4801 

798 

636804 

508169592 

28.2489 

9.2754 

853 

727609 

620650477 

29.2062 

9.4838 

799 

638401 

510082399 

28.2666 

9.2793 

854 

729316 

622835864 

79.2233 

9.4875 

800 

640000 

512000000 

28.2843 

9.2832 

855 

731025 

625026375 

29.2404 

9.4912 

801 

641601 

513922401 

28.3019 

9.2870 

856 

732736 

627222016 

29.2575 

9.4949 

802 

643204 

515849608 

28.3196 

9.2909 

857 

734449 

629422793 

29.2746 

9.4986 

803 

644809 

517781627 

28.3373 

9.2948 

858 

736164 

631628712 

29.2916 

9.5023 

804 

646416 

519718464 

28.3549 

9.2986 

859 

737881 

633839779 

29.3087 

9.5060 

805 

648025 

521660125 

28.3725 

9.3025 

860 

739600 

636056000 

29.3258 

9.5097 

806 

649636 

523606616 

28.3901 

9.3063 

861 

741321 

638277381 

29.3428 

9.5134 

807 

651249 

525557943 

28.4077 

9.3102 

862 

743044 

640503928 

29.3598 

9.5171 

808 

652864 

527514112 

28.4253 

9.3140 

863 

744769 

642735647 

29.3769 

9.5207 

809 

654481 

529475129 

28.4429 

9.3179 

864 

746496 

644972544 

29.3939 

9.5244 

810 

656100 

531441000 

28.4605 

5.3217 

865 

748225 

647214625 

9.4109 

9.5231 

811 

657721 

533411731 

28.4781 

5.3255 

866 

49956 

49461896 

9.4279 

9.5317 

812 

659344 

35387328 

28.4956  9.3294 

867 

51689 

51714363  29.4449 

9.5354 

813 
814 

660969  37367797 
662596  539353144 

28.51329.3332 
28.5307  9.3370 

868  5342465397203229.4618 
8691  755  1  6  1  1  656234909!  29.4788 

9.5391 
9.5427 

102 


MATHEMATICAL   TABLES. 


No. 

870 

871 
872 
873 
874 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

~925 
926 
927 
928 
929 

Square 

Cube. 

Sq. 
Root. 

Cube 
Root. 

756900 
758641 
760384 
762129 
763876 

658503000 
660776311 
663054848 
665338617 
667627624 

29.4958 
29.5127 
29.5296 
29.5466 
29.5635 

9.5464 
9.5501 
9.5537 
9.5574 
9.5610 

855625 
857476 
859329 
861184 
863041 

791453125 
794022776 
796597983 
799178752 
801765089 

30.4138 
30.4302 
30.4467 
30.4631 
30.4795 

9.7435 
9.7470 
9.7505 
9.7540 
9.7575 

875 

876 
877 
878 
879 

765625 
767376 
769129 
770884 
772641 

669921875 
672221376 
674526133 
676836152 
679151439 

29.5804 
29.5973 
29.6142 
29.63  1  1 
29.6479 

9.5647 
9.5683 
9.5719 
9.5756 
9.5792 

930 
931 
932 
933 
934 

864900 
866761 
868624 
870489 
872356 

804357000 
806954491 
809557568 
812166237 
814780504 

30.4959 
30.5123 
30.5287 
30.5450 
30.5614 

9.76M 
9.7645 
9.7680 
9.7715 
9.7750 

880 
881 
882 
883 
884 

774400 
776161 
777924 
779689 
781456 

681472000 
683797841 
686128968 
688465387 
690807104 

29.6648 
29.6816 
29.6985 
29.7153 
29.7321 

9.5828 
9.5865 
9.5901 
9.5937 
9.5973 

935 
936 
937 
938 
939 

874225 
876096 
877969 
879844 
881721 

817400375 
820025856 
822656953 
825293672 
827936019 

30.5778 
30.5941 
30.6105 
30.6268 
30.6431 

9.7785 
9.7819 
9.7854 
9.7889 
9.7924 

885 
886 
887 
888 
889 

783225 
784996 
786769 
788544 
790321 

693154125 
695506456 
697864103 
700227072 
702595369 

29.7489 
29.7658 
29.7825 
29.7993 
29.8161 

9.6010 
9.6046 
9.6082 
9.6118 
9.6154 

940 
941 
942 
943 
944 

883600 
885481 
887364 
889249 
891136 

830584000 
833237621 
835896888 
838561807 
841232384 

30.6594 
30.6757 
30.6920 
30.7083 
30.7246 

9.7959 
9.7993 
9.8028 
9.8063 
9.8097 

890 
891 
892 
893 
694 

792100 
793881 
795664 
797449 
799236 

704969000 
707347971 
709732288 
712121957 
714516984 

29.8329 
29.8496 
29.8664 
29.8831 
29.8998 

9.6190 
9.6226 
9.6262 
9.6298 
9.6334 

945 
946 
947 
948 
949 

893025 
894916 
896809 
898704 
900601 

843908625 
846590536 
849278123 
851971392 
854670349 

30.7409 
30.7571 
30.7734 
30.7896 
30.8058 

9.8132 
9.8167 
9.8201 
9.8236 
9.8270 

895 
896 
897 
898 
899 

801025 
802816 
804609 
806404 
808201 

716917375 
719323136 
721734273 
724150792 
726572699 

29.9166 
29.9333 
29.9500 
29.9666 
29.9833 

9.6370 
9.6406 
9.6442 
9.6477 
9.6513 

950 
951 
952 
953 
954 

902500 
904401 
906304 
908209 
910116 

857375000 
860085351 
862801408 
865523177 
868250664 

30.8221 
30.8383 
30.8545 
30.8707 
30.8869 

9.8305 
9.8339 
9.8374 
9.8408 
9.8443 

900 
901 
902 
903 
904 

810000 
811801 
813604 
815409 
817216 

729000000 
731432701 
733870808 
736314327 
738763264 

30.0000 
30.0167 
30.0333 
30.0500 
30.0666 

9.6549 
9.6585 
9.6620 
9.6656 
9.6692 

955 
956 
957 
958 
959 

912025 
913936 
915849 
917764 
919681 

870983875 
873722816 
876467493 
879217912 
881974079 

30.9031 
30.9192 
30.9354 
30.9516 
30.9677 

9.8477 
9.8511 
9.8546 
9.8580 
9.8614 

905 
906 
907 
908 
909 

819025 
820836 
822649 
824464 
826281 

741217625 
743677416 
746142643 
748613312 
751089429 

30.0832 
30.0998 
30.1164 
30.1330 
30.1496 

9.6727 
9.6763 
9.6799 
9.6834 
9.6870 

960 
961 
962 
963 
964 

921600 
923521 
925444 
927369 
929296 

884736000 
887503681 
890277128 
893056347 
895841344 

30.9839 
31.0000 
31.0161 
31.0322 
31.0483 

9.8648 
9.8683 
9.8717 
9.8751 
9.8785 

910 
911 
912 
913 
914 

828100 
829921 
831744 
833569 
835396 

753571000 
75605803  1 
758550528 
761048497 
763551944 

30.1662 
30.1828 
30.1993 
30.2159 
30.2324 

9.6905 
9.6941 
9.6976 
9.7012 
9.7047 

965 
966 
967 
968 
969 

931225 
933156 
935089 
937024 
938961 

898632125 
901428696 
904231063 
907039232 
909853209 

3  1  .0644 
3  1  .0805 
3  1  .0966 
31.1127 
31.1288 

9.8819 
9.8854 
9.8888 
9.8922 
9.8956 

915 
916 
917 
918 
919 

837225 
839056 
840889 
842724 
844561 

766060875 
768575296 
771095213 
773620632 
776151559 

30.2490 
30.2655 
30.2820 
30.2985 
30.3150 

9.7082 
9.7118 
9.7153 
9.7188 
9.7224 

970 
971 
972 
973 

974 

940900 

942841 
944784 
946729 
948676 

912673000 
915498611 
918330048 
921167317 
924010424 

31.1448 
31.1609 
31.1769 
31.1929 
31.2090 

9.8990 
9.9024 
9.9058 
9.9092 
9.9126 

920 
921 
922 
923 
924 

846400 
848241 
850084 
851929 
853776 

778688000 
781229961 
783777448 
786330467 
7888890241 

30.3315 
30.3480 
30.3645 
30.3809 
30.3974 

9.7259 
9.7294 
9.7329 
9.7364 
9.7400 

975 
976 
977 
978 
979 

950625 
952576 
954529 
956484 
958441 

926859375 
929714176 
932574833 
935441352 
938313739 

31.2250 
31.2410 
31.2570 
31.2730 
31.2890 

9.9160 
99194 
9.9227 
9.9261 
9.9293 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.        103 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

980 

960400 

941  192000 

31.3050 

9.9329 

1035 

1071225 

1108717875 

32.1714 

10.1153 

981 

962361 

944076141 

31.3209 

9.9363 

1036 

10732% 

1111934656 

32.1870 

10.1186 

982 

964324 

946966168 

31.3369 

9.93% 

1037 

1075369 

1115157653 

32.2025 

10.1218 

983 

966289 

949862087 

31.3528 

9.9430 

1038 

1077444 

1  1  18386872 

32.2180 

10.1251 

984 

968256 

952763904 

31.3688 

9.9464 

1039 

1079521 

1121622319 

32.2335 

10.1283 

985 

970225 

955671625 

31.3847 

9.9497 

1040 

1081600 

1124864000 

32.2490 

10.1316 

986 

9721% 

958585256 

31.4006 

9.9531 

1041 

1083681 

1128111921 

32.2645 

10  1348 

987 

974169 

%1  504803 

31.4166 

9.9565 

1042 

1085764 

1131366088 

32.2800 

10.1381 

988 

976144 

964430272 

31.4325 

9.9598 

1043 

1087849 

1134626507 

32.2955 

10.1413 

989 

978121 

%7361669 

31.4484 

9.%32 

1044 

1089936 

1137893184 

32.3110 

10.1446 

990 

980100 

970299000 

31.4643 

9.%66 

1045 

1092025 

1141166125 

32.3265 

10.1478 

991 

982081 

973242271 

31.4802 

9.%99 

1046 

1094116 

1144445336 

32.3419 

10.1510 

992 

984064 

976191488 

31.4960 

9.9733 

1047 

10%209 

1147730823 

32.3574 

10.1543 

993 

986049 

979146657 

31.5119 

9.9766 

1048 

1098304 

1151022592 

32.3728 

10.1575 

994 

988036 

982107784 

31.5278 

9.9800 

1049 

ir00401 

1154320649 

32.3883 

10.1607 

995 

990025 

985074875 

31.5436 

9.9833 

1050 

1  102500 

1157625000 

32.4037 

10.1640 

9% 

992016 

988047936 

31.5595 

9.9866 

1051 

1104601 

1160935651 

32.4191 

10.1672 

997 

994009 

991026973  31.5753 

9.9900 

1052 

1  106704 

1164252608 

32.4345 

10.1704 

998 

996004 

99401  1992 

31.5911 

9.9933 

1053 

1108809 

1167575877 

32.4500 

10.1736 

999 

998001 

997002999 

31.6070 

9.9%7 

1054 

1110916 

1170905464 

32.4654 

10.1769 

1000 

1000000 

1000000000 

31.6228 

10.0000 

1055 

1  1  13025 

1174241375 

32.4808 

10.1801 

1001 

1002001 

1003003001 

31.6386 

10.0033 

1056 

1115136 

1177583616 

32.4%2 

10.1833 

1002 

1004004 

1006012008 

31.6544 

10.0067 

1057 

1117249 

1180932193 

32.5115 

10.1865 

1003 

1006009 

1009027027 

31.6702 

10.0100 

1058 

1  1  19364 

1184287112 

32.5269 

10.1897 

1004 

1008016 

1012048064 

31.6860 

10.0133 

1059 

1121481 

1  187648379 

32.5423 

10.1929 

1005 

1010025 

1015075125 

31.7017 

10.0166 

1060 

1123600 

1191016000 

32.5576 

10.1%1 

1006 

1012036 

1018108216 

31.7175 

10.0200 

1061 

1125721 

1  194389981 

32.5730 

10.1993 

1007 

1014049 

1021147343 

31.7333 

10.0233 

1062 

1127844 

1  197770328 

32.5833 

10.2025 

1008 

1016064 

1024192512 

31.7490 

10.0266 

1063 

1129%9 

1201157047 

32.6036 

10.2057 

1009 

1018081 

1027243729 

31.7648 

10.0299 

1064 

11320% 

1204550144 

32.6190 

10.2089 

1010 

T020100 

1030301000 

31.7805 

10.0332 

1065 

1134225 

120794%25 

32  6343 

10.2121 

1011 

1022121 

1033364331 

31.7962 

10.0365 

1066 

1136356 

12113554% 

32.6497 

10.2153 

1012 

1024144 

1036433728 

31.8119 

10.0398 

1067 

1138489 

1214767763 

32.6650 

10.2185 

1013 

1026169 

1039509197 

31.8277 

10.0431 

1063 

1140624 

1218186432 

32.6803 

10.2217 

1014 

10281% 

1042590744 

31.8434 

10.0465 

1069 

1142761 

1221611509 

32.6956 

10.2249 

1015 

1030225 

1045678375 

31.8591 

10.0498 

1070 

1144900 

1225043000 

32.7109 

10.2281 

1016 

1032256 

10487720% 

31.8748 

10.0531 

1071 

1  147041 

1228480911 

32.7261 

10.2313 

1017 

1034289 

1051871913 

31.8904 

10.0563 

1072 

1149184 

1231925248 

32.7414 

10.2345 

1018 

1036324 

1054977832 

31.9061 

10.0596 

1073 

1151329 

1235376017 

32.7567 

10.2376 

1019 

1038361 

1058089859 

31.9218 

10.0629 

1074 

1153476 

1238833224 

32.7719 

10.2408 

1020 

1040400 

1061208000 

31.9374 

10.0662 

1075 

1155625 

1242296875 

32.7872 

10.2440 

1021 

1042441 

1064332261 

31.9531 

10.0695 

1076 

1157776 

1245766976 

32.8024 

10.2472 

1022 

1044484 

1067462648 

31.9687 

10.0728 

1077 

1159929 

1249243533 

32.8177 

10.2503 

1023 

1046529 

1070599167 

31.9844 

10.0761 

1078 

1162084 

1252726552 

32.8329 

10.2535 

1024 

1048576 

1073741824 

32.0000 

10.0794 

1079 

1  164241 

1256216039 

32.8481 

10.2567 

1025 

1050625 

1076890625 

32.0156 

10.0826 

1080 

1166400 

1259712000 

32.8634 

10.2599 

1026 

1052676 

1080045576 

32.0312 

10.0859 

1081 

1  168561 

1263214441 

32.8786 

10.2630 

1027 

1054729 

1083206683 

32.0468 

10.0892 

1032 

1170724 

1266723368 

32.8938 

10.2662 

1028 

1056784 

1086373952 

32.0624 

10.0925 

1033 

1172889 

1270238787 

32.9090 

10.2693 

1029 

1058841 

1089547389 

32.0780 

10.0957 

1084 

1175056 

1273760704 

32.9242 

10.2725 

1030 

1060900 

1092727000 

32.0936 

10.0990 

1035 

1177225 

1277289125 

32.9393 

10.2757 

1031 

1062%! 

1095912791 

32.1092 

10.1023 

1036 

11793% 

1280824056 

32.9545 

10.2788 

1032 

1065024 

1099104768 

32.1248 

10.1055 

1037 

1181569 

1284365503 

32.%97 

10.2820 

1033 

10670S9 

1  102302937 

32.1403 

10.1088 

1088 

1183744 

1287913472 

32.9848 

10.2851 

1034 

1069156 

1105507304 

32.1559 

10.1121 

1089 

11  8592  11  1291  467969 

33.0000 

10.2883 

104 


MATHEMATICAL   TABLES. 


No. 
T090 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1188100 

1295029000 

33.0151 

10.2914 

1145 

1311025 

1501123625 

33.8378 

10.4617 

1091 

1  190281 

12985%571 

33.0303i  10.2946 

1146 

1313316 

1505060136 

33.8526 

10.4647 

1092 
1093 

1192464 
1194649 

1302170688 
1305751357 

33.0454 
33.0606 

10.297/ 
10.3009 

1147 
1148 

1315609 
1317904 

1509003523 
1512953792 

33.8674 
33.882 

10.4678 
10.4708 

1094 

1196836 

1309338584 

33.0757 

10.3040 

1149 

132020 

1516910949 

33.8%9 

10.4739 

1095 

1199025 

1312932375 

33.0908 

10.307 

1150 

1322500 

1520875000 

33.9116 

10.4769 

10% 

1201216 

1316532736 

33.1059 

10.3103 

1151 

1324801 

1524845951 

33.9264 

10.4799 

1097 

1203409 

1320139673 

33.1210 

10.3134 

1152 

1327104 

1528823808 

33.9411 

10.4830 

1098 

1205604 

1323753192 

33.1361 

10.3165 

1153 

1329409 

1532808577 

33.9559 

10.4860 

1099 

1207801 

1327373299 

33.1512 

10.3197 

1154 

1331716 

1536800264 

33.9706 

10.4890 

1100 

1210000 

1331000000 

33.1662 

10.3228 

1155 

1334025 

1540798875 

33.9853 

10.4921 

1101 

1212201 

1334633301 

33.1813J  10.3259 

1156 

1336336 

1544804416 

34.0000 

10.4951 

1102 

1214404 

1338273208 

33.1964!  10.3290 

1157 

1338649 

1548816893 

34.0147 

10.4981 

1103 

1216609 

1341919727 

33  .21141  10.3322 

1158 

1340964 

1552836312 

34.0294 

10.5011 

1104 

1218816 

1345572864 

33.2264 

103353 

1159 

1343281 

1556862679 

34.0441 

10.5042 

1105 

1221025 

1349232625 

33.2415 

10.3384 

1160 

1345600 

1560896000 

34.0588 

10.5072 

1106 

1223236 

1352899016 

33.2566 

10.3415 

1161 

1347921 

1564936281 

34.0735 

10.5102 

1107 

1225449 

1356572043 

33.2716 

10.3447 

1162 

1350244 

1568933528 

34.0881 

10.5132 

1108 

1227664 

1360251712 

33.2866 

10.3478 

1163 

1352569 

1573037747 

34.1028 

1  0.5  162 

1109 

1229881 

1363938029 

33.3017 

10.3509 

1164 

13548% 

1577098944 

34.1174 

10.5192 

1110 

1232100 

1367631000 

33.3167 

10.3540 

1165 

1357225 

1581167125 

34.1321 

10.5223 

1111 

1234321 

1371330631 

33.3317 

10.3571 

1166 

1359556 

15852422% 

34.1467 

10.5253 

1112 

1236544 

1375036928 

33.3467 

10.3602 

1167 

1361889 

1589324463 

34.1614 

10.5283 

1113 

1238769 

1378749897 

33.3617 

10.3633 

1168 

1364224 

1593413632 

34.1760 

10.5313 

1114 

12409% 

1382469544 

33.3766 

10.3664 

1169 

1366561 

1597509809 

34.1906 

10.5343 

1115 

1243225 

1386195875 

33.3916 

10.3695 

1170 

1368900 

1601613000 

34.2053 

10.5373 

1116 

1245456 

13899288% 

33.4066 

10.3726 

1171 

1371241 

1605723211 

34.2199 

10.5403 

1117 

1247689 

1393668613 

33.4215 

103757 

1172 

1373584 

1609840448 

34.2345 

10.5433 

1118 

1249924 

1397415032 

33.4365 

10.3788 

1173 

1375929 

1613964717 

34.2491 

10.5463 

1119 

1252161 

1401168159 

33.4515 

10.3819 

1174 

1378276 

1618096024 

34.2637 

10.5493 

1120 

1254400 

1404928000 

33.4664 

10.3850 

1175 

1380625 

1622234375 

34.2783 

10.5523 

1121 

1256641 

408694561 

33.4813 

10.3881 

1176 

1382976 

1626379776 

34.2929 

10.5553 

1122 

1258884 

412467848 

33.4%3 

10.3912 

1177 

1385329 

1630532233 

34.3074 

10.5583 

1123 

1261  129 

416247867 

33.5112 

10.3943 

1178 

1387684 

1634691752 

34.3220 

10.5612 

1124 

1263376 

420034624 

33.5261 

10.3973 

1179 

1390041 

638858339 

34.3366 

10.5642 

1125 

1265625 

423828125 

33.5410 

10.4004 

1180 

1392400 

643032000 

34.3511 

10.5672 

1126 

1267876 

427628376 

33.5559 

10.4035 

1181 

1394761 

647212741 

34.3657 

10.5702 

1127 

1270129 

431435383 

33.5708 

10.4066 

1182 

1397124 

65140056834.3802 

10.5732 

1128 

1272384 

435249152 

33.5857 

10.4097 

1183 

1399489 

655595487 

34.3948 

0.5762 

1129 

1274641 

439069689 

33.6006 

10.4127 

1184 

1401856 

659797504 

34.4093 

0.5791 

1130 

1276900 

442897000 

33.6155 

10.4158 

1185 

1404225 

664006625 

34.4238 

0.5821 

\\3\ 

1279161 

446731091 

33.6303 

10.4189 

1186 

1406596 

668222856 

34.4384 

0.5851 

1132 

1281424 

450571968  33.6452 

10.4219 

1187 

140S%9 

672446203 

34.4529 

0.5881 

1133 

1283689 

4544  1%37|  33  .6601 

10.4250 

1158 

1411344 

676676672 

34.4674 

0.5910 

1134 

1285956 

458274104 

33.6749 

10.4281 

1189 

1413721 

680914269 

34.4819 

0.5940 

1135 

1288225 

462135375 

33.6898 

10.4311 

1190 

1416100 

685159000 

34.4964 

0.5970 

1136 

12904% 

466003456133.7046 

10.4342 

1191 

1418481 

689410871 

34.5109 

0.6000 

1137 

1292769 

469878353  33.7174 

10.4373 

1192 

1420864 

693669888 

34.5254 

0.6029 

1138 

1295044 

473760072  33.7342 

10.4404 

1193 

1423249 

697936057 

34.5398 

0.6059 

1139 

1297321 

477648619 

33.7491 

10.4434 

1194 

1425636 

702209384 

34.5543 

0.6088 

1140 

1299600 

481544000 

33.7639 

10.4464 

1195 

1428025 

706489875 

34,5688 

0.6118 

1141 

1301881 

485446221  33.7787 

10.4495 

11% 

1430416 

710777536 

34.5832 

0.6148 

1142 

1304164 

489355288  33.7935 

10  4525 

1197 

1432809 

715072373 

34.5977 

0.6177 

1143 

1306449 

493271207  33.8083 

10.4556 

1198 

1435204 

719374392 

34.6121 

0.6207 

1144 

1308736 

497193934338231 

10.4586 

1199 

1437601  '1723683599 

34.6266 

0.6236 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.       105 


No 
1200 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1440000 

1728000000 

34.6410 

10.6266 

1255 

1575025 

1976656375 

35.4260 

10.7865 

1201 

1442401 

1732323601 

34.6554 

10.6295 

1256 

1577536 

1981385216 

35.4401 

10.7894 

1202 

1444804 

1  736654408 

34.6699 

10.6325 

1257 

1580049 

1986121593 

35.4542 

10.7922 

1203 

1447209 

1740992427 

34.6843 

10.6354 

1258 

1582564 

1990865512 

35.4683 

10.7951 

1204 

1449616 

1745337664 

34.6987 

10.6384 

1259 

1585081 

1995616979 

35.4824 

10.7980 

1205 

1452025 

1749690125 

34.7131 

10.6413 

1260 

1587600 

2000376000 

35.4%5 

10.8008 

1206 

1454436 

1754049816 

34.7275 

10.6443 

1261 

1590121 

2005142581 

35.5106 

10.8037 

1207 

1456849 

1758416743 

34.7419 

10.6472 

1262 

1592644 

2009916728 

35.5246 

10.8065 

1208 

1459264 

1762790912 

34.7563 

1C.6501 

1263 

1595169 

2014698447 

35.5387 

10.8094 

1209 

1461631 

1767172329 

34.7707 

10.6530 

1264 

15976% 

2019487744 

35.5528 

10.8122 

1210 

1464100 

1771561000 

34.7851 

10.6560 

1265 

1600225 

202428.4625 

35.5668 

10.8151 

1211 

1  466521 

1775956931 

34.7994 

10.6590 

1266 

1602756 

2029089096 

35.5809 

10.8179 

1212 

1463944 

1780360128 

34.8138 

10.6619 

1267 

1605289 

2033901163 

35.5949 

10.8208 

1213 

1471369 

1784770597 

34.8281 

10.6648 

1268 

1607824 

2038720832 

35.6090 

10.8236 

1214 

1473796 

1789188344 

34.8425 

10.6678 

1269 

1610361 

2043548109 

35.6230 

10.8265 

1215 

1476225 

1793613375 

34.8569 

10.6707 

1270 

1612900 

2048383000 

35.6371 

10.8293 

1216 

1478656 

17980456% 

34.8712 

10.6736 

1271 

1615441 

2053225511 

35.6511 

10.8322 

1217 

1481089 

1802485313 

34.8855 

10.6765 

1272 

1617984 

2058075648 

35.6651 

10.8350 

1218 

1433524 

1806932232 

34.8999 

10.6795 

1273 

1620529 

2062933417 

35.6791 

10.8378 

1219 

1485%! 

1811386459 

34.9142 

10.6324 

1274 

1623076 

2067798824 

35.6931 

10.8407 

1220 

1438400 

1815848000 

34.9285 

10.6853 

1275 

1625625 

2072671875 

35.7071 

10.8435 

1221 

1490841 

1820316861 

34.9428 

10.6882 

1276 

1628176 

2077552576 

35.7211 

10.8463 

1222 

1493284 

1824793048 

34.9571 

10.691  1 

1277 

1630729 

2082440933 

35.7351 

10.8492 

1223 

1495729 

1829276567 

34.9714 

10.6940 

1278 

1633284 

2087336952 

35.7491 

10.8520 

1224 

1498176 

1833767424 

34.9357 

10.6970 

1279 

1635841 

2092240639 

35.7631 

10.8548 

1225 

1500625 

1838265625 

35.0000 

10.6999 

1280 

1638400 

2097152000 

35.7771 

10.857; 

1226 

1503076 

1842771176 

35.0143 

10.7028 

1281 

1640%! 

2102071041 

35.791  1 

10.8605 

1227 

1505529 

1847284033 

35.0286 

10.7057 

1282 

1643524 

2106997768 

35.8050 

10.8633 

1223 

1507984 

1851804352 

35.0428 

10.7086 

1283 

1646089 

2111932187 

35.8190 

10.8661 

1229 

1510441 

1856331989 

35.0571 

10.7115 

1284 

1648656 

21  16874304 

35.8329 

10.8690 

1230 

1512900 

1860867000 

35.0714 

10.7144 

1285 

1651225 

2121824125 

35.8469 

10.8718 

1231 

1515361 

1865409391 

35.0856 

10.7173 

1286 

1653796 

2126781656 

35.8608 

10.8746 

1232 

1517824 

1869959163 

35.0999 

10.7202 

1287 

1656369 

2131746903 

35.8748 

10.8774 

1233 

1520239 

1874516337 

35.1141 

10.7231 

1238 

1658944 

2136719872 

35.8887 

10.8802 

1234 

1522756 

1879080904 

35.1283 

10.7260 

1289 

1661521 

2141700569 

35.9026 

10.8831 

1235 

1525225 

1833652875 

35.1426 

10.7289 

1290 

1664100 

2146689000 

35.9166 

10.8859 

1236 

1527696 

1838232256 

35.1568 

10.7318 

1291 

1666681 

2151685171 

35.9305 

10.8887 

1237 

1530169 

1892819053 

35.1710 

10.7347 

1292 

1669264 

2156689088 

35.9444 

10.8915 

1233 

1532644 

1897413272 

35.1852 

10.7376 

1293 

1671849 

2161700757 

35.9583 

10.8943 

1239 

1535121 

1902014919 

35.1994 

10.7405 

1294 

1674436 

2166720184 

35.9722 

10.8971 

1240 

1537600 

1906624000 

35.2136 

10.7434 

1295 

1677025 

2171747375 

35.9fBl 

10.8959 

1241 

1540081 

1911240521 

35.2278 

10.7463 

1296 

167%16 

2176782336 

36.0000 

10.9027 

1242 

1542564 

1915864438 

35.2420 

10.7491 

1297 

1682209 

2181825073 

36.0139 

10.9055 

1243 

1545049 

1920495907 

35.2562 

10.7520 

1298 

1684804 

2186875592 

36.0278 

10.9083 

1244 

1547536 

1925134784 

35.2704 

10.7549 

1299 

1687401 

2191933899 

36.0416 

10.9111 

1245 

1550025 

1929781125 

35.2846 

10.7578 

1300 

1690000 

2197000000 

36.0555 

10.9139 

1246 

1552516 

1934434936 

35.2987 

10.7607 

1301 

1692601 

2^02073901 

36.0694 

10.9167 

1247 

1555005 

1939096223 

35.3129 

10.7635 

1302 

1695204 

2207155608 

36.0832 

10.9195 

1243 

1557504 

1  943764992 

35.3270 

10.7664 

1303 

1697809 

2212245127 

36.0971 

10.9223 

1249 

1560001 

1948441249 

35.3412 

10.7693 

1304 

1700416 

2217342464 

36.1109 

10.9251 

1250 

1562509 

1953125000 

35.3553 

10.7722 

1305 

1703025 

2222447625 

36.1248 

10.9279 

1251 

1555011 

1957816251 

35.3695 

10.7750 

1306 

1705636 

2227560616 

36.1386 

10.9307 

1252 

1567504 

1962515008 

35.3836 

10.7779 

1307 

1708249 

2232681443 

36.1525 

10.9335 

1253 

1570009 

1967221277 

35.3977 

10.7808 

1308 

1710864 

22378101  12 

36.1663 

10.9363 

1254 

1572516 

197193506435.4119 

10.7837 

1309 

1713481 

2242946629 

36.1801 

10.9391 

106 


MATHEMATICAL  TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
.Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

T310 

1716100 

2248091000 

36.1939 

10.9418 

1365 

1863225 

2543302125 

36.9459 

1  1  .0929 

1311 

1718721 

2253243231 

36.2077 

10.9446 

1366 

1865956 

25488958% 

36.9594 

1  1  .0956 

1312 

1721344 

2258403328 

36.2215 

10.9474 

1367 

1868689 

2554497863 

36.9730 

1  1  .0983 

1313 

1723969 

2263571297 

36.2353 

10.9502 

1368 

1871424 

2560108032 

36.9865 

11.1010 

1314 

17265% 

2268747144 

36.2491 

10.9530 

1369 

1874161 

2565726409 

37.0000 

11.1037 

1315 

1729225 

2273930875 

36.2629 

10.9557 

1370 

1876900 

2571353000 

37.0135 

11.1064 

1316 

1731856 

22791224% 

36.2767 

10.9585 

1371 

1879641 

257698781  1 

37.0270 

11.1091 

1317 

1734489 

2284322013 

36.2905 

10.%13 

1372 

1882384 

2582630848 

37.0405 

11.1118 

1318 

1737124 

2289529432 

36.3043 

10.9640 

1373 

1885129 

2588282117 

37.0540 

11.1145 

1319 

1739761 

2294744759 

36.3180 

10.9668 

1374 

1887876 

2593941624 

37.0675 

11.1172 

1320 

1742400 

2299968000 

36.3318 

10.%% 

1375 

1890625 

2599609375 

37.0810 

11.1199 

1321 

1745041 

2305199161 

36.3456 

10.9724 

1376 

1893376 

2605285376 

37.0945 

11.1226 

1322 

1747684 

2310438248 

36.3593 

10.9752 

1377 

18%129 

261096%33 

37.1080 

11.1253 

1323 

1750329 

2315685267 

36.3731 

10.9779 

1378 

1898884 

2616662152 

37.1214 

11.1280 

1324 

1752976 

2320940224 

36.3868 

10.9807 

1379 

1901641 

2622362939 

37.1349 

11.1307 

1325 

1755625 

2326203125 

36.4005 

10.9834 

1380 

1904400 

2628072000 

37.1484 

11.1334 

1326 

1758276 

2331473976 

36.4143 

10.9862 

1381 

1907161 

2633789341 

37.1618 

11.1361 

1327 

1760929 

2336752783 

36.4280 

10.9890 

1382 

1909924 

2639514968 

37.1753 

11.1387 

1328 

1763584 

2342039552 

36.4417 

10.9917 

1383 

1912689 

2645248887 

37.1887 

11.1414 

1329 

1766241 

2347334289 

36.4555 

10.9945 

1384 

1915456 

2650991104 

37.2021 

11.1441 

1330 

1768900 

2352637000 

36.4692 

10.9972 

1385 

1918225 

2656741625 

37.2156 

11.1468 

1331 

1771561 

2357947691 

36.4829 

11.0000 

1386 

1920996 

2662500456 

37.2290 

11.1495 

1332 

1774224 

2363266368 

36.4966 

1  1  .0028 

1387 

1923769 

2668267603 

37.2424 

11.1522 

1333 

1776889 

2368593037 

36.5103 

11.0055 

1388 

1926544 

2674043072 

37.2559 

11.1548 

1334 

1779556 

2373927704 

36.5240 

11.0083 

1389 

1929321 

2679826869 

37.2693 

11.1575 

1335 

1782225 

2379270375 

36.5377 

11.0110 

1390 

1932100 

2685619000 

37.2827 

11.1602 

1336 

1784896 

2384621056 

36.5513 

11.0138 

1391 

1934881 

2691419471 

37.2961 

11.1629 

1337 

1787569 

2389979753 

36.5650 

11.0165 

1392 

1937664 

2697228288 

37.3095 

11.1655 

1338 

1790244 

2395346472 

36.5787 

11.0193 

1393 

1940449 

2703045457 

37.3229 

11.1682 

1339 

1792921 

2400721219 

36.5923 

11.0220 

1394 

1943236 

2708870984 

37.3363 

11.1709 

1340 

1795600 

2406104000 

36.6060 

11.0247 

1395 

1946025 

2714704875 

37.3497 

11.1736 

1341 

1798281 

2411494821 

36.6197 

1  1  .0275 

1396 

1948816 

2720547136 

37.3631 

11.1762 

1342 

1800964 

2416893688 

36.6333 

1  1  .0302 

1397 

1951609 

2726397773 

37.3765 

11.1789 

1343 

1803649 

2422300607 

36.6469 

1.0330 

1398 

1954404 

2732256792 

37.3898 

11.1816 

1344 

1806336 

2427715584 

36.6606 

1  .0357 

1399 

1957201 

2738124199 

37.4032 

11.1842 

1345 

1809025 

2433138625 

36.6742 

.0384 

1400 

1960000 

2744000000 

37.4166 

11.1869 

1346 

1811716 

2438569736 

36.6879 

.0412 

1401 

1962801 

2749884201 

37.4299 

11.1896 

1347 

1814409 

2444008923 

36.7015 

.0439 

1402 

1%5604 

2755776808 

37.4433 

11.1922 

1348 

1817104 

2449456192 

36.7151 

.0466 

1403 

1%8409 

2761677827 

37.4566 

11.1949 

1349 

1819801 

2454911549 

36.7287 

.0494 

1404 

1971216 

2767587264 

37.4700 

11.1975 

1350 

1822WO 

2460375000 

36.7423 

.0521 

1405 

1974025 

2773505125 

37.4833 

11.2002 

1351 

1825201 

2465846551 

36.7560 

1  .0548 

1406 

1976836 

2779431416 

37,4967 

1  1  .2028 

1352 

1827904 

2471326208 

36.76% 

1  .0575 

1407 

1979649 

2785366143 

37.5100 

1  1  .2055 

1353 

1830609 

2476813977 

36.7831 

.0603 

1408 

1982464 

2791309312 

37.5233 

1  1  .2082 

1354 

1833316 

2482309864 

36.7967 

1.0630 

1409 

1985281 

2797260929 

37.5366 

11.2108 

1355 

1836025 

2487813875 

36.8103 

.0657 

1410 

1988100 

2803221000 

37.5500 

11.2135 

1356 

1838736 

2493326016 

36.8239 

1.0684 

1411 

1990921 

2809189531 

37.5633 

11.2161 

1357 

1841449 

2498846293 

36.8375 

1.0712 

1412 

1993744 

2815166528 

37.5766 

11.  2  188 

1358 

1844164 

2504374712 

36.8511 

1.0739 

1413 

19%569 

2821151997 

37.5699 

11.2214 

1359 

1846881 

2509911279 

36.8646 

1  .0766 

1414 

1999396 

2827145944 

37.6032 

1  1  .2240 

1360 

1849600 

2515456000 

36.8782 

1  .0793 

1415 

2002225 

2833148375 

37  6165 

11.2267 

1361 

1852321 

2521008881 

36.8917 

1  .0820 

1416 

2005056 

28391592% 

37.6298 

11.2293 

1362 

1855044 

2526569928 

36.9053 

1  .0847 

1417 

2007889 

2845178713 

37.6431 

11.2320 

1363 

1857769 

2532139147 

36.9188  11.0875 

1418 

2010724 

2851206632 

37.6563 

1  1  2346 

1364  18604% 

2537716544 

36.9324  1  1  .0902 

1419 

2013561 

2857243059 

37.66% 

1  1  2373 

SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS.       107 


No. 

Square. 

Cube. 

Sq.  | 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1420 
1421 
1422 
1423 
1424 

2016400 
2019241 
2022084 
2024929 
2027776 

2863288000 
2869341461 
2875403448 
2881473967 
2887553024 

37.6829 
37.6962 
37.7094 
37.7227 
37.7359 

1  1  .2399 
1  1  .2425 
1  1  .2452 
11.2478 
11.2505 

1475 
1476 
1477 
1478 
1479 

2175625 
2178576 
2181529 
2184484 
2187441 

3209046875 
3215578176 
3222118333 
3228667352 
3235225239 

38.4057 

38  4187 
38.4318 
38.4448 
38.4578 

1  1  .3832 
1  1  .3858 
1  1  .3883 
11.3909 
11.3935 

1425 
1426 
1427 
1428 
1429 

2030625 
2033476 
2036329 
2039184 
2042041 

2893640625 
2899736776 
2905841483 
2911954752 
2918076589 

37.7492 
37.7624 
37.7757 
37.7889 
37.8021 

11.2531 
11.2557 
1  1  .2583 
11.2610 
11.2636 

1480 
1481 
1482 
1483 
1484 

2190400 
2193361 
21%324 
2199289 
2202256 

3241792000 
3248367641 
3254952168 
3261545587 
3268147904 

38.4708 
38.4838 
38.4968 
38.5097 
38.5227 

11.3960 
11.3986 
11.4012 
11.4037 
11.4063 

1430 
1431 
1432 
1433 
1434 

2044900 
2047761 
2050624 
2053489 
2056356 

2924207000 
2930345991 
2936493568 
2942649737 
2948814504 

37.8153 
37.8286 
37.8418 
37.8550 
37.8682 

11.2662 
11.2689 
11.2715 
11.2741 
11.2767 

1485 
1486 
1487 
1488 
1489 

2205225 
2208196 
2211169 
2214144 
2217121 

3274759125 
3281379256 
3288008303 
3294646272 
3301293169 

38.5357 
38.5487 
38.5616 
38.5746 
38.5876 

11.4089 
11.4114 
11  4140 
11.4165 
11.4191 

1435 
1436 
1437 
1438 
1439 

2059225 
20620% 
2064969 
2067844 
2070721 

2954987875 
2961169856 
2967360453 
2973559672 
29797675  19 

37.8814 
37.8946 
37.9078 
37.9210 
37.9342 

11.2793 
11.2820 
1  1  .2846 
11.2872 
1  1  .2898 

1490 
1491 
1492 
1493 
1494 

2220100 
2223081 
2226064 
2229049 
2232036 

3307949000 
3314613771 
3321287488 
3327970157 
3334661784 

386005 
38.6135 
386264 
38.6394 
38.6523 

11.4216 
11.4242 
1  1  .4268 
1  1  .4293 
11.4319 

1440 
1441 
1442 
1443 
1444 

2073600 
2076481 
2079364 
2032249 
2085136 

2985984000 
2992209121 
2998442888 
3004685307 
3010936384 

37.9473 
37.9605 
37.9737 
37.9868 
38.0000 

1  1  .2924 
11.2950 
1  1  .2977 
1  1  .3003 
11.3029 

1495 
1496 
1497 
1493 
1499 

2235025 
2238016 
2241009 
2244004 
2247001 

3341362375 
3348071936 
3354790473 
3361517992 
3368254499 

38.6652 
38.6782 
38.691  1 
38.7040 
38.7169 

1  1  .4344 
1  1  .4370 
11.4395 
11.4421 
11.4446 

1445 
1446 
1447 
1448 
1449 

2088025 
2090916 
2093809 
2096704 
2099601 

3017196125 
3023464536 
3029741623 
3036027392 
3042321849 

38.0132 
38.0263 
38.0395 
38  0526 
38.0657 

1  1  .3055 
11.3081 
11.3107 
11.3133 
11.3159 

1500 
1501 
1502 
1503 
1504 

2250000 
2253001 
2256004 
2259009 
2262016 

3375000000 
3381754501 
3388518008 
3395290527 
3402072064 

38.7298 
38.7427 
38.7556 
38.7685 
38.7814 

11.4471 
1  1  .4497 
11.4522 
1  1  .4548 
11.4573 

1450 
1451 
1452 
1453 
1454 

2102500 
2105401 
2108304 
2111209 
2114116 

3048625000 
3054936851 
3061257408 
3067586677 
3073924664 

38.0789 
38.0920 
38.1051 
38.1182 
38.1314 

11.3185 
11.3211 
1  1  .3237 
1  1  .3263 
11.3289 

1505 
1506 
1507 
1508 
1509 

2265025 
2268036 
2271049 
2274064 
2277081 

3408862625 
3415662216 
3422470843 
3429288512 
3436115229 

38.7943 
38.8072 
38  8201 
38.8330 
38.8458 

11.4598 
11.4624 
11.4649 
11.4675 
11.4700 

1455 
1456 
1457 
1458 
1459 

2117025 
2119936 
2122849 
2125764 
2128681 

3080271375 
3086626816 
3092990993 
3099363912 
3105745579 

38.1445 
38.1576 
38.1707 
38.1838 
38.1969 

11.3315 
11.3341 
1  1  .3367 
11.3393 
11.3419 

1510 
1511 
1512 
1513 
1514 

2280100 
2283121 
2286144 
2289169 
22921% 

3442951000 
3449795831 
3456649728 
3463512697 
3470384744 

38.8587 
38.8716 
38.8844 
38.8973 
38.9102 

11.4725 
11.4751 
11  ,4776 
11.4801 
11.4826 

1460 
1461 
1462 
1463 
1464 

2131600 
2134521 
2137444 
2140369 
2143296 

3112136000 
3118535181 
3124943128 
3131359847 
3137785344 

38.2099 
38.2230 
38.2361 
38.2492 
38.2623 

11.3445 
11.3471 
11.34% 
11.3522 
11.3548 

1515 

1516 
1517 
1518 
1519 

2295225 
2298256 
2301289 
2304324 
2307361 

3477265875 
34841560% 
3491055413 
3497%3832 
3504881359 

38.9230 
38.9358 
38.9487 
38.%15 
38.9744 

11.4852 
11.4877 
11.4902 
11.4927 
11.4953 

1465 
1466 
1467 
1468 
1469 

2146225 
2149156 
2152089 
2155024 
2157%1 

3144219625 
3150662696 
3157114563 
3163575232 
3170044709 

38.2753 
38.2884 
38.3014 
38.3145 
38.3275 

11.3574 
11.3600 
11.3626 
1  1  .3652 
11.3677 

1520 
1521 
1522 
1523 
1524 

2310400 
2313441 
2316484 
2319529 
2322576 

3511808000 
3518743761 
3525688648 
3532642667 
3539605824 

38.9872 
39.0000 
39.0128 
39.0256 
39.0384 

11.4978 
11.5003 
11.5028 
11.5054 
11.5079 

1470 
1471 
M72 
1473 
1474 

2160900 
2163841 
2166784 
2169729 
2172676 

3176523000 
3183010111 
3189506048 
3196010817 
3202524424 

38.3406 
38.3536 
38.3667 
38.3797 
38  3927 

11.3703 
1  1  .3729 
1  1  .3755 
1  1  3780 
11.3806 

1525 
1526 
1527 
4528 
1529 

2325625 
2328676 
2331729 
2334784 
2337841 

3546578125 
3553559576 
3560550183 
3567549952 
3574558889 

39.0512 
39.0640 
39.0768 
39.08% 
39.1024 

11.5104 
11.5129 
11.5154 
11.5179 
11.5204 

108 


MATHEMATICAL  TABLES, 


No. 

1530 
1531 
1532 
1533 
1534 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

"7565 
1566 
1567 
1568 
1569 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

2340900 
2343961 
2347024 
2350089 
2353156 

3581577000 
3588604291 
3595640768 
3602686437 
3609741304 

39.1152 
39.1280 
39.1408 
39.1535 
39.1663 

1  1  .5230 
11.5255 
11.5280 
11.5305 
11.5330 

2449225 
2452356 
2455489 
2458624 
2461761 

3833037125 
38403894% 
3847751263 
3855123432 
3862503009 

39.5601 
39.5727 
39.5854 
39.5980 
39.6106 

11.6102 
11.6126 
11.6151 
11.6176 
11.6200 

1535 
1536 
1537 
1538 
1539 

2356225 
23592% 
2362369 
2365444 
2368521 

3616805375 
3623878656 
3630%  11  53 
3638052872 
3645153819 

39.1791 
39.1918 
39.2046 
39.2173 
39.2301 

11.5355 
1  1  .5380 
1  1  .5405 
1  1  .5430 
1  1  .5455 

1570 
1571 
1572 
1573 
1574 

2464900 
2468041 
2471184 
2474329 
2477476 

3869893000 
3877292411 
3884701248 
3892119517 
3899547224 

39.6232 
39.6358 
39.6485 
39.661  1 
39.6737 

11.6225 
1  1  .6250 
1  1  .6274 
1  1  .6299 
11.6324 

1540 
1541 
1542 
1543 
1544 

2371600 
2374681 
2377764 
2380849 
2383936 

3652264000 
3659383421 
3666512088 
3673650007 
3680797184 

39.2428 
39.2556 
39.2683 
39.2810 
39.2938 

1  1  .5480 
11.5505 
11.5530 
11.5555 
11.5580 

1575 
1576 
1577 
1578 
1579 

2480625 
2483776 
2486929 
2490084 
2493241 

3906984375 
3914430976 
3921887033 
3929352552 
3936827539 

39.6863 
39.6989 
39.7115 
39.7240 
39.7366 

1  1  .6348 
1  1  .6373 
1  1  .6398 
1  1  .6422 
1  1  .6447 

1545 
1546 
1547 
1548 
154Q 

2387025 
2390116 
2393209 
2396304 
2399401 

3687953625 
3695119336 
3702294323 
3709478592 
3716672149 

39.3065 
393192 
39.3319 
39.3446 
39.3573 

1  1  .5605 
1  1  .5630 
1  1  .5655 
11.5680 
11.5705 

1580 
1581 
1582 
1583 
1584 

2496400 
2499561 
2502724 
2505889 
2509056 

3944312000 
3951805941 
3959309368 
3966822287 
3974344704 

39.7492 
39.7618 
39.7744 
39.7869 
39.7995 

11.6471 
11.64% 
11.6520 
1  1  .6545 
1  1  .6570 

1550 
1551 
1552 
1553 
1554 

2402500 
2405601 
2408704 
2411809 
2414916 

3723875000 
3731087151 
3738308608 
3745539377 
3752779464 

39.3700 
39.3827 
39.3954 
39.4081 
39.4208 

1  1  .5729 
11.5754 
1  1  .5779 
1  1  .5804 
1  1  .5829 

1585 
1586 
1587 
1588 
1589 

2512225 
25153% 
2518569 
2521744 
2524921 

3981876625 
3989418056 
3996%9003 
4004529472 
4012099469 

39.8121 
39.8246 
39.8372 
39.8497 
39.8623 

1  1  .6594 
11.6619 
1  1  .6643 
11.6668 
1  1  .6692 

1555 
1556 
1557 
1558 
1559 

2418025 
2421136 
2424249 
2427364 
2430481 

3760028875 
3767287616 
3774555693 
3781833112 
37891  19879 

39.4335 
39.4462 
39.4588 
39.4715 
39.4842 

11.5854 
1  1  .5879 
1  1  .5903 
1  1  .5928 
1  1  .5953 

1590 
1591 
1592 
1593 
1594 

2528100 
2531281 
2534464 
2537649 
2540836 

401%79000 
4027268071 
4034866688 
4042474857 
4050092584 

39.8748 
39.8873 
39.8999 
39.9124 
39.9249 

11.6717 
1  1  .6741 
1  1  .6765 
1  1  .6790 
11.6814 

1560 
1561 
1562 
1563 
1564 

2433600 
2436721 
2439844 
2442969 
24460% 

3796416000 
3803721481 
381  1036328 
3818360547 
3825694144 

39.4968 
39.5095 
39.5221 
39.5348 
39.5474 

1  1  .5978 
11.6003 
11.6027 
1  1  .6052 
11.6077 

1595 
15% 
1597 
1598 
1599 

2544025 
2547216 
2550409 
2553604 
2556801 

4057719875 
4065356736 
4073003173 
4080659192 
4088324799 

39.9375 
39.9500 
39.%25 
39.9750 
39.9875 

1  1  .6839 
1  1  .6863 
11  6888 
11.6912 
11.6936 

1600 

2560000 

4096000000 

40.0000 

11.6961 

SQUARES  AND  CUBES  OF  DECIMALS. 


No. 

Square 

Cube. 

No. 

Square 

Cube. 

No. 

Square. 

'  Cube. 

\2 

.01 
.04 

.001 
.008 

.01 
.02 

.0001 
.0004 

.000  001 
.000  008 

.001 
.002 

.00  00  01 
.00  00  04 

.000  000  001 
.000  000  008 

.09 

.027 

.03 

.0009 

.000  027 

.003 

.00  00  09 

.000  000  027 

*4 

.16 

.064 

.04 

.0016 

.000  064 

.004 

.00  00  16 

,000  000  064 

.5 

.25 

.125 

.05 

.0025 

.000  125 

.005 

.00  00  25 

.000  000  125 

6 

.36 

.216 

.06 

.0036 

.000  216 

.006 

.00  00  36 

.000  000  216 

.7 

.49 

.343 

.07 

.0049 

.000  343 

.007 

.00  00  49 

.000  000  343 

8 

.64 

.512 

.08 

.0064 

.000  512 

.008 

.00  00  64 

.000  000  512 

.9 

.81 

.729 

.09 

.0081 

.000  729 

.009 

.00  00  81 

.000  000  729 

1  0 

1  00 

1.000 

.10 

.0100 

.001  000 

.010 

.00  01  00 

.000  001  000 

1.44 

1.728 

.12 

.0144 

.001  728 

.012 

.00  01  44 

.000  001  728 

Note  that  the  square  has  twice  as  many  decimal  places,  and  the  cube 
.three times  as  many  decimal  places,  as  the  root. 


FIFTH  ROOTS   AND   FIFTH   POWERS, 


109 


FIFTH  ROOTS  AND  FIFTH  POWERS. 

(Abridged  from  TRAUTWINB.) 


*i 
&& 

Power. 

o  3 

£« 

Power. 

(H   . 

o  -^ 

ll 

Power. 

S<i 

ll 

Power. 

li 

Itf 

Power. 

.10 

.000010 

3.7 

693.440 

9.8 

90392 

21.8 

4923597 

40 

102400000 

.15 

.000075 

3.8 

792.352 

9.9 

95099 

22.0 

5153632 

41 

115856201 

.20 

.000320 

3.9 

902.242 

10.0 

100000 

22.2 

5392186 

42 

130691232 

.25 

.000977 

4.0 

1024.00 

10.2 

110408 

22.4 

5639493 

43 

147008443 

.30 

.002430 

4.1 

1158.56 

10.4 

121665 

22.6 

5895793 

44 

164916224 

.35 

.005252 

4.2 

1306.91 

10.6 

133823 

22.8 

6161327 

45 

184528125 

.40 

.010240 

4.3 

1470.08 

10.8 

146933 

23.0 

6436343 

46 

205962976 

.45 

.018453 

4.4 

1649.16 

11.0 

161051 

23.2 

6721093 

47 

229345007 

.50 

.031250 

4.5 

1845.28 

11.2 

176234 

23.4 

7015834 

48 

254803968 

.55 

.050328 

4.6 

2059.63 

11.4 

192541 

23.6 

7320825 

49 

282475249 

.60 

.077760 

4.7 

2293.45 

11.6 

210034 

23.8 

7636332 

50 

312500000 

.65 

.116029 

4.8 

2548.04 

11.8 

228776 

24.0 

7962624 

51 

345025251 

.70 

.168070 

49 

2824.75 

12.0 

248832 

24.2 

8299976 

52 

380204032 

.75 

.237305 

5.0 

3125.00 

12.2 

270271 

24.4 

8648666 

53 

418195493 

.80 

.327680 

5.1 

3450.25 

12.4 

293163 

24.6 

9008978 

54 

459165024 

.85 

.443705 

5.2 

3802.04 

12.6 

317580 

24.8 

9381200 

55 

503284375 

.90 

.590490 

5.3 

4181.95 

12.8 

343597 

25.0 

9765625 

56 

550731776 

.95 

.773781 

5.4 

4591  65 

13.0 

371293 

25.2 

10162550 

57 

601692057 

.00 

1.00000 

5.5 

5032.84 

13.2 

400746 

25.4 

10572278 

58 

656356768 

.05 

1.27628 

5.6 

5507.32 

13.4 

432040 

25.6 

10995116 

59 

714924299 

.10 

1.61051 

5.7 

6016.92 

13.6 

465259 

25.8 

11431377 

60 

777600000 

.15 

2.01135 

5.8 

6563.57 

13.8 

500490 

26.0 

11881376 

61 

844596301 

.20 

2.48832 

5.9 

7149.24 

14.0 

537824 

26.2 

12345437 

62 

916132832 

.25 

3.05176 

6.0 

7776.00 

14.2 

577353 

26.4 

12823886 

63 

992436543 

.30 

3.71293 

6.1 

8445.96 

14.4 

619174 

26.6 

13317055 

64 

1073741824 

.35 

4.48403 

6.2 

9161.33 

14.6 

663383 

26.8 

13825281 

65 

1160290625 

.40 

5.37824 

6.3 

9924.37 

14.8 

710082 

27.0 

14348907 

66 

1252332576 

.45 

6.40973 

6.4 

10737 

15.0 

759375 

27.2 

14888280 

67 

1350125107 

.50 

7.59375 

6.5 

11603 

15.2 

811368 

27.4 

15443752 

68 

1453933568 

.55 

8.94661 

6.6 

12523 

15.4 

866171 

27.6 

16015681 

69 

1564031349 

.60 

10.4858 

6.7 

13501 

15.6 

923896 

27.8 

1  6604430 

70 

1680700000 

.65 

12.2298 

6.8 

14539 

15.8 

984658 

28.0 

17210368 

71 

1804229351 

.70 

14.1986 

6.9 

15640 

16.0 

1048576 

28.2 

17833868 

72 

1934917632 

.75 

16.4131 

7.0 

16807 

16.2 

1115771 

28.4 

18475309 

73 

2073071593 

.80 

18.8957 

7.1 

18042 

16.4 

1186367 

28.6 

19135075 

74 

2219006624 

.85 

21.6700 

7.2 

19349 

16.6 

1260493 

28.8 

19813557 

75 

2373046875 

.90 

24.7610 

7.3 

20731 

16.8 

1338278 

29.0 

20511149 

76 

2535525376 

.95 

28.1951 

7.4 

22190 

17.0 

1419857 

29.2 

21228253 

77 

2706784157 

2.00 

32.0000 

7.5 

23730 

17.2 

1  505366 

29.4 

21965275 

78 

2887174368 

2.05 

36.2051 

7.6 

25355 

17.4 

1594947 

29.6 

22722628 

79 

3077056399 

2.10 

40.8410 

7.7 

27068 

17.6 

1688742 

298 

23500728 

80 

3276800000 

2.15 

45.9401 

7.8 

28872 

17.8 

1  786899 

30.0 

24300000 

81 

3486784401 

2.20 

51.5363 

7.9 

30771 

18.0 

1889568 

30.5 

26393634 

82 

3707398432 

2.25 

57.6650 

8.0 

32768 

18.2 

1996903 

31.0 

28629151 

83 

3939040643 

2.30 

64.3634 

8.1 

34868 

18.4 

2109061 

31.5 

31013642 

84 

4182119424 

2.35 

71.6703 

8.2 

37074 

18.6 

2226203 

32.0 

33554432 

85 

4437053125 

2.40 

79.6262 

8.3 

39390 

18.8 

2348493 

32.5 

36259082 

86 

4704270176 

2.45 

88.2735 

8.4 

41821 

19.0 

2476099 

33.0 

39135393 

87 

4984209207 

2.50 

97.6562 

8.5 

44371 

19.2 

2609193 

33.5 

42191410 

88 

5277319168 

2.55 

107.820 

8.6 

47043 

19.4 

2747949 

34.0 

45435424 

89 

5584059449 

2.60 

118.814 

8.7 

49842 

19.6 

2892547 

34.5 

48875980 

90 

5904900000 

2.70 

143.489 

8.8 

52773 

19.8 

3043168 

35.0 

52521875 

91 

6240321451 

2.80 

172.104 

8.9 

55841 

20.0 

3200000 

35.5 

56382167 

92 

6590815232 

2.90 

205.111 

9.0 

59049 

20.2 

3363232 

36.0 

60466176 

93 

6956883693 

3.00 

243.000 

9.1 

62403 

20.4 

3533059 

36.5 

64783487 

94 

7339040224 

3.10 

286.292 

9.2 

65908 

20.6 

3709677 

37.0 

69343957 

95 

7737809375 

3.20 

335.544 

9.3 

69569 

20.8 

3893289 

37.5 

74157715 

96 

8153726976 

3.30 

391.354 

9.4 

73390 

21.0 

4084101 

38.0 

79235168 

97 

8587340257 

3.40 

454.354 

9.5 

77378 

21.2 

4282322 

38.5 

84587005 

98 

9039207968 

3.50 

525.219 

9.6 

81537 

21.4 

4488  1  66 

39.0 

90224199 

99 

9509900499 

3.60 

604.662 

9.7 

85873 

21.6 

4701850 

39.5 

96158012 

110 


MATHEMATICAL  TABLES. 


tt 

|- 

53 


1    O 

!l 


81 
Bl 

0 
0 


I 


LO  CO  C 

O  —  r 


-''  — 


--- 


OI>«.O^ 

m  !>•  co  c 

CNt^  — C 


o  o  O  •-  «ri  i 

• 


OvO 
^O  —  C 
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ooow^oooooomom.  oooinoomoooomtnoro  c^.o 
-1  —  !>.  —  mo^-OiAOPOOoor^oot>NO'^-vOfNOOio'Tt' 

-<        —  '- 


«—  —  -•  —  —  «N  «N  <N  (N  <S  (S  (S  fS  <N  C 


,.. 

f^t^.t^.0  —  (NpTiOO'^TOOO  —  <N 

oo  —  covo  —  <NPM  —  ir^rt-r>.in 

O  O  O  O  O  —  fS  CO  vO  00  -O  CO  <N  r 

—  fT 


d  OO  CO  —  ' 

U^ICN  — 


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C.S 


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o  —  oooo 


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Is 

1.- 


CIRCUMFERENCES   AND   AREAS   OF   CIRCLES. 
CIRCUMFERENCES  AND  AREAS  OF  CIRCLES. 


Ill 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

1/64 

.04909 

.00019 

23/8 

7.4613 

4.4301 

6Vs 

19.242 

29  465 

1/32 

.  098  1  8 

.00077 

7/16 

7.6576 

4  .  6664 

1/4 

19.635 

30  680 

3/64 

.14726 

.00173 

i/3 

7.8540 

4.9087 

3/8 

20.028 

31   919 

Vl6 

.19635 

.00307 

9/16 

8.0503 

5.1572 

V2 

20.420 

33    183 

3/32 

.29452 

.00690 

5/8 

8.2467 

5.4119 

5/8 

20.813 

34.472 

Vs 

.39270 

.01227 

H/16 

8.4430 

5.6727 

3/4 

21.206 

35  785 

5/32 

.49087 

.01917 

3/4 

8.6394 

5.9396 

7/8 

21.598 

37.  122 

3/16 

.  58905 

.02761 

13/16 

8.8357 

6.2126 

21.991 

38.485 

7/32 

.  68722 

.03758 

7/8 

9.0321 

6.4918 

*l/8 

22.384 

39.871 

15/16 

9.2284 

6.7771 

V4 

22.776 

41.282 

1/4 

.78540 

.  04909 

3/8 

23  .  1  69 

42.718 

»/32 

.88357 

.06213 

3. 

9.4248 

7.0686 

V2 

23.562 

44.  179 

5/16 

.98175 

.07670 

Vl6 

9.6211 

7.3662 

5/8 

23.955 

45  .  664 

H/32 

.0799 

.09281 

Vs 

9.8175 

7  .  6699 

3/4 

24.347 

47.173 

3/8 

.  1781 

.11045 

3/16 

10.014 

7.9798 

7/8 

24.740 

48.707 

13/32 

.2763 

.12962 

!/4 

10.210 

8.2958 

8. 

25.133 

50.265 

7/16 

.3744 

..15033 

5/16 

10.407 

8.6179 

V8 

25.525 

51.849 

15/32 

.4726 

.17257 

3/8 

10.603 

8.9462 

1/4 

25.918 

53.455 

7/16 

10.799 

9.2806 

3/8 

26.311 

55.088 

1/2 

.5708 

.19635 

1/2 

10.996 

9.6211 

V2 

26.704 

56.745 

17/32 

.6690 

.22166 

9/16 

11.  192 

9.9678 

5/8 

27.096 

58.426 

9/18 

.7671 

.24850 

5/8 

1  1  .  388 

10.321 

3/4 

27.489 

60.  132 

19/32 

.8653 

.27688 

H/16 

11.585 

10.680 

7/8 

27.882 

61.862 

5/8 

.9635 

.30680 

3/4 

11.781 

11.045 

9. 

28.274 

63.617 

21/32 

2.0617 

.33824 

13/16 

11.977 

11.416 

1/8 

28.667 

65.397 

H/16 

2.1598 

.37122 

7/8 

12.174 

1  1  .  793 

1/4 

29.060 

67.201 

23/32 

2.2580 

.40574 

15/16 

12.370 

12.177 

3/8 

29.452 

69.029 

4. 

12.566 

12.566 

1/2 

29.845 

70.882 

3/4 

2.3562 

.44179 

Vl6 

12.763 

12.962 

5/8 

30.238 

72.760 

25/32 

2.4544 

.47937 

1/8 

12.959 

13.364 

3/4 

30.631 

74.662 

13/16 

2.5525 

.51849 

3/16 

13.  155 

13.772 

•7/8 

3  1  .  023 

76.589 

27/32 

2.6507 

.55914 

1/4 

13.352 

14.  186 

10. 

31.416 

78.540 

7/8 

2.7489 

.60132 

5/16 

13.548 

14.607 

V8 

3  1  .  809 

80.516 

29/32 

2.8471 

.64504 

3/8 

13.744 

15.033 

1/4 

32.201 

82.516 

15/16 

2.9452 

.  69029 

7/16 

13.941 

15.466 

3/8 

32.594 

84.541 

31/32 

3.0434 

.73708 

1/2 

14.137 

1  5  .  904 

V2 

32.987 

86.590 

9/16 

14.334 

16.349 

5/8 

33.379 

88,664 

1. 

3.1416 

.7854 

5/8 

14.530 

16.800 

3/4 

33.772 

90.763 

Vl6 

3.3379 

.8866 

U/16 

14.726 

17.257 

7/8 

34.  165 

92.886 

•1/8 

3.5343 

.9940 

3/4 

14.923 

17.721 

11. 

34.558 

95.033 

3/16 

3.7306 

.1075 

13/16 

15.119 

18.  190 

1/8 

34.950 

97.205 

1/4 

3.9270 

.2272 

7/8 

15.315 

18.665 

1/4 

35.343 

99.402 

5/16 

4.1233 

.3530 

15/16 

15.512 

19.147 

3/8 

35.736 

101.62 

3/8 

4.3197 

.4849 

5. 

15.708 

19.635 

V2 

36.  128 

103.87 

7/16 

4.5160 

.6230 

Vl6 

1  5  .  904 

20.  129 

5/8 

36.521 

106.14 

1/2 

4.7124 

.7671 

1/8 

16.  101 

20.629 

3/4 

36.914 

108.43 

'•Vie 

4.9087 

.9175 

3/16 

16.297 

21.135 

7/8 

37.306 

110.75 

5/8 

5.1051 

2.0739 

1/4 

16.493 

21.648 

13. 

37.699 

113.10 

H/16 

5.3014 

2.2365 

5/l6 

16.690 

22  .  1  66 

V8 

38.092 

115.47 

3/4 

5.4978 

2.4053 

3/8 

16.886 

22.691 

1/4 

38.485 

117.86 

13/16 

5.6941 

2.5802 

7/16 

17.082 

23.221 

3/8 

38.877 

120.28 

7/8 

5.8905 

2.7612 

1/2 

17.279 

23.758 

1/2 

39.270 

122.72 

15/16 

6.0868 

2.9483 

9/16 

17.475 

24.301 

5/8 

39.663 

125.19 

5/8 

17.671 

24.850 

3/4 

40.055 

127.68 

3. 

6.2832 

3.1416 

n/ie 

17.868 

25.406 

7/8 

40.448 

130.19 

Vl6 

6.4795 

3.3410 

3/4 

18.064 

25.967 

13. 

40.841 

132.73 

1/8 

6.6759 

3.5466 

13/16 

18.261 

26.535 

V8 

41.233 

135  30 

3/16 

6.8722 

3.7583 

7/8 

18.457 

27.  109 

1/4 

41.626 

137.89 

1/4 

7  .  0686 

3.9761 

15/16 

18.653 

27.688 

3/8 

42.019 

140.50 

5/16 

7.2649 

4.2000 

6. 

18.850 

28.274 

1/2 

42.412 

143.14 

112 


MATHEMATICAL  TABLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam 

Circum. 

Area. 

135/8 

42.804 

145.80 

217/8 

68.722 

375.83 

30  Vs 

94.640 

712.76 

3/4 

43.197 

148.49 

23. 

69.  115 

380.13 

1/4 

95.033 

718.69 

7/8 

43.590 

151.20 

1/8 

69.508 

384.46 

3/8 

95.426 

724  64 

14. 

43  ,  982 

153.94 

1/4 

69.900 

388.82 

1/2 

95.819 

730.62 

1/8 

44.375 

156.70 

3/8 

70.293 

393.20 

5/8 

96.211 

736.62 

1/4 

44.768 

159.48 

1/2 

70.686 

397.61 

3/4 

96.604 

742.64 

3/8 

45.160 

162.30 

5/8 

71.079 

402.04 

7/8 

96.997 

748.69 

V2 

45.553 

165.13 

3/4 

71.471 

406.49 

31. 

97.389 

754.77 

5/8 

45.946 

167.99 

7/8 

71.864 

410.97 

V8 

97.782 

760.87 

3/4 

46.338 

170.87 

23. 

72.257 

415.48 

1/4 

98.175 

766.99 

7/8 

46.731 

173.78 

1/8 

72.649 

420.00 

3/8 

98.567 

773.  14 

15. 

47.124 

176.7! 

1/4 

73.042 

424.56 

1/2 

98.960 

779.31 

J-/8 

47.517 

179.67 

3/8 

73.435 

429.13 

5/8 

99.353 

785.51 

1/4 

47.909 

182.65 

1/2 

73.827 

433.74 

3/4 

99.746 

791    73 

3/8 

48.302 

185.66 

5/8 

74.220 

438.36 

7/8 

100.  138 

797.98 

V2 

48.695 

188.69 

3/4 

74.613 

443.01 

32. 

100.531 

804.25 

5/8 

49.087 

191.75 

7/8 

75.006 

447.69 

Vs 

100.924 

810.54 

3/4 

49.480 

194.83 

24. 

75.398 

452.39 

1/4 

101.316 

816.86 

7/8 

49.873 

197.93 

1/8 

75.791 

457.11 

3/8 

101.709 

823.21 

16. 

50.265 

201.06 

1/4 

76.  184 

461.86 

1/2 

102.102 

829.58 

Vs 

50.658 

204.22 

3/8 

76.576 

466.64 

5/8 

102.494 

835.97 

V4 

51.051 

207.39 

1/2 

76.969 

471.44 

3/4 

102.887 

842.39 

3/8 

51.444 

210.60 

5/8 

77.362 

476.26 

7/8 

103.280 

848.83 

V2 

51.836 

213.82 

3/4 

77.754 

481.11 

33. 

103.673 

855.30 

5/8 

52.229 

217.08 

7/8 

78.147 

485.98 

1/8 

104.065 

861.79 

3/4 

52.622 

220.35 

25. 

78.540 

490.87 

1/4 

104.458 

868.31 

7/8 

53.014 

223.65 

1/8 

78.933 

495.79 

3/8 

104.851 

874.85 

17. 

53.407 

226.98 

1/4 

79.325 

500.74 

V2 

105.243 

881.41 

Vs 

53.800 

230.33 

3/8 

79.718 

505.71 

5/8 

105.636 

888.00 

1/4 

54.192 

233.71 

1/2 

80.111 

510.71 

3/4 

106.029 

894.62 

3/8 

54.585  - 

237.10 

5/8 

80.503 

515.72 

7/8 

106.421 

901.26 

1/2 

54.978 

240.53 

3/4 

80.896 

520.77 

34. 

106.814 

907.92 

5/8 

55.371 

243.98 

7/8 

81.289 

525.84 

V8 

107.207 

914.61 

3/4 

55.763 

247.45 

26. 

81.681 

530.93 

1/4 

107.600 

921.32 

7/8 

56.156 

250.95 

1/8 

82.074 

536.05 

3/8 

107.992 

928.06 

18. 

56.549 

254.47 

1/4 

82.467 

541.19 

1/2 

108.385 

934.82 

1/8 

56.941 

258.02 

3/8 

82.860 

546.35 

5/8 

108.778 

941.61 

1/4 

57.334 

261.59 

1/2 

83.252 

551.55 

3/4 

109.  170 

948.42 

3/8 

57.727 

265.18 

5/8 

83.645 

556.76 

7/8 

109.563 

955.25 

1/2 

58.119 

268.80 

3/4 

-84.038 

562.00 

35. 

109.956 

962  .  1  1 

5/8 

58.512 

272.45 

7/8 

84.430 

567.27 

1/8 

110.348 

969  .  00 

3/4 

58.905 

276.12 

27. 

84.823 

572.56 

1/4 

110.741 

975.91 

7/8 

59.298 

279.81 

Vs 

85.216 

577.87 

3/8 

111.  134 

982.84 

19. 

59.690 

283.53 

1/4 

85.608 

583.21 

1/2 

111.527 

989.80 

1/8 

60.083 

287.27 

3/8 

86.001 

588.57 

5/8 

111.919 

996.78 

1/4 

60.476 

291.04 

1/2 

86.394 

593.96 

3/4 

112.312 

1003.8 

3/8 

60.868 

294.83 

5/8 

86.786 

599.37 

7/8 

112.705 

1010.8 

1/2 

61.261 

298.65 

3/4 

87.179 

604.81 

36. 

113.097 

1017.9 

5/8 

61.654 

302.49 

7/8 

87.572 

610.27 

1/8 

113.490 

1025.0 

3/4 

62  .  046 

306.35 

28. 

87.965 

615.75 

1/4 

113.883 

1032.1 

7/8 

62.439 

310.24 

V8 

88.357 

621.26 

3/8 

114.275 

1039.2 

20. 

62.832 

314.16 

1/4 

88.750 

626.80 

1/2 

114.  668 

1046.3 

1/8 

63.225 

318.10 

3/8 

89.143 

632.36 

5/8 

115.061 

1053.5 

1/4 

63.617 

322.06 

1/2 

89.535 

637.94 

3/4 

115.454 

1060.7 

3/8 

64.010 

326.05 

5/8 

89.928 

643.55 

7/8 

115.846 

1068.0 

1/2 

64.403 

330.06 

3/4 

90.321 

649.18 

37. 

116.239 

1075.2 

5/8 

64.795 

334.10 

7/8 

90.713 

654.84 

1/8 

116.632 

1082.5 

3/4 

65.188 

338.16 

29. 

91.106 

660.52 

1/4 

117.024 

1089.8 

7/8 

65.581 

342.25 

1/8 

91.499 

666.23 

3/8 

117.417 

1097.1 

21. 

65.973 

346.36 

V4 

91  .892 

671.96 

1/2 

17.810 

1104.5 

1/8 

66.366 

350.50 

3/8 

92.284 

677.71 

5/8 

18.202 

1111.8 

1/4 

66.759 

354.66 

1/2 

92.677 

683  .  49 

3/4 

1-8.596 

1119.2 

3/8 

67.152 

358.84 

5/8 

93.070 

689.30 

7/8 

18.988 

1126.7 

1/2 

67.544 

363.05 

3/4 

93.462 

695.13 

38. 

19.381 

1134.1 

5/8 

67.937 

367.28 

7/8 

93.855 

700.98 

1/8 

19.773 

1141.6 

3/4 

68.330 

371.54 

30. 

94.248 

706  .  86 

V4 

120.166 

1149.1 

CIRCUMFERENCES   AND  AREAS   OF   CIRCLES.       113 


Dtam 

Circuin. 

Area. 

Diara 

Circum. 

Area. 

Diam 

Circum. 

Area. 

883/8 

120.559 

1136.6 

465/8 

146.477 

1707.4 

547/g 

172.395 

2365.0 

1/2 

120.951 

1164.2 

3/4 

146.869 

1716.5 

55. 

172.788 

2375.8 

5/8 

121.344 

1171.7 

7/8 

147.262 

1725.7 

1/8 

173.180 

2386.6 

3/4 

121.737 

1179.3 

47. 

147.655 

1734.9 

V4 

173.573 

2397.5 

7/8 

122.129 

1186.9 

Vs 

148.048 

1744.2 

3/8 

173.966 

2408.3 

39. 

122.522 

1194.6 

V4 

148.440 

1753.5 

V2 

174.358 

2419.2 

l/8 

122.915 

1202.3 

3/8 

148.833 

1762.7 

5/8 

174.751 

2430.  1 

1/4 

123.308 

1210.0 

V2 

149.226 

1772.  1 

3/4 

175.  144 

2441.  1 

3/8 

123.700 

1217.7 

5/8 

149.618 

1781.4 

7/8 

175.536 

2452.0 

1/2 

124.093 

1225.4 

3/4 

150.011 

1790.8 

56. 

175.929 

2463.0 

5/8 

124.486 

1233.2 

7/8 

150.404 

1800.  1 

Vs 

176.322 

2474.0 

3/4 

124.878 

1241.0 

48. 

150.796 

1809.6 

1/4 

176.715 

2485.0 

7/8 

125.271 

1248.8 

Vs 

151.189 

1819.0 

3/8 

177.  107 

2496.  1 

40. 

125.664 

1256.6 

1/4 

151.582 

1828.5 

1/2 

177.500 

2507.2 

Vs 

126.056 

1264.5 

$ 

151.975 

1837.9 

5/8 

177.893 

2518.3 

1/4 

126.449 

1272.4 

1/2 

152.367 

1847.5 

3/4 

178.285 

2529.4 

3/8 

126.842 

1280.3 

5/8 

152.760 

1857.0 

7/8 

178.678 

2540.6 

1/9 

127.235 

1288.2 

3/4 

153.  153 

1866.5 

57. 

179.071 

2551.8 

5/8 

127.627 

1296.2 

7/8 

153.545 

1876.  1 

1/8 

1  79.  463 

2563.0 

3/4 

128.020 

1304.2 

49. 

153.938 

1885.7 

V4 

179.856 

2574.2 

7/a 

128.413 

1312.2 

Vs 

154.331 

1895.4 

3/8 

180.249 

2585.4 

41. 

128.805 

1320.3 

V4 

154.723 

1905.0 

1/2 

180.642 

2596.7 

Vs 

129.198 

1328.3 

3/8 

155.116 

1914.7 

5/8 

181.034 

2608.0 

V4 

129.591 

1336.4 

V2 

155.509 

1924.4 

3/4 

181.427 

2619.4 

3/8 

129.983 

1344.5 

5/8 

155.902 

1934.2 

7/8 

181.820 

2630.7 

I/O 

130.376 

1352.7 

3/4 

156.294 

1943.9 

58. 

182.212 

2642.  1 

5/8 

130.769 

1360.8 

7/8 

156.687 

1953.7 

VS 

182.605 

2653.5 

3/4 

131.161 

1369.0 

50. 

157  080 

1963.5 

V4 

182.998 

2664.9 

7/8 

131.554 

1377.2 

Vs 

157.472 

1973.3 

3/8 

183.390 

2676.4 

42. 

131.947 

1385.4 

1/4 

157.865 

1983.2 

1/2 

183.783 

2687.8 

1/8 

132.340 

1393.7 

3/jj 

158.258 

1993.1 

5/8 

184.176 

2699.3 

V? 

132.732 

1  402  .  0 

1/9 

158.650 

2003.0 

3/4 

184.569 

2710.9 

3/8 

133.125 

1410.3 

5/8 

159.043 

2012.9 

7/8 

184.961 

2722.4 

1/9 

133.518 

1418.6 

8/4 

159.436 

2022.8 

59. 

185.354 

2734.0 

5/8 

133.910 

1427.0 

7/8 

159.829 

2032.8 

i/a 

185.747 

2745.6 

3/4 

134.303 

1435.4 

51. 

160.221 

2042.8 

1/4 

186.139 

2757.2 

7/8 

134.696 

1443.8 

Vs 

160.614 

2052.8 

3/8 

186.532 

2768.8 

43. 

135.088 

1452.2 

*/4 

161.007 

2062.9 

1/2 

186.925 

2780.5 

Vs 

135.481 

1460.7 

3/8 

161.399 

2073.0 

5/8 

187.317 

2792.2 

1/4 

135.874 

1469.  1 

1/2 

161.792 

2083.1 

3/4 

187.710 

2803.9 

3/8 

136.267 

1477.6 

5/8 

162.185 

2093.2 

7/8 

188.103 

2815.7 

V2 

136.659 

1486.2 

3/4 

162.577 

2103.3 

60. 

188.496 

2827.4 

5/8 

137.052 

1494.7 

7/8 

162.970 

2113.5 

Vs 

188.888 

2839.2 

3/4 

137.445 

1503.3 

53. 

163.363 

2123.7 

1/4 

189.281 

2851.0 

7/8 

137.837 

1511.9 

Vs 

163.756 

2133.9 

3/8 

189.674 

2862.9 

44. 

138.230 

1520.5 

V4 

164.148 

2144.2 

1/2 

190.066 

2874.8 

Vs 

138.623 

1529.2 

3/8 

164.541 

2154.5 

5/8 

190.459 

2886.6 

V4 

139.015 

1537.9 

1/2 

164.934 

2164.8 

3/4 

190.852 

2898.6 

3/8 

139.408 

1546.6 

5/8 

165.326 

2175.1 

7/8 

191.244 

2910.5 

V2 

139.801 

1555.3 

3/4 

165.719 

2185.4 

61. 

191.637 

2922.5 

5/8 

140.194 

1564.0 

7/8 

166.112 

2195.8 

1/8 

192.030 

2934.5 

3/4 

140.586 

1572.8 

53. 

166.504 

2206.2 

V4 

192.423 

2946.5 

7/8 

140.979 

1581.6 

Vs 

166.897 

2216.6 

3/8 

192.815 

2958.5 

45. 

141.372 

1590.4 

V4 

167.290 

2227.0 

1/2 

193.208 

2970.6 

Vs 

141.764 

1599.3 

3/8 

167.683 

2237.5 

5/8 

193.601 

2982  .  7 

V4 

142.157 

1608.2 

1/2 

168.075 

2248.0 

3/4 

193.993 

2994.8 

3/8 

142.550 

1617.0 

5/8 

1  68  .  468 

2258.5 

7/8 

194.386 

3006.9 

Va 

142.942 

1626.0 

3/4 

168.861 

2269.1 

62. 

194.779^ 

3019.1 

5/8 

143.335 

1634.9 

7/8 

169.253 

2279.6 

Vs 

195.  171 

3031.3 

3/4 

143.728 

1643.9 

54. 

169.646 

2290.2 

V4 

195.564 

3043.5 

7/8 

144.  121 

1652.9 

1/8 

170.039 

2300.8 

3/8 

195.957 

3055.7 

46. 

144.513 

1661.9 

1/4 

170.431 

2311.5 

V2 

196.350 

3068.0 

Vs 

144.906 

1670.9 

3/8 

170.824 

2322.1 

5/8 

196.742 

3080.3 

V4 

145.299 

1680.0 

1/2 

171.217 

2332.8 

8/4 

197.135 

3092.6 

3/8 

145.691 

1689.1 

5/8 

171.609 

2343.5 

7/8 

197.528 

3  1  04  .  9 

,      V2 

146.084 

1698.2 

3/4 

172.002 

2354.3 

63. 

197.920 

3117.2 

114 


MATHEMATICAL  TABLES. 


Diam. 

63V8~ 

Circum. 

Area. 

Diam 

Circum. 

Area. 

Diam 

Circum. 

Area. 
"4979.1 

198.313 

3129.6 

713/8 

224.231 

4001.1 

795/8 

250.149 

1/4 

198.706 

3142.0 

1/2 

224.624 

4015.2 

3/* 

250.542 

4995  .  2 

3/8 

199.098 

3154.5 

5/8 

225.017 

4029.2 

7/8 

250.935 

5010.9 

1/2 

199.491 

3166.9 

3/4 

225.409 

4043.3 

80. 

251.327 

5026.5 

5/8 

199.884 

3179.4 

7/8 

225.802 

4057.4 

1/8 

251.720 

5042.3 

3/4 

200.277 

3191.9 

73. 

226.  195 

4071.5 

1/4 

252.  113 

5058.0 

7/8 

200.669 

3204.4 

Vs 

226.587 

4085.7 

3/8 

252.506 

5073.8 

64. 

201.062 

3217.0 

1/4 

226.980 

4099.8 

!/2 

252.898 

5089.6 

1/8 

201.455 

3229.6 

3/8 

227.373 

4114.0 

5/8 

253.291 

5105.4 

V4 

201.847 

3242.2 

V2 

227.765 

4128.2 

3/4 

253.684 

5121.2 

3/8 

202.240 

3254.8 

5/8 

228.158 

4142.5 

7/8 

254.076 

5137.  1 

Va 

202.633 

3267.5 

3/4 

228.551 

4156.8 

81. 

254.469 

5153.0 

5/8 

203.025 

3280.1 

7/8 

228.944 

4171.1 

V8 

254.862 

5  1  68  .  9 

3/4 

203.418 

3292.8 

73. 

229.336 

4185.4 

1/4 

255.254 

5184.9 

7/8 

203.811 

3305.6 

1/8 

229.729 

4199.7 

3/8 

255.647 

5200.8 

65. 

204.204 

3318.3 

1/4 

230.122 

4214.1 

1/2 

256.040 

5216.8 

Vs 

204.596 

3331.1 

3/8 

230.514 

4228.5 

5/8 

256.433 

5232.8 

V4 

204.989 

3343.9 

V2 

230.907 

4242.9 

3/4 

256.825 

5248.9 

3/8 

205.382 

3356.7 

5/8 

231.300 

4257.4 

7/8 

257.218 

5264.9 

V2 

205.774 

3369.6 

3/4 

231.692 

4271.8 

83. 

257.611 

5281.0 

5/8 

206.167 

3382.4 

7/8 

232.085 

4286.3 

1/8 

258.003 

5297.  1 

3/4 

206.560 

3395.3 

74. 

232.478 

4300.8 

1/4 

258.396 

5313.3 

7/8 

206.952 

3408.2 

1/8 

232.871 

4315.4 

3/8 

258.789 

5329.4 

66. 

207.345 

3421.2 

1/4 

233.263 

4329.9 

1/2 

259.181 

5345.6 

1/8 

207.738 

3434.2 

3/8 

233.656 

4344.5 

5/8 

259.574 

5361.8 

1/4 

208.131 

3447.2 

1/2 

234.049 

4359.2 

3/4 

259.967 

5378.  1 

3/8 

208.523 

3460.2 

5/8 

234.441 

4373.8 

7/8 

260.359 

5394.3 

1/2 

208.916 

3473.2 

3/4 

234.834 

4388.5 

83. 

260.752 

5410.6 

5/8 

209.309 

3486.3 

7/8 

235.227 

4403  .  1 

1/8 

261.145 

5426.9 

3/4 

209.701 

3499.4 

75. 

235.619 

4417.9 

l/4 

261.538 

5443.3 

7/8 

210.094 

3512.5 

1/8 

236.012 

4432.6 

3/8 

261.930 

5459.6 

67. 

210.487 

3525.7 

1/4 

236.405 

4447.4 

1/2 

262.323 

5476.0 

1/8 

210.879 

3538.8 

3/8 

236.798 

4462.2 

5/8 

262.716 

5492.4 

1/4 

211.272 

3552.0 

V2 

237.190 

4477.0 

3/4 

263.108 

5508.8 

3/8 

211.665 

3565.2 

5/8 

237.583 

-^491.8 

7/8 

263.501 

5525.3 

1/2 

212.058 

3578.5 

3/4 

237.976 

4506.7 

84. 

263.894 

5541.8 

5/8 

212.450 

3591.7 

7/8 

238.368 

4521.5 

1/8 

264.286 

5558.3 

3/4 

212.843 

3605.0 

76c 

238.761 

4536.5 

V4 

264.679 

5574.8 

7/8 

213.236 

3618.3 

1/8 

239.154 

4551.4 

3/8 

265.072 

5591.4 

68. 

213.628 

3631.7 

V4 

239.546 

4566.4 

1/2 

265.465 

5607.9 

Vs 

214.021 

3645.0 

3/8 

239.939 

4581.3 

5/8 

265.857 

5624.5 

V4 

214.414 

3658.4 

1/2 

240.332 

4596.3 

3/4 

266.250 

5641.2 

3/8 

214.806 

3671.8 

5/8 

240.725 

4611.4 

7/8 

266.643 

5657.8 

1/2 

215.199 

3685.3 

3/4 

241.  117 

4626.4 

85. 

267.035 

5674.5 

5/8 

215.592 

3698.7 

7/8 

241.510 

4641.5 

1/8 

267.428 

5691.2 

3/4 

2  1  5  .  984 

3712.2 

77. 

241.903 

4656.6 

V4 

267.821 

5707.9 

7/8 

216.377 

3725.7 

1/8 

242.295 

4671.8 

3/8 

268.213 

'5724.7 

69. 

216.770 

3739.3 

1/4 

242.688 

4686.9 

V2 

268.606 

5741.5 

Vs 

217.163 

3752.8 

3/8 

243.081 

4702.1 

5/8 

268.999 

5758.3 

V4 

217.555 

3766.4 

1/2 

243.473 

4717.3 

3/4 

269.392 

5775.1 

3/8 

2  1  7  .  948 

3780.0 

5/8 

243.866 

4732.5 

7/8 

269.784 

5791.9 

1/2 

218.341 

3793.7 

3/4 

244.259 

4747.8 

86. 

270.177 

5808.8 

5/8 

218.733 

3807.3 

7/8 

244.652 

4763.1 

1/8 

270.570 

5825.7 

3/4 

219.126 

3821.0 

78. 

245.044 

4778.4 

1/4 

270.962 

5842.6 

7/8 

219.519 

3834.7 

1/8 

245.437 

4793.7 

3/8 

271.355 

5859.6 

70. 

219.911 

3848.5 

1/4 

245.830 

4809.0 

1/9 

271.748 

5876.5 

V8 

220.304 

3862.2 

3/8 

246.222 

4824.4 

5/J 

272.140 

5893.5 

1/4 

220.697 

3876.0 

i/2 

246.615 

4839.8 

3/4 

272.533 

5910.6 

3/8 

221.090 

3889.8 

5/8 

247.008 

4855.2 

7/8 

272.926 

5927.6 

V2 

221.482 

3903.6 

3/4 

247   400 

4870.7 

87. 

273.319 

5944.7 

5/8 

221.375 

3917.5 

7/8 

247.793 

4886.2 

Vs 

273.711 

5961.8 

3/4 

222.268 

3931.4 

79. 

248.  186 

4901.7 

1/4 

274.  104 

5978.9 

7/8 

222  .  660 

3945.3 

!/8 

248.579 

4917.2 

3/8 

274.497 

5996.0 

71. 

223.053 

3959  2 

1/4 

248.971 

4932.7 

1/2 

274.889 

6013.2 

V8 

223  .  446 

3973   1 

3/8 

249.364 

4948.3 

5/8 

275.282 

6030.4 

1/4 

223.838 

3987.1 

V2 

249.757 

4963.9 

3/4 

275.675 

6047.6 

CIRCUMFERENCES    AND   AREAS   OF   CIRCLES.       115 


Diani 

Circum. 

Area. 

Diam 

Circum. 

Area. 

Diam 

Circum. 

Area. 

877/s 

276.067 

6064.9 

957/s 

301.200 

7219.4 

130 

408.41 

13273.23 

88. 

276.460 

6082.1 

96. 

301.593 

7238.2 

131 

411.55 

13478.22 

1/8 

276.853 

6099.4 

1/8 

301.986 

7257.1 

132 

414.69 

13684.78 

1/4 

277.246 

6116.7 

1/4 

302.378 

7276.0 

133 

417.83 

13892.91 

3/8 

277.638 

6134.1 

3/8 

302.771 

7294.9 

134 

420.97 

1  4  1  02  .  6  1 

1/2 

278.031 

6151.4 

1/2 

303.  164 

7313.8 

135 

424.  12 

14313.88 

5/8 

278.424 

6168.8 

5/8 

303.556 

7332.8 

136 

427.26 

14526.72 

3/4 

278.816 

6186.2 

3/4 

303.949 

7351.8 

137 

430.40 

!4741  .  14 

7/8 

279.209 

6203  .  7 

7/8 

304.342 

7370.8 

138 

433.54 

14957.12 

89. 

279.602 

6221.1 

97. 

304.734 

7389.8 

139 

436.68 

15174.68 

V8 

279.994 

6238.6 

1/8 

305.  127 

7408.9 

140 

439.82 

15393.80 

1/4 

280.387 

6256.1 

1/4 

305.520 

7428.0 

141 

442.96 

15614.50 

3/8 

280.780 

6273.7 

3/8 

305.913 

7447.1 

142 

446.  11 

15836.77 

Vz 

281.  173 

6291.2 

1/2 

306.305 

7466.2 

143 

449.25 

16060.61 

5/8 

281.565 

6308.8 

5/8 

306.698 

7485.3 

144 

452.39 

16286.02 

3/4 

281.958 

6326.4 

3/4 

307.091 

7504.5 

145 

455.53 

16513.00 

7/8 

282.351 

6344.1 

7/8 

307.483 

7523.7 

146 

458.67 

16741.55 

90. 

282.743 

6361.7 

98. 

307.876 

7543.0 

147 

461.81 

16971.67 

Vs 

283.136 

6379.4 

1/8 

308.269 

7562.2 

148 

464.96 

17203.36 

1/4 

283.529 

6397.1 

1/4 

308.661 

7581.5 

149 

468.10 

17436.62 

3/8 

283.921 

64  1  4  .  9 

3/8 

309.054 

7600.8 

150 

471.24 

17671.46 

1/2 

284.314 

6432.6 

1/2 

309.447 

7620.  1 

151 

474.38 

17907.86 

5/8 

284.707 

6450.4 

5/8 

309.840 

7639.5 

152 

477.52 

18145.84 

3/4 

285.100 

6468.2 

3/4 

310.232 

7658.9 

153 

480.66 

18385.39 

7/8 

285.492 

6486.0 

7/8 

310.625 

7678.3 

154 

483.81 

18626.50 

91. 

285.885 

6503.9 

99. 

311.018 

7697.7 

155 

486.95 

18869.19 

Vs 

286.278 

6521.8 

1/8 

311.410 

7717.1 

156 

490  .  09 

19113.45 

1/4 

286.670 

6539.7 

1/4 

311.803 

7736.6 

157 

493.23 

19359.28 

3/8 

287.063 

6557.6 

3/8 

312.  196 

7756.1 

158 

496.37 

19606.68 

V2 

287.456 

6575.5 

1/2 

312.588 

7775.6 

159 

499.51 

19855.65 

5/8 

287.848 

6593.5 

5/8 

312.981 

7795.2 

160 

502.65 

20106.  19 

3/4 

288.241 

6611.5 

3/4 

313.374 

7814.8 

161 

505  .  80 

20358.31 

7/8 

288.634 

6629.6 

7/8 

313.767 

7834.4 

162 

508.94 

20611.99 

93. 

289.027 

6647.6 

100 

314".  159 

7854.0 

163 

512.08 

20867.24 

Vs 

289.419 

6665  .  7 

101 

317.30 

8011  .85 

164 

515.22 

21124.07 

V4 

289.812 

6683.8 

102 

320.44 

8171.28 

165 

518.36 

21382.46 

3/8 

290.205 

6701.9 

103 

323.58 

8332.29 

166 

521.50 

21642.43 

V2 

290.597 

6720.  1 

104 

326.73 

8494.87 

167 

524.65 

21903.97 

5/8 

290.990 

6738.2 

105 

329.87 

8659.01 

168 

527.79 

22167.08 

3/4 

291.383 

6756.4 

106 

333.01 

8824.73 

169 

530.93 

22431.76 

7/8 

291.775 

6774.7 

107 

336.15 

8992.02 

170 

534.07 

22698.01 

93. 

292.168 

6792.9 

108 

339.29 

9160.88 

171 

537.21 

22965  .  83 

V8 

292.561 

6811.2 

109 

342.43 

9331.32 

172 

540.35 

23235.22 

V4 

292.954 

6829.5 

110 

345.58 

9503.32 

173 

543.50 

23506.18 

3/8 

293.346 

6847.8 

111 

348.72 

9676.89 

174 

546.64 

23778.71 

1/2 

293.739 

6866.1 

112 

351.86  > 

9852.03 

175 

549.78 

24052.82 

5/8 

294.  132 

6884.5 

113 

355.00 

0028.75 

176 

552.92 

24328.49 

3/4 

294.524 

6902  .  9 

114 

358.14 

0207.03 

177 

556.06 

24605  .  74 

7/8 

294.917 

6921.3 

115 

361.28 

0386.89 

178 

559.20 

24884.56 

94. 

295.310 

6939.8 

116 

364.42 

0568.32 

179 

562.35 

25164.94 

1/8 

295  .  702 

6958.2 

117 

367.57 

0751.32 

ISO 

565  .  49 

25446.90 

1/4 

296.095 

6976.7 

118 

370.71 

0935.88 

181 

568.63 

25730.43 

3/8 

296.488 

6995.3 

119 

373.85 

1122.02 

182 

571.77 

26015.53 

1/2 

296.881 

701.3.8 

120 

376.99 

1309.73 

183 

574.91 

26302.20 

5/8 

297.273 

7032.4 

121 

380.13 

1499.01 

184 

578.05 

26590.44 

3/4 

297.666 

7051.0 

122 

383.27 

1689.87 

185 

581.19 

26880.25 

7/8 

298.059 

7069.6 

123 

386.42 

1882.29 

186 

584.34 

27171.63 

95. 

298.451 

7088.2 

124 

389.56 

2076.28 

187 

587.48 

27464.59 

1/8 

298.844 

7106.9 

125 

392.70 

2271.85 

188 

590.62 

27759.11 

1/4 

299.237 

7125.6 

126 

395.84 

2468.98 

189 

593  .  76 

28055.21 

3/8 

299.629 

7144.3 

127 

398.98 

2667.69 

190 

596.90 

28352.87 

1/2 

300.022 

7163.0 

128 

402.  12 

2867.96 

191 

600.04 

28652.  11 

5/8 

300.415 

7181.8 

129 

405.27 

3069.81 

192 

603.19 

28952.92 

3/4 

•  n      i 

300.807 

7200.6 

116 


MATHEMATICAL  TABLES. 


Diam 

Circum 

Area. 

Diam 

Circum 

Area. 

Diam 

Circum. 

Area. 

193 

606.33 

29255.30 

260 

816.81 

53092.92 

327 

1027.30 

83961.84 

194 

609.47 

29559.25 

261 

819.96 

53502.11 

328 

1030.44 

84496.28 

195 

612.61 

29864.77 

262 

823.10 

53912.87 

329 

1033.58 

85012.28 

196 

615.75 

30171.86 

263 

826.24 

54325.  21 

330 

1036.73 

85529.86 

197 

618.89 

30480.52 

264 

829.38 

54739.11 

331 

1039.87 

86049.01 

193 

622.04 

30790.75 

265 

832.52 

55154.59 

332 

1043.01 

86569.73 

199 

625.  18 

31102.55 

266 

835.66 

55571.63 

333 

1046.  15 

87092.02 

200 

628.32 

31415.93 

267 

838.81 

55990.25 

334 

1049.29 

87615.88 

201 

631.46 

31730.87 

268 

841.95 

56410.44 

335 

1052.43 

88141.31 

202 

634.60 

32047.39 

269 

845.09 

56832.20 

336 

1055.58 

88668.31 

203 

637.74 

32365.47 

270 

848.23 

57255.53 

337 

1058.72 

89196.88 

204 

640.88 

32685.  13 

271 

851.37 

57680.43 

338 

1061  .86 

89727.03 

205 

644.03 

33006.36 

272 

854.51 

58106.90 

339 

1065.00 

90258.74 

206 

647.  17 

33329.  16 

273 

857.65 

58534.94 

340 

1068.  14 

90792.03 

207 

650.31 

33653.53 

274 

860.80 

58964.55 

341 

1071.28 

91326.88 

203 

653.45 

33979.47 

275 

863  .  94 

59395.74 

342 

1074.42 

91863.31 

209 

656.59 

34306.98 

276 

867.08 

59828.49 

343 

1077.57 

92401.31 

210 

659.73 

34636.06 

277 

870.22 

60262.82 

344 

1080.71 

92940.88 

211 

662.88 

34966.71 

278 

873.36 

60698.71 

345 

1083.85 

93482.02 

212 

666.02 

35298.94 

279 

876.50 

61136.  18 

346 

1086.99 

94024.73 

213 

669.  16 

35632.73 

280 

879.65 

61575.22 

347 

1090.  13 

94569.01 

214 

672.30 

35968.09 

281 

882.79 

62015.82 

348 

1093.27 

95114.86 

215 

675.44 

36305.03 

282 

885.93 

62458.00 

349 

1096.42 

95662.28 

216 

678.58 

36643.54 

283 

889.07 

62901.75 

350 

1099.56 

96211.28 

217 

681.73 

36983.61 

284 

892.21 

63347.07 

351 

1102.70 

96761.84 

218 

684.87 

37325.26 

285 

895.35 

63793.97 

352 

1105.84 

97313.97 

219 

688.01 

37668.48 

286 

898.50 

64242.43 

353 

1108.98 

97867.68 

230 

691.  15 

38013.27 

287 

901.64 

64692.46 

354 

1112.  12 

98422.96 

221 

694.29 

38359.63 

288 

904.78 

65144.07 

355 

1115.27 

98979.80 

222 

697.43 

38707.56 

289 

907.92 

65597.24 

356 

1118.41 

99538.22 

223 

700.58 

39057.07 

290 

911.06 

66051.99 

357 

1121.55 

100098.21 

224 

703.72 

39408.  14 

291 

914.20 

66508.30 

358 

1124.69 

100659.77 

225 

706.86 

39760.78 

292 

917.35 

66966.  19 

359 

1127.83 

101222.90 

226 

710.00 

401  15.00 

293 

920.49 

67425.65 

360 

1130.97 

101787.60 

227 

713.  14 

40470.78 

294 

923.63 

67886.68 

361 

1134.11 

102353.87 

228 

716.28 

40828.  14 

295 

926.77 

68349.28 

362 

1137.26 

102921.72 

229 

719.42 

41187.07 

296 

929.91 

68813.45 

363 

1140.40 

103491.  13 

230 

722.57 

41547.56 

297 

933.05 

69279.  19 

364 

1143.54 

1  04062  .  1  2 

231 

725.71 

41909.63 

298 

936.  19 

69746.50 

365 

1146.68 

104634.67 

232 

728.85 

42273.27 

299 

939.34 

70215.38 

366 

1149.82 

105208.80 

233 

73  1  .  99 

42638.48 

300 

942.48 

70685.83 

367 

1152.96 

105784.49 

234 

735.13 

43005.26 

301 

945.62 

71157.86 

368 

1156.11 

106361.76 

235 

738.27 

43373.61 

302 

948.76 

71631.45 

369 

1159.25 

106940.60 

236 

741.42 

43743.54 

303 

951.90 

72106.62 

370 

1162.39 

107521.01 

237 

744.56 

44115.03 

304 

955.04 

72583.36 

371 

1165.53 

108102.99 

238 

747.70 

44488.09 

305 

958.  19 

73061.66 

372 

1  168.67 

108686.54 

239 

750.84 

44862.73 

306 

961.33 

73541  .54 

373 

1171.81 

109271.66 

240 

753.98 

45238.93 

307 

964.47 

74022.99 

374 

1174.96 

109858.35 

241 

757.  12 

45616.71 

308 

967.61 

74506.01 

375 

1178.10 

1  10446.62 

242 

760.27 

45996.06 

309 

970.75 

74990.60 

376 

1181.24 

111036.45 

243 

763.41 

46376.98 

310 

973.89 

75476.76 

377 

1184.33 

1  1  1627.86 

244 

766.55 

46759.47 

311 

977.04 

75964.50 

378 

1187.52 

112220.83 

245 

769.69 

47143.52 

312 

980.  18 

76453.80 

379 

1190.66 

112815.38 

246 

772.  S3 

47529.  16 

313 

983.32 

76944.67 

380 

1193.81 

113411.49 

247 

775.97 

47916.36 

314 

986.46 

77437.12 

381 

1196.95 

114009.18 

248 

779.  11 

48305.13 

315 

989.60 

77931.  13 

382 

1200.09 

1  14608.44 

249 

782.26 

48695.47 

316 

992  .  74 

78426.72 

383 

1203.23 

115209.27 

250 

785.40 

49087.39 

317 

995.88 

78923.88 

384 

1206.37 

115811;67 

251 

788.54 

49480.87 

318 

999.03 

79422.60 

385 

1209.51 

116415.64 

252 

791.68 

49875.92 

319 

1002.17 

79922  .  90 

386 

1212.65 

117021.18 

253 

794.82 

50272.55 

320 

1005.31 

80424.77 

387 

1215.80 

117628.30 

254 

797.96 

50670.75 

321 

1008.45 

80928.21 

388 

1218.94 

18236.98 

255 

801.  11 

51070.52 

322 

1011.59 

81433.22 

389 

1222.08 

18847.24 

256 

804.25 

51471.85 

323 

1014.73 

81939.80 

390 

1225.22 

19459.06 

257 

807.39 

51874.76 

324 

1017.88 

82447.96 

391 

1228.36 

20072.46 

258 

810.53 

52279.24 

325 

1021.02 

82957.68 

392 

1231.50 

20687.46 

259 

813.67 

52685  .  29 

326 

1024.  16 

83468.98 

393 

1234.65 

21303.96 

CIRCUMFERENCES  AND   AREAS  OF  CIRCLES. 


117 


Diam 

Circum 

Area. 

Diam 

Circum 

Area. 

Diam 

Circum 

Area. 

"394" 

1237.79 

121922.07 

461 

1448.27 

166913.60 

528 

1658.76 

218956.44 

395 

1240.93 

122541.75 

462 

1451.42 

167638.53 

529 

1661.90 

219786.61 

396 

1244.07 

123163.00 

463 

1454.56 

168365.02 

530 

1665.04 

220618.34 

397 

1247.21 

123785.82 

464 

1457.70 

1  69093  .  08 

531 

1668.  19 

221451.65 

398 

1250.35 

124410.21 

465 

1460.84 

169822.72 

532 

1671.33 

222286.53 

399 

1253.50 

125036.  17 

466 

1463.98 

170553.92 

533 

1674.47 

223122.98 

400 

1256.64 

125663.71 

467 

1467.  12 

171286.70 

534 

1677.61 

223961.00 

401 

1259.78 

126292.81 

468 

1470.27 

172021.05 

535 

1680.75 

224800.59 

402 

1262.92 

126923.48 

469 

1473.41 

172756.97 

536 

1683.89 

225641.75 

403 

1266.06 

127555.73 

470 

1476.55 

173494.45 

537 

1687.04 

226484.48 

404 

1269.20 

128189.55 

471 

1479.69 

174233.51 

538 

1690.18 

227328.79 

405 

1272.35 

128824.93 

472 

1482.83 

174974.  14 

539 

1693.32 

228174.66 

406 

1275.49 

129461  .89 

473 

1485.97 

175716.35 

540 

1696.46 

229022.  10 

407 

1278.63 

130100.42 

474 

1489.11 

176460.12 

541 

1699.60 

229871.12 

408 

1281.77 

130740.52 

475 

1492.26 

177205.46 

542 

1702.74 

230721.71 

409 

1284.91 

131382.  19 

476 

1495.40 

177952.37 

543 

1705.88 

231573.86 

410 

1288.05 

132025.43 

477 

1498.54 

178700.86 

544 

1709.03 

232427.59 

411 

1291.  19 

132670.24 

478 

1501.68 

179450.91 

545 

1712.17 

233282.89 

412 

1294.34 

133316.63 

479 

1504.82 

180202.54 

546 

1715.31 

234139.76 

413 

1297.48 

133964.58 

480 

1507.96 

180955.74 

547 

1718.45 

234998.20 

414 

1300.62 

134614.10 

481 

1511.11 

181710.50 

548 

1721.59 

235858.21 

415 

1303.76 

135265.20 

482 

1514.25 

182466.84 

549 

1724.73 

236719.79 

416 

1306.90 

135917.86 

483 

1517.39 

183224.75 

550 

1727.88 

237582.94 

417 

1310.04 

136572.10 

484 

1520.53 

183984.23 

551 

1  73  1  .  02 

238447.67 

418 

1313.19 

137227.91 

485 

1523.67 

184745.28 

552 

1734.16 

239S13.96 

419 

1316.33 

137885.29 

486 

1526.81 

185507.90 

553 

1737.30 

240181.83 

420 

1319.47 

138544.24 

487 

1529.96 

186272.10 

554 

1740.44 

241051.26 

421 

1322.61 

139204.76 

488 

1533.10 

187037.86 

555 

1743.58 

241922.27 

421 

1325.75 

139866.85 

489 

1536.24 

187805.19 

556 

1746.73 

242794.85 

423 

1328.89 

140530.51 

49O 

1539.38 

188574.10 

557 

1749.87 

243668.99 

424 

1332.04 

141195.74 

491 

1542.52 

169344.5. 

558 

1753.01 

244544.71 

425 

1335.  18 

141862.54 

492 

1545.66 

1901  16.62 

559 

1756.15 

245422.00 

426 

1338.32 

142530.92 

493 

1548.81 

190890.2 

560 

1759.29 

246300.86 

427 

1341.46 

143200.86 

494 

1551.95 

191665.43 

561 

1  762  .  43 

247181.30 

428 

1344.60 

143872.38 

495 

1555.09 

192442.  18 

562 

1765.58 

248063.30 

429 

1347.74 

1  44545.  46 

496 

1558.23 

193220.51 

563 

1768.72 

248946.87 

430 

1350.88 

145220.  12 

497 

1561.37 

194000.41 

564 

1771  .86 

249832.01 

431 

1354.03 

145896.35 

498 

1564.51 

194781.89 

565 

1775.00 

250718.73 

432 

1357.17 

146574.15 

499 

1567.65 

195564.93 

566 

1778.14 

251607.01 

433 

1360.31 

147253.52 

500 

1570.80 

196349.54 

567 

1781.28 

252496.87 

434 

1363.45 

147934.46 

501 

1573.94 

197135.72 

568 

1784.42 

253388.30 

435 

1366.59 

148616.97 

502 

1577.03 

197923.48 

569 

1787.57 

254281.29 

436 

1369.73 

149301.05 

503 

1580.22 

198712.80 

570 

1790.71 

255175.86 

437 

1372  88 

149986.70 

504 

1583.36 

199503.70 

571 

1793.85 

256072.00 

438 

1376.02 

150673.93 

505 

1586.50 

200296.17 

572 

1796.99 

256969.71 

439 

1379.  16 

151362.72 

506 

1589.65 

201090.20 

573 

1800.  13 

257868.99 

440 

1382.30 

152053.08 

507 

1592.79 

201885.81 

574 

1803.27 

258769.85 

441 

1385.44 

152745.02 

508 

1595.93 

202682.99 

575 

1806.42 

259672.27 

442 

1388.58 

153438.53 

509 

1599.07 

203481.74 

576 

1809.56 

260576.26 

443 

1391.73 

154133.60 

510 

1602.21 

204282.06 

577 

1812.70 

261481.83 

444 

1394.87 

154830.25 

511 

1605.35 

205083.95 

578 

1815.84 

262388.96 

445 

1398.01 

155528.47 

512 

1608.50 

205887.42 

579 

1818.93 

263297.67 

446 

1401.  15 

156228.26 

513 

1611.64 

206692.45 

580 

1822.12 

264207.94 

447 

1404.29 

156929.62 

514 

1614.78 

207499.05 

581 

1825.27 

265119.79 

448 

1407.43 

157632.55 

515 

1617.92 

208307.23 

582 

1828.41 

266033.21 

449 

1410.58 

158337.06 

516 

1  62  1  .  06 

209116.97 

583 

1831.55 

266948.20 

450 

1413.72 

159043.13 

517 

1624.20 

209928.29 

584 

1834.69 

267864.76 

451 

1  4  1  6  .  86 

159750.77 

518 

1627.34 

210741.18 

585 

1837.83 

268782.89 

452 

1420.00 

160459.99 

519 

1630.49 

211555.63 

586 

1840.97 

269702.59 

453 

1423.14 

161170.77 

520 

1633.63 

212371.66 

587 

1844.11 

270623.86 

454 

1426.28 

161883.  13 

521 

1636.77 

213189.26 

588 

1847.26 

271546.70 

455 

1429.42 

162597.05 

522 

1639.91 

214008.43 

589 

1850.40 

272471.  12 

456 

1432.57 

163312.55 

523 

1643.05 

214829.  17 

59O 

1853.54 

273397.10 

457 

1435.71 

164029.62 

524 

1646.  19 

215651.49 

591 

1856.68 

274324.66 

458 

1438  85 

164748  26 

525 

1649.34 

216475.37 

592 

1859.82 

275253.78 

459 
460 

1441.99 
1445.13 

165468.47 
166190.25 

526 
527 

1652.48 
1655.62 

217300.82 
218127.85 

593 
594 

1862.96  276184.48 
1866.1l'277l16.75 

118 


MATHEMATICAL  TABLES. 


Diam 

Circum. 

Area. 

Diam 

Circum, 

Area. 

Diam 

Circum 

Area. 

595 

1869.25 

278050.58 

663 

2082.88 

345236.69 

731 

2296.50 

419686.  13 

596 

1872.39 

278985.99 

664 

2086.02 

346278.91 

732 

2299.65 

420835  19 

597 

1875.53 

279922.97 

665 

2089.16 

347322.70 

733 

2302.79 

421985*  79 

598 

1878.67 

280861.52 

666 

2092.30 

348368.07 

734 

2305.93 

423137.97 

599 

1881.81 

281801.65 

667 

2095.44 

349415.00 

735 

2309.07 

424291.72 

600 

1884.96 

282743.34 

668 

2098.58 

350463.51 

736 

2312.2 

425447.04 

601 

1888.  10 

283686.60 

669 

2101.73 

351513.59 

737 

2315.35 

426603  .  94 

602 

1891.24 

284631.44 

670 

2104.87 

352565.24 

738 

2318.50 

427762.40 

603 

1894.38 

285577.84 

671 

2108.01 

353618.45 

739 

2321.64 

428922.43 

604 

1897.52 

286525.82 

672 

2111.15 

354673.24 

740 

2324.78 

430084.03 

605 

1900.66 

287475.36 

673 

2114.29 

355729.60 

741 

2327.92 

431247.21 

606 

1903.81 

288426.48 

674 

2117.43 

356787.54 

742 

233  1  .  06 

432411.95 

607 

1906.95 

289379.17 

675 

2120.58 

357847.04 

743 

2334.20 

433578.27 

608 

1910.09 

290333.43 

676 

2123.72 

358908.11 

744 

2337.34 

434746.  \6 

609 

1913.23 

291289.26 

677 

2126.86 

359970.75 

745 

2340.49 

435915.62 

610 

1916.37 

292246.66 

678 

2130.00 

361034.97 

746 

2343.63 

437086.64 

611 

1919.51 

293205.63 

679 

2133.14 

362100.75 

747 

2346.77 

438259.24 

612 

1922.65 

294166.17 

680 

2136.28 

363168.11 

748 

2349.91 

439433.41 

613 

1925.80 

295128.28 

681 

2139.42 

364237.04 

749 

2353.05 

440609.16 

614 

1928.94 

296091.97 

682 

2142.57 

365307.54 

750 

2356.19 

441786.47 

615 

1932.08 

297057.22 

683 

2145.71 

366379.60 

751 

2359.34 

442965.35 

616 

1935.22 

298024.05 

684 

2148.85 

367453.24 

752 

2362.48 

444145.80 

617 

1938.36 

298992.44 

685 

2151.99 

368528.45 

753 

2365.62 

445327.83 

618 

1941.50 

299962.41 

686 

2155.13 

369605.23 

754 

2368.76 

446511.42 

619 

1944.65 

300933.95 

687 

2158.27 

370683.59 

755 

2371.90 

447696.59 

620 

1947.79 

301907.05 

688 

2161.42 

371763.51 

756 

2375.04 

448883.32 

621 

1950.93 

302881.73 

689 

2164.56 

372845.00 

757 

2378.19 

450071.63 

622 

1954.07 

303857.98 

690 

2167.70 

373928.07 

758 

2381.33 

451261.51 

623 

1957.21 

304835.80 

691 

2170.84 

375012.70 

759 

2384.47 

452452.96 

624 

1960.35 

305815.20 

692 

2173.98 

376098.91 

760 

2387.61 

453645.98 

625 

1963.50 

306796.16 

693 

2177.12 

377186.68 

761 

2390.75 

454840.57 

626 

1966.64 

307778.69 

694 

2180.27 

378276.03 

762 

2393.89 

456036.73 

627 

1969.78 

308762.79 

695 

2183.41 

379366.95 

763 

2397.04 

457234.46 

628 

1972.92 

309748.47 

696 

2186.55 

380459.44 

764 

2400.18 

458433.77 

629 

1976.06 

310735.71 

697 

2189.69 

381553.50 

765 

2403.32 

459634.64 

630 

1979.20 

311724.53 

698 

2192.83 

382649.13 

766 

2406.46 

460837.08 

631 

1982.35 

312714.92 

699 

2195.97 

383746.33 

767 

2409.60 

462041.10 

632 

1985.49 

313706.88 

700 

2199.11 

384845.10 

768 

2412.74 

463246.69 

633 

1988.63 

314700.40 

701 

2202.26 

385945.44 

769 

2415.88 

464453.84 

634 

1991.77 

315695.50 

702 

2205.40 

387047.36 

770 

2419.03 

465662.57 

635 

1994.91 

316692.17 

703 

2208.54 

388150.84 

771 

2422.17 

466872.87 

636 

1998.05 

317690.42 

704 

2211.68 

389255.90 

772 

2425.31 

468084.74 

637 

2001.  19 

318690.23 

705 

2214.82 

390362.52 

773 

2428.45 

469298.  18 

638 

2004.34 

319691.61 

706 

2217.96 

391470.72 

774 

2431.59 

470513.19 

639 

2007.48 

320694.56 

707 

2221.11 

392580.49 

775 

2434.73 

471729.77 

640 

2010.62 

321699.09 

708 

2224.25 

393691.82 

776 

2437.88 

472947.92 

641 

2013.76 

322705.18 

709 

2227.39 

394804.73 

777 

2441.02 

474167.65 

642 

2016.90 

323712.85 

710 

2230.53 

395919.21 

778 

2444.16 

475388.94 

643 

2020.04 

324722.09 

711 

2233.67 

397035.26 

779 

2447.30 

476611.81 

644 

2023.  19 

325732.89 

712 

2236.81 

398152.89 

780 

2450.44 

477836.24 

645 

2026.33 

326745.27 

713 

2239.96 

399272.08 

781 

2453.58 

479062.25 

646 

2029.47 

327759.22 

714 

2243.10 

400392.84 

782 

2456.73 

480289.83 

647 

2032.61 

328774.74 

715 

2246.24 

401515.18 

783 

2459.87 

481518.97 

648 

2035.75 

329791.83 

716 

2249.38 

402639.08 

784 

2463.01 

482749.69 

649 

2038.89 

330810.49 

717 

2252.52 

403764.56 

785 

2466.15 

483981.98 

650 

2042.04 

331830.72 

718 

2255.66 

404891.60 

786 

2469.29 

485215.84 

651 

2045.  18 

332852.53 

719 

2258.81 

406020.22 

787 

2472.43 

48645  1  .  28 

652 

2048.32 

333875.90 

720 

2261.95 

407150.41 

788 

2475.58 

487688.28 

653 

2051.46 

334900.85 

721 

2265  .  09 

408282.17 

789 

2478.72 

488926.85 

654 

2054.60 

335927.36 

722 

2268.23 

409415.50 

790 

2481.86 

490166.99 

655 

2057.74 

336955.45 

723 

2271.37 

410550.40 

791 

2485.00 

491408.71 

656 

2060.88 

337985.10 

724 

2274.51 

411686.87 

792 

2488.14 

492651.99 

657 

2064.03 

339016.33 

725 

2277.65 

412824.91 

793 

2491.28 

493896.85 

.  658 

2067.17 

340049.13 

726 

2280.80 

413964.52 

794 

2494.42 

495143.28 

659 

2070.31 

341083.50 

727 

2283.94 

415105.71 

795 

2497.57 

496391.27 

660 

2073.45 

342119.44 

728 

2287.085416248.46 

796 

2500.71 

497640.84 

661 

2076.59 

343156.95 

729 

2290.22 

417392.79 

797 

2503.85 

498891.98 

£62 

2079.73  344196.03 

730  2293.36 

418538.68 

798 

2506.99500144.69 

CIRCUMFERENCES    AND    AREAS   OP  CIRCLES.       119 


Diam 

Circum. 

Area. 

Diam.  I  Circum. 

Area. 

Diam 

Circum.  1  Area. 

799 

2510.13 

501398.97 

867 

2723.76 

590375.16 

935 

2937.39 

686614.71 

8OO 

2513.27 

502654.82 

868 

2726.90 

591737.83 

936 

2940.53 

688084.  19 

801 

2516.42 

503912.25 

869 

2730.04 

593102.06 

937 

2943.67 

689555.24 

802 

2519.56 

505171.24 

870 

2733.19 

594467.87 

938 

2946.81 

691027.86 

803 

2522.70 

50643  1  .  80 

871 

2736.33 

595835.25 

939 

2949.96 

692502  05 

804 

2525.84 

507693.94 

872 

2739.47 

597204.20 

940 

2953.10 

693977.82 

805 

2528.98 

508957.64 

873 

2742.61 

598574.72 

941 

2956.24 

695455.  15 

806 

2532.12 

510222.92 

874 

2745.75 

599946.81 

942 

2959.38 

696934.06 

807 

2535.27 

511489.77 

875 

2748.89 

601320.47 

943 

2962.52 

698414.53 

808 

2538.41 

512758.19 

876 

2752.04 

602695.70 

944 

2965  .  66 

699896.58 

809 

2541.55 

514028.18 

877 

2755.18 

604072.50 

945 

2968.81 

701380.19 

810 

2544.69 

515299.74 

878 

2758.321605450.88 

946 

2971.95 

702865  38 

811 

2547.83 

516572.87 

879 

2761.46 

606830.82 

947 

2975.09 

704352.14 

812 

2550.97 

517847.57 

88O 

2764.60 

608212.34 

948 

2978.23 

705840  47 

813 

2554.11 

519123.84 

881 

27  '67.7  'A 

609595.42 

949 

2981.37 

707330  37 

814 

2557.26 

520401.68 

882 

2770.88 

610980.08 

05O 

2984.51 

708821.84 

815 

2560.40 

521681.10 

883 

2774.03 

612366.31 

951 

2987.65 

7  1  03  1  4  .  88 

816 

2563.54 

522962.08 

884 

2777.  17 

613754.11 

952 

2990.80 

711809.50 

817 

2566.68 

524244.63 

885 

2780.31 

615143.48 

953 

2993  .  94 

713305.68 

818 

2569.82 

525528.76 

886 

2783.45 

616534.42 

954 

2997.08 

714803.43 

819 

2572,96 

526814.46 

887 

2786.59 

617926.93 

955 

3000.22 

716302.76 

820 

2576.11 

528101.73 

888 

2789.73 

619321.01 

956 

3003.36 

717803.66 

821 

2579.25 

529390.56 

889 

2792.88 

620716.66 

957 

3006.50 

719306.12 

822 

2582.39 

530680.97 

890 

2796.02 

622113.89 

958 

3009.65 

720810.16 

823 

2585.53 

531972.95 

891 

2799.16 

623512.68 

959 

3012.79 

722315.77 

824 

2588.67 

533266.50 

892 

2802.30 

624913.04 

960 

3015.93 

723822.95 

825 

2591.81 

534561.62 

893 

2805.44 

626314.98 

961 

3019.07 

725331.70 

826 

2594.96 

535858.32 

894 

2808.58 

627718.49 

962 

3022.21 

726842.02 

827 

2598.10 

537156.58 

895 

2811.73 

629123.56 

963 

3025.35 

728353.91 

828 

2601.24 

538456.41 

896 

2814.87 

630530.21 

964 

3028.50 

729867.37 

829 

2604.38 

539757.82 

897 

2818.01 

631938.43 

965 

3031.64 

731382.40 

830 

2607.52 

541060.79 

898 

2821.15 

633348.22 

966 

3034.78 

732899.01 

831 

2610.66 

542365.34 

899 

2824.29 

634759.58 

967 

3037.92 

734417.18 

832 

2613.81 

543671.46 

900 

2827.43 

636172.51 

968 

3041.06 

735936.93 

833 

2616.95 

544979.15 

901 

2830.58 

637587.01 

969 

3044.20 

737458.24 

834 

2620.09 

546288.40 

902 

2833.72 

639003.09 

970 

3047.34 

738981.13 

835 

2623.23 

547599.23 

903 

2836.86 

640420.73 

971 

3050.49 

740505.59 

836 

2626.37 

548911.63 

904 

2840.00 

641839.95 

972 

3053.63 

74203  1  .  62 

837 

2629.51 

550225.61 

905 

2843.14 

643260.73 

973 

3056.77 

743559.22 

838 

2632.65 

551541.15 

906 

2846.28 

644683  .  09 

974 

3059.91 

745088.39 

839 

2635.80 

552858.26 

907 

2849.42 

646107.01 

975 

3063.05 

746619.  13 

840 

2638.94 

554176.94 

908 

2852.57 

647532.51 

976 

3066.19 

748151.44 

841 

2642.08 

555497.20 

909 

2855.71 

648959.58 

977 

3069.34 

749685.32 

842 

2645.22 

556819.02 

910 

2858.85 

650388.22 

978 

3072.48 

751220.78 

843 

2648.36 

558142.42 

911 

2861.99 

651818.43 

979 

3075.62 

752757.80 

844 

2651.50 

559467.39 

912 

2865.13 

653250.21 

98O 

3078.76 

754296.40 

845 

2654.65 

560793.92 

913 

2868.27 

654683.56 

981 

3081.90 

755836.56 

846 

2657.79 

562122.03 

914 

2871.42 

656118.48 

982 

3085.04 

757378.30 

847 

2660.93 

563451.71 

915 

2874.56 

657554.98 

983 

3088.19 

758921.61 

848 

2664.07 

564782.96 

916 

2877.70 

658993  .  04 

984 

3091  .33 

760466.48 

849 

2667.21 

566115.78 

917 

2880.84 

660432.68 

985 

3094.47 

762012.93 

850 

2670.35 

567450.17 

918 

2883.98 

661873.88 

986 

3097.61 

763560.95 

851 

2673.50 

568786.14 

919 

2887.12 

663316.66 

987 

3100.75 

765110.54 

852 

2676.64 

570123.67 

92O 

2890.27 

664761.01 

988 

3103.89 

766661.70 

853 

2679.78 

571462.77 

921 

2893.41 

666206.92 

989 

3107.04 

768214.44 

854 

2682.92 

572803.45 

922 

2896.55 

667654.41 

99O 

3110.18 

769768.74 

855 

2686.06 

574145.69 

923 

2899.69 

669103.47 

991 

3113.32 

771324.61 

856 

2689.20 

575489.51 

924 

2902.83 

670554.10 

992 

3116.46 

772882.06 

857 

2692.34 

576834.90 

925 

2905.97 

672006.30 

993 

3119.60 

774441.07 

858 

2695.49 

578181.85 

926 

2909.11 

673460.08 

994 

3122.74 

776001.66. 

859 

2698.63 

579530.38 

927 

2912.26 

674915.42 

995 

3125.88 

777563.82 

860 
861 

2701.77 
2704.91 

580880.48 
582232.15 

928 
929 

2915.40676372.33 
2918.54  677830.82 

996 
997 

3129.03 
3132.17 

779127.54 
780692  84 

862 

2708.05 

583585.39 

930 

2921.68:679290.87 

998 

3135.31 

782259.7? 

863 

2711.19 

584940.20 

931 

2924.82  680752.50 

999 

3138.45 

783828  15 

864 

2714.34 

586296.59 

932 

2927.96682215.69 

1000 

3141.59 

785398.16 

865 

2717.48 

587654.54 

933 

2931  .  11  683680.46 

866 

m 

2720.62 

589014.07 

934 

2934.25  685146.80 

120     CIRCUMFERENCE  OF  CIRCLES,  FEET  AND  INCHED 


—  ^OG  —  <*JiN.OenNOOe^\NOONcNmoo^~moo  —  ^  t>.  o  m  r^  o  m 


—  —  —  CN  CN  «N  en 


•1-— OOONooh-.NOm-'^-eneN  —  OONOOooi^NOin-feneN  —  o  ON~OO  r  „  -  , 


rNNOenot^'3-  — ooineNC 


V  in  t>.'  a^  —  o  CN 
•CNmoo  —  •^•oo  —  ^4 


rNOoeN-<rmi>.ONOOcNcnmt>.ONOc 


- 

^B  —  oo  in  CN  ON  vo  co  o  r>.  •*  —  oo  in  C 


^jesmoo  —  •<j-f>.O'<j-t>.oen\ooNeNNOONeNinoo  —  -<roo  — •«j-h>.oenNooenNOONeN 
p^  mmmi  r>,r>,      oo      ONONQNONO 


r;oNONoooooooooooooooooooooor>.r>«rs«.r>^r>.t>.r>»r>»r<«t>«rs».NONONONONONONONONO 

£^*^3^*^w^^^*^or^^"«^«N^^f<\o^^^^^^^Ndf^ 


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m  in  o  vo  so  i>«  t>«  t>«  oo  oo  oo  oo  ON  ON  ON 


N  —  ooNoooor>«NO>n^tTncN  —  ON 

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ocnr>iOfnNOONCNinoNCNmoo  —  -*r>.o-^-t>.oenvOONCNvOONCNino    — 
—  —  —  CN  CN  CN  CN  en  en  en  -«r  if  -^-  m  m  m  NO  NO  NO  t>.  i>.  t>«  r>.  oo  oo  oo  ON  ON  ON  o 


<  — 

ONONONONOu^u 
O  en  o  r^  ^  •—  o 

'    '        * 


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-—  oo  in  CN 

* 


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o  —  moo  —  -<i 
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ooin<NONNOenor>.-«r  — 
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—  —  —  CN  CN  CN  en  en  en  -<r  ^n-  >n  in  m  in  NO  NO  NO  t>.  t>.  t>,  oo  oo  oo  ON  ON  ON  o 


AREAS  OF  THE  SEGMENTS  OF  A  CIRCLE. 


121 


AREAS  OF  THE   SEGMENTS  OF  A  CIRCLE. 

(Diameter=l;  Rise  or  Height  in  parts  of  Diameter  being  given.) 

RULE  FOR  USE  OF  THE  TABLE. — Divide  the  rise  or  height  of  the  segment 
by  the  diameter.  Multiply  the  area  in  the  table  corresponding  to  the 
quotient  thus  found  by  the  square  of  the  diameter. 

//  the  segment  exceeds  a  semicircle  its  area  is  area  of  circle  —  area  of  seg- 
ment whose  rise  is  (diarn.  of  circle  —  rise  of  given  segment). 

Given  chord  and  rise,  to  find  diameter.     Diam.  =  (square  of  half  chord -*- 
rise)  +  rise.    The  half  chord  is  a  mean  proportional  between  the  two  parts  . 
into  which  the  chord  divides  the  diameter  which  is  perpendicular  to  it. 


Rise 
-f- 

Diam. 

Area. 

Rise 
^ 
Diam. 

Area. 

Rise 
Diam. 

Area. 

Rise 
Diam. 

Area. 

Rise 
-i- 

Diam. 

Area. 

.001 

.00004 

.054 

•01646 

.107 

.04514 

.16 

.08111 

.213 

.12235 

.002 

.00012 

.055 

.01691 

.108 

.04576 

.161 

.08185 

.214 

.12317 

.003 

.00022 

.056 

.01737 

.109 

.04638 

.162 

.08258 

.215 

.12399 

.004 

.00034 

.057 

.01783 

.11 

.04701 

.163 

.08332 

.216 

.12481 

.005 

.00047 

.058 

.01830 

.111 

.04763 

.164 

.08406 

.217 

.12563 

.006 

.00062 

.059 

.01877 

.112 

.04826 

.165 

.08480 

.218 

.12646 

.007 

.00078 

.06 

.01924 

.113 

.04889 

.166 

.08554 

.219 

.12729 

.008 

.00095 

.061' 

.01972 

.114 

.04953 

.167 

.08629 

.22 

.12811 

.009 

.00113 

.062 

.02020 

.115 

.05016 

.168 

.08704 

.221 

.12894 

.01 

.00133 

.063 

.02068 

.116 

.05080 

.169 

.08779 

.222 

.12977 

.011 

.00153 

.064 

.02117 

.117 

.05145 

.17 

.08854 

.223 

.13060 

.012 

.00175 

.065 

.02166 

.118 

.05209 

.171 

.08929 

.224 

.13144 

.013 

.00197 

.066 

.02215 

.119 

.05274 

.172 

.09004 

.225 

.13227 

.014 

.0022 

.067 

.02265 

.12 

.05338 

.173 

.09080 

.226 

.13311 

.015 

.00244 

.068 

.02315 

.121 

.05404 

.174 

.09155 

.227 

.13395 

.016 

.00268 

.069 

.02366 

.122 

.05469 

.175 

.0923  1 

.228 

.13478 

.017 

.00294 

.07 

.02417 

.123 

.05535 

.176 

.09307 

.229 

.13562 

.018 

.0032 

.071 

.02468 

.124 

.05600 

.177 

.09384 

.23 

.13646 

.019 

.00347 

.072 

.02520 

.125 

.05666 

.178 

.09460 

.231 

.13731 

.02 

.00375 

.073 

.02571 

.126 

.05733 

.179 

.09j37 

.232 

.13815 

.021 

.00403 

.074 

.02624 

.127 

.05799 

.18 

.09613 

.233 

.13900 

.022 

00432 

.075 

.02676 

.128 

.05866 

.181 

.09690 

.234 

.13984 

.023 

.00462 

.076 

.02729 

.129 

.05933 

.182 

.09767 

.235 

.14069 

.024 

.00492 

.077 

.02782 

.13 

.06000 

.183 

.09845 

.236 

.14154 

.025 

.00523 

.078 

.02836 

.131 

.06067 

.184 

.09922 

.237 

.14239 

.026 

.00555 

.079 

.02889 

.132 

.06135 

.185 

.10000 

.238 

.14324 

.027 

.00587 

.08 

.02943 

.133 

.06203 

.186 

.10077 

.239 

.14409 

.028 

.00619 

.081 

.02998 

.134 

.06271 

.187 

.10155 

.24 

.14494 

,029 

.00653 

.082 

.03053 

.135 

.06339 

.188 

.10233 

.241 

.14580 

.03 

.00687 

.083 

.03108 

.136 

.06407 

.189 

.10312 

.242 

.14666 

.031 

.00721 

.084 

.03163 

.137 

.06476 

.19 

.10390 

.243 

.14751 

.032 

.00756 

.085 

.03219 

.138 

.06545 

.191 

.10469 

.244 

.14837 

.033 

.00791 

.086 

.03275 

.139 

.06614 

.192 

.10547 

.245 

.14923 

.034 

.00827 

.087 

.03331 

.14 

.06683 

.193 

.10626 

.246 

.15009 

.035 

.00864- 

.088 

.03387 

.141 

.06753 

.194 

.10705 

.247 

.15095 

.036 

.00901 

.089 

.03444 

.142 

.06822 

.195 

.10784 

.248 

.15182 

.037 

.00938 

.09 

.03501 

.143 

.06892 

.196 

.10864 

.249 

.15268 

.038 

.00976 

091 

.03559 

.144 

.06963 

.197 

.10943 

.25 

.15355 

.039 

.01015 

.092 

.03616 

.145 

.07033 

.198 

.11023 

.251 

.15441 

.04 

.01054 

.093 

.03674 

.146 

.07103 

.199 

.11102 

.252 

.15528 

.041 

.01093 

.094 

.03732 

.147 

.07174 

.2 

.11182 

.253 

.15615 

.042 

.01133 

.095 

.03791 

.148 

.07245 

.201 

.11262 

.254 

.15702 

.043 

.01173 

.096 

.03850 

.149 

.07316 

.202 

.11343 

.255 

.15789 

.044 

.01214 

.097 

.03909 

.15 

.07387 

.203 

.11423 

.256 

.15876 

.045 

.01255 

.098 

.03968 

.151 

.07459 

.204 

.11504 

.257 

.15964 

.046 

.01297 

.099 

.04028 

.152 

.07531 

.205 

.11584 

.258 

.16051 

.047 

.01339 

| 

.04087 

.153 

.07603 

.206 

.11665 

.259 

.16139 

.048 

.01382 

J01 

.04148 

.154 

.07675 

.207 

.  1  1  746 

.26 

.16226 

.049 

.01425 

.102 

.04208 

.155 

.07747 

.208 

.11827 

.261 

.16314 

.05 

.01468 

.103 

.04269 

.156 

.07819 

.209 

.11908 

.262 

.16402 

.051 

.01512 

.104 

.04330 

.157 

.07892 

.21 

.11990 

.263 

.16490 

.052 

.01556 

.105 

.04391 

.158 

.07965 

.211 

.12071 

.264 

.16578 

.053 

.01601 

.106 

.04452 

.159 

.08038 

.212 

.12153 

.265 

.16666 

122 


MATHEMATICAL  TABLES, 


Rise 

•4- 

Diam. 

Area. 

Rise 
Diam. 

Area. 

Rise 

•*- 
Diam. 

Area. 

Rise 

•*• 
Diana. 

Area. 

Rise 

•*• 
Diam. 

Area. 

.266 

.16755 

.313 

.21015 

.36 

.25455 

.407 

.30024 

.454 

.34676 

.267 

.16643 

.314 

.21108 

.361 

.25551 

.408 

.30122 

.455 

-.34776 

.268 

.16932 

.315 

.21201 

.362 

.25647 

.409 

.30220 

.456 

.34876 

.269 

17020 

316 

.21294 

.363 

.25743 

.41 

.30319 

.457 

.34975 

.27 

.17109 

.317 

.21387 

.364 

.25839 

.411 

.30417 

.458 

.35075 

.271 

.17198 

.318 

.21480 

.365 

.25936 

.412 

.30516 

.459 

.35175 

.272 

.17287 

.319 

.21573 

.366 

.26032 

.413 

.30614 

.46 

.35274 

.273 

.17376 

.32 

.21667 

.367 

.26128 

.414 

.30712 

.461 

.35374 

.274 

.17465 

.321 

.21760 

.368 

.26225 

.415 

.30811 

.462 

.35474 

.275 

.17554 

.322 

.21853 

.369 

.26321 

.416 

.30910 

.463 

.35573 

.276 

.17644 

.323 

,21947 

.37 

.26418 

.417 

.3  1  008 

.464 

.35673 

.277 

.17733 

.324 

.22040 

.37! 

.265  1  4 

.418 

.31107 

.465 

.35773 

.278 

.17823 

.325 

.22134 

.372 

.26611 

.419 

.31205 

.466 

.35873 

.279 

.17912 

.326 

.22228 

.373 

.26708 

.42 

.31304 

.467 

.35972 

.28 

.18002 

.327 

.22322 

.374 

.26805 

.421 

.31403 

.468 

.36072 

.281 

.18092 

.328 

.22415 

.375 

.26901 

.422 

.31502 

.469 

.36172 

.282 

.18182 

.329 

.22509 

.376 

.26998 

.423 

.31600 

.47 

.36272 

.283 

.18272 

.33 

.22603 

.377 

.27095 

.424 

.31699 

.471 

.36372 

.284 

.18362 

.331 

.22697 

.378 

.27192 

.425 

.3  1  798 

.472 

.36471 

.285 

.18452 

.332 

.22792 

.379 

.27289 

.426 

.31897 

.473 

.36571 

.286 

.18542 

.333 

.22886 

.38 

.27386 

.427 

.31996 

.474 

.36671 

.287 

.18633 

.334 

.22980 

.381 

.27483 

.428 

.32095 

.475 

.36771 

.288 

.18723 

.335 

.23074 

.382 

.27580 

.429 

.32194 

.476 

.36871 

.289 

.18814 

.336 

.23169 

.383 

.27678 

.43 

.32293 

.477 

.36971 

.29 

.18905 

.337 

.23263 

.384 

.27775 

.431 

.32392 

.478 

.37071 

.291 

.18996 

.338 

.23358 

.385 

.27872 

.432 

.32491 

.479 

.37171 

.292 

.19086 

.339 

.23453 

.386 

.27969 

.433 

.32590 

.48 

.37270 

293 

.19177 

.34 

.23547 

.387 

.28067 

.434 

.32689 

.481 

.37370 

294 

.19268 

.341 

.23642 

.388 

.28164 

.435 

.32788 

.482 

.37470 

.295 

.19360 

.342 

.23737 

.389 

.28262 

.436 

.32887 

.483 

.37570 

.296 

.19451 

.343 

.23832 

.39 

.28359 

.437 

.32987 

.484 

.37670 

.297 

.19542 

.344 

.23927 

.391 

.28457 

.438 

.33086 

.485 

.37770 

.298 

.19634 

.345 

.24022 

.392 

.28554 

.439 

.33185 

.486 

.37870 

.299 

.19725 

.346 

.24117 

.393 

.28652 

.44 

.33284 

.487 

.37970 

.3 

.19817 

.347 

.24212 

.394 

.28750 

.441 

.33384 

.488 

.38070 

.301 

.19908 

.348 

.24307 

.395 

.28848 

.442 

.33483 

.489 

.38170 

.302 

.20000 

.349 

.24403 

.396 

.28945 

.443 

.33582 

.49 

.38270 

.303 

.20092 

.35 

.24498 

.397 

.29043 

.444 

.33682 

.491 

.38370 

,304 

.20184 

.351 

.24593 

.398 

.29141 

.445 

.33781 

.492 

.38470 

.305 

.20276 

.352 

.24689 

.399 

.29239 

.446 

.33880 

.493 

.38570 

.306 

.20368 

.353 

.24784 

.4 

.29337 

.447 

.33980 

.494 

.38670 

.307 

.20460 

.354 

.24880 

".401 

.29435 

.448 

.34079 

.495 

.38770 

.308 

.20553 

.355 

.24976 

.402 

.29533 

.449 

.34179 

.496 

.38870 

.309 

.20645 

.356 

.25071 

.403 

.29631 

.45 

.34278 

.497 

.38970 

.31 

.20738 

.357 

.25167 

.404 

.29729 

.451 

.34378 

.498 

.39070 

.311 

.20830 

.358 

.25263 

.405 

.29827 

.452 

.34477 

.499 

.39170 

.312 

.20923 

.359 

.25359 

.406 

.29926 

.453 

.34577 

.5 

.39270 

For  rules  for  finding  the  area  of  a  segment  see  Mensuration,  page  60. 

LENGTHS  OF  CIRCULAR  ARCS. 

(Degrees  being  given.     Radius  of  Circle  =  1.) 

FORMULA.  —  Length  of  arc  =          g          X  radius  X  number  of  degrees. 

RULE.  —  Multiply  the  factor  in  the  table  (see  next  page)  for  any  given 
number  of  degrees  by  the  radius. 
EXAMPLE.  —  Given  a  curve  of  a  radius  of  55  feet  and  an  angle  of  7  8°  20'. 

r  Factor  from  table  for  78° 1 .3613568 

Factor  from  table  for  20' .0058178 

Factor. 1.3671740 

1.3671746X55  = 


LENGTHS   OP  CIRCULAR  ARCS. 


FACTORS  FOR  LENGTHS  OF  CIRCULAR  ARCS. 


123 


Degrees. 

Minutes. 

1 

.0174533 
.0349066 

61 
62 

1  .0646508 
1.0821041 

121 
122 

2.1118484 
2.1293017 

1 
2 

.0002909 
.0005818 

3 

.0523599 

63 

1.0995574 

123 

2.1467550 

3 

.0008727 

A 

.0698132 

64 

1.1170107 

124 

2.1642083 

4 

.0011636 

5 

.0872665 

65 

1.1344640 

125 

2.1816616 

5 

.0014544 

6 

.1047198 

66 

1.1519173 

126 

2.1991149 

6 

.0017453 

7 

.1221730 

67 

1.1693706 

127 

2.2165682 

7 

.0020362 

8 

.1396263 

68 

1.1868239 

128 

2.2340214 

8 

.0023271 

9 

.1570796 

69 

1.2042772 

129 

2.2514747 

9 

.0026  1  80 

10 

.1745329 

70 

1.2217305 

130 

2.2689280 

10 

.0029089 

11 

.1919862 

71 

1.2391838 

131 

2.2863813 

11 

.0031998 

12 

.2094395 

72 

1.2566371 

132 

2.3038346 

12 

.0034907 

13 

.2268928 

73 

1  .2740904 

133 

2.3212879 

13 

.0037815 

14 

.2443461 

74 

1.2915436 

134 

2.3387412 

14 

.0040724 

15 

.2617994 

75 

1.3089969 

135 

2.3561945 

15 

.0043633 

16 

.2792527 

'  76 

1.3264502 

136 

2.3736478 

16 

.0046542 

17 

.2967060 

77 

1.3439035 

137 

2.3911011 

17 

.0049451 

18 

.3141593 

78 

1.3613568 

138 

2.4085544 

18 

.0052360 

19 

.3316126 

79 

1.3788101 

139 

2.4260077 

19 

.0055269 

20 

.3490659 

80 

1.3962634 

140 

2.4434610 

20 

.0058178 

21 

.3665191 

81 

1.4137167 

141 

2.4609142 

21 

.0061087 

22 

.3839724 

82 

1  .43  1  1  700 

142 

2.4783675 

22 

.0063995 

23 

.4014257 

83 

1  .4486233 

143 

2.4958208 

23 

.0066904 

24 

.4188790 

84 

1  .4660766 

144 

2.5132741 

24 

.0069813 

25 

.4363323 

85 

1.4835299 

145 

2.5307274 

25 

.0072722 

26 

.4537856 

86 

1.5009832 

146 

2.5481807 

26 

.0075631 

27 

.4712389 

87 

1.5184364 

147 

2.5656340 

27 

.007854(1 

28 

.4886922 

88 

1.5358897 

148 

2.5830873 

28 

.0081449 

29 

.5061455 

89 

1.5533430 

149 

2.6005406 

29 

.0084358 

30 

.5235988 

90 

1.5707963 

150 

2.6179939 

30 

.008726(1 

31 

.5410521 

91 

1  .5882496 

151 

2.6354472 

31 

.0090175 

32 

.5585054 

92 

1.6057029 

152 

2.6529005 

32 

.0093084 

33 

.5759587 

93 

1.6231562 

153 

2.6703538 

33 

.0095993 

34 

.5934119 

94 

1  .6406095 

154 

2.6878070 

34 

.0098902 

35 

.6108652 

95 

1.6580628 

155 

2.7052603 

35 

.0101811 

36 

.6283185 

96 

1.6755161 

156 

2.7227136 

36 

.0104720 

37 

.6457718 

97 

1  .6929694 

157 

2.7401669 

37 

.0107629 

38 

.6632251 

98 

1.7104227 

158 

2.7576202 

38 

.0110538 

39 

.6806784 

99 

1.7278760 

159 

2.7750735 

39 

.0113446 

40 

.6981317 

100 

1.7453293 

160 

2.7925268 

40 

.0116355 

41 

.7155850 

101 

1.7627825 

161 

2.8099801 

41 

.0119264 

42 

.7330383 

102 

1.7802358 

162 

2.8274334 

42 

.0122173 

43 

.7504916 

103 

1.7976891 

163 

2.8448867 

43 

.0125082 

44 

.7679449 

104 

1.8151424 

164 

2.8623400 

44 

.0127991 

45 

.7853982 

105 

1.8325957 

165 

2.8797933 

45 

.0130900 

46 

.8028515 

106 

1  .8500490 

166 

"2.8972466 

46 

.0133809 

47 

.8203047 

107 

1.8675023 

167 

2.9146999 

47 

.0136717 

48 

.8377580 

108 

1.8849556 

168 

2.9321531 

48 

.0139626 

49 

.8552113 

109 

1  .9024089 

169 

2.9496064 

49 

.0142535 

50 

.8726646 

110 

1.9198622 

170 

2.9670597 

50 

.0145444 

51 

.8901179 

111 

1.9373155 

171 

2.9845130 

51 

.0148353 

52 

.9075712 

112 

1.9547688 

172 

3.0019663 

52 

.0151262 

53 

.9250245 

113 

1  19722221 

173 

3.0194196 

53 

.0154171 

54 

.9424778 

114 

1  .9896753 

174 

3.0368729 

54 

.0157080 

55 

.9599311 

115 

2.0071286 

175 

3.0543262 

55 

.0159989 

56 

.9773844 

116 

2.0245819 

176 

3.0717795 

56 

.0162897 

57 

.9948377 

117 

2.0420352 

177 

3.0892328 

57 

.0165806 

58 

1.0122910 

118 

2.0594885 

178 

3.1066861 

58 

.0168715 

59 

1.0297443 

119 

2.0769418 

179 

3.1241394 

59 

.0171624 

60 

1.0471976 

120 

2.0943951 

180 

3.1415927 

60 

.0174533 

124 


MATHEMATICAL 


LENGTHS  Off  CtHCtJLAll  ARCS. 

(Diameter  =-  1.    Given  the  Chord  and  Height  of  the  Arc.) 

RULE  FOR  USE  OF  THE  TABLE.  —  Divide  the  height  by  the  chord.  Find 
In  the  column  of  heights  the  number  equal  to  this  quotient.  Take  out  the 
corresponding  number  from  the  column  of  lengths.  Multiply  this  last 
number  by  the  length  of  the  given  chord;  the  product  will  be  length  of  the 

If  the  arc  is  greater  than  a  semicircle,  first  find  the  diameter  from  the 
formula,  Diam.  =  (square  of  half  chord  -f-  rise)  +  rise;  the  formula  is  true 
whether  the  arc  exceeds  a  semicircle  or  not.  Then  find  the  circumference. 
From  the  diameter  subtract  the  given  height  of  arc,  the  remainder  will  be 
height  of  the  smaller  arc  of  the  circle;  find  its  length  according  to  the  rule, 
and  subtract  it  from  the  circumference. 


Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

0.001 

.00002 

0.15 

.05896 

0.238 

.14480 

0.326 

.26288 

0.414 

.40788 

.005 

.00007 

.152 

.06051 

.24 

.14714 

.328 

.26588 

.416 

.41145 

.01 

.00027 

.154 

.06209 

.242 

.14951 

.33 

.26892 

.418 

.41503 

.015 

.00061 

.156 

.06368 

.244 

.15189 

.332 

.27196 

.42 

.41861 

.02 

.00107 

.158 

.06530 

.246 

.15428 

.334 

.27502 

.422 

.42221 

.025 

.00167 

.16 

.06693 

.248 

.15670 

.336 

.27810 

.424 

.42583 

.03 

.00240 

.162 

.06858 

.25 

.15912 

.338 

.28118 

.426 

.42945 

.035 

.00327 

.164 

.07025 

.252 

.16156 

.34 

.28428 

.428 

.43309 

.04 

.00426 

.166 

.07194 

.254 

.16402 

:342 

.28739 

.43 

.43673 

.045 

.00539 

.168 

.07365 

.256 

.16650 

.344 

.29052 

.432 

.44039 

.05 

.00665 

.17 

.07537 

.258 

.16899 

.346 

.29366 

.434 

.44405 

.055 

.00805 

.172 

.07711 

.26 

.17150 

.348 

.29681 

.436 

.44773 

.06 

.00957 

.174 

.07888 

.262 

.17403 

.35 

.29997 

.438 

.45142 

.065 

.01123 

.176 

.08066 

.264 

.17657 

.352 

.30315 

.44 

.45512 

.07 

.01302 

.178 

.08246 

.266 

.17912 

.354 

.30634 

.442 

.45883 

.075 

.01493 

.18 

.08428 

.268 

.18169 

.356 

.30954 

.444 

.46255 

.08 

.01698 

.182 

.08611 

.27 

.18429 

.358 

.31276 

.446 

.46628 

.085 

.01916 

.184 

.08797 

.272 

.18689 

.36 

.31599 

.448 

.47002 

.09 

.02146 

.186 

.08984 

.274 

.18951 

.362 

.31923 

.45 

.47377 

.095 

.02389 

.188 

.09174 

.276 

.19214 

.364 

.32249 

.452 

.47753 

.10 

.02646 

.19 

.09365 

.278 

.19479 

.366 

.32577 

.454 

.48131 

.102 

.02752 

.192 

.09557 

.28 

.19746 

.368 

.32905 

.456 

.48509 

.104 

.02860 

.194 

.09752 

.282 

.20014 

.37 

.33234 

.458 

.48889 

.106 

.02970 

.196 

.09949 

.284 

.20284 

.372 

.33564 

.46 

.49269 

.108 

.03082 

.198 

.10147 

.286 

.20555 

.374 

.33896 

.462 

.49651 

.11 

.03196 

.20 

.10347 

.288 

.20827 

.376 

.34229 

.464 

.50033 

.112 

.03312 

.202 

.10548 

.29 

.21102 

.378 

.34563 

.466 

.50416 

.114 

.03430 

.204 

.10752 

.292 

.21377 

.38 

.34899 

.468 

.50800 

.116 

.03551 

.206 

.10958 

.294 

.21654 

.382 

.35237 

.47 

.51185 

.118 

.03672 

.208 

.11165 

.296 

.21933 

.384 

.35575 

.472 

.51571 

.12 

.03797 

.21 

.11374 

.298 

.22213 

.386 

.35914 

.474 

.51958 

.122 

.03923 

.212 

.11584 

.30 

.22495 

.388 

.36254 

.476 

.52346 

.124 

.04051 

.214 

.11796 

.302 

.22778 

.39 

.36596 

.478 

.52736 

.126 

.04181 

.216 

.12011 

.304 

.23063 

.392 

.36939 

.48 

.53126 

.128 

.04313 

.218 

.12225 

.306 

.23349 

.394 

.37283 

.482 

.53518 

.13 

.04447 

.22 

.12444 

.308 

.23636 

.396 

.37628 

.484 

.53910 

.132 

.04584 

.222 

.12664 

.31 

.23926 

.398 

.37974 

.486 

.54302 

.134 

.04722 

.224 

.12885 

.312 

.24216 

>  .40 

.38322 

.488 

.54696 

.136 

.04862 

.226 

.13108 

.314 

.24507 

.402 

.38671 

.49 

.55091 

.138 

.05003 

.228 

.13331 

.316 

.24801 

.404 

.39021 

.492 

.55487 

.14 

.05147 

.23 

.13557 

.318 

.25095 

.406 

.39372 

.494 

.55854 

.142 

.05293 

.232 

.13785 

.32 

.25391 

.408 

.39724 

.496 

.56282 

.144 

.05441 

.234 

.14015 

.322 

.25689 

.41 

.40077 

.498 

.56681 

.146 

.05591 

.236 

.14247 

.324 

.25988 

.412 

.40432 

.50 

.57080 

.148 

.05743 

CIRCLES  AND  SQUARES   OF   EQUAL  AREA.         125 


Diameters  of  Circles  and  Sides  of  Squares  of  Same  Area. 

Diameter  of  circle  *  1.128379  X  side  of  square  of  same  area. 
Side  of  square        «  0.886227  X  diameter  of  circle  of  same  area. 


Diam.  of  Cir- 
cle or  Side 
of  Square. 

Side  of 
Square 
Equiva- 
lent to 
Circle. 

Diam.  of 
Circle 
Equiva- 
lent to 
Square. 

Diam.  of  Cir- 
cle or  Side 
of  Square. 

Side  of 
Square 
Equiva- 
lent to 
Circle. 

Diam.  of 
Circle 
Equiva- 
lent to 
Square. 

Diam.  of  Cir- 
cle or  Side 
of  Square. 

Side  of 
Square 
Equiva- 
lent to 
Circle. 

Diam.  of 
Circle 
Equiva- 
lent to 
Square. 

1 

0.886 

1  .128 

34 

30.132 

38.365 

67 

59.377 

75.601 

2 

1.772 

2.257 

35 

31.018 

39.493 

68 

60.263 

76.730 

3 

2.659 

3.385 

36 

31.904 

40.622 

69 

61  .150 

77.858 

4 

3.545 

4.514 

37 

32.790 

41.750 

70 

62  .  036 

78.987 

5 

4.431 

5.642 

38 

33.677 

42.878 

71 

62.922 

80.115 

6 

5.317 

6.770 

39 

34.563 

44.007 

72 

63.808 

81.243 

7 

6.204 

7.899 

40 

35.449 

45.135 

73 

64.695 

82.372 

8 

7.090 

9.027 

41 

36.335 

46  .  264 

74 

65.581 

83.500 

9 

7.976 

10.155 

42 

37.222 

47.392 

75 

66.467 

84.628 

10 

8.862 

11.284 

43 

38.108 

48.520 

76 

67.353 

85.757 

11 

9.748 

12.412 

44 

38.994 

49.649 

77 

68.239 

86.885 

12 

10.635 

13.541 

45 

39.880 

50.777 

78 

69.126 

tttt.014 

13 

11.521 

14.669 

46 

40.766 

51  .905 

79 

70.012 

89.142 

14 

12.407 

15.797 

47 

41  .653 

53.034 

80 

70.898 

90.270 

15 

13.293 

16.926 

48 

42.539 

54.162 

81 

71  .784 

91  .399 

16 

14.180 

18.054 

49 

43.425 

55.291 

82 

72.671 

92.527 

17 

15.066 

19.182 

50 

44.311 

56.419 

83 

73.557 

93.655 

18 

15.952 

20.311 

51 

45.198 

57.547 

84 

74.443 

94.784 

19 

16.838 

21.439 

52 

46.084 

58.676 

85 

75.330 

95.912 

20 

17.725 

22.568 

53 

46.970 

59.804 

86 

76.216 

97.041 

21 

18.611 

23.696 

54 

47.856 

60.932 

87 

77.102 

98.169 

22 

19.497 

24.824 

55 

48.742 

62.061 

88 

77.988 

99.297 

23 

20.383 

25.953 

56 

49.629 

63.189 

89 

>8.874 

100.426 

24 

21.269 

27.081 

57 

50.515 

64.318 

90 

79.760 

101  .554 

25 

22.156 

28.209 

58 

51.401 

65.446 

91 

80.647 

102.682 

26 

23.042 

29.338 

59 

52.287 

66.574 

92 

81.533 

103.811 

27 

23.928 

30.466 

60 

53.174 

67.703 

93 

82.419 

104.939 

28 

24.814 

31.595 

61 

54.060 

68.831 

94 

83.305 

106.068 

29 

25.701 

32.723 

62 

54.946 

69.959 

95 

84  192 

107.196 

30 

26.587 

33.851 

63 

55.832 

71  .088 

96 

85.078 

108.324 

31 

27.473 

34.980 

64 

56  719 

72.216 

97 

85.964 

109.453 

32 

28.359 

36.108 

65 

57.605 

73.345 

98 

86.850 

110.581 

33 

29.245 

37.237 

66 

58.491 

74.473 

99 

87.736 

111.710 

Number  of  Circles  that  can  be  Inscribed  within  a  Larger  Circle.  • 

N  =  Number  of  circles;  D  =  diam.  of  enclosing  circle;  d  =  diam.  of 
inscribed  circles. 

Obtain  the  ratio  of  D  -5-  d  and  find  the  value  nearest  to  it  in  the 
table.  Opposite  this  value  under  Ar,  find  the  number  of  circles  of 
diameter  d  that  can  be  inscribed  in  a  circle  of  diameter  D. 


N 

D/d 

N 

D/d 

N 

D/d 

N 

D/d 

N 

D/d 

N 

D/d 

N 

D/d 

2 

2.00 

13 

4.23 

24 

5.72 

35 

6.86 

46 

7.81 

85 

10.46 

140 

13.26 

3 

2.15 

14 

4.41 

25 

5.81 

36 

7.00 

47 

7.92 

90 

10.73 

145 

13.49 

4 

2.41 

15 

4.55 

26 

5.92 

37 

7.00 

48 

8.00 

95 

11.15 

150 

13.72 

-  5 

2.70 

16 

4.70 

27 

6.00 

38 

7.08 

49 

8.03 

100 

11.34 

155 

13.95 

6 

3.00 

17 

4.86 

28 

6.13 

39 

7.18 

50 

8.13 

105 

11.60 

160 

14.17 

7 

3.00 

18 

5.00 

29 

6.23 

40 

7.31 

55 

8.21 

110 

11.85 

165 

14.39 

8 

3.31 

19 

5.00 

30 

6.40 

41 

7.39 

60 

8.94 

115 

12.10 

170 

14.60 

9 

3.61 

20 

5.18 

31 

6.44 

42 

7.43 

65 

9.25 

120 

12.34 

175 

14.81 

10 

3.80 

21 

5.31 

32 

6.55 

43 

7.61 

70 

9.61 

125 

12.57 

180 

15.01 

11 

3.92 

22 

5.49 

33 

6.70 

44 

7.70 

75 

9.93 

130 

12.80 

185 

15.20 

12 

4.05 

23 

5.61 

34 

6.76 

45 

7.72 

80 

10.20 

135 

13.06 

190 

15.39 

126 


MATHEMATICAL  TABLES. 


SPHERES. 

(Some  errors  of  1  in  the  last  figure  only.    From  TRAUTWINE.) 


Diam 

Sur- 
face. 

Vol- 
ume. 

Diam 

Sur- 
face. 

Vol- 
ume. 

Diam. 

Sur- 
face. 

Vol- 
ume. 

V32 

.0030 

.0000 

31/4 

33.18 

17.97 

97/8 

306.36 

504.21 

Vie 

.0122 

.0001 

5/16 

34.47 

19.03 

10. 

314.16 

523.60 

3/32 

.0276 

.0004 

3/8 

35.78 

20.129 

1/8 

322.06 

543.48 

1/8 

.0490 

.0010 

7/16 

37.122 

21.268 

1/4 

330.06 

563.86 

5/32 

.0767 

.0020 

1/2 

38.484 

22.449 

3/8 

338.16 

584.74 

3/16 

.1104 

.0034 

9/16 

39.872 

23.674 

1/2 

346.36 

606.13 

7/32 

.1503 

.0054 

5/8 

41.283 

24.942 

5/3 

354.66 

628.04 

1/4 

.1963 

.0081 

H/16 

42.719 

26.254 

3/4 

363.05 

650.46 

9/32 

.2485 

.0116 

3/4 

44.179 

27.61 

7/8 

371.54 

673.42 

5/16 

.3068 

.0159 

13/16 

45.664 

29.016 

11. 

380.13 

696.91 

U/32 

.3712 

.0212 

7/8 

47.173 

30.466 

1/8 

388.83 

720.95 

3/8 

.44179 

.0276 

15/16 

48.708 

31.965 

1/4 

397.61 

745.51 

13/32 

.51848 

.0351 

4. 

50.265 

33.510 

3/8 

406.49 

770.64 

7/16 

.60132 

.0438 

1/8 

53.456 

36.751 

V2 

415.48 

796.33 

15/32 

.69028 

.0539 

V4 

56.745 

40.195 

5/8 

424.50 

822.58 

1/2 

.78540 

.0654 

3/8 

60.133 

43.847 

3/4 

433.73 

849.40 

9/16 

.99403 

.0931 

1/2 

63.617 

47.713 

7/8 

443.01 

876.79 

5/8 

1.2272 

.12783 

5/8 

67.201 

51.801 

12. 

452.39 

904.78 

H/16 

1.4849 

.17014 

3/4 

70.883 

56.116 

1/4 

471.44 

962.52 

3/4 

1.7671 

.22089 

7/8 

74.663 

60.663 

V2 

490.87 

1  022.7 

13/16 

2.0739 

.28084 

5. 

78.540 

65.450 

3/4 

510.71 

1085.3 

7/8 

2.4053 

.35077 

1/8 

82.516 

70.482 

13. 

530.93 

1150.3 

15/16 

2.7611 

.43  143 

V4 

86.591 

75.767 

V4 

551.55 

1218.0 

1 

3.1416 

.52360 

3/8 

90.763 

81  .308 

1/2 

572.55 

1288.3 

Vl6 

3.5466 

.62804 

1/2 

95.033 

87.113 

3/4 

593.95 

1361.2 

1/8 

3.9761 

.7455 

5/8 

99.401 

93.189 

14. 

615.75 

1436.8 

3/16 

4.4301 

.8768 

3/4 

103.87 

99.541 

1/4 

637.95 

1515.1 

1/4 

4.9088 

.0227 

7/8 

108.44 

106.18 

1/2 

660.52 

1596.3 

5/16 

5.4119 

.1839 

6. 

113.10 

113.10 

3/4 

683.49 

1680.3 

3/8 

5.9396 

.3611 

1/8 

117.87 

120.31 

15. 

706.85 

1767.2 

7/16 

6.4919 

.5553 

1/4 

122.72 

127.83 

1/4 

730.63 

1857.0 

1/2 

7.0686 

.7671 

3/8 

127.68 

135.66 

1/2 

754.77 

1949.8 

9/16 

7.6699 

.9974 

1/2 

132.73 

143.79 

3/4 

779.32 

2045.7 

5/8 

8.2957 

2.2468 

5/8 

137.89 

152.25 

16. 

804.25 

2144.7 

,     U/16 

8.9461 

2.5161 

3/4 

143.14 

161.03 

1/4 

829.57 

2246.8 

I             Q/ 

3/4 

9.6211 

2.8062 

7/8 

148.49 

170.14 

1/2 

855.29 

2352.1 

13/16 

0.321 

3.1177 

7. 

153.94 

179.59 

3/4 

881.42 

2460.6 

'7/8 

1.044 

3.4514 

1/8 

159.49 

189.39 

17. 

907.93 

2572.4 

15/16 

1.793 

3.8083 

1/4 

165.13 

199.53 

1/4 

934.83 

2687.6 

2. 

2.566 

4.1888 

3/8 

1  70.87 

210.03 

1/2 

962.12 

2806.2 

1/16 

3.364 

4.5939 

1/2 

176.71 

220.89 

3/4 

989.80 

2928.2 

1/8 

4.186 

5.0243 

5/8 

182.66 

232.13 

18. 

1017.9 

3053.6 

3/16 

5.033 

5.4809 

3/4 

188.69 

243.73 

1/4 

1046.4 

3182.6 

1/4 

5.904 

5.9641 

7/8 

194.83 

255.72 

1/2 

1075.2 

3315.3 

5/16 

6.800 

6.4751 

8. 

201.06 

268.08 

3/4 

1  104.5 

3451.5 

3/8 

7.721 

7.0144 

V8 

207.39 

280.85 

19. 

1  134.1 

3591.4 

Vl6 

8.666 

7.5829 

1/4 

213.82 

294.01 

1/4 

1164.2 

3735.0 

1/2 

9.635 

8.1813 

3/8 

220.36 

307.58 

1/2 

1  194.6 

3882.5 

9/16 

0.629 

8.8103 

1/2 

226.98 

321.56 

3/4 

1225.4 

4033.7 

5/8 

1.648 

9.4708 

5/8 

233.71 

335.95 

20. 

1256.7 

4188.8 

U/16 

2.691 

0.154 

3/4 

240.53 

350.77 

V4 

1288.3 

4347.8 

3/4 

3.758 

0.889 

7/8 

247.45 

366.02 

1/2 

1320.3 

4510.9 

13/16 

4.850 

1.649 

9. 

254.47 

381.70 

3/4 

352.7 

4677.9 

7/8 

5.967 

2.443 

1/8 

261.59 

397.83 

21. 

385.5 

4849.1 

15/16 

7.109 

3.272 

1/4 

268.81 

414.41 

1/4 

418.6 

5024.3 

3. 

8.274 

4.137 

3/8 

270.12 

431.44 

1/2 

452.2 

5203.7 

1/16 

9.465 

5.039 

1/2 

283.53 

448.92 

3/4 

486.2 

5387.4 

1/8 

0.680 

5.979 

5/8 

291.04 

466.87 

23. 

520.5 

5575.3 

3/16 

1.919 

6.957 

3/4 

289.65 

485.31 

1/4 

555.3 

5767.6 

SPHERES. 


SPHERES  —  Continued. 


127 


Diam 

Sur- 
face. 

Vol- 
urne 

Diam 

Sur- 
face 

Vol- 
ume 

Diam 

Sur- 
face. 

Vol. 
ume. 

22  1/2 

1590.4 

5964. 

40  1/2 

5153.1 

34783 

70  1/2 

15615 

183471 

3/4 

1626.0 

6165.2 

41. 

5281.1 

36087 

71. 

15837 

187402 

23. 

1661.9 

6370.6 

V2 

5410.7 

37423 

1/2 

16061 

191389 

1/4 

1698.2 

6580.6 

43. 

5541.9 

38792 

73. 

16286 

195433 

1/2 

1735.0 

6795.2 

1/2 

5674.5 

40194 

V2 

16513 

199532 

3/4 

1772. 

7014.3 

43. 

5808.8 

41630 

73. 

16742 

203689 

24. 

1809.6 

7238.2 

1/2 

5944.7 

43099 

1/2 

16972 

207903 

V4 

1847.5 

7466.7 

44. 

6082.1 

44602 

74. 

17204 

212175 

1/2 

1885.8 

7700. 

1/2 

6221.2 

46141 

1/2 

17437 

216505 

3/4 

1924.4 

7938.3 

45. 

6361.7 

47713 

75. 

17672 

220894 

25. 

1963.5 

8181.3 

V2 

6503.9 

49321 

1/2 

17908 

225341 

V4 

2002.9 

8429.2 

46. 

6647.6 

50965 

76. 

18146 

229848 

!/2 

2042.6 

8682.0 

1/2 

6792.9 

52645 

V2 

18386 

234414 

3/4 

2083.0 

8939.9 

47. 

6939.9 

54362 

77. 

18626 

239041 

26. 

2123.7 

9202.8 

1/2 

7088.3 

56115 

V2 

18869 

243728 

1/4 

2164.7 

9470.8 

48. 

7238.3 

57906 

78. 

19114 

248475 

1/2 

2206.2 

9744.0 

1/2 

7389.9 

59734 

1/2 

19360 

253284 

3/4 

2248.0 

10022 

49. 

7543.1 

61601 

79. 

19607 

258155 

27. 

2290.2 

10306 

1/2 

7697.7 

63506 

1/2 

19856 

263088 

1/4 

2332.8 

10595 

50. 

7854.0 

65450 

80. 

20106 

268083 

1/2 

2375.8 

10889 

1/2 

8011.8 

67433 

1/2 

20358 

273147 

3/4 

2419.2 

11189 

51. 

8171.2 

69456 

81. 

20612 

278263 

28. 

2463.0 

11494 

1/2 

8332.3 

71519 

V2 

20867 

283447 

1/4 

2507.2 

11805 

52. 

8494.8 

73622 

83. 

2i<24 

288696 

1/2 

2551.8 

12121 

1/2 

8658.9 

75767 

1/2 

21382 

294010 

3/4 

2596.7 

12443 

53. 

8824.8 

77952 

83. 

21642 

299388 

29. 

2642.1 

12770 

1/2 

8992.0 

80178 

1/2 

21904 

304831 

1/4 

2687.8 

13103 

54. 

9160.8 

82448 

84. 

22167 

310340 

1/2 

2734.0 

13442 

V2 

9331.2 

84760 

1/2 

22432 

315915 

3/4 

2780.5 

13787 

55. 

9503.2 

87114 

85. 

22698 

321556 

30. 

2827.4 

14137 

V2 

9676.8 

89511 

1/2 

22966 

327264 

1/4 

2874.8 

14494 

56. 

9852.0  ' 

91953 

86. 

23235 

333039 

1/2 

2922.5 

14856 

V2 

10029 

94438 

1/2 

23506 

338882 

3/4 

2970.6 

15224 

57. 

10207 

96967 

87. 

23779 

344792 

31. 

3019.1 

15599 

1/2 

10387 

99541 

1/2 

24053 

350771 

1/4 

3068.0 

15979 

58. 

10568 

102161 

88. 

24328 

356819 

1/2 

3117.3 

16366 

1/2 

10751 

104826 

1/2 

24606 

362935 

3/4 

3166.9 

16758 

59. 

10936 

107536 

89. 

24885 

369122 

33. 

3217.0 

17157 

1/2 

11122 

110294 

1/2 

25165 

375378 

V4 

3267.4 

17563 

60. 

11310 

113098 

90. 

25447 

381704 

1/2 

3318.3 

17974 

V2 

11499 

115949 

1/2 

25730 

388102 

3/4 

3369.6 

18392 

61. 

11690 

118847 

91. 

26016 

394570 

33. 

3421.2 

18817 

1/2 

11882 

121794 

V2 

26302 

401109 

V4 

3473.3 

19248 

63. 

12076 

124789 

93. 

26590 

407721 

V2 

3525.7 

19685 

1/2 

12272 

127832 

1/2 

26880 

4  1  4405 

8/4 

3578.5 

20129 

63. 

12469 

130925 

93. 

27172 

421161 

34. 

3631.7 

20580 

1/2 

12668 

134067 

1/2 

27464 

427991 

1/4 

3685.3 

21037 

64. 

12868 

137259 

94. 

27759 

434894 

1/2 

3730.3 

21501 

1/2 

13070 

140501 

1/2 

28055 

441871 

35. 

3848.5 

22449 

65. 

13273 

143794 

95. 

28353 

448920 

V2 

3959.2 

23425 

1/2 

13478 

147138 

V2 

28652 

456047 

36. 

4071.5 

24429 

66. 

13685 

1  50533 

96. 

28953 

463248 

*/2 

4185.5 

25461 

1/2 

13893 

153980 

1/2 

29255 

470524 

37. 

4300.9 

26522 

67. 

14103 

157480 

97. 

29559 

477874 

V2 

4417.9 

27612 

V2 

14314 

161032 

1/2 

29865 

485302 

38. 

4536.5 

28731 

68. 

14527 

164637 

98. 

30172 

492808 

V2 

4656.7 

29880 

1/2 

14741 

168295 

1/2 

30481 

500388 

39. 

4778.4 

31059 

69. 

14957 

1  72007 

99. 

30791 

508047 

V2 

4901.7 

32270 

1/2 

15175 

175774 

V2 

31103 

515785 

40. 

5026.5 

33510 

70. 

15394 

1  79595 

00. 

31416 

523598 

128 


MATHEMATICAL   TABLES. 


NUMBER  OF  SQUARE  FEET  IN  PLATES  3  TO  32  FEET 
LONG,  AND   1  INCH  WIDE. 

For  other  widths, multiply  by  the  width  in  inches.  1  sq .  in.  =  0.00694/9  sq.  ft, 


Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long; 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

3.  0 

36 

.25 

7.  10 

94 

.6528 

12.  8 

152 

.056 

37 

.2569 

11 

95 

.6597 

9 

153 

.063 

2 

38 

.2639 

8.  0 

96 

.6667 

10 

154 

.069 

3 

39 

.2708 

1 

97 

.6736 

11 

155 

,076 

4 

40 

.2778 

2 

98 

.6806 

13.  0 

156 

,083 

5 

41 

.2847 

3 

99 

.6875 

1 

157 

09 

6 

42 

.2917 

4 

100 

.6944 

2 

158 

.097 

7 

43 

.2986 

5 

101 

.7014 

3 

159 

.104 

8 

44 

.3056 

6 

102 

.7083 

4 

160 

.1  14 

9 

45 

.3125 

7 

103 

.7153 

5 

161 

.ua 

10 

46 

.3194 

8 

104 

.7222 

6 

162 

.125 

11 
4.  0 

47 
48 

.3264 
.3333 

9 
10 

105 
106 

.7292 
.7361 

7 
8 

163 
•164 

.13.? 
.  1  3V 

49 

.3403 

11 

107 

.7431 

9 

165 

.146 

2 

50 

.3472 

9.  0 

108 

.75 

10 

166 

.153 

3 

51 

.3542 

1 

109 

.7569 

11 

167 

.159 

4 

52 

.3611 

2 

110 

.7639 

14.  0 

168 

.167 

5 

53 

.3681 

3 

111 

.7708 

1 

169 

.174 

6 

54 

.375 

4 

112 

.7778 

2 

170 

.181 

7 

55 

.3819 

5 

113 

.7847 

3 

171 

.188 

8 

56 

.3889 

6 

114 

.7917 

4 

172 

.194 

9 

57 

.3958 

7 

115 

.7986 

5 

173 

.201 

10 

58 

.4028 

8 

116 

.8056 

6 

174 

.208 

It 

59 

.4097 

9 

117 

.8125 

7 

175 

.215 

5.  0 

60 

.4167 

10 

•  118 

.8194 

8 

176 

.222 

61 

.4236 

11 

119 

.8264 

9 

177 

.229 

2 

62 

.4306 

10.  0 

120 

.8333 

10 

178 

.236 

3 

63 

.4375 

121 

.8403 

11 

179 

.243 

4 

64 

.4444 

2 

122 

.8472 

15.  0 

180 

.25 

5 

65 

.4514 

3 

123 

.8542 

181 

.257 

6 

66 

.4583 

4 

124 

.8611 

2 

182 

.264 

7 

67 

.4653 

5 

125 

.8681 

3 

183 

.271 

8 

68 

.4722 

6 

126 

.875 

4 

184 

.278 

9 

69 

.4792 

7 

127 

.8819 

5 

185 

.285 

10 

70 

.4861 

8 

128 

.8889 

6 

186 

.292 

11 

71 

.4931 

9 

129 

.8958 

7 

187 

.299 

8.  0 

72 

.5 

10 

130 

.9028 

8 

188 

.306 

1 

73 

.5069 

11 

131 

.9097 

9 

189 

.313 

2 

74 

.5139 

11.  0 

132 

.9167 

10 

190 

.319 

3 

75 

.5208 

133 

.9236 

11 

191 

.326 

4 

76 

.5278 

2 

134 

.9306 

16.  0 

192 

.333 

5 

77 

.5347 

3 

135 

.9375 

1 

193 

.34 

6 

78 

.5417 

4 

136 

.9444 

2 

194 

.347 

7 

79 

.5486 

5 

137 

.9514 

3 

195 

.354 

8 

80 

.5556 

6 

138 

.9583 

4 

196 

.361 

9 

81 

.5625 

7 

139 

.9653 

5 

197 

.368 

10 

82 

.5694 

8 

140 

.9722 

6 

198 

.375 

11 

83 

.5764 

9 

141 

.9792 

7 

199 

.382 

7.  0 

84 

.5834 

10 

142 

.9861 

8 

200 

.389 

85 

.5903 

11 

143 

.9931 

9 

201 

.396 

2 

86 

.5972 

12.  0 

144 

.000 

10 

202 

.403 

3 

87 

.6042 

145 

.007 

11 

203 

.41 

4 

88 

.6111 

2 

146 

.014 

17.  0 

204 

.417 

5 

89 

.6181 

3 

147 

.021 

1 

205 

.424 

6 

90 

.625 

4 

148 

.028 

2 

206 

.431 

7 

91 

.6319 

5 

149 

.035 

3 

207 

.438 

8 

92 

.6389 

6 

150 

1.042 

4 

208 

.444 

9 

93 

.6458 

7 

151 

1.049 

5 

209 

K451 

NUMBER   OF   SQUARE    FEET   IN   PLATES. 


120 


SQUARE  FEET  IN  PLATES.  —  Continued. 


Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins.. 
Long. 

Ins. 
Long 

Square 
Feet. 

17.  6 

210 

1.458 

22.  5 

269 

1.868 

27.  4 

328 

2.278 

7 

211 

1.465 

6 

270 

1.875 

5 

329 

2.285 

8 

212 

1.472 

7 

271 

1.882 

6 

330 

2.292 

9 

213 

1.479 

8 

272 

1.889 

7 

331 

2.299 

10 

214 

1.486 

9 

273 

1.896 

8 

332 

2.306 

11 

215 

1.493 

10 

274 

1.903 

9 

333 

2.313 

18.  0 

216. 

1.5 

11 

275 

1.91 

10 

334 

2.319 

217 

1.507 

23.  0 

276 

1.917 

11 

335 

2.326 

2 

218 

1.514 

277 

1.924 

28.  0 

336 

2.333 

3 

219 

1.521 

2 

278. 

1.931 

1 

337 

2.34 

4 

220 

1.528 

3 

279 

1.938 

2 

338 

2.347 

5 

221 

1.535 

4 

280 

1.944 

3 

339 

2.354 

6 

222 

1.542 

5 

281 

1.951 

4 

340 

2.361 

7 

223 

1.549 

6 

282 

1.958 

5 

341 

2.368 

8 

224 

1.556 

7 

283 

1.965 

6 

342 

2.375 

9 

225 

1.563 

8 

284 

1.972 

7 

343 

2.382 

10 

226 

1.569 

9 

285 

1.979 

8 

344 

2.389 

11 

227 

1.576 

10 

286 

1.986 

9 

345 

2.396 

19.  0 

228 

1.583 

11 

287 

1.993 

10 

346 

2.403 

229 

1.59 

24.  0 

288 

2. 

11 

347 

2.41 

2 

230 

1.597 

1 

289 

2.007 

29.  0 

348 

2.417 

3 

231 

1.604 

2 

290 

2.014 

349 

2.424 

4 

232 

1.611 

3 

291" 

2.021 

2 

350 

2.431 

5 

233 

1.618 

4 

292 

2.028 

3 

351 

2.438 

6 

234 

1.625 

5 

293 

2.035 

4 

352 

2.444 

7 

235 

1.632 

6 

294 

2'.042 

5 

353 

2.451 

8 

236 

1.639 

7 

295 

2.049 

6 

354 

2.458 

9 

237 

1.645 

8 

296 

2.056 

7 

355 

2.465 

10 

238 

1.653 

9 

297 

2.063 

8 

356 

2.472 

11 

239 

1  .659 

10 

298 

2.069 

9 

357 

2.479 

20.  0 

240 

1.667 

11 

299 

2.076 

10 

358 

2.486 

241 

1.674 

25.  0 

300 

*2.083 

11 

359 

2.493 

2 

242 

1.681 

1 

301 

2.09 

30.  0 

360 

2.5 

3 

243 

1.688 

2 

302 

2.097 

1 

361 

2.507 

4 

244 

1.694 

3 

303 

2.104 

2 

362 

2.514 

5 

245 

1.701 

4 

304 

2.111 

3 

363 

2.521 

6 

246 

1.708 

5 

305 

2.118 

4 

364 

2.528 

7 

247 

1.715 

6 

306 

2.125 

5 

365 

2.535 

8 

248 

1.722 

7 

307 

2.132 

6 

366 

2.542 

9 

249 

1.729 

8 

308 

2.139 

7 

367 

2.549 

10 

250 

1.736 

9 

309 

2.146 

8 

368 

2.556 

II 

251 

1.743 

10 

310 

2.153 

9 

369 

2.563 

21.  0 

252 

1.75 

11 

311 

2.16 

10 

370 

2.569 

253 

1.757 

26.  0 

312 

2.167 

11 

371 

2.576 

2 

254 

1.764 

313 

2.174 

31.  0 

372 

2.583 

3 

255 

1.771 

2 

314 

2.18V 

373 

2.59 

4 

256 

1.778 

3 

315 

2.188 

2 

374 

2.597 

5 

257 

1.785 

4 

316 

2.194 

3 

375 

2.604 

6 

258 

1.792 

5 

317 

2.201 

4 

376 

2.611 

7 

259 

1.799 

6 

318 

2.208 

5 

377 

2.618 

8 

260 

1.806 

7 

319 

2.215 

6 

378 

2.625 

9 

261 

1.813 

8 

320 

2.222 

7 

379 

2.632 

10 

262 

1.819 

9 

321 

2.229 

8 

380 

2.639 

11 

263 

1.826 

10 

322 

2.236 

9 

381 

2.646 

23.0 

264 

1.833 

11 

323 

2.243 

10 

382 

2.653 

1 

265 

1.84 

27.  0 

324 

2.25 

11 

383 

2.66 

2 

266 

1.847 

325 

2.257 

32.  0 

384 

2.667 

3 

267 

1.854 

2 

326 

2.264 

1 

385 

2.674 

4 

268 

1.861 

3 

327 

2.271 

2 

386 

2.681 

130 


MATHEMATICAL   TABLES. 


GALLONS  AND   CUBIC  FEET, 

United  States  Gallons  in  a  given  Number  of  Cubic  Feet. 

1  cubic  foot  =  7. 4805 19  U.S.  gallons;  1  gallon  =  231  cu.ir  .  =  0.13368056cu. ft. 


Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

0.1 

0.75 

50 

374.0 

8,000 

59,844.2 

0.2 

1.50 

60 

448.8 

9,000 

67,324.7 

0.3 

2.24 

70 

523.6 

10,000 

74,805.2 

0.4 

2.99 

80 

598.4 

20,000 

.••      149,610.4 

0.5 

3.74 

90 

673.2 

30,000 

224,415.6 

0.6 

4.49 

100 

748.0 

40,000 

299,220.8 

0.7 

5.24 

200 

1,496.1 

50,000 

374,025.9 

0.8 

5.98 

300 

2,244.2 

60,000 

448,831.1 

0.9 

6.73 

400 

2,992.2 

70,000 

523,636.3 

1 

7.48 

500 

3,740.3 

80,000 

598,441.5 

2 

14.96 

600 

4,488.3 

90,000 

673,246. 

3 

22.44 

700 

5,236.4 

100,000 

748,051.9 

4 

29.92 

800 

5,984.4 

200,000 

1,496,103.8 

5 

37.40 

900 

6,732.5 

300,000 

2,244,155.7 

6 

44.88 

1,000 

7,480.5 

400,000 

2,992,207.6 

7 

52.36 

2,000 

14,961.0 

500,000 

3,740,259.5 

8 

59.84 

3,000 

22,441.6 

600,000 

4,488,311.4 

9 

67.32 

4,000 

29,922.1 

700,000 

5,236,363.3 

10 

74.80 

5,000 

37,402.6 

800  000 

5,984,415.2 

20 

149.6 

6,000 

44,883.1 

900,000 

6,732,467.1 

30 

224.4 

7,000 

52,363.6 

1,000,000 

7,480,519.0 

40 

299.2 

Cubic  Feet  in  a  given  Number  of  Gallons. 


Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

1 
2 

.134 
.267 

1,000 
2,000 

133.681 
267.361 

1,000,000 
2,000,000 

133,680.6 
267,361.1 

3 

.401 

3,000 

401.042 

3,000,000 

401,041.7 

4 

.535 

4,000 

534.722 

4,000,000 

534,722.2 

5 

.668 

5,000 

668.403 

5,000,000 

668,402.8 

6 

.802 

6,000 

802.083 

6,000,000 

802,083.3 

7 

.936 

7,000 

935.764 

7,000,000 

935,763.9 

8 

1.069 

'    8,000 

1,069.444 

8,000,000 

1,069,444.4 

9 

1.203 

9,000 

1,203.125 

9,000,000 

1,203,125.0 

10 

1.337 

10,000 

1,336.806 

10,000,000 

1,336,805.6 

Cubic  Feet  per  Second,  Gallons  in  24  hours,  etc. 

1/60  I  1.5472  2.2800 

1  60  92.834  133.681 

7.480519  448.83  694.444  1,000. 

10,771.95  646,317  1,000,000  1,440,000 

62.355      3741.3          5788.66  8335.65 


Cu.  ft.  per  sec. 
Cu.  ft.  per  min. 
U.  S*  Gals,  per  min. 

"  "  "  24  hrs. 
Pounds  of  water  ) 
(at  62°  F.)  per  min.  J 


The  gallon 'is  a  troublesome  and  unnecessary  measure.  If  hydraulic 
engineers  and  pump  manufacturers  would  stop  using  it,  and  use  cubig 
Jeet  instead,  many  tedious  calculations  would  be  saved. 


CAPACITY   OF   CYLINDKICAL   VESSELS. 


131 


CONTENTS  IN   CUBIC  FEET  AND  U.  S.  GALLONS  OF  PIPES 

AND   CYLINDERS  OF  VARIOUS  DIAMETERS  AND  ONE 

FOOT  IN  LENGTH. 

1  gallon  =  231  cubic  inches.     1  cubic  foot  =  7.4805  gallons. 


For  1  Foot  in 

For  1  Foot  in 

For  1  Foot  in 

d 

Length. 

.S 

Length. 

d 

Length. 

5  as 

0>  3? 

fc« 

•»•»  2 
§•§ 

Cu.Ft. 

U.S. 

-t~    O 

oj^j 
Jo 

Cu.Ft. 

U.S. 

•S  2 

d  « 

Cu.Ft. 

U.S. 

c  c 

also 

Gals., 

d 

also 

Gals., 

d  d 

also 

Gals.. 

Q 

Area  in 

231 

p 

Area  in 

231 

Area  in 

231 

M 

Sq.Ft. 

Cu.In. 

Sq.Ft. 

Cu.In. 

. 

Sq.Ft. 

Cu.  In. 

V4 

.0003 

.0025 

63/4 

.2485 

1.859 

19 

1.969 

14.73 

5/16 

.0005 

.004 

7 

.2673 

1.999 

191/2 

2074 

15.51 

3/8 

.0008 

.0057 

7V4 

.2867 

2.145 

20 

2.182 

16.32 

7/16 

.001 

.0078 

71/2 

.3068 

2.295 

201/2 

2.292 

17.15 

1/2 

.0014 

.0102 

73/4 

.3276 

2.45 

21 

2.405 

17.99 

9/16 

.0017 

.0129 

8 

.3491 

2.611 

2U/2 

2.521 

18.86 

5/8 

.0021 

.0159 

8l/4 

.3712 

2.777 

22 

2.640 

19.75 

11/16 

.0026 

;0193 

81/2 

.3941 

2.948 

221/2 

2.761 

20.66 

3/4 

.0031 

.0230 

83/4 

.4176 

3.125 

23 

2.885 

21.58 

«/16 

.0036 

.0269 

9 

.4418 

3.305 

231/2 

3.012 

22.53 

7/8 

.0042 

.0312 

91/4 

.4667 

3.491 

24 

3.142 

23.50 

15/16 

.0048 

.0359 

91/2 

.4922 

3.682 

25 

3.409 

25.50 

1 

.0055 

.0408 

93/4 

.5185 

3.879 

26 

3.687 

27.58 

U/4 

.0085 

.0638 

10 

.5454 

4.08 

27 

3.976 

29.74 

U/2 

.0123 

.0918 

101/4 

.5730 

4.286 

28 

4.276 

31.99 

13/4 

.0167 

.1249 

101/2 

.6013 

4.498 

29 

4.587 

34.31 

2 

.0218 

.1632 

103/4 

.6303 

4.715 

30 

4.909 

36.72 

2V4    - 

.0276 

.2066 

11 

.66 

4.937 

31 

5.241 

39.21 

21/2 

.0341 

.2550 

111/4 

.6903 

5.164 

32 

5.585 

41.78 

23/4 

.0412 

.3085 

111/2 

.7213 

5.396 

33 

5.940 

44.43 

3 

.0491 

.3672 

113/4 

.7530 

5.633 

34 

6.305 

47.16 

31/4 

.0576 

.4309 

12 

.7854 

5.875 

35 

6.681 

49.98 

31/2 

.0668 

.4998 

121/2 

.8522 

6.375 

36 

7.069 

52.88 

33/4 

.0767 

.5738 

13 

.9218 

6.895 

37 

7.467 

55.86 

4 

.0873 

.6528 

13V2 

.994 

7.436 

38 

7.876 

58.92 

41/4 

.0985 

.7369 

14 

1.069 

7.997 

39 

8.296 

62.06 

4V2 

.1104 

.8263 

141/2 

1.147 

8.578 

40 

8.727 

65.28 

43/4 

.1231 

.9206 

15 

1.227 

9.180 

41 

9.168 

68.58 

5 

.1364 

.020 

15l/2 

1.310 

9.801 

42 

9.621 

71.97 

5V4 

.1503 

.125 

16 

1.396 

10.44 

43 

10.085 

75.44 

5i/2 

.1650 

.234 

161/2 

.485 

11.11 

44 

10.559 

78.99 

53/4 

.1803 

.349 

17 

.576 

11.79 

45 

11.045 

82.62 

6 

.1963 

.469 

171/2 

.670 

12.49 

46 

11.541 

86.33 

61/4 

.2131 

.594 

18 

.768 

13.22 

47 

12.048 

90.10 

61/2 

.2304 

.724 

18l/2 

.867 

13.96 

48 

12.566 

94.00 

To^find  the  capacity  of  pipes  greater  than  the  largest  given  in  the  table, 


aer  n  any  o  z, 

in  cubic  feet  by  621/4  or  the  gallons  by  8 1/3,  or,  if  a  closer  approximation  is 
required,  by  the  weight  of  a  cubic  foot  of  water  at  the  actual  temperature 
in  the  pipe. 

Given  the  dimensions  of  a  cylinder  in  inches,  to  find  its  capacity  in  U.  8. 
gallons:  Square  the  diameter,  multiply  by  the  length  and  by  0.0034.  If  d= 

diameter,  I  -  length,  gallons-  d*  X  °^54  X  *  - 0.0034  &  1.  If  D  and  L  are 
in  feet,  gallons  -  5.875  D*L. 


.132 


MATHEMATICAL  TABLES. 


CYLINDRICAL,  VESSELS,  TANKS,  CISTERNS,  ETC. 

Diameter  In  Feet  and  Inches,  Area  in  Square  Feet,  and  U.  S, 
Gallons  Capacity  for  One  Foot  in  Depth. 


1  gallon  =  231  cubic  inches  = 


1  cubic  foot 

7.4805 


'  0.13368  cubic  feet. 


Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Ft.  In. 

Sq.ft. 

1  foot 
depth. 

Ft.  In. 

Sq.  ft. 

1  foot 
depth. 

Ft.  In. 

Sq.ft. 

1  foot 
depth. 

1 

.785 

5.87 

5    8 

25.22 

188  .66 

19 

283  .53 

2120.9 

1 

.922 

6.89 

5    9 

25.97 

194.25 

19    3 

291.04 

2177.1 

2 

.069 

8.00 

510 

26.73 

199.92 

19    6 

298.65 

2234.0 

3 

.227 

9.18 

5  11 

27.49 

205.67 

19    9 

306.35 

2291.7 

A 

.396 

10.44 

6 

28.27 

211.51 

20 

314.16 

2350.1 

5 

.576 

11.79 

6    3 

30.68 

229.50 

20    3 

322.06 

2409.2 

6 

.767 

13.22 

6    6 

33.18 

248.23 

20    6 

330.C6 

2469.1 

7 

.969 

14.73 

6    9 

35.78 

267.69 

20    9 

338.16 

2529,6 

8 

2.182 

16.32 

7 

38.48 

287.88 

21 

346.36 

2591.0 

9 

2.405 

17.99 

7    3 

41.28 

308.81 

21    3 

354.66 

2653.0 

10 

2.640 

19.75 

7    6 

44.18 

330.48 

21    6 

363.05 

2715.8 

11 

2.885 

21.58 

7    9 

47.17 

352.88 

21    9 

371.54 

2779.3 

3.142 

23.50 

8 

50.27 

376.01 

22 

380.13 

2843.6 

1 

3.409 

25.50 

8    3 

53.46 

399.88 

22    3 

388.82 

2908.6 

2      2 

3.687 

27.58 

8    6 

56.75 

424.48 

22    6 

397.61 

2974.3 

2      3 

3.976 

29.74 

8    9 

60.13 

449.82 

22    9 

406.49 

3040.8 

2      4 

4.276 

31.99 

9 

63.62 

475.89 

23 

415.48 

3108.0 

2      5 

4.587 

34.31 

9    3 

67.20 

502.70 

23    3 

424.56 

3175.9 

2      6 

4.909 

36.72 

9    6 

70.88 

530.24 

23    6 

433.74 

3244.6 

2      7 

5.241 

39.21 

9    9 

74.66 

558.51 

23    9 

443.01 

3314.0 

2      8 

5.585 

41.78 

10 

78.54 

587.52 

24 

452.39 

3384.1 

2      9 

5.940 

44.43 

10    3 

82.52 

617.26 

24    3 

461.86 

3455.0 

2     10 

6.305 

47.16 

10-   6 

86.59 

647.74 

24    6 

471.44 

3526.6 

2    11 

6.681 

49.98 

10    9 

90.76 

678.95 

24    9 

481.11 

3598.9 

3 

7.069 

52.88 

11 

95.03 

710.90 

25 

490.87 

3672.0 

1 

7.467 

55.86 

11    3 

99.40 

743.58 

25    3 

500.74 

3745.8 

2 

7.876 

58.92 

11    6 

103.87 

776.99 

25    6 

510.71 

3820.3 

3 

8.296 

62.06 

11    9 

108.43 

811.14 

25    9 

520.77 

3895.6 

A 

8.727 

65.28 

12 

113.10 

846.03 

26 

530.93 

3971.6 

5 

9.168 

68.58 

12    3 

117.86 

881.65 

26    3 

541.19 

4048.4 

6 

9.621 

71.97 

12    6 

122.72 

918.00 

26    6 

551.55 

4125.9 

7 

10.085 

75.44 

12    9 

127.68 

955.09 

26    9 

562.00 

4204.  1 

8 

10.559 

78.99 

13 

132.73 

992.91 

27 

572.56 

4283.0 

9 

1  1  .045 

82.62 

13    3 

137.89 

1031.5 

27    3 

583.21 

4362.7 

10 

11.541 

86.33 

13    6 

143.14 

1070.8 

27    6 

593.96 

4443.1 

11 

12.048 

90.13 

13    9 

1  48.49 

1110.8 

27    9 

604.81 

4524.3 

12.566 

94.00 

14 

153.94 

1151.5 

28 

615.75 

4606.2 

1 

13.095 

97.96 

14    3 

159.48 

1193.0 

28    3 

626.80 

4688.8 

2 

13.635 

102.00 

14    6 

165.13 

1235.3 

28    6 

637.94 

4772.1 

3 

14.186 

106.12 

14    9 

170.87 

1278.2 

28    9 

649.18 

4856.2 

4 

14.748 

110.32 

15 

176.71 

1321.9 

29 

660.52 

4941.0 

5 

15.321 

114.61 

15    3 

182.65 

1366.4 

29   3 

67  1  .96 

5026.6 

6 

15.90 

118.97 

15    6 

188.69 

1411.5 

29    6 

683.49 

5112.9 

7 

16.50 

123.42 

15    9 

194.83 

1457.4 

29    9 

695.13 

5199.9 

8 

17.10 

127.95 

16 

201.06 

1504.1 

30 

706.86 

5287.7 

9 

17.72 

132.56 

46    3 

207.39 

1551.4 

30    3 

718.69 

5376.2 

10 

18.35 

137.25 

16    6 

213.82 

1  599.5 

30    6 

730.62 

5465.4 

11 

18.99 

142.02 

16    9 

220.35 

1648.4 

30    9 

742.64 

5555.4 

19.63 

146.88 

17 

226.98 

1697.9 

31 

754.77 

5646.1 

1 

20.29 

151.82 

17    3 

233.71 

1748.2 

31    3 

766.99 

5737.5 

2 

20.97 

156.83 

17    6 

240.53 

1799.3 

31    6 

779.31 

5829.7 

3 

21.65 

161.93 

17    9 

247.45 

1851.1 

31    9 

791.73 

5922.6 

4 

22.34 

167.12 

18 

254.47 

1903.6 

32 

804.25 

6016.2 

5 

23.04 

172.38 

18    3 

261.59 

1956.8 

32    3 

816.86 

6110.6 

6 

23.76 

177.  ,72 

18    6 

268.80 

2010.8 

32    6 

829.58 

6205.7 

7 

24.48 

183.15 

18   9 

276.12 

2065.5 

32    9 

842.39 

6301.5 

CAPACITIES   OF  RECTANGULAR  TANKS. 


133 


CAPACITIES  OF  RECTANGULAR  TANKS  IN  U.  S. 
GALLONS,  FOB  EACH  FOOT  IN  DEPTH. 

1  cubic  foot  =-  7.4805  U.  S.  gallons 


Vidth 
of 
Fank. 

Length  of  Tank. 

feet. 

2 

ft.  in. 
2  6 

feet. 
3 

ft.  in. 
3  6 

feet. 
4 

ft.  in. 
4     6 

feet. 
5 

ft.  in. 
5  6 

feet. 
6 

ft.  in. 
6  6 

feet. 
7 

t.   in. 
2    6 

3    6 
4 

4    6 

5    6 
6 
6    6 

7 

29.92 

37.40 
46.75 

44.88 
56.10 
67.32 

52.36 
65.45 
78.54 
91.64 

59.84 
74.80 
89.77 
104.73 
119.69 

67.32 
84.16 
1  00.99 
117.82 
134.65 

151.48 

74.81 
93.51 
112.21 
130.91 
149.61 

168.31 
187.01 

82.29 
102.86 
123.43 
144.00 
164.57 

185.14 
205.71 
226.28 

89.77 
112.21 
134.65 
157.09 
179.53 

201.97 
224.41 
246.86 
269.30 

97.25 
121.56 
145.87 
170.18 
194.49 

218.80 
243.11 
267.43 
291.74 
316.05 

104.73 
130.91 
157.09 
183.27 
209.45 

235.62 
261.82 
288.00 
314.18 
340.36 

366.54 

... 

Width 
of 
Tank. 

Length  of  Tank. 

ft.  in 
7   6 

feet. 
8 

ft.  in. 
8  6 

feet. 
9 

ft.  in 
9  6 

feet. 
10 

ft.  in 
10  6 

feet. 
11 

ft.  in 
11  6 

feet. 
13 

179.53 
224.41 
269.30 
314.18 
359.06 

403.94 
448.83 
493.  7  1 
538.59 
583.47 

628.36 
673.24 
718.12 
763.00 
807.89 

852.77 
897.66 
942.56 
987.43 
1032.3 

1077.2 

ft.  in 
2 
2  6 
3 
3  6 
4 

4  6 

5  6 
6 
6  6 

7  6 
8 
8  6 
9 

9  6 
10 
10  6 
11 
11  6 

12 

112.21 
140.26 
168.31 
196.36 
224.41 

25247 
280.52 
308.57 
336.62 
364.67 

392.72 
420.78 

119.69 
149.61 
179.53 
209.45 
239.37 

269.30 
299.22 
329.14 
359.06 
388.98 

418.91 
448.83 
478.75 

127.17 
158.96 
190.75 
222.54 
254.34 

286.13 
317.92 
349.71 
381.50 
413.30 

445.09 
476.88 
508.67 
540.46 

134.65 
168.31 
202.97 
235.63 
269.30 

302.96 
336.62 
370.28 
403.94 
437.60 

471.27 
504.93 
538.59 
572.25 
605.92 

142.13 
177.66 
213.19 
248.73 
284.26 

319.79 
355.32 
390.85 
426.39 
461.92 

497.45 
532.98 
568.51 
604.05 
639.58 

675.11 

149.61 
187.01 
224.41 
261.82 
299.22 

336.62 
374.03 
411.43 
448.83 
486.23 

523.64 
561.04 
598.44 
635.84 
673.25 

710.65 
748.05 

157.09 
196.36 
235.63 
274.90 
314.18 

353.45 
392.72 
432.00 
471.27 
510.54 

549.81 
589.08 
628.36 
667.63 
706.90 

746.17 

785.45 
824.73 

164.57 
205.71 
246.86 
288.00 
329.14 

370.28 
411.43 
452.57 
493.71 
534.85 

575.99 
617.14 
658.28 
699.42 
740.56 

781.71 
822.86 
864.00 
905.14 

172.05 
215.06 
258.07 
301.09 
344.10 

387.11 
430.13 
473.14 
516.15 
559.16 

602.18 
645.19 
688.20 
731.21 
774.23 

817.24 
860.26 
903.26 
946.27 
989.29 

134 


MATHEMATICAL   TABLES. 


NUMBER  OF  BARRELS    (31  1-3  GALLONS)  IN 
CISTERNS  AND  TANKS. 


I  barrel  =  31^  gallons  > 


31.5X  231 
1728 


=  4.21094  cu.  ft.  Reciprocal -0.2  37 477 


Diameter  in  Feet. 


Feet. 

5 

6 

7 

8 

9 

10 

11 

13 

13 

14 

, 

4.663 

6.714 

9.139 

11.937 

15.108 

18.652  , 

>2.569 

26.859 

31.522 

36.557 

5 

23.3 

33.6 

45.7 

59.7 

75.5 

93.3 

12.8 

134.3 

157.6 

182.8 

6 

28.0 

40.3 

54.8 

71.6 

90.6 

111.9 

35.4 

161.2 

189.1 

219.3 

7 

32.6 

47.0 

64.0 

83.6 

105.8 

130.6 

58.0 

188.0 

220.7 

255.9 

8 

37.3 

53.7 

73.1 

95.5 

120.9 

149.2 

80.6 

214.9 

252.2 

292.5 

9 

42.0 

60.4 

82.3 

107.4 

136.0 

167.9    ; 

>03.1 

241.7 

283.7 

329.0 

10 

46.6 

67.1 

91.4 

119.4 

151.1 

186.5    ; 

Z25.7 

268.6 

315.2 

365.6 

11 

51.3 

73.9 

100.5 

131.3 

166.2 

205.2    ; 

548.3 

295.4 

346.7 

402.1 

12 

56.0 

80.6 

109.7 

143.2 

181.3 

223.8    ; 

570.8 

322.3 

378.3 

438.7 

13 

60.6 

87.3 

118.8 

155.2 

196.4 

242.5    : 

593.4 

349.2 

409.8 

475.2 

14 

65.3 

94.0 

127.9 

167.1 

211.5 

261.1    I 

16.0 

376.0 

44  K3 

511.8 

15 

69.9 

100.7 

137.1 

179.1 

226.6 

279.8    2 

38.5 

402.9 

472.8 

548.4 

16 

74.6 

107.4 

146.2 

191.0 

241.7 

298.4    2 

61.1 

429.7 

504.4 

584.9 

17 

79.3 

114.1 

155.4 

202.9 

256.8 

317.1     2 

83.7 

456.6 

535.9 

621.5 

18 

83.9 

120.9 

164.5 

214.9 

271.9 

335.7    ^ 

K)6.2 

483.5 

567.4 

658.0 

19 

88.6 

127.6 

173.6 

226.8 

287.1 

354.4    ^ 

128.8 

510.3 

598.9 

694.6 

20 

93.3 

134.3 

182.8 

238.7 

302.2 

373.0    * 

151.4 

537.2 

630.4 

731.1 

Depth 
in 

Diameter  in  Feet. 

Feet. 

15 

16 

17 

18 

19 

20 

21 

22 

1 

41.966 

47.748 

53.903 

60.431 

67.33. 

I      74.606 

82.253 

90.273 

5 

209.8 

238.7 

269.5 

302.2 

336.7 

373.0 

411.3 

451.4 

6 

251.8 

286.5 

323.4 

362.6 

404.0 

447.6 

493.5 

541.6 

7 

293.8 

334.2 

377.3 

423.0 

471.3 

522.2 

575.8 

631.9 

8 

335.7 

382.0 

431.2 

483.4 

538.7 

596.8 

658.0 

722.2 

9 

377.7 

429.7 

485.1 

543.9 

606.0 

671.5 

740.3 

812.5 

10 

419.7 

477.5 

539.0 

604.3 

673.3 

746.1 

822.5 

902.7 

11 

461.6 

525.2 

592.9 

664.7 

740.7 

820.7 

904.8 

993.0 

12 

503.6 

573.0 

646.8 

725.2 

808.0 

895.3 

987.0 

1083.3 

13 

545.6 

620.7 

700.7 

785.6 

875.3 

969.9 

1069.3 

1173.5 

14 

587.5 

668.5 

754.6 

846.0 

942.6 

1044.5 

1151.5 

1263.8 

15 

629.5 

716.2 

808.5 

906.5 

1010.0 

1119.1 

1233.8 

1354.1 

16 

671.5 

764.0 

862.4 

966.9 

1077.3 

1193.7 

1316.0 

1444.4 

17 

713.4 

811.7 

916.4 

1027.3 

1144.6 

1268.3 

1398.3 

1534.5 

18 

755.4 

859.5 

970.3 

1087.8 

1212.0 

1342.9 

1480.6 

1624.9 

19 

797.4 

907.2 

1024.2 

1148.2 

1279.3 

1417.5 

1562.8 

1715.2 

20 

839.3 

955.0 

1078.1 

1208.6 

1346.6 

1492.1 

1645.1 

1805.5 

i 

LOGARITHMS    OF   NUMBERS. 


135 


NUMBER  OF  BARBELS   (31  1-2  GALLONS)  IN  CISTERNS 
AND  TANKS.  —  Continued. 


Depth 
in 
Feet. 

Diameter  in  Feet. 

23 

24 

25 

26 

27 

28 

29 

30 

1 
5 

98.666 
493.3 

107.432 
537.2 

116.571 
582.9 

126.083 
630.4 

135.968 
679.8 

146.226 
731.1 

156.858 
784.3 

167.863 
839.3 

6 

592.0 

644.6 

699.4 

756.5 

815.8 

877.4 

941.1 

1007.2 

7 

690.7 

752.0 

316.0 

882.6 

951.8 

1023.6 

1098.0 

1175.0 

8 

789.3 

859.5 

932.6 

1008.7 

1087.7 

1169.8 

1254.9 

1342.9 

9 

888.0 

966.9 

1049.1 

1134.7 

1223.7 

1316.0 

1411.7 

1510.8 

to 

986.7 

1074.3 

1165.7 

1260.8 

1359.7 

1462.2 

1  568.6 

1678.6 

11 

1085.3 

1  181.8 

1282.3 

1386.9 

1495.6 

1608.5 

1725.4 

1846.5 

12 

1184.0 

1289.2 

1398.8 

1513.0 

1631.6 

1754.7 

1882.3 

2014.4 

13 

1282.7 

1396.6 

1515.4 

1639.1 

1767.6 

1900.9 

2039.2 

2182.2 

14 

1381.3 

1504.0 

1632.0 

1765.2 

1903.6 

2047.2 

2196.0 

2350.1 

15 

1480.0 

1611.5 

1  748.6 

1891.2 

2039.5 

2193.4 

2352.9 

2517.9 

16 

1578.7 

1718.9 

1865.1 

2017.3 

2175.5 

2339.6 

2509.7 

2685.8 

17 

1677.3 

1826.3 

1981.7 

2143.4 

2311.5 

2485.8 

2666.6 

2853.7 

18 

1776.0 

1933.8 

2098.3 

2269.5 

2447.4 

2632.0 

2823.4 

3021.5 

19 

1874.7 

2041.2 

2214.8 

2395.6 

2583.4 

2778.3 

2980.3 

3189.4 

20 

1973.3 

2148.6 

2321.4 

2521.7 

2719.4 

2924.5 

3137.2 

3357.3 

LOGARITHMS. 

Logarithms  (abbreviation  log).  —  The  log  of  a  number  is  the  exponent 
of  the  power  to  which  it  is  necessary  to  raise  a  fixed  number  to  produce 
the  given  number.  The  fixed  number  is  called  the  base.  Thus  if  the 
base  is  10,  the  log  of  1000  is  3,  for  103  =  1000.  There  are  two  systems 
of  logs  in  general  use,  the  common,  in  which  the  base  is  10,  and  the  Naperian, 
or  hyperbolic,  in  which  the  base  is  2.718281828  ....  The  Naperian  base 
is  commonly  denoted  by  e,  as  in  the  equation  ey  —  x,  in  which  y  is  the 
Nap.  log  of  a:.  The  abbreviation  loge  is  commonly  used  to  denote  the 
Nap  log. 

In  any  system  of  logs,  the  log  of  1  is  0;  the  log  of  the  base,  taken  in  that 
system,  is  1.  In  any  system  the  base  of  which  is  greater  than  1,  the  logs  of 
all  numbers  greater  than  1  are  positive  and  the  logs  of  all  numbers  less 
than  1  are  negative. 

The  modulus  of  any  system  is  equal  to  the  reciprocal  of  the  Naperian  log 
of  the  base  of  that  system.  The  modulus  of  the  Naperian  system  is  1 ,  that 
of  the  common  system  is  0.4342945. 

The  log  of  a  number  in  any  system  equals  the  modulus  of  that  system  X 
the  Naperian  log  of  the  number. 

The  hyperbolic  or  Naperian  log  of  any  number  equals  the  common 
logX  2.3025851. 

Every  log  consists  of  two  parts,  an  entire  part  called  the  characteristic. 
or  index,  and  the  decimal  part,  or  mantissa.  The  mantissa  only  is  given 
in  the  usual  tables  of  common  logs,  with  the  decimal  point  omitted.  The 
characteristic  is  found  by  a  simple  rule,  viz.,  it  is  one  less  than  the  number 
of  figures  to  the  left  of  the  decimal  point  in  the  number  whose  log  is  to  be 
found.  Thus  the  characteristic  of  numbers  from  1  to  9.99  +  is  0,  from 
10  to  99.99  4-  is  1,  from  100  to  999  -f  is  2,  from  0.1  to  0.99  +  is  -  1,  from 
0.01  to  0.099  +  is  -2,  etc.  Thus 


log  of    2000  is  3.30103;  log  of  0.2 
••     "     oon   "  2.30103;     "    "  0.02 


200         , 

20  "  1.30103; 

2  "  Q.30103; 


is  -  1.30103,  or  9.30103  -  10 
"  -  2.30103,  "  8.30103  -  10 
0.002  "  -  3.30103,  "  7.30103  -  10 
1*  0,0002  "  -  4,30103,  '!  Q.301Q3  -  IQ 


136  LOdARITHMS   OF    NUMBERS. 

The  minus  sign  is  frequently  written  above  the  characteristic  thusi 
log  0.002  =  3.30103.  The  characteristic  only  is  negative,  the  decimal  part, 
or  mantissa,  being  always  positive. 

When  a  log  consists  of  a  negative  index  and  a  positive  mantissa,  it  is 
usual  to  write  the  negative  sign  over  the  index,  or  else  to  add  10  to  the 
index,  and  to  indicate  the  subtraction  of  10  from  the  resulting  logarithm. 

Thus  log  0.2  =  1.30103,  and  this  may  be  written  9.30103  -  10. 

In  tables  of  logarithmic  sines,  etc.,  the  —  10  is  generally  omitted,  as 
being  understood. 

Rules  for  use  of  the  table  of  logarithms.  — To  find  the  log  of  any 
whole  number.  —  For  1  to  100  inclusive  the  log  is  given  complete  in  the 
small  table  on  page  137. 

For  100  to  999  inclusive  the  decimal  part  of  the  log  is  given  opposite  the 
given  number  in  the  column  headed  0  in  the  table  (including  the  two 
figures  to  the  left,  making  six  figures).  Prefix  the  characteristic,  or 
index,  2. 

For  1000  to  9999  inclusive:  The  last  four  figures  of  the  log  are  found 
•  opposite  the  first  three  figures  of  the  given  number  and  in  the  vertical 
column  headed  with  the  fourth  figure  of  the  given  number ;  prefix  the  two 
figures  under  column  0,  and  the  index,  which  is  3. 

For  numbers  over  10,000  having  five  or  more  digits:  Find  the  decimal 
part  of  the  log  for  the  first  four  digits  as  above,  multiply  the  difference 
figure  in  the  last  column  by  the  remaining  digit  or  digits,  and  divide  by  10 
if  there  be  only  one  digit  more,  by  100  if  there  be  two  more,  and  so  on; 
add  the  quotient  to  the  log  of  the  first  four  digits  and  prefix  the  index, 
which  is  4  if  there  are  five  digits,  5  if  there  are  six  digits,  and  so  on.  The 
table  of  proportional  parts  may  be  used,  as  shown  below. 

To  find  the  log  of  a  decimal  fraction  or  of  a  whole  number  and  a 
'decimal.  —  First  find  the  log  of  the  quantity  as  if  there  were  no  decimal 
Doint,  then  prefix  the  index  according  to  rule:  the  index  is  one  less  than 
the  number  of  figures  to  the  left  of  the  decimal  point. 

Example,     log  of  3.14159.     log  of  3.141      =0.497068.    Diff.  =-138 
From  proportional  parts  5    =  690 

09=  1242 


log  3. 14159       0.4971494 

If  the  number  is  a  decimal  less  than  unity,  the  index  is  negative 
and  is  one  more  than  the_  number  of  zeros  to  the  right  of  the  decimal 
point.  Log  of  0.0682  =  2.833784  =  8.833784  -  10. 

To  find  the  number  corresponding  to  a  given  log. —  Find  in  the 
table  the  log  nearest  to  tne  decimal  part  of  the  given  log  and  take  the 
first  four  digits  of  the  required  number  from  the  column  N  and  the  top  or 
foot  of  the  column  containing  the  log  which  is  the  next  less  thanthegiven 
log.  To  find  the  5th  and  6th  digits  subtract  the  log  in  the  table  from  the 
given  log,  multiply  the  difference  by  100,  and  divide  by  the  figure  in  the 
Diff.  column  opposite  the  log;  annex  the  quotient  to  the  four  digits 
already  found,  and  place  the  decimal  point  according  to  the  rule;  the 
number  of  figures  to  the  left  of  the  decimal  point  is  one  greater  than  the 
index.  The  number  corresponding  to  a  log  is  called  the  anti-logarithm. 

Find  the  anti-log  of 0.497150 

Next  lowest  log  in  table  corresponds  to  3141 0.497068      Diff.  =  82 

Tabular  diff.  =  138;  82  -f-  138  =  0.59  -f- 
The  index  being  0,  the  number  is  therefore  3.14159  -f . 

To  multiply  two  numbers  by  tlie  use  of  logarithms.  —  Add  together 
the  logs  of  the  two  numbers,  and  find' the  number  whose  log  is  the  sum. 

To  divide  two  numbers.  —  Subtract  the  log  of  the  divisor  from  the 
log  of  the  dividend,  and  find  the  number  whose  log  is  the  difference. 
Log  of  a  fraction.     Log  of  a/b  =  log  a  —  log  b. 

To  raise  a  number  to  any  given  power.  —  Multiply  the  log  of  the 
number  by  the  exponent  of  the  power,  and  find  the  number  whose  log 
is  the  product. 

To  find  any  root  of  a  given  number.  —  Divide  the  log  of  the  number 
index  of  the  root.    The  quotient  is  tlje  log,  of  tfce  root. 


IiOGAUITHMS   OP  NUMBERS. 


137 


To  find  the  reciprocal  of  a  number.  —  Subtract  the  decimal  pait 
of  the  log  of  the  number  from  0,  add  1  to  the  index  and  change  the  sign  of 
the  index.  The  result  is  the  log  of  the  reciprocal. 

Required  the  reciprocal  of  3.141593. 

Log  of  3.141593,  as  found  above 0.4971498 

Subtract  decimal  part  from  0  gives 0.5028502 

Add  1  to  the  index,  and  changing  sign  of  the  index  gives. .  1. 5028502 
which  is  the  log  of  0.31831. 

To  find  the  fourth  term  of  a  proportion  by  logarithms.  —  Add 
the  logarithms  of  the  second  and  third  terms,  and  from  their  sum  subtract 
the  logarithm  of  the  first  term. 

When  one  logaithm  is  to  be  subtracted  from  another,  it  may  be  more 
convenient  to  convert  the  subtraction  into  an  addition,  which  may  be 
done  by  first  subtracting  the  given  logarithm  from  10,  adding  the  difference 
to  the  other  logarithm,  and  afterwards  rejecting  the  10. 

The  difference  between  a  given  logarithm  and  .10  is  called  its  arithmetical 
complement,  or  cologarithm. 

To  subtract  one  logarithm  from  another  is  the  same  as  to  add  its  com- 
plement and  then  reject  10  from  the  result.  For  a  —  b  =  10  —  b+  a  — 10. 

To  work  a  proportion,  then,  by  logarithms,  add  the  complement  of  the 
logarithm  of  the  first  term  to  the  logarithms  of  the  second  and  third  terms. 
The  characteristic  must  afterwards  be  diminished  by  10. 

Example     in    logarithms    with  a    negative    index.  —  Solve    by 


logarithms 


Vioii 
quotient  to  the  2.45  power. 

log  526    =       2.720986 
log  1011    =       3.004751 


which  means  divide  526  by  1011  and  raise  the 


log  of  quotient  = 
Multiply  by 


9.716235  -  10 
2.45 


.48581175 
3.8864940 
19.432470 


23. 80477575  -(10X2.45)  =  1.30477575  =  0.20173,  Ans. 
LOGARITHMS  OF  NUMBERS  FROM  1  TO  100. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

! 

0.000000 

21 

.322219 

41 

.612784 

61 

.785330 

81 

.908485 

2 

0.301030 

22 

.342423 

42 

.623249 

62 

.792392 

82 

.913814 

0.477121 

23 

.361728 

43 

.633468 

63 

.799341 

83 

.919078 

4 

0.602060 

24 

.380211 

44 

.643453 

64 

.806180 

84 

.924279 

0.698970 

25 

.397940 

45 

.653213 

65 

.812913 

85 

.929419 

6 

0.778151 

26 

.414973 

46 

.662758 

66 

.819544 

86 

.934498 

7 

0.845098 

27 

.431364 

47 

.672098 

67 

.826075 

87 

.939519 

8 

0.903090 

28 

.447158 

48 

.681241 

68 

.832509 

88 

.944483 

9 

0.954243 

29 

.462398 

49 

.690196 

69 

.838849 

89 

.949390 

10 

1  .000000 

30 

.477121 

50 

.698970 

70 

.845098 

90 

.954243 

11 

.041393 

31 

.491362 

51 

.707570 

71 

.851258 

91 

.959041 

12 

.079181 

32 

.505150 

52 

.716003 

72 

.857332 

92 

.963788 

13 

.113943 

33 

.518514 

53 

.724276 

73 

.863323 

93 

.968483 

14 

.146128 

34 

.531479 

54 

.732394 

74 

.869232 

94 

.973128 

15 

.176091 

35 

.544068 

55 

.740363 

75 

.875061 

95 

977724 

16 

.204120 

36 

.556303 

56 

.748188 

76 

.880814 

96 

.982271 

17 

230449 

37 

.568202 

57 

.755875 

77 

.886491 

97 

.966772 

18 

.255273 

38 

.579784 

58 

.763428 

78 

.892095 

98 

.991226 

19 

.278754 

39 

.591065 

59 

.770852 

79 

.897627 

99 

.995635 

20 

1.301030 

40 

.602060 

60 

.778151 

80 

.903090 

100 

2.000000 

For  four-place  logarithms  see  page 


138 


LOGARITHMS   OF  NUMBERS. 


No.  100  L.  OOO.j 


[No.  109  L.  040. 


N. 

0 

1 

3 

0868 
5181 
9451 

3 

4 

5 

6 

7 

8 

346~1 

7748 

9 

3891 
8174 

Diff. 

432' 
428 

424 
420 

416 
412 
408 

404 
400 

397 

100 
1 
2 

3 

4 

5 
6 

8 
9 

000000 
4321 
8600 

0434 
4751 
9026 

1301 
5609 
9876 

1734 
6038 

2166 
6466 

2598 
6894 

3029 
7321 

0300 

4521 
8700 

0724 
4940 
9116 

1147 
5360 
9532 

1570 
5779 
9947 

1993 
6197 

2415 
6616 

012837 
7033 

3259 
7451 

3680 
7868 

4100 

8284 

0361 

4486 
8571 

2619 
6629 

0775 

4896 
8978 

021189 
5306 
9384 

1603 
5715 
9789 

2016 
6125 

2428 
6533 

2841 
6942 

3252 
7350 

3664 
7757 

4075 
8164 

0195 
4227 
8223 

0600 
4628 
8620 

1004 
5029 
9017 

1408 
5430 
9414 

1812 
5830 
9811 

2216 
6230 

3021 

7028 

033424 
7426 
04 

3826 
7825 

0207 

0602 

0998 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

434" 

43.4 

86.8 

130.2 

173.6 

217.0 

260.4 

303.8 

347.2 

390.6 

433 

43.3 

86.6 

129.9 

173.2 

216.5 

259.8 

303.1 

346.4 

389.7 

432 

43.2 

86.4 

129.6 

172.8 

216.0 

259.2 

302.4 

345.6 

388.8 

431 

43.1 

86.2 

129.3 

172.4 

215.5 

258.6 

301.7 

344.8 

387.9 

430 

43.0 

86.0 

129.0 

172.0 

215.0 

258.0 

301.0 

344.0 

387.0 

429 

42.9 

85.8 

128.7 

171.6 

214.5 

257.4 

300.3 

343.2 

386.1 

428 

42.8 

85.6 

128.4 

171.2 

214.0 

256.8 

299.6 

342.4 

385.2 

427 

42.7 

85.4 

128.1 

170.8 

213.5 

256.2 

298.9 

341.6 

384.3 

426 

42.6 

85.2 

127.8 

170.4 

213.0 

255.6 

298.2 

340.8 

383.4 

425 

42.5 

85.0 

127.5 

170.0 

212.5 

255.0 

297.5 

340.0 

382.5 

424 

42.4 

84.8 

127.2 

169.6 

212.0 

254.4 

296.8 

339.2 

381.6 

423 

42.3 

84.6 

126.9 

169.2 

211.5 

253.8 

296.1 

338.4 

380.7 

422 

42.2 

84.4 

126.6 

168.8 

211.0 

253.2 

295.4 

337.6 

379.8 

421 

42.1 

84.2 

126.3 

168.4 

210.5 

252.6 

294.7 

336.8 

378.9 

420 

42.0 

84.0 

126.0 

168.0 

210.0 

252.0 

294.0 

336.0 

373.0 

419 

41.9 

83.8 

125.7 

167.6 

209.5 

251.4 

293.3 

335.2 

377.1 

418 

41.8 

83.6 

125.4 

167.2 

209.0 

250.8 

292.6 

334.4 

376.2 

417 

41.7 

83.4 

125.1 

166.8 

208.5 

250.2 

291.9 

333.6 

375.3 

416 

41.6 

83.2 

124.8 

166.4 

208.0 

249.6 

291.2 

332.8 

374.4 

415 

41.5 

83.0 

124.5 

166.0 

207.5 

249.0 

290.5 

332.0 

373.5 

414 

41.4 

82.8 

124.2 

165.6 

207.0 

248.4 

289.8 

331.2 

372.6 

413 

41.3 

82.6 

123.9 

165.2 

206.5 

247.8 

289.1 

330.4 

371.7 

412 

41.2 

82.4 

123.6 

164.8 

206.0 

247.2 

288.4 

329.6 

370.8 

>11 

41.1 

82.2 

123.3 

164.4 

205.5 

246.6 

287.7 

328.8 

369.9 

410 

41.0 

82.0 

123.0 

164.0 

205.0 

246.0 

287.0 

328.0 

369.0 

409 

40.9 

81.8 

122.7 

163.6 

204.5 

245.4 

286.3 

327.2 

368.1 

408 

40.8 

81.6 

122.4 

163.2 

204.0 

244.8 

285.6 

326.4 

367.2 

407 

40.7 

81.4 

122.1 

162.8 

203.5 

244.2 

284.9 

325.6 

366.3 

406 

40.6 

81.2 

121.8 

162.4 

203.0 

243.6 

284.2 

324.8 

365.4 

405 

40.5 

81.0 

121.5 

162.0 

202.5 

243.0 

283.5 

324.0 

364.5 

404 

40.4 

80.8 

121.2 

161.6 

202.0 

242.4 

282.8 

323.2 

363.6 

403 

40.3 

80.6 

120.9 

161.2 

201.5 

241.8 

282.1 

322.4 

362.7 

402 

40.2 

80.4 

120.6 

160.8 

201.0 

241.2 

281.4 

321.6 

361.8 

401 

40.1 

80.2 

120.3 

160.4 

200.5 

240.6 

280.7 

320.8 

360.9 

400 

40.0 

80.0 

120.0 

160.0 

200.0 

240.0 

280.0 

320.0 

360.0 

399 

39.9 

79.8 

119.7 

159.6 

199.5 

239.4 

279.3 

319.2 

359.1 

398 

39.8 

79.6 

119.4 

159.2 

199.0 

238.8 

278.6 

318.4 

358.2 

397 

39.7 

79.4 

119.1 

158.8 

198.5 

238.2 

277.9 

317.6 

357.3 

396 

39.6 

79.2 

118.8 

158.4 

198.0 

237.6 

277.2 

316.8 

356.4 

395 

39.5 

79.0 

118.5 

158.0 

197.5 

237.0 

276.5 

316.0 

355.5 

LOGARITHMS   OF   NUMBERS. 


139 


No.  110  L.  041.] 


[No.  119  L.  078. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

no 
i 

2 

3 
4 

5 

6 
7 

8 
9 

041393 
5323 
9218 

1787 
5714 
9606 

2182 
6105 
9993 

2576 
6495 

0380 
4230 
8046 

2969 
6885 

0766 
4613 
8426 

3362 
7275 

3755 
7664 

4148 
8053 

4540 
8442 

4932 
8830 

393 
390 

386 
383 

379 
376 
373 

370 
366 
363 

1153 
4996 
8805 

1538 
5378 
9185 

1924 
5760 
9563 

2309 
6142 
9942 

2694 
6524 

0320 
4083 
7815 

053078 
6905 

3463 
7286 

3846 
7666 

060698 
4458 
8186 

1075 
4832 
8557 

1452 
5206 
8928 

1829 
5580 
9298 

2206 
5953 
9668 

2582 
6326 

2958 
6699 

3333 
7071 

3709 
7443 

0038 
3718 
7368 

0407 
4085 
7731 

0776 
4451 
8094 

1145 
4816 
8457 

1514 
5182 
8819 

071882 
5547 

2250 
5912 

2617 
6276 

2985 
6640 

3352 
7004 

PROPORTIONAL   PA.RTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

395 

39.5 

79.0 

118.5 

158.0 

197.5 

237.0 

276.5 

316.0 

355.5 

394 

39.4 

78.8 

T18.2 

157.6 

197.0 

236.4 

275.8 

315.2 

354.6 

393 

39.3 

78.6 

1  17.9 

157.2 

196.5 

235.8 

275.1 

314.4 

353.7 

392 

39.2 

78.4 

117.6 

156.8 

196.0 

235.2 

274.4 

313.6 

352.8 

391 

39.1 

78.2 

117.3 

156.4 

195.5 

234.6 

273.7 

312.8 

351.9 

390 

39.0 

78.0 

117.0 

156.0 

195.0 

234.0 

273.0 

312.0 

351.C 

389 

38.9 

77.8 

116.7 

155.6 

194.5 

233.4 

272.3 

311.2 

350.1 

388 

38.8 

77.6 

116.4 

155.2 

194.0 

232.8 

271.6 

310.4 

349.2 

387 

38.7 

77.4 

116.1 

154.8 

193.5 

232.2 

270.9 

309.6 

348.3 

386 

38.6 

77.2 

115.8 

154.4 

193.0 

231.6 

270.2 

308.8 

347.4 

385 

38.5 

77.0 

115.5 

154.0 

192.5 

231.0 

269.5 

308.0 

346.? 

384 

38.4 

76.8 

115.2 

153.6 

192.0 

230.4 

268.8 

307.2 

345.6 

383 

38.3 

76.6 

114.9 

153.2 

191.5 

229.8 

268.1 

306.4 

344.7 

382 

38.2 

76.4 

114.6 

152.8 

191.0 

229.2 

267.4 

305.6 

343.8 

381 

38.1 

76.2 

114.3 

152.4 

190.5 

228.6 

266.7 

304.8 

342.9 

380 

38.0 

76.0 

114.0 

152.0 

1900 

228.0 

266.0 

304.0 

342.0 

379 

37.9 

75.8 

113.7 

151.6 

189.5 

227.4 

265.3 

303.2 

341.1 

378 

37.8 

75.6 

113.4 

151.2 

189.0 

226.8 

264.6 

302.4 

340.2 

377 

37.7 

75.4 

113.1 

150.8 

188.5 

226.2 

263.9 

301.6 

339.3 

376 

37.6 

75.2 

112.8 

150.4 

188.0 

225.6 

263.2 

300.8 

338.4 

375 

37.5 

75.0 

112.5 

150.0 

187.5 

225.0 

262.5 

300.0 

337.5 

374 

37.4 

74.8 

112.2 

149.6 

187.0 

224.4 

261.8 

299.2 

336.6 

373 

37.3 

74.6 

111.9 

149.2 

186.5 

223.8 

261.1 

298.4 

335.7 

372 

37.2 

74.4 

111.6 

148.8 

186.0 

223.2 

260.4 

297.6 

334.8 

371 

37.1 

74.2 

111.3 

148.4 

185.5 

222.6 

259.7 

296.8 

333.9 

370 

37.0 

74.0 

111.0 

148.0 

185.0 

222.0 

259.0 

296.0 

333.0 

369 

36.9 

73.8 

110.7 

147.6 

184.5 

221.4 

258.3 

295.2 

332.1 

368 

36.8 

73.6 

110.4 

147.2 

184.0 

220.8 

257.6 

294.4 

331.2 

367 

36.7 

73.4 

110.1 

146.8 

183.5 

220.2 

256.9 

293.6 

330.3 

366 

36.6 

73.2 

109.8 

146.4 

183.0 

219.6 

256.2 

292.8 

329.4 

365 

36.5 

73.0 

109.5 

146.0 

182.5 

219.0 

255.5 

292.0 

328.5 

364 

36.4 

72.8 

109.2 

145.6 

182.0 

218.4 

254.8 

291.2 

327.6 

363 

36.3 

72.6 

108.9 

145.2 

181.5 

217.8 

254.1 

290.4 

326.7 

362 

36.2 

72.4 

108.6 

144.8 

181.0 

217.2 

253.4 

289.6 

325.8 

361 

36.1 

72.2 

108.3 

144.4 

180.5 

216.6 

252.7 

288.8 

324.9 

360 

36.0 

72.0 

108.0 

144.0 

180.0 

216.0 

252.0 

288.0 

324.0 

359 

35.9 

71.8 

107.7 

143.6 

179.5 

215.4 

251.3 

287.2 

323.1 

358 

35.8 

71.6 

107.4 

143.2 

179.0 

214.8 

250.6 

286.4 

322.2 

357 

35.7 

71.4 

107.1 

142.8 

178.5 

214.2 

249.9 

285.6 

32!.  3 

356 

35.6 

71.2 

106.8 

142.4 

178.0 

213.6 

249.2 

284.8 

320.4 

140 


LOGARITHMS    OF   NUMBERS. 


No.  120  L.  079.] 


[No.  134  L.  130. 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

120 
2 

4 

5 

6 
7 

8 

9 

130 

1 

2 
3 

4 

079181 

9543 

9904 

0266 
3861 
7426 

0626 
4219 
7781 

0987 
4576 
8136 

1347 
4934 
8490 

1707 
5291 
8845 

2067 
5647 
9198 

2426 
6004 
9552 

360 
357 
355 

352 
349 

346 
343 
341 

338 
335 

333 

330 
328 
325 

323 

082785 
6360 
9905 

3144 
6716 

3503 
7071 

0258 

3772 
7257 

0611 

4122 
7604 

0963 

4471 
7951 

1315 
4820 
8298 

1667 
5169 
8644 

2018 
5518 
8990 

2370 
5866 
9335 

2721 
6215 
9681 

3071 
6562 

093422 
6910 

0026 
3462 
6871 

100371 
3804 
7210 

0715 
4146 
7549 

1059 
4487 
7888 

1403 
4828 
8227 

1747 
5169 
8565 

2091 
5510 
8903 

2434 
5851 
9241 

2777 
6191 
9579 

3119 
6531 
9916 

0253 
3609 

6940 

110590 

3943 
725  '1 

0926 

4277 
7603 

1263 

4611 
7934 

1599 

4944 
8265 

1934 

5278 
8595 

2270 

5611 

8926 

2605 

5943 
9256 

2940 

6276 
9586 

3275 

6608 
9915 

0245 
3525 
6781 

120574 
3852 
7105 
13 

0903 
4178 
7429 

1231 
4504 
7753 

1560 
4830 
8076 

1888 
5156 
8399 

2216 
5481 
8722 

2544 
5806 
9045 

2871 
6131 
9368 

3198 
6456 
9690 

0012 

PROPORTIONAL  PARTS. 


Diff. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

355" 

35.5 

71.0 

106.5 

142.0 

177.5 

213.0 

248.5 

284.0 

319.5 

354 

35.4 

70.8 

106.2 

141.6 

177.0 

212.4 

247.8 

283.2 

318.6 

353 

35.3 

70.6 

105.9 

141.2 

176.5 

211.8 

247.1 

282.4 

317.7 

352 

35.2 

70.4 

105.6 

140.8 

176.0 

211.2 

246.4 

281.6 

316.8 

351 

35.1 

70.2 

105.3 

140.4 

175.5 

210.6 

245.7 

280.8 

315.9 

350 

35.0 

70.0 

105.0 

140.0 

175.0 

210.0 

245.0 

280.0 

315.0 

349 

34.9 

69.8 

104.7 

139.6 

174.5 

209.4 

244.3 

279.2 

314.1 

348 

34.8 

69.6 

104.4 

139.2 

174.0 

208.8 

243.6 

278.4 

313.2 

347 

34.7 

694 

104.1 

138.8 

173.5 

208.2 

242.9 

277.6 

312.3 

346 

34.6 

69.2 

103.8 

138.4 

173.0 

207.6 

242.2 

276.8 

311  4 

345 

34.5 

69.0 

103.5 

138.0 

172.5 

207.0 

241.5 

276.0 

310.5 

344 

34.4 

68.8 

103.2 

137.6 

172.0 

206.4 

240.8 

275.2 

309.6 

343 

34.3 

68.6 

102.9 

137.2 

171.5 

205.8 

240.1 

274.4 

308.7 

342 

34.2 

68.4 

102.6 

136.8 

171.0 

205.2 

239.4 

273.6 

307.8 

341 

34.1 

68.2 

102.3 

136.4 

170.5 

204.6 

238.7 

272.8 

306.9 

340 

34.0 

68.0 

102.0 

136.0 

170.0 

204.0 

238.0 

272.0 

306.0 

339 

33.9 

67.8 

101.7 

135.6 

169.5 

203.4 

237.3 

271.2 

305.1 

338 

33.8 

67.6 

101.4 

135.2 

169.0 

202.8 

236.6 

270.4 

304.2 

337 

33.7 

67.4 

101.1 

134.8 

168.5 

202.2 

235.9 

269.6 

303.3 

336 

33.6 

67.2 

100.8 

134.4 

168.0 

201.6 

235.2 

268.8 

302.4 

335 

33.5 

67.0 

100.5 

134.0 

167.5 

201.0 

234.5 

268.0 

301.5 

334 

33.4 

66.8 

100.2 

133.6 

167.0 

200.4 

233.8 

267.2 

300.6 

333 

33.3 

66.6 

99.9 

133.2 

166.5 

199.8 

233.1 

266.4 

299.7 

332 

33.2 

66.4 

99.6 

132.8 

166.0 

199.2 

232.4 

265.6 

298.8 

331 

33.1 

66.2 

99.3 

132.4 

165.5 

198.6 

231.7 

264.8 

297.9 

330 

33.0 

66.0 

99.0 

132.0 

165.0 

198.0 

231.0 

264.0 

297.0 

329 

32.9 

65.8 

98.7 

131.6 

164.5 

197.4 

230.3 

263.2 

296.1 

328 

32.8 

65.6 

98.4 

131.2 

164.0 

196.8 

229.6 

262.4 

295.2 

327 

32.7 

65.4 

98.1 

130.8 

163.5 

196.2 

228.9 

261.6 

294.3 

326 

32.6. 

65.2 

97.8 

130.4 

163.0 

195.6 

228.2 

260.8 

293.4 

325 

32.5 

65.0 

97.5 

130.0 

162.5 

195.0 

227.5 

260.0 

292.5 

324 

32.4 

64.8 

97.2 

129.6 

162.0 

194.4 

226.8 

259.2 

291.6 

323 

32.3 

64.6 

96.9 

129.2 

161.5 

193.8 

226.1 

258.4 

290.7 

322 

32.2 

64.4 

96.6 

128.8 

161.0 

193.2 

225.4 

257.6 

289.8 

LOGARITHMS    OF  NUMBERS. 


141 


No.  135  L.  130.] 


[No.  149  L.  175. 


N. 

O 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

~32T 
318 
316 

314 
311 

309 

307 
305 
303 

301 
299 
297 
295 

293 
291 

135 
6 

7 
8 

9 
140 

2 
3 
4 

5 
6 

7 

8 
9 

130334 
3539 
6721 
9879 

0655 
3858 
7037 

0977 
4177 
7354 

1298 
4496 
7671 

1619 
4814 
7987 

1939 
5133 
8303 

2260 
5451 
8618 

2580 
5769 
8934 

2900 
6086 
9249 

3219 
6403 
9564 

0194 
3327 

6438 
9527 

0508 
3639 

6748 
9835 

0822 
3951 

7058 

1136 
4263 

7367 

1450 
4574 

7676 

1763 
4885 

7985 

2076 
5196 

8294 

2389 
5507 

8603 

2702 
5818 

8911 

143015 

6128 
9219 

0142 
3205 
6246 
9266 

0449 
3510 
6549 
9567 

0756 
3815 
6852 
9868 

1063 
4120 
7154 

1370 
4424 
7457 

1676 
4728 
7759 

1982 
5032 
8061 

152288 
5336 
8362 

2594 
5640 
8664 

2900 
5943 
8965 

0168 
3161 
6134 
9086 

0469 
3460 
6430 
9380 

0769 
3758 
6726 
9674 

1068 
4055 
7022 
9968 

161368 
4353 
7317 

1667 
4650 
7613 

1967 
4947 
7908 

2266 
5244 
8203 

2564 

5541 
8497 

2863 
5838 
8792 

1  70262 
3186 

0555 

3478 

0348 
3769 

1141 
4060 

1434 
4351 

1726 
4641 

2019 
4932 

2311 
5222 

2603 
5512 

2895 
5802 

PROPORTIONAL  PARTS. 


Diff. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

321 

32.1 

64.2 

96.3 

128.4 

160.5 

192.6 

224.7 

256.8 

288.9 

320 

32.0 

64.0 

96.0 

128.0 

160.0 

192.0 

224.0 

256.0 

2880 

319 

31.9 

63.8 

95.7 

127.6 

159.5 

191.4 

223.3 

255.2 

287.1 

318 

31.8 

63.6 

95.4 

127.2 

159.0 

190.8 

222.6 

254.4 

286.2 

317 

31.7 

63.4 

95.1 

126.8 

158.5 

190.2 

221.9 

253.6 

285.3 

316 

31.6 

63.2 

94.8 

126.4 

158.0 

189.6 

221.2 

252.8 

284.4 

315 

31.5 

63.0 

94.5 

126.0 

157.5 

189.0 

220.5 

252.0 

283.5 

314 

31.4 

62.8 

94.2 

125.6 

157.0 

188.4 

219.8 

251.2 

282.6 

313 

31.3 

62.6 

93.9 

125.2 

156.5 

187.8 

219.1 

250.4 

281.7 

312 

31.2 

62.4 

93.6 

124.8 

156.0 

187.2 

218.4 

249.6 

280.8 

311 

31.1 

62.2 

93.3 

124.4 

155.5 

186.6 

217.7 

248.8 

279.9 

310 

31.0 

62.0 

93.0 

124.0 

155.0 

186.0 

217.0 

248.0 

279.0 

309 

30.9 

61.8 

92.7 

123.6 

154.5 

185.4 

216.3 

247.2 

278.1 

308 

30.8 

61.6 

92.4 

123.2 

154.0 

184.8 

215.6 

246.4 

277.2 

307 

30.7 

61.4 

92.1 

122.8 

153.5 

184.2 

214.9 

245.6 

276.3 

306 

30.6 

61.2 

91.8 

122.4 

153.0 

183.6 

214.2 

244.8 

275.4 

305 

30!5 

61.0 

91.5 

122.0 

152  5 

183.0 

213.5 

244.0 

274.5 

304 

30.4 

60.8 

91.2 

121.6 

152.0 

182.4 

212.8 

243.2 

273.6 

303 

30.3 

60.6 

90.9 

121.2 

151.5 

181.8 

212.1 

242.4 

272.7 

302 

30.2 

60.4 

90.6 

120.8 

151.0 

181.2 

211.4 

241.6 

271.8 

301 

30.1 

60.2 

90.3 

120.4 

150.5 

1806 

210.7 

240.8 

270.9 

300 

30.0 

60.0 

90.0 

120.0 

150.0 

180.0 

210.0 

240.0 

270.0 

299 

29.9 

59.8 

89.7 

119.6 

149.5 

179.4 

209.3 

239.2 

269.1 

298 

29.8 

59.6 

89.4 

119.2 

149.0 

178.8 

208.6 

238.4 

268.2 

297 

29.7 

59.4 

89.1 

118.8 

148.5 

178.2 

207.9 

237.6 

267.3 

296 

29.6 

59.2 

88.8 

118.4 

148.0 

177.6 

207.2 

236.8 

266.4 

295 

29.5 

590 

88.5 

118.0 

147.5 

177.0 

206.5 

236.0 

265.5 

294 

29.4 

58.8 

88.2 

117.6 

147.0 

176.4 

205.8 

235.2 

264.6 

293 

29.3 

58.6 

87.9 

117.2 

146.5 

175.8 

205.1 

234.4 

263.7 

292 

29.2 

58.4 

87.6 

116.8 

146,0 

175.2 

204.4 

233.6 

262.8 

291 

29.1 

58.2 

87.3 

116.4 

145.5 

174.6 

203.7 

232.8 

261.9 

290 

29.0 

58.0 

87.0 

116.0 

145.0 

174.0 

203.0 

232.0 

261.. 

289 

28.9 

57.8 

86.7 

115.6 

144.5 

173.4 

202.3 

231.2 

260.1 

288 

28.8 

57.6 

86.4 

115.2 

144.0 

172.3 

201.6 

230.4 

259.2 

287 

28.7 

57.4 

86.1 

114.8 

143.5 

172.2 

200.9 

229.6 

258.3 

286 

28.6 

57.2 

85.8 

114.4 

143.0 

171.6 

200.2 

228.8 

2*7.4 

142 


LOGARITHMS   OP  NUMBERS. 


Wo.  150  L.  176.] 


[No.  109  L.  230 


N. 
~T50" 

2 

4 

5 
6 
7 

8 

9 
160 
2 

3 

4 

6 

8 
9 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

DiflF. 
-28T 

287 
285 

283 

281 
279 
278 
276 

274 
272 

271 
269 

267 
266 
264 
262 

261 
259 
258 

256 

176091 
8977 

6381 
9264 

6670 
9552 

6959 
9839 

7248 

7536 

7825 

8113 

8401 

8689 

0126 
2985 
5825 
8647 

0413 
3270 
6108 
8928 

0699 
3555 
6391 
9209 

0986 
3839 
6674 
9490 

1272 
4123 
6956 
9771 

1558 
4407 
7239 

181844 
4691 
7521 

2129 
4975 
7803 

2415 
5259 
8084 

2700 
5542 
8366 

0051 
2846 
5623 
8382 

190332 
3125 
5900 
8657 

0612 
3403 
6176 
8932 

0892 
3681 
6453 
9206 

1171 
3959 
6729 
9481 

1451 
4237 
7005 
9755 

1730 
4514 
7281 

2010 
4792 
7556 

2289 
5069 
7832 

2567 
5346 
8107 

0029 
2761 

5475 
8173 

0303 
3033 

5746 
8441 

0577 
3305 

6016 
8710 

0850 
3577 

6286 
8979 

1124 
3848 

6556 
9247 

201397 

4120 
6826 
9515 

1670 

4391 
7096 
9783 

1943 

4663 
7365 

2216 

4934 
7634 

2488 

5204 
7904 

0051 
2720 
5373 
8010 

0319 
2986 
5638 
8273 

0586 
3252 
5902 
8536 

0853 
3518 
6166 
8798 

1121 
3783 
6430 
9060 

1388 
4049 
6694 
9323 

1654 
4314 
6957 
9585 

1921 
4579 
7221 
9846 

212188 
4844 
7484 

2454 
5109 
7747 

220108 
2716 
5309 
7887 
23 

0370 
2976 
5568 
8144 

0631 
3236 
5826 
8400 

0892 
3496 
6084 
8657 

1153 
3755 
6342 
8913 

1414 
4015 
6600 
9170 

1675 
4274 
6858 
9426 

1936 
4533 
7115 
9682 

2196 
4792 
7372 
9938 

2456 
5051 
7630 

0193 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

285 

28.5 

57.0 

85.5 

114.0 

142.5 

171.0 

199.5 

228.0 

256.5 

,784 

28.4 

56.8 

85.2 

113.6 

142.0 

170.4 

198.8 

227.2 

255.6 

283 

28.3 

56.6 

84.9 

113.2 

141.5 

169.8 

198.1 

226.4 

254.7 

282 

28.2 

56.4 

84.6 

112.8 

141.0 

169.2 

197.4 

225.6 

253.8 

281 

28.1 

56.2 

84.3 

112.4 

140.5 

168.6 

196.7 

224.8 

252.9 

280 

28.0 

56.0 

84.0 

112.0 

140.0 

168.0 

196.0 

224.0 

252.0 

279 

27.9 

55.8 

83.7 

111.6 

139.5 

167.4 

195.3 

223.2 

251.1 

278 

27.8 

55.6 

83.4 

111.2 

139.0 

166.8 

194.6 

222.4 

250.2 

277 

27.7 

55.4 

83.1 

110.8 

138.5 

166.2 

193.9 

221.6 

249.3 

276 

27.6 

55.2 

82.8 

110.4 

138.0 

165.6 

193.2 

220.8 

248.4 

275 

27.5 

55.0 

82.5 

110.0 

137.5 

165.0 

192.5 

220.0 

247.5 

274 

27.4 

54.8 

82.2 

109.6 

137.0 

164.4 

191.8 

219.2 

246.6 

273 

27.3 

54.6 

81.9 

109,2 

136.5 

163.8 

191.1 

218.4 

245.7 

272 

27.2 

54.4 

81.6 

108.8 

136.0 

163.2 

190.4 

217.6 

244.8 

271 

27.1 

54.2 

81.3 

108.4 

135.5 

162.6 

189.7 

216.8 

243.9 

270 

27.0 

54.0 

81.0 

108.0 

135.0 

162.0 

189.0 

216.0 

243.0 

269 

26.9 

53.8 

80.7 

107.6 

134.5 

161.4 

188.3 

215.2 

242.1 

268 

26.8 

53.6 

80.4 

107.2 

134.0 

160.8 

187.6 

214.4 

241.2 

267 

26.7 

53.4 

80.1 

106.8 

133.5 

160.2 

186.9 

213.6 

240.3 

266 

26.6 

53.2 

79.8 

106.4 

133.0 

159.6 

186.2 

212.8 

239.4 

265 

26.5 

53.0 

79.5 

106.0 

132.5 

159.0 

185.5 

212.0 

238.5 

264 

26.4 

52.8 

79.2 

105.6 

132.0 

158.4 

184.8 

211.2 

237.6 

263 

26.3 

52.6 

78.9 

105.2 

131.5 

157.8 

184.1 

210.4 

236.7 

262 

26.2 

52.4 

78.6 

104.8 

131.0 

157.2 

183.4 

209.6 

235.8 

261 

26.1 

52.2 

78.3 

104.4 

130.5 

156.6 

182.7 

208.8 

234.9 

260 

26.0 

52.0 

78.0 

104.0 

130.0 

156.0 

182.0 

208.0 

234.0 

259 

25.9 

51.8 

77.7 

103.6 

129.5 

155.4 

181.3 

207.2 

233.1 

258 

25.8 

51.6 

77.4 

103.2 

129.0 

154.8 

180.6 

206.4 

232.2 

257 

25.7 

51.4 

77.1 

102.8 

128.5 

154.2 

179.9 

205.6 

231.3 

256 

25.6 

51.2 

76,8 

102.4 

128.0 

153.6 

179.2 

204.8 

230.4 

255 

25.5 

51.0 

76.5  ' 

102.0 

127.5  ' 

153.0 

178.5 

204.0  i 

229J 

LOGARITHMS   OF  NUMBERS. 


143 


No.  I  VOL.  230.] 


[No.  189L.278. 


N. 

17o~ 

i 

2 
3 

4 

6 
7 

8 
9 

180 
1 

2 
3 

4 
5 
6 

8 
9 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

230449 
2996 
5528 
8046 

0704 
3250 
5781 
8297 

0960 
3504 
6033 
8548 

1215 
3757 
6285 
8799 

1470 
4011 
6537 
9049 

1724 
4264 
6789 
9299 

1979 
4517 
7041 
9550 

2234 
4770 
7292 
9800 

2488 
5023 
7544 

2742 
5276 
7795 

255 
253 
252 

250 

249 
248 
246 

245 
243 
242 

241 
239 

238 
237 
235 
234 

233 
232 
230 
229 

0050 
2541 
5019 
7482 
9932 

0300 
2790 
5266 
7728 

240549 
3038 
5513 
7973 

0799 
3286 
5759 
8219 

1048 
3534 
6006 
8464 

1297 
3782 
6252 
8709 

1546 
4030 
6499 
8954 

1795 
4277 
6745 
9198 

2044 
4525 
6991 
9443 

2293 
4772 
7237 
9687 

0176 
2610 
5031 

7439 
9833 

250420 
2853 

5273 
7679 

0664 
3096 

5514 
7918 

0908 
3338 

5755 
8158 

1151 
3580 

5996 
8398 

1395 

3822 

6237 
8637 

1638 
4064 

6477 
8877 

1881 
4306 

6718 
9116 

2125 
4548 

6958 
9355 

2368 
4790 

7198 
9594 

260071 
2451 
4818 
7172 
9513 

0310 
2688 
5054 
7406 
9746 

0548 
2925 
5290 
7641 
9980 

0787 
3162 
5525 
7875 

1025 
3399 
5761 
81  10 

1263 
3636 
5996 
8344 

1501 
3873 
6232 
8578 

1739 
4109 
6467 
8812 

1976 
4346 
6702 
9046 

2214 
4582 
6937 
9279 

0213 
2538 
4850 
7151 

0446 
2770 
5081 
7380 

0679 
3001 
5311 
•7609 

0912 
3233 
5542 
7838 

1144 
3464 
5772 
8067 

1377 
3696 
6002 
8296 

1609 
3927 
6232 
8525 

271842 
4158 
6462 

2074 
4389 
6692 

2306 
4620 
6921 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

255 

25.5 

51.0 

76.5 

102.0 

127.5 

153.0 

178.5 

204.0 

229.5 

254 

25.4 

50.8 

76.2 

101.6 

127.0 

152.4 

177.8 

203.2 

228.6 

253 

25.3 

50.6 

75.9 

101.2 

126.5 

151.8 

177.1 

202.4 

227.7 

252 

25.2 

50.4 

75.6 

100.8 

126.0 

151.2 

176.4 

201.6 

226.8 

251 

25.1 

50.2 

75.3 

100.4 

125.5 

150.6 

175.7 

200.8 

225.9 

250 

25.0 

50.0 

75.0 

100.0 

125.0 

150.0 

175.0 

200.0 

225.0 

249 

24.9 

49.8 

74.7 

99.6 

124.5 

149.4 

174.3 

199.2 

224.1 

248 

24.8 

49.6 

74.4 

99.2 

124.0 

148.8 

173.6 

198.4 

223.2 

247 

24.7 

49.4 

74.1 

98.8 

123.5 

148.2 

172.9 

197.6 

222.3 

246 

24.6 

49.2 

73.8 

98.4 

123.0 

147.6 

172.2 

196.8 

221.4 

245 

24.5 

49.0 

73.5 

98.0 

122.5 

147.0 

171.5 

196.0 

220.5 

244 

24.4 

48.8 

73.2 

97.6 

122.0 

146.4 

170.8 

195.2 

219.6 

243 

24.3 

48.6 

72.9 

97.2 

121.5 

145.8 

170.1 

194.4 

218.7 

242 

24.2 

48.4 

72.6 

96.8 

121.0 

145.2 

1694 

193.6 

217.8 

241 

24.1 

48.2 

72.3 

96.4 

120.5 

144.6 

168.7 

192.8 

216.9 

240 

24.0 

48.0 

72.0 

96.0 

120.0 

144.0 

168.0 

192.0 

216.0 

239 

23.9 

47.8 

71.7 

95.6 

119.5 

143.4 

167.3 

191.2 

215.1 

238 

23.8 

47.6 

71.4 

95.2 

119.0 

142.8 

166.6 

190.4 

214.2 

237 

23.7 

47.4 

71.1 

94.8 

118.5 

142.2 

165.9 

189.6 

213.3 

236 

23.6 

47.2 

70.8 

94.4 

118.0 

141.6 

165.2 

188.8 

212.4 

235 

23.5 

47.0 

70.5 

94.0 

117.5 

141.0 

164.5 

188.0 

211.5 

234 

23.4 

46.8 

70.2 

93.6 

117.0 

140.4 

163.8 

187.2 

210.6 

233 

23.3 

46.6 

69.9 

93.2 

116.5 

139.8 

163.1 

186.4 

209.7 

232 

23.2 

46.4 

69.6 

92.8 

116.0 

139.2 

162.4 

185.6 

208.8 

231 

23.1 

46.2 

69.3 

92.4 

115.5 

138.6 

161.7 

184.8 

207.9 

230 

23.0 

46.0 

69.0 

920 

115.0 

138.0 

161.0 

184.0 

207.0 

229 

22.9 

45.8 

68.7 

91.6 

114.5 

137.4 

160.3 

183.2 

206.1 

228 

22.8 

45.6 

68.4 

91.2 

114.0 

136.8 

159.6 

182.4 

205.2 

227 

22.7 

45.4 

68.1 

90.8 

113.5 

136.2 

158.9 

181.6 

204.3 

226 

22.6 

45.2 

67.8 

90.4 

113.0 

135.6 

158.2 

180.8 

203.4 

144 


LOGARITHMS   OF  NUMBERS. 


No.  190  L.  278.] 


[No.  214  L.332. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

190 

278754 

898;; 

921  1 

9439 

9667 

9895 

m  j-i 

nae 

n^7« 

flQflA 

2 
3 
4 

281033 
3301 
5557 
7802 

1261 
3527 
5782 
8026 

1488 
3753 
6007 
8249 

1715 
3979 
6232 
8473 

1942 
4205 
6456 
8696 

2169 
4431 
6681 
8920 

2396 
4656 
6905 
9143 

2622 
4882 
7130 
9366 

2849 
5107 
7354 
9589 

3075 
5332 

7578 
9812 

227 
226 
225 
223 

5 
6 
7 
8 
9 

290035 
2256 
4466 
6665 
8853 

0257 
2478 
4687 
6884 
9071 

0480 
2699 
4907 
7104 
9289 

0702 
2920 
5127 
7323 
9507 

0925 
3141 
5347 
7542 
9725 

1147 
3363 
5567 
7761 
9943 

1369 
3584 
5787 
7979 

1591 
3804 
6007 
8198 

1813 
4025 
6226 
8416 

2034 
4246 
6446 
8635 

222 
221 
220 
219 

0161 

0-170 

ft^QS 

no  i  q 

9  t  A 

200 
1 
2 
3 
4 

301030 
3196 
5351 
7496 
9630 

1247 
3412 
5566 
7710 
9843 

1464 
3628 
5781 
7924 

1681 
3844 
5996 
8137 

1898 
4059 
6211 
8351 

2114 
4275 
6425 
8564 

2331 

4491 
6639 

8778 

2547 
4706 
6854 
8991 

2764 
4921 
7068 
9204 

2980 
5136 
7282 
9417 

217 
216 
215 
213 

0056 

0268 

048  1 

0693 

0906 

1  1  j  o 

i  -2ar\ 

1  ^49 

919 

5 
6 
7 
8 

311754 
3867 
5970 
8063 

1966 
4078 
6180 

8272 

2177 
4289 
6390 
8481 

2389 
4499 
6599 
8689 

2600 
4710 
6809 
8898 

2812 
4920 
7018 
9106 

3023 
5130 

7227 
9314 

3234 
5340 
7436 
9522 

3445 
5551 
7646 
9730 

3656 
5760 

7854 
9938 

211 
210 
209 
208 

9 
210 

2 
3 

320146 

2219 
4282 
6336 
8380 

0354 

2426 
4488 
6541 
8583 

0562 

2633 
4694 
6745 
8787 

0769 

2839 
4899 
6950 

8991 

t)977 

3046 
5105 
7155 
9194 

1184 

3252 
5310 
7359 
9398 

1391 

3458 
5516 
7563 
9601 

1598 

3665 
5721 
7767 
9805 

1805 

3871 
5926 
7972 

2012 

4077 
6131 
8176 

207 

206 
205 
204 

noftP. 

O9  i  i 

9flT 

4 

330414 

0617 

0819 

1022 

1225 

1427 

1630 

1832 

2034 

2236 

202 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

225 

22.5 

45.0 

67.5 

90.0 

112.5 

135.0 

157.5 

180.0 

202.5 

224 

22.4 

44.8 

67.2 

89  6 

112.0 

134.4 

156.8 

179.2 

201.6 

223 

22.3 

44.6 

66.9 

89.2 

111.5 

133.8 

156.1 

178.4 

200.7 

222 

22.2 

44.4 

66.6 

88.8 

1110 

133.2 

155.4 

177.6 

199.8 

221 

22.1 

44.2 

66.3 

88.4 

110.5 

132.6 

154.7 

176.8 

198.9 

220 

22.0 

44.0 

66.0 

88.0 

110.0 

132.0 

154.0 

176.0 

198.0 

219 

21.9 

43.8 

65.7 

87.6 

109.5 

131.4 

153.3 

175.2 

197.1 

218 

21.8 

43.6 

65.4 

87.2 

109.0 

130.8 

152.6 

174.4 

196.2 

217 

21.7 

43.4 

65.1 

86.8 

108.5 

130.2 

151.9 

173.6 

195.3 

216 

21.6 

43.2 

64.8 

86.4 

108.0 

129.6 

151.2 

172.8 

194.4 

215 

21.5 

43.0 

64.5 

86.0 

107.5 

129.0 

150.5 

172.0 

193.5 

214 

21.4 

42.8 

64.2 

85.6 

107.0 

128.4 

149.8 

171.2 

192.6 

213 

21.3 

42.6 

63.9 

85.2 

106.5 

127.8 

149.1 

170.4 

191.7 

212 

21.2 

42.4 

63.6 

84.8 

106.0 

127.2 

148.4 

169.6 

190.8 

211 

21.1 

42.2 

63.3 

84.4 

105.5 

126.6 

147.7 

168.8 

189.9 

210 

21.0 

42.0 

63.0 

84.0 

105.0 

126.0 

147.0 

168.0 

189.0 

209 

20.9 

41.8 

62.7 

83.6 

104.5 

125.4 

146.3 

167.2 

188.1 

208 

20.8 

41.6 

62.4 

83.2 

104.0 

124.8 

145.6 

166.4 

187.2 

207 

20.7 

41.4 

62.1 

82.8 

103.5 

124.2 

144.9 

165.6 

186.3 

206 

20.6 

41:2 

61.8 

82.4 

103.0 

123.6 

144.2 

164.8 

185.4 

205 

20.5 

41.0 

61.5 

82.0 

102.5 

123.0 

143  5 

164.0 

184.5 

204 

20.4 

40.8 

61.2 

81.6 

102.0 

122.4 

142.8 

163.2 

183.6 

203 

20.3 

40.6 

60.9 

81.2 

101.5 

121.8 

142.1 

162.4 

182.7 

202 

20.2 

40.4 

60.6 

80.8 

101.0 

121.2   1 

141.4 

161.6 

181.8 

LOGARITHMS   OF   NUMBERS. 


145 


No.  215  L.  332.] 


[No.  239  L.  380. 


N. 

0 

1 

3 

3 

4 

5 

"3447 
5458 
7459 
9451 

6 

73649 
5658 
7659 
9650 

7 

~3850 
5859 
7858 
9849 

8 

~~4Q5~1 
6059 
8058 

9 

"4253 
6260 

S257 

Diff. 

~202" 
201 
200 

199 
198 

197 
196 
195 

194 
193 
193 
192 
191 
190 

189 

188 
188 
187 
186 

215 
6 

8 
9 
220 

2 
3 

4 
6 

8 
9 

230 

2 
3 
4 

5 
6 
7 
8 
9 

332438 
4454 
6460 
8456 

2640 
4655 
6660 
8656 

2842 
4856 
6860 
8855 

3044 
5057 
7060 
9054 

3246 
5257 
7260 
9253 

0047 
2028 

3999 
5962 
7915 
9860 

1796 
3724 
5643 
7554 
9456 

0246 
2225 

4195 
6157 
8110 

340444 

2423 
4392 
6353 
8305 

0642 

2620 
4589 
6549 
8500 

0841 

2817 
4785 
6744 
8694 

1039 

3014 
4981 
6939 
8889 

1237 

3212 
5178 
7135 
9083 

1435 

3409 
5374 
7330 
9278 

1632 

3606 
5570 
7525 
9472 

1830 

3802 
5766 
7720 
9666 

1603 
3532 
5452 
7363 
9266 

0054 
1989 
3916 
5834 
7744 
9646 

350248 
2183 
4108 
6026 
7935 
9835 

0442 
2375 
4301 
6217 
8125 

0636 
2568 
4493 
6408 
8316 

0829 
2761 
4685 
6599 
8506 

1023 
2954 
4876 
6790 
8696 

1216 
3147 
5068 
6981 
8886 

1410 
3339 
5260 
7172 
9076 

0025 

1917 
3800 
5675 
7542 
9401 

0215 

2105 
3988 
5862 
7729 
9587 

0404 

2294 
4176 
6049 
7915 
9772 

0593 

2482 
4363 
6236 
8101 
9958 

0783 

2671 
4551 
6423 

8287 

0972 

2859 
4739 
6610 
8473 

1161 

3048 
4926 
6796 
8659 

1350 

3236 
5113 
6983 
8845 

0698 
2544 
4382 
6212 
8034 
9849 

1539 

3424 
5301 
7169 
9030 

361728 
3612 
5488 
7356 
9216 

0143 
1991 
3831 
5664 
7488 
9306 

0328 
2175 
4015 
5846 
7670 
9487 

0513 
2360 
4198 
6029 
7852 
9668 

0883 
2728 
4565 
6394 
8216 

185 
184 
184 
183 
182 

181 

37106S 
2912 
4748 
6577 
8398 
38 

1253 
3096 
4932 
6759 
8580 

1437 
3280 
5115 
6942 
8761 

1622 
3464 
5298 
7124 
8943 

1806 
3647 
5481 
7306 
9124 

0030 

PROPORTIONAL  PARTS. 


Diff. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

*202~ 
201 

20.2 
20.1 

40.4 
40.2 

60.6 
60.3 

80.8 
80.4 

101.0 
100.5 

121.2 
120.6 

141.4 
140.7 

161.6 
160.8 

181.8 
180.9 

200 

20.0 

40.0 

60.0 

80.0 

100.0 

120.0 

140.0 

160.0 

180.0 

199 

19.9 

39.8 

59.7 

79.6 

99.5 

119.4 

139.3 

159.2 

179.{ 

198 

19.8 

39.6 

59.4 

79.2 

99.0 

118.8 

138.6 

158.4 

178.2 

197 

19.7 

39.4 

59.1 

78.8 

98.5 

118.2 

137.9 

157.6 

177.3 

196 

19.6 

39.2 

58.8 

78.4 

98.0 

117.6 

137.2 

156.8 

176.4 

195 

19.5 

39.0 

58.5 

78.0 

97.5 

117.0 

136.5 

1  56.0 

175.5 

194 

19.4 

38.8 

58.2 

77.6 

97.0 

116.4 

135.8 

155.2 

174.6 

193 

19.3 

38.6 

57.9 

77.2 

96.5 

115.8 

135.1 

154.4 

173.7 

192 

19.2 

38.4 

57.6 

76.8 

96.0 

'  115.2 

134.4 

153.6 

172.8 

191 

19.1 

38.2 

57.3 

76.4 

95.5 

114.6 

133.7 

152.8 

171.9 

190 

190 

38.0 

57.0 

76.0 

95.0 

114.0 

133.0 

152.0 

171.0 

189 

18.9 

37.8 

56.7 

75.6 

94.5 

113.4 

132.3 

151.2 

170.1 

188 

18.8 

37.6 

56.4 

75.2 

940 

112.8 

131.6 

150.4 

169.2 

187 

18.7 

37.4 

56.1 

74.8 

93.5 

112.2 

130.9 

149.6 

168.3 

186 

18.6 

37.2 

55.3 

74.4 

93.0 

111.6 

130.2 

148.8 

167.4 

185 

18.5 

37.0 

55.5 

74.0 

92.5 

111.0 

129.5 

148.0 

166.5 

184 

18.4 

36.8 

55.2 

73.6 

92.0 

110.4 

128.8 

147.2 

165.6 

183 

18.3 

36.6 

54.9 

73.2 

91.5 

109.8 

128.1 

146.4 

164.7 

182 

18.2 

36.4 

54.6 

72.8 

91.0 

109.2 

127.4 

145.6 

163.8 

181 

18.1 

36.2 

54.3 

72.4 

90.5 

108.6 

126.7 

144.8 

162.9 

180 

18.0 

36.0 

54.0 

72.0 

90.0 

108.0 

126.0 

1440 

162.0 

179 

17.9 

35.8 

53.7 

71.6 

89.5 

107.4 

125.3 

143.2 

161.1 

146 


LOGARITHMS   OF  NUMBERS. 


No.  240  L.  380.J 


[No.  269  L.  431, 


N. 

1 

3 
4 
5 

6 

7 
8 
9 

250 

1 

2 
3 

5 
6 

7 

8 
9 

260 

2 
3 

4 
6 

8 
9 

0 

1 

2 

~0573 
2377 
4174 
5964 
7746 
9520 

3 

4 

5 

6 

7 

8 

T656 
3456 
5249 
7034 
8811 

9 

Diff. 

IsT 

180 
179 
178 
178 

177 
176 
176 
175 
174 

173 

173 
172 
171 

17! 
170 
169 

169 
168 
167 

167 
166 
165 

165 
164 
164 
163 
162 
162 

161 

380211 
2017 
3815 
5606 
7390 
9166 

0392 
2197 
3995 
5785 
7568 
9343 

0754 
2557 
4353 
6142 
7924 
9698 

0934 
2737 
4533 
6321 
8101 
9875 

1115 
2917 
4712 
6499 
8279 

1296 
3097 
4891 
6677 
8456 

1476 
3277 
5070 
6856 
8634 

1837 
3636 
5428 
7212 
8989 

0051 
1817 
3575 
5326 
7071 

8808 

0228 
1993 
3751 
5501 
7245 

8981 

0405 
2169 
3926 
5676 
7419 

9154 

0582 
2345 
4101 
5850 
7592 

9328 

0759 
2521 
4277 
6025 
7766 

9501 

390935 
2697 
4452 
6199 

7940 
9674 

1112 
2873 
4627 
6374 

8114 
9847 

1288 
3048 
4802 
6548 

8287 

1464 
3224 
4977 
6722 

8461 

1641 
3400 
5152 
6896 

8634 

0020 
1745 
3464 
'5176 
6881 
8579 

0192 
1917 
3635 
5346 
7051 
8749 

0365 
2089 
3807 
5517 
7221 
8918 

0538 
2261 
3978 
5688 
7391 
9087 

0711 
2433 
4149 
5858 
7561 
9257 

0883 
2605 
4320 
6029 
7731 
9426 

1056 
2777 
4492 
6199 
7901 
9595 

1228 
2949 
4663 
6370 
8070 
9764 

401401 
3121 
4834 
6540 
8240 
9933 

1573 
3292 
5005 
6710 
8410 

0102 
1788 
3467 

5140 
6807 
8467 

0271 
1956 
3635 

5307 
6973 
8633 

0440 
2124 
3803 

5474 
7139 
8798 

0609 
2293 
3970 

5641 
7306 
8964 

0777 
2461 
4137 

5808 
7472 
9129 

0946 
2629 
4305 

5974 
7638 
9295 

11  14 
2796 
4472 

6141 
7804 
9460 

1110 
2754 
4392 
6023 
7648 
9268 

1283 
2964 
4639 

6308 
7970 
9625 

1451 
3132 
4806 

6474 
8135 
9791 

1439 
3082 
4718 
6349 
7973 
9591 

411620 
3300 

4973 
6641 
8301 
9956 

0121 
1768 
3410 
5045 
6674 
8297 
9914 

0286 
1933 
3574 
5208 
6836 
8459 

0451 
2097 
3737 
5371 
6999 
8621 

0616 
2261 
3901 
5534 
7161 
8783 

0781 
2426 
4065 
5697 
7324 
8944 

0945 
2590 
4228 
5860 
7486 
9106 

1275 
2918 
4555 
6186 
7811 
9429 

421604 
3246 
4882 
6511 
8135 
9752 
43 

0075 

0236 

0398 

0559 

0720 

0881 

1042 

1203 

PROPORTIONAL  PARTS. 


Diff. 
T78~ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

17.8 

35.6 

53.4 

71.2 

89.0 

106.8 

124.6 

142.4 

160.2 

177 

17.7 

35.4 

53.1 

70.8 

88.5 

106.2 

•  23.9 

141.6 

159.3 

176 

17.6 

35.2 

52.8 

70.4 

88.0 

105.6 

123.2 

140.8 

158.4 

175 

17.5 

35.0 

52.5 

70.0 

87.5 

105.0 

122.5 

140.0 

157.5 

174 

17.4 

34.8 

52.2 

69.6 

87.0 

104.4 

121.8 

139.2 

156.6 

173 

173 

34.6 

51.9 

69.2 

86.5 

103.8. 

121.1 

138.4 

155.7 

172 

17.2 

34.4 

51.6 

68.8 

86.0 

103.2 

120.4 

137.6 

154.8 

171 

17.1 

34.2 

51.3 

68.4 

85.5 

102.6 

119.7 

136.8 

153.V 

170 

17.0 

34.0 

51.0 

68.0 

85.0 

102.0 

119.0 

136.0 

153.0 

169 

16.9 

33.8 

50.7 

67.6 

84.5 

101.4 

118.3 

135.2 

152.1 

168 

16.8 

33.6 

50.4 

67.2 

84.0 

100.8 

117.6 

134.4 

151.2 

167 

16.7 

33.4 

50.1 

66.8 

83.5 

100.2 

116.9 

133.6 

150.3 

166 

16.6 

33.2 

49.8 

66.4 

830 

99.6 

116.2 

132.8 

149.4 

165 

16.5 

33.0 

49.5 

66.0 

82.5 

99.0 

115.5 

132.0 

148.5 

164 

16.4 

32.8 

49.2 

65.6 

82.0 

98.4 

114.8 

131.2 

147.6 

163 

16.3 

32.6 

48.9 

65.2 

81.5           97.8 

114.1 

130.4 

146.7 

162 

16.2 

32.4 

48.5 

64.8 

81.0           97.2 

113.4 

129.6 

1458 

161 

16.1 

32.2 

48.3 

64.4 

80.5  1        96.6 

112.7 

128.8 

144.9 

LOGARITHMS   OF  NUMBERS.  147 

No.  270  L.  431.]  [No.  299  L.  476. 


N. 

?70 
1 
2 
3 
4 
5 

6 

8 
9 

280 

2 

4 
5 
6 
7 
8 

9 

290 

1 

3 

4 
5 

6 

8 
9 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

431364 
2969 
4569 
6163 
7751 
9333 

1525 
3130 
4729 
6322 
7909 
9491 

1685 
3290 
4888 
6481 
8067 
9648 

1846 
3450 
5048 
6640 
8226 
9806 

2007 
3610 
5207 
6799 
8384 
9964 

2167 
3770 
5367 
6957 
8542 

2328 
3930 
5526 
7116 
8701 

24tte> 
4090 
5685 

7275 
8859 

2649 
4249 
5844 
7433 
9017 

2809 
4409 
6004 
7592 
9175 

161 
160 
159 
159 
158 

158 
157 
157 
156 
155 

155 

154 
154 
153 
153 
152 
152 
15} 

151 
150 

150 
149 
149 
148 
148 

147 
146 
146 
146 
145 

0122 
1695 
3263 
4825 
6382 

7933 
9478 

0279 
1852 
3419 
4981 
6537 

8088 
9633 

0437 
2009 
3576 
5137 
6692 

8242 
9787 

0594 
2166 
3732 
5293 
6848 

8397 
9941 

0752 
2323 
3889 
5449 
7003 

8552 

440909 
2480 
4045 
5604 

7158 
8706 

1066 
2637 
4201 
5760 

7313 
8861 

1224 
2793 
4357 
5915 

7468 
QQ15 

1381 
2950 
4513 
6071 

7623 
9170 

1538 
3106 
4669 
6226 

7778 
9324 

0095 
1633 
3165 
4692 
6214 
7731 
9242 

450249 
1786 
3318 
4845 
6366 
7882 
9392 

0403 
1940 
3471 
4997 
6518 
8033 
9543 

0557 
2093 
3624 
5150 
6670 
8184 
9694 

0711 
2247 
3777 
5302 
6821 
8336 
9845 

0865 
2400 
3930 
5454 
6973 
8487 
9995 

1018 
2553 
4082 
5606 
7125 
8638 

1172 
2706 
4235 
5758 
7276 
8789 

1326 
2859 
4387 
5910 
7428 
8940 

1479 
3012 
4540 
6062 
7579 
9091 

0146 
1649 

3146 
4639 
6126 
7608 
9085 

0296 
1799 

3296 
4788 
6274 
7756 
9233 

0447 
1948 

3445 
4936 
6423 
7904 
9380 

0597 
2098 

3594 
5085 
6571 
8052 
9527 

0748 
2248 

3744 
5234 
6719 
8200 
•9675 

460898 

2398 
3893 
5383 
6868 
8347 
9322 

1048 

2548 
4042 
5532 
7016 
8495 
9969 

1198 

2697 
4191 
5680 
7164 
8643 

1348 

2847 
4340 
5829 
7312 
8790 

1499 

2997 
4490 
5977 
7460 
8938 

0116 
1585 
3049 
4508 
5962 

0263 
1732 
3195 
4653 
6107 

0410 
1878 
3341 
4799 
6252 

0557 
2025 
3487 
4944 
6397 

0704 
2171 
3633 
5090 
6542 

0851 
2318 
3779 
5235 
6687 

0998 
2464 
3925 
5381 
6832 

1145 
2610 
4071 
5526 
6976 

471292 
2756 
4216 
5671 

1438 
2903 
4362 
5816 

PROPORTIONAL,  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7. 

8 

9 

161 
160 

16.1 
16.0 

32.2 
32.0 

48.3' 
48.0 

64.4 
64.0 

80.5 
80.0 

96.6 
96.0 

112.7 
112.0 

128.8 
128.0 

144.9 
144.0 

159 

15.9 

31.8 

47.7 

63.6 

79.5 

95.4 

111.3 

127.2 

143.1 

158 

15.8 

31.6 

47.4 

63.2 

79.0 

94.8 

110.6 

126.4 

142.2 

157 

15.7 

31.4 

47.1 

62.8 

78.5 

94.2 

109.9 

125.6 

141.3 

156 

15.6 

31.2 

46.8 

62.4 

78.0 

93.6 

109.2 

124.8 

140.4 

155 

15.5 

31.0 

46.5 

62.0 

77.5 

93.0 

108  5 

124.0 

139.5 

154 

15.4 

30.8 

46.2 

61.6 

77.0 

92.4 

107.8 

123.2 

138.6 

153 

15.3 

30.6 

45.9 

61.2 

76:5 

91.8 

107.1 

122.4 

137.7 

152 

15.2 

30.4 

45.6 

60.8 

76.0 

91.2 

106.4 

121.6 

136.8 

151 

15.1 

30.2 

45.3 

60.4 

75.5' 

90.6 

105.7 

120.8 

135.9 

150 

15.0 

30.0 

450 

60.0 

75.0 

90.0 

105.0 

120.0 

135.0 

149 

14.9 

29.8 

44.7 

59.6 

74.5 

89.4 

104.3 

119.2 

134.1 

148 

14.8 

29.6 

44.4 

59.2 

74.0 

88.8 

103.6 

118.4 

133.2 

147 

14.7 

29.4 

44.1 

58.8 

73.5 

88.2 

102.9 

117.6 

132.3 

146 

14.6 

29.2 

43.8 

58.4 

73.0 

87.6 

102.2 

116.8 

131.4 

145 

14.5 

29.0 

43.5 

58.0 

72.5 

87.0 

101.5 

1160 

1305 

144 

14.4 

28.8 

43.2 

57.6 

72.0 

86.4 

100.8 

115.2 

129.6 

143 

14.3 

28.6 

42.9 

57.2 

71.5 

85.8 

100.1 

114.4 

128.7 

142 

14.2 

28.4 

42.6 

56.8 

71.0 

85.2 

99.4 

113.6 

127.8 

141 

14.1 

28.2 

42.3 

56.4 

70.5 

84.6 

98.7 

112.8 

126.9 

140 

14.0 

28.0 

42.0 

56.0 

70.0 

84.0 

98.0 

112.0  ! 

126.0 

LOGARITHMS   OF  NUMBERS. 


No.  300  L.  477.] 


[No.  339  L.  531. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

300 

1 

477121 
8566 

7266 
8711 

7411 
8855 

7555 
8999 

7700 
9143 

7844 
9287 

7989 
9431 

8133 
9575 

8278 
9719 

8422 
9863 

1  145' 
144 

2 
3 
4 
5 
6 
7 
8 

480007 
1443 
2874 
4300 
5721 
7138 
8551 

0151 
1586 
3016 
4442 
5863 
7280 
8692 

0294 
1729 
3159 
4585 
6005 
7421 
8833 

0438 
1372 
3302 
4727 
6147 
7563 
8974 

0582 
2016 
3445 
4869 
6289 
7704 
91  14 

0725 
2159 
3587 
5011 
6430 
7845 
9255 

0369 
2302 
3730 
5153 
6572 
7986 
9396 

1012 
2445 
3872 
5295 
6714 
8127 
9537 

1156 
2588 
4015 
5437 
6355 
8269 
9677 

1299 
2731 
4157 
5579 
6997 
8410 
9818 

144 
143 
143 
142 
142 
141 
141 

9 

9958 

0099 

0239 

0380 

0520 

0661 

0801 

0941 

1081 

1222 

140 

310 
1 
2 
3 
4 
5 

491362 
2760 
4155 
5544 
6930 
8311 

1502 
2900 
4294 
5683 
7068 
8448 

1642 
3040 
4433 
5822 
7206 
8586 

1782 
3179 
4572 
5960 
7344 
8724 

1922 
3319 
4711 
6099 
7483 
8862 

2062 
3458 
4850 
6238 
7621 
8999 

2201 
3597 
4989 
6376 
7759 
9137 

2341 
3737 
5128 
6515 
7897 
9275 

2481 
3876 
5267 
6653 
8035 
9412 

2621 
4015 
5406 
6791 
8173 
9550 

140 
139 
139 
139 
138 
138 

6 

9687 

9824 

9962 

0099 

0236 

0374 

0511 

0648 

0785 

0922 

137 

7 
8 
9 

320 
1 
2 

501059 
2427 
3791 

5150 
6505 
7856 

1  196 
2564 
3927 

5286 
6640 
7991 

1333 
2700 
4063 

5421 
6776 
8126 

1470 

2837 
4199 

5557 
6911 
8260 

1607 
2973 
4335 

5693 
7046 
8395 

1744 
3109 
4471 

5828 
7181 
8530 

1880 
3246 
4607 

5964 
7316 
8664 

2017 
3382 
4743 

6099 

7451 
8799 

2154 
3518 
4878 

6234 
7586 
8934 

2291 
3655 
5014 

6370 
7721 
9068 

137 
136 
136 

136 
135 
135 

3 

9203 

9337 

947  1 

9606 

9740 

9874 

0009 

0143 

0277 

041  1 

134 

4 
5 
6 
7 
8 
9 

330 

510545 
1883 
3218 
4548 
5874 
7196 

8514 

0679 
2017 
3351 
4681 
6006 
7328 

8646 

0813 
2151 
3484 
4813 
6139 
7460 

8777 

0947 
2284 
3617 
4946 
6271 
7592 

8909 

1081 
2418 
3750 
5079 
6403 
7724 

9040 

1215 
2551 
3883 
5211 
6535 
7855 

9171 

1349 
2684 
4016 
5344 
6668 
7987 

9303 

1482 
2818 
4149 
5476 
6800 
8119 

9434 

1616 
2951 
4282 
5609 
6932 
8251 

9566 

1750 
3084 
4415 
5741 
7064 
8382 

9697 

134 
133 
133 
133 
132 
132 

131 

1 

9828 

9959 

0090 

0221 

0353 

0484 

0615 

0745 

0876 

1007 

131 

2 
3 
4 
5 
6 
7 

521138 
2444 
3746 
5045 
6339 
7630 

1269 
2575 
3876 
5174 
6469 
7759 

1400 
2705 
4006 
5304 
6598 
7888 

1530 
2835 
4136 
5434 
6727 
8016 

1661 
2966 
4266 
5563 
6856 
8145 

1792 
3096 
4396 
5693 
6985 
8274 

1922 
3226 
4526 
5822 
7114 
8402 

2053 
3356 
4656 
5951 
7243 
8531 

2183 
3486 
4785 
6081 
7372 
8660 

2314 
3616 
4915 
6210 
7501 
8788 

131 
130 
130 
129 
129 
129 

8 

8917 

9045 

9174 

9302 

9430 

9559 

9687 

9815 

9943 

0072 

128 

9 

530200 

0328 

0456 

0584 

0712 

0840 

0968 

1096 

1223 

1351 

128 

PROPORTIONAL  PARTS. 


Diff 

1 

3 

3 

4 

5 

6 

7 

,      8 

9 

139 

13.9 

27.8 

41.7 

55.6 

69.5 

83.4 

97.3 

11  1.2 

125.1 

138 

13.8 

27.6 

41.4 

55.2 

69.0 

82.8 

96.6 

110.4 

124.2 

137 

13.7 

27.4 

41.1 

54.8 

68.5 

82.2 

95.9 

109.6 

123.3 

136 

13.6 

27.2 

40.8 

54.4 

68.0 

81.6 

95.2 

108.8 

122.4 

135 

13.5 

27.0 

40.5 

54.0 

67.5 

81.0 

94.5 

108.0 

121.5 

134 

13.4 

26.8 

40.2 

53.6 

67.0 

80.4 

93.8 

107.2 

120.6 

133 

13.3 

26.6 

39.9 

53.2 

66.5 

79.8 

93.1 

106.4 

119.7 

132 

13.2 

26.4 

39.6 

52.8 

66.0 

79.2 

92.4 

105.6 

118.8 

131 

13.1 

26.2 

39.3 

52.4 

65.5 

78.6 

91.7 

104.8 

117.9 

130 

13.0 

26.0 

39.0 

52.0 

65.0 

78.0 

91.0 

1040 

117.0 

129 

12.9 

25.8 

38.7 

51.6 

64.5 

77.4 

90.3 

103.2 

M6.1 

128 

12.8 

25.6 

38.4 

51.2 

64  0 

76.8 

89.6 

102.4 

115.2 

127 

12.7 

25.4  * 

38.1 

50.8  1 

63.5 

76.2 

88.9     1 

101.6 

114.3 

LOGARITHMS    OF   NUMBERS. 


149 


No.  340  L.  531.J  ' 


[No. 379  L.  579. 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

340 
2 

4 
5 
6 

7 
8 
9 

350 
1 

3 
4 

5 
6 

8 
9 

360 
1 
2 
3 

4 
5 

6 

8 
9 

370 

I 

2 

4 
5 
6 

8 
9 

531479 
2754 
4026 
5294 
6558 
7819 
9076 

1607 
2882 
4153 
5421 
6685 
7945 
9202 

1734 
3009 
4280 
5547 
6811 
8071 
9327 

1862 
3136 
4407 
5674 
6937 
8197 
9452 

1990 
3264 
4534 
5800 
7063 
8322 
9578 

2117 
3391 
4661 
5927 
7189 
8448 
9703 

2245 
3518 
4787 
6053 
7315 
8574 
9829 

2372 
3645 
4914 
6180 
7441 
8699 
9954 

2500 
3772 
5041 
6306 
7567 
8825 

2627 
3899 
5167 
6432 
7693 
8951 

128 
127 
127 
126 
126 
126 

125 
125 
125 
124 

124 
124 
123 
123 

123 
122 
122 
121 
121 
121 

120 
120 
120 

119 
119 
119 

m 

118 
118 
118 

117 

117 
117 
116 
116 
116 
115 
115 
115 
114 

0079 
1330 
2576 
3820 

5060 
6296 
7529 
8758 
9984 

0204 
1454 
2701 
3944 

5183 
6419 
7652 
8881 

540329 
1579 
2825 

4068 
5307 
6543 
7775 
9003 

0455 
1704 
2950 

4192 
5431 
6666 
7898 
9126 

0580 
1829 
3074 

4316 
5555 
6',  89 
8021 
9249 

0705 
1953 
3199 

4440 
5678 
6913 
8144 
9371 

0830 
2078 
3323 

4564 
5802 
7036 
8267 
9494 

0955 
2203 

3447 

4688 
5925 
7159 
8389 
9616 

1080 
2327 
3571 

4812 
6049 
7282 
8512 
9739 

1205 
2452 
3696 

4936 
6172 
7405 
8635 
9861 

0106 
1328 
2547 
3762 
4973 
6«82 

7387 
8589 
9787 

550228 
1450 
2668 
3883 
5094 

6303 
7507 
8709 
9907 

0351 
1572 
2790 
4004 
5215 

6423 
7627 
8829 

0473 
1694 
2911 
4126 
5336 

6544 
7748 
8948 

0595 
1816 
3033 

4247 
5457 

6664 
7868 
9068 

0717 
1938 
3155 
4368 
5578 

6785 
7988 
9188 

0840 
2060 
3276 
4489 
5699 

6905 
8108 
9308 

0962 
2181 
3398 
4610 
5820 

7026 
8228 
9428 

1084 
2303 
3519 
4731 
5940 

7146 
8349 
9548 

1206 
2425 
3640 
4852 
6061 

7267 
8469 
9667 

0026 
1221 
2412 
3600 
4784 
5966 
7144 

8319 
9491 

0146 
1340 
2531 
3718 
4903 
6084 
7262 

8436 
9608 

0265 
1459 
2650 
3837 
5021 
6202 
7379 

8554 
9725 

0385 
1578 
2769 
3955 
5139 
6320 
7497 

8671 
9842 

0504 
1698 
2887 
4074 
5257 
6437 
7614 

8788 
9959 

0624 
1817 
3006 
4192 
5376 
6555 
7732 

8905 

0743 
1936 
3125 
4311 
5494 
6673 
7849 

9023 

0863 
2055 
3244 
4429 
5612 
6791 
7967 

9140 

0982 

2174 
3362 
4548 
5730 
6909 
8084 

9257 

561101 
2293 
3481 
4666 
5848 
7026 

8202 
9374 

0076 
1243 
2407 
3568 
4726 
5880 
7032 
8181 
9326 

0193 
1359 
2523 
3684 
4841 
5996 
7147 
8295 
9441 

0309 
1476 
2639 
3800 
4957 
6111 
7262 
8410 
9555 

0426 
1592 
2755 
3915 
5072 
6226 
73,77 
8525 
9669 

570543 
1709 
2872 
4031 
5188 
6341 
7492 
8639 

0660 
1825 
2988 
4147 
5303 
6457 
7607 
8754 

0776 
1942 
3104 
4263 
5419 
6572 
7722 
8868 

0893 
2058 
3220 
4379 
5534 
6687 
7836 
8983 

1010 
2174 
3336 
4494 
5650 
6802 
7951 
9097 

1126 
2291 
3452 
4610 
5765 
6917 
8066 
9212 

PROPORTIONAL  PARTS. 


Diff. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

128 

12.8 

25.6 

38.4 

51.2 

64.0 

76.8 

89.6 

102.4 

115.2 

127 

12.7 

25.4 

38.1 

50.8 

63.5 

76.2 

88:9 

101.6 

114.3 

126 

12.6 

25.2 

37.8 

50.4 

63.0 

75.6 

88.2 

100.8 

113.4 

125 

12.5 

25.0 

37.5 

50.0 

62.5 

75.0 

87.5 

100.0 

112.5 

124 

12.4 

24.8 

37.2 

49.6 

62.0 

74.4 

86.8 

99.2 

111.6 

123 

12.3 

24.6 

36.9 

49.2 

61.5 

73.8 

86.1 

98.4 

110.7 

122 

12.2 

24.4 

36.6 

48.8 

61.0 

73.2 

85.4 

97.6 

109.8 

121 

12.1 

24.2 

36.3 

48.4 

60.5 

72.6 

84.7 

96.8 

108.9 

120 

12.0 

24.0 

36.0 

48.0 

60.0 

72.0 

84.0 

96.0 

108.0 

119 

11.9 

23.8 

35.7 

47.6 

59.5 

71.4 

83.3 

95.2 

107.1 

150 


LOGARITHMS    OF   NUMBERS. 


No.  380  L.  579.J 


[No.  414  L.  617. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 
114 

113 
112 

111 

110 
109 

108 
107 

106 
105 

380 

1 
2 

4 

6 

7 
8 
9 

390 
1 
2 
3 
4 
5 
6 
7 
8 

9 

400 
1 
2 
3 
4 
5 
6 
7 

8 
9 

410 
2 
4 

579784 

9898 

0012 
1153 
2291 
3426 
4557 
5686 
6812 
7935 
9056 

0126 
1267 
2404 
3539 
4670 
5799 
6925 
8047 
9167 

0241 
1381 
2518 
3652 
4783 
5912 
7037 
8160 
9279 

0355 
1495 
2631 
3765 
4896 
6024 
7149 
8272 
9391 

0469 
1608 
2745 
3879 
5009 
6137 
7262 
8384 
9503 

0583 
1722 
2858 
3992 
5122 
6250 
7374 
8496 
9615 

0697 
1836 
2972 
4105 
5235 
6362 
7486 
8608 
9726 

0811 
1950 
3085 
4218 
5348 
6475 
7599 
8720 
9838 

580925 
2063 
3199 
4331 
5461 
6587 
7711 
8832 
9950 

1039 
2177 
3312 
4444 
5574 
6700 
7823 
8944 

0061 

1176 
2288 
3397 
4503 
5606 
6707 
7805 
8900 
9992 

~\OS2 

2169 
3253 
4334 
5413 
6489 
7562 
8633 
9701 

0173 

1287 
2399 
3508 
4614 
5717 
6817 
7914 
9009 

0284 

1399 
2510 

3618 
4724 
5827 
6927 
8024 
9119 

0396 

1510 
2621 
3729 
4834 
5937 
7037 
8134 
9228 

0507 

1621 
2732 
3840 
4945 
6047 
7146 
8243 
9337 

0619 

1732 
2843 
3950 
5055 
6157 
7256 
8353 
9446 

0730 

1843 
2954 
4061 
5165 
6267 
7366 
8462 
9556 

0842 

1955 
3064 
4171 
5276 
6377 
7476 
8572 
9665 

0953 

2066 
3175 
4282 
5386 
6487 
7586 
8681 
9774 

591065 
2177 
3286 
4393 
5496 
6597 
7695 
8791 
9883 

0101 
1191 

2277 
3361 
4442 
5521 
6596 
7669 
8740 
9808 

0210 
1299 

2386 
3469 
4550 
5628 
6704 
7777 
8847 
9914 

0319 
1406 

2494 
3577 
4658 
5736 
681  1 
7884 
8954 

0428 
1517 

2603 
3686 
4766 
5844 
6919 
7991 
9061 

0537 
1625 

2711 
3794 
4874 
5951 
7026 
8098 
9167 

0646 
1734 

2819 
3902 
4982 
6059 
7133 
8205 
9274 

0755 
1843 

2928 
4010 
5089 
6166 
7241 
8312 
9381 

0864 
1951 

3036 
4118 
5197 
6274 
7348 
8419 
9488 

600973 

2060 
3144 
4226 
5305 
6381 
7455 
8526 
9594 

0021 
1086 
2148 

3207 
4264 
5319 
6370 
7420 

0128 
1192 
2254 

3313 
4370 
5424 
6476 
7525 

0234 
1298 
2360 

3419 
4475 
5529 
6581 
7629 

0341 
1405 
2466 

3525 
4581 
5634 
6686 
7734 

0447 
1511 
2572 

3630 
4686 
5740 
6790 
7839 

0554 
1617 
2678 

3736 
4792 
5845 
6895 
7943 

610660 
1723 

2784 
3842 
4897 
5950 
7000 

0767 
1829 

2890 
3947 
5003 
6055 
7105 

0873 
1936 

2996 
4053 
5108 
6160 
7210 

0979 
2042 

3102 
4159 
5213 
6265 
7315 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

118 

11.8 

23.6 

35.4 

47.2 

59.0 

70.8 

82.6 

94.4 

106.2 

117 

11.7 

23.4 

35.1 

46.8 

58.5 

70.2 

81.9 

93.6 

105.3 

116 

11.6 

23.2 

34.8 

46.4 

58.0 

69.6 

81.2 

92.8 

104.4 

115 

11.5 

23.0 

34.5 

46.0 

57.5 

69.0 

80.5 

92.0 

103.5 

114 

11.4 

22.8 

34.2 

45.6 

57.0 

68.4 

79.8 

9,  7 

102.6 

113 

11.3 

22.6 

33.9 

45.2 

56.5 

67.8 

79.1 

90.4 

101.7 

112 

11.2 

22.4 

33.6 

44.8 

56.0 

67.2 

78.4 

89.6 

100.8 

111 

11.1 

22.2 

33.3 

44.4 

55.5 

66.6 

77.7 

88.8 

99.9 

110 

11.0 

22.0 

33.0 

44.0 

55.0 

66.0 

77.0 

88.0 

99.0 

109 

10.9 

21.8 

32.7 

43.6 

54.5 

65.4 

76.3 

87.2 

98.1 

108 

10.8 

21.6 

32.4 

43.2 

54.0 

64.8 

75.6 

86.4 

97.2 

107 

10.7 

21.4 

32.1 

42.8 

53.5 

64.2 

74.9 

85.6 

96.3 

106 

10.6 

21.2 

31.8 

42.4 

53.0 

63.6 

74.2 

84.8 

95.4 

105 

10.5 

21.0 

31.5 

42.0 

52.5 

63.0 

73.5 

84.0 

94.5 

104 

10.4 

20.8 

31.2 

41.6 

52.0 

62.4 

72.8 

83.2 

93.6 

LOGARITHMS    OF    NUMBERS. 


151 


No.  415  L.  618.] 


[No.  459  L.  662. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

415 

618048 

8153 

8257 

8362 

8466 

8571 

8676 

8780 

8884 

8989 

~105 

6 

9093 

9198 

9302 

9406 

9511 

9615 

9719 

9824 

9928 

"0032 

7 

620136 

0240 

0344 

0448 

0552 

0656 

0760 

0864 

0968 

1072 

104 

8 

1176 

1280 

1384 

1488 

1592 

1695 

1799 

1903 

2007 

2110 

9 

2214 

2318 

2421 

2525 

2628 

2732 

2835 

2939 

3042 

3146 

420 

3249 

3353 

3456 

3559 

3663 

3766 

3869 

3973 

4076 

4179 

1 

4282 

4385 

4488 

4591 

4695 

4793 

4901 

5004 

5107 

5210 

103 

2 

5312 

5415 

5518 

5621 

5724 

5827 

5929 

6032 

6135 

6238 

3 

6340 

6443 

6546 

6648 

6751 

6853 

6956 

7058 

7161 

7263 

4 

7366 

7463 

7571 

7673 

7775 

7878 

7980 

8082 

8185 

8287 

5 

8389 

8491 

8593 

8695 

8797 

8900 

9002 

9104 

9206 

9308 

.102 

6 

9410 

9512 

9613 

9715 

9817 

9919 

0021 

0123 

0224 

0326 

7 

630428 

0530 

~063T 

0733 

0835 

0936 

1038 

1139 

1241 

1342 

8 

1444 

1545 

1647 

1748 

1849 

1951 

2052 

2153 

2255 

2356 

9 

2457 

2559 

2660 

2761 

2862 

2963 

3064 

3165 

3266 

3367 

430 

3468 

3569 

3670 

3771 

3872 

3973 

4074 

4175 

4276 

4376 

101 

1 

4477 

4578 

4679 

4779 

4880 

4981 

5081 

5182 

5283 

5383 

2 

5484 

5584 

5635 

5785 

5886 

5986 

6087 

6187 

6287 

6388 

3 

6488 

6588 

6638 

6789 

6889 

6989 

7089 

7189 

7290 

7390 

4 

7490 

7590 

7690 

7790 

7890 

7990 

8090 

8190 

8290 

8389 

100 

5 

8489 

8589 

8689 

8789 

8888 

8988 

9088 

9188 

9287 

9387 

6 

9486 

9586 

9686 

9785 

9885 

9984 

0084 

0183 

0283 

0382 

7 

640431 

0581 

0680 

0779 

0879 

0978 

1077 

1177 

1276 

1375 

8 

1474 

1573 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

9 

2465 

2563 

2662 

2761 

2860 

2959 

3058 

3156 

3255 

3354 

99 

440 

3453 

3551 

3650 

3749 

3847 

3946 

4044 

4143 

4242 

4340 

1 

4439 

4537 

4636 

4734 

4832 

4931 

5029 

5127 

5226 

5324 

2 

5422 

5521 

5619 

5717 

5815 

5913 

6011 

6110 

6208 

6306 

3 

6404 

6502 

6600 

6698 

6796 

6894 

6992 

7089 

7187 

7285 

98 

4 

7333 

7481 

7579 

7676 

7774 

7872 

7969 

8067 

8165 

8262 

5 

8360 

8458 

8555 

8653 

8750 

8848 

8945 

9043 

9140 

9237 

6 

9335 

9432 

9530 

9627 

9724 

9821 

9919 

0016 

0113 

0210 

7 

650303 

0405 

0502 

"0599 

0696 

0793 

0890 

0987 

1084 

1181 

8 

1278 

1375 

1472 

1569 

1666 

1762 

1859 

1956 

2053 

2150 

97 

9 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3019 

3116 

450 

3213 

3309 

3405 

3502 

3598 

3695 

3791 

3888 

3984 

4080 

4177 

4273 

4369 

4465 

4562 

4658 

4754 

4850 

4946 

5042 

2 

5138 

5235 

5331 

5427 

5523 

5619 

5715 

5810 

5906 

6002 

96 

3 

6098 

6194 

6290 

6386 

6482 

6577 

6673 

6769 

6864 

6960 

4 

7056 

7152 

7247 

7343 

7438 

7534 

7629 

7725 

7820 

7916 

5 

8011 

8107 

8202 

8298 

8393 

8488 

8584 

8679 

8774 

8870 

6 

8965 

9060 

9155 

9250 

9346 

9441 

9536 

9631 

9726 

9821 

7 

9916 

0011 

0106 

0201 

0296 

0391 

0486 

0581 

0676 

"0771 

95 

8 

660865 

0960 

1055 

1150 

1245 

1339 

1434 

1529 

1623 

1718 

9 

1813 

1907 

2002 

2096 

2191 

2286 

23801  2475 

2569 

2663 

PROPORTIONAL  PARTS. 


Diff. 

1 

10.5 
10.4 
10.3 
10.2 
10.1 
10.0 
9.9 

2 

3 

4 

5 

6 

7 

8 

9 

105 
104 
103 
102 
101 
100 
99 

21.0 
20.8 
20.6 
20.4 
20.2 
20.0 
19.8 

31.5 
31.2 
30.9 
30.6 
30.3 
30.0 
29.7 

42.0 
41.6 
41.2 
40.8 
40.4 
40.0 
39.6 

52.5 
52.0 
51.5 
51.0 
50.5 
50.0 
49.5 

63.0 
62.4 
61.8 
61.2 
60.6 
60.0 
59.4 

73.5 
72.8 
72.1 
71.4 
70.7 
70.0 
69.3 

84.0 
83.2 
82.4 
81.6 
80.8 
80.0 
79.2 

94.5 
93.6 
92.7 
91.8 
90.9 
90.0 
89.1 

152 


LOGARITHMS   OF  NUMBERS. 


No.  460  L.  662.] 


[No.  499  L.  698 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff< 

"46CT 

'  662758 

2852 

2947 

3041 

3135 

3230 

"3324 

3418 

3512 

3607 

3701 

3795 

3889 

3983 

4078 

4172 

4266 

4360 

4454 

4548 

2 

4642 

4736 

4830 

4924 

5018 

5112 

5206 

5299 

5393 

5487 

94 

3 

5581 

5675 

5769 

5862 

5956 

6050 

6143 

6237 

6331 

6424 

4 

•6518 

6612 

6705 

6799 

6892 

6986 

7079 

7173 

7266 

7360 

5 

7453 

7546 

7640 

7733 

7826 

7920 

8013 

8106 

8199 

8293 

6 

8386 

8479 

8572 

8665 

8759 

8852 

8945 

9038 

9131 

9224 

7 

9317 

94  1C 

9503 

9596 

9689 

9782 

9875 

9967 

0060 

fil  53 

Ql 

8 

670246 

0339 

0431 

0524 

0617 

0710 

0802 

0895 

0988 

U  1  Jj 

1080 

7J 

9 

1173 

1265 

1358 

1451 

1543 

1636 

1728 

1821 

1913 

2005 

470 

2098 

2190 

2283 

2375 

2467 

2560 

2652 

2744 

2836 

2929 

1 

3021 

3rl13 

3205 

3297 

3390 

3482 

3574 

3666 

3758 

3850 

2 

3942 

4934 

4126 

4218 

4310 

4402 

4494 

4586 

4677 

4769 

92 

3 

4861 

4953 

5045 

5137 

5228 

5320 

5412 

5503 

5595 

5687 

4 

5778 

5870 

5962 

6053 

6145 

6236 

6328 

6419 

6511 

6602 

5 

6694 

6785 

6876 

6968 

7059 

7151 

7242 

7333 

7424 

7516 

6 

7607 

7698 

7789 

7881 

7972 

8063 

8154 

8245 

8336 

8427 

7 

8518 

8609 

8700 

8791 

8882 

8973 

9064 

9155 

9246 

9337 

9! 

3 

9428 

9519 

9610 

9700 

9791 

9882 

9973 

0063 

01  54 

0745 

9 

680336 

0426 

0517 

0607 

0698 

0789 

0879 

0970 

1060 

\)mj 

1151 

480 

1241 

1332 

1422 

1513 

1603 

1693 

1784 

1874 

1964 

2055 

1 

2145 

2235 

2326 

2416 

2506 

2596 

2686 

2777 

2867 

2957 

2 

3047 

3137 

3227 

3317 

3407 

3497 

3587 

3677 

3767 

3857 

90 

3 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

4 

4845 

4935 

5025 

5114 

5204 

5294 

5383 

5473 

5563 

5652 

5 

5742 

5831 

5921 

601-0 

6100 

6189 

6279 

6368 

6458 

6547 

6 

6636 

6726 

6815 

6904 

6994 

7083 

7172 

7261 

7351 

7440 

7 

7529 

7618 

7707 

77% 

7886 

7975 

8064 

8153 

8242 

8331 

8 

8420 

8509 

8598 

8687 

8776 

8865 

8953 

9042 

9131 

9220 

89 

9 

9309 

9398 

9486 

9575 

9664 

9753 

9841 

9930 

0019 

01(17 

490 

690196 

0285 

0373 

0462 

0550 

0639 

0728 

0816 

0905 

U  1  U/ 

0993 

1 

1081 

1170 

1258 

1347 

1435 

1524 

1612 

1700 

1789 

1877 

2 

1965 

2053 

2142 

2230 

2318 

2406 

2494 

2583 

2671 

2759 

3 

2847 

2935 

3023 

3111 

3199 

3287 

3375 

3463 

3551 

3639 

88 

4 

3727 

3815 

3903 

3991 

4078 

4166 

4254 

4342 

4430 

4517 

5 

4605 

4693 

4781 

4868 

4956 

5044 

5131 

5219 

5307 

5394 

6 

5482 

5569 

5657 

5744 

5832 

5919 

6007 

6094 

6182 

6269 

7 

6356 

6444 

6531 

6618 

6706 

6793 

6880 

6968 

7055 

7142 

8 

7229 

7317 

7404 

7491 

7578 

7665 

7752 

7839 

7926 

8014 

87 

9 

8100 

8188 

8275 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

PROPORTIONAL  PARTS. 


Diff. 

1 

3 

3 

4 

5 

6 

7 

8 

9 

^98 

9.8 

19.6 

29  A 

39.2 

49.0 

58.8 

68.6 

78.4 

88.2 

97 

9.7 

19.4 

29.1 

38.8 

48.5 

58.2 

67.9 

77.6 

87.3 

96 

9.6 

19.2 

28.8 

38.4 

48.0 

57.6 

67.2 

76.8 

86.4 

95 

9.5 

19.0 

28.5 

38.0 

47.5 

57.0 

66.5 

76.0 

85.5 

94 

9.4 

18.8 

28.2 

37.6 

47.0 

56.4 

65.8 

75.2 

84.6 

93 

9.3 

18.6 

27.9 

37.2 

46.5 

55.8 

65.1 

74.4 

83.7 

92 

9.2 

18.4 

27.6 

36.8 

46.0 

55.2 

64.4 

73.6 

82.8 

91 

9.1 

18.2 

27.3 

36.4 

45.5 

54.6 

63.7 

72.8 

81.9 

90 

9.0 

18.0 

27.0 

36.0 

45.0 

54.0 

63.0 

72.0 

81.0 

89 

8.9 

17.8 

26.7 

35.6 

44.5 

53.4 

62.3 

71.2 

80.1 

88 

8.8 

17.6 

26.4 

35.2 

44.0 

52.8 

61.6 

70.4 

79.2 

87 

8.7 

17.4 

26.1 

34.8 

43.5 

52.2 

60.9 

69.6 

78.3 

66 

8.6 

17.2 

25.8 

34.4 

43.0 

51.6 

60.2 

68.8 

77.4 

LOGARITHMS   OF   NUMBERS. 


153 


No.  500  L.  698.1 


[No.  544  L.  736 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

DiS. 

500 

698970 

QO-1Q 

9057 

QQ9.4 

9144 

9231 

9317 

9404 

9491 

"9578 

~9664 

9751 

t 

yoJO 

yy^^t 

001  1 

0098 

0184 

0271 

0358 

0444 

0531 

0617 

2 

700704 

0790 

0877 

0963 

1050 

1136 

1222 

1309 

1395 

1482 

3 

1568 

1654 

1741 

1827 

1913 

1999 

2086 

2172 

2258 

2344 

4 

243  1 

2517 

2603 

2689 

2775 

2861 

2947 

3033 

3119 

3205 

5 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

3893 

3979 

4065 

86 

6 

4151 

4236 

4322 

4408 

4494 

4579 

4665 

4751 

4837 

4922 

7 

5008 

5094 

5179 

5265 

5350 

5436 

5522 

5607 

5693 

5778 

8 

5864 

5949 

6035 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

9 

6718 

6803 

6888 

6974 

7059 

7144 

7229 

7315 

7400 

7485 

510 

7570 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

8251 

8336 

1 

8421 

8506 

8591 

8676 

8761 

8846 

8931 

9015 

9100 

9185 

85 

O?7fl 

Q-l  CC 

Q44O 

QCTX 

9609 

9694 

9779 

9863 

9948 

y^/U 

\TJ  JJ 

y^fnU 

•  y.?<6if 

0033 

3 

710117 

0202 

0287 

0371 

0456 

0540 

0625 

0710 

0794 

0879 

4 

0963 

1048 

1132 

1217 

1301 

1385 

1470 

1554 

1639 

1723 

5 

1807 

1892 

1976 

2060 

2144 

2229 

2313 

2397 

2481 

2566 

6 

2650 

2734 

2818 

2902 

2986 

3070 

3154 

3238 

3323 

3407 

7 

3491 

3575 

3659 

3742 

3826 

3910 

3994 

4078 

4162 

4246 

84 

8 

4330 

4414 

4497 

4581 

4665 

4749 

4833 

4916 

5000 

5084 

9 

5167 

5251 

5335 

5418 

5502 

5586 

5669 

5753 

5836 

5920 

520 

6003 

6087 

6170 

6*254 

6337 

6421 

6504 

6588 

6671 

6754 

6838 

6921 

7004 

7088 

7171 

7254 

7338 

7421 

7504 

7587 

2 

7671 

7754 

7837 

7920 

8003 

8086 

8169 

8253 

8336 

8419 

83 

3 

8502 

8585 

8668 

875T 

8834 

8917 

9000 

9083 

9165 

9248 

Qa-i  | 

QA1  / 

Q  AQ7 

QCOA 

Qf\f\^ 

Q7  AC* 

QQOQ 

991  1 

9994 

yjJ  1 

y^f  1  f 

y^ty/ 

VDOL 

yOO.7 

y/T-j 

yo^o 

0077 

5 

720159 

0242 

0325 

0407 

0490 

0573 

0655 

0738 

0821 

0903 

6 

0986 

1068 

1151 

1233 

1316 

1398 

1481 

1563 

1646 

1728 

7 

1811 

1893 

1975 

2058 

2140 

2222 

2305 

2387 

2469 

2552 

8 

2634 

2716 

2798 

2881 

2963 

3045 

3UZ7 

3209 

3291 

3374 

9 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4030 

4112 

4194 

82 

530 

4276 

4358 

4440 

4522 

4604 

4685 

4767 

4849 

4931 

5013 

1 

5095 

5176 

5258 

5340 

5422 

5503 

5585 

5667 

5748 

5830 

5912 

5993 

6075 

6156 

6238 

6320 

6401 

6483 

6564 

6646 

3 

6727 

6809 

6890 

6972 

7053 

7134 

7216 

7297 

7379 

7460 

7541 

7623 

7704 

7785 

7866 

7948 

8029 

8110 

8191 

8273 

5 

8354 

8435 

8516 

8597 

8678 

8759 

8841 

8922 

9003 

9084 

6 
7 

9165 
9974 

9246 

9327 

9408 

9489 

9570 

9651 

9732 

9813 

9893 

81 

005 

0136 

021  7 

029? 

0376 

045C 

0540 

0621 

0702 

8 

730782 

0863 

094^ 

1024 

1105 

1186 

1266 

1347 

1428 

1508 

9 

1589 

1669 

1750 

1830 

1911 

1991 

2072 

2152 

2233 

2313 

540 

2394 

2474 

2555 

2635 

2715 

2796 

2876 

2956 

3037 

3117 

3197 

3278 

3358 

3438 

3518 

3598 

3679 

3759 

3839 

3919 

2 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

4560 

4640 

4720 

80 

3 

4800 

4880 

4960 

5040 

5120 

5200 

5279 

5359 

5439 

5519 

4 

5599 

5679 

5759 

5838 

5918 

5998 

6078 

6157 

6237 

6317 

PROPORTIONAL  PARTS. 


DIS. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

87 
86 
85 
84 

8.7 
8.6 
8.5 
8.4 

17.4 
17.2 
17.0 
16.8 

26.1 
25.8 
25.5 
25.2 

34.8 
34.4 
34.0 
33.6 

43.5 
43.0 
42.5 
42.0 

52.2 
51.6 
51.0 
50.4 

60.9 
60.2 
59.5 
58.8 

69.6 
68.8 
68.0 
67.2 

78.3 
77.4 
76.5 
75.6 

154 


LOGARITHMS   OF   NUMBERS. 


No.  545  L.  736.] 


[No  584  L.  767 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9  • 

Diff. 

$45 
6 

8 
9 

736397 
7193 
7987 
8781 
9572 

6476 
7272 
8067 
8860 
9651 

6556 
7352 
8146 
8939 
9731 

6635 
7431 
8225 
9018 
9810 

6715 

7511 
8305 
9097 
9889 

6795 
7590 
8384 
9177 
9968 

6874 
7670 
8463 
9256 

6954 
7749 
8543 
9335 

7034 
7829 
8622 
9414 

7113 
7908 
8701 
9493 

0047 

0126 

07OS 

nooj 

7O 

550 

740363 

0442 

0521 

0600 

0678 

0757 

Uvn/ 

0836 

0915 

U<iUJ 

0994 

v^OH 

1073 

/y 

1152 

1230 

1309 

1388 

1467 

1546 

1624 

1703 

1782 

1860 

2 

1939 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2647 

3 

2725 

2804 

2882 

2961 

3039 

3118 

3196 

3275 

3353 

3431 

4 

3510 

3588 

3667 

3745 

3823 

3902 

3980 

4058 

4136 

4215 

5 

4293 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

4919 

4997 

6 

5075 

5153 

5231 

5309 

5387 

5465 

5543 

5621 

5699 

5777 

78 

7 

5855 

5933 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

8 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7179 

7256 

7334 

9 

7412 

7489 

7567 

7645 

7722 

7800 

7878 

7955 

8033 

8110 

560 

8188 

8266 

8343 

8421 

8498 

8576 

8653 

8731 

8808 

8885 

8963 

9040 

9118 

9195 

9272 

9350 

9427 

9504 

9582 

9659 

2 

9736 

9814 

9891 

9968 

0045 

0123 

0200 

0277 

0354 

0431 

3 

750508 

0586 

0663 

0740 

0817 

0894 

0971 

1048 

1125 

1202 

4 

1279 

1356 

1433 

1510 

1587 

1664 

.  1741 

1818 

1895 

1972 

77 

5 

2048 

2125 

2202 

2279 

2356 

2433 

2509 

2586 

2663 

2740 

6 

2816 

2893 

2970 

3047 

3123 

3200 

3277 

3353 

3430 

3506 

7 

3583 

3660 

3736 

3813 

3889 

3966 

4042 

4119 

4195 

4272 

8 

4348 

4425 

4501 

4578 

4654 

4730 

4807 

4883 

4960 

5036 

9 

5112 

5189 

5265 

5341 

5417 

5494 

5570 

5646 

5722 

5799 

570 

5875 

5951 

6027 

6103 

6180 

6256 

6332 

6408 

6484 

6560 

1 

6636 

6712 

6758 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

2 

7396 

7472 

7548 

7624 

7700 

7775 

7851 

7927 

8003 

8079 

3 

8155 

8230 

8306 

8382 

8458 

8533 

8609 

8685 

8761 

8836 

4 

8912 

8988 

9063 

9139 

9214 

9290 

9366 

9441 

9517 

9592 

i 

QAA« 

074-1 

9819 

9894 

QQ7O 

9 

7ODO 

7/*1J 

77/\J 

0045 

0121 

0196 

0272 

0347 

6 

760422 

0498 

0573 

0649 

0724 

0799 

0875 

0950 

1025 

1101 

7 

1176 

1251 

1326 

1402 

1477 

1552 

1627 

1702 

1778 

1853 

8 

1928 

2003 

2078 

2153 

2228 

2303 

2378 

2453 

2529 

2604 

73 

9 

2679 

2754 

2829 

2904 

2978 

3053 

3128 

3203 

3278 

3353 

580 

3428 

3503 

3578 

3653 

3727 

3802 

3877 

3952 

4027 

4101 

1 

4176 

4251 

4326 

4400 

4475 

4550 

4624 

4699 

4774 

4848 

2 

4923 

4998 

5072 

5147 

5221 

5296 

5370 

5445 

5520 

5594 

3 

5669 

5743 

5818 

5892 

5966 

6041 

6115 

6190 

6264 

6338 

4 

6413 

6487 

6562 

6636 

6710 

6785 

6859 

6933 

7007 

7082 

PROPORTIONAL,  PARTS. 


Diff. 
1ST- 

1 

3 

~T6T 

3 

4 

5 

6 

7 

8 

9 

8.3 

24.9 

33.2 

41.5 

49.8 

58.1 

66.4 

74.7" 

82 

8.2 

16.4 

24.6 

32.8 

41.0 

49.2 

57.4 

65.6 

73.8 

81 

8.1 

16.2 

24.3 

32.4 

40.5 

48.6 

56.7 

64.8 

72.9 

80 

8.0 

16.0 

24.0 

32.0 

40.0 

48.0 

56.0 

64.0 

72.0 

79 

7.9 

15.8 

23.7 

31.6 

39.5 

47.4 

55.3 

63.2 

71.1 

78 

7.8 

15.6 

23.4 

31.2 

39.0 

46.8 

54.6 

62.4 

70.2 

77 

7.7 

15.4 

23.1 

30.8 

38.5 

46.2 

53.9 

61.6 

69.3 

76 

7.6 

15.2 

22.8 

30.4 

38.0 

45.6 

53.2 

60.8 

68.4 

75 

7.5 

15.0 

22.5 

30.0 

37.5 

45.0 

52.5 

60.0 

67.5 

74 

7.4 

14,8 

22,2 

29.6 

37.0 

44.4 

51.8 

59.3 

66* 

LOGARITHMS   OF   NUMBERS. 


155 


No.  585  L.  767.] 


[No.  629  L.  79ft 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

585 

767156 

7230 

~730~4 

7379 

7453 

7527 

7601 

7675 

7749 

7823 

6 

7898 

7972 

8046 

8120 

8194 

8268 

8342 

8416 

8490 

8564 

74 

7 

8638 

8712 

8786 

8860 

8934 

9008 

9082 

9156 

9230 

9303 

9377 

945  1 

9525 

9599 

9673 

9746 

9820 

9894 

9968 

0042 

9 

770115 

0189 

0263 

0336 

0410 

0484 

0557 

0631 

0705 

0778 

590 

0852 

0926 

0999 

1073 

1146 

1220 

1293 

1367 

1440 

1514 

1 

1587 

1661 

1734 

1808 

1881 

1955 

2028 

2102 

2175 

2248 

2 

2322 

2395 

2468 

2542 

2615 

2688 

2762 

2835 

2908 

2981 

3 

3055 

3128 

3201 

3274 

3348 

3421 

3494 

3567 

3640 

3713 

4 

3786 

3860 

3933 

4006 

4079 

4152 

4225 

4298 

4371 

4444 

73 

5 

4517 

4590 

4663 

4736 

4809 

4882 

4955 

5028 

5100 

5173 

6 

5246 

5319 

5392 

5465 

5538 

5610 

5683 

5756 

5829 

5902 

7 

5974 

6047 

6120 

6193 

6265 

6338 

6411 

6483 

6556 

6629 

8 

6701 

6774 

6846 

6919 

6992 

7064 

7137 

7209 

7282 

7354 

9 

7427 

7499 

7572 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

600 

8151 

8224 

8296 

8368 

8441 

8513 

8585 

8658 

8730 

8802 

1 

8874 

8947 

9019 

9091 

9163 

9236 

9308 

9380 

9452 

9524 

9596 

9669 

9741 

9813 

9885 

9957 

0029 

0101 

0173 

0245 

3 

780317 

0389 

0461 

0533 

0605 

0677 

0749 

0821 

0893 

0965 

72 

4 

1037 

1109 

1181 

1253 

1324 

1396 

1468 

1540 

1612 

1684 

5 

1755 

1827 

1899 

1971 

2042 

2114 

2186 

2258 

2329 

2401 

6 

2473 

2544 

2616 

268  T 

2759 

2831 

2902 

2974 

3046 

3117 

7 

3189 

3260 

3332 

3403 

3475 

3546 

3618 

3689 

3761 

3832 

8 

3904 

3975 

4046 

4118 

4189 

4261 

4332 

4403 

4475 

4546 

9 

4617 

4689 

4760 

4831 

4902 

4974 

5045 

5116 

5187 

5259 

610 

5330 

5401 

5472 

5543 

5615 

5686 

5757 

5828 

5899 

5970 

6041 

6112 

6183 

6254 

6325 

6396 

6467 

6538 

6609 

6680 

71 

2 

6751 

6822 

6893 

6964 

7035 

7106 

7177 

7248 

7319 

7390 

7460 

7531 

7602 

7673 

7744 

7815 

7885 

7956 

8027 

8098 

4 

8168 

8239 

8310 

8381 

8451 

8522 

8593 

8663 

8734 

8804 

5 

8875 

8946 

9016 

9087 

9157 

9228 

9299 

9369 

9440 

9510 

9581 

965  1 

9722 

9792 

986- 

9933 

0004 

0074 

0144 

0215 

7 

790285 

0356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

8 

0988 

1059 

1129 

1199 

1269 

1340 

1410 

1480 

1550 

1620 

9 

1691 

1761 

1831 

1901 

1971 

2041 

2111 

2181 

2252 

2322 

620 

2392 

2462 

2532 

2602 

2672 

2742 

2812 

2882 

2952 

3022 

70 

1 

3092 

3162 

3231 

3301 

3371 

3441 

3511 

3581 

3651 

3721 

2 

3790 

3860 

3930 

4000 

4070 

4139 

4209 

4279 

4349 

4418 

4488 

4558 

4627 

4697 

4767 

4836 

4906 

4976 

5045 

5115 

4 

5185 

5254 

5324 

5393 

5463 

5532 

5602 

5672 

5741 

5811 

5 

5880 

5949 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

6505 

6 

6574 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7129 

7198 

7 

7268 

7337 

7406 

7475 

7545 

7614 

7683 

7752 

7821 

7890 

8 

7960 

8029 

8098 

8167 

8236 

8305 

8374 

8443 

8513 

8582 

9 

8651 

8720 

8789 

8858 

8927 

8996 

9065 

9134  9203 

9272 

69 

PROPORTIONAL  PARTS. 


Diff. 

74 
73 
72 
71 
70 
69 

1 

2 

3 

4 

5 

6 

7 

8 

9 

7.5 

7.4 
7.3 
7.2 
7.1 
7.0 
6.9 

15.0 

14.8 
14.6 
14.4 
14.2 
14.0 
13.8 

22.5 
22.2 
21.9 
21.6 
21.3 
21.0 
20.7 

30.0 
29.6 
29.2 
28.8 
28.4 
28.0 
27.6 

37.5 
37.0 
36.5 
36.0 
35.5 
35.0 
34.5 

45.0 
44.4 
43.8 
43.2 
42.6 
42.0 
41.4 

52.5 

51.8 
51.1 
50.4 
49.7 
49.0 
48.3    . 

60.0 
59.2 
58.4 
57.6 
56.8 
56.0 
55.2 

67.5 
66.6 
65.7 
64.8 
63.9 
63.0 
62.1 

156 


LOGAK1THMS   OF   NUMBERS. 


No.  630  L.  799.1 


lNo.674L.829, 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

"630 

799341 

9409 

9478 

9547 

9616 

9685 

9754 

9823 

9892 

9961 

1 

800029 

0098 

0167 

0236 

0305 

0373 

0442 

0511 

0580 

0648 

2 

0717 

0786 

0854 

0923 

0992 

1061 

1129 

1198 

1266 

1335 

3 

1404 

1472 

1541 

1609 

1678 

1747 

1815 

1884 

1952 

2021 

4 

2089 

2158 

2226 

2295 

2363 

2432 

2500 

2568 

2637 

2705 

5 

2774 

2842 

2910 

2979 

3047 

3116 

3184 

3252 

3321 

3389 

6 

3457 

3525 

3594 

3662 

3730 

3798 

3867 

3935 

4003 

4071 

7 

4139 

4208 

4276 

4344 

4412 

4480 

4548 

4616 

4685 

4753 

8 

4821 

4889 

4957 

5025 

5093 

5161 

5229 

5297 

5365 

5433 

68 

9 

5501 

5569 

5637 

5705 

5773 

5841 

5908 

5976 

6044 

6112 

640 

806180 

6248 

6316 

6384 

6451 

6519 

6587 

6655 

6723 

6790 

1 

6858 

6926 

6994 

7061 

7129 

7197 

7264 

7332 

7400 

7467 

2 

7535 

7603 

7670 

7738 

7806 

7873 

7941 

8008 

8076 

8143 

3 

8211 

8279 

8346 

8414 

8481 

8549 

8616 

8684 

8751 

8818 

4 

8886 

8953 

9021 

9088 

9156 

9223 

9290 

9358 

9425 

9492 

5 

9560 

9627 

9694 

9762 

9829 

9896 

9964 

0031 

0098 

0165 

6 

810233 

0300 

0367 

0434 

0501 

0569 

0636 

0703 

0770 

0837 

7 

0904 

0971 

1039 

1106 

1173 

1240 

1307 

1374 

1441 

1508 

6: 

8 

1575 

1642 

•1709 

1776 

1843 

1910 

1977 

2044 

2111 

2178 

9 

2245 

2312 

2379 

2445 

2512 

2579 

2646 

2713 

2780 

2847 

650 

2913 

2980 

3047 

3114 

3181 

3247 

3314 

3381 

3448 

3514 

1 

3581 

3648 

3714 

3781 

3848 

3914 

3981 

4048 

4114 

4181 

2 

4248 

4314 

4381 

4447 

4514 

4581 

4647 

4714 

4780 

4847 

3 

4913 

4980 

5046 

5113 

5179 

5246 

5312 

5378 

5445 

5511 

4 

5578 

5644 

5711 

5777 

5843 

5910 

5976 

6042 

6109 

6175 

5 

6241 

6308 

6374 

6440 

6506 

6573 

6639 

6705 

6771 

6838 

6 

6904 

6970 

7036 

7102 

7169 

7235 

7301 

7367 

7433 

7499 

7 

7565 

7631 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

8 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

9 

8885 

8951 

9017 

9083 

9149 

9215 

9281 

9346 

9412 

9478 

660 

9544 

9610 

9676 

9741 

9807 

9873 

9939 

0004 

0070 

0136 

1 

820201 

0267 

0333 

0399 

0464 

0530 

0595 

0661 

0727 

0792 

2 

0858 

0924 

0989 

1055 

1120 

1186 

1251 

1317 

1382 

1448 

3 

1514 

-1579 

1645 

1710 

1775 

1841 

1906 

1972 

2037 

2103 

4 

2168 

2233 

2299 

2364 

2430 

2495 

2560 

2626 

2691 

2756 

5 

2822 

2887 

2952 

3018 

3083 

3148 

3213 

3279 

3344 

3409 

6 

3474 

3539 

3605 

3670 

3735 

3800 

3865 

3930 

3996 

4061 

7 

4126 

4191 

4256 

4321 

4386 

4451 

4516 

4581 

4646 

4711 

8 

4776 

4841 

4906 

4971 

5036 

5101 

5166 

5231 

5296 

5361 

65 

9 

5426 

5491 

5556 

5621 

5686 

5751 

5815 

5880 

5945 

6010 

670 

6075 

6140 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

1 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7175 

7240 

7305 

2 

7369 

7434 

7499 

7563 

7628 

7692 

7757 

7821 

7886 

7951 

3 

8015 

8080 

8144 

8209 

8273 

8338 

8402 

8467 

8531 

8595 

4 

8660 

8724 

8789 

8853 

8918 

8982'  9046 

9111 

9175 

9239 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

G 

7 

8 

9 

68 
67 
66 
65 
64 

6.8 
6.7 
6.6 
6.5 
6.4 

13.6 
13.4 
13.2 
13.0 
12.8 

20.4 
20.1 
19.8 
19.5 
19.2 

27.2 
26.8 
26.4 
26.0 
25.6 

34.0 
33.5 
33.0 
32.5 
32.0 

40.8 
40.2 
39.6 
39.0 

38.4 

47.6 
46.9 
46.2 
45.5 
44.8 

54.4 
53.6 
52.8 
52.0 
51.2 

61.2 
60.3 
59.4 
58.5 
57.6 

LOGARITHMS   Ofr  NtJMSERS. 


15? 


No.  675  L.  829.] 


[No.  719  L.  857. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

~67T 

829304 
9947 

9368 

9432 

9497 

9561 

9625 

9690 

9754 

9818 

9882 

6 

001  1 

0075 

0139 

0204 

0268 

0332 

0396 

0460 

"TTT 

7 

830589 

0653 

0717 

0781 

0845 

0909 

0973 

1037 

1102 

1166 

3 

1230 

1294 

.  1358 

1422 

1486 

1550 

1614 

1678 

1742 

1806 

64 

9 

1870 

1934 

1998 

2062 

2126 

2189 

2253 

2317 

2381 

2445 

680 

2509 

2573 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3083 

1 

3147 

3211 

3275 

3338 

3402 

3466 

3530 

3593 

3657 

3721 

2 

3784 

3848 

3912 

3975 

4039 

4103 

4166 

4230 

4294 

4357 

3 

4421 

4484 

4548 

4611 

4675 

.4739 

4802 

4866 

4929 

4993 

4 

5056 

5120 

5183 

5247 

5310 

5373 

5437 

5500 

5564 

5627 

5 

5691 

5754 

5817 

5881 

5944 

6007 

6071 

6134 

6197 

6261 

6 

6324 

6387 

6451 

6514 

6577 

6641 

6704 

6767 

6830 

6894 

7 

6957 

7020 

7083 

7146 

7210 

7273 

7336 

7399 

7462 

7525 

8 

7588 

7652 

7715 

7778 

7841 

7904 

7967 

8030 

8093 

8156 

63 

9 

8219 

8282 

8345 

8408 

8471 

8534 

8597 

8660 

8723 

8786 

690 

8849 

8912 

8975 

9038 

9101 

9164 

9227 

9289 

9352 

9415 

1 

94/8 

9541 

9604 

9667 

9729 

9792 

9855 

9918 

9981 

0043 

2 

840106 

0169 

0232 

0294 

0357 

0420 

0482 

0545 

0608 

0671 

3 

0733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

4 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

1860 

1922 

5 

1985 

2047 

2110 

2172 

2235 

2297 

2360 

2422 

2484 

2547 

6 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

7 

3233 

3295 

3357 

3420 

3482 

3544 

3606 

3669 

3731 

3793 

8 

3855 

3918 

3980 

4042 

4104 

4166 

4229 

4291 

4353 

4415 

9 

4477 

4539 

4601 

4664 

4726 

4788 

4850 

4912 

4974 

5036 

700 

5098 

5160 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

62 

1 

5718 

5780 

5842 

5904 

5966 

6028 

6090 

6151 

6213 

6275 

2 

6337 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

3 

6955 

7017 

7079 

7141 

7202 

7264 

7326 

7388 

7449 

7511 

4 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8004 

8066 

8128 

5 

8189 

8251 

8312 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

6 

8805 

8366 

8928 

8989 

9051 

9112 

9174 

9235 

9297 

9358 

7 

9419 

9431 

9542 

9604 

9665 

9726 

9788 

9849 

9911 

9972 

8 

850033 

0095 

0156 

0217 

0279 

0340 

0401 

0462 

0524 

0585 

9 

0646 

0707 

0769 

0830 

0891 

0952 

1014 

1075 

1136 

1197 

710 

1258 

1320 

1381 

1442 

1503 

1564 

1625 

1686 

1747 

1809 

1 

1870 

1931 

1992 

2053 

2114 

2175 

2236 

2297 

2358 

2419 

61 

2 

2480 

2541 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3029 

3 

3090 

3150 

3211 

3272 

3333 

3394 

3455 

3516 

3577 

3637 

4 

3698 

3759 

3820 

3881 

3941 

4002 

4063 

4124 

4185 

4245 

5 

4306 

4367 

4428 

4488 

4549 

4610 

4670 

4731 

4792 

4852 

6 

4913 

4974 

5034 

5095 

5156 

5216 

5277 

5337 

5398 

5459 

7 

5519 

5580 

5640 

5701 

5761 

5822 

5882 

5943 

6003 

6064 

8 

6124 

6185 

6245 

6306 

6366 

6427 

6487 

6548 

6608 

6668 

9 

6729   6789J  6850 

6910 

6970 

7031 

7091 

7152 

7212 

7272 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

65 
64 
63 
62 
61 
60 

6.5 
6.4 
6.3 
6.2 
6.1 
6.0  1 

13.0 
12.8 
12.6 
12.4 
12.2 
12.0 

19.5 
19.2 
18.9 
18.6 
18.3 
18.0 

26.0 
25.6 
25.2 
24.8 
24.4 
24.0 

32.5 
32.0 
31.5 
31.0 
30.5 
30.0 

39.0 
38:4 
37.8 
37.2 
36.6 
36.0 

45.5 

44.8 
44.1 
43.4 
42.7 
42.0 

52.0 
51.2 
50.4 
49.6 
48.8 
48.0 

58.5 
57.6 
56.7 
55.8 
54.9 
54.0 

158 


LOGARITHMS   OF   NUMBERS. 


Ho.  720  L.  857.] 


(No.  764  L. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

720 

857332 

7393 

7453 

7513 

7574 

7634 

7694 

7755 

7815 

7875 

7935 

7995 

8056 

8116 

S176 

8236 

8297 

8357 

8417 

8477 

2 

8537 

8597 

8657 

8718 

8778 

8838 

8898 

8958 

9018 

9078 

3 

9138 

9198 

9258 

9318 

9379 

9439 

9499 

9559 

9619 

9679 

60 

4 

9739 

9799 

9859 

9918 

9978 

0038 

0098 

0158 

021fi 

fl?7fl 

5 

860338 

0398 

0458 

0518 

0578 

0637 

0697 

0757 

0817 

U^/O 

0877 

6 

0937 

0996 

1056 

1116 

1176 

1236 

1295 

1355 

1415 

1475 

7 

1534 

1594 

1654 

1714 

1773 

1833 

1893 

1952 

2012 

2072 

8 

2131 

2191 

2251 

2310 

2370 

2430 

2489 

2549 

2608 

2668 

9 

2728 

2787 

2847 

2906 

2966 

3025 

3085 

3144 

3204 

3263 

730 

3323 

3382 

3442 

3501 

3561 

3620 

3680 

3739 

3799 

3858 

1 

3917 

3977 

4036 

4096 

4155 

4214 

4274 

4333 

4392 

4452 

2 

4511 

4570 

4630 

4689 

4748 

4808 

4867 

4926 

4985 

5045 

3 

5104 

5163 

5222 

5282 

5341 

5400 

5459 

5519 

5578 

5637 

4 

5696 

5755 

5814 

5874 

5933 

5992 

6051 

6110 

6169 

6228 

5 

6287 

6346 

6405 

6465 

6524 

6583 

6642 

6701 

6760 

6819 

6 

6878 

6937 

6996 

7055 

7114 

7173 

7232 

7291 

7350 

7409 

59 

7 

7467 

7526 

7585 

7644 

7703 

7762 

7821 

7880 

7939 

7998 

8 

8056 

8115 

8174 

8233 

8292 

8350 

8409 

8468 

8527 

8586 

9 

8644 

8703 

8762 

8821 

8879 

8938 

8997 

9056 

9114 

9173 

740 

9232 

9290 

9349 

9408 

9466 

9525 

9584 

9642 

9701 

9760 

1 

9818 

9877 

9935 

9994 

0053 

01  1  1 

0170 

0228 

0287 

0345 

2 

870404 

0462 

0521 

0579 

0638 

0696 

0755 

0813 

0872 

0930 

3 

0989 

1047 

1106 

1164 

1223 

1281 

1339 

1398 

1456 

1515 

4 

1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2098 

5 

2156 

2215 

2273 

2331 

2389 

2448 

2506 

2564 

2622 

2681 

6 

2739 

2797 

2855 

2913 

2972 

3030 

3088 

3146 

3204 

3262 

7 

3321 

3379 

3437 

3495 

3553 

3611 

3669 

3727 

3785 

3844 

8 

3902 

3960 

4018 

4076 

4134 

4192 

4250 

4308 

4366 

4424 

58 

9 

4482 

4540 

4598 

4656 

4714 

4772 

4830 

4888 

4945 

5003 

750 

5061 

5119 

5177 

5235 

5293 

5351 

5409 

5466 

5524 

5582 

1 

5640 

5698 

5756 

5813 

5871 

5929 

5987 

6045 

6102 

6160 

2 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

3 

6795 

6853 

6910 

6968 

7026 

7083 

7141 

7199 

7256 

7314 

- 

4 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

5 

7947 

8004 

8062 

8119 

8177 

8234 

8292 

8349 

8407 

8464 

6 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

8981 

9039 

7 

9096 

9153 

9211 

9268 

9325 

9383 

9440 

9497 

9555 

9612 

9669 

9726 

9784 

9841 

9898 

9956 

0013 

0070 

0127 

0185 

9 

880242 

0299 

0356 

0413 

0471 

0528 

0585 

0642 

0699 

0756 

760 

0814 

0871 

0928 

0985 

1042 

1099 

1156 

1213 

1271 

1328 

1385 

1442 

1499 

1556 

1613 

1670 

1727 

1784 

1841 

1898 

2 

1955 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

3 

2525 

2581 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3037 

4 

3093 

3150 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

3605 

PROPORTIONAL,  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

59 
58 
57 
56 

5.9 
5.8 
5.7 
5.6 

11.8 
11.6 
11.4 
11.2 

17.7 
17.4 
17.1 

16.8 

*23.6 
23.2 
22.8 
22.4 

29.5 
29.0 
28.5 
28.0 

35.4 
34.8 
34.2 
33.6 

41.3 
40.6 
39.9 
39.2 

47.2 
46.4 
45.6 
44.8 

53.1 
52.2 
51.3 
50.4 

LOGARITHMS   OF   NUMBERS. 


159 


No.  765  L.  883.] 


[No.  809  L.  908. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

765 

883661 

3718 

3775 

3832 

3888 

3945 

4002 

4059 

4115 

4172 

6 

4229 

4285 

4342 

4399 

4455 

4512 

4569 

4625 

4682 

4739 

7 

4795 

4852 

4909 

4965 

5022 

5078 

5135 

5192 

5248 

5305 

8 

5361 

5418 

5474 

5531 

5587 

5644 

5700 

5757 

5813 

5870 

9 

5926 

5983 

6039 

6096 

6152 

6209 

6265 

6321 

6378 

6434 

770 

6491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

1 

7054 

7111 

7167 

7223 

7280 

7336 

7392 

7449 

7505 

7561 

2 

7617 

7674 

7730 

7786 

7842 

-7898 

7955 

8011 

8067 

8123 

3 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

8573 

8629 

8685 

A 

8741 

8797 

8853 

8909 

8965 

9021 

9077 

9134 

9190 

9246 

9302 
9862 

9358 
9918 

9414 
9974 

9470 

9526 

9582 

9638 

9694 

9750 

9806 

56 

0030 

0086 

0141 

0197 

0253 

0309 

0365 

7 

890421 

0477 

0533 

0589 

0645 

0700 

0756 

0812 

0868 

0924 

8 

0980 

1035 

1091 

1147 

1203 

1259 

1314 

1370 

1426 

1482 

9 

1537 

1593 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

780 

2095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

2595 

2651 

2707 

2762 

2818 

2873 

2929 

2985 

3040 

3096 

3151 

2 

3207 

3262 

3318 

3373 

3429 

3484 

3540 

3595 

3651 

3706 

3 

3762 

3817 

3873 

3928 

3984 

4039 

4094 

4150 

4205 

4261 

4 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

5 

4870 

4925 

4980 

5036 

5091 

5146 

5201 

5257 

5312 

5367 

6 

5423 

5478 

5533 

5588 

5644 

5699 

5754 

5809 

5864 

5920 

7 

5975 

6030 

6085 

6140 

6195 

6251 

6306 

6361 

6416 

6471 

8 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 

9 

7077 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7572 

55 

790 

7627 

7682 

7737 

7792 

7847 

7902 

7957 

8012 

8067 

8122 

1 

8176 

8231 

8286 

8341 

8396 

8451 

8506 

8561 

8615 

8670 

2 

8725 

8780 

8835 

8890 

8944 

8999 

9054 

9109 

9164 

9218 

3 

9273 

9328 

9383 

9437 

9492 

9547 

9602 

9656 

9711 

9766 

4 

9821 

9875 

9930 

9985 

0039 

0094 

0149 

0203 

0258 

0312 

5 

900367 

0422 

0476 

0531 

0586 

0640 

0695 

0749 

0804 

0859 

6 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

1295 

1349 

1404 

7 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

8 

2003 

2057 

2112 

2166 

2221 

2275 

2329 

2384 

2438 

2492 

9 

2547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3036 

800 

3090 

3144 

3199 

3253 

3307 

3361 

3416 

3470 

3524 

3578 

1 

3633 

3687 

3741 

3795 

3849 

3904 

3958 

4012 

4066 

4120 

2 

4174 

4229 

4283 

4337 

4391 

4445 

4499 

4553 

4607 

4661 

3 

4716 

4770 

4824 

4878 

4932 

4986 

5040 

5094 

5148 

5202 

4 

5256 

5310 

5364 

5418 

5472 

5526 

5580 

5634 

5688 

5742 

54 

5 

5796 

5850 

5904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

6 

6335 

6389 

6443 

6497 

6551 

6604 

6658 

6712 

6766 

6820 

7 

6874 

6927 

6981 

7035 

7089 

7143 

7196 

7250 

7304 

7358 

8 

7411 

7465 

7519 

7573 

7626 

7680 

7734 

7787 

7841 

7895 

9 

7949 

8002 

8056 

8110 

8163 

8217 

8270 

8324 

8378 

8431 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

57 
56 
55 
54 

5.7 
5.6 
5.5 
5.4 

11.4 
11.2 
11.0 
10.8 

17.1 
16.8 
16.5 
16.2 

22.8 
22.4 
22.0 
21.6 

28.5 
28.0 
27.5 
27.0 

34.2 
33.6 
33.0 
32.4 

39.9 
39.2 
38.5 
37.8 

45.6 
44.8 
44.0 
43.2 

51.3 
50.4 
49.5 
48.6 

LOGARITHMS    OF   NUMBERS. 


No.  810  L.  908.) 


[No.  854  L.  93* 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

810 

908485 

8539 

8592 

8646 

8699 

8753 

8807 

8860 

8914 

8967 

9021 

9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

9503 

2 

9556 

9610 

9663 

9716 

9770 

9823 

9877 

9930 

9984 

0037 

3 

910091 

0144 

0197 

0251 

0304 

0358 

0411 

0464 

0518 

0571 

4 

0624 

0678 

0731 

0784 

0838 

0891 

0944 

0998 

1051 

1104 

5 

1158 

1211 

1264 

1317 

1371 

1424 

1477 

1530 

1584 

1637 

6 

1690 

1743 

1797 

1850 

1903 

1956 

2009 

2063 

2116 

2169 

7 

2222 

2275 

2328 

2381 

2435 

2488 

2541 

2594 

2647 

2700 

8 

2753 

2806 

2859 

2913 

2966 

3019 

3072 

3125 

3178 

3231 

9 

3284 

3337 

3390 

3443 

3496 

3549 

3602 

3655 

3708 

3761 

53 

820 

3814 

3867 

3920 

3973 

4026 

4079 

4132 

4184 

4237 

4290 

1 

4343 

4396 

4449 

4502 

4555 

4608 

4660 

4713 

4766 

4819 

2 

4872 

4925 

4977 

5030 

5083 

5136 

5189 

5241 

5294 

5347 

3 

5400 

5453 

5505 

5558 

5611 

5664 

5716 

5769 

5822 

5875 

4 

5927 

5980 

6033 

6085 

6138 

6191 

6243 

6296 

6349 

6401 

5 

6454 

6507 

6559 

6612 

6664 

6717 

6770 

6822 

6875 

6927 

6 

6980 

7033 

7085 

7138 

7190 

7243 

7295 

7348 

7400 

7453 

7 

7506 

7558 

7611 

7663 

7716 

7768 

7820 

7873 

7925 

7978 

8 

8030 

8083 

8135 

8188 

8240 

8293 

8345 

8397 

8450 

8502 

9 

8555 

8607 

8659 

8712 

8764 

8816 

8869 

8921 

8973 

9026 

830 

9078 

9130 

9183 

9235 

9287 

9340 

9392 

9444 

9496 

9549 

1 

9601 

9653 

9706 

9758 

9810 

9862 

9914 

9Q67 

0019 

0071 

2 

920123 

0176 

0228 

0280 

0332 

0384 

0436 

0489 

0541 

0593 

3 

0645 

0697 

0749 

0801 

0853 

0906 

0958 

1010 

1062 

1114 

5*- 

4 

1166 

1218 

1270 

1322 

1374 

1426 

1478 

1530 

1582 

1634 

5 

1686 

1738 

1790 

1842 

1894 

1946 

1998 

2050 

2102 

2154 

6 

2206 

2258 

2310 

2362 

2414 

2466 

2518 

2570 

2622 

2674 

7 

2725 

2777 

2829 

2881 

2933 

2985 

3037 

3089 

3140 

3192 

8 

3244 

3296 

3348 

3399 

3451 

3503 

3555 

3607 

3658 

3710 

9 

3762 

3814 

3865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

840 

4279 

4331 

4383 

4434 

4486 

4538 

4589 

4641 

4693 

4744 

1 

4796 

4848 

4899 

4951 

5003 

5054 

5106 

5157 

5209 

5261 

2 

5312 

5364 

5415 

5467 

5518 

5570 

5621 

5673 

5725 

5776 

3 

5828 

5879 

5931 

5982 

6034 

6085 

6137 

6188 

6240 

6291 

4 

6342 

6394 

6445 

6497 

6548 

6600 

6651 

6702 

6754 

6805 

5 

6857 

6908 

6959 

7011 

7062 

7114 

7165 

7216 

7268 

7319 

6 

7370 

7422 

7473 

7524 

7576 

7627 

7678 

7730 

7781 

7832 

7 

7883 

7935 

7986 

8037 

8088 

8140 

8191 

8242 

8293 

8345 

8 

8396 

8447 

8498 

8549 

8601 

8652 

8703 

8754 

8805 

8857 

9 

8908 

8959 

9010 

9061 

9112 

9163 

9215 

9266 

9317 

9368 

850 

9419 

9470 

9521 

9572 

9623 

9674 

9725 

9776 

9827 

9879 

1 

9930 

9981 

51 

0032 

0083 

0134 

0185 

0236 

0287 

0338 

0389 

2 

930440 

0491 

0542 

0592 

0643 

0694 

0745 

0796 

0847 

0898 

3 

0949 

1000 

1051 

1102 

1153 

1204 

1254 

1305 

1356 

1407 

4 

1458 

1509 

1560 

1610 

1661 

1712 

1763 

1814 

1865 

1915 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

» 

9 

53 
52 
51 
50 

5.3 
5.2 
5.1 
5.0 

10.6 
.10.4 
10.2 
10.0 

15.9 
15.6 
15.3 
15.0 

21.2 
20.8 
20.4 
20.0 

26.5 
26.0 
25.5 
25.0 

31.8 
31.2 
30.6 
30.0 

37.1 
36.4 
35.7 
35.0 

42.4 
41.6 
40.8 
40.0 

47.7 
46.8 
45.9 
45.0 

LOGARITHMS    OF   NUMBERS. 


161 


No.  855  L.  931. J 


[No.  899  L.  954, 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

855 

931966 

2017 

2068 

2118 

2169 

2220 

2271 

2322 

2372 

2423 

6 

2474 

2524 

2575 

2626 

2677 

2727 

2778 

2829 

2879 

2930 

7 

2981 

3031 

3082 

3133 

3183 

3234 

3285 

3335 

3386 

3437 

8 

3487 

3538 

3589 

3639 

3690 

3740 

3791 

3841 

3892 

3943 

9 

3993 

4044 

4094 

4145 

4195 

4246 

4296 

4347 

4397 

4448 

860 

4498 

4549 

4599 

4650 

4700 

4751 

4801 

4852 

4902 

4953 

1 

5003 

5054 

5104 

5154 

5205 

5255 

5306 

5356 

5406 

5457 

2 

5507 

5558 

5608 

5658 

5709 

5759 

5809 

5860 

5910 

5960 

3 

6011 

6061 

6111 

6162 

6212 

6262 

6313 

6363 

6413 

6463 

4 

6514 

6564 

6614 

6665 

6715 

6765 

6815 

6865 

6916 

6966 

5 

7016 

7066 

7116 

7167 

7217 

7267 

7317 

7367 

7418 

7468 

6 

7518 

7568 

7618 

7668 

7718 

7769 

7819 

7869 

7919 

7969 

7 

8019 

8069 

8119 

8169 

8219 

8269 

8320 

8370 

8420 

8470 

50 

6 

8520 

8570 

8620 

8670 

8720 

8770 

8820 

8870 

8920 

8970 

9 

9020 

9070 

9120 

9170 

9220 

9270 

9320 

9369 

9419 

9469 

870 

9519 

9569 

9619 

9669 

9719 

9769 

9819 

9869 

9918 

9968 

1 

940018 

0068 

0118 

0168 

0218 

0267 

0317 

0367 

0417 

0467 

2 

0516 

0566 

0616 

0666 

0716 

0765 

0815 

0865 

0915 

0964 

3 

1014 

1064 

1114 

1163 

1213 

1263 

1313 

1362 

1412 

1462 

4 

1511 

1561 

1611 

1660 

1710 

1760 

1809 

1859 

1909 

1958 

3 

2003 

2058 

2107 

2157 

2207 

2256 

2306 

2355 

2405 

2455 

6 

2504 

2554 

2603 

2653 

2702 

2752 

2801 

2851 

2901 

2950 

7 

3000 

3049 

3099 

3148 

3198 

3247 

3297 

3346 

3396 

3445 

8 

3495 

3544 

3593 

3643 

3692 

3742 

3791 

3841 

3890 

3939 

9 

3989 

4038 

4088 

4137 

4186 

4236 

4285 

4335 

4384 

4433 

880 

4483 

4532 

4581 

4631 

4680 

4729 

4779 

4828 

4877 

4927 

1 

4976 

5025 

5074 

5124 

5173 

5222 

5272 

5321 

5370 

5419 

2 

5469 

5518 

5567 

5616 

5665 

5715 

5764 

5813 

5862 

5912 

3 

5961 

6010 

6059 

6108 

6157 

6207 

6256 

6305 

6354 

6403 

4 

6452 

6501 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

5 

6943 

6992 

7041 

7090 

7139 

7189 

7238 

7287 

7336 

7385 

6 

7434 

7483 

7532 

7581 

7630 

7679 

7728 

7777 

7826 

7875 

49 

7 

7924 

7973 

8022 

8070 

8119 

8168 

8217 

8266 

8315 

8364 

8 

8413 

8462 

8511 

8560 

8608 

8657 

8706 

8755 

8804 

8853 

9 

8902 

8951 

8999 

9048 

9097 

9146 

9195 

9244 

9292 

9341 

690 

9390 

9439 

9488 

9536 

9585 

9634 

9683 

9731 

9780 

9829 

1 

9878 

9926 

9975 

0024 

0073 

0121 

0170 

0219 

0267 

0316 

2 

950365 

0414 

0462 

0511 

0560 

0608 

0657 

0706 

0754 

0303 

3 

0851 

0900 

0949 

0997 

1046 

1095 

1143 

1192 

1240 

1289 

4 

1338 

1386 

1435 

1483 

1532 

1580 

1629 

1677 

1726 

1775 

5 

1823 

1872 

1920 

1969 

2017 

2066 

2114 

2163 

2211 

2260 

6 

2308 

2356 

2405 

2453 

2502 

2550 

2599 

2647 

2696 

2744 

7 

2792 

2841 

2889 

2938 

2986 

3034 

3083 

3131 

3180 

3228 

8 

3276 

3325 

3373 

3421 

3470 

3518 

3566 

3615 

3663 

3711 

9 

3760 

3808 

3856 

3905 

3953 

4001 

4049 

4098 

4146 

4194 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

45.9 
45.0 
44.1 
43.2 

51 
50 
49 
48 

5.1 
5.0 
4.9 
48 

10.2 
10.0 
9.8 
9.6 

15.3 
15.0 
14.7 
14.4 

20.4 
20.0 
19.6 
19.2 

25.5 
25.0 
24.5 
24.0 

30.6 
30.0 
29.4 
28.8 

35.7 
35.0 
34.3 
33.6 

40.8 
40.0 
39.2 
38.4 

162 


LOGARITHMS    OF    NUMBERS. 


Ho.  900  L.  954.J 


[No.  944  L.  975. 


N. 

1   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

900 

954243 

4291 

4339 

4387 

4435 

4484 

4532 

4580 

4628 

4677 

. 

1 

4725 

4773 

4821 

4869 

4918 

4966 

5014 

5062 

5110 

5158 

2 

5207 

5255 

5303 

5351 

5399 

5447 

5495 

5543 

5592 

5640 

3 

5688 

5736 

5784 

5832 

5880 

5928 

5976 

6024 

6072 

6120 

4 

6168 

6216 

6265 

6313 

6361 

6409 

6457 

6505 

6553 

6601 

5 

6649 

6697 

6745 

6793 

6840 

6888 

6936 

6984 

7032 

7080 

48 

6 

7128 

7176 

7224 

7272 

7320 

7368 

7416 

7464 

7512 

7559 

7 

7607 

7655 

7703 

7751 

7799 

7847 

7894 

7942 

7990 

8038 

8 

8086 

8134 

8181 

8229 

8277 

8325 

8373 

8421 

8468 

8516 

9 

8564 

8612 

8659 

8707 

8755 

8803 

8850 

8898 

8946 

8994 

910 

9041 

9089 

9137 

9185 

9232 

9280 

9328 

9375 

9423 

9471 

I 

9518 

9566 

9614 

9661 

9709 

9757 

9804 

9852 

9900 

9947 

2 

9995 

0042 

0090 

Atao 

ni  oe 

n?^ 

A7Af 

rjaoo 

n^7A 

3 

960471 

0518 

0566 

V  1  JO 

0613 

U  1  O  J 

0661 

\jLjj 

0709 

UZOU 

0756 

\)jZ,c 

0804 

U.3/O 

0851 

0423 
0899 

4 

0946 

0994 

1041 

1089 

1136 

1184 

1231 

1279 

1326 

1374 

5 

1421 

1469 

1516 

1563 

1611 

1658 

1706 

1753 

1801 

1848 

6 

1895 

1943 

1990 

2038 

2085 

2132 

2180 

2227 

2275 

2322 

7 

2369 

2417 

2464 

2511 

2559 

2606 

2653 

2701 

2748 

2795 

8 

2843 

2890 

2937 

2985 

3032 

3079 

3126 

3174 

3221 

3268 

9 

3316 

3363 

3410 

3457 

3504 

3552 

3599 

3646 

3693 

3741 

920 

3788 

3835 

3882 

3929 

3977 

4024 

4071 

4118 

4165 

4212 

1 

4260 

4307 

4354 

4401 

4448 

4495 

4542 

4590 

4637 

4684 

2 

4731 

4778 

4825 

4872 

4919 

4966 

5013 

5061 

5108 

5155 

3 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

5531 

5578 

5625 

4 

5672 

5719 

5766 

5813 

5860 

5907 

5954 

6001 

6048 

6095 

47 

5 

6142 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

6 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7033 

7 

7080 

7127 

7173 

7220 

7267 

7314 

7361 

7408 

7454 

7501 

8 

7548 

7595 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

9 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

8343 

8390 

8436 

930 

8483 

8530 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

8903 

1 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9323 

9369 

2 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

3 

9882 

9928 

9975 

0021 

0068 

01  14 

0161 

0207 

0254 

0300 

4 

970347 

0393 

0440 

0486 

0533 

0579 

0626 

0672 

0719 

0765 

5 

0812 

0858 

0904 

0951 

0997 

1044 

1090 

1137 

1183 

1229 

6 

1276 

1322 

1369 

1415 

1461 

1508 

1554 

1601 

1647 

1693 

7 

1740 

1786 

1832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

8 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 

2573 

2619 

9 

2666 

2712 

2758 

2804 

2851 

2897 

2943 

2989 

3035 

3082 

940 

3128 

3174 

3220 

3266 

3313 

3359 

3405 

3451 

3497 

3543 

1 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

3913 

3959 

4005 

2 

4051 

4097 

4143 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

3 

4512 

4558 

4604 

4650 

4696 

4742 

4788 

4834 

4880 

4926 

4 

4972 

5018 

5064 

5110 

5156 

5202 

5248 

5294 

5340 

5386 

46 

PROPORTIONAL  PARTS. 


Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

47 
46 

4.7 
4.6 

9.4 
9.2 

14.1 
13.8 

18.8 
18.4 

23.5 
23.0 

28.2 
27.6 

32.9 
32.2 

37.6 
36.8 

42.3 
41.4 

LOGARITHMS    OF   NUMBERS. 


163 


No.  945  L.  975.J 


(No.  989  L.  995. 


N. 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

Diff. 

945 

975432 

5478 

5524 

5570 

5616 

5662 

5707 

5753 

5799 

5845 

6 

5891 

5937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

6304 

7 

6350 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

8 

6808 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

7220 

9 

7266 

7312 

7358 

7403 

7449 

7495 

7541 

7586 

7632 

7678 

950 

7724 

7769 

7815 

7861 

7906 

7952 

7998 

8043 

8089 

8135 

1 

8181 

8226 

8272 

8317 

8363 

8409 

8454 

8500 

8546 

8591 

2 

8637 

8683 

8728 

8774 

8819 

8865 

8911 

8956 

9002 

9047 

3 

9093 

9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9503 

4 

9548 

9594 

9639 

9685 

9730 

9776 

9821 

9867 

9912 

9958 

5 

980003 

0049 

0094 

0140 

0185 

0231 

0276 

0322 

0367 

0412 

6 

0458 

0503 

0549 

0594 

0640 

0685 

0730 

0776 

0821 

0867 

7 

0912 

0957 

1003 

1048 

1093 

1139 

1184 

1229 

1275 

1320 

8 

1366 

1411 

1456 

1501 

1547 

1592 

1637 

1683 

1728 

1773 

9 

1819 

1864 

1909 

1954 

2000 

2045 

2090 

2135 

2181 

2226 

960 

2271 

2316 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

1 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3040 

3085 

3130 

2 

3175 

3220 

3265 

3310 

3356 

3401 

3446 

3491 

3536 

3581 

3 

3626 

3671 

3716 

3762 

3807 

3852 

3897 

3942 

3987 

4032 

4 

4077 

4122 

4167 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

5 

4527 

4572 

4617 

4662 

4707 

4752 

4797 

4842 

4887 

4932 

45 

6 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

7 

5426 

5471 

5516 

5561 

5606 

5651 

5696 

5741 

5786 

5830 

8 

5875 

5920 

5965 

6010 

6055 

6100 

6144 

6189 

6234 

6279 

9 

6324 

6369 

6413 

6458 

6503 

6548 

6593 

6637 

6682 

6727 

6772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7130 

7175 

1 

7219 

7264 

7309 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

2 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

3 

8113 

8157 

8202 

8247 

8291 

8336 

8381 

8425 

8470 

8514 

8559 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

5 

9005 

9049 

9094 

9138 

9183 

9227 

9272 

9316 

9361 

9405 

9450 

9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

9850 

7 
7 

9395 

9939 

9983 

0028 

0072 

01  17 

0161 

0206 

025C 

O7O4 

8 

990339 

0383 

0428 

0472 

0516 

0561 

0605 

0650 

0694 

U^Vn 

0738 

9 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

980 

1226 

1270 

1315 

1359 

1403 

1448 

1492 

1536 

1580 

1625 

1 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

1979 

2023 

2067 

2 

2111 

2156 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

2509 

3 

2554 

2598 

2642 

2686 

2730 

2774 

2819 

2863 

2907 

2951 

4 

2995 

3039 

3083 

3127 

3172 

3216 

3260 

3304 

3348 

3392 

5 

3436 

3480 

3524 

3568 

3613 

3657 

3701 

3745 

3789 

3833 

6 

3877 

3921 

3965 

4009 

4053 

4097 

4141 

4185 

4229 

4273 

7 

4317 

4361 

4405 

4449 

4493 

4537 

4581 

4625 

4669 

4713 

44 

8 

4757 

4801 

4845 

4889 

4933 

4977 

5021 

5065 

5108 

5152 

9 

5196 

5240 

5284 

5328 

5372 

5416 

5460 

5504 

5547 

5591 

PROPORTIONAL  PARTS. 


Diff. 

46 
45 
44 
43 

1 

3 

3 

4 

5 

6 

7 

8 

9 

4.6 
4.5 
4.4 
4.3 

9.2 
9.0 
8.8 
8.6 

13.8 
13.5 
13.2 
12.9 

18.4 
18.0 
17.6 
17.2 

23.0 
22.5 
22.0 
21.5 

27.6 
27.0 
26.4 
25.8 

32.2 
31.5 
30.8 
30.1 

36.8 
36.0 
35.2 
34.4 

41.4 
40.5 
39.6 
38.7 

164 


HYPERBOLIC   LOGARITHMS. 


No. 990  L. 995 J 


[No.999L.999. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

990 

995635 

5679 

5723 

5767 

5811 

5854 

5898 

5942 

5986 

6030 

1 

6074 

6117 

6161 

6205 

6249 

6293 

6337 

6380 

6424 

6468 

44 

2 

6512 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

3 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

4 

7386 

7430 

7474 

7517 

7561 

7605 

7648 

7692 

7736 

7779 

3 

7823 

7867 

7910 

7954 

7998 

8041 

8085 

8129 

8172 

8216 

6 

8259 

8303 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

7 

8695 

8739 

8782 

8826 

8869 

8913 

8956 

9000 

9043 

9087 

8 

9131 

9174 

9218 

9261 

9305 

9348 

9392 

9435 

9479 

9522 

9 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

9913 

9957 

43 

HYPERBOLIC  LOGARITHMS. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1.01 

.0099 

1.45 

.3716 

.89 

.6366 

2.33 

.8458 

2.77 

.0188 

1.02 

.0198 

1.46 

.3784 

.90 

.6419 

2.34 

.8502 

2.78 

.0225 

1.03 

.0296 

1.47 

.3853 

.91 

.6471 

2.35 

.8544 

2.79 

.0260 

1.04 

.0392 

1.48 

.3920 

.92 

.6523 

2.36 

.8587 

2.80 

.0296 

1.05 

.0488 

1.49 

.3988 

.93 

.6575 

2.37 

.8629 

2.81 

.0332 

1.06 

.0583 

1.50 

.4055 

.94 

.6627 

2.38 

.8671 

2.82 

.0367 

1.07 

.0677 

1.51 

.4121 

.95 

.6678 

2.39 

.8713 

2.83 

.0403 

1.08 

.0770 

1.52 

.4187 

.96 

.6729 

2.40 

.8755 

2.84 

.0438 

1.09 

.0862 

1.53 

.4253 

.97 

.6780 

2.41 

.8796 

2.85 

.0473 

1.10 

.0953 

1.54 

.4318 

.98 

.6831 

2.42 

.8838 

2.86 

.0508 

1.11 

.1044 

1.55 

.4383 

1.99 

.6881 

2.43 

.8879 

2.87 

.0543 

1.12 

.1133 

1.56 

.4447 

2.00 

.6931 

2.44 

.8920 

2.88 

.0578 

1.13 

.1222 

1.57 

.4511 

2.01 

.6981 

2.45 

.8961 

2.89 

.0613 

1.14 

.1310 

1.58 

.4574 

2.02 

.7031 

2.46 

.9002 

2.90 

.0647 

1.15 

.1398 

1.59 

.4637 

2.03 

.7080 

2.47 

.9042 

2.91 

.0682 

1.16 

.1484 

1.60 

.4700 

2.04 

.7129 

2.48 

.9083 

2.92 

.0716 

1.17 

.1570 

1.61 

.4762 

2.05 

.7178 

2.49 

.9123 

2.93 

.0750 

1.18 

.1655 

1.62 

.4824 

2.06 

.7227 

2.50 

.9163 

2.94 

.0784 

1.19 

.1740 

1.63 

.4886 

2.07 

.7275 

2.51 

.9203 

2.95 

.0818 

1.20 

.1823 

1.64 

.4947 

2.08 

.7324 

2.52 

.9243 

2.96 

.0852 

1.21 

.1906 

1.65 

.5008 

2.09 

.7372 

2.53 

.9282 

2.97 

.0886 

1.22 

.1988 

J.66 

.5068 

2.10 

.7419 

2.54 

.9322 

2.98 

.0919 

1.23 

.2070 

1.67 

.5128 

2.11 

.7467 

2.55 

.9361 

2.99 

.0953 

1.24 

.2151 

1.68 

.5188 

2.12 

.7514 

2.56 

.9400 

3.00 

.0986 

1.25 

.2231 

1.69 

.5247 

2.13 

.7561 

2.57 

.9439 

3.01 

.1019 

1.26 

.2311 

1.70 

.5306 

2.14 

.7608 

2.58 

.9478 

3.02 

.1056 

1.27 

.2390 

1.71 

.5365 

2.15 

.7655 

2.59 

.9517 

3.03 

.1081 

1.28 

.2469 

1.72 

.5423 

2.16 

.7701 

2.60 

.9555 

3.04 

.1113 

1.29 

.2546 

1.73 

.5481 

2.17 

.7747 

2.61 

.9594 

3.05 

.1154 

1.30 

.2624 

1.74 

.5539 

2.18 

.7793 

2.62 

.9632 

3.06 

.1187 

1.31 

.2700 

1.75 

.5596 

2.19 

.7839 

2.63 

.9670 

3.07 

.1219 

1.32 

.2776 

1.76 

.5653 

2.20 

.7885 

2.64 

.9708 

3.08 

.1246 

1.33 

.2852 

1.77 

.5710 

2.21 

.7930 

2.65 

.9746 

3.09 

.1284 

1.34 

.2927 

1.78 

.5766 

2.22 

.7975 

2.66 

.9783 

3.10 

.1312 

1.35 

.3001 

1.79 

.5822 

2.23 

.8020 

2.67 

.9821 

3.11 

.1349 

1.36 

.3075 

1.80 

.5878 

2.24 

.8065 

2.68 

.9858 

3.12 

.1378 

1.37 

.3148 

1.81 

.5933 

2.25 

.8109 

2.69 

.9895 

3.13 

.1410 

1.38 

.3221 

1.82 

.5988 

2.26 

.8154 

2.70 

.9933 

3.14 

.1442 

1.39 

.3293 

1.83 

.6043 

2.27 

.8198 

2.71 

.9969 

3.15 

.1474 

1.40 

.3365 

1.84 

.6098 

2.28 

.8242 

2.72 

1  .0006 

3.16 

.1506 

1.41 

.3436 

1.85 

.6152 

2.29 

.8286 

2.73 

1  .0043 

3.17 

.1537 

1.42 

.3507 

1.86 

.6206 

2.30 

.8329 

2.74 

1  .0080 

3.18 

.1569 

1.43 

.3577 

1.87 

.6259 

2.31 

.8372 

2.75 

1.0116 

3.19 

.1600 

1.44 

.3646 

1.88 

.6313 

2.32 

.8416 

2.76 

1.0152 

3.20 

.1632 

HYPERBOLIC  LOGARITHMS. 


165 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

3.21 

.1663 

3.87 

.3533 

4.53 

.5107 

5.19 

.6467 

5.85 

.7664 

3.22 

.1694 

3.88 

.3558 

4.54 

.5129 

5.20 

.6487 

5.86 

.7681 

3.23 

.1725 

3.89 

.3584 

4.55 

.5151 

5.21 

.6506 

5.87 

.7699 

3.24 

.1756 

3.90 

.3610 

4.56 

.5173 

5.22 

.6525 

5.88 

.7716 

3.25 

.1787 

3.91 

.3635 

4.57 

.5195 

5.23 

.6544 

5.89 

.7733 

3.26 

.1817 

3.92 

.3661 

4.58 

.5217 

5.24 

.6563 

5.90 

.7750 

3.27 

.1848 

3.93 

.3686 

4.59 

.5239 

5.25 

.6582 

5.91 

.7766 

3.28 

.1878 

3.94 

.3712 

4.60 

.5261 

5.26 

.6601 

5.92 

.7783 

3.29 

.1909 

3.95 

.3737 

4.61 

.5282 

5.27 

.6620 

5.93 

.7800 

3.30 

.1939 

3.96 

.3762 

4.62 

.5304 

5.28 

.6639 

5.94 

.7817 

3.31 

.1969 

3.97 

.3788 

4.63 

.5326 

5.29 

.6658 

5.95 

.7834 

3.32 

.1999 

3.98 

.3813 

4.64 

.5347 

5.30 

.6677 

.  5.96 

.7851 

3.33 

.2030 

3.99 

.3838 

4.65 

.5369 

5.31 

.6696 

5.97 

.7867 

3.34 

.2060 

4.00 

.3863 

4.66 

.5390 

5.32 

.6715 

5.98 

.7884 

3.35 

.2090 

4.01 

.3888 

4.67 

.5412 

5.33 

.6734 

5.  99' 

.7901 

3.36 

.2119 

4.02 

.3913 

4.68 

.5433 

5.34 

.6752 

6.00 

.7918 

3.37 

.2149 

4.03 

.3938 

4.69 

.5454 

5.35 

.6771 

6.01 

.7934 

3.38 

.2179 

4.04 

.3962 

4.70 

.5476 

5.36 

.6790 

6.02 

.7951 

3.39 

.2208 

4.05 

.3987 

4.71 

.5497 

5.37 

.6808 

6.03 

.7967 

3.40 

.2238 

4.06 

.4012 

4.72 

.5518 

5.38 

.6827 

6.04 

.7984 

3.41 

.2267 

4.07 

.4036 

4.73 

.5539 

5.39 

.6845 

6.05 

.8001 

3.42 

.2296 

4.08 

.4061 

4.74 

.5.560 

5.40 

.6864 

606 

.8017 

3.43 

.2326 

4.09 

.4085 

4.75 

.5581 

5.41 

.6882 

6.07 

.8034 

3.44 

.2355 

4.10 

.4110 

4.76 

.5602 

5.42 

.6901 

6.08 

.8050 

3.45 

.2384 

4.11 

.4134 

4.77 

.5623 

5.43 

.6919 

6.09 

.8066 

3.46 

.2413 

4.12 

.4159 

4.78 

.5644 

5.44 

.6938 

6.10 

.8083 

3.47 

.2442 

4.13 

.4183 

4.79 

.5665 

5.45 

.6956 

6.11 

.8099 

3.48 

.2470 

4.14 

.4207 

4.80 

.5686 

5.46 

.6974 

6.12 

.8116 

3.49 

.2499 

4.15 

.4231 

4.81 

.5707 

5.47 

.6993 

6.13 

.8132 

3.50 

.2528 

4.16 

.4255 

4.82 

.5728 

5.48 

.7011 

6.14 

.8148 

3.51 

.2556 

4.17 

.4279 

4.83 

.5748 

5.49 

.7029 

6.15 

.8165 

3.52 

.2585 

4.18 

.4303 

4.84 

.5769 

5.50 

.7047 

6.16 

.8181 

3.53 

.2613 

4.19 

.4327 

4.85 

.5790 

5.51 

.7066 

6.17 

.8197 

3.54 

.2641 

4.20 

.4351 

4.86 

.5810 

5.52 

.7084 

6.18 

.8213 

3.55 

.2669 

4.21 

.4375 

4.87 

.5831 

5.53 

.7102 

6.19 

.8229 

3.56 

.2698 

4.22 

.4398 

4.88 

5851 

5.54 

.7120 

6.20 

.8245 

3.57 

.2726 

4.23 

.4422 

4.89 

.5872 

5.55 

.7138 

6.21 

.8262 

3.58 

.2754 

4.24 

4446 

4.90 

.5892 

5.56 

.7156 

6.22 

.8278 

3.59 

.2782 

4.25 

.4469 

4.91 

.5913 

5.57 

.7174 

6.23 

.8294 

3.60 

.2809 

4.26 

.4493 

4.92 

.5933 

5.58 

.7192 

6.24 

.8310 

3.61 

.2837 

4.27 

.4516 

4.93 

.5953 

5.59 

.7210 

6.25 

.8326 

3.62 

.2865 

4.28 

.4540 

4.94 

.5974 

5.60 

.7228 

6.26 

.8342 

3.63 

.2892 

4.29 

.4563 

4.95 

.5994 

5.61 

.7246 

6.27 

.8358 

3.64 

.2920 

4.30 

.4586 

4.96 

.6014 

5.62 

.7263 

6.28 

.8374 

365 

.2947 

4.31 

.4609 

4.97 

.6034 

5.63 

.7281 

6.29 

.8390 

3.66 

.2975 

4.32 

.4633 

4.98 

.6054 

5.64 

.7299 

6.30 

.8405 

3.67 

.3002 

4.33 

.4656 

4.99 

.6074 

5.65 

.7317 

6.31 

.8421 

3.68 

.3029 

4.34 

.4679 

5.00 

.6094 

5.66 

.7334 

6.32 

.8437 

3.69 

.3056 

4.35 

.4702 

5.01 

.6114 

5.67 

.7352 

6.33 

.8453 

3.70 

.3083 

4.36 

.4725 

5.02 

.6134 

5.68 

.7370 

6.34 

8469 

3.71 

.3110 

4.37 

.4748 

5.03 

.6154 

5.69 

.7387 

6.35 

.8485 

3.72 

.3137 

4.38 

.4770 

5.04 

.6174 

5.70 

.7405 

6.36 

.8500 

3.73 

.3164 

4.39 

.4793 

5.05 

.6194 

5.71 

.7422 

6.37 

.8516 

3.74 

.3191 

4.40 

.4816 

5.06 

.6214 

5.72 

.7440 

6.38 

.8532 

3.75 

.3218 

4.41 

.4839 

5.07 

.6233 

5.73 

.7457 

6.39 

.8547 

3.76 

.3244 

4.42 

.4861 

5.08 

.6253 

5.74 

.7475 

6.40 

.8563 

3.77 

.3271 

4.43 

.4884 

5.09 

.6273 

5.75 

.7492 

6.41 

.8579 

3.78 

.3297 

4.44 

.4907 

5.10 

.6292 

5.76 

.7509 

6.42 

.8594 

3.79 

.3324 

4.45 

.4929 

5.11 

.6312 

5.77 

.7527 

6.43 

.8610 

3.80 

.3350 

4.46 

.4951 

5.12 

.6332 

5.78 

.7544 

6.44 

.8625 

3.81 

.3376 

4.47 

.4974 

5.13 

.6351 

5.79 

.7561 

6.45 

.8641 

3.82 

.3403 

4.48 

.4996 

5.14 

.6371 

5.80 

.7579 

6.46 

.8656 

3.83 

.3429 

4.49 

.5019 

5.15 

.6390 

5.81 

.7596 

6.47 

.8672 

3.84 

.3455 

4.50 

.5041 

5.16 

.6409 

5.82 

.7613 

6.48 

8687 

3.85 

.3481 

4.51 

.5063 

5.17 

.6429 

5.83 

1  .7630 

6.49 

.8703 

3.86 

.3507 

4.52 

.5085 

5.18 

.6448 

5.84 

1.7647 

6.50 

.8718 

106 


HYPERBOLIC  LOGARITHMS. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No 

Log. 

6.51 

1.8733 

7.15 

.9671 

7.79 

2.0528 

8.66 

2.1587 

9.94 

2.2966 

6.52 

1.8749 

7.16 

.9685 

7.80 

2.0541 

8.68 

2.1610 

9.96 

2.2986 

6.53 

1  .8764 

7.17 

.9699 

7.81 

2.0554 

8.70 

2.1633 

9.98 

2.3006 

6.54 

1.8779 

7.18 

.9713 

7.82 

2.0567 

8.72 

2  1656 

10.00 

2.3026 

6.55 

1.8795 

7.19 

.9727 

7.83 

2.0580 

8.74 

2.1679 

10.25 

2.3279 

6.56 

1.8810 

7.20 

.9741 

7.84 

2.0592 

8.76 

2.1702 

10.50 

2.3513 

6.57 

1.8825 

7.21 

.9754 

7.85 

2.0605 

8.78 

2.1725 

10.75 

2.3749 

6.58 

1  .8840 

7.22 

.9769 

7.86 

2.0618 

8.80 

2.1748 

11.00 

2.3979 

6.59 

1.8856 

7.23 

.9782 

7.87 

2.0631 

8.82 

2.1770 

11.25 

2.4201 

6.60 

1.8871 

7.24 

.9796 

7.88 

2.0643 

8.84 

2.1793 

11.50 

2.4430 

6.61 

1  .8886 

7.25 

.9810 

7.89 

2.0656 

8.86 

2.1815 

11.75 

2.4636 

6.62 

1.8901 

7.26 

.9824 

7.90 

2.0669 

8.88 

2.1838 

12.00 

2.4849 

6.63 

1.8916 

7.27 

.9838 

7.91 

2.0681 

8.90 

2.1861 

12.25 

2.5052 

6.64 

1  .893  1 

7.28 

.9851 

7.92 

2.0694 

8.92 

2.1883 

12.50 

2.5262 

6.65 

1  .8946 

7.29 

.9865 

7.93 

2.0707 

8.94 

2.1905 

12.75 

2.5455 

6.66 

1  8961 

7.30 

.9879 

7.94 

2.0719 

8.96 

2.1928 

13.00 

2.5649 

6.67 

1.8976 

7.31 

.9892 

7.95 

2.0732 

8.98 

2.1950 

13.25 

2.5840 

6.68 

1.8991 

7.32 

.9906 

7.96 

2.0744 

9.00 

2.1972 

13.50 

2.6027 

6.69 

1  .9006 

7.33 

.9920 

7.97 

2.0757 

9.02 

2.1994 

13.75 

2.621  1 

6.70 

1.9021 

7.34 

.9933 

7.98 

2.0769 

9.04 

2.2017 

14.00 

2.6391 

6.71 

1  .9036 

7.35 

.9947 

7.99 

2.0782 

9.06 

2.2039 

14.25 

2.6567 

6.72 

1.9051 

7.36 

.9961 

800 

2.0794 

9.08 

2.2061 

14.50 

2.6740 

6.73 

1  .9066 

7.37 

.9974 

8.01 

2.0807 

9.10 

2.2083 

14.75 

2.6913 

6.74 

1.9081 

7.38 

.9988 

8.02 

2.0819 

9.12 

2.2105 

15.00 

2.7081 

6.75 

1  .9095 

7.39 

2.0001 

8.03 

2.0832 

9.14 

2.2127 

15.50 

2.7408 

6.76 

1.9110 

7.40 

2.0015 

8.04 

2.0844 

9.16 

2.2148 

16.00 

2.7726 

6.77 

1.9125 

7.41 

2.0028 

8.05 

2.0857 

9.18 

2.2170 

16.50 

2.8034 

6.78 

1.9140 

7.42 

2.0041 

8.06 

2.0869 

9.20 

2.2192 

17.00 

2.8332 

6.79 

1.9155 

7.43 

2.0055 

8.07 

2.0882 

9.22 

2.2214 

17.50 

2.8621 

6.80 

1.9169 

7.44 

2.0069 

8.08 

2.0894 

924 

2.2235 

18.00 

2.8904 

6.81 

1.9184 

7.45 

2.0082 

8.09 

2.0906 

9.26 

2.2257 

18.50 

2.9178 

6.82 

1.9199 

7.46 

2.0096 

8.10 

2.0919 

9.28 

2.2279 

19.00 

2.9444 

6.83 

1.9213 

7.47 

2.0108 

8.11 

2.0931 

9.30 

2.2300 

19.50 

2.9703 

6.84 

1  .9228 

7.48 

2.0122 

8.12 

2.0943 

9.32 

2.2322 

20.00 

2.9957 

6.85 

1  .9242 

7.49 

2.0136 

8.13 

2.0956 

9.34 

2.2343 

21 

3.0445 

6.86 

1.9257 

7.50 

2.0149 

8,14 

2.0968 

9.36 

2.2364 

22 

3.0910 

6.87 

1.9272 

7.51 

2.0162 

8.15 

2.0980 

9.38 

2.2386 

23 

3.1355 

6.88 

1  .9286 

7.52 

2.0176 

8.16 

2.0992 

9.40 

2.2407 

24 

3.1781 

6.89 

1.9301 

7.53 

2.0189 

8.17 

2.1005 

9:42 

2.2428 

25 

3.2189 

6.90 

1  .93  1  5 

7.54 

2.0202 

8.18 

2.1017 

9.44 

2.2450 

26 

3.2581 

N6.91 

1  .9330 

7.55 

2.0215 

8.19 

2.1029 

9.46 

2.2471 

27 

3.2958 

6.92 

1.9344 

7.56 

2.0229 

8.20 

2.1041 

9.48 

2.2492 

28 

3.3322 

6.93 

1.9359 

7.57 

2.0242 

8.22 

2.1066 

9.50 

2.2513 

29 

3.3673 

6.94 

1.9373 

7.58 

2.0255 

8.24 

2.1090 

9.52 

2.2534 

30 

3.4012 

6.95 

1.9387 

7.59 

2.0268 

8.26 

2.1114 

9.54 

2.2555 

31 

3.4340 

6.96 

1  .9402 

7.60 

2.0281 

8.28 

2.1138 

9.56 

2.2576 

32 

3.4657 

6.97 

1.9416 

7.61 

2.0295 

8.30 

2.1163 

9.58 

2.2597 

33 

3.4965 

6.98 

1  .9430 

7.62 

2.0308 

8.32 

2.1187 

9.60 

2.2618 

34 

3.5263 

6.99 

1  .9445 

7.63 

2.0321 

8.34 

2.1211 

9.62 

2.2638 

35 

3.5553 

7.00 

1  .9459 

7.64 

2.0334 

8.36 

2.1235 

9.64 

2.2659 

36 

3.5835 

7.01 

1  .9473 

7.65 

2.0347 

8.38 

2.1258 

9.66 

2.2680 

37 

3.6109 

7.02 

1  .9488 

7.66 

2.0360 

8.40 

2.1282 

9.68 

2.2701 

38 

3.6376 

7.03 

1  .9502 

7.67 

2.0373 

8.42 

2.1306 

9.70 

2.2721 

39 

3.6636 

7.04 

1.9516 

7.68 

2.0386 

8.44 

2.1330 

9.72 

2.2742 

40 

3.6889 

7.05 

1.9530 

7.69 

2.0399 

8.46 

2.1353 

9.74 

2.2762 

41 

3.71J6 

7.06 

1.9544 

7.70 

2.0412 

8.48 

2.1377 

9.76 

2.2783 

42 

3.7377 

7.07 

1.9559 

7.71 

2.0425 

8.50 

2.1401 

9.78 

2.2803 

43 

3.7612 

7.08 

1.9573 

7.72 

2.0438 

8.52 

2.1424 

9.80 

2.2824 

44 

3.7842 

7.09 

1.9587 

7.73 

2.0451 

8.54 

2.1448 

9.82 

2.2844 

45 

3.8067 

7.10 

1.9601 

7.74 

2.0464 

8.56 

2.1471 

9.84 

2.2865 

46 

3.8286 

7.11 

1.9615 

7.75 

2.0477 

8.58 

2.1494 

9.86 

2.2885 

47 

3.8501 

7.12 

1  .9629 

7.76 

2.0490 

8.60 

2.1518 

9.88 

2.2905 

48 

3.8712 

7.13 

1  .9643 

7.77 

2.0503 

8.62 

2.1541 

9.90 

2.2925 

49 

3.8918 

7.14 

1.9657 

7.78 

2.0516 

8.64 

2.1564 

9.92 

2.2946 

50 

3.9120 

LOGARITHMIC    TRIGONOMETRICAL   FUNCTIONS. 


167 


LOGARITHMIC   SINES,  ETC. 


1 

Sine. 

Cosec. 

Versin. 

Tangent 

Cotan. 

Covers. 

Secant. 

Cosine. 

bb 

0) 

Q 

o 

n.Neg. 

nfinite. 

n.Neg. 

In.Neg. 

Infinite. 

0.00000 

1  0.00000 

0.00000 

90 

1 

.24186 

1.75814 

6.18271 

8.24192 

11.75808 

9.99235 

10.00007 

9.99993 

89 

2 

.54282 

1.43718 

6.78474 

8.54308 

1  1  .45692 

9.98457 

10.00026 

9.99974 

88 

3 

.71880 

1.28120 

7.13687 

8.71940 

1  1  .28060 

9.97665 

10.00060 

9.99940 

87 

4 

.84358 

1.15642 

7.38667 

8.84464 

11.15536 

9.96860 

10.00106 

9.99894 

80 

5 

.94030 

1.05970 

7.58039 

8.94195 

1  1  .05805 

9.96040 

10.00166 

9.99834 

85 

6 

.01923 

0.98077 

7.73863 

9.02162 

10.97838 

9.95205 

10.00239 

999761 

84 

7 

9.08589 

0.91411 

7.87238 

9.08914 

10.91086 

9.94356 

10.00325 

9.99675 

83 

8 

.14356 

0.85644 

7.98820 

9.14780 

10.85220 

9.93492 

10.00425 

9.99575 

82 

9 

.19433 

0.80567 

8.09032 

9.19971 

10.80029 

9.92612 

0.00538 

9.99462 

81 

10 

9.23967 

0.76033 

8.18162 

9.24632 

10.75368 

9.91717 

10.00665 

9.99335 

80 

11 

9.28060 

0.71940 

8.26418 

9.28865 

10.71135 

9.90805 

10.00805 

9.99195 

79 

12 

9.31788 

0.68212 

8.33950 

9.32747 

10.67253 

9.89877 

10.00960 

9.99040 

78 

13 

9.35209 

0.64791 

8.40875 

9.36336 

0.63664 

9.88933 

10.01128 

9.98872 

77 

14 

9.38368 

0.61632 

8.47282 

9.39677 

0.60323 

9.87971 

10.01310 

9.98690 

76 

15 

9.41300 

0.58700 

8.53243 

9.42805 

10.57195 

9.86992 

10.01506 

9.98494 

75 

16 

9.44034 

0.55966 

8.58814 

9.45750 

10.54250 

9.85996 

10.01716 

9.98284 

74 

17 

9.46594 

0.53406 

8.64043 

9  48534 

10.51466 

9.84981 

10.01940 

9.98060 

73 

18 

9  48998 

0.51002 

8.68969 

9.51178 

10.48822 

9.83947 

10.02179 

9.97821 

72 

19 

9.51264 

10.48736 

8.73625 

9.53697 

10.46303 

9.82894 

10.02433 

9.97567 

71 

20 

9.53405 

10.46595 

8.78037 

9.56107 

10.43893 

9.81821 

10.02701 

9.97299 

70 

21 

9.55433 

10.44567 

8.82230 

9.58418 

10.41582 

9.80729 

10.02985 

9.97015 

69 

22 

9.57358 

10.42642 

8.86223 

9.60641 

10.39359 

9.79615 

10.03283 

9.96717 

68 

23 

9.59188 

10.40812 

8.90034 

9.62785 

10.37215 

9.78481 

10.03597 

9.96403 

67 

24 

9.6093  1 

10.39069 

8.93679 

9.64858 

10.35142 

9.77325 

10.03927 

9.96073 

66 

25 

9.62595 

10.37405 

8.97170 

9.66867 

10.33133 

9.76146 

10.04272 

9.95728 

65 

26 

9.64184 

10.35816 

9.00521 

9.68818 

10.31182 

9.74945 

10.04634 

9.95366 

64 

27 

9.65705 

10.34295 

9.03740 

9.70717 

10.29283 

9.73720 

10.05012 

9.94988 

63 

28 

9.67161 

10.32839 

9.06838 

9.72567 

10.27433 

9.72471 

10.05407 

9.94593 

62 

29 

9.68557 

10.31443 

9.09823 

9.74375 

10.25625 

9.71197 

10.05818 

9.94182 

61 

30 

9.69897 

10.30103 

9.12702 

9.76144 

10.23856 

9.69897 

10.06247 

9.93753 

60 

31 

9.71184 

10.28816 

9.15483 

9.77877 

10.22123 

9.68571 

10.06693 

9.93307 

59 

32 

9.72421 

10.27579 

9.18171 

9.79579 

10.20421 

9.67217 

10.07158 

9.92842 

58 

33 

9.73611 

10.26389 

9.20771 

9.81252 

10.18748 

9.65836 

10.07641 

9.92359 

57 

34 

9.74756 

10.25244 

9.23290 

9.82899 

10.17101 

9.64425 

10.08143 

9.91857 

56 

35 

9.75859 

10.24141 

9.25731 

9.84523 

10.15477 

9.62984 

10.08664 

9.91336 

55 

36 

9.76922 

10.23078 

9.28099 

9.86126 

10.13874 

9.61512 

10.09204 

9.90796 

54 

37 

9.77946 

10.22054 

9.30398 

9.87711 

10.12289 

9.60008 

10.09765 

9.90235 

53 

38 

9.78934 

10.21066 

9.32631 

9.89281 

10.10719 

9.58471 

10.10347 

9.89653 

52 

39 

9.79887 

10.20113 

9.34802 

9.90837 

10.09163 

9.56900 

10.10950 

9.89050 

51 

40 

9.80807 

10.19193 

9.36913 

9.92381 

10.07619 

9.55293 

10.11575 

9.88425 

50 

41 

9.81694 

10.18306 

9.38968 

9.93916 

10.06084 

9.53648 

10.12222 

9.87778 

49 

42 

9.82551 

10.17449 

9.40969 

9.95444 

10.04556 

9.51966 

10.12893 

9.87107 

48 

43 

9.83378 

10.16622 

9.42918 

9.96966 

10.03034 

9.50243 

10.13587 

9.86413 

47 

44 

9.84177 

10.15823 

9.44818 

9.98484 

10.01516 

9.48479 

10.14307 

9.85693 

46 

45 

9.84949 

10.15052 

9.4667 

10.00000 

10.00000 

9.46671 

10.15052 

9.84949 

45 

Cosine 

Secant. 

Covers 

Cotan. 

Tangent 

Versin. 

Cosec. 

Sine. 

From  45°  to  90°  read  from  bottom  of  table  upwards. 


168 


LOGARITHMS   OF  NUMBERS. 


Four-place  Logarithms  of  Numbers  to   1000. 

For  six-place  logarithms  of  numbers  to  10,000,  see  pp.  137  to  164. 


No. 

0 

1 

2 

3 

4 

5 

6 

1 

8 

9 

No. 

0 

0000 

3010 

4771 

6021 

6990 

7782 

8451 

9031 

9542 

0 

2 
3 

4 
5 
6 
7 
8 
9 

0000 
3010 
4771. 
6021 
6990 
7782 
8451 
9031 
9542 

0414 
3222 
4914 
6128 
7076 
7853 
8513 
9085 
9590 

0792 
3424 
5052 
6232 
7160 
7924 
8573 
9138 
9638 

1139 
3617 
5185 
6335 
7243 
7993 
8633 
9191 
9685 

1461 
3802 
5315 
6435 
7324 
8062 
8692 
9243 
9731 

1761 
3979 
5441 
6532 
7404 
8129 
8751 
9294 
9777 

2041 
4150 
5563 
6628 
7482 
8195 
8808 
9345 
9823 

2304 
4314 
5682 
6721 
7559 
8261 
8865 
9395 
9868 

2553 
4472 
5798 
6812 
7634 
8325 
8921 
9445 
9912 

2788 
4624 
5911 
6902 
7709 
8388 
8976 
9494 
9956 

1 
2 
3 
4 
5 
6 
7 
8 
9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

10 

It 
12 
13 
14 
15 
16 
17 
18 
19 

0414 
0792 
1139 
1461 
1761 
2041 
2304 
2553 
2788 

0453 
0828 
1173 
1492 
1790 
2068 
2330 
2577 
2810 

0492 
0864 
1206 
1523 
1818 
2095 

2355 
2601 
2833 

0531 
0899 
1239 
1553 
1847 
2122 
2380 
2625 
2856 

0569 
0934 
1271 
1584 
1875 
2148 
2405 
2648 
2878 

0607 
0969 
1303 
1614 
1903 
2175 
2430 
2672 
2900 

0645 
1004 
1335 
1644 
1931 
2201 
2455 
2695 
2923 

0682 
1038 
1367 
1673 
1959 
2227 
2480 
2718 
2945 

0719 
1072 
1399 
1703 
1987 
2253 
2504 
2742 
2967 

0755 
1106 
1430 
1732 
2014 
2279 
2529 
2765 
2989 

11 

12 
13 
14 
15 
16 
17 
18 
19 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

3222 

3424 
3617 
3802 
3979 
4150 
4314 
4472 
4624 

3243 
3444 
3636 
3820 
3997 
4166 
4330 
4487 
4639 

3263 
3464 
3655 
3838 
4014 
4183 
4346 
4502 
4654 

3284 
3483 
3674 
3856 
4031 
4200 
4362 
4518 
4669 

3304 
3502 
3692 
3874 
4048 
4216 
4378 
4533 
4683 

3324 
3522 
3711 
3892 
4065 
4232 
4393 
4548 
4698 

3345 
3541 
3729 
3909 
4082 
4249 
4409 
4564 
4713 

3365 
3560 
3747 
3927 
4099 
4265 
4425 
4579 
4728 

3385 
3579 
3766 
3945 
4116 
4281 
4440 
4594 
4742 

3404 
3598 
3784 
3962 
4133 
4298 
4456 
4609 
4757 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 

4914 
5052 
5185 
5315 
5441 
5563 
5682 
5798 
5911 

4928 
5065 
5198 
5328 
5453 
5575 
5694 
5809 
5922 

4942 
5079 
5211 
5340 
5465 
5587 
5705 
5821 
5933 

4955 
5092 
5224 
5353 
5478 
5599 
5717 
5832 
5944 

4969 
5105 
5237 
5366 
5490 
5611 
5729 
5843 
5955 

4983 
5119 
5250 
5378 
5502 
5623 
5740 
5855 
5966 

4997 
5132 
5263 
5391 
5515 
5635 
5752 
5866 
5977 

5011 
5145 
5276 
5403 
5527 
5647 
5763 
5877 
5988 

5024 
5159 
5289 
5416 
5539 
5658 
5775 
5888 
5999 

5038 
5172 
5302 
5428 
5551 
5670 
5786 
5899 
6010 

31 
32 
33 
34 
35 
36 
37 
38 
39 

40 

6021- 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

40 

41 
42 
43 
44 
45 
46 
47 
48 
49 

6128 
6232 
6335 
6435 
6532 
6628 
6721 
6812 
6902 

6138 
6243 
6345 
6444 
6542 
6637 
6730 
6821 
6911 

6149 
6253 
6355 
6454 
6551 
6646 
6739 
6830 
6920 

6160 
6263 
6365 
6464 
6561 
6656 
6749 
6839 
6928 

6170 
6274 
6375 
6474 
6571 
6665 
6758 
6848 
6937 

6180 
6284 
6385 
6484 
6580 
6675 
6767 
6857 
6946 

6191 
6294 
6395 
6493 
6590 
6684 
6776 
6866 
6955 

6201 
6304 
6405 
6503 
6599 
6693 
6785 
6875 
6964 

6212 
6314 
6415 
6513 
6609 
6702 
6794 
6884 
6972 

6222 
6325 
6425 
6522 
6618 
6712 
6803 
6893 
6981 

41 
42 
43 
44 
45 
46 
47 
48 
49 

50 

6990 

6998 

7007 

7016' 

7024 

7033 

7042 

7050 

7059 

7067 

50 

LOGARITHMS  OP  NUMBERS. 


169 


Four-place  Logarithms  of  Numbers  to  1000. 

For  six-place  logarithms  of  numbers  to  10,000,  see  pp.  137  to  164. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

No. 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

50 

51 
52 
53 

7076 
7160 

7243 

7084 
7168 
7251 

7093 
7177 
7259 

7101 

7185 
7267 

7110 
7193 
7275 

7118 
7202 
7284 

7126 
7210 
7292 

7135 
7218 
7300 

7143 
7226 
7308 

7152 
7235 
7316 

51 

52 
53 

54 
55 
56 

7324 
7404 
7482 

7332 
7412 
7490 

7340 
7419 
7497 

7348 
7427 
7505 

7356 
7435 
7513 

7364 
7443 
7520 

7372 
7451 
7528 

7380 
7459 
7536 

7388 
7466 
7543 

7396 
7474 
7551 

54 
55 
56 

57 
58 
59 

7559 
7634 
7709 

7566 
7642 
7716 

7574 
7649 
7723 

7582 
7657 
7731 

7589 
7664 
7738 

7597 
7672 

7745 

7604 
7679 
7752 

7612 
7686 
7760 

7619 
7694 
7767 

7627 
7701 
7774 

57 
58 
59 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

60 

61 
62 
63 

7853 
7924 
7993 

7860 
7931 
8000 

7868 
7938 
8007 

7875 
7945 
8014 

7882 
7952 
8021 

7889 
7959 
8028 

7896 
7966 
8035 

7903 
7973 
8041 

7910 
7980 
8048 

7917 
7987 
8055 

61 
62 
63 

64 
65 
66 

8062 
8129 
8195 

8069- 
8136 
8202 

8075 
8142 
8209 

8082 
8149 
8215 

8089 
8156 
8222 

8096 
8162 
8228 

8102 
8169 
8235 

8109 
8176 
8241 

8116 
8182 
8248 

8122 
8189 
8254 

64 
65 
66 

67 
68 
69 

8261 
8325 
8388 

8267 
8331 
8395 

8274 
8338 
8401 

8280 
8344 
8407 

8287 
8351 
8414 

8293 
8357 
8420 

8299 
8363 
8426 

8306 
8370 
8432 

8312 
8376 
8439 

8319 

8382 
8445 

67 
68 
69 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

70 

71 
72 
73 

8513 
8573 
8633 

8519 
8579 
8639 

8525 
8585 
8645 

8531 
8591 
8651 

8537 
8597 
8657 

8543 
8603 
8663 

8549 
8609 
8669 

8555 
8615 
8675 

8561 
8621 
8681 

8567 
8627 
8686 

71 
72 
73 

74 
75 
76 

8692 
8751 
8808 

8698 
8756 
8814 

8704 
8762 
8820 

8710 
8768 
8825 

8716 
8774 
8831 

8722 
8779 
8837 

8727 
8785 
8842 

8733 
8791 
8848 

8739 
8797 
8854 

8745 
8802 
8859 

74 
75 
76 

77 
78 
79 

8865 
8921 
8976 

8871 
8927 
8982 

8876 
8932 
8987 

8882 
8938 
8993 

8887 
8943 
8998 

8893 
8949 
9004 

8899 
8954 
9009 

8904 
8960 
9015 

8910 
8965 
9020 

8915 
8971 
9025 

77 
78 
79 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

80 

81 
82 
83 

9085 
9138 
9191 

9090 
9143 
9196 

9096 
9149 
9201 

9101 
9154 
9206 

9106 
9159 
9212 

9112 
9165 
9217 

9117 
9170 
9222 

9122 
9175 
9227 

9128 
9180 
9232 

9133 
9186 
9238 

81 
82 
83 

84 
85 
86 

9243 
9294 
9345 

9248 
9299 
9350 

9253 
9304 
9355 

9258 
9309 
9360 

9263 
9315 
9365 

9269 
9320 
9370 

9274 
9325 
9375 

9279 
9330 
9380 

9284 
9335 
9385 

9289 
9340 
9390 

84 
85 
86 

87 
88 
89 

9395 
9445 
9494 

9400 
9450 
9499 

9405 
9455 
9504 

9410 
9460 
9509 

9415 
9465 
9513 

9420 
9469 
9518 

9425 
9474 
9523 

9430 
9479 
9528 

9435 
9484 
9533 

9440 
9489 
9538 

87 
88 
89 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

90 

91 
92 
93 

9590 
9638 
9685 

9595 
9643 
9689 

9600 
9647 
9694 

9605 
9652 
9699 

9609 
9657 
9703 

9614 
9661 
9708 

9619 
9666 
9713 

9624 
9671 
9717 

9628 
9675 
9722 

9633 
9680 
9727 

91 
92 
93 

94 
95 
96 

9731 
9777 
9823 

9736 
9782 
9827 

9741 
9786 
9832 

9745 
9791 
9836 

9750 
9795 
9841 

9754 
9800 
9845 

9759 
9805 
9850 

9764 
9809 
9854 

9768 
9814 
9859 

9773 
9818 
9863 

94 
95 
96 

97 
98 
99 

9868 
9912 
9956 

9872 
9917 
9961 

9877 
9921 
9965 

9881 
9926 
9969 

9886 
9930 
9974 

9890 
9934 
9978 

9894 
9939 
9983 

9899 
9943 
9987 

9903 
9948 
9991 

9908 
9952 
9996 

97 
98 
99 

100 

0000 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

0035 

0039 

100 

170          NATURAL   TRIGONOMETRICAL   FUNCTIONS. 


NATURAL  TRIGONOMETRICAL,  FUNCTIONS. 


• 

M. 

Sine. 

Co- 
Vers. 

Cosec. 

Tang. 

Co  tan. 

Se- 
cant. 

Ver. 

Sin. 

Cosine. 

o 

0 

.00000 

1  .0000 

Infinite 

.00000 

Infinite 

.0000 

.00000 

1.0000 

1)0 

^ 

15 

.00436 

.99564 

229.18 

.00436 

229.18 

.0000 

.00001 

.99999 

45 

30 

.00873 

.99127 

114.59 

.00873 

114.59 

.0000 

.00004 

.99996 

30 

45 

.01309 

.98691 

76.397- 

.01309 

76.390 

.0001 

.00009 

.99991 

15 

1 

0 

.01745 

.98255 

57.299 

.01745 

57.290 

.0001 

.00015 

.99985 

89 

0 

15 

.02181 

.97819 

45.840. 

.02182 

45.829 

.0002 

.00024 

.99976 

45 

30 

.02618 

.97382 

38.202 

.02618 

38.188 

.0003 

.00034 

.99966 

30 

45 

.03054 

.96946 

32.746 

.03055 

32.730 

.0005 

.00047 

.99953 

15 

2 

0 

.03490 

.96510 

28.654 

.03492 

28.636 

.0006 

.00061 

.99939 

88 

0 

15 

.03926 

.96074 

25.471 

.03929 

25.452 

.0008 

.00077 

.99923 

45 

30 

.G4362 

.95638 

22.926 

.04366 

22.904 

.0009 

.00095 

.99905 

30 

45 

.04798 

.95202 

20.843 

.04803 

20.819 

.0011 

.00115 

.99885 

15 

3 

0 

.05234 

.94766 

19.107 

.05241 

19.081 

.0014 

.00137 

.99863 

87 

0 

15 

.05669 

.9433  1 

17.639 

.05678 

17.611 

.0016 

.00161 

.99839 

45 

30 

.06105 

.93895 

16.380 

.06116 

16.350 

.0019 

.00187 

.9981.3 

30 

45 

.06540 

.93460 

15.290 

.06554 

15.257 

.0021 

.00214 

.99786 

15 

4 

0 

.06976 

.93024 

14.336 

.06993 

14.301 

.0024 

.00244 

.99756 

80 

0 

15 

.07411 

.92589 

13.494 

.07431 

13.457 

.0028 

.00275 

.99725 

45 

30 

.07846 

.92154 

12.745 

.07870 

12.706 

.0031 

.00308 

.99692 

30 

45 

.08281 

.91719 

12.076 

.08309 

12.035 

.0034 

.00343 

.99656 

15 

5 

0 

.08716 

.91284 

11.474 

.08749 

11.430 

.0038 

.00381 

.99619 

85 

0 

15 

.09150 

.90850 

10.929 

.09189 

10.883 

.0042 

.00420 

.99580 

45 

30 

.09585 

.90415 

10.433 

.09629 

10.385 

.0046 

.00460 

.99540 

30 

45 

.10019 

.89981 

9.9812 

.10069 

9.9310 

.0051 

.00503 

.99497 

15 

6 

0 

.10453 

.89547 

9.5668 

.10510 

9.5144 

.0055 

.00548 

.99452 

84 

0 

15 

.10887 

.89113 

9.1855 

.10952 

9.1309 

.0060 

.00594 

.99406 

45 

30 

.11320 

.88680 

8.8337 

.11393 

8.7769 

.0065 

.00643 

.99357 

30 

45 

.11754 

.88246 

8.5079 

.11836 

8.4490 

.0070 

.00693 

.99307 

15 

7 

0 

.12187 

.87813 

8.2055 

.12278 

8.1443 

.0075 

.00745 

.99255 

83 

0 

15 

.12620 

.87380 

7.9240 

.12722 

7.8606 

.0081 

.00800 

.99200 

45 

30 

.13053 

.86947 

7.6613 

.13165 

7.5958 

.0086 

.00856 

.99144 

30 

45 

.13485 

.86515 

7.4156 

.13609 

7.3479 

.0092 

.00913 

.99086 

15 

8 

0 

.13917 

.86083 

7.1853 

.14054 

7.1154 

.0098 

.00973 

.99027 

82 

0 

15 

.14349 

.85651 

6.9690 

.14499 

6.8969 

.0105 

.01035 

.98965 

45 

30 

.14781 

.85219 

6.7655 

.14945 

6.6912 

.0111 

.01098 

.98902 

30 

45 

.15212 

.84788 

6.5736 

.15391 

6.4971 

.0118 

.01164 

.98836 

15 

9 

0 

.15643 

.84357 

6.3924 

.15838 

6.3138 

.0125 

.01231 

.98769 

81 

0 

15 

.16074 

.83926 

6.2211 

.16286 

6.1402 

.0132 

.01300 

.98700 

45 

30 

.16505 

.83495 

6.0589 

.16734 

5.9758 

.0139 

.01371 

.98629 

30 

45 

.16935 

.83065 

5.9049 

.17183 

'5.8197 

.0147 

.01444 

.98556 

15 

10 

0 

.17365 

.82635 

5.7588 

.17633 

5.6713 

.0154 

.01519 

.98481 

80 

0 

15 

.17794 

.82206 

5.6198 

.18083 

5.5301 

.0162 

.01596 

.98404 

45 

30 

.18224 

.81776 

5.4874 

.18534 

5.3955 

.0170 

.01675 

.98325 

30 

45 

.18652 

.81348 

5.3612 

.18986 

5.2672 

.0179 

.01755 

.98245 

15 

11 

0 

.19081 

.80919 

5.2408 

.19438 

5.1446 

.0187 

.01837 

.98163 

79 

0 

15 

.19509 

.80491 

5.1258 

.19891 

5.0273 

.0196 

,01921 

.98079 

45 

30 

.19937 

.80063 

5.0158 

.20345 

4.9152 

.0205 

.02008 

.97992 

30 

45 

.20364 

.79636 

4.9106 

.20800 

4.8077 

.0214 

.02095 

.97905 

15 

13 

0 

.20791 

.79209 

4.8097 

.21256 

4.7046 

.0223 

.02185 

.97815 

78 

0 

15 

.21218 

.78782 

4.7130 

21712 

4.6057 

.0233 

.02277 

.97723 

45 

30 

.21644 

.78356 

4.6202 

.22169 

4.5107 

.0243 

.02370 

.97630 

30 

45 

.22070 

.77930 

4.5311 

.22628 

44194 

.0253 

.02466 

.97534 

15 

13 

0 

.22495 

.77505 

4.4454 

.23087 

4.3315 

.0263 

.02563 

.97437 

77 

0 

15 

.22920 

.77080 

4.3630 

.23547 

4.2468 

.0273 

.02662 

.97338 

45 

30 

.23345 

.76655 

4.2837 

.24008 

4.1653 

.0284 

.02763 

.97237 

30 

45 

.23769 

.76231 

4.2072 

.24470 

4.0867 

.0295 

.02866 

.97134 

15 

14 

0 

24192 

.75808 

4.1336 

.24933 

4.0108 

.0306 

.02970 

.97030 

76 

0 

15 

.24615 

.75385 

4.0625 

25397 

3.9375 

.0317 

.03077 

.96923 

45 

30 

.25038 

.74962 

3.9939 

.25862 

3.8667 

.0329 

.03185 

.96815 

30 

45 

.25460 

.74540 

3.9277 

.26328 

3.7983 

.0341 

.03295 

.96705 

15 

15 

0 

.25882 

.74118 

3.8637 

.26795 

3.7320 

1.0353 

.03407 

.96593 

!•> 

0 

Co- 
sine. 

Ver. 

Sin. 

Secant. 

Cotan 

Tang. 

Cosec. 

Co- 
Vers. 

Sine. 

0 

M; 

From  75°  to  90°  read  from  bottom  of  table  upwards. 


NATURAL  TRIGONOMETRICAL   FUNCTIONS. 


171 


• 

M. 

Sine. 

Co- 
Vers. 

Cosec 

Tang 

Cotan 

Secant 

Ver. 

Sin. 

Cosine 

I 

15~ 

~0~ 

.25882 

.74118 

3.8637 

.26795 

3.7320 

1.0353 

.03407 

.96593 

75 

~ 

15 

.26303 

.73697 

3.8018 

.27263 

3.6680 

1.0365 

.03521 

.96479 

45 

30 

.26724 

.73276 

3.7420 

.27732 

3.6059 

1.0377 

.03637 

.96363 

30 

45 

.27144 

.72856 

3.6840 

.28203 

3.5457 

1.C390 

.03754 

.96246 

15 

16 

0 

.27564 

.72436 

3.6280 

.28674 

3.4874 

1  .0403 

.03874 

.96126 

74 

0 

15 

.27983 

.72017 

3.5736 

.29147 

3.4308 

1.0416 

.03995 

.96005 

45 

30 

.28402 

.71598 

3.5209 

.29621 

3.3759 

1.0429 

.04118 

.95882 

30 

45 

.28820 

.71180 

3.4699 

.30096 

3.3226 

1  .0443 

.04243 

.95757 

15 

17 

0 

.29237 

.70763 

3.4203 

.30573 

3.2709 

1.0457 

.04370 

.95630 

73 

0 

15 

.29654 

.70346 

3.3722 

.31051 

3.2205 

1.0471 

.04498 

.95502 

45 

30 

.30070 

.69929 

3.3255 

.31530 

3.1716 

1  .0485 

.04628 

.95372 

30 

45 

.30486 

69514 

3.2801 

.32010 

3.1240 

1.0500 

.04760 

.95240 

15 

18 

0 

.30902 

69098 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

.95106 

72 

0 

15 

31316 

68684 

3.1932 

.32975 

3.0326 

1.0530 

.05030 

.94970 

45 

30 

31730 

.68270 

3.1515 

.33459 

2.9887 

1.0545 

.05168 

.94832 

30 

45 

32144 

67856 

3.1110 

.33945 

2.9459 

1  .0560 

.05307 

.94693 

15 

19 

0 

32557 

67443 

3.0715 

34433 

2.9042 

1.0576 

.05448 

.94552 

71 

0 

15 

32969 

67031 

3.0331 

.34921 

2.8636 

1  .0592 

.05591 

.94409 

45 

30 

33381 

66619 

2.9957 

35412 

2.8239 

1  .0608 

.05736 

.94264 

30 

45 

33792 

66208 

2.9593 

35904 

2.7852 

1  .0625 

.05882 

.94118 

!5 

20 

0 

34202 

65798 

2.9238 

36397 

2.7475 

1  .0642 

.0603  1 

.93969 

70 

0 

15 

34612 

65388 

2.8892 

36892 

2.7106 

1  .0659 

.06181 

.93819 

45 

30 

35021 

64979 

2.8554 

37388 

2.6746 

1.0676 

.06333 

.93667 

30 

45 

35429 

64571 

2.8225 

37887 

2.6395 

1  .0694 

,.06486 

.93514 

1) 

21 

0 

35837 

64163 

2.7904 

38386 

2.6051 

1.0711 

.06642 

.93358 

69 

0 

15 

36244 

63756 

2.7591 

38888 

2.5715 

1.0729 

.06799 

.93201 

45 

30 

36650 

63350 

2.7285 

39391 

2.5386 

1.0748 

.06958 

.93042 

30 

45 

37056 

62944 

2.6986 

39896 

2.5065 

1.0766 

.07119 

.92881 

13 

22 

0 

37461 

62539 

2.6695 

40403 

2.4751 

1.0785 

.07282 

.92718 

68 

0 

15 

37865 

62135 

2.6410 

40911 

2.4443 

1  .0804 

.07446 

.92554 

45 

30 

38268 

61732 

2.6131 

41421 

2.4142 

1  .0824 

.07612 

.92388 

30 

45 

38671 

61329 

2.5859 

41933 

2.3847 

1  .0844 

.07780 

.92220 

15 

23 

0 

39073 

60927 

2.5593 

42447 

2.3559 

1  .0864 

.07950 

.92050 

67 

0 

15 

39474 

60526 

2.5333 

42963 

2.3276 

1  .0884 

.08121 

.91879 

45 

30 

39875 

60125 

2.5078 

43481 

2.2998 

1  .0904 

.08294 

.91706 

30 

45 

40275 

59725 

2.4829 

44001 

2.2727 

1  .0925 

.08469 

.91531 

15 

24 

0 

40674 

59326 

2.4586 

44523 

2.2460 

1.0946 

.08645 

.91355 

66 

0 

15 

41072 

58928 

2.4348 

45047 

2.2199 

1.0968 

.08824 

.91176 

45 

30 

41469 

58531 

2.4114 

45573 

2.1943 

1  .0989 

.09004 

.90996 

30 

45 

41866 

58134 

2.3886 

46101 

2.1692 

1.1011 

.09186 

.90814 

15 

25 

0 

42262 

57738 

2.3662 

46631 

2.1445 

1.1034 

.09369 

.90631 

65 

0 

15 

42657 

57343 

2.3443 

47163 

2.1203 

1.1056 

.09554 

.90446 

45 

30 

43051 

56949 

2.3228 

47697 

2.0965 

1.1079 

.09741 

.90259 

30 

45 

43445 

56555 

2.3018 

48234 

2.0732 

1.1102 

.09930 

.90070 

15 

26 

0 

43837 

56163 

2.2812 

48773 

2.0503 

1.1126 

.10121 

.89879 

64 

0 

15 

44229 

55771 

2.2610 

49314 

2.0278 

1.115.0 

.10313 

.89687 

45 

30 

44620 

55380 

2.2412 

49858 

2.0057 

1.1174 

.10507 

.89493 

30 

45 

45010 

54990 

2.2217 

50404 

1  .9840 

1.1198 

.10702 

.89298 

15 

27 

0 

45399 

54601 

2.2027 

50952 

1  .9626 

1.1223 

.10899 

.89101 

63 

0 

15 

45787 

54213 

2.1840 

51503 

1.9416 

1.1248 

.11098 

88902 

45 

30 

46175 

53825 

2.1657 

52057 

1.9210 

1.1274 

.11299 

.88701 

30 

45 

46561 

53439 

2.1477 

52612 

1  .9007 

1.1300 

.11501 

.88499 

15 

23 

0 

46947 

53053 

2.1300 

53171 

1  .8807 

1.1326 

.11705 

.88295 

62 

0 

15 

47332 

52668 

2.1127 

53732 

1.8611 

1.1352 

.11911 

.88089 

45 

30 

47716 

52284 

2.0957 

54295 

1.8418 

1.1379 

.12118 

.87882 

30 

45 

48099 

51901 

2.0790 

54862 

1.8228 

1.1406 

.12327 

.87673 

15 

29 

0 

48481 

51519 

2.0627 

55431 

1  .8040 

1.1433 

.12538 

.87462 

61 

0 

15 

48862 

51138 

2.0466 

56003 

1.7856 

1.1461 

.12750 

.87250 

45 

30 

49242 

50758 

2.0308 

56577 

1.7675 

1.1490 

.12964 

.87036 

30 

45 

49622 

.50378 

2.0152 

57155 

1.7496 

1.1518 

.13180 

.86820 

15 

30 

0 

50000 

.50000 

2.0000 

57735 

1.7320 

1.1547 

.13397 

.86603 

60 

_0 

Co- 
sine. 

Ver. 
Sin. 

Se- 
cant. 

Co  tan. 

Tang.. 

Cosec. 

Co- 
Vers. 

Sine. 

o 

M. 

From  60°  to  75°  read  from  bottom  of  table  upwards. 


172         NATUKAL   TRIGONOMETRICAL    FUNCTIONS. 


o 

M. 

Sine. 

Co- 
Vers. 

Cosec. 

Tang. 

Co  tan. 

Secant. 

Ver. 
Sin. 

Cosine 

80~ 

0 

.50000 

.50000 

2.0000 

.57735 

.7320 

.1547 

.13397 

.86603 

60 

0 

15 

.50377 

.49623 

.9850 

.58318 

.7147 

.1576 

.13616 

.86384 

45 

30 

.50754 

.49246 

.9703 

.58904 

.6977 

.1606 

.13837 

.86163 

30 

45 

.51129 

.48871 

.9558 

.59494 

.6808 

.1636 

.14059 

.85941 

15 

31 

0 

.51504 

.48496 

.9416 

.60086 

.6643 

.1666 

.14283 

.85717 

59 

0 

15 

.51877 

.48123 

.9276 

.60681 

.6479 

.1697 

.14509 

.85491 

45 

30 

.52250 

.47750 

.9139 

.61280 

.6319 

.1728 

.14736 

.85264 

30 

45 

.52621 

.47379 

.9004 

.61882 

.6160 

.1760 

.14965 

.85035 

15 

33 

0 

.52992 

.47008 

.8871 

.62487 

.6003 

.1792 

.15195 

.84805 

58 

0 

15 

.53361 

.46639 

.8740 

.63095 

.5849 

.1824 

.15427 

.84573 

45 

30 

.53730 

.46270 

.8612 

.63707 

.5697. 

.1857 

.15661 

.84339 

30 

45 

.54097 

.45903 

.8485 

.64322 

.5547 

.1890 

.15896 

.84104 

15 

33 

0 

.54464 

.45536 

.8361 

.64941 

5399 

.1924 

.16133 

.83867 

67 

0 

15 

.54829 

.45171 

.8238 

.65563 

.5253 

.1958 

.16371 

.83629 

45 

30 

.55194 

.44806 

.8118 

.66188 

.5108 

.1992 

.16611 

.83389 

30 

45 

.55557 

.44443 

.7999 

.66818 

.4966 

.2027 

.16853 

.83147 

15 

34 

0 

.55919 

.44081 

.7883 

.67451 

.4826 

.2062 

.17096 

.82904 

56 

0 

15 

.56280 

.43720 

.7768 

.68087 

.4687 

.2098 

.17341 

.82659 

45 

30 

.56641 

.43359 

.7655 

.68728 

.4550 

.2134 

.17587 

.82413 

30 

45 

.57000 

.43000 

.7544 

.69372 

.4415 

.2171 

.17835 

.82165 

15 

35 

0 

.57358 

.42642 

.7434 

.70021 

.4281 

.2208 

.18085 

.81915 

55 

0 

15 

.57715 

.42285 

.7327 

.70673 

.4150 

.2245 

.18336 

.81664 

45 

30 

.58070 

.41930 

.7220 

.71329 

.4019 

.2283 

.18588 

.81412 

30 

45 

.58425 

.41575 

.7116 

.71990 

.3891 

.2322 

.18843 

.81157 

15 

36 

0 

.58779 

.41221 

.7013 

.72654 

.3764 

.2361 

.19098 

.80902 

54 

0 

15 

.59131 

.40869 

.6912 

.73323 

.3638 

.2400 

.19356 

.80644 

45 

30 

.59482 

.40518 

.6812 

.73996 

.3514 

.2440 

.19614 

.80386 

30 

45 

.59832 

.40168 

.6713 

.74673 

.3392 

.2480 

.19875 

.80125 

15 

37 

0 

.60181 

.39819 

.6616 

.75355 

.3270 

.2521 

.20136 

.79864 

53 

0 

15 

.60529 

.39471 

.6521 

.76042 

.3151 

.2563 

.20400 

.79600 

45 

30 

.60876 

.39124 

.6427 

.76733 

.3032 

.2605 

.20665 

.79335 

30 

45 

.61222 

.38778 

.6334 

.77428 

.2915 

.2647 

.20931 

.79069 

15 

38 

0 

.61566 

.38434 

.6243 

.78129 

.2799 

.2690 

.21199 

.78801 

52 

0 

15 

.61909 

.38091 

.6153 

78834 

.2685 

.2734 

.21468 

.78532 

45 

30 

.62251 

.37749 

.6064 

.79543 

.2572 

.2778 

.21739 

.78261 

30 

45 

.62592 

.37408 

5976 

.80258 

.2460 

2822 

.22012 

.77988 

15 

39 

0 

.62932 

.37068 

.5890 

.80978 

.2349 

.2868 

.22285 

.77715 

51 

0 

15 

.63271 

.36729 

.5805 

.81703 

.2239 

.2913 

.22561 

.77439 

45 

30 

.63608 

.36392 

.5721 

.82434 

.2131 

.2960 

.22833 

.77162 

30 

45 

.63944 

.36056 

.5639 

.83169 

.2024 

.3007 

.23116 

.76884 

15 

40 

0 

.64279 

.35721 

.5557 

.83910 

.1918 

.3054 

.23396 

.76604 

50 

0 

15 

.64612 

.35388 

.5477 

.84656 

.1812 

.3102 

.23677 

.76323 

45 

30 

.64945 

.35055 

.5398 

.85408 

.1708 

.3151 

.23959 

.76041 

30 

45 

.65276 

.34724 

.5320 

.86165 

.1606 

.3200 

.24244 

.75756 

15 

41 

0 

.65606 

.34394 

.5242 

.86929 

.1504 

.3250 

.24529 

.75471 

49 

0 

15 

.65935 

.34065 

.5166 

.87698 

.1403 

.3301 

.24816 

.75184 

45 

30 

.66262 

.33738 

.5092 

.88472 

.1303 

.3352 

.25104 

.74896 

30 

45 

.66588 

.33412 

.5018 

.89253 

.1204 

.3404 

.25394 

.74606 

15 

42 

0 

.66913 

.33087 

.4945 

.90040 

.1106 

.3456 

.25686 

.74314 

48 

0 

15 

.67237 

.32763 

.4873 

.90834 

.1009 

.3509 

.25978 

.74022 

45 

30 

.67559 

.32441 

.4802 

.91633 

.0913 

.3563 

.26272 

.73728 

30 

45 

.67880 

.32120 

.4732 

.92439 

.0818 

.3618 

.26568 

.73432 

15 

43 

0 

.68200 

.31800 

.4663 

.93251 

.0724 

.3673 

.26865 

.73135 

47 

0 

15 

.68518 

.31482 

.4595 

.94071 

.0630 

.3729 

.27163 

.72837 

45 

30 

.68835 

.31165 

.4527 

.94896 

.0538 

.3786 

.27463 

.72537 

30 

45 

.69151 

.30849 

.4461 

.95729 

.0446 

.3843 

.27764 

.72236 

15 

44 

0 

.69466 

.30534 

.4396 

.96569 

.0355 

.3902 

.28066 

.71934 

46 

0 

15 

.69779 

.30221 

.4331 

.97416 

.0265 

.3961 

.28370 

.71630 

45 

30 

.70091 

.29909 

.4267 

.98270 

.0176 

.4020 

.28675 

.71325 

30 

45 

.70401 

.29599 

.4204 

.99131 

.0088 

.4081 

.28981 

.71019 

15 

45 

0 

.70711 

.29289 

.4142 

1  .0000 

.0000 

.4142 

.29289 

.70711 

45 

0 

Cosine 

Ver. 
Sin. 

Se- 
cant. 

Cotan. 

Tang. 

Cosec. 

Co- 
Vers. 

Sine. 

• 

M. 

From  45°  to  60°  read  from  bottom  of  table  upwards. 


SPECIFIC    GRAVITY. 


173 


MATERIALS. 

THE   CHEMICAL  ELEMENTS. 

Common  Elements  (42). 


•11 

«£ 

12 

«£ 

V 

OrC 

Name. 

|-s 

IJ 

Name. 

1^ 

fl 

Name. 

J't? 

Al 

Sb 

Aluminum 
Antimony 

27.1 
120.2 

F 
Au 

Fluorine 
Gold 

19. 
197.2 

Pd 
P 

Palladium 
Phosphorus 

106.7 
31. 

As 

Arsenic 

75.0 

H 

Hydrogen 

1.01 

Pt 

Platinum 

195.2 

Ba 

Barium 

137.4 

I 

Iodine 

126.9 

K 

Potassium 

39.1 

Bi 

Bismuth 

208.0 

Ir 

Iridium 

193.1 

Si 

Silicon 

28.3 

B 

Boron 

11.0 

Fe 

Iron 

55.84 

Ag 

Silver 

107.9 

Br 

Bromine 

79.9 

Pb 

Lead 

207.2 

Na 

Sodium 

23. 

Cd 

Cadmium 

112.4 

Li 

Lithium 

6.94 

Sr 

Strontium 

87.6 

Ca 

Calcium 

40.1 

Mg 

Magnesium 

24.34 

S 

Sulphur 

32.1 

C 

Carbon 

12. 

Mn 

Manganese 

54.9 

Sn 

Tin 

119. 

Cl 

Chlorine     • 

35.5 

Hg 

Mercury 

200.6 

Ti 

Titanium 

48.1 

Cr 

Chromium 

52.0 

Ni 

Nickel 

58.7 

W 

Tungsten 

184.0 

Co 

Cobalt 

59. 

N 

Nitrogen 

14.01 

Va 

Vanadium 

51.0 

Cu 

Copper 

63.6 

0 

Oxygen 

16. 

Zn     1 

Zinc 

65.4 

The  atomic  weights  of  many  of  the  elements  vary  in  the  decimal 
place  as  given  by  different  authorities.  The  above  are  the  most  recent 
values  referred  to  O  =  16  and  H  =  1.008.  When  H  is  taken  as  1, 
O  =  15.879,  and  the  other  figures  are  diminished  proportionately. 

Rare  Elements  (37). 

Beryllium,  Be.  Indium,  In.  Ruthenium,  Ru.  Thallium,  Tl. 

Caesium,  Cs.  Lanthanum,  La.  Samarium,  Sm.  Thorium,  Th. 

Cerium,  Ce.  Molybdenum,  Mo.  Scandium,  Sc.  Uranium,  U. 

Erbium,  Er.  Niobium,  Nb.  Selenium,  Se.  Ytterbium,  Yr. 

Gallium,  Ga.  Osmium,  Os.  Tantalum,  Ta.  Yttrium,  Y. 

Germanium,  Ge.  Rhodium,  R.  Tellurium,  Te.  Zirconium,  Zr. 

Glucinum,  G.  Rubidium,  Rb.  Terbium,  Tb. 

Elements  recently  discovered  (1895-1900):  Argon,  A,  39.9;  Krypton 
Kr,  81.8;  Neon,  Ne,  20.0;  Xenon,  X,  128.0;  constituents  of  the  atmos- 
phere, which  contains  about  1  per  cent  by  volume  of  Argon,  and  very 
small  quantities  of  the  others.  Helium,  He,  4.0;  Radium,  Ra,  225.0; 
Gadolinium,  Gd,  156.0;  Neodymium.  Nd,  143.6;  Praesodymium,  Pr, 
110.5;  Thulium,  Tm,  171.0. 


SPECIFIC  GRAVITY. 

The  specific  gravity  of  a  substance  is  its  weight  as  compared  with  the 
weight  of  an  equal  bulk  of  pure  water.  In  the  metric  system  it  is  the 
weight  in  grammes  per  cubic  centimeter. 

To  find  the  specific  gravity  of  a  substance; 

W  =  weight  of  body  in  air ;  w  =  weight  of  body  submerged  in  water. 


Specific  gravity  = 


W 


W  -w' 


If  the  substance  be  lighter  than  the  water,  sink  it  by  means  of  a 
heavier  substance,  and  deduct  the  weight  of  the  heavier  substance. 

Specific  gravity  determinations  are  usually  referred  to  the  standard  of 
the  weight  of  water  at  62°  F.,  62.355  Ib.  per  cubic  foot.  Some  expert- 


174 


MATERIALS. 


menters  have  used  60°  F.  as  the  standard,  and  others  32°  and  39.1°  F. 
There  is  no  general  agreement. 

Given  sp.  gr.  referred  to  water  at  39.1°  F.,  to  reduce  it  to  the  standard 
of  62°  F.  multiply  it  by  1.00112. 

Given  sp.  gr.  referred  to  water  at  62°  F.,  to  find  weight  per  cubic  foot 
multiply  by  62.355.  Given  weight  per  cubic  foot,  to  find  sp.  gr.  multiply 
by  0.016037.  Given  sp.  gr.,  to  find  weight  per  cubic  inch  multiply  by 

Weight  and  Specific  Gravity  of  Metals. 


Specific  Gravity. 
Range  accord- 
ing to 
several 
Authorities. 

Specific  Grav- 
ity.    Approx. 
Mean  Value, 
used  in 
.    Calculation 
of  Weight. 

Weight 
per 
Cubic 
Foot, 
Ibs. 

Weight 
per 
Cubic 
Inch, 
Ibs. 

2.56     to     2.71 

2.67 

166.5 

00963 

Antimony  

6.66     to     6.86 

6  76 

421  6 

02439 

Bismuth  

9.74     to     9.90 

9.82 

612.4 

0.3544 

Brass:  Copper  +  Zinc-K 
80             20 
70             30L  . 
60             40 
50             50* 

Cadmium    .  . 

7.8       to     8.6 

8.52     to     8.96 
8.6       to     8.7 

{8.60 
8.40 
8.36 
8.20 

8.853 
865 

536.3 
523.8 
521.3 
511.4 

552. 
539 

0.3103 
0.3031 
0.3017 
0.2959 

0.3195 
03121 

Calcium  

1.58 

1.58 

98.5 

0.0570 

Ch  rom  i  um 

50 

5  0 

311  8 

0  1804 

Cobalt       

85       to     8  6 

8.55 

533  1 

0  3085 

19.245  to   19.361 

19.258 

1200.9 

06949 

Copper    .    .  . 

8.69     to     8  92 

8853 

552 

03195 

Iridium     

22.38     to  23. 

22.38 

1396 

08076 

Iron   Cast 

6  85     to     7  48 

7218 

450 

02604 

Iron   Wrought  

7.4       to     7.9 

7  70 

480 

02779 

Lead  

11.07     to   11.44 

11.38 

709.7 

04106 

Manganese  ... 

7.         to     8. 

8. 

499 

02887 

Magnesium.  .  , 

1  .69     to     1  .75 

1.75 

109. 

0.0641 

j  32° 
Mercury  <  60° 
1212° 
Nickel 

13.61 
13.58 
13.37     to  13.38 
8.279  to     8.93 

13.61 
13.58 
13.38 
8.8 

848.6 
846.8 
834.4 
548  7 

0.4908 
0.49  1  1 
0.4828 
03175 

Platinum  

20.33     to  22.07 

21.5 

1347.0 

07758 

0.865 

0.865 

53.9 

0.0312 

Silver  

10.474  to   10.511 

10.505 

655.1 

03791 

Sodium  

0.97 

0.97 

60.5 

0.0350 

Steel... 

7  69*  to     7.932t 

7.854 

4896 

02834 

Tin  

7.291  to     7.409 

7.350 

458.3 

0.2652 

Titanium  .    . 

5.3 

5.3 

330  5 

0  1913 

17.        to  17.6 

17.3 

1078.7 

0.6243 

Zinc.  .  . 

6.86     to     7.20 

7.00 

436.5 

0.2526 

*  Hard  and  burned. 

t  Very  pure  and  soft.     The  sp.  gr.  decreases  as  the  carbon  is  increased. 

In  the  first  column  of  figures  the  lowest  are  usually  those  of  cast  metals, 
which  are  more  or  less  porous;  the  highest  are  of  metals  finely  rolled  or 
drawn  into  wire. 

The  weight  of  1  cu.  cm.  of  mercury  at  0°  C.  is  13.59545  grams  (Thiessen). 
Taking  atmosphere  =  29.92  in.  of  mercury  at  32°  F.  =  14.6963  Ib.  per 
sq.  in.,  1  cu.  im  of  mercury  =  0.49117  Ib.  Taking  water  at  0.036085  Ib. 
per  cu.  in.  at  62°  F.,  the  specific  gravity  of  mercury  is  at  32°  F.  13.611. 


SPECIFIC   GKAVITY. 


175 


Specific  Gravity  of  Liquids  at  60°  F. 


A   'r\    AT   *•'   tV 

I  200 

Naphtha           

0.670  to  0.737 

"      Nitric 

1.54 

0.93 

"     Sulphuric 

1  849 

"     Olive        

0.92 

Alcohol  pure 

0.794 

"    Palm  

0.97 

"        95  per  cent  .  . 
"        50  per  cent 

0.816 
0.934 

'    Petroleum,  crude. 
"    Rape 

0.78  to   1.00 
0.92 

Ammonia   27  9  per  ct 

0.891 

*    Turpentine  

0.86 

Bromine 

2.97 

"    Whale  

0.92 

Carbon  disulphide 

1.26 

Tar    

1.0 

Ether  Sulphuric 

0  72 

Vinegar 

1.08 

Gasoline 

0  660  to  0.670 

Water  

1.0 

Kerosene.  . 

0.753  to  0.864 

Water,  Sea  ... 

1.026  to  1.03 

Compression  of  the  following  Fluids  under  a  Pressure  of  15  Ib. 
per  Square  Inch. 

Water     0.00004663    I    Ether 0.00006158 

Alcohol 0.0000216      |    Mercury 0.00000265 

The  Hydrometer. 

The  hydrometer  is  an  instrument  for  determining  the  density  of 
liquids.  It  is  usually  made  of  glass,  and  consists  of  three  parts:  (1) 
the  upper  part,  a  graduated  stem  or  fine  tube  of  uniform  diameter; 
(2)  a  bulb,  or  enlargement  of  the  tube,  containing  air,  and  (3)  a  small 
bulb  at  the  bottom,  containing  shot  or  mercury  which  causes  the  in- 
strument to  float  in  a  vertical  position.  The  graduations  are  figures 
representing  either  specific  gravities,  or  the  numbers  of  an  arbitrary  scale, 
as  in  Baume's,  Twaddell's,  Beck's,  and  other  hydrometers. 

There  is  a  tendency  to  discard  all  hydrometers  with  arbitrary  scales 
and  to  use  only  those  which  read  in  terms  of  the  specific  gravity 
directly. 

Baume's  Hydrometer  and  Specific  Gravities  Compared. 


5  Heavy  liquids,  Sp.  gr. 
l  Light    liquids,  Sp.  gr. 


145  -r  (145  -deg.  Be.) 
140  -r  (130  +  deg.  Be.) 


Degrees 
Baume* 

Liquids 
Heavier 
than 
Water, 
Sp.  Gr. 

Liquids 
Lighter 
than 
Water, 
Sp.  Gr. 

Degrees 
Baume* 

Liquids 
Heavier 
than 
Water, 
Sp.  Gr 

Liquids 
Lighter 
than 
Water, 
Sp.  Gr. 

Degrees 
Baume* 

Liquids 
Heavier 
than 
Water, 
Sp.  Gr. 

Liquids 

Htr 

Water, 
Sp.  Gr. 

00 

000 

190 

151 

0940 

380 

355 

0833 

1.0 

.007 

20.0 

.160 

0.933 

39.0 

.368 

0.828 

2.0 
3.0 

.014 
021 

21.0 
22.0 

.169 
.179 

0.927 
0.921 

40.0 
41  0 

.381 
394 

0.824 
0  819 

4.0 

.028 

23.0 

189 

0915 

42  0 

408 

0  814 

5.0 

.036 

24.0 

.198 

0.909 

44.0 

.436 

0805 

6.0 
7.0 

.043 
.051 

25.0 
26.0 

.208 
.219 

0.903 
0.897 

46.0 
48.0 

.465 
.495 

0.796 
0.787 

8.0 
9.0 

.058 
.066 

27.0 
28.0 

.229 
.239 

0.892 
0.886 

50.0 
52.0 

.526 
.559 

0.778 
0.769 

10.0 
11.0 
12.0 
13.0 
14.0 
15.0 
16.0 
17.0 

.074 
.082 
.090 
.099 
.107 
.115 
.124 
.133 

1.000 
0.993 
0.986 
0.979 
0.972 
0.966 
0.959 
0.952 

29.0 
30.0 
31.0 
32.0 
330 
34.0 
35.0 
36.0 

.250 
.261 
.272 
.283 
.295 
.306 
1.318 
1.330 

0.881 
0.875 
0.870 
0.864 
0,859 
0.854 
0.849 
0.843 

54.0 
56.0 
58.0 
60.0 
65.0 
70.0 
75.0 

.593 
.629 
.667 
.706 
.813 
.933 
2.071 

0761 
0.753 
0.745 
0.737 
0.718 
0.700 
0.683 

18.0 

142 

0946 

370 

1  343 

0838 

170 


MATERIALS. 


Specific  Gravity  and  Weight  of  Gases  at  Atmospheric  Pressure 
and  33°  F. 

(For  other  temperatures  and  pressures  see  Physical  Properties  of  Gases.) 


Density, 
Air  =>  1. 

Density, 
H  =  f. 

Grammes 
per  Litre. 

Lbs.  per 
Cu.  Ft. 

Cubic  Ft. 
per  Lb. 

Air  

1  .0000 

1  4.444 

.2931 

0.080728 

12388 

1.1052 

15.963 

.4291 

0.08921 

11  209 

Hydrogen,  H  

0.0692 

1  000 

0.0895 

0.00559 

1  78  93  1 

Nitrogen,  N  

0.9701 

14.012 

.2544 

0.07831 

12  770 

Carbon  monoxide,  CO  . 
Carbon  dioxide,  CO2  .  . 
Metha  ne,marsh-gas,  CtU 
Ethyl  ene  C2EU  

0.9671 
1.5197 
0.5530 
0.9674 

13.968 
21.950 
7.987 
13.973 

.2505 
.9650 
0.7150 
.2510 

0.07807 
0.12267 
C.04464 
0  07809 

12.810 
8.152 
22.429 
12  805 

08982 

12.973 

.1614 

0.07251 

13.792 

0.5889 

8.506 

0.7615 

0  04754 

21  036 

Water  vapor,  HtO  .  .  ,  . 
Sulphur  dioxide,  SO2  .  . 

0.6218 
2.213 

8.981 
31.965 

0.8041 
2.862 

0.05C20 
0.1787 

19.922 
5.597 

Specific  Gravity  and  Weight  of  Wood. 


Specific 
Gravity. 

rii 

Sl| 

QjOPn 
£ 

Specific 
Gravity, 

&4 
%as 

«•§! 

uoPk 

Alder  

Avge. 
0.56  to  0.80  0.68 
0.73  to  0.79  0.76 
0.60  to  0.84  0.72 
0.31  to  0.40  0.35 
0.62  to  0.85   0.73 
0.56  to  0.74  0.65 
0.91  to  1.33    1.12 
0.49  to  0.75   0.62 
0.61  to  0.72   0.66 
0.46  to  0.66  0.56 
0.24                0.24 
0.41  to  0.66  0.53 
0.76                0.76 
1.13  to  1.33    1.23 
0.55  to  0.78  0.61 
0.48  to  0.70  0.59 
0.84  to  1  .00  0.92 
0.59                 0.59 
0.36  to  0.41    0.38 
0.69  to  0.94  0.77 
0.76                0.76 

42 
47 
45  • 
22 
46 
41 
70 
39 
41 
35 
15 
33 
47 
76 
33 
37 
57 
37 
24 
48 
47 

Hornbeam.  . 
Juniper  .... 
Larch  
Lignum  vita? 
Linden     .  .  . 
Locust  
Mahogany.  . 
Maple  

Avge. 
0.76                0.76 
0.56                0.56 
0.56                0.56 
0.65  to  1.33    1.00 
0.604 
0.728 
0.56  to  1.06  0.81 
0.57  to  0.79  0.68 
0.56  to  0.90   0.73 
0.96  to  1.26    1.11 
0.69  to  0.86  0.77 
0.73  to  0.75   0.74 
0.35  to  0.55   0.45 
0.46  to  0.76   0.61 
0.38  to  0.58  0.48 
0.40  to  0.50   0.45 
0.59  to  0.62   0.60 
0.66  to  0.98   0.82 
0.50  to  0.67   0.58 
0.49  to  0.59   0.54 

47 
35 
35 
62 
37 
46 
51 
42 
46 
69 
48 
46 
28 
38 
30 
28 
37 
51 
36 
34 

Ash  

Bamboo  .... 
Beech  

Birch  
Box 

Cedar. 

Cherry  
Chestnut.  .  .  . 
Cork 

Mulberry.  .  . 
Oak,  Live  .  . 
Oak,  White. 
Oak,  Red  .  . 
Pine,   White 
"  Yellow 
Poplar  
Spruce  
Sycamore  .  . 
Teak  

Cypress  
Dogwood  .  .  . 
Ebony.    . 

Elm.  .  . 

Fir  

Gum 

Hackmatack 
Hemlock.  .  .  . 
Hickory  
Holly.      . 

Walnut  
Willow  

OP   THE   USEFUL  METALS. 


177 


Weight  and  Specific  Gravity  of  Stones,  Brick,  Cement,  etc. 
Water  =  1.00.) 


(Pure 


Lb.  per  Cu.  Ft. 

Sp.  Gr. 

Ashes  

43 

87 

1.39 

Brick,  Soft                         

100 

1  .6 

112 

1.79 

Hard        

125 

2.0 

"       Pressed  

135 

2.16 

"       Fire                         

140  to  150 

2.  24  to  2  4 

Sand-lime  

136 

2.18 

Brickwork  in  mortar 

100 

1  6 

"    cement  .  .  %  

112 

1.79 

Cement,  American,  natural 

28    to  3  2 

"         Portland 

3  .  05  to  3   15 

loose  

92 

"         in  barrel 

115 

Clay  

120  to  150 

'  1  .92  to  2.4 

Concrete 

120  to  155 

1   92  to  2  48 

Earth,  loose  .        ... 

72  to     80 

1  .  1  5  to  1   28 

rammed 

90  to  110 

1   44  to  1   76 

Emery  . 

250 

4. 

Glass 

1  56  to  1  72 

25    to  2  75 

flint  

180  to  196 

2.88  to  3   14 

Gneiss    1 

160  to  170 

2.  56  to  2.72 

Granite  f  
Gravel  

100  to  120 

1.6    to  1.92 

Gypsum 

130  to   150 

2  08  to  2  4 

Hornblende  

200  to  220 

3.2    to  3.  52 

Ice      . 

55  to     57 

0  88  to  0  92 

Lime,  quick,  in  bulk  

50  to     60 

0.8    to  0.96 

Limestone 

140  to   185 

2  30  to  2  90 

Magnesia,  Carbonate  

150 

2.4 

Marble 

160  to   180 

2  56  to  2  88 

Masonry,  dry  rubble  

140  to   160 

2.24  to  2.56 

"         dressed 

140  to   180 

2  24  to  2  88 

Mica  

175 

2.80 

Mortar 

90  to   100 

44  to  1   6 

Mud,  soft  flowing  

104  to   120 

.67  to  1  .92 

Pitch 

72 

15 

Plaster  of  Paris  

93  to   113 

.50  to  T.81 

Quartz  

165 

2.64 

Sand                  .    .                .... 

90  to   110 

44  to  1   76 

"     wet  

118  to   129 

.89  to  2.  07 

Sandstone  .... 

140  to   150 

2  24  to  2.4 

Slate  

170  to   180 

2.72  to  2.88 

Soapstone  ... 

166  to   175 

2  65  to  2.8 

Stone,  various  

135  to  200 

2.16to3.4 

"      crushed  

100 

Tile 

1  10  to   120 

1   76  to  1   92 

Trap  Rock  

1  70  to  200 

2.72  to  3.  4 

PROPERTIES   OF  THE  USEFUL  METALS. 

Aluminum,  AI.  —  Atomic  weight  27.1.  Specific  gravity  2.6  to  2.7. 
The  lightest  of  all  the  useful  metals  except  magnesium.  A  soft,  ductile, 
malleable  metal,  of  a  white  color,  approaching  silver,  but  with  a  bluish 
cast.  Very  non-corrosive.  Tenacity  about  one-third  that  of  wrought 
iron.  Formerly  a  rare  metal,  but  since  1890  its  production  and  use 
have  greatly  increased  on  account  of  the  discovery  of  cheap  processes 
for  reducing  it  from  the  ore.  Melts  at  1215°  F.  For  further  description 
see  Aluminum,  under  Strength  of  Materials,  page  380. 

Antimony  (Stibium),  Sb. — At.  wt.  120.2  Sp.  gr.  6.7  to  6.8.  A 
brittle  metal  of  a  bluish-white  color  and  highly  crystaline  or  laminated 
structure.  Melts  at  842°  F.  Heated  in  the  open  air  it  burns  with  a 


178  MATERIALS. 

bluish-white  flame.  Its  chief  use  is  for  the  manufacture  of  certain  alloys,  j 
as  type-metal  (antimony  1,  lead  4),  britannia  (antimony  1,  tin  9),  and  4 
various  anti-friction  metals  (see  Alloys).  Cubical  expansion  by  heat  3 
from  32°  to  212°  F.,  0.0070.  Specific  heat  0.050. 

Bismuth,  Bi.  —  At.  wt.  208.5.  Bismuth  is  of  a  peculiar  light  reddish  I 
color,  highly  crystalline,  and  so  brittle  that  it  can  readily  be  pulverized,  j 
It  melts  at  510°  F.,  and  boils  at  about  2300°  F.  Sp.  gr.  9.823  at  54°  F.,  ] 
and  10.055  just  above  the  melting-point.  Specific  heat  about  0.0301  at  j 
ordinary  temperatures.  Coefficient  of  cubical  expansion  from  32°  to  i 
212°,  0.0040.  Conductivity  for  heat  about  1/56  and  for  electricity  only  .] 
about  i/so  of  that  of  silver.  Its  tensile  strength  is  about  6400  IDS.  per  | 
square  inch.  Bismuth  expands  in  cooling,  and  Tribe  has  shown  that  } 
this  expansion  does  not  take  place  until  after  solidification.  Bismuth  is  \ 
the  most  diamagnetic  element  known,  a  sphere  of  it  being  repelled  by  a  ; 
strong  magnet. 

Cadmium,  Cd.  —  At.  wt.  112.4.     Sp.  gr.  8.6  to  8.7.     A  bluish-white 
metal,  lustrous,  with  a  fibrous  fracture.     Melts  below  500°  F.  and  vola- 
tilizes at  about  680°  F.     It  is  used  as  an  ingredient,  in  some  fusible  alloys 
with  lead,  tin,  and  bismuth.     Cubical  expansion  from  32°  to  212°  F.,  • 
0.0094. 

Copper,  Cu.  —  At.  wt.  63.6.     Sp.  gr.  8.81  to  8.95.     Fuses  at  about  ; 
1930^  F.     Distinguished  from  all  other  metals  by  its  reddish  color.     Very 
ductile  and  malleable,  and  its  tenacity  is  next  to  iron.     Tensile  strength 
20,000  to  30,000  Ibs.  per  square  inch.     Heat  conductivity  73.6%  of  that  i 
of  silver,  and  superior  to  that  of  other  metals.     Electric  conductivity 
equal  to  that  of  gold  and  silver.     Expansion  by  heat  from  32°  to  212°  F., 
0.0051  of  its  volume.     Specific  heat  0.093.     (See  Copper  under  Strength 
of  Materials;  also  Alloys.) 

Gold  (Aurum),  Au.  —  At.  wt.  197.2.  Sp.  gr.,  when  pure  and  pressed 
in  a  die,  19.34.  Melts  at  about  1915°  F.  The  most  malleable  and  duc- 
tile of  all  metals.  One  ounce  Troy  may  be  beaten  so  as  to  cover  160  sq. 
ft.  of  surface.  The  average  thickness  of  gold-leaf  is  1/282000  of  an  inch,  i 
or  100  sq.  ft.  per  ounce.  One  grain  may  be  drawn  into  a  wire  500  ft.  in 
length.  The  ductility  is  destroyed  by  the  presence  of  1/2000  part  of  lead, 
bismuth,  or  antimony.  Gold  is  hardened  by  the  addition  of  silver  or  of 
copper.  U.  S.  gold  coin  is  90  parts  gold  and  10  parts  alloy,  which  is 
chiefly  copper  with  a  little  silver.  By  jewelers  the  fineness  of  gold  is 
expressed  in  carats,  pure  gold  being  24  carats,  three-fourths  fine  18 
carats,  etc. 

Iridium,  Ir.  —  Iridium  is  one  of  the  rarer  metals.  It  has  a  white 
lustre,  resembling  that  of  steel;  its  hardness  is  about  equal  to  that  of  the 
ruby;  in  the  C9ld  it  is  quite  brittle,  but  at  white  heat  it  is  somewhat 
malleable.  It  is  one  of  the  heaviest  of  metals,  having  a  specific  gravity 
of  22.38.  It  is  extremely  infusible  and  almost  absolutely  inoxidizable. 

For  uses  of  iridium,  methods  of  manufacturing  it,  etc.,  see  paper  by 
W.  L.  Dudley  on  the  "Iridium  Industry,"  Trans.  A.  I.  M.  E.,  1884. 

Iron  (Ferrum),Fe.  —  At.  wt.  55.9.  Sp.  gr.:  Cast,  6.85  to  7.48;  Wrought, 
7.4  to  7.9.  Pure  iron  is  extremely  infusible,  its  melting  point  being  above 
3000°  F.,  but  its  fusibility  increases  with  the  addition  of  carbon,  cast 
iron  fusing  ab9ut  2500°  F.  Conductivity  for  heat  11.9,  and  for  electricity 
12  to  14.8,  silver  being  100.  Expansion  in  bulk  by  heat:  cast  iron 
0.0033,  and  wrought  iron  0.0035,  from  32°  to  212°  F.  Specific,  heat: 
cast  iron  0.1298,  wrought  iron  0.1138,  steel  0.1165.  Cast  iron  exposed 
to  continued  heat  becomes  permanently  expanded  1  1/2  to  3  per  cent  of  its 
length.  Grate-bars  should  therefore  be  allowed  about  4  per  cent  play. 
(For  other  properties  see  Iron  and  Steel  under  Strength  of  Materials.) 

Lead  (Plumbum),  Pb.  —  At.  wt  206.9.  Sp.  gr.  11.07  to  11.44  by  dif- 
ferent authorities.  Melts  at  about  625°  F.,  softens  and  becomes  pasty 
at  about  617°  F.  If  broken  by  a  sudden  blow  when  just  below  the 
melting-point  it  is  quite  brittle  and  the  fracture  appears  crystalline. 
Lead  is  very  malleable  and  ductile,  but  its  tenacity  is  such  that  it  can 
be  drawn  into  wire  with  great  difficulty.  Tensile  strength,  1600  to 
2400  Ibs.  per  square  inch.  Its  elasticity  is  very  low,  and  the  metal 
flows  under  very  slight  strain.  Lead  dissolves  to  some  extent  in  pure 
water,  but  water  containing  carbonates  or  sulphates  forms  over  vt  » 
film  of  insoluble  salt  which  prevents  further  action. 


PROPERTIES   OF  THE  USEFUL  METALS.  179 

Magnesium,  Mg.  —  At.  wt.  24.36.  Sp.  gr.  1.69  to  1.75.  Silver-white, 
brilliant,  malleable,  and  ductile.  It  is  one  of  the  lightest  of  metals, 
weighing  only  about  tvyo  thirds  as  much  as  aluminum.  In  the  form  of 
filings,  wire,  9r  thin  ribbons  it  is  highly  combustible,  burning  with  a 
light  of  dazzling  brilliancy,  useful  for  signal-lights  and  for  flash-lights 
for  photographers.  It  is  nearly  non-corrosive,  a  thin  film  of  carbonate 
of  magnesia  forming  on  exposure  to  damp  air,  which  protects  it  from 
further  corrosion.  It  may  be  alloyed  with  aluminum,  5  per  cent  Mg 
added  to  Al  giving  about  as  much  increase  of  strength  and  hardness  as 
10  per  cent  of  copper.  Cubical  expansion  by  heat  0.0083,  from  32°  to 
212°  F.  Melts  at  1200°  F.  Specific  heat  0.25. 

Manganese,  Mn.  —  At.  wt.  55.  Sp.  gr.  7  to  8.  The  pure  metal  is  not 
used  in  the  arts,  but  alloys  of  manganese  and  iron,  called  spiegeleisen 
when  containing  below  25  per  cent  of  manganese,  and  ferro-manganese 
when  containing  from  25  to  90  per  cent,  are  used  in  the  manufacture  of 
steel.  Metallic  manganese,  when  alloyed  with  iron,  oxidizes  rapidly  in 
the  air,  and  its  function  in  steel  manufacture  is  to  remove  the  oxygen 
from  the  bath  of  steel  whether  it  exists  as  oxide  of  iron  or  as  occluded 
gas. 

Mercury  (Hydrargyrum),  Hg.  —  At.  wt.  199.8.  A  silver-white  metal, 
liquid  at  temperatures  above  —  39°  F.,  and  boils  at  680°  F.  Unchange- 
able as  gold,  silver,  and  platinum  in  the  atmosphere  at  ordinary  tem- 
peratures, but  oxidizes  to  the  red  oxide  when  near  its  boiling-point. 
Sp.  gr.:  when  liquid  13.58  to  13.59,  when  frozen  14.4  to  14.5.  Easily 
tarnished  by  sulphur  fumes,  also  by  dust,  from  which  it  may  be  freed 
by  straining  through  a  cloth.  No  metal  except  iron  or  platinum  should 
be  allowed  to  touch  mercury.  The  smallest  portions  of  tin,  lead,  zinc, 
and  even  copper  to  a  less  extent,  cause  it  to  tarnish  and  lose  its  perfect 
liquidity.  Coefficient  of  cubical  expansion  from  32°  to  212°  F.  0.0182; 
per  deg.  0.000101. 

Nickel,  Ni.  —  At.  wt.  58.7.  Sp.  gr.  8.27  to  8.93.  A  silvery-white 
metal  with  a  strong  lustre,  not  tarnishing  on  exposure  to  the  air.  Duc- 
tile, hard,  and  as  tenacious  as  iron.  It  is  attracted  to  the  magnet  and 
may  be  made  magnetic  like  iron.  Nickel  is  very  difficult  of  fusion,  melt- 
ing at  about  3000°  F.  Chiefly  used  in  alloys  with  copper,  as  german- 
silver,  nickel-silver,  etc.,  and  also  in  the  manufacture  of  steel  to  increase 
its  hardness  and  strength,  also  for  nickel-plating.  Cubical  expansion 
from  32°  to  212°  F.,  0.0038.  Specific  heat  0.109. 

Platinum,  Pt.  —  At.  wt.  194X  A  whitish  steel-gray  metal,  malleable, 
very  ductile,  and  as  unalterable  by  ordinary  agencies  as  gold.  When 
fused  and  refined  it  is  as  soft  as  copper.  Sp.  gr.  21.15.  It  is  fusible  only 
by  the  oxyhydrogen  blowpipe  or  in  strong  electric  currents.  When  com- 
bined with  iridium  it  forms  an  alloy  of  great  hardness,  which  has  been 
used  for  gun- vents  and  for  standard  weights  and  measures.  The  most 
important  uses  of  platinum  in  the  arts  are  for  vessels  for  chemical  labo- 
ratories and  manufactories,  and  for  the  connecting  wires  in  incandescent 
electric  lamps  and  for  electrical  contact  points.  Cubical  expansion  from 
32°  to  212°  F.,  0.0027,  less  than  that  of  any  other  metal  except  the  rare 
metals,  and  almost  the  same  as  glass. 

Silver  (Argentum),  Ag.  —  At.  wt.  107.9.  Sp.  gr.  10.1  to  11.1,  accord- 
ing to  condition  and  purity.  It  is  the  whitest  of  the  metals,  very  malle- 
able and  ductile,  and  in  hardness  intermediate  between  gold  and  copper. 
Melts  at  about  1750°  F.  Specific  heat  0.056.  Cubical  expansion  from 
32°  to  212°  F.,  0.0058.  As  a  conductor  of  electricity  it  is  equal  to  copper. 
As  a  conductor  of  heat  it  is  superior  to  all  other  metals. 

Tin  (Stannum),  Sn.  —  At.  wt.  119.  Sp.  gr.  7.293.  White,  lustrous, 
soft,  malleable,  of  little  strength,  tenacity  about  3500  Ibs.  per  square 
inch.  Fuses  at  442°  F.  Not  sensibly  volatile  when  melted  at  ordinary 
heats.  Heat  conductivity  14.5,  electric  conductivity  12.4;  silver  being 
100  in  each  case.  Expansion  of  volume  by  heat  0.0069  from  32°  to  212°  F. 
Specific  heat  0.055.  Its  chief  uses  are  for  coating  of  sheet-iron  (called 
tin  plate)  and  for  making  alloys  with  copper  and  other  metals. 

Zinc,  Zn.— At.  wt.  65.4.  Sp.  gr.  7.14.  Melts  at  780°  F.  Volatilizes 
and  burns  in  the  air  when  melted,  with  bluish-white  fumes  of  zinc  oxide. 
It  is  ductile  and  malleable,  but  to  a  much  less  extent  than  copper,  and 


180 


MATERIALS. 


its  tenacity,  about  5000  to  6000  Ibs.  per  square  inch,  is  about  one  tenth 
that  of  wrought  iron.  It  is  practically  non-corrosive  in  the  atmosphere, 
a  thin  film  of  carbonate  of  zinc  forming  upon  it.  Cubical  expansion 
between  32°  and  212°  F.,  0.0088.  Specific  heat  0.096.  Electric  conduc- 
tivity 29,  heat  conductivity  36,  silver  being  100.  Its  principal  uses  are 
for  coating  iron  surfaces,  called  "galvanizing,"  and  for  making  brass  and 
other  alloys. 

Table  Showing  the  Order  of 

Tenacity.  Infusibility. 

Iron  Platinum 

Copper  Iron 

Aluminum  Copper 

Platinum  Gold 

Silver  Silver 

Zinc  Aluminum 

Gold  Zinc 

Tin  Lead 

Lead  Tin 

MEASURES   AND  WEIGHTS   OF    VARIOUS  MATERIALS 
(APPROXIMATE). 


Malleability. 

Ductility. 

Gold 

Platinum 

Silver 

Silver 

Aluminum 

Iron 

Copper 
Tin 

Copper 
Gold 

Lead 

Aluminum 

Zinc 

Zinc 

Platinum 

Tin 

Iron 

Lead 

Brickwork.  —  Brickwork    is    estimated 
various  thicknesses  of  wall  runs  as  follows: 


by    the    thousand,    and    for 


8i/4-in.  wall,  or  1  brick  in  thickness,  14  bricks  per  superficial  foot. 
123/4  "  ••  11/2"  21       " 

17  "         "          "    9          "         "  "  Oft          "  "  "  «• 


17 

2U/2 


28 
35 


An  ordinary  brick  measures  about  81/4X4  X  2  inches,  which  is  equal 
to  66  cubic  inches,  or  26.2  bricks  to  a  cubic  foot.  The  average  weight  is 
4 1/2  Ibs. 

Fuel.  —  A  bushel  of  bituminous  coal  weighs  76  pounds  and  contains 
2688  cubic  inches  =  1.554  cubic  feet.  29.47  bushels  =  1  gross  ton. 

One  acre  of  bituminous  coal  contains  1600  tons  of  2240  pounds  per 
foot  of  thickness  of  coal  worked.  15  to  25  per  cent  must  be  deducted  for 
waste  in  mining. 

41  to  45  cubic  feet  bituminous  coal  when  broken  down  =  1  ton,  2240  Ibs. 


34  t< 
123 
70.9 
1  cu 
1 
1 

a 

i 
i 

3  41 

bic  fo 

'    anthracite  prepared  for  market  .  . 
'    of  charcoal 

.    =  1  ton,  2240  Ibs. 
=  1  ton   2240  Ibs 

"        "    "  coke           .        

.    =  1  ton,  2240  Ibs 

ot  of  anthracite  coal 

=  55  to  66  Ibs 

"  bituminous  coal                                 .  .  . 

«=  50  to  55  Ibs 

Cumberland  (semi-bituminous)  coal.  .  .  . 
Cannel  coal                               .          

=  53  Ibs. 
=  50  3  Ibs 

Charcoal  (hardwood)  

=  18.5  Ibs. 

"         (nine)  .  . 

=  18  Ibs. 

A  bushel  of  coke  weighs  40  pounds  (35  to  42  pounds). 

A  bushel  of  charcoal.  - —  In  1881  the  American  Charcoal-Iron  Work- 
ers' Association  adopted  for  use  in  its  official  publications  for  the  stand- 
ard bushel  of  charcoal  2748  cubic  inches,  or  20  pounds.  A  ton  of  char- 
coal is  to  be  taken  at  2000  pounds.  This  figure  of  20  pounds  to  the 
bushel  was  taken  as  a  fair  average  of  different  bushels  used  throughout 
the  country,  and  it  has  since  been  established  by  law  in  some  States. 

Cement. — Portland,  per  bbl.  net,  376  Ibs.,  per  bag,  net 94  Ibs. 

Natural,  per  bbl.  net,  282  Ibs.,  per  bag  net 94  Ibs. 

Lime. — A  struck  bushel 72  to  75  Ibs. 

Grain. — A  struck  bushel  of  wheat  =  60  Ibs.;  of  corn  =  56  Ibs.;  of 
oats  =  30  Ibs. 

Salt. — A  struck  bushel  of  salt,  coarse,  Syracuse,  N.  Y.  =  56  Ibs.; 
Turk's  Island  =  76  to  80  Ibs. 


MEASUKES  AND   WEIGHTS   OF   VARIOUS   MATERIALS.    181 


Ores,  Earths,  etc. 

13  cubic  feet  of  ordinary  gold  or  silver  ore,  in  mine    =  1  ton  =  2000  Ibs. 

20  "  broken  quartz =1  ton  =  2000  Ibs. 

18  feet  of  gravel  in  bank =1  ton. 

27  cubic  feet  of  gravel  when  dry =1  ton. 

25  "  sand 

18  "  earth  in  bank 

27  "  earth  when  dry 

17  "  clay 

Except  where  otherwise  stated,  a  ton  =  2240  Ibs. 

WEIGHTS   OF  LOGS,   LUMBER,    ETC. 

Weight  of  Green  Logs  to  Scale  1000  Feet,  Board  Measure. 

Yellow  pine  (Southern) 8,000  to  10,0001bs. 


1  ton. 

1  ton. 
=  1  ton. 
=  1  ton. 


, 

Norway  pine  (Michigan) 7,000  to    8,000 

WhitP  ninp  nVTirhiffaTi^  I  off  of  stumP 7'000  to     7,000 

(Micnigan)  j  QUt  of  water 7  000  to    g  000 

White  pine  (Pennsylvania),  bark  off 5,000  to    6,000 

Hemlock  (Pennsylvania),  bark  off . 6,000  to    7,000 

Four  acres  of  water  are  required  to  store  1,000,000  feet  of  logs. 

Weight  of  1000  Feet  of  Lumber,  Board  Measure. 

Yellow  or  Norway  pine Dry,  3,000  Ibs.       Green,  5,000  Ibs. 

White  pine '     2,500    "  4,000    " 

Weight  of  1  Cord  of  Seasoned  Wood,  128  Cu.  Ft.  per  Cord,  Ibs. 


Hickory  or  sugar  maple. .  .  .  4,500 

White  oak 3,850 

Beech,  red  oak  or  black  oak  .  3,250 


Poplar,  chestnut  or  elm. .  .  2,350 
Pine  (white  or  Norway)..  .  2,000 
Hemlock  bark,  dry 2,200 


WEIGHT  OF  RODS,   BARS,   PLATES,   TUBES,   AND   SPHERES 
OF   DIFFERENT   MATERIALS. 

Notation:  b  =  breadth,  t  =  thickness,  s  =  side  of  square,  D  =  ex- 
ternal diameter,  d  =  internal  diameter,  all  in  inches. 

Sectional  areas:  of  square  bars  =  s2;  of  flat  bars  =  W;  of  round  rods 
=  0.7854  Z>2;  of  tubes  •=  0.7854  (D2  -  rf2)  =  3.1416  (Dt  -Z2). 

Volume  of  1  foot  in  length:  of  square  bars  =  12s2;  of  flat  bars  =  12bt; 
of  round  bars  =  9.4248D2;  of  tubes  =  9.4248  (D2  -  d2)  =  37.699 
(Dt  -22),  in  cu.  in. 

Weight  per  foot  length  =  volume  +  weight  per  cubic  inch  of  mate- 
rial. Weight  of  a  sphere  =  diam.3  X  0.5236  X  weight  per  cubic  inch. 


3 

$& 

r.g 

. 

4 

. 

d 

u  . 

*?  rX 

[Vj    f^.O 

fe  PQ 

U    . 

j>  -fj  iH 

JV   'tf      » 

Material. 

P| 

5  > 

^ 

fctrf 

g| 

If  fa 

y  • 

"gjj 

JJ 

ge 

g-w 

+i«*H   ^ 

i*s 

i* 

I^-S 

£-3« 

4J  a 

82  X 

btX 

D*X 

D*X 

Cast  iron  

7.218 

450. 

37.5 

31/8 

31/8 

0.2604 

15-16 

2.454 

0.1363 

Wrought  iron.  . 

7.7 

480. 

40. 

31/3 

31/3 

.2779 

1. 

2.618 

.1455 

Steel 

7.854 

489.6 

40.8 

3.4 

3.4 

.2833 

1.02 

2.670 

.1484 

Copper  &  Bronze 
(copper  and  tin) 

8.855 

552. 

46. 

3.833 

3.833 

.3195 

1.15 

3.011 

.1673 

Brass  (  £  zm^* 

8.393 

523.2 

43.6 

3.633 

3.633 

«3029 

1.09 

2.854 

.1586 

Monel  metal,  rolled 

8.95 

558. 

46.5 

3.87 

3.87 

.323 

1.16 

3.043 

.1691 

Lead... 

1  1.38 

709.6 

59.1 

493 

493 

.4106 

1  48 

3.870 

.2150 

Aluminum  

2.67 

166.5 

13.9 

1.16 

1.16 

.0963 

0.347 

0.908 

.0504 

Glass. 

2.62 

163.4 

13.6 

1.13 

1  13 

.0945 

0.34 

0.891 

.0495 

Pine  wood,  dry  

0.481 

30.0 

2.5 

0.21 

0.21 

.0174 

1-16 

0.164 

.0091 

Weight  per  cylindrical  in.,  1  in.  long,  =  coefficient  of  D2  in  next  to 
last  column  -7- 12. 


182  MATERIALS. 

FOP  tubes  use  the  coefficient  of  D2  in  next  to  last  column,  as  for  rods, 
and  multiply  it  into  (D2  —  d2) ;  or  multiply  it  by  4  (Dt  -  22) . 

For  hollow  spheres  use  the  coefficient  of  D3  in  the  last  column  and 
multiply  it  into  (D3  -  d3). 

For  hexagons  multiply  the  weight  of  square  bars  by  0.866  (short 
diam.  of  hexagon  =  side  of  square).  For  octagons  multiply  by  0.8284. 

COMMERCIAL    SIZES    OF  MERCHANT  IRON  AND  STEEL 

BARS. 

Steel  Bars. 

Flats,  Square  Edge. — s/g  to  3  in.  wide,  by  any  thickness  from 
1/8  in.  up  to  width;  3  to  5  in.  wide  by  any  thickness  1/4  t9  3  in. 
inclusive;  5  to  7  in.  wide,  by  any  thickness,  1/4  to  2  in.  inclusive. 

Flats,  Band  Edge. — Thicknesses  are  in  B.  W.  G.,  3/8  in.  wide  by 
No.  18  to  No.  4.  7/i6  in.  by  No.  19  to  No.  4.  1/2  in.  by  No.  22  to  No. 
4.  9/i6  to  1  in.  by  No.  23  to  No.  4.  1 1/16  to  2  in.  by  No.  22  to  No.  4. 
2Vi6  to  3  in.  by  No.  21  to  No.  1.  39/16  to  4  in.  by  No.  19  to  No.  1. 
4Vi6  to  41/2  in.  by  No.  18  to  No.  1.  49/i6  to  5  Vie  in.  by  No.  17  to  No.  1. 
5 i/s  to  6 3/4  in.  by  No.  16  to  No.  1.  7  in.,  7 1/4  in.,  7 1/2  in.,  7  5/8  in.,  7 3/4  in., 
7 7/8  in.,  8  in.,  81/4  in.,  81/2  in.,  85/8  in.,  each  by  No.  14  to  No.  1.  95/8 
in.  by  No.  12  to  No.  1. 

Squares. — Widths  across  faces:  3/ie  to  2  in.,  advancing  by  1/64  in.; 
21/32  to  3  1/2  in.,  advancing  by  1/32  in.;  3  9/ie  to  51/2  in.,  advancing  by 
Vie  in. 

Round-cornered  Squares. — 1/4  to  3/4  in.,  across  faces,  advancing 
by  1/64  in. 

Rounds. — Diameters:  7/32  to  13/4  in.,  inclusive,  advancing  by  1/64 
in.;  1  25/32  in.  to  31/2  in.  inclusive,  advancing  by  1/32;  3  9/ie  to  7  in., 
inclusive,  advancing  by  Vie  in. 

Half  Rounds. — Diameters:  5/16  to  7/s  in.,  inclusive,  advancing  by 
1/64  in. ;  15/16  to  1 3/4  in . ,  advancing  by  Vie  in. ;  2  in. ;  2 1/2  in. ;  3  in. 

.Hexagons. — Width  across  faces:  1/4  to  13/ie  in.,  inclusive,  advanc- 
ing by  1/32  in.;  1  1/4  in.  to  3 Vie  in.,  advancing  by  Vie  in. 

Iron  Bars. 

Round. — 3/i6  to  1 7/8  in.,  advancing  by  Vs2  in.;  1 15/i6  to  2 3/4  in.,  advancing 
by  Vie  in.;  2  7/8  to  3  3/4  in.,  advancing  by  Vs  in.;  4  to  5  in.,  advancing  by 
1/4  in. 

Squares. — Vie  to  5/s  in.,  advancing  by  1/32  in.;  n/ie  in.  to  1  in.,  advancing 
by  Vie  in.;   1  Vg  in.  to  2  1/2  in.,  advancing  by  Vs  in.;  2  3/4  in.  to  4  */2  in.,  ad- 
vancing by  1/4  in- 
Half  Rounds.— -8/g,   7/16,   l/2,   5/8,   11/16,   3/4,   7/8f   1,   1  l/g,    1  \j£\  3/g,    1  l/2, 

1 3/4,  2  in. 

OvalS.— V2  X  V4,   5/8  X  5/16,  3/4  X  3/8  and  7/8  X  7/16  in. 


Half  Ovals.— 1/2  X  Vie,  Vs  X  Vie,  3/4  X  Vie,  Vs  X  Vie,  1  X  Vie, 
3/4  X  V4,  Vs  X  i/4,  1  X  i/4,  1  Vs  X  1/4.  1  X  Vie,  1  Vs  X  Vie,  1  V4  X  Vie, 
1  X  Vs,  1  Vs  X  Vs,  1  V4  X  Vs,  1  V2  X  Vs,  1  3/4  X  V*  2  X  Vs  in. 


Flats.— 1/2  X  Vie  to  Vs  in.;  Vs  X  Vie  to  1/2  in.;  3/4  X  Vie  to  Vs  in.; 
Vs  X  Vie  to  3/4  in.;  1  X  Vie  to  Vs  in.;  1  Vie  X  i/4  to  Vs  in-;  1  Vs  X  Vie  to 
1  in.;  1  1/4  X  Vie  to  1  in.;  1  3/s  X  Vie  to  1  Vs  in.;  1  1/2  X  Vie  to  1  1/4  in.; 

1  Vs  X  V4  to  1  1/2  in.;   1  3/4  X  Vie  to  1  1/2  in.;   1  Vs  X  I/A  to  1  1/2  in.;  2  X  Vie 
to  1  3/4  in.;  2  Vs  X  V4  to  1  1/4  in.;  2  i/4  X  Vie  to  2  in.;  2  Vs  X  V4  to  1  3/4  in.; 
2V2  XVie  to  2V4  in.;    2  Vs  X  V4  to  2  i/4  in.;    2  3/4  X  Vie  to  2  1/2  in.; 

2  7/8  X  V8  to  1/2  in.;  2  Vs  X  Vs  to  2  i/4  in.;  3  X  Vie  to  2  3/4  in.;  3  Vs  X  1  V2 
to  2  Vs  in.;  3 1/4  X  */4  to  2 3/4  in.;  3  1/2  X  Vie  to  2  Vs  in.;  3  3/4  X  V4  to  3  in.; 

•4  X  V4  to  3  in.;  4  1/4  X  V4  to  2  in.;  4  1/2  X  J/4  to  2  1/2  in.;  4  3/4  X  V4  to  2 
in.;  5  X  x/4  to  2  3/4  in.;  5  1/2  X  V4  to  2  in.;  6  X  V4  to  2  in.;  6  1/2  X  V4  to 
1  in.;  7  X  !/4  to  2  in.;  7  1/2  X  x/4  to  1  in.;  8  X  V4  to  2  in. 

Round  Edge  Flats. — 1  to  2  in.  wide  by  V4  to  1  V4  in.  thick;  2 1/4  to 
4  1/2  in.  wide  by  3/s  to  1 1/4  in.  thick. 


WEIGHT   OP  IRON   AND   STEEL   SHEETS. 


183 


WEIGHT  OF  IRON  AND  STEEI,  SHEETS. 

Weights  in  Pounds  per  Square  Foot. 

(For  weights  by  the  Decimal  Gauge,  see  page  33.) 


Thickness  by  Birmingham  Gauge. 

U.  S.  Standard  Gauge,  1893.     (See 
p.  32.) 

No.  of 
Gauge. 

Thick- 
ness in 
Inches. 

Iron. 

Steel. 

No.  of 
Gauge. 

Thick- 
ness, In. 
(Approx.) 

Iron. 

Steel. 

0000 

0.454 

18.16 

18.52 

0000000 

0.5 

20. 

20.40 

000 

.425 

17.00 

17.34 

000000 

0.4688 

18.75 

19.125 

00 

.38 

15.20 

15.50 

00000 

0.4375 

17.50 

17.85 

0 

.34 

13.60 

13.87 

0000 

0.4063 

16.25 

16.575 

1 

.3 

12.00 

12.24 

000 

0.375 

15. 

15.  3C 

2 

.284 

11.36 

11.59 

00 

0.3438 

13.75 

14.025 

3 

.259 

10.36 

10.57 

0 

0.3125 

12.50 

12.75 

4 

.238 

9.52 

9.71 

1 

0.2813 

11.25 

11.475 

5 

.22 

8.80 

8.98 

2 

0.2656 

10.625 

10.837 

6 

.203 

8.12 

8.28 

3 

0.25 

10. 

10.20 

7 

.18    ' 

7.20 

7.34 

4 

0.2344 

9.375 

9.562 

8 

.165 

6.60 

6.73 

5 

0.2188 

8.75 

8.925 

9 

.148 

5.92 

6.04 

6 

0.2031 

8.125 

8.287 

10 

.134 

5.36 

5.47 

7 

0.1875 

7.5 

7.65 

11 

.12 

4.80 

4.90 

8 

0.1719 

6.875 

7.012 

12 

.109 

4.36 

4.45 

9 

0.1563 

6.25 

6.375 

13 

.095 

3.80 

3.88 

10 

0.1405 

5.625 

5.737 

14 

.083 

3.32 

3.39 

11 

0.125 

5. 

5.10 

15 

.072 

2.88 

2.94 

12 

0.1094 

4.375 

4.462 

16 

.065 

2.60 

2.65 

13 

0.0938 

3.75 

3.825 

17 

.058 

2.32 

2.37 

14 

0.0781 

3.125 

3.187 

18 

.049 

.96 

2.00 

15 

0.0703 

2.8125 

2.869 

19 

.042 

.68 

1.71 

16 

0.0625 

2.5 

2.55 

20 

.035 

.40 

1.43 

17 

0.0563 

2.25 

2.295 

21 

.032 

.28 

1.31 

18 

0.05 

2. 

2.04 

22 

.028 

.12 

1.14 

19 

0.0438 

.75 

.785 

23 

.025 

.00 

1.02 

20 

0.0375 

.50 

.53 

24 

.022 

.88 

.898 

21 

0.0344 

.375 

.402 

25 

.02 

.80 

.816 

22 

0.0312 

.25 

.275 

26 

.018 

.72 

.734 

23 

0.0281 

.125 

.147 

27 

.016 

.64 

.653 

24 

0.025 

.02 

28 

.014 

.56 

.571 

25 

0.0219 

0^875 

0.892 

29 

.013 

.52 

.530 

26 

0  0188 

0.75 

0.765 

30 

.012 

.48 

.490 

27 

0.0172 

0.6875 

0.701 

31 

.01 

.40 

.408 

28 

0.0156 

0.625 

0.637 

32 

.009 

.36 

.367 

29 

0.0141 

0.5625 

0.574 

33 

.008 

.32 

.326 

30 

0.0125 

0.5 

0.51 

34 

.007 

.28 

.286 

31 

0.0109 

0.4375 

0.446 

35 

.005 

.20 

.204 

32 

0.0102 

0.40625 

0.414 

36 

.004 

.16 

.163 

33 

0.0094 

0.375 

0.382 

34 

0.0086 

0.34375 

0.351 

35 

0.0078 

0.3125 

0.319 

36 

0.0070 

0.28125 

0.287 

37 

0.0066 

0.26562 

0.271 

38 

0.0063 

0.25 

0.255 

Iron.           Steel. 

Specific  gravity  .  .                                7.7                7.854 

489.6 
Weight  per  cubic  inch 0.2778          0.2833 

As  there  are  many  gauges  in  use  differing  from  each  other,  and  even  the 
thicknesses  of  a  certain  specified  gauge,  as  the  Birmingham,  are  not  assumed 
the  same  by  all  manufacturers,  orders  for  sheets  and  wires  should  always 
state  the  weight  per  square  foot,  or  the  thickness  in  thousandths  of  an  inch. 


184 


MATERIALS. 


WEIGHTS  OF  SQUARE  AND  ROUND  BARS  OP  WROUGHT 
IRON  IN  POUNDS   PER  LINEAL  FOOT. 

Iron  weighing  480  Ib.  per  cubic  foot.     For  steel  add  2  per  cent. 


Thickness  or 
Diameter 
in  Inches. 

2l? 

Sgj 
*& 

°ii 

!§e^ 

£J! 

Thickness  or 
Diameter 
in  Inches. 

*H  e8  M 
5«§ 

•ajM 

'8  3^ 

*Jt 

Weight  of 
Round  Bar 
1  Ft.  Long. 

Thickness  or 
Diameter 
in  Inches. 

!lf 
»IJ 
II! 

Weight  of 
Round  Bar  I 
1  Ft.  Long.  [ 

0 

H/16 

24.08 

18.91 

3/8 

96.30 

75.64 

Vl6 

0.013 

0.010 

3/4 

25.21 

19.80 

7/16 

08.55 

77.40 

VS 

.052 

.041 

13/16 

26.37 

20.71 

1/2 

100.8 

79.19 

3/16 

.117 

.092 

7/8 

27.55 

21.64 

/16 

103.1 

81.00 

1/4 

.208 

.164 

15/16 

28.76 

22.59 

5/8 

105.5 

82.83 

5/16 

.326 

.256 

3 

30.00 

23.56 

H/16 

107.8 

84  69 

3/8 

.469 

.368 

1/16 

31.26 

24.55 

3/4 

110.2 

86.56 

7/16 

.638 

.501 

1/8 

32.55 

25.57 

13/16 

112.6 

88.45 

>/2 

.833 

.654 

3/16 

33.87 

26.60 

7/8 

115.1 

9036 

9/16 

1.055 

.828 

1/4 

35.21 

27.65 

15/16 

117.5 

92.29 

5/8 

1.302 

1.023 

5/16 

36.58 

28.73 

6 

120.0 

94.25 

H/16 

1.576 

1.237 

3/8 

37.97 

29.82 

1/8 

125.1 

98.22 

3/4 

1.875 

1.473 

7/16 

39.39 

30.94 

1/4 

130.2 

102.3 

13/16 

2.201 

1.728 

1/2 

40.83 

32.07 

3/8 

135.5 

106.4 

7/8 

2.552 

2.004 

9/16 

42.30 

33.23 

V2 

140.8 

110.6 

15/16 

2.930 

2.301 

5/8 

43.80 

34.40 

5/8 

146.3 

114.9 

1 

3.333 

2.618 

H/16 

45.33 

35.60 

3/4 

151.9 

119.3 

Vl6 

3.763 

2.955 

3/4 

46.88 

36.82 

7/8 

157*6 

123.7 

1/8 

4.219 

3.313 

13/16 

48.45 

38.05 

163.3 

128.3 

3/16 

4.701 

3.692 

7/8 

50.05 

39.31 

1/8 

169.2 

132.9 

1/4 

5.208 

4.091 

15/16 

51.68 

40.59 

1/4 

175.2 

137.6 

5/16 

5.742 

4.510 

4 

53.33 

41.89 

3/8 

181.3 

1424 

3/8 

6.302 

4.950 

1/16 

55.01 

43.21 

1/2 

187  5 

147.3 

7/16 

6.888 

5.410 

1/8 

56.72 

44.55 

5/8 

193.8 

152.2 

1/2 

7.500 

5.890 

3/16 

58.45 

45.91 

3/4 

200.2 

157.2 

9/16 

8.138 

6.392 

1/4 

60.21 

47.29 

7/8 

206.7 

162.4 

5/8 

8.802 

6.913 

5/16 

61.99 

48.69 

213.3 

167.6 

H/16 

9.492 

7.455 

3/8 

63.80 

50.11 

1/4 

226.9 

178.2 

3/4 

10.21 

8.018 

7/16 

65.64 

51.55 

1/2 

240.8 

189.2 

13/16 

10.95 

8.601 

V2 

67.50 

53.01 

3/4 

255.2 

200.4 

7/8 

11.72 

9.204 

9/16 

69.39 

54.50 

9 

270.0 

212.1 

15/16 

12.51 

9.828 

5/8 

.71.30 

56.00 

1/4 

285.2 

224.0 

2 

13.33 

10.47 

U/16 

73.24 

57.52 

1/9 

300.8 

236.3 

1/16 

14.18 

11.14 

3/4 

75.21 

59.07 

3/4 

316.9 

248.9 

1/8 

15.05 

11.82 

13/16 

77.20 

60.63 

10 

333.3 

261.8 

3/16 

15.95 

12.53 

7/8 

79.22 

62.22 

1/4 

350.2 

275.1 

1/4 

16.88 

13.25 

15/16 

81.26 

63.82 

1/9 

367.5 

288.6 

5/16 

17.83 

14.00 

5 

83.33 

65.45 

3/4 

385.2 

302.5 

3/8 

18.80 

14.77 

Vl6 

85.43 

67.10 

11 

403  3 

3168 

7/16 

1980 

15.55 

1/8 

87.55 

68.76 

1/4 

421.9 

331.3 

1/2 

20.83 

16.36 

3/16 

89.70 

70.45 

1/2 

440.8 

346.2 

9/16 

21.89 

17.19 

1/4 

91.88 

72.16 

3/4 

460.2 

361.4 

5/8 

22.97 

18.04 

5/16 

94.08 

73.89 

12 

480. 

377. 

WEIGHT  OF  STEEL   BARS. 


185 


WEIGHT  OP  SQUARE  AND  ROUND  STEEL  BARS   PER   LINEAL 
FOOT.      (Steel  Weighing  489.6  Ib.  per  cu.  ft.) 


Thickness  or 
Diameter 
in  Inches. 

Weight  of 
Square  Bar 
1  Ft.  Long. 

Weight  of 
Round  Bar 
1  Ft.  Long. 

Thickness  or 
Diameter 
in  Inches. 

Weight  of 
Square  Bar 
1  Ft.  Long. 

°«*e 
•s    s 
Sl% 

!§£ 
^«- 

Thickness  or 
Diameter 
in  Inches. 

Weight  of 
Square  Bar 
1  Ft.  Long. 

Weight  of 
Round  Bar 
1  Ft.  Long. 

0 

H/16 

24.56 

19.29 

3/8 

98.23 

77.15 

1/16 

0.013 

0.010 

3/4 

25.71 

20.20 

7/16 

100.5 

78.95 

1/8 

.053 

.042 

13/16 

26.90 

21.12 

1/2 

102.8 

80.77 

3/16 

.119 

.094 

7/8 

28.10 

22.07 

9/16 

105.2 

82.62 

V4 

.212 

.167 

15/16 

29.34 

23.03 

5/8 

107.6 

84.49 

5/16 

.333 

.261 

3 

30.60 

24.03 

U/ifl 

110.0 

86.38 

3/8 

.478 

.375 

1/16 

31  .89 

25.04 

3/4 

112.4 

88.29 

7/16 

.651 

.511 

1/8 

33.20 

26.08 

13/16 

114.9 

90.22 

1/2 

.850 

.667 

3/16 

34.55 

27.13 

7/8 

117.4 

92.17 

9/16 

1.076 

.845 

1/4 

35.91 

28.20 

15/16 

119.9 

94.14 

5/8 

1.328 

1  .043 

5/16 

37.31 

29.30 

6 

122.4 

96.14 

H/16 

1.608 

1.262 

3/8 

38.73 

30.42 

1/8 

127.6 

100.2 

3/4 

1  .913 

1  .502 

7/16 

40.18 

31  .56 

1/4 

132.8 

104.3 

13/16 

2.245 

1.763 

1/2 

41  .65 

32.71 

3/8 

138.2 

108.5 

7/8 

2.603 

2.044 

9/16 

43.15 

33.89 

1/2 

143.6 

112.8 

15/16 

2.989 

2.347 

5/8 

44.68 

35.09 

5/8 

149.2 

117.2 

1 

3.400 

2.670 

U/16 

46.24 

36.31 

3/4 

154.9 

121.7 

1/16 

3.838 

3.014 

3/4 

47.82 

37.56 

7/8 

160.8 

126.2 

1/8 

4.303 

3.379 

13/16 

49.42 

38.81' 

7 

166.6 

130.9 

3/16 

4.795 

3.766 

7/8 

51  .05 

40.10 

1/8 

172.6 

135.6 

1/4 

5.312 

4.173 

15/16 

52.71 

41  .40 

1/4 

178.7 

140.  < 

5/16 

5.857 

4.600 

4 

54.40 

42.73 

3/8 

184.9 

145.1 

3/8 

6.428 

5.049 

1/16 

56.11 

44.07 

1/2 

191.3 

150.2 

7/16 

7.026 

5.518 

1/8 

57.85 

45.44 

5/8 

197.7 

155.2 

1/2 

7.650 

6.008 

3/16 

59.62 

46.83 

3/4 

204.2 

159.3 

9/16 

8.301 

6.520 

1/4 

61:41 

48.24 

7/8 

210.8 

165.6 

5/8 

8.978 

7.051 

5/16 

63.23 

49.66 

8 

217.6 

171.0 

H/16 

9.682 

7.604 

3/8 

65.08 

51.11 

1/4 

231.4 

181.8 

3/4 

10.41 

8.178 

7/16 

66.95 

52.58 

1/2 

245.6 

193.0 

13/16 

11  .17 

8.773 

1/2 

68.85 

54.07 

3/4 

260.3 

204  .4 

7/8 

11  .95 

9.388 

9/16 

70.78 

55.59 

9 

275.4 

216.3 

15/16 

12.76 

10.02 

5/8 

72.73 

57.12 

1/4 

290.9 

228.5 

2 

13.60 

10.68 

n/i6 

74.70 

58.67 

1/2 

306.8 

241.0 

1/16 

14.46 

11  .36 

3/4 

76.71 

60.25 

3/4 

323.2 

253.9 

1/8 

15.35 

12.06 

13/16 

78.74 

61.84 

10 

340.0 

267.0 

3/16 

16.27 

12.78 

7/8 

80.80 

63.46 

1/4 

357.2 

280.6 

1/4 

17.22 

13.52 

15/16 

82.89 

65.10 

1/2 

374.9 

294.  4 

5/16 

18.19 

14.28 

5 

85.00 

66.76 

3/4 

392.9 

308.6 

3/8 

19.18 

15.07 

Vl6 

87.14 

68.44 

11 

411.4 

323.1 

7/16 

20.20 

15.86 

'   1/8 

89.30 

70.14 

1/4 

430.3 

337.9 

1/2 

21.25 

16.69 

3/16 

91  .49 

71.86 

1/2 

449.6 

353.1 

9/16 

22.33 

17.53 

1/4 

93  72 

73.60 

3/4 

469.4 

368.6 

5/8 

23.43 

18.40 

5/16 

95.96 

75.37 

12 

489.6 

384.5 

Weight  of  Fillets. 


Ra- 
dius, 
In. 

Area, 
Sq.  In. 

Weight  per  In.,  Lb. 

Ra- 
dius, 
In. 

Area, 
Sq.  In. 

Weight  per  In.,  Lb. 

Cast 
Iron. 

Steel. 

Brass. 

Cast 
Iron. 

Steel. 

Brass. 

1/4 

0.0134 

0.0035 

0.0038 

0.0040 

13/16 

0.1416 

0.0369 

0.0401 

0.0414 

5/16 

.0209 

.0054 

.0059 

.0061 

7/8 

.1634 

.0428 

.0465 

.0479 

3/8 

.0302 

.0078 

.0085 

.0088 

15/16 

.1886 

.0491 

.0534 

.0550 

7/16 

.0411 

.0107 

.0116 

.0120 

1 

.2146 

.0559 

.0608 

.0626 

1/2 

.0536 

.0140 

.0152 

.0157 

1  1/8 

.2716 

.0709 

.0771 

.0794 

9/1  fi 

.0679 

.0177 

.0192 

.0200 

1  1/4 

.3353 

.0874 

.0950 

.0979 

5/8 

.0834 

.0218 

.0237 

.0244 

1  3/8 

.4057 

.0920 

.1000 

.1030 

H/16 

.1014 

.0264 

.0287 

.0300 

1  1/2 

.4828 

.1259 

.1368 

.1410 

3/4 

.1207 

.0315 

.0342 

.0352 

15/8 

.5668 

.1479 

.1608 

.1657 

Continued  on  next  page. 


186 


MATERIALS. 


Weights  per  Lineal  Inch  of  Bound,  Square  and  Hexagon  Steel. 

Weight  of  1  cu.  in.  =  0.2836  Ib.  Weight  of  1  cu.  ft.  »  490  Ib. 


Thick- 
ness or 
Diam- 
eter. 

Round. 

Square. 

Hexagon 

Thick- 
ness or 
Diam- 
eter. 

Round. 

Square. 

Hexagon. 

V32 

0.0002 

0.0003 

0.0002 

17/8 

0  .  783  1 

0.9970 

0.8635 

1/16 

.0009 

.0011 

.0010 

115/ 

.8361 

.0646 

.9220 

3/32 

.0020 

.0025 

.0022 

2 

.8910 

.1342 

.9825 

1/8 

.0035 

.0044 

.0038 

21/16 

.9475 

.2064 

.0448 

5/32 

.0054 

.0069 

.0060 

21/8 

.0058 

.2806 

.1091 

3/16 

.0078 

.0101 

.0086 

23/i6 

.0658 

.3570 

.1753 

7/32 

.0107 

.0136 

.0118 

21/4 

.1276 

.4357 

.2434 

1/4 

.0139 

.0177 

.0154 

25/ie 

.1911 

.5165 

.3135 

9/32 

.0176 

.0224 

.0194 

23/8 

.2564 

.6569 

.3854 

5/16 

.0218 

.0277 

.0240 

27/ie 

.3234 

.6849 

.4593 

H/32 

.0263 

.0335 

.0290 

21/2 

.3921 

.7724 

.5351 

3/8 

.0313 

.0405 

.0345 

25/8 

.5348 

1.9541 

.6924 

13/32 

.0368 

.0466 

.0405 

23/i 

.6845 

2.1446 

.8574 

7/16 

.0426 

.0543 

.0470 

27/8 

.8411 

2.3441 

2.0304 

15/32 

.0489 

.0623 

.0540 

3 

2.0046 

2.5548 

2.2105 

1/2 

.0557 

.0709 

.0614 

31/8 

2.1752 

2.7719 

2.3986 

17/32 

.0629 

.0800 

.0693 

31/4 

2.3527 

2.9954 

2.5918 

9/16 

.0705 

.0897 

.0777 

33/g 

2.5371 

3.2303 

2.7977 

19/32 

.0785 

.1036 

.0866 

31/2 

2.7286 

3.4740 

3.0083 

5/8 

.0870 

.1108 

.0959 

35/8 

2.9269 

3.7265 

3.2275 

21/32 

.0959 

.1221 

.1058 

33/4 

3.1323 

3.9880 

3.4539 

11/16 

.1053 

.1340 

.1161 

37/g 

3.3446 

4.2582 

3.6880 

23/32 

.1151 

.1465 

.1270 

4 

3.5638 

4.5374 

3.9298 

3/4 

.1253 

.1622 

.1382 

41/8 

3.7900 

4.8254 

4.1792 

25/32 

.1359 

.1732 

.1499 

41/4 

4.0232 

5.1223 

4.4364 

13/16 

.1470 

.1872 

.1620 

43/8 

4.2634 

5.4280 

4.7011 

27/32 

.1586 

.2019 

.1749 

41/2 

4.5105 

5.7426 

4.9736 

7/8 

.1705 

.2171 

.1880 

45/8 

4.7645 

6.0662 

5.2538 

29/32 

.1829 

.2329 

.2015 

43/4 

5.0255 

6.6276 

5.5416 

15/16 

.1958 

.2492 

.2159 

47/8 

5.2935 

6.7397 

5.8371 

31/32 

.2090 

.2661 

.2305 

5 

5.5685 

7.0897 

6.1403 

9 

.2227 

.2836 

.2456 

51/8 

5.8504 

7.4496 

6.4511 

1  1/16 

.2515 

.3201 

.2773 

51/4 

6.1392 

7.8164 

6.7697 

1  1/8 

.2819 

.3589 

.3109 

53/8 

6.4351 

8.1930 

7.0959 

1  3/16 

.3141 

.4142 

.  .3464 

51/2 

6.7379 

8.5786 

7.4298 

U/4 

.3480 

.4431 

.3838 

55/8 

7.0476 

8.9729 

7.7713 

1  5/16 

.3837 

.4885 

.4231 

53/4 

7.3643 

9.3762 

8.1214 

1  3/8 

.4211 

.5362 

.4643 

57/8 

7.6880 

9  .  7883 

8.4774 

1  7/16 

.4603 

.5860 

.5076 

6 

8.0186 

10.2192 

8.8420 

1  V2 

.5012 

.6487 

.5526 

61/4 

8  .  7007 

11.0877 

9.5943 

1  9/16 

.5438 

.6930 

.5996 

6l/2 

9.4107 

11.9817 

10.3673 

1  5/8 

.5882 

.7489 

.6480 

63/4 

10.1485 

12.9211 

11.1908 

1  H/16 

.6343 

.8076 

.6994 

7 

10.9142 

13.8960 

12.0351 

1  3/4 

.6821 

.8685 

.7521 

71/2 

12.5291 

15.9520 

13.8158 

1  13/16 

.7317 

.9316 

.8069 

8 

14.2553 

18.1497 

15.7192 

Weight  of  Fillets.— Continued  from  page  185.   . 


Ra- 
dius, 
In. 

Area, 
Sq.  In. 

Weight  per  In.,  Lb. 

Ra- 
dius, 
In. 

Area, 
Sq.  In. 

Weight  per  In.,  Lb. 

Cast 
Iron. 

Steel. 

Brass. 

Cast 
Iron. 

Steel. 

Br.ass. 

13/4 

0.6572 

0.1713 

0.1862 

0.1920 

27/8 

1.774 

0.4621 

0.5022 

0.5017 

1  7/8 

.7545 

.1970 

.2137 

.2202 

3 

1.931 

.4950 

.5471 

.5635 

2 

.8585 

.2237 

.2431 

.2504 

31/4 

2.267 

.5903 

.6417 

.6609 

21/8 

.9692 

.2502 

.2743 

.2826 

31/2 

2.629 

.6926 

.7438 

.7661 

US 

1.086 

.2832 

.3079 

.3172 

33/4 

3.018 

.7873 

.8523 

.8817 

23/8 

1.210 

.3155 

.3429 

.3532 

3.434 

.8933 

.9709 

1.000 

21/2 

1.341 

.3496 

.3800 

.3914 

41/4 

3.876 

1.008 

1.096 

1.130 

25/8 

1.478 

.3857 

.4192 

.4317 

41/2 

4.346 

1.132 

1.231 

1.270 

23/4 

1.623 

.4222 

.4589 

.4727 

43/4 

4.842 

1.261 

1.371 

1.421 

WEIGHT   OF   PLATE   IKON. 


187 


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MATERIALS. 


WEIGHTS  OF  STEEL  BLOOMS. 

Soft  steel.     1  cubic  inch  —  0.284  Ib.     1  cubic  foot  =  490.75  Ibs. 


Size, 
Inches 

Lengths. 

1" 

6" 

13" 

18" 

24" 

30" 

36" 

42" 

48" 

54" 

60" 

66" 

12  X6 
X5 

20.45 
17.04 

123 
102 

245 
204 

368 
307 

491 
409 

613 
511 

736 
613 

~859 
716 

982 

818 

1104 
920 

1227 
1022 

1350 
1125 

X4 

13.63 

82 

164 

245 

327 

409 

491 

573 

654 

736 

818 

900 

11   X6 

18.75 

113 

225 

338 

450 

563 

675 

788 

900 

1013 

1  125 

1238 

X5 

15.62 

94 

188 

281 

375 

469 

562 

656 

750 

843 

937 

1031 

X4 

12.50 

75 

150 

225 

300 

375 

450 

525 

600 

675 

750 

825 

10  X8 

22.72 

136 

273 

409 

545 

682 

818 

954 

1091 

1227 

1363 

1500 

X7 

19.88 

120 

239 

358 

477 

596 

715 

835 

955 

1074 

1193 

1312 

X6 

17.04 

102 

204 

307 

409 

511 

613 

716 

818 

920 

1022 

1125 

X5 

14.20 

85 

170 

256 

341 

426 

511 

596 

682 

767 

852 

937 

X4 

11.36 

68 

136 

205 

273 

341 

409 

477 

546 

614 

682 

750 

K3 

8.52 

51 

102 

153 

204 

255 

306 

358 

409 

460 

511 

562 

9  X8 

20.45 

123 

245 

368 

491 

613 

736 

859 

982 

1104 

1227 

1350 

X7 

17.89 

107 

215 

322 

430 

537 

644 

751 

859 

966 

1073 

1181 

X6 

15.34 

92 

184 

276 

368 

460 

552 

644 

736 

828 

920 

1012 

X5 

12.78 

77 

153 

230 

307 

383 

460 

537 

614 

690 

767 

844 

X4 

10.22 

61 

123 

184 

245 

307 

368 

429 

490 

552 

613 

674 

X3 

7.66 

46 

92 

138 

184 

230 

276 

322 

368 

414 

460 

506 

8  X8 

18.18 

109 

218 

327 

436 

545 

655 

764 

873 

982 

1091 

1200 

X7 

15.9 

95 

191 

286 

382 

477 

572 

668 

763 

859 

954 

1049 

X6 

13.63 

82 

164 

245 

327 

409 

491 

573 

654 

736 

818 

900 

X5 

11.36 

68 

136 

205 

273 

341 

409 

477 

546 

614 

682 

750 

X4 

9.09 

55 

109 

164 

218 

273 

327 

382 

436 

491 

545 

600 

X3 

6.82 

41 

82 

123 

164 

204 

245 

286 

327 

368 

409 

450 

7  X7 

13.92 

83 

167 

251 

334 

418 

501 

585 

668 

752 

835 

919 

X6 

11.93 

72 

143 

215 

286 

358 

430 

501 

573 

644 

716 

788 

X5 

9.94 

60 

119 

179 

7,38 

298 

358 

417 

477 

536 

596 

656 

X4 

7.95 

48 

96 

143 

191 

239 

286 

334 

382 

429 

477 

525 

X3 

5.96 

36 

72 

107 

143 

179 

214 

250 

286 

322 

358 

393 

61/2X61/2 

12. 

72 

144 

216 

288 

360 

432 

504 

576 

648 

720 

792 

X4 

7.38 

44 

89 

133 

177 

221 

266 

310 

354 

399 

443 

487 

6  X6 

10.22 

61 

123 

184 

245 

307 

368 

429 

490 

551 

613 

674 

X5 

8.52 

51' 

102 

153 

204 

255 

307 

358 

409 

460 

511 

562 

X4 

6.82 

41 

82 

123 

164 

204 

245 

286 

327 

368 

409 

450 

X3 

5.11 

31 

61 

92 

123 

153 

184 

214 

245 

276 

307 

337 

5i/2X5i/2 

8.59 

52 

103 

155 

206 

258 

309 

361 

412 

464 

515 

567 

X4 

6.25 

37 

75 

112 

150 

188 

225 

262 

300 

337 

375 

412 

5  X5 

7.10 

43 

85 

128 

170 

213 

256 

298 

341 

383 

426 

469 

X4 

5.68 

34 

68 

102 

136 

170 

205 

239 

273 

307 

341 

375 

41/2X41/2 

5.75 

35 

69 

104 

138 

173 

207 

242 

276 

311 

345 

380 

X4 

5.11 

31 

61 

92 

123 

153 

184 

215 

246 

276 

307 

338 

4  X4 

4.54 

27 

55 

82 

109 

136 

164 

191 

218 

246 

272 

300 

X31/2 

3.97 

24 

48 

72 

96 

119 

143 

167 

181 

215 

238 

262 

X3 

3.40 

20 

41 

61 

82 

102 

122 

143 

163 

184 

204 

224 

31/2X31/2 

3.48 

21 

42 

63 

84 

104 

125 

146 

167 

188 

209 

230 

X3 

2.98 

18 

36 

54 

72 

89 

107 

'  125 

143 

161 

179 

197 

3  X3 

2.56 

15 

31 

46 

61 

77 

92 

108 

123 

138 

154 

169 

ROOFING   MATERIALS   AND   ROOF   CONSTRUCTION.     191 


ROOFING  MATERIALS  AND  ROOF  CONSTRUCTION. 

Approximate  Weight  of  Roofing  Materials. 

(American  Sheet  &  Tin  Plate  Co.) 


Material. 


Lb.  per 

sq.  ft. 


Corrugated  galvanized  iron,  No.  20,  unbearded 

Copper,  16  oz.  standing  seam .  .  .  .  , 

Felt  and  asphalt,  without  sheathing 

Glass,  i/s  in.  thick 

Hemlock  sheathing,  1  in.  thick 

Lead,  about  l/s  in.  thick 

Lath  and  plaster  ceiling  (ordinary) 

Mackite,  1  in.  thick,  with  plaster 

Neponset  roofing,  felt,  2  layers 

Spruce  sheathing,  1  in.  thick 

Slate,  3/i6  in.  thick,  3  in.  double  lap 

Slate,  l/s  in.  thick,  3  in.  double  lap 

Shingles,  6  in.  X  18  in.,  1/3  to  weather 

Skylight  of  glass,  3/ie  to  1/2  in.,  including  frame 

Slag  roof,  4-ply 

Terne  plate,  1C,  without  sheathing 

Terne  plate,  IX,  without  sheathing 

Tiles  (plain),  10  1/2  in.  X  6  1/4  in.  X  5/8  in.  -  5  1/4  in.  to  weather . 

Tiles  (Spanish),  14  1/2  in.  X  10  l/2  in.-  7  1/4  in.  to  weather 

White  pine  sheathing,  1  in.  thick 

Yellow  pine  sheathing,  1  in.  thick 


21/4 

,./< 
<»/< 

6  to  8 
6  to  8 
10 

1/2 
21/2 
63/4 

4l/2 

4  to  10 
4 
1/2 

5/8 
18 

81/2 
21/2 


Snow  and  Wind  Loads  on  Roofs. 

In  designing  roofs,  in  addition  to  the  weight  of  roofing  material  to 
be  supported,  recognition  must  be  given  to  possible  snow  and  wind  loads. 

In  snowy  localities  the  minimum  snow  load  per  horizontal  sq.  ft.  of 
roof  should  be  considered  as  25  Ib.  for  slopes  up  to  20  degrees.  For 
each  degree  increase  in  slope  up  to  45  degrees,  this  load  may  be  reduced 
1  Ib.  Above  45-degree  slope  no  snow  load  need  be  considered.  In 
especially  severe  climates  these  allowances  should  be  increased  in  ac- 
cordance with  actual  conditions. 

The  wind  load  is  the  pressure  normal  to  the  surface  of  the  roof  pro- 
duced by  a  wind  blowing  horizontally.  The  wind  pressure  against  a 
vertical  plane  as  determined  by  the  U.  S.  Signal  Service  at  Mt.  Wash- 
ington, N.  H.,  is  for  various  velocities  of  wind: 

Velocity,  miles  per  hr ..  10     20     30     40     50       60       80      100 

Pressure,  Ib.  per  sq.  ft 0.4    1.6    3.6    6.4    10.0    14.4    25.6    40.0 

The  pressure  on  a  flat  surface  is  twice  that  on  a  cylindrical  surface 
of  the  same  projected  area.  For  further  information  regarding  wind 
pressure,  see  page  626.  As  the  slope  of  the  roof  increases,  the  greater 
becomes  the  wind  pressure  on  it.  The  pressure  normal  to  the  surface 
of  roofs  of  different  slopes  exerted  by  a  wind  velocity  of  100  miles  per 
hour  (40  Ib.  per  sq.  ft.  on  a  vertical  plane)  is 

Rise,  in.  per  ft. .       4  6  8  12  16  18  24 

Angle  with 

horizontal.  . 
Pitch  (Rise  -j- 

Span) 1/6  1/4  V3  1/2  V3  V4  1 

Wind  pressure. .    16.8        23.7        29.1        36.1        38.7        39.3        40.0 

Roof  Construction.  (N.  G.  Taylor  Co.,  Philadelphia.) — Roofs  with 
less  than  1/3  pitch  are  made  with  flat  seams,  and  should  preferably  be 
covered  with  14  X  20  in.  sheets,  rather  than  with  20  X  28-in.  sheets,  as 
the  larger  number  of  seams  tend  to  stiffen  the  surface  and  prevent 
buckles.  For  a  flat  seam  roof  the  edges  of  the  sheets  are  turned  1/2  in., 
locked  together  and  soldered.  The  sheets  are  fastened  to  the  sheath.- 


.  18°  26'  26°  34'  33°  41'  45°  0'     53°  8'     56°  19'  63°  26' 


192 


MATERIALS, 


ing  boards  by  cleats  8  in.  apart  and  locked  in  the  seams.  Two  1-in 
barbed  and  tinned  nails  are  driven  in  each  cleat.  Steep  tin  roofs 
should  be  made  with  standing  seams  and  from  28  X  20-in.  sheets.  The 
sheets  are  first  single  or  double  seamed  and  soldered  together  in  a  long 
strip  reaching  from  eave  to  ridge.  The  sloping  seams  are  composed 
of  two  "upstands"  interlocked  at  the  upper  edge  and  held  to  the  sheath- 
ing boards  by  cleats.  No  solder  is  used  in  standing  seams  as  a  rule 
In  soldering  tin  roofs,  only  a  good  rosin  flux  should  be  used.  The  use 
of  acid  must  be  carefully  avoided. 

ttoof  Paints. — The  American  Sheet  and  Tin  Plate  Co.  recommends 
for  painting  metal  work  and  tin  roofs  metallic  brown,  Venetian  red,  or 
red  oxide  paint,  ground  in  pure  linseed  oil.  The  paint  should  be 
rubbed  well  in,  and  should  not  be  spread  thin.  See  also  Preservative 
Coatings,  page  471. 

Tin  Plates  are  made  of  soft  sheet  steel  coated  with  tin,  and  are 
called  in  the  trade  "coke"  or  "charcoal"  plates  according  to  the  weight 
of  coating.  These  terms  have  survived  from  the  time  when  the  highest 
quality  of  plate  was  made  from  charcoal-iron,  while  the  lower  grades 
were  made  from  coke-iron.  Consequently,  plates  to-day  with  the 
lighter  coatings  are  known  as  coke-plates,  and  are  used  for  tin  cans,  etc. 
The  various  grades  of  charcoal-plates  are  designated  by  the  letters  A  to 
AAAAA,  the  latter  having  the  heaviest  coating  and  the  highest  polish. 
There  is  one  other  brand  made  with  a  heavier  coating  than  5A,  which  is 
especially  adapted  for  nickel-plating.  The  unit  9f  value  and  measure- 
ment of  tin  plates  is  the  "base-box,"  which  will  hold  112  sheets  of 
14  X  20  in.  plate,  or  31360  sq.  in.  of  any  size.  Plates  lighter  than  65  Ib. 
per  base  box  (No.  36  gage)  are  known  as  taggers  tin. 

Weights  of  Standard  Galvanized  Sheets. 

(American  Sheet  &  Tin  Plate  Co.) 


1 

o 

M 

$£ 

&B 

d* 

| 

d 

O 

1* 

§£ 

fc^ 

5 

1 
O 

&£ 
$$ 

I* 

a* 

O 

M 

«s 

I* 
tf 

8 
9 
10 
11 
12 
13 
14 

112.5 
102.5 
92.5 
82.5 
72.5 
62.5 
52.5 

7.031 
6.406 
5.781 
5.156 
4.531 
3.906 
3.281 

15 
16 
17 
18 
19 
20 
21 

47.5 
42.5 
38.5 
34.5 
30.5 
26.5 
24.5 

2.969 
2.656 
2.406 
2.156 
1.906 
1.656 
1.531 

22 
23 
24 
25 
26 
27 
28 

22.5 
20.5 
18.5 
16.5 
14.5 
13.5 
12.5 

1.406 
1.281 
1.156 
1.031 
0.906 
.844 
.781 

29 
30 
31 
32 
33 
34 

11.5 
10.5 
9.5 
9.0 
8.5 
8.0 

0.719 
.656 
.594 
.563 
.531 
.500 

Standard  Weights  and  Gages  of  Tin  Plate. 

(American  Sheet  &  Tin  Plate  Co.,  Pittsburgh.) 


II 

Nearest 
Wire 
Gage  No. 

cr 

O3 

I* 
^ 

S.g 

PQo 

^(N 

°x 

F£ 

<u  £ 

T3   S 

^ 

Nearest 
Wire 
Gage  No. 

a1 

CO 

fe£ 
a  ... 

^ 

gfl 

«i 
°X 

^a 

100 
107 
118 
135 
128 
139 
155 
148 
175 

•§§ 

g 

Nearest 
Wire 
Gage  No. 

O" 

CQ   . 

§53 
P.  r 

^ 

Sg 

§ 

F* 

55  Ib. 
60 
65 
70 
75 
80 
85 
90 
95 

38 
37 
36 
35 
34 
33 
32 
31 
31 

0.252 
.275 
.298 
.321 
.344 
.367 
.390 
.413 
.436 

55 

60 
65 
70 
75 
80 
85 
90 
95 

lOOlb. 
1C 
1181b. 
IX 
IXL 
DC 
2X 
2XL 
3X 

30V2 
30 
29 
28 
28 
28 
27 
27 
26 

0.459 
.491 
.542 
.619 
.588 
.638 
.711 
.679 
.803 

3XL 
DX 
4X 
4XL 
D2X 
D3X 
D4X 

26 
26 
25 
25 
24 
23 
22 

0.771 
.826 
.895 
.863 
.964 
1.102 
1.239 

168 
180 
195 
188 
210 
240 
270 

TIN   AND   TERNE   PLATES. 


193 


Sizes  and  Net  Weight  per  Box  of  100  Ib.  (0.459  Ib.  per  sq.  ft.) 
Tin  Plates. 


Size  of 
Sheets. 

Sheets 
per 
Box. 

Weight 
per 
Box. 

Size  of 
Sheets. 

Sheets 
per 
Box. 

Weight 
per 
Box. 

Size  of 
Sheets. 

Sheets 
per 
Box. 

Weight 
per 
Box. 

10       X14 

225 

100 

15X15 

225 

161 

14       X31 

112 

155 

14       X20 

112 

100 

16X16 

225 

183 

111/4X223/4 

112 

91 

20       X28 

112 

200 

17X17 

225 

206 

131/4x173/4 

112 

84 

10      X20 

225 

143 

18X18 

112 

116 

131/4X191/4 

112 

91 

11       X22 

225 

172 

19X19 

112 

129 

131/2x191/2 

112 

94 

11i/2'X23 

225 

189 

20X20 

112 

143 

131/2x193/4 

112 

95 

12       X12 

225 

103 

21X21 

112 

158 

14       Xl83/4 

124 

103 

12       X24 

112 

103 

22X22 

112 

172 

14       X19V4 

120 

103 

13       X13 

225 

121 

23X23 

112 

189 

14       X21 

112 

105 

13       X26 

H2 

121 

24X24 

112 

204 

14       X22 

.112 

110 

14       X14 

225 

140 

26X26 

112 

241 

14       X221/4 

112 

111 

14       X28 

112 

140 

16X20 

112 

114 

15V2X23 

112 

127 

For  weight  per  box  of  other  than  100-lb.  plates  multiply  by  the 
figures  in  the  column  "Weight  per  Box"  in  the  preceding  table,  and 
divide  by  100.  Thus  for  IX  plates  20  X  28  in.,  200  X  135  +  100  =  270. 

Sheets  Required  for  Tin  Roofing. 

(American  Sheet  &  Tin  Plate  Co.,  1914.) 


Sheets 

Sheets 

Sheets 

Sheets 

Sheets 

e 

Required. 

£ 

Required 

.j 

Required. 

+1 

Required. 

42 

Required. 

S_4 

R 

g^_. 

, 

£_; 

w 

g^_. 

£H 

Is 

CO 

1^ 

s^ 

cr 

CO 

1^ 

2^ 

s 

1 

S&H 

1 

§^ 

s^ 

D* 
CO 

1^ 

*o 

^X 

^* 

"o 

^  V 

T3  V 

*o 

co^ 

'O  V 

"o 

^  V 

3* 

"8 

co§ 

^ 

1 

£~ 

CO 

6 
fc 

"S 
ST 

S3  •*• 

CO^ 

6 

I- 

co^ 

6 
fc 

!- 

Is 

CO 

1 

ICTJ- 

Is 

CO 

100 

59 

31 

280 

164 

86 

460 

269 

141 

640 

374 

197 

820 

479 

252 

110 

65 

34 

290 

170 

89 

470 

275 

144 

650 

379 

200 

830 

484 

255 

120 

70 

37 

300 

175 

92 

480 

280 

148 

660 

385 

203 

840 

490 

258 

130 

76 

40 

310 

181 

95 

490 

286 

151 

670 

391 

206 

850 

496 

26! 

140 

82 

43 

320 

187 

99 

500 

292 

154 

680 

397 

209 

860 

502 

264 

150 

88 

46 

330 

193 

102 

510 

298 

157 

690 

403 

212 

870 

508 

267 

160 

94 

50 

340 

199 

105 

520 

304 

160 

700 

409 

215 

880 

514 

270 

170 

100 

53 

350 

205 

108 

530 

309 

163 

710 

414 

218 

890 

519 

273 

180 

105 

56 

360 

210 

540 

315 

166 

720 

420 

221 

900 

525 

276 

190 

111 

59 

370 

216 

114 

550 

321 

169 

730 

426 

224 

910 

531 

279 

200 

117 

62 

380 

222 

'117 

560 

327 

172 

740 

432 

227 

920 

537 

282 

210 

123 

65 

390 

228 

120 

570 

333 

175 

750 

438 

230 

930 

543 

285 

220 

129 

68 

400 

234 

123 

580 

339 

178 

760 

444 

233 

940 

549 

288 

230 

135 

71 

410 

240 

126 

590 

344 

181 

770 

449 

236 

950 

554 

291 

240 

140 

74 

420 

245 

129 

600 

350 

184 

780 

455 

239 

960 

560 

295 

250 

146 

77 

430 

251 

132 

610 

356 

187 

790 

461 

243 

970 

566 

298 

260 

152 

80 

440 

257 

135 

620 

362 

190 

800 

467 

246 

980 

572 

301 

270 

158 

83 

450 

263 

138 

630 

368 

194 

810 

473 

249 

990 

578 

304 

Terne  Plates,  or  Roofing  Tin,  are  coated  with  an  alloy  of  tin  and  lead. 
In  the  "U.  S.  Eagle,  N.M."  brand  the  alloy  is  32%  tin,  68%  lead. 
The  weight  per  112  sheets  of  this  brand  before  and  after  coating  is  as 
follows: 

1C  14  X  20  1C  20  X  28  IX  14  X  20  IX  20  X  28 
Black  plates ...  95  to  100  Ib.  190  to  200  Ib.  125  to  130  Ib.  250  to  260  Ib. 
After  coating. .  .  115  to  120  230  to  240  145  to  150  290  to  300 

Terne  plates  are  made  in  two  thicknesses:  1C,  in  which  the  iron  body 
weighs  about  50  Ib.  per  100  sq.  ft.,  and  IX,  in  which  it  weighs  62  1/2  Ib. 
per  1.00  sq.  ft.  The  1C  grade  is  preferred  for  roofing,  wnile  the  !?C 


194 


MATERIALS. 


grade  is  used  for  spouts,  valleys,  gutters,  and  flashings.  The  standard 
weight  of  14  X  20  in.  1C  plates  is  107  Ib.  per  base-box,  and  of  14  x  20- 
in.  IX  plate  135  Ib. 

Long  terne  sheets  are  made  in'gages,  Nos.  14  to  32,  from  10  to  40  in. 
wide  and  up  to  120  in.  long.  They  are  made  in  five  grades  with  coat- 
ings of  8,  12,  15,  20,  and  25  Ib. 

A  box  of  112  sheets  14  X  20  in.  will  cover  approximately  192  sq.  ft. 
of  roof,  flat  seam,  or  583  sheets  1000  sq.  ft.  For  standing  seam  roofing 
a  sheet  20  X  28  in.  will  cover  475  sq.  in.,  or  303  sheets  1000  sq.  ft.  A 
box  of  112  sheets  20  X  28  in.  will  cover  approximately  366  sq.  ft. 

The  common  sizes  of  tin  plates  are  10  X  14  in.  and  multiples  of  that 
measure.  The  sizes  most  generally  used  are  14  x  20  and  20  X  28  in. 

Specifications  for  Tin  and  Terne  Plate.     (Penna.  R.R.,  1903.) 


Material  Desired. 

Rejected  if  less  than 

Tin 
Plate. 

No.  1 
Terne. 

No.  2 
Terne. 

Tin 
Plate. 

No.  1 

Terne. 

No.  2 
Terne. 

Coating: 
Tin,  per  cent  

100 
0 
0.023 

0.496 
.625 
.716 
.808 
.900 

26 
74 
0.046 

0.519 
.648 
.739 
.831 
.923 

16 
84 
0.023 

0.496 
.625 
.716 
.808 
.900 

Lead,  per  cent  

Amount  per  sq.  ft.,  Ib.  . 
Weight,  Ib.  per  sq.  ft.  of 
Grade  1C... 

0.0183 

0.468 
.590 
.676 
.763 
.850 

0.0413 

0.490 
.612 
.699 
.787 
.874 

0.083 

0.468 
.590 
.676 
.763 
.850 

Grade  IX  ... 

Grade  IXX  

Grade  IXXX  .  . 

Grade  IXXXX  

Each  sheet  in  a  shipment  of  tin  or  terne  plate  must  (1)  be  cut  as 
nearly  exact  to  size  ordered  as  possible;  (2)  must  be  rectangular,  flat, 
and  free  from  flaws;  (3)  must  double  seam  successfully  under  reason- 
able treatment;  (4)  must  show  a  smooth  edge  with  no  sign  of  fracture 
when  bent  through  an  angle  of  180  degrees  and  flattened  down  with  a 
wooden  mallet ;  (5)  must  be  so  nearly  like  every  other  sheet  in  the  ship- 
ment, both  in  thickness  and  in  uniformity  and  amount  of  coating,  that 
110  difficulty  will  arise  in  the  shops  due  to  varying  thickness  of  sheets. 

Corrugated  Sheets. — Weight  per  100  Sq.  Ft.,  Lb. 

(American  Sheet  &  Tin  Plate  Co.,  Pittsburgh,  1914.) 


Corruga- 
tions. 

5/8  in. 

1V4  in. 

2  in. 

2  i/2  in.* 
26  in. 
wide. 

2  1/2  in.f 
27  i/2  in. 
wide. 

3  in. 

5  in. 

U.  S.  Std. 
Sheet 
Metal 
Gage. 

"8 
a 

& 

jh 

eft  N 

o 

1 

a 
'3 
ft 

i 

11 

o'rt 

! 

ia 

PH 

li 

O'~ 

I 
1 

jb 

5* 

1 

& 

ji 

1 

1 
PH 

li 

0'" 

1 
'<« 

PH 

"68 
75 
81 
95 
108 
122 
135 
148 
162 
215 
269 
336 
470 

h 

73  N 

0'~ 

~~77 

84 
91 
97 
111 
124 
137 
151 
164 
178 
231 
285 
352 
486 

29 
28 
27 
26 
25 
24 
23 
22 
21 
20 
18 
16 
14 
12 
10 

"i\ 

78 
85 
99 
113 

81 
88 
95 
102 
116 
130 

"7\ 
78 
85 
99 
113 
127 
141 
155 
169 

81 
88 
95 
102 
116 
130 
144 
158 
172 
186 

"68 
75 
82 
95 
109 
122 
136 
149 
163 
216 
270 

77 
84 
91 
98 
111 
125 
138 
151 
165 
178 
232 
286 

"68 
75 
82 
95 
109 
122 
136 
149 
163 
216 
270 
338 
472 
607 

77 
84 
91 
98 
111 
125 
138 
151 
165 
178 
232 
286 
353 
488 
623 

69 
76 
83 
97 
110 
124 
137 
151 
165 
219 
274 
342 
478 
615 

78 
85 
92 
99 
113 
126 
140 
153 
167 
181 
235 
290 
358 
494 
631 

"68 
75 
82 
95 
109 
122 
136 
149 
163 
216 
270 
338 
472 

77 
84 
91 
98 
111 
125 
138 
151 
165 
178 
232 
286 
353 
488 

.... 

.... 

*  Siding.        t  Roofing, 


SLATE. 


195 


Covering  width  of  plates,  lapped  one  corrugation.  24  in.  Standard 
lengths,  5,  6,  7,  8,  9,  and  10  ft.;  maximum  length,  12  ft. 

Ordinary  corrugated  sheets  should  have  a  lap  of  1 1/2  or  2  corrugations 
side-lap  for  roofing  in  order  to  secure  water-tight  side  seams ;  if  the  roof 
is  rather  steep  1 1/2  corrugations  will  answer.  Some  manufacturers 
make  a  special  high-edge  corrugation  on  sides  of  sheets,  and  thereby  are 
enabled  to  secure  a  water-proof  side-lap  with  one  corrugation  only,  thus 
saving  from  6%  to  12%  of  material  to  cover  a  given  area. 

No.  28  gage  corrugated  iron  is  generally  used  for  applying  to  wooden 
buildings;  but  for  applying  to  iron  framework  No.  24  gage  or  heavier 
should  be  adopted. 

Galvanizing  sheet  iron  adds  about  21/2  oz.  to  its  weight  per  square 
foot. 

Slate. 

Slate  in  roofs  is  measured  by  the  square,  1  square  being  equal  to  100 
superficial  square  feet.  In  measuring,  the  width  of  the  eaves  is  allowed 
at  the  widest  part.  Hips,  valleys,  and  cuttings  are  measured  lineally 
and  6  in.  extra  is  allowed.  The  thickness  of  slate  for  roofing  varies 
usually  from  1/8  to  3/16  in.  The  weight  varies,  when  lapped,  from 
4  1/2  to  63/4  lb.  per  sq.  ft.  The  laps  range  from  2  to  4  in.,  3  in.  being 
the  standard.  As"  slate  is  usually  laid,  the  number  of  square  feet  of  roof 
covered  by  one  slate  is  w  (I  —  3)  -~  288,  w  and  I  being  the  width  and 
length  respectively  of  the  slate  in  inches. 

Number  and  Superficial  Area  of  Slate  for  One  Square  of  Roof. 


Size, 
In. 

No. 
per 
Sq. 

Area, 

£ 

Size, 
In. 

No. 

K 

Area, 
Sq. 
Ft. 

Size, 
In. 

No. 

I? 

Area, 

1?: 

Size, 
In. 

No. 

per 
Sq. 

Area, 
Sq. 
Ft. 

6X12 
7X12 

533 
457 

267 

10X14 
8X16 

261 

277 

246 

10X20 
11  X20 

169 
154 

235 

12X24 
14X24 

114 
98 

228 

8X12 
9X12 
7X14 
8X14 

400 
355 
374 
327 

'254' 

9X16 
10X16 
9X18 
10X18 

246 
221 
213 
192 

'240' 

12X20 
14X20 
16X20 
12  X22 

141 
121 
137 
126 

23J 

16X24 
14X26 
16X26 

86 
89 
78 

'225' 

9X14 

291 

12X18 

160 

240 

14X22 

108 

Weight  of  Slate,  in  Pounds,  for  One  Square  of  Roof. 

(1  cu.  ft.  slate   =  175  lb.) 


Length 
of 
Slate,  In. 

Thickness  of  Slate,  Inch. 

Vs 

3/16 

V4 

3/8 

Va 

5/8 

3/4 

1 

!>4' 

16 
18 
20 
22 
24 
26 

483 
460 
445 
434 
425 
418 
412 
407 

724 
688 
667 
650 
637 
626 
617 
610 

967 
920 
890 
869 
851 
836 
825 
815 

1450 
1379 
1336 
1303 
1276 
1254 
1238 
1222 

1936 
1842 
1784 
1740 
1704 
1675 
1653 
1631 

2419 
2301 
2229 
2174 
2129 
2093 
2066 
2039 

2902 
2760 
2670 
2607 
2553 
2508 
2478 
2445 

3872 
3683 
3567 
3480 
3408 
3350 
3306 
3263 

Corrugated  Arches. 

For  corrugated  curved  sheets  for  floor  and  ceiling  construction  in 
fireproof  buildings,  No.  16,  18,  or  20  gage  iron  is  commonly  used,  and 
sheets  may  be  curved  from  4  to  10  in.  rise — the  higher  the  rise  the 
stronger  the  arch.  By  a  series  of  tests  it  has  been  demonstrated  that 
corrugated  arches  give  the  most  satisfactory  results  with  a  base  length 
not  exceeding  6  ft.,  and  5  ft.  or  even  less  is  preferable  where  great 
strength  is  required.  These  corrugated  arches  are  made  with  1 1/4  X  3/8, 


196 


MATERIALS. 


2  1/2  X  1/2,  3  X  3/4,  and  5  X  Vs  in.  corrugations,  and  in  the  same  width 
of  sheet  as  above  mentioned. 

Terra-Cotta. 

Porous  terra-cotta  roofing  3  in.  thick  weighs  16  Ib.  per  square  foot  and 
2  in.  thick  12  Ib.  per  square  foot. 

Ceiling  made  of  the  same  material  2  in.  thick  weighs  11  Ib.  per  square 
foot. 

Tiles. 

Flat  tiles  61/4  X  101/2  X  5/8  in.  weigh  from  1480  to  1850  Ib.  per  square 
of  roof  (100  square  feet),  the  lap  being  one-half  the  length  of  the  tile. 

Tiles  with  grooves  and  fillets  weigh  from  740  to  925  Ib.  per  square  of 
roof. 

Pan-tiles  141/2  X  101/2  laid  10  in.  to  the  weather  weigh  850  Ib.  per 
square. 

Pine  Shingles. 

The  figures  below  give  the  weight  of  shingles  required  to  cover  one 
square  of  a  common  gable  roof.  For  hip  roofs  add  5  per  cent. 

Inches  exposed  to  weather.  .  .............     4      41/2      5      51/2      6 

No.  of  shingles  per  square  of  roof  .........   900     800     720     655     600 

Weight  of  shingles  per  square,  Ib  .........   216     192     173     157     144 

Skylight  Glass  Required  for  One  Square  of  Roof. 

Dimensions,  in  ...............  12  X  48  15  X  60  20  X  100  94  X  156 

Thickness,  in  ........  ,  ........        3/16  i/4             3/8  l/2 

Area,  sq.  ft  ..................  3.997  6.246        13.880  101.768 

Weight  per  square,  Ib  .........        250  350            500  700 

No  allowance  has  been  made  in  the  above  figures  for  lap.  If  ordinary 
window-glass  is  used,  single  thick  glass  (about  Vie  inch)  will  weigh  about 
82  Ib.  per  square,  and  double  thick  glass  (about  i/s  inch)  will  weigh 
about  164  Ib.  per  square,  no  allowance  being  made  for  lap.  A  box  of 
ordinary  window-glass  contains  as  nearly  50  square  feet  as  the  size  of 
the  panes  will  admit.  Panes  of  any  size  are  made  to  order  by  the 
manufacturers,  but  a  great  variety  of  sizes  are  usually  kept  in  stock, 
ranging  from  6X8  inches  to  36  X  60  inches. 

THICKNESS  OF  CAST-IRON  WATER-PIPES. 

P.  H.  Baermann,  in  a  paper  read  before  the  Engineers'  Club  of  Phila- 
delphia in  1882,  gave  twenty  different  formulae  for  determining  the 
thickness  of  cast-iron  pipes  under  pressure.  The  formulae  are  of  three 
classes: 

1.  Depending  upon  the  diameter  only. 

2.  Those  depending  upon  the   diameter  and  head  and  which  add  a 
constant. 

3.  Those  depending  upon  the  diameter  and  head  contain  an  additive 
or  subtractive  term  depending  upon  the  diameter,  and  add  a  constant. 

The  more  modern  formulae  are  of  the  third  class,  and  are  as  follows: 

t  =  0.00008/id  +  O.Old  +  0.36  ................  Shedd,  No.  1. 

t  =  0.00006/id  +  0.0133d  +  0.296  .............  Warren  Foundry,  No.  2. 

t  =  0.000058M  +  0.0152d  4-  0.312  ............  Francis,  No.  3. 

t  =  0.000048/id  4-  0.013d  +  0.32  ..............  Dupuit,  No.  4. 

t  =  0.00004/id  4-  0.1    Vd~4-  0.15  .....  .........  Box,  No.  5. 

t  =  0.000135/id  4-  0.4  -  0.001  Id  ..............  Whitman,  No.  6. 

t  =  0.00006  (h  4-  230)  d  4-  0.333  -  0.0033d  ......  Fanning,  No.  7. 

t  =  O.OOOlSftd  +  0.25  -  0.0052d  ...............  Meggs,  No.  8. 

In  which  t  =  thickness  in  inches,  h  =  head  in  feet,  d  =  diameter  in 
inches.  For  h  =  100  ft.,  and  d  =  10  in.,  formulas  Nos.  1  to  7  inclusive 
give  to  from  0.49  to  0.54  in.,  but  No.  8  gives  only  0.35  in.  Fanning's 
formula,  now  (1908)  in  most  common  use,  gives  0.50  in. 

Rankine  (Civil  Engineering},  p.  721,  says:  "Cast-iron  pipes  should  be 
made  of  a  soft  and  tough  quality  of  iron.  Great  attention  should  be  paid 


THICKNESS  OF  CAST-IRON  WATEB-HPES.        1Q7 


to  molding  them  C9rrectly,  so  that  the  thickness  may  be  exactly  uniform 
all  round.  Each  pipe  should  be  tested  for  air-bubbles  and  flaws  by  ring- 
ing it  with  a  hammer,  and  for  strength  by  exposing  it  to  double  the 
intended  greatest  working  pressure."  The  rule  for  computing  the  thick- 
ness of  a  pipe  to.  resist  a  given  working  pressure  is  t  =  rp/f,  where  r  is 
the  radius  in  inches,  p  the  pressure  in  pounds  per  square  inch,  and /the 
tensile  strength  of  the  iron  per  square  inch.  When  /  =  18,000,  and  a 
factor  of  safety  of  5  is  used,  the  above  expressed  in  terms  of  d  and  h 
becomes  t  =  0.5d  X  0.433/1  -T-  3600  =  0.00006d/i. 

"There  are  limitations,  however,  arising  from  difficulties  in  casting, 
and  by  the  strain  produced  by  shocks,  which  cause  the  thickness  to  be 
made  greater  than  that  given  by  the  above  formula."  (See  also  Burst- 
ing Strength  of  Cast-iron  Cylinders,  under  "Cast  Iron.") 

The  most  common  defect  of  cast-iron  pipes  is  due  to  the  "shifting  of 
the  core,"  which  causes  one  side  of  the  pipe  to  be  thinner  than  the  other. 
Unless  the  pipe  is  made  of  very  soft  iron  the  thin  side  is  apt  to  be  chilled 
in  casting,  causing  it  to  become  brittle  and  it  may  contain  blow-holes 
and  "  cold-shots."  This  defect  should  be  guarded  against  by  inspection 
of  every  pipe  for  uniformity  of  thickness. 

Standard  Thicknesses  and  Weights  of  Cast-iron  Pipe. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1915.) 


:§  . 

Class  A. 

Class  B. 

Class  C. 

Class  D. 

100  Ft.  Head. 

200  Ft.  Head. 

300  Ft.  Head. 

400  Ft.  Head. 

££ 

43  Lb.  Pressure. 

86  Lb.  Pressure. 

130  Lb.  Pressure. 

1  73  Lb.  Pressure 

•rt  c 

.6  c3 

** 

Pounds  per 

AS 

Pounds  per 

%& 

Pounds  per 

%* 

Pounds  per 

|S 

£ 

•S         - 

Ft. 

L'gth. 

2  if 

El 

Ft. 

L'gth. 

PH  ® 

Ft. 

L'gth. 

g| 

Ft. 

Lgfch. 

3 

0.39 

14.5 

175 

0.42 

16.2 

194 

0.45 

17.1 

205 

0.48 

18.0 

216 

4 

.42 

20.0 

240 

.45 

21.7 

260 

.48 

23.3 

280 

.52 

25.0 

300 

6 

.44 

30.8 

370 

.48 

33.3 

400 

.51 

35.8 

430 

.55 

38.3 

460 

8 

.46 

42.9 

515 

.51 

47.5 

570 

.56 

52.1 

625 

.60 

55.8 

670 

10 

.50 

57.1 

685 

.57 

63.8 

765 

.62 

70.8 

850 

.68 

76.7 

920 

12 

.54 

72.5 

870 

.62 

82.1 

985 

.68 

91.7 

1100 

.75 

100.0 

1200 

14 

.57 

89.6 

1075 

.66 

102.5 

1230 

.74 

116.7 

1400 

.82 

129.2 

1550 

16 

.60 

108.3 

1300 

.70 

125.0 

1500 

.80 

143.8 

1725 

.89 

158.3 

1900 

18 

.64 

129.2 

1550 

.75!    150.0 

1800 

.87 

175.0 

2100 

.96 

191.7 

2300 

20 

.67 

150.0 

1800 

.80 

175.0 

2100 

.92 

208.3 

2500 

.03 

229.2 

2'/50 

24 

.76 

204.2 

2450 

.89 

233.3 

2800 

.04 

279.2 

3350 

.16 

306.7 

3680 

30 

.88 

291.7 

3500 

.03 

333.3 

4000 

.20 

400.0 

4800 

.37 

450.0 

5400 

36 

.99    391.7 

4700 

.15 

454.2 

5450 

.36 

545.8 

6550 

.58 

625.0 

7500 

42 

.10'    512.5 

6150 

.28 

591.7 

7100 

.54 

716.7 

8600 

.78 

825.0 

9900 

48 

.26!    666.7 

8000 

.42 

750.0 

9000 

.71 

908.3 

10900 

.96  1050.0 

12600 

54 

.35    800.0 

9600 

.55 

933.3 

11200 

.90 

1141.7 

13700 

2.23il341.7 

16100 

60 

.39    916.7 

11000 

.67 

1104.2 

13250 

2.00 

1341.7 

16100 

2.38 

1583.3 

19000 

72 

.62  1281.9 

15380 

.95 

1547.3 

18570 

2.39 

1904.3 

22850 

. 

84 

.72!  1635.8 

19630 

2.22 

2104.1 

25250 

The  above  weights  are  per  length  to  lay  12  feet,  including  standard 
sockets;  proportionate  allowance  to  be  made  for  any  variation. 

Weight  of  Underground  Pipes.  (Adopted  by  the  Natl.  Fire  Pro- 
tection Association,  1913.)  Weights  are  not  to  be  less  than  those 
specified  when  the  normal  pressures  do  not  exceed  125  Ib.  per  sq.  in. 
When  the  normal  pressures  are  in  excess  of  125  Ib.  heavier  pipes  should 
be  used.  The  weights  given  include  sockets. 

Pipe,  in. . ,  46  8  10         12  14  16 

Weights  per  foot,  Ib....   23     35.8     52.1     70.8     91.7     116.7     143.8 


198 


MATERIALS. 


Standard  Thicknesses  and  Weights  of  Cast  Iron  Pipe. 
For  Fire  Lines  and  High-Pressure  Service. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1915.) 


Nominal  Inside 
Diam.,  In. 

Class  E. 
500  ft.  Head. 
217-lb.  Pressure. 

Class  F. 
600  ft.  Head. 
260-lb.  Pressure. 

Class  G. 
700  ft.  Head. 
3044b.  Pressure. 

Class  H. 
800  ft.  Head. 
347-lb.  Pressure. 

ft 

r  .    O> 

&  c 

Lb.  per 

A& 

_o    - 

Lb.  per 

if 

Hg 

Lb.  per 

ii 

r.    0> 
^    C 

Lb.  per 

Ft. 

Lgth. 

Ft. 

Lgth. 

Ft. 

Lgth. 

Ft. 

Lgth. 

6 
8 
10 
12 
14 
16 
18 
20 
24 
30 
36 

0.58 
.66 
.74 
.82 
.90 
.98 
.07 
.15 
.31 
.55 
.80 

42.5 
60.9 
86.9 
114.6 
145.6 
180.7 
221.8 
265.8 
359.1 
530.9 
738.1 

510 
731 

1043 
1375 
1747 
2168 
2662 
3190 
4309 
6371 
8857 

0.61 
.71 
.80 
.89 
.99 
1.08 
1.17 
1.27 
1.45 
1.73 
2.02 

44.3 
66.8 
92.8 
122.8 
158.8 
196.5 
239.3 
287.3 
392.3 
588.8 
821.0 

531 

802 
1114 
1474 
1905 
2358 
2872 
3448 
4707 
7065 
9852 

0.65 
.75 
.86 
.97 
.07 
.18 
.28 
.39 
.75 

48.1 
72.3 
101.4 
136.2 
175.1 
218.0 
268.2 
321.8 
479.8 

577 

868 
1217 
1634 
2101 
2616 
3218 
3862 
5758 

0.69 
.80 
.92 
.04 
.16 
.27 
.39 
.51 
.88 

50.5 
76.1 
107.3 
144.4 
187.5 
233.8 
287.8 
345.8 
510.6 

606 
913 
1288 
1733 
2250 
2805 
3453 
4149 
6127 

All  lengths  to  lay  12  ft.  Weights  are  approximate;  those  per  foot 
include  allowance  for  bell;  those  per  length  include  bell.  Propor- 
tionate allowance  is  to  be  made  for  variations  from  standard  length. 


Standard  and  Heavy  Cast  Iron  Bell  and  Spigot  Gas  Pipe. 
Weights  and  Dimensions. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1914.) 


Actual  Out- 

Thickness, 

Dia.  of  Sock- 

A 

Weight  per 

Weight  per 

,—  fi 

side  Dia.,  In. 

In. 

ets,  In. 

*o  w" 

Foot,  Lb. 

Length,  Lb. 

•p 

$4 

£ 

'O    . 

CT3 

£ 

"O    . 

CTJ 

i 

O  4_> 

fl 

^  . 

fl"rt 

£ 

ro  . 

CTJ 

>» 

> 

§s 

11 

o> 

3a 

8 

la 

0) 

&o 

3s 

8 

OS  £ 

8 

fc 

&« 

w 

wrt 

w 

oa* 

w 

pW 

£* 

W 

02* 

w 

4 

4.80 

5.00 

0.40 

0.42 

5.80 

5.80    4.00 

19.33 

20.0 

232 

240 

6 

6.90,     7.10 

.43 

.47 

7.90 

7.90    4.00 

30.25 

32.8 

363 

394 

8 

9.05     9.05 

.45 

.49 

10.05 

9.85    4.00 

42.08 

45.3 

505 

544 

10 

11  .10i  11  .10 

.49 

.51 

12.10 

11  .90    4.00 

55.91 

58.7 

671 

703 

12 

13.20 

13.20 

.54 

.57 

14.20 

14.00    4.50 

73.83 

76.1 

886 

913 

16 

17.40 

17.40 

.62 

.65 

18.40 

18.40    4.50 

112.58 

117.2 

1351 

1406 

20 

21.60 

21  .60 

.6G 

.75 

22.85 

22.60    4.50 

153.83 

166.7    1846!  2000 

24 

25.80 

25.80 

.76 

.82 

27.05 

26.80    5.00 

206.41 

224.0    2477;  2688 

30 

31  .74 

32.00 

.85 

1  .00 

32.99 

33.00    5.00 

284.001323.9 

3408  3887 

36 

37.96 

38.30 

.95 

1.05 

39.21 

39.30    5.00 

379.25  442.7    4551    5312 

42 

44.20  44.50 

1  .07 

1  .26 

45.45 

45.50    5.00 

497.66  581  .3    5972  6975 

48 

50.50  50.80 

1.26 

1.38 

51  .75i   51  .80    5.00 

663.50!  739.  6    7962  8875 

The  Standard  pipe  listed  above  conforms  to  the  standard  adopted  by 
the  American  Gas  Institute  in  1911.  The  heavy  pipe  given  is  not  in- 
cluded in  the  A.  G.  I.  standards  but  is  used  by  many  gas  engineers  for 
service  under  paved  streets  with  heavy  traffic,  or  where  subsoil  condi- 
tions make  the  heavier  pipe  desirable.  Pipes  are  made  to  lay  12  ft. 
length.  Weights  per  foot  include  bell  and  bead.  Length  of  bead  = 
0.75  in.  for  4-  and  6-in.  pipe;  1.00  in.  for  8-  to48-in.  pipe.  Thickness  of 
bead  =  0.19  in.  for  4-  and  6-in.  pipe;  0.25-in.  for  8-  to  48-in.  pipe. 


LEAD   REQUIRED   FOR   CAST   IRON   PIPE  JOINTS.    199 


Standard  Flanged  Cast  Iron  Pipe  for  Gas. 

(United  Cast  Iron  Pipe  &  Foundry  Co.,  1914,  Am.  Gas.  Inst.  Std.,  1913.) 


Nomi- 
nal 

Thick- 
ness, 

Flange 
Diam., 

Flange 
Thick- 

Bolt 
Circle 

Bolts 

Wgt. 
Single 

Approx.  Wgt., 
Lb. 

Diam., 
In. 

In. 

In. 

ness, 

In.   ' 

No. 

Size, 
In. 

r  lange, 
Lib. 

Foot. 

Lgth. 

4 

0.40 

9.00 

0.72 

7.125 

~T~ 

0.625 

8.19 

18.62 

223 

6 

.43 

11.00 

.72 

9.125 

4 

.625 

10.46 

29.01 

348 

8 

.45 

13.00 

.75 

11  .125 

8 

.625 

12.65 

40.05 

481 

10 

.49 

16.00 

.86 

13.75 

8 

.625 

22.53!     54.71 

656 

12 

.54 

18.00 

.875 

15.75 

8 

.625 

25.96      71.34 

856 

16 

.62 

22.50 

.00 

20.00 

12 

.75 

39.68 

108.61 

1303 

20 

.68 

27.00 

.00 

24.50 

16 

.75 

51.10!    147.95 

1775 

24 

.76 

31  .00 

.125 

28.50 

16 

.75 

65.00 

197.38 

2369 

30 

.85 

37.50 

.25 

35.00 

20 

.875 

96.70 

273.45 

3281 

36 

.95 

44.00 

.375 

41  .25 

24 

.875 

132.26 

366.67 

4400 

42 

1.07 

50.75 

.56 

47.75 

28 

1.00 

186.83    483.48 

5802 

48 

1  .26 

57.00 

.75 

54.00 

32 

1  .00 

235.23 

647.36 

7768 

Pipe  is  made  in  12-ft.  lengths,  and  faced  Vie  in.  short  for  gaskets. 
Weight  per  foot  includes  flanges.  Flanges  are  Am.  Gas.  Inst.,  and  are 
different  from  the  "American  1914"  standard  for  water  and  steam  pipe. 
Pipes  heavier  than  above  may  be  made  by  reducing  internal  diameters. 

Threaded  Cast  Iron  Pipe. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1914.) 


Nominal  diam.,  in  

3 

4 

6 

8 

10 

12 

Actual  outside  diam.,  in 

3.96 

5.00 

7.10 

9.30 

11   40 

13.50 

Thickness,  in.,  Class  B  

0.42 

0.45 

0.48 

0.51 

0.57 

0.62 

Wt.  per  foot,  Class  B    .  . 

14.6 

20.1 

31  .2 

43.9 

60.5 

78.9 

Thickness  in    Class  D 

0  48 

0  52 

0  55 

0  60 

0  68 

0  75 

Wt.  per  foot,  Class  D  

16.4 

22.8 

35.3 

51.2 

71.4 

93.7 

Quantity  of  Lead  Required  for  Cast  Iron  Pipe  Bell  and  Spigot  Joints. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1914.) 


S 

Depth  of  Joint 

i 

Depth  of  Joint 

§  c 

2  In.    1  2  1/4  In.  |  2  1/2  In.  |  Solid. 

§« 

2  In. 

2  1/4  In.  |  2  1/2  In.  |  Solid. 

p 

Approx.  Weight  of  Lead  in  Joint.—  Lb. 

3~ 

Approx.  Weight  of  Lead  in  Joint.  —  Lb. 

3 

6.00 

6.50        7.00 

10.25 

74 

44.00     48.00      52.50 

95.00 

4 

7.50 

8.00 

8.75 

13.00 

30 

54.25 

59.50 

64.75 

117.50 

6 

10.25 

11.25 

12.25 

18.00 

36 

64.75 

71  .00 

77.25 

140.25 

8 

13.25 

14.50 

15.75 

23.00 

42 

75.25 

78.75 

85.50 

155.25 

10 

16.00 

17.50 

19.00 

31  .00 

48 

85.50 

94.00 

102.25 

202.25 

12 

19.00 

20.50 

22.50 

36.50 

54 

97.60 

107.10 

116.60 

238.60 

14 

22.00 

24.00 

26.00 

38.50 

60 

108.30 

118.80 

129.50 

255.50 

16 

30.00 

33.00 

35.75 

64.75 

72 

128.00 

140.50 

153.00 

302.50 

18 

33.80 

36.90 

40.00 

72.00 

84 

147.00 

161  .50 

175.60 

348.00 

20 

37.00 

40.50 

44.00 

80.00 

The  above  table  gives  the  calculated  weight  of  lead  required  for  pipe 
joints  both  with  and  without  gasket.  Weight  of  lead  taken  at  0.41 
Ib.  per  cu.  in.  Allowance  has  been  made  for  lead  to  project  beyond  the 
face  of  the  bell  for  calking.  Pipe  specifications  allow  lead  space  to  vary 
from  those  given  in  tables,  hence  the  weights  of  lead  may  vary  ap- 
proximately 11  to  16  per  cent  from  those  given  above, 


200 


MATERIALS 


Cast-iron  Pipe  Columns,  Weight  and  Safe  Loads,  Pounds. 

(U.  S.  Cast  Iron  Pipe  and  Foundry  Co.,  1914.) 


T  onrrfVi 

4-Inch  Pipe. 

6-Inch  Pipe. 

8-Inch  Pipe. 

1  0-Inch  Pipe. 

ijGngtn. 

Wgt. 

Load. 

Wgt. 

Load. 

Wgt. 

Load. 

Wgt. 

Load. 

6  ft.  0  in. 

160 

56070 

245 

100100 

359 

164410 

428 

224200 

6   6 

171 

54130 

262 

98310 

385 

162400 

464 

222300 

7   0 

183 

52190 

280 

96270 

410 

160350 

500 

220300 

7   6 

194 

50250 

298 

94100 

436 

1  58200 

535. 

218300 

8   0 

206 

48320 

316 

92040 

462 

1  56000 

571 

216200 

8   6 

217 

46440 

333 

89820 

487 

153600 

607 

213900 

9   0 

229 

44590 

351 

87620 

513 

1  5  1  200 

643 

211600 

9   6 

240 

42800 

368 

85450 

539 

148760 

678 

209300 

10   0 

251 

41050 

386 

83260 

564 

146260 

714 

206900 

10   6 

262 

39360 

404 

81040 

590 

143700 

750 

204500 

11   0 

274 

37730 

421 

78840 

615 

141160 

785 

202200 

11   6 

285 

36160 

439 

76700 

642 

138570 

821 

199800 

12   0 

297 

34670 

457 

74580 

667 

135920 

857 

197400 

12   6 

308 

33220 

474 

71600 

692 

133340 

893 

195000 

Base  and  Top  Castings. 

Ins.  square        10 

12 

14 

16 

Wt.,  Ibs.         65 

100 

145 

200 

Add  weight  of  base  and  top  castings  f9r  complete  weight  of  column. 
Loads  are  based  on  Gordon's  formula,  with  a  factor  of  safety  of  8. 


Weight  of  Open  End  Cast-Iron  Cylinders. 

Cast  iron  =  450  Ibs.  per  cubic  foot. 
Pounds  per  Lineal  Foot. 


Thick. 

Wgt. 

Thick. 

Wgt. 

Thick. 

Wgt. 

Thick. 

Wgt. 

Bore. 

of 
Metal. 

per 
Foot. 

Bore. 

of 
Metal. 

per 
Foot. 

Bore. 

of 

Metal. 

Foot. 

Bore. 

of 
Metal. 

per 
Foot. 

In. 

In. 

Lb. 

In. 

"in*. 

Lb. 

In. 

In. 

Lb. 

In. 

In. 

Lb. 

4 

3/8 

16.1 

11 

V2 

56.5 

17 

V8 

153.6 

24 

7/8 

213.7 

!/2 

22.1 

5/8 

71.3 

18 

5/8 

114.3 

1 

245.4 

5/8 

28.4 

3/4 

86.5 

3/4 

138.1 

26 

3/4 

197.0 

5 

3/8 

19.8 

12 

V2 

61.4 

7/8 

162.1 

7/8 

230.9 

1/2 

27.0 

5/8 

77.5 

19 

5/8 

120.4 

1 

265.1 

5/8 

34.4 

3/4 

93.9 

3/4 

145.4 

28 

3/4 

211.7 

6 

3/8 

23.5 

13 

V2 

66.3 

7/8 

170.7 

7/8 

248.1 

1/2 

31.9 

5/8 

83.6 

20 

5/8 

126.6 

1 

284.7 

5/8 

40.7 

3/4 

101.2 

3/4 

152.8 

30 

7/8 

265.2 

7 

3/8 

27.2 

14 

V2 

71.2 

7/8 

179.3 

304.3 

V2 

36.8 

5/8 

89.7 

21 

5/8 

132.7 

U/8 

343.7 

5/8 

46.8 

3/4 

108.6 

3/4 

160.1 

32 

7/8 

282.4 

8 

3/8 

30.8 

15 

5/8 

95.9 

7/8 

187.9 

1 

324.0 

1/2 

41.7 

3/4 

116.0 

22 

5/8 

138.8 

H/8 

365.8 

5/8 

52.9 

7/8 

136.4 

3/4 

167.5 

34 

7/8 

299.6 

9 

V2 

46.6 

16 

5/8 

102.0 

7/8 

196.5 

1 

343.7 

5/8 

59.1 

3/4 

123.3 

23 

3/4 

174  9 

H/8 

388.0 

3/4 

71.8 

7/8 

145.0 

7/8 

205.1 

36 

7/8 

316.6 

TO 

1/2 

51.5 

17 

5/8 

108.2 

235.6 

] 

363.1 

5/8 

65.2 

3/4 

130.7 

24 

8/4 

182.2 

H/8 

410.0 

3/4 

79.2 

The  weight  of  two  flanges  may  be  reckoned  =  weight  of  one  foot, 


WELDED   PIPE. 


201 


WROUGHT-IRON  (OR  STEEL)  WELDED  PIPE. 

For  discussion  of  the  Briggs  Standard  of  Wrought-iron  Pipe  Dimen- 
sions, see  Report  of  the  Committee  of  the  A.  S.  M.  E.  in  "Standard 
Pipe  and  Pipe  Threads,"  1886.  Trans.,  Vol.  VIII,  p.  29.  The  diameter 
of  the  bottom  of  the  thread  is  derived  from  the  formula  D  — 

(0.05D+  1.9)  x  i,  in  which  D  =  outside  diameter  of  the  tubes,  and  n 
the  number  of  threads  to  the  inch.  The  diameter  of  the  top  of  the 
thread  is  derived  from  the  formula  0.8  ^  X  2  +  d,  or  1.6  i  +  d,  in  which 

d  is  the  diameter  at  the  bottom  of  the  thread  at  the  end  of  the  pipe. 
The  sizes  for  the  diameters  at  the  bottom  and  top  of  the  thread  at  the 
end  of  the  pipe  are  as  follows : 

Standard  Pipe  Threads. 


Nom- 

m^3 

Diam. 

Diam. 

Nom- 

OS'S 

Diam. 

Diam. 

inal 

ijl 

of  Pipe 

of  Pipe 

inal 

6f  Pipe 

of  Pipe 

Size. 

Ex- 

at Root 

at  Top 

Size. 

Ex- 

QJ*""1 

at  Root 

at  Top 

ternal 

-C  ^ 

of 

of 

ternal 

S  cD 

of 

of 

Diam. 

Ha 

Thread. 

Thread. 

Diam. 

Hft 

Thread. 

Thread. 



1/8 

0.405 

27 

0.3339 

0.3931 

5 

5.563 

8 

5.2907 

5.4907 

1/4 

.540 

18 

.4329 

.5218 

6 

6.625 

8 

6.3460 

6.5460 

3/8 

.675 

18 

.5676 

.6565 

7 

7.625 

8 

7.3398 

7.5398 

1/2 

.840 

14 

.7013 

.8156 

8 

8.625 

8 

8.3336 

8.5336 

3/4 

1.050 

14 

.9105 

1.0248 

9 

9.625 

8 

9.3273 

9.5273 

1 

1.315 

111/2 

1  .  1  440 

1.2832 

10 

10.750 

8 

10.4453 

10.6453 

H/4 

1.660  111/2 

1  .4876 

1  .6267 

11 

11.750 

8 

11.4390 

11.6390 

H/2 

1.900;i1l/2 

1.7265 

1  .8657 

12 

12.750 

8 

12.4328 

12.6328 

2 

2.375I1U/2 

2.1995 

2.3386 

13 

14.000 

8 

13.6750 

13.8750 

21/2 

2.875      8 

2.6195 

2.8195 

14 

15.000 

8 

14.6688 

14.8688 

3 

3.500      8 

3.2406 

3.4406 

15 

16.000 

8 

15.6625 

15.8625 

31/2 

4.000      8 

3.7375 

3.9375 

170.D. 

17.000 

8 

16.6563 

16.8563 

4 

4.500      8 

4.2343 

4.  4343 

18O.D. 

18.000 

8 

17.6500 

17.8500 

4l/2 

5.000      8 

4.7313 

4.9313 

20  O.D. 

20.000 

8 

19.6375 

19.8375 

Tap  Drills  for  Pipe  Taps  (Briggs'  Standard) . 


Size  of 
Tap, 
In. 

Size  of 
Drill, 
In. 

Size  of 
Tap,  . 
In. 

Size  of 
Drill, 
In. 

Size  of 
Tap, 
In. 

Size  of 
Drill, 
In. 

Size  of 
Tap, 
In. 

Siz^of 
Drill, 
In. 

1/8 

V4 
3/8 
1/2 

21/64 
29/64 
19/32 
23/32 

3/4 

1  1/4 

1  V2 

,%« 

1    3/16 
1  15/32 
1  23/32 

2 

21/2 

31/2 

2  3/16 
2H/16 
3  5/16 
313/ifi 

4 

41/2 

6 

4  3/16 
4H/16 
5  1/4 
6  5/ii 

Having  the  taper,  length  of  full-threaded  portion,  and  the  sizes  at 
bottom  and  top  of  thread  at  the  end  of  the  pipe,  as  given  in  the  table, 
taps  and  dies  can  be  made  to  secure  these  points  correctly,  the  length 
of  the  imperfect  threaded  portions  on  the  pipe,  and  the  length  the  tap 
is  run  into  the  fittings  beyond  the  point  at  which  the  size  is  as  given,  or, 
in  other  words,  beyond  the  end  of  the  pipe,  having  no  effect  upon  the 
standard.  The  angle  of  the  thread  is  60°,  and  it  is  slightly  rounded  off 
at  top  and  bottom,  so  that,  instead  of  its  depth  being  0.866  its  pitch,  as 
is  the  case  with  a  full  V-thread,  it  is  4/5  the  pitch,  or  equal  to  0.8  -r-  n,  n 
being  the  number  of  threads  per  inch. 

Taper  of  conical  tube  ends,  1  in  32  to  axis  of  tube  =  %  inch  to  the 
foot  total  taper. 

The  thread  is  perfect  for  a  distance  (L)  from  the  end  of  the  pipe,  ex- 
pressed by  the  rule,  L  =  (0.8  D  +  4.8)  -j-n;  where  D  =  outside  diameter 


202 


MATERIALS. 


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WELDED  PIPE. 


203 


in  inches.  Then  come  two  threads,  perfect  at  the  root  or  bottom, 
but  imperfect  at  the  top,  and  then  come  three  or  four  threads  imperfect 
at  both  top  and  bottom.  These  last  do  not  enter  into  the  joint  at  all, 
but  are  incident  to  the  process  of  cutting  the  threads.  The  thickness 
of  the  pipe  under  the  root  of  the  thread  at  the  end  of  the  pipe  =  0.0175 
D  +  0.025  in. 

Briggs'  standard  gages  are  made  by  Pratt  &  Whitney  Co.,  Hartford, 
Conn. 

Standard  Welded  Pipe. — The  permissible  variation  in  weights  is  5% 
above  and  5%  below  those  given  in  the  table  on  the  opposite  page. 
Pipe  is  furnished  with  threads  and  couplings,  and  in  random  lengths 
unless  otherwise  ordered.  Weights  are  figured  on  the  basis  of  one 
cubic  inch  of  steel  weighing  0.2833  lb.,  and  the  weight  per  foot  with 
threads  and  couplings  is  based  on  a  length  of  20  feet,  including  the 
coupling,  but  shipping  lengths  of  small  sizes  will  usually  average  less 
than  20  feet.  Taper  of  threads  is  %  inch  diameter  per  foot  length  for 
all  sizes.  The  weight  of  water  contained  in  one  lineal  foot  is  based 
on  a  weight  of  62.425  pounds  per  cubic  foot,  which  is  the  weight  at  its 
maximum  density  (39.1°  F.) 

The  steel  used  for  lap-welded  pipe  has  the  following  average  analysis 
and  physical  properties: 

El.         Tens.    Elong. 
C        Mn     "'  S  P         Lim.         Str.     in  8  in. 

Bessemer 0.07     0.30     0.045     0.100     36,000     58,000     22% 

Open-hearth 0.09     0.40     0.035     0.025     33,000     53,000     25% 

Extra  Strong~Plpe.     (National  Tube  Company,  1915) 


. 

Length  of 

*  bc-w 

Diameter. 

i 

^J 

Circum- 
ference. 

Transverse  Area. 

Pipe  per 
Sq.  Foot. 

sfj 

. 

41 

|| 

1 

9 

|| 

ll 

t<  £ 

bi 

0) 

J 

J 

sUO 

53 

W 

& 

s 

^ 

& 

£ 

W 

^ 

^ 

Hw 

&W 

J 

In. 

In. 

In. 

Lb. 

In. 

In. 

Sq.In. 

Sq.  In. 

Sq.In 

Ft. 

Ft. 

Ft. 

Va 

0.405 

0.215 

.095 

0.314 

1.272 

0.675 

0.129 

0.036 

0.093 

9.431 

17.766 

3966.393 

1/4 

.540 

.302 

.119 

.535 

1.696 

.949 

.229 

.072 

.157 

7.073 

12.648 

2010.290 

3/8 

.675 

.423 

.126 

.738 

2.121 

1.329 

.358 

.141 

.217 

5.658 

9.030 

1024.689 

1/2 

.840 

.546 

.147 

1.087 

2.639 

1.715 

.554 

.234 

.320 

4.547 

6.995 

615.017 

'      3/4 

1.050 

.742 

.154 

1.473 

3.299 

2.331 

.866 

.433 

.433 

3.637 

5.147 

333.016 

1.315 

.957 

.179 

2.171 

4.131 

3.007 

1.358 

.719 

.639 

2.904 

3.991 

200.193 

1  1/4 

1.660 

1.278 

.191 

2.996 

5.215 

4.015 

2.164 

1.283 

.881 

2.301 

2.988 

112.256 

U/2 

1.900 

1.500 

.200 

3.631 

5.969 

4.712 

2.835 

1.767 

1.068 

2.010 

2.546 

81  .487 

2 

2.375 

1.939 

.218 

5.022 

7.461 

6.092 

4.430 

2.953 

1.477 

1.608 

1.969 

48.766 

21/2 

2.875 

2.323 

.276 

7.661 

9.032 

7.298 

6.492 

4.238 

2.254 

1.328 

1.644 

33.976 

3 

3.500 

2.900 

.300 

10.252 

10.996 

9.111 

9.621 

6.605 

3.016 

1.091 

1.317 

21.801 

31/2 

4.000 

3.364 

.318 

12.505 

12.566 

10.568 

12.566 

8.888 

3.678 

0.954 

1.135 

16.202 

4 

4.500 

3.826 

.337 

14.983 

14.137 

12.020 

15.904 

1  1  .497 

4.407 

.848 

0.998 

12.525 

41/2 

5.000 

4.290 

.355 

17.611 

15.708 

13.477 

19.635 

14.455 

5.180 

.763 

.890 

9.962 

5 

5.563 

4.813 

.375 

20.778 

17.477 

15.120 

24.306 

18.194 

6.112 

.686 

.793 

7.915 

6 

6.625 

5.761 

.432 

28.573 

20.813 

18.099 

34.472 

26.067 

8.405 

.576 

.663 

5.524 

7 

7.625 

6.625 

.500  38.048 

23.955 

20.813 

45.664 

34.472 

11.192 

.500 

.576 

4.177 

8 
9 

8.625 
9.625 

7.625 
8.625 

.500  43.388 
.50048.728 

27.096 
30.238 

23.955 
27.096 

58.426 
72.760 

45.663 
58.426 

12.763 
14.334 

.442 
.396 

.500 
.442 

3.154 
2.465 

10 

10.750 

9.750 

.500  54.735  33.772 

30.631 

90.763 

74.662 

16.101 

.355 

.391 

1.929 

11 

11.750 

10.750 

.50060.07536.914 

33.772 

108.434 

90.763 

17.671 

.325 

.355 

1.587 

12 

12.750  11.7*0 

.50065.415 

40.055 

36.914 

127.676 

108.434 

19.242 

.299 

.325 

1.328 

13 

14.  000  Si  3.  000 

.50072.091 

43.982 

40.841 

153.938 

132.732 

21.206 

.272 

.293 

1.085 

14 

15.000'  14.0001  .500  77.431  147.124 

43.982 

176.715 

153.93822.777 

.254 

.272 

0.935 

15 

16.000!  15.0001  .500182.771  50.265 

47.124 

201  .062 

176.715l24.347 

.238 

.254 

.815 

The  permissible  variation  in  weight  is  5%  above  and  5%  below. 
Furnished  with  plain  ends!  and  in  random  lengths  unless  otherwise 
ordered. 


204 


MATERIALS, 


Double  Extra  Strong  Pipe.    (National  Tube  Company,  1915.) 


Diameter. 

1 

li 

3 

Circum- 
ference. 

Transverse  Area. 

Length  of 
Pipe  per 
Sq.  Foot. 

J..& 

*-M 

1 

i* 

H 

i" 

Thickn 

s 

^ 

& 

11 

h-t 

il 

*  a 
H 

6-d 

£* 

HH 

-3 
% 

% 

-1 

a 

Int. 
Surface. 

O.SU 

43  C  « 

|35 
1 

In. 

In. 

In. 

Lb. 

In. 

In. 

Sq.In  Sq.In 

Sq.In 

Ft. 

Ft. 

Feet. 

1/2 

0.840 

0.2520.294 

1.714    2.639 

0.792 

0.554 

0.050 

0.504 

4.547 

15.157 

2887.165 

3/4 

1.050 

.4341   .308 

2.440    3.299 

1.363 

.8661     .148 

.718 

3.637 

8.801 

973.404 

1.315 

.599    .358 

3.659    4.131 

1.882 

1.358 

.282 

1.076 

2.904 

6.376 

510.998 

U/4 

1.660 

.896 

.382 

5.214    5.215 

2.815 

2.164      .630 

1.534 

2.301 

4.263 

228.379 

H/2 

1.900 

1.100 

.400    6.408;  5.969 

3.456 

2.835 

.950 

1.885 

2.010 

3.472 

151.526 

2 

2.375 

1.503 

.436    9.029   7.461 

4.722 

4.430 

1.774 

2.656 

1.608 

2.541 

81.162 

21/2 

2.875 

1.771 

.552.13.695!  9.032 

5.564 

6.492    2.464 

4.028 

1.328 

2.156 

58.457 

3 

3.500 

2.300    .60018.58310.996 

7.226 

9.621 

4.155 

5.4t>6 

1.091 

1.660 

34.659 

31/2 

4.000 

2.728!   .63622.850  12.  5b6 

8.570 

12.566    5.845 

6.721 

0.954 

1.400 

24.637 

4 

4.500 

3.152    .67427.541  14.137 

9.902 

15.904 

7.803 

8.101 

.848 

1.211 

18.454 

41/2 

5.000 

3.5801    .71032.53015.708 

1  1  .247 

19.635 

10.066 

9.569 

.763 

1.066 

14.306 

5 

5.563 

4.063    .75038.55217.477 

12.764 

24.306 

12.966 

1  1  .340 

.686 

0.940 

11.107 

6 

6.625 

4.897    .86453.16020.813 

15.384 

34.472 

18.835 

15.637 

.576 

.780 

7.646 

7 

7.625 

5.875 

.875  63.079  23.955 

18.457 

45.664 

27.109 

18.555 

.500 

.650 

5.312 

8 

8.625 

6.875    .875  72  424127.096  21  .598  58.426 

37.12221.304    .442      .555 

3.879 

The  permissible  variation  in  weight  is  10%  above  and  10%  below. 
Furnished  with  plain  ends  and  in  random  lengths  unless  otherwise 
ordered. 

Standard  Boiler  Tubes  and  Flues — Lap- Welded. 

(National  Tube  Company,  1915.) 


Diameter. 

1 

1 

Circum- 
ference. 

Transverse  Area. 

Length  of  Tube 
per  Sq.  Foot. 

|:K 

jN 

QjlS 

z* 

.5?  §3 

ii 

JB 

fa 

£-3 

3 

8 

§ 

fig 

*O  4J  O 

"5  §  S 

<§§ 

1° 

1 

f 

ia 

£j 

Ia 

3* 

B 

a 

l| 

*l 

J0' 

In. 

In. 

In. 

Lb. 

In. 

In. 

Sq.In. 

Sq.  In. 

Sq.In 

Ft. 

Ft. 

Ft. 

Ft. 

13/4 

1.560 

0.095 

1.679 

5.498 

4.901 

2.405 

1.911 

.494 

2.182 

2.448 

2.315 

75.340 

1.8.0 

.095 

1.932 

6.283 

5.686 

3.142 

2.573 

.569 

1.90912.110 

2.010 

55.965 

21/4 

2.0oO 

.095 

2.186 

7.0o9 

6.472 

3.976 

3.333 

.643 

1  .697  1  .854 

1.775 

43.205 

21/2 

2.282 

.109 

2.783 

7.854 

7.109 

4.909 

4.090 

.819 

1.527 

1.673 

1.600 

35.208 

23/4 

2.532 

.109 

3.074 

8.639 

7.955 

5.940 

5.036 

.904 

1.388 

1.508 

1.448 

28.599 

3 

2.782 

.109 

3.365 

9.425 

8.740 

7.0b9 

6.079 

.990 

1.273 

1.373 

1.323 

23.690 

31/4 

3.010 

.120 

4.011 

10.210 

9.456 

8.296 

7.116 

1.180 

1.175 

1.269 

1.222 

20.237 

31/2 

3.260 

.120 

4.331 

10.996 

10.242 

9.621 

8.347 

1.274 

1.091 

1.171 

1.131 

17.252 

33/4 

3.510 

.120 

4.652 

1  1  .781 

1  1  .027 

1  1  ,045 

9.677 

1.368 

1.018 

1.088 

1.053 

14.882 

4 

3.732 

.134 

5.532 

12.5o6 

1  1  .724 

12.5ob 

10.939 

1.627 

0.954 

.023 

0.989 

13.164 

4l/2 

4.232 

.134 

6.2t8 

14.137 

13.295 

15.904 

14.0b6 

1.838 

.848 

0.902 

.875 

10.237 

5 

4.704 

.148 

7.6o9 

15.708 

14.776 

19.b35 

17.379 

2.256 

.763 

.812 

.787 

8.286 

6 

5.670 

.165 

10.282 

18.850 

17.813 

28.274 

25.249 

3.025 

.636 

.673 

.655 

5.703 

7 

6.670 

.165 

12.044 

21.991 

20.954 

38.485 

34.942 

3.543 

.545 

.572 

.559 

4.12t 

8 

7.670 

165 

13.807 

25.133 

24.096 

50.265 

46.204 

4.061 

.477 

.498 

.487 

3.117 

9 

8.640 

.180 

16.955 

28.274 

27.143 

63.617 

58.629 

4.988 

.424 

.442 

.433 

2.456 

10 

9.594 

.203 

21  .240 

31.416 

30.140 

78.540 

72.292 

6.248 

.381 

.398 

.390 

1.992 

11 

10.560 

.220 

-25.329  34.5^8 

33.175 

95.033 

87.582 

7.451 

.347 

.361 

.354 

1.644 

12 

1  1  .542 

.229 

28.788  37.699 

36.2oO 

113.097 

104.629 

8.468 

.318 

.330 

.324 

1.376 

13 

12.524 

.238 

32.439  40.841 

39.3*5  132.732 

123.190 

9.542 

.293 

.304 

.299 

1.169 

14 

13.504 

.248 

36.424 

43.982 

42.424 

153.938 

143.224 

10.714 

.272 

.282 

.277 

1.005 

15 
16 

14.482 
15.460 

.25940.775 
.270145.359 

47.124 
50.265 

45.497 
48.509 

176.715 
201.062 

164.721 
187.719 

1  1  .994 
13.343 

.254 
.238 

.263 
.247 

.259 
.242 

0.874 
.767 

LAP-WELDED  STEEL  PIPE. 


205 


Weights  and  Bursting  Strength  of  Lap-Welded  Steel  Pipe. 

(American  Spiral  Pipe  Works,  Chicago,  1911.) 

20-Pt.  Lengths,  Plain  Ends  without  Connections.  Thicknesses  in 
U.  S.  Standard  Gage  or  Inches.  Bursting  Strength  in  Lb.  per  Sq.  Jn. 
Internal  Pressure. 


Inside  Dia., 
Ins. 

Thickness, 
Ins. 

d 

i< 

r 

Bursting 
Strength. 

Inside  Dia., 
Ins. 

Thickness, 
Ins. 

3 
s*f 
ft§ 
.pfc 
^ 

Bursting 
Strength. 

Inside  Dia., 
Ins. 

Thickness, 
Ins. 

a 

M 

r 

Bursting 
Strength. 

12 

10G 

19.3 

1172 

28 

3/4 

244 

2678 

42 

1/4 

119 

595 

" 

3/16 

25.8 

1562 

" 

329 

3570 

" 

1/2 

239 

1190 

11 

1/4 

34.6 

2083 

" 

H/4 

416 

4462 

" 

3/4 

362 

1784 

14 

10G 

22.4 

1005 

30 

3/16 

64 

625 

*• 

1 

486 

2380 

" 

V4 

40.2 

1785 

" 

1/4 

85 

833 

" 

1  1/4 

612 

2976 

" 

3/8 

61.0 

2678 

" 

1/2 

172 

1666 

44 

1/4 

124 

568 

11 

1/2 

82.0 

3568 

" 

3/4 

261 

2500 

" 

1/2 

250 

1136 

16 

10G 

25.6 

879 

" 

352 

3328 

" 

3/4 

378 

1705 

" 

I/I 

45.8 

1562 

" 

H/4 

444 

4160 

" 

1 

508 

2277 

" 

3/8 

69.4 

2344 

32 

3/16 

68 

586 

" 

U/4 

640 

2840 

" 

1/2 

93.5 

3124 

" 

1/4 

91 

781 

48 

V4 

135 

520 

M 

5/8 

118.0 

3904 

" 

V2 

183 

1562 

" 

1/2 

273 

1040 

18 

10G 

28.7 

781 

" 

3/4 

278 

2344 

" 

3/4 

412 

1562 

M 

1/4 

51.4 

1388 

" 

1 

374 

3125 

" 

553 

2080 

" 

3/8 

77.8 

2082 

" 

U/4 

472 

3906 

" 

U/4 

696 

2604 

" 

1/2 

104.7 

2776 

34 

3/16 

72 

551 

50 

1/4 

141 

500 

" 

5/8 

132.0 

3472 

" 

1/4 

96 

735 

" 

1/2 

284 

1000 

20 

10G 

31.9 

703 

*• 

1/2 

194 

1470 

" 

3/4 

429 

1500 

M 

1/4 

57.0 

1250 

" 

3/4 

294 

2206 

« 

1 

576 

2000 

" 

1/2 

116.2 

2500 

" 

1 

396 

2942 

" 

11/4 

724 

2500 

•* 

3/4 

177.0 

3736 

" 

U/4 

500 

3678 

54 

1/4 

152 

463 

22 

10G 

35.0 

639 

36 

3/16 

76 

520 

1/2 

306 

926 

" 

1/4 

62.6 

1136 

" 

1/4 

102 

694 

« 

3/4 

462 

1390 

" 

1/2 

127.0 

2272 

" 

1/2 

206 

1388 

" 

1 

620 

1852 

" 

3/4 

194.0 

3410 

« 

3/4 

311 

2080 

" 

U/4 

780 

2315 

" 

1 

262.0 

4555 

'• 

419 

2776 

60 

V4 

169 

416 

24 

10G 

38.0 

586 

« 

U/4 

528 

3472 

1/2 

340 

832 

** 

V4 

68.0 

1041 

38 

s/rt 

80 

493 

'« 

3/4 

513 

1250 

" 

1/2 

138.0 

2082 

« 

1/4 

107 

658 

« 

688 

1664 

" 

3/4 

210.0 

3124 

" 

1/2 

217 

1316 

" 

U/4 

864 

2080 

M 

1 

284.0 

4160 

*< 

3/4 

328 

1972 

66 

1/4 

186 

379 

26 

3/16 

55.0 

721 

" 

441 

2632 

" 

!/2 

374 

758 

1/4 

74.0 

961 

«« 

U/4 

556 

3288 

" 

3/4 

563 

1132 

'* 

1/2 

150.0 

1922 

40 

3/16 

84 

467 

" 

1 

755 

1516 

" 

3/4 

227.0 

2885 

" 

1/4 

113 

625 

'« 

U/4 

948 

1892 

" 

307.0 

3847 

" 

1/2 

228 

1250 

72 

V4 

203 

347 

" 

H/4 

388.0 

4809 

«' 

3/4 

345 

1868 

1/2 

407 

694 

28 

3/16 

60.0 

669 

" 

1 

464 

2500 

*« 

3/4 

614 

1040 

" 

V4 

80.0 

892 

" 

U/4 

584 

3124 

«< 

822 

1388 

" 

1/2 

161  .0 

1784 

42 

3/16 

89 

446 

" 

U/4 

1032 

1736 

For  dimensions  of  extra  heavy  rolled  steel  flanges  for  above  pipe, 
see  table  page  211. 

Square  Pipe,  external  size,  7/g,  1,  H/4,  li/2,  Hl/ie,  2,  21/2,  3  in. 

Rectangular  Pipe,  external  size,  1 1/4  X  1,  11/2X1 V4,  2X1 1/4, 
2X1 1/2,  21/2X1 1/2,  3X2. 

Two  or  more  thicknesses  of  each  size. 

Pipe  Specialties. — Hand  railings  and  their  fittings;  ladders  with  flat 
or  round  pipe  bars  and  runners;  seamless  cylinders,  with  flat,  domed, 
disked,  or  necked  ends;  special  shapes  for  automobiles,  to  replace  drop 
forgings ;  tapered  tubes,  and  other  specialties  are  illustrated  in  National 
Tube  Co.'s  Book  of  Standards. 


206 


MATERIALS. 


Special  Sizes  of  Lap-welded  Pipe — Boston  Casing.   (National  Tube  Co.) 


£    N 

§1 

•«  8 

ss 

tfiS 

5.  a 

li 

68* 

!'! 

M      • 

!§  8 

as 

ll 

£  1 

la 

Is 

ga 

Is 

SQ 

e" 

la 

&* 

E-i  C 

IJ 

*Q 
w 

E-<  fl 

2 

21/4 

0.100 

4l/2 

43/4 

0.145 

55/8 

6 

0.224 

81/4 

85/s 

0.217 

21/4 

21/2 

.108 

41/2 

43/4 

.193 

55/8 

6 

.275 

81/4 

85/8 

.264 

21/2 

23/4 

.113 

43/4 

5 

.152 

61/4 

65/8 

.169 

85/8 

9 

.196 

23/4 

3 

.116 

5 

51/4, 

.153 

61/4 

65/s 

.185 

95/8 

10 

.209 

3 

31/4 

.120 

5 

51/4 

.182 

65/8 

7 

.174 

105/8 

11 

.224 

31/4 

31/2 

.125 

5 

51/4 

.182 

65/8 

7 

.231 

115/8 

12 

.243 

31/2 

33/4 

.129 

5 

51/4 

.241 

7V4 

75/8 

.181 

121/2 

13 

.259 

33/4 

4 

.134 

5 

51/4 

.301 

75/8 

8 

.186 

131/2 

14 

.276 

4 

41/4 

.138 

53/18 

5l/2 

.154 

75/8 

8 

.236 

141/2 

15 

.291 

41/4 

4l/2 

.142 

55/8 

6 

.164 

81/4 

85/8 

.188 

15l/2 

16 

.302 

41/4 

4l/2 

.205 

55/8 

6 

.190 

Other  sizes  of  lap- welded  pipe:  Inserted  Joint  Casing,  external 
diameters  same  as  Boston  Casing,  with  the  least  thickness.  The  5  5/g 
casing  is  made  0.164  and  0.190  in.  thick.  California  Diamond  X  Casing, 
sizes  5  5/8  to  15  1/2,  all  heavier  than  Boston.  Oil  Well  Tubing,  11/4  to  4  in. ; 
Bedstead  Tubing,  3/8  to  3  in.;  Flush  Joint  Tubing,  3  to  18  in.;  Allison 
Vanishing  Thread  Tubing,  2  to  8  in.,  ends  upset,  11/4  to  8  in.,  ends  not 
upset;  Special  Rotary  Pipe,  2  1/2  to  6  in.;  South  Penn  Casing,  53/i6  to 
12 1/2  in. ;  Reamed  and  Drifted  Pipe,  2  to  6  in. ;  Air-line  Pipe,  1 1/2  to  6  in. ; 
Drill  Pipe,  4  to  6  in. ;  Dry-kiln  Pipe,  1  and  1 1/4  in. ;  Tuyere  Pipe,  1  and 
H/4  in. 

TUBULAR  ELECTRIC  LINE  POLES. 

For  railway  work  the  poles  most  used  are  30  ft.  long,  and  are  com- 
posed of  7-in.,  6-in.,  and  5-in.  pipe.  Anchor  poles  are  usually  8-in., 
7-in.,  and  6-in.,  but  often  they  are  made  of  larger  pipe.  Full  directions 
for  designing  such  poles  are  given  in  the  National  Tube  Co.'s  Book  of 
Standards,  which  contains  38  pages  of  tables  of  dimensions,  load,  de- 
flection, etc.,  of  poles  of  different  sizes  and  weights. 

PROTECTIVE  COATINGS  FOR  PIPE. 

(1)  Galvanizing — The  pipe  cleaned  from  scale  and  rust  by  pickling 
in  warm  dilute  sulphuric  acid,  washed,  immersed  in  an  alkaline  bath, 
dried  and  immersed  in  molten  zinc.  (2)  Bituminous  Coating — The 
cleaned,  dried  and  warmed  pipe  is  dipped  in  a  bath  of  refined  coal  tar 
pitch,  free  from  water  and  the  lighter  oils,  at  a  temperature  not  below 
212°,  and  then  baked.  (3)  "National  Coating." — The  bituminous 
coated  pipe,  after  baking  is  wrapped  with  a  strip  of  fabric  saturated 
with  the  hot  compound,  the  edges  of  the  fabric  overlapping. 

VALVES  AND  FITTINGS. 

(From  Information  Furnished  by  National  Tube  Co.,  1915.) 

Wrought  pipe  is  usually  connected  in  one  of  three  ways,  screwed, 
flanged  or  leaded  joints. 

Screwed. — Pipe  in  sizes  from  i/g  m.  to  15  in.  inclusive  is  regularly 
threaded  on  the  ends,  and  is  connected  by  means  of  threaded  couplings. 

Flanged. — Pipe  in  sizes  11/4  inches  and  larger  is  frequently  connected 
by  drilled  flanges  bolted  together,  the  joint  being  made  by  a  gasket 
between  the  flange  faces. 

Flanges  are  attached  to  the  pipe  in  a  variety  of  ways.  The  most 
common  method  for  sizes  of. pipe  from  U/4  in.  to  15  in.  inclusive 
is  by  screwing  them  on  the  pipe.  Many  prefer  peened  flanges  for 
pipe  larger  than  6  in.  The  peened  flange  is  shrunk  on  the  end  of 
the  pipe,  and  the  latter  is  then  peened  over  or  expanded  into  a  recess 
in  the  flange  face.  Steel  flanges  are  also  welded  to  pipe  and  loose 
flanges  are  used  by  flanging  over  the  pipe  ends.  When  no  method 
of  attaching  is  stated,  screwed  flanges  are  always  furnished. 


VALVES  AND   FITTINGS.  207 

Working  Pressures. — All  valves  and  fittings  are  classified,  as  a  rule, 
under  five  general  headings,  representing  the  working  pressures  for 
which  they  are  suitable,  as  follows:  Low  Pressure,  up  to  25  pounds 
per  square  inch.  Standard,  up  to  125  pounds  per  square  inch.  Medium 
Pressure,  from  125  pounds  to  175  pounds  per  square  inch.  Extra 
Heavy,  from  175  pounds  to  250  pounds  per  square  inch.  Hydraulic, 
for  high  pressure  water  up  to  800  pounds  per  square  inch. 

The  following  table  gives  the  names  of  different  valves  and  fittings, 
the  material  of  which  they  are  made,  and  the  regular  sizes  manu- 
factured for  the  different  pressures  (L,  low;  S,  standard;  M,  medium; 
E,  extra  heavy ;  H ,  hydraulic) : 

SCREWED  FITTINGS. 

Malleable  Iron S,  E,  H,  sizes  1/8  to    8  in. 

Cast  Iron S,  E,  1/4  to  12  in. 

FLANGED  FITTINGS. 

Cast  Iron L,  S,  E,  H,  sizes  2  in.  and  larger. 

GATE  VALVES. 

Brass L  S  M  E        If  up  to  3  in. 

Iron  Body,  sizes. .    12  to  48     2  to  30  2  to  18    1 1/4  to  24    H/2  to  12  in. 

GLOBE  AND  ANGLE  VALVES. 

Brass S,  i/s  to  4;  M,  1/4  to  3;  E,  1/2  to  3;  H,  1/2  to  2 

Iron  Body S,  2  to  12;  E,  2  to  12 

CHECK  VALVES. 

Brass S,  M,  E,  H,  sizes  l/s  to    3  in. 

Iron  Body L,  S,  M ,  E,  H,     '      2    to  12  in. 

COCKS,  STEAM  AND  GAS. 

Brass sizes  1/4  to  3  in. 

Iron  Body *      1/2  to  3  in. 

Nipples. — Nipples  are  made  in  all  sizes  from  i/g  in.  to  12  in.  in- 
clusive, in  all  lengths,  either  black  or  galvanized,  and  regular  right- 
hand  or  right-  and  left-hand  threads.  (For  table  of  nipples  see  National 
Tube  Co.'s  Book  of  Standards.)  Long  screws  or  tank  nipples  are  made 
of  extra  heavy  pipe  because  there  is  less  danger  of  crushing  or  splitting 
them  when  screwing  up. 

Screwed  Fittings — Malleable  Iron. — Standard  Malleable  Iron  Fittings 
are  made  both  plain  and  beaded.  The  former  are  generally  used  for 
low  pressure  gas  and  water,  as  in  house  plumbing  and  railing  work.  The 
beaded  is  the  standard  steam,  air,  gas,  or  oil  fitting.  Beaded  fittings, 
in  sizes  4  in.  and  smaller,  are  made  in  nearly  every  useful  combination  of 
openings.  Sizes  larger  than  4  in.  are  not  usually  made  reducing  except 
by  means  of  bushing.  Extra  heavy  and  hydraulic  malleable  iron 
fittings  are  flat  bead,  or  banded. 

Screwed  Fittings — Cast  Iron. — It  is  not  considered  good  practice  to 
use  screwed  cast-iron  fittings  of  any  kind  in  sizes  larger  than  6  in. 

Flanged  Fittings. — The  flanges  of  the  low  pressure  and  standard  are 
the  same  with  the  exception  of  the  flange  thickness,  which  is  less  on  the 
low  pressure.  These  flanges  are  known  as  the  American  Standard. 
(See  pp.  209,  210.) 

There  is  no  recognized  standard  for  flanges  in  hydraulic  work. 

Unions. — Unions  are  usually  classified  under  two  headings,  Nut  unions 
and  Flange  unions.  Nut  unions  are  commonly  used  in  sizes  2  in.  and 
smaller,  and  flange  unions  in  sizes  larger  than  2  in.  However,  many 
manufacturers  make  nut  unions  as  large  as  4  in.  and  flange  unions 
smaller  than  2  in. 

Nut  unions  are  made  in  malleable  iron,  brass,  and  malleable  iron, 
and  ail  brass.  The  all  malleable  iron  union  (lip  union)  is  the  standard 
malleable  iron  union  of  the  trade  and  requires  a  gasket.  The  brass 
and  malleable  iron  union  is  a  better  union,  because  no  gasket  is  re- 
quired and  there  is  no  possibility  of  the  parts  rusting  together.  The 
pipe  end  of  this  union  which  carries  an  external  thread,  called  the 


208  MATERIALS. 

thread  end,  upon  which  the  ntit  or  ring  screws,  is  made  of  brass,  and  the 
other  pipe  end  (called  the  bottom)  and  nut  ring  are  made  of  malleable 
iron.  The  seat  formed  by  the  brass  and  iron  pipe  ends,  when  brought 
together,  is  truly  spherical  and  the  harder  iron  is  sure  to  make  a  perfect 
joint  with  the  softer  brass. 

All-brass  unions  are  made  with  a  spherical  or  conical  seat,  no  gaskets 
being  required.  The  finished  all-brass  union  is  often  used  where  showy 
work  is  desired,  such  as  oil  piping  for  engines,  etc. 

Flange  unions  are  made  of  malleable  iron,  malleable  iron  and  brass, 
cast  iron,  and  cast  iron  and  brass. 

The  type  of  flange  union  recommended  for  standard  work  is  made 
with  a  brass  to  iron  non-corrosive  ball  joint  seat  which  requires  no 
gasket  to  make  a  tight  joint  even  when  the  pipe  alignment  is  imperfect. 
The  flange  is  loose  on  the  collar,  so  that  the  bolts  match  the  holes  in 
any  position. 

Valves  and  Cocks. — The  most  common  means  for  regulating  the  flow 
of  fluids  in  pipes  is  by  means  of  valves  and  cocks,  valves  being  pre- 
ferred because  of  the  easier  operation  and  greater  reliability.  The 
common  types  of  valves  are  straightway  or  gate,  globe,  and  angle.  A 
globe  valve  offers  more  resistance  to  the  flow  of  any  fluid  than  the 
straightway  valve. 

Globe  and  Angle  Valves. — Many  manufacturers  make  a  globe  and 
angle  valve  known  as  light  standard  or  competition  valve,  but  it  is 
not  recommended  for  any  work  except  the  lowest  pressures,  or  where 
the  valve  will  not  be  often  opened  or  closed. 

Cocks. — Among  the  modern  types  of  cocks  is  one  made  with  iron 
body  and  brass  plug.  This  cock  has  an  inverted  plug  with  a  spring 
at  the  bottom  constantly  pressing  the  plug  against  the  seat,  which 
reseats  the  plug  if  it  should  stick.  These  cocks  are  tested  to  250  Ib. 
cold-water  pressure,  and  125  Ib.  compressed-air  pressure  under  water, 
and  are  recommended  for  125  Ib.  working  pressure. 

Blast  Furnace  Fittings. — Tuyere  cocks  and  tuyere  unions  used  in 
blast  furnace  piping  are  always  made  of  brass  on  account  of  ease  in 
disconnecting,  greater  reliability  of  metal  and  resistance  to  corrosion 
from  the  impurities  in  the  water,  such  as  sulphuric  acid. 

STANDARD   PIPE   FLANGES   (CAST  IRON). 

The  following  tables  showing  dimensions  of  standard  pipe  flanges 
were  adopted  by  the  American  Society  of  Mechanical  Engineers,  the 
Master  Steam  and  Hot  Water  Fitters'  Association,  and  a  committee 
representing  the  manufacturers  of  pipe  fittings.  They  represent  a 
compromise  between  the  standards  adopted  by  the  American  Society  of 
Mechanical  Engineers  and  the  Master  Steam  and  Hot  Water  Fitters' 
Association  hi  1912,  known  as  the  1912  U.  S.  Standard,  and  the  stand- 
ards adopted  by  a  conference  of  manufacturers  in  July,  1912,  known 
as  the  Manufacturers'  standard.  The  new  standards,  given  in  the 
tables,  are  called  the  American  Standard,  and  became  effective  Jan.  1, 
1914.  The  table  of  flanges  for  extra  heavy  fittings  is  for  working 
pressures  up  to  250  Ib.  per  sq.  in.  The  table  for  ordinary  fittings  is  for 
working  pressures  up  to  125  Ib.  per  sq.  in.  In  the  tables,  the  values  of 

T  X  T) 

stresses  in  pipe  walls  were  calculated   from  the  formula  S  =  - — .—  > 

where  p  =  working  pressure,  Ib.  per  sq.  in.,  t  =  thickness  of  pipe, 
in.,  and  r  =  radius  of  pipe,  in.  The  highest  stress  was  found  to  be 
2000  Ib.  per  sq.  in.  on  the  250-lb.,  46-  and  48-in.  pipe  walls,  giving  a 
factor  of  safety  of  about  10.  The  desirable  thickness  of  pipe  (Col.  2) 

is  calculated  from  the  formula  T  =  PA* 3°  -P  +  0.333/1  -  -^  Jl.2. 

where  p  =  pressure,  Ib.,  per  sq.  in.,  5  =  1800,  and  d  =  diameter 
of  pipe.  The  minimum  thickness  in  even  fractions  of  an  inch  is  given 
in  Col.  3.  The  following  approximate  formulae  were  also  used  for 
ordinary  fittings:  Diam.  of  bolt  circles  =  1.10  d  +  3.  Flange  thick- 
ness (for  pipe  diameters  26  to  100  in.  inclusive)  =  0.0315  d  +  1.25. 
For  extra  heavy  fittings  the  formulae  are:  Bolt  circle  =  1.171d+3.75; 
Flange  thickness  =  0.0546  d  +  1.375  (for  sizes  10  to  48  in.  inclusive). 


American  Standard  Cast  Iron  Pipe  flanges  for  Pressures  Up  to  ™ 

Lb.  per  Sq.  In.      (All  Dimensions  in  Inches.) 


r  r    Pipe 

£« 

Flanges. 

Bolts. 

fc 

Thickness 

E  • 

jj 

i 

o 

Jj 

^ 

£ 

.S 

a£ 

f- 

See  Fig.  75, 
p.  210 

S 

& 

|i 

n  & 

W    OH 

! 

Q 

IS 
H 

if 

0) 

g 

5 

I! 

CU     *M 

g& 

A 

B 

C 

1 

0.43 

7/16 

143 

4 

7/16 

I  1/2 

3 

~4 

7/16 

0.093 

264 

9/16 

2.12 

^9l 

U2T 

1  1/4 

0.44 

7/16 

178 

41/2 

1/2 

15/8 

33/8 

4 

7/16 

0.093 

412 

9/16 

2.38  0.91 

L47 

H/2 

0.45 

7/16 

214 

9/16 

13/4 

37/8 

4 

1/2  0.126; 

438 

5/82.731.00 

1.73 

2 

0.46 

7/16 

286 

6 

5/8 

2 

43/4 

4 

5/81 

0.202 

486 

3/4! 

3.35 

1.21 

2.14 

21/2 

0.48 

7/16 

357 

7 

11/16 

21/4 

51/2 

4 

5/8  0.202 

750 

3/4  3.88 

1.21 

2.67 

'3 

0.50 

7/16 

428 

71/2 

3/4 

21/4 

6 

4 

5/8  i  0.202 

1093 

3/4 

4.23 

1.21 

3.02 

31/2 

0.52 

7/16 

500 

81/2 

13/16 

21/2 

7 

4 

5/8 

0.202 

1488 

3/4 

4.94 

1.21 

3.73 

4 

0.53 

1/2 

500 

9 

15/16 

21/2 

71/2 

8 

5/8  '0.202 

972 

3/4 

2.87 

1.21 

1.56 

41/2 

0.55 

1/2 

562 

91/4 

15/16 

23/8 

73/4 

8 

3/4 

0.302 

823 

7/8^2.96 

1.44 

1.52 

5 

0.56 

1/2 

625 

10 

15/16 

21/2 

81/2 

8 

3/4 

0.302 

1016 

7/8 

3.25 

1.44 

1.81 

6 

0.60 

9/16 

667 

11 

21/2 

91/2 

8 

3/4 

0.302 

1463 

7/8 

3.63 

1.44 

2.19 

7 

0.63 

5/8 

700 

12l/2 

1/16 

23/4 

103/4 

8 

3/4  '0.302 

1991 

7/84.11 

1.44 

2.67 

8 

0.66 

5/8 

800 

131/2 

1/8 

23/4 

113/4 

8 

3/4!  0.302  2600 

7/8  4.50 

1.44 

3.06 

9 

0.70 

H/16 

818 

15 

1/8 

3 

131/4112 

3/4  0.302  2194 

7/8|3.43 

1  .44  1  .99 

10 

0.73 

3/4 

833 

16 

8/18 

3 

141/4112 

7/8 

0.420 

1948 

3.69 

1  .66  2.03 

12 

0.80 

13/16 

923 

19 

1/4 

31/2 

17 

12 

7/8 

0.420 

2805 

4.40 

1.66 

2.74 

14 

0.86 

7/8 

1000 

21 

3/8 

31/2 

183/4 

12 

0.5502915 

1/8 

4.86  1  .88 

2.98 

15 

0.90 

7/8    1072 

221/4 

3/8 

35/8 

20 

16 

1 

0.5502510 

1/83.90  1.88 

2.02 

16 

0.93 

1000 

231/2 

7/16 

33/4 

21  1/4 

16 

1 

0.550 

2856 

1/8 

4.14 

1.88 

2.26 

18 

1.00 

1/16 

1059 

25 

9/16 

31/2 

223/4 

16 

1  l/s  0.694 

2865 

1/44.44 

2.09 

2.35 

20 

1.07 

1/8 

1111 

271/2 

H/16 

33/4 

25 

20 

1  1/8 

0.694 

2829 

1/4 

3.91 

2.09 

1.82 

22 
24 

1.13 
1.20 

3/16 
1/4 

1158 
1200 

13/16 
7/8 

33/4 

271/4 
291/2 

20 
20 

1  1/4  0.893  2660 
l/iO.8933166 

1  3/8  4.2612.31 
1  3/8;4.62l2.31 

1.95 
2.31 

26 

1.27 

5/16 

1238 

341/4 

2 

41/8 

313/4 

24 

1  1/4 

0.893 

3096 

13/8 

4.14 

2.31 

1.83 

28 
30 

1.33 
1.40 

3/8 
7/16 

1273 
1304 

361/2 

383/4 

2    1/16 
2    1/8 

4i/4|  34  ' 
43/8l  36 

28 
28 

1  l  /4  10.  893  1  3078 
13/8  1.057  12985 

1  3/8  3.81 
1/2  4.03 

2.31 
2.53 

1.50 
1.50 

32 

1.47 

1/2 

1333 

413/4J2    1/4 

47/8 

381/2 

28 

1  1/2 

1.294 

2775 

5/8 

4.31 

2.75 

1.56 

34 

1.54 

9/16 

1360 

433/42   5/i6 

47/8 

401/2 

32 

H/2 

.294274 

1  5/8  3.97 

2.75 

1.22 

36 

1.60 

5/8 

1385 

46 

2    3/8 

5 

423/4 

32 

1  1/2 

.294 

3073 

15/8 

4.19 

2.75 

1.44 

38 

1.67 

H/16 

1407 

483/4 

2  3/8 

53/8 

451/4 

32 

1  5/8 

.515 

2924 

1  3/4  4.43 

2.96 

1.47 

40 

1.73 

3/4 

1428 

503/42    1/2 

53/8    471/4 

36 

1  5/8 

.515 

2880 

13/4 

4.11 

2.96 

1.15 

42 

1.82 

13/16 

1448 

53 

2    5/8 

5l/2    49i/2 

36 

1  5/8 

.5153175 

13/4 

4.31 

2.96 

1.35 

44 

1.87 

7/8  11467 

551/4 

2    5/8 

5  5/8    51  3/4 

40 

15/8 

.515 

3136 

1  3/4  4.06 

2.96 

1.10 

46 

1.94 

115/ie  1484 

571/42H/16 

55/8    533/4 

40 

1  5/8 

.515 

3428 

18/4 

4.22 

2.96 

1.26 

48 

2.00 

2 

1500 

591/212  3/4 

53/4 

56 

44 

1  5/8 

.515 

3393 

13/4 

3.98 

2.96 

1.02 

50 
52 

2.07 
2.14 

21/16 
21/8 

1515 
1530 

SI'" 

2   3/4 
2   7/8 

57/8 
6 

581/444 
60  1/2  44 

13/4J   .746)3195 
1  3/4{   .746  3456 

7/8|4.14 
7/84.30 

3.19 
3.19 

0.95 
1.11 

54 

2.20 

23/16  1543   661A3         161/s 

62  3/4  44 

13/4 

.746 

3726 

17/8 

4.45 

3.19 

1.26 

56 

2.27 

21/4 

1555    683/4 

3           163/8 

65 

48 

13/4 

.746 

3674 

1  7/8  4.26 

3.19 

1.07 

58 

2.34 

2  5/16  1567 

71 

3   1/8    61/2 

671/4 

48 

1  3/4 

.746 

394 

17/fi 

4.4013.19 

1.21 

60 

2.41 

27/ie  1538 

73 

3    1/8    61/2 

691/4 

52 

13/4 

.7463892 

1  7/8  4.19 

3.19 

1.00 

62 

2.47 

2  1/2    1550 

753/4 

3   1/4 

67/8 

713/4 

52 

1  7/8  12.  051  3538 

2 

4.34 

3.41 

0.93 

64 

2.54 

2  9/16 

1561 

78 

3    1/4 

7 

74 

52 

7/8 

2.051 

3770 

2 

4.48 

3.41 

1.07 

66 

2.61 

25/8 

1572 

80 

3  3/g 

7 

76 

52 

7/82.051 

4010 

2 

4.60 

3.41 

1.19 

68 

2.68 

2H/16H582 

821/43   3/8 

71/8 

781/4 

56 

7/8 

2.051 

3952 

2 

4.38 

3.41 

0.97 

70 

2.74 

23/4  11591 

84l/213  1/2 

71/4 

801/2 

56 

7/8  !  2.  051 

4188 

2 

4.51 

3.41 

1.10 

72 

2.81 

213/ie  '1600    86  1/2  3   1/2 

71/4 

821/2 

60 

7/82.051 

4136 

2 

4.33 

3.41 

0.92 

74 

2.88 

27/8    1609    881/213  5/8 

71/4 

841/2 

60 

7/8 

2.051 

4368 

2 

4.44 

3.41 

1.03 

76 

2.94 

215/16 

1617    903/43  5/8 

73/8 

861/260 

7/82.051 

4608 

2 

4.54 

3.41 

1.13 

78 

3.01 

3 

1625    93    - 

3  3/4 

71/2 

883/4 

60 

2 

2.302 

432 

21/8 

4.66 

3.63 

1.03 

80 

3.08 

31/16 

1633    951/4 

3  3/4 

75/8 

91 

60 

2 

2.302 

4549 

2l/8!4.78 

3.63 

1.15 

82 

3.15 

31/8 

1640    971/23   7/8 

73/4    931/4 

60 

2 

2.302 

4779 

2  l/s  4.90 

3.63 

1.27 

84 

3.21 

33/16 

1647    993/43  7/8 

77/8    951/2 

64 

2 

2.302 

4702 

21/8 

4.68 

3.63 

1.05 

86 

3.28 

31/4 

1653  102 

4 

8        973/4 

64 

2 

2.302 

4928 

2  l/8,'4.79 

3.63 

1.16 

88 

3.35 

35/16 

1660  1041/4 

4 

81/8  100 

68 

2 

2.302 

4857 

2  l/s 

4.60 

3.63 

0.97 

90 

3.41 

33/8 

1667s  106  1/2  4  1/8 

81/411021/4 

6821/s 

2.648  4416 

21/4 

!4.71 

3.83 

0.88 

92 

3.48 

31/2 

16431083/44  l/s 

83/8  104  1/2  68  21/8^2.648  4615 

2  1/4  4.81 

3.83 

0.98 

94 

3.55 

39/16 

1649  111 

4    1/4 

8.1/2  1061/468  21/8 

2.648 

4817 

21/4 

4.89 

3.83 

1.06 

96 
98 
100 

3.62 
3.68 
3.75 

35/8 
3H/16 
33/4 

1655  1131/4 
1661  1151/s 
1667J1173/4 

41/4    85/81081/216821/43.023440 
4  S/g  Is  3/4  110  3/4|68  2  1/4  3.023  4587 
4  3/8  |87/8;113      |68l2  1/413.023  4776 

2  3/8  4.99  4.06 
23/85.094.06 
23/85.20l4.06 

0.93 
1.03 
1.14 

210 


MATERIALS. 


The  last  three  columns  of  the  table  refer  to  the  sketch  Fig.  75,  and  show 

the  distances  between  bolt  holes,  the  maximum 

space  occupied   by  the  nuts  and  the  minimum 

t-*-B->j       space   between   adjacent   nuts,   all  measured  on 

/-f-\       '/i~\!       tne  cnord-     Bolt  holes  are  to  straddle  the  center 

/.  ;   \ — !(--}— V-      une'  ancl  are  to  De  Vs  in.  larger  in  diameter  than 

\     /^CJ\     /        the  bolts.     Standard  weight  fittings  and  flanges 

j~     ^  are  to  be  plain  faced,  but  extra  heavy  fittings  and 

flanges  are  to  have  a  raised  surface  i/ie  in.  high 

(On  Chord)  inside  of  bolt  holes  for  gaskets.    Square  head  bolts 

with  hexagonal  nuts  are  recommended,  but  for 

Fig.  75.  bolts  is/g  in.  diameter  and  larger,  studs  with  a  nut 

on  each  end  may  be  substituted.     Flanges  are  to 

be  spot  bored  for  nuts  for  sizes  32  in.  to  100  in.  inclusive.     For  super- 
heated steam,  steel  flanges,  fittings  and  valves  are  recommended. 

American  Standard  Extra  Heavy  Cast  Iron  Pipe  Flanges 
For  Pressures  up  to  250  Lb.  per  Sq.  In.     (All  Dimensions  in  Inches.) 


Pipe             |d 

Flanges. 

Bolts. 

See  Fig.  75, 
p.  210. 

g 

Thickness.^ 

i 

"8 

1 

. 

fe 

d 

•  d 

0) 

o 

8 

ij 

•sl 

•I 

w  P< 

i 

Thickn. 

8 

0  g 

|  Numbe 

IA 

>  a1 
43  co 

*»  °* 

4J>  rt 

55 

PQ 

A 

B 

C 

~y 

0.45 

1/2 

250 

41/2 

H/16 

13/4    31/4 

4     1/2 

0.126 

389 

5/8 

2.29 

.00 

1.29 

H/4 

0.47 

1/2 

312 

5 

3/4 

17/8 

33/4    4!     1/2 

0.126 

609 

5/8 

2.65 

.00 

1.65 

,  U/2 

0.49 

1/2 

375    6 

13/18 

21/4 

41/2    4    5/80.202 

547 

3/43.17 

.21 

1.96 

0.51 

1/2 

500 

61/2 

7/8 

21/4 

5 

4     5/8 

0.202 

972 

3/4 

3.53 

.21 

2.32 

21/2 

0.53 

9/16 

555 

71/2 

|      ' 

21/2 

57/g 

4 

3/4,0.302 

1016 

7/8 

4.15 

.442.71 

3 

0.56 

9/16 

667 

81/4 

1  1/8 

25/8 

65/8!  8 

3/4 

0.302 

731 

7/8 

2.53 

.44 

.09 

31/2 

0.59 

9/16 

778 

9 

13/16 

23/4|   71/4|   8 

3/40.302 

995     7/8;2.77 

.44 

.33 

0.61 

5/8 

800 

10 

1  1/4 

3 

77/8 

0 

3/4 

0.302 

1300!    7/8 

3.01 

.44 

.57 

41/2 

0.64 

5/8 

900 

101/2 

1  5/16 

3 

81/2 

8 

3/t  0.302 

1646     7/8  '3.  25 

.44 

.81 

5 

0.67 

909 

11 

13/8 

3 

91/4 

8 

3/4!0.302|2032 

7/8  3.53 

.44  2.09 

6 

0.72 

3/4 

1000 

121/2 

1  7/16 

31/4 

105/8 

12 

3/4  0.302 

1950     7/82.75 

1.44 

.31 

7 

0.78 

13/16 

1077 

14 

31/2J  11  7/8 

12 

7/80.420 

1909 

3.07 

1.66 

.41 

8 

0.83 

13/16 

1230  15 

15/8 

31/213 

12 

7/8  0.420  2493 

3.36 

1.66 

.70 

9 

0.89 

7/8 

1285 

161/4 

1  3/4 

35/8:i4 

12 

1 

0.550 

2410     l/s 

3.62 

1.88 

.74 

10 

0.94 

15/16 

1333 

171/2 

17/8 

33/4151/4 

16 

1 

0.5502231     1/8,2.97 

1.88 

.09 

12 

1.05 

| 

1500 

201/2 

2 

41/4 

173/4 

16 

11/80.6942546     1/4  3.46 

2.09 

.37 

14 
15 
16 

1.16 
1.21 
1.27 

U/8 
13/16 

HA 

155523 
1579  24  1/2 

1600:25  1/2 

21/8 
23/16 
21/4 

41/2!20l/420  1  i/sO.6942773     1/4  3.17  2.09 
43/4  21  1/2  20  1  1  A  1  0.  893  1  2473!    3/8  3.36  2.31 
43/4J22  1/2120  1  1/4  10.  893  2814    3/8|3.52  2.31 

.08 
.05 
.21 

18 

1.37 

13/8 

1636 

28 

23/8 

5 

243/4 

24 

1  1/4  0.893  j  2968     3/8|3.232.31 

0.92 

20 
22 

1.48H/2     1666301/2 
1.5919/16    176033 

21/2 
25/8 

5  1/4  27 

5  1/4  29  1/4 

24 
24 

13/8 
1  1/2 

.057  3096 
.295  3058 

1/2  3.52  2.53  0.99 
5/8  3.81  2.75    .06 

24 

1  .70  1  5/8 

1846 

36 

23/4 

5  3/4  32 

24 

1  5/8 

.515 

3110il  3/4 

4.18296 

.22 

26 

1.81  1  13/ie 

1793381/4 

2  13/16 

61/8341/2 

28 

15/8 

.5153126  1  3/4  3.86!  2.96  0.9  J 

28 

1.91 

17/8 

1866 

403/4 

215/1663/8 

37 

28 

15/8 

.515!3629j1  3/44.142.96 

.18 

30 

2.02 

2 

1875 

43 

3 

61/2 

391/4 

28 

1  3/4 

1.7463615  1  7/8!4.38  3.19 

.19 

32 

2.1321/s.     1882451/4 

31/8 

65/841  1/228 

1  7/82.051 

3501  2 

4.64,341 

.26 

34 
36 

2.2421/4    1  1889  47  1/2 
2.35123/s     189450 

31/4 
33/8 

63/4 

43i/2 
46 

28 
32 

1  7/8  2.051 
1  7/82.051 

39522 

38772 

4.873.41 
4.503.41 

.46 
.09 

38 

2.4627/16    1948521/4 

37/ie  71/848 

32  1  7/8  2.051 

43202 

4.703.41 

.29 

40 
42 
44 
46 
48 

2.562  9/161953541/2 
2.67  2  n/16  1953  57 
2.78:213/161955591/1 
2.8912  7/8   200061  1/2 
3.003         :  2000  65 

3    9/i67l/4 
3  11/16  7  1/2 
33/4     .75/8 
37/8      73/4 
4          l81/2 

501/4  36  1  7/8!2.051  4255  2       4.38  3.41  0.97 
523/4J36  1  7/8  2.051  4691  2        4.59  3.41    .18 
55       1362       2.302458721/84.793.63    .16 
57  1/4  40  2       ;2.302  4512  2  1/8  4.49  3.63  0.86 
603/4402       12.302  4913  2  i/s  4.76  3.63  1.13 

*  Thickness  of  flange  given  in  table  includes  raised  face. 


FORGED  AND  ROLLED  STEEL  FLANGES. 


211 


Forged  Steel  Flangeslfor  Riveted  Pipe. 

Riveted  Pipe  Manufacturers'  Standard.* 


ll 

II 

£72 

0) 
T3   g 

3  i 
£5 

Thickness 
of  Flange.* 

•83 

|3 

•3<2 

IS 

Diam.  of 
Bolt  Circle. 

-2 

g£ 
11 

£W 

Outside 
Diam. 

Thickness 
of  Flange.* 

o» 

& 

0-2 

IS 

Diam.  of 
Bolt  Circle. 

4 
5 
6 
7 
8 
9 
10 
j  ] 

6 

8 
9 
10 
11 
13 
14 
J5 

5/16  .... 
5/16  9/16 
5/16  9/16 
3/8  9/16 
3/8  9/i6 
3/8  5/8 
3/8  5/8 
3/8  11/16 
7/16 

4 
8 
8 
8 
8 
8 
8 
8 
12 

V/18 

7/16 
7/16 
1/2 
1/2 
1/2 
1/2 
1/2 
1/2 

43/4 
5  15/16 
6  15/16 

7T,, 

10 

M   1/4 
121/4 
13  3/8 

16 
18 
20 
22 
24 
26 
28 
30 
32 

211/4 

%,\ 
%'< 

32 
34 
36 
38 

V8        3/4 
V8        3/4 
5/8        V8 
H/16      7/8 
11/16      7/8 

1 

1 

12 
16 
16 
16 
16 
24 
28 
28 
28 

V2 
5/8 
5/8 
5/8 

V8 
3/4 

3/4 
3/4 
3/4 

191/4 
2H/4 

231/8 
26 
273/4 
293/4 
313/4 
333/4 
353/4 

12 
13 
14 
15 

16 
17 
18 
19 

7/16  3/4 
7/16  .... 
7/16  3/4 
9/16  3/4 

12 
12 
12 
12 

1/2 
1/2 
1/2 
1/2 

141/4 

15  1/4 

161/4 

177/16 

34 
36 
40 
42 

40 
42 
46 
48 

H/8 

H/8 
M/8 

28 
32 
32 
36 

3/4 
3/4 
3/4 

3/4 

373/4 
393/4 
433/4 
453/4 

*  Flanges  for  riveted  pipe  are  also  made  with  the  outside  diameter  and 
the  drilling  dimensions  the  same  as  those  of  the  A.  S.  M.  E.  standard 
(page  209) ,  and  with  the  thickness  as  given  in  the  second  column  of  fig- 
ures under  "Thickness  of  Flange"  in  the  above  table. 

Curved  Forged  Steel  Flanges  are  also  made  for  boilers  and  tanks. 
See  catalogue  of  American  Spiral  Pipe  Works,  Chicago. 

Forged  and  Rolled  Steel  Flanges. 

Dimensions  in  Inches.     (American  Spiral  Pipe  Works,  1913.) 


Standard  Companion  Flanges. 

Standard  Shrink  Flanges. 

"3          DD 

•g 

•8 

-.                 . 

•3 

•8 

1      .| 

T3  PJ 

•a  a? 

1 

^3    • 

S3        8 

-8  a 

a 

i     , 

fd   • 

.  . 

|l 

OQ 

|i 

p 

|I 

n 

5w 

III 

l| 

iP 

"a^ 

|1 

A 

B 

C 

D 

E 

A 

B 

C 

D 

E 

2 

6 

21/8 

5/8 

1 

31/8 

4 

9 

43/8 

15/16 

23/i6 

53/4 

21/2 

7 

21/2 

H/16 

1  Vl6 

35/8 

41/2 

91/4 

47/8 

15/16 

21/4 

61/8 

^ 

71/3 

31/8 

3/4 

1  1/8 

45/16 

5 

10 

57/16 

15/16 

25/i6 

67/8 

31/2 

81/2 

35/8 

13/16 

13/16 

47/8 

6 

It 

61/2 

27/ie 

77/8 

4 

9 

41/8 

15/16 

13/16 

53/8 

7 

121/2 

71/2 

1/16 

21/2 

9 

41/2 

91/4 

45/8 

15/16 

5  13/16 

8 

131/2 

81/2 

1/8 

25/8 

10 

5 

10 

51/8 

15/16 

1  5/16 

67/ie 

9 

15 

91/2 

1/8 

23/4 

11  1/8 

6 

11 

I  7/16 

7  9/16 

10 

16 

Id  5/8 

3/16 

3 

121/4 

7 

121/2 

7  3/1J 

1/16 

H/2 

85/8 

12 

19 

125/8 

1/4 

33/8 

141/2 

8 

131/2 

1/8 

15/8 

9  H/16 

14 

21 

137/s 

3/8 

33/8 

157/s 

9 

15 

9  3/i6 

1/8 

13/4 

105/s 

15 

221/4 

147/8 

3/8 

31/2 

167/8 

10 

16 

105/18 

3/16 

1  7/8 

1  1  15/16 

16 

231/2 

157/8 

7/16 

35/8 

18 

12 

19 

125/i6 

1/4 

21/16 

141/8 

18 

25 

177/s 

9/16 

37/8 

201/8 

14 

21 

131/2 

13/8 

157/16 

20 

271/2 

197/s  J 

11/16 

41/8 

22  1/4 

212 


MATERIALS, 


Forged  and  Rolled  Steel  Flanges.— Continued. 
Extra  Heavy  Companion  Flanges. 


Is 
iff 

233 

Outside 
Diam. 

Js 

Thick- 
ness. 

*o  . 

J3-^5 

•s  3 

1* 

*8  . 

c-a 

I* 

Nominal 
Size,  Ins. 

Outside 
Diam. 

.1 

IQ 

Thick- 
ness. 

o 
£•§ 

1* 

i 

# 

A 

B 

C 

D 

E 

A 

B 

C 

D 

E 

91/8 

101/8 

113/16 
129/ia 
145/8 
1513/w 
17  3/i6 
181/4 

j* 

31/2 
4l/2 
6 

61/2 

71/2 
81/4 

9 
10 

,o./, 

121/2 

21/8 
21/2 
31/8 
35/8 
41/8 
45/8 
51/8 
63/16 

7/8 

1/8 
1/8 
1/4 
1/4 
H/4 

3/8 
7/16 
9/16 
5/8 
3/4 
13/16 

2?/8 

33/8 
41/16 
4H/16 
55/16 
5  13/16 
61/4 
6  13/16 
77/8 

7 

8 
9 
10 
12 
14 
15 
16 

14 
15 
16 

171/2 

20 

221/2 

£1/2 

73/16 
83/i6 
93/16 
105/ie 
I25/16 

131/2 
141/2 
151/2 

1  5/16 
13/8 
17/16 
H/2 
1V8 
13/4 
1  13/16 
17/8 

21/16 
23/16 
21/4 
23/8 
29/16 
2  H/16 
2  13/16 
31/16 

Extra  Heavy  High  Hub  Flanges. 


Size. 

A 

B 

C 

D 

E 

Size. 

A 

B 

C 

D 

E 

4 

10 

43/8 

I  1/8 

31/8 

53/4 

18 

27 

177/8 

2 

5 

203/4 

"  4  1/2 

101/2 

47/8 

H/4 

31/4 

61/4 

20 

291/2 

197/g 

21/4 

5l/2 

22i/2 

5 

11 

57/16 

H/4 

31/4 

7 

22 

3H/2 

21/4 

51/2 

243/4 

6 

12l/2 

61/2 

H/4 

31/4 

7  15/16 

24 

34 

27/16 

61/4 

27 

7 

14 

71/2 

15/16 

33/8 

.91/8 

30 

40 

27/W    61/4 

33 

8 

15 

81/2 

13/8 

3l/2 

105/i6 

36 

46 

2  7/16 

61/4 

39 

9 

16 

91/2 

17/16 

35/8 

113/8 

42 

52 

27/16    61/4 

45 

10 

17V2 

105/g 

H/2 

33/4 

125/s 

48 

581/4 

27/16 

61/2 

5H/4 

11 

183/4 

115/8 

19/16 

37/8 

135/8 

54 

641/2 

27/16 

61/2 

571/4 

12 

20 

125/8 

15/8 

4 

143/4 

60 

703/s 

27/16 

.61/2 

633/8 

14 

221/2 

137/8 

13/4 

43/8 

I63/i6 

66 

77 

27/16 

71/2 

69l/2 

15 

23.1/2 

147/8 

1  13/16 

41/2 

171/4 

72 

831/s 

27/16 

71/2 

755/8 

16 

25 

15  7/8  j 

17/8 

43/4 

181/2 

The  Rockwood  Pipe  Joint.  —  Tfle  system  of  flanged  joints  now  in 
common  use  for  high  pressures,  made  by  slipping  a  flange  over  the  pipe, 
expanding  the  end  of  the  pipe  by  rolling  or  peening,  and  then  facing  it  in 
a  lathe,  so  that  when  the  flanges  of  two  pipes  are  bolted  together  the 
bearing  of  the  joint  is  on  the  ends  of  the  pipes  themselves  and  not  on  the 
flanges,  was  patented  by  George  I.  Rockwood,  April  5,  1897,  No.  580,058, 
and  first  described  in  Eng.  Rec.,  July  20,  1895.  The  joint  as  made  by 
different  manufacturers  is  known  by  various  trade  names,  as  Walmanco, 
Van  Stone,  etc. 

Matheson  Joint  and  Converse  Lock-joint  Pipe. — Sizes,  external 
diameters  2  to  20  in.,  22,  24,  26,  28,  and  30  in.  Kimberley  Joint  Pipe, 
6  to  30  in.  These  pipes  are  considerably  lighter  than  standard  pipe. 
The  Converse  and  Kimberley  joints  are  made  with  special  forms  of  ex- 
ternal hubs,  filled  and  calked  with  lead.  The  Matheson  joint  is  also 
a  lead-packed  joint,  but  the  bell  or  socket  is  made  by  expanding  one  of 
the  pipes,  the  end  being  reinforced  by  a  steel  band.  The  lead  required 
per  joint  is  less  than  for  other  lead- joint  pipes  of  the  same  diameter. 


PIPE   FITTINGS. 

Dimensions  of  Standard  Cast-Iron  Flanged  Pipe  Fittings,  for  Pres- 
sures up  to  125  Lb.  per  Sq.  In.  (Adopted  March  20,  1914,  by  a 
joint  committee  of  manufacturers  and  of  the  Am.  Soc.  M.  E.) 
Dimensions  in  the  tables,  pages  213  and  214,  refer  t9  corresponding 
letters  on  the  sketches  on  page  215.  For  dimensions  of  flanges 
and  bolts  see  Table  of  Standard  Flanges,  pages  209  and  210. 


213 
Standard  Cast  Iron  Flanged  Pipe  Fittings  for  Pressures  up  to  125  lb. 

per  Sq.  In.  (see  sketches  p.  215.) 


Size. 

Tees,  Crosses 
and  Ells. 

Long 
Radius 
Ells. 

45 
degree 
Ells. 

Laterals. 

Re- 
ducers. 

Min. 
Thick- 
ness of 
Metal. 

H/4 

j* 

f>/2 

3./2 

41/2 

6 
7 

8 
9 
10 
12 
14 
15 
16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 
74 
76 
78 
80 
82 
84 
86 
88 
90 
92 
94 
96 
98 
100 

A-A 

fy 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
20 
22 
24 
28 
29 
30 
33 
36 
40 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
74 
78 
82 
84 
88 
90 
94 
96 

too 

102 
106 
108 
112 
116 
118 
120 
124 
126 
130 
134 
136 
138 
142 
146 
148 

A 

31/2 
33/4 

4l/2 

51/2 

6 

61/2 
71/2 

8 

81/2 

9 
10 
11 
12 

14 

g.A 

161/2 

18 
20 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
37 
39 
41 
42 
44 
45 
47 
48 
50 
51 
53 
54 
56 
58 
59 
60 
62 
63 
65 
67 
68 
69 
71 
73 
74 

B 
5 

51/2 
61/2 

73/4 
81/2 

91/2 
101/4 
11  V2 
123/4 
14 
151/4 
161/2 

19 

21  1/2 
223/4 

261/2 

IV/2 
36l/2 
39 

4H/2 

44 

£'/' 
5siI/2 

56* 

61  1/2 
64 

6V/2 
Jl  A 

76l/2 
79 

8H/2 

84 

86  1/2 
89 

9H/2 

94 
96l/2 
99 

101  1/2 

104 
1061/2 
109  . 

!!11/2 

1161/2 

119 

!ir/2 

!£'/2 

C 

]3/4 

21/4 
21/2 

3 

31/2 

4 

41/2 

51/2 
51/2 

6 

61/2 

71/2 
71/2 

8 
8 

81/2 
91/2 

10 
11 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

D 

JV, 
}|V, 

13 

Hl/2 

15 
|5./2 

18 

g* 

24 
251/2 
30 
33 

341/2 

*>/, 

43 
46 
491/2 
53 
56 
59 

E 

53/4 

61/4 

8 

,r/2 
a* 

12i/2 

131/2 
141/2 
161/2 
171/2 
191/2 

201/2 
2?./, 

281/2 
30 
32 
35 
371/2 
401/2 
44 
461/2 
49 

F 

13/4 
13/4 

21/2 
21/2 

3 
3 
3 

31/2 
31/2 

41/2 
41/2 

51/2 

6 
6 

61/2 

8 

81/2 

9 
9 

91/2 

10 

G 
"6  " 

61/2 

J.A 

9 
10 
11 

M'/2 

14 
16 
17 
18 
19 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 
68 
70 
72 
74 
76 
78 
80 
82 
84 
86 
88 
90 
92 
94 
% 
98 
100 

7/16 

l^ 
7/16 

MM 

7/16 

!/!« 
7/16 
1/2 
1/2 
1/2 
9/16 
5/8 
5/8 

$' 

%16 

7/8 

1/16 
1/8 
3/16 

1/4 
5/16 

y? 

7/16 
1/2 
9/16 
5/8 

"/" 

8r 

'     15/16 

21/16 
21/8 
23/16 
21/4 
25/16 
27/i6 
21/2 
29/16 
25/8 
2  H/16 
23/4 
2  13/16 
27/8 
2  15/16 

31/16 
31/8 
33/is 
31/4 
35/ia 
33/8 
31/2 
39/16 
35/8 
3  11/16 
33/4 

214 


MATERIALS. 


Dimensions  of  American  Standard  Flanged  Reducing  Fittings.     Short 
Body  Pattern.      (All  Dimensions  in  Inches.) 

Long  body  patterns  are  used  when  outlets  are  larger  than  those  in 
table,  and  have  the  same  dimensions  as  straight  size  fittings.  All  re- 
ducing fittings  from  1  to  16  in.  inclusive  have  same  dimensions  as 
straight  size  fittings.  The  dimensions  of  reducing  fittings  are  always 
regulated  by  the  reduction  of  the  outlet. 


18 
20 
22 
24 
26 
28 
30 
32 
34 
56 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 

Tees,  Ells,  Crosses. 

Laterals. 

i 

w 

~60~ 
62 
64 
66 
68 
70 
72 
74 
76 
78 
80 
82 
84 
86 
88 
90 
92 
94 
96 
98 
100 

Tees,  Ells, 
and  Crosses. 

J* 

Cfl+3 

*3 

S-o 

12 
14 
15 
16 
18 
18 
20 
20 
22 
24 
24 
26 
28 
28 
30 
32 
32 
34 
36 
36 
38 

AA 

26 
28 
28 
30 
32 
32 
36 
36 
38 
40 
40 
44 
46 
46 
48 
52 
52 
54 
58 
58 
62 

A 

13 
14 
14 
15 
16 
16 
18 
18 
19 
20 
20 
22 
23 
23 
24 
26 
26 
27 
29 
29 
31 

B 

N  "£ 
W^ 

So 

a* 

9 
10 
10 
12 
12 
14 
15 

D 

26 
28 
29 
32 
35 
37 
39 

E 

F 

1 

V2 

o'/2 

0 
0 

H 

271/2 
291/2 
31  1/2 
34  i/2 
38 
40 
42 

S4^ 

w5 

& 

S-8 

40 
40 
42 
44 
44 
46 
48 
48 
50 
52 
52 
54 
56 
56 
58 
60 
60 
62 
64 
64 
66 

AA 

66 
66 
68 
70 
70 
74 
80 
80 
84 
86 
86 
88 
94 
94 
96 
100 
100 
104 
106 
106 
110 

A 

~33 
33 
34 
35 
35 
37 
40 
40 
42 
43 
43 
44 
47 
47 
48 
50 
50 
52 
53 
53 
55 

B 

"4? 

42 
44 
45 
46 
47 
48 
49 
50 
52 
53 
54 
56 
57 
58 
61 
62 
63 
64 
65 
67 

17  l/2 

18 
19 
20 

11 

24 
25 
26 
28 
29 
30 
31 
33 
34 
35 
36 
37 
39 
40 

25 
27 

281/2 

\Vh 

37 
39 

Extra  Heavy  American  Standard  Flanged  Reducing  Fittings. 
Body  Pattern.      (All  Dimensions  in  Inches.) 


Short 


1 

CO 

Tees,  Ells  and  Crosses. 

Laterals. 

| 

c/5 

Tees,  Ells  and  Crosses. 

ti 

05^3 

go 

^"o 

AA 

A 

K 

S-^ 

.3   Q) 
C/253 

So 

&£ 

D 

E 

F 

H 

II 

a* 

§3 

AA 

A 

K 

18 
20 
22 
24 
26 
28 
30 
32 

12 
14 
15 
16 
18 
18 
20 
20 

28 
31 
33 
34 
38 
38 
41 
41 

14 

151/2 
161/2 

17 
19 
19 

20  l/2 
201/2 

17 

1SV2 
gv, 

24 

251/2 
26i/2 

9 
10 
10 
12 

34 
37 
40 
44 

31 
34 
37 
41 

3 
3 
3 
3 

8'" 

39 

43 

34 
36 
38 
40 
42 
44 
46 
48 

22 
24 
24 
26 
28 
28 
30 
32 

44 
47 
47 
50 
53 
53 
55 
58 

22 

231/2 

•§>* 

2$ 
i172 

28 
291/2 
301/2 

31  1/2 
331/2 

341/2 

351/2 
37i/2 

Standard  Brass  Flanges  as  adopted  Sept.  17,  1913,  by  the  Committee 
of  manufacturers  on  the  standardization  of  Valves  and  Fittings,  to  be- 
come effective  Jan.  1,  1914  are  listed  on  page  215.  The  bolt  holes  for 
these  flanges  are  to  be  drilled  i/ie  in.  greater  than  the  bolt  diameter  for 
sizes  2  in.  and  smaller,  and  %  in.  greater  than  the  bolt  diameter  for 
sizes  2l/2  in.  and  larger.  The  flanges  have  smooth,  plain  faces,  and  when 
coupled  to  extra  heavy  iron  flanges,  the  latter  should  have  the  raised 
surface  faced  off. 


STANDARD   BRASS  FLANGES. 


215 


Side  Outlet 

Tee 
STEAIGHT  SIZE  FITTINGS. 

J±H      'M**: 


Laterals 
REDUCING  FITTINGS. 


Jfoducers 


The  dimensions  on  these  sketches  refer  to  the  corresponding  letters 
in  the  tables  of  flanged  fittings,  pages  213  and  214,  and  also  to  the 
reference  letters  in  the  tables  of  screwed  fittings,  page  216. 

Standard  Brass  Flanges. 


Standard  —  For  Pressures  up 
to  125  Lb. 

Extra  Heavy  —  For  Pressures 
up  to  250  Lb. 

Size, 
In. 

Diam., 
In. 

Thick- 
ness, 
In. 

Bolt 
Circle  , 
In. 

No. 
of 
Bolts. 

Size 
of 
Bolts, 
In. 

Diam., 
In. 

Thick- 
ness, 
In. 

Bolt 
Circle, 
In. 

No. 
of 
Bolts. 

Size 
of 
Bolts, 
In. 

V4&3/8 

2V2 

9/32 

1  n/16 

4 

3/8 

3 

3/8 

2 

4 

7/16 

1/2 

3/4 

3 

3V2 

5/16 
H/32 

2V8 
2V2 

4 
4 

3/8 
3/8 

jv, 

13/32 
7/16 

23/8 

27/8 

4 
4 

'£ 

1 

4 

3/8 

3 

4 

7/16 

41/2 

V2 

3V4 

4 

V2 

H/4 

4V2 

1V32 

33/8 

4 

7/16 

5 

n/32 

33/4 

4 

V2 

H/2 

5 

Vl6 

37/8 

4 

V2 

6 

9/16 

4V2 

4 

5/8 

2 

6 

V2 

43/4 

4 

5/8 

6V2 

5/8 

5 

4 

5/8 

2V2 

7 

9/16 

5V2 

4 

5/8 

7V2 

n/16 

57/8 

4 

3/4 

3 

?V2 

5/8 

6 

4 

'5/8 

8V4 

3/4 

6Vs 

8 

3/4 

3V2 

81/2 

H/16 

7 

4 

5/8 

9 

13/16 

7V4 

8 

3/4 

4 

9 

n/16 

7V2 

8 

5/8 

10 

7/8 

7V8 

8 

3/4 

4V2 

9V4 

23/32 

73/4 

8 

3/4 

10V2 

7/8 

8V2 

8 

3/4 

5 

10 

3/4 

8V2 

8 

3/4 

11 

15/16 

9V4 

8 

3/4 

6 

11 

.13/16 

9i/2 

8 

3/4 

12V2 

105/8 

12 

3/4 

7 

12V2 

7/8 

10:V4 

8 

3/4 

14 

Vl6 

11  7/8 

12 

7/8 

8 

131/2 

16/16 

11  3/4 

8 

3/4 

15 

1/8 

13 

12 

7/8 

9 

15 

15/16 

131/4 

12 

3/4 

16i/4 

1/8 

14 

12 

1 

10 

16 

141/4 

12 

7/8 

17V2 

3/16 

15V4 

16 

1 

12 

19 

1Vl6 

17 

12 

7/8 

201/2 

V4 

173/4 

16 

IV8 

'216 


MATERIALS. 


Dimensions  of  Screwed  Cast  Iron  and  Malleable  Pipe  Fittings,  For 
Steam  and  Water.      (Crane  Co.,  Chicago,  1914.) 

R  =  regular  fitting;  E.H.  ~  extra  heavy  fitting.     For  meaning  of 
dimensions  see  sketches  p.  215.     Dimensions  in  inches. 


. 

Long 

51*"      Tee,  Cross,  Ell. 

Rad. 

45  Deg.  Ell. 

Lateral. 

Reducer.* 

wng. 

Ell. 

Dimension.       A 

B 

C 

D 

E 

G 

Size, 
Ins. 

Cast  Iron. 

Mall. 

Mall. 

Cast  Iron. 

Mall. 

C.I. 

C.I. 

C.I. 

Mall. 

R. 

E.  H. 

E.H. 

E.  H. 

R. 

E.H. 

E.H. 

R. 

R. 

R. 

E.  H. 

1/4 

13/16 

1  i/ifi 

3/4 

3/4 

3/8 

15/ie 

1  1/4 

13/16 

7/8 

1/2 

1  1/8 

1  1/2 

7/8 

1    ' 

21/2 

1  7/8 

3/4 

15/16 

13/4 

1 

U/8 

3 

21/4 

1  H/16 

1 

1  7/16 

2" 

2 

2  1/2 

U/8 

13/8" 

15/16 

31/2 

23/4 

2 

1   1/4 

13/4 

21/4 

21/4 

3 

15/16 

H/2 

41/4 

31/4 

21/8  ' 

23/8 

1   V2 

1  15/16 

29/16 

31/2 

17/16 

15/8 

1  H/16 

47/8 

313/16 

21/4 

2  H/16 

2 

21/4 

3 

3 

4 

1  15/16 

2 

53/4 

41/2 

27/16 

23/16 

2l/2 

2  H/16 

31/2 

31/2 

43/4 

1  IS/16 

21/4 

21/4 

61/4 

53/16 

2  H/16 

3 

31/8 

41/8 

41/8 

51/2 

2  3/16 

21/2 

21/2 

77/8 

61/8 

2  15/16 

3l/2 

37/16 
33/4 

4H/16 
51/8 

45/8 
51/8 

61/423/8 
7         25/8 

"29/ie 
23/4 

25/8 
2  13/16 

87/8 
93/4 

67/8 
75/8 

31/8 
33/8 

41/2 

41/16 

51/2 

55/8 

73/4!213/i63 

115/8 

91/4 

35/8 

5 

47/16 

61/8 

61/4 

31/16    35/ie 

115/8 

91/t 

37/8 

6 

51/8 

71/4 

71/4 

91/2 

37/16  133/4 

137/16 

103/4 

43/8 

7 

5  13/16 

81/8 

37/8 

4 

151/4 

121/4 

4  13/16 

8 

61/2 

91/8 

41/4 

43/4 

1615/i6 

135/8 

51/4 

9 
10 

73/16 
77/8 

4H/16 
53/16 

47/8  ' 

20H/16 

163/4 
163/4 

5  H/16 
63/ie 

12 

91/4 

133/8 

6 

51/2 

1 

195/s 

71/8 

*  The  reducers  are  for  reducing  from  the  size  of  pipe  given  to  the 
next  smaller  size.  In  addition,  malleable  reducers  are  listed  for  1  %  X 
Vi,^lA  X  1,  1  Yi  X  Vi,  2  x  1,  2  X  Vi-  The  dimension  G  given  in  the 
table  is  the  same  for  these  special  fittings  as  for  the  regular  fittings 
given  above. 

Strength  of  Pipe  Fittings. — To  determine  the  actual  bursting  strength 
of  cast  iron  fittings,  and  also  to  determine  the  influence  of  form  upon 
the  strength,  Crane  Co.  conducted  experiments  in  which  flanged 
fittings  of  different  sizes  and  forms  were  tested  to  destruction  by  inter- 
nal pressure.  The  experiments  showed  that  the  strength  of  ells  is 
practically  the  same,  regardless  of  degree,  or  whether  the  ell  is  straight 
or  reducing  sizes.  Fittings  of  the  same  general  shape  as  the  tee  or 
cross  are  of  nearly  the  same  strength,  and  relatively  of  about  two-thirds 
the  strength  of  an  ell.  The  straight  lateral  has  about  one-third  the 
strength  of  the  ell.  The  following  average  figures  of  bursting  strength 
of  extra  heavy  tees  and  ells  are  condensed  from  the  company  s  1914 
catalogue: 


12       14        16        18        20       24 

1        H/8     13/16     H/4     15/16     H/2 


Size  of  fitting,  ins.,          6       8       10 
Thickness  of  metal,  in.  3/4   13/16    15/16 

Tees,  Perro-steel: 
Burst  at,  Ib.  per  sq.in.2733  2250  2160  2033  1825  1700  1450  1275  1300 

Tees,  Cast  Iron: 
Burst  at,  lb.persq.in.1687  1350  1306  1380  1100  1025     600     750     700 

Ells,  Ferro-steel: 
Burst  at,  Ib.  per  sq.in.3266  2725  2350  2133 

Ells,  Cast  Iron: 
Burst  at,  Ib.  per  sq.  in. 2275  1625  1541   1275   1075  1250 


STANDARD   STRAIGHT-WAY   GATE   VALVES.         217 


Length  of  Thread  on   Pipe  that-  should  be  screwed  into  fittings  to 
make  a  tight  joint  is  given  by  Crane  Co.  as  follows: 


Size  of  pipe,  in 1/8 

Length  of  thread,  in.1/4 


1/4 
3/8 


3/8 


Size  of  pipe,  in 31/2    4        41/2 

Length  of  thread,  in.  11/16  11/ie  IVs 


'2     3/4     1  H/4        H/2       2       21/2       3 

'2     V2  Vl6  5/8         5/8     11/16    15/16        1 

5        6  7  8        9        10       12 

13/16  H/4  H/4  15/16   13/8      1  1/2   15/8 


VALVES. 

Dimensions  of  Standard  Globe,  Angle  and  Cross  Valves. 

(Crane  Co.,  1914.) 

Iron  Body,  Brass  Trimmings,  with  Yoke. 

Dimensions  in  Inches:  B,  face  to  face,  flanged;  B/2,  center  to  face, 
flanged  (Angle  and  Cross  Valves) ;  C,  diameter  of  flanges;  D,  thickness 
of  flanges;  S,  center  to  top  of  stem,  open;  O,  diameter  of  wheel. 


Size. 
2 

21/2 
31/2 
41/2 

6 

B 

8 

81/2 
91/2 
101/2 

11 

12 
13 
14 

B/2 

C 

6 

7 

71/2 
Bl/2 

9 

91/4 

10 
11 

D 

S 

O 

Size. 

7 
8 
10 
12 
14 
15 
16 

B 

B/2 

C 

D 

11/16 
H/8 
13/16 
H/4 
13/8 
13/8 
17/16 

S 

4 

41/4 
43/4 

51/4 
51/2 

6 

61/2 

5/8 
H/16 
3/4 
13/16 
15/16 
15/16 
15/16 

103/4 
1U/4 

g* 

151/4 
151/4 
171/4 

19 

61/2 

6l/2 

71/2 
71/2 

9 
9 
10 
12 

16 
17 
20 
24 
28 
30 
32 

8 

81/2 
10 
12 
14 
15 
16 

121/2 
131/2 

16 
19 
21 

221/4 
231/2 

201/2 
23  3/4 
28 
34 
38l/2 
381/2 
41  1/2 

Standard  Straight- Way  Gate  Valves.     (Crane  Co.,  1914.) 
Iron  Body.     Brass  Trimmings.     Wedge  Gate. 

Dimensions  in  Inches:  A,  nominal  size;  B,  face  to  face,  flanged;  C, 
diam.  of  flanges;  D,  thickness  of  flanges;  K,  end  to  end,  screwed;  N, 
center  to  top  of  non-rising  stem;  O,  diam.  of  wheel;  S,  center  to  top  of 
rising  stem,  open;  Y,  center  to  outside  of  by-pass;  P,  size  of  by-pass; 
X,  number  of  turns  to  open. 


A 

B 

C 

D 

K 

N 

O 

S 

Y 

P 

X 

2 

7 

6 

5/8 

57/i6 

113/4 

61/2 

141/2 

7 

21/2 

71/2 

7 

H/16 

57/8 

123/4 

61/2 

16 

8 

3 

8 

71/2 

3/4 

61/8 

141/4 

71/2 

19 

101/4 

31/2 

81/2 

81/2 

13/16 

61/2 

151/4 

71/2 

2U/4 

101/8 

4 

9 

9 

15/10 

67/8 

161/t 

9 

24 

83/4 

41/2 

91/2 

91/4 

15/16 

71/8 

175/s 

9 

251/2 

9 

5 

10 

10 

15/16 

73/8 

19 

10 

28  l/2 

11 

6 

101/2 

11 

1 

73/4 

203/4 

12 

313/4 

125/8 

7 

11 

121/2 

H/16 

81/4 

23 

12 

371/4 

151/4 

8. 

1H/2 

131/2 

H/8 

83/4 

26 

14 

41 

16 

9 

12 

15 

H/8 

91/4 

28 

14 

443/4 

183/4 

10 

13 

16 

13/16 

97/8 

301/4 

16 

50 

20l/2 

12 

14 

19 

H/4 

115/8 

351/4 

18 

571/4 

241/8 

14 

15 

21 

13/8 

391/4 

20 

663/4 

19l/2 

2 

281/4 

15 

15 

221/4 

13/8 

4U/8 

20 

693/4 

21 

2 

3H/2 

16 

16 

231/2 

17/16 

441/4 

22 

751/4 

233/4 

3 

331/4 

18 

17 

25 

19/16 

483/t 

24 

86 

243/4 

3 

351/2 

20 

18 

271/2 

1  n/io 

521/2 

24 

91 

273/4 

4 

421/4 

22 

19 

291/2 

1  13/16 

551/2 

27 

100 

29 

4 

46 

24 

20 

32 

1    V8 

62 

30 

109 

301/2 

4 

50 

26 

23 

341/4 

2 

657/s 

30 

1171/2 

32 

4 

65 

28 

26 

361/2 

2    1/16 

70 

36 

125 

33 

4 

80 

30 

30 

383/4 

2    1/8 

75l/2 

36 

133 

34 

4 

921/2 

36 

36 

453/4 

2  3/8 

83 

158  l/2 

39 

6 

108 

218 


MATERIALS. 


Extra  Heavy  Straight-Way  Gate  Valves. 

Ferro-steel.  Hard  Metal  Seats.  Wedge  Gate.  (For  meaning  of  letters,  see  p.  217.) 


A 

B 

K 

C 

D 

N 

s 

0 

P 

Y 

X 

U/4 

6l/2 

51/2 

5 

3/4 

83/4 

105/8 

5 

12 

1  V2 

.  71/2 

61/4 

6 

13/16 

95/8 

121/4 

51/2 

11 

2 

81/2 

7 

61/2 

7/8 

101/2 

133/4 

61/2 

14 

21/2 

91/2 

8 

71/2 

127/s 

16 

71/2 

15 

3 

111/8 

9 

81/4 

H/8 

145/8 

191/2 

9 

14 

31/2 

11V8 

10 

9 

13/16 

151/2 

22 

10 

16 

12 

11 

10 

H/4 

173/4 

241/2 

12 

18 

41/2 

131/4 

121/4 

101/2 

15/16 

183/4 

27 

12 

21 

5 

15 

13l/2 

11 

13/8 

201/4 

293/4 

14 

23 

6 

157/8 

l57/8 

12l/2 

17/16 

23 

341/8 

16 

H/4 

13 

28 

7 

161/4 

161/4 

14 

H/2 

243/4 

38 

18 

H/4 

141/8 

30 

8 

161/2 

161/2 

15 

15/8 

283/4 

423/4 

20 

H/2 

157/8 

34 

9 

17 

17 

161/4 

13/4 

301/2 

47 

20 

H/2 

163/8 

40 

10 

18 

18 

171/2 

17/8 

333/4 

523/4 

22 

H/3 

167/8 

39 

12 

193/4 

201/2 

2 

371/4 

60 

24 

2 

197/8 

46 

14 

221/2 

23 

21/8 

423/4 

673/4 

24 

2 

205/8 

52 

15 

221/2 

241/2 

23/16 

423/4 

673/4 

24 

2 

205/8 

52 

16 

24 

251/2 

21/4 

751/4 

27 

3 

251/4 

60 

18 

26 

28 

23/8 

821/4 

30 

3 

26  1/2!    67 

20 

28 

301/2 

21/2 

91  1/2 

30 

4 

30  1/2     74 

22 

291/2 

33 

25/8 

101 

36 

4 

32  1/4 

82 

24 

31 

36 

23/4 

109 

36 

4 

33 

88 

For  dimensions  of  Medium  Valves  and  Extra  Heavy  Hydraulic 
Valves,  see  Crane  Company's  catalogue. 

NATIONAL   STANDARD   HOSE   COUPLINGS 

Adopted  by  the  National  Board  of  Fire  Underwriters,  American 
Waterworks  Association,  New  England  Waterworks  Association,  Na- 
tional Firemen's  Association,  National  Fire  Protection  Association. 


Dimensions  in  Inches. 


2V2 

V4 
31/1, 


35/8 


1  V 


1 

7V2 

7/8 

3.0925  3.6550 


1 


3V2 
l/4 

4V4 


2.87153.37634.00135.3970 


6 
1 
4.28 


4V2 

V4 
53/4 


5.80 


,'  The  threads  to  be  of  the  60°  V.  pattern  with  0.01  in.  cut  off  the  top 
of  thread  and  0.01  in.  left  in  the  bottom  of  the  2  y2-m.,  3-in.,  and  3  lA-ir\. 
couplings,  and  0.02  in.  in  like  manner  for  the  4  l/2-m.  couplings. 

A  =  inside  diameter  of  hose  couplings,  N  =  number  of  threads  per 

WOODEN   STAVE   PIPE. 

Pipes  made  of  wooden  staves,  banded  with  steel  hoops,  are  made  by 
the  Excelsior  Wooden  Pipe  Co.,  San  Francisco,  in  sizes  from  10  inches  to 
10  feet  in  diameter,  and  are  extensively  used  for  long-distance  Piping, 
especially  in  the  Western  States.  The  hoops  are  made  of  steel  rods  witl 
upset  and  threaded  ends.  When  buried  below  the  hydraulic  grade  line 
and  kept  full  of  water,  these  pipes  are  practically  indestructible.  J 
the  economic  design  and  use  of  stave  pipe  see  paper  by  A,  L,  Adams, 
Trans.  4.  S,  C,  £.,  vcH,  xU, 


RIVETED   HYDRAULIC   PIPE. 


219 


Weight  and  Strength  of  Riveted  Hydraulic  Pipe. 

(Pelton  Water  Wheel,  San  Francisco,  1915.) 


Thickness. 

4-in. 

5-in. 

6-in. 

7- 

n. 

8-in. 

Gauge. 

In. 

18 
16 
14 
12 
10 

0.050 
.062 
.078 
.109 
.140 

S 
555 
693 
866 

W 

2.8 
3.7 

4.4 

S 
444 
555 
693 

W 
3.5 
4  4 
5.5 

S 
370 
462 
578 
.808. 

W 
4.1 
5.2 
6.4 
8.8 

S 
317 
396 
495 
693 

W 
4.7 
5.9 
7.3 
10.0 

5 
277 
346 
433 
606 
777 

W 
5.3 
6.7 

8.2 
11.5 
14.5 

9-in. 

10-in. 

11  -in. 

12-in. 

14-in. 

"    16 
14 
12 
10 
8 

0.062 
.078 
.109 
.140 
.171 
3/16 

308 
385 
539 
693 

7.5 
9.2 
12.6 
16.4 

277 
346 
485 
623 
761 
832 

8.3 
10.2 
14.2 
18.0 
21.5 
23.5 

252 
314 
439 
565 
693 
757 

9.0 
11.0 
15.2 
19.3 
23.5 
25.5 

231 

289 
404 
519 
635 
693 

9.9 
1Z.2 
16.7 
21.0 
25.6 
27.7 

198 

248 
346 
445 
543 
594 

11.4 
14.0 
19.2 
24.2 
29.5 
31.9 

15-in. 

16-in. 

18-in. 

20-in. 

22-in. 

16 
14 
12 
10 
8 

0.062 
.078 
.109 
.140 
.171 
3/16 
1/4 
5/16 
3/8 
7/16 

185 
231 
323 
415 
507 
555 
739 

12.0 
14.0 
20.3 
25.7 
30.4 
34.0 
45.5 

173 
217 
303 
388 
475 
520 
693 
866 

12.8 
16.0 
21.5 
27.3 
33.3 
36.0 
48.2 
60.6 

154 
193 
270 
346 
422 
462 
616 
770 
924 

14.5 
17.8 
24.4 
30.7 
38.4 
40.5 
54.1 
67.7 
81.3 

139 
173 
242 
311 
380 
416 
555 
693 
831 
970 

16.0 
19.6 
27.3 
34.5 
41.5 
45.0 
59.6 
74.6 
89.5 
105.0 

126 
157 
220 
283 
346 
378 
505 
631 
757 
883 

17.7 
21.2 
29.2 
37.1 
45.2 
49.0 
65.5 
81.5 
98.0 
114.5 

24-in. 

26-in. 

30-in. 

36-in. 

42-in. 

14 
12 
10 
8 

0.078 
.109 
.140 
.171 
3/16 
V4 
5/16 
3/8 
7/16 
1/2 
5/8 
3/4 

7/8 

144 
202 
259 
317 
346 
462 
578 
693 
808 
924 

23.7 
32.5 
40.5 
49.2 
53.0 
71.0 
88.5 
106.0 
124.5 
142.0 

133 

186 
239 
293 
320 
427 
533 
640 
747 
854 
1066 

25.5 
34.5 
43.7 
53.0 
57.5 
76.5 
95.5 
114.5 
134.0 
153.0 
191.0 

162 

208 
254 
277 
370 
462 
555 
647 
739 
924 
1108 

39.5 
50.3 
60.5 
65.5 
87.5 
109.0 
130.5 
151.5 
174.5 
220.0 
264.0 

134 
173 
211 
231 
308 
385 
462 
539 
616 
770 
924 
1078 

47.7 
60.0 
75.0 
79.0 
105.5 
130.0 
156.0 
182.5 
207.0 
260.0 
312.5 
366.0 

148 
181 
198 
264 
330 
396 
462 
528 
660 
792 
924 

69.5 
84.7 
91.5 
122.0 
151.0 
180.5 
211.0 
240.5 
302.0 
361.5 
424.0 

48-in. 

54-in. 

60-in. 

66-in. 

72-in. 

8 

0.171 
3/16 

V4 
5/16 
3/8 
7/16 
1/2 
5/8 
3/4 

7/8 

158 
173 
231 
289 
346 
404 
462 
578 
693 
808 
924 

98  0 
106.0 
142.0 
177.0 
212.0 
249.0 
284.0 
354.0 
430.0 
505.0 
582.0 

141 
154 
205 
256 
308 
359 
411 
513 
616 
719 
822 

110.0 
119.0 
159.0 
198.0 
237.0 
277.5 
316.5 
399.5 
479.5 
563.5 
647.5 

127 
139 
185 
231 
277 
323 
370 
462 
555 
647 
739 

121.0 
131.0 
175.0 
218.0 
261.0 
303.0 
349.0 
440.0 
528.0 
620.0 
712.0 

127 

168 
210 
252 
294 
336 
420 
504 
588 
672 

144.5 
193.0 
239.0 
286.5 
334.0 
382.0 
480.0 
577.5 
677.0 
777.5 

115 

154 
193 
231 
270 
308 
385 
462 
539 
616 

158.0 
211.0 
260.0 
312.0 
365.0 
414.0 
520.0 
624.0 
732.0 
840.0 

Pipe  made  of  sheet  steel  plate,  ultimate  tensile  strength  55,000  Ibs.  per 
sq.  in.,  double-riveted  longitudinal  joints  and  single-riveted  circular  joints. 
Strength  of  longitudinal  joints,  70%.  Strain  by  safe  pressure,  1/4  of  ulti- 
mate strength. 


220 


MATERIALS. 


Riveted  Iron  Pipe. 
(Abendroth  &  Root  Mfg.  Co.) 

Sheets  punched  and  rolled,  ready  for  riveting,  are  packed  in  con- 
venient form  for  shipment.  The  following  table  shows  the  iron  and 
rivets  required  for  punched  and  formed  sheets. 


Number  Square  Feet  of 
Iron  Required  to  Make 
100  Lineal  Feet  Punched 

^       »-i  302 

Number  Square  Feet  of 
Iron  Required  to  Make 
100  Lineal  Feet  Punched 

£  *  u  GJ3 

and    Formed    Sheets 

and    Formed    Sheets 

"O   OPH 

when  put  Together. 

fl      || 

when  put  Together. 

1~  il 

Diam- 
eter in 
Inches. 

Width 
of  Lap 
in 
Inches. 

Square 
Feet. 

Q,  >    ^  C"3 

Diam- 
eter in 
Inches. 

Width 
of  Lap 
in 
Inches. 

Square 
Feet. 

allll 

3 

1 

90 

1600 

14 

U/2 

397 

2800 

4 

1 

116 

1700 

15 

U/2 

423 

2900 

5 

11/2 

150 

1800 

16 

U/2 

452 

3000 

6 

U/2 

178 

1900 

18 

U/2 

506 

3200 

7 

U/2 

206 

2000 

20 

U/2 

562 

3500 

8 

U/2 

234 

2200 

22 

U/2 

617 

3700 

9 

U/2 

258 

2300 

24 

U/2 

670 

3900 

10 

H/2 

289 

2400 

26 

U/2 

725 

4100 

11 

11/2 

314 

2500 

28 

U/2 

779 

4400 

12 

1  1/2 

343 

2600 

30 

U/2 

836 

4600 

13 

369 

2700 

36 

U/2 

998 

5200 

Spiral  Riveted  Pipe. 

Approximate  Bursting  Strength.     Pounds  per  Square  Inch. 
(American  Spiral  Pipe  Works,  Chicago,  1915.) 


Inside 
Diam. 
Inches. 

iniCKness.  —  \j.  &.  oiaiiuaru  oauge. 

No.20. 

No.  18. 

No.  16. 

No.  14. 

No.  12. 

No.  10. 

No.  8. 

No.  6. 

No.  3 

(V4"). 

3 

1500 

2000 

4 

1125 

1500 

1875 

5 

900 

1200 

1500 

6 

1000 

1250 

1560 

2170 

7 

860 

1070 

1340 

1860 

8 

750 

935 

1170 

1640 

9 

835 

1045 

1460 

10 

750 

935 

1310 

11 

680 

850 

1200 

12 

625 

780 

1080 

1410 

13 

575 

720 

1010 

1295 

14 

535 

670 

940 

1210 

15 

625 

875 

1125 

16 

585 

820 

1050 

1290 

1520 

1880 

18 

520 

730 

940 

1140 

1360 

1660 

20 

470 

660 

840 

1030 

1220 

1500 

22 

425 

595 

765 

940 

1108 

1364 

24 

390 

540 

705 

820 

1015 

1250 

26 

505 

650 

795 

935 

1154 

28 

470 

605 

735 

870 

1071 

30 

435 

560 

685 

810 

1000 

32 

410 

525 

645 

760 

940 

34 

380 

490 

600 

715 

880 

36 

365 

470 

570 

680 

830 

40 

330 

420 

515 

610 

750 

BENT  'AND   COILED   PIPES. 


221 


Weight  per  Sq.  Ft.  of  Sheet  Steel  for  Riveted  Pipe. 

(American  Spiral  Pipe  Works,  Chicago,  1915.) 


Thick- 
ness 
B.W.G. 

Thick- 
ness, 
In. 

Weight 
in  Lb., 
Black. 

Weight 
in  Lb., 
Galvan- 
ized. 

Thickness 
B.W.G. 

Thick- 
ness, 
In. 

Weight 
in  Lb., 
•  Black. 

Weight 
inLb., 
Galvan- 
ized. 

26 
24 
22 
20 

0.018 
.022 
.028 
.035 

0.7344 
0.8976 
1.1424 
1.428 

0.8844 
1.0476 
1.2924 
1.578 

18 
16 
14 
12 

0.049 
.065 
.083 
.109 

1.9992 
2.652 
3.3864 
4.4472 

2.1492 
2.802 
3.5364 
4.5972 

Weights  based  on  steel  of  489.6  Ib.  per  cu.  ft.    Weights  of  galvanized 
sheets  based  on  an  addition  of  0.075  Ib.  per  sq.  ft.  of  surface. 

BENT   AND    COILED   PIPES. 

(National  Pipe  Bending  Co.,  New  Haven,  Conn.) 
Coils  and  Bends  of  Iron  and  Steel  Pipe. 


Size  of  pipe  Inches 

Vi 

3/9 

1/2 

3/1 

j 

1  If* 

1  lh 

2 

71/? 

1 

Least  outside  diameter 

7 

?.ih 

3V-> 

41/2 

6 

8 

12 

16 

74 

37 

31/o 

4 

41  A> 

5 

6 

7 

8 

9 

10 

17 

Least  outside  diameter 
of  coil  Inches 

40 

48 

52 

58 

66 

80 

9? 

10*5 

HO 

H6 

Lengths  continuous  welded  up  to  3-in.  pipe  or  coupled  as  desired. 

90*  Bends  in  Iron  or  Steel  Pipe. 

(Whitlock  Coil  Pipe  Co.,  Hartford,  Conn.) 


Size  pipe,  I.D  

3 

}!/ 

4 

41/o 

5 

6 

8 

Q 

10 

1? 

Radius  of  bend  .  .  , 

1? 

13 

15 

17 

?0 

71 

7f 

30 

36 

4"? 

48 

End  

3 

31/2 

31/o 

4 

4 

4 

I 

5 

5 

6 

6 

Center  to  face  

15 

161/2 

181/o 

21 

74 

77 

31 

35 

41 

48 

54 

Size  pipe,  O  D 

14 

16 

18 

20 

?? 

?< 

| 

26 

78 

30 

Radius  of  bend  .  .  . 

60 

70 

80 

90 

100 

IK 

) 

70 

140 

160 

End  

7 

7 

7 

8 

8 

f 

| 

10 

10 

10 

Center  to  face  

67 

77 

87 

98 

108 

11* 

! 

30 

150 

170 

The  radii  given  are  for  the  center  of  the  pipe.  "End"  means  the 
length  of  straight  pipe,  in  addition  to  the  90°  bend,  at  each  end  of  the 
pipe.  "Center  to  face"  means  the  perpendicular  distance  from  the 
center  of  one  end  of  the  bent  pipe  to  a  plane  passing  across  the  other  end. 
The  dimensions  given  are  the  minimums  recommended.  Larger  radii 
than  are  shown  are  recommended  for  flexibility  and  lesser  friction. 

Flexibility  of  Pipe  Bends.  (Valve  World,  Feb.,  1906.)— So  far  as 
can  be  ascertained,  no  thorough  attempt  has  ever  been  made  to  de- 
termine the  maximum  amount  of  expansion  which  a  U-loop,  or  quarter 
bend,  would  take  up  in  a  straight  run  of  pipe  having  both  ends  anchored. 
The  Crane  Company  has  adopted  five  diameters  of  the  pipe  as  a  stand- 
ard radius,  which  comes  nearer  than  any  other  to  suiting  average  re- 


222 


MATERIALS. 


quirements,  and  at  the  same  time  produces  a  symmetrical  article.  Bends 
shorter  than  this  can  be  made,  but  they  are  extremely  stiff,  tend  to 
buckle  in  bending,  and  the  metal  in  the  outer  wall  is  stretched  beyond- 
a  desirable  point. 

In  1905  the  Crane  Company  made  a  few  experiments  with  8-inch  U 
and  quarter  bends  to  ascertain  the  amount  of  expansion  they  would  take 
up.  The  U-bend  was  made  of  steel  pipe  0.32  inch  thick,  weighing  28 
Ibs.  per  foot,  with  extra  heavy  cast-iron  flanges  screwed  on  and  refaced. 
It  was  connected  by  elbows  to  two  straight  pipes,  N,  67  ft.,  5.  82  ft., 
which  were  firmly  anchored  at  their  outer  ends.  Steam  was  then  let 
into  the  pipes  with  results  as  follows: 
80  Ib.  Expansion, 

Expansion,  N,     7/8  ,  S,  U/s  . 

Expansion,  N,  13/ie,  S,  11/2  . 

Expansion,  JV,  11/8  ,  S,  17/8  . 

Expansion,  N,  11/2  .  S,  17/8  . 


50  Ib. 
100  Ib. 
150  Ib. 
200  Ib. 


Total  1  7/8  in. 
Total  2  in. 
Total  2  H/iein. 
Total  3  in. 
Total  3  3/8  in. 


Flange  broke. 


Flange   broke 
at  208  Ibs. 


Straight  pipe  148  ft.,  one  end.    80 


Quarter  bend,  full  weight  pipe. 
Ibs.     Total  expansion,  1 3/8.     Flange  leaked. 

Quarter  bend,  extra  heavy  pipe.  Expanded  7/8  in.  when  a  flange 
broke.  Replaced  with  a  new  flange,  which  broke  when  the  expansion 
was  \y%  in. 

Wrought  Pipe  Bends.  (National  Tube  Co.).  —  The  following  are 
given  as  the  advisable  (R)  and  the  least  allowable  (Ri)  radii  in  inches 
to  which  pipe  should  be  bent: 


Size. 

R. 

Ri. 

Size. 

R. 

Ri. 

Size. 

R. 

Ri. 

Size. 

R. 

Ri. 

Size. 

R. 

Ri. 

iv. 

3V. 

15 

18 
21 

24 

10 
12 
14 
16 

4V. 

6 
7 

27 
30 
36 
42 

18 
20 
24 
28 

8 
9 
10 
11 

48 
54 
60 
66 

32 
36 
40 
44 

12 
13 
14 
15 

72 
84 
90 
100 

48 
60 
68 
76 

180.D. 
200.D. 
22O.D. 
24  0.  D. 

125 
150 
165 
180 

90 
120 
132 
144 

Bends  of  12-in.  pipe  and  smaller  to  be  of  full  weight  pipe;  14  to  16 
In.  outside  diameter,  not  less  than  3/8  in.  thick;  18  in.  and  larger,  not 
less  than  7/i6  to  1/2  in.  thick.  With  welded  flanges  there  must  be  a 
short  straight  length  of  pipe,  preferably  equal  to  two  diameters  of  the 
pipe,  between  the  flange  and  the  bend. 

Coils  and  Bends  of  Drawn  Brass  and  Copper  Tubing. 


Size  of  tube,  outside  diameter.  .Inches 
Least  outside  diameter  of  coil  .  .  Inches 

1/4 

3/8 
H/2 

2V2 

5/8 
21/2 

33/4 

1 
4 

H/4 
6 

13/8 

Size  of  tube,  outside  diameter..  Inches 
Least  outside  diameter  of  coil.  .Inches 

H/2 

95/8 

li3/4 

2 
12 

,2* 

P 

21/2 
18 

23/4 
20 

Lengths  continuous  brazed,  soldered,  or  coupled  as  desired. 

SEAMLESS  TUBES. 

Locomotive  Boiler  Tubes,  Seamless.— Diameters,  external,  11/2,  13A, 
17/8,  2,  21/4,  21/2,  and  3  in. 

Nine  thicknesses  of 

each  size,  inch..  .0.095  .109  .110  .120  .125  .134  .135  .148  .150 
Birmingham  wire 

gage 13       12      ...        11      ,..        10      ...          9      ... 

Shelby  Seamless  Steel  Tubes  are  made  of  three  classes  of  open- 
hearth  steel:  0.17  C  (0.14  to  O'.19%);  0.35  C  (0.30  to  0.40%);  and 
31/2%  nickel  (0.20  to  0.30  C,  3  to  4%  nickel).  In  all,  manganese  is 
from  0.40  to  0.60%;  sulphur,  0.015  to  0.040;  phosphorus,  0.010  to 
0.035%.  Hot  finished  tubes  are  not  given  any  heat  treatment  after 


COLD-DRAWN   SEAMLESS   STEEL  TUBES.  223 

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224 


MATERIALS. 


leaving  the  hot  mills.  Cold-drawn  tubes  are  annealed  before  and  heat- 
treated  after  drawing.  .The  physical  properties  of  finished  material  are 
as  follows: 


Temper 

Tensile 
Strength. 

Elastic 
Limit. 

Elong.  in 
8  In.,  %. 

0.17  C 

0.35  C 

3l/2%Ni. 

(  S,    unannealed  .  .  . 
1  T,    finish  anneal  .  . 
j  W,  soft  anneal  .  .  . 
(  Y,    retort  anneal  . 
!S,     unannealed.  .  . 
T,    finish  anneal  .  . 
U,    med.  anneal  .  . 
!S,    unannealed  .  .  . 
W,  finish  anneal  .  . 
U,    med.  anneal  .  . 

65,000  to    80,000 
60,000  to    75,000 
47,000  to    55,000 
45,000  to    52,000 
85,000  to  100,000 
80,000  to    95,000 
65,000  to    80,000 
95,000  to  110.000 
85,000  to  105,000 
70,000  to    85,000 

60,000  to    70,000 
50,000  to    65,000 
27,000  to    35,000 
22,000  to    28,000 
75,000  to    90,000 
70,000  to    85,000 
50,000  to    60,000 
85,000  to  100,000 
75,000  to    90,000 
45,000  to    60,000 

3  to  7 
10  to  16 
28  to  33 
30  to  40 
Low 
12  to  18 
20  to  30 
10  to  18  in  2" 
15  to  25  in  2" 
40  to  50  in  2" 

The  0.17  C  tube  is  also  furnished  in  intermediate  tempers.  U,  V, 
and  X,  between  T  and  Y,  and  special  treatments  are  given  to  order. 

In  estimating  the  effective  steam-heating  or  boiler  surface  of  tubes, 
the  surface  in  contact  with  air  or  gases  of  combustion  (whether  internal 
or  external  to  the  tubes)  is  to  be  taken. 

For  heating  liquids  by  steam,  superheating  steam,  or  transferring  heat 
from  one  liquid  or  gas  to  another,  the  mean  surface  of  the  tubes  is  to  be 
taken. 

Outside  Area  of  Tubes. 

To  find  the  square  feet  of  surface,  S,  in  a  tube  of  a  given  length,  L,  in 
ieet,  and  diameter,  d,  in  inches,  multiply  the  length  in  feet  by  the  diam- 
eter in  inches  and  by  0.2618.  Or,  S  =  3-141^dL  =0.2618  dL.  For  the 

diameters  in  the  table  below,  multiply  the  length  in  feet  by  the  figures 
given  opposite  the  diameter. 

Area  of  Tubes  per  Lineal  Foot. 


Diam. 

Area, 

Dia. 

Area, 

Dia. 

Area, 

Dia. 

Area, 

,Dia. 

Area, 

Dia. 

Area, 

In. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In. 

Sq.  Ft. 

In.   Sq.Ft. 

1'4 

0.0654 

11/4 

0.3272 

21/4 

0.5890 

31/4 

0.8508 

5 

1  .3090 

9 

2.3562 

1/2 

.1309 

1  1/2 

.3927 

21/3 

.6545 

31  /a 

.9163 

6 

1.5708 

10 

2.6180 

8/4 

.1963 

13  //| 

.4581 

23/4 

.7199 

33/4 

.9817 

7 

1  .8326 

11 

2.8798 

1 

.2618 

2 

.5236 

3 

.7854 

4 

1  .0472 

8 

2.0944 

12 

3.1416 

Seamless  Brass  and  Copper  Tube,  Iron  Pipe  Sizes. 


Nominal 

Diam.,  In. 

Wt.  per  Ft., 
Lb. 

Nominal 

Diam.,  In. 

Wt.  per  Ft., 
Lb. 

Size, 
In. 

Out- 
side. 

In- 
side. 

Brass 

Cop- 
per. 

Size, 
In. 

Out- 
side. 

In- 
side. 

Brass 

Cop- 
per. 

1/g 

0.405 

0.281 

0.246 

0.259 

3 

3.500 

3.062    8.314 

8.741 

1/4 

.540 

.375 

.437 

.459 

3*/2 

4.000 

3.500  10.85 

11.41 

3/8 

.675 

.494 

.612 

.644 

4 

4.500 

4.000  12.29 

12.93 

1/2 

.840 

.625 

.911 

.958 

*Vi 

5.000 

4.500  13.74 

14.44 

3/4 

1.050 

.822 

1.235 

1.298 

5 

5.563 

5.062  15.40 

16.19 

1 

1.315 

1  .062 

1  .740 

1.829 

6 

6.625 

6.125  18.44 

19.39 

11/4 

1.660 

1  .368 

2.557 

2.698 

7 

7.625 

7.06223.92 

25.15 

U/2 

1.900 

1.600 

3.037 

3.193 

8 

8.625 

8.00030.05 

31  .60 

2 

2.375 

2.062 

4.017 

4.224 

9 

9.625 

8.937 

36.94 

38.84 

2i/2 

2.875 

2.500 

5.830 

6.130 

10 

10.750  10.019 

43.91 

46.17 

SEAMLESS   BRASS   TUBES. 


225 


Weight  per  Foot  of  Seamless  Brass  Tubes. 

(Condensed  from  Manufacturers'  Standard  Tables,  1915.) 


A.W.G. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

Wall.* 

0.2576 

0.2043 

0.1620 

0.1285 

0.1019 

.0808 

.0641 

.0508 

.0403 

.0320 

.0253 

.0201 

Diam.f 

1/g 

0.044 

0.039 

0.034 

0.029 

0.024 

3/i6 

0!692 

.080 

.069 

.058 

.048 

.039 

1/4 

0.175 

OJ58 

.138 

.117 

.098 

.081 

.066 

.053 

5/i6 

.248 

.217 

.184 

.154 

.127 

.104 

.084 

.068 

3/8 

0.376 

.322 

.275 

.231 

.191 

.156 

.127 

.103 

.083 

1/2 

6!  634 

.562 

.469 

.392 

.323 

.264 

.214 

.173 

.139 

.112 

5/8 

i'.io 

6!  994 

.868 

.748 

.617 

.509 

.416 

.338 

.273 

.219 

.176 

.141 

3/4 

1.47 

1.29 

1.10 

.934 

.764 

.  .626 

.509 

.411 

.331 

.266 

.213 

.170 

7/8 

1.84 

1.59 

1.34 

.12 

.911 

.743 

.601 

.485 

.389 

.312 

.249 

.199 

2.21 

1.88 

1.57 

.31 

.06 

.859 

.694 

.558 

.448 

.358 

.286 

.228 

11/8 

2.59 

2.18 

1.81 

.49 

.21 

.976 

.787 

.632 

.506 

.404 

.322 

.257 

1  V4 

2.96 

2.47 

2.04 

.68 

.35 

.09 

.879 

.705    .564 

.450 

.359 

.286 

13/8 

3.33 

2.77 

2.27 

.86 

.50 

.21 

.972 

.779 

.622 

.497 

.396 

.315 

1  V2 

3.70 

3.06 

2.51 

2.05 

.65 

.33 

.06 

.852 

.681 

.543 

.432 

.344 

13/4 

4.45 

3.65 

2.98 

2.42 

.94 

.56 

.25 

.999 

.797 

.635 

.506 

.402 

2 

5.19 

4.24 

•3.45 

2.79 

2.24 

.79 

.44 

.15 

.914 

.728 

.579 

.460 

21/4 

5.94 

4.84 

3.91 

3.16 

2.53 

2.03 

.62 

.29 

.03 

.820 

.652 

.519 

21/2 

6.68 

5.43 

4.38 

3.54 

2.83 

2.26 

.81 

.44 

.15 

.913 

.722 

.577 

23/4 

7.43 

6.02 

4.85 

3.91 

3.12 

2.50 

.99 

.59 

.26 

.01 

.799 

.635 

3 

8.17 

6.61 

5.32 

4.28 

3.42 

2.73 

2.18 

.73 

.38 

.10 

.872 

.693 

31/4 

8.92 

7.20 

5.79 

4.65 

3.71 

2.96 

2.36 

.88 

.50 

.19 

.946 

.751 

31/2 

9.66 

7.79 

6.26 

5.02 

4.01 

3.20 

2.55 

2.03 

.61 

.28 

.02 

.809 

33/4 

10.4 

8.38 

6.73- 

5.39 

4.30 

3.43 

2.73 

2.18 

.73 

.37 

.09 

.867 

4 

11.2 

8.97 

7.19 

5.77 

4.60 

3.66, 

2.92 

2.32 

.85 

.47 

.17 

.926 

41/4 

11.9 

9.56 

7.66 

6.14 

4.89 

3.90 

3.10 

2.47 

.96 

.56 

.24 

.984 

41/2 

12.6 

10.2 

8.13 

6.51 

5.19 

4.13 

3.29 

2.62 

2.08 

.65 

.31 

1.04 

43/4 

13.4 

10.7 

8.60 

6.88 

5.48 

4.37 

3.47 

2.76    2.20 

.74 

.39 

1.10 

14.1 

11.3 

9.07 

7.25 

5.78 

4.60 

3.66 

2.91 

2.31 

.84 

.46 

1.16 

51/4 

14.9 

11.9 

9.54 

7.62 

6.07 

4.83 

3.85 

3.06 

2.43 

.93 

51/2 

15.6 

12.5 

10.0 

8.00 

6.36  (5.07 

4.03 

3.20 

2.55 

2.02 

53/4 

16.4 

13.1 

10.5 

8.37 

6.66  |5.30 

4.22 

3.35 

2.66 

2.11 

6 

17.1 

13.7 

10.9 

8.74 

6.95    5.53 

4.40 

3.50 

2.78    2.21 

61/4 

17.9 

14.3 

11.4 

9.11 

7  25  15.77 

4.59 

3.65  J2.90 

6l/2 

18.6 

14.9 

11.9 

9.48 

7.54  16.00 

4.77 

3.79 

3.01 

63/4 
0   /4 

19  4 

15  5 

12  3 

9  85 

7  84  !*  ?4 

4  96 

3  94 

20.1 

16  1 

12  8 

10  2 

8.13 

6  47 

5.14 

4.09 

71/4 

20  8 

16  7 

13  3 

10  6 

8  43 

6  70 

5  33 

4  23 

71/2 

21.6 

17^2 

13.8 

11.0 

S.72 

6.94 

5.51 

4.38 

73/4 

22  3 

17  8 

14  2 

11  .3 

9  02 

7  17 

5.70 

4  53 

8 

23  1 

18-4 

14-7 

11  7 

9  31 

7*40 

5  88 

4  67 

81/4 

23.8 

19  0 

15.2 

12.1 

9  61 

7  64 

6  07 

4  82 

81/2 

24  6 

19  6 

15  6 

12  5 

9  90 

7  87 

6  25 

4  97 

83/4 

25  3 

20  2 

16.1- 

12  8 

10  2 

8.11 

6.44 

5  12 

9 

26  1 

20  8 

16  6 

13  2 

10  5 

8  34 

6  63 

5  26 

91/4 

26  8 

21  4 

17  0 

13  6 

10.8 

8.57 

6  81 

5  41 

91/2 

27  6 

22  0 

17  5 

13  9 

11   1 

8  81 

7  00 

5  56 

93/4 

28.3 

22.6 

18.0 

14.3 

11.4 

9.04 

7.18 

5.70 

10 

29.0 

23.2 

18.4 

14.7 

11.7 

9.27 

7.37 

5.85 

*  Thickness  in  inches.  t  Outside  diameter,  inches. 

Seamless  brass  tubes  are  made  from  H  in.  to  1  in.  outside  diameter, 
varying  by  i/ie  in.,  and  from  1 H  in.  to  10  in.  outside  diameter,  varying  by 
K  in.,  and  in  all  gages  from  No.  2  to  No.  24  A.  W.  G.  witnin  the  limits 
of  the  above  table.  To  determine  the  weight  per  foot  of  a  tube  of  a 
given  inside  diameter,  add  to  the  weights  given  above  the  weights  given 
below,  under  the  corresponding  gage  numbers. 

A.W.G.          2       4       6       8        10      12      14      16      18      20      22      24       26 
Lb.perft.  1.54  .966  .607  .382  .240  .151   .095  .060  .038  .024  .015  .009  .0059 

For  copper  tubing  add  5  %  to  the  weights  given  above. 


226 


MATERIALS. 


Aluminum  Tubing  is  made  in  sizes  from  %  to  2  in.  diatn.,  advanc- 
ing  by  i/g  inch,  and  from  2  to  6  in.  diam.,  advancing  by  y±  in.,  in 
practically  all  thicknesses  from  No.  24  to  No.  1  B.W.G.  Aluminum 
pipe  is  made  in  sizes  to  correspond  with  iron-pipe  fittings,  ranging  in 
diameter  from  i/s  to  4  in.  Aluminum  pipe  fittings  are  made  in  prac- 
tically all  standard  pipe  sizes.  Details  of  sizes,  weights,  strength, 
etc.,  of  these  tubes,  pipes,  and  fittings  are  given  in  the  pamphlets  of 
the  Aluminum  Co.  of  America,  Pittsburgh. 

Lead  and  Tin-Lined  Lead  Pipe. 

(United  Lead  Company,  New  York,  1915.) 


In- 

8£ 

In- 

8£ 

In- 

% a 

side 
Dia., 
In. 

Let- 
ter. 

Weight 
per  Ft. 

l| 

side 
Dia., 
In. 

Let- 
ter. 

Weight 
per  Ft. 

j§ 

H^ 

side 
Dia., 
In. 

Let- 
ter. 

Weight 
per  Ft. 

-1  1 
3> 

3/8 

D 

10       oz. 

9 

5/8 

AA 

2  3/4  Ib. 

21 

1/4 

AA 

5  3/4  Ib. 

25 

3/8 

C 

12 

10 

5/8 

AAA 

31/2  "t 

26 

1/4 

AAA 

63/4   " 

28 

3/8 

B 

1        Ib. 

13 

3/4 

E 

8 

1/2 

E 

3 

12 

3/8 

'    A 

1  1/4  " 

15 

3/4 

D 

1  1/4  " 

9 

1/2 

D 

3  1/2  " 

14 

3/8 

AA 

1  1/2   " 

17 

3/4 

C 

13/4 

13 

1/2 

C 

4  1/4   " 

16 

3/8 

AAA 

1  3/4   " 

20 

3/4 

Spec'l 

14 

1/2 

B 

5 

19 

7/16 

13         OZ. 

10 

3/4 

B 

21/4 

16 

1/2 

A 

61/2    " 

24 

7/16 

1          Ib. 

12 

3/4 

A 

20 

1/2 

AA 

7  1/2  " 

27 

1/2 

E 

9       oz. 

6 

3/4 

AA 

31/2 

23 

1/2 

AAA 

81/2    " 

30 

1/2 

D 

12 

8 

3/4 

AAA 

43/4 

29 

3/4 

D 

4 

14 

1/2 

C 

1        Ib. 

11 

E 

1  1/2 

9 

3/4 

C 

5 

17 

1/2 

B 

1  1/4   " 

13 

D 

2 

12 

3/4 

B 

6 

20 

1/2 

Spec'l 

I  V2    " 

15 

C 

21/2 

14 

3/4 

A 

7 

23 

1/2 

A 

1  3/4   " 

17 

B 

31/4 

18 

3/4 

AA 

81/2     '. 

27 

1/2 

AA 

2        " 

19 

A 

4 

21 

13/4 

AAA 

10 

31 

1/2 

Spec'l 

2l/2  " 

22 

AA 

43/4 

25 

2 

D 

43/4     ' 

14 

1/2 

AAA 

3 

26 

AAA 

6 

30 

2 

C 

6 

18 

5/8 

E 

3/4  " 

7 

V4 

E 

2 

10 

2 

B 

7 

21 

5/8 

D 

1          " 

9 

V4 

D 

2.1/2 

12 

2 

A 

8 

23 

5/8 

C 

1  V2   " 

13 

1/4 

C 

3 

14 

2 

AA 

9 

26 

5/8 

B 

2        " 

16 

1/4 

B 

33/4 

17 

2 

AAA 

113/4   " 

33 

5/8 

A 

21/2    " 

20 

1/4  J 

A 

43/4 

21 

Weight  of  lead  is  taken  0.4106  Ib.  per  cu.  in.  The  safe  working 
strength  of  lead  is  about  K  the  elastic  limit,  or  225  Ib.  per  sq.  in. 

To  find  the  thickness  of  lead  pipe  required  when  the  head  of 
water  is  given.  (Chadwick  Lead  Works.) 

RULE. — Multiply  the  head  in  feet  by  size  of  pipe  wanted,  expressed 
decimally,  and  divide  by  750;  the  quotient  will  be  the  thickness  re- 
quired, in  one-hundredths  of  an  inch.  Thus  the  thickness  of  a  half-inch 
pipe  for  a  head  of  25  feet  will  be  25X0. 50-5-750  =  0.016  inch. 

This  rule  corresponds  to  a  safe  working  stress  of  165  Ibs.  per  sq.in. 
It  gives  thicknesses  of  small  diameter  pipes  that  are  much  less  than 
those  given  iii  the  table  below. 

Weight  of  Lead  Pipe  Which  Should  Be  Used  for  a  Given 
Head  of  Water      (United  Lead  Co.,  New  York,  1915.) 


Head  or 
Number 
of  Feet 
Fall. 

Pres- 
sure 
per  sq. 
inch. 

Caliber  and  Weight  per  Foot. 

Letter. 

Vs  in. 

1/2  in. 

Vs  in. 

3/4  in. 

1  in. 

11/4  in. 

30ft. 
50ft. 
75ft. 
100ft. 
]50  ft. 
200ft. 

131b. 
22  Ib. 
32  Ib. 
44  Ib. 
65  Ib. 
87  Ib. 

D 

C 
B 
A 
AA 
AAA 

10       oz. 
12       oz. 
1        Ib. 

11/4lb. 
1  1/2  Ib. 
1  3/4  Ib. 

3/4  Ib. 
1  Ib. 
1  1/4  Ib. 

1  3/4  Ib. 

2  Ib. 
3  Ib. 

1  Ib. 

1  1/2  Ib. 
2  Ib. 
2  l/2  Ib. 
23/4lb. 
3  i/2  Ib. 

1  1/4  Ib. 
1  3/4  Ib. 
2  1/4  Ib 
3        Ib. 
3  l/2  Ib. 
4  3/4  Ib. 

2       Ib. 

2  1/2  Ib. 
3l/4lb. 
4       Ib. 
43/ilb. 
6       Ib- 

2  1/2  Ib. 
3  Ib. 
33/4lb. 
43/4Ib. 
5  3/4  Ib. 
63/4lb. 

LEAD  AND  TIN-LINED  PIPE. 


227 


1 1/2  in.,  2  and  3  pounds  per  foot. 

"    3  and  4  pounds  per  foot. 

*'   3 1/2,  5,  and  6  pounds  per  foot. 
3 1/2   "   4  pounds  per  foot. 


Lead  Waste-Pipe. 

4  in.,  5,  6,  and  8  pounds  per  foot. 
4 1/2    "    6  and  8  pounds  per  foot. 

5  "    8,  1 0,  and  1 2  pounds  per  foot. 

6  "12  pounds  per  foot. 


Tin-Lined  and  Lead-Lined  Iron  Pipe. 

(United  Lead  Co.,  New  York,  1915.) 


Size, 
In. 

Wt.  per  ft.,  Ib. 

Size, 
In. 

Wt.perft.,lb. 

Size, 
In. 

Wt.perft.,lb. 

Size, 
In. 

Wt.  per 
ft.,  Ib. 
Lead 
Lined. 

Lead 
Lined. 

Tin 
Lined. 

Lead 
Lined. 

Tin 
Lined. 

Lead 
Lined. 

Tin 

Lined. 

1/2- 

•A 
!|g 

,   13/8 

1  V8 
21/2 

3-1/2 

43/8 

1 

13/8 

|U 

33/41 

f'A 

31/2 

61/8 
81/2 
111/2 

14l/2 

152/3 

51/4 
71/2 
101/6 
128/10 
141/6 

41/2 

6 
7 
8 

18 

21  l/2 
293/4 
36 
47 

16 

26  l/io 
191/6 

9 
10 
12 

66 
75 

88 

Block  Tin  Pipe  and  Tubing. 


Diam.,  In. 

Thick- 

Wt. 

Diam.,  In. 

Thick- 

Wt. 

Diam.,  In. 

Thick- 

Wt. 

In- 

Out- 

ness, 
i.- 

ftT 

In- 

Out- 

ness, 

ir\ 

per 

ft., 

In- 

Out- 

ness, 

?^f 

side. 

side. 

n. 

oz. 

side. 

side. 

in. 

oz. 

side. 

side. 

in. 

oz. 

Tubing. 

Pipe. 

Pipe. 

1/8 

0.25 

0.062 

1.9 

3/8 

0.495 

0.06 

4 

5/8 

0.800 

0.037 

10 

1/8 

.202 

.0385 

| 

3/8 

.503 

.064 

41/2 

5/8 

.831 

.103 

12 

3/16 

.292 

.053 

2 

3/8 

.515 

.07 

5 

3/4 

.901 

.076 

10 

3/16 

.331 

.072 

3 

3/8 

.539 

.082 

6 

3/4 

.928 

.089 

12 

3/16 

.367 

.09 

4 

3/8 

.561 

.093 

7 

.172 

.086 

15 

.388 

.069 

3.1/2 

3/8 

.584 

.104 

8 

.204 

.102 

18 

Pir»P 

1/2 

.632 

.066 

6 

1/4 

.436 

.093 

20 

ripe. 

1/2 

.670 

.085 

8 

!/4 

.471 

.110 

24 

1/4 

.400 

.075 

4 

1/2 

.707 

.103 

10 

1/2 

.746 

.123 

32 

1/4 

.433 

.091 

5 

1/2 

.741 

.120 

12 

1/2 

.802 

.151 

40 

5/16 

.444 

.066 

4 

5/8 

.735 

.055 

6 

2 

2.236 

.118 

40 

Vl6 

.562 

.065 

5 

5/8 

.768 

.071 

8 

2 

2.280 

.140 

48 

Weight  of  tin  taken  as  0.2652  Ib.  per  cubic  inch. 


Weight  Per  Foot  of  Brass-  and  Copper-Lined  Iron  Pipe. 

(United  Lead  Co.,  New  York,  1915.) 


1/2 

3/4 


1 

13/8 


13/8 


H/4 
H/2 


22/3    22/3 

3  l/4i  3  1/4 

4  1/3!  4  3/8 


21/2 

4 


67/10  63/4 
83/4  88/10 
126/10!  |27/io 


191/2 

32i1A 


Sll 


193/4 

25  6/10 
381/2 


228 


MATERIALS. 


Lead-Lined  pipe  is  particularly  adapted  for  use  in  contact  with  acids, 
mine  water,  salt  water,  or  any  liquid  which  has  a  corrosive  action  on 
iron  pipe. 

Lead  Covered  iron  pipe  for  use  in  bleacheries,  etc.,  where  steam 
passes  through  the  pipe  and  the  exterior  is  in  contact  with  acid  or  cor- 
rosive solutions  is  made  in  commercial  sizes  of  H,  %,  1,  1%,  1  ^,  2 
and  3  inches. 

Brass  and  Copper  Pipes,  Lined  with  Tin  or  Lead,  are  made  in  com- 
mercial sizes  of  y^,  y±,  1,  11A,  1^,  and  2  inches. 

Sheet  Lead  is  rolled  to  any  weight  per  sq.  ft.  from  1  to  7  Ib.  in  any 
width  up  to  11  ft.  6  in.,  and  from  8  Ib.  up,  12  ft.  wide.  A  square  foot  of 
rolled  sheet  lead  1  in.  thick  weighs  approximately  59  Y2  Ib. 

Approximate  Weight  of  Sheet  Zinc. 

(Aluminum  Co.  of  America,  1914.) 


o* 

fc 

•    o 

1| 
*s 

o"  . 
w  -a 

NM 

a> 

ft4a 

6 
2 

o 

Is 

11 

w-a 

£  r 

6 

0 

Is 

5-S. 
«•>  g 

1 

d 

1  g 
If 

a*  • 

I* 

i 

^j1"1 

-4-Jfe 

i 

g 
N 

£HH 

H 

£^ 

N 

S 

£ 

_c 

H 

£ 

i 

0.002 

0.075 

8 

0.016 

0.60 

15 

0.040 

1.50 

22 

0.090 

3.37 

2 

.004 

.15 

9 

.018 

.67 

16 

.045 

1.68 

23 

.100 

3.75 

3 

.006 

.225 

10 

.020 

.75 

17 

.050 

1.87 

24 

.125 

4.70 

4 

.008 

.30 

11 

.024 

.90 

18 

.055 

2.06 

25 

.250 

9.41 

5 

.010 

.37 

12 

.028 

1.05 

19 

.060 

2.25 

26 

.375 

14.11 

6 

.012 

.45 

13 

.032 

1.20 

20 

.070 

2.62 

27 

.500 

18.  8( 

7 

.014 

.52 

14 

.034 

1.35 

21 

.080 

3.00 

28 

1.000 

37.60 

Weight  of  Sheet  or  Bar  Brass. 

(Compiled  from  Manufacturers'  Standard  Tables.) 


A 

£•* 

-bi 

oi 

.^ 

bib 

kA 

aa 

£i* 

bib 

-A 

*Q 

08  3 

a 

P 

j2M 
J* 

^ 

0)   t-, 

II 

1» 

aJ     . 

cr— 

OQ 

|S 

1:- 
m 

11 

CO 

$ 

1 

In. 
1/16 

2.77 

Lb. 
0.014 

Lb. 
0.011 

In. 

3/4 

33.21 

Lb. 
2.075 

Lb. 
1.630 

In. 

17/16 

63.66 

Lb. 
7.623 

Lb. 
5.987 

1/8 

5.54 

.058 

.045 

13/16 

35.98 

2.435 

1.913 

H/2 

66.42 

8.300 

6.519 

3/16 

8.30 

.130 

.102 

38.75 

2.824 

2.218 

19/16 

69.19 

9.006 

7.073 

1/4 

11.07 

.231 

.181 

15/16 

41.51 

3.242 

2.546 

15/8 

71.96 

9.741 

7.651 

5/16 

13.84 

.360 

.283 

44.28 

3.689 

2.897 

74.73 

10.50 

8.250 

3/8 

16.61 

.519 

.407 

'1/16 

47.05 

4.164 

3.271 

1  3/416 

77.49 

11.30 

8.873 

7/16 

19.37 

.706 

.555 

11/8 

49.82 

4.669 

3.667 

1  13/16 

80.26  12.12 

9.518 

1/2 

22.14 

.922 

.724 

13/16 

52.59 

5.202 

4.086 

17/8 

83.03  12.97 

10.19 

9/16 

24.91 

1.167 

.917 

U/4 

55.35 

5.764 

4.527 

1  15/16 

85.80  13.85 

10.88 

5/8 

27.68 

1.441 

1.132 

15/16 

58.12 

6.355 

4.991 

2 

88.56  14.76 

11.59 

11/16 

30.44 

1.744 

1.369 

13/8 

60.89 

6.974 

5.478 

WEIGHT  OF  COPPER  AND  BRASS  WIRE  AND  PLATES.   229 


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5       H,-^g 

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on          i— 'oooooO-^-OMncNO^t^iriTrcocNCN  —  —  ~- 
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a       H^  —  co  co  o^  ro  —  <^'  \o  a  <^  co  o  o>  •-  -<*•  a^  «A  CN  av  t^  vc  -^  co  co 

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230 


MATERIALS. 


Weight  of  Aluminum  Plates.     (Brown  &  Sharpe  Gage.) 
(Aluminum  Co.  of  America,  1914.) 


Gage. 

Thick- 
ness, 
In. 

Wgt., 
Lb. 

Gage. 

Thick- 
ness, 
In. 

'^ 

Gage. 

Thick- 
ness, 
In. 

Wgt., 
Lb. 

0000 

0.46000 

6.406 

12 

0.080808 

1.126 

27 

0.014195 

0.1976 

000 

.40964 

5.704 

13 

.071961 

1.002 

28 

.012641 

.1760 

00 

.36480 

5.080 

14 

.064084 

.8924 

29 

.011257 

.1567 

0 

.32486 

4.524 

15 

.057068 

.7946 

30 

.010025 

.1396 

1 

.28930 

4.029 

16 

.050820 

.7078 

31 

.008928 

.1244 

2 

.25763 

3.588 

17 

.045257 

.6302 

32 

.007950 

.1107 

3 

.22942 

3.195 

18 

.040303 

.5612 

33 

.007080 

.09854 

4 

.20431 

2.845 

19 

.035890 

.4998 

34 

.006304 

.08778 

5 

.18194 

2.534 

20 

.031961 

.4450 

35 

.005614 

.07817 

6 

.16202 

2.256 

21 

.028462 

.3964 

36 

.005000 

.06962 

7 

.14428 

2.009 

22 

.025347 

.3530 

37 

.004453 

.06201 

8 

.12849 

1.789 

23 

.022571 

.3143 

38 

.003965 

.05521 

9 

.11443 

1.594 

24 

.020100 

.2798 

39 

.003531 

.04917 

10 

.10189 

1.418 

25 

.017900 

.2492 

40 

.003144 

.04378 

11 

.090742 

1.264 

26 

.015940 

.2219 

Weight  of  Sheet  or  Bar  Aluminum  (Sp.  Gr.  2.68). 
(Aluminum  Co.  of  America,  1914.) 


tess, 
or  Dia. 

& 

o* 

bi 

A 

o?  ti 

U 

eJ 

g3 

,+J 

s*. 

O4 

b£ 

ts 

t-i  be 

wjj 

a 

.-s 

03    j_ 

2  o 

4 

bD 

£3 

£  ti 

«J 

II 

ofGQ 
a  t-> 

*£ 

T3  ,? 

g£ 

!v>2 

£CQ 

$  « 

5    . 

«£ 

^^5 
§£ 

c 

l| 

oo  M 

J4^    JH 
O 

3 

«S 

1* 

ea 

JB  ft 

GO 

CT,-| 

QQ 

&H 

2«S 

£02 

JSft 
CQ 

£* 

1? 

S33 

a 

OQ 

c^^ 

1- 

In. 

Lb. 

Lb. 

In. 

~LbT 

Lb. 

In. 

Lb. 

"EET 

1/16 

0.8690.004 

0.003 

3/4 

10.436 

0.652 

0.516 

1Vl6 

20.002 

2.396    1.882 

1/8 

1.739 

.018 

.014 

IS/IB  '11.  306    .766 

.601 

1  1/2      20.872    2.609    2  049 

3/16 

2.609 

.041 

.032 

7/8    12.175 

.888 

.697 

l»/16 

21.741    2.831    2.223 

V4 

3.479 

.072 

.057 

15/16'  13.  045    .019 

.800 

1  5/8      22.611    3.062    2  405 

8/16 

4.348 

.114 

.089 

1 

13.915    .159      .911 

1  n/16  123.481    3.302    2.593 

3/8 

5.218    .163 

.128 

11/16   14.784    .309      .028 

13/4     24.350    3  550    2  7£9 

Vl6 

6.0881    .222 

.174 

1  1/8     15.654    .467      .152 

1  13/16  25.250    3.810   2.992 

1/2 

6.958    .290 

.227 

13/15    16.524    .635      .284 

17/8 

26.090 

4.075    3.202 

9/16 

7.827    .367 

.288 

11/4 

17.934    .812      .423 

1  15/16 

26.960 

4.352    3.417 

"   5/8 

8.697|    .453 

.356 

15/16 

18.263    .997      .569 

2 

27.829 

4.638    3.642 

H/16 

9.5671    .548 

.430 

13/8 

19.133^2.192  1   .722 

1 

For  further  particulars  regarding  aluminum  see  pp.  380-383;  396-401. 

Weight  Per  Foot  of  Copper  Rods,  Pounds. 

(From  tables  of  manufacturers,  1914.) 


In. 

Round. 

Square. 

In. 

Round. 

Square. 

In. 

Round. 

Square. 

1/8 
1/4 
3/8 

1/2 
5/8 
3/4 
7/8 

0.04735 
.1894 
.4261 
.7576 
1.184 
1  .705 
2.320 
3.030 

0.06028 
.2411 
'    .5424 
.9644 
1.507 
2.170 
2.953 
3.857 

1/8 
1/4 
3/8 
1/2 
5/8 
3/4 

a778 

3.835 
4.735 
5.729 
6.818 
8.002 
9.281 
10.65 
12.12 

4.882 
6.028 
7.293 
8.679 
10.19 
11  .81 
13.56 
15.53 

2V8 
21/4 
23/8 
21/2 
25/8 
23/4 
27/8 

13.68 
15.34 
17.09 
18.94 
20.88 
22.92 
25.05 
27.27 

17.41 
19.53 
21.76 
24.11 
26.58 
29.18 
31.89 
34.71 

For  weight  of  octagon  rod,  multiply  the  weight  of  round  rod  by  1.081. 
For  weight  of  hexagon  rod,  multiply  the  weight  of  round  rod  by  1.12. 


SCREW   THREADS. 


231 


SCREW  THREADS. 

Sellers  or  U.  S.  Standard. 

The  system  of  screw  threads  devised  by  William  Sellers  and  recom- 
mended for  adoption  by  a  committee  of  the  Franklin  Institute  in  1864 
is  now  in  general  use  in  the  United  States  and  is  known  as  the  U.  S. 
standard.  The  angle  of  the  thread  is  60  deg.  The  thread  is  flat- 
tened at  the  top,  the  width  of  flat  being  one-eighth  the  pitch.  The 
bottom  of  the  thread  is  filled  in,  the  width  of  flat  at  the  bottom  also 
being  one-eighth  the  pitch.  The  wearing  surface  of  the  thread  is  thus 
three-quarters  the  pitch. 

Diana,  at  root  of  thread  =  diam.  of  bolt-  (1.299  -~  No.  of  threads 
per  in.).  Depth  of  thread  =  0.6495  X  pitch. 

For  a  sharp  V  thread,  with  an  angle  of  60  deg.  the  formula  is 
Diam.  at  root  of  thread  =  diam.  of  bolt  —  (1.733  -s-  No.  of  threads  per  in.). 

The  rules  for  dimensioning  nuts  and  heads  given  in  the  Franklin 
Institute  report  are: 

Let  d  =  diameter  of  bolt,  D  =  short  diameter  of  rough  nut  or  head, 

(Continued  on  page  232.) 

Dimensions  of  Screw-Threads,  Sellers  or  U.  S.  Standard. 


BOLTS  AND  THREADS. 

NUTS  AND  BOLT 
HEADS. 

T3 

^j 

.JJ 

^j 

a* 

_p  g 

*  . 

"£ 

S 

"o 

PQ 

$ 

OS'S 

A 

JS  o 

Sea 

Ij 

S 

fc 

w 

cv 

§)M 

.2  g 

.2 

f. 

8 

"o 

CO 

*sj 

"8 

««"*  oa 

d 

Q  £ 

£ 

1 

|| 

Ctf  «*-i 

S 

go« 

S^  1 

£3 

M| 

if! 

1 

5 

H 

3° 

| 

^PQw 

^  "oca 

£w 

^W 

0M 

S 

i 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

1/4 

20 

0.185 

0.0062 

0.049 

0.027 

1/2 

0.578 

0.707 

V4 

V4 

5/16 

18 

.240 

.0059 

.077 

.045 

19/32 

.686 

.840 

5/16 

19/64 

3/8 

16 

.294 

.0078 

.110 

.068 

H/16 

.794 

.972 

3/8 

n/32 

7/16 

14 

.345 

.0089 

.150 

.093 

25/32 

.902 

.105 

7/16 

25/64 

1/2 

13 

.400 

.0096 

.196 

.126 

7/8 

.011 

.237 

V2 

7/16 

9/16 

12 

.454 

.0104 

.249 

.162 

31/32 

.119 

.370 

9/16 

31/64 

5/8 

11 

.507 

.0113 

.307 

.202 

1  Vl6 

.227 

.502 

5/8 

17/32 

3/4 

10 

.620 

.0125 

.442 

.302  1  1/4 

.444 

.768 

3/1 

5/8 

7/8 

9 

.731 

.0139 

.601 

.420 

1  7/16 

.660 

2.033 

7/8 

23/32 

8 

.837 

.0156 

.785 

.550 

1  5/8 

.877 

2.298 

13/16 

1  1/8 

7 

.939 

.0178 

.994 

.694  1  13/1  « 

2.093 

2.563 

V8 

29/32 

H/4 

7 

.065      .0178 

1.227 

.891 

2 

2.310 

2.828 

1/4 

13/8 

6 

.160 

.0208 

1.485 

1.057 

23/16 

2.527 

3.093      3/8  i    3/3? 

I  1/2 

6 

.284 

.0208 

1.767 

1.295 

23/8 

2.743 

3.358       1/2      3/,fi 

15/8 

51/2 

.389 

.0227 

2.074 

1.515 

2.960 

3.623 

5/8       9/*2 

13/4 

5 

.491 

.0250 

2.405 

1.746 

23/f 

3.176 

3.889 

13/4 

3/8 

17/8 

5 

.616 

.0250 

2.761 

2.051 

2  15/16 

3.393 

4.154 

1  7/8 

15/32 

2 

41/2 

.712 

.0278 

3.142 

2.302 

31/8 

3.609 

4.419 

2 

9/l6 

21/4 

41/2 

.962 

.0278 

3.976 

3.023 

31/2 

4.043 

4.949 

21/4 

3/4 

21/2 

4  ' 

2.176 

.0312 

4.909 

3.719 

37/s 

4.476 

5.479 

21/2 

J5/16 

23/4 

4 

2.426 

.0312 

5.940 

4.622 

41/4 

4.909 

6.010 

3 

31/2 

2.629 

.0357 

7.069 

5.428 

45/8 

5.342 

6.540 

3 

25/16 

31/4 

31/2 

2.879 

.0357 

8.296 

6.510 

5 

5.775 

7.070    31/4 

2  !/2 

31/2 

31/4 

3.100 

.0384 

9.621 

7.548 

53/8 

6.208 

7.600 

31/2 

2U/16 

33/4 

3 

3.317 

.0417 

11.045 

8.641 

53/4 

6.641 

8.131 

33/4 

27/s 

4 

3 

3.567 

.0417 

12.566 

9.993 

61/8 

7.074 

8.661 

4 

3  VIP 

41/4 

27/8 

3.798 

.0435 

14.186 

11.328 

61/2 

7.508 

9.191 

41/4 

3V4 

41/2 

23/4 

4.028 

.0454  115.904 

12.743 

67/8 

7.941 

9.721 

41/2 

43/4 

25/8 

4.256 

.0476    17.721 

14.250 

71/4 

8.374 

10.252 

43/4 

3  5/g 

5 

21/2 

4.480 

.0500    19.635 

15.763 

75/8 

8.807 

10.782 

5 

3  13/16 

51/4 

21/2 

4.730 

.0500    21.648 

17.572 

8 

9.240 

11.312 

5V4 

4 

51/2 

23/8 

4.953 

.0526  '23.758 

19.267 

83/8 

9.673 

11.842 

51/2 

4Vl6 

53/4 

23/8 

5.203 

.0526    25.967 

21.262 

83/4 

10.106 

12.373 

53/4 

6 

21/4 

5.423!     .0555    28.274 

23.098 

91/8 

10.539 

12.903 

6 

49/l6 

232 


MATERIALS. 


Di  =  short  diameter  of  finished  nut  or  head ;  T  —  thickness  of  rough 
nut;  Ti  =  thickness  of  finished  nut;  t  =  thickness  of  rough  head,  U 
thickness  of  finished  head;  D  =  1.5  d  +  i/s;  A  =  1.5  d  4-  i/ie;  T  =  d- 
Ti  =  d-  i/i6;  t  =  y2  D,  ti  =  1/2  d  -  i/ie. 

The  dimensions  given  by  the  above  formulae  for  nuts  and  heads  are 
not  generally  accepted  by  the  makers  of  nuts  and  bolts.  The  general 
practice  is  to  make  the  rough  and  finished  nuts  of  the  same  dimensions, 
otherwise  different  wrenches  would  be  required  for  the  same  size  of 
nut.  The  dimensions  of  nuts  and  bolt  heads  given  in  the  above  table 
are  those  adopted  by  the  Upson  Nut  Co.,  Hoopes  and  Townsend,  and 
the  U.  S.  Navy,  and  agree  with  the  formulae  D  =  1.5  d  +  1/3,  T  =  Ti  = 
d,t  =  ti  =  1/2  -D. 

Screw-Threads,  Whitworth  (English)  Standard. 


g' 

,d 

j 

,d 

j 

4 

j 

jg 

^ 

^ 

• 

1 

9 

1 

• 

5 

9 

5 

• 

^ 

S 

8 

S 

a 

S 

S 

Q 

S 

1/4 

20 

5/8 

11 

i 

8 

13/4 

5 

3 

3V? 

5/16 

ft 
7/16 

1/2 

18 
16 
14 
12 

H/16 
3/4 
13/16 

7/8 

11 

10 
10 
9 

H/8 
H/4 
13/8 
H/2 

7 
7 
6 
6 

21/4 
21/2 

4 

3V4 
33/4 

31/4 
3V4 

'.2 

15/16 

9 

15/8 

5 

23/4 

31/2 

In  the  Whitworth  or  English  system  the  angle  of  the  thread  is  55 
degrees,  and  the  point  and  root  of  the  thread  are  rounded  to  a  radius  of 
0.1373  X  pitch.  The  depth  of  the  thread  is  0.6403  X  pitch. 

International  Standard  Thread  (Metric  System). 

The  form  of  thread  is  the  same  as  the  U.  S.  Standard.  P  =  pitch, 
in  millimetres  =  25.4  +  no.  of  threads  per  in.  No.  of  threads  per  in.  =* 
25.4  H-P: 

Diam.,  mm.  67  8  9  10  11  12  14  16  18  20  22  24  27 
Pitch,  mm.  1.0  1.0  1.25  1.25  1.5  1.5  1.75  2.  2.  2.5  2.5  2.5  3.  3. 
Diam.,  mm.  30  33  36  39  42  45  48  52  56  60  64  68  72  76  80 
Pitch,  mm.  3.5  3.5  4.  4.  4.5  4.5  5.  5.  5.5  5.5  6.  6.  6.5  6.5  7. 

British  Association  Standard  Thread. 

The  angle  between  the  threads  is  47  1A°.  The  depth  of  the  thread  is 
0.6  X  the  pitch.  The  tops  and  bottoms  of  the  threads  are  rounded  with 
a  radius  of  2/11  of  the  pitch. 

Number 0124556 

Diameter,  mm 6.0       5.3       4.7       4.1       3.64     3.2     2.8 

Pitch,  mm 1.00     0.90     0.81     0.73     0.66     0.590.53 

Number 7  8  9  10         12         14         19 

Diameter,  mm 2.5       2.2       1.9       1.7       1.3       1.0       0.79 

Pitch,  mm 0.48     0.43     0.39     0.35     0.28     0.23     0.19 


Limit  Gages  for  Iron  for  Screw-Threads. 

In  ad9pting  the  Sellers,  or  Franklin  Institute,  or  United  States  Stand- 
ard, as  it  is  variously  called,  a  difficulty  arose  from  the  fact  that  it  is 
the  habit  of  iron  manufacturers  to  make  iron  over-size,  and  as  there  are 
no  over-size  screws  in  the  Sellers  system,  if  iron  is  too  large  it  is  necessary 
to  cut  it  away  with  the  dies.  So  great  is  this  difficulty,  that  the  practice 
of  making  taps  and  dies  over-size  has  become  very  general.  If  the 
Sellers  system  is  adopted  it  is  essential  that  iron  should  be  obtained  of 
the  correct  size,  or  very  nearly  so.  Of  course  no  high  degree  of  precision 
is  possible  in  rolling  iron,  and  when  exact  sizes  were  demanded,  the  ques- 
tion arose  how  much  allowable  variation  there  should  be  from  the  true 
size.  It  was  proposed  to  make  limit-gages  for  inspecting  iron  with  two 
openings,  one  larger  and  the  other  smaller  than  the  standard  size,  and 


SCREW  THREADS. 


233 


then  specify  that  the  iron  should  enter  the  large  end  and  not  enter  the 
small  one.  The  following  table  of  dimensions  for  the  limit-gages  was 
adopted  by  the  Master  Car-Builders'  Association  in  1883. 


"o  . 

fl)  C 

11 
a° 
S* 

II 

-  _O 

13^ 

1° 

Difference. 

1 

1* 

w 

~5/8 
3/4 

,7/8 

H/8 

H/4 

11 
f 

If 
£ 

Difference. 

Size  of  Iron, 
In. 

11 

QjO 

II 

--  .O 

1° 

Difference. 

1/4 

5/16 
3/8 
7/16 
V2 
9/16 

0.2550 
0.3180 
0.3810 
0.4440 
0.5070 
0.5700 

0.2450 
0.3070 
0.3690 
0.4310 
0.4930 
0.5550 

0.010 
0.011 
0.012 
0.013 
0.014 
0.015 

0.6330 
0.7585 
0.8840 
1  .0095 
1.1350 
1  .2605 

0.6170 
0.7415 
0.8660 
0.9905 
1  .1150 
1  .2395 

0.016 
0.017 
0.018 
0.019 
0.020 
0.021 

13/8 
H/2 
15/8 
13/4 
17/8 

.3860 
.5115 
.6370 
.7625 
.8880 

1  .3640 
1  .4885 
1  .6130 
1  .7375 
1  .8620 

0.022 
0.023 
0.024 
0.025 
0.026 

Caliper  gages  with  the  above  dimensions,  and  standard  reference 
gages  for  testing  them,  are  made  by  the  Pratt  &  Whitney  Co.,  Hartford. 

Automobile  Screws  and  Nuts. — The  Society  of  Automobile  Engi- 
neers (1912)  adopted  standard  specifications  for  hexagon  head  screws, 
castle  and  plain  nuts  known  as  the  A.L.A.M.  standard.  Material  to 
be  steel,  elastic  limit  not  less  than  60,000  Ibs.  per  sq.  in.,  tensile  strength 
not  less  than  100,000  Ibs.  per  sq.  in.  U.  S.  Standard  thread  is  used,  the 
threaded  portion  of  screws  being  1 K  times  the  diameter.  The  castle 
nut  has  a  boss  on  the  upper  surface  with  six  slots  for  a  locking  pin 
through  the  bolt. 

Standard  Automobile  Screws,  Castle  and  Plain  Nuts. 

All  dimensions  in  inches.  P  =  pitch,  or  number  of  threads  per  inch. 
d  =  diam.  of  cotter  pin.  P  -4-  8  =  flat  top  of  thread.  The  body 
diam.  of  screws  is  0.001  in.  less  than  nominal  diam.,  with  a  plus 
tolerance  of  zero  and  a  minus  tolerance  of  0.002  in.  The  top  shall  be 
between  0.003  in.  and  0.003  in.  large. 


D 

P 

B 

Ai 

H 

K 

I 

A 

c 

E 

d 

1/4 

28 

7/13 

7/32 

3/16 

1/16 

3/32 

9/32 

5/64 

1/16 

Vl6 

24 

1/2 

17/64 

15/64 

Vl6 

7/64 

21/64 

3/32 

5/64 

1/16 

3/8 

24 

9/16 

21/61 

9/32 

3/32 

1/8 

13/32 

1/8 

1/8 

3/32 

7/16 

20 

5/8 

3/8 

21/64 

3/32 

1/8 

29/64 

1/8 

1/8 

3/32 

1/2 

20 

3/4 

7/16 

3/8 

3/32 

1/8 

9/16 

3/16 

1/8 

3/32 

9/16 

18 

7/8 

31/64 

27/64 

3/32 

1/8 

39/04 

3/16 

5/32 

1/8 

5/8 

18 

15/16 

35/64 

15/32 

3/32 

1/8 

23/32 

1/4 

5/32 

1/8 

H/16 

16 

1 

19/32 

33/64 

3/32 

1/8 

49/64 

1/4 

5/32 

1/8 

3/1 

16 

H/16 

21/32 

9/16 

3/32 

1/8 

13/16 

Vl 

5/32 

1/8 

7/8 

14 

1  V4 

49/o 

21/32 

3/32 

1/8 

29/32 

1/4 

5/32 

1/8 

1 

14 

17/10 

7/8 

3/4 

3/32 

Vs 

1 

1/4 

5/32 

1/8 

H/8 

12 

15/8 

63/64 

27/32 

5/32 

7/32 

15/32 

5/16 

7/32 

H/04 

M/4 

12 

1  13/16 

1  3/32 

15/16 

5/32 

7/32 

H/4 

5/16 

7/32 

H/64 

13/8 
U/2 

12 
12 

2 
23/16 

1  13/64 
15/16 

H/32 
H/8 

3/16 
3/16 

1/4 
1/4 

1  13/32 
H/2 

3/8 
3/8 

1/4 
1/4 

13/04 
13/64 

234 


MATERIALS. 


The  Acme  Screw  Thread. 

The  Acme  Thread  is  an  adaptation  of  the  commonly  used  style  of  worm 
thread  and  is  intended  to  take  the  place  of  the  square  thread.  It  is  a 
little  shallower  than  the  Worm  thread,  but  the  same  depth  as  the  square 
thread  and  much  stronger  than  the  latter.  The  angle  of  the  thread  is  29°. 

The  various  parts  of  the  Acme  .Thread  are  obtained  as  follows: 

Width  of  point  of  tool  for  screw*  or  tap  thread  •=« 
(0.3707  -5-  No.  of  Threads  per  in.)  -  0.0052. 

Width  of  screw  or  nut  thread  =  0.3707  •*-  No.  of  Threads  per  in. 

Diam.  of  Tap  =  Diam,  of  Screw  +  0.020. 


Diam-  of  Screw- 


-0.020 


*F  —  F-H  —  - 

No.  of  Threads  per  in. 

Depth  of  Thread  =  |  1  -5-  (2  X  No.  of  Threads  per  in.)  j-  +  0.010. 
The  angle  of  the  thread  is29  deg. 

MACHINE  SCREWS.—  A.  S.M.E.  Standard. 

Ther  American  Society  of  Mechanical  Engineers  (1907)  received  a  report 
on  standard  machine  screws  from  its  committee  on  that  subject.  The 
included  angle  of  the  thread  is  60  degrees  and  a  flat  is  made  at  the  top 
and  bottom  of  the  thread  of  one-eighth  of  the  pitch  for  the  basic  diameter. 
A  uniform  increment  of  0.013  inch  exists  between  all  sizes  from  0  to  10 
and  0.026  inch  in*  the  remaining  sizes.  .  The  pitches  are  a  function  ot  the 
diameter  as  expressed  by  the  formula 

Threads  per  inch 

The  minimum  tap  conforms  to  the  basic  standard  in  all  respects  except 
diameter.  The  difference  between  the  minimum  tap  and  the  maximum 
screw  provides  an  allowance  for  error  in  pitch  and  for  wear  of  the  tap  in 
service. 

A.  S.  M.  E.  Standard  Machine  Screws. 
(Corbin  Screw  Corporation.) 


Size. 

Outside  Diameters. 

Pitch  Diameters. 

Root  Diameters. 

Out. 

No. 

Dia. 
and 
Thds. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

per  In. 

0 

0.060-80 

0.0572 

0.060 

0.0028 

0.0505 

0.0519 

0.0014 

0.0410 

0.0438 

0.0028 

1 

.073-72 

.070 

.073 

.003 

.06251  .064 

.0015 

.052 

.055 

.0030 

2 

.086-64 

.0828 

.086 

.0032 

.0743 

.0759 

.0016 

.0624 

.0657 

.0033 

3 

.099-56 

.0955 

099 

.0035 

.0857 

.0874 

.0017 

.0721 

.0758 

.0037 

4 

.112-48 

.1082 

.112 

.0038 

.0966 

.0985 

.0019 

.0807 

.0849 

.0042 

5 

.125-44 

.1210 

.125 

.0040 

.1082 

.1102 

.0020 

.0910 

.0955 

.0045 

6 

.138-40 

.1338 

.138 

.0042 

.1197 

.1218 

.0021 

.1007 

.1055 

.0048 

7 

.151-36 

.1466 

.151 

.0044 

.1308 

.1330 

.0022 

.1097 

.1149 

.0052 

8 

.164-36 

.1596 

.164 

.0044 

.1438 

.146 

.0022 

.1227 

.1279 

.0052 

9 

.177-32 

.1723 

.177 

.0047 

.1544 

.1567 

.0023 

.1307 

.1364 

.0057 

10 

.190-30 

.1852 

.190 

.0048 

.166 

.1684 

.0024 

.1407 

.1467 

.0060 

12 

.216-28 

.2111 

.216 

.0049 

.1904 

.1928 

.0024 

.1633 

.1696 

.0063 

14 

.242-24 

.2368 

.242 

.0052 

.2123 

.2149 

.0026 

.1808 

.1879 

.0071 

16 

.268-22 

.2626 

.268 

.0054 

.2358 

.2385 

.0027 

.2014 

.209 

.0076 

18 

.294-20 

.2884 

.294 

.0056 

.2587 

.2615 

.0028 

.2208 

.229 

.0082 

20 

.320-20 

.3144 

.320 

.0056 

.2847 

.2875 

.0028 

.2468 

.255 

.0082 

22 

.346-18 

.3402 

.346 

.0058 

.3070 

.3099 

.0029 

.2649 

.2738 

.0089 

24 

.372-16 

.366 

.372 

.0060 

.3284 

.3314 

.0030 

.281 

.2908 

.0098 

26 

.398-16 

.392 

.398 

.0060 

.3544 

.3574 

.0030 

.307 

.3168 

.0098 

28 

.424-14 

.4178 

.424 

.0062 

.3745 

.3776 

.0031 

.3204 

.3312 

.0108 

30 

.450-14 

.4438 

.450 

.0062 

.4005 

.4036 

.0031 

.3464 

.3572 

.0108 

A.   S.   M.   E.    STANDARD   TAPS. 


235 


A.  S.  M.  E.  Special  Screws. 

(All  Dimensions  in  Inches.) 


Old 

No. 

New. 

Outside  Diameters. 

Pitch  Diameters. 

Root  Diameters. 

Outside 
Diam.  and 
Threads 
per  In. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

Mini- 
mum. 

Maxi- 
mum. 

Dif- 
fer- 
ence. 

*~j 

0.073-64 

0.0698 

0.073 

0.0032 

0.0613 

0.0629 

0.0016 

0.0494 

0.0527|0.0033 

2 

.086-56 

.0825 

.086 

.0035 

.0727 

.0744 

.0017 

.0591 

.0628 

.0037 

3 

.099-48 

.0952 

.099 

.0038 

.0836 

.0855 

.0019 

.0677 

.0719 

.0042 

4 

.112-40 

.1078 

.112 

.0042 

.0937 

.0958 

.0021 

.0747 

.0795 

.0048 

36 

.1076 

.112 

.0044  .0918 

.0940 

.0022 

.0707 

.0759 

.0052 

5 

.125-40 

.1208 

.125 

.0042  .1067 

.1088 

.0021  .0877 

.0925 

.0048 

36 

.1206 

.125  .0044  .1048 

.1070 

.0022  .0837 

.0889 

.0052 

6 

.138-36 

.1336 

.138  .0044!  .1178 

.1200 

.0022  .0967 

.1019  .0052 

32 

.1333 

.138;  .0047!  .1154 

.1177 

.0023 

.0917 

.0974  .0057 

7 

.151-32 

.1463 

.151  .0047  .1284 

.1307 

.0023 

.1047 

.1104 

.0057 

30 

.1462 

.151  .0048  .1270 

.1294 

.0024 

.1017 

.1077 

.0060 

8 

.164-32 

.1593 

.164  .0047  .1414 

.1437 

.0023 

.1177 

.1234 

.0057 

30 

.1592 

.164  .0048  .1400 

.1  424 

.0024 

.1147 

.1207 

.0060 

9 

.177-30 

.1722 

.177  .0048  .1529 

.1553 

.0024 

.1277 

.1337 

.0060 

24 

.1718 

.177 

.0052  .1473 

.1499 

.0026 

.1158 

.1229 

.0071 

10 

.190-32 

.1853 

.190  .0047  .1674 

.1697 

.0023 

.1437 

.1494 

.0057 

24 

.1848 

.190  .0052  .1603 

.1629 

.00261  .1288 

.1359 

.0071 

12 

.216-24 

.21Q8 

.216 

.0052  .1863 

.1889 

.0026 

.1548 

.1619 

.0071 

14 

.242-20  !  .2364 

.242 

.0056  .2067 

.2095 

.0028 

.1688 

.1770 

.0032 

16 

.268-20 

.2624 

.268 

.0056  .2327 

.2355 

.0028 

.1948 

.2030 

.0082 

18 

.294-18 

.2882 

.294 

.0058  .2550 

.2579 

.0029 

.2129 

.2218 

.0089 

20 

.320-18 

.3142 

.320 

.0058  .2810 

.2839 

.0029 

.2389 

.2478 

.0089 

22 

.346-16 

.3400 

.346 

.0060 

.3024 

.3054 

.0030 

.2550 

.2648 

.0098 

24 

.372-18 

.3662 

.372 

.0058  .3330 

.3359 

.0029 

.2909 

.2998 

.0089 

26 

.398-14 

.3918 

.398 

.0062  .3485 

.3516 

.0031 

.2944 

.3052 

.0108 

28 

.424-16 

.4180 

.424]  .0060 

.3804 

.3834 

.0030 

.3330 

.3428  .0098 

30 

.450-16 

.4440 

.450!  .0060  .4064 

.4094  .0030 

.3590 

.3688 

.0098 

A.  S.  M.  E.  Standard  Taps. 

(Corbin  Screw  Corporation.) 


Size. 

Outside  Diameters. 

Pitch  Diameters. 

Root  Diameters. 

Tap  Drill 
.  Diameters. 

No. 

Out.  Dia. 
and 
Thds. 
per  In. 

Mini- 
mum, 
In. 

Maxi- 
mum, 
In. 

Dif- 
fer- 
ence. 

Mini- 
mum, 
In. 

Maxi- 
mum, 
In. 

Dif- 
fer- 
ence. 

Mini- 
mum, 
In. 

Maxi- 
mum, 
In. 

Dif- 
fer- 
ence. 

0 

0.060-80 

0.0609 

0.0632 

0.0023 

0.0528 

0.0538 

0.0010 

0.0447 

0.0466 

0.0019 

0.0465 

1 

.073-72 

.0740 

.0765 

.0025 

.0650 

.0660 

.0010 

.0560 

.0580 

.0020 

.0595 

2 

.086-64 

.0871 

.0898 

.0027 

.0770 

.0781 

.0011 

.0668 

.Oo89 

.0021 

.0700 

3 

.099-56 

.1002 

.1033 

.0031 

.0886 

.0897 

.0011 

.0770 

.0793 

.0023 

.0785 

4 

.112-48 

.1133 

.1168 

.0035 

.0998 

.1010 

.0012 

.0862 

.0887 

.0025 

.0890 

5 

.125-44 

.1263 

.1301 

.0038 

.1116 

.1129 

.0013 

.0968 

.0995 

.0027 

.0995 

6 

.138-40 

.1394 

.1435 

.0041 

.1232 

.1246 

.0014 

.1069 

.1097 

.0028 

.1100 

7 

.151-36 

.1525 

.1569 

.0044 

.1345 

.1359 

.0014 

.1164 

.1193 

.0029 

.1200 

8 

.164-36 

.1655 

.1699 

.0044 

.1475 

.1489 

.0014 

.1294 

.1323 

.0029 

.1360 

9 

.177-32 

.1786 

.1835 

.0049 

.1583 

.1598 

.0015 

.1380 

.1411 

.0031 

.1405 

10 

.  190-30 

.1916 

.1968 

.0052 

.1700 

.1716 

.0016 

.1483 

.1515 

.0032 

.1520 

12 

.216-28 

.2176 

.2232 

.0056 

.1944 

.1961 

.0017 

.1712 

.1745 

.0033 

.1730 

14 

.242-24 

.2438 

.2500 

.0062 

.2167 

.2184 

.0017 

.1896 

.1931 

.0035 

.1935 

16 

.268-22 

.2698 

.2765 

.0067 

.2403 

.2421 

.0018 

.2108 

.2144 

.0036 

.2130 

18 

.294-20 

.2959 

.3031 

.0072 

.2634 

.2652 

.0018 

.2309 

.2346 

.0037 

.2340 

20 

.320-20 

.3219 

.3291 

.0072 

.2894 

.2912 

.0018 

.2569 

.2606 

.0037 

.2610 

22 

.346-18 

.3479 

.3559 

.0080 

.3118 

.3138 

.0020!  .2757 

.27.96 

.0039 

.2810 

24 

.372-16 

.374 

.3828 

.0088 

.3334 

.3354 

.0020 

.2928 

.2968 

.0040 

.2968 

26 

.398-16 

.400 

.4088 

.0088 

.3594 

.3614 

.0020 

.3188 

.3228 

.0040 

.3230 

28 

.424-14  .4261 

.4359 

.0098 

.3797 

.3818 

.00211  .3333 

.3374 

.0041 

.3390 

30 

.450-14 

.4521 

.4619 

-.0098 

.4057 

.4078 

.00211  .3593 

.3634 

.0041 

.3680 

236 


MATERIALS. 


A.  S.  M.  E.  Special  Taps. 

(Corbin  Screw  Corporation.) 


Size. 

Outside  Diameters. 

Pitch  Diameters. 

Root  Diameters. 

*t 

No. 

Out.  Dia. 
and 
Thds. 

Min., 
In. 

Max., 
In. 

Dif- 
fer- 

Min., 
in. 

Max., 
In. 

Dif- 
fer- 

Min., 
In. 

Max., 
In. 

Dif- 
fer- 

Q| 

Sg 

per  In. 

ence. 

ence. 

ence. 

HM 

j~ 

0.073-64 

0.0741 

0.0768 

0.0027 

0.0640 

0.0651 

0.0011 

0.0538 

0.0559 

0.0021 

0  0550 

2 

.086-56 

.0872 

.09031  .0031 

.0756 

.0767 

.0011 

.0640 

.0663 

.00231  .0670 

3 

.099-48 

.1003 

.1038 

.0035 

.0868 

.0880 

.0012 

.0732 

.0757 

.0025!  0760 

4 

.112-40 

.1134 

.1175 

.0041 

.0972 

.0986 

.0014 

.0809 

.08371  .0028 

.0820 

36 

.1135 

.1179 

.0044 

.0955 

.0969 

.0014 

.0774 

.0803!  .0029 

.0810 

5 

.125-40 

.1264 

.1305 

.0041 

.1102 

.1116 

.0014 

.0939 

.0967 

.0028 

.0980 

36 

.  1  2o5 

.1309 

.0044 

.1085 

.1099 

.0014 

.0904 

.0933 

.0029 

.0935 

6 

.138-36 

.13*> 

.14:>y 

.Ou44 

.1215 

.1229 

.0014 

.1034 

.1003 

.0029 

.1065 

32 

.1395 

.14*5 

.00^9 

.1193 

.12u8 

.0015 

.0990 

.1021 

.0031 

.1015 

7 

.151-32 

.1526 

.1575 

.0049 

.1323 

.1338 

.0015 

.1120 

.1151 

.0031!  .1160 

30 

.1526 

.1578 

.0052 

.1310 

.1326 

.0016 

.1093 

.1125 

.0032  .1130 

8 

.164-32 

.1656 

.1705 

.0049 

.1453 

.1468 

.0015 

.1250 

.1281 

.0031 

.1285 

30 

.1656 

.1708 

.0052 

.1440 

.1456 

.0016 

.1223 

.1255 

.0032 

.1285 

9 

.  177-30 

.1786 

.1838 

.0052 

.1569 

.1585 

.0016 

.1353 

.1385 

.0032 

.1405 

24 

.1788 

.1850 

.0062 

.1517 

.1534 

.0017 

.1247 

.1282 

.0035 

.1285 

10 

.  190-32 

.1916 

.1965 

.0049 

.1713 

.1728 

.0015 

.1510 

.1541 

.0031 

.1540 

24 

.1918 

.1980 

.0062 

.1647 

.1664 

.0017 

.1377 

.1412 

.0035 

.1405 

12 

.216-24 

.2178 

.2240 

.00o2 

.1907 

.1924 

.0017 

.1637 

.1672 

.0035 

.1660 

14 

.242-20 

.2439 

.2511 

.0072 

.2114 

.2132 

.0018 

.1789 

.1826 

.0037 

.1820 

16 

.268-20 

.2699 

.2771 

.0072 

.2374 

.2392 

.0018 

.2049 

.2086 

.0037 

.2093 

18 

.294-18 

.2959 

.3039 

.0080 

.2598 

.2618 

.0020 

.2237 

.2276 

.0039  .2280 

20 

.320-18 

.3219 

.3299 

.0080 

.2858 

.2878 

.0020 

.2497 

.2536 

.0039  .2570 

22 

.346-16 

.3480 

.3568 

.0088 

.3074 

.3094 

.0020 

.2668 

.2708 

.0040 

.2720 

24 

.372-18 

.3739  .3819 

.0080 

.3378 

.3398 

.0020 

.3017 

.3056 

.0039 

.3125 

26 

.398-14 

.4u01 

.4099 

.0098 

.3537 

.3558 

.0021 

.3073 

.3114 

.0041 

.3125 

28 

.424-16 

.42oO 

.4348 

.0088 

.3854 

.3874 

.0020 

.3448 

.3488 

.0040 

.3480 

30 

.450-16 

.4520 

.4dOo 

.00o8 

.4114 

.4134 

.0020 

.3708 

.3748 

.0040 

.3770 

Wood  Screws. 

Two  systems  of  wood  screw  threads  are  in  common  use,  that  of  the 
American  Screw  Co.  and  that  of  the  Asa  I.  Cook  Co.  They  are  alike 
as  to  diameters  but  differ  in  the  number  of  threads  per  inch. 


Threads 

Threads 

Threads 

per  In. 

per  In. 

per  In. 

No. 

Diam., 
In. 

po- 

rt  §O 

No. 

Diam., 
In. 

llo 

^1°; 

No. 

Diam., 
In. 

g  CU  o* 

-i<? 

«<co 

%u 

<& 

<!u 

<£ 

4Jo 

0 

0.058 

32 

30 

11 

0.203 

12 

12.5 

22 

0.347 

7 

7.5 

1 

.071 

28 

28 

1? 

.216 

11 

12 

7.3 

.361 

7 

2 

.084 

26 

26 

13 

.229 

11 

11 

24 

.374 

7 

7 

3 

.097 

24 

24 

14 

.242 

10 

10 

25 

.387 

7 

4 

.110 

22 

22 

15 

.255 

10 

9.5 

7.6 

.400 

6 

6.5 

5 

.124 

20 

20 

16 

.268 

9 

9 

27 

.413 

6 

6 

.137 

18 

18 

17 

.282 

9 

8.5 

78 

.426 

6 

6.5 

7 

.150 

16 

17 

18 

.295 

8 

8 

29 

.439 

6 

8 

.163 

15 

15 

19 

.308 

8 

30 

.453 

6 

6 

9 

.176 

14 

14 

?0 

321 

8 

7  5 

10 

.189 

13 

13 

21 

.334 

8 

STANDARD   STUDS. 


237 


Dimensions  of  Machine  Screw  Heads,  A.  S.  M.  E.  Standard 


FLAT   HEAD.  ROUND   HEAD.*          OVAL   FILLISTER  FLAT   FILLIS- 

(1)  (2)  HEAD.  TER  HEAD. 

(3)  (4) 

*  Form  of  head  is  semi-elliptical  in  axial  cross  section. 


Dimensions 


A  =  Diam.  of  Body.     D   = 
B   =  Diam.  of/        (1) 
Head  and  rad.  V2A  -0.008 
of  oval  (3J. 
C   =  Height  of  i    A  -0.008 

=  Width  of  Slot 
(2) 
1.85A  -0.005 

0.7A 

MC  +  o.oi 

,  =  0.173  A  + 
(3) 
1.64A  -0.009 

0.66A  -0.002 

HF 
0.134B  +C 

0.015. 
(4) 
1.64A  -0.009 

0.66A  -0.002 

1AG 

Head  or  Side  V      1.739 
of  Head   (3).  I 
E   =  Depth  of  Slot.   K  C 
F   =  Height  of  ) 

Head  (3).       I     

H 

B 

B 

C 

C 

C 

E 

E 

E 

E 

F 

(D 

(2) 

(3,4) 

(D 

(2) 

(3,4) 

D 

(D 

(2) 

(3) 

(4) 

(3) 

0.0600.112 

0.106 

0.0894 

0.030 

0.042 

0.03760.025 

0.010 

0  031 

0  025 

0  019 

0.0496 

.073i  .138 

.130 

.1107 

.037 

.051 

.0461 

.028 

.012 

.035 

.030 

.023 

.Oo09 

.0861  .164 

.154 

.1320 

.045 

.060 

..0548  .030 

.015 

040 

036 

027 

.0725 

099 

190 

,178 

.1530 

052 

.069 

.0633  .032 

017 

044 

04? 

03? 

.0838 

.112 

.216 

.202 

.1747 

.060 

.078 

.0719  .034 

.020 

.049 

.048 

.036 

.0953 

.125 

.242 

.226 

.1960 

.067 

.087 

.0805 

.037 

.022 

053 

053 

.040 

.1068 

.138 

.268 

.250 

.2170  .075 

.097 

.0890 

.039 

.025 

.058 

.059 

.044 

.1180 

.151 

.294 

.274 

.2386  .082 

.106 

.0976 

.041 

.027 

063 

065 

.049 

.1296 

.164 

.320 

.298 

.2599;  .090 

.115 

.1062 

.043 

.030 

.067 

.071 

.053 

.1410 

.177 

.346 

.  322 

.  2813 

.097 

.124 

.1148  .046 

.032 

.072 

.076 

.057 

.1524 

.190 

.372 

.346 

.3026 

.105 

.133 

.1234  .048 

035 

076 

082 

062 

.1639 

.216 

.424 

.394 

.3452 

.120 

.151 

.1405 

.052 

.040 

.085 

.093 

.070 

.1868 

.242 

.476 

.443 

.3879 

135 

.169 

.1577  .057 

045 

094 

105 

079 

.2097 

.268 

.528 

.491 

.4305  .150 

.188 

.17^8  .061 

.050 

.104 

.116 

.087 

.2325 

.294 

.580 

.539 

.4731  .164 

.206 

.1920 

.066 

.055 

.113 

.128 

.0% 

.2554 

.320 

.632 

.587 

.5158 

179 

.224 

.2092 

070 

060 

.122 

.140 

.104 

.2783 

.346 

684 

635 

.5584  .194 

.242 

.2263'  .075 

065 

131 

150 

113 

.3011 

.372 

.736 

.683 

.6010  .209 

.260 

.2435S  .079 

.070 

.140 

.162 

.122 

.3240 

.398 

.788 

731 

.6437  .224 

.279 

.2606  .084 

075 

149 

,173 

.130 

.3469 

.424 

.840 

.779 

.6863  .239 

.297   .2778  .088 

.080 

.158 

.185 

.139 

.3698 

.450  .892 

.827 

.7290  .254 

.315 

.2950  .093  .0851  .167 

.196 

.147 

.3927 

Standard  Studs.— The  Ups9n  Nut  Co.,  Cleveland,  gives  (1914)  the 
f9llowing  formulae  for  the  dimensions  of  standard  stud  bolts  with 
either  V  or  U.  S.  Standard  threads:  A  =  diam.  of  stud;  B  = 
length  of  short  thread ;  C  =  length  of  unthreaded  portion ;  D  =  length 
of  long  thread;  E  =  total  length  of  stud,  all  in  inches.  B  =  A  -\-  1A\ 
C  =  A;  D  =  E-  (B+  C). 


238 


MATERIALS. 


Dimensions  of  Standard  Set  and  Cap-Screws. 

Compiled  from  tables  of  leading  manufacturers.  All  dimensions 
in  inches.  D  =  short  diam.  of  head,  square  and  hex.  heads,  or  diam. 
of  round  head;  L  =  maximum  length,  I  =  minimum  length  under  head; 
//,  r,  maximum  and  minimum  length  over  all;  H  =  length  of  head. 


Diam.  of  Screws  .  .  . 
Threads  per  In  .... 

Vs 
40 

VlG 

24 

V4 

20 

Vie 
18 

3/8 

16 

VlG 

14 

^ 
or  13 

VlG 

12 

5/8 
11 

3/4 

10 

Vs 
9 

1 

8 

IVs 
7 

»V4 

7 

Sq.  Head        j  ? 
Set-Screws.  |j" 

V 

V2 

*£i. 
Vs 

Vs 

V2 

'£• 

5/8 

V2 

5/8 

9/16 

3/4 

Vs 
4V2 

3/4 

V4 
43/4 

V5s 

1V4 

1 
5 

IVs 

U/8 
13/4 

IV, 

Sq.  Head 
Cap-Screws. 

D 
H 
L 

Z 

Vs 

* 

3/4 

7/16 
VlG 

3/4 

V2 

$ 

3/4 

V2 

^ 

3/4 

> 
3/8 

3/4 

Via 

^ 

3/4 

5/8 

Vi 

3/4 
3/4 

¥ 

3/4 

n/16 
V4!G 

1 

13/16 

$ 

i 

3/4 

Vs 

4V2 

Vs 
4% 

IV4 

'/: 

1V2 

T 

!3/4 

IVs 
IVs 

2 

1V2 

T 

LL^ 

1^1 

Hexagon 
Head 
Cap-Screws. 

D 
H 
L 

I 

VlG 

^ 
3/4 

5/8 

'£ 

3/4 

Vs 
Vs 
4V2 

1 

3/4 

tf: 

IVs 
V5s 

IV* 

T 
1V4 

IVs 
IVs 

2 

IVs 
IV, 

2 

Round  and 
Filister 
Head 
Cap-Screws. 

D 
H 
L 

I 

''? 

3/4 

V4 

% 

Vs 
V4 

^ 

5//16 

$! 

3/4 

9/16 
3/8 

3/4 

% 
4# 

3/4 

'£ 

3/4 

w/i, 
•£„ 

1 

? 

n/4 

i< 

iVj 

IVs 
Vs 
6 

1V4 

1V4 

6 
2 

Flat  Head      f  9, 
Cap-Screws.  |£ 

V4 
1»/4 

3/4 

Vs 

3/4 

2ft 

3/4 

6/8 
2V4 
3/4 

V 

3/4 

13/16 
1 

Vs 

n/4 

1 

3 

U/2 

IVs 

!3/4 

'i4 

Button-Head 
Cap-Screws. 

D 
L 

I 

7/32 
1V4 
3/4 

VlG 
3/4 

VlG 

% 

Vl6 
2V2 
3/4 

5/8 
23/4 
3/4 

•£ 

3/4 

13/16 
1 

15/16 
IV4 

1 

3 

1V« 

£ 

13/4 

Socket  Set-Screws, 
Length. 

U/32 

Vl6 

Va 

9/16 

Vs 

n/16 

Vs 

1 

IV4 

Threads  are  U.  S.  Standard.  On  all  cap-screws  of  1  in.  and  less  in 
diam.  and  4  in.  long  and  under,  threads  are  cut  %  of  the  length  of  body; 
longer  than  4  in.  threads  are  cut  1A  of  the  length  of  body.  Lengths 
advance  by  y±  in.  from  minimum  to  maximum. 

Oval  Head  Rivets — Approximate  Number  in  One  Pound 

(Garland  Nut  &  Rivet  Co.,  Pittsburgh.) 


Diam. 

7/16 

3/8 

Vl6 

V4 

3/16 

1/8 

Diam. 

7/16 

3/8 

5/16 

V4 

3/16 

V8 

Length 

Length 

V4 

123 

262 

630 

15/8 

101/2 

16 

23 

40 

71 

166 

3/8 

56 

102 

210 

500 

1  3/8 

10 

15 

21 

36 

68 

160 

1/2 

21  "  ' 

34" 

49 

9Q 

177 

415 

17/8 

91/2 

141/2 

20 

35 

62 

145 

5/8 

19 

30 

45 

78 

150 

350 

2 

9 

14 

18 

32 

60 

140 

3/4 

17 

27 

39 

70 

132 

300 

21/4 

81/2 

13 

16 

29 

55 

V8 

16 

24 

35 

6* 

110 

280 

21/2 

8 

12 

15 

27 

48 

1 

15 

22 

33 

56 

100 

250 

23/4 

71/2 

11 

14 

25 

44 

1  Vs 

14 

21 

31 

50 

96 

3 

10 

13 

23 

42 

H/4 

13 

20 

27 

46 

88 

205 

31/2 

6 

9 

12 

20 

'13/8 

12 

18 

26 

44 

80 

4 

8 

18 

... 

... 

H/2 

11 

17 

24 

42 

77 

J78 

Small  rivets  are  made  to  fit  holes  of  their  rated  size;  the  actual  diameter 
may  vary  slightly  from  the  decimals  given  below: 

Size 3/32         7/64  l/8          9/64         5/33         11/M        3/10 

Approx.  diam 094     .109       125     .140     .155     .170     .185 

Size 7/32       •    1/4         9/32         5/ie          3/g         7/ie 

Approx.  diam,,., 215     .245     ,275     .305     ,365     .425 


WEIGHT  OF  RIVETS. 


239 


Weight  of  100  Cone  Head  Rivets. 

(Hoopes  &  Townsend,  Philadelphia,  1914.) 


L'gth 
Under 

Scant  Diameter,  In. 

Head 
In. 

Vl 

9/16 

5/s 

U/16 

3/4 

13/16 

7/8 

1 

U/8* 

11/4* 

3/4 

8.6 

11  .9 

15.5 

7/8 

9.3 

12.7 

16.5 

1 

9.9 

13.6 

17.6 

22.4 

28.1 

34  5 

1  l/8 

10.6 

14.4 

18.6 

23.6 

29.6 

36.3 

•  1  V4 

11   2 

15.2 

19.6 

24.9 

31    1 

38  1 

46 

65 

13/8 

11  .9 

16.1 

20.7 

26.1 

32.6 

39.8 

48 

68 

93 

1  V2 

12.5 

16.9 

21  .7 

27.4 

34. 

41  .6 

50 

70 

96 

J27 

15/8 

13.2 

17.7 

22.7 

28.6 

35.6 

43  .4 

52 

73 

100 

132 

13/4 

13.8 

18.6 

23.8 

29.9 

37.1 

45.1 

54 

76 

103 

136 

17/8 

14.5 

19.4 

24.8 

31.1 

38.6 

46.9 

56 

78 

107 

-140 

2 

15.1 

20.2 

25.8 

32.4 

40.1 

48.7 

58 

81 

110 

145 

21/8 

15.8 

21  :0 

26.9 

33.7 

41.6 

50.5 

60 

84 

114 

149 

21/4 

16.4 

21.9 

27.9 

34.9 

43.1 

52.2 

62 

87 

117 

153 

23/8 

17.1 

22.7 

28.9 

36.2 

44.6 

54.0 

64 

89 

121 

158 

21/2 

17.8 

23.5 

30.0 

37.4 

46.1 

55.8 

66 

92 

124 

162 

25/8 

18.4 

24.4 

31.0 

38.7 

47.6 

57.5 

68 

95 

128 

166 

23/4 

19.1 

25.2 

32.0 

39.9 

49.1 

59.3 

70 

97 

132 

171 

27/8 

19.7 

26.0 

33.1 

41  .2 

50.6 

61.1 

72 

100 

135 

175 

3 

20.4 

26.9 

34.1 

42.5 

52. 

62.8 

74 

103 

139 

179 

31/4 

21.7 

28.5 

36.2 

45.0 

55. 

66.4 

78 

108 

146 

188 

31/2 

22.9 

30.2 

38.2 

47.5 

58. 

69.9 

83 

114 

153 

197 

33/4 

24.3 

31.9 

40.3 

50.0 

61. 

73.4 

87 

119 

160 

205 

4 

25.6 

33.5 

42.4 

52.5 

64. 

77.0 

91 

124 

167 

214 

41/4 

26.9 

35.2 

44.4 

55.0 

67. 

80.5 

95 

130 

174 

223 

41/2 

28.2 

36.9 

46.5 

57.5 

70. 

84.0 

99 

135 

181 

232 

43/4 

29.5 

38.5 

48.6 

60.0 

73. 

87.6 

103 

141 

188 

240 

5 

30.8 

40.2 

50.6 

62.6 

76. 

91  .1 

107 

146 

195 

249 

51/4 

32.1 

41  .9 

52.7 

65.1 

.79. 

94.6 

1  1  1 

151 

202 

258 

51/2 

33.4 

43.5 

54.8 

67.6 

82. 

98.2 

115 

157 

209 

266 

53/4 

34.7 

45.2 

56.8 

70.1 

85. 

101.7 

120 

162 

216 

275 

6 

36.0 

46.8 

58.9 

72.6 

88. 

105.2 

124 

167 

223 

284 

6l/2 

38.7 

50.2 

63.0 

77.6 

94. 

112.3 

132 

178 

237 

301 

7 

41.3 

53.5 

67.2 

82.7 

100^ 

119.4 

140 

189 

251 

319 

Wgt. 

of 

4.7 

6.9 

9.3 

12.3 

16.1 

20.4 

26 

38 

54 

75 

Hds. 

*  All  Rivets  larger  than  one  inch  are  made  to  exact  diameter. 

Tinners'  Rivets.     Flat  Heads.     (Garland  Nut  &  Rivet  Co.) 


k 

i 

!• 

b 

j?2 

|  d 

SM 

A 

P 

£2 

3  s 

SM 

* 

f* 
g2 

31bs. 

31/2 

5 
6 

7  ' 

Id 

er 

ji 

~s>  . 

p 

l| 
£- 

8 
9 
10 
12 
14 
16 

0.070 
.080 
.090 
.094 
J01 
.109 

1/8 
9/64 
5/32 
H/64 
3/16 
3/16 

4  oz. 
6 
8 
10 
12 
14 

0.115 
.120 
.125 
.133 
.140 
.147 

13/64 

7/32 
15/64 
1/4 
17/64 
9/32 

1  lb. 

1  V4 
1  1/2 
,3/4 

21/2 

0.160 
.163 
.173 
.185 
.200 
.215 

5/16 
21/64 
H/32 
3/8 
25/64 
13/32 

0.225 
.230 
.233 
.253 
.275 
.293 

7/16 
29/64 
15/32 
1/2 
33/64 
17/32 

240 


MATERIALS. 


Shearing  Value,  Area  of  Rivets,  and  Bearing  Value  of  Riveted  Plates. 

Shearing  Value  =  Area  of  Rivet  X  Allowable  Shearing  Stress  Per  Sq.  In. 
Bearing  Value  =  Diameter  of  Rivet  X  Thickness  of  Plate  X  Allowable 
Bearing  Stress  Per  Square  Inch. 


Di- 
am. 
of 
Riv- 
et. 
In. 

Area. 
Sq. 
In. 

Single 
Shear 
6,000 
Lbs. 
Sq.In. 

Double 
Shear 
6,000 
Lbs. 
Sq.In. 

Bearing  Value  for  Different  Thicknesses  of  Plate 
in  Inches  at  1  2,000  Lb.  per  Square  Inch. 

i/4 

In. 

Vie 
In. 

«/8 
In. 

Vl6 

In. 

J/2 
In. 

Vs 
In. 

Vl 
In. 

Vs 
In. 

1 
In. 

V2 
5/8 
3/4 

Vs 

0.1964 
0.3068 
0.4418 
0.6013 
0.7854 

1178 
1841 
2651 
3608 
4712 

2356 
3682 
5301 
7216 
9425 

1500 
1875 

1875 
2344 
2813 

2250 
2813 
3375 
3938 

2625 
3281 
3938 
4594 
5250 

3000 
3750 

4688 
5625 

2250 
2625 
3000 

4500 
5250 
6000 

6750 
7875 

3281 
3750 

6563 

9188 
10500 

12000 

4500 

75001 

900(J| 

Di- 
am. 
of 
Riv- 
et, 
In. 

Area, 
Sq. 
In. 

Single 
Shear 
7,500 
Lbs. 
Sq. 
In. 

Double 
Shear 
7,500 
Lbs. 
.  Sq. 
In. 

2945 
4602 
6627 
9020 
11781 

Bearing  Value  for  Different  Thicknesses  of  Plate 
in  Inches  at  15,000  Lbs.  per  Square  Inch. 

1/4 
In. 

Vl6 

In. 

J/8 
In. 

Vie 
In. 

y* 

In. 

Vs 
In. 

J/4 
In. 

T/8 

In. 

1 
In. 

V2 

5/8 
3/4 

,'/8 

0.1964 
0.3068 
0.4418 
0.6013 
0.7854 

1473 
2301 
3313 
4510 
5891 

1875 
2344 

2344 
2930 
3516 

2813 
3516 
4219 
4922 
5625] 

3781 

3750 

4102 
4922 
5742 
6563 

4688 

5859 
7031 

8438 
9844 

11484 
13125 

15000 

2813 
3281 
3750 

5625 
6563 
7500 

4102 
4688 

8203 
9375 

11  250J 

Di- 
am. 
of 
Riv- 
et, 
In. 

V2 
5/8 
3/4 

V8 

Area, 
Sq. 
In. 

Single 
Shear 
10,000 
Lbs. 
Sq. 
In. 

Double 
Shear 
10,000 
Lbs. 
Sq. 
In. 

Bearing  Value  for  Different  Thicknesses  of  Plate 
in  Inches  at  20,000  Lbs.  per  Square  Inch. 

i/4 

In. 
2500 
3125 

Vl6 
In. 

3l25 
3906 

4688 

Vs 
In. 

37501 
4688 
5625 
6563 
7500 

Vl6 

In. 

1/2 

In. 

Vs 
In. 

V< 
In. 

T/8 

In. 

1 

In. 

0.1964 
0.3068 
0.4418 
0.6013 
0.7854 

1964 
3068 
4418 
6013 
7854 

3927 
6136 
8836 
12026 
15708 

4375 

5000 
6250 

5469 

7813 
9375 

11250 
13125 

.... 

3750 
4375 
5000 

6563 
7656 
8750 

7500 
8750 
10000 

5469 
6256 

10938 
12500 

15313 
17500 

20000 

15000| 

Dia. 
of 
Riv- 
et. 

371? 

1/4- 
5/16 
11/32 
3/8 
Vl6 

Area 
in 
Square 
Inches. 

6,000  Lbs. 
per  Sq.  In. 

Bearing  Value  for  Different  Thicknesses  of  Plate 
in  Inches  at  1  2,000  Lb.  per  Square  Inch. 

Single 
Shear 

Double 
Shear. 

Vs 
In. 

3/l6 

In. 

i/4 

In. 

Vl6 

In. 

n/32 

In. 

'  Vs 
In. 

Vl6 
In. 

0.0274 
0.0491 
0.0764 
0.0924 
0.1104 
0.1499 

164 
295 
458 
554 
662 
899 

328 
589 
917 
1109 
1325 
1799 

281 
375 

468 

42?. 

563 
703 

750 
938 

1172 
1289 
1406 

515 
563 
656 

773 

844 
984 

1031 
1125 
1313 

1418 
1547 
1804 

1687 
1969 

2297 

1640 

All  bearing  values  above  or  to  right  of  zigzag  lines  are  greater  than 
double  shear.  Values  between  upper  and  lower  zigzag  lines  are  less 
than  double  and  greater  than  single  shear.  Values  below  and  to  left 
of  lower  zigzag  lines  are  less  than  single  shear. 


WEIGHT   OF  LAG   SCREWS 


241 


LENGTH  OF  RIVETS  REQUIRED  FOR  VARIOUS  GRIPS 

(American  Bridge  Co.  Standard — Dimensions  in  Inches.) 


Grip 
a 

Diameter,  In. 

Grip 
b 

Diameter,  In. 

1/2 

5/8 

3/4 

7/8 

1 

1/2 

5/8 

3/4 

7/8 

1 

1/2 

1  1/2 

13/4 

17/8 

2 

21/8 

1/2 

1/8 

"Tl/4 

1  V4 

13/8 

Ts78 

5/8 

15/8 

17/8 

2 

21/8 

21/4 

5/8 

1/4 

1  3/8 

1  3/8 

1  V2 

1  1/2 

3/4 

13/4 

2 

21/8 

21/4 

23/g. 

3/4 

3/8 

H/2 

1  V2 

1  5/8 

15/8 

7/8 

17/8 

21/8 

21/4 

23/8 

21/2 

7/8 

1/2 

15/8 

15/8 

13/4 

1  3/4 

1 

2 

21/4 

23/8 

21/2 

25/8 

1 

5/8 

13/4 

13/4 

1  7/8 

1  7/8 

1/4 

21/4 

21/2 

25/8 

23/4 

27/8 

1/4 

7/8 

2 

2 

21/8 

21/8 

1/2 

25/8 

27/8 

3 

3  1/8 

31/4 

1/2 

21/8 

21/4 

23/8 

23/8 

21/2 

3/4 

3 

31/4 

33/8 

31/2 

35/8 

3/4 

21/2 

2  5/8 

23/4 

23/4 

27/8 

2 

31/4 

31/2 

35/8 

33/4 

37/8 

2 

23/4 

27/8 

3 

3 

31/8 

1/4 

31/2 

33/4 

37/8 

4 

41/8 

1/4 

3 

31/8 

31/4 

31/4 

33/8 

1/2 

33/4 

4 

41/8 

4  1/4 

43/8 

1/2 

3  1/4 

33/8 

31/2 

31/2 

35/8 

3/4 

4 

41/4 

'43/8 

41/2 

45/8 

3/4 

31/2 

35/3 

33/4 

33/4 

37/8 

3 

43/8 

45/8 

43/4 

47/8 

5 

3 

37/g 

4 

4 

41/8 

41/4 

1/4 

45/g 

47/8;   5 

51/8 

51/4 

1/4 

41/8 

41/4 

41/4 

43/8 

41/2 

1/2 

47/8 

51/8 

51/4 

53/8 

51/2 

1/2 

43/8 

41/2 

41/2 

45/8 

43/4 

3/4 

51/8 

53/8 

51/2 

55/8 

53/4 

3/4 

45/8 

43/4 

43/4 

47/8 

5 

4 

53/8 

55/8 

53/4 

57/8 

6 

4 

47/8 

5 

5 

51/8 

51/4 

1/4 

53/4 

6 

61/8 

61/4 

63/8 

1/4 

51/4 

•53/8 

53/8 

51/2 

55/8 

1/2 

61/8 

6  3/8 

61/2 

65/8 

63/4 

1/2 

55/8 

53/4 

53/4 

53/4 

57/8 

3/4 

63/8 

65/8 

63/4 

67/8 

7 

3/4 

57/8 

6 

6 

6 

61/8 

5 

65/8 

67/g 

7 

71/8 

71/4 

5 

61/8 

61/4 

61/4 

61/4 

63/8 

Weight  of  100  Lag  Screws. 

(Hoopes  &  Townsend,  Philadelphia,  1914.) 


Diameter,  Inches. 

Vl6 

3/8 

Vl8 

V2 

9/16 

5/8 

3/4 

7/8 

1 

H/8 

iV4 

Length  Under  Head  to  Point. 

Ib. 
4.2 
4.7 
5.2 
5.7 
6.2 
7.2 
8.2 
9.2 
10.2 
11.3 
12.4 
13.5 

Ib. 
6.5 
7.1 
7.7 
8.4 
9.2 
10.6 
12.0 
13.5 
15.0 
16.5 
18.0 
19.5 

Ib. 
9.2 
10.0 
10.9 
11.8 
12.7 
14.6 
16.6 
18.8 
20.7 
22.8 
24.9 
27.0 
31.1 
35.2 

Ib. 
13.0 
13.8 
14.9 
16.1 
17.4 
19.0 
21.5 
24.0 
26.5 
29.0 
31.5 
34.0 
39.0 
44.0 
49.0 
54.0 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

23.0 
24.5 
26.0 
29.2 
32.5 
35.9 
39.3 
42.7 
46.1 
49.5 
56.3 
63.1 
69.9 
76.7 
83.5 
90.5 

24.8 
27.3 
29.0 
32.9 
36.9 
41.0 
44.9 
48.8 
52.7 
56.6 
64.5 
72.5 
80.5 
88.5 
96.5 
104.5 
112.5 
121.0 
129.5 
138.0 

43.0 
48.3 
53.8 
59.6 
65.5 
71.5 
77.5 
83.5 
95.5 
107.6 
119.8 
131.0 
143.1 
155.4 
167.6 
179.8 
192.0 
204.0 

75.0 
78.5 
82.0 
86.0 
90.0 
98.0 
106.0 
122.5 
139.0 
155.5 
172.0 
188.5 
205.0 
221.5 
238.0 
255.0 
272.0 

"96" 
99 
108 
118 
128 
138 
158 
178 
198 
219 
240 
261 
282 
304 
326 
348 

150 
163 
176 
203 
230 
257 
284 
311 
338 
365 
393 
421 
449 

'246' 
270 
300 
332 
365 
395 
425 
459 
493 
527 
562 

Thds. 
per  in. 

10 

7 

7 

6 

5 

5 

4V2 

4V2 

3 

3 

3 

242 


MATERIALS 


Approximate  Weight  of  Machine  Bolts  per  100,  Square  Heads  and 
Square  Nuts.      (Hoopes  &  Townsend,  Philadelphia,  1914.) 


Length  Under 
Head  to 
Point,  In. 

Diameter. 

In! 

4/8 
In. 

7/16 
In. 

1/2 
In. 

Vie 

In. 

V8 
In. 

3/4 
In. 

7/8 
In. 

In. 

H/4 
In. 

11/2 
In. 

13/4 
In. 

2 

In. 

H/4 

3.1 

8.4 

12.5 

17.7 

24.3 

30.7 

50.4 

« 

[1  V2 

3.4 

9.2 

13.6 

19.1 

26.0 

32.8 

53.5 

2 

4.1 

10.8 

15.7 

21.8 

29.5 

37.1 

59.7 

89.4 

125.7 

21/2 

4.8 

12.3 

17.8 

24.6 

33.0 

41.4 

65.9 

97.3 

136.8 

246.3 

3 

5.5 

13.8 

19.9 

27.4 

36.5 

45.7 

72.1 

105.7 

147.8    263.5 

'476 

31/2 

6.2 

15.3 

21.8 

29.8 

40.0 

50.0 

78.3 

114.2 

158.9:  280.8 

495 

4 

6.9  '16.9 

24.0 

32.6 

43.5 

54.4 

84.5 

122.6 

169.9    298.1 

520 

720 

41/2 

7.5!  18.4 

26.1 

35.4 

46.7 

58.3 

90.3 

H0.5 

179.4    314.1 

545 

753 

5 

8.2  19.9 

28.2 

38.1 

50.2 

62.6 

96.5 

138.9 

190.4    331.4 

570 

786 

1180 

5l/2 

8.9'21.5 

30.3 

40.9 

53.7 

66.9 

102.7 

147.4201.5    348.6    595 

820 

1225 

6 

9.6'23.0 

32.4 

43.7 

57.2 

71.3 

108.9 

155.8 

212.5    365.9    620 

854 

1270 

61/2 

10.3 

24.6 

34.5 

46.4 

60.7 

75.6 

115.1 

164.3223.6    383.1    645 

888 

1315 

7 

11.0 

26.1 

36.6    49.2 

64.2 

79.9 

121.3 

172.7  234.6    400.4    670 

922 

1360 

71/2 

11.7 

27.7 

38.8    51.9 

67.6 

84.2 

127.6 

181.2 

245.6    417.7 

695 

956 

1405 

8 

12.4 

29.2 

40.9    54.7 

71.1 

88.5 

133.8 

189  .6  256.71  434.9 

725 

990 

1450 

9 

13.7 

32.4 

44.9   60.0 

77.8 

96.8 

145.7 

205  .9  278.0    468.2 

775 

1058 

1540 

10 

15.1 

35.5 

49.1  1  65.5 

84.8 

105.4 

158.2 

222.8 

300.0 

502.7 

825 

1126 

1630 

11 

16.5 

38.6 

53.4   71.0 

91.8 

114.1 

170.6 

239.8322.2 

537.3 

875 

1194 

1720 

12 

17.941.7 

57.6 

76.5 

98.8  122.7 

183.0 

256.7 

344.3 

571.8 

925 

1262 

1810 

13 
14 

19.3144.8 
20.6547.9 

61.8   82.0 
66.0   87.6 

105.5  131.0  195.4 
112.51139.6207.9 

273.6(366.3 
290.5388.4 

606.3 
640.8 

975 
1025 

1330 
1398 

1900 
1990 

15 

22.051.0 

70.3   93.1 

119.5J  148  .2  220  .3 

307.4410.5 

675.3 

1075 

1468  2080 

16 

23.454.1 

74.5    98.6 

126.4 

156.9 

232.7 

324.3 

432.6 

709.8 

1125 

1536 

2170 

17 

24.857.2 

78.7  104.1 

133.4 

165.5245.1 

341.2454.7 

744.3 

1175 

1604  2260 

18 

26.260.3 

82.9  109.7 

140.4  174.1 

257  .6  1  358.1 

476.8 

778.9 

1225 

1672  2350 

20 

28.966.5 

91.4  120.7 

154.4  191.4 

282.4  392.0 

521.0 

847.9  1325 

1808 

2530 

22 

31.772.7 

99.9  131.7 

168.4208.6307.3 

425.8565.1 

916.9  1425 

19442710 

24 

34.4  78.9 

108.3  142.8 

182.4 

225.9 

332.1 

459.6 

609.3 

986.01525 

2080 

2890 

26 

37.2  85.2 

116.8  153.8 

196.3 

243.1 

357.0 

493.4653.5 

1055.0  16252216  3070 

28 

40.091.4 

125.2  164.9 

210.3 

260.4381.8 

527  .3  697  .7  1124.0  17252352 

3250 

30 

42.7  97.6 

133.7  175.9 

224.3 

277.7  406.7 

561.  1  741  .9i  1193  .01825  2488  3450 

Weight  per  1 00  Nuts. 


Square 
Hexagon 

Diff. 

0.7 
0.6 

0.1 

2.5 
2.1 

~QA 

3.9 
3.2 

~07 

5.7 

4.8 

~<K9 

8.1 
6.7 

1.4 

9.9 

8.3 

1.6 

16.8 
14.0 

26.9 
22.3 

4.6 

40.1 
33.4 

~6.7 

77.8 
64.0 

162 
134 

28 

257 
207 

50 

381 
307 

74 

2.8 

13.8 

Weight  of  100  Heads. 


Square 
Hexagon 

0.8 
0.7 

2.4 
2.2 

4.01  5.9 

3.5  5.3 

8.8 
7.9 

11.4 
10.3 

20.0 
17.0 

31.4 
28.2 

44.9 
39.4 

90.9 
83.9 

144 
132 

231 
215 

345 
302 

Diff. 

0.1 

0.2 

0.5]  0.6 

0.9 

1.1 

3.0 

3.2 

5.5 

7.0 

12 

16 

43 

For  Weight  of  Bolts  with  Hex.  Heads  and  Hex.  Nuts. 
Subtract         |  0.2  |  0.6|     1 .2|     1.5|    2.3|    2.7|    5.81    7.8|  12.2|     20  8[    40|    66|  117 

Sizes  of  Cast  Washers.     (Upson  Nut  Co.,  Cleveland,  1914  ) 


Diam. 

Hole. 

Thick. 

Bolt. 

Weight. 
Lbs. 

Diam. 

Hole. 

Thick. 

Bolt. 

Weight. 
Lbs. 

In. 
21/4 
23/4 

31/2 

In. 

l',l 
T* 

In. 

11/16 
3/4 

13/16 

7/8 

In. 

1/2 
5/8 
3/4 

7/8 

V2 

5/8 
3/4 

11/4 

In. 

4 
41/2 

6 

In. 

U/8 
H/4 
13/8 
13/4 

In. 

15/16 

U/8 
H/4 

In. 
1 
U/8 
H/4 
11/2 

15/8 

T 

WBOUGHT   WASHERS. 


243 


Weight  and  Dimensions  of  Hanger  Bolts. 

(Hoopes  &  Townsend,  Philadelphia,  1914.) 

One  end  cut  with  deep  wood  screw  thread,  the  other  fitted  with  a 
standard  cold  punched,  chamfered  and  trimmed  square  nut. 


Diameter,  In. 

Vl 

5/8 

3/4 

7/8 

1 

1  1/8 

1  1/4 

13/g 

M/2 

Length  Over  All,  In. 

~ 

Approximate  Weight  per  100. 

4 
6 
8 
10 
12 
14 
16 

24 
34 
44 
54 

53 
67 
81 
95 

80 
97 
114 
134 
154 

106 
138 
166 
196 
226 
256 

174 
217 
259 
295 
329 

257 
299 
332 
374 
417 

301 
351 
401 
451 
501 

456 
511 
566 
621 

532 
597 
677 
747 

Threads  per  inch: 
Nut  end      

13 
6 

11 
5 

10 

41/2 

9 

41/2 

8 
3 

7 
3 

7 
3 

6 

21/2 

6 

21/2 

Screw  end  

Turnbuckles. 

(Cleveland  City  Forge  and  Iron  Co.) 
Standard  sizes  made  with  right  and  left  threads.     D  =  outside  diamete^ 


FIG.  76. 

of  screw.     A  =  length  in  clear  between  heads  =  6  ins.  for  all  sizes, 
B  =  length  of  tapped  heads  =  1 1/2  D  nearly.     C  =  6  ins.  +  3  D  nearly- 


Wrought  Washers,  Manufacturers'  Standard. 

(Upson  Nut  Co.,  Cleveland,  1914.) 


|0 

£ 

13 

|0 

,£ 

13 

6 

o> 

1^ 

.So 

if 

i 

o> 

_o   • 

^ 

•S§ 

If 

.2 

'o 

is  w 

'o 

Q  — 

• 

'o 

»2 

o~~ 

53  «— 

b 

B 

p 

W 

55 

r 

5 

W 

H 

W 

^ 

^ 

In. 

In. 

No. 

In. 

In. 

In. 

No 

In. 

9/16 

1/4 

18 

3/16 

39400 

2.53 

21/2 

1  Vl6 

8 

1 

568 

176 

3/4 

5/16 

16 

V4 

15600 

6.4 

23/4 

8 

H/8 

473 

211 

7/8 

3/8 

16 

5/16 

11250 

8.8 

3 

13/8 

8 

U/4 

364 

261 

1 

7/16 

14 

3/8 

6800 

14.7 

31/4 

H/2 

7 

13/8 

275 

364 

M/4 

1/2 

14 

7/16 

4300 

21. 

31/2 

1V8 

7 

H/2 

256 

390 

13/8 

9/16 

12 

1/2 

2600 

38.4 

33/4 

13/4 

7 

15/8 

220 

454 

H/2 

5/8 

12 

9/16 

2250 

44.4 

4 

17/8 

7 

13/4 

197 

508 

13/4 

H/16 

10 

5/8 

1300 

77. 

41/4 

2 

7 

17/8 

174 

575 

2 

13/16 

9 

3/4 

900 

111. 

41/2 

21/8 

7 

2 

160 

625 

21/4 

15/16 

8 

7/8 

782 

153. 

43/4 

23/8 

5 

21/4 

122 

820 

5 

25/8 

4 

21/2 

106 

943 

244 


MATERIALS. 


Track  Bolts  and  V.  S.  Standard  Hexagon  Nuts,  Sizes  and  Weights  for 
Different  Weights  of  Kail.      (Upson  Nut  Co.,  Cleveland,  1914.) 


Size  of  Bolts,  In. 

Diam.  of  Nuts, 
In. 

.d 

fM   W) 

d 

1 

Size  of  Bolts,  In. 

Diam.  of  Nuts, 
In. 

i* 

d 

.2   • 

c 

~3 

pq 

00 

Diam.  of  Nuts, 
In. 

!i 

d 

Kegs  per  Mile, 
4-bolt  Joint. 

Rails  70  to  lOOlb.  per  Yard. 

Rails-45  to  85  lb.  per  Yard. 

Rails  20to  301b.  per  Yard. 

X5 

X43/4 

X  4  1/2 
X  4  1/4 
X4 

X33/4 

X31/2 
X31/4 
X3 

7/8  X  5  1/2 
7/8  X  5  1/4 
7/8X5 
7/8  X  4  3/4 
7/8  X  4  1/2 
7/8  X  4  1/4 
7/8X4 

15/8 
15/8 
15/8 
15/8 
15/8 
15/8 
15/8 
15/8 
15/8 
1  7/18 
1  7/15 
17/13 
17/16 
17/16 
17/16 
17/16 

110 
115 
120 
125 
130 
H5 
140 
145 
150 
143 
148 
153 
158 
163 
168 
173 

13.0 
12.3 
11.8 
11.2 
10.8 
10.4 
10.0 
9.7 
94 
9.8 
95 
9.2 
89 
8.6 
8.4 
8.1 

XXXXXXXXXXXXXX 

tinue 

1/4 

V4 

1/4 

1/4 
1/4 
V4 
1/4 
1/4 
1/4 
1/4 
1/4 

d) 
205 
210 
215 
220 
225 
230 
235 
240 
247 
254 
257 
260 
266 
283 

6.8 
6.7 
6.6 
6.4 
6.3 
6.2 
6.1 
6.0 
5.8 
5.7 
5.6 
55 
5.3 
5.0 

5/8  X  2  1/4 
5/8X2 
1/2X3 

1/2X23/4 
1/2  X  2  1/2 
1/2  X  2  1/4 
1/2X2 

1/16 
H/16 

7/8 
7/8 
7/8 
7/8 
7/8 

495 
525 
715 
737 
760 
800 
820 

2.8 
2.7 

^9 
.8 
.7 

Rails  12  to  161b.  per  Yd. 

V2  X  13/4 
1/2  X  1  V2 
1/2  X  1  3/8 
1/2  X  1  V4 
3/8X2 
3/8  X  1  3/4 
3/8  X  1  V2 

7/8 
7/8 
7/8 
7/8 
H/16 
H/16 
H/16 

890 
980 
1070 
1160 
1590 
1710 
1830 

.6 
.4 
.2 
.2 
.0 
.0 
.0 

Rails  30  to  40  lb.  per  Yard. 

Rails  45  to  85  lb.  per  Yard. 

3/4  X  2  3/4 
3/4  X  2  1/2 
5/8  X  3  1/2 
5/8  X  3  1/4 
5/8X3 
5/8  X  2  3/4 
5/8  X  2  1/2 

H/4 
V4 
1/16 
1/16 
1/16 
1/16 
1/16 

300 
317 
375 
392 
410 
435 
465 

4.7 
4.4 
3.8 
3.6 
3.4 
3.2 
30 

Rails  8  to  121b.  per  Yard. 

7/8X37/8 
7/8X33/4 
7/8  X  3  1/2 
7/8  X  3  1/4 
7/8X3 
3/4  X  5  3/4 

17/16 
17/16 
17/16 
17/16 
17/16 
H/4 

178 
183 
188 
193 
198 
200 

79 
7.7 
7.5 
7.3 
7.1 
7.0 

3/8  X  1  1/4|    H/16 

2010 

1.0 

Length  and  Number  of  Cut  Nails  to  the  Pound. 


Size. 

Length. 

Common. 

Clinch. 

Fence. 

Finishing. 

g 

E 

« 

M 

1 
u 

k 

1 
« 

Tobacco. 

Cut  Spikes. 

3/4 

3/4  in. 

800 

v« 

7/8 

500 

2d 

800 

1100 

1000 

376 

3d 

1  1/4 

480 

720 

760 

224 

4d 

1  1/2 

288 

523 

368 

180 

398 

5d 

1  »>i 

200 

410 

130 

6d 
7d 

2  '' 

2i/4 

168 
124 

95 

74 

84 
64 

268 
188 

224 

126 
98 

96 
82 

8d 
9d 

2V2 

23/4 

88 
70 

62 
53 

48 
36 

146 
130 

128 
110 

75 
65 

68 

lOd 

^    '* 

58 

46 

30 

102 

91 

55 

28 

12d 

31/4 

44 

42 

24 

76 

71 

40 

16d 

3  I'/o 

34 

38 

20 

62 

54 

27 

22 

20d 

4 

23 

33 

16 

54 

40 

14V2 

30d 

4  l/9 

18 

20 

33 

121/2 

40d 

5  " 

14 

27 

9V2 

50d 

51/2 

10 

8 

60d 

6  _ 

8 

6 

EAILROAD   MATERIAL. 


245 


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246 


NUMBER  OF  WIRE  NAILS  PER  POUND. 


APPROXIMATE  NUMBER  OF  WIRE  NAILS  PER  POUND. 

(American  Steel  and  Wire  Co.,  ]  908.) 

These  approximate  numbers  are  an  average  only, 
and  the  figures  given  may  be  varied  either  way  by 
changes  in  the  dimensions  of  the  heads  or  points 
Brads  and  no-head  nails  will  run  more  to  the  pound 
than  the  table  shows,  and  large  or  thick-headed 
nails  will  run  less. 

Length,  Inches. 

- 

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STEEL   WIRE   NAILS. 


247 


248 


MATERIALS. 


WROUGHT    SPIKES. 

Number  of  Nails  in  Keg  of  150  Pounds. 


Length, 
Inches. 

V4  in. 

5/16  in. 

3/8  in. 

Length, 
Inches. 

1/4  in. 

5/i6  in. 

3/8  in. 

7/i6  in. 

1/2  in. 

3 

2250 

7 

1161 

662 

482 

445 

306 

31/2 

1890 

1208 

8 

635 

455 

3«4 

256 

4 

41/9 

1650 
1464 

1135 
1064 

9 
10 

573 

424 
391 

300 
270 

240 
222 

5 

1380 

930 

"742 

11 

249 

203 

6 

1292 

868 

570 

12 

236 

180 

For  sizes  and  weights  of  wire  spikes  see  Steel  Wire  Nails,  page  235. 

BOAT    SPIKES. 

Number  in  Keg  of  200  Pounds. 


Length. 

1/4 

5/16 

3/8 

V2 

2375 

2050 

1230 

940 

6   *  

1825 

1175 

800 

450 

990 

650 

375 

8   '  ..  .   . 

880 

600 

333 

9   *  .     ..,  

525 

300 

10  "  

475 

275 

WIRES  OF  DIFFERENT  METALS  AND  ALLOYS. 

(J.  Bucknall  Smith's  Treatise  on  Wire.) 

Brass  Wire  is  commonly  composed  of  an  alloy  of  1  %  to  2  parts  of 
copper  to  one  part  of  zinc.  The  tensile  strength  ranges  from  20  to  40 
tons  per  square  inch,  increasing  with  the  percentage  of  zinc  in  the  alloy. 

German  or  Nickel  Silver,  an  alloy  of  copper,  zinc,  and  nickel,  is 
practically  brass  whitened  by  the  addition  of  nickel.  It  has  been 
drawn  into  wire  as  fine  as  0.002  inch  diameter. 

Platinum  wire  may  be  drawn  into  the  finest  sizes.  On  account  of  its 
high  price  its  use  is  practically  confined  to  special  scientific  instruments 
and  electrical  appliances  in  which  resistances  to  high  temperature, 
oxygen,  and  acids  are  essential.  It  expands  less  than  other  metals 
when  heated.  Its  coefficient  of  expansion  being  almost  the  same  as 
that  of  glass  permits  its  being  sealed  in  glass  \v  ithout  fear  of  cracking 
the  latter.  It  is  therefore  used  in  incandescent  electric  lamps. 

Phosphor-bronze  Wire  contains  from  2  to  6  per  cent  of  tin  and 
from  1/20  to  i/s  per  cent  of  phosphorus.  •  The  presence  of  phosphorus 
is  detrimental  to  electric  conductivity. 

"Delta-metal"  wire  is  made  from  an  alloy  of  copper,  iron,  and  zinc, 
Its  strength  ranges  from  45  to  62  tons  per  square  inch.  It  is  used  for 
some  kinds  of  wire  rope,  also  for  wire  gauze.  It  is  not  subject  to 
deposits  of  verdigris.  It  has  great  toughness,  even  when  its  tensile 
strength  is  over  60  tons  per  square  inch. 

Aluminum  Wire. —  Specific  gravity  2.68.  Tensile  strength  between 
10  and  15  tons  per  square  inch.  It  has  been  drawn  as  fine  as  11,401 
yards  to  the  ounce,  or  0.042  grain  per  yard. 

Aluminum  Bronze,  90  copper,  10  aluminum,  has  high  strength  and 
ductility;  is  inoxidizable,  sonorous.  Its  electric  conductivity  is  12.6 
per  cent.  See  page  396. 

Silicon  Bronze,  patented  in  1882  by  L.  Weiler  of  Paris,  is  made  as 
follows:  Fluosilicate  of  potash,  pounded  glass,  chloride  of  sodium  and 
calcium,  carbonate  of  soda  and  lime,  are  heated  in  a  plumbago  crucible, 
and  after  the  reaction  takes  place  the  contents  are  thrown  into  the 
molten  bronze  to  be  treated.  Silicon-bronze  wire  has  a  conductivity 
of  from  40  to  98  per  cent  of  that  of  copper  wire  and  four  times  more 
than  that  of  iron,  while  its  tensile  strength  is  nearly  that  of  steel,  or 

(Continued  on  page  250.) 


PROPERTIES   OF   STEEL   WIRE. 


249 


PROPERTIES    OF    STEEL  WIRE. 

(John  A.  Roebling's  Sons  Co.,  1908.) 


No., 
Roebling 
Gauge. 

Diam., 
in. 

Area, 
square 
inches. 

Breaking 
strain,  100, 
000  Ib.  per 
sq.  inch. 

Weight  in  pounds. 

Feet    in 
2000  Ib. 

Per 
1000ft. 

Per 

mile. 

000000 

0.460 

0.166191 

16,619 

558.4 

2,948 

3,582 

00000 

0.430 

0.145221 

14,522 

487.9 

2,576 

4,099 

0000 

0  393 

0.121304 

12,130 

407.6 

2,152 

4,907 

000 

0.362 

0.102922 

10,292 

345.8 

1,826 

5,783 

00 

0.331 

0.086049 

8,605 

289.1 

1,527 

6,917 

0 

0.307 

0.074023 

7,402 

248.7 

1,313 

8,041 

1 

0.283 

0.062902 

6,290 

211.4 

1,116 

9,463 

2 

0.263     ' 

0.054325 

5,433 

182.5 

964 

10,957 

3 

0.244 

0.046760 

4,676 

157.1 

830 

12,730 

4 

0.225 

0.039761 

3,976 

133.6 

705      . 

14,970 

5 

0.207 

0.033654 

3,365 

113.1 

597 

17,687 

6 

0.192 

0.028953 

2,895 

97.3 

514 

20,559 

7 

0.177 

0.024606 

2,461 

82.7 

437 

24,191 

v        8 

0.162 

0.020612 

2,061 

69.3 

366 

28,878 

9 

0  148 

0.017203 

1,720 

57.8 

305 

34,600 

10 

0.135 

0.014314 

1,431 

48.1 

254 

41,584 

11 

0.120 

O.C11310 

1,131 

38.0 

201 

52,631  ' 

12 

0.105 

0.008659 

866 

29.1 

154 

68,752 

13 

0.092 

0.006648 

665 

22.3 

118 

89,525 

14 

0.080 

0.005027 

503 

16.9 

89.2 

118,413 

15 

0.072 

0.004071 

407 

13.7 

72.2 

146,198 

16 

0.063 

0.003117 

312 

10.5 

55.3 

191,022 

17 

0.054 

0.002290 

229 

7.70 

40.6 

259,909 

18 

0.047 

0.001735 

174 

5.83 

30.8 

343,112 

19 

0.041 

0.001320 

132 

4.44 

23.4 

450,856 

20 

0.035 

0.000962 

96 

3.23 

17.1 

618,620 

21 

0.032 

0.000804 

.80 

2.70 

14.3 

740,193 

22 

0.028 

0.000616 

62 

2.07 

10.9 

966,651 

23 

0.025 

0  000491 

49 

1.65 

8.71 

24 

0.023 

0.000415 

42 

1.40 

7.37 

t< 

25 

0.020 

0.000314 

31 

1.06 

5.58 

t 

26 

0.018 

0.000254 

25 

0.855 

4.51 

t 

27 

0.017 

0.000227 

23 

.763 

4.03 

t 

28 

0.016 

0.000201 

20 

.676 

3.57 

u 

29 

0.015 

0.000177 

18 

.594 

3.14 

30 

0.014 

0.000154 

15 

.517 

2.73 

• 

31 

0.0135 

0.000143 

14 

.481 

2.54 

32 

0.013 

0.000133 

13 

.446 

2.36 

33 

0.011 

0.000095 

9.5 

.319 

1.69 

34 

0.010 

0.000079 

7.9 

.264 

1.39 

35 

0.0095 

0.000071 

7.1 

.238 

1.26 

36 

0.009 

0.000064 

6.4 

.214 

1.13 

The  above  table  was  calculated  on  a  basis  of  483.84  Ib.  per  cu.  ft.  for  steel 
wire.  Iron  wire  is  a  trifle  lighter.  The  breaking  strains  are  calculated  for 
100,000  Ib.  per  sq.  in.  throughout,  simply  for  convenience,  so  that  the 
breaking  strains  or  wires  of  any  strength  per  sq.  in.  may  be  quickly  deter- 
mined by  multiplying  the  values  given  in  the  tables  by  the  ratio  between 
the  strength  per  square  inch  and  100,000.  Thus,  a  No.  15  wire,  with  a 


strength  per  sq.  in.  of  150,000  Ib.,  ha,?  »  breaking  strain  of  407  X 


,,,. 
Ol°00 


250 


MATERIALS. 


28  to  55  tons  per  square  inch  of  section.  The  conductivity  decreases 
as  the  tensile  strength  increases.  Wire  whose  conductivity  equals  95 
per  cent  of  that  of  pure  copper  gives  a  tensile  strength  of  28  tons  per 
square  inch,  but  when  its  conductivity  is  34  per  cent  of  pure  copper, 
its  strength  is  50  tons  per  square  inch.  It  is  being  largely  used  for 
telegraph  wires.  It  has  great  resistance  to  oxidation. 

Ordinary  Drawn  and  Annealed  Copper  Wire  has  a  strength  of  from 
15  to  20  tons  per  square  inch. 

"  PLOW  "-STEEL  WIRE. 

Experiments  by  Dr.  Percy  on  the  English  plow-steel  (so-called) 
gave  the  following  results:  Specific  gravity,  7.814;  carbon,  0.828  per 
cent;  manganese!  0.587  per  cent;  silicon,  0.143  per  cent;  sulphur,  0.009 
per  cent;  phosphorus,  nil;  copper,  0.030  per  cent.  No  traces  of  chro- 
mium, titanium,  or  tungsten  were  found.  The  breaking  strains  of  the 
wire  were  as  follows: 

Diameter,  inch 0.093          0.132          0.159          0.191 

Pounds  per  sq.  inch.     344,960      257,600      224,000      201,600 
The   elongation  was  only  from  0.75  to  1.1  per  cent. 

STRENGTH  OF  PIANO-WIRE. 

The  average  strength  of  English  piano-wire  is  given  as  follows  by 
Webster,  Horsfals  &  Lean: 


Size, 
Music-wire 
Gauge. 

Equivalent 
Diameters, 
Inch. 

Ultimate 
Tensile 
Strength, 
Pounds. 

Size, 
Music-wire 
Gauge. 

Equivalent 
Diameters, 
Inch. 

Ultimate 
Tensile 
Strength, 
Pounds. 

12 

0.029 

225 

18 

0.041 

395 

13 

.031 

250 

19 

.043 

425 

14 

.033 

285 

20 

.045 

500 

15 

.035 

305 

21 

.047 

540 

16 

.037 

340 

22 

.052 

650 

17 

.039 

360 

These  strength  range  from  300,000  to  340,000  Ibs.  per  sq.  in.  The 
composition  of  this  wire  is  as  follows:  Carbon,  0.570;  silicon,  0.090; 
sulphur,  0.011;  phosphorus,  0.018;  manganese,  0.425. 

GALVANIZED  IRON  WIRE  FOR  TELEGRAPH  AND 
TELEPHONE  LINES. 

(Trenton  Iron  Co.) 

WEIGHT  PER  MILE-OHM.  —  This  term  is  to  be  understood  as  dis- 
tinguishing the  resistance  of  material  only,  and  means  the  weight  of  such 
material  required  per  mile  to  give  the  resistance  of  one  ohm.  To  ascer- 
tain the  mileage  resistance  of  any  wire,  divide  the  "  weight  per  mile- 
ohm"  by  the  weight  of  the  wire  per  mile.  Thus  in  a  grade  of  Extra 
Best  Best,  of  which  the  weight  per  mile-ohm  is  5000,  the  mileage  ..resist- 
ance of  No.  6  (weight  per  mile  525  Ibs.)  would  be  about  91/2  ohms;  and 
No.  14  steel  wire,  6500  Ibs.  weight  per  mile-ohm  (95  Ibs.  weight  per  mile), 
would  show  about  69  ohms. 

Sizes  of  Wire  used  in  Telegraph  and  Telephone  Lines. 

No.  4.  Has  not  been  much  used  until  recently;  is  now  used  on 
important  lines  where  the  multiplex  systems  are  applied. 

No.  5.    Little  used  in  the  United  States. 

No.  6.    Used  for  important  circuits  between  cities. 

No.  8.    Medium  size  for  circuits  of  400  miles  or  less. 

No.  9.  For  similar  locatipns  to  No.  8,  but  on  somewhat  shorter  cir- 
cuits; until  lately  was  the  size  most  largely  used  in  this  country. 

Nos.  10,  11.  For  shorter  circuits,  railway  telegraphs,  private  lines, 
police  and  fire-alarm  lines,  etc. 

No,  12.    For  telephone  lines,  police  and  fire-alarm  lines,  etc. 


TELEGRAPH  AND  TELEPHONE  WIRE. 


251 


Nos.  13,  14.  For  telephone  lines  and  short  private  lines;  steel  wire  is 
used  most  generally  in  these  sizes. 

The  coating  of  telegraph  wire  with  zinc  as  a  protection  against  oxida- 
tion is  now  generally  admitted  to  be  the  most  efficacious  method. 

The  grades  of  line  wire  are  generally  known  to  the  trade  as  "Extra 
Best  Best  '  (E.  B.  B.),  "Best  Best"  (B.  B.),  and  "Steel." 

"Extra  Best  Best"  is  made  of  the  very  best  iron,  as  nearly  pure  as 
any  commercial  iron,  soft,  tough,  uniform,  and  of  very  high  conduc- 
tivity, its  weight  per  mile-ohm  being  about  5000  Ibs. 

The  "Best  Best"  is  of  iron,  showing  in  mechanical  tests  almost  as 
good  results  as  the  E.  B.  B.,  but  is  not  quite  as  soft,  and  somewhat  lower 
in  conductivity;  weight  per  mile-ohm  about  5700  Ibs. 

The  "Steel"  wire  is  well  suited  for  telephone  or  short  telegraph  lines, 
and  the  weight  per  mile-ohm  is  about  6500  Ibs. 

The  following  are  (approximately)   the  weights  per  mile  of  various 
sizes  of  galvanized  telegraph  wire,  drawn  by  Trenton  Iron  Co.'s  gauge: 
No.         4,        5,       6,         7,      8,         9,        10,      11,      12,       13,      14. 

Lbs.      720,    610,    525,    450,   375,    310,    250,    200,    160,    125,    95. 

Tests  of  Telegraph  Wire. 

The  following  data  are  taken  from  a  table  given  by  Mr.  Prescott  relat- 
ing to  tests  of  E.  B.  B.  galvanized  wire  furnished  the  Western  Union 
Telegraph  Go. 


Size 
of 
Wire 

Diam., 
Inch. 

Weight. 

Length. 
Feet 
per 
pound. 

Resistance. 
Temp.  75.8°  Fahr. 

Ratio  of 
Breaking 
Weight  to 
Weight 
per  mile. 

Grains 
per  foot. 

Pounds 
per  mile. 

Feet 
per  ohm 

Ohms 
per  mile. 

4 

0.238 

1043.2 

886.6 

6.00 

958 

5.51 

5 

.220 

891.3 

673.0 

7.85 

727 

7.26 

6 

.203 

758.9 

572.2  ' 

9.20 

618 

8.54 

3.05 

7 

.180 

595.7 

449.9 

11.70 

578 

10.86 

3.40 

8 

.165 

501.4 

378.1 

14.00 

409 

12.92 

3.07 

9 

.148 

403.4 

304.2 

17.4 

328 

16.10 

3.38 

10 

.134 

330.7 

249.4 

21.2 

269 

19.60 

3.37 

11 

.120 

265.2 

200.0 

26.4 

216 

24.42 

2.97 

12 

.109 

218.8 

165.0 

32.0 

179 

29.60 

3.43 

14 

083 

126.9 

95.7 

55.2 

104 

51.00 

3.05 

Sizes,    Weights    and    Strengths    of    Hard-Copper    Telegraph    and 
Telephone  Wire. 

(J.  A.  Roebling's  Sons  Co.,  1908.) 


a 

^g 

*-! 

g||| 

K 

_G 
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BO 

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13     . 

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X  -Sp*]  O  e^ 

NO 

§ 

«  g 

££ 

15'S'S 

P.  o       .—  "^ 
Q.^  »g  >  a. 

So 

1 

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i^^^ 

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72 

Q 

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^Pn  0  £  * 

9 

0.114 

208 

653 

4.39 

2 

13 

0.072 

83 

274 

11.01 

61/2 

10 

0.102 

166 

540 

5.49 

3 

14 

0.064 

65 

220 

13.94 

8 

11 

0.091 

132 

426 

6.90 

4 

15 

0.057 

52 

174 

17.57 

9 

12 

0.081 

105 

334 

8.70 

6 

16 

0.051 

42 

139 

21.95 

10 

In  handling  this  wire  the  greatest  care  should  be  observed  to  avoid 
kinks,  bends,  scratches  or  cuts.  Joints  should  be  made  only  with 
Mclntire  connectors.  On  account  of  its  conductivity  being  about  five 


252 


MATERIALS. 


times  that  of  E.  B.  B.  iron  wire,  and  its  breaking  strength  over  three 
times  its  weight  per  mile,  copper  may  be  used  of  which  the  section  is 
smaller  and  the  weight  less  than  an  equivalent  iron  wire,  allowing  a 
greater  number  of  wires  to  be  strung  on  the  poles.  Besides  this  advan- 
tage, the  reduction  of  section  materially  decreases  the  electrostatic 
capacity,  while  its  non-magnetic  character  lessens  the  self-induction  of 
the  line,  both  of  which  features  tend  to  increase  the  possible  speed  of 
signaling  in  telegraphing,  and  to  give  greater  clearness  of  enunciation 
over  telephone  lines,  especially  those  of  great  length. 

Weight  of  Bare  and  Insulated  Copper  Wire*  Pounds. 

(John  A.  Roebling's  Sons  Co.,  1908.) 


Weight  per  1000  Feet,  Solid. 

Weight  per  Mile,  Solid. 

02 

Weather- 

Weather- 

proof. 

-a  % 

bb 

proof. 

^  0) 

hb 

sj 

6 

ll 

11 

111 

d 

ll 

g 

o>  . 

33 

3  oj 

ll 

g||' 

C 
I'g 

& 

QPQ 

HPQ 

£££ 

Spq 

& 

Srt 

Htt 

E££ 

sta 

0000 

641 

723 

767 

862 

925 

3384 

3817 

4050 

4550 

4890 

000 

509 

587 

629 

710 

760 

2687 

3098 

3320 

3750 

4020 

00 

403 

467 

502 

562 

600 

2127 

2467 

2650 

2970 

3170 

0 

320 

377 

407 

462 

495 

1689 

1989 

2150 

2440 

2610 

1 

253 

294 

316 

340 

365 

1335 

1553 

1670 

1800 

1930 

2 

202 

239 

260 

280 

300 

1066 

1264 

1370 

1480 

1585 

3 

159 

185 

199 

230 

270 

840 

977 

1050 

1220 

1425 

4 

126 

151 

164 

190 

220 

665 

795 

865 

1000 

1160 

5 

100 

122 

135 

155 

190 

528 

646 

710 

820 

1000 

6 

79 

100 

112 

127 

160 

417 

529 

590 

670 

840 

8 

50 

66 

75 

85 

110 

264 

349 

395 

450 

580 

9 

39 

54 

62 

^206 

283 

325 

10 

32 

46 

53 

60 

"so 

169 

241 

280 

3i5 

420 

12 

20 

30 

35 

42 

55 

106 

158 

185 

220 

290 

14 

12.4 

20 

25 

30 

40 

66 

107 

130 

160 

210 

16 

7.9 

16 

20 

24 

30 

42 

83 

105 

130 

160 

18 

4.8 

12 

16 

19 

24 

25 

64 

85 

100 

130 

20 

3.1 

9 

12 

16 

48 

65 

Specifications  for  Hard-Drawn  Copper  Wire. 

The  British  Post  Office  authorities  require  that  hard-drawn  copper 
wire  supplied  to  them  shall  be  of  the  lengths,  sizes,  weights,  strengths, 
and  conductivities  as  set  forth  in  the  annexed  table. 


Weight  per  Statute 
Mile,  Ib. 

Approximate  Equiv- 
alent Diameter,  mils. 

W) 
Cj 

13 

°| 

'»  ®  e8  S 

1! 

vji 

6^ 

q>  .--.  _g  r; 

i>  s 

•si 

| 

i 

^ 

| 

§ 

si 

s-s 

|||^' 

g^j 

sl 

| 

i 

s 

1 

1 

II 

II 

I  sis 

i  ^.i 

ST  -2 

'S 

3 

'S 

2 

-a 

.'s  ^ 

rt  §^  "S 

£3  ^g^ 

tim 

S 

* 

02 

S 

s 

S 

SH 

* 

i 

100 

971/2 

1021/2 

79 

78 

80 

330 

30 

9.10 

50 

150 
200 

1461/4 
195 

1533/4 
205 

97 
112 

951/2 

1101/2 

98 
1131/4 

490 
650 

25 
20 

6.05 
4.53 

50 
50 

400 

390 

410 

158 

1551/2 

1601/4 

1300 

10 

2.27 

50 

WIRE  ROPE. 


253 


Stranded  Copper  Feed  Wire,  Weight  in  Pounds. 

(John  A.  Roebling's  Sons  Co.,  1908.) 


^  Weight  per  1000  Feet. 

Weight  per  Mile. 

Weather- 

Weather- 

M 

proof 

proof 

1 

U 

oT  o  o5 

9 

IT 

*s 

!lN 

.2 

i 

£  • 

1,3 

lls 

m 

o  8 

'E  8 

o  3 

• 

'E  t-i 

o 

SoS 

CQ 

HPQ 

£jfc& 

fl 

fi« 

Htt 

£^P< 

53 

2,000,000 

6100 

6690 

7008 

7540 

2208 

35323 

37000 

39800 

1  750,000 

5338 

5894 

6193 

6700 

28184 

31119 

32700 

35400 

1,500,000 

4375 

5098 

5380 

5830 

24156 

26915 

28400 

30800 

1,250,000 

3813 

4264 

4508 

4940 

20132 

22516 

23800 

20000 

1.000.00C 

3050 

3456 

3674 

3860 

3980 

6104 

18246 

19400 

20400 

26100 

900,000 

2745 

3127 

3332 

3520 

3640 

4493 

16513 

17600 

18600 

11000 

800,000 

2440 

2799 

2992 

3180 

3280 

2883 

14779 

15800 

16800 

19200 

750,000 

2288 

2635 

2822 

3000 

3100 

12080 

13913 

14900 

15850 

17300 

700,000 

2135 

2471 

2650 

2820 

2920 

11272 

13045 

14000 

14900 

16300 

600,000 

1830 

2093 

2235 

2350 

2450 

9662 

11052 

11800 

12400 

15400 

500,000 

1525 

1765 

1894 

1990 

2080 

8052 

9318 

10000 

10500 

13100 

450,000 

1373 

1601 

1724 

1820 

1900 

7249 

8452 

9100 

9600 

10000 

400,000 

1220 

1436 

1553 

1650 

1700 

6441 

7584 

8200 

8700 

9000 

350,000 

1068 

1248 

1345 

1440 

1500 

5639 

6589 

7100 

7600 

7900 

300,000 

915 

1083 

1174 

1270 

1310 

4831 

5721 

6200 

6700 

6900 

250,000 

762 

907 

985 

1060 

1120 

4023 

4788 

5200 

5600 

5900 

B.&S. 

Gauge. 

0000 

645 

745 

800 

900 

960 

3405 

3935 

4220 

4750 

5070 

000 

513 

604 

653 

735 

785 

2708 

3190 

3450 

3880 

4150 

00 

406 

482 

522 

583 

625 

2143 

2544 

2760 

3080 

3300 

0 

322 

388 

424 

480 

510 

1700 

2051 

2240 

2530 

2700 

1 

255 

303 

328 

355 

380 

1346 

1599 

1735 

1870 

2000 

2 

203 

246 

270 

290 

335 

1071 

1301 

1425 

1540 

1770 

3 

160 

190 

206 

240 

280 

844 

1004 

1090 

1270 

1480 

4 

127 

155 

170 

195 

230 

670 

820 

900 

1030 

1220 

5 

101 

126 

140 

160 

195 

533 

668 

740 

845 

1030 

6 

80 

103 

115 

132 

165 

422 

544 

610 

695 

870 

8 

50 

68 

78 

87 

105 

264 

359 

410 

460 

555 

WIRE  ROPE. 

The  following  notes  and  tables  are  compiled  from  data  furnished 
by  the  American  Steel  &  Wire  Co.,  Cleveland,  1915. 

Wire  ropes,  which  have  almost  entirely  superseded  chains  and 
manila  rope  for  haulage  and  hoisting  purposes,  are  made  with  a  vary- 
ing number  of  wires  to  the  strand,  and  a  varying  number  of  strands 
to  the  rope,  according  to  the  service  in  which  they  are  to  be  used  and 
the  degree  of  flexibility  required.  Five  grades  of  rope  are  usually 
manufactured,  as  regards  the  material  used,  viz.:  Iron,  crucible 
cast  steel,  extra  strong  crucible  cast  steel,  "plow-steel,"  and  an  improved 
grade  of  plow-steel  called  "Monitor."  Haulage  rope,  for  mines, 
docks,  etc.,  usually  consists  of  6  strands  of  7  wires  each  laid  around  a 
hemp  core.  Hoisting  rope,  for  elevators,  mines,  coal  and  ore  hoists, 
conveyors,  derricks,  steam  shovels,  dredges,  logging,  etc.,  consists  of 
6  strands  of  19  wires  each,  with  a  single  hemp  core.  A  more  flexible 
rope,  for  crane  service,  etc.,  consists  of  6  3 7- wire  strands  wound  around 
a  single  hemp  core.  In  general,  the  flexibility  of  the  rope  is  increased 
by  increasing  the  number  of  wires  in  the  strands.  The  most  flexiblo 


254  MATERIALS. 

standard  rope  made  consists  of  6  61- wire  strands  and  one  hemp  core. 
Other  varieties  comprise  flattened  strand  ropes  for  haulage,  hoisting, 
and  transmission,  non-spinning  rope  for  the  suspension  of  loads  at  the 
end  of  a  single  line,  steel  clad  rope  for  severe  conditions  of  service, 
guy  and  rigging  ropes,  and  hawsers  for  towing  or  mooring. 

Breaking  Strength  of  Wire  Rope. — The  various  manufacturers 
have  adopted  standard  figures  for  the  strength  of  all  sizes  and  qualities 
of  wire  rope.  Formerly,  it  was  the  custom  to  test  the  individual  wires 
and  to  consider  their  combined  strength  as  the  strength  of  the  rope 
as  a  whole.  These  strengths  were  greater  than  the  actual  strength 
obtained  by  breaking  the  finished  rope.  The  figures  given  in  the 
tables  herewith  represent  actual  breaks  of  the  various  ropes,  and  range 
from  95  to  80  per  cent  or  less  of  the  combined  strength  of  the  single 
wires,  depending  on  the  construction.  The  figures,  which  were 
adopted  May  1,  1910,  are  considerably  lower  than  those  given  in 
earlier  tables.  In  general,  a  factor  of  safety  of  five  is  allowed  in  giving 
the  working  loads. 

Lay  of  Wire  Rope. — Lang  Lay. — The  regular  lay  of  wire  rope  com- 
prises wires  in  the  strands  laid  to  the  left,  the  strands  being  laid  to 
the  right,  known  as  right-hand  rope;  or  wires  laid  to  the  right,  and 
strands  laid  to  the  left,  known  as  left-hand  rope.  In  Lang  lay  rope 
the  wires  in  the  strands  and  the  strands  themselves  are  laid  in  the 
rope  in  the  same  direction,  either  right  or  left.  Lang  lay  rope  is  some- 
what more  flexible  than  ordinary  rope,  and  as  the  wires  are  laid  more 
axially  in  the  rope,  longer  surfaces  are  exposed  to  wear,  and  the  en- 
durance is  thereby  increased. 

Sheaves  and  Drums. — Drums  and  sheaves  of  the  largest  practicable 
diameter  are  recommended  in  all  wire  rope  installations.  If  possible, 
drums  should  be  lagged,  and  where  feasible,  a  grooved  drum  on  hoists 
is  more  desirable  than  a  flat  drum.  The  grooves  should  give  ample 
clearance  between  successive  windings ;  thus  a  drum  for  %-inch  rope 
should  have  the  grooves  at  least  7/g-inch  apart  on  centers.  The 
grooves  should  be  made  smooth  in  order  not  to  cut  the  rope,  and  they 
should  be  of  slightly  larger  radius  than  the  rope  in  order  to  avoid  wedg- 
ing or  pinching  it.  Overwinding,  that  is,  the  winding,  of  the  rope  in 
more  than  one  layer,  is  to  be  avoided  if  possible,  by  making  the  drum 
large  enough  to  take  all  the  rope  in  a  single  layer.  Overwinding  will 
rapidly  destroy  the  rope,  and  the  extra  cost  of  the  larger  drum  will  be 
more  than  compensated  by  the  greater  life  of  the  rope.  The  best 
possible  alignment  of  sheaves  and  drums  should  be  made  to  avoid 
undue  wear  on  the  sides  of  the  sheaves  and  the  rope.  In  general,  the 
lead  sheaves  over  which  the  rope  runs  from  the  drum  should  be  aligned 
with  the  center  of  the  drum,  or  if  the  drum  is  not  entirely  filled,  with 
the  center  of  the  portion  on  which  the  rope  is  wound.  The  distance 
between  the  drum  and  lead  sheave  should  be  such  as  to  cause  an  angle 
not  exceeding  1°  30'  between  the  line  from  the  center  of  .the  sheave  to 
the  center  of  the  drum,  and  the  line  from  the  center  of  the  sheave  to  the 
outer  side  of  the  drum.  When  the  sheaves  become  worn,  they  should 
be  replaced  or  the  grooves  turned  before  they  are  used  with  a  new 
wire  rope,  otherwise  the  rope  will  not  work  properly.  For  many 

Surposes,  particularly  mine  service,  the  grooves  can  advantageously 
e  lined  with  well-seasoned,  hardwood  blocks  set  on  end,  which  can 
be  renewed  when  worn.  Large  sheaves,  running  at  high  velocity, 
should  be  lined  with  leather  set  on  end,  or  with  india-rubber.  This 
is  the  practice  for  power  transmission  between  distant  points,  where 
the  rope  frequently  runs  at  a  velocity  of  4,000  feet  per  minute. 

Reversed  Bending. — Reverse  bending,  that  is,  bending  the  wire 
rope  first  in  one  direction  over  sheaves  and  then  in  the  opposite  direc- 
tion, is  to  be  avoided  wherever  possible.  This  practice  will  wear  out 
a  rope  more  quickly  than  any  other  known  method.  A  little  care  in 
design  will  usually  eliminate  all  situations  which  call  for  reversed 
bending,  and  it  is  even  desirable  to  change  existing  constructions  if 
necessary  to  remove  this  condition.  .The  expense  of  rope  renewals 
will  more  than  equal  the  cost  of  change  as  a  rule. 

Handling  Wire  Rope. — Wire  rope  must  not  be  coiled  or  uncoiled 
like  hemp  rope.     When  received  in  a  coil  it  should  be  rolled  on  the  - 
ground  like  a  hoop  and  straightened  out  before  being  put  on  the 
sheaves.     If  on  a  reel,  it  should  be  mounted  on  a  spindle  or  a  flat 


GALVANIZED   WIRE   ROPE. 


255 


Galvanized  Iron  and  Steel  Wire  Rope. 

For  Ship  and  Yacht  Rigging,  Guys,  etc. 

6  Strands,  7  or  12  Wires  per  Strand,  1  Hemp  Core;  6  Strands, 
19  Wires  per  Strand,  1  Hemp  Core. 


Diameter,  In. 

Approx.  Circum.,  In. 

J 

CM 

£ 

4.85 
4.42 
4.15 
3.55 
3.24 
3.00 
2.45 
2.21 
2.00 
1.77 
1.58 
1.20 

7  or  12-  Wire 
Strand,  Iron 

19-  Wire 

Strand,  Steel 

d 

i 

4 

7  or  12-  Wire 
Strand,  Iron. 

19-  Wire 
Strand,  Steel 

fi 

!tg 

g^-5 

H 

*o 

!«s 

i 

^     i—  i 

Xs"' 

II 

Sp 

0*043 

2S 

a  o 

O  OJ3 

£  CD  c 
3  a  & 

•r*  P5  t/} 

rt 

13 

u 

g 

a 

i 
$ 

ii 

4* 

o  0^3 

6a)| 
|&| 

ii 

o  ox" 
III 

13/4 
HI/16 
5/8 
1/2 
7/16 
3/8 
1/4 
3/16 
1/8 
1/16 

7/8 

51/2 
51/4 

43/4 
41/0 
4.,, 

33/4 

31/2 

3V, 

23/4 

42.0 
38.0. 
35.0 
30.0 
28.0 
26.0 
23.0 
19.0 
18.0 
16.1 
14.1 
11.1 

11.0 
10.5 
10.0 
9.5 
9.0 
8.5 
8.0 
7.5 
6.5 
6.0 
5.75 
5.25 

42^0 
38.0 
34.0 
31.0 
28.0 
22.0 

J3" 
12 
11 
10 
9 
8.5 

13/1G 
3/4 
5/8 
9/16 
V2 
7/16 
3/8 
5/16 
9/32 
1/4 
7/22 
3/16 

21/2 
21/4 

13/4 

H/2 
H/4 
H/8 

7/8 
3/4 

5/8 
1/2 

1.03 
0.89 
0.62 
0  50 
0.39 
0.30 
0.22 
0.15 
0.125 
0.09 
0.063 
0.04 

9.4 
7.8 
5.7 
4.46 
3.39 
2.35 
1.95 
1.42 
1.20 
0.99 
0.79 
0.61 

5 

4.75 
4.5 
3.75 
3 
2.5 
2.25 
2 
1.75 
1.5 
1.25 
1.125 

19.0 
16.8 
11.7 
9.0 
7.0 
5.0 
4.2 
3.2 

8.0 
7.0 
6.0 
5.25 

4.75 
4.25 
3.75 
3.0 

Galvanized  Steel  Wire  Strand. 

7  or  19  Wires  Twisted  into  a  Single  Strand. 


3/4 

5/8 


2100 
1610 
1200 
800 


9/16 

1/2 
7/16 
3/8 


650 
510 
415 
295 


Ma 

C  m 


11000 
8500 
6500 
5000 


P 


5/16 
1/4 
7/32 
3/16 


210 
125 
95 
75 


3800 
2300 
1800 
1400 


5/32 
1/8 
3/32 


900 
500 
400 


19-wire  strand  is  made  only  from  1  to  H  in.  diam.,  7-  wire  strand  is 
made  only  -from  %  to  3/32  in.  diam. 


Galvanized  Steel  Cables  for  Suspension  Bridges. 

Composed  of  6  Strands  —  with  Wire  Center. 


. 

Approx. 

Appro. 

Approx. 

Diam., 
In. 

Wt.  per 
Foot, 
Lb. 

Breaking 
Strain, 
Tons 

Diam., 
In. 

Wt.  per 
Foot, 
Lb. 

Break- 
ing 
Strain, 

Diam., 
In. 

Wt.  per 
Foot, 
Lb 

Break- 
ing 
Strain, 

(2000  Lb.). 

Tons. 

Tons. 

73/, 

12.7 

310 

21/4 

8.52 

208 

13/4 

5.10 

124 

25/8 

11.6 

283 

21/8 

7.60 

185 

15/8 

4.34 

106 

21/2 

10.5 

256 

2 

6.73 

164 

1  1/2 

3.70 

90 

23/8 

9.50 

232 

17/8 

5  90 

144 

13/8 

3.10 

75 

256  MATERIALS* 

turntable  and  properly  unwound.  Kinking  or  untwisting  must  be 
avoided. 

Protection  of  Wire  Rope. — Wire  rope  should  -be  protected  by  a 
suitable  lubricant,  both  internally  and  externally,  to  prevent  rust  and 
to  keep  it  pliable.  If  this  is  omitted  rust  will  set  in  and  stiffen  the 
rope,  resulting  in  poor  service.  Raw  linseed  oil,  applied  with  a  piece 
of  sheepskin,  the  wool  inside,  is  a  good  preservative;  the  oil  also  may 
be  mixed  with  Spanish  brown  or  lamp-black.  Wire  rope  running 
under  water  should  be  treated  with  mineral  or  vegetable  tar,  one 
bushel  of  fresh  slacked  lime  being  added  to  each  barrel  of  tar  to 
neutralize  the  acid.  The  tar  is  well  boiled  and  the  rope  saturated 
with  it.  Wire  rope  manufacturers  furnish  special  compounds  for  the 
treatment  of  wire  ropes. 

Exposure  to  Heat. — Where  wire  rope  is  exposed  to  intense  heat,  as 
in  foundry  or  steel  mill  service,  a  soft  iron  core  is  often  substituted  for 
the  hemp  core.  Asbestos  also  is  sometimes  used,  but  it  rapidly  dis- 
integrates and  is  not  recommended.  The  use  of  the  iron  core  adds 
from  7  to  10  per  cent  to  the  strength  of  the  rope,  but  the  wear  on  the 
center  is  as  great  as  on  the  outside  strands,  and  the  hemp  center 
is  to  be  preferred  wherever  possible. 


VARIETIES  AND  USES  OF  WIRE  ROPE. 

Transmission,  Haulage  or  Standing  Rope. — Usually  made  of  6 
7-wire  strands  and  one  hemp  core,  in  all  five  grades  noted  above.  Iron 
rope  is  comparatively  little  used  except  in  the  smaller  sizes.  It  is 
composed  of  very  soft  wires  of  low  tensile  strength.  Crucible  cast 
steel  rope  is  particularly  adapted  to  mine  haulage  work,  including  tail 
rope  and  endless  haulage  systems,  gravity  hoists,  and  coal  and  ore  dock 
haulage,  roads  operating  small  grip  cars.  The  sizes,  3/8  to  5/8  inch 
inclusive,  are  used  for  sand  lines  in  oil  wells,  and  from  5/8  to  1  inch  for 
oil-well  drilling.  In  general  it  can  be  used  for  severe  service,  and 
where  the  flexibility  required  is  a  minimum.  Extra  strong  crucible 
cast  steel  rope  has  practically  the  same  applications  as  the  preceding 
rope,  .except  that  being  stronger  a  smaller  rope  can  be  used  for  the 
same  service.  The  plow-steel  rope  is  advised  for  situations  similar 
to  those  for  which  the  cast  steel  ropes  are  used,  but  where  it  is  neces- 
sary to  secure  increased  strength,  without  altering  the  working  con- 
ditions. The  wires  are  harder  and  capable  of  standing  greater  wear 
than  any  of  the  foregoing  ropes.  Monitor  plow-steel  rope  is  the 
strongest  and  stiffest  of  all  and  is  used  for  work  demanding  the  greatest 
strength  and  lightest  rope  possible.  Sheaves  for  this  rope  should,  if 
possible,  be  somewhat  larger  than  for  other  grades.  For  working  loads, 
strength,  etc.,  of  these  ropes,  see  table,  page  257. 

Standard  Hoisting  Rope. — Composed  of  6  19-wire  strands  and  a 
hemp  core;  made  in  the  following  grades:  Iron,  mild  steel,  crucible 
cast  steel,  extra  strong  crucible  cast  steel,  plow-steel,  and  Monitor 
plow-steel.  The  wires  are  smaller  than  those  in  transmission  ropes  of 
the  same  size,  and  it  is  more  flexible.  It  will  not  stand  as  much 
abrasion  as  transmission  rope.  The  iron  rope  is  used  for  elevator 
hoisting,  where  the  strength  is  sufficient,  and  is  almost  universally 
employed  for  counterweights,  except  on  traction  elevators.  Where 
the  pulleys  are  comparatively  small  it  is  sometimes  used  for  power 
transmission.  The  mild  steel  rope  is  made  especially  for  traction 
elevators,  where  quick  starting  and  stopping  is  required.  The  cru- 
cible cast  steel  rope  is  adapted  to  mine  hoisting,  logging,  elevators, 
derricks,  hay  presses,  dredges,  cableways,  inclined  planes,  coal  hoists, 
conveyors,  ballast  unloaders,  ship  hoists,  and  similar  applications. 
The  extra  strong  crucible  cast  steel  rope  is  adapted  to  the  same  pur- 
poses and  may  be  used  for  heavier  loads  than  the  former  rope.  It  is 
extensively  used  for  oil-well  drilling  and  tubing  lines.  Plow-steel  rope 
is  used  for  heavy  mine  work,  inclined  planes,  dredges,  cableways,  for 
heavy  logging,  etc.  It  is  especially  desirable  for  deep  mine  shafts 
and  long  inclines  on  account  of  its  great  strength  per  unit  of  weight. 
It  is  the  most  economical  rope  where  the  weight  of  the  rope  is  to  be 
considered  or  the  capacity  of  the  machinery  is  to  be  increased  without 
Changing  sheaves  or  drums.  Monitor  plow-steel  rope  is  somewhat 


TRANSMISSION,  HAULAGE  AND  HOISTING  ROPE.    257 


Transmission,  Haulage,  OP  Standing  Rope. 

6  Strands,  7  Wires  per  Strand,  1  Hemp  Core. 


d 
i—  i 

-P 

Approximate  Breaking 
Strength,  Tons 
(2000  Ibs.) 

Allowable  Working 
Load,  Tons  (2000  Ibs.) 

Min.  Dia. 
Drum  or 
Sheave,In. 

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63.0 

73.0 

82  0 

90.0 

64 

12  6 

14.6 

16  4 

18  0 

16  0 

11  0 

13/8 

41/4 

3.00 

28.053.0 

63.0 

72.0 

79.0 

5.6 

10.6 

12.6 

14  4 

16  0 

15  0 

10  0 

U/4 

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2.45 

23.046.0 

54.0 

60.0 

67.0 

4  6 

9  2 

10.8 

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13  0 

13  0 

9  0 

H/8 

31/2 

2.00 

19.0 

37.0 

43.0 

47.0 

52.0 

3.8 

7.4 

8.6 

9  4 

10  0 

1  20 

8  0 

1 

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1.58 

15.0 

31.0 

35.0 

38,0 

42.0 

3  0 

6  2 

7.0 

7  6 

8  4 

10  5 

7  0 

7/8 

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1.20 

12.0 

24.0 

28.0 

31.0 

33.0 

2.4 

4.8 

5.6 

6  2 

6  6 

9  0 

6  0 

3/4 

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8.8 

18.6 

21.0 

23  0 

25  0 

1  7 

3  7 

4.2 

4  6 

5  0 

7  5 

5  0 

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21/8 

0.75 

7.3 

15.4 

16.7 

18.0 

20.0 

1.5 

31 

3.3 

3  6 

4  0 

7  25 

4  75 

9/16 

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16  0 

17  5 

1  2 

2  6 

2.9 

3  ? 

3  5 

7  0 

4  50 

13/4 

0.50 

4.8 

10.0 

11.0 

12.0 

13.0 

0.96 

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2  4 

2  6 

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4  00 

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2.2 

4.6 

5.25 

5  9 

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0  44 

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1.05 

1  2 

1  3 

4  0 

2  75 

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1 

0.15 

1.7 

3.5 

3.95 

4.4 

0  34 

0  70 

0.79 

0  88 

3.5 

2.25 

9/32 

7/8 

0.125 

1.2 

2.5 

2.95 

3.4 

0.24 

0.50 

0.59 

0.68 

3.0 

1.75 

Standard  Hoisting  Rope. 

6  Strands,  19  Wires  per  Strand,  1  Hemp  Core. 


A 

i 

Approximate  Breaking 
Strength,  Tons  (2000  Lbs). 

Allowable  Working  Loads 
Tons  (2000  Lbs). 

Min.  Dia. 
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11.95 

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211.0 

243.0 

275.0 

315.0 

22.2 

42.2 

48.6 

55.0 

63.0 

17.0 

11  0 

21/2 

77/8 

9.85 

92.0 

170.0 

200.0 

229.0 

263.0 

18.4 

34.0 

40.0 

46.0 

53.0 

15.0 

10.0 

21/4 

71/8 

8.00 

72.0 

133.0 

160.0 

186.0 

210.0 

14.4 

26.6 

32.0 

37.0 

42.0 

14.0 

9.0 

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61/4 

6.30 

55.0 

106.0 

123.0 

140.0 

166.0 

11.0 

21.2 

24.6 

28.0 

33.0 

12.0 

8.0 

17/8 

53/4 

5.55 

50.0 

96.0 

112.0 

127.0 

150.0 

10.0 

19.0 

22.4 

25.0 

30.0 

12.0 

8.0 

13/4 

51/2 

4.85 

44.0 

85.0 

99.0 

112.0 

133.0 

8.8 

17.0 

19.8 

22.0 

27.0 

11.0 

7-0 

15/8 

5 

4.15 

38.0 

72.0 

83.0 

94.0 

110.0 

7.6 

14.4 

16.6 

19.0 

22.0 

10.9 

6.5 

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43/4 

3.55 

33.0 

64.0 

73.0 

82.0 

98.0 

6.6 

12.8 

14.6 

16.0 

20.0 

9.0 

6.0 

13/8 

41/4 

3.00 

28.0 

56.0 

64.0 

72.0 

84.0 

5.6 

11.2 

12.8 

14.0 

17.0 

8.5 

5.5 

U/4 

4 

2.45 

22.8 

47.0 

53.0 

58.0 

69.0 

4.56 

9.4 

10.6 

12.0 

14.0 

7.5 

5.0 

H/8 

31/2 

2.00 

18.6 

38.0 

43.0 

47.0 

56.0 

3.72 

7.6 

8.6 

9.4 

11.0 

7.0 

4.5 

3 

1.58 

14.5 

30.0 

34.0 

38.0 

45.0 

2.90 

6.0 

6.80 

7.6 

9.0 

6.0 

4.0 

7/8 

23/4 

1.20 

11.8 

23.0 

26.0 

29.0 

35.0 

2.36 

4.6 

5.20 

5.8 

7.0 

55 

3.5 

3/4 

21/4 

0.89 

8.5 

17.5 

20.2 

23.0 

26.3 

1.70 

3.5 

4.04 

4.6 

5.3 

4.5 

3.0 

5/8 

2 

0.62 

6.0 

12.5 

14.0 

15.5 

19.0 

1.20 

2.5 

2.80 

3.1 

3.8 

4.0 

2.5 

9/16 

13/4 

0.50 

4.7 

10.0 

11.2 

12.3 

14.5 

0.94 

2.0 

2.24 

2.4 

2.9 

3.5 

2.25 

V2 

H/2 

0.39 

3.9 

8.4 

9.2 

10.0 

12.1 

0.78 

1.68 

1.84 

2.0 

2.4 

3.0 

2.0 

7/16 

U/4 

0.30 

2.9 

6.5 

7.25 

8.0 

9.4 

0.58 

1.30 

1.45 

1.6 

1.9 

2.75 

1.75 

3/8 

H/8 

0.22 

2.4 

4.8 

5.30 

5.75 

6.75 

0.48 

0.96 

1.06 

1.15 

1.35 

2.25 

1.50 

5/16 

1 

0.15 

1.5 

3.1 

3.50 

3.80 

4.50 

0.30 

0.62 

0.70 

0.76 

0.9 

2.0 

1.25 

V4 

3/4 

0.10 

1.1 

2.2 

2.43 

2.65 

3.15 

0.22 

0.44 

0.49 

0.53 

0.63 

1.5 

1.00 

258  MATERIALS. 

stiff er  than  the  same  diameter  of  crucible  and  plow-steel  ropes,  but 
strength  for  strength,  it  is  equally  flexible.  A  smaller  rope  of  this 
grade  than  any  of  the  others  can  be  used  for  a  given  service.  It  is 
particularly  adapted  to  derricks,  dredges,  skidders,  and  stump  pullers. 
The  sheaves  should  be  somewhat  larger,  if  possible,  than  for  the  other 
grades.  See  tables,  page  257. 

Extra  Flexible  Hoisting  Rope. — Consists  of  8  19-wire  strands  and 
one  hemp  core.  The  greater  flexibility  permits  its  use  on  smaller 
sheaves  and  drums,  such  as  are  usually  found  on  derricks.  It  is  not 
advisable  to  use  it  where  there  is  much  overwinding,  as  it  will  flatten 
much  more  quickly  than  the  6  X  19  standard  rope.  It  is  made  in 
the  five  grades  of  iron,  crucible  cast  steel,  extra  strong  crucible  cast 
steel,  plow-steel,  and  Monitor  plow-steel.  Its  uses  are  the  same  as 
those  of  standard  hoisting  rope,  noted  above.  See  tables,  page  259. 

Special  Flexible  Hoisting  Rope. — Consists  of  6  37-wire  strands  and 
one  hemp  core.  It  is  extremely  flexible,  and  is  especially  adapted 
to  service  on  cranes  where  the  sheaves  are  rather  small.  It  is  made 
in  the  grades  crucible  cast  steel,  extra  strong  crucible  cast  steel,  plow- 
steel,  and  Monitor  plow-steel.  It  will  not  stand  as  much  abrasion 
as  the  6  19-wire  strand  rope,  but  it  is  particularly  efficient,  as  over 
50  per  cent  of  the  wires  are  in  the  inner  layers  and  are  protected  from 
abrasion.  The  crucible  steel  ropes  are  used  for  general  hoisting  work 
where  the  sheaves  are  small,  while  the  plow-steel  varieties  are  recom- 
mended for  crane  service.  The  Monitor  plow-steel  rope  is  largely 
used  on  dredges  for  both  main  and  spud  ropes.  See  table,  page  259. 

Flattened  Strand  Rope. — Flattened  strand  ropes  are  used  where  an 
increased  wearing  surface  is  desired  above  that  obtained  with  a  round 
strand  rope.  They  are  made  both  for  haulage  and  transmission, 
and  for  hoisting,  and  are  always  made  Lang  lay. 

The  haulage  rope  is  made  in  three  types,  each  of  which  has  one 
hemp  core.  The  first  has  5  9-wire  strands,  the  center  wire  being 
of  elliptical  section;  the  second  has  6  8- wire  strands,  the  center  wire 
being  of  triangular  section;  the  third  has  5  11 -wire  strands,  the  three 
center  wires  being  of  smaller  diameter  than  the  others  and  laid  along- 
side of  each  other  in  the  same  plane.  These  ropes  are  made  in  the 
iron,  crucible  cast  steel,  extra  strong  crucible  cast  steel,  and  Monitor 
plow-steel  grades.  They  are  made  in  diameters  ranging  from  1  K 
inch,  down  to  3/8  inch.  The  1-inch  6  8-wire  strand  rope  weighs 
1.80  Ib.  per  ft.  and  has  an  approximate  strength  of  34  tons,  in  the 
crucible  cast  steel  grade.  Monitor  plow-steel  rope  of  the  same  diam- 
eter and  weight  has  an  approximate  breaking  strength  of  36  tons. 
The  similar  figures  for  3/Hnch  rope,  weighing  0.45  Ib.  per  ft.,  are: 
Crucible  cast  steel,  9.6  tons;  Monitor  plow -steel,  11.9  tons. 

Flattened  strand  hoisting  rope  is  made  in  two  types,  each  with 
one  hemp  core:  (A)  5  28-wire  strands,  the  center  wire  being  of  ellip- 
tical section;  and  (B)  6  25-wire  strands,  the  center  wire  being  of 
triangular  section,  and  the  12  wires  immediately  surrounding  it  being 
of  smaller  diameter  than  the  outer  wires.  These  ropes  compare  in 
flexibility  with  the  standard  hoisting  ropes,  but  have  about  150  per 
cent  greater  wearing  surface.  Type  A  is  made  in  the  grades  of  iron, 
crucible  cast  steel,  extra  strong  crucible  cast  steel,  and  Monitor  plow 
steel.  Type  B  is  made  in  the  grades  of  crucible  cast  steel,  extra  strong 
crucible  cast  steel,  and  Monitor  plow  steel.  They  are  made  in  sizes 
ranging  from  21/4  in.  diam.  down  to  3/8  inch.  Type  B  rope,  2  in. 
diam.,  weighing  7.25  Ib.  per  ft.,  has  the  following  breaking  strength: 
Crucible  cast  steel,  117  tons;  Monitor  plow  steel,  183  tons.  The 
similar  figures  for  H-inch  rope  of  the  same  type,  weighing  0.45  Ib. 
per  ft.,  are:  Crucible  cast  steel,  9.3  tons;  Monitor  plow  steel,  13.3 
tons. 

Non-Spinning  Hoisting  Rope. — Comprises  18  7- wire  strands  and 
one  hemp  core,  6  strands,  long  lay,  being  laid  around  the  core  to  the 
left,  and  12  strands,  regular  lay  being  laid  to  the  right  around  them. 
A  free  object  suspended  from  the  end  of  a  rope  of  this  character  will 
not  rotate  and  endanger  the  lives  of  persons  below  it.  Furthermore, 
the  attention  required  to  handle  and  guide  the  load  is  decreased. 
This  rope  is  recommended  for  back  haul  or  single-line  derricks,  and 
for  shaft  sinking  and  mine  hoisting,  where  the  bucket  swings  without 
guides.  This  rope  works  best  where  it  does  not  overwind  on  the 


FLEXIBLE   HOISTING   ROPE. 


259^ 


Extra  Flexible  Steel  Hoisting  Rope. 

8  Strands,  19  Wires  per  Strand,  1  Hemp  Core. 


4 
1 

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Approximate  Strength, 
Tons  (2000  Lbs.). 

Allowable  Working 
Load,  Tons  (2000  Lbs.). 

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1.6 

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1.9 

.33 

7/16 

1  V4 

0.27 

5.7 

6.30 

6.90 

1.14 

1.26 

1.38 

.16 

3/8 

1  1/8 

0.20 

4.2 

4.66 

5.12 

0.84 

0.93 

1.02 

.00 

6/10 

1 

0.13 

2.75 

3.05 

3.35 

0.55 

0.61 

0.67 

0.83 

3/4 

0.09 

1.80 

2.02 

2.25 

0.36 

0.40 

0.45 

0.75 

Special  Flexible  Steel  Hoisting  Rope. 

6  Strands,  37  Wires  per  Strand,  1  Hemp  Core. 


C 

,* 

Breaking  Strength, 

Allowable  Working  Load, 

g 

Wr 

S 

Tons  (2000  Lbs.). 

Tons  (2000  Lbs.). 

O  _iJ 

S 

Q, 

^j 

•a 

2s 

HH 

5 

^3 

^i 

U  §< 

|Si 

S  00 

| 

o  o5 

li 

§5£ 

£  0>  0 

1 

E! 

o   „ 

is 

Q 

g 

I 

r 

Crucible 
Steel  R 

£?tf 

cs'S'S 

is  S^ 
w0c/2 

02  o5 

|i 

Monitor 
Steel  R 

Crucible 
Steel  R 

Extra  St 
Crucibl 
Steel  R 

m  oJ 
*§• 
& 

Monitor 
Steel  R 

51 

!: 

23/4 

85/8 

11.95 

200  0 

233.0 

265.0 

278.0 

40.0 

47.0 

53.0 

55.0 

21/2 

77/8 

9.85 

160.0 

187.0 

214.0 

225.0 

32.0 

37.0 

43.0 

45.0 

21/4 

71/8 

8.00 

125.0 

150.0 

175.0 

184.0 

25.0 

30.0 

35.0 

37.0 

2 

61/4 

6.30 

105.0 

117.0 

130.0 

137.0 

21.0 

23.0 

26.0 

27.0 

17/8 

53/4 

5.55 

94.0 

106.0 

119.0 

125.0 

18.8 

21.2 

23.8 

25.0 

13/4 

51/2 

4.85 

84.0 

95.0 

108.0 

113.0 

17.0 

19.0 

22.0 

23.0 

15/8 

5 

4.15 

71.0 

79.0 

90.0 

95.0 

14.0 

16.0 

18.0 

19.0 

H/2 

43/4 

3.55 

63.0 

71.0 

80.0 

84.0 

12.0 

14.0 

16.0 

17.0 

3.  75. 

13/8 

41/4 

3.00 

55.0 

61.0 

68.0 

71.0 

11.0 

12.0 

14.0 

14.0 

3.50 

H/4 

4 

2.45 

45.0 

50.0 

55.0 

58.0 

9.0 

10.0 

11.0 

11.0 

3.20 

U/8 

31/2 

2.00 

34.0 

39.0 

44.0 

46.0 

7.0 

8.0 

9.0 

9.2 

2.83 

3 

1.58 

29.0 

32.0 

35.0 

37.0 

6.0 

6.4 

7.0 

7.4 

2.50 

7/8 

23/4 

1.20 

23.0 

25.0 

27.0 

29.0 

5.0 

5.0 

5.0 

5.8 

2.16 

3/4 

21/4 

0.89 

17.5 

19.0 

21.0 

23.0 

3.5 

3.8 

4.0 

4.6 

.83 

5/8 

2 

0.62 

11.2 

12.6 

14.0 

16.0 

2.2 

2.5 

3.0 

3.2 

75 

13/4 

0.50 

9.5 

10.5 

11.5 

12.5 

1.9 

2.1 

2.3 

2.5 

.50 

1/26 

0.39 

7.25 

8.25 

9.25 

9.75 

1.45 

1.65 

1.85 

1.9 

.33 

7/16 

1  1/4 

0.30 

5.5 

6.35 

7.2 

7.50 

1.1 

1.27 

1.4 

1.5 

.15 

3/8 

H/8 

0.22 

4.2 

4.65 

5.1 

5.30 

0.84 

0.93 

1.0 

1.06 

.00 

260 


MATERIALS. 


drum.  The  best  fastening  is  an  open  or  closed  socket,  but  the  wire 
rope  makers  recommend  that  fastenings  be  attached  at  the  factory. 
This  rope  should  not  be  as  heavily  loaded  as  ordinary  hoisting  rope. 
It  is  made  in  the  grades  of  iron,  crucible  cast  steel,  extra  strong  crucible 
cast  steel,  plow  steel,  and  Monitor  plow  steel.  See  table,  page  261. 

Extra  Flexible  Iron  Hoisting  Rope. 

8  Strands,  19  Wires  per  Strand,  1  Hemp  Core. 

Diam.  In 1  7/8        3/4      5/8         9/16        i/2 

Approx.  Circum.,  in 3  2  %       2  M       2  1%         H/2 

Weight  per  ft.,  Ib 1.42     1.08     0.80     0.56     0.45     0.35 

Approximate    Strength,   tons 

(2000  Ibs.) 16.0     13.0       9.5       7.0        6.0       5.0 

Working  Load,  tons  (2000  Ibs.)  3 . 1       2.6       1.9       l."4         1.2       1.0 
Min.  Diam  of  Drum,  ft 6.0       5.5       4.5       4.0        3.5      3.0 

Steel-Clad  Hoisting  Rope. — The  regular  grades  of  hoisting  ropes, 
as  well  as  the  special  flexible  and  extra  flexible,  are  furnished,  if  de- 
sired, with  a  flat  strip  of  steel  wound  spirally  around  each  strand. 
These  give  additional  wearing  surface  without  sacrificing  the  flexibility. 
When  the  flat  winding  is  worn  through,  a  complete  rope  remains  with 
unimpaired  strength.  These  ropes  are  designed  for  severe  conditions 
of  service,  and  an  additional  service  of  50  to  100  per  cent  over  that  of 
the  unprotected  rope  is  frequently  obtained.  The  hoisting  rope 
tables  on  pages  257  and  259  may  be  used  for  the  strength  of  steel- 
clad  rope,  by  referring  to  the  diameter  of  the  rope,  as  it  would  be  were 
no  wrapping  applied.  The  steel  wrapping  is  not  considered  as  adding 
any  strength  to  the  rope,  but  merely  serving  to  increase  its  life. 

Flat  Rope. — Flat  rope  consists  of  a  number  of  "flat-rope"  strands, 
twisted  alternately  right  and  left,  placed  side  by  side  and  served  with 
soft  Swedish  iron  or  steel  wire,  to  form  a  flat  rope  of  the  desired  width 
and  thickness.  The  soft  sewing  wires  wear  much  quicker  than  the 
rope  wire,  and  have  to  be  replaced  from  time  to  time,  at  which  time 
worn  strands  can  also  be  renewed.  Flat  rope  is  used  principally  for 
hoisting  heavy  loads  out  of  deep  shafts,  it  requiring  a  reel  but  little 
larger  than  the  width  of  the  rope,  whereas  round  rope  necessitates 
the  use  of  a  large  drum.  Its  use  is  recommended  where  saving  of 
machinery  space  is  an  object.  It  does  not  twist  or  spin  in  the  shaft, 
It  is  also  used  for  operating  spouts  on  coal  and  ore  docks,  and  for  raising 
and  lowering  emergency  gates  on  canals  and  similar  machinery.  For 
details  of  methods  of  fastening  it  to  drums,  the  manufacturers  should 
be  consulted.  Drums  and  sheaves  should  be  as  large  as  possible.  A 
rule  for  the  diameter  of  the  drum  is  D  =  c  t,  where  D  is  diameter  of 
drum  at  bottom;  ft.,  t  =  thickness  of  rope;  in.  and  c  =  100  for  drums 
and  160  for  sheaves.  Sheaves  should  be  crowned  at  the  center  and 
have  deep  flanges  to  guide  the  rope.  See  table,  page  261. 

Track  Cable  for  Aerial  Tramways. — Composed  of  several  successive 
layers  of  wires  wrapped  around  a  single  wire  core,  the  number  of 
wires  varying  with  the  diameter  of  the  cable.  The  cable  is  made  in 
plow  steel  and  crucible  steel  grades 

Track  Cable  for  Aerial  Tramways. 


21/2 
21/4 


Breaking 
Stress  Tons 
(2000  Lbs.). 


1310 
1036 
935 
840 
728 


161.0    189.0 


13/4 

1V8 
H/2 
13/8 
U/4 


Breaking 
Stress  Tons 
(2000  Lbs.). 


145.8 
124.0 
108.4 
88.8 
.71.8 


171.0 
146.0 
127.5 
105.0 
84.6 


H/8 

V8 
3/4 

5/8 


Breaking 
St'ssTons 
(2000  Lbs.) 


60.0 
49.2 
37.6 
27.6 
19.2 


STEEL  FLAT  EOPB. 


261 


Non-Spinning  Hoisting  Rope. 

18  Strands,  7  Wires  per  Strand,  1  Hemp  Core. 


d 

Approximate  Breaking 
Strength,  Tons  (2000  Lb.). 

Allowable  Working  Load, 
Tons  (2000  Lb.). 

4 

d 

M 

5  . 

\ 

i 
& 

;ble  Cast 
;1  Rope. 

4 

1 
£o5 

tor  PlowT 
;1  Rope. 

1 

rt 

ible  Cast 
;1  Rope. 

2^o;  o 

L 

tor  Plow 
;1  Rope. 

Diameter 
m  or  Shea  A 

1 

a 

£ 

P 

Ceo 

lol 

°ft 

§3 

e  S 

el 

lul 

11 

§| 

!« 

3 

p 

>H 

0 

w 

S 

^ 

M 

0 

w 

S 

^ 

S 

13/4 

51/2 

5.50 

45.80 

85.90 

101.00 

111.10 

122.00 

9.1 

17.1 

20.2 

22.2 

24.04 

7.00 

15/8 

5 

4.90 

39.80 

74.40 

87.60 

96.30 

7.9 

14.8 

17.5 

19.2 

6.50 

43/4 

4.32 

34.00 

63.80 

75.00 

82.50 

90  '.70 

6.8 

12.7 

15.0 

16.5 

18J 

6.00 

13/8 

41/4 

3.60 

28.20 

52.00 

62.40 

68.60 

75.50 

5.6 

10.4 

12.4 

13.7 

15.1 

5.50 

U/4 

4 

2.80 

23.40 

43.80 

51.60 

56.80 

62.50 

4.6 

8.7 

10.3 

11.3 

12.5 

5.00 

H/8 

31/2 

2.34 

19.60 

36.80 

43.20 

47.50 

52.20 

3.9 

7.3 

8.6 

9.5 

10.4 

4.50 

1 

3 

1.73 

14.95 

28.00 

33.00 

36.30 

39.00 

2.9 

5.6 

6.6 

7.2 

7.8 

4.00 

7/8 

23/4 

1.44 

11.95 

22.50 

26.50 

31.80 

35.00 

2.3 

4.5 

5.3 

6.3 

7.0 

3.50 

3/4 

21/4 

1.02 

8.85 

16.70 

19.60 

24.60 

27.00 

1.7 

3.3 

3.9 

4.9 

5.4 

3.00 

!   5/8 

2 

0.70 

5.90 

11.10 

13.10 

15.75 

17.30 

1.1 

2.2 

2.6 

3.1 

3.4 

2.50 

9/16 

13/4 

0.57 

4.85 

9.10 

10.70 

12.80 

0.97 

1.8 

2.1 

2.5 

2.25 

1/2 

U/2 

0.42 

3.65 

6.90 

8.10 

9.75 

iojo 

0.73 

1.3 

1.6 

1.9 

2.\ 

2.00 

7/16 

U/4 

0.31 

2.63 

4.90 

5.80 

6.85 

0.52 

0.98 

1.1 

1.3 

1.75 

3/8 

H/8 

0.25 

2.10 

3.90 

4.60 

5.55 

6.16 

0.42 

0.78 

0.92 

1.1 

\'.2 

1.50 

Steel  Flat  Kope. 


A 

V 

g 

1/4 
1/4 
1/4 
1/4 

JJ/16 
5/16 
5/16 
5/16 

^16 
5/16 

d 
4 

1 

U/2 

h 

U/2 

21/2 

31/2 

i 

er 
1 
^ 

0.65 
0.82 
1.06 
1.23 

Allow- 
able 
Working 
Load, 
Tons 
(2000 
Lbs.). 

d 
1 

'rS 

3/8 
3/8 
3/8 
3/8 

1/2 

V2 
1/2 
V2 
1/2 
V« 
1/2 
1/2 
1/2 

d 

H-  1 

1 

g 

41/2 
51/2 

6 

d 

d 

5 

? 

Allow- 
able 
Working 
Load, 
Tons 
(2000 
Lbs.). 

d 

1 

1 
1 

5/8 
5/8 
5/8 
5/8 
5/8 
5/8 

1/4 
3/4 
3/4 
3/4 

S 

M 
£ 

3 
$ 

£ 

1 
£ 

Allow- 
able 
Working 
Load, 
Tons 
(2000 
Lbs.). 

ll 
f 

2.6 
3.4 
4.4 
5.2 

|S 

S 

®  ^4 

rJ2     Q} 

I1 

O 

|l 

S 

£~ 

11 

5M 

O 

|oa 
S 

21.0 

23.8 
26.4 
29.0 
34.2 
39.4 

3.10 
4.00 
5.30 
6.20 

2.85 
3.10 
3.50 
3.73 

12.6 
13.6 
15.4 
16.2 

6.6 
16.2 
18.4 
19.4 

41/2 
51/2 

6 
7 
8 

4.55 
5.10 
5.65 
6.15 
7.30 
8.40 

18.2 
20.4 
22.8 
25.0 
29.6 
34.0 

0.79 
1.10 
1.35 
1.60 
1.88 
2.15 

3.6 
4.6 
6.0 
7.2 
8.2 
9.6 

4.4 
5.6 
7.0 
8.6 
10.0 
11.4 

21/2 

31/2 

41/2 

51/2 

6 
7 

2.20 
2.50 
2.80 
3.15 
3.85 
4.20 
4.55 
4.90 
5.90 

9.0 
10.4 
12.0 
13.8 
16.6 
18.0 
19.6 
21.0 
25.6 

10.8 
12.6 
14.4 
16.4 
19.8 
21.6 
23.6 
25.2 
30.6 

5 
6 
7 
8 

6.85 
7.50 
8.25 
9.75 

27.0 
30.2 
33.6 
40.4 

31.4 
35.0 
38.8 
46.8 

3/8 
3/8 

3/8 
3/8 
3/8 

2 

21/2 
31/2 

1.30 
1.70 
1.89 
2.30 
2.43 

5.4 
7.2 
8.2 
10.0 
10.8 

6.6 
8.6 
9.8 
12.0 
13.0 

V8 
7/8 
7/8 
7/8 

5 
6 
7 
8 

7.50 
9.53 
9.56 
10.60 

31.0 
36.0 
40.6 
45.0 

34.4 
41.8 
46.6 
51.6 

5/8 
5/8 

31/2 

3.50 
4.00 

13.6 
15.8 

15.8 
18.4 

The  allowable  working  load  in  the  above  table  is  1/5  of  the  approxi- 
mate breaking  stress  of  the  rope. 


262^ 


MATERIALS. 


Locked  Wire  Cable. — Locked  wire  cable  and  locked  coil-track 
cable,  of  the  general  form  shown  in  Fig.  77,  are  used  as  track  cables 
for  aerial  tramways.  They  differ  only  in  the  number  and  size  of 


Fig.  77. 

wires  used,  and  both  are  made  of  crucible  cast  steel.  The  locked 
wire  cable  is  the  more  flexible  of  the  two.  These  cables  are  smoother 
than  the  track  cable  described  on  page  260. 

Locked  Coil  and  Locked  Wire  Cable. 


d 

Wt.  per 
Ft.,  Lb. 

Break- 
ing 

Stress, 
Tons 
(2000 

Lbs.). 

^ 
j 

3 

Wt. 
Ft., 

per 
Lb. 

Break- 
ing 
Stress, 
Tons 
(2000 
Lbs.). 

d 

3 

Wt.  per 
Ft.,  Lbs. 

Break- 
ing 
Stress 
Tons 
(2000 
Lbs.). 

TJ 

0)_i 

9 

fl 

Id 
o  o 
oO 

0)  OJ 

x.% 

$* 

Ji 

2° 

'd  • 
o>  o> 

ja.SJ 

P 

h 

^ 

Locked 
Wire. 

*j 

•8? 

J° 

82 

3s 

Ij 

•a? 

J° 

'O    • 
0)  0) 
-M.S3 

S* 

21/2 

2.A 

13/4 
15/8 

6.30 

15.60 
12.50 
10.00 
7.65 
6.60 

J03 

240 
190 
160 
120 
103 

H/2 
13/8 
U/4 
H/8 

5.30 
4.40 
3.70 
3.00 
2.35 

5:S 

3.80 
3.15 
2.50 

89 
75 
62 
50 
40 

89 
75 
62 
50 
40 

7/8 
3/4 
5/8 
9/16 
V2 

.  1.80 

1.88 
1.30 
0.90 
0.72 
0.57 

30 

30 

22 
15.5 
12.5 
10 

Galvanized  Steel  Hawser. 

For  Lake  and  Deep  Sea  Towing  and  Mooring  Lines. 


fi 

Q 

C 

0 

Six  3  7-  Wire 
Strands,  1 
Hemp  Core 

Six  24-  Wire 
Strands,  7 
Hemp  Cores. 

d 

B 

3 

Circum.,  In. 

Six  3  7-  Wire 
Strands,  1 
Hemp  Core. 

Six  24-  Wire 
Strands,  7 
Hemp  Cores 

£ 

i 

jja 

^^ 

1 

HA 

«rg3 
c  M^: 
S|| 

«^ 

£ 

1. 

4J.«fl 

^^ 

1 

H  -A 

1^ 

•311 

JcotJ. 

£ 

*. 

4J^5 

^ 

| 

E?A 

^ 

•§!§ 

M^^ 

£ 

1  . 

.ij-Q 

pH 

0) 

I. 

9& 

1^1 
w^^ 

23/8 
25/16 
21/4 
21/8 
21/16 

1  15/16 
1  13/16 
13/4 
1  H/16 
15/8 

71/2 
71/4 
71/8 
63/4 
61/2 
61/4 

6 

53/4 
51/2 

jvi 

8.82 
8.36 
8.00 
7.06 
6.65 
6.30 
5.84 
5.13 
4.85 
4.42 
4.15 

188 
182 
171 
155 
140 
132 
125 
112 
104 
97 
87 

5^8i 
5.51 
5.09 
4.48 
4.24 
3.86 
3.63 

ii3 

106 
98 
88 
82 
76 
74 

H/2 
17/16 
13/8 
H/4 
13/16 
H/8 
H/16 

7/8 
13/16 
3/4. 

43/4 
41/2 
41/4 

33/4 

31/2 

3.  A 

23/4 

21/2 
21/4 

3.55 
3.24 
3.00 
2.45 
2.21 
2.00 
1.77 
1.58 
1.20 
1.03 
0.89 

76 
72 
66 
54 
47 
42 
38 
31.5 
26 
22 
20 

3.10 
2.92 
2.62 
2.15 
.93 
.75 
.54 
.38 
.05 
0.90 
0  78 

63 
55 
50 
42 
38 
34 
27 
25 
20 
17 
14 

SPLICING   WIRE   ROPES. 


203 


To  Splice  a  Wire  Rope.  —  The  tools  required  will  be  a  email  marline 
spike,  nipping  cutters,  and  either  clamps  or  a  small  hemp-rope  sling  with 
which  to  wrap  around  and  untwist  the  rope.  If  a  bench-vise  is  acces- 
sible it  will  be  found  convenient. 

In  splicing  rope,  a  certain  length  is  used  up  in  making  the  splice.  An 
allowance  of  not  less  than  16  feet  for  i/2-mch  rope,  and  proportionately 
longer  for  larger  sizes,  must  be  added  to  the  length  of  an  endless  rope  in 
ordering. 

Having  measured,  carefully,  the  length  the  rope  should  be  after  splicing, 
and  marked  the  points  M  and  M',  Fig.  78,  unlay  the  strands  from  each 
end  E  and  E'  to  M  and  M'  and  cut  off  the  center  at  M  and  M',  and  then: 

(1).  Interlock  the  six  unlaid  strands  of  each  end  alternately  and  draw 
them  together  so  that  the  points  M  and  M'  meet,  as  in  Fig.  79. 

(2).  Unlay  a  strand  from  one  end,  and  following  the  unlay  closely,  lay 
into  the  seam  or  groove  it  opens,  the  strand  opposite  it  belonging  to  the 
other  end  of  the  rope,  until  within  a  length  equal  to  three  or  four  times 
the  length  of  one  lay  of  the  rope,  and  cut  the  other  strand  to  about  the 
same  length  from  the  point  of  meeting  as  at  A,  Fig.  80. 

(3).  Unlay  the  adjacent  strand  in  the  opposite  direction,  and  following 
the  unlay  closely,  lay  in  its  place  the  corresponding  opposite  strand,  cut- 
ting the  ends  as  described  before  at  B,  Fig.  80. 

There  are  now  four  strands  laid  in  place  terminating  at  A  and  B,  with 
the  eight  remaining  at  MM',  as  in  Fig.  80. 

It  will  be  well  after  laying  each  pair  of  strands  to  tie  them  temporarily 
"  the  points  A  and  B. 

M 


\B 


FIG.  80. 


A  A  A% 


A       A'      A"       M       B       B'      B" 


FIG.  81.       SPLICING  WIRE  ROPE.       FIG.  82. 

Pursue  the  same  course  with  the  remaining  four  pairs  of  opposite 
strands,  stopping  each  pair  about  eight  or  ten  turns  of  the  rope  short  of 
the  preceding  pair,  and  cutting  the  ends  as  before. 

We  now  have  all  the  strands  laid  in  their  proper  places  with  their  re- 
spective ends  passing  each  other,  as  in  Fig.  81. 

All  methods  of  rope-splidng  are  identical  to  this  point:  their  variety 
consists  in  the  method  of  tucking  the  ends.  The  one  given  below  is  the 
one  most  generally  practiced. 

Clamp  the  rope  either  in  a  vise  at  a  point  to  the  left  of  A,  Fig.  81,  and 
by  a  hand-clamp  applied  near  A,  open  up  the  rope  by  untwisting  suffi- 
ciently to  cut  the  core  at  A,  and  seizing  it  with  the  nippers,  let  an  assis- 
tant draw  it  out  slowly,  you  following  it  closely,  crowding  the  strand  in 
its  place  until  it  is  all  laid  in.  Cut  the  core  where  the  strand  ends,  and 
push  the  end  back  into  its  place.  Remove  the  clamps  and  let  the  rope 
close  together  around  it.  Draw  out  the  core  in  the  opposite  direction 
and  lay  the  other  strand  in  the  center  of  the  rope,  in  the  same  manner. 
Repeat  the  operation  at  the  five  remaining  points,  and  hammer  the  rope 
lightly  at  the  points  where  the  ends  pass  each  other  at  A,  A,  B,  B,  etc., 
with  small  wooden  mallets,  and  the  splice  is  complete,  as  shown  in  Fig.  82. 

If  a  clamp  and  vise  are  not  obtainable,  two  rope  slings  and  short 
wooden  levers  may  be  used  to  untwist,  and  open  up  the  rope. 

A  rope  spliced  as  above  will  .be  nearly  as  strong  as  the  original  rope 
and  smooth  everywhere.  After  running  a  few  days,  the  splice,  if  well 
made,  cannot  be  found  except  by  close  examination. 

The  above  instructions  have  been  adopted  by  the  leading  rope  manu- 
facturers of  America. 


264 


MATERIALS. 


CHAINS. 

Weight  per  Foot,  Proof  Test  and  Breaking  Weight. 

(Pennsylvania  Railroad  Specifications,  1903.) 


Nominal 
Diameter 
of  Wire. 
Inches. 

Description. 

Maximum 
Length  of 
100  Links. 
Inches. 

Weight 
per 
Foot. 
Lbs. 

Proof 
Test. 
Lbs. 

Breaking 
Weight. 
Lbs. 

5/00 

Twisted  chain 

1  03  1/8 

020 

3/16 

961/4 

0.35 

3/16 

V4 
5/16 
3/8 
3/s 

Perfection  twisted  chain 
Straight-link  chain  .... 

Crane  chain 

151  1* 
102 
1143/4 
1143/4 
1135/0 

0.27 
0.70 
1.10 
1.60 
1.60 

1,600 
2,500 
3,600 
4,140 

3,200 
5,000 
7,200 
8,280 

7/16 
7/16 

Straight-link  chain  .... 
Crane  chain 

127l/2 
1261/4 

2.07 
2.07 

4,900 
5,635 

9,800 
11,270 

V2 
1/2 

Straight-link  chain  .... 
.Crane  chain  

153  /4 
1511/2 

2.50 
2.60 

6,400 
7,360 

12,800 
14,720 

5/8 

5/0 

Straight-link  chain  .... 
Crane  chain             

1781/2 
1763/4 

4.08 
4.18 

10,000 
11,500 

20,000 
23,000 

3/4 
3/i 

Straight-link  chain  .... 
Crane  chain 

204 
202 

5.65 
5.75 

14,400 
16,560 

28,800 
33,120 

7/8 

2521/2 

7.70 

22,540 

45,080 

1 

•I          K 

277  ?/4 

9.80 

29,440 

58,880 

1 

1  I/a 

Straight-Jink  chain  
Crane  chain  

280l/2 
303 

9.80 
12.65 

25,600 
38,260 

51,200 
76,520 

1  1/4 

3531/2 

15.50 

46,000 

92,000 

1  1/2 

•  i          « 

4165/8 

22.50 

66  240 

132,480 

1  3/1 

<i          « 

4793/4 

30.00 

90,  1  60 

180,320 

2  /4 

"          " 

5551/2 

39.00 

117,760 

235,520 

Elongation  of  all  sizes,  10  per  cent.  All  chain  must  stand  the  proof 
test  without  deformation.  A  piece  2  ft.  long  out  of  each  200  ft.  is 
tested  to  destruction. 

British  Admiralty  Proving   Tests  of  Chain  Cables.  —Stud-links. 
Minimum  size  in  inches  and  16ths.     Proving  test  in  tons  of  2240  Ibs. 
Min.  Size:      H        *        H      '«      it        l-    l&     H     JA       H    1A    II 
Test,  tons:     8£    10.1     11.9    13f    15|       18    20.3   22f  25*fe    28.1      31    34 
Min.  Size:     1&       1*      lT9s     if    Hi       If     Hi     H     Hi        2     2$ 
Test,  tons:  37*fc      40£    43.9    474    51*    55.1     59.1   63*    6743        72    81* 

Wrought-iron  Chain  Cables.  —  The  strength  of  a  chain  link  is  less 
than  twice  that  of  a  straight  bar  of  a  sectional  area  equal  to  that  of  one 
side  of  the  link.  .  A  weld  exists  at  one  end  and  a  bend  at  the  other,  each 
requiring  at  least  one  heat,  which  produces  a  decrease  in  the  strength. 
The  report  of  the  committee  of  the  U.  S.  Testing  Board  (1879),  on  tests 
of  wrought-iron  and  chain  cables,  contains  the  following  conclusions. 
That  beyond  doubt,  when  made  of  American  bar  iron,  with  cast-iron 
studs,  the  studded  link  is  inferior  in  strength  to  the  unstudded  one. 

"That  when  proper  care  is  exercised  in  the  selection  of  material,  a  varia- 
tion of  5  to  17  per  cent  of  the  strongest  may  be  expected  in  the  resistance 
of  cables.  Without  this  care,  the  variation  may  rise  to  25  per  cent. 

"That  with  proper  material  and  construction  the  ultimate  resistance  of 
the  chain  may  be  expected  to  vary  from  155  to  170  per  cent  of  that  of  the 
bar  used  in  making  the  links,  and  show  an  average  of  about  163  per  cent. 

"That  the  proof  test  of  a  chain  cable  should  be  about  50  per  cent  of 
the  ultimate  resistance  of  the  weakest  link." 

The  decrease  of  the  resistance  of  the  studded  below  the  unstudded 
cable  is  probably  due  to  the  fact  that  in  the  former  the  sides  of  the  link 
do  not  remain  parallel  to  each  other  up  to  failure,  as  they  do  in  the  latter. 
The  result  is  an  increase  of  stress  in  the  studded  link  over  the  unstudded 
in  the  proportion  of  unity,  to  the  secant  of  half  the  inclination  of  the 
sides  of  the  former  to  each  other. 

From  a  great  number  of  tests  of  bars  and  unfinished  cables,  the  commit- 
tee considered  that  the  average  ultimate  resistance,  and  proof  tests  of 
chain  cables  made  of  the  bars,  whose  diameters  are  given,  should  be 
such  as  are  shown  in  the  accompanying  table. 


CHAINS. 


265 


ULTIMATE    RESISTANCE    AND   PROOF   TESTS   OF    CHAIN    CABLES. 


Diam. 
of 
Bar. 

Average  resist. 
=  163%  of  Bar. 

Proof  Test. 

Diam. 
of 
Bar. 

Average  resist. 
=  163%  of  Bar. 

Proof  Test 

Inches. 

Pounds. 

Pounds. 

Inches. 

Pounds. 

Pounds. 

71,172 

33,840 

19/16 

162,283 

77,159 

U/16 

79,544 

37,820 

15/8 

174,475 

82,956 

U/8 

88,445 

42,053 

1  H/16 

187,075 

88,947 

13/16 

97,731 

46,468 

13/4 

200,074 

95,128 

11/4 

107,440- 

51,084 

1  13/16 

213,475 

101,499 

15/16 

117,577 

55,903 

17/8 

227,271 

108,058 

13/8 

128,129 

60,920 

1  15/16 

241,463 

114,806 

17/16 

139,103 

66,  1  38 

2 

256,040 

121,737 

U/2 

150,485 

71,550 

Pitch,  Breaking,  Proof  and  Working  Strains  of  Chains. 

(Bradlee  &  Co.,  Philadelphia.) 


JO 

D.B.G.  Special  Crane. 

Crane. 

.2 

0> 

ft 

.2 

^ 

|, 

•  g 

,0 

Jt 

!p  n 

"i 

.2 

• 

73 

t->~* 

*o3  C 

(-<•—* 

CJ5  fl 

3 

. 

f* 

P 

1 

1 

Mo 

1 

.s" 

O 

? 

.rH 

X 

o 

0> 

12 

H 

hc£ 
o3C/} 

&^£ 

OJ  S 

W)£ 

*•"      ^Q 

S-2" 

V 

O 

ft 

'5 

o 

<3  bfl 

*rt  rt  * 

O 

(B   hO 

^  0  m 

N 

ft 

^.2 

>a 

^5p 

w 

K 

A 

O 

P4 

o 

OH 

1/4 

25/32 

3/4 

15/16 

1,932 

3,864 

1,288 

1,680 

3,360 

1,120 

5/16 

27/32 

1 

U/8 

2,898 

5,796 

1,932 

2,520 

5,040 

1,680 

3/8 

31/32 

U/2 

15/16 

4,186 

8,372 

2,790 

3,640 

7,280 

2,427 

7/16 

15/32 

2 

U/2 

5,796 

11,592 

3,864 

5,040 

10,080 

3,360 

1/2 

1  H/32 

21/2 

1  13/16 

7,728 

15,456 

5,152 

6,720 

13,440 

4,480 

9/16 

1  15/32 

33/io 

2 

9,660 

19,320 

6,440 

8,400 

16,800 

5,600 

5/8 

I  23/3«> 

41/10 

23/16 

11,914 

23,828 

7,942 

10,360 

20,720 

6,907 

H/16 

1  13/16 

5 

23/8 

14,490 

28,980 

9,660 

12,600 

25,200 

8,400 

3/4 

1  15/16 

62/io 

29/16 

17,388 

34,776 

11,592 

15,120 

30,240 

10,080 

13/16 

21/16 

67/io 

23/4 

20,286 

40,572 

13,524 

17,640 

35,280 

11,760 

7/8 

23/16 

83/8 

215/16 

22,484 

44,968 

14,989 

20,440 

40,880 

13,627 

15/16 

27/ie 

9 

33/16 

25,872 

51,744 

17,248 

23,520 

47,040 

15,680 

21/2 

101/2 

33/8 

29,568 

59,136 

19,712 

26,880 

53,760 

17,920 

11/16 

25/8 

12 

39/16 

33,264 

66,538 

22,176 

30,240 

60,480 

20,160 

U/8 

23/4 

135/g 

313/16 

37,576 

75,152 

25,050 

34,160 

68,320 

22,773 

13/16 

31/16 

137/io 

4 

41,888 

83,776 

27,925 

38,080 

76,160 

25,387 

11/4 

31/8 

16 

43/ie 

46,200 

92,400 

30,800 

42,000 

84,000 

28,000 

33/8 

161/9 

43/8 

50,512 

101  024 

33,674 

45,920 

91,840 

30,613 

13/J6 

39/16 

191/4 

49/i6 

55,748 

111,496 

37,165 

50,680 

101,360 

33,787 

1  7/16 

311/16 

43/4 

60,368 

120,736 

40,245 

54,880 

109,760 

36,587 

U/2 

37/8 

23 

51/8 

66,528 

133,056 

44,352 

60,480 

120,960 

40,320 

19/16 

4 

25 

55/ie 

70,762 

141,524 

47,174 

65,520 

131,140 

43,180 

13/4 

43/4 

31 

57/8 

82,320 

164,640 

54,880 

2 

53/4 

40 

63/4 

107,520 

215,040 

71,680 

21/4 

63/4 

523/4 

75/8 

136,080 

272,160 

90,720 

2l/2 

7 

641/2 

83/8 

168,000 

336,000 

112,000 

23/4 

71/4 

73 

91/8 

193,088 

386,  1  76 

128,725 

3 

73/4 

86 

97/8 

217,728 

435,456 

145,152 

The  distance  from  center  of  one  link  to  center  of  next  is  equal  to  the 
inside  length  of  link,  but  in  practice  1/32  in.  is  allowed  for  weld.  This  is 
approximate,  and  where  exactness  is  required,  chain  should  be  made  so. 

FOR  CHAIN  SHEAVES.  —  The  diameter,  if  possible,  should  be  not  less 
than  thirty  times  the  diameter  of  chain  used. 

EXAMPLE.  —  For  1-inch  chain  use  30-inch  sheaves. 


T&, 

~      ^ '  %J 


^,< 


WTHEBEOOE 


MATERIALS. 

SHAPES  AND  SIZES  OF   FIRE-BRICK. 

(Stowe-Fuller  Co.,  Cleveland,  1914.) 


Name  of 
Brick 
or 

Length, 
Inches. 

Width, 
Inches. 

Thick-' 
ness, 
Inches. 

_«  . 

o| 

0)   t< 

n& 

ta 

M0> 

*-  be 

'£  S 

'?  S 

Tile. 

j>tj 

>3§ 

IS 

26 

Ss 

62 

'2u 

a 

6 

c 

d 

c 

/ 

£ 

HH    0 

STRAIGHT  BRICK. 


9-inch  . 

9 

4l/o 

21/2 

Large  9-inch  .  . 
Small  9-    "    .  . 

9 
9 

63/4" 

31/0 

21/2 

Checker  .  . 

9 

3 

3 

Soap  .  .  .,  
No.  1  Split 

9 
9 

21/2 

41/0 

21/4 

No.  2    "     ... 

9 

4l'/o 

2 

Checker  Tile  .  I 

1820, 

} 

6 

3 

Mill 

24 
1820, 

) 

(. 

9 

3 

Mill  Block  . 

24 

' 

9 

6 

No.  1  Bridgewall 
No.  2 

13 
13 

61/2 
61/2 

6 
3 

WEDGE  SHAPE  AND  TAPER  BRICKS. 
Large  9-in.  No 

1  Wedge  . . . 
Large  9-in.  No 

2  Wedge... 
No.  1  Wedge . 
No.  2       "      . 
No.  1  Key*.  . 
No.  2     "  * . . 
No.  3     "  * . . 
No.  4     "  *  .  . 
No.  1  Archf. . 
No.  2     "     t- . 
Side  Skew  .  .  . 
End  Skew  .  .  . 
Skew  Back.  .  . 
No.  1  Neck  .  . 
No.  2      "      .  . 
No.  3      "     . . 
Feather  Edge . 
Jamb  . 


Edge  Arch 


63/4 

63/4 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41A> 

4'" 

31/2 
21/4 

13/4 

ii/2 
V" 

21/2 

21/2 
21/2 

21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 

21/0 

17/8 
U/2 
U/2 

2" 

../, 

0 

102 

63 
102 
63 
112 
65 
41 
26 
72 
42 

60 

30 
60 
30 
144 
72 
36 
18 
48 
24 

'5/8 

1/8 

2" 

36 

CIRCLE  BRICK,  Curved  Edges. 


No.  1  . 
No.  2. 

No!  4 '. 
No.  5. 


81/2 

9 

9 
9 
9 


51/4  4i/2!.. 
69/1641/2.. 

73/1641/2  .. 
79/16  41/2  .  . 
75/8  41/2  . . 


.  2l/2    . 

.  21/2'  . 

.  2l/2  . 

.  21/2    . 

:  21/2  . 


9 
II 
14 
20 

24 


CUPOLA  BLOCKS. 


No.  1  
No.  2  .  . 

9 

63/8 

63/4 

6 
6 

4 
4 

15 
17 

30 
36 

No.  3  . 

9 

71/8 

6 

4 

71 

48 

No.  4  

9 

71/2 

6 

4 

52 

60 

*  Tapers  lengthwise,     t  Tapers  breadthwise. 

Other  special  shapes  of  brick  and  tile  manufactured  are:  Locomo- 
tive tile,  32,  34,  and  40  in.  X  10  in.  X  3  in. ;  34  and  36  in.  X  8  in.  X  3  in. 
Blast  Furnace  Shapes,  13  H  X  6  X  2^  in.  straight;  No.  1,  12  ft.  Key 


NUMBER  OF  FIEE  BRICK  FOR  CIRCLES. 


267 


13^X6  X5X2H  in.  thick,  91  brick  to  circle;  No.  2,  6  ft.  Key 
13  J^  X  6  X  43/8  X  2%  in.  thick,  53  brick  to  circle;  bottom  blocks, 
18  X  9  X  4  1A  in.  straight.  Standard  Block  Linings,  9X9,  12  X  9, 
15  X  9,  18  X  9,  all  4  V£  in.  thick,  made  straight,  and  as  key-brick 
for  use  with  straight  brick  to  line  any  diameter  of  furnace ;  the  key- 
bricks  are  made  for  radii  of  5,  7  1A,  and  10  ft.  Pottery  Kiln  Brick, 
flat  back,  9X6  X  2  H  in. ;  flat  back  arch,  9X6X3^X2^  in.; 
56  brick  to  a  32-inch  inside  diam.  circle,  No.  2  flat  back  arch,  9X6 
X  3  y±  X  2  in.,  31  brick  to  a  22-inch  inside  diam.  circle. 

A  straight  9-inch  fire-brick  weighs  7  Ibs.,  a  silica  brick,  6.2  Ibs.;  a 
magnesia  brick,  9  Ibs. ;  a  chrome  brick,  10  Ibs.  A  silica  brick  expands 
about  i/s  inch  per  foot  when  heated  to  2,500°  F. 

Clay  brick  expand  or  shrink,  dependent  upon  the  proportion  of 
silica  to  alumina  contained  in  the  brick;  but  most  fire  clay  brick 
contain  alumina  sufficient  to  show  some  shrinkage. 

One  cubic  foot  of  wall  requires  17,  9-inch  bricks;  one  cubic  yard, 
requires  460.  Where  keys,  wedges,  and  other  "shapes"  are  used,  add 
10  per  cent,  in  estimating  the  number  required. 

To  secure  the  best  results,  fire-brick  should  be  laid  in  the  same  clay 
from  which  they  are  manufactured.  One  ton  of  ground  clay  should 
be  sufficient  to  lay  3,000  ordinary  bricks.  It  should  be  used  as  a 
thin  paste  and  not  as  mortar.  The  thinner  the  joint  the  better  the 
furnace  wall.  In  ordering  bricks,  the  service  for  which  they  are  to  be 
used  should  be  stated. 

Silica  brick  should  be  laid  in  silica  cement  and  with  the  smallest 
joint  possible. 

Ground  fire-brick  or  old  cupola  blocks  mixed  with  fire-clay  make 
the  best  cupola  daub  known. 

NUMBER   OF    FIRE-BRICK   REQUIRED    FOR   VARIOUS 
CIRCLES. 


Diam. 
of 
Circle. 

Key  Bricks. 

Arch  Bricks. 

Wedge  Bricks. 

-T 

d 
£ 

cK 

6 
£ 

<M 

6 
fc 

6 

"ttf 
1 

«s 

6 

6 

.s 

Ov 

la 
"o 
H 

<s 

6 

d 
fc 

.s 

0> 

3 
S 

ft.  in. 
1   6 
2  0 
2   6 
3   0 
3   6 
4  0 
4  6 
5   0 
5   6 
6  0 
6   6 
7   0 
7   6 
8   0 
8   6 
9   0 
9   6 
10   0 
10   6 
II   0 
11   6 
12   0 
12   6 

25 
17 
9 

"\3 
25 
^8 

25 
30 
34 
38 
42 
46 

42 
31 
21 
10 

42 

18 
36 
54 
7? 

49 
57 
64 
72 
80 
87 
95 
102 
110 
117 
125 
132 
140 
147 
155 
162 
170 
177 
185 
193 

60 

48 
36 
24 
12 

'26' 
40 
59 
79 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 

'"s" 

15 

23 
30 
38 
46 
53 
61 
68 
76 
83 
91 
98 
106 

60 
68 
76 
83 
91 
98 
106 
113 
121 
128 
136 
144 
151 
159 
166 
174 
181 
189 
196 
204 

32 
25 
19 
13 
6 

10 
21 
32 
42 
53 
63 

51 
55 
59 
63 

72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 

8 
15 
23 
30 
38 
45 
53 
60 
68 
75 
83 
90 
98 
105 
113 
121 

58 
52 
47 
42 
37 
31 
26 
21 
16 
11 
5 

9 
19 
29 
38 
47 
57 
66 
76 
85 
94 
104 
113 
113 

67 
71 
76 
80 
84 
88 
92 
97 
101 
105 
109 
113 
117 

For  larger  circles  than  12  feet  use  113  No.  1  Key,  and  as  many  9-inch 
brick  as  may  be  needed  in  addition. 


268 


MATERIALS. 


Refractoriness  of  Some  American  Fire-Brick. —  (R.  F.  Weber, 
A.  I.  M.  E.,  1904.)  Prof.  Heinrich  Ries  notes  that  the  fusibility  of  New 
Jersey  brick  is  influenced  largely  by  its  percentage  of  silica,  but  also  in 
part  by  the  texture  of  the  clay.  It  was  found  that  the  fustion-point  of 
almost  any  of  the  New  Jersey  fire-bricks  could  be  reduced  four  or  five 
Seger  cones  by  grinding  the  brick  sufficiently  fine  to  pass  through  a 
700-mesh  sieve. 

Mr.  Weber  draws  the  conclusion  from  his  tests  of  44  bricks  that  it  is 
evident  that  the  refractoriness  of  a  fire-brick  depends  on  the  total  quan- 
tity of  fluxes  present,  the  silica  percentage  and  the  coarseness  of  grain; 
moreover,  chemical  analysis  alone  cannot  be  used  as  an  index  of  the 
refractoriness  except  within  rather  wide  limits.  The  following  table 
shows  the  composition,  fusion-point,  and  physical  properties  of  six 
most  refractory  and  of  five  least  refractory  of  the  44  bricks. 


J.3 

1 

Locality. 

Si02. 

A12O3. 

Fe.03. 

TiO2. 

ill 

•J3t«J& 

4 

«*-!    fl 

6  5? 

J^ra5 

eg 

'   Cr^ 

55 

< 

sT 

3 

Per 

Per 

Per 

Per 

Per 

Per 

No. 

cent. 

cent. 

cent. 

cent. 

cent. 

cent. 

1.... 

Missouri  . 

51   59 

38  26 

1  84 

1  97 

6  34 

10  25 

32  to  33 

Kentucky  

54.90 

38.19 

2J8 

K55 

3J8 

6.91 

32  to  33 

y'.'.'. 

Pennsylvania  

53.05 

41.16 

2.65 

•  1.80 

1.34 

5.79 

32  to  33 

4.... 

Colorado  

93.57 

2.53 

0.62 

0.27 

3.01 

3.90 

32  to  33 

5... 

Ken  tucky  

44  77 

43  08 

2  78 

2  54 

6  83 

12.15 

31  to  32 

6 

New  York 

68  70 

20  75 

1  20 

5  54 

3  81 

10  55 

31  to  32 

40.... 

Pennsylvania  

61.28 

27.13 

2.90 

1.37 

7.31 

11.58 

26 

41.... 

Pennsylvania  

74.83 

16.40 

3.26 

0.77 

4.74 

8.77 

26 

42... 

Alabama  

67  19 

25.05 

2  83 

0  71 

4.22 

7  76 

26 

43 

Indiana 

60  76 

31  66 

5  67 

1  58 

0  33 

7  58 

26 

44.  ... 

Kentucky  

60.58 

32.49 

2.25 

1.69 

2.99 

6.93 

26 

1  Fairly   uniform,   angular   flint-clay   particles,   constituting  body  of 
brick.     Largest  pieces  5  to  6  mm.  in  diameter.     White. 

2  Coarse-grained ;   angular  pieces  of  flint-clay  as  large  as  9  mm.     Aver- 
age 4  to  5  mm.     Light  buff. 

3  Coarse,   angular  flint-clay  particles,   varying  from   1   to  5  mm.  in 
diameter.     Average  4  to  5  mm.     Buff. 

4  Fine-grained  quartz  particles.      Largest  2  to  3  mm.  in  diameter. 
White. 

6  Medium  grain;  flint-clay  particles,  fairly  uniform  in  size,  3  to  4  mm. 
Light  buff. 

6  Coarse  grain;  quartz  particles,  4  to  5  mm.  in  diameter,  forming 
about  50  per  cent  of  brick.  White. 

40  Fine  grain;    small,  white  flint-clay  particles,  not   over   2  mm.   in 
diameter  and  not  abundant.     Buff. 

41  Medium  grain;   pieces  of  quartz  with  pinkish  color  and  angular  flint- 
clay  particles.     About  3  mm.  in  diameter.     Buff. 

42  Fine  grain;   even  texture.     Few  coarse  particles.     Brown. 

tt  Fine  grain;  some  particles  as  large  as  1  to  2  mm.  in  diameter.     Buff. 
44  Angular,  dark-colored,  flinty-clay  particles.     Maximum  size  5  mm. 
Throughout  a  reddish-brown  matrix. 

SLAG  BRICKS  AND   SLAG  BLOCKS. 

Slag  bricks  are  made  by  mixing  granulated  basic  slag  and  slaked  lime, 
molding  the  mixture  in  a  brick  press  or  by  hand,  and  drying.  The  silica 
in  the  slag  ranges  from  22.5%  to  35%;  the  alumina  andiron  oxide  together, 
from  16.1%  to  21%;  the  lime,  from  40%  to  51.5%.  The  granulated  slag 
is  dried  and  pulverized.  Powdered  slaked  lime  is  added  in  sufficient  quan- 


ANALYSES  OF  FIRE  CLAYS. 


269 


tity  to  bring  the  total  calcium  oxide  in  the  mixture  up  to  about  55%. 
Usually  a  small  amount  of  -water  is  added.  The  mixture  is  then  molded 
into  shape,  and  the  bricks  are  then  dried  for  six  to  ten  days  in  the  open 
air.  Slag  bricks  weigh  less  than  clay  bricks  of  equal  size,  require  less 
mortar  in  laying  up,  and  are  at  least  equal  to  them  in  crushing  strength. 

Slag  blocks  are  made  by  running  molten  slag  direct  from  the  furnaces 
into  molds.  If  properly  made,  they  are  stronger  than  slag  bricks.  They 
are,  however,  impervious  to  air  and  moisture;  and  on  that  account 
dwellings  constructed  of  them  are  apt  to  be  damp.  Their  chief  uses  are 
for  foundations  or  for  paving  blocks.  The  properties  required  in  a  slag 
paving  block,  viz:  density,  resistance  to  abrasion,  toughness,  and  rough- 
ness of  surface,  vary  with  the  chemical  composition  of  the  slag,  the 
rapidity  of  cooling,  .and  the  character  of  the  molds  used.  Blocks  cast  in 
sand  molds,  and  heavily  covered  with  loose  sand,  cool  slowly,  and  give 
much  better  results  than  those  cast  in  iron  molds.  —  E.  C.  Eckel,  Ena. 
News,  April  30,  1903. 

ANALYSES  OF  FIRE  CLAYS. 


Brand. 

Titanic  Acid, 
TiO2 

O 
33 

i 

s 

m 

Alumina, 
A1203  • 

B 

•p 

O 
1 

I 

S 

0 
oT 

'3 

lo 

!* 

9, 
W 

•§ 

n 

1 

9, 

1 

C8 

1 

Total  Im- 
purities. 

1 

Mt  Savage^- 

50.46 
56.80 
44.40 
56.15 
55.87 
56.80 
67.84 
68.01 
48.35 
44.80 

51.50 
63.18 
44.61 
45.26 
67.47 
65.60 
73.82 
65.41 
53.40 
55.46 

73.71 
67.12 

35.90 
30.08 
33.56 
33.30 
41.39 
30.08 
21.83 
24.09 
36.37 
39.00 

44.85 
23.70 
38.01 
37.85 
19.33 
20.75 
15.88 
30.55 
26.40 
31.74 

18.33 
21.18 

12.744 
10.50 
14.575 
9.68 

'  '7.69 
5.98 
3.03 
10.56 
14.70 

1.94 
6.87 
13.63 
13.30 
10.45 
11.00 
6.45 

.50 
.12 
.08 
0.59 
.60 
.67 
.57 
.01 
2.00 
0.30 

0.33 
1.20 
1.25 
2.03 
2.56 
2.00 
2.95 
70 

0.13 

0.02 

Trace 
0.80 

1.65 
1  9? 

Mt.  Savage2  .  .  . 
Mt.  Savages.  .  . 
Mt.  Savage*  .  .  . 
Strasburg,  O.  .  . 
Cumberland,  Md 
Woodbridge.NJ 
Carter  Co.,  Ky  . 
ClearfieldCo.,Pa 
Clearfield5  and. 
Cambria     Cos., 
Pa6 

1.15 
1.53 

6.'45 
1.15 

Tr. 
0.17 
0.40 

6.'28 
3.01 
0.07 
0.20 

0.23 
0.17 
0.08 
0.08 
0.41 
1.65 
Tr. 

0.11 
0.12 
0.30 

6.24 

6!  12 
1.00 

1.15 

0.47 
0.41 
0.02 
0.07 
Tr. 
Tr. 

0.2 

6.'29 
2.30 
2.24 

'  2.5 

47 
0.20 

4'" 

1.47 
0.88 
2.79 
3.97 
4.33 
4.02 
4.73 

Clinton  Co.,  Pa. 
Clarion  Co.,  Pa. 
FarrandsvillePa 
St.LouisCo.,Mo 
Gottwerth,  Aus. 
Stourbridge,  En. 
Glenboig,   Scot. 
La  Bouchade,Fr 
Coblentz,     Ger. 
Diesdorf  ,  Rhine- 
land  .  . 

1.46 
1.02 

\33 

2.52 
1.74 
1.26 
1.07 
Tr. 
0.90 

4.55 
3.47 
3.59 
5.14 

3.85 
3  58 

S020.19 

0.20 

3.65 

12.00 
9.37 

5.17 
6.21 

4.20 
0.59 

0.89 
1.85 

0.69 
0.19 

Tr. 
0.32 

0.64 
0.14 

0.10 
0.84 

0. 
2.49 

2.12 
2.02 

>5 
0.68 

0.24 

4.20 
4.09 

3.85 
5.93 

0.90 

Dowlair,  Wales. 

1  Mass.  Inst.  of  Technology,  1871.  2  Report  on  Clays  of  New  Jersey. 
Prof.  G.  H.  Cook,  1877.  *  Second  Geological  Survey  of  Penna.,  1878. 
*  Dr.  Otto  Wuth  (2  samples),  1885.  5  Flint  clay  from  Clea.rfleld  and 
Cambria  counties,  Pa.,  average  of  hundreds  of  analyses  by  Harbison- 
Walker  Refractories  Co.,  Pittsburg,  Pa.  6  Same  material  calcined. 
All  other  analyses  from  catalogue  of  Stowe-Fuller  Co.,  1914. 

MAGNESIA  BRICKS. 

"Foreign  Abstracts"  of  the  Institution  of  Civil  Engineers,  1893,  gives  a 
paper  by  C.  Bischof  on  the  production  of  magnesia  bricks.  The  material 
most  in  favor  at  present  is  the  magnesite  of  Styria,  which,  although  less 
pure  considered  as  a  source  of  magnesia  than  the  Greek,  has  the  property 
of  fritting  at  a  high  temperature  without  melting. 

At  a  red  heat  magnesium  carbonate  is  decomposed  into  carbonic  acid 
and  caustic  magnesia,  which  resembles  lime  in  becoming  hydrated  and 


270  MATERIALS. 

recarbonated  when  exposed  to  the  air,  and  possesses  a  certain  plasticity, 

so  that  it  can  be  moulded  when  subjected  to  a  heavy  pressure.  By  long- 
continued  or  stronger  heating  the  material  becomes  dead-burnt,  giving  a 
form  of  magnesia  of  high  density,  sp.  gr.  3.8,  as  compared  with  3.0  in  the 
plastic  form,  which  is  unalterable  in  the  air  but  devoid  of  plasticity.  A 
mixture  of  two  volumes  of  dead-burnt  with  one  of  plastic  magnesia  can 
be  moulded  into  bricks  which  contract  but  little  in  firing.  Other  binding 
materials  that  have  been  used  are:  clay  up  to  10  or  15  per  cent;  gas-tar, 
perfectly  freed  from  water,  soda,  silica,  vinegar  as  a  solution  of  magnesium 
acetate  which  is  readily  decomposed  by  heat,  and  carbolates  of  alkalies 
or  lime.  Among  magnesium  compounds  a  weak  solution  of  magnesium 
chloride  may  also  be  used.  For  setting  the  bricks  lightly  burnt,  caustic 
magnesia,  with  a  small  proportion  of  silica  to  render,  it  less  refractory,  is 
recommended.  The  strength  of  the  bricks  may  be  increased  by  adding 
iron,  either  as  oxide  or  silicate.  If  a  porous  product  is  required,  sawdust 
or  starch  may  be  added  to  the  mixture.  When  dead-burnt  magnesia  is 
used  alone,  soda  is  said  to  be  the  best  binding  material.  See  also  papers 
by  A.  E.  Hunt,  Trans.  A.  I.  M.  E.t  xvi,  720,  and  by  T.  Egleston,  Trans. 
A.  I.  M.E.,  xiv,  458. 

The  average  composition  of  magnesite,  crude  and  calcined,  is  given  as 
follows  by  the  Harbison-Walker  Refractories  Co.,  Pittsburg  (1907). 


Gre 
Crude. 
Carbonate  of  magnesia     97.00% 
Magnesia  
Silica      1  25 

cian. 
Calcined. 

94'.66'% 
2.75 
0.70 
0.80 
1.50 
0.40 

Styrian. 
Crude.     Calcined. 
92.50%      
85.50% 
1.50           3.00 
0.50           1.00 
3.90           8.00 
1.25           2.50 
0.50 

Alumina  

0.40 

Iron  Oxide  

...       0  40 

Lime  

0.75 

Loss  ....'.  

100.05       100.15  99.65       100.50 

With  the  calcined  Styrian  magnesite  of  the  above  analysis  it  is  not 
necessary  to  use  a .  binder  either  for  making  brick  or  for  forming  the 
bottom  of  an  open-hearth  furnace. 

ZIRCONIA. 

Zirconiaore  (84.1  ZrO2;  7.74  SiO2;  3.10Fe2O3;  1.21  TiO2;  0.66A12O3: 
loss  on  ignition  2.72)  vitrifies  slightly  at  1830°  C.  (3326°  F) .  Mixed  with 
different  percentages  of  clay  and  molded  into  cones  it  vitrifies  at  some- 
what lower  temperatures.  A  zirconia  brick  containing  5%  clay  be- 
came plastic  on  its  face  at  1800°  C.  (3272°F;).  (H.  Conrad  Meyer, 
j\fet.  &  Chem.  Eng.,  Vol.  xii,  No.  12,  1914,  Vol.  xiii,  No.  4,  1915; 
Circular  of  Foote  Mineral  Co.,  Philadelphia.) 

ASBESTOS. 

The  following  analyses  of  asbestos  aregiven~by  J.  T.  Donald.  Eng.  and 
M.  Jour.,  June  27,  1891. 

Canadian. 
Italian.      Broughton.    Templeton. 

Silica 40.30%          40.57%  40.52% 

Magnesia 43.37  41.50  42.05 

Ferrous  oxide 87  2.81  1.97 

Alumina 2.27  .90  2..10 

Water 13.72  13.55  13.46 

100.53  99.33  100.10 

Chemical  analysis  throws  light  upon  an  important  point  in  connection 
with  asbestos,  i.e.,  the  cause  of  the  harshness  of  the  fibre  of  some  varieties. 
Asbestos  is  principally  a  hydrous  silicate  of  magnesia,  i.e.,  silicate  of  mag- 
nesia combined  with  water.  When  harsh  fibre  is  analyzed  it  is  found  to 
contain  less  water  than  the  soft  fibre.  In  fibre  of  very  fine  quality  from 
Black  Lake  analysis  showed  14.38%  of  water,  while  a  harsh-fibred  sa>mple 
gave  only  11.70%.  If  soft  fibre  be  heated  to  a  temperature  that  will  drive 
off  a  portion  of  the  combined  water,  there  results  a  substance  so  brittle 
that  it  may  be  crumbled  between  thumb  and  finger.  There  is  evidently 
some  connection  between  the  consistency,  of  the  fibre  and  the  amount  of 
water  in  its  composition, 


STANDARD  CROSS  SECTIONS. 

Recommended  by  a  Committee  of  the  Am.  Soc.  M.  B.;  1912. 


271 


Cast  Iron 


Wrought  Iron 


Cast  Steel 


Wrought  Steel 


Aluminum       Rubber,  Vulcanite 


Rock 


Original       Filling 

Earth 


Sand 


Other  Materials 


Wrought  Steel        Nickel  Steel 


Chrome  Steel        Vanadium  Steel 


fill 


;.M::&V;; 


wws 


Concrete         Concrete  Blocks 


Cyclopean  Expanded     Wire  or 

PonorpfA  Metal  Rods 

concrete      Reinf  orced  concrete 


272  STKENGTH  OF  MATERIALS. 


STRENGTH  OP  MATERIALS. 

Stress  and  Strain.  —  There  is  much  confusion  among  writers  on 
strength  of  materials  as  to  the  definition  of  these  terms.  An  external 
force  applied  to  a  body,  so  as  to  pull  it  apart,  is  resisted  by  an  internal 
force,  or  resistance,  and  the  action  of  these  forces  causes  a  displacement 
of  the  molecules,  or  deformation.  By  some  writers  the  external  force  is 
called  a  stress,  and  the  internal  force  a  strain;  9thers  call  the  external 
force  a  strain,  and  the  internal  force  a  stress;  this  confusi9n  of  terms  is 
not  of  importance,  as  the  words  stress  and  strain  are  quite  commonly 
used  synonymously,  but  the  use  of  the  word  strain  to  mean  molecular 
displacement,  deformation,  or  distortion,  as  is  the  custom  of  some,  is  a 
corruption  of  the  language.  See  Engineering  News,  June  23,  1892. 
Some  authors  in  order  to  avoid  confusion  never  use  the  word  strain  in 
their  writings.  Definitions  by  leading  authorities  are  given  below. 

Stress.  —  A  stress  is  a  force  which  acts  in  the  interior  of  a  body,  and 
resists  the  external  forces  which  tend  to  change  its  shape.  A  deformation 
is  the  amount  of  change  of  shape  of  a  body  caused  by  the  stress.  The 
word  strain  is  often  used  as  synonymous  with  stress,  and  sometimes  it  is 
also  used  to  designate  the  deformation.  (Merriman.) 

The  force  by  which  the  molecules  of  a  body  resist  a  strain  at  any  point 
is  called  the  stress  at  that  point. 

The  summation  of  the  displacements  of  the  molecules  of  a  body  for  a 
given  point  is  called  the  distortion  or  strain  at  the  point  considered. 
(Burr.) 

Stresses  are  the  forces  which  are  applied  to  bodies  to  bring  into  action 
their  elastic  and  cohesive  properties.  These  forces  cause  alterations  of 
the  forms  of  the  bodies  upon  which  they  act.  Strain  is  a  name  given  to 
the  kind  of  alteration  produced  by  the  stresses.  The  distinction  between 
stress  and  strain  is  not  always  observed,  one  being  used  for  the  other. 
(Wood.) 

The  use  of  the  word  stress  as  synonymous  with  "  stress  per  square  inch," 
or  with  "strength  per  square  inch,"  should  be  condemned  as  lacking  in 
precision. 

Stresses  are  of  different  kinds,  viz.:  tensile,  compressive,  transverse,  tor- 
sional,  and  shearing  stresses. 

A  tensile  stress,  or  pull,  is  a  force  tending  to  elongate  a  piece.  A  com- 
pressive  stress,  or  push,  is  a  force  tending  to  shorten  it.  A  transverse  stress 
tends  to  bend  it.  A  torsional  stress  tends  to  twist  it.  A  shearing  stress 
tends  to  force  one  part  of  it  to  slide  over  the  adjacent  part. 

Tensile,  compressive,  and  shearing  stresses  are  called  simple  stresses. 
Transverse  stress  is  compounded  of  tensile  and  compressive  stresses,  and 
torsional  of  tensile  and  shearing  stresses. 

To  these  five  varieties  of  stresses  might  be  added  tearing  stress,  which  is 
either  tensile  or  shearing,  but  in  which  the  resistance  of  different  portions 
of  the  material  are  brought  into  play  in  detail,  or  one  after  the  other, 
instead  of  simultaneously,  as  in  the  simple  stresses. 

Effects  of  Stresses.  —  The  following  general  laws  for  cases  of  simple 
tension  or  compression  have  been  established  by  experiment  (Merriman) : 

1.  When  a  small  stress  is  applied  to  a  body,  a  small  deformation  is  pro- 
duced, and  on  the  removal  of  the  stress  the  body  springs  back  to  its  original 
form.     For  small  stresses,  then,  materials  may  be  regarded  as  perfectly 
elastic. 

2.  Under  small  stresses  the  deformations  are  approximately  proportional 
to  the  forces  or  stresses  which  produce  them,  and  also  approximately  pro- 
portional to  the  length  of  the  bar  or  body. 

3.  When  the  stress  is  great  enough  a  deformatipn  is  produced  which  is 
partly  permanent,  that  is,  the  body  does  not  spring  back  entirely  to  its 
original  form  on  removal  of  the  stress.    This  permanent  part  is  termed  a 
set.    In  such  cases  the  deformations  are  not  proportional  to  the  stress. 

4.  When  the  stress  is  greater  still  the  deformation  rapidly  increases  and 
the  body  finally  ruptures. 

5.  A  sudden  stress,  or  shock,  is  more  injurious  than  a  steady  stress  or 
than  a  stress  gradually  applied. 


ELASTIC    LIMIT   AND    YIELD    POINT. 


273 


Elastic  Limit.  —  The  elastic  limit  is  defined  as  that  load  at  which 
the  deformations  cease  to  be  proportional  to  the  stresses,  or  at  which 
the  rate  of  stretch  (or  other  deformation)  begins  to  increase.  It  is  also 
defined  as  the  load  at  which  a  permanent  set  first  becomes  visible.  The 
last  definition  is  not  considered  as  good  as  the  first,  as  it  is  found  that  with 
some  materials  a  set  occurs  with  any  load,  no  matter  how  small,  and  that 
with  others  a  set  which  might  be  called  permanent  vanishes  with  lapse  of 
time,  and  as  it  is  impossible  to  get  the  point  of  first  set  without  removing 
the  whole  load  after  each  increase  of  load,  which  is  frequently  inconven- 
ient. The  elastic  limit,  defined,  however,  as  that  stress  at  which  the 
extensions  begin  to  increase  at  a  higher  rate  than  the  applied  stresses, 
usually  corresponds  very  nearly  with  the  point  of  first  measurable  per- 
manent set. 

Apparent  Elastic  TJmit.  —  Prof.  J.  B.  Johnson  (Materials  of  Con- 
struction, p.  19)  defines  the  "  apparent  elastic  limit  "  as  "  the  point  on  the 
stress  diagram  [a  plotted  diagram  in  which  the  ordinates  represent  loads 
and  the  abscissas  the  corresponding  elongations]  at  which  the  rate  of 
deformation  is  50%  greater  than  it  is  at  the  origin,"  [the  minimum  rate]. 
An  equivalent  definition,  proposed  by  the  author,  is  that  point  at  which 
the  modulus  of  extension  (length  X  increment  of  load  per  unit  of  section 
-=-  increment  of  elongation)  is  two  thirds  of  the  maximum.  Fcr  steel, 
with  a  modulus  of  elasticity  of  30,000,000,  this  is  equivalent  to  that 
point  at  which  the  increase  of  elongation  in  an  8-inch  specimen  for  1000 
Ibs.  per  sq.  in.  increase  of  load  is  0.0004  in. 

Yield-point.  —  The  term  yield-point  has  recently  been  introduced  into 
the  literature  of  the  strength  of  materials.  It  is  defined  as  that  point  at 
which  the  rate  of  stretch  suddenly  increases  rapidly  with  no  increase  of 
the  load.  The  difference  between  the  elastic  limit,  strictly  defined  as 
the  point  at  which  the  rate  of  stretch  begins  to  increase,  and  the  yield- 
point,  may  in  some  cases  be  considerable.  This  difference,  however,  will 
not  be  discovered  in  short  test-pieces  unless  the  readings  of  elongations 
are  made  by  an  exceedingly  fine  instrument,  as  a  micrometer  reading  to 
0.0001  inch.  In  using  a  coarser  instrument,  such  as  calipers  reading  to 
1/100  of  an  inch,  the  elastic  limit  and  the  yield-point  will  appear  to  be 
simultaneous.  Unfortunately  for  precision  of  language,  the  term  yield- 
point  was  not  introduced  until  long  after  the  term  elastic  limit  had  been 
almost  universally  adopted  to  signify  the  same  physical  fact  which  is  now 
defined  by  the  term  yield-point,  that  is,  not  the  point  at  which  the  first 
change  in  rate,  observable  9iily  by  a  microscope,  occurs,  but  that  later 
point  (more  or  less  indefinite  as  to  its^  precise  position)  at  which  the 
increase  is  great  enough  to  be  seen  by  the  naked  eve.  A  most  convenient 
method  of  determining  the  point  at  which  a  sudden  increase  of  rate  of 
stretch  occurs  in  short  specimens,  when  a  testing-machine  in  which  the 
pulling  is  done  by  screws  is  used,  is  to  note  the  weight  on  the  beam  at 
the  instant  that  the  beam  "drops."  During  the  earlier  portion  of  the 
test,  as  the  extension  is  steadily  increased  by  the  uniform  but  slow  rota- 
tion of  the  screws,  the  poise  is  moved  steadily  along  the  beam  to  keep  it 
in  equipoise;  suddenly  a  point  is  reached  at  which  the  beam  drops,  and 
will  not  rise  until  the  elongation  has  been  considerably  increased  by  the 
further  rotation  of  the  screws,  the  advancing  of  the  poise  meanwhile 
being  suspended.  This  point  corresponds  practically  to  the  point  at  which 
the  rate  of  elongation  suddenly  increases,  and  to  the  point  at  which 
an  appreciable  permanent  set  is  first  found.  It  is  also  the  point 
which  has  hitherto  been  called  in  practice  and  in  text-books  the  elastic 
limit,  and  it  will  probably  continue  to  be  so  called,  although  the  use  9f 
the  newer  term  "  yield-point "  for  it,  and  the  restriction  of  the  term  elastic 
limit  to  mean  the  earlier  point  at  which  the  rate  of  stretch  begins  to 
increase,  as  determinable  only  by  micrometric  measurements,  is  more 
precise  and  scientific.  In  order  to  obtain  the  yield-point  by  the  drop  of 
the  beam  with  approximate  accuracy,  the  screws  of  the  testing  machine 
must  be  run  very  slowly  as  the  yield-point  is  approached,  so  as  to  cause 
an  elongation  of  not  more  than,  say,  0.005  in.  per  minute. 

In  tables  of  strength  of  materials  hereafter  given,  the  term  elastic  limit 
is  used  in  its  customary  meaning,  the  point  at  which  the  rate  of  stress  has 
begun  to  increase  as  pbservable  by  ordinary  instruments  or  by  the  drop  of 
the  beam.  With  this  definition  it  is  practically  synonymous  with  yield- 
point. 


274  STRENGTH    <  >F    MATERIALS. 

Coefficient  (or  Modiilii-0  of  Klasticity.  --This  is  a  term  express- 
ing  the  relation  between  the  amount  of  extension  or  compression  of  a  mate- 
rial and  the  load  producing  that  extension  or  compression. 

It  is  defined  as  the  load  per  unit  of  section  divided  bv  the  extension  per 
unit  of  length. 

Let  P  be  the  applied  load,  k  the  sectional  area  of  the  piece,  I  the  length 
of  the  part  extended,  A  the  amount  of  the  extension,  and  E  the  coefficient 
of  elasticity.  Then  P  •*•  k  =  the  load  on  a  unit  of  section;  A  ~  /  =  the 
elongation  of  a  unit  of  length. 

p  •  A      Pl 


The  coefficient  of  elasticity  is  sometimes  denned  as  the  figure  ex: 


slant.  This  definition  follows  from  the  formula  above  given,  thus: 
If  k  =  one  square  inch.  (  and  A  each  =  one  inch,  then  E  =  P. 

Within  the  elastic  limit,  when  the  deformations  are  proportional  to  the 
stresses,  the  coefficient  of  elasticity  is  constant,  but  beyond  the  elastic 
..imit  it  decreases  rapidly. 

In  cast  iron  there  is  generally  no  apparent  limit  of  elasticity,  the  defor- 
mations increasing  at  a  faster  rate  than  th«  .rid  a  permanent 

set  being  produced  by  small  loads.  The  coefficient  of  elasticity  therefore 
is  not  constant  during  any  portion  of  a  test,  but  grows  smaller  as  the  load 
increases.  The  same  is  true  in  the  case  of  timber.  In  wrought  iron  and 
steelj  however,  there  is  a  well-defined  elastic  limit,  and  the  coefficient  of 
elasticity  within  that  limit  is  nearly  constant. 

Resilience,  or  Work  of  Resistance  of  a  Material.  —  Within  the 
elastic  limit,  the  resistance  increasing  uniformly  from  zero  stress  to  the 
stress  at  the  elastic  limit  .  the  work  done  by  a  load  applied  gradually  is 
equal  to  one  half  the  product  of  the  final  stress  by  the  extension  or  other 
deformation.  Beyond  the  elastic  limit,  the  extensions  increasing  more 
rapidly  than  the  loads,  and  the  strain  diagram  (a  plotted  diagram  showing 
the  relation  of  extensions  to  stresses)  approximating  a  parabolic  form,  the 
work  is  approximately  equal  to  two  thirds  the  product  of  the  maximum 
stress  by  the  extension. 

The  amount  of  work  required  to  break  a  bar,  measured  usually  in  inch- 
pounds,  is  called  its  resilience:  the  work  required  to  strain  it  to  the  elastic 
limit  is  called  its  elastic  resilience.  (See  below.) 

Under  a  load  applied  suddenly  the  momentary  elastic  distortion  is 
equal  to  twice  that  caused  by  the  same  load  applied  gradually. 

When  a  solid  material  is  exposed  to  percussive  stress,  as  when  a  weight 
falls  upon  a  beam  transversely,  the  work  of  resistance  is  measured  by  the 
product  of  the  weight  into  the  total  fall. 

Elastic  Resilience.  —  In  a  rectangular  beam  tested  by  transverse 
stressrsupported  at  the  ends  and  loaded  in  the  middle, 


in  which,  if  P  is  the  load  in  pounds  at  the  elastic  limit.  R  =  the  modulus  of 
transverse  strength,  or  the  stress  on  the  extreme  fibre,  at  the  elastic  limit, 
B  =  modulus  of  elasticity,  A  =  deflection,  I,  6,  and  <1  =  length,  breadth. 
and  depth  in  inches.     Substituting  for  P  ia  (2)  its  value  in  (1),  A=  ] 
+  Ed. 

The  elastic  resilience  =  half  the  product  of  the  load  and  deflection  = 
l/2P  A,  and  the  elastic  resilience  per  cubic  inch  =  1/2  PA  -5-  Ibd. 

Substituting  the  values  of  P  and  A,  this  reduces  to  elastic  resilience  per 

1      02 

cubic  inch  =  —  =,  w  ,  which  is  independent  of  the  dimensions;  and  therefore 

18  bj 

the  elastic  resilience  per  cubic  inch  for  transverse  strain  may  be  used  as  a 
modulus  expressing  one  valuable  quality  of  a  material, 


ELEVATION    OF   THE    ELASTIC    LIMIT.  275 

Similarly  for  tension:  Let  P  =  tensile  stress  in  pounds  per  square  inch 
at  the  elastic  limit;  e  =  elongation  per  unit  of  length  at  the  elastic  limit: 
E  =  modulus  of  elasticity  =  P  -*-  e\  whence  e  =  P  +  E 

Then  elastic  resilience  per  cubic  inch  =  1/2  Pe  =  5  #~ 

Elevation    of   Ultimate  Resistance   and  Elastic   Limit.  —  It  was 

first  observed  by  Prof.  R.  H.  Thurston,  and  Commander  L.  A.  Beardslee, 
U.S.  N.,  independently,  in  1873,  that  if  wrought  iron  be  subjected  to  a 
stress  beyond  its  elastic  limit,  but  not  beyond  its  ultimate  resistance,  and 
then  allowed  to  "rest"  for  a  definite  interval  of  time  a  considerable 
increase  of  elastic  limit  and  ultimate  resistance  may  be  experienced.  In 
other  words,  the  application  of  stress  and  subsequent  "rest"  increases 
the  resistance  of  wrought  iron.  This  "rest"  may  be  an  entire  release 
from  stress  or  a  simple  holding  the  test-piece  at  a  given  intensity  of 
stress. 

Commander  Beardslee  prepared  twelve  specimens  and  subjected  them 
to  a  stress  equal  to  the  ultimate  resistance  of  the  material,  vuthout 
breaking  the  specimens.  These  were  then  allowed  to  rest,  entirely  free 
from  stress,  from  24  to  30  hours,  after  which  they  were  again  stressed 
until  broken.  The  gain  in  ultimate  resistance  by  the  rest  was  found  to 
vary  from  4.4  to  17  per  cent. 

This  elevation  of  elastic  and  ultimate  resistance  appears  to  be  peculiar 
to  iron  and  steel;  it  has  not  been  found  in  other  metals. 

Relation  of  the  Elastic  Limit  to  Endurance  under  Repeated 
Stresses  (condensed  from  Engineering,  August  7,  1891).  —  When  engi- 
neers first  began  to  test  materials,  it  was  soon  recognized  that  if  a  speci- 
men was  loaded  beypnd  a  certain  point  it  did  not  recover  its  original 
dimensions  on  removing  the  load,  but  took  a  permanent  set;  this  point 
was  called  the  elastic  limit.  Since  below  this  point  a  bar  appeared  to 
recover  completely  its  original  form  and  dimensions  on  removing  the 
load,  it  appeared  obvious  that  it  had  not  been  injured  by  the  load,  and 
hence  the  working  load  might  be  deduced  from  the  elastic  limit  by  using 
a  small  factor  of  safety. 

Experience  showed,  however,  that  in  many  cases  a  bar  would  not  carry 
safely  a  stress  anywhere  near  the  elastic  limit  of  the  material  as-  deter- 
mined by  these  experiments,  and  the  whole  theory  of  any  connection 
between  the  elastic  limit  of  a  bar  and  its  working  load  became  almost 
discredited,  and  engineers  employed  the  ultimate  strength  only  in  deduc- 
ing the  safe  working  load  to  which  their  structures  might  be  subjected. 
Still,  as  experience  accumulated  it  was  observed  that  a  higher  factor  of 
safety  was  required  for  a  live  load  than  for  a  dead  one. 

In  1871  Wohler  published  the  results  of  a  number  of  experiments  on 
bars  of  iron  and  steel  subjected  to  live  loads.  In  these  experiments  the 
stresses  were  put  on  and  removed  from  the  specimens  without  impact, 
but  it  was,  nevertheless,  found  that  the  breaking  stress  of  the  materials 
was  in  every  case  much  below  the  statical  breaking  load.  Thus,  a  bar 
of  Krupp's  axle  steel  having  a  tenacity  of  49  tons  per  square  inch  broke 
with  a  stress  of  28.6  tons  per  square  inch,  when  the  load  was  completely 
removed  and  replaced  without  impact  170,000  times.  These  expenments 
were  made  on  a  large  number  of  different  brands  of  iron  and  steel,  and 
the  results  were  concordant  in  showing  that  a  bar  would  break  with  an 
alternating  stress  of  only,  say,  one  third  the  statical  breaking  strength  of 
the  material,  if  the  repetitions  of  stress  were  sufficiently  numerous.  At 
the  same  time,  however,  it  appeared  from  the  general  trend  of  the  experi- 
ments that  a  bar  would  stand  an  indefinite  number  of  alternations  of 
stress,  provided  the  stress  was  kept  below  the  limit. 

Prof.  Bauschinger  defines  the  elastic  limit  as  the  point  at  which  stress 
ceases  to  be  sensibly  proportional  to  extension,  the  latter  being  measured 
with  a  mirror  apparatus  reading  to  1/5000  of  a  millimetre,  or  about 
1/100000  in.  This  limit  is  always  below  the  yield-point,  and  may  on 
occasion  be  zero.  On  loading  a  bar  above  the  yield -point,  this  point 
rises  with  the  stress,  and  the  rise  continues  for  weeks,  months,  and 
possibly  for  years  if  the  bar  is  left  at  rest  under  its  load.  On  the  other 
hand,  when  a  bar  is  loaded  beyond  its  true  elastic  limit,  but  below  its 
yield-point,  this  limit  rises,  but  reaches  a  maximum  as  the  yield-point  is 
approached,  and  then  falls  rapidly,  reaching  even  to  zero.  On  leaving 
the  bar  at  rest  under  a  stress  exceeding  that  of  tys  primitive 


276 


STRENGTH    OF  MATERIALS. 


down  point  the  elastic  limit  begins  to  rise  again,  and  may,  if  left  a  sufifl* 
cient  time,  rise  to  a  point  much  exceeding  its  previous  value. 

A  bar  has  two  limits  of  elasticity,  one  for  tension  and  one  for  com- 
pression. Bauschinger  loaded  a  number  of  bars  in  tension  until  stress 
ceased  to  be  sensibly  proportional  to  deformation.  The  load  was  then 
removed  and  the  bar  tested  in  compression  until  the  elastic  limit  in  this 
direction  had  been  exceeded.  This  process  raises  the  elastic  limit  in 
compression,  as  would  be  found  on  testing  the  bar  in  compression  a  second 
time.  In  place  of  this,  however,  it  was  now  again  tested  in  tension,  when 
it  was  found  that  the  artificial  raising  of  the  limit  in  compression  had 
lowered  that  in  tension  below  its  previous  value.  By  repeating  the 
process  of  alternately  testing  in  tension  and  compression,  the  two  limits 
took  up  points  at  equal  distances  from  the  line  of  no  load,  both  in  tension 
and  compression.  These  limits  Bauschinger  calls  natural  elastic  limits 
of  the  bar,  which  for  wrought  iron  correspond  to  a  stress  of  about  81/2  tons 
per  square  inch,  but  this  is  practically  the  limiting  load  to  which  a  bar 
of  the  same  material  can  be  strained  alternately  in  tension  and  com- 
pression, without  breaking  when  the  loading  is  repeated  sufficiently  often, 
as  determined  by  Wohler's  method. 

As  received  from  the  rolls  the  elastic  limit  of  the  bar  in  tension  is  above 
the  natural  elastic  limit  of  the  bar  as  defined  by  Bauschinger,  having  been 
artificially  raised  by  the  deformations  to  which  it  has  been  subjected  in 
the  process  of  manufacture.  Hence,  when  subjected  to  alternating 
stresses,  the  limit  in  tension  is  immediately  lowered,  while  that  in  com- 
pression is  raised  until  they  both  correspond  to  equal  loads.  Hence,  in 
Wohler's  experiments,  in  which  the  bars  broke  at  loads  nominally  below 
the  elastic  limits  of  the  material,  there  is  every  reason  for  concluding  that 
the  loads  were  really  greater  than  true  elastic  limits  of  the  material. 
This  is  confirmed  by  tests  on  the  connecting-rods  of  engines,  which  work 
under  alternating  stresses  of  equal  intensity.  Careful  experiments  on 
old  rods  show  that  the  elastic  limit  in-  compression  is  the  same  as  that  in 
tension,  and  that  both  are  far  below  the  tension  elastic  limit  of  the 
material  as  received  from  the  rolls. 

The  common  opinion  that  straining  a  metal  beyond  its  elastic  limit 
injures  it  appears  to  be  untrue.  It  is  not  the  mere  straining  of  a  metal 
beyond  one  elastic  limit  that  injures  it,  but  the  straining,  many  times 
repeated,  beyond  its  two  elastic  limits.  Sir  Benjamin  Baker  has  shown 
that  in  bending  a  shell  plate  for  a  boiler  the  metal  is  of  necessity  strained 
beyond  its  elastic  limit,  so  that  stresses  of  as  much  as  7  tons  to  15  tons 
per  square  inch  may  obtain  in  it  as  it  comes  from  the  rolls,  and  unless  the 
plate  is  annealed,  these  stresses  will  still  exist  after  it  has  been  built  into 
the  boiler.  In  such  a  case,  however,  when  exposed  to  the  additional  - 
stress  due  to  the  pressure  inside  the  boiler,  the  overstrained  portions  of 
the  plate  will  relieve  themselves  by  stretching  and  taking  a  permanent 
set,  so  that  probably  after  a  year's  working  very  little  difference  could  be 
detected  in  the  stresses  in  a  plate  built  into  the  boiler  as  it  came  from  the 
bending  rolls,  and  in  one  which  had  been  annealed,  before  riveting  into 
lace,  and  the  first,  in  spite  of  its  having  been  strained  beyond  its  elastic 
mits,  and  not  subsequently  annealed,  would  be  as  strong  as  the  other. 


p 
li 


Resistance  of  Metals  to  Repeated  Shocks. 

More  than  twelve  years  were  spent  by  Wohler  at  the  instance  of  the 
Prussian  Government  in  experimenting  upon  the  resistance  of  iron  and 
steel  to  repeated  stresses.  The  results  of  his  experiments  are  expressed 
in  what  is  known  as  Wohler's  law,  which  is  given  in  the  following  words 
in  Dubois's  translation  of  Weyrauch: 

"  Rupture  may  be  caused  not  only  by  a  steady  load  which  exceeds  the 
carrying  strength,  but  also  by  repeated  applications  of  stresses,  none  of 
which  are  equal  to  the  carrying  strength.  The  differences  of  these  stresses 
are  measures  of  the  disturbance  of  continuity,  in  so  far  as  by  their  increase 
the  minimum  stress  which  is  still  necessary  for  rupture  diminishes." 

A  practical  illustration  of  the  meaning  of  the  first  portion  of  this  law 
may  be  given  thus:  If  50,000  pounds  once  applied  will  just  break  a  bar 
of  iron  or  steel,  a  stress  very  much  less  than  50,000  pounds  will  break  it 
if  repeated  sufficiently  often. 


EFFECT   OF   VIBEATION  AND  LOAD.  277 

|  This  is  fully  confirmed  by  the  experiments  of  Fairbairn  and  Spangenberg, 
as  well  as  those  of  Wohler;  and,  as  is  remarked  by  Weyrauch,  it  may  be 
considered  as  a  long-known  result  of  common  experience.  It  partially 
accounts  for  what  Mr.  Holley  has  called  the  "intrinsically  ridiculous 
factor  of  safety  of  six." 

Another  "  long-known  result  of  experience"  is  the  fact  that  rupture  may 
be  caused  by  a  succession  of  shocks  or  impacts,  none  of  which  alone  would 
be  sufficient  to  cause  it.  Iron  axles,  the  piston-rods  of  steam  hammers, 
and  other  pieces  of  metal  subject  to  continuously  repeated  shocks, 
invariably  break  after  a  certain  length  of  service.  They  have  a  "life" 
which  is  limited. 

Several  years  ago  Fairbairn  wrote:   "  We  know   that   in  some  cases 
•.  wrought  iron  subjected  to  C9ntinuous  vibration   assumes  a  crystalline 
structure,  and  that  the  cohesive  powers  are  much  deteriorated,  but  we 
j  are  ignorant  of  the  causes  of  this  change."     We  are  still  ignorant,  not 
i  only  of  the  causes  of  this  change,  but  of  the  conditions  under  which  it 
i  takes  place.     Who  knows  whether  wrought  iron  subjected  to  very  slight 
continuous  vibration  will   endure   forever?   or   whether   to   insure  final 
i  rupture  each  of  the  continuous  small  shocks  must  amount  at  least  to  a 
f  certain  percentage  of  single  heavy  shock  (both  measured  in  foot-ppunds), 
which  would  cause  rupture  with  one  application?     Wohler  found  in  test- 
ing iron  by  repeated    stresses   (not   impacts)    that   in  one  case  400,000 
applications  of  a  stress  of  500  centners  to  the  square  inch  caused  rupture, 
!  while  a  similar  bar  remained  sound  after-  48,000,000  applications  of  a 
stress  of  300  centners  to  the  square  inch  (1  centner  =  110.2  Ibs.). 

Who  knows  whether  or  not  a  similar  law  holds  true  in  regard  to  repeated 
!..  shocks?     Suppose  that  a  bar  of  iron  would  break  under  a  single  impact  of 
f  1000  foot-pounds,  how  many  times  would  it  be  likely  to  bear  the  repetition 
I  of  100  foot-pounds,  or  would  it  be  safe  to  allow  it  to  remain  for  fifty  years 
subjected  to  a  continual  succession  of  blows  of  even  10  foot-pounds  each? 
Mr.  William  Metcalf  published  in  the  Metallurgical  Review,  Dec.,  1877, 
the  results  of  some  tests  of  the  life  of  steel  of  different  percentages  of 
1  carbon  under  impact.     Some  small  steel  pitmans  were  made,  the  specifi- 
cations for  which  required  that  the  unloaded  machine  should  run  4^ 
I   hours  at  the  rate  of  1200  revolutions  per  minute  before  breaking. 

The  steel  was  all  of  uniform  quality,  except  as  to  carbon.  Here  are  the 
results.  The 

0.30  C.  ran     1  h.  21  m.     Heated  and  bent  before  breaking. 

0.49  C.  1  h.  28  m. 

0.53  C.  4  h.  57  m.     Broke  without  heating. 

0.65  C.  3  h.  50  m.     Broke  at  weld  where  imperfect. 

0.80  C.  5  h.  40  m. 

0.84  C.  18  h. 

0.87  C.  Broke  in  weld  near  the  end. 

0.96  C.  Ran  4.55  m.,  and  the  macnine  broke  down. 

Some  other  experiments  by  Mr.  Metcalf  confirmed  his  conclusion,  viz. 
that  high-carbon  steel  was  better  adapted  to  resist  repeated  shocks  and 
vibrations  than  low-carbon  steel. 

These  results,  however,  would  scarcely  be  sufficient  to  induce  any 
engineer  to  use  0.84  carbon  steel  in  a  car-axle  or  a  bridge-rod.  Further 
experiments  are  needed  to  confirm  or  overthrow  them. 

(See  description  of  proposed  apparatus  for  such  an  investigation  in  the 
author's  paper  in  Trans.  A.  /.  M.  E.,  vol.  viii,  p.  76,  from  which  the  above 
extract  is  taken.) 

Effect  of  Vibration  and  Load  on  Steel.  (Prof.  P.  R.  Alger,  U.  S. 
Navy,  U.  S.  Naval  Inst.  Proc.,  Dec.,  1910.)— In  1883,  or  thereabouts, 
a  test  of  the  theory  that  guns  are  weakened  by  the  shock  and  vibration 
of  repeated  firing  was  made  at  the  Washington  Navy  Yard  as  follows: 
Heavy  weights,  sufficient  to  strain  the  wire  nearly  to  its  elastic  limit, 
were  suspended  by  pieces  of  wire,  and  small  hammers  were  arranged 

that,  actuated  by  the  machinery  of  the  shop,  they  struck  the  taut 
wires  at  regular  and  frequent  intervals.  After  months  of  constant 
vibration,  all  the  time  under  severe  strain,  the  wires,  when  tested 
showed  unchanged  physical  qualities.  Moreover,  every  gun,  army 
and  navy,  that  has  suffered  accident,  since  we  first  began  to  build 


278  STKENGTH   OF  MATERIALS. 

steel  guns,  has  had  the  metal  of  the  part  that  failed  tested,  and  neve* 
has  there  been  a  case  when  any  material  difference  was  found  between 
the  physical  qualities  shown  by  the  last  tests  and  those  shown  by  the 
original  tests  for  acceptance.  One  of  these  guns,  a  12-in.,  had  been 
fired  481  rounds  when  its  muzzle  was  blown  off.  (The  fact  stated  in 
the  last  sentence  tends  to  confirm  the  "theory"  that  guns  are  weakened 
by  repeated  firing,  although  the  weakening  may  not  be  discovered  by 
physical  tests.) 

Stresses  Produced  by  Suddenly  Applied  Forces  and  Shocks. 

(Mansfield  Merriman,  R.  R.  &  Eng.  Jour.,  Dec.,  1889.) 

Let  P  be  the  weight  which  is  dropped  from  a  height  h  upon  the  end  of  a 
bar,  and  let  y  be  the  maximum  elongation  which  is  produced.  The  work 
performed  by  the  falling  weight,  then,  is  W  =  P(h  +  y),  and  this  must 
equal  the  internal  work  of  the  resisting  molecular  stresses.  The  stress  in 
the  bar,  which  is  at  first  0,  increases  up  to  a  certain  limit  Q,  which  is 
greater  than  P;  and  if  the  elastic  limit  be  not  exceeded  the  elongation 
increases  uniformly  with  the  stress,  so  that  the  internal  work  is  equal  to 
the  mean  stress  1/2  Q  multiplied  by  the  total  elongation  y,  or  TP=i/2  Qv. 
Whence,  neglecting  the  work  that  may  be  dissipated  in  heat, 

J/2  Qy  =  Ph  +  Py. 

If  e  be  the  elongation  due  to  the  static  load  P,  within  the  elastic  limit 
V  =  -pe;  whence  Q  =  P  (l  +  y  1  +2-V  which  gives  the  momentary 
maximum  stress.  Substituting  this  value  of  Q,  there  results  y  =  e 
fl  +  y  1  +2-V  which  is  the  value  of  the  momentary  maximum  elon- 
gation. 

A  shock  results  when  the  force  P,  before  its  action  on  the  bar,  is  moving 
with  velocity,  as  is  the  case  when  a  weight  P  falls  from  a  height  h.  The 
above  formulas  show  that  this  height  h  may  be  small  if  e  is  a  small  quan- 
tity, and  yet  very  great  stresses  and  deformations  be  produced.  For 
Instance,  let  h  =  4e,  then  Q  =  4P  and  y  =  4e;  also  let  h  =  12e,  then 
Q  =  6P  and  y  =  6e.  Or  take  a  wrought-iron  bar  1  in.  square  and  5  ft. 
long:  under  a  steady  load  of  5000  Ibs.  this  will  be  compressed  about  0.012 
in.,  supposing  that  no  lateral  flexure  occurs;,  but  if  a  weight  of  5000  Ibs. 
drops  upon  its  end  from  the  small  height  of  0.048  in.  there  will  be  produced 
the  stress  of  20,000  Ibs. 

A  suddenly  applied  force  is  one  which  acts  with  the  uniform  intensity  P 
upon  the  end  of  the  bar,  but  which  has  no  velocity  before  acting  upon  it. 
This  corresponds  to  the  case  of  h  =  0  in  the  above  formulas,  and  gives 
Q  =  2P  and  y  =  2e  for  the  maximum  stress  and  maximum  deforma- 
tion. Probably  the  action  of  a  rapidly  moving  train  upon  a  bridge 
produces  stresses  of  this  character.  For  a  further  discussion  of  this 
subject,  in  which  the  inertia  of  the  bar  is  considered,  see  Merriman's 
Mechanics  of  Materials,  10th  ed.,  1908. 


TENSILE  STRENGTH. 

The  following  data  are  usually  obtained  in  testing  by  tension  in  a  testing- 
machine  a  sample  of  a  material  of  construction: 

The  load  and  the  amount  of  extension  at  the  elastic  limit. 

The  maximum  load  applied  before  rupture. 

The  elongation  of  the  piece,  measured  between  gauge-marks, placed  a 
stated  distance  apart  before  the  test;  and  the  reduction  of  area  at  the 
point  of  fracture. 

The  load  at  the  elastic  limit  and  the  maximum  load  are  recorded  in 
pounds  per  square  inch  of  the  original  area.  The  elongation  is  recorded 
as  a  percentage  of  the  stated  length  between  the  gauge-marks,  and  the 
reduction  of  area  as  a  percentage  of  the  original  area.  The  coefficient  of 
elasticity  is  calculated  from  the  ratio  the  extension  within  the  elastic 


PRECAUTIONS  IN  MAKING  TENSILE  TESTS.         279 


limit  per  inch  of  length  bears  to  the  load  per  square  inch  producing  that 
extension. 

On  account  of  the  difficulty  of  making  accurate  measurements  of  the 
fractured  area  of  a  test-piece,  and  of  the  fact  that  elongation  is  more 
valuable  than  reduction  of  area  as  a  measure  of  ductility  and  of  resilience 
or  work  of  resistance  before  rupture,  modern  experimenters  are  abandoning 
the  custom  of  reporting  reduction  of  area.  The  data  now  calculated 
from  th?  results  of  a  tensile  test  for  commercial  purposes  are:  1.  Tensile 
strength  in  pounds  per  square  inch  of  original  area.  2.  Elongation  per 
cent  of  a  stated  length  between  gauge-marks,  usually  8  inches.  3.  Elastic 
limit  in  pounds  per  square  inch  of  original  area. 

The  short  or  grooved  test  specimen  gives  with  most  metals,  especially 
with  wrought  iron  and  steel,  an  apparent  tensile  strength  much  higher 
than  the  real  strength.  This  form  of  test-piece  is  now  almost  entirely 
abandoned.  Pieces  2  in.  in  length  between  marks  are  used  for  forgings. 

The  following  results  of  the  tests  of  six  specimens  from  the  same  i/4-in. 
steel  bar  illustrate  the  apparent  elevation  of  elastic  limit  and  the  changes 
in  other  properties  due  to  change  in  length  of  stems  which  were  turned 
down  in  each  specimen  to  0.798  in.  diameter.  (Jas.  E.  Howard,  Eng. 
Congress  1893,  Section  G.) 


Description  of  Stem. 

Elastic  Limit, 
Lbs.  per  Sq.  In. 

Tensile  Strength, 
Lbs.  per  Sq.  In. 

Contraction  of 
Area,  per  cent. 

1  .00  in.  long  

64,900 

94,400 

49.0 

0  50  in.  long  

65,320 

97,800 

43.4 

68,000 

102,420 

39.6 

Semicircular  groove,  0.4 

75,000 

116,380 

31.6 

Semicircular  groove,  1/8 

86,000,  about 

134,960 

23.0 

V-shaped  groove  

90,000,  about 

117,000 

Indeterminate. 

Test  plates  made  by  the  author  in  1879  of  straight  and  grooved  test- 
pieces  of  boiler-plate  steel  cut  from  the  same  gave  the  following  results: 

5  straight  pieces,  56,605  to  59,012  Ibs.  T.  S.    Aver.  57,566  Ibs. 

4  grooved     "         64,341  to  67,400    "       "  "      65,452  " 

Excess  of  the  short  or  grooved  specimen,  21  per  cent,  or  12,114  Ibs. 

Measurement  of  Elongation.  —  In  order  to  be  able  to  compare 
records  of  elongation,  it  is  necessary  not  only  to  have  a  uniform  length  of 
section  between  gauge-marks  (say  8  inches),  but  to  adopt  a  uniform 
method  of  measuring  the  elongation  to  compensate  for  the  difference 
between  the  apparent  elongation  when  the  piece  breaks  near  one  of  the 
gauge-marks,  and  when  it  breaks  midway  between  them.  The  following 
method  is  recommended  (Trans.  A.  S.  M.  E.,  vol.  xi,  p.  622): 

Mark  on  the  specimen  divisions  of  1/2  inch  each.  After  fracture  measure 
from  the  point  of  fracture  the  length  of  8  of  the  marked  spaces  on  each 
fractured  portion  (or  7  +  on  one  side  and  8  4-  on  the  other  if  the  fracture 
is  not  at  one  of  the  marks).  The  sum  of  these  measurements,  less  8 
inches,  is  the  elongation  of  8  inches  of  the  original  length.  If  the  fracture 
is  so  near  one  end  of  the  specimen  that  7  +  spaces  are  not  left  on  the 
shorter  portion,  then  take  the  measurement  of  as  many  spaces  (with  the 
fractional  part  next  to  the  fracture)  as  are  left,  and  for  the  spaces  lacking 
add  the  measurement  of  as  many  corresponding  spaces  of  the  longer 
portion  as  are  necessary  to  make  the  7  -f-  spaces. 

Precautions  Required  in  making  Tensile  Tests. — The  testing- 
machine  itself  should  be  tested,  to  determine  whether  its  weighing 
apparatus  is  accurate,  and  whether  it  is  so  made  and  adjusted  that 
in  the  test  of  a  properly  made  specimen  the  line  of  strain  of  the  testing- 
machine  is  absolutely  in  line  with  the  axis  of  the  specimen. 


280 


STRENGTH   OF  MATERIALS. 


The  specimen  should  be  so  shaped  that  it  will  not  give  an  incorrect 
record  of  strength. 

It  should  be  of  uniform  minimum  section  for  not  less  than  eight  inches 
of  its  length.  Eight  inches  is  the  standard  length  for  bars.  For  forgings 
and  castings  and  in  special  cases  shorter  lengths  are  used;  these  show 
greater  percentages  of  elongation,  and  the  length  between  gauge  marks 
should  therefore  always  be  stated  in  the  record. 

Regard  must  be  had  to  the  time  occupied  in  making  tests  of  certain 
materials.  Wrought  iron  and  soft  steel  can  be  made  to  show  a  higher 
than  their  actual  apparent  strength  by  keeping  them  under  strain  for  a 
great  length  of  time. 

In  testing  soft  alloys,  copper,  tin,  zinc,  and  the  like,  which  flow  under 
constant  strain,  their  highest  apparent  strength  is  obtained  by  testing 
them  rapidly.  In  recording  tests  of  such  materials  the  length  of  time 
occupied  in  the  test  should  be  stated. 

For  very  accurate  measurements  of  elongation,  corresponding  to  incre- 
ments of  load  during  the  tests,  the  electric  contact  micrometer,  described 
in  Trans.  A.  S.  M.  E.,  vol.  vi.  p.  479,  will  be  found  convenient.  When 
readings  of  elongation  are  then  taken  during  the  test,  a  strain  diagram 
may  be  plotted  from  the  reading,  which  is  useful  in  comparing  the  quali- 
ties of  different  specimens.  Such  strain  diagrams  are  made  automatically 
by  the  new  Olsen  testing-machine,  described  in  Jour.  Frank.  Inst.  1891. 

The  coefficient  of  elasticity  should  be  deduced  from  measurement 
observed  between  fixed  increments  of  load  per  unit  section,  say  between 
2000  and  12,000  pounds  per  square  inch  or  between  1000  and  11,000 
pounds  instead  of  between  0  and  10,000  pounds. 

Shapes  of  Specimens  for  Tensile  Tests.  —  The  shapes  shown  be- 
low were  recommended  by  the  author  in  1882  when  he  was  connected 
With  the  Pittsburgh  Testing  Laboratory.  They  are  now  in  most  general 
use;  the  earlier  forms,  with  5  inches  or  less  in  length  between  shoulders, 
being  almost  entirely  abandoned. 


No.  1.   Square  or  flat  bar.  as 
rolled. 


No.  2.     Round  bar,  as  rolled. 


No.  3.  Standard  shape  for 
flats  or  squares.  Fillets 
1/2  inch  radius. 

No.  4.  Standard  shape  for 
rounds.  Fillets  1/2  inch 
radius. 

No.  5.  Government  shape 
formerly  used  for  marine 
boiler-plates  of  iron.  Not 
recommended,  as  results 
are  generally  in  error. 


Increasing  the  Tensile  Strength  of  Iron  Bars  by  Twisting  them. 

—  Ernest  L.  Ransome  of  San  Francisco  obtained  a  patent,  in  1888,  for 
an  "improvement  in  strengthening  and  testing  wrought  metal  and  steel 
rods  or  bars,  consisting  in  twisting  the  same  in  a  cold  state.  .  .  .  Any 
defect  in  the  lamination  of  the  metal  which  would  otherwise  be  concealed 
is  revealed  by  twisting,  and  imperfections  are  shown  at  once.  The 
treatment  may  be  applied  to  bolts,  suspension-rods  or  bars  subjected  to 
tensile  strength  of  any  description." 
Jesse  J.  Shuman  (Am.  Soc.  Test.  Mat.,  1907)  describes  several  series  of 


COMPKESSIVE  STRENGTH.  281 

experiments  on  the  effect  of  twisting  square  steel  bars.     Following  are 
some  of  the  results: 

Soft  Bessemer  steel  bars  1/2  in.  square.    Tens.  Strength,  plain  bar,  60,400, 

No.  of  turns  per  foot 3  43/4  5  53/4          57/8 

Yield  point,  Ibs.  per  sq.  in 65,600     72,400     84,800     84,000     80,800 

Ult.  strength  "      "  "     83,200     89,600     92,000     90,000     88,800 

Elongation  in  8  in.,  % 10          5.75        6.25         7.5          3.75 

Bessemer,  0.25  carbon,  1/2 in.  sq.    Tens,  strength,  plain  bar,  75,000. 

No.  of  turns  per  foot 3          41/2          47/8  5  51/2 

Yield  point,  Ibs.  per  sq.  in 83,600     83,200     88,800     84,200    84,200 

Ult.  strength  "  "     99,600     99,200  104,000  102,000  100,800 

Elongation  in  8  in.,  % 8  4.5  4          5.75          6 

Bars  of  each  grade  twisted  off  when  given  more  turns  than  stated. 
Soft  Bessemer,  square  bars,  different  sizes. 

Size.in.sq 1/4    3/8    i/2      5/8     3/4    7/8     1     H/8li/4 

No.  of  turns  per  ft 4     31/23     21/4    1 1/2  1 V4    1       7/8    3/4 

Yield  rjint,  increase  %* 11182      6483      85.577      82      64      59 

Ult.  strength     "        %* 37  38.6  41  33.5  34.3  29.7  22.8  20.1  28.9 

*  Average  of  two  tests  each. 

Mr.  Schuman  recommends  that  in  twisting  bars  for  reinforced  concrete, 
in  order  not  to  be  in  danger  of  approaching  the  breaking  point,  the  num- 
ber of  turns  should  be  about  half  the  number  at  which  the  steel  is  at  its 
maximum  strength,  which  for  Bessemer  of  about  60,000  Ibs.  tensile 
strength  means  one-complete  twist  in  8  to  10  times  the  size  of  the  bar. 

Steel  bars  strengthened  by  twisting  are  largely  used  in  reinforced 
concrete. 

COMPRESSIVE  STRENGTH. 

What  is  meant  by  the  term  "compressive  strength"  has  not  yet  been 
settled  by  the  authorities,  and  there  exists  more  confusion  in  regard  to 
this  term  than  in  regard  to  any  other  used  by  writers  on  strength  of 
materials.  The  reason  of  this  may  be  easily  explained.  The  effect  of  a 
compressive  stress  upon  a  material  varies  with  the  nature  of  the  material, 
and  with  the  shape  and  size  of  the  specimen  tested.  While  the  effect  of  a> 
tensile  stress  is  to  produce  rupture  or  separation  of  particles  in  the  direc- 
tion of  the  line  of  strain,  the  effect  of  a  C9mpressive  stress  on  a  piece  of 
material  may  be  either  to  cause  it  to  fly  into  splinters,  to  separate  into 
two  or  more  wedge-shaped  pieces  and  fly  apart,  to  bulge,  buckle,  or  bend, 
or  to  flatten  out  and  utterly  resist  rupture  or  separation  of  particles.  A 
piece  of  speculum  metal  (copper  2,  tin  1)  under  compressive  stress  will 
exhibit  no  change  of  appearance  until  rupture  takes  place,  and  then  it 
will  fly  to  pieces  as  suddenly  as  if  blown  apart  by  gunpowder.  A  piece 
of  cast  iron  or  of  stone  will  generally  split  into  wedge-shaped  fragments. 
A  piece  of  wrought  iron  will  buckle  or  bend.  A  piece  of  wood  or  zinc 
may  bulge,  but  its  action  will  depend  upon  its  shape  and  size.  A  piece 
of  lead  will  flatten  out  and  resist  compression  till  the  last  degree;  that  is, 
the  more  it  is  compressed  the  greater  becomes  its  resistance. 

Air  and  other  gaseous  bodies  are  compressible  to  any  extent  as  long  as 
they  retain  the  gaseous  condition.  Water  not  confined  in  a  vessel  is  com- 
pressed by  its  own  weight  to  the  thickness  of  a  mere  film,  while  when 
confined  in  a  vessel  it  is  almost  incompressible. 

It  is  probable,  although  it  has  not  been  determined  experimentally, 
that  solid  bodies  when  confined  are  at  least  asr  incompressible  as  water. 
When  they  are  not  confined,  the  effect  of  a  compressive  stress  is  not  only 
to  shorten  them,  but  also  to  increase  their  lateral  dimensions  or  bulge 
them.  Lateral  stresses  are  therefore  induced  by  compressive  stresses. 

The  weight  per  square  inch  of  original  section  required  to  produce  any 
given  amount  or  percentage  of  shortening  of  any  material  is  not  a  constant 
quantity,  but  varies  with  both  the  length  and  the  sectional  area,  with  the 
shape  of  the  sectional  area,  and  with  the  relation  of  the  area  to  the  length. 
The  "compressive  strength"  of  a  material,  if  this  term  be  supposed  to 
mean  the  weight  in  pounds  per  square  inch  necessary  to  cause  runture, 
may  vary  with  every  size  and  shape  of  specimen  experimented  upon. 


282  STRENGTH   OF   MATERIALS. 

Still  more  difficult  would  it  be  to  state  what  is  the  " compressive  strength" 
of  a  material  which  does  not  rupture  at  all,  but  flattens  out.  Suppose  we 
are  testing  a  cylinder  of  a  soft  metal  like  lead,  two  inches  in  length  and 
one  inch  in  diameter,  a  certain  weight  will  shorten  it  one  per  cent,  another 
weight  ten  per  cent,  another  fifty  per  cent,  but  no  weight  that  we  can 
place  upon  it  will  rupture  it,  for  it  will  flatten  out  to  a  thin  sheet.  What, 
then,  is  its  compressive  strength?  Again,  a  similar  cylinder  of  soft 
wrought  iron  would  probably  compress  a  few  per  cent,  bulging  evenly 
all  around;  it  would  then  commence  to  bend,  but  at  first  the  bend  would 
be  imperceptilbe  to  the  eye  and  too  small  to  be  measured.  Soon  this 
bend  would  be  great  enough  to  be  noticed,  and  finally  the  piece  might  be 
bent  nearly  double,  or  otherwise  distorted.  What  is  the  "compressive 
strength"  of  this  piece  of  iron?  Is  it  the  weight  per  square  inch  which 
compresses  the  piece  one  per  cent  or  five  per  cent,  that  which  causes  th'e 
first  bending  (impossible  to  be  discovered),  or  that  which  causes  a  per- 
ceptible bend? 

As  showing  the  confusion  concerning  the  definitions  of  compressive 
strength,  the  following  statements  from  different  authorities  on  the 
strength  of  wrought  iron  are  of  interest. 

Wood's  Resistance  of  Materials  states,  "  Comparatively  few  experiments 
have  been  made  to  determine  how  much  wrought  iron  will  sustain  at  the 
point  of  crushing.  Hodgkinson  gives  65,000,  Rondulet  70,800,  Weisbach 
72,000,  Rankine  30,000  to  40,000.  It  is  generally  assumed  that  wrought 
iron  will  resist  about  two  thirds  as  much  crushing  as  to  tension,  but  the 
experiments  fail  to  give  a  very  definite  ratio." 

The  following  values,  said  to  be  deduced  from  the  experiments  of  Major 
Wade,  Hodgkinson,  and  Capt.  Meigs,  are  given  by  Haswell: 


American  wrought  iron  127,720  Ibs. 

"     (mean) 85,500  " 

™      ,.  u  (     65,200   " 

English  {     40!000  " 

Stoney  states  that  the  strength  of  short  pillars  of  any  given  material, 
all  having  the  same  diameter,  does  not  vary  much,  provided  the  length  of 
the  piece  is  not  less  than  one  and  does  not  exceed  four  or  five  diameters, 
and  that  the  weight  which  will  just  crush  a  short  prism  whose  base  equals 
one  square  inch,  and  whose  height  is  not  less  than  1  to  1V£  and  does  not 
exceed  4  or  5  diameters,  is  called  the  crushing  strength  of  the  material. 
It  would  be  well  if  experimenters  would  all  agree  upon  some  such  defi- 
nition of  the  term  "crushing  strength,"  and  insist  that  all  experiments 
which  are  made  for  the  purpose  of  testing  the  relative  values  of  different 
materials  in  compression  be  made  on  specimens  of  exactly  the  same 
shape  and  size.  An  arbitrary  size  and  shape  should  be  assumed  and 
agreed  upon  for  this  purpose.  The  size  mentioned  by  Stoney  is  definite 
as  regards  area  of  section,  viz.,  one  square  inch,  but  is  indefinite  as  re- 
gards length,  viz.,  from  one  to  five  diameters.  In  some  metals  a  speci- 
men five  diameters  long  would  bend,  and  give  a  much  lower  apparent 
strength  than  a  specimen  having  a  length  of  one  diameter.  The  words 
"will  just  crush"  are  also  indefinite  for  ductile  materials,  in  which  the 
resistance  increases  without  limit  if  the  piece  tested  does  not  bend.  In 
such  cases  the  weisht  which  causes  a  certain  percentage  of  compression, 
as  five,  ten,  or  fifty  per  cent,  should  be  assumed  as  the  crushing  strength. 

For  future  experiments  on  crushing  strength  three  things  are  desir- 
able: First,  an  arbitrary  standard  shape  and  size  of  test  specimen  for 
comparison  of  all  materials.  Secondly,  a  standard  limit  of  compression 
for  ductile  materials,  which  shall  be  considered  equivalent  to  fracture 
in  brittle  materials.  Thirdly,  an  accurate  knowledge  of  the  relation 
of  the  crushing  strength  of  a  specimen  of  standard  shape  and  size  to 
the  crushing  strength  of  specimens  of  all  other  shapes  and  sizes.  The 
latter  can  only  be  secured  by  a  very  extensive  and  accurate  series  of 
experiments  upon  all  kinds  of  materials,  and  on  specimens  of  a  great 
number  of  different  shapes  and  sizes. 

The  author  proposes,  as  a  standard  shape  and  size,  for  a  compressive 


COLUMNS,    PILLARS,    OH   STRUTS.  283 

test  specimen  for  all  metals,  a  cylinder  one  inch  in  length,  and  one  half 
square  inch  in  sectional  area,  or  0.798  inch  diameter;  and  for  the  limit 
of  compression  equivalent  to  fracture,  ten  per  cent  of  the  original  length. 
The  term  "  compressive  strength,"  or  "  compressive  strength  of  standard 
specimen,"  would  then  mean  the  weight  per  square  inch  required  to 
fracture  by  compressive  stress  a  cylinder  one  inch  long  and  0.798  inch 
diameter,  or  to  reduce  its  length  to  0.9  inch  if  fracture  does  not  take 
place  before  that  reduction  in  length  is  reached.  If  such  a  standard,  or 
any  standard  size  whatever,  had  been  used  by  the  earlier  authorities  on 
the  strength  of  materials,  we  never  would  have  had  such  discrepancies 
in  their  statements  in  regard  to  the  compressive  strength  of  wrought 
iron  as  those  given  ab9ve. 

The  reasons  why  this  particular  size  is  recommended  are:  that  the 
sectional  area,  one-half  square  inch,  is  as  large  as  can  be  taken  in  the 
ordinary  testing-machines  of  100,000  pounds  capacity,  to  include  all 
the  ordinary  metals  of  construction,  cast  and  wrought  iron,  and  the 
softer  steels;  and  that  the  length,  one  inch,  is  convenient  for  calcula- 
tion of  percentage  of  compression.  If  the  length  were  made  two  inches, 
many  materials  would  bend  in  testing,  and  give  incorrect  results.  Even 
in  cast  iron  Hodgkinson  found  as  the  mean  of  several  experiments  on 
various  grades,  tested  in  specimens  %  inch  in  height,  a  compressive 
strength  per  square  inch  of  94,730  pounds,  while  the  mean  of  the  same 
number  of  specimens  of  the  same  irons  tested  in  pieces  iy2  inches  in 
height  was  only  88., 800  pounds.  The  best  size  and  shape  of  standard 
specimen  should,  however,  be  settled  upon  only  after  consultation  and 
agreement  among  several  authorities. 

The  Committee  on  Standard  Tests  of  the  American  Society  of  Me- 
chanical Engineers  say  (vol.  xi,  p.  624) : 

"Although  compression  tests  have  heretofore  been  made  on  diminu- 
tive sample  pieces,  it  is  highly  desirable  that  tests  be  also  made  on  long 
pieces  from  10  to  20  diameters  in  length,  corresponding  more  nearly  with 
actual  practice,  in  order  that  elastic  strain  and  change  of  shape  may  be 
determined  by  using  proper  measuring  apparatus. 

"The  elastic  limit,  modulus  or  coefficient  of  elasticity,  maximum  and 
ultimate  resistances,  should  be  determined,  as  well  as  the  increase  of 
section  at  various  points,  viz.,  at  bearing  surfaces  and  at  crippling  point. 

"  The  use  of  long  compression- test  pieces  is  recommended,  because  the 
investigation  of  short  cubes  or  cylinders  has  led  to  no  direct  application 
of  the  constants  obtained  by  their  use  in  computation  of  actual  struc- 
tures, which  have  always  been  and  are  now  designed  according  to  em- 
pirical formulse  obtained  from  a  few  tests  of  long  columns." 

COLUMNS,  PILLARS,   OR  STRUTS. 

Notation. -^-P  =  crushing  weight  in  pounds;  d  =  exterior  diameter 
in  inches;  a  =  area  in  square  inches;  L  =  length  in  feet;  I  =  length  in 
inches;  S  =  compressive  stress,  Ibs.  per  sq.  in.;  E  =  modulus  of  elasticity 
in  tension  or  compression;  r  =  least  radius  of  gyration;  <£,  an  experimental 
coefficient. 

For  a  short  column  centrally  loaded  S  =  P/a,  but  for  a  long  column 
which  tends  to  bend  under  load ,  the  stress  on  the  concave  side  is  greater^ 
and  on  the  convex  side  less  than  P/a. 

Hodgkinson's  Formula  for  Columns. 

Both  ends  rounded,  the  Both  ends  flat,  the  length 

•u-  A    t  n  i.  ™               length   of   the   column  of   the  column   exceed- 

,olumn.          exceeding  15  times  its  ing  30  times  its  diam- 

diameter.  eter. 


Solid    cylindrical    col-  )  &       --  -af.  d3'7* 

= 


l    col-  ) 

> 

on  .  .  .  J 


.  .  >  f    =  jJfj  .  _ 

umns  of  cast  iron  .  .  .  J  L1  7 


Solid     cylindrical    col-  | 


p  _  ne  ocn 

'  2 


r/3'55 


P  =  98,920   j~ 
P  =  299,600  - 


umns  of  wrought  iron  J  L2 

These  formulae  apply  only  in  cases  in  which  the  length  is  so  great  that 


'284 


STRENGTH   OF   MATERIALS. 


the  column  breaks  by  bending  and  not  by  simple  crushing.  Hodgkinson's 
tests  were  made  on  small  columns,  and  his  results  are  not  now  con- 
sidered reliable. 

Euler's  Formula  for  Long  Columns. 

7T2  E  (r/l)2  for  columns  with  round  or  hinged  ends. 


with  fixed  ends,  multiply  by  4;  with  one  end  round  and  the  other  fixed, 
multiply  by  21/4;  for  one  end  fixed  and  the  other  free,  as  a  post  set  in  the 
ground,  divide  by  4.  P  is  the  load  which  causes  a  slight  deflection:  a 


load  greater  than  P  will  cause  an  increase  of  deflection  until  the  column 
fails  by  bending.  The  formula  is  now  little  used. 

Christie's  Tests  (Trans.  A.  S.  C.  E.  1884:  Merriman's  Mechanics 
of  Materials}.  —  About  300  tests  of  wrought-iron  struts  were  made,  the 
duality  of  the  iron  being  about  as  follows:  tensile  strength  per  sq.  in., 
49,600  IDS.,  elastic  limit  32,000  Ibs.,  elongation  18%  in  8  ins. 

The  following  table  gives  the  average  results. 


Ratio  I  IT 
Length  to 
Least  JJ,a- 

Ultimate  Load,  P/a,  in  Pounds  per  Square  Inch. 

Gyraticra. 

Fixed  Ends, 

Flat  Ends. 

Hinged  Ends. 

Round  Ends. 

20 

46,000 

46,000 

46,000 

44,000 

40 

40,000 

40,000 

40,000 

36,500 

eo 

36,000 

36,000 

36,000 

30,500 

80 

32,000 

32,000 

31,500 

25,000 

100 

30,000 

29,800 

28,000 

20,500 

120 

28,000 

26,300 

24,300 

16,500 

140 

25,500 

23,500 

21,000 

12,800 

160 

23,000 

20,000 

16,500 

9,500 

180 

20,000  % 

16,800 

12,800 

7,500 

200 

17,500 

14,500 

10,800 

6,000 

220 

15,000 

12,700 

8,800 

5,000 

240 

13,000 

11,200 

7,500 

4,300 

260 

11,000 

9,800 

6,500 

3,800 

280 

10,000 

8,500 

5,700 

3,200 

300 

9,000 

7,200 

5,000 

2,800 

320 

8,000 

6,000 

4,500 

2,500 

360 

6,500 

4,300 

3,500 

1,900 

400 

5.200 

3,000 

2,500 

1,500 

The  results  of  Christie's  tests  agree  with  those  computed  by  Euler's 
formula  for  round-end  columns  with  llr  between  150  and  400,  but 
differ  widely  from  them  in  shorter  columns,  and  still  more  widely  in 
columns  with  fixed  ends. 

Rankine's  Formula  (sometimes  called  Gordon's),  S  =  —  fl  +<£  f-j  J 

n  rr 

or  —  = .      Applying    Rankine's   formula   to   the   results   of 

experiments,  wide  variations  are  found  in  the  values  of  the  empirical 
coefficient  <£.  Merriman  gives  the  following  values,  which  are  extensively 
employed  in  practice. 

VALUES  OF  <f>  FOR  RANKINE'S  FORMULA. 


Material. 

Both  Ends 
Fixed. 

Fixed  and 
Round. 

Both  Ends 
Round. 

Timber  

1/3  000 

1  78/3  000 

4/3  000 

1  /5.000 

1.78/5  000 

4/5  000 

Wrought  Iron  .  . 

1/36,000 

1.78/36,000 

4/36,000 

Steel  !.. 

1  /25.000 

1.78/25,000 

4/25  000 

The  value  to  be  taken  for  S  is  the  ultimate  compressive  strength  of  the 


WORKING  FORMULAE  FOR  STRUTS.  285 

material  for  cases  of  rupture,  and  the  allowable  compressive  unit  stress 
for  cases  of  design. 

Burr  gives  the  following  values  as  commonly  taken  for  S  and  <f>. 

For  solid  wrought-iron  columns,  S  =  36,000  to  40,000,  tf>  =  1/36,000  to 
1/40,000. 

For  solid  cast-iron  columns,    .  S  =  80,000,  <j>  =  1/6,400. 

For  hollow  cast-iron  columns,  P  /a  =  80,000  •*-  1  +  ^Q  ^  (d  =  outside 
diam.  in  inches). 

The  coefficient  of  P/d2  is  given  by  different  writers  as  1/400,  1/500, 
1/600  and  1/800.  (See  Strength  of  Cast-iron  Columns,  below.) 

Sir  Benjamin  Baker  gives  for  mild  steel,  S  =  67,000  Ibs.,  <£  =  1/22,400; 
for  strong  steel,  S  =  114,000  Ibs.,  d>  =  1/14,400.  Prof.  Burr  considers 
these  only  loose  approximations.  (See  Straight-line  Formula,  below). 

For  dry  timber,  Rankine  gives  8  =  7200  Ibs.,  </>  =  1/3000. 

The  Straight-line  Formula.  —  The  results  of  computations  by  Euler's 
or  Rankine's  formulas  give  a  curved  line  when  pk)tted  on  a  diagram 
with  values  of  l/r  as  abscissas  and  value  of  P/a  as  ordinates.  The  Average 
results  of  experiments  on  columns  within  the  limits  of  l/r  commonly 
used  in  practice,  say  from  50  to  200,  can  be  represented  by  a  straight  line 
about  as  accurately  as  by  a  curve.  Formulas  derived  from  such  plotted 
lines,  of  the  general  form  P/a  =  S  -  C  l/r,  in  which  C  is  an  experimental 
coefficient,  are  in  common  use,  but  Merriman  says  it  is  advisable  that  the 
use  of  this  formula  should  be  limited  to  cases  in  which  the  specifications 
require  it  to  be  employed,  and  for  rough  approximate  computations. 
Values  of  S  and  C  given  by  T.  H.  Johnson  are  as  follows: 

F      H       R  F      H    R 

Wrought  Iron: 

S  =  42,000  Ibs.,  C  =  128,  157,  203;  limit  of  l/r  =  218,  178,138 
Structural  Steel: 

5=52,500"      C  =  179,  220,  284;      ......        195,159,123 

Cast  Iron:       5=80,000"      C  =  438,  537,  693;      ......        122,    99,    77 

Oak,  flat  ends: 

S  =  5,400  "     C  =  28:  128 

F,  flat  ends;  H,  hinged  ends;  R,  round  ends. 

Merriman  says:  "The  straight-line  formula  is  not  suitable  for  investi- 
gating a  column,  that  is  for  determining  values  of  S  due  to  given  loads, 
because  S  enters  the  formula  in  such  a  manner  as  to  lead  to  a  cubic 
equation  when  it  is  the  only  unknown  quantity.  It  may  be  used  to  find 
the  safe  load  for  a  given  column  to  withstand  a  given  unit  stress,  or  to 
design  a  column  for  a  given  load  and  unit  stress.  When  so  used,  it  is 
customary  to  divide  the  values  of  S  and  C  given  in  the  table  by  an 
assumed  factor  of  safety.  For  example,  Cooper's  specifications  require 
that  the  sectional  area  a  for  a  medium-steel  post  of  a  through  railroad 
bridge  shall  be  found  from  P/a  =  17,000  -  90  l/r  Ibs.  per  sq.  in.,  in 
which  P  is  the  direct  dead-load  compression  on  the  post  plus  twice  the 
live-load  compression;  the  values  of  S  and  C  here  used  are  a  little  less 
than  one-third  of  those  given  in  the  table  for  round  ends." 

Working^  Formulae  for  Wrought-iron  and  Steel  Struts  of  Various 
Forms.  —  Burr  gives  the  following  practical  formulae: 


p.  =  Ultimate 

Kind  of  Strut.  Ibs?  W'in.  ™mate 

of  Section. 


Flat  and  fixed  end  iron  angles  and  tees  44000  -  140  £  (1)    8800  -28^     (2) 
Hinged-end  iron  angles  and  tees  ......  46000  -175^  (3)    9200  -  35  ^     (4) 

Flat-end  iron  channels  and  I-beams  .  .  .  40000  -  1  10  -  (5)    8000  -  22  -     (6) 


286 


STRENGTH  OF  MATERIALS. 


Flat-end  mild-steel  angles  .............  52000  -  180  l-  (7)  10400  -  36^     (8) 

Flat-end  high-steel  angles  ...........  76000-290  l-  (9)  15200  -58  £  (10) 


Pin-end  solid  wrought-iron  columns  .  .  .32000  -  80  - 


6400  -  16  - 


32000- 277 


6400-55^1 


Equations  (1)  to  (4)  are  to  be  used  only  between  -  =40  and  -  =  200 

11       (5)  and  (6)       "    "    "     "        "  "  =  20   "    "  =  200 

(7)  to  (10)         "     "    "     "        "  "  =  40    "    "  =  200 

(11)  and  (12)  "    !!    !!     !!       !'  "  =  20   "   "  =  200 

or  ~  =  6  and  -  =>    65 
d  d 

Comparison  of  Column  Compression  Formulae. — The  Carnegie 
Steel  Co.  gives  in  its  Pocket  Companion  (1913)  a  table  comparing  the 
allowable  unit  stresses  in  columns  calculated  from  the  formulae  of  the 
American  Bridge  Co.,  American  Railway  Engineering  Association, 
Gordon,  and  the  New  York,  Philadelphia,  and  Boston  Building  Laws, 
for  various  values  of  l/r.  The  table  below  is  condensed  from  this 
table  and  compares  the  values  obtained  by  the  American  Bridge  Co. 
formula  with  the  average  of  all  those,  except  that  of  the  American 
Bridge  Co.  for  values  of  l/r  up  to  120,  and  with  the  values  obtained 
by  Gordon's  formula  for  values  of  l/r  from  125  to  200. 

Allowable  Unit  Stresses — Pounds  per  Sq.  In. 


l/r 

Am.  Bridge 
Co. 

Average. 

\l/r 

Am.  Bridge 
Co. 

Average. 

l/r 

Am.  Bridge 
Co. 

Gordon. 

0 

14,000 

14,790 

65 

1  1,450 

11,803 

125 

6,750 

8,715 

5 

14,000 

14,719 

70 

11,100 

11,466 

130 

6,500 

8,510 

10 

14,000 

14,620 

75 

10,750 

11,130 

135 

6,250 

8,300 

15 

14,000 

14,499 

80 

10,400 

10,794 

140 

6,000 

8,095 

20 

14,000 

14,355 

85 

10,050 

10,459 

145 

5,750 

7,890 

25 

14,000 

14,185 

90 

9,700 

10,127 

150 

5,500 

7,690 

30 

13,900 

13,977 

95 

9,350 

9,785 

155 

5,250 

7,495 

35 

13,550 

13,701 

100 

9,000 

9,473 

160 

5,000 

7,305 

40 

13,200 

13,410 

105 

8,650 

9,150 

165 

4,750 

7,120 

45 

12,850 

13,106 

110 

8,300 

8,837 

170 

4,500 

6,935 

50 

12,500 

12,790 

115 

7,950 

8,528 

180 

4,000 

6,580 

55 

12,150 

12,467 

120 

7,600 

8,221 

190 

3,500 

6,240 

60 

11,800 

12,137 

200 

3,000 

5,920 

Built  Columns  (Burr).  —  Steel  columns,  properly  made,  of  steel 
ranging  in  specimens  from  65,000  to  73,000  Ib.  per  square  inch,  should 
give  a  resistance  25  to  33  per  cent  in  excess  of  that  of  wrought-iron 
columns  with  the  same  value  of  I  •*-  r,  provided  that  ratio  does  not  exceed 
140. 

The  unsupported  width  of  a  plate  in  a  compression  member  should  not 
exceed  30  times  its  thickness. 

In  built  columns  the  transverse  distance  between  center  lines  of  rivets 
securing  plates  to  angles  or  channels,  etc.,  should  not  exceed  35  times  the 
plate  thickness.  If  this  width  is  exceeded,  longitudinal  buckling  of  the 
plate  takes  place,  and  the  column  ceases  to  fail  as  a  whole,  but  yields  in 
detail. 

The  thickness  of  the  leg  of  an  angle  to  which  latticing  is  riveted  should 
not  be  less  than  1/9  of  the  length  of  that  leg  or  side  if  the  column  is  purely 
a  compression  member.     The  above  limit  may  be  passed  somewhat  in  stiff 
ties  and  compression  members  designed  to  carry  transverse  loads. 
^  The  panel  points  of  latticing  should  not  be  separated  by  a  greater  clis- 


WORKING  STRAINS  ALLOWED  IN  BRIDGE  MEMBERS.    287 

tance  than  60  times  the  thickness  of  the  angle-leg  to  which  the  latticing 
is  riveted,  if  the  column  is  wholly  a  compression  member. 

The  rivet  pitch  should  never  exceed  16  times  the  thickness  of  the 
thinnest  metal  pierced  by  the  rivet,  and  if  the  plates  are  very  thick  it 
should  never  nearly  equal  that  value. 

Burr  gives  the  following  general  principles  which  govern  the  resistance 
of  built  columns: 

The  material  should  be  disposed  as  far  as  possible  from  the  neutral  axis 
of  the  cross-section,  thereby  increasing  r; 

There  should  be  no  initial  internal  stress; 

The  individual  portions  of  the  column  should  be  mutually  supporting; 

The  individual  portions  of  the  column  should  be  so  firmly  secured  to 
each  other  that  no  relative  motion  can  take  place,  in  order  that  the 
column  may  fail  as  a  whole,  thus  maintaining  the  original  value  of  r. 

Stoney  says:  "  When  the  length  of  a  rectangular  wrought-iron  tubular 
column  does  not  exceed  30  times  its  least  breadth,  it  fails  by  the  bulging  or 
buckling  of  a  short  portion  of  the  plates,  not  by  the  flexure  of  the  pillar 
as  a  whole." 

Tests  of  Five  Large  Built  Steel  Columns.  (Proc.  A.  S.  C.  E.,  Feb., 
1911;  Eng.  News,  Mar.  16,  1911). — The  lateral  dimensions  of  the 
columns  were -about  20  X  30  in.,  and  their  sectional  area  90  sq.  in. 
They  were  made  of  two  ribs  30  in.  deep,  spaced  207/g  in.,  laced  by  two 
lines  of  2  1/2  X  3/8  in.  lacing.  Each  rib  was  made  of  an  outside  plate, 
30  XH/16  in.,  and  an  inside  plate,  I7l/z  X  5/8  in.,  and  two  inner  edging 
angles,  6  X  6  X  5/8  in.  Transverse  plate  diaphragms,  6  ft.  apart,  gave 
additional  lateral  rigidity.  The  test  columns  were  fitted  with  10-in. 
pins  set  parallel  to  the  plane  of  the  lacing.  The  columns  were  tested 
in  the  1,200-ton  hydraulic  machine  at  Phcenixville,  Pa.;  two  of  them 
(Nos.  1  and  2)  did  not  reach  failure.  The  results  are  as  below: 


No. 
1 

Section 
Area  Sq.  In. 
90  73 

Length 
Ft.   In. 
20     0 

l/f 

26  2 

Max.  Load 
Lb. 
2  600  962 

Lb.  per 
Sq.  In. 

28  667 

2  

90  33 

36     5 

47.2 

2  600,962 

28,794 

3  

90.78 

36     5 

47.2 

2,675,183 

29,469 

4    . 

90  32 

36     5 

47.2 

2  726  815 

30,191 

5.  . 

89.96 

36     5 

47.1 

2,742,950 

30,490 

Nos.  3  and  4  failed  by  bulging  of  plates  in  front  of  pins;  No.  5  by 
web-plates  bulging  inward  121/2  in.  from  one  end.  The  columns  de- 
parted from  strictly  proportional  compression  at  a  load  as  low  as  20,000 
Ib.  per  sq.  in.  Plotted  curves  of  the  tests  show  that  all  the  columns 
reached  their  elastic  limit  at  about  this  figure,  and  an  ultimate  strength 
at  about  30,000  Ib.  per  sq.  ill.  Eng.  News  says  that  it  does  not  appear 
that  the  lacing  contributed  to  the  failure.  It  shows  that  the  com- 
pressive  strength  of  these  columns  did  not  exceed  60%  of  the  tensile 
strength  of  the  metal. 

WORKING  STRAINS  ALLOWED  IN  BRIDGE  MEMBERS. 

Theodore  Cooper  gives  the  following  in  his  Bridge  Specifications: 
Compression  members  shall  be  so  proportioned  that  the  maximum  load 
shall  in  no  case  cause  a  greater  strain  than  that  determined  by  the  follow- 
ing formula: 

8000  * 

P  =    Tjj for  square-end  compression  members; 


1  + 


40,000  r2 


8000 
p  =   -  _  -  for  compression  members  with  one  pin  and  one  square 


30,000r2  en; 
8000 
P  =  -  •£  -  for  compression  members  with  pin-bearings; 


1  + 


20,000  r* 


288  STRENGTH    OF   MATERIALS. 

(These  values  may  be  increased  in  bridges  over  150  ft.  span.  See 
Cooper's  Specifications.) 

P  —  the  allowed  compression  per  square  inch  of  cross-section; 
I  =  the  length  of  compression  member,  in  inches; 

r  =  the  least  radius  of  gyration  of  the  section  in  inches. 

No  compression  member,  however,  shall  have  a  length  exceeding  25 
times  its  least  width. 

Tension  Members.  —  All  parts  of  the  structure  shall  be  so  proportioned 
that  the  maximum  loads  shall  in  no  case  cause  a  greater  tension  than  the 
following  (except  in  spans  exceeding  150  feet): 

Pounds  per 

sq.  in. 
On  lateral  bracing  .......................  ........  "  ...........  15,000 

On  solid  rolled  beams,  used  as  cross  floor-beams  and  stringers  ....    9,000 

On  bottom  chords  and  main  diagonals  (forged  eye-bars)  .........  10,000 

On  bottom  chords  and  main  diagonals  (plates  or  shapes),  net  section  8,000 
On  counter  rods  and  long  verticals  (forged  eye-bars)  ....  ........   8,000 

On  counter  and  long  verticals  (plates  or  shapes),  net  section  .....   6,500 

On  bottom  flange  of  riveted  cross-girders,  net  section  ..........  .  .   8,000 

On  bottom  flange  of  riveted  longitudinal  plate  girders  over  20  ft. 

long,  net  section  ...........................................   8,000 

On  bottom  flange  of  riveted  longitudinal  plate  girders  under  20  ft. 

long,  net  section  ..........................................   7,000 

On  floor-beam  hangers,  and  other  similar  members  liable  to  sudden 

loading  (bar  iron  with  forged  ends)  .........................   6,000 

On  floor-beam  hangers,  and  other  similar  members  liable  to  sudden 

loading  (plates  or  shapes),  net  section  .......................   5,000 

Members  subject  to  alternate  strains  of  tension  and  compression  shall  be 
proportioned  to  resist  each  kind  of  strain.  Both  of  the  strains  shall,  how- 
ever, be  considered  as  increased  by  an  amount  equal  to  8/10  of  the  least  of 
the  two  strains,  for  determining  the  sectional  area  by  the  above  allowed 
strains. 

The  Phcenix  Bridge  Co.  (Standard  Specifications,  1895)  gives  the  follow- 
ing: 

The  greatest  working  stresses  in  pounds  per  square  inch  shall  be  £  s 
follows: 

Tension. 

Steel.  Iron. 

p    Q  nno  Fi  4.  Min'  stress"|     For  bars»        p_7  500  f  i  +  Min-  Stress1 
F-9,000  ^1  +  Max  stressj  forged  ends-          T*«W  L1  t  Max.  stress] 

P~8  500  Fl  4-  Min-  Stress1       Plates  or      >  =  7  000  Fl  +  Min"  Stress1 
F-8,500     1  +  7.UUU     l  + 


8,500  pounds.  Floor-beam  hangers,  forged  ends  ......  7,000  pounds. 

7,500        "  Floor-beam  hangers,  plates  or  shapes,  net 

section  ............................  6,000 

10,000  Lower  flanges  of  rolled  beams  .........  8,000 

20,000        "  Outside  fibres  of  pins  ................  15,000 

30,000        "  Pins  for  wind-bracing  ................  22,500 

20,000  Lateral  bracing  ............  .  ........  15,000 

Shearing. 

9,000  pounds.     Pins  and  rivets  ......................     7,500  pounds. 

Hand-driven    rivets  20%    less   unit   stresses. 

For  bracing  increase  unit  stresses  50%. 
$,000  pounds.     Webs  of  plate  girders  ................     5,000  pounds. 

Bearing. 

16  000  pounds.     Projection  semi-intrados  pins  and  rivets,  12,000  pounds. 
Hand-driven  rivets  20%  less  unit  stresses.     For 
bracing  increase  unit  stresses  50%, 


STRENGTH    OF   CAST-IRON   COLUMNS.  289 

Compression. 

Lengths  less  than  forty  times  the  least  radius  of  gyration,  P  previously 
found.  See  Tension. 

Lengths  more  than  forty  times  the  least  radius  of  gyration,  P  reduced 
by  following  formulae: 

P 

For  both  ends  fixed,       b  =   75 


36,000  r2 

p 
For  one  end  hinged,        b  =  -^ — 


1 


24,000  r2 

P 
For  both  ends  hinged,    b  = 


18,000  r2 

P  =  permissible  stress  previously  found  (see  Tension);  b  =  allowable 
working  stress  per  square  inch;  I  =  length  of  member  in  inches;  r  =  least 
radius  of  gyration  of  section  in  inches.  No  compression  member,  how- 
ever, shall  have  a  length  exceeding  45  times  its  least  width. 

Pounds  per 
sq.  in. 

In  counter  web  members 10,500 

In  long  verticals 10,000 

In  all  main-web  and  lower-chord  eye-bars ,   13,200 

In  plate  hangers  (net  section} 9,000 

In  tension  members  of  lateral  and  transverse  bracing 19,000 

In  steel-angle  lateral  ties  (net  section) 15,000 

For  spans  over  200  feet  in  length  the  greatest  allowed  working  stresses 
per  square  inch,  in  lower-chord  and  end  main-web  eye-bars,  shall  be  taken 
at 

min.  total  stressX 


10,000  (l 


max.  total  stress/ 


whenever  this  quantity  exceeds  13,200. 

The  greatest  allowable  stress  in  the  main-web  eye-bars  nearest  the  centre 
of  such  spans  shall  be  taken  at  13,200  pounds  per  square  inch;  and  those 
for  the  intermediate  eye-bars  shall  be  found  by  direct  interpolation 
between  the  preceding  values. 

The  greatest  allowable  working  stresses  in  steel  plate  and  lattice  girders 
and  rolled  beams  shall  be  taken  as  follows: 

Pounds  per 
sq.  in. 

Upper  flange  of  plate  girders  (gross  section) 10,000 

Lower  flange  of  plate  girders  (net  section) 10,000 

In  counters  and  long  verticals  of  lattice  girders  (net  section)     9,000 
In  lower  chords  and  main  diagonals  of  lattice  girders  (net 

section) 10,000 

In  bottom  flanges  of  rolled  beams 10,000 

In  top  flanges  of  rolled  beams 10,000 


THE   STRENGTH  OF  OAST-IRON  COLUMNS. 

Hodgkinson's  experiments  (first  published  in  Phil.  Trans.  Royal  Socy., 
1840,  and  condensed  in  Tredgold  on  Cast  Iron,  4th  ed.,  1846),  and  Gordon's 
formula,  based  upon  them,  are  still  used  (1898)  in  designing  cast-iron  col- 
umns. They  are  entirely  inadequate  as  a  basis  of  a  practical  formula 
suitable  to  the  present  methods  of  casting  columns. 

Hodgkinson's  experiments  were  made  on  nine  "long"  pillars,  about  71/2 
ft.  long,  whose  external  diameters  ranged  from  1.74  to  2.23  in.,  and 
average  thickness  from  0.29  to  0.35  in.,  the  thickness  of  each  column  also 
Varying,  and  on  13  "sljort"  pillars,  0.733  fy.  to  2,251  ft.  long,  with  exter- 


290 


STRENGTH    OF   MATERIALS. 


nal  diameters  from  1.08  to  1.26  in.,  all  of  them  less  than  1/4  in.  thick. 
The  iron  used  was  Low  Moor,  Yorkshire,  No.  3,  said  to  be  a  good  iron,  not 
very  hard,  earlier  experiments  on  which  had  given  a  tensile  strength  of 
14,535  and  a  crushing  strength  of  109,801  Ibs.  per  sq.  in.  Modern  cast- 
iron  columns,  such  as  are  used  in  the  construction  of  buildings,  are  very 
different  in  size,  proportions,  and  quality  of  iron  from  the  slender  "long" 
pillars  used  in  Hodgkinson's  experiments.  There  is  usually  no  check,  by 
actual  tests  or  by  disinterested  inspection,  upon  the  quality  of  the  material. 
The  tensile,  compressive,  and  transverse  strength  of  cast  iron  varies 
through  a  great  range  (the  tensile  strength  ranging  from  less  than  10,000 
to  over  40,000  Ibs.  per  sq.  in.),  with  variations  in  the  chemical  composition 
of  the  iron,  according  to  laws  which  are  as  yet  very  imperfectly  under- 
stood, and  with  variations  in  the  method  of  melting  and  of  casting. 
There  is  also  a  wide  variation  in  the  strength  of  iron  of  the  same  melt 
when  cast  into  bars  of  different  thicknesses. 

Another  difficulty  in  obtaining  a  practical  formula  f9r  the  strength  of 
cast-iron  columns  is  due  to  the  uncertainty  of  the  quality  of  the  casting, 
and  the  danger  of  hidden  defects,  such  as  internal  stresses  due  to  unequal 
cooling,  cinder  or  dirt,  blow-holes,  "cold-shuts,"  and  cracks  on  the  inner 
surface,  which  cannot  be  discovered  by  external  inspection.  Variation 
in  thickness,  due  to  rising  of  the  core  during  casting,  is  also  a  common 
defect 

In  addition  to  these  objections  to  the  use  of  Gordon's  formula,  for  cast- 
iron  columns,  we  have  the  data  of  experiments  on  full-sized  columns, 
made  by  the  Building  Department  of  New  York  City  (Eng'g  News,  Jan.  13 
and  20,  1898).  Ten  columns  in  all  were  tested,  six  15-inch,  1901/4  inches 
long,  two  8-inch,  160  inches  long,  and  two  6-inch,  120  inches  long.  The 
tests  were  made  on  the  large  hydraulic  machine  of  the  Phoenix  Bridge  Co., 
of  2,000,000  pounds  capacity,  which  was  calibrated  for  frictionai  error  by 
the  repeated  testing  within  the  elastic  limit  of  a  large  Phoenix  column, 
and  the  comparison  of  these  tests  with  others  made  on  the  government 
machine  at  the  Watertown  Arsenal.  The  average  frictionai  error  was 
calculated  to  be  15.4  per  cent,  but  Engineering  News,  revising  the  data, 
makes  it  17.1  per  cent,  with  a  variation  of  3  per  cent  either  way  from  the 
average  with  different  loads.  The  results  of  the  tests  of  the  columns  are 
given  below. 

TESTS  OF  CAST-IRON   COLUMNS. 


Thickness. 

Breaking  Load. 

her. 

Inches. 

Max. 

Min. 

Average. 

Pounds. 

Pounds 
per  Sq.  In. 

j 

15 

1 

, 

,356,000 

30,830 

2 

15 

1  5/16 

H/8 

,330,000 

27,700 

3 

15 

H/4 

H/8 

,198,000 

24,900 

4 

151/s 

17/32 

H/8 

,246,000 

25,200 

5 

15 

1  H/16 

1  H/64 

,632,000 

32,100 

6 

15 

H/4 

H/8 

13/16 

2,082,000  + 

40,400  + 

7 
8 

73/4to81/4 
8 

U/4 
13/32 

1 
13/64 

651,000 
612,800 

31,900 
26,800 

9 

61/16 

15/32 

11/8     . 

19/64 

400,000 

22,700 

10 

63/32 

H/8 

H/16 

17/64 

455,200 

26,300 

Column  No.  6  was  not  broken  at  the  highest  load  of  the  testing 
machine. 

Columns  Nos.  3  and  4  were  taken  from  the  Ireland  Building,  which 
collapsed  on  August  8,  1895;  the  other  four  15-inch  columns  were  made 
from  drawings  prepared  by  the  Building  Department,  as  nearly  as  possible 
s  of  Nos.  3  and  4.  Nos.  1  and  2  were  made  by  a  foundry  in  New 


duplicates  of        .  .  . 

York  with  no  knowledge  of  their  ultimate  use. 


Nos.  5  a.nc}  6  were 


SAFE    LOADS    FOB    CAST-IRON    COLUMNS. 


291 


by  a  foundry  in  Brooklyn  with  the  knowledge  that  they  were  to  be  tested. 
Nos.  7  to  10  were  made  from  drawings  furnished  by  the  Department. 
Applying   Gordon's  formula,  as  used   by   the  Building   Department, 

S  =-. a    ,  to  these  columns  gives  for  the  breaking  strength  per  square 

1  +  400  eP 

inch  of  the  15-inch  columns  57,143  pounds,  for  the  8-inch  columns  40,000 
pounds,  and  for  the  6-inch  columns  40,000.  The  strength  of  columns  Nos. 
3  and  4  as  calculated  is  128  per  cent  more  than  their  actual  strength;  their 
actual  strength  is  less  than  44  per  cent  of  their  calculated  strength;  and 
the  factor  of  safety,  supposed  to  be  5  in  the  Building  Law,  is  only  2.2  f9r 
central  loading,  no  account  being  taken  of  the  likelihood  of  eccentric 
loading. 

Prof.  Lanza,  Applied  Mechanics,  p.  372,  quotes  the  records  of  14 
tests  of  cast-iron  mill  columns,  made  on  the  Watertown  testing-machine  in 
1887-88,  the  breaking  strength  per  square  inch  ranging  from  25,100  to 
63,310  pounds,  and  showing  no  relation  between  the  breaking  strength 
per  square  inch  and  the  dimensions  of  the  columns.  Only  3  of  the  14 
columns  had  a  strength  exceeding  33,500  pounds  per  square  inch.  The 
average  strength  of  the  other  11  was  29,600  pounds  per  square  inch.  Prof. 
Lanza  says  that  it  is  evident  that  in  the  case  of  such  columns  we  cannot 
rely  upon  a  crushing  strength  of  greater  than  25,000  or  30,000  pounds 
per  square  inch  of  area  of  section. 

He  recommends  a  factor  of  safety  of  5  or  6  with  these  figures  for  crush- 
ing strength,  or  5000  pounds  per  square  inch  of  area  of  section  as  the 
highest  allowable  safe  load,  and  in  addition  makes  the  conditions  that 
the  length  of  the  column  shall  not  be  greatly  in  excess  of  20  times  the 
diameter,  that  the  thickness  of  the  metal  shall  be  such  as  to  insure  a  good 
strong  casting,  and  that  the  sectional  area  should  be  increased  if  necessary 
to  insure  that  the  extreme  fibre  stress  due  to  probable  eccentric  loading 
shall  not  be  greater  than  5000  pounds  per  square  inch. 

Prof.  W.  H.  Burr  (Eng'g  News,  June  30,  1898)  gives  a  formula  derived 
from  plotting  the  results  of  the  Watertown  and  Phoenixville  tests,  above 
described,  which  represents  the  average  strength  of  the  columns  in  pounds 
per  square  inch.  It  is  p  =  30,500  -  160  l/d.  It  is  to  be  noted  that  this 
is  an  average  value,  and  that  the  actual  strength  of  many  of  the  columns 
was  much  lower.  Prof.  Burr  says:  "If  cast-iron  columns  are  designed 
with  anything  like  a  reasonable  and  real  margin  of  safety,  the  amount  of 
metal  required  dissipates  any  supposed'  economy  over  columns  of  mild 
steel." 

Square  Columns.  —  Square  cast-iron  columns  should  be  abandoned. 
They  are  liable  to  have  serious  internal  strains  from  difference  in  con- 
traction on  two  adjacent  sides.  John  F.  Ward,  Eng.  News,  Apr.  16,  1896. 

Safe  Load,  in  Tons  of  2000  Lbs.,   for  Round  Cast-iron  Columns* 
with  Turned  Capitals  and  Bases. 

Loads  being  not  eccentric,  and  length  of  column  not  exceeding  20  times 
the  diameter.  Based  on  ultimate  crushing  strength  of  25,000  Ibs.  per 
sq.  in.  and  a  factor  of  safety  of  5. 


Thick- 


Diameter,  Inches. 


ness, 
Inches. 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

18 

5/8 
3/4 
7/8 

11/8 
11/4 

26.4 
30.9 
35.2 
39.2 

31.3 
36.8 
42.1 
47.1 

42.7 
48.9 
55.0 
60.8 

48.6 
55.8 
62.8 
69.6 
76  1 

54.5 
62.7 
70.7 
78.4 
85  9 

69.6 
78.5 
87.2 
95.7 

76.5 
86.4 
96.1 
105.5 

94.2 
104.9 
115.3 

102.1 

113.8 
125.2 

110.0 
122.6 
135.0 

131.4 
144.8 

1644 

13/8 

93  1 

103.9 

114.7 

125.5 

136.3 

147.1 

157.9 

179.5 

11/2 

123.7 

135.5 

147.3 

159.0 

170.8 

194.4 

13/4 

168.4 

182.1 

195  8 

223  3 

2 

204.2 

219.9 

251.3 

292  STRENGTH   OF  MATERIALS. 

For  lengths  greater  than  20  diameters  the  allowable  loads  should  be 
decreased.  How  much  they  should  be  decreased  is  uncertain,  since  suffi- 
cient data  of  experiments  on  full-sized  very  long  columns,  from  which  a 
formula  for  the  strength  of  such  columns  might  be  derived,  are  as  yet 
lacking.  There  is,  however,  rarely,  if  ever,  any  need  of  proportioning 
cast-iron  columns  with  a  length  exceeding  20  diameters. 


Safe  Loads  in  Tons  of  200O  Pounds  for  Cast-iron  Columns. 

(By  the  Building  Laws  of  New  York  City,  Boston,  and  Chicago,  1897.) 

New  York.  Boston.            Chicago. 

(         8a  5  a                    5  a 

Square  columns. ...  )  ~     — /r~"  — 12 —               — JT~ 

114-  i    _L  _                    la. 

r          '      Knn  ^/2  *    ~    i  ncfi^n          ±     * 


Round  columns 

)  1  + 


500  cP  T  1067cP  800  d2 

Ba  5a  5a 

— ~~  — 


400  d*  800  d2  T  600  & 


a  =  sectional  area  in  square  inches;  1=  unsupported  length  of  column 
in  inches;  d  =  side  of  square  column  or  thickness  of  round  column  in 
inches. 

The  safe  load  of  a  15-inch  round  column  iy2  inches  in  thickness,  16 
feet  long,  according  to  the  laws  of  these  cities  would  be,  in  New  York,  361 
tons;  in  Boston,  264  tons;  in  Chicago,  250  tons. 

The  allowable  stress  per  square  inch  of  area  of  such  a  column  would  be, 
in  New  York,  11,350  pounds;  in  Boston,  8300  pounds;  in  Chicago,  7850 
pounds.  A  safe  stress  of  5000  pounds  per  square  inch  would  give  for  the 
safe  load  on  the  column  159  tons. 

Strength  of  Brackets  on  Cast-iron  Columns.  —  The  columns  tested 
by  the  New  York  Building  Department  referred  to  above  had  brackets 
cast  upon  them,  each  bracket  consisting  of  a  rectangular  shelf  sup- 
ported by  one  or  two  triangular  ribs.  These  were  tested  after  the 
columns  had  been  broken  in  the  principal  tests.  In  17  out  of  22  cases  the 
brackets  broke  by  tearing  a  hole  in  the  body  of  the  column,  instead  of  by 
shearing  or  transverse  breaking  of  the  bracket  itself.  The  results  were 
surprisingly  low  and  very  irregular.  Reducing  them  to  strength  per 
square  inch  of  the  total  vertical  section  through  the  shelf  and  rib  or  ribs, 
they  ranged  from  2450  to  5600  Ibs.,  averaging  4200  Ibs.,  for  a  load  con- 
centrated at  the  end  of  the  shelf,  and  4100  to  10,900  Ibs.,  averaging  8000 
.Ibs.,  for  a  distributed  load.  (Eng'g  News,  Jan.  20,  1898.) 

Maximum  Permissible  Stresses  in  columns  used  in  buildings. 
(Building  Ordinances  of  City  of  Chicago,  1893.) 

For  riveted  or  other  forms  of  wrought-iron  columns: 

g  r=      12000  a     ^        i  —  length  of  column  in  inches; 

Z2  r  =  least  radius  of  gyration  in  inches; 

36000  r2         a  =  area  °*  c°lumn  in  square  inches. 

For  riveted  or  other  steel  columns,  if  more  than  60  r  in  length: 

s  =  17,ooo  -  521 

If  less  than  60  r  in  length:  S  =  13,500  a. 
For  wooden  posts: 

e  ac  a  =  area  of  post  in  square  inches; 

»  •"  72"'  d  =  least  side  of  rectangular  post  in  inches; 

1  •+  ocn^o  I   =  length  of  post  in  inches; 

250  d2  <  600  for  white  or  Norway  pine; 

C   =  {  800  for  oak  ; 

(900  for  long-leaf  yellow  pine, 


MOMENT  OF  INERTIA  AND  RADIUS  OF  GYRATION.  293 

MOMENT  OF  INERTIA  AND  RADIUS  OF  GYRATION. 

The  moment  of  inertia  of  a  section  is  the  sum  of  the  products  of 
each  elementary  area  of  the  section  into  the  square  of  its  distance  from  an 
assumed  axis  of  rotation,  as  the  neutral  axis. 

Assume  the  section  to  be  divided  into  a  great  many  equal  small  areas, 
a,  and  that  each  such  area  has  its  own  radius,  r,  or  distance  from  the 
assumed  axis  of  rotation,  then  the  sum  of  all  the  products  derived  by 
multiplying  each  a  by  the  square  of  its  r  is  the  moment  of  inertia,  7,  or 
7  =  2  ar2,  in  which  2  is  the  sign  of  summation. 

For  moment  of  inertia  of  the  weight  or  mass  of  a  body  se£  Mechanics. 

The  radius  of  gyration  of  the  section  equals  the  square  root  of  the 
quotient  of  the  moment  of  inertia  divided  by  the  area  of  the  section.  If 
R  =  radius  of  gyration,  7  =  moment  of  inertia  and  A  =  area 

R  =V/7Z    II A  =  R2. 

The  center  of  gyration  is  the  point  where  the  entire  area  might  be 

concentrated  and  have  the  same  moment  of  inertia  as  the  actual  area. 

The  distance  of  this  center  from  the  axis  of  rotation  is  the  radius  of 

gyration. 

The  moments  of  inertia  of  various  sections  are  as  follows: 

d  =  diameter,  or  outside  diameter;  d\  =  inside  diameter;  6  =  breadth; 

h  =  depth;  61,  hi,- inside  breadth  and  depth; 

Solid  rectangle   7  =  Vi2&/i3;       Hollow  rectangle   7  =  Vi2(&&8  -  &i/ti3); 

Solid  square        7  =  Vi2&4;         Hollow  square       7  =  1/12(6*     —  6i4); 

Solid  cylinder     7  =  i/Qi^d4;      Hollow  cylinder     7  =  i/w^Cd4  —  di4). 

Moment  of  Inertia  about  any  Axis.  —  If  b  —  breadth  and  h  = 
depth  of  a  rectangular  section  its  moment  of  inertia  about  its  central 
axis  (parallel  to  the  breadth)  is  1/12  bh*;  and  about  one  side  is  1/3  bhz.  If 
a  parallel  axis  exterior  to  the  section  is  taken,  and  d  =  distance  of  this 
axis  from  the  farthest  side  and  d\  =  its  distance  from  the  nearest  side, 
(d  —  di  =  h},  the  moment  of  inertia  about  this  axis  is  1/36  (d3  —  di3). 

The  moment  of  inertia  of  a  compound  shape  about  any  axis  is  equal  to 
the  sum  of  the  moments  of  inertia,  with  reference  to  the  same  axis,  of  all 
the  rectangular  portions  composing  it. 

Moment  of  Inertia  of  Compound  Shapes.  (Pencoyd  Iron 
Works.)  —  The  moment  of  inertia  of  any  section  about  any  axis  is  equal 
to  the  7  about  a  parallel  axis  passing  through  its  centre  of  gravity  4-  (the 
area  of  the  section  X  the  square  of  the  distance  between  the  axes). 

By  this  rule,  the  moments  of  inertia  or  radii  of  gyration  of  any  single 
sections  being  known,  corresponding  values  may  be  obtained  for  any 
combination  of  these  sections. 

E.  A.  Dixon  (Am.  Mach.,  Dec.  15,  1898)  gives  the  following  formula  for 
the  moment  of  inertia  of  any  rectangular  element  of  a  built  up  beam: 
7  =  1/3  (h3  —  h\3)b,  I  =  moment  of  inertia  about  any  axis  parallel  to  the 
neutral  axis,  h  =  distance  from  the  assumed  axis  to  the  farthest  fiber, 
h\  =  distance  to  nearest  fiber,  b  =  breadth  of  element.  The  sum  of  the 
moments  of  inertia  of  ail  the  elements,  taken  about  the  center  of  gravity 
or  neutral  axis  of  the  section,  is  the  moment  of  inertia  of  the  section. 

The  polar  moment  of  inertia  of  a  surface  is  the  sum  of  the  products 
obtained  by  multiplying  each  elementary  area  by  the  square  of  its  dis- 
tance from  the  center  of  gravity  of  the  surface;  it  is  equal  to  the  sum  of 
the  moments  of  inertia  taken  with  respect  to  two  axes  at  right  angles  to 
each  other  passing  through  the  center  of  gravity.  It  is  represented  by 
J.  For  a  solid  shaft  J  =  1/32  ^d4;  for  a  hollow  shaft,  J  =  1/32  *(d*  —  ofi4), 
5n  which  d  is  the  outside  andr/i  the  inside  diameter. 

The  polar  radius  of  gyration,  Rp  =  \/J/A,  is  defined  as  the  radius  of 
a  circumference  along  which  the  entire  area  might  be  concentrated  and 
have  the  same  polar  moment  of  inertia  as  the  actual  area. 

For  a  solid  circular  section  Rp2  =  i/s  7J>2;  for  a  hollow  circular  sec- 
tion Rp*  =  l/8(d2  +  di2). 

Moments  of  Inertia  and  Radius  of  Gyration  for  Various  Sec- 
tions, and  their  Use  in  the  Formulas  for  Strength  of  Girders  and 
Columns.  —  The  strength  of  sections  to  resist  strains,  either  as 
girders  or  as  columns,  depends  not  only  on  the  area  but  also  on  the 
form  of  the  section,  and  the  property  of  the  section  which  forms  the 


294  STRENGTH   OF   MATERIALS. 

basis  of  the  constants  used  in  the  formulas  for  strength  of  girders  and 
columns  to  express  the  effect  of  the  form,  is  its  moment  of  inertia  about 
its  neutral  axis.  The  modulus  of  resistance  of  any  section  to  transverse 
bending  is  its  moment  of  inertia  divided  by  the  distance  from  the  neutral 
axis  to  the  fibres  farthest  removed  from  that  axis;  or 

Section  modulus  =  •=- Moment  of  inertia _  ;        z  =  7 

Distance  of  extreme  fibre  from  axis  c 

Moment  of  resistance  =  section  modulus  X  unit  stress  on  extreme  fibre. 

Radius  of*  Gyration  of  Compound  Shapes.  —  In  the  case  of  a 
pair  of  any  shape  without  a  web  the  value  of  R  can  always  be  found  with- 
out considering  the  moment  of  inertia. 

The  radius  of  gyration  for  any  section  around  an  axis  parallel  to  another 
axis  passing  through  its  centre  of  gravity  is  found  as  follows: 

Let  r  =  radius  of  gyration  around  axis  through  centre  of  gravity;  R  = 
radius  of  gyration  around  another  axis  parallel  to  above;  d  =  distance 
between  axes:  R  =  Vrf2  +  r2. 

When  r  is  small,  R  may  be  taken  as  equal  to  d  without  material  error. 

Graphical  Method  for  Finding  Radius  of  Gyration.  —  Benj.  F. 
La  Rue,  Eng.  News-,  Feb.  2,  1893,  gives  a  short  graphical  method  for 
finding  the  radius  of  gyration  of  hollow,  cylindrical,  and  rectangular 
columns,  as  follows: 

For  cylindrical  columns: 

Lay  off  to  a  scale  of  4  (or  40)  a  right-angled  triangle,  in  which  the  base 
equals  the  outer  diameter,  and  the  altitude  equals  the  inner  diameter 
of  the  column,  or  vice  versa.  The  hypothenuse,  measured  to  a  scale  of 
unity  (or  10),  will  be  the  radius  of  gyration  sought. 

This  depends  upon  the  formula 


G=  VMom.  of  inertia  -*-  Area  =  1/4 
in  which  A  =  area  and  D  =  diameter  of  outer  circle,  a  =  area  and  d  =* 
diameter  of  inner  circle,  and  G  =  radius  of  gyration.  V/)2  +  ^2  is  the 
expression  for  the  hypothenuse  of  a  right-angled  triangle,  in  which  D  and 
d  are  the  base  and  altitude. 

The  sectional  area  of  a  hollow  round  column  is  0.7854(Z)2  —  d2).  By 
constructing  a  right-angled  triangle  in  which  D  equals  the  hypothenuse 
and  d  equals  the  altitude,  the  base  will  equal  V£)2  _  &  Calling  the 
value  of  this  expression  for  the  base  B,  the  area  will  equal  0.7854.82. 

Value  of  G  for  square  columns: 

Lay  off  as  before,  but  using  a  scale  of  10,  a  right-angled  triangle  of  which 
the  base  equals  D  or  the  side  of  the  outer  square,  and  the  altitude  equals  d, 
the  side  of  the  inner  square.  With  a  scale  of  3  measure  the  hypothenuse, 
which  will  be,  approximately,  the  radius  of  gyration. 

This  process  for  square  columns  gives  an  excess  of  slightly  more  than 
4%.  By  deducting  4%  from  the  result,  a  close  approximation  will  be 
obtained. 

A  very  close  result  is  also  obtained  by  measuring  the  hypothenuse  with 
the  same  scale  by  which  the  base  and  altitude  were  laid  off,  and  multiplying 
by  the  decimal  0.29';  more  exactly,  the  decimal  is  0.28867. 

The  formula  is 


VMom.  of  ii 
Area 


of  inertia  1        . 

D2  +  eJ2,  =  0.28867 


This  may  also  be  applied  to  any  rectangular  column  by  using  the  lesser 
diameters  of  an  unsupported  column,  and  the  greater  diameters  if  the 
column  is  supported  in  the  direction  of  its  least  dimensions. 

ELEMENTS  OF  USUAL  SECTIONS. 

Moments  refer  to  horizontal  axis  through  centre  of  gravity.  This  table 
is  intended  for  convenient  application  where  extreme  accuracy  is  not 
important.  Some  of  the  terms  are  only  approximate;  those  marked  *  are 
correct.  Values  for  radius  of  gyration  in  flanged  beams  apply  to  standard 
minimum  sections  only.  A  =  area  of  section;  b  =  breadth;  h  =  depth: 
D  •=  diameter. 


ELEMENTS    OF    USUAL   SECTIONS. 


295 


Shape 

of  Section. 

Moment 
of  Inertia. 

Section 
Modulus. 

Square  of 
Least 
Radius  of 
Gyration. 

Least 
Radius  of 
Gyration. 

4 

Solid  Rect- 

6^3* 

6A2* 

(Least  side)2* 

Least  side  * 

i 

angle. 

12 

6 

12 

3.46 

En  t 

Hr»llr*OT  T?  £»<••+ 

bW    bh** 

h*+h«* 

h+hl 

i 

angle. 

12 

6h 

12 

4.89 

0 

Solid  Circle. 

1/64  irZ)** 
=  0.049  ID* 

=  (?U982£>3 

~I6~ 

D* 
4 

y^Si 

Hollow  Circle. 
A,  area  of 

AD*  -ad** 

AD*-a#* 

D2-f^2* 

D+d 

1JP 

a,  area  of 
small  section. 

16 

SO 

16 

5.64 

^ 

Solid  Triangle. 

.   6fc3 
36 

24~ 

The  least  of 
the   two  ; 

T82°rl4 

The  least 
of  the  two; 
h           b 
4^4°r4T9 

o 

Even  Angle. 

Ah* 
1  0.2 

•7T     . 

25" 

6 
5 

tT 

Ah* 

^^ 

(hb}* 

hb 

J 

Uneven  Angle. 

9.5 

6.5 

\3(h*+b*) 

2.6(h+b) 

•B 

Even  Cross. 

\9 

93 

223 

474 

eP 

Even  Tee. 

Ah* 
U.I 

T" 

b* 
223 

6 
4.74 

^ 

I  Beam. 

Ah* 
6.66 

^^ 
3.2 

62 

21 

6 
438 

TO 

Channel. 

Ah* 
7.34 

A* 

3.67 

62 
12.5 

6 
334 

<f|Hq 
>-ft—  i 

Deck  Beam. 

Ah* 
6.9 

Ah 
4 

62 
363 

6 
6 

Distance  of  base  from  centre  of  gravity,  solid  triangle,  -;  even  angle,  ^-^. 

o  o.o' 

uneven   angle,  ^-r ;   even  tee,  77-5 ;    deck  beam,  — ;  all    other   shapes 

'      O.O  O.O  .i.O 

given  in  the  table,  -  or  — • 


296  STRENGTH  OF   MATERIALS. 

ECCENTRIC  LOADING  OF  COLUMNS. 

In  a  given  rectangular  cross-section,  such  as  a  masonry  joint  under 
pressure,  the  stress  will  be  distributed  uniformly  over  the  section  only 
when  the  resultant  passes  through  the  centre  of  the  section;  any  deviation 
from  such  a  central  position  will  bring  a  maximum  unit  pressure  to  one 
edge  and  a  minimum  to  the  other;  when  the  distance  of  the  resultant 
from  one  elge  is  one  third  of  the  entire  width  of  the  joint,  the  pressure  at 
the  nearer  edge  is  twice  the  mean  pressure,  while  that  at  the  farther  edge 
is  zero,  and  that  when  the  resultant  approaches  still  nearer  to  the  edge 
the  pressure  at  the  farther  edge  becomes  less  than  zero:  in  fact,  becomes 
a  tension,  if  the  material  (mortar,  etc.)  there  is  capable  of  resisting  tension. 
Or,  if,  as  usual  in  masonry  joints,  the  material  is  practically  incapable  of 
resisting  tension,  the  pressure  at  the  nearer  edge,  when  the  resultant 
approaches  it  nearer  than  one  third  of  the  width,  increases  very  rapidly 
and  dangerously,  becoming  theoretically  infinite  when  the  resultant 
reaches  the  edge. 

With  a  given  position  of  the  resultant  relatively  to  one  edge  of  the  joint 
or  section,  a  similar  redistribution  of  the  pressures  throughout  the  section 
may  be  brought  about  by  simply  adding  to  or  diminishing  the  width  of 
the  section. 

Let  P  =  the  total  pressure  on  any  section  of  a  bar  of  uniform  thickness. 

w  =-  the  width  of  that  section  =  area  of  the  section,  when  thickness  =  1. 
p  =.  p/w  =  the  mean  unit  pressure  on  the  section. 

M  =  the  maximum  unit  pressure  on  the  section. 

m  =  the  minimum  unit  pressure  on  the  section. 
d  =  the  eccentricity  of  the  resultant  =  its  distance  from  the  centre  of 
the  section 


When  d  =  -  w  then  M  =  2p  and  m  =  O. 
6 

When  d  is  greater  than  1/6  iff,  the  resultant  in  that  case  being  less  than 
one  third  of  the  width  from  one  edge,  p  becomes  negative.  (J.  C.  Traut- 
wine,  Jr.,  Engineering  News,  Nov.  23,  1893.) 

Eccentric  Loading  of  Cast-iron  Columns.  —  Prof.  Lanza  writes 
the  author  as  follows:  The  table  on  page  276  applies  when  the  result- 
ant of  the  loads  upon  the  column  acts  along  its  central  axis,  i.e.,  passes 
through  the  centre  of  gravity  of  every  section.  In  buildings  and  other 
constructions,  however,  cases  frequently  occur  when  the  resultant  load 
does  not  pass  through  the  centre  of  gravity  of  the  section:  and  then  the 
pressure  is  not  evenly  distributed  over  the  section,  but  is  greatest  on  the 
side  where  the  resultant  acts.  (Examples  occur  when  the  loads  on 
the  floors  are  not  uniformly  distributed.)  In  these  cases  the  outside 
fibre  stresses  of  the  column  should  be  computed  as  follows,  viz.: 
Let  P  =  total  pressure  on  the  section; 

d  =  eccentricity    of    resultant  =  its    distance   from   the   centre   of 

gravity  of  the  section; 

A  =  area  of  the  section,  and  /  its  moment  of  inertia  about  an  axis  in 
its  plane,  passing  through  its  centre  of  gravity,  and  perpendic- 
ular to  d; 
ci  =  distance  of  most  compressed  and  ci  =  that  of  least  compressed 

fibre  from  above  stated  axis; 
si  =*  maximum  and  sz  =  minimum  pressure  oer  unit  of  area.     Then 

P  ,    (Pd)ci  P       (Pd)ca. 

Sl  -  A  +   —I"       and      S2  =  A  ~  -J- 

Having  assumed  a  certain  trial  section  for  the  column  to  be  designed,  si 
should  be  computed,  and,  if  it  exceed  the  proper  safe  value,  a  different 
section  should  be  used  for  which  si  does  not  exceed  this  value. 

The  proper  safe  value,  in  the  case  of  cast-iron  columns  whose  ratio  of 
length  to  diameter  does  not  greatly  exceed  20,  is  5000  pounds  per  square 
inch  when  the  eccentricity  u^ed  in  the  computation  of  si  is  liable  to  occur 
frequently  in  the  ordinary  uses  of  the  structure;  but  when  it  is  one  which 
can  only  occur  in  rare  cases  the  value  8000  Ibs.  per  sq.  in.  may  be  used. 

A  long  cap  on  a  column  is  more  conducive  to  the  production  of  eccen- 
tricity of  loading  than  a  short  one,  hence  a  long  cap  is  a  source  of  weakness, 


TRANSVERSE  STRENGTH.  297 


TRANSVERSE  STRENGTH. 

In  transverse  tests  the  strength  of  bars  of  rectangular  section  is  found  to 
vary  directly  as  the  breadth  of  the  specimen  tested,  as  the  square  of  its 
depth,  and  inversely  as  its  length.  The  deflection  under  any  load  varies 
as  the  cube  of  the  length,  and  inversely  as  the  breadth  and  as  the  cube  of 
the  depth.  Represented  algebraically,  if  S  =  the  strength  and  D  the 
deflection,  /  the  length,  b  the  breadth,  and  d  the  depth, 

bd2  Is 

S  varies  as  —  r-  and  D  varies  as  ,—  ^- 
I  bd3 

For  the  purpose  of  reducing  the  strength  of  pieces  of  various  sizes  to 
a  common  standard,  the  term  modulus  of  rupture  (represented  by  R)  is 
used.  Its  value  is  obtained  by  experiment  on  a  bar  of  rectangular  section 
supported  at  the  ends  and  loaded  in  the  middle  and  substituting  numerical 
values  in  the  following  formula: 


in  which  P  =  the  breaking  load  in  pounds,  I  =  the  length  in  inches,  b  the 
breadth,  and  d  the  depth. 

The  modulus  of  rupture  is  sometimes  defined  as  the  strain  at  the  instant 
of  rupture  upon  a  unit  of  the  section  which  is  most  remote  from  the  neu- 
tral axis  on  the  side  which  first  ruptures.  This  definition,  however,  is 
based  upon  a  theory  which  is  yet  in  dispute  among  authorities,  and  it  is 
better  to  define  it  as  a  numerical  value,  or  experimental  constant,  found 
by  the  application  of  the  formula  above  given. 

From  the  above  formula,  making  /  12  inches,  and  b  and  d  each  1  inch,  it 
follows  that  the  modulus  of  rupture  is  18  times  the  load  required  to  break 
a  bar  one  inch  square,  supported  at  two  points  one  foot  apart,  the  load 
being  applied  in  the  middle. 

,  ,      span  in  feet  X  load  at  middle  in  Ibs. 

Coefficient  of  transverse  strength  =  ^-      -77—.  —  r 

breadth  in  inches  X  (depth  in  inches)2 

=  —  th  of  the  modulus  of  rupture. 

lo 

Fundamental  Formulae  for  Flexure  of  Beams  (Merriman). 

Resisting  shear  =  vertical  shear; 

Resisting  moment  =  bending  moment; 

Sum  of  tensile  stresses  =  sum  of  compressive  stresses: 

Resisting  shear  =  algebraic  sum  of  all  the  vertical  components  of  the 
internal  stresses  at  any  section  of  the  beam. 

If  A  be  the  area  of  the  section  and  Ss  the  shearing  unit  stress,  then 
resisting  shear  =  ASS;  and  if  the  vertical  shear  =  F,  then  V=  ASS. 

The  vertical  shear  is  the  algebraic  sum  of  all  the  external  vertical  forces 
on  one  side  of  the  section  considered.  It  is  equal  to  the  reaction  of  one 
support,  considered  as  a  force  acting  upward,  minus  the  sum  of  all  the 
vertical  downward  forces  acting  between  the  support  and  the  section. 

The  resisting  moment  =  algebraic  sum  of  all  the  moments  of  the  inter- 
nal horizontal  stresses  at  any  section  with  reference  to  a  point  in  that 

section,  =  —  •  in  which  S  =  the  horizontal  unit  stress,  tensile  or  com- 

c 

pressive  as  the  case  may  be,  upon  the  fibre  most  remote  from  the  neutral 
axis,  c  =  the  slwrtest  distance  from  that  fibre  to  said  axis,  and  7  =  the 
moment  of  inertia  of  the  cross-section  with  reference  to  that  axis. 

The  bending  moment  M  is  the  algebraic  sum  of  the  moment  of  the 
external  forces  on  one  side  of  the  section  with  reference  to  a  point  in  that 
section  =  moment  of  the  reaction  of  one  support  minus  sum  of  moments 
of  loads  between  the  support  and  the  section  considered. 


The  bending  moment  is  a  compound  quantity  =  product  of  a  force  by 
the  distance  of  its  point  of  application  from  the  section  considered,  the 
distance  being  measured  on  a  line  drawn  from  the  section  perpendicular 
to  the  direction  of  the  action  of  the  force, 


298 


STRENGTH   OF   MATERIALS. 


Concerning  the  formula,  M=*SI/c,  p.  297,  Prof.  Merriman,  £"710.  News, 
July  21,  1894,  says:  The  formula  quoted  is  true  when  the  unit-stress  S  on 
the  part  of  the  beam  farthest  from  the  neutral  axis  is  within  the  elastic  limit 
of  the  material.  It  is  not  true  when  this  limit  is  exceeded,  because  then 
the  neutral  axis  does  not  pass  through  the  center  of  gravity  of  the  cross- 
section,  and  because  also  the  different  longitudinal  stresses  are  not  pro- 
portional to  their  distances  from  that  axis,  these  two  requirements  being 
involved  in  the  deduction  of  the  formula.  But  in  all  cases  of  design  the 
permissible  unit-stresses  should  not  exceed  the  elastic  limit,  and  hence 
the  formula  applies  rationally,  without  regarding  the  ultimate  strength 
of  the  material  or  any  of  the  circumstances  regarding  rupture.  Indeed, 
so  great  reliance  is  placed  upon  this  formula  that  the  practice  of.  testing 
beams  by  rupture  has  been  almost  entirely  abandoned,  and  the  allowable 
unit-stresses  are  mainly  derived  from  tensile  and  compressive  tests. 


APPROXIMATE  GREATEST  SAFE  LOADS  IN  LBS.  ON  STEEL 
BEAMS.     (Pencoyd  Iron  Works.) 

Based  on  fiber  strains  of  16,000  Ibs.  for  steel.  (For  iron  the  loads  should 
bo  one-eighth  less,  corresponding  to  a  fibre  strain  of  14,000  Ibs.  per  square 
inch.)  Beams  supported  at  the  ends  and  uniformly  loaded. 

L  =  length  in  feet  between  supports;  a  =  interior    area    in    square 
A  =  sectional  area  of  beam  in  square  inches; 

inches;  d  —  interior  depth  in  inches. 

D  =  depth  of  beam  in  inches.  w  =  working  load  in  net  tons. 


Shape  of 
Section. 

Greatest  Safe  Load  in  Pounds. 

Deflection  in  Inches. 

Load  in 
Middle. 

Load 
Distributed. 

Load  in 
Middle. 

Load 
Distributed. 

Solid  Rect- 
angle. 

890  AD 

1780  AD 

wL* 

wL* 

L 

L 

32  AD2 

52AD2 

Hollow 
Rectangle. 

890(AZ)-acO 

1780(AZ>-ad) 

wtf 

wL* 

L 

L 

32(AD'2-aa'2) 

52(AD2-ad2) 

Solid 
Cylinder. 

667AD 

\333AD 

wtf 

wL3 

L 

L 

•  24  AD2 

38  AD2 

Hollow 
Cylinder. 

667(AD-ad) 
L 

]333(AD-ad) 

wU 

wL* 

L 

24(AD2-ad*) 

38(AD'2-ad2) 

Even- 
legged 
Angle  or 
Tee. 

885AD 

1770AD 

wL* 

wL3 

L 

L 

32AD2 

52AD2 

Channel  or 
Z  bar 

1525AD 

3050AD 

wL* 

wL* 

L 

L 

53  AD2 

85AD2 

Deck 
Beam. 

1380AD 

276QAD 

wLs 

wlfi 

L 

L 

50AZ>2 

SOAD2 

I  Beam. 

1695  AD 

3390AD 

wL* 

wU 

L 

L 

58  AD2 

93AD2 

I 

11 

III 

IV 

V 

The  above  formulas  for  the  strength  and  stiffness  9f  rolled  beams  of 
various  sections  are  intended  for  convenient  application  in  cases  where 
gtrict  accuracy  is  not  required. 


TBANSVERSE   STRENGTH   OF    BEAMS. 


299 


A  IS 


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£ 


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CQ 


t 


300 


STRENGTH   OF   MATERIALS. 


The  rules  for  rectangular  and  circular  sections  are  correct,  while  those 
for  the  flanged  sections  are  approximate,  and  limited  in  their  application 
to  the  standard  shapes  as  given  in  the  Pencoyd  tables.  When  the  section 
of  any  beam  is  increased  above  the  standard  minimum  dimensions,  the 
flanges  remaining  unaltered,  and  the  web  alone  being  thickened,  the  ten- 
dency will  be  for  the  load  as  found  by  the  rules  to  be  in  excess  of  the 
actual;  but  within  the  limits  that  it  is  possible  to  vary  any  section  in  the 
rolling;  the  rules  will  apply  without  any  serious  inaccuracy. 

The  calculated  safe  loads  will  be  approximately  one  half  of  loads  that 
would  injure  the  elasticity  of  the  materials. 

The  rules  for  deflection  apply  to  any  load  below  the  elastic  limit,  or 
less  than  double  the  greatest  safe  load  by  the  rules. 

If  the  beams  are  long  without  lateral  support,  reduce  the  loads  for  the 
ratios  of  width  to  span  as  follows: 


Length  of  Beam. 
20  times  flange  width. 
30 

40  " 
50  " 
60  " 
70  " 


Proportion  of  Calculated  Load 
forming  Greatest  Safe  Load. 

Whole  calculated  load. 

9-10 

8-10 

7-10 

6-10 

5-10 


These  rules  apply  to  beams  supported  at  each  end.  For  beams  supported 
otherwise,  alter  the  coefficients  of  the  table  as  described  below,  referring 
to  the  respective  columns  indicated  by  number. 


Changes  of  Coefficients  for  Special  Forms  of  Beams. 


Kind  of  Beam. 

Coefficient  for  Safe 
Load, 

Coefficient  for  Deflec- 
tion. 

Fixed  at  one  end,  loaded 
at  the  other. 

One  fourth  of  the  coeffi- 
cient, col.  II. 

One  sixteenth  of  the  co- 
efficient of  col.  IV. 

Fixed  at  one  end,  load 
evenly  distributed. 

One  fourth  of  the  coeffi- 
cient of  col.  III. 

Five  forty-eighths  of  the 
coefficient  of  col.  V. 

Both  ends  rigidly  fixed, 
or  a  continuous  beam, 
with  a  load  in  middle. 

Twice  the  coefficient  of 
col.  II. 

Four  times  the  coeffi- 
cient of  col.  IV. 

Both  ends  rigidly  fixed, 
or  a  continuous  beam, 
with  load  evenly  dis- 
tributed. 

One  and  one-half  times 
the  coefficient  of  col. 
III. 

Five  times  the  coefficient 
of  col.  V. 

Formulae  for  Transverse  Strength  of  Beams.  —  Referring  to  table 
on  page  299, 

P  =  load  at  middle; 

W  =»  total  load,  distributed  uniformly; 

I  =•  length,  b  =  breadth,  d  «  depth,  in  inches; 
B  =»  modulus  of  elasticity; 
R  =  modulus  of  rupture,  or  stress  per  square  inch  of  extreme  fiber; 

7  =  moment  of  inertia; 

c  =  distance  between  neutral  axis  and  extreme  fibre. 
For  breaking  load  of  circular  section,  replace  bd?  by 


BEAMS   OF   UNIFORM   STRENGTH. 


301 


The  value  of  R  at  rupture,  or  the  modulus  of  rupture  (see  page  282), 
is  about  60,000  for  structural  steel,  and  about  110,000  for  strong  steel. 
(Merriman.) 

For  cast  iron  the  value  of  R  varies  greatly  according  to  quality.  Thurs- 
ton  found  45,740  and  67,980  in  No.  2  and  No.  4  cast  iron,  respectively. 

For  beams  fixed  at  both  ends  and  loaded  in  the  middle,  Barlow,  by 
experiment,  found  the  maximum  moment  of  stress  =  1/6  PI  instead  of 
1/8  PI,  the  result  given  by  theory.  Prof.  Wood  (Resist.  Matls.  p.  155) 
says  of  this  case:  The  phenomena  are  of  too  complex  a  character  to  admit 
of  a  thorough  and  exact  analysis,  and  it  is  probably  safer  to  accept  the 
results  of  Mr.  Barlow  in  practice  than  to  depend  upon  theoretical  results. 


BEAMS  OP  UNIFORM  STRENGTH  THROUGHOUT  THEIR 
LENGTH. 


The  section  is  supposed  in  all  cases  to  be  rectangular  throughout.  The 
beams  shown  in  plan  are  of  uniform  depth  throughout.  Those  shown  in 
elevation  are  of  uniform  breadth  throughout. 

B  =•  breadth  of  beam.     D  =  depth  of  beam. 


ELEVATION. 


Fixed  at  one  end,  loaded  at  the  other* 
curve  parabola,  vertex  at  loaded  end ;  BD 
proportional  to  distance  from  loaded  end- 
The  beam  may  be  reversed,  so  that  the 
upper  edge  is  parabolic,  or  both  edges  may 
be  parabolic. 

Fixed  at  one  end,  loaded  at  tne  other; 
triangle,  apex  at  loaded  end ;  BD2  propor- 
tional to  the  distance  from  the  loaded  end. 

Fixed  at  one  end ;  load  distributed ;  tri- 
angle, apex  at  unsupported  end ;  BD2  pro- 
portional to  square  of  distance  from  unsup- 
ported end. 

Fixed  at  one  end;  load  distributed; 
curves  two  parabolas,  vertices  touching 
each  other  at  unsupported  end;  BD* 
proportional  to  distance  from  unsupported 
end. 

Supported  at  both  ends;  load  at  any  one 
point;  two  parabolas,  vertices  at  the 
points  of  support,  bases  at  point  loaded; 
BD2  proportional  to  distance  from  nearest 
point  of  support.  The  upper  edge  or 
both  edges  may  also  be  parabolic. 

Supported  at  both  ends ;  load  at  any  one 
point;  two  triangles,  apices  at  points  of 
support,  bases  at  point  loaded;  BD2  pro- 
portional to  distance  from  the  nearest 
point  of  support. 

Supported  at  both  ends;  load  distri- 
buted; curves  two  parabolas,  vertices  at 
the  middle  of  the  beam;  bases  centre  line 
of  beam;  BD2  proportional  to  product  of 
distances  from  points  of  support. 

Supported  at  both  ends;  load  distri- 
buted; curve  semi-ellipse:  BD2  propor- 
tional to  the  product  of  the  distances 
from  the  points  of  support. 


302 


STRENGTH   OF   MATERIALS. 


DIMENSIONS  AND  WEIGHTS  OF  STEUCTUEAL  STEEL 
SECTIONS   COMMONLY   EOLLED. 

(  Carnegie  Steel  Co.,  1913.) 


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STRENGTH   OF   MATERIALS. 


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PROPERTIES   Otf  ROLLED   STRUCTURAL   STEEL.     305 


Weights  and  Dimensions  of  I-Beams. 


Size, 
In. 

Wt. 

f£ 

Lb. 

Size, 
In. 

Wt. 

ST. 

Lb. 

Size, 
In. 

Wt. 
per 
Ft., 
Lb. 

Size, 
In. 

Wt. 

IE 

Lb. 

Size, 
In. 

Wt. 

f£ 

Lb. 

Size, 
In. 

Wt. 
per 
Ft., 
Lb. 

27 
24 

83.0 
115.0 
110.0 
105.0 
100.0 
95.0 
90.0 
85.0 
80.0 
69  5 

20 
18 

90.0 
85.0 
8D.O 
75.0 
70.0 
65.0 
90.0 
85.0 
80.0 
75  0 

18 
15 

55.0 
46.0 
75.0 
70.0 
65.0 
60.0 
55.0 
50.0 
45.0 
42  0 

12 
10 

45.0 
40.0 
35.0 
31.5 
27.5 
40.0 
35.0 
30.0 
25.0 
22  0 

9 
8 

7 
6 

21.0 
25.5 
23.0 
20.5 
18.0 
17.5 
20.0 
17.5 
15.0 
17.25 

5 

4 

3 

12.25 
9.75 
10.5 
9.5 
8.5 
7.5 
7.5 
6.5 
5.5 

21 

57  5 

70  0 

36  0 

9 

35  0 

14.75 

20 

100.0 
95.0 

65.0 
60.0 

12 

55.0 
50.0 

30.0 
25.0 

5 

12.25 
14.75 

Weights  and  Dimensions  of  Channels. 


15 

55.0 
50.0 
45.0 
40.0 
35  0 

13  • 
12 

37.0 
35.0 
32.0 
40.0 
35  0 

10 
9 

30.0 
25.0 
20.0 
15.0 
25  0 

8 
7 

18.75 
16.25 
13.75 
11.25 
19  75 

6 
5 

15.5 
13.0 
10.5 
8.0 
11  5 

4 
3 

5.25 
6.0 
5.0 
4.0 

13 

33.0 
50  0 

' 

30.0 
25  0 

20.0 
15  0 

17.25 
14  75 

9.0 
6  5 

45  0 

20  5 

13  25 

12  25 

4 

7  25 

40.0 

10 

35.0 

8 

21.25 

9.75 

6.25 

PROPERTIES  OF  ROLLED  STRUCTURAL  STEEL. 

Explanation  of  Tables  of  the  Properties  of  I-Beams,  Channels, 
Angles,  Z-Bars,  Tees,  etc.      (Carnegie  Steel  Co.) 

The  tables  of  properties  of  I-beams  and  channels,  pp.  307  to  313, 
are  calculated  for  all  standard  sizes  and  weights  to  which  each  pattern 
is  rolled,  excepting  for  five  weights  of  the  13-in.  channel  which  is  omitted 
in  the  tables.  The  table  of  properties  of  angles  are  calculated  for  the 
maximum,  intermediate,  and  minimum  weights  of  each  size,  excepting 
that  only  maximum  and  minimum  weights  are  given  for  a  few  of  the 
smaller  sizes  as  noted  in  the  tables.  The  properties  of  Z-bars  are  given 
for  thicknesses  differing  by  Vi6  in.  The  table  of  properties  of  Tee  shapes 
lists  the  lightest  section  of  each  size.  In  the  case  of  angles  there  will 
be  two  section  moduli  for  each  position  of  the  neutral  axis,  since  the 
distance  between  the  neutral  axis  and  the  extreme  fiber  is  different  on 
either  side  of  the  axis.  With  T-sections  there  are  two  section  moduli 
where  the  neutral  axis  is  parallel  to  the  flange.  In  these  cases  only 
the  smaller  section  moduli  are  given. 

The  column  headed  x,  in  the  table  of  the  properties  of  standard 
channels,  giving  the  distance  of  the  center  of  gravity  of  channel  from 
the  outside  of  web,  is  used  to  obtain  the  radius  of  gyration  for  columns 
or  struts  consisting  of  two  channels  latticed,  for  the  case  of  the  neutral 
axis  passing  through  the  center  of  the  cross-section  parallel  to  the  webs 
of  the  channels.  This  radius  of  gyration  is  equal  to  the  distance  be- 
tween the  center  of  gravity  of  the  channel  and  the  center  of  the  section, 
i.e.,  neglecting  the  moments  of  inertia  of  the  channels  around  their  own 
axes,  thereby  introducing  a  slight  error  on  the  side  of  safety. 

In  the  tables  of  safe  loads  of  beams  and  channels,  the  safe  loads  for 
various  lengths  of  span  are  given  only  for  the  lightest  weight  of  each 
section  rolled  in  the  various  sizes.  The  safe  loads  of  the  heavier  weights 
of  each  section  can  be  calculated  from  the  data  given  in  the  tables  of 
properties.  The  safe  loads  given  in  the  tables  are  for  a  uniform  load 
per  running  foot  on  the  beam  or  channel.  If  the  load,  instead  of  being 
uniform,  is  concentrated  at  the  center  of  the  span,  multiply  it  by  2 
and  then  consider  it  as  a  uniform  load.  The  deflection  will  be  0,8  X 


306 


STRENGTH   OF   MATERIALS* 


the  deflection  for  the  uniform  load.  The  safe  loads  in  the  tables  are 
calculated  solely  with  reference  to  the  safe  unit  stresses  due  to  flexure, 
and  the  values  given  will  not  produce  average  shearing  stresses  in  the 
web  greater  than  -10, 000  Ib.  per  sq.  in.,  the  maximum  allowed  in  the 
American  Bridge  Co.'s  specifications.  When  the  beams  carry  con- 
centrated loads,  the  buckling  or  shearing  stresses  in  the  web,  rather 
than  the  resistance  of  the  flanges  to  bending  stresses  may  limit  the 
carrying  capacity. 

The  tables  of  safe  loads  for  angles,  tees,  and  Z-bars  give  the  safe  loads 
on  a  span  of  1  ft.,  from  which  the  safe  load  for  any  length  of  span  may 
be  obtained  by  direct  division.  They  also  give  the  values  at  which 
the  allowed  safe  load  will  produce  the  maximum  allowable  deflection 
of  1/360  of  the  span  length. 

The  tables  are  based  on  an  extreme  fiber  stress  of  16,000  Ib.  per  sq.  in., 
which  is  the  customary  figure  for  quiescent  loads,  as  in  buildings. 
Where  running  loads  are  involved,  as  in  bridges,  crane  runways,  etc.,  an 
extreme  fiber  stress  of  12,500  Ib.  per  sq.  in.  should  be  used  and  the  values 
reduced  accordingly.  For  suddenly  applied  loads,  the  extreme  fiber 
stresses  should  be  reduced  to  8,000  Ib.  per  sq.  in. 

It  is  assumed  in  the  tables  that  the  load  is  applied  normal  to  the 
neutral  axis  perpendicular  to  the  web  at  the  center,  and  that  the  beam 
deflects  only  vertically  in  the  plane  of  bending.  For  other  conditions 
of  loading,  the  safe  load  must  be  determined  by  the  general  theory  of 
flexure  (see  page  297)  in  accordance  with  the  mode  of  application  of  the 
load  and  its  character.  Under  these  conditions  the  safe  loads  will  be 
considerably  lower  than  those  given  in  the  tables.  It  is  also  assumed 
in  the  tables  that  the  compression  flanges  of  the  various  sections  are 
secured  against  lateral  deflection  by  the  use  of  the  rods  at  proper  inter- 
vals. The  lateral  unsupported  length  of  beams  and  girders  should  not 
exceed  forty  times  the  width  of  the  compression  flange.  When  thj 
unsupported  length  exceeds  ten  times  this  width,  the  tabular  safe  loads 
should  be  reduced  as  follows,  W  being  the  width  of  the  compression 
flange: 
Length  of  unsupported 

•  flange 5W  WW  15W  20W  25W  'SOW  35W  40W 

Percentage  of  full  safe 

load  allowed 100     100    90.6    81.2    71.9    62.5    53.1    43.8 

In  addition  to  the  lateral  deflection  induced  by  pure  bending  stresses 
in  the  beam,  there  may  be  deflection  due  to  the  thrust  of  arches  or 
other  loads  acting  on  a  line  perpendicular  to  the  line  of  the  principal 
stresses.  These  should  be  neutralized  by  tie  rods  so  that  in  no  case 
will  the  unit  stresses  exceed  16,000  Ib.  per  sq.  in. 

(For  much  other  important  information  concerning  rolled  structural 
shapes,  see  the  "Pocket  Companion"  of  the  Carnegie  Steel  Co.,  Pitts- 
burgh, Pa.,  price  $2.) 

Allowable  Tension  Values  in  Bars— Thousands  of  Pounds. 

(Carnegie  Steel  Co.,  1913.) 


Round  Bars. 

Square  Bars. 

Round  Bars. 

Square  Bars. 

Size, 

Unit 

Unit 

Unit 

Unit 

Size, 

Unit 

Unit 

Unit 

Unit 

In. 

Stress 

Stress 

Stress 

Stress 

In. 

Stress 

"  Stress 

Stress 

Stress 

16,000 

20,000 

16,000 

20,000 

16,000 

20,000 

16,000 

20,000 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

Lb.  per 
Sq.  In. 

1/4 

0.8 

1.0 

1  .0 

1.3 

13/4 

38.5 

48.1 

49.0 

61.3 

1/fl 

3.1 

3.9 

4.0 

5.0 

2 

50.3 

62.8 

64.0 

80.0 

3/4 

7.1 

8.8 

9.0 

11  .3 

2l/4 

63.6 

79.5 

81  .0 

101.3 

12.6 

15.7 

16.0 

20.0 

21/2 

78.5 

98.2 

100.0 

125.0 

11/4 

19.6 

24.5 

25.0 

31  .3 

23/4 

95.0 

118.8 

121  .0 

151,3 

U/2 

28.3 

35.3 

36.0 

45.0 

3 

113.1 

141.4 

144.0 

180.0 

PKOPERTIES  OF  ROLLED  STRUCTURAL  STEEL.    307 


Properties  of  Carnegie  Standard  I-Beams  —  Steel.* 


. 

Neutral  Axis  Per- 

Neutral Axis  Coin- 

• 

•g 

Q) 

5 

pendicular  to  Web 

cident  with  Center 

1 

1 

a 
.2 

P? 

at  Center. 

Line  of  Web. 

2 

& 

E 
*s 

"o 

"o   . 

-§ 

m 

o   . 

-§ 

1 

o 

1 

? 

03 

o 
1 

u 

4J    03 

n 

11 

|f 

•ft 

|! 

if 

|1 

Q 

£ 

1 

If 

1 

r 

1° 

1^ 

1" 

JjO 

1^ 

in. 

Ib 

sq.  in. 

in. 

in. 

in.* 

in. 

in.3 

in.* 

in. 

in.3 

27 

83.0 

24.41 

7.500 

0.424 

2888.6 

10.88 

214.0 

53.1 

1.47 

14.1 

24 

115.0 

33.98 

8.000 

0.750 

2955.5 

9.33 

246.3 

83.2 

1.57 

20.8 

110.0 

32.48 

7.938 

0.688 

2883.5 

9.42 

240.3 

81.0 

1.58 

20.4 

«« 

105.0 

30.98 

7.875 

0.625 

2811.5 

9.53 

234.3 

78.9 

1.60 

20.0 

M 

100.0 

29.41 

7.254 

0.754 

2379.6 

9.00 

198.3 

48.6 

1.28 

13.4 

«« 

95.0 

27.94 

7.193 

0.693 

2309.0 

9.09 

192.4 

47.1 

1.30 

13.1 

«« 

90.0 

26.47 

7.131 

0.631 

2238.4 

9.20 

186.5 

45.7 

1.31 

12.8 

«« 

85.0 

25.00 

7.070 

0.570 

2167.8 

9.31 

180.7 

44.4 

1.33 

12.6 

«« 

80.0 

23.32 

7.000 

0.500 

2087.2 

9.46 

173.9 

42.9 

1.36 

12.3 

«« 

69.5 

20.44 

7.000 

0.390 

1928.0 

9.71 

160.7 

39.3 

1.39 

11.2 

2\ 

57.5 

16.85 

6.500 

0.357 

1227.5 

8.54 

116.9 

28.4 

1.30 

8.8 

20 

100.0 

29.41 

7.284 

0.884 

1655.6 

7.50 

165.6 

52.7 

1.34 

14.5 

95.0 

27.94 

7.210 

0.810 

1606.6 

7.58 

160.7 

50.8 

1.35 

14.1 

*» 

90.0 

26.47 

7.137 

0.737 

1557.6 

7.67 

155.8 

49.0 

1.36 

13.7 

«« 

85.0 

25.00 

7.063 

0.663 

1508.5 

7.77 

150.9 

47.3 

1.37 

13.4 

«« 

80.0 

23.73 

7.000 

0.600 

1466.3 

7.86 

146.6 

45.8 

.39 

13.1 

M 

75.0 

22.06 

6.399 

0.649 

1268.8 

7.58 

126.9 

30.3 

.17 

9.5 

" 

70.0 

20.59 

6.325 

0.575 

1219.8 

7.70 

122.0 

29.0 

.19 

9.2 

« 

65.0 

19.08 

6.250 

0.500 

1169.5 

7.83 

117.0 

27.9 

.21 

8.9 

18 

90.0 

26.47 

7.245 

0.807 

1260.4 

6.90 

140.0 

52.0 

.40 

14.4 

85.0 

25.00 

7.163 

0.725 

1220.7 

6.99 

135.6 

50.0 

.42 

14.0 

« 

80.0 

23.53 

7.082 

0.644 

1181.0 

7.09 

131.2 

48.1 

.43 

13.6 

« 

75.0 

22.05 

7.000 

0.562 

1141.3 

7.19 

126.8 

46.2 

.45 

13.2 

«< 

70.0 

20.59 

6.259 

0.719 

921.2 

6.69 

102.4 

24.6 

.09 

7.9 

«< 

65.0 

19.12 

6.177 

0.637 

881.5 

6.79 

97.9 

23.5 

.11 

7.6 

«« 

60.0 

17.65 

6.095 

0.555 

841.8 

6.91 

93.5 

22.4 

.13 

7.3 

«« 

55.0 

15.93 

6.000 

0.460 

795.6 

7.07 

88.4 

21.2 

.15 

7.1 

« 

46.0 

13.53 

6.000 

0.322 

733.2 

7.36 

81.5 

19.9 

.21 

6.6 

15 

75.0 

22.06 

6.292 

0.882 

691.2 

5.60 

92.2 

30.7 

.18 

9.8 

70.0 

20.59 

6.194 

0.784 

663.7 

5.68 

88.5 

29.0 

.19 

9.4 

« 

65.0 

19.12 

6.096 

0.686 

636.1 

5.77 

84.8 

27.4 

.20 

9.0 

M 

60.0 

17.67 

6.000 

0.590 

609.0 

5.87 

81.2 

26.0 

.21 

8.7 

" 

55.0 

16.18 

5.746 

0.656 

511.0 

5.62 

68.1 

17.1 

.02 

5.9 

M 

50.0 

14.71 

5.648 

0.558 

483.4 

5.73 

64.5 

16.0 

.04 

5.7 

«« 

45.0 

13.24 

5.550 

0.460 

455.9 

5.87 

60.8 

15.1 

.07 

5.4 

«« 

42.0 

12.48 

5.500 

0.410 

441.8 

5.95 

58.9 

14.6 

.08 

5.3 

«« 

36.0 

10.63 

5.500 

0.289 

405.1 

6.17 

54.0 

13.5 

.13 

4.9 

12 

55.0 

16.18 

5.611 

0.821 

321.0 

4.45 

53.5 

17.5 

.04 

6.2 

50.0 

14.71 

5.489 

0.699 

303.4 

4.54 

50.6 

16.1 

.05 

5.9 

« 

45.0 

13.24 

5.366 

0.576 

285.7 

4.65 

47.6 

14.9 

.06 

5.6 

«« 

40.0 

11.84 

5.250 

0.460 

269.0 

4.77 

44.8 

13.8 

.08 

5.3 

«« 

35.0 

10.29 

5.086 

0.436 

228.3 

4.71 

38.0 

10.1 

0.99 

4.0 

« 

31.5 

9.26 

5.000 

0.350 

215.8 

4.83 

36.0 

9.5 

.01 

3.8 

«« 

27.5 

8.04 

5.000 

0.255 

199.6 

4.98 

33.3 

8.7 

.04 

3.5 

10 

40.0 

11.76 

5.099 

0.749 

158.7 

3.67 

31.7 

9.5 

0.90 

3.7 

«« 

35.0 

10.29 

4.952 

0.602 

146.4 

3.77 

29.3 

8.5 

0.91 

3.4 

«« 

30.0 

8.82 

4.805 

0.455 

134.2 

3.90 

26.8 

7.7 

0.93 

3.2 

« 

25.0 

7.37 

4.660 

0310 

122.1 

4.07 

24.4 

6.9 

0.97 

3.0 

" 

22.0 

6.52 

4.670 

0.232 

113.9 

4.18 

22.8 

6.4 

0.99 

2.7 

*  See  notes  on  next  page. 


(Table  continued  on  next  page.') 


308 


STRENGTH   OF  MATERIALS, 


Properties  of  Carnegie  Standard  I-Beams— Steel.— Continued. 


Neutral  Axis  Per- 

Neutral Axis  Coin- 

. 

o3 

1 

pendicular  to  Web 

cident  with  Center 

i 

§ 

g 

i 

p» 

at  Centeix 

Line   of  Web. 

1 

E 

o 

o   . 

_  fl 

. 

o 

d 

. 

•s 

p, 

J 

•s 

S 

^•~ 

3 

-u.rt 

•8-S 

•g 

f 

"M 

"* 

1 

11 

$  8 

|1. 

<u  "E 
S  o> 

ss 

ll 

M 

S 

'S 

<u 

25 

P 

55 

P 

lo 

t5^ 

Q 

£ 

< 

^ 

H 

£ 

PH 

|! 

S 

$ 

"m7 

Ib. 

sq.  in. 

in. 

in. 

in.* 

in. 

in.3 

in.* 

in  i 

in.3 

9 

35.0 

10.29 

4.772 

0.732 

111.8 

3.29 

24.8 

7.3 

0.84 

3.1 

" 

30.0 

8.82 

4.609 

0.569 

101.9 

3.40 

22.6 

6.4 

0.85 

2.8 

" 

25.0 

7.35 

4.446 

0.406 

91.9 

3.54 

20.4 

5.7 

0.88 

2.5 

" 

21.0 

6.31 

4.330 

0.290 

84.9 

3.67 

18.9 

5.2 

0.90 

2.4 

8 

25.5 

7.50 

4.271 

0.541 

68.4 

3.02 

17.1 

4.8 

0.80 

2.2 

*' 

23.0 

6.76 

4.179 

0.449 

64.5 

3.09 

16.1 

4.4 

0.81 

2.1 

" 

20.5 

6.03 

4.087 

0.357 

60.6 

3.17 

15.2 

4.1 

0.82 

2.0 

'« 

18.0 

5.33 

4.000 

0.270 

56.9 

3.27 

14.2 

3.8 

0.84 

1.9 

" 

17.5 

5.15 

4.330 

0.210 

58.3 

3.37 

14.6 

4.5 

.0.93 

2.1 

7 

20.0 

5.88 

3.868 

0.458 

42.2 

2.68 

12.1 

3.2 

0.74 

.7 

•« 

17.5 

5.15 

3.763 

0.353 

39.2 

2.76 

11.2 

2.9 

0.76 

.6 

" 

15.0 

4.42 

3.660 

0.250 

36.2 

2.86 

10.4 

2.7 

0.78 

.5 

6 

17.25 

5.07 

3.575 

0.475 

26.2 

2.27 

8.7 

2.4 

0.68 

.3 

*« 

14.75 

4.34 

3.452 

0.352 

24.0 

2.35 

8.0 

2.1 

0.69 

.2 

«« 

12.25 

3.61 

3.330 

0.230 

21.8 

2.46 

7.3 

.9 

0.72 

5 

14.75 

4.34 

3.294 

0.504 

15.2 

1.87 

6.1 

.7 

0.63 

!o 

" 

12.25 

3.60 

3.147 

0.357 

13.6 

1.94 

5.5 

.5 

0.63 

0.92 

«« 

9.75 

2.87 

3.000 

0.210 

12.1 

2.05 

4.8 

.2 

0.65 

0.82 

4 

10.5 

3.09 

2.880 

0.410 

7.1 

.52 

3.6 

.0 

0.57 

0.70 

«« 

9.5 

2.79 

2.807 

0.337 

6.8 

.55 

3.4 

0.93 

0.58 

0.66 

«* 

8.5 

2.50 

2.733 

0.263 

6.4 

.59 

3.2 

0.85 

0.58 

0.62 

•f 

7.5 

2.21 

2.660 

0.190 

6.0 

.64 

3.0 

0.77 

0.59 

0.58 

3 

7.5 

2.21 

2.521 

0.361 

2.9 

.15 

1.9 

0.60 

0.52 

0.48 

<« 

6.5 

1.91 

2.423 

0.263 

2.7 

.19 

1.8 

0.53 

0.52 

0.44 

" 

5.5 

1.63 

2.330 

0.170 

2.5 

.23 

1.7 

0.46 

0.53 

0.40 

L  =  safe  loads  in  pounds,  uniformly  distributed ;  I  =  span  in  feet; 
M  =  moments  of  forces  in  foot-pounds ;  /  =  fiber  stress. 
S  —  section  modulus. 


=  S£?;    L  =  ~  f~;  for/=  16,0001b.per  sq.  in.  (for  build- 

J.&  O         I 

ings)  •  L  =  32)^°7°  3  for/  =  12,500  Ib.  per  sq.  in.  (for  bridges) ;  L  =  25^°70  3 

pi  o  I 

Properties  of  Carnegie  Trough  Plates  —  Steel. 


Moment  of 

Sec- 
tion 
Index. 

Size,  in 
Inches. 

Weight 
per 
Foot. 

Area 
of  Sec- 
tion. 

Thick- 
ness   in 
Inches. 

Inertia, 
Neutral 
Axis 
Parallel    to 

Section 
Modulus, 
Axis  as 
before. 

Radius 
of  Gy- 
ration, 
Axis   as 

Length. 

before. 

Ib. 

sq.  in. 

/ 

S 

r 

M  10 

91/2X33/4 

16.3 

4.78 

V2 

3.7 

1.4 

0.91 

M  11 

91/2X3  3/4 

18.0 

5.28 

9/16 

4.1 

1.6 

0.91 

M  12 

91/2X33/4 

19.7 

5.79 

5/8 

4.6 

1.8 

0,90 

M  13 

91/2X33/4 

21.4 

6.30 

H/16 

5.0 

2.0 

0.90 

M  14 

91/2X33/4 

23.2 

6.97 

3/4 

5.5 

2.2 

0.90 

PROPERTIES  OF  ROLLED  STRUCTURAL  STEEL.   309 


Safe  Loads,  in  Thousands  of  Pounds,  Uniformly  Distributed  for 
Carnegie  Steel  I-Beams. 


e 
I 

27  in. 

83 
Ib. 

24-inch. 

21  in. 

57^ 
Ib. 

20-inch. 

18-inch. 

1  5-inch. 

105 

Ib. 

80  Ib. 

69K 

)b. 

80  Ib. 

65  Ib. 

75  Ib. 

46  Ib. 

60  Ib: 

42  Ib. 

36 

Ib. 

4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

177  0 

173.2 
144.4 
123.7 
108.3 
96.2 
86.6 
78.7 
72.2 
66.6 
61.9 
57.7 
54.1 
50.9 
48.1 
45.6 
43.3 
41.2 
39.4 
37.7 
36.1 
34.6 
33.3 
32.1 
30.9 
29.9 
28.9 

123.0 
104.8 
89.8 
78.5 
69.8 
62.8 
57.1 
52.4 
48.3 
44.9 
41.9 
39.3 
37.0 
34.9 
33.1 
31.4 
29.9 
28.6 
27.3 
26.2 
25.1 
24.2 
23.3 
22.4 
21.7 
20.9 

86.7 
823 
72.0 
64.0 
57.6 
52.4 
48.0 
44.3 
41.2 
38.4 
36.0 
33.9 
32.0 
30.3 
28.8 
27.4 
26.2 
25.1 
24.0 
23.0 
22.2 
21.3 
20.6 
19.9 
19.2 
18.6 
18.0 

240.0 
223.4 
195.5 
173.8 
156.4 
142.2 
130.3 
120.3 
111.7 
104.3 
97.7 
92.0 
86.9 
82.3 
78.2 
74.5 
71.1 
68.0 
65.2 
62.6 
60.2 
57.9 
55.9 
53.9 
52.1 
50.5 
48.9 
47.4 
46.0 
44.7 
43.4 
42.3 
41.2 
40.1 
39.1 

200.0 

202.3 

115.9 

229.0 
228.2 
207.5 
190.2 
175.6 
163.0 
152.2 
142.6 
134.3 
126.8 
120.1 
114.1 
108.7 
103.7 
99.2 
95.1 
91.3 
87.8 
84.5 
81.5 
78.7 
76.1 
73.6 
71.3 
69.2 
67.1 
65.2 
63.4 
61.7 
60.1 
58.5 
57.1 
55.7 
54.3 
53.1 
51.9 
50.7 
49.6 
48.6 
47.5 
46.6 
45.6 

300.0 

240.0 

187.2 
171.4 
155.8 
142.8 
131.8 
122.4 
114.3 
107.1 
100.8 
95.2 
90.2 
85.7 
81.6 
77.9 
74.5 
71.4 
68.6 
65.9 
63.5 
61.2 
59.1 
57.1 
55.3 
53.6 
51.9 
50.4 
49.0 
47.6 
46.3 
45.1 
43.9 
42.8 
41.8 
40.8 
39.9 
38.9 
38.1 
37.3 
36.5 
35.7 
35.0 
34.3 

150.0 

178.2 
155.9 
138.6 
124.7 
113.4 
104.0 
96.0 
89. 
83.2 
78.0 
73.4 
69.3 
65.7 
62.4 
59.4 
56.7 
54.2 
52.0 
49.9 
48.0 
46.2 
44.6 
43.0 
41.6 
40.2 
39.0 
37.8 
36.7 
35.6 
34.7 
33.7 
32.8 
32.0 
31.2 
30.4 
29.7 

193.2 
169.1 
150.3 
135.3 
123.0 
112.7 
104.1 
96.6 
90.2 
845 
79.6 
75.1 
71.2 
67.6 
64.4 
61.5 
58.8 
56.4 
54.1 
52.0 
50.1 
48.3 
46.6 
45.1 
43.6 
42.3 
41.0 
39.8 
38.6 
37.6 

231.9 
206.1 
185.5 
168.7 
154.6 
142.7 
132.5 
123.7 
116.0 
10X1 
103.1 
97.6 
92.8 
88.3 
84.3 
80.7 
77.3 
74.2 
71.4 
68.7 
66.3 
64.0 
61.8 
59.8 
58.0 
56.2 
54.6 
53.0 
51.5 
50.1 
48.8 
47.6 
46.4 
45.3 
44.2 
43.1 
42.2 
41.2 
40.3 
39.5 
387 

108.6 
96.6 
86.9 
79.0 
72.4 
66.8 
62.1 
57.9 
54.3 
51.1 
48.3 
45.7 
43.4 
41.4 
39.5 
37.8 
3&.2 
34.8 
33.4 
32.2 
31.0 
30.0 
29.0 
28.0 
27.2 
26.3 
25.6 
24.8 
24.1 

277.7 
249.9 
227.2 
208.3 
192.2 
178.5 
166.6 
156.2 
147.0 
138.8 
131.5 
125.0 
119.0 
113.6 
108.7 
104.1 
100.0 
96.1 
92.6 
89.3 
86.2 
83.3 
80.6 
78.1 
75.7 
73.5 
71.4 
69.4 
67.5 
65.8 
64.1 
62.5 
61.0 
59.5 
58.1 
56.8 
55.5 
54.3 
53.2 
52.1 

138.6 
124.7 
113.4 
103.9 
95.9 
89.1 
83.1 
77.9 
73.4 
69.3 
65.6 
62.4 
59.4 
56.7 
54.2 
52.0 
49.9 
48.0 
46.2 
44.5 
43.0 
41.6 
.40.2 
39.0 
37.8 
36.7 
35.6 
34.6 
33.7 
32.8 
32.0 
31.2 
30.4 
29.7 

27.9 
27.1 

20.3 
19.6 

36.6 
35.6 

23.5 
22.9 

38.1 
37.2 

29.0 
28.3 

Table  con- 
tinued   on 
next  page. 

51.0 
50.0 

37.9 
37.1 

Loads  above  upper  horizontal  lines  will  produce  maximum  allow- 
able shear  in  webs.  Loads  below  lower  horizontal  lines  will  produce 
excessive  deflections  and  must  not  be  used  with  plastered  ceilings. 
Maximum  fiber  stress,  16,000  Ib.  per  sq.  in.  Safe  loads  given  include 
the  weight  of  beam,  which  should  be  deducted  to  give  net  load. 


310 


STRENGTH   OF  MATERIALS. 


Safe  Loads,  in  Thousands  of  Pounds,  Uniformly  Distributed  for 
Carnegie  Steel  I-Beams. — Continued. 


i 

a 
^ 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
r  j 
J2 
13 
14 
15 
16 

r 

18 
19 
20 
21 
22 
23 
24 
25 
26 

12-inch. 

1  0-inch. 

9-in. 

8-inch. 

7-in. 

6-in. 

5-in. 

4-in. 

3-in. 

40  Ib. 

31^ 
Ib. 

27y2 

Ib. 

25 

Ib. 

22 
Ib. 

21 
Ib. 

18 

Ib. 

17^ 
Ib. 

15 

Ib. 

12M 
Ib. 

9M 
Ib. 

7Yz 
Ib. 

5^ 
Ib. 

10.2 
— 
5.9 
4.4 
3.5 
2.9 
— 
2.2 

27.6 
25.8 
19.4 
15.5 
12.9 
11.1 
9.7 
8.6 
7.7 

7.0 
6.5 

21.0 
17.2 
12.9 
10.3 
8.6 
7.4 
6.4 
5.7 
5.2 
4.7 
4.3 

15.2 
10.6 
8.0 
6.4 
5.3 
4.5 
4.0 
3.5 
3.2 

52.2 
50.3 
40.3 
33.6 
28.8 
25.2 
22.4 
20.1 
18.3 
16.8 
15.5 
14.4 
13.4 
12.6 
11.8 
11.2 

43.2 
37.9 
30.3 
25.3 
21.7 
19.0 
16.9 
15.2 
13.8 
12.6 
11.7 
10.8 
10.1 
9.5 
8.9 
8.4 

33.6 

35.0 
27.6 
22.1 
18.4 
15.8 
13.8 
12.3 
11.0 
10.0 
9.2 

8.5 
7.9 

110.4 

84.0 

61.2 
59.1 
50.7 
44.4 
39.4 
35.5 
32.3 
29.6 
27.3 
25.3 
23.7 
22.2 
20.9 
19.7 
18.7 
17.7 
16.9 
16.1 
15.4 
14.8 

62.0 

46.4 

"4U3 

34.7 
30.4 
27.0 
24.3 
22.1 
20.2 
18.7 
17.4 
16.2 
15.2 
14.3 
13.5 
12.8 
12.1 
11.6 
11.0 

95.6 
79.7 
68.3 
59.8 
53.1 
47.8 
43.5 
39.8 
36.8 
34.2 
31.9 
29.9 
28.1 
26.6 
25.2 
23.9 
22.8 
21.7 
20.8 
19.9 

76.7 
63.9 
54.8 
48.0 
42.6 
38.4 
34.9 
32.0 
29.5 
27.4 
25.6 
24.0 
22.6 
21.3 
20.2 
19.2 
18.3 
17.4 
16.7 
16.0 

52.1 
43.4 
37.2 
32.6 
28.9 
26.0 
23.7 
21.7 
20.0 
18.6 
17.4 
16.3 
15.3 
14.5 
13.7 
13.0 

12.4 
11.8 

31.1 
25.9 
22.2 
19.4 
17.3 
15.6 
14.1 
13.0 
12.0 
11.1 
10.4 
9.7 
9.2 
8.6 

6.0 
5.5 

Loads  above 
the    upper 
zontal    lines 
produce  maxi- 
Q  allowable 
ar   in  webs, 
is  below  lower 
I  produce  ex- 
and    should 
stered  ceilings. 
?ss,  16,000  Ib. 
>  given  include 
which  should 
net  load. 

7.4 
6.9 

hor 
will 
mur 
she 
Loa 

5S    Wil 

tions, 
hplaj 
r  stn 
loads 
)eam, 
)  give 

10.6 
10.1 

horizontal  line 
cessive    deflec 
not  be  used  wit 
Maximum  flbe 
persq.  in.  Safe 
the  weight  of  t 
be  deducted  tc 

19.1 
18.4 

15.3 
14.8 

14.2 
13.6 

Properties  of  Carnegie  Corrugated  Plates  —  Steel. 


Moment  of 

Sec- 
tion 
Index. 

Size,  in 
Inches. 

Weight 
Foot. 

Area 
of  Sec- 
tion. 

Thick- 
ness in 
Inches. 

Inertia, 
Neutral 
Axis 
Parallel  to 

Section 
Modulus, 
Axis  as 
before. 

Radius 
of  Gy- 
ration, 
Axis  as 

Length. 

before. 

M30 

83/i  XI  1/2 

Ib. 
8.1 

sq.  in. 
2.38 

1/4 

0.64 

S 
0.8 

O.r52 

M31 

83/4    XI  9/16 

10.1 

2.96 

5/16 

0.95 

1.1 

0.57 

M32 

83/4    XI  5/8 

12.0 

3.53 

3/8 

1.3 

1.4 

0.62 

M33 

123/i6X23/4 

17.8 

5.22 

V8 

4.8 

3.3 

0.96 

M34 

123/16X2l3/i6 

20.8 

6.10 

7/16 

5.8 

3.9 

0.98 

M35 

123/16X27/8 

23.7 

6.97 

1/2 

6.8 

4.5 

0.99 

SPACING   OF  I-BEAMS   FOR   UNIFORM  LOAD.       311 


Spacing  of  Carnegie  Steel  I-Beams  for  Uniform  Load  of  100  Lbs. 
per  Square  Foot. 

(Figures  in  table  give  the  proper  distance,  feet,  center  to  center  of  beams.) 


Ill 

Ft. 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

27-in. 
83  Ib. 

228.2 
188.6 
158.5 
135.0 
116.4 
101.4 
89.2 
79.0 
70.4 
63.2 
57.1 
51.8 
47.2 
43.1 
39.6 
36.5 
33.8 
31.3 
29.1 

24-inch. 

21  -in. 

20-inch. 

18-inch. 

1  5-inch. 

105 

Ib. 

249.9 
206.5 
173.6 
147.9 
127.5 
111.1 
97.6 
86.5 
77.1 
69.2 
62.5 
56.7 
51.6 
47.2 
43.4 
40.0 
37.0 
34.3 
31  9 

80 
Ib. 

185.5 
153.3 
128.8 
109.8 
94.7 
82.5 
72.5 
64.2 
57.3 
51.4 
46.4 
42.1 
38.3 
35.1 
32.2 
29.7 
27.5 
25.5 
23.7 

69^ 

Ib. 

171.4 
141.6 
119.0 
101.4 
87.4 
76.2 
66.9 
53.3 
52.9 
47.5 
42.8 
38.9 
35.4 
32.4 
29.8 
27.4 
25.4 
23.5 
21.9 

57^ 
Ib. 

80 
Ib. 

65 

Ib. 

75 

Ib. 

46 

Ib. 

60 

Ib. 

42 
Ib. 

36 

Ib. 

57.6 
47.6 
40.0 
34.1 
29.4 
25.6 
22.5 
19.9 
17.8 
16.0 
14.4 
13.1 
11.9 
10.9 
10.0 
9.2 
8.5 

124.7 
103.1 
86.6 
73.8 
63.6 
55.4 
48.7 
43.2 
38.5 
34.5 
31.2 
28.3 
25.8 
23.6 
21.7 
20.0 
18.5 
17.1 
15.9 

156.4 
129.3 
108.6 
92.6 
79.8 
69.5 
61.1 
54.1 
48.3 
43.3 
39.1 
35.5 
32.3 
29.6 
27.2 
25.0 
23.1 
21.5 
700 

124.8 
103.1 
86.6 
73.8 
63.7 
54.4 
48.7 
43.2 
38.5 
34.6 
31.2 
28.3 
25.8 
23.6 
21.7 
20.0 
18.5 
17.1 
159 

135.3 
111.8 
93.9 
80.0 
69.0 
60.1 
52.8 
46.8 
41.8 
37.5 
33.8 
30.7 
28.0 
25.6 
23.5 
21.6 
20.0 
18.6 
17.3 

e 

7 
6 
5 
4 
3 
3 
3 
2 
2 
2 
1 
1 
1 
1 
1 
1 
1 
1 

6.9 
1.8 
0.4 
1.4 
4.3 
8.6 
3.9 
0.1 
6.8 
4.1 
1.7 
9.7 
8.0 
6.4 
5.1 
3.9 
2.9 
1  9 

86.6 
71.6 
60.1 
51.3 
44.2 
38.5 
33.8 
30.0 
26.7 
24.0 
21.7 
19.6 
17.9 
16.4 
15.0 
13.9 
12.8 

62.8 
51.9 
43.6 
37.2 
32.1 
27.9 
24.5 
21.7 
19.4 
17.4 
15.7 
14.3 
13.0 
11.9 
10.9 
10.1 
9.3 

1  1 

Distance  f 
between 
supports. 

12-inch. 

10-inch. 

9-in 

8-inch. 

7-in. 

6-in. 

5-in. 

4-in 

3-in 

40 
Ib. 

^ 

27^ 
Ib. 

25 
Ib. 

22 
Ib. 

21 

Ib. 

18 
Ib. 

17^ 
Ib. 

15 

Ib. 

W 

ft 

7H 
Ib. 

5^ 
Ib. 

Ft. 

!"• 

61/2 

8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 

60.7 
5%1 
42.1 
35.9 
31.0 
23.7 
18.7 
15.2 
12.5 
10.5 
9.0 
7.7 
6.7 
5.9 

'"53 

4.7 

62 
51 
43 
36 

l\ 

19 
15 
12 
10 
9 
7 
6 
6 
-5 

4 

.2 
.4 
.2 
.8 
.8 
.3 
.2 
.6 
.9 
.8 
.2 
•9 
.9 
.1 

"4 

44.2 
36.5 
30.7 
26.1 
22.5 
17.3 
13.6 
11.0 
9.1 
7.7 
6.5. 
5.6: 

31.0 
25.6 
21.5 
18.3 
15.8 
12.1 
9.6 
7.8 
6.4 
5.4 
'"4.6 
40 

20.6 
17.1 
14.3 
12.2 
10.5 
8.1 
6.4 
5.2 
""4.3 
3.6 

12.7 
10.5 
8.8 
7.5 
6.5 
5.0 

"3.9 

3.2 

.. 

7.1 
5.8 
4.9 

JT.2 
:  3.6 
• 

132.8 

97i6 
74.7 
59.0 
47.8 
39.5 
33.2 
28.3 
24.4 
21.3 
18.7 
165 
14.8 
13.2 
12.0 
10.8 
9.9 
9.0 
8.3 

106.6 

783 
60.0 
47.4 
38.4 
31.7 
26.6 
22.7 
19.6 
17.1 
15.0 
13.3 
11.8 
10.6 
9.6 
8.7 
7.9 
7.3 
6.7 

98.6 

72^4 
55.4 
43.8 
35.5 
29.3 
24.6 
21.0 
18.1 
15.8 
13.9 
12.3 
11.0 
9.8 
8.9 
8.1 
7.3 
6.7 
6.2 

72.4 

532 
40.7 
32.2 
26.1 
21.5 
18.1 
15.4 
13.3 
11.6 
10.2 
9.0 
8.0 
7.2 
6.5 
"5."9 
5.4 

67.5 

49^6 
38.0 
30.0 
24.3 
20.1 
16.9 
14.4 
12.4 
10.8 
9.5 
8.4 
7.5 
6.7 
6.1 
"T.5 
5.0 

55.9 

4l!l 
31.5 
24.9 
20.1 
16.6 
14.0 
11.9 
10.3 
9.0 
7.9 
7.0 
6.2 
•5.6 
5.0 

4.9 
4.3 

8 

For  any  other  load  than  100  Ib.  per  sq.  ft.,  divide  the  spacing  given 
by  the  ratio  the  given  load  per  sq.  ft.  bears  to  100.  Thus  for  a  load 
of  150  Ib.  per  sq.  ft.  divide  by  1.5.  Maximum  fiber  stress  16,000  Ib. 
per  sq.  in. 

Spacings  given  below  the  dotted  horizontal  lines  will  produce  exces- 
sive deflection,  and  should  not  be  used  with  plastered  ceilings. 


312 


STRENGTH  OP  MATERIALS. 


Properties  of  Carnegie  Standard  Channels  —  Steel. 


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430.2 

12.2 

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312.6 

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40. 

11.76 

0.76 

3.42 

196.9 

6.6 

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0.751 

32.8 

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35. 

10.29 

0.64 

3.30 

179.3 

5.9 

4.17 

0.757 

29.9 

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30. 

8.82 

0.51 

3.17 

161.7 

5.2 

4.28 

0.768 

26.9 

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7.35 

0.39 

3.05 

144.0 

4.5 

4.43 

0.785 

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6.03 

0.28 

2.94 

128.1 

3.9 

4.61 

0.805 

21.4 

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0.70 

10 

35. 

10.29 

0.82 

3.18 

115.5 

4.7 

3.35 

0.672 

23.1 

.9 

0.70 

30. 

8.82 

0.68 

3.04 

103.2 

4.0 

3.42 

0.672 

20.7 

.7 

0.65 

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25. 

7.35 

0.53 

2.89 

91.0 

3.4 

3.52 

0.680 

18.2 

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0.62 

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20. 

5.88 

0.38 

2.74 

78.7 

2.9 

3.66 

0.696 

15.7 

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0.61 

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15. 

4.46 

0.24 

2.60 

66.9 

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3.87 

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13.4 

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20. 

5.88 

0.45 

2.65 

60.8 

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3.21 

0.646 

13.5 

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15. 

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2.49 

50.9 

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11.3 

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3.89 

0.23 

2.43 

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0.674 

10.5 

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8 

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183/4 

6.25 
5.51 

0.58 
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2.62 
2.53 

as 

2.3 
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2.77 
2.82 

0.600 
0.603 

11.9 
11.0 

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0.59 
0.57 

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161/4 

4.78 

0.40 

2.44 

39.9 

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2.89 

0.610 

10.0 

0.95 

0.56 

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133/4 

4.04 

0.31 

2.35 

36.0 

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2.98 

0.619 

9.0 

0.87 

0.56 

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1H/4 

3.35 

0.22 

2.26 

32.3 

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3.11 

0.630 

8.1 

0.79 

0.58 

7 

193/4 

5.81 

0.63 

2.51 

33.2 

.9 

2.39 

0.565 

9.5 

0.96 

0.58 

** 

171/4 

5.07 

0.53 

2.41 

30.2 

.6 

2.44 

0.564 

8.6 

0.87 

0.56 

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143/4 

4.34 

0.42 

2.30 

27.2 

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2.50 

0.568 

7.8 

0.79 

0.54 

" 

121/4 

3.60 

0.32 

2.20 

24.2 

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2.59 

0.575 

6.9 

0.71 

0.53 

" 

93/4 

2.85 

0.21 

2.09 

21.1 

0.98 

2.72 

0.586 

6.0 

0.63 

0.55 

6 

151/2 

4.56 

0.56 

2.28 

19.5 

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2.07 

0.529  - 

6.5 

0.74 

0.55 

" 

13. 

3.82 

0.44 

2.16 

17.3 

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2.13 

0.529 

5.8 

0.65 

0.52 

" 

101/2 

3.09 

0.32 

2.04 

15.1 

0.88 

2.21 

0.534 

5.0 

0.57 

0.50 

" 

8. 

2.38 

0.20 

1.92 

13.0 

0.70 

2.34 

0.542 

4.3 

0.50 

0.52 

5 

111/2 

3.38 

0.48 

2.04 

10.4 

0.82 

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0.493 

4.2 

0.54 

0.51 

" 

9. 

2.65 

0.33 

.89 

8.9 

0.64 

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0.493 

3.6 

0.45 

0.48 

" 

61/2 

1.95 

0.19 

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7.4 

0.48 

.95 

0.498 

3.0 

0.38 

0.49 

4 

71/4 

2.13 

0.33 

.73 

4.6 

0.44 

.46 

0.455 

2.3 

0.35 

0.46 

" 

61/4 

1.84 

0.25 

.65 

4.2 

0.38 

.51 

0.454 

2.1 

0.32 

0.46 

" 

51/4 

1.55 

0.18 

.58 

3.8 

0.32 

.56 

0.453 

1.9 

0.29 

0.46 

3 

6. 

1.76 

0.36 

.60 

2.1 

0.31 

.08 

0.421 

1.4 

0.27 

0.46 

f* 

5. 

1.47 

0.26 

.50 

IJS- 

0.25 

.12 

0.415 

1.2 

0.24 

0.44 

" 

4. 

1.19 

0.17 

.41 

1.6 

0.20 

.17 

0.409 

1.1 

0.21 

0.44 

I/  =  safe  load  in  pounds,  uniformly  distributed;  Z  =  span  in  feet; 

M=  moment  of  forces   in   foot-pounds;   /  =  fiber  stress;    S  =  section 

modulus. 

~^  -          ,  ^,  —          ;  for/ =  16,000  Ibs.  per  sq.  in.  (for  buildings); 

14  O    I 

=  32^°70>S  for  /  =  12,500  Ib.  per  sq.  in.  (fo*  bridges),  L  =  ^OpOS 


PROPERTIES  OF  ROLLED  STRUCTURAL  STEEL.       313 
Maximum  Safe  Load  for  Carnegie  Channels  in  thousands  of  Pounds. 


Span, 
Ft. 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 
32 

Depth  and  Weight  of  Sections. 

3  in. 
41b. 

15  in. 
33  Ib. 

13  in. 

32  Ib. 

12  in. 

20^ 
Ib. 

10  in. 
151b. 

9  in. 

13M 
Ib. 

8  in. 

1IM 
Ib. 

7  in. 
9M 
Ib. 

6  in. 
81b. 

5  in. 

ft 

4  in. 
5M 
Ib. 

24.0 

19.0 

14.4 

10.2 

4S.O 

41.4 

35.2 

29.4 

23.1 
15.4 
11.6 
9.2 
7.7 
6.6 
5.8 
5.1 
4.6 
4.2 
3.9 

15.8 
10.5 
7.9 
6.3 
5.3 
4.5 
4.0 
3.5 
3.2 
2.9 
2.6 

10.1 
6.7 
5.1 
4.1 
3.4 
2.9 
2.5 

5.8 
3.9 
2.9 
2.3 
1.9 

L5 

120.0 

97.5 

67.2 

47.6 
35.7 
28.5 
23.8 
20.4 
17.8 
15.9 
14.3 
13.0 
11.9 
11.0 
10.2 
9.5 
8.9 
8.4 
7.9 
7.5 
7  1 

37.4 
28.0 
22.4 
18.7 
16.0 
14.0 
12.5 
11.2 
10.2 
9.3 
8.6 
8.0 
7.5 
7.0 
6.6 
62 

28.7 
21.5 
17.2 
14.4 
12.3 
10.8 
9.6 
8.6 
7.8 
7.2 
6.6 
6.2 
5.7 
5.4 

21.4 
16.1 
12.9 
10.7 
9.2 
8.0 
7.1 
6.4 
5.8 
5.4 
4.9 
4.6 

111.1 
88.9 
74.1 
63.5 
55.6 
49.4 
44.5 
40.4 
37.0 
34.2 
31.8 
29.6 
27.8 
26.1 
24.7 
23.4 
22.3 
21.2 
20.2 
19.3 
18.5 
17.8 
17.1 
16.5 
15.9 
15.3 
14.8 

97.5 
78.0 
65.0 
55.7 
48.7 
43.3 
39.0 
35.4 
32.5 
30.0 
27.9 
26.0 
24.4 
22.9 
21.7 
20.5 
19.5 
18.6 
17.7 
17.0 
16.2 
15.6 
15.0 

56.9 
45.5 
38.0 
32.5 
28.5 
25.3 
22.8 
20.7 
19.0 
17.5 
16.3 
.15.2 
14.2 
13.4 
12.7 
12.0 
11.4 
10.8 
10.4 
9.9 
9.5 

2.2 
2.0 

3.6 
3.3 

4.3 
4.0 

5.1 
4.8 

5.9 
5.6 

6.8 
6.5 

.... 

9.1 
8.8 

Loads  above  upper  horizontal  lines 
will  produce  maximum  allowable  shear 
in  webs.     Loads  below  lower  horizontal 
lines  will  produce  excessive  deflections. 
Maximum    bending    stress,    16,000  Ib. 
per  sq.  in. 

14.4 
13.9 

14.3 
13  9 

Properties  of  Carnegie  T-Shapes  —  Steel. 


Size, 

Mini- 
mum 
Thick- 
ness, In. 

CA 

Neutral  Axis  through  C. 
of  G.  Parallel  to  Flange. 

Neutral    Axis   Co- 
incident with  Cen- 
ter Line  of  Stem. 

i    p. 

Flange 
by 

*3 

H-l 

. 

m 

Stem. 

O.^ 

o   . 

** 

3 

5  <jT 

cfl 

HI    § 

1 

i 

| 

ll 

og 
e«  cr 

S+3 

81 

•i'f 

n3  >> 

el 

.2  ° 

PI 

"£•£ 

n 

It 

ll 

In. 

1 

00 

'j* 

O»H 
% 

£° 

1 

3^ 

S 

5° 

&* 

5      ><  3 

1/2 

13/3* 

13.4 

3.93 

2.4 

0.78 

1.1 

0.73 

5.4 

.17 

2.2 

5      X  21/2 

3/8 

7/16 

10.9 

3.18 

1.5 

0.68 

0.78 

0.63 

4.1 

.14 

.6 

41  /2X  31/2 

7/16 

H/16 

15.7 

4.60 

5.1 

1.05 

2.1 

1.11 

3.7 

0.90 

.7 

41/2X3 

3/8 

3/8 

9.8 

2.88 

2.1 

0.84 

0.91 

0.74 

3.0 

.02 

.3 

41/2X3 

5/16 

5/16 

8.4 

2.46 

1.8 

0.85 

0.78 

0.71 

2.5 

.01 

.1 

41/2  X  2l/2 

3/8 

3/8 

9.2 

2.68 

1.2 

0.67 

0.63 

0.59 

3.0 

.05 

.3 

41/2X21/2 

5/16 

5/16 

7.8 

2.29 

1.0 

0.68 

0.54 

0.57 

2.5 

.05 

•' 

(Table  continued  on  next  page.) 


314 


STRENGTH    OF   MATERIALS. 


Properties  of  Carnegie  T-Shapes — Steel. — Continued. 


Q;_« 

Mini- 
mum 
Thick- 
ness, In. 

at 

Neutral  Axis  through  C. 
of  G.  Parallel  to  Flange. 

Neutral    Axis   Co- 
incident with  Cen- 
ter Line  of  Stem. 

bize, 
Flange 

l-s 

d 

H-  | 

*l« 

d 

by 

St)61Tl 

&3 

1 

o   . 

ri 

*^~ 

•g 

w 

& 

tf 

M  0 

*! 

-p  c3 

I'-d 

0   I- 

5  0) 

°'3 

•§S 

J1 

S.s& 
fl  *  2 
%<£ 

4*    « 

il 

c  & 

°£ 
32 

II 

§ 

| 

'S  fe 

CUC/2 

§5 

to 

$% 

S-3* 

o£ 

lio* 

J^ 

In. 

E 

C/2 

£ 

«i 

2 

K 

t 

Qis-S 

s 

K 

4      X5 

1/2 

1/2 

15.3 

4.50 

10.8 

1.55 

3.1 

.56 

2.8 

0.79 

.4 

4      X5 

3/8 

3/8 

11.9 

3.49 

8.5 

1.56 

2.4 

.51 

2.1 

0.78 

.1 

4      X  41/2 

1/2 

1/2 

14.4 

4.23 

7.9 

1.37 

2.5 

.37 

2.8 

0.81 

.4 

4      X41/2 

3/8 

3/8 

11.2 

3.29 

6.3 

1.39 

2.0 

.31 

2.1 

0.80 

.1 

4      X  4 

1/2 

1/2 

13.5 

3.97 

5.7 

1.20 

2.0 

.18 

2.8 

0.84 

.4 

4      X4 

3/8 

3/8 

10.5 

3.09 

4.5 

1.21 

1.6 

.13 

2.1 

0.83 

.1 

4      X3 

3/8 

3/8 

9.2 

2.68 

2.0 

0.86 

0.90 

0.78 

2.1 

0.89 

.1 

4      X  3 

5/16 

5/16 

7.8 

2.29 

1.7 

0.87 

0.77 

0.75 

1.8 

0.88 

0.88 

4      X  21/2 

3/8 

3/8 

8.5 

2.48 

1.2 

0.69 

0.62 

0.62 

2.1 

0.92 

1.0 

4      X  21/2 

5/16 

5/16 

7.2 

2.12 

1.0 

0.69 

0.53 

0.60 

1.8 

0.91 

0.88 

4      X  2 

3/8 

3/8 

7.8 

2.27 

0.60 

0.52 

0.40 

0.48 

2.1 

0.96 

4      X2 

5/16 

5/16 

6.7 

1.95 

0.53 

0.52 

0.34 

0.46 

.8 

0.95 

0^88 

31/2X4 

1/2 

1/2 

12.6 

3.70 

5.5 

1.21 

2.0 

.24 

.9 

0.72 

1.1 

31/2  X  4 

3/8 

3/8 

9.8 

2.88 

4.3 

1.23 

.5 

.19 

.4 

0.70 

0.81 

31/2  X  31/2 

1/2 

1/2 

11.7 

3.44 

3.7 

1.04 

.5 

.05 

.9 

0.74 

1.1 

3i/2  X  31/2 

3/8 

3/8 

9.2 

2.68 

3.0 

1.05 

.2 

.01 

.4 

0.73 

0.81 

3l/2X3 

1/2 

1/2 

10.8 

3.17 

2.4 

0.87 

] 

0.88 

.9 

0.77 

1.1 

31/2X3 

3/8 

3/8 

8.5 

2.48 

1.9 

0.88 

0'.89 

0.83 

.4 

0.75 

0.81 

31/2  X  3 

5/16 

3/8 

7.5 

2.20 

1.8 

0.91 

0.85 

0.85 

.2 

0.74 

0.68 

3      X4 

1/2 

1/2 

11.7 

3.44 

5.2 

1.23 

1.9 

.32 

.2 

0.59 

0.81 

3      X4 

7/16 

7/16 

10.5 

3.06 

4.7 

1.23 

.7 

.29 

.1 

0.59 

0.70 

3      X4 

3/8 

3/8 

9.2 

2.68 

4.1 

1.24 

.5 

.27 

0.90 

0.58 

0.60 

3      X  3i/2 

1/2 

1/2 

10.8 

3.17 

3.5 

1.06 

.5 

.12 

.2 

0.62 

0.80 

3      X  3i/2 

7/16 

7/16 

9.7 

2.83 

3.2 

1.06 

.3 

.10 

.0 

0.60 

0.69 

3      X  3i/2 

3/8 

3/8 

8.5 

2.48 

2.8 

1.07 

.2 

.07 

0.93 

0.61 

0.62 

3      X  3 

1/2 

1/2 

9.9 

2.91 

2.3 

0.88 

.1 

0.93 

.2 

0.64 

0.80 

3      X3 

7/16 

7/16 

8.9 

2.59 

2.1 

0.89 

0.98 

0.91 

.0 

0.63 

0.70 

3      X3 

3/8 

3/8 

7.8 

2.27 

1.8 

0.90 

0.86 

0.88 

0.90 

0.63 

0.60 

3      X3 

5/16 

5/16 

6.7 

1.95 

1.6 

0.90 

0.74 

0.86 

0.75 

0.62 

0.50 

3      X  21/2 

3/8 

3/8- 

7.1 

2.07 

1.1 

0.72 

0.60 

0.71 

0.89 

0.66 

0.59 

3      X  21/2 

5/16 

5/16 

6.1 

1.77 

0.94 

0.73 

0.52 

0.68 

0.75 

0.65 

0.50 

3      X  2i/2 

1/4 

1/4 

5.0 

1.47 

0.78 

0.73 

0.43 

0.66 

0.61 

0.64 

0.40 

21/2X3 

3/8 

3/8 

7.1 

2.07 

1.7 

0.91 

0.84 

0.95 

0.53 

0.51 

0.42 

21/2  X  3 

5/16 

5/16 

6.1 

1.77 

1.5 

0.92 

0.72 

0.92 

0.44 

0.50 

0.35 

21/2  X  21/2 

3/8 

3/8 

6.4 

1.87 

1.0 

0.74 

0.59 

0.76 

0.52 

0.53 

0.42 

21/2  X   H/4 

3/16 

3/16 

2.87 

0.84 

0.08 

0.31 

0.09 

0.32 

0.29 

0.58 

0.23 

21/4X21/4 

5/16 

5/16 

4.9 

1.43 

0.65 

0.67 

0.41 

0.68 

0.33 

0.48 

0.29 

2      X  2 

5/16 

5/16 

4.3 

1.26 

0.44 

0.59 

0.31 

0.61 

0.23 

0.43 

0.23 

2      X  U/2 

1/4 

1/4 

3.09 

0.91 

0.16 

0.42 

0.15 

0.42 

0.18 

0.45 

0.18 

13/4  X   13/4 

1/4 

1/4 

3.09 

0.91 

0.23 

0.51 

0.19 

0.54 

0.12 

0.37 

0.14 

U/2X   U/2 

1/4 

1/4 

2.47 

0.73 

0.15 

0.45 

0.14 

0.47 

0.08 

0.32     6.JO 

H/4  X   11/4 

1/4 

1/4 

2.02 

0.59 

0.08 

0.37 

0.10 

0.40 

0.05 

0.28 

0.07 

1        X    1        3/18 

3/ieJ 

1.25 

0.37 

0.03 

0.29 

0.05 

0.32 

0.02 

0.22 

0.04 

Ten  light-weight  T's  of  sizes  under  2K  X  2K  in,  are  omitted. 


PROPERTIES   OF  ROLLED   STRUCTURAL  STEEL.    315 


Maximum  Safe  Loads  on  Carnegie  T-Shapes. 

Allowable  Uniform  Load  in  Thousands  of  Pounds.    Neutral  Axis  Parallel 
to  Flange.    Maximum  Bending  Stress,  16,000  Pounds  Per  Square  Inch. 


Maximum 

Maximum 

Size. 

Wgt. 

IFt. 

Span 

Span. 
360  X  De- 
flection. 

Size. 

Wgt. 

1  Ft. 
Span 

Span. 
360  X  De- 
flection. 

Foot, 

Foot, 

n 

1 

oT 

|d 

Stem, 
Tn. 

Lb. 

Safe 
Load. 

Safe  iLgth., 
Load.!  Feet. 

S  . 

Stem, 
Tn. 

Lb. 

Safe 
Load. 

Safe 
Load. 

Lgth., 
Feet. 

E 

1 

fe 

3 

13.4 

II  .41 

.25     9.1 

3  1/2 

9.7 

14.19 

.46 

9.7 

5 

21/2 

10.9 

8.96 

1.20 

7.5 

31/2 

2-5 

12.37 

.26 

9.8 

31/2 

15.7 
9.8 

22.72 
9.71 

2.37 
.07 

~9.6 
9.1 

3 
3 

9.9 
8.9 

11  .73 
10.45 

.41 
.24 

8.3 
8.4 

41/2 

3 

21/2 

21/2 

8.4 
9.2 
7.8 

8.32 
6.72 
5.76 

0.90 
0.87 
0.74 

9.2 

7.7 
7.8 

3 

3 
3 

21/2 
21/2 
21/2 

7.8 
6.7 
7.1 
6.1 
5.0 

9.17 
7.89 
6.40 
5.55 
4.59 

.08 
0.92 
0.89 
0.76 
0.62 

8.5 
8.6 
7.2 
7.3 
7.4 

5 
5 

15.3 
1  1   9 

33.39    2.40   13.9 
25  92        RA.   \A  \ 

4 

41/2 

41/2 

4 
3 

14.4 
11.2 
13.5 
10.5 
9.2 

27.09 
21.12 
21  .55 
'6.85 
9.60 

2.15 
.65 
1  .89 
.45 
1  .08 

12.6 
12.8 
11.4 
11.6 
8.9 

2  1/2 

3 
3 

21/2 
21/2 
1  1/4 

7.1 
6.1 
6.4 
5.5 

2.87 

8.96 
7.63 
6.29 
5.33 
0.93 

1.08 
0.91 
0.90 
0.75 
0.25 

8  '.4 
7.0 
7.1 
3.7 

3 

7  8 

8.21 

0.90 

9.1 

9  i  /  , 

21/.1 

49 

4.37 

0.69 

6.3 

21/2 

8.5 

6.61 

0.87 

7.6 

L  1/4 

21/4 

4.1 

3.41 

0.53 

6.4 

21/2 

7.2 

5.65 

0.73 

7.7 

2 

4.3 

3  31 

0.59 

5.6 

2 

7.8 

4.27 

0.70 

6.  1 

2          2 

3.56 

2.77 

0.49 

5.7 

2 

6.7 

3.63 

0.59 

6.2 

IV, 

3.09 

1  .60 

0.36 

4.4 

,, 

4 
4 

31/2 

31/2 

3 

12.6 
9.8 
11.7 
9.2 
10.8 
85 

21  .12 
16.53 
16.32 
12.69 
12.05 
9.49 

.90 
.46 
.65 
.27 

.42 
09 

11.1 
11.3 
9.9 
10.0 
8.5 
8.7 

1  3/4 

13/4 

3.09 

~T:Q3 
^703 
1  .49 
1.17 
0.57 

~OT41 
07 
0.36 
0.27 
0.15 

4.9 

4ll 
4.3 
3.7 

1  1/2 

2 

1  1/42 

2.45 
2.47 
1  .94 
1.25 

3 

7.5 

9.07 

.04 

8.7 

1  1/4 

2.02 

1  .01 

0.30 

3.4 

4 
4 

11.7 
10.5 

20.69 
18  35 

.92    10.8 
68    10  9 

1  1/4 

5/8 

1  .59 
0.88 

0.78 
0.14 

0.22 
0.07 

3.5 

1.9 

3 

4 

9,2 

16.11 

.47 

11.0 

1 

T~25 

"0749 

ins 

27T 

31/2 

10.8 

15.89 

.66 

9.6 

1 

0.89 

0.35 

0.12 

2.9 

316 


STRENGTH   OF  MATERIALS. 


Properties  of  Carnegie  Z-fiars. 


• 

.2  i 

•2-g 

.2  A 

.a* 

<J| 

.   . 

^bi 

J$  ~ 

x  g 

<-2 

<!! 

i<s 

II 

fl 

•  '3 

•  J3 

^.'3 

/5   nj 

XH 

MH 

tj  * 

3-S 

~3  rv 

fl| 

"o   . 

m 

££ 

0>  0 

*& 

11 

is 

Sol 

g^ 

3 

53 

'-p 

4J 

1 

I 

V 

*o 

1 

1 

.*  ^ 

hi 

.SO 

Jo 

fH 

l« 

S 

111 

J-U 
D 

11 

"8 

1 

"o 

§ 

J>. 

hickness 

1 

1 

'*o 
t 

III 

3 

1*2: 
1^5 

111 

111 

1 

M     '3 
|.2| 

•§i 

t3  c* 

M 

1? 

H 

& 

< 

% 

§ 

CO 

CO 

K 

« 

tf 

in. 

in. 

in. 

lb. 

sq.  in. 

/ 

/ 

S 

S 

r 

r 

r 

6 

31/2 

3/8 

15.7 

4.59 

25.32 

9.11 

8.44 

2.75 

2.35 

.41 

0.83 

61/1639/ie 

7/16 

18.4 

5.39 

29.80 

10.95 

9.83 

3.27 

2.35 

.43 

0.83 

61/8 

35/8 

1/2 

21.1 

6.19 

34.36 

12.87 

11.22 

3.81 

2.36 

.44 

0.84 

6 

31/2 

9/16 

22.8 

6.68 

34.64 

12.59 

11.52 

3.91 

2.28 

.37 

0.81 

61/16 

39/16 

5/8 

25.4 

7.46 

38.86 

14.42 

12.82 

4.43 

2.28 

.39 

0.82 

61/8 

35/8 

H/16 

28.1 

8.25 

43.18 

16.34 

14.10 

4.98 

2.29 

.41 

0.84 

6 

31/2 

3/4 

29.4 

8.63 

42.12 

15.44 

14.04 

4.94 

2.21 

.34 

0.81 

6i/i639/i6 

13/16 

32.0      9.40 

46.13 

17.27 

15.22 

5.47 

2.22 

.36 

0.82 

61/8 

35/8 

7/8 

34.6 

10.17 

50.22 

19.18 

16.40 

6.02 

2.22 

.37 

0.83 

5 

31/4 

5/16 

11.6 

3.40 

13.36 

6.18 

5.34 

2.00 

.98 

.35 

0.75 

5  1/16 

35/16 

3/8 

14.0 

4.10 

16.18 

7.65 

6.39 

2.45 

.99 

.37 

0.76 

51/8 

33/8 

7/16 

16.4 

4.81 

19.07 

9.20 

7.44 

2.92 

.99        .38 

0.77 

5 

31/4 

•    1/2 

17.9 

5.25 

19.19 

9.05 

7.68 

3.02 

.91        .31 

0.74 

5'1/ie 

35/16 

9/16 

20.2 

5.94 

21.83 

10.51 

8.62 

3.47 

.91        .33 

0.75 

51/8 

33/8 

5/8 

22.6 

6.64 

24.53 

12.06 

9.57 

3.94 

.92 

.35 

0.76 

5 

31/4 

H/16 

23.7 

6.96 

23.68 

11.37 

9.47 

3.91 

.84 

.28 

0.73 

51/16 

3  5/16 

3/4 

26.0 

7.64 

26.16 

12.83 

10.34 

4.37 

.85 

.30 

0.74 

51/8 

33/8 

13/16 

28.4 

8.33 

28.70 

14.36 

11.20 

4.84 

.86 

.31 

0.76 

4 

31/16 

1/4 

8.2 

2.41 

6.28 

4.23 

3.14 

1.44 

.62 

.33 

0.67 

41/16 

31/8 

5/16 

10.3 

3.03 

7.94 

5.46 

3.91 

1.84 

.62 

.34 

0.68 

41/8 

33/16 

3/8 

12.5 

3.66 

9.63 

6.77 

4.67 

2.26 

.62 

.36 

0.69 

4 

31/16 

7/16 

13.8 

4.05 

9.66 

6.73 

4.83 

2.37 

.55 

.29 

0.66 

41/16 

31/8 

1/2 

15.9 

4.66 

11.18 

7.96 

5.50 

2.77 

.55 

.31 

0.67 

41/8 

33/16 

Vl6 

18.0 

5.27 

12.74 

9.26 

6.18 

3.19 

.55 

.33 

0.68 

4 

31/16 

5/8 

18.9 

5.55 

12.11 

8.73 

6.05 

3.18 

.48 

.25 

0.66 

41/16 

31/8 

H/16 

20.9 

6.14 

13.52 

9.95 

6.65 

3.58 

.48 

.27 

0.67 

41/8 

33/16 

3/4 

23.0 

6.75 

14.97 

11.24 

7.26 

4.00 

.49 

.29 

0.68 

3 

2H/16 

1/4 

6.7 

1.97 

2.87 

2.81 

1.92 

1.10 

.21 

.19 

0.55 

31/16 

23/4 

5/16 

8.5 

2.48 

3.64 

3.64 

2.38 

1.40 

.21 

.21 

0.56 

3 

2  H/16 

3/8 

9.8 

2.86 

3.85 

3.92 

2.57 

1.57 

.16 

.17 

0.54 

31/16 

23/4 

7/16 

11.5 

3.36 

4.57 

4.75 

2.98 

1.88 

.17 

.19 

0.55 

3 

2  H/16 

1/2 

12.6 

3.69 

4.59 

4.85 

3.06 

1.99 

.12 

15 

0.53 

31/16 

23/4 

9/16 

14.3 

4.18 

5.26 

5.70 

3.43 

2.31 

.12 

17 

0.54 

PROPERTIES  OF  ROLLED  STRUCTURAL  STEEL.  317 


Properties  of  Carnegie  Unequal  Angles;  Minimum,  Intermediate, 
and  Maximum  Thicknesses  and  Weights. 


J 

Moment  of 

Section 

Radius  of  Gyra- 

,fj 

.§ 

•  s 

Inertia.  —  /. 

Modulusl-S. 

tion.  —  r. 

Size, 
In. 

Q 

£ 

If 

w  v 

•85"! 

<!     ^s 

!;! 

rt 

•35  fc 

OB    0    g, 

'8  **  c? 
***£ 

•5S  8 

*r| 

^J      rt 
"oJfe 

|| 

1 

1)1 

^  1 

if* 

Ill 

III 

I'gt 

Hi 

£  2~£ 

^Q 

o 

IS 

|* 

S^ 

i" 

|&g 

1*1 

II 

8       X6 

1 

44.2 

13.00 

38.8 

80.8 

8.9 

15.1 

1.73 

2.49 

1.28 

3/4 

33.8 

9.94 

30.7 

63.4 

6.9 

11.7 

1.76 

2.53 

1.29 

7/16 

20.2 

5.93 

19.3 

39.2 

4.2 

7.1 

1.80 

2.57 

1.30 

8       X  3  1/2 

35.7 

10.50 

7.8 

66.2 

3.0 

13.7 

0.86 

2.51 

0.73 

3/4 

27.5 

8.06 

6.3 

52.3 

2.3 

10.6 

0.88 

2.55 

0.73 

7/16 

16.5 

4.84 

4.1 

32.5 

1.5 

6.4 

0.92 

2.59 

0.74 

7       X31/2 

32.3 

9.50 

7.5 

45.4 

3.0 

10.6 

0.89 

2.19 

0.74 

H/16 

23.0 

6.75 

5.7 

33.5 

2.1 

7.6 

0.92 

2.23 

0.74 

3/8 

13.0 

3.80 

3.5 

19.6 

1.3 

4.3 

0.96 

2.27 

0.76 

6       X4 

30.6 

9.00 

10.8 

30.8 

3.8 

8.0 

.09 

1.85 

0.85 

H/16 

21.8 

6.40 

8.1 

22.8 

2.8 

5.8 

.13 

.89 

0.86 

3/8 

12.3 

3.61 

4.9 

13.5 

1.6 

3.3 

.17 

.93 

0.88 

6       X31/2 

28.9 

8.50 

7.2 

29.2 

2.9 

7.8 

0.92 

.85 

0.74 

H/16 

20.6 

6.06 

5.5 

21.7 

2.1 

5.6 

0.95 

.89 

0.75 

9.8 

2.87 

2.9 

10.9 

1.0 

2.7 

.00 

.95 

0.77 

5       X4 

7/86 

24.2 

7.11 

9.2 

16.4 

3.3 

5.0 

.14 

.52 

0.84 

5/8 

17.8 

5.23 

7.1 

12.6 

2.5 

3.7 

.17 

.55 

0.84 

3/8 

11.0 

3.23 

4.7 

8.1 

1.6 

2.3 

.20 

.59 

0.86 

5       X31/2 

7/8 

22.7 

6.67 

6.2 

15.7 

2.5 

4.9 

0.96 

.53 

0.75 

5/8 

16.8 

4.92 

4.8 

12.0 

.9 

3.7 

0.99 

.56 

0.75 

5/16 

8.7 

2.56 

2.7 

6.6 

.0 

1.9 

1.03 

.61 

0.76 

5       X3 

13/16 

19.9 

5.84 

3.7 

14.0 

.7 

4.5 

0.80 

.55 

0.64 

9/16 

14.3 

4.18 

2.8 

10.4 

.3 

3.2 

0.82 

.58 

0.65 

5/16 

8.2 

2.40 

1.8 

6.3 

0.75 

1.9 

0.85 

.61 

0.66 

«2X3 

13/16 

18.5 

5.43 

3.6 

10.3 

.7 

3.6 

0.81 

.38 

0.61 

9/16 

13.3 

3.90 

2.8 

7.8 

.3 

2.6 

0.85 

.41 

0.6* 

5/16 

7.7 

2.25 

1.7 

4.7 

0.75 

1.5 

0.87 

.44 

0.65 

X31/2 

13/16 

18.5 

5.43 

5.5 

7.8 

2.3 

2.9 

1.01 

.19 

0.72 

13.3 

3.90 

4.2 

5.9 

.7 

2.1 

1.03 

.23 

0.72 

5/16 

7.7 

2.25 

2.6 

3.6 

.0 

1.3 

1.07 

.26 

0.73 

X3 

13/16 

17.1 

5.03 

3.5 

7.3 

.7 

2.9 

0.83 

.21 

0.64 

9/16 

12.4   i 

3.62 

2.7 

5.6 

.2 

2.1 

0.86 

.24 

0.64 

1/4 

5.8 

1.69 

1.4 

2.8 

0.60 

1.0 

0.89 

.28 

0.65 

3V2X3 

13/16 

15.8 

4.62 

3.3 

5.0 

.7 

2.2 

0.85 

.04 

0.62 

9/16 

11.4 

3.34 

2.5 

3.8 

.2 

1.6 

0.87 

.07 

0.62 

1/4 

5.4 

1.56 

.3 

.9 

0.58 

0.78 

0.91 

.11 

0.63 

12X21/2 

H/16 

1/2 

12.5 
9.4 

3.65 
2.75 

.7 
.4 

4.1 
3.2 

0.99 
0.76 

1.9 
1.4 

0.69 
0.70 

.06 
.09 

0.53 
0.53 

1/4 

4.9 

1.44 

0.78 

1.8 

0.41 

0.75 

0.74 

.12 

0.54 

X2i/2 

9/16 

9.5 

2.78 

.4 

2.3 

0.82 

1.2 

0.72 

0.91 

0.52 

7/16 

7.6 

2.21 

.2 

.9 

0.66 

0.93 

0.73 

0.92 

0.52 

4.5 

1.31 

0.74 

.2 

0.40 

0.56 

0.75 

0.95 

0.53 

X2 

1/2 

7.7 

2.25 

0.67 

.9 

0.47 

1.0 

0.55 

0.92 

0.43 

3/8 

5.9 

1.73 

0.54 

.5 

0.37 

0.78 

0.56 

0.94 

0.43 

1/4 

4.1 

1.19 

0.39 

.1 

0.25 

0.54 

0.57 

0.95 

0.43 

2X2 

1/2 

6.8 

2.00 

0.64* 

0.46 

0.70 

0.56 

0.75 

0.42 

5/16 

4.5 

1.31 

0.45 

0^79 

0.31 

0.47 

0.58 

0.78 

0.42 

1/8 

1.86 

0.55 

0.20 

0.35 

0.13 

0.20 

0.61 

0.89 

0.43 

21/2XH/2 

5/16 

3.92 

1.15 

0.19 

0.71 

0.17 

0.44 

0.41 

0.79 

0.32 

3/16 

2.44 

0.72 

0.13 

0.46 

0.11 

0.28 

0.42 

0.80 

0.33 

2V4X  U/2 

1/2 

5.6 

1.63 

0.26 

0.75 

0.26 

0.54 

0.40 

0.68 

0.32 

3/16 

2.28 

0.67 

0.12 

0.34 

0.11 

0.23 

0.43 

0.72 

0.33 

(Table  continued  on  next  page.) 


318 


STRENGTH   OF  MATERIALS. 


Properties  of  Carnegie  Unequal  Angles.—  Continued. 


Size, 
In. 

Thickness,  Inches. 

"o 

& 

b 

P.J 

*! 
g 

Area  of  Section, 
Square  Inches. 

Moment  of 
Inertia.  —  /. 

Section 
Modulus.-/!?. 

Radius  of  Gyra- 
tion. —  r. 

w  0  ft*. 

.»3| 

<J      § 

"sS 

llg 
J&s 

•3*1 

<5  ^ 

•sS 
111 

3f*-JC 

o;P-tGQ 

flj| 

%! 

-^^ 

2*3  M 

,3  C  C 

S(£>3 

S5 

w  o  ft, 
3^c 

<J       cd 

•Sfe 

git 

£  i  ° 
3  tf,c 

gHHGG 

w  o  ft. 

3"*" 

<5        rt 
2^ 

£«*? 

3  efl  o 
ajpLiJ 

•gs| 

M 
SP 

3  «*  J3 
EPkCQ 

oa'-j 
3  w 

'S  § 

oJ  tsa 

«.2 
^Q 

hJ  ^ 

032 
0.33 
0.27 
0.27 
0.27 
0.27 
0.26 
0.26 

2       X  1  1/2 
2       X  1  1/4 

1  3/4Xll/4 

1V2XU/4 

3/8 
1/8 
1/4 
3/16 
1/4 
1/8 
Vl6 
3/16 

3.99 
1.44 
2.55 
1.96 
2.34 
1.23 
2.59 
1.64 

1.17 
0.42 
0.75 
0.57 
0.69 
0.36 
0.76 
0.48 

0.21 
0.09 
0.09 
0.07 
0.09 
0.05 
0.10 
0.07 

0.43 
0.17 
0.30 
0.23 
0.20 
0.11 
0.16 
0.10 

0.20 
0.08 
0.10 
0.08 
0.10 
0.05 
0.11 
0.07 

0.34 
0.13 
0.23 
0.18 
0.18 
0.09 
0.!6 
0.10 

0.42 
0.45 
0.34 
0.35 
0.35 
0.37 
0.35 
0.37 

0.61 
0.64 
0.63 
0.64 
0.54 
0.56 
0.45 
0.46 

Maximum  and  minimum  sizes  only  are  given  for  angles  less  than 

Safe  Loads,  in  Thousands  of  Pounds,  for  Carnegie  Unequal  Angles 
Used  as  Beams.  Minimum,  Intermediate,  and  Maximum  Thick- 
ness and  Weights. 


Neutral  Axis  Parallel 

Neutral  Axis  Parallel 

to  Shorter  Leg. 

to  Longer  Leg. 

Size  of  Angle, 

Safe 

Maximum  Span, 
360  X  Deflec- 

Safe 

Maximum  Span, 
360    X   Deflec- 

Inches. 

Load, 
1  Foot 

tion. 

Load, 
1  Foot 

tion. 

Span. 

Safe 

Lgth., 

Span. 

Safe 

Lgth.; 

Load. 

Feet. 

Load. 

Feet. 

8X6X1 

161.17 

7.49 

21.5 

95.15 

5.44 

17.5 

8       X6       X    3/4 

124.48 

5.68 

21.9 

73.92 

4.13 

17.9 

8       X6       X     7/16 

75.41 

3.37 

22.4 

45.12 

2.47 

18.3 

8       X  3  l/2  X  1 

146.03 

7.53 

19.4 

32.21 

3.10 

10.4 

X3i/2x    3/4 

113.17 

5.72 

19.8 

25.07 

2.33 

10.8 

8       X31/2X     Vl6 

68.80 

3.39 

20.3 

15.57 

1.38 

11.3 

7       X  3  i/2  X  1 

112.85 

6.52 

17.3* 

31.57 

3,10 

10.2 

7       X3i/2X    n/16 

81.07 

4.58 

17.7 

22.83 

2.14 

10.7 

7       X31/2X    3/8 

46.19 

2.54 

18.2 

13.44 

1.19 

11.2 

6       X4       XI 

85.55 

5.56 

15.4 

40.43 

3.55 

11.4 

6       X4        X    n/16 

61.65 

3.88 

15.9 

29.44 

2.47 

11.9 

6       X4        X     3/8 

35.41 

2.16 

16.4 

17.07 

1.39 

12.3 

6       X  3  1/2  X  1 

83.52 

5.57 

15.0 

30.93 

3.09 

10.0 

6       X31/2X   11/16 

60.27 

3.89 

15.5 

22.51 

2:14 

10.5 

6       X31/2X    Vl6 

29.23 

1.83 

16.0 

11.09 

1.00 

11.1 

5       X4       X     7/8 

53.23 

4.00 

13.3 

35.31 

3.15 

11.2 

5       X  4       X     V8 

39.79 

2.92 

13.6 

26.45 

2.28 

11.6 

5       X4       X    3/8 

24.96 

1.78 

14.0 

16.75 

1.40 

12.0 

5       X3l/2X    7/8 

52.05 

4.04 

12.9 

26.88 

2.71 

99 

5       X31/2X    5/s 

38.93 

2.93 

13.3 

20.27 

1.97 

10.3 

5         X31/2X     5/16 

20.69 

1.51 

13.7 

10.88 

1.02 

10.7 

(Table  continued  on  next  page.} 

Maximum  bending  stress,  16,000  Ib.  per  sq.  in.    Safe  loads  for  other 
spans  - 
the  \\    _ 
"Which  can  be  carried." 


ns  are  inversely  proportional  to  the  span  in  feet.    Safe  loads  include 
weight  of  the  angle,  which  should  be  deducted  to  give  net  load 


PROPERTIES  OF  ROLLED  STRUCTURAL  STEEL.  319 


Safe  Loads,  in  Thousands  of  Pounds,  for  Carnegie  Unequal  Angles 
Used  as  Beams. — Continued. 


Neutral  Axis  Parallel 

Neutral  Axis  Parallel 

to  Shorter  Leg. 

to  Longer  Leg. 

Size  of  Angle, 

Safe 

Maximum  Span, 
360  X  Deflec- 

Safe 

Maximum  Span, 
360  X  Deflec- 

Inches. 

Load, 
1  Foot 

tion. 

Load 
1  Foot 

tion. 

Span. 

Safe 

Lgth., 

Span. 

Safe 

Lgth., 

Load. 

Feet. 

Load. 

Feet. 

5       X3       X    lVl6 

47.47 

3.77 

12.6 

18.56 

2.16 

8.6 

5       X  3        X     9/i6 

34.45 

2.65 

13  0 

13.55 

1.51 

9.0 

5       X3       X     5/16 

20.16 

1.51 

13.4 

8.00 

0.85 

9.4 

41/2X3        X    13/18 

38.61 

3.36 

11.5 

18.24 

2.15 

8.5 

4  1/2  X  3       X     9/l6 

28.16 

2.38 

11.8 

13.33 

1.51 

8.8 

41/2X3       X     Vie 

16.43 

1.35 

12.2 

8.00 

0.87 

9.2 

4         X31/2X    13/16 

31.15 

2.94 

10.6 

24.53 

2.56 

9.6 

4        X31/2X     9/iG  . 

22.93 

2.08 

11.0 

17.92 

1.79 

10.0 

4       X  3  1/2  X     5/16 

13.44 

1.18 

11.4 

10.67 

1.03 

10.4 

4       X  3        X    i3/i6 

30.61 

2.97 

10.3 

17.92 

2.15 

8.3 

4       X  3       X     9/iii 

22.40 

2.09 

10.7 

13.12 

1.51 

8.7 

4       X  3       X     1/4 

10.67 

0.96 

11.1 

6.40 

0.70 

9.1 

31/2X3        X    13/16 

23.47 

2.57 

9.1 

17.60 

2.17 

8.1 

31/2X3         X      9/16 

17.17 

1.81 

9.5 

12.91 

1.52 

8.5 

31/2X3       X     V4 

8.32 

0.84 

9.9 

6.19 

0.70 

8.9 

3  1/2  X  2  1/2  X    n/16 

19.73 

2.19 

9.0 

10.56 

1.51 

7.0 

31/2X2  1/2  X      1/2 

15.04 

1.63 

92 

8.11 

1.13 

7.2 

3  1/2  X  2  1/2  X     1/4 
3       X  2  1/2  X     9/i6 

3         X21/2X      7/16 

3       X  2  1/2  X     1/4 

3       X2       X     1/2 
3       X2       X     3/8 
3       X2       X     V4 

21/2X2       X     1/2 
21/2X2         X      5/i6 

8.00 

12.27 
9.92 
5.97 

10.67 
8.32 
5.76 

7.47 
5.01 

0.83 

1.53 

1.22 
0.71 

1.39 
1.05 
0.71 

1.15 
0.74 

9.6 

8.0 
8.1 
8.4 

7.7 
7.9 
8.1 

6.5 
6.8 

4.37 

8.75 
7.04 
4.27 

5.01 
3.95 
2.77 

4.91 
3.31 

0.58 

1.25 
0.99 
0.58 

0.88 
0.67 
0.46 

0.89 
0.57 

7.6 

7.0 
7.1 

7.4- 

5.7 
5.9 
6.1 

5.5 
5.8 

21/2X2       X     1/8 

2.13 

0.30 

7.1 

1.49 

0.23 

6.1 

*21/2XH/2X      5/16 

4.69 

0.73 

6.4 

1.81 

0.41 

4.4 

*21/2XH/2X      3/16 

2.99 

0.45 

6.6 

1.17 

0.25 

4.6 

*21/4XH/2X      1/2 

5.76 

1.02 

5.6 

2.77 

0.67 

4.1 

*2  1/4  X  1  1/2  X      3/16 

2.45 

0.40 

6.0 

1.17 

0.25 

4.6 

*2         X  1  1/2  X      3/8 

3.63 

0.70 

5.2 

2.13 

0.51 

4.2 

*2       X  1  V2  X     1/8 

1.39 

0.24 

5.6 

0.80 

0.17 

4.6 

*2       X  1  1/4  X     1/4 

2.45 

0.47 

5.2 

1.04 

0.28 

3.7 

*2       X  1  1/4  X     3/16 

1.92 

0.36 

5.3 

0,.80 

0.21 

3.8 

*13/4XH/4X      1/4 

1.92 

0.42 

4.6 

1.01 

0.28 

3.6 

*13/iXH/4X      1/8 

1.00 

0.21 

4.8 

0.56 

0.15 

3.8 

*H/2X11/4X      5/ie 

1.71 

0.44 

3.9 

1.17 

0.34 

3.4 

*l  V2  X  1  V4  X      3/16 

1.07 

0.26 

4.1 

0.78 

0.22 

3.6 

Maximum  bending  stress,  16,000  Ib.  per  sq.  in.  Safe  loads  for  other 
spans  are  inversely  proportional  to  the  span  in  feet.  Safe  loads  include 
the  weight  of  the  angle,  which  should  be  deducted  to  give  net  load 
which  can  be  carried. 

*  Only  maximum  and  minimum  sizes  are  given  for  angles  smaller 
than  2^x2  in. 


320 


STRENGTH   OF   MATERIALS. 


Properties  of  Carnegie  Angles  with  Equal  Legs.     Minimum,  Inter* 
mediate  and  Maximum  Thicknesses  and  Weights. 


o  o 

i  S*® 

3  G~ 

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1^11 

Q 

EH 

f* 

<i 

Q 

* 

ft 

3 

8      X8 

U/8 

56.9 

16.73 

2.41 

98.0 

17.5 

2.42 

.55 

8      X8 

13/16 

42.0 

12.34 

2.30 

74.7 

13.1 

2.46 

.57 

8      X8 

1/2 

26.4 

7.75 

2.19 

48.6 

8.4 

2.51 

.58 

6      X6 

1 

37.4 

11.00 

.86 

35.5 

8.6 

.80 

.16 

6      X6 

11/16 

26.5 

7.78 

.75 

26.2 

6.2 

.83 

.17 

6      X6 

3/8 

14.9 

4.36 

.64 

15.4 

3.5 

.88 

.19 

5      X5 

1 

30.6 

9.00 

.61 

19.6 

5.8 

.48 

0.96 

LI/16 

21.8 

6.40 

.50 

14.7 

4.2 

.51 

0.97 

5      X5 

3/8 

12.3 

3.61 

.39 

8.7 

2.4 

.56 

0.99 

4      X4 

13/16 

19.9 

5.84 

.29 

8.1 

3.0 

.18 

0.77 

4      X4 

9/16 

14.3 

4.18 

.21 

6.1 

2.2 

.21 

0.78 

4      X4 

6.6 

1.94 

.09 

3.0 

1.0 

.25 

0.79 

31/2X31/2 

13/16 

17.1 

5.03 

.17 

5.3 

2.3 

.02 

0.67 

31/2X31/2 

9/16 

12.4 

3.62 

.08 

4.0 

1.6 

.05 

0.68 

31/2X31/2 

V4 

5.8 

1.69 

0.97 

2.0 

0.79 

.09 

0.69 

3      X3 

5/8 

11.5 

3.36 

0.98 

2.6 

1.3 

0.88 

0.57 

3      X3 

7/16 

8.3 

2.43 

0.91 

2.0 

0.95 

0.91 

0.58 

3      X3 

1/4 

4.9 

1.44 

0.84 

1.2 

0.58 

0.93 

0.59 

21/2X21/2 

1/2 

7.7 

2.25 

0.81 

1.2 

0.73 

0.74 

0.47 

2l/2X2i/2 

5/16 

5.0 

1.47 

0.74 

0.85 

0.48 

0.76 

0.49 

21/2X21/2 

1/8 

2.08 

0.61 

0.67 

0.38 

0.20 

0.79 

0.50 

2      X2 

7/16 

5.3 

1.56 

0.66 

0.54 

0.40 

0.59 

0.39 

2      X2 

1/1 

3.19 

0.94 

0.59 

0.35 

0.25 

0.61 

0.39 

2      X2 

1/8 

1.65 

0.48 

0.55 

0.19 

0.13 

0.63 

0.40 

13/4X13/4 

7/16 

4.6 

1.34 

0.59 

0.35 

0.30 

0.51 

0.33 

13/4X1  3/4 

5/16 

3.39 

1.00 

0.55 

0.27 

0.23 

0.52 

0.34 

13/4X13/4 

1/8 

1.44 

0.42 

0.48 

0.13 

0.10 

0.55 

0.35 

11/2XH/2 

3/8 

3.35 

0.98 

0.51 

0.19 

0.19 

0.44 

0.29 

11/2XU/2 

1/4 

2.34 

0.69 

0.47 

0.14 

0.13 

0.45 

0.29 

11/2XU/2 

1/8 

1.23 

0.36 

0.42 

0.08 

0.07 

0.46 

0.30 

U/4X1V4 

5/16 

2.33 

0.68 

0.42 

0.09 

0.11 

0.36 

0.24 

H/4XH/4 

3/16 

1.48 

0.43 

0.38 

0.06 

0.07 

0.38 

0.24 

11/4XH/4 

1/8 

1.01 

0.30 

0.35 

0.04 

0.05 

0.38 

0.25 

1      XI 

1/4 

1.49 

0.44 

0.34 

0.04 

0.06 

0.29 

0.19 

1       XI 

3/16 

1.16 

0.34 

0.32 

0.03 

0.04 

0.30 

0.19 

1       XI 

1/8 

0.80 

0.23 

0.30 

0.02 

0.03 

0.31 

0.19 

RIVET  SPACING   FOR   STRUCTURAL   WORK.         321 


Safe  Loads,  in  Thousands  of  Pounds,  Uniformly  Distributed  for 
Carnegie  Equal  Angles  Used  as  Beams. 

(Maximum,  Intermediate  and  Minimum  Thicknesses  and  Weights.) 


Maximum 

Maximum 

Safe 

Span, 

Safe 

Span, 

Size  of  Angle, 
Inches. 

Load 
One- 
Foot 

360  X  De- 
flection. 

Size  of  Angle, 
Inches. 

Load 
One- 
Foot 

360  XDe- 
flection. 

Span. 

Safe 

Lgth. 

Span. 

Safe 

Lgth. 

+ 

Load 

Feet. 

Load 

Feet. 

8       X  8      X  1  1/8 

186.99 

8.31 

22.5 

21/2X21/2X1/2 

7.79 

1.15 

6.8 

113/16 

139.84 

6.08 

23.0 

5/16 

5.12 

0.72 

7.1 

X6       XI 

11/16 

X4       X  13/16 

89.28 
91.41 
65.81 
37.65 
61.87 
44.80 
25.81 
32.11 

3.82 
5.48 
3.85 
2.14 
4.55 
3.  IS 
1.78 
2.95 

23.4 
16.7 
17.1 
17.6 
13.6 
14.1 
14.5 
10.9 

1/8 

2      X2        X7/16 
1/4 
1/8 
13/4X13/4XV16 
5/16 
1/8 
11/2XH/2X3/8 

2.13 
4.27 
2.67 
1.39 
3.20 
2.45 
1.07 
2.03 

0.29 
0.79 
0.46 
0.24 
0.68 
0.51 
0.21 
0.51 

7.4 
5.4 
5.7 
5.8 
4.7 
4.8 
5.1 
4.0 

9/16 

23.36 

2.07 

11.3 

V4 

1.39 

0.33 

4.2 

1/4 

11.20 

0.96 

11.7 

1/8 

0.77 

0.17 

4.4 

31/2X31/2X13/16 

24.00 

2.55 

9.4 

H/4X1  1/4XV16 

1.17 

0.36 

3.3 

3        X3      X  5/8 

7/16 
V4 

17.60 
8.43 
13.87 
10.13 
6.19 

1.81 
0.83 
1.69 
1.21 
0.71 

9.7 
10.2 
8.2 
8.4 
8.7 

3/16 

1/8 

1      XI      X  1/4 

3/16 
1/8 

0.76 
0.52 
0.60 
0.47 
0.33 

0.22 
0.14 
0.22 
0.17 
0.12 

3.5 
3.6 
2.6 
2.7 
2.8 

Maximum  bending  stress,    16,000  Ib.   per  sq.   in.      Safe  loads  for 

other  spans  are  inversely  proportional  to  the  span  in  feet.     Safe  loads 

given  include  weight  of  angle  which  should  be  deducted  to  give  net 

•  load  that  can  be  carried. 

Rivet  Spacing  for  Structural  Work. — The  following  rules  are  con- 
densed from  those  of  the  Cambria  Steel  Co.  The  minimum  pitch  of 
rivets  should  be  at  least  three  times  the  diameter,  and  in  bridge  work 
should  not  exceed  6  in.,  or  16  times  the  thickness  of  the  thinnest  outside 
plate.  The  minimum  distance  between  edge  of  any  piece  and  the 
center  of  the  rivet  is  11/4  in.  for  3/4  and  7/g  in.  rivets  except  in  bars 
less  than  21/2  in.  wide.  If  possible  this  distance  should  be  at  least 
two  rivet  diameters  for  all  sizes,  and  should  not  exceed  eight  times  the 
thickness  of  the  plate.  The  maximum  pitch  for  flanges  of  girders  and 
chords  carrying  floors  is  4  in.  Where  plates  are  in  compression,  the 
maximum  pitch  in  the  lines  of  stress  is  sixteen  times  the  plate  thickness, 
and  in  the  line  at  right  angles  to  the  line  of  stress,  thirty-two  times  the 
plate  thickness,  except  in  the  case  of  cover  plates,  top  chords,  and 
end  posts,  where  the  maximum  pitch  may  be  forty  times  the  plate 
thickness.  The  minimum  space  between  the  rivet  center  and  the  ad- 
jacent leg  when  rivets  are  adjacent  to  the  corners  of  angles  is  1/2  the 
diameter  of  the  head,  plus  3/g  in.  clearance.  When  there  is  a  row  of 
rivets  in  the  adjacent  leg,  the  3/g  in.  clearance  should  be  measured  from 
the  rivet  heads. 

The  table  below,  and  those  on  page  322,  give  the  standards  adopted 
by  the  American  Bridge  Co.  for  rivet  spacing  in  structural  and  bridge 
work: 

Gages  for  Angles,  Inches. 


i*Pr*i 

Leg 

gi 

g2 

Max. 
Rivet 

8 

41/2 

3 

1  1/8 

7 

4 

21/2 

1 

6 

31/2 

21/2 
21/4 

7/8 

5 
3 

2 

13/4 

7/8 

4 

21/2 

31/2 

3 

1V4 

21/2 
13/8 

2 

H/8 

13/4 

'ft 

'% 

1 

5/8 

3/4 

V2 

4- 
1 

- 

7/8 

7/8 

7/8 

3/4 

5/8 

V2 

3/8 

3/8 

l/l 

V4 

322 


STRENGTH  OF  MATERIALS. 


Minimum  Spacing,  Clearance  and  Stagger  for  Rivets. 

Distance  c,  Inches. 

0 

CN 

~co 

CN 

CS 

~co 

_WJ 

T3 
rt 

•s 

I 

1 

$ 
•S 

rs 

o 

J 

CO                CO 

CN  CN  CN  en 

<o          «a 

00      2      *° 

en  en  en 

Values  below  and  to  right  of  upper  zigzag  line  are  large  enough  for  %-inch  rivets.  Values  below  and  to  right  of  lower 
zigzag  line  are  large  enough  for  %-inch  rivets. 

Minimum  Staeger.  d.  Inches.  U—  OJ—  *. 

k%      ^ 
$-tii  }  _1 

i-^.  %!I 

l^-jjj^-2^^ 

-o 

rs 

CO                 CO 

CN    CN    CN    CN 

<        '          00       % 

M<      00      S 
«H      CO      t» 

« 

M 

CO                     - 

CS    CS    CN    CN 

™ 

CO 

en 

co 

en 

^ 

h  en 

\ 

:  :  :  :  :   ^ 

CS 

CN 

CN    CN    CN    CN 

CN 

CD 

co 
CS 

en 

cc, 

en 

co 

en 

m 

o     — 

CO 

.....     CO 

oc 

CO                 CO                 CC 

oo 

* 

2 

co 

00 

CC 

_ 

:  :  :  :  :^^ 

CS 

CN    CN    CN    CN 

rs 

CS 

CN 

CN 

en  en  en 

•"••" 

CC 

CO 

- 

00 

,* 

S 

2 

en 

00 

en 

CD 

rt    JO    CO 

0        —  — 

rs 

CN    CN    CN    CN 

CS 

CN    CN    CN 

CN 

CO 

< 

CO 

00       «       *       00       2 

cc 

CO      ^ 



Center  to  Center  Distance  (a*)  of  Staggered  Rivets 

Distance  a,  In 

- 

Values  of  x,  In 

CS 

CS    CN    CS    CN 

CN 

CN 

N 

CN 

CN 

CN  en 

ov 

-C    ^^" 

oc 

CS 

co           co    ce 
CN    CN    CS    CN 

CO 

CN 

CN 

CO 
CS 

CO 

CN 

CN 

CN  en 

]H 

CO 

- 

00<                  00       2 

—    —    CN    CN    CN 

CO 
CN 

CN 

CS 

CS 

co 
CN 

CO 
CN 

CO 
CN 

— 

^><>l 

<<  ^.2  oo 

CO 
CO 

<:^£    ^ 

cc 

22. 

00      ^      00 

- 

•—    «—   CN    CN 

CN 

CN 

CN 

CS 

CN 

CN 

CS 

><J^ 

1 

js  ^  ^js  «  M 

CS 

CN 

CO 

CN 

CC 

CN 

O       CO 

CN    CN 

"  CO 

%ff 

CC 

1 

-5    ^    oo 

2 

2 

CO 

oo     •»* 

^fM 

CS 

CS 

CS 

CN 

CN 

CS 

CS 

> 

co     co 

CS 

CO        CO 

CC 

cc 
CS 

1 

CO                       CO 

10   \\co~~^ 

CS 

CS 

CN 

CS 

CS 

aouBJBa^ 
uinuiiuiT\ 

;^iin 

CO      CO      ^      ^      ^   ^S      CO 

CO 

CO      CO 

CS 

l^ 

- 



- 

CS 

CS 

CN 

CS 

CS 

"UT  '(X* 

umuiiuij) 

^^^c^m 

Distance 
b,  In. 

^ 

^^^^ 

PS"" 

^ 

CS 

00 

CS 

CS 

CN 

CN 

'UI"^JC 

[s»?SS?_f 

PLATE   AND    ANGLE    COLUMNS.  323 


Notes  on  Tables  of  Channel  and  Plate  and  Angle  Columns. 


(Carnegie  Steel  Co.) 

The  tables  on  pages  324  to  330  give  the  safe  loads  in  thousands  of 
pounds  which  can  be  imposed  on  channel  and  plate  and  angle  columns 
of  the  form  and  dimensions  shown  in  the  illustrations,  which  experience 
has  shown  to  be  desirable  for  ordinary  bridges  and  buildings.  They 
also  give  the  moments  of  inertia  and  radii  of  gyration  about  both  axes 
of  symmetry,  areas  of  section  and  weights  per  foot  without  allowances 
for  rivet  heads,  or  other  details.  The  tables  have  been  computed  for 
the  least  radius  of  gyration  in  accordance  with  the  American  Bridge  Co. 
formula  for  ratios  of  l/r  up  to  120,  S  =  19,000  -  100  l/r,  in  which  S  is 
the  axial  compressive  strength,  Ib.  per  sq.  in.,  I  is  the  length,  in.,  and 
r  is  the  radius  of  gyration,  in.  The  maximum  value  of  S  is  not  to 
exceed  13,000.  For  ratios  of  l/r  up  to  120  and  for  greater  ratios  up 
to  200  the  maximum  values  of  »S  allowed  are  as  follows : 


l/r 

S 

l/r 

S 

l/r 

S 

l/r 

S 

60 
70. 
80 
90 

13,000 
12,000 
1  1  ,000 
10,000 

100 
110 
120 
130 

9,000 
8,000 
7,000 
6.500 

140 
150 
160 
170 

6,000 
5,500 
5,000 
4,500 

180 
190 

4,000 
3,500 

The  values  given  in  the  table  may  be  compared  with  the  values  given 
by  other  formulae  by  means  of  the  comparative  table  on  page  286. 
It  is  assumed  in  the  tables  that  the  loads  are  direct  and  equally  dis- 
tributed over  the  cross  section  of  the  column  or  balanced  on  opposite 
sides  of  it.  In  the  case  of  unbalanced  loads  bending  stresses  are  pro- 
duced, and  the  column  must  be  so  proportioned  that  the  combined  fiber 
stresses  do  not  exceed  the  allowable  axial  compression.  (See  page  296.) 

The  ratio  l/r  =120  should  not  be  exceeded  for  main  members  under 
heavy  stress.  For  secondary  members  such  as  wind  bracing,  under 
higher  ratios,  which,  however,  must  not  exceed  200,  may  be  used. 


Fig.  84 


Fig.  85 


Fig.  86 


*  ^>>> 

(*3 

[ 

—11'^ 

S 

0 

Fig.  87 


18-'— --H 

Fig.  88 


)      C 


Fig.  89 


DIMENSIONS  OF  CHANNEL  COLUMNS. 
(See  tables,  pages  324—327.) 


324 


STRENGTH  OF  MATERIALS. 


Safe  Loads  on  Carnegie  10-Inch  Channel  Columns  in  Thousands 
of  Pounds.    (See  Figs.  83  and  84,  page  323.) 


k 

*g  0> 

«d 

!_ 

15 

20 

25 
30 
35 

15 
20 

!:;; 

M  c 

a 

•ep^ 
5 

Thickness  of 
Side  Plate,  Ib. 

Effective  Length  of  Column,  Feet. 

.&..&.-&.  *<jv4t|  Radius  of  Gyr. 
'•vj'o^ui  In  bo  Axis  Parallel  to 
-UK*  oj^|  Side  Plate. 

£fl'S 

O  Sj5 

|S 

ffla 

£<3 

1T72" 
3.60 
3.59 
3.58 
3.58 

Weight  per  Ft. 
Ib. 

18 
TT6 

20 
TT2 

22 

24 

Too 

181 

197 
213 
229 

26 

~95 
170 

185 
200 
215 

28 

~89 
159 

173 
187 
201 

30 

-83 
148 

161 
174 
187 

32 
~77 

34 

Lat. 

106 
192 
209 
226 
243 

72 

37.8 

12 
12 

5/16 
3/8 

7/16 
1/2 

213 

•m 

252 
271 
152 
286 
305 
324 
343 

203 
221 
239 
257 
T44 

137 
149 
161 
173 
96 
179 
191 
203 
215 
114 

126 
137 
148 
159 

55.5 
60.6 
65.7 
70.8 
47.8 

Lat. 

136  128 

120  112 

104 
195 
207 
220 
233 
124 

88 
164 
174 
185 
196 
103 

3.66 

3.55 

Vl6 

i/a 

9/16 

5/8 

271 
289 
307 
325 

256 

272 
289 
307 
165 

240225210 
256240223 
272  255  237 
288  270  252 

4.46 
4.53 
4.60 
4.66 

3.51 
3.50 
3.50 
3.50 

75.7 
80.8 
85.9 
91.0 

Lat. 

186 

176 

155 

145 

134 
260 
274 

3.52 

3.41 

57.8 

12 
12 
12 

14 
14 

9/15 
5/8 

359 
378 

339 
357 

319 
336 

300280 
316295 

241 
253 

221 
233 

201 
212 

4.45 
4.52 

3.44 
3.44 

95.9 
101.0 

9/16 

5/8 

392 
411 

424 
444 

370 
388 

348 
364 

326  303 
341  318 

281 
295 

259 
271 
276 
289 
87 

237J  216 
248    227 
251  "232 
263    243 

4.33 
4.39 
4.22 
4.29 

3.37 
3.37 

105.9 
111.0 

9/16 
5/8 

400 
418 

375 
392 

350 
366 

325 
341 
~98 
230 
250 
270 

301 
315 
"92 

3.30 
3.31 

115.9 
121.0 

Lat. 

116 

114 
^252 
275 
298 
|I46 
312 
335 
358 
380 

109 
251 
273 
295 

103 
241 
261 
282 

81 
T98 
214 
231 
100 

75 
187 
203 
219 
~92 

3.87 

4.70 

39.3 

3/8 
7/16 

1/2 

252 
275 
298 

219 
238 
257 
115 

209 
226 
244 
~T08 
255 
272 
290 
308 
~T29 

4.63 
4.70 
4.76 

4.36 
4.33 
4.31 
4.53 

65.7 
71.7 
77.6 

Lat. 

153 

139 

131 

123 

3.66 

49.4 

7/16 
1/2 
9/16 
5/8 

312 
335 
358 
380 

308 
330 
352 
374 

295 
316 
337 
357 

282  268 
301  287 
321  306 
341  324 

241 
258 
275 
291 

228 
243 
259 
274 

4.52 
4.59 
4.66 
4.72 

4.29 
4.27 
4.26 
4.24 

81.7 
87.6 
93.6 
99.5 

25 

Lat. 

189J179 

169 

159 

149 

139 

119 

109 

3.52 

4.39 

59.4 

14 

9/16 
5/8 
H/16 
3/4 

396 

419 
441 
464 

396 
419 
441 
464 

388 
410 

432 
453 

371 
392 
412 
433 

353 
373 
393 
412 

336 
355 
373 
392 

319 
336 
354 
372 

301    284 
318    300 
3351  315 
35l|  331 

4.52 
4.58 
4.64 
4.70 

4.22 
4.21 
4.20 
4.19 

103.6 
109.5 
115.5 
121.4 

30 
35 

Lat. 

224J21I 

199 

187 

174 

162 

149 

137 

125 

3.42 

4.28 

69.4 
"7253 
131.4 
137.4 
143.3 
149.3 
155.2 

14 
14 

H/16 

3/4 

13/16 
7/8 
15/16 

480 

502 
525 
548 
571 
593 

480 
502 
525 
548 
571 
593 

467  446 
488  466 
510487 
532;  508 
554  529 
575:549 

424  403 
444  421 
464  440 
483  459 
503  478 
522  496 

382 
399 
417 
434 
452 
469 
~479 
496 
514 
532 
549 
567 

360 
377 
394 
410 
427 
443 
~45T 
468 
485 
502 
517 
534 

339 
354 
370 
385 
401 
416 
424 
440 
455 
471 
486 
502 

4.53 
4.59 
4.65 
4.70 
4.76 
4.81 
4.66 
4.72 
4.77 
4.82 
4.87 
4.92 

4.16 
4.15 
4.15 
4.14 
4.14 
4.13 

15/16 

U/16 

H/8 
13/16 

U/4 

609 
632 
654 
677 
700 
723 

609 
632 
654 
677 
700 
723 

588  561  533  506 
610  582  553  525 
632  603  573  544 
654624  593  '563 
675  644612  581 
697  665i  63  2  '599 

4.10 
4.10 
4.10 
4.  IP 
4.09 
4.09 

159.3 
165.2 
171.2 
177.1 
183.1 
189.0 

Safe  loads  enclosed  between  heavy  lines  are  for  ratios  of  l/r  riot  over 
60;  between  the  dotted  lines  are  for  ratios  of  l/r  not  over  200;  all 
other  safe  loads  are  for  ratios  l/r  up  to  120.  Allowable  fiber  stress 
13,000  Ib.  for  lengths  of  60  radii  or  over.  Weights  do  not  include  rivet 
heads  or  other  details. 


SAFE  LOADS  ON  CHANNEL  COLUMNS. 


325 


Safe  Loads  for  Carnegie  12-Inch  Channel  Columns  in  Thousands 
of  Pounds.    (See  Figs.  85  and  86,  page  323.) 


Weight  of  Channel, 
Ib.  per  ft. 

Width  of  Side  Plate. 

Thickness  of  Side 
Plate,  in. 

Effective  Length  of  Column,  Feet. 

Radius  of  Gyration, 
Axis  Parallel  to 
Side  Plate. 

Radius  of  Gyration, 
Perpendicular  to 
Side  Plate. 

Weight  per  Ft.,  Ib. 

18 

20 

22 

24 

26 

28 

30 

32 

34 

2<>y2 

25 
30 

30 

- 

' 

In. 

Lat. 

157 

157|    157 

152 

146 

139 

133 

126 

120 

4.61 

4.50 

50.4 

14 

3/8 
7/16 
1/2 
9/16 

5/8 

Tat: 

293;  293 
316!  316 
339    339 
362    362 
384    384 
191     191 

290 
312 
334 
355 
377 
190 

277 
298 
319 
339 
360 
182 
370 
390 
411 
432 
453 
215 
465 
486 
506 
527 
548 

265 

284 
304 
324 
344 
174 

252 
271 
290 
308 
327 
166 

239 
257 
275 
292 
310 
158 

227 
243 
260 
277 
293 
150 

214 
230 
246 
261 
277 
142 

5.40 
5.48 
5.55 
5.62 
5.68 
4.43 
5.47 
5.53 
5.60 
5.66 
5.71' 

4.29 
4.27 
4.26 
4.24 
4.23 
~4~36 

76.7 
82.7 
88.6 
94.6 
100.5 
59.4 

14 
14 

9/16 

5/8 
H/16 

3/4 

13/16 

396 

419 
441 
464 
487 

396 

419 
441 
464 
487 

387 
409 
431 
.453 
474 
^25 

352 
372 
392 
412 
431 

335 
354 
372 
391 
410 
195 

318 
335 
353 
371 
388 

300 
317 
333 
350 
367 
175 
375 
392 
408 
425 
442 

283 
298 
314 
330 
345 
165 
352 
368 
383 
399 
415 

4.20 
4.19 
4.18 
4.18 
4.17 
~T.23~ 
4.13 
4.13 
4.12 
4.12 
4.12 

103.6 
109.5 
115.5 
121.4 
127.4 
69.4 
131.4 
137.4 
143.3 
149.3 
155.2 
"7974 

Lat. 

~3/T 
13/16 
7/8 
15/16 

229|  229 

205 

185 

4.28 

502 
525 

548 
571 
593 
268 

502 
525 
548 
571 
593 

487 
509 
531 
553 
575 

442 
462 
482 
502 
522 

420 
439 
457 
476 
495 

397 
415 
432 
450 
468 

5.52 
5.58 
5.64 
5.70 
5.75 
4.17 

Lat. 

268 
609 
632 
654 
677 
700 
723 
745 
768 
791 
814 

259 
587 
609 
631 
653 
674 
695 
717 
739 
761 
783 

248 

236 

224 

212 
477 
494 
512 
530 
547 
564 
582 
600 
618 
635 

200 

188 

4.13 

H 

15/16 

1/16 

1/8 
3/16 
1/4 
5/16 
3/8 
7/16 
1/2 

609 
632 
654 
677 
700 
723 
745 
768 
791 
814 

559 
580 
601 
622 
642 
663 
684 
704 
725 
746 

532 
552 
571 
591 
610 
630 
650 
670 
689 
709 

504 
523 
542 
561 
578 
597 
616 
635 
654 
672 

599 
622 
646 
669 
693 
703 
726 
750 
773 
797 
820 
844 
867 
891 
914 
937 
961 
985 
1007 

449 
466 
483 
499 
515 
532 
548 
565 
582 
599 

421 
437 
453 
469 
483 
499 
515 
530 
546 
562 

5.50 
5.64 
5.69 
5.74 
5.80 
5.85 
5.89 
5.94 
5.99 
6.04 

4.03 
4.08 
4.08 
4.08 
4.07 
4.07 
4.07 
4.07 
4,07 
4.07 

159.3 
165.2 
171.2 
177.1 
183.1 
189.0 
195.0 
200.9 
206.9 
212.8 

16 

15/16 

1/16 

1/8 
3/16 

1/4 

619 
645 
671 
697 
723 
749 

619 
645 
671 
697 
723 
749 
762 
788 
814 
840 
866 
892 
918 
944 
970 
996 
1022 
1048 
1074 
1100 

619 
645 
671 
697 
723 
749 
~762 
788 
814 
840 
866 
892 
918 
944 
970 
996 
1022 
1048 
1074 
|I100 

619 
645 
671 
697 
723 
749 
762 

599 
623 
648 
673 
697 
721 
~732 
756 
781 
805 
830 
854 
879 
903 
928 
953 
977 
1002 
1027 
1050 

552 
574 
596 
619 
642 
664 
674 
696 
719 
741 
764 
785 
808 
830 
853 
876 
897 
920 
943 
965 

528 
549 
571 
593 
614 
635 
644 
665 
687 
708 
730 
751 
773 
794 
815 
837 
858 
880 
901 
922 

504 
525 
545 
566 
5«6 
606 

5.76 
5.81 
5.87 
5.92 
5.97 
6.01 
~5~.~87~ 
5.91 
5.96 
6.01 
6.06 
6.10 
6.15 
6.19 
6.24 
6.28 
6.32 
6.36 
6.41 
6.45 

4.85 
4.84 
4.83 
4.83 
4.82 
4.81 

162.0 
168.8 
175.6 
182.4 
189.2 
196.0 
199.2 
206.0 
212.8 
219.6 
226.4 
233.2 
240.0 
246.8 
253.6 
260.4 
267.2 
274.0 
280.8 
287.6 

16 

3/16 
1/4 

5/16 
3/8 
7/16 
1/2 
9/16 
5/8 
111/16 
1  3/4 
113/16 
7/8 
H5/16 

762 
788 
814 
840 
866 
892 
918 
944 
970 
996 
1022 
1048 
1074 
HOC 

615 
635 
656 
676 
697 
716 
737 
757 
778 
799 
818 
839 
860 
879 

4.80 
4.79 
4.79 
4.78 
4.78 
4.77 
4.77 
4.76 
4.76 
4.76 
4.75 
4.75 
4.75 
4.74 

787 
813 
838 
864 
889 
915 
940 
966 
992 
1017 
1042 
1068 
1093 

•Safe  loads  enclosed  between  heavy  lines  are  for  ratios  of  l/r  not 
over  60;  all  others  are  for  ratios  l/r  not  over  120.  Allowable  fiber  stress 
13,000  Ib.  for  lengths  of  60  radii  or  over.  Weights  do  not  include  rivet 
head  or  other  details. 


326 


STRENGTH  OF   MATERIALS. 


Safe  Loads  on  15-Inch  Carnegie  Channel  Columns  in  .Thousands 
of  Pounds.*     (See  Figs.  87  and  88,  page  323.) 


si 

I 

£ 

u 

*o 

+9 

•S 
£ 

Width  of  Side  Plate,  in. 

Thickness  of  Side 
Plate,  in. 

Effective  Length  of  Column,  Feet. 

Radius  of  Gyration,  Axis 
Parallel  to  Side  Plate. 

Radius  of  Gyration, 
Axis  Perpendicular  to 
Side  Plate. 

£ 

£ 

& 

a 

! 
1 

18 

20 

22 

24 

26 

28 

30 

32 

34 

33 

16 

Lat. 

257 
413 
439 
465 
491 
517 

257 

257 

257 

252 
"400 
424 
448 
473 
498 

243 
384 
407 
431 
454 
478 

251 

233 
368 
390 
413 
435 
458 

224 
352 
3/3 
395 
416 
438 

231 

214 

5.62 
6.48 
6.57 
6.66 
6.74 
6.81 

4.98 
4.85 
4.83 
4.82 
4.81 
4.80 

80.2 
106.8 
113.6 
120.4 
127.2 
134.0 

3/8 
7/16 
1/2 
9/16 

V8 

413 
439 
465 
491 
517 

413 
439 
465 
491 

±1 

268 
528 
554 
580 
606 
632 

306 

413 
439 
465 
491 
517 

337 
357 

377 
398 

418 

~22? 

35 

40 

45 

16 

Lat. 

268 
"328 
554 
580 
606 
632 

268 
528 
554 
580 
606 
632 

268 
[517 
552 
578 
604 
629 

"306 

261 

241 

5.58 

4.95 

84.2 

5/8 
H/16 

3/4 

13/16 

7/8 

LaT 

507 
531 
555 
580 
605 

295 

486 
510 
533 
557 
580 

466 
488 
511 
533 
556 

272 

446 
467 
488 
510 
531 

260 

425 
446 
466 
487 
507 

~249 

6.77 
6.84 
6.91 
6.98 
7.04 

5743 

4.79 
4.78 
4.77 
4.77 
4.76 

138.0 
144.8 
151.6 
158.4 
165.2 

306 

306 

284 

4.84 

92.1 

16 

13/16 

V8 
15/13 

11/16 

H/8 

644 
670 
696 
722 
748 
774 

644 
670 
696 
722 
748 
774 

644 
670 
696 
722 
748 
774 

344 

639 
665 
690 
715 
741 
767 

614 
638 
663 
687 
712 
737 

589 
612 
636 
659 
683 
706 

316 
715 
738 
761 
785 
808 
832 
856 
879 

564 
586 
609 
631 
653 
676 

^302 
-684 
705 
728 
751 
773 
796 
818 
841 

539 
560 
581 
602 
624 
646 

5146.85 
5346.91 
5546.97 
57417.03 
595  7.09 
615  7.15 

4.73 
4.72 
4.72 
4.71 
4.71 
4.71 

168.4 
175.2 
182.0 
188.8 
195.6 
202.4 

16 

Lat. 

344|   344 

343 

329 

289 
"653 
673 
695 
716 
738 
760 
781 
803 

276 

5.32 

4.75 

102.2 

H/16 

H/8 
13/15 
H/4 
15/16 
13/8 
17/16 
H/2 

786 
812 
838 
864 
890 
916 
942 
968 

786 
812 
838 
864 
890 
916 
942 
968 

786 
812 
838 
864 
890 
916 
942 
968 

777 
802 
827 
853 
879 
904 
930 
956 

746 
770 
794 
819 
844 
868 
893 
918 

622 
641 
662 
682 
703 
723 
744 
764 

6.98 
7.04 
7.09 
7.15 
7.20 
7.25 
7.30 
7.35 

4.68 
4.67 
4.67 
4.67 
4.67 
4.67 
4.67 
4.67 

205.6 
212.4 
219.2 
226.0 
232.8 
239.6 
246.4 
253.2 

33 

18 

3/8 
7/16 
1/2 
9/16 

5/8 

433 
462 
491 
521 
550 

433 
462 
491 
521 
550 

433' 
462 
491 
521 
550 

433 
462 
491 
521 
550 

433    433 
462    462 
491    491 

421 
449 
476 
503 
530 

407 
433 
459 
486 
512 

3936.54 
4186.63 
4436.72 
46916.80 
4946.87 

5.67 
5.64 
5.61 
5.59 
5.57 

111.9 
119.6 
127.2 
134.9 
142.5 

521 
550 

520 
549 

35 

18 

5/8 
H/16 
3/4 
13/16 
7/8 

560 
589 
619 
648 
677 

560 
589 
619 
648 
677 

560 
589 
619 
648 
677 

560 
589 
619 
648 
677 

560 
589 
619 
648 
677 

558 
586 
615 
643 
671 

680 
708 
736 
764 
793 
821 

540 
567 
594 
621 
649 

521 

547 
574 
599 
626 

502 
527 
553 
578 
603 

6.84 
6.91 
6.98 
7.04 
7.10 

5.56 
5.54 
5.53 
5.51 
5.50 

146.5 
154.2 
161.8 
169.5 
177.1 

40 

18 

13/16 

7/8 
15/16 

1  1/16 
1   1/8 

686 
715 
745 
774 
803 
832 

686 
715 
745 
774 
803 
832 

686 
715 
745 
774 
803 
832 

686 
715 
745 
774 
803 
832 

686 
715 

745 
774 
803 
832 

657 
684 
711 
738 
766 
793 

634 
660 
685 
712 
738 
764 

6106.92 
6366.98 
660  7.04 
685  7.10 
711  7.16 
73617.21 

5.49 
5.48 
5.46 
5.45 
5.45 
5.44 

179.5 
187.1 
194.8 
202.4 
210.1 
1217.7 

*  Table  continued  on  next  page.     See'  note  at  foot  of  page. 


SAFE    LOADS    ON    CHANNEL    COLUMNS. 


327 


Safe   Loads   on   15-Inch    Carnegie  Channel  Columns  in  Thousands 
of  Pounds.*    (See  Figs.  87  and  88,  page  323 . ) 


1 

.£ 

3 

Effective  Length  of  Column,  Feet. 

.2 

S 

;2 

« 

r§ 

.2  & 

.2  3 

j2 

g 

s 

0) 

CO 

II 

si  . 

J 

& 

T3 

*o    . 

r*?  ^ 

O    Cn4-* 

>*4 

u 

W 

$-s 

18 

20 

22 

24 

26 

28 

30 

32 

34 

'S'S 

£ 
a 

IL 

O 

3 

Is 

ll 

||| 

ta 
'3 

£ 

£ 

H 

& 

« 

1/16 

841 

841 

841 

841 

841 

829 

800 

771 

743  7.05 

5.42 

220.1 

1/8 

871 

871 

871 

871 

871 

857 

828 

798 

7687.11 

5.42 

227.7 

3/16 

900 

900 

900 

900 

900 

885 

855 

824 

793  7.17 

5.41 

235.4 

1/4 

929 

929 

929 

929 

929 

913 

882 

850 

8187.22 

5.40 

243.0 

5/16 

958 

958 

958 

958 

958 

942 

909 

877 

844  7.27 

5.40 

250.0 

3/8 

988 

988 

988 

988 

988 

970 

936 

902 

86817.32 

5.39 

258.3 

45 

18 

7/16 

1017 

1017 

1017 

1017 

1017 

998 

963 

928 

893 

7.37 

5.38 

266.0 

1/2 

1046 

1046 

1046 

1046 

1046 

1026 

991 

955 

919 

7.42 

5.38 

273.6 

9/16 

1075 

1075 

1075 

1075 

1075 

1054 

1017 

980 

943  7.47 

5.37 

281.3 

5/8 

1105 

1105 

1105  1105 

1105 

1083  1045 

1007 

969:7.52 

5.37 

288.9 

H/16 

1134 

1134 

1134  1134 

1134 

1112  1073 

1034 

995  7.57 

5.37 

296.6 

3/4 

1163 

1163  1163 

1163 

1163 

1139 

1099  1059 

101917.61 

5.36 

304.2 

7/8 

1222 

1222  1222 

1222 

1222 

1195 

1153  1111  106917.70 

5.35 

319.5 

2 

1280  1280  1280 

1280 

1280 

1253 

1208  1164  112017.79 

5.35 

334.8 

Safe 


Loads  on  15-Inch  Carnegie  Channel  Columns  with  Flange  Plates 
in  Thousands  of  Pounds.*     (See  Fig.  89,  page  323.) 


Weight  of  Chan.,  Ib.  per  ft. 

Width  of  Side  Plate,  in. 

Thickness  of  Side  Plate,  in. 

Width  of  Web  Plate,  in. 

Thickness  of  Web  Plate,  in. 

Effective  Length  of  Column,  Feet. 

Radius  of  Gyration,  Axis 
Parallel  to  Side  Plate. 

Radius  of  Gyration,  Axis 
Perpendicular  to  Side  Plate 

Weight  per  Ft.,  Ib. 

18 

20 

22 

24 

26 

28 

30 

32 

-34 

35 
45 

18 

2 

14 

3/8 
9/16 

1340 
1408 

1340 
1408 

1340 
1408 

1340 
1408 

1340 
1408 

1307 
1369 

1261 
1320 

1214 
1270 

1168 
1221 

7.65 
7.52 

5.32350.5 
5.28368.4 

18 

2 

14 

9/16 

1485 

1485 

1485 

1485 

1485 

1439 

1387 

1335 

1283 

7.39 

5.25 

388.4 

20 

17/8 

21/8 
21/4 
23/8 
21/2 
25/8 
23/4 
27/8 

14 

5/8 
5/8 
5/8 
5/8 
5/8 
5/8 
5/8 
5/8 
5/8 
5/8 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1547 
1612 
1677 
1742 
1807 
1872 
1937 
2002 
2067 
2132 

1543 
1607 
1670 
1735 
1798 
1863 
1926 
1991 
2054 
2118 

1495 
1557 
1618 
1681 
1742 
1805 
1866 
1929 
1989 
2052 

1447 
1507 
1566 
1627 
1686 
1747 
1806 
1866 
1925 
1985 

7.33 
7.43 
7.52 
7.61 
7.70 
7.79 
7.88 
7.97 
8.05 
8.13 

5.97 
5.96 
5.95 
5.95 
5.94 
5.94 
5.93 
5.93 
5.92 
5.92 

404.5 
421.5 
438.5 
455.5 
472.5 
489.5 
506.5 
523.5 
540.5 
557.5 

*Safe  load  values  enclosed  within  the  heavy  lines  are  for  ratios  of 
l/r  not  over  60;  all  others  are  for  ratios  of  l/r  not  over  120.  Allowable 
fiber  stress  per  sq.  in.,  13,000  Ib.  for  lengths  of  60  radii  or  over.  Weights 
do  not  include  rivet  heads  OP  other  details, 


328 


STRENGTH   OF   MATERIALS. 


Safe  Loads  on  Carnegie  Plate  and  Angle  Columns  In 
Thousands  of  Pounds.* 


Web  +  )£  for 
|2'kngle  Leg; 

*|~\ 

+  •3 

22  / 

sy 

Angle 

r 

}=> 

s. 

Web 
Plate. 

Effective  Length  in  Feet. 

Radius  of  Gyration, 
Axis  Perpendicular 
to  Web  Plate. 

13 
|| 

°P-IP£ 

|  23-C 
^'<$ 

I  Weight,  Pounds 

per  Foot.  „  j 

a 

£ 

ii 

£  s 

H 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

2  V2X2      X  1/4 
3       X2       X  V4 
3        X2  1/2XV4 

6 
8 

8 

69 

1/4   flf 
!    88 

56 

72 
76 

43 
60 
63 

|J3, 

49 
50 

El 

62 
70 
85 

28 
40 
42 
"43 
52 
57 
70 

22 
34 

I 
I 

60 

2.45 
2.50 
2.51 

.04 
.28 
.24 
.19 
.23 
.44 
.49 

19.6 
21.5 

23.1 
24.5 
29.2 
26.4 
31.2 
32.  S 
37.2 
37.3 
42.  f 

29 
29 
28 
36 
43 
52 

23 

22 

28 
36 
45 
47 
55 
63 
74 

"77 

88 
100 

3      X2  1/2X  1/4 
3        X2  1/2XV16 
3  1/2X2  1/2X  1/4 

31/2X21/2XV16 

rJRJ  79   65 
l/4  p70|  95    78 
101  1  96   83 
j  1191115  100 
1  125J120  104 
6/1Bl  H2J138  121 
j  WlllfifZB 
161  16l!l49 

3.35 
3.38 
3.41 
3.43 

30 
_38 
39 
47 
55 
66 

1! 

89 

23 
30 
31 
38 
48 
57 

"59 

68 
78 

31/2X21/2X  5/16 
3  1/2X2  V2X  3/8 

4      X3      X  5/i6 
4      X3      X  3/8 

89 
104 
113 
131 

73 
86 
97 
114 

62 
73 
81 
97 

54 

64 

71 
83 

3.38 
3.40 
3.35 

3.36 

.47 
.51 
.67 
.71 

4 
4 
4 

X3 
X3 
X3 

X3/8 
X7/16 
XV2 

8 

168  168 
3/8     188  188 
'208208 

154 
175 
196 

136  118 
155  135 
174  152 

100 
114 
130 

86 
98 
110 

3.33 
3.34 
3.33 

.70 
1.73 
1.77 

44.2 
49.4 
54.6 

3      X2  1/2X1/4 

31/2X31/2XV4 
31/2X21/2X5/16 
"3  1/2X2  1/2X  5/16 

4      X3      X  5/16 
4      X3      X  3/s 

10 
10 

10 

V4 
5/16 

Effective  Length  in  Feet. 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

82 
100 
119 
125 

749 
|J70 
1  178 
1198 
'207 
232 
[236 
1266 
1296 

66 
86 
103 
108 
133 
154 
160 
181 

'207 

232 

236 
'266 
296 
312 
341 

!386 
89 
106 
J131 

52 
71 
87 
91 
116 
135 
140 
160 
194 
220 
23b 
266 
296 
312 
341 
37C 
386 

44 

57 

TT 

73 
99 
117 
121 
138 
175 
200 
226 
|257 
|288 
1302 
1333 
363 

36 
50 
61 

M 

82 
98 
101 
116 
157 
180 
209 
238 
267 
-280 
309 
337 
351 

28 
43 
53 
55 

73 
85 
88 
101 

36 
45 

47 
64 
76 
78 
90 

29 
37 
~38 
56 
67 
68 
79 
107 
123 

4.16 
4.23 
4.28 
4.20 
4.18 
4.22 

1.15 

.39 
.45 
.42 
.62 
.67 

26.5 
28.1 
32.  S 
35.1 
39.4 
44.6 
46  .f 
52.  ( 
54.4 
60.  £ 
62.  C 
70.  ( 
77.  t 

30 

47 
57 

39 
48 
48 
57 

,S 

126 
144 
164 

4 
4 
5 
5 
6 
.6 
6 

X3      X  3/8 
X3      X  Vie 
X3  1/2X  3/8 
X3  1/2X  Vl6 

X4      X  3/8 
X4       X  7/16 
X4      X  V2 

3/8 

58 
68 
98 
113 

4.17 
4.19 
4.18 
4.20 
4.19 
4.20 
4.20 

.65 
.69 
2.10 
2.15 
2.56 
2.61 
2.65 

139 
160 
192 
220 
247 
258 
285 
312 

121 
140 
175 
201 
226 

158 
182 
206 

141 
163 
185 
~T92 
214 
236 
"245 

6 
6 
6 

X4 
X4 
X4 

XV2 
X»/16 
X5/8 

10 

[312 
1/2    341 

370 

236 
262 
287 

214 
238 
261 
"272 

170 
191 
210 

4.14 
4.15 
4.15 

2.62 
2.66 
2.69 

81.  t 
89.4 
97.  C 

6 

X4 

X5/8 

10   5/8 

1336 

J7ol 

Ls 

I  148 
Tl"7 

UZ2 

|378 

3251298 

218 

4.10 

2.68 

101.: 

"29.  1 
34.6 

39.  ( 

31/2X21/2X  1/4 
3  1/2X2  1/2X  5/16 
4      X3      X  5/i6 

12 
12 

1/4 
5/1(3 

73 
89 
114 

]59j  52 
72(63 
97J80 

44 
54 

371 

T5 
j  87 

36 
45 
63 

28 
37 
55 
"56 
67 

5.04 
5.11 
5.09 

.35 

.41 
.61 

46 
~47 
57 

38 

~38 
47 

4 
4 

X3 
X3 

X  Vl6 
X3/8 

|138 
(159 

120 
139 

101Q4 
119199 

65 
77 

5.01 
5.06 

.58 
.63 

41.  t 
46.6 

*Safe  loads  enclosed  within  dotted  lines  are  for  ratios  of  l/r  of  not 
over  60.  Those  enclosed  within  heavy  lines  are  for  ratios  of  l/r  not 
over  200.  All  others  are  for  ratios  of  l/r  up  to  120.  Allowable  fiber 
stress  13,000  Ib.  per  sq.  in.  for  lengths  of  60  radii  or  less.  Eack  column 
consists  of  four  angles  and  one  web  plate.  AVeights  given  do  not 
include  rivet  heads  or  other  details, 


SAFE  LOADS  ON  PLATE  AND  ANGLE  COLUMNS.     329 


Safe  Loads  on  Carnegie  Plate  and  Angle  Columns  in 
Thousands  of  Pounds. — Continued. 


&$' 
**1 

^"CTlT 
*J  ^ 

lii 

i.jt~~~^ 

Angle 

r 
u 

Web 
Plate. 

Effective  Length  in  Feet. 

Radius  of  Gyration, 
Axis  Perpendicular 
to  Web  Plate. 

1- 

*%* 

1 

51 

Is. 
£ 

+  To 

.0  5 

&** 

P  a*_\ 

A 
TJ 
g 

•&  18 

O  <p 

3  « 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

|ia 

|n 

s. 

4  • 
5 

5 
6 
6 

X3       X  3/8 
X3  1/2X  3/8 
X31/2X  Vl6 
X3  1/2XV2 

X4      X  Vl6 
X4      X  1/2 

12 

J  187 

217 

3/8  I  |g 
1276 
j  305 

167 

145 
201 
226 
252 
2/6 
305 

124 
181 
205 
229 
264 
295 

102] 
162 
184 
206 

244 
274 

-9i|~5o 

69 
110 
125 
141 

58 
100 
114 
129 

"IS 
91 
104 
118 
147 
166 
173 
"797 
213 
234 
254 
162 
172 

4.99 
5.02 
5.05 
5.07 
5.06 
5.07 

1.61 
2.06 
2.10 
2.15 
2.56 
2.61 

49.3 
56.9 
63.3 
69.7 
72.5 
80.1 

217 
242 
266 
276 
305 

142 
162 

184 
224 
252 

123 
141 
161 
204 
230 

184 
209 
118 
242 
266 
290 
314 
~325 

164 
187 

6 
6 
6 
6 
6 

X4 
X4 
X4 
X4 
X4 

X  V2 
X  9/16 
X5/8 
X«/16 
X3/4 

12 

V2 

325 
354 
383 

43_9 
458 

325 
354 
383 
411 
439 

325 
354 
383 
411 
439 

312 
342 
373 
403 
43_3 
451 

288 
317 
346 
375 
403 
419 

265 

292 
319 
347 
373 

388 

242 

267 
293 
318 
344 

195 
217 
239 
262 
284 
194 
~305 

!4.99 
5.01 
5.02 
5.01 
5.01 

2.57 
2.61 
2.65 
2.69 
2.72 

85.2 
92  R 
100  \ 
107.6 
114.8 

6 

X4 

X3/4 

12 
12 

5/8 
3/4 

458 

458 

357 

4.96 

2.70 

119  ^ 

6 

X4 

X3/4 

1478 

478 

478|469  436 

403 

370   338 

4.91 

2.69 

125  3 

Safe  loads  enclosed  within  dotted  lines  are  for  ratios  of  l/r  of  not  over 
60.  Those  enclosed  within  heavy  lines  are  for  ratios  of  l/r  not  over  200. 
All  others  are  for  ratios  of  l/r  up  to  120.  Allowable  fiber 

stress  13,000  Ib.  per  sq.  in.  for  lengths  of  60  radii  or  less.      t-r-T^ ^~ 

Each  column  consists  of  four  angles  and  one  web  plate.       3Sr 
Weights  given  do  not  include  rivet  heads  or  other  details.       + 


Safe  Loads  on  Carnegie  Plate  and  Angle  Columns 
with  Side  Plates  in  Thousands  of  Pounds. 


Angles. 

Web 
Plate. 

Side 
Plates. 

Effective  Length  in  Feet. 

RadiusofGyration, 
Axis  Perpendic- 
ular to  Web  Plate. 

RadiusofGyration, 
Axis  Parallel  to 
Web  Plate. 

Weight,  Pounds 
per  Foot. 

£ 
•d 

P 

-^ 

13 
H 

JS 

•S 

iS 

1 

16 

18 

20 

22 

24 

~289 
334 
355 
377 

26 

28 

30 

6X4X  3/8 
6X4X  3/8 
6X4X  7/16 
6X4X  1/2 

12 
12 
12 

3/8 

1/2 

5/8 

14 

3/8 
1/2 
V2 
1/2 

379 

"428 
458 
487 

I0! 
553 
582 
610 
'630 
675 
721 
766 

357 

407 
434 
461 

334 
383 
407 
433 
447 
495 
520 
544 

312 
358 
381 
405 
417 
463 
487 
509 

267 
310 
329 
349 

244 
285 
303 
321 
329 
369 
388 
405 

222 
261 
277 
293 

5.58 
5.71 
5.68 
5.65 

3.14 
3.25 
3.23 
3.22 

100.2 
112.1 
120.1 
127  7 
132.8 
144.7 
152.3 
159  9 

6X4X  V2 
6X4X  V2 
6X4X  9/J6 
6X4X  5/8 

14 

V2 
5/8 
5/8 
5/S 

ft 

,7/8 

476 
526 
553 
579 

388 
432 
454 
475 

358 
401 
421 
440 

299 
338 
354 
370 

5.58 
5.69 
5.67 

5.64 

3.18 
3.26 
3.25 
3.24 

6X4X  Vs 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 

14 

594 
644 
694 
742 

558 
606 
654 
700 

522 
568 
614 
658 

486 
529 
574 
616 

450 
491 
534 
574 

413 
453 
494 
532 

377 
415 
454 
490 

5.59 
5.69 
5.79 
5.88 

3.21 
3.27 
3.33 
3.37 

165  0 
176.9 
188.8 
209.7 

Safe  loads  enclosed  in  dotted  lines  are  for  ratios  of  l/r  not  over  60. 
Those  enclosed  in  -heavy  lines  are  for  ratios  of  l/r  not  over  200.  All 
others  are  for  ratios  of  l/r  up  to  120.  Allowable  fiber  stress,  13,000  Ib. 
per  sq.  in.  for  length  of  60  radii  and  under.  Each  column  consists  of 
four  angles,  two  side  plates,  and  one  web  plate  except  those  marked  *, 
which  have  tw9  web  plates.  Weights  given  do  not  include  rivet  heads 
and  other  details.  Table  continued  on  next  page. 


330 


STRENGTH   OF  MATERIALS. 


Safe  Loads  on  Carnegie  Plate  and  Angle  Columns  with 
Side  Plates  in  Thousands  of  Pounds.  *— Continued. 


Angles. 

Web 
Plate. 

Side 
Plates. 

Effective  Length  in  Feet. 

RadiusofGyration 
Axis  Perpendic- 
ular to  Web  Plate 

Radius  of  Gyration 
Axis  Parallel  to 
Web  Plate. 

Weight,  Pounds  | 
per  Foot. 

,19 

73 
g 

J2 

g 

3 

T3 

£ 

1 
H 

18 

20 

22 

24 

26 

28 

30 

32 

6X4X  Vs 
6X4X  5/s 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/s 
6X4X  5/8 
6X4X  5/8 

12 

5/8 

14 

11/8 
H/4 

13/8 
11/2 
15/8 
13/4 
17/8 

2 

719 
840 
888 
937 
986 
1034 
1082 
1l30 
"353 
390 
417 
442 
468 

747 
794 
840 
887 
934 
980 
1026 
!1072 

703 
748 
793 
837 
882 
926 
970 
1014 

659 
702 
745 
787 
830 
872 
914 
956 

615 
657 
697 
738 
779 
818 
858 
898 

571 
611 
649 
688 
727 
764 
802 
840 

527 
565 
601 
638 
675 
710 
746 
782 

483 
519 
553 
588 
623 
657 
690 
725 

5.97 
6.06 
6.14 
6.22 
6.30 
6.38 
6.46 
6.54 

3.14 
3.45 
3.48 
3.51 
3.54 
3.56 
3.58 
3.60 

212.6 
224.5 
236.4 
248.3 
260.2 
272  1 
284.0 
295.9 

6X4X  V8 
6X4X  Vie 
6X4X  Va 
6X4X  V2 
6X4X  1/2 

14 

3/8 

14 

3/8 
3/8 
3/8 
7/16 
1/2 

340 
365 
390 
415 
439 

317 
340 
363 
387 
410 

293 
314 
336 
359 
381 

270 
289 
309 
.331 
353 

246 
264 
282 
303 
324 

223 
239 
255 
275 
295 

205 
220 
236 
251 
267 
-284 
303 

6.46 
6.45 
6.43 
6.49 
6.55 

3.10 
3.09 
3.09 
3.14 
3.19 

102.8 
110.8 
118  4 
124.3 
130.3 

6X4X  V2 
6X4X  V2 

14 

3/8 

14 

9/16 
5/8 

493|  453 
517|  487 

433 
456 

403  1  374 
426    395 

344 
364 

314 

334 

6.61 

6.67 

3.23 
3.27 

136.2 
142.2 

6X4X  V2 
6X4X  9/l6 
6X4X  5/g 

14 

1/2 

5/8 

5/8 

14 
14 

14 

5/8 
5/8 
5/8 

535    502 
561    527 
587    551 

470 
493 
515 
530 
576 
622 
668 
713 
758 
802 
847 
892 
935 
981 
1025 

437 
459 
479 

405 
424 
443 
455 
497 
540 
581 
622 
664 
704 

373 
390 
407 

340 
356 
372 

308 
322 
336 

f345 
378 
415 
452 
487 
522 
556 
591 
626 
659 
696 
730 

6.58 
6.56 
6.54 

3.22 
3.21 
3.20 

148.1 
155.7 
163.3 

6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/s 

14 
14 

5/8 
3/4 

17/8 
H/8 
H/4 

13/8 

606 
655 
705 
754 
803 
852 
901 
949 
998 
1046 
1095 
1144 
Tl98" 
1250 
1315 
1367 
1419 
1471 
1523 

568 
615 
664 
711 
758 
805 
851 

493 
536 
581 
625 
667 
711 
753 

417 
457 
493 
538 
577 
617 
655 

380 
418 
457 
495 
532 
569 
605 
642 
679 
715 
753 
789 

6.47 
6.58 
6.68 
6.78 
6.87 
6.96 
7.05 

3.17 
3.23 
3.29 
3.34 
3.38 
3.42 
3.45 

169.3 
181.2 
193.1 
205.0 
216.9 
228.8 
240.7 

6X4X  5/s 
6X4X  5/8 
6X4X  5/s 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X4X  5/8 
6X6X  5/8 
6X6X  5/8 
6X6X  5/8 
6X6X  5/8 
6X6X  Vs 

H/2 
15/8 
13/4 
17/8 

898 
945 
991 
1038 
1084 
"1198 

!S2 

1308 
1364 

HI  9" 
1471 
1523 
"590 
T6"57" 
1728 
1787 
1845 
1904 

796 
839 
880 
924 
966 

744 
786 
825 
867 
907 

693 
732 
770 
810 
848 

7.13 
7.22 
7.30 
7.38 
7.46 

3.48 
3.51 
3.53 
3.56 

3.58 

252.6 
264.5 
276.4 
288.3 
300.2 

16 

JV.J 

2 

21/8| 
21/41 
23/8| 
21/2  1 

1146  1091  1036 
1201  1144  1087 
1246  1185  1123 
1301  1237  1174 
1356  1290  1225 
1  409|  1  342  ,  1274 
1463  139311324 

981    926 
1030    973 
1062  1000 
1111  1047 
1160  1094 
1207  1139 
1254  1185 

871 
916 
939 
984 
1029 
1072 
1115 

7.45 
7.53 
7.36 
7.44 
7.53 
7.61 
7.69 

4.02 
4.05 
3.95 
3.98 
4.01 
4.03 
4.05 

313.8 
327.4 
344.2 
357.8 
371.4 
385.0 
398.6 

6X6X  5/8 
8X6X  5/8 
8X6X  5/8 
8X6X  5/8 
8X6X  5/8 
8X6X  5/s 

*14 

1/2 

]6 
18 

21/2*1592 
21/2  ,1657 
23/8  M728 
21/2  11787 
25/8  M845 
23/4  11904 

1516  1443  1369  1295 
1616  1543  1470  1397 

1222 
1324 

1148 
1251 

7.57 
7.54 

3.99    416.4 
4.18    433.6 

172811695  1626  1557  1488  1419 
1787  1756  1685  1614  1543  1471 
1845  1818  1744  16711598  1525 
1904  1879  1804!  1729  1653  1578 

7.54 
7.62 
7.70 
7.78 

4.61    452.3 
4.63   467.6 
4.65    482.9 
4.67    498,2 

8X6X  5/8 
8X6X  5/s 
8X6X  5/s 
8X6X  5/s 
8X6X  5/8 
8X6X  5/s 

*14 

5/8 

18 

23/4  J1949 

1949  1949H918 

1841  1763  1686  1608 

7.71 

4.64    510.1 

20 

25/8    20272027,2027 
23/4   2092:  2092  12092 
27/8    21572157  2157 
3         2222;22222222 
3  l/s    2287  2287  2287 

2027|2009  1935  1862 
2092)2077  2002  1926 
21571214620681991 
2222|2214  2135  2055 
2287)2283  2202  2120 

1789 
1851 
1913 
1976 
2039 

7.70 
7.78 
7.86 
7.94 
8.01 

5.10 
5.12 
5.14 
5.16 

5.18 

530.5 
547.5 
564.5 
581.5 
598.5 

*See  note  at  foot  of  page  329. 


PROPERTIES   OF  BETHLEHEM   GIRDER   BEAMS.    331 


Bethlehem,  Girder  and  I-Beams,  and  H- Columns. — The  tables  of 
special  and  girder  beams  give  the  sections  and  weights  usually  rolled. 
Intermediate  and  heavier  weights  may  be  obtained  by  special  arrange- 
ment. The  table  of  H-columns  gives  only  the  minimum  and  maximum 
weights  for  each  section  number.  Many  intermediate  weights  are 
regularly  made. 

The  coefficients  of  strength  given  n  the  tables  are  based  on  a  maxi- 
mum fiber  stress  of  16,000  Ib.  per  sq.  in.,  which  is  allowable  for  quies- 
cent loads,  as  in  buildings.  For  moving  loads  the  fiber  stress  of  12,500 
Ib.  per  sq.  in.  should  be  used,  and  the  coefficients  reduced  proportion- 
ately. For  suddenly  applied  loads,  as  in  railroad  bridges,  they  should 
be  still  further  reduced.  For  a  fiber  stress  of  8000  Ib.  per  sq.  in.  the 
coefficients  would  be  one-half  those  given  in  the  tables.  The  quotient 
obtained  by  d  viding  the  coefficient  given  for  the  beam  by  the  span  in 
feet  will  give  the  uniformly  distributed  safe  load  in  pounds,  including 
the  weight  of  the  beam.  If  the  load  is  concentrated  at  the  middle  of  the 
span  the  safe  load  is  one  half  the  uniformly  distributed  load. 

For  further  information  see  handbook  of  Structural  Steel  Shapes, 
Bethlehem  Steel  Co.,  South  Bethlehem,  Pa.,  1911. 

Properties  of  Bethlehem  Girder  Beams. 


£•3 

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200.0 

58.71 

0.75 

15.00 

9150.6 

12.48 

610.0 

6,507,100 

94.65 

630.2 

3.28 

30 

180.0 

53.00 

.69 

13.00 

8194.5 

12.43 

546.3 

5,827,200 

82.60 

433.3 

2.86. 

28 

180.0 

52.86      .69 

14.35 

7264.7 

11.72 

518.9 

5,535,000 

80.75 

533.3 

3.18 

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165.0 

48.47 

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12.50 

6562.7 

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468.8 

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75.15 

371.9 

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46.91 

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5620.8 

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432.4 

4,611,900 

67.95 

435.7 

3.05 

26 

150.0 

43.94 

.63 

12.00 

5153.9 

10.83 

396.5 

4,228,800 

67.95 

314.6 

2.68 

24 

140.0 

41.16 

.60 

13.00 

4201.4 

10.10 

350.1 

3,734,600 

60.85 

346.9 

2.90 

24 

120.0 

35.38 

.53 

12.00 

3607.3 

10.10 

300.6 

3,206,500 

49.25 

249.4 

2.66 

20 

140.0 

41.19 

.64 

12.50 

2934.7 

8.44 

293.5 

3,130,300 

62.10 

348.9 

2.91 

20 

112.0 

32.81 

.55 

12.00 

2342.1 

8.45 

234.2 

2,498,300 

49.25 

239.3 

2.70 

18 

92.0 

27.12 

.48 

11.50 

1591.4 

7.66 

176.8 

1,886,100 

38.05 

182.6 

2.59 

15 
15 

140.  Q!  41.27 
104.0   30.50 

.80 
.60 

11.75 
11.25 

1592.7 
1220.1 

6.21 
6.32 

212.4 
162.7 

2,265,200 
1,735,300 

67.10 
47.15 

331.0 
213.0 

2.83 
2.64 

15 

73.0 

21.49 

.43 

10.50 

883.4 

6.41 

117.8 

1,256,600 

29.60 

123.2 

2.39 

12 

70.0 

20.58 

.46 

10.00 

538.8 

5.12 

89.8 

957,800 

28.60 

114.7 

2.36 

12 

55.0 

16.18 

.37 

9.75 

432.0 

5.17 

72.0 

768,000 

21.15 

81.1 

2.24 

10 

44.0 

12.95 

.31 

9.00 

244.2 

4.34 

48.8 

521,000 

14.90 

57.3 

2.10 

9 

38.0 

11.22 

.30 

8.50 

170.9 

3.90 

38.0 

405,000 

13.35 

44.1 

1.98 

8 

32.5 

9.54 

.29 

8.00 

114.4 

3.46 

28.6 

305,100 

11.80 

32.9 

1.86 

W=Safe  load  in  pounds  uniformly  distributed,  including  weight  of  beam. 
L  =  Span  in  feet.  M— Moment  of  forces  in  foot-pounds.  /= fiber  stress,  . 
W=C/L;  M=C/8;  C=  WL  = 


332 


STRENGTH   OF  MATERIALS. 


Properties  of  Bethlehem  I-Beams. 


f  -      o5 

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5239.6 

12.18 

349.3 

3,726,000 

51.90 

165.0 

2.16 

28 

105.0 

30.88 

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10.000 

4014.1 

11.40 

286.7 

3,058,400 

44.50 

131.5 

2.06 

26 

90.0 

26.49 

.460 

9.500 

2977.2 

10.60 

229.0 

2,442,800 

37.65 

101.2 

.95 

24 

84.0 

24.80 

.460 

9.250 

2381.9 

9.80 

198.5 

2,117,300 

37.55 

91.1 

.92 

24 

83.0 

24.59 

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9.130 

2240.9 

9.55 

186.7 

1,991,900 

46.55 

78.0 

.78 

24 

73.0 

21.47 

.390 

9.000 

2091.0 

9.87 

174.3 

1,858,700 

27.00 

74.4 

.86 

20 

82.0 

24.17 

.570 

8.890 

1559.8 

8.03 

156.0 

1,663,800 

51.20 

79.9 

.82 

20 

72.0 

21.37 

.430 

8.750 

1466.5 

8.28 

146.7 

1,564,300 

32.45 

75.9 

.88 

20 
20 

69.0 
64.0 

20.26 
18.86 

.520 
.450 

8.145 
8.075 

1268.9 
1222.1 

7.91 
8.05 

126.9 
122.2 

1,353,500 
1,303,600 

44.10 
34.70 

51.2 
49.8 

.59 
.62 

23 

59.0 

17.36 

.375 

8.000 

1172.2 

8.22 

117.2 

1,250,300 

25.00 

48.3 

.66 

18 

59.0 

17.40 

.495 

7.675 

883.3 

7.12 

98.1 

1,046,900 

39.00 

39.1 

.50 

18 

54.0 

15.87 

.410 

7.590 

842.0 

7.28 

93.6 

997,900 

28.75 

37.7 

.54 

18 

52.0 

15.24 

V375 

7.555 

825.0 

7.36 

91.7 

977,700 

24.60 

37.1 

.56 

18 

48.5 

14.25 

.320 

7.500 

798.3 

7.48 

88.7 

946,100 

18.35 

36.2 

.59 

15 

71.0 

20.95 

.520 

7.500 

796.2 

6.16 

106.2 

1,132,400 

38.95 

61.3 

.71 

15 

64.0 

18.81 

.605 

7.195 

664.9 

5.95 

88.6 

945,600 

46.95 

41.9 

.49 

15 

54.0 

15.88 

.410 

7.000 

610.0 

6.20 

81.3 

867,600 

27.40 

38.3 

.55 

15 

45.0 

13.52 

.440 

6.810 

484.8 

5.99 

64.6 

689,500 

30.00 

25.2 

.36 

15 

41.0 

12.02 

.340 

6.710 

456.7 

6.16 

60.9 

649,400 

19.95 

24.0 

.41 

15 

38.0 

11.27 

.290 

6.660 

442.6 

6.27 

59.0 

629,500 

15.05 

23.4 

.44 

12 

36.0 

10.61 

.310 

6.300 

269.2 

5.04 

44.9 

478,600 

16.10 

21.3 

.42 

12 

32.0 

9.44 

.335 

6.205 

228.5 

4.92 

38.1 

406,200 

17.90 

16.0 

.30 

12 

28.5 

8.42 

.250 

6.120 

216.2 

5.07 

36.0 

384,400 

11.10 

15.3 

.35 

10 

28.5 

8.34 

.390 

5.990 

134.6 

4.02 

26.9' 

287,100 

19.90 

12.1 

.21 

10 

23.5 

6.94 

.250 

5.850 

122.9 

4.21 

24.6 

262,200 

10.50 

11.2 

.27 

9 

24.0 

7.04 

.365 

5.555 

92.1 

3.62 

20.5 

218,300 

16.95 

8.8 

.12 

9 

20.0 

6.01 

.250 

5.440 

85.1 

3.76 

18.9 

201,800 

10.05 

8.2 

.17 

8 

19.5 

5.78 

.325 

5.325 

60.6 

3.24 

15.1 

161,600 

13.45 

6.7 

.08 

8 

17.5 

5.18 

.250 

5.250 

57.4 

3.33 

14.3 

153,000 

9.45 

6.4 

.11 

W  =  Safe  load  in  pounds  uniformly  distributed,  including  weight  of  beam. 
L  =  Span  in  feet.  M=  Moment  of  forces  in  foot-pounds.  /  =  fiber  stress. 
C  =  Coefficients  given  in  the  table. 
W  =  C/L;  M  =  C/8;  C=  WL  =  8M 


PROPERTIES   OF   BETHLEHEM   H-COLUMNS. 


333 


Dimensions  and  Properties  of  Bethlehem  Boiled  Steel  H-Columns.* 


o 

Dimensions,  in  Inches. 

cj 

Neutral  Axis 
Perpen.  to  Web. 

Neutral  Axis  on 
Center  Line  of  Web. 

& 

A  & 

«-i 

i     -g 

T3  t> 

-MO, 

! 

Mean  Thic 
ness  of  Flan} 

Breadth  of 
Flange. 

Thickness  c 
Web 

&£ 

J~l 

|3S 

fi 

O  OS 

OJ  CP 

S-Oi 

Moment  of 
Inertia. 

Section 
Modulus. 

Radius  of 
Gyration. 

Moment  of 
Inertia. 

Section 
Modulus. 

Radius  of 
Gyration 

14-Inch  H-Columns 


83.5 
91.0 

133/4 

137/8 

H/16 

3/4 

13.92 
13.96 

0.43 
.-47 

11.06 
11.06 

24.46 
26.76 

884.9 
976.8 

128.7 
140.8 

6.01 
6.04 

294.5 
325.4 

42.3 
46.6 

3.47 
3.49 

99.0 
162.0 

14 
15 

13/16 
15/16 

14.00 
14.31 

.51 

.82 

11.06 
11.06 

29.06 
47.71 

1070.6 
1894.0 

153.0 

252.5 

6.07 
6.30 

356.9 
626.1 

51.0 
87.5 

3.50 
3.62 

170.5 
227.5 

151/8 

16 

13/8 
1  13/16 

14.35 
14.62 

.86 
1.13 

11.06 
11.06 

50.11 
66.98 

2007.0 
2859.6 

265.4 
357.5 

6.33 
6.53 

662.3 
929.4 

92.3 
127.1 

3.64 
3.72 

236.0 
287.5 

161/8 
167/s 

17/8 
21/4 

14.66 
14.90 

1.17 
1.41 

11.06 
11.06 

69.45 
84.50 

2991.5 
3836.1 

371.0 
454.7 

6.56 
6.74 

970.0 
1226.7 

132.3 
164.7 

3.74 
3.81 

12-Inch  H-Columns 


64.5 
71.5 

M  3/4 

117/8 

5/8 
H/16 

11.92 
11.96 

0.39 
.43 

9.21 
9.21 

19.00 
20.96 

499.0 
556.6 

84.9 
93.7 

5.13 
5.15 

168.6 
188.2 

28.3 
31.5 

2.98 
3.00 

78.0 
132.5 

12 
13 

3/4 
U/4 

12.00 
12.31 

.47 
.78 

9.21 
9.21 

22.94 
38.97 

615.6 
1141.3 

102.6 
175.6 

5.18 
5.41 

208.1 
380.7 

34.7 
61.9 

3.01 
3.13 

139.5 
161.0 

131/8 
131/2 

15/16 

11/2 

12.35 
12.47 

.82 
.94 

9.21 
9.21 

41.03 
47.28 

1214.5 
1444.3 

185.0 
214.0 

5.44 
5.53 

404.1 
477.0 

65.4 
76.5 

3.14 
3.18 

10-Inch  H-Columns 


49.0 

97/8 

9/16 

9.97 

0.36 

7.67 

14.37 

263.5 

53.4 

4.28 

89.1 

17.9 

2.49 

54.0 
99.5 

10 
11 

5/8 
H/8 

10.00 
10.31 

.39 
.70 

7.67 
7.67 

15.91 
29.32 

296.8 
607.0 

59.4 
110.4 

4.32 
4.55 

100.4 
201.7 

20.1 
39.1 

2.51 
2.62 

105.5 
123.5 

111/8 

11  1/2 

13/16 
1  3/8 

10.35 
10.47 

.74 
.86 

7.67 
7.67 

31.06 
36.32 

651.0 
790.4 

117.0 
137.5 

4.58 
4.67 

215.6 
259.3 

41.7 
49.5 

2.64 
2.67 

8-Inch  H-Columns 


32.0 

77/8 

7/16 

8.00 

0.31 

6.14 

9.17 

105.7 

26.9 

3.40 

35.8 

8.9 

1.98 

34.5 
71.5 

8 
9 

,V2 

8.00 
8.32 

.31 
.63 

6.14 
6.14 

10.17 
21.05 

121.5 
285.6 

30.4 
63.5 

3.46 
3.68 

41.1 
94.4 

10.3 
22.7 

2.01 
2.12 

76.5 
90.5 

91/8 
91/2 

H/16 
H/4 

8.36 
8.47 

.67 
.78 

6.14 
6.14 

22.46 
26.64 

309.5 
385.3 

67.8 
81.1 

3.71 
3.80 

101.9 
125.1 

24.4 
29.6 

2.13 
2.17 

*  The  tables  are  greatly  condensed  from  the  original.  The  depth 
of  section  regularly  rolled  in  each  size  advances  by  l/%  inch  from  the 
smallest  to  the  largest  section  shown  in  each  table.  The  increased 
depth  of  each  section  in  a  given  size  is  obtained  by  adding  metal  to 
the  flanges,  the  depth  of  web  remaining  constant  in  each  size, 


334  STRENGTH   OF   MATERIALS. 


TORSIONAL  STRENGTH. 

Let  a  horizontal  shaft  of  diameter  =  d  be  fixed  at  one  end,  and  at  the 
other  or  free  end,  at  a  distance  =  I  from  the  fixed  end,  let  there  be  fixed 
a  horizontal  lever  arm  with  a  weight  =  P  acting  at  a  distance  =  a  from 
the  axis  of  the  shaft  so  as  to  twist  it;  then  Pa  =  moment  of  the  applied 
force. 

Resisting  moment  =  twisting  moment  =  SJ/c,  in  which  S  =  unit 
shearing  resistance,  J  =  polar -moment  of  inertia  of  the  section  with 
respect  to  the  axis,  and  c  =  distance  of  the  most  remote  fiber  from  the 
axis,  in  a  cross-section.  For  a  circle  with  diameter  d 


For  hollow  shafts  of  external  diameter  d  and  internal  diameter  (&, 


Pa  =  0.1963  S;     d  =    «         5.1 


1  ~^)S 

In  solving  the  last  equation  the  ratio  di/d  is  first  assumed. 

For  a  rectangular  bar  in  which  b  and  d  are  the  long  and  short  sides  of 
the  rectangle,  Pa  =  0.2222  bdzS;  and  for  a  square  bar  with  side  d,  Pa  = 
0.2222  dsS.  (Merriman,  "Mechanics  of  Materials,"  10th  ed.) 

The  above  formulae  are  based  on  the  supposition  that  the  shearing 
resistance  at  any  point  of  the  cross-section  is  proportional  to  its  distance 
from  the  axis;  but  this  is  true  only  within  the  elastic  limit.  In  mate- 
rials capable  of  flow,  while  the  particles  near  the  axis  are  strained  within 
the  elastic  limit  those  at  some  distance  within  the  circumference  may  be 
strained  nearly  to  the  ultimate  resistance,  so  that  the  total  resistance  is 
something  greater  than  that  calculated  by  the  formulae.  For  working 
strength,  however,  the  formulae  may  be  used,  with  S  taken  at  the  safe 
working  unit  resistance. 

The  ultimate  torsional  shearing  resistance  5  is  about  the  same  as  the 
direct  shearing  resistance,  and  may  be  taken  at  20,000  to  25,000  Ibs.  per 
square  inch  for  cast  iron,  45,000  Ibs.  for  wrought  iron,  and  50,000  to 
150,000  Ibs.  for  steel,  according  to  its  carbon  and  temper.  Large  factors 
of  safety  should  be  taken,  especially  when  the  direction  of  stress  is  re- 
versed, as  in  reversing  engines,  and  when  the  torsional  stress  is  com- 
bined with  other  stresses,  as  is  usual  in  shafting.  (See  "Shafting.") 

Elastic  Resistance  to  Torsion.  —  Let  I  =  length  of  bar  being 
twisted,  d  =  diameter,  P  =  force  applied  at  the  extremity  of  a  lever  arm 
of  length  =  a,  Pa  =  twisting  moment,  G  =  torsional  modulus  of  elas- 
ticity, 9  =  angle  through  which  the  free  end  of  the  shaft  is  twisted, 
measured  in  arc  of  radius  ==  1. 

For  a  cylindrical  shaft, 

P^       **gd4          A       32PaE  32  Pal.        32 

P°  =  -32T;         *  =  -^G-;        (?  =  -^oT*        T  =  10.186. 

If  a  =  angle  of  torsion  in  degrees, 

4__^L-  1 80  9        180X32PaZ       583.6  Pal 

""180'  *  *2d<G  d*G 

The  value  of  G  is  given  by  different  authorities  as  from  1/8  to  2/5  of  E, 
the  modulus  of  elasticity  for  tension.  For  steel  it  is  generally  taken  a* 
12,000,000  Ibs.  per  sq.  in. 


COMBINED   STRESSES.  335 


COMBINED    STRESSES. 

Combined  Tension  and  Flexure.  —  Let  A  =  the  area  of  a  bar 
subjected  to  both  tension  and  flexure,  P  =  tensile  stress  applied  at  the 
ends,  P  -*•  A  =  unit  tensile  stress,  S  =  unit  stress  at  the  fiber  on  the 
tensile  side  most  remote  from  the  neutral  axis,  due  to  flexure  alone,  then 
maximum  tensile  unit  stress  =  (P  -T-  A)  +  S.  A  beam  to  resist  com- 
bined tension  and  flexure  should  be  designed  so  that  (P  •*•  A)  +  S  shall 
not  exceed  the  proper  allowable  working  unit  stress. 

Combined  Compression  and  Flexure.  —  If  P  •*•  A  =  unit  stress 
due  to  compression  alone,  and  S  =  unit  compressive  stress  at  fiber  most 
remote  from  neutral  axis,  due  to  flexure  alone,  then  maximum  compres- 
sive unit  stress  =  (P  -*-  A)  +  S. 

Combined  Tension  (or  Compression)  and  Cross  Shear.  —  If 
applied  tension  (or  compression)  unit  stress  =  p,  applied  shearing  unit 
stress  =  v,  then  from  the  combined  action  of  the  two  forces 


Max.  S  =  Vp2  +  V4P2,     Maximum  shearing  unit  stress; 
Max.  t  =  1/2  P  +vV  4-  1/4P2,  Maximum  tensile  (or  compressive)  unit  stress. 
Combined  Flexure  and  Torsion.  —  If  S  =  greatest  unit  stress  due 
to  flexure  alone,  and  Ss  =  greatest  torsional  shearing  unit  stress  due  to 
torsion  alone,  then  for  the  combined  stresses 

Max.  tension  or  compression  unit  stress  t  =  1/28  + 


Max.  shear  s  =  ±*Sss*  +  V4S2. 

Equivalent  bending  moment  =  1/2  M  +  1/2  ^M2  +  T2,  where  M=  bending 
noment  and  T  =  torsional  moment. 

Formula  f9r  diameter  of  a  round  shaft  subjected  to  transverse  load 
while  transmitting  a  given  horse-power  (see  also  Shafts  of  Engines): 


,73  _  16  M        16  J5ff        402,500,000  H* 
xt  t    V   n2    •*  H2 

where  M  =  maximum  bending  moment  of  the  transverse  forces  in 
pound-inches,//  =  horse-power  transmitted,  n  =  No.  of  revs,  per  minute, 
and  t  =  the  safe  allowable  tensile  or  compressive  working  strength  of 
the  material. 

Guest's  Formula  for  maximum  tension  or  compression  unit  stress  is 
<=\/4<Ss2  +  S9(Phil.  Afa0.,July,  1900).  It  is  claimed  by  many  writers  to 
be  more  accurate  than  Rankine's  formula,  given  above.  Equivalent 
bending  moment  =  V^P  +  T2.  (Eng'g.,  Sept.  13  and  27,  1907;  July  10, 
1908;  April  23,  1909.) 

Combined  Compression  and  Torsion.  —  For  a  vertical  round  shaft 
carrying  a  load  and  also  transmitting  a  given  horse-power,  the  result- 
ant maximum  compressive  unit  stress 

2P  I  J72          4P2 

».^+y  321.000.^  +  ^, 

in  which  P  is  the  load.  From  this  the  diameter  d  may  be  found  when  t 
and  the  other  data  are  given. 

Stress  due  to  Temperature.  —  Let  I  =  length  of  a  bar,  A  =  its  sec- 
tional area,  c  —  coefficient  of  linear  expansion  for  one  degree,  t  =  rise  or 
fall  in  temperature  in  degrees,  E  —  modulus  of  elasticity,  A  the  change 
of  length  due  to  the  rise  or  fall  t:  if  the  bar  is  free  to  expand  or  contract. 
A  =  ca. 

If  the  bar  is  held  so  as  to  prevent  its  expansion  or  contraction  the 
stress  produced  by  the  change  of  temperature  =  -S  =  ActE.  The  fol- 
lowing are  average  values  of  the  coefficients  of  linear  expansion  for  a 
change  in  temperature  of  one  degree  Fahrenheit: 

For  brick  and  stone a  =  0.0000050, 

For  cast  iron a  =  0. 0000056, 

For  wrought  iron  and  steel.... a= 0.0000065. 


336  STRENGTH   OF   MATERIALS. 

The  stress  due  to  temperature  should  be  added  to  or  subtracted  from 
the  stress  caused  by  other  external  forces  according  as  it  acts  to  increase 
or  to  relieve  the  existing  stress. 

What  stress  will  be  caused  in  a  steel  bar  1  inch  square  in  area  by  a 
change  of  temperature  of  100°  F.?  S  =  ActE  =  IX  0.0000065  X  100  X 
30,000,000  =  19,500  Ibs.  Suppose  the  bar  is  under  tension  of  19,500 
Ibs.  between  rigid  abutments  before  the  change  in  temperature  takes 
place,  a  cooling  of  100°  F.  will  double  the  tension,  and  a  heating  of  100° 
will  reduce  the  tension  to  zero. 


STRENGTH  OF  FLAT  PLATES. 

For  a  circular  plate  supported  at  the  edge,  uniformly  loaded,  according 
to  Grashof,    , 


_ 
6/    '         ~~5rt' 

For  a  circular  plate  fixed  at  the  edge,  uniformly  loaded, 
2r2  A/2  r2p  3ft2 

•f  —    _  _  v)'        f    —     V—  •        71    —  ' 

f-3t2P,    <    -  y3  /  ,    P  -  2r2> 

in  which  /  denotes  the  working  stress;  r,  the  radius  in  inches;  t,  the  thick- 
ness in  inches;    and  p,  the  pressure  in  pounds  per  square  inch. 
For  mathematical  discussion,  see  Lanza,  "  Applied  Mechanics." 
Lanza  gives  the  following  table,  using  a  factor  of  safety  of  8,  with  ten- 
sile strength  of  cast  iron  20,000,  of  wrought  iron  40,000,  and  of  steel  80,000: 

Supported.  Fixed. 

Cast  iron  ............  t  =  0.0182570  r  v/p  t  =  0.0163300  r  V£" 

Wrought  iron  ........  t  =  0.0117850  r  ^p__  t  =  0.0105410  r  V£ 

Steel  ................  t  =  0.0091287  rVp  t  =  0.0081649  r  Vp 

For  a  circular  plate  supported  at  the  edge,  and  loaded  with  a  concen- 
trated load  P  applied  at  a  circumference  the  radius  of  which  is  TO: 


for  -  =    10       20       so       40 

TO 
c  =  4.07      5.00      5.53      5.92 

•      7T/  C 

The  above  formulae  are  deduced  from  theoretical  considerations,  and 
give  thicknesses  much  greater  than  are  generally  used  in  steam-engine 
cylinder-heads.  (See  empirical  formulae  under  Dimensions  of  Parts  of 
Engines.)  The  theoretical  formulae  seem  to  be  based  on  incorrect  or 
incomplete  hypotheses,  but  they  err  in  the  direction  of  safety. 

Thickness  of  Flat  Cast-iron  Plates  to  resist  Bursting  Pressures. 
—  Capt.  John  Ericsson  (Church's  Life  of  Ericsson)  gave  the  following 
rules:  The  proper  thickness  of  a  square  cast-iron  plate  will  be  obtained 
by  the  following:  Multiply  the  side  in  feet  (or  decimals  pf  a  foot)  by 
1/4  of  the  pressure  in  pounds  and  divide  by  850  times  the  side  in  inches; 
the  quotient  is  the  square  of  the  thickness  in  inches. 

For  a  circular  plate,  multiply  11-14  of  the  diameter  in  feet  by  1/4  of 
the  pressure  on  the  plate  in  pounds.  Divide  by  850  times  11-14  of  the 
diameter  in  inches.  [Extract  the  square  root.] 


STRENGTH  OF  FLAT  SURFACES.         337 

Prof.  Wm.  Harkness;  Eng'g  News,  Sept.  5,  1895,  shows  that  these  rules 
can  be  put  in  a  more  convenient  form,  thus:  For  square  plates  T  =» 
0.00495  S  ^p,  and  for  circular  plates  T  =  0.00439  D^p,  where  T  = 
thickness  of  plate,  S  =  side  of  the  square,  D  =  diameter  of  the  circlev 
and  p  =  pressure  in  Ibs.  per  sq.  in.  Professor  Harkness,  however, 
doubts  the  value  of  the  rules,  and  says  that  MO  satisfactory  theoretical 
solution  has  yet  been  obtained. 

The  Strength  of  Unstayed  Flat  Surfaces.  —  Robert  Wilson 
(Bng'g,  Sept.  24,  1877)  draws  attention  to  the  apparent  discrepancy 
between  the  results  of  theoretical  investigations  and  of  actual  experi- 
ments on  the  strength  of  unstayed  flat  surfaces  of  boiler-plate,  such  as 
the  unstayed  flat  crowns  of  domes  and  of  vertical  boilers. 

On  trying  to  make  the  rules  given  by  the  authorities  agree  with  the 
results  of  his  experience  of  the  strength  of  unstayed  flat  ends  of  cylin- 
drical boilers  and  domes  that  had  given  way  after  Ions  use,  Mr.  Wilson 
was  led  to  believe  that  the  rules  give  the  breaking  strength  much  lower 
than  it  actually  is.  He  describes  a  number  of  experiments  made  by 
Mr.  Nichols  of  Kirkstall,  which  gave  results  varying  widely  from  each 
Other,  as  the  method  of  supporting  the  edges  of  the  plate  was  varied, 
and  also  varying  widely  from  the  calculated  bursting  pressures,  the 
actual  results  being  in  all  cases  very  much  the  higher.  Some  conclusions 
drawn  from  these  results  are: 

1.  Although  the  bursting  pressure  has  been  found  to  be  so  high,  boiler- 
makers  must  be  warned  against  attaching  any  importance  to  this,  since 
the  plates  deflected  almost  as  soon  as  any  pressure  was  put  upon  them 
and  sprang  back  again  on  the  pressure  being  taken  off.     This  springing 
of  the  plate  in  the  course  of  time  inevitably  results  in  grooving  or  chan- 
neling, which,  especially  when  aided  by  the  action  of  the  corrosive  acids 
in  the  water  or  steam,  will  in  time  reduce  the  thickness  of  the  plate,  and 
bring  about  the  destruction  of  an  unstayed  surface  at  a  very  low  pressure. 

2.  Since  flat  plates  commence  to  deflect  at  very  low  pressures,  they 
should  never  be  used  without  stays;    but  it  is  better  to  dish  the  plates 
when  they  are  not  stayed  by  flues,  tubes,  etc. 

3.  Against  the  commonly  accepted  opinion  that  the  limit  of  elasticity 
should  never  be  reached  in  testing  a  boiler  or  other  structure,  these  ex- 
periments show  that  an  exception  should  be  made  in  the  case  of  an  un- 
stayed flat  end-plate  of  a  boiler,  which  will  be  safer  when  it  has  assumed 
a  permanent  set  that  will  prevent  its  becoming  grooved  by  the  continual 
variation  of  pressure  in  working.     The  hydraulic  pressure  in  this  case 
simply  does  what  should  have  been  done  before  the  plate  was  fixed, 
that  is,  dishes  it. 

4.  These  experiments  appear  to  show  that  the  mode  of  attaching  by 
flange  or  by  an  inside  or  outside  angle-iron  exerts  an  important  influence 
on  the  manner  in  which  the  plate  is  strained  by  the  pressure. 

When  the  plate  is  secured  to  an  angle-iron,  the  stretching  under  pres- 
sure is,  to  a  certain  extent,  concentrated  at  the  line  of  rivet-holes,  and 
the  plate  partakes  rather  of  a  beam  supported  than  fixed  round  the  edge. 
Instead  of  the  strength  increasing  as  the  square  of  the  thickness,  when 
the  plate  is  attached  by  an  angle-iron,  it  is  probable  that  the  strength 
does  not  increase  even  directly  as  the  thickness,  since  the  plate  gives 
way  simply  by  stretching  at  the  rivet-holes,  and  the  thicker  the  plate, 
the  less  uniformly  is  the  strain  borne  by  the  different  layers  of  which  the 
plate  may  be  considered  to  be  made  up.  When  the  plate  is  flanged,  the 
flange  becomes  compressed  by  the  pressure  against  the  body  of  the  plate, 
and  near  the  rim,  as  shown  by  the  contrary  flexure,  the  inside  of  the  plate 
is  stretched  more  than  the  outside,  and  it  may  be  by  a  kind  of  shearing 
action  that  the  plate  gives  way  along  the  line  where  the  crushing  and 
stretching  meet. 

5.  These  tests  appear  to  show  that  the  rules  deduced  from  the  theo- 
retical investigations  of  Lame",  Rankine,  and  Grashof  are  not  confirmed 
by  experiment,  and  are  therefore  not  trustworthy. 

The  rules  of  Lame",  etc.,  apply  only  within  the  elastic  limit.  (Eng'g, 
Dec.  13,  1895.) 

Unbraced  Wrought-iron  Heads  of  Boilers,  etc.  (The  Locomo- 
tive, Feb.,  1890).  —  Few  experiments  have  been  made  on  the  strength 
of  flat  heads,  and  our  knowledge  of  them  comas  largely  from  theory. 
Experiments  have  been  made  on  small  plates  Vie  of  an  inch  thick, 


338  STRENGTH   OF   MATERIALS. 

yet  the  data  so  obtained  cannot  be  considered  satisfactory  when  we 
consider  the  far  thicker  heads  that  are  used  in  practice,  although  the 
results  agreed  weli  with  Rankine's  formula.  Mr.  Nichols  has  made  ex- 
periments on  larger  heads,  and  from  them  he  has  deduced  the  following 
rule:  "To  find  the  proper  thickness  for  a  flat  unstayed  head,  multiply 
the  area  of  the  head  by  the  pressure  per  square  inch  that  it  is  to  bear 
safely,  and  multiply  this  by  the  desired  factor  of  safety  (say  8):  then 
divide  the  product  by  ten  times  the  tensile  strength  of  the  material 
used  for  the  head."  His  rule  for  finding  the  bursting  pressure  when  the 
dimensions  of  the  head  are  given  is:  "Multiply  the  thickness  of  the  end- 
plate  in  inches  by  ten  times  the  tensile  strength  of  the  material  used, 
and  divide  the  product  by  the  area  of  the  head  in  inches." 

In  Mr.  Nichols's  experiments  the  average  tensile  strength  of  the  iron 
used  for  the  heads  was  44,800  pounds.  The  results  he  obtained  are 
giren  below,  with  the  calculated  pressure,  by  his  rule,  for  comparison. 

1.  An  unstayed  flat  boiler-head  is  341/2  inches  in  diameter   and  9/io 
inch  thick.     What  is  its  bursting  pressure?     The  area  of  a  circle  341/2 
inches   in  diameter  is    935    square   inches;    then  9/ie  X  44,800  X  10  = 
252,000,    and    252,000  -f-  935  =  270    pounds,    the    calculated    bursting 
pressure.     The  head  actually  burst  at  280  pounds. 

2.  Head  341/2  inches  in  diameter  and  3/8  inch  thick.     The  area  =  935 
square   inches;    then,  3/8  x  44,800  X  10  =  168,000,    and    168,000  -f-  935 
=  180  pounds,  calculated  bursting  pressure.     This  head  actually  burst 
at  200  pounds. 

3.  Head  261/4  inches  in  diameter,  and  3/8  inch  thick.     The  area  541 
square  inches;    then,   3/8  x  44,800  X  10  =  168,000,   and  168,000  •*-  541 
=  311  pounds.     This  head  burst  at  370  pounds. 

4.  Head  281/2  inches  in  diameter  and  3/8  inch  thick.     The  area  =  638 
square  inches;    then,  3/8  x  44,800  X  10  =  168,000,  and   168,000  -*•  638 
=  263  pounds.     The  actual  bursting  pressure  was  300  pounds. 

In  the  third  experiment,  the  amount  the  plate  bulged  under  different 
pressures  was  as  follows: 

At  pounds  per  sq.  in 10        20       40       80       120       140       170       200 

Plate  bulged 1/32      Vie      Vs      J/4        3/8        V2        5/8        3/4 

The  pressure  was  now  reduced  to  zero,  and  the  end  sprang  back  3/18 
inch,  leaving  it  with  a  permanent  set  of  9/16  inch.  The  pressure  of 
200  Ibs.  was  again  applied  on  36  separate  occasions  during  an  interval  of 
five  days,  the  bulging  and  permanent  set  being  noted  on  each  occasion, 
but  without  any  appreciable  difference  from  that  noted  above. 

The  experiments  described  were  confined  to  plates  not  widely  different 
in  their  dimensions,  so  that  Mr.  Nichols's  rule  cannot  be  relied  upon  for 
heads  that  depart  much  from  the  proportions  given  in  the  examples. 

Strength  of  Stayed  Surfaces.  —  A  flat  plate  of  thickness  t  is  sup- 
ported uniformly  by  stays  whose  distance  from  center  to  center  is  a, 
uniform  load  p  IDS.  per  square  inch.  Each  stay  supports  pa2  Ibs.  The 
greatest  stress  on  the  plate  is 

/  =  f|V     (Unwin.) 

For  additional  matter  on  this  subject  see  strength  of  Steam  Boilers. 

Stresses  in  Steel  Plating  due  to  Water-pressure,  as  in  plating  of 
vessels  and  bulkheads  (Engineering,  May  22,  1891,  page  629). 

Mr.  J.  A.  Yates  has  made  calculations  of  the  stresses  to  which  steel 
plates  are  subjected  by  external  water-pressure,  and  arrives  at  the 
following  conclusions: 

Assume  2a  inches  to  be  the  distance  betvyeen  the  frames  or  other 
rigid  supports,  and  let  d  represent  the  depth  in  feet,  below  the  surface 
of  the  water,  of  the  plate  under  consideration,  t  =  thickness  of  plate  in 
inches,  D  the  deflection  from  a  straight  line  under  pressure  in  inches, 
and  P  =  stress  per  square  inch  of  section. 

For  outer  bottom  and  ballast-tank  plating,  a  =  420  t/d,  D  should  not 
be  greater  than  0.05  X  2  a/12,  and  P/2  not  greater  than  2  to  3  tons; 
while  for  bulkheads,  etc.,  a  =  2352 //d,  D  should  not  be  greater  than 


THICK   HOLLOW   CYLINDERS   UNDER   TENSION.     339 


0.1  X  2  a/ 12,  and  P/2  not  greater  than  7  tons.     To  illustrate  the  appli- 
cation of  these  formulae  the  following  cases  have  been  taken: 


For  Outer  Bottom,  etc. 

For  Bulkheads,  etc. 

Thick- 
ness of 
Plating. 

Depth 
below 
Water. 

Spacing  of 
Frames  should 
not  exceed 

Thick- 
ness of 
Plating. 

Depth  of 
Water. 

Maximum  Spac- 
ing of  Rigid 
Stiff  en  ers. 

in. 

ft. 

in. 

in. 

ft. 

ft.     in. 

1/2 

20 

About  2  1 

1/2 

20 

9     10 

1/2 

10 

42 

3/8 

20 

7       4 

3/8 

18 

18 

3/8 

10 

14       8 

3/8 

9 

36 

1/4 

20 

4     10 

V4 

10 

20 

1/4 

10 

9       8 

1/4 

5 

40 

V8 

10 

4     10 

It  would  appear  that  the  course  which  should  be  followed  in  stiffening 
bulkheads  is  to  fit  substantially  rigid  stiffening  frames  at  comparatively 
wide  intervals,  and  only  work  such  light  angles  between  as  are  necessary 
for  making  a"  fair  job  of  the  bulkhead. 


SPHERICAL,    SHELLS   AND   DOMED   BOILER-HEADS. 

To  find  the  Thickness  of  a  Spherical  Shell  to  resist  a  given 
Pressure.  —  Let  d  =  diameter  in  inches,  and  p  the  internal  pressure 
per  square  inch.  The  total  pressure  which  tends  to  produce  rupture 
around  the  great  circle  will  be  i/4rcd2p.  Let  5  =  safe  tensile  stress  per 
square  inch,  and  t  the  thickness  of  metal  in  inches;  then  the  resistance 
to  the  pressure  will  be  n  d  t  S.  Since  the  resistance  must  be  equal  to  the 
pressure, 

iUnd*p  =  *dtS.     Whence*  =  ^. 

4o 

The  same  rule  is  used  for  finding  the  thickness  of  a  hemispherical  head 
to  a  cylinder,  as  of  a  cylindrical  boiler. 

Thickness  of  a  Domed  Head  of  a  Boiler.  —  If  S  =  safe  tensile 
stress  per  square  inch,  d  =  diameter  of  the  shell  in  inches,  and  t  =  thick- 
ness of  the  shell,  t  =  pd  -s-  2/S;  but  the  thickness  of  a  hemispherical 
head  of  the  same  diameter  is  t  =  pd  •+•  4£.  Hence  if  we  make  the 
radius  of  curvature  of  a  domed  head  equal  to  the  diameter  of  the  boiler, 

we  shall  have  i  =  -f^  =  •?«  ,  or  the  thickness  of  such  a  domed  head 

4o  zo 

will  be  equal  to  the  thickness  of  the  shell. 


THICK   HOLLOW   CYLINDERS   UNDER   TENSION. 

Lamg's  formula,  which  is  generally  used,  gives 

t  =  thickness;  n=  inside  and  r2  =  outside  radius; 
^  =  maximum  allowable  hoop  tension  at  the 

interior  of  the  cylinder  ; 
p  =  intensity  of  interior  pressure; 
s  =*  tension  at  the  exterior  of  the  cylinder. 


t  _  r  J  (h+  P\^       i  1 
"    1  1  W^p/  5 


340  STRENGTH   OF  MATERIALS. 

EXAMPLE:  Let  maximum  unit  stress  at  the  inner  edge  of  the  annulus 
=  8000  lbs.  per  square  inch,  radius  of  cylinder  =  4  inches,  interior 
pressure  =  4000  lbs.  per  square  inch.  Required  the  thickness  and  the 
tension  at  the  exterior  surface. 

^{{^^'-il-^-i)-™.^ 

2n2  2X16         4000  lbs. 


For  short  cast-iron  cylinders,  such  as  are  used  in-  hydraulic  presses,  it  is 
doubtful  if  the  above  formulae  hold  true,  since  the  strength  of  the  cylindri- 
cal portion  is  reinforced  by  the  end.  In.  that  case  the  strength  would  be 
higher  than  that  calculated  by  the  formula.  A  rule  used  in  practice 
for  such  presses  is  to  make  the  thickness  =  Vio  of  the  inner  circum- 
ference, for  pressures  of  3000  to  4000  lbs.  per  square  inch. 

Hooped  Cylinders.  —  For  very  high  pressures,  as  in  large  guns,  hoops 
or  outer  tubes  of  forged  steel  are  shrunk  on  inner  tubes,  thus  bringing  a 
compressive  stress  on  the  latter  which  assists  in  resisting  the  tension  due 
to  the  internal  pressure.  For  discussion  of  Lame"s,  and  other  formulae 
lor  built-up  guns,  see  Merriman's  "Mechanics  of  Materials." 

THIN   CYLINDERS   UNDER   TENSION. 

Let  p  =  safe  working  pressure  in  lbs.  per  sq.  in.; 
d  =  diameter  in  inches; 

T  =  tensile  strength  of  the  material,  lbs.  per  sq.  in.; 
t  =  thickness  in  inches; 
/  =  factor  of  safety; 
c  =  ratio  of  strength  of  riveted  joint  to  strength  of  solid  plate. 


If  T  =  50,000,  /  =  5,  and  c  =  0.7;  then 

_  1  4.0001         •        dp 
d       ;  \  ~  14^000* 

The  above  represents  the  strength  resisting  rupture  along  a  longitudinal 
seam.  For  resistance  to  rupture  in  a  circumferential  seam,  due  to 

pressure  on  the  ends  of  the  cylinder,  we  have  ^—  =  —  ^—  -  ;    • 

4  Tt  c 
whence  p  =  . 

Or  the  strength  to  resist  rupture  around  a  circumference  is  twice  as  great 
as  that  to  resist  rupture  longitudinally;  hence  boilers  are  commonly 
single-riveted  in  the  circumferential  seams  and  double-riveted  in  the 
longitudinal  seams. 

CARRYING  CAPACITY  OF  STEEL  ROLLERS  AND  BALLS. 

Carrying  Capacity  of  a  Steel  Roller  between  Flat  Plates.  —  (Mem- 
man,  Mech.  of  Mails.)  Let  S  =  maximum  safe  unit  stress  of  the  mate- 
rial, I  =  length  of  the  roller  in  inches,  d  =  diameter,  E  =  modulus  of 


elasticity,  W  =  load,  then  W  =  2/3  idS  (2  S/E)*.  Taking  w  =  W/l, 
and  S  =  15,000  and  E  =  30,000,000  lbs.  per  sq.  in.  for  steel  the  formula 
reduces  to  w  =  316  d.  Cooper's  specifications  for  bridges,  1901,  gives 
w  =  300  d.  (The  rule  given  in  some  earlier  specifications,  w  =  1200  v'd, 
Is  erroneous.)  The  formula  assumes  that  only  the  roller  is  deformed  by 
the  load,  but  experiments  show  that  the  plates  also  are  deformed,  and 
that  the  formula  errs  on  the  side  of  safety.  Experiments  by  CrandaU 


RESISTANCE   OF  HOLLOW   CYLINDERS.  341 

and  Marston  on  steel  rollers  of  diameters  from  1  to  16  in.  show  that 
their  crushing  loads  are  closely  given  by  the  formula  W  =  880  Id.  (See 
Holler  Bearings.) 

Spherical  Rollers. — With  the  same  notation  as  above,  d  being  the 
diameter  of  the  sphere,  S  =  VWE+i/tndZ',  W  =  1/4  nd2S2  +  E.  The 
diameter  of  a  sphere  to  carry  a  given  load  with  an  allowable  unit- 
stress  S  is  d  ='2  \/WE+irS2.  This  rule  assumes  that  there  is  no  de- 
formation of  the  plates  between  which  the  sphere  acts,  hence  it  errs  on 
the  side  of  safety.  (See  Ball  Bearings.) 

RESISTANCE  OF  HOLLOW  CYLINDERS  TO  COLLAPSE. 

Fairbairn's  empirical  formula  (Phil.  Trans.,  1858)  is 

p  =  9,675,600  ^. (1) 

where  p  =  pressure  in  Ib.  per  square  inch,  t  =  thickness  of  cylinder, 
d  =  diameter,  and  /  =  length,  all  in  inches. 
He  recommends  the  simpler  formula 

p  =  9,675,600 1|       (2) 

as  sufficiently  accurate  for  practical  purposes,  for  tubes  of  considerable 
diameter  and  length. 

The  diameters  of  Fairbairn's  experimental  tubes  were  4,  6,  8,  10,  and 
12  inches,  and  their  lengths  ranged  between  19  and  60  inches. 

His  formula  (2)  was  until  about  1908  generally  accepted  as  the  basis  of 
rules  for  strength  of  boiler-flues.  In  some  cases,  however,  limits  were 
fixed  to  its  application  by  a  supplementary  formula. 

Lloyd's  Register  contains  the  following  formula  for  the  strength  of 
circular  boiler-flues,  viz., 

_  89.600  V 

Ld       

The  English  Board  of  Trade  prescribes  the  following  formula  for  cir- 
cular flues,  when  the  longitudinal  joints  are  welded,  or  made  with  riveted 
butt-straps,  viz., 

90,000  t2 
(L  +  Vd  * 

For  lap-joints  and  for  inferior  workmanship  the  numerical  factor  may 
be  reduced  as  low  as  60,000. 

The  rules  of  Lloyd's  Register,  and  those  of  the  Board  of  Trade,  pre- 
scribe further,  that  in  no  case  the  value  of  P  must  exceed  800  t/d.  (5) 

In  formulae  (3),  (4),  (5)  P  is  the  highest  working  pressure  in  pounds 
per  square  inch,  t  and  d  are  the  thickness  and  diameter  in  inches,  L  is 
the  length  of  the  flue  in  feet  measured  between  the  strengthening  rings, 
in  case  it  is  fitted  with  such.  Formula  (3)  is  the  same  as  formula  (2), 
with  a  factor  of  safety  of  9. 

Nystrom  has  deduced  from  Fairbairn's  experiments  the  following 
formula  for  the  collapsing  strength  of  flues : 

p  =692,800  —~     .   .    . (6) 

d  v  I 

where  p,  t,  I,  and  d  have  the  same  meaning  as  in  formula  (1),  Nystrom 
considers  a  factor  of  safety  of  4  sufficient  in  applying  his  formula.  (See 
"A  New  Treatise  on  Steam  Engineering,"  by  J.  W.  Nystrom,  p.  106.) 

Formulse  (1),  (3),  and  (6)  have  the  common  defect  that  they  make 
the  collapsing  pressure  decrease  indefinitely  with  Increase  of  length,  and 
vice  versa. 

D.  K.  Clark,  in  his  "Manual  of  Rules,"  etc.,  p.  696,  gives  the  dimen- 
sions of  six  flues,  selected  from  the  reports  of  the  Manchester  Steam- 
users'  Association,  1862-69.  which  collapsed  while  in  actual  use  in  boil- 
ers. These  flues  varied  from  24  to  60  inches  in  diameter,  and  from 
3/16  to  3/8  inch  in  thickness.  They  consisted  of  rings  of  plates  riveted 
together,  with  one  or  two  longitudinal  seams,  but  all  of  them  unfortified 
by  intermediate  flanges  or  strengthening  rings.  From  the  data  Clark 


342  STRENGTH  OF  MATERIALS. 

deduced   the  following  formula  "for  the  average  resisting  force  of 
common  boiler-flues,"  viz., 


where  p  is  the  collapsing  pressure  in  pounds  per  square  inch,  and  d  and  t 
are  the  diameter  and  thickness  expressed  in  inches. 

Instances  of  collapsed  flues  of  Cornish  and  Lancashire  boilers  collated 
by  Clark  (S.  E.,  vol.  i,  p.  643),  showed  that  the  resistance  to  collapse 
of  flues  of  3/g-in.  plates,  18  to  43  ft.  long,  and  30  to  50  in.  diameter  varied 
as  the  1.75  power  of  the  diameter.  Thus, 

For  diameters  of  ..............   30     35     40     45     50    in. 

The  collapsing  pressures  were  ...   76     58     45     37     30    Ib.  per  sq.  in. 
For  7/16-in.  plates  the  collapsing 

pressures  were  ........  ..........      60     49     42    Ib.  per  sq.  in. 

C.  R.  Roelker,  in  Van  Nostrand's  Magazine,  March,  1881,  says  that 
Nystrom's  formula,  (6)  ,  gives  a  closer  agreement  of  the  calculated  with 
the  actual  collapsing  pressures  in  experiments  on  flues  of  every  descrip- 
tion than  any  of  the  other  formulae. 

Formula  for  Corrugated  Furnaces  (Eng'g,  July  24,  1891,  p.  102).  — 
As  the  result  of  a  series  of  experiments  on  the  resistance  to  collapse 
of  Fox's  corrugated  furnaces,  the  Board  of  Trade  and  Lloyd's  Register 
altered  their  formulae  for  these  furnaces  in  1891  as  follows: 

Board  of  Trade  formula  is  altered  from 


T  =  thickness  in  inches;  D  =  mean  diameter  of  furnace;  W  P  =  work- 
ing pressure,  Ib.  per  sq.  in. 

Lloyd's  formula  is  altered  from 

looo  xcr  -  2)  _  wp  toi234Xj(r-2)  =  wpf 

T  =  thickness  in  sixteenths  of  an  inch; 
D  =  greatest  diameter  of  furnace; 
WP  —  working  pressure  in  pounds  per  square  inch. 

Stewart's  Experiments.  —  Prof  .  Reid  T.  Stewart  (Trans.  A.S.M.E,, 


5,  10,  15  and  20  ft.  between  transverse  joints  tending  to  hold  the  tube  in 
a  circular  form.  A  second  series  was  made  on  single  lengths  of  20  ft. 
Seven  sizes,  from  3  to  10  in.  outside  diam.,  in  all  the  commercial  thick- 
nesses obtainable,  were  tested.  The  tests  showed  that  all  the  old  for- 
mulae were  inapplicable  to  the  wide  range  of  conditions  found  in  modern 
practice.  The  principal  conclusions  drawn  from  the  research  are  as 
follows: 

1.  The  length  of  tube,  between  transverse  joints  tending  to  hold  it 
in  circular  form,  has  no  practical  influence  upon  the  collapsing  pressure 
of  a  commercial  lap-welded  tube  so  long  as  this  length  is  npt  less  than 
about  six  diameters  of  tube. 

2.  The  formulas,  based  upon  this  research,  for  the  collapsing  pres- 
sures of  modern  lap-welded  Bessemer  steel  tubes,  for  aii  lengths  greater 
than  six  diameters,  are  as  follows: 


P= 


l,00o(l  -  y/1    -1600^)    ........     (A) 

P  =  86,670  t  -  1386      ............     (B) 

Where  P  -»  collapsing  pressure,    pounds   per  sq.  inch,  d  •=*  outside 
diameter  of  tube  in  inches,  t.  =  thickness  of  wall  in  inches* 

Formula  A  is  for  values  of  P  less  than  581  pounds,  or  for  values  of 


RESISTANCE  OF  HOLLOW   CYLINDERS.  343 

less  than  0.023,  while  formula  B  is  for  values  greater  than  these.  When 
applying  .these  formulae,  to  practice,  a  suitable  factor  of  safety  must  be 
applied. 

3.  The  apparent  fibre  stress  under  which  the  different  tubes  failed 
varied  from  about  7000  Ibs.  for  the  relatively  thinnest  to  35,000  Ibs. 
pep  sq.  ?n.  for  the  relatively  thickest  walls.  Since  the  average  yield 
point  of  the  material  was  37,000  and  the  tensile  strength  58,000  Ibs. 
per  sq.  in.,  it  would  appear  that  the  strength  of  a  tube  subjected  to  a 
fluid  collapsing  pressure  is  not  dependent  alone  upon  either  the  elastic 
limit  or  ultimate  strength  of  the  material  constituting  it.  The  element 
of  greatest  weakness  in  a  tube  is  its  departure  from  roundness,  even 
when  this  departure  is  relatively  small. 

The  table  on  the  following  page  is  a  condensed  statement  of  the  principal 
results  of  the  tests. 

Rational  Formulae  for  Collapse  of  Tubes.     (S.  E.  Slocum,  Eng'g, 
Jan.  8,  1909.) 

Heretofore  designers  have  been  forced  to  rely  either  upon  the  anti- 
quated experiments  of  Fairbairn,  which  were  known  to  be  in  error  bv 
as  much  as  100%  in  many  cases,  or  else  to  apply  the  theoretical  formu- 
lae  of  Love  and  others,  without  knowing  how  far  the  assumptions  on 
which  these  formulae  are  based  are  actually  realized. 

A  rational  formula  for  thin  tubes  under  external  pressure,  due  to  A.  E.  H. 
Love,  is 

P  =  [2  E/(l  -  m2)]  (*/D)»,    .......     (1) 


in  which  P  =  collapsing  pressure  in  Ibs.  per  sq.  in. 

E  =  modulus  of  elasticity  in  Ibs.  per  sq.  in. 

Nm  =  Poisson's  ratio  of  lateral  to  transverse  deformation. 
t  =  thickness  of  tube  wall  in  ins. 
D  =  external  tube  diameter  in  ins. 
or  thick  tubes  a  special  case  of  Lame"s  general  formula  is 
P  =  2u[(t/D)  -  (£/D)2J,       .........     (2) 

in  which  u  =  ultimate  compressive  strength  in  Ibs.  per  sq.  in. 

The  average  values  of  the  elastic  constants  are  for  steel,  E  =  30,000,000, 
m  =  0.295,  u  =  40,000;  and  for  brass,  E  =  14,000,000,  m  =  0.357, 
u  =  11,000. 

Hence,  for  thin  steel  tubes,  P  =  65,720,000  (f/Z>)»      .....     (3) 

For  thick  steel  tubes,  P  =  80,000  [(t/D)  -  (t/D)*]  ....     (4) 

For  thin  brass  tubes,  P  =  32,090,000  (t/D)  3.     .     ....     (5) 

For  thick  brass  tubes,  P  =  22,000  [(t/D)  -  (t/D)*]  ....     (6) 

It  is  desirable  to  introduce  a  correction  factor  C  in  (1)  which  shall 
allow  for  the  average  ellipticity  and  variation  in  thickness.  The  cor- 
rection for  ellipticity  =  d  —  (I>min/£>max)3,  and  that  for  variation  in 
thickness  =  C2  =  (tmin/kver.)3.  From  Stewart's  twenty-five  experiments 
Ci  =  0.967  and  Cz  =  0.712.  The  correction  factor  C  =  Ci  Cz  =  0.69; 
and  (1)  becomes 

P  =  C[2£Y(1  -  m2)](i/D)3        ......     (7) 

in   which    C  =  0.69   for   Stewart's   lap-welded   steel   flues,   t  =  average 
thickness  in  ins.,  and  D  =  maximum  diameter  in  ins. 

The  empirical  formulas  obtained  by  Carman  (Univ.  of  Illinois,  Bull. 
No.  17,  1906),  are  for  thin  cold-drawn  seamless  steel  tubes, 

P  =  50,200,000  (t/D)3, 
and  for  thin  seamless  brass  tubes, 

P  =  25,150,000  (£/D)3. 

Carman  assigns  0.025  as  the  upper  limit  of  t/D  for  thin  tubes  and  0.03 
as  the  lower  limit  of  t/D  for  thick  tubes.  Stewart  assigns  0.023  as  the 
limit  of  t/D  between  thin  and  thick  tubes. 

Comparing  these  with  (3)  and  (5),  it  is  evident  that  they  correspond 
to  a  correction  factor  of  0.76  for  the  steel  tubes  and  0.78  for  the  brass 
tubes.  Since  Carman's  experiments  were  performed  on  seamless  drawn 
tubes,  while  Stewart  used  lap-welded  tubes,  it  might  have  been  antici- 


344 


STRENGTH   OF  MATERIALS. 


COLLAPSING  PRESSURE  OF  LAP- WELDED  STEEL  TUBES. 
Outside  Diameter,  85/8  In.;    Length  of  Pipe,  20  Ft. 


Thick- 
ness, 
In. 

Length, 
Ft. 

Bursting 
Pressure, 
Lbs.  per 
Sq.  In. 

Aver- 
age. 

Outside 
Diam. 
In. 

Thick- 
ness. 

Bursting 
Pressure. 

Aver- 
age. 

0.176 

2.21 

815-1085 

977 

3 

0.112 

1550-2175 

1860 

0.180 

4.70 

525-705 

792 

3 

O.H3 

2575-3350 

2962 

0.181 

10.03 

455-650 

565 

3 

0.188 

3700-4200 

4095 

0.184 

14.71 

425-610 

548 

4 

0.119 

860-1030 

964 

0.185 

19.72 

450-625 

536 

4 

0.175 

2050-2540 

2280 

0.212 

2.21 

1240-1353 

1314 

4 

0.212 

3075-3375 

3170 

0.212 

4.70 

805-975 

907 

4 

0.327 

5425-5625 

5560 

0.217 

10.50 

700-960 

841 

6 

0.130 

450-640 

524 

0.219 

12.79 

750-1115 

905 

6 

0.167 

715-1110 

928 

0.268 

2.14 

1475-2200 

'    1872 

6 

0.222 

1200-2075 

1797 

0.274 

4.64 

1345-2030 

1684 

6 

0.266 

1750-2890 

2441 

0.272 

9.64 

1150-1908 

1583 

7 

0.160 

515-675 

592 

0.273 

14.64 

1250-1725 

1485 

7 

0.242 

1525-1850 

1680 

0.268 

19.64 

1250-1520 

1419 

7 

0.279 

1835-2445 

2147 

0.311 

2.16 

2290-2490. 

2397 

8.64 

0.185 

450-625 

536 

0.306 

4  64 

1795-2325 

2073 

8.66 

0.268 

1250-1520 

1419 

0.306 

9.64 

1585-2055 

1807 

8.67 

0.354 

1830-2180 

2028 

0.309 

14.64 

1520-2025 

1781 

10 

0.165 

210-240 

225 

0.302 

19.75 

1575-1960 

1762 

10 

0.194 

305-425 

383  • 

10 

0.316 

1275-1385 

1319 

COLLAPSING  PRESSURE  OF  LAP- WELDED  STEEL  TUBES  <,LBS.  PER  SQ.  IN.) 
Calculated  by  Stewart's  Formulae. 


Outside  Diameters,  Inches. 


ickness. 

2  In. 

21/2 
In. 

3  In. 

4  In. 

5  In. 

6  In. 

7  In. 

8  In. 

9  In. 

10  In. 

11  In 

H 

0  10 

2947 

2081 

1503 

781 

0  12 

3814 

2774 

2081 

1214 

694 

400 

0.14 

4671 

3468 

2659 

1647 

1041 

636 

400 

286 

217 

0.16 

5548 

4161 

3236 

2081 

1387 

925 

595 

400 

297 

232 

J87 

0.18 

6414 

4854 

3814 

3514 

1734 

1214 

843 

564 

400 

306 

244 

0.20 

7281 

5548 

4392 

2947 

2081 

1503 

1090 

781 

542 

400 

314 

0.22 

8148 

6241 

4970 

3381 

2427 

1792 

1338 

997 

733 

525 

400 

0.24 

9014 

6934 

5548 

3814 

2774 

2081 

1586 

1214 

935 

694 

512 

0.26 

9881 

7628 

6125 

4248 

3121 

2370 

1833 

1431 

1118 

867 

633 

0.28 

8321 

6703 

4681 

3468 

2669 

2081 

1647 

1310 

1041 

820 

0.30 

9014 

7281 

5114 

3814 

2947 

2328 

1864 

1503 

1214 

978 

0.32 

9708 

7859 

5548 

4161 

3236 

2576 

2081 

1696 

1387 

1135 

0  34 

8437 

5981 

4508 

3525 

2824 

2297 

1888 

1561 

1293 

0  36 

9014 

6414 

4854 

3814 

3071 

2514 

2081 

1734 

1450 

0  38 

9592 

6848 

5201 

4103 

3319 

2731 

2273 

1907 

1608 

0.40 

7281 

5548 

4392 

3567 

2947 

2466 

2081 

1766 

0.42 

7714 

5894 

4681 

3814 

3164 

2659 

2254 

1923 

0  44 

8148 

6241 

4970 

4062 

3381 

2851 

2427 

2081 

0  46 

8581 

6588 

5259 

4309 

3598 

3044 

2601 

2238 

0  48 

9014 

6934 

5548 

4557 

3814 

3236 

2774 

2396 

0.50 

9448 

7281 

5887 

4805 

4031 

3429 

2947 

2554 

HOLLOW   COPPER  BALLS.  345 

pated  that  the  latter  would  develop  a  smaller  percentage  of  the  theo- 
retical strength  for  perfect  tubes  than  the  former. 

Formula  (2)  for  thick  tubes  when  corrected  for  ellipticity  and  varia^ 
tion  in  thickness  reads 

P  =  2ucC  (t/D)  [1  -  C  (t/D)] (8) 

in   which  t  =  average  thickness,   and   C  =  Cit   Cz,   Ci  being  equal  to 

•Pminx-OmaxI    Cz  =  ^average/train- 

From  Stewart's  experiments,  average  ellipticity  C\  =  0.9874,  and 
average  variation  in  thickness  Ci  =  0.9022;  .'.  C  =  0.9874  X  0.9022 
=  0.89. 

We  have  then,  for  thick  lap-welded  steel  flues, 

P  =  2wc0.89  (t/D)  [I  - 
knd  for  thin  lap-welded  steel  flues, 

P  =  0.69  [2  E/(l  -  m*) 
in  which  E  =  30,000,000,  m  =  0.295,  and  uc  =  38,500  Ibs.  per  sq.  in. 

The  experimental  data  of  Stewart  and  Carman  have  made  it  possible 
to  correct  the  rational  formulas  of  Love  and  Lam6  to  conform  to  actual 
conditions;  and  the  result  is  a  pair  of  supplementary  formulas  (7)  and 
(8),  which  cover  the  entire  range  of  materials,  diameters,  and  thicknesses 
for  long  tubes  of  circular  section.  All  that  now  remains  to  be  done  is 
the  experimental .  determination  of  the  correction  constants  for  other 
types  of  commercial  tubes  than  those  already  tested. 

HOLLOW  COPPER  BALLS. 

Hollow  copper  balls  are  used  as  floats  in  boilers  or  tanks,  to  control 
feed  and  discharge  valves,  and  regulate  the  water-level. 

They  are  spun  up  in  halves  from  sheet  copper,  and  a  rib  is  formed  on 
one  half.  Into  this  rib  the  other  half  fits,  and  the  two  are  then  soldered 
or  brazed  together.  In  order  to  facilitate  the  brazing,  a  hole  is  left  on 
one  side  of  the  ball,  to  allow  air  to  pass  freely  in  or  out;  and  this  hole  is 
made  use  of  afterwards  to  secure  the  float  to  its  stem.  The  original 
thickness  of  the  metal  may  be  anything  up  to  about  Vie  of  an  inch,  if 
the  spinning  is  done  on  a  hand  lathe,  though  thicker  metal  may  be  used 
when  special  machinery  is  provided  for  forming  it.  In  the  process  of 
spinning,  the  metal  is  thinned  down  in  places  by  stretching;  but  the 
thinnest  place  is  neither  at  the  equator  of  the  ball  (i.e.,  along  the  rib) 
nor  at  the  poles.  The  thinnest  points  lie  along  two  circles,  passing 
around  the  ball  parallel  to  the  rib,  one  on  each  side  of  it,  from  a  third 
to  a  half  of  the  way  to  the  poles.  Along  these  lines  the  thickness  may 
be  10,  15,  or  20  per  cent  less  than  elsewhere,  the  reduction  depending 
somewhat  on  the  skill  of  the  workman. 

The  Locomotive  for  October,  1891,  gives  two  empirical  rules  for  deter- 
mining the  thickness  of  a  copper  ball  which  is  to  work  under  an  external 
pressure,  as  follows: 

,_,,  .  diameter  in  inches  X  pressure  in  pounds  per  sq.  in. 

16.000 
2.   Thickness  -  diameter  xVpressure. 

These  rules  give  the  same  result  for  a  pressure  of  166  Ibs.  only.  EX- 
AMPLE: Required  the  thickness  of  a  5-inch  copper  ball  to  sustain 

Pressures  of 50      100      150      166      200      250  lbs.persq.in. 

Answer  by  first  rule 0156  .0312  .0469  .0519  .0625  .0781  inch. 

Answer  by  second  rule  .0285  .0403  .0494  .0518  .0570  ,0637     " 


346  STRENGTH  OF  MATERIALS. 

HOLDING-POWER   OF  NAILS,    SPIKES,   AND    SCREWS. 

(A.  W.  Wright,  Western  Society  of  Engineers,  1881.) 
Spikes.  —  Spikes  driven  into  dry  cedar  (cut  18  months): 

Size  of  spikes 5  X  V4in.  sq.  6  X  1/4  6  X  1/2    5  X3/S 

Length  driven  in 41/4 in.       5  in.       5  in.  4i/4in. 

Pounds  resistance  to  drawing.  Av'ge.  Ibs.     857  821       1691     1202 

Frnm  fi  tn  Q  tp«tq  Pflrh  I  Max-     "      1159  923          2129       1556 

I rom  6  to  9  tests  each {Min     „      ?66  766       U20       68? 

A.  M.  Wellington  found  the  force  required  to  draw  spikes  9/ig  X  9/i6  in., 
driven  41/4  inches  into  seasoned  oak,  to  be  4281  Ibs.;  same  spikes,  etc., 
in  unseasoned  oak,  6523  Ibs. 

"Professor  W.  R.  Johnson  found  that  a  plain  spike  3/8  inch  square 
driven  33/g  inches  into  seasoned  Jersey  yellow  pine  or  unseasoned  chest- 
nut required  about  2000  Ibs.  force  to  extract  it;  from  seasoned  white 
oak  about  4000  and  from  well-seasoned  locust  6000  Ibs." 

Experiments  in  Germany,  by  Funk,  give  from  2465  to  3940  Ibs.  (mean 
of  many  experiments  about  3000  Ibs.)  as  the  force  necessary  to  extract  a 
plain  i/2-inch  square  iron  spike  6  inches  long,  wedge-pointed  for  one  inch 
and  driven  41/2  inches  into  white  or  yellow  pine.  When  driven  5  inches 
the  force  required  was  about  Vio  part  greater.  Similar  spikes  9/16  inches 
square}  7  inches  long,  driven  6  inches  deep,  required  from  3700  to  6745 
Ibs.  to  extract  them  from  pine;  the  mean  of  the  results  being  4873  Ibs. 
In  ail  cases  about  twice  as  much  force  was  required  to  extract  them 
from  oak.  The  spikes  were  all  driven  across  the  grain  of  the  wood. 
When  driven  with  the  grain,  spikes  or  nails  do  not  hold  with  more  than 
half  as  much  force. 

Boards  of  oak  or  pine  nailed  together  by  from  4  to  16  tenpenny  com- 
mon cut  nails  and  then  pulled  apart  in  a  direction  lengthwise  of  the 
boards,  and  across  the  nails,  tending  to  break  the  latter  in  two  by  a 
shearing  action,  averaged  ab9ut  300  to  400  Ibs.  per  nail  to  separate 
them,  as  the  result  of  many  trials. 

Resistance  of  Drift-bolts  in  Timber.  —  Tests  made  by  Rust  and 
Coolidge,  in  1878. 

White      Norway 
Pine.         Pine. 

1  in.  square  iron  drove  30  in.  in  15/ie-in.  hole,  Ibs 26,400       19,200 

1  in.  round      "         "      34    "   "  !3/i6-in.  " 16,800       18,720 

1  in.  square     "         "      18    "   "  i5/16_in.  "  14,600       15,600 

1  in.  round  22    "    "  i3/i6-in.  " 13,200       14,400 

Holding-power  of  Bolts  in  White  Pine.     (Eng'g  News,  Sept.  26,  1891.) 

Round.        Square. 
Lbs.  Lbs. 

Average  of  all  plain  1-in.  bolts 8224  8200 

Average  of  all  plain  bolts,  5/8  to  1  ifo  in 7805  8110 

Average  of  all  bolts 8383  8598 

Round  drift-bolts  should  be  driven  in  holes  i3/ie  of  their  diameter,  and 
square  drift-bolts  in  holes  whose  diameter  is  14/16  of  the  side  of  the  square. 

Force  required  to  draw  Screws  out  of  Norway  Pine. 

1/2"  diam.  drive  screw  4  in.  in  wood.       Power  required,  average  2424  Ibs. 

4  threads  per  in.  5  in.  in  wood.    "  2743 

1     D'blethr'd,3perin.,  4in.  in  "  2730 

Lag-screw,  7  per  in.,  1 1/2   "  1465 

6    "     "  21/2     ""        "  "        2026 

1/2  inch  R.R.  spike 5  2191 

Force  required  to  draw  Wood  Screws  out  of  Dry  Wood.  —  Tests 
made  by  Mr.  Bevan.  The  screws  were  about  two  inches  in  length,  0.22 
diameter  at  the  exterior  of  the  threads,  0.15  diameter  at  the  bottom,  the 
depth  of  the  worm  or  thread  being  0.035  and  the  number  of  threads  in  one 
inch  equal  12.  They  were  passed  through  pieces  of  wood  half  an  inch 
in  thickness  and  drawn-out  by  the  weights  stated:  Beech,  460  Ibs.;  ash, 


STRENGTH   OF   BOLTS.  347 

790  Ibs.;  oak,  760  Ibs.;  mahogany,  770  Ibs.;  elm,  665  Ibs.;  sycamore, 
830  Ibs. 

Tests  of  Lag-screws  in  Various  Woods  were  made  by  A.  J.  Cox, 
University  of  Iowa,  1891: 

Kind  of  Wood.  |£V     jg       «     St. 

Seasoned  white  oak . ...  5/8  in.       1/2  in.        4 1/2  in.      8037          3 

7/i6  "         3  6480          1 


1/2  "         3/8     '          41/2  "        8780          2 

5/8 


Yellow-pine  stick 5/8  "        l/2    '          4  3800          2 

White  cedar,  unseasoned 5/s  "        J/2    '         4  3405          2 

Cut  versus  Wire  Nails.  —  Experiments  were  made  at  the  Watertown 
Arsenal  in  1893  on  the  comparative  direct  tensile  adhesion,  in  pine  and 
spruce,  of  cut  and  wire  nails.  The  results  are  stated  by  Prof.  W.  H.  Burr 
as  follows: 

There  were  58  series  of  tests,  ten  pairs  of  nails  (a  cut  and  a  wire  nail 
in  each)  being  used.  The  tests  were  made  in  spruce  wood  in  most  in- 
stances. The  nails  were  of  all  sizes,  from  li/s  to  6  in.  in  length.  In 
every  case  the  cut  nails  showed  the  superior  holding  strength  by  a  large 
percentage.  In  spruce,  in  nine  different  sizes  of  nails,  b9th  standard 
and  light  weight,  the  ratio  of  tenacity  of  cut  to  wire  nail  was  about 
3  to  2.  With  the" finishing"  nails  the  ratio  was  roughly  3.5  to  2.  With 
box  nails  (l\  to  4  inches  long)  the  ratio  was  roughly  3  to  2.  The  mean 
superiority  in  spruce  wood  was  61%.  In  white  pine,  cut  nails,  driven 
with  taper  along  the  grain,  showed  a  superiority  of  100%,  and  with 
taper  across  the  grain  of  135%.  Also  when  the  nails  were  driven  in  the 
end  of  the  stick,  i.e.,  along  the  grain,  the  superiority  of  cut  nails  was 
100%,  or  the  ratio  of  cut  to  wire  was  2  to  1.  Thfc  total  of  the  results 
showed  the  ratio  of  tenacity  to  be  about  3.2  to  2  for  the  harder  wood, 
and  about  2  to  1  for  the  softer,  and  for  the  whole  taken  together  the 
ratio  was  3.5  to  2. 

Nail-holding  Power  of  Various  Woods.  —  Tests  at  the  Watertown 
Arsenal  on  different  sizes  of  nails  from  8d.  to  60d.,  reduced  to  holding 
power  per  sq.  in.  of  surface  in  wood,  gave  average  results,  in  pounds, 
as  follows:  white  pine,  wire,  167;  cut,  405.  Yellow  pine,  wire,  318;  cut, 
662.  White  oak,  wire,  940;  cut,  1216.  Chestnut,  cut,  683.  Laurel, 
wire,  651;  cut,  1200. 

Experiments  by  F.  W.  Clay.     (Eng'g  News,  Jan.  11,  1894.) 

t Tenacity  of  6d  nails— \ 

Plain.  Barbed.  Blued.  Mean. 

White  pine 106          94         135         111 

Yellow  pine 190         130         270         196 

Basswood 78         132         219         143 

White  oak .-226         300         555         360 

Hemlock 141         201         319         220 

STRENGTH   OF   BOLTS. 

Effect  of  Initial  Strain  in  Bolts.  —  Suppose  that  bolts  are  used  to 
connect  two  parts  of  a  machine  and  that  they  are  screwed  up  tightly 
before  the  effective  load  comes  on  the  connected  parts.  Let  Pi  =  the 
initial  tension  on  a  bolt  due  to  screwing  up,  and  Pz  —  the  load  after- 
wards added.  The  greatest  load  may  vary  but  little  from  Pi  or  Pz, 
according  as  the  former  or  the  latter  is  greater,  or  it  may  approach  the 
value  Pi  +  Pz,  depending  upon  the  relative  rigidity  of  the  bolts  and  of 
the  parts  connected.  Where  rigid  flanges  are  bolted  together,  metal  to 
metal,  it  is  probable  that  the  extension  of  the  bolts  with  any  additional 
tension  relieves  the  initial  tension,  and  that  the  total  tension  is  Pi  or  Pz, 
but  in  cases  where  elastic  packing,  as  india  rubber,  is  interposed,  the 
extension  of  the  bolts  may  very  little  affect  the -initial  tension,  and  the 
total  strain  may  be  nearly  Pi  +  Pz.  Since  the  latter  assumption  is 
more  unfavorable  to  the  resistance  of  the  bolt,  this  contingency  should 
usually  be  provided  for.  (See  Unwin,  "Elements  of  Machine  Design," 
for  demonstration.) 


348 


STRENGTH   OF  MATERIALS. 


Forrest  E.  Cardullo  (Machinery's  Reference  Series  No.  22,  1908)  states 
the  effect  of  initial  stress  in  bolts  due  to  screwing  them  tight  as  follows: 

1.  When  the  bolt  is  more  elastic  than  the  material  it  compresses,  the 
stress  in  the  bolt  is  either  the  initial  stress  or  the  force  applied,  whichever 
is  greater. 

2.  When  the  material  compressed  is  more  elastic  than  the  bolt,  the 
stress  in  the  bolt  is  the  sum  of  the  initial  stress  and  the  force  applied. 

Experiments  on  screwing  up  1/2,  8/4,  1  and  1 1/4  in.  bolts  showed  that  the 
stress  produced  is  often  sufficient  to  break  a  i/2-in...bolt,  and  that  the  stress 
varies  about  as  the  square  of  the  diameter.  From  these  experiments 
Prof.  Cardullo  calculates  what  he  calls  the  "working  section"  of  a  bolt  as 
equal  to  its  area  at  the  root  of  the  thread,  less  the  area  of  a  i/2-in.  bolt 
at  the  root  of  the  thread  times  twice  the  diameter  of  the  bolt,  and  gives 
the  following  table  based  on  this  rule. 

Working  Strength  of  Bolts.     U.  S.  Standard  Threads. 


„ 

tat 

a 

V 

. 

. 

, 

„ 

"o 

n 

st 

.2  • 

"o 

I 

1. 

1- 

1-3 

!« 

Q 

1". 

to| 

"oil 

*8la 

'o'S 

*! 

*s  1 

'o  § 

Si      . 

a'Ss 

bc'o 

ri  O     • 

rd     O        ' 

^  §,« 

sL 

•5  ft« 

•^  °*  m 

2-2 

0  o 

Mi£j 

II 

w>0  g 

||| 

||| 

fcj[lo  ® 

c  §  1 

c  §  £ 

11 

£H.S 

o  S* 

£§to 

H^to 

^§to 

^2"to 

^^Tto 

p 

< 

^ 

ro 

^ 

to 

to 

to 

1/2 

0.126 

0 

0 

0 

0 

0 

0 

0 

5/8 

0.202 

0.044 

220 

264 

308 

352 

440 

528 

3/4 

0.302 

0.113 

565 

678 

791 

904 

1,130 

1,356 

7/8 

0.420 

0.200 

1,000 

1,200 

1,400 

1,600 

2,000 

2,400 

1 

0.550 

0.298 

1,490 

1,788 

2,086 

2,384 

2,980 

3,476 

U/8 

0.694 

0.411 

2,055 

2,466 

2,877 

3,288 

4,110 

4,932 

11/4 

0.893 

0.578 

2,890 

3,468 

4,046 

4,624 

5,780 

6,936 

1.057 

0.710 

3,550 

4,260 

4,970 

5,680 

7,100 

8,520 

H/2 

1.295 

0.917 

4,585 

5,502 

6,419 

7,336 

9,170 

10,504 

15/8     . 

1.515 

1.105 

5,525 

6,630 

7,735 

8,840 

11,050 

13,2oO 

1.746 

1.305 

6,525 

7,830 

9,135 

10,440 

13,050 

15,660 

17/8 

2.051 

1.578 

7,890 

9,468 

11,046 

12,624 

15,780 

18,936 

2 

2.302 

1.798 

8,990 

10,788 

12,586 

14,384 

17,980 

21,576 

21/4 

3.023 

2.456 

12,280 

14,736 

17,192 

19,648 

24,560 

29,472 

21/2 

3.719 

3.089 

15,445 

18,534 

21,623 

24,712 

30,890 

37,068 

23/4 

4.620 

3.927 

19,635 

23,562 

27,489 

31,416 

39,270 

47,124 

3 

5.428 

4.672 

23,360 

28,032 

32,704 

37,376 

46,720 

56,064 

31/4 

6.510 

5.690 

28,450 

34,140 

39,830 

45,520 

56,900 

68,280 

31/2 

7.548 

6.666 

33,330 

39,996 

46,664 

53,328 

66,660 

79,992 

The  stresses  on  bolts  caused  by  tightening  the  nuts  by  a  wrench  may 
be  calculated  as  follows:  Let  L  =  the  effective  length  of  the  wrench  in 
inches,  P  =  the  force  in  pounds  applied  at  the  distance  L,  n  =  no.  of 
threads  per  inch  of  the  bolt,  T  =  total  tension  on  the  bolt  if  there  were 
no  friction,  then  T  =  2  nnLP.  Wilfred  Lewis,  Trans.  A.  S.  M.  E.,  gives 
for  the  efficiency  of  a  bolt  E  =  1  -f-  (1  +  nd),  where  d  =  external  diameter 
of  the  screw.  T  X  E  =  2nnLP  -4-  (1  +  nd)  is  the  tension  corrected 
for  friction.  It  also  expresses  the  load  that  can  be  lifted  by  screwing  a 
nut  on  a  bolt  or  a  bolt  into  a  nut. 

STRENGTH  OF  CHAINS. 

Formulas  for  Safe  Load  on  Chains. — Writing  the  formula  for  the  safe 
lead  on  chains  P  —  Kd2,  P  in  pounds,  d  in  inches,  the  following  figures  for 
K  are  given  by  the  authorities  named. 

Open  link  Stud  link 

Unwin  '     13,440;  11,200*  20,160. 

Weisbach  13,350  17,800 

Bach  13,750;  11,000*  16,500;  13,200* 

*  The  lower  figures  are  for  much  used  chain,  subject  frequently  to  the 
maximum  load.  G.  A  Goodenough  and  L.  E.  Moore,  Univ.  of  Illinois 


STAND-PIPES   AND  THEIR  DESIGN.  349 


STAND-PIPES  AND   THEIR  DESIGN. 

(Freeman  C.  Coffin,  New  England  Water  Works  Assoc.,  Eng.  News, 
March  16,  1893.)  See  also  papers  by  A.  H.  Rowland,  Eng.  Club  of  Phil., 
1887;  B.  F.  Stephens,  Amer.  Water  Works  Assoc.,  Eng.  News,  Oct.  6 
and  13,  1888;  W.  Kiersted,  Rensselaer  Soc.  of  Civil  Eng.,  Eng'g  Record, 
April  25  and  May  2,  1891,  and  W.  D.  Pence,  Eng.  News,  April  and  May, 
1894-  also,  J.  N.  Hazlehurst's  "  Towers  and  Tanks  for  Water  Works." 

The  question  of  diameter  is  almost  entirely  independent  of  that  of 
height.  The  efficient  capacity  must  be  measured  by  the  length  from  the 
high- water  line  to  a  point  below  which  it  is  undesirable  to  draw  the 
water  on  account  of  loss  of  pressure  for  fire-supply,  whether  that  point 
is  the  actual  bottom  of  the  stand-pipe  or  above  it.  This  allowable 
fluctuation  ought  not  to  exceed  50  ft.,  in  most  cases.  This  makes  the 
diameter  dependent  upon  two  conditions,  the  first  of  which  is  the  amount 
of  the  consumption  during  the  ordinary  interval  between  the  stopping  and 
starting  of  the  pumps.  This  should  never  draw  the  water  below  a  point  that 
will  give  a  good  fire  stream  and  leave  a  margin  for  still  further  draught 
for  fires.  The  second  condition  is  the  maximum  number  of  fire  streams 
and  their  size  which  it  is  considered  necessary  to  provide  for,  and  the 
maximum  length  of  time  which  they  are  liable  to  have  to  run  before  the 
pumps  can  be  relied  upon  to  reinforce  them. 

Another  reason  for  making  the  diameter  large  is  to  provide  for  stability 
against  wind-Dressiire  when  empty. 

The  following  table  gives  the  height  of  stand-pipes  beyond  which  they 
are  not  safe  against  wind-pressures  of  40  and  50  Ibs.  per  square  foot. 
The  area  of  surface  taken  is  the  height  multiplied  by  one  half  the 
diameter. 

Diameter,  feet 20         25  30  35 

Max.  height,  wind  40  Ibs 45         70         150 

1     50    " 35         55  80         160 

Any  form  of  anchorage  that  depends  upon  connections  with  the  side 
plates  near  the  bottom  is  unsafe.  By  suitable  guys  the  wind-pressure  is 
resisted  by  tension  in  the  guys,  and  the  stand-pipe  is  relieved  from 
wind  strains  that  tend  to  overthrow  it.  The  guys  should  be  attached  to 
a  band  of  angle  or  other  shaped  iron  that  completely  encircles  the  tank, 
and  rests  upon  some  sort  of  bracket  or  projection,  and  not  be  riveted  to 
the  tank.  They  should  be  anchored  at  a  distance  from  the  base  equal 
to  the  height  of  the  point  at  which  they  are  attached,  if  possible. 

The  best  plan  is  to  build  the  stand-pipe  of  such  diameter  that  it  will 
resist  the  wind  by  its  own  stability. 

Thickness  of  the  Side  Plates. 

The  pressure  on  the  sides  tending  to  rupture  the  plates  by  tension,  due 
to  the  weight  of  the  water,  increases  in  direct  ratio  to  the  height,  and 
also  to  the  diameter.  The  strain  upon  a  section  1  inch  in  height  at  any 
point  is  the  total  strain  at  that  point  divided  by  two  —  for  each  side  is 
supposed  to  bear  the  strain  equally.  The  total  pressure  at  any  point  is 
equal  to  the  diameter  in  inches,  multiplied  by  the  pressure  per  square 
inch,  due  to  the  height  at  that  point.  It  may  be  expressed  as  follows: 

H  —  height  in  feet,  and  /  =  factor  of  safety; 
d  =  diameter  in  inches; 
p  =  pressure  in  Ibs.  per  square  inch; 
0.434  =  p  for  1  ft.  in  height; 

s  =  tensile  strength  of  material  per  square.inch; 
T  =  thickness  of  plate. 

Bulletin,  No.  18,  1907,  after  an  extensive  theoretical  and  experimental 
Investigation,  find  that  these  values  give  maximum  stresses  in  the  external 
fibers  of  from  26,400  to  40,320  Ibs.  per  sq.  in.,  which  they  consider  much 
too  high  for  safety.  Taking  20,000  as  a  permissible  maximum  stress, 
they  give  the  formulae  for  safe  load  P  =  8000  d2  for  open  links  and 
P  =  10,000  dz  for  stud  links.  They  say  that  the  stud  link  will  within 
the  elastic  limit  bear  from  20  to  25%  more  load  than  the  open  link,  but 
that  the  ultimate  strength  of  the  stud'link  is  probably  less  than  that  of  the 
open  link.  See  also  tables  of  Size  and  Strength  of  Chains,  page  264. 


350  STRENGTH   OF   MATERIALS. 

Then  the  total  strain  on  each  side  per  vertical  inch 

=  0.434  Hd  =  pd  ,        T  =  OA34Hdf  =  pdf 
2  2   '  2s          ~    2s' 

Mr.  Coffin  takes  /  =  5,  not  counting  reduction  of  strength  of  joint, 
equivalent  to  an  actual  factor  of  safety  of  3  if  the  strength  of  the  riveted 
joint  is  taken  as  60  per  cent  of  that  of  the  plate. 

The  amount  of  the  wind  strain  per  square  inch  of  metal  at  any  joint 
can  be  found  by  the  following  formula,  in  which 

H  =  height  of  stand-pipe  in  feet  above  joint; 
T  =  thickness  of  plate  in  inches; 
p    =  wind-pressure  per  square  foot; 
W  =  wind-pressure  per  foot  in  height  above  joint; 
W  —  Dp  where  D  is  the  diameter  in  feet; 
m  =  average  leverage  or  movement  about  neutral  axis 

or  central  points  in  the  circumference;  or, 
m  =  sine  of  45°,  or  0.707  times  the  radius  in  feet. 

Then  the  strain  per  square  inch  of  plate 
(Hw)  f 


circ.  in  ft.  X  mT 

Mr.  Coffin  gives  a  number  of  diagrams  useful  in  the  design  of  stand- 
pipes,  together  with  a  number  of  instances  of  failures,  with  discussion 
of  their  probable  causes. 

Mr.  Kiersted's  paper  contains  the  following:  Among  the  most  promi- 
nent strains  a  stand-pipe  has  to  bear  are:  that  due  to  the  static  pressure 
of  the  water,  that  due  to  the  overturning  effect  of  the  wind  on  an  empty 
stand-pipe,  and  that  due  to  the  collapsing  effect,  on  the  upper  rings,  of 
violent  wind  storms. 

For  the  thickness  of  metal  to  withstand  safely  the  static  pressure  of 
water,  let  t  =  thickness  of  the  plate  iron  in  inches;  H  =  height  of  stand- 
pipe  in  feet;  D  =  diameter  of  stand-pipe  in  feet. 

Then,  assuming  a  tensile  strength  of  48,000  Ibs.  per  square  inch,  a 
factor  of  safety  of  4,  and  .efficiency  of  double-riveted  lap-joint  equaling 
0.6  of  the  strength  of  the  solid  plate,  t  =  0.00036  H  X  D;  H  =  10,000  t 
-+-3.6D;  which  will  give  safe  heights  for  thicknesses  up  to  5/8  to  3/4  of  an 
inch.  The  same  formula  may  also  apply  for  greater  heights  and  thick- 
nesses within  practical  limits,  if  the  joint  efficiency  be  increased  by  triple 
riveting. 

The  conditions  for  the  severest  overturning  wind  strains  exist  when 
the  stand-pipe  is  empty. 

Formula  for  wind-pressure  of  50  pounds  per  square  foot,  whend  = 
diameter  of  stand-pipe  in  inches;  x  =  any.  unknown  height  of  stand- 
pipe;  x  =  VsOTrctf  =  15.85  V(#. 

Failures  of  Stand-pipes.  —  A  list  showing  23  important  failures 
inside  of  nine  years  is  given  in  a  paper  by  Prof.  W.  D.  Pence,  Eng'g 
News,  April  5,  12,  19  and  26,  May  3,  10  and  24,  and  June  7,  1894.  His 
discussion  of  the  probable  causes  of  the  failures  is  most  valuable. 

Water  Tower  at  Yonkers,  N.Y.  —  This  tower,  with  a  pipe  122  feet 
high  and  20  feet  diameter,  is  described  in  Engineering  News,  May  18,  1892. 

The  thickness  of  the  lower  rings  is  u/16  of  an  inch,  based  on  a  tensile 
strength  of  60,000  Ibs.  per  square  inch  of  metal,  allowing  65%  for  the 
strength  of  riveted  joints,  using  a  factor  of  safety  of  31/2  and  adding  a 
constant  of  l/g  inch.  The  plates  diminish  in  thickness  by  Vie  inch  to 
the  last  four  plates  at  the  top,  which  are  1/4  inch  thick. 

The  contract  for  steel  requires  an  elastic  limit  of  at  least  33,000  Ibs. 
per  square  inch;  an  ultimate  tensile  strength  of  from  56,000  to  66,000  Ibs. 
per  square  inch;  an  elongation  in  8  inches  of  at  least  20%,  and  a  reduc- 
tion of  area  of  at  least  45%.  The  inspection  of  the  work  was  made  by  the 
Pittsburgh  Testing  Laboratory.  According  to  their  report  the  actual 
conditions  developed  were  as  follows:  Elastic  limit  from  34,020  to  39,420; 


WROUGHT-IRON    AND    STEEL    WATER    PIPES. 


351 


the  tensile  strength  from  58,330  to  65,390;  the  elongation  in  8  inches 
from  221/2  to  32%;  reduction  in  area  from  52.72  to  71.32%;  17  plates 
out  of  141  were  rejected  in  the  inspection. 

The  following  table  is  calculated  by  Mr.  Kiersted's  formulae.  The 
stand-pipe  is  intended  to  be  self-sustaining;  that  is,  without  guys  or 
stiff  eners. 

Heights  of  Stand-pipes  for  Various  Diameters  and  Thicknesses  of 
Plates. 


Thickness 
of  Plate 
in  Frac- 
tions of 
an  Inch. 

Diameters  in  Feet. 

5 

6 

7 

8 

9 

10 

12 

14 

15 

16 

18 

20 

25 

3/16  
7/32  

50 
55 

55 

60 

65 

55 
65 
75 
90 
100 
110 
115 
125 
130 

50 
60 
70 
85 
100 
115 
120 
130 
135 
145 
150 

35 
50 
55 
70 
85 
100 
115 
130 
145 
155 
165 

40 
50 
60 
75 
85 
100 
110 
120 
135 
145 
160 

40 

45 
55 
70 
80 
90 
100 
115 
125 
135 
150 
160 

1/4  •  .  .  - 
5/16-  ..  . 
3/8-  ..  • 
7/16-  .-  • 
V2  .... 
9/16   •  • 

60 
70 
75 
80 
85 

65 
75 
80 
90 
95 

70 
80 
90 
95 
100 

75 

85 
95 
100 
110 
115 

40 
50 
65 
75 
85 
95 
105 
120 
130 
140 
150 
160 

35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 

35 
40 
50 
60 
70 
80 
85 
95 
105 
110 
120 
130 
140 

25 
35 
40 
45 
55 
60 
65 
75 
80 
90 
95 
105 
110 

5/8  

11/16  

3/4  

13/16  

7/8.  ..., 

15/16  

1  

Heights  to  nearest  5  feet.     Rings  are  to  build  5  feet  vertically. 


WROUGHT-IRON  AND    STEEL  WATER-PDPES. 

Riveted  Steel  Water-pipes  (Engineering  News,  Oct.  11,  1890,  and 
Aug.  1,  1891).  —  The  use  of  riveted  wrought-iron  pipe  has  been  common 
in  the  Pacific  States  for  many  years,  the  largest  being  a  44-inch  conduit 
in  connection  with  the  works  of  the  Spring  Valley  Water  Co.,  which 
supplies^San  Francisco.  The  use  of  wrought  iron  and  steel  pipe  has  been 
necessary  in  the  West,  owing  to  the  extremely  high  pressures  to  be  with- 
stood and  the  difficulties  of  transportation.  As  an  example:  In  connec- 
tion with  the  water  supply  of  Virginia  City  and  Gold  Hill,  Nev.,  there 
was  laid  in  1872  an  lli/2-inch  riveted  wrought-iron  pipe,  a  part  of  which 
is  under  a  head  of  1720  feet. 

In  the  East,  an  important  example  of  the  use  of  riveted  steel  water 
pipe  is  that  of  the  East  Jersey  Water  Co.,  which  supplies  the  city  of 
Newark.  The  contract  provided  for  a  maximum  high  service  supply  of 
25,000,000  gallons  daily.  In  this  case  21  miles  of  48-inch  pipe  was  laid, 
some  of  it  under  340  feet  head.  The  plates  from  which  the  pipe  is  made 
are  about  13  feet  long  by  7  feet  wide,  open-hearth  steel.  Four  plates 
are  used  to  make  one  section  of  pipe  about  27  feet  long.  The  pipe  is 
riveted  longitudinally  with  a  double  row,  and  at  the  end  joints  with  a 
single  row  of  rivets.  Before  being  rolled  into  the  trench,  two  of  the 
27-feet  lengths  are  riveted  together,  thus  diminishing  the  number  of 
joints  to  be  made  in  the  trench  and  the  extra  excavation  to  give  room 
for  joining. 

The  thickness  of  the  plates  varies  with  the  pressure,  but  only  three 
thicknesses  are  used,  1/4  ,  5/16,  and  3/8  inches,  the  pipe  made  of  these 
thicknesses  having  a  weight  of  160,  185,  and  225  IDS.  per  foot,  respec- 
tively. At  the  works  all  the  pipe  was  tested  to  pressure  11/2  times  that 
to  which  it  is  to  be  subjected  when  in  place. 

An  important  discussion  of  the  design  of  large  riveted  steel  pipes  t< 


352  STRENGTH   OF   MATERIALS. 

resist  not  only  the  internal  pressure  but  also  the  external  pressure  from 
moist  earth  in  which  they  are  laid,  together  with  notes  on  the  design  of  a 
pipe  18ft.  diam.  6000  ft.  long  for  the  Ontario  Water  Power  Co.,  Niagara 
Falls,  by  Joseph  Mayer,  will  be  found  in  Eng.  News,  April  26, 1906. 

STRENGTH     OF     VARIOUS    MATERIALS.     EXTRACTS    FROM 
KIRKALDY'S   TESTS. 

The  publication,  in  a  book  by  W.  G.  Kirkaldy,  of  the  results  of  many 
thousand  tests  made  during  a  quarter  of  a  century  by  his  father,  David 
Kirkaldy,  has  made  an  important  contribution  to  our  knowledge  con- 
cerning the  range  of  variation  in  strength  of  numerous  materials.  A 
condensed  abstract  of  these  results  was  published  in  the  American  Ma- 
chinist, May  11  and  18,  1893,  from  which  the  following  still  further  con- 
densed extracts  are  taken: 

The  figures  for  tensile  and  compressive  strength,  or,  as  Kirkaldy  calls 
them,  pulling  and  thrusting  stress,  are  given  in  pounds  per  square  inch  of 
original  section,  and  for  bending  strength  in  pounds  of  actual  stress  or 
pounds  per  BD2  (breadth  X  square  of  depth)  for  length  of  36  inches 
between  supports.  The  contraction  of  area  is  given  as  a  percentage  of 
the  original  area,  and  the  extension  as  a  percentage  in  a  length  of  10 
inches,  except  when  otherwise  stated.  The  abbreviations  T.  S.,  E.  L., 
Contr.,  and  Ext.  are  used  for  the  sake  of  brevity,  to  represent  tensile 
strength,  elastic  limit,  and  percentages  of  contraction  of  area,  and  elon- 
gation, respectively. 

Cast  Iron.  —  44  tests:  T.  S.  15,468  to  28,740  pounds;  17  of  these 
were  unsound,  the  strength  ranging  from  15,468  to  24,357  pounds. 
Average  of  all,  23,805  pounds. 

Thrusting  stress,  specimens  2  inches  long,  1.34  to  1.5  in.  diameter; 
43  tests,  all  sound,  94,352  to  131,912;  one,  unsound,  93,759;  average  of 
all,  113,825. 

Bending  stress,  bars  about  1  in.  wide  by  2  in.  deep,  cast  on  edge. 
Ultimate  stress  2876  to  3854;  stress  per  BD*  =  725  to  892;  average, 
820.  Average  modulus  of  rupture,  R,  =  3/2  stress  per  BD2  X  length, 
=  44,280.  Ultimate  deflection,  0.29  to  0.40  in.;  average,  0.34  inch. 

Other  tests  of  cast  iron,  460  tests,  16  lots  from  various  sources,  gave 
results  with  total  range  as  follows:  Pulling  stress,  12,688  to  33,616 
pounds;  thrusting  stress,  66,363  to  175,950  pounds;  bending  stress,  per 
BD2,  505  to  1128  pounds;  modulus  of  rupture,  R,  27,270  to  61,912. 
Ultimate  deflection,  0.21  to  0.45  inch. 

The  specimen  which  was  the  highest  in  thrusting  stress  was  also  the 
highest  in  bending,  and  showed  the  greatest  deflection,  but  its  tensile 
Strength  was  only  26,502. 

The  specimen  with  the  highest  tensile  strength  had  a  thrusting  stress  of 
143,939  and  a  bending  strength,  per  BD2,  of  979  pounds  with  0.41  de- 
flection. The  specimen  lowest  in  T.  S.  was  also  lowest  in  thrusting  and 
bending,  but  gave  0.38  deflection.  The  specimen  which  gave  0.21  deflec- 
tion had  T.  S.,  19,188:  thrusting,  104,281;  and  bending,  561. 

Iron  Castings.  —  69  tests;  tensile  strength,  10,416  to  31,652;  thrust- 
Ing  stress,  ultimate  per  square  inch,  53,502  to  132,031. 

Channel  Irons.  —  Tests  of  18  pieces  cut  from  channel  irons.  T.  S. 
40,693  to  53,141  pounds  per  square  inch;  contr.  of  area  from  3.9  to 
32.5%.  Ext.  in  10  in.  from  2.1  to  22.5%.  The  fractures  ranged  all  the 
way  from  100%  fibrous  to  100%  crystalline.  The  highest  T.  S.,  53,141, 
with  8.1%  contr.  and  5.3%  ext.,  was  100%  crystalline;'  the  lowest  T.  S., 
iO, 693,  with  3.9  contr.  and  2.1%  ext.,  was  75%  crystalline.  All  the 
fibrous  irons  showed  from  12.2  to  22.5%  ext.,  17.3  to  32.5  contr.,  and 
T.  S.  from  43,426  to  49,615.  The  fibrous  irons  are  therefore  of  medium 
tensile  strength  and  high  ductility.  The  crystalline  irons  are  of  variable 
T.  S.,  highest  to  lowest,  and  low  ductility. 

Lowmoor  Iron  Bars.  —  Three  rolled  bars  21/2  inches  diameter;  ten- 
Bile  tests:  elastic,  23,200  to  24,200;  ultimate,  50,875  to  51,905;  contrac- 
tion, 44.4  to  42.5;  extension,  29.2  to  24.3.  Three  hammered  bars,  41/2 
Inches  diameter,  elastic  25,100  to  24,200;  ultimate,  46,810  to  49,223; 
contraction,  20.7  to  46.5;  extension,  10.8  to  31.6.  Fractures  of  all,  100 
per  cent  fibrous.  In  the  hammered  bars  the  lowest  T.  S,  was  accom- 
panied by  lowest  ductility. 


KIRKALDY'S  TESTS. 


353 


Iron  Bars,  Various.  —  Of  a  lot  of  80  bars  of  various  sizes,  some 
rolled  and  some  hammered  (the  above  Lowmoor  bars  included),  the 
lowest  T.  S.  (except  one)  40,808  pounds  per  square  inch,  was  shown  by 
the  Swedish  "hoop  L"  bar  31/4  inches  diameter,  rolled.  Its  elastic  limit 
was  19,150  pounds;  contraction  68.7%  and  extension  37.7%  in  10 
inches.  It  was  also  the  most  ductile  of  all  the  bars  tested,  and  was  100% 
fibrous.  The  highest  T.  S.,  60,780  pounds,  with  elastic  limit,  29,400; 
contr.,  36.6;  and  ext.,  24.3%,  was  shown  by  a  "  Farnley "  2-inch  bar, 
rolled.  It  was  also  100%  fibrous.  The  lowest  ductility  2.6%  contr., 
and  4.1%  ext.,  was  shown  by  a  33/4-inch  hammered  bar,  without  brand. 
It  also  had  the  lowest  T.  S.,  40,278  pounds,  but  rather  high  elastic  limit, 
25,700  pounds.  Its  fracture  was  95%  crystalline.  Thus  of  the  two  bars 
showing  the  lowest  T.  S.,  one.  was  the  most  ductile  and  the  other  the 
least  ductile  in  the  whole  series  of  80  bars. 

Generally,  high  ductility  is  accompanied  by  low  tensile  strength,  as  in 
the  Swedish  bars,  but  the  Farnley  bars  showed  a  combination  of  high 
ductility  and  high  tensile  strength. 

Locomotive  Forgings,  Iron.  — -17  tests  average,  E.  L.,  30,420; 
T.  S.,  50,521;  contr.,  36.5:  ext.  in  10  inches,  23.8. 

Broken  Anchor  Forcings,  Iron.  — 4  tests:  average,  E.  L.,  23,825; 
T.  S.,  40,083;  contr.,  3.0;  ext.  in  10  inches,  3.8. 

Kirkaldy  places  these  two  irons  in  contrast  to  show  the  difference 
between  good  and  bad  work.  The  broken  anchor  material,  he  says,  is 
of  a  most  treacherous  character,  and  a  disgrace  to  any  manufacturer. 

Iron  Plate  Girder.  —  Tensile  tests  of  pieces  cut  from  a  riveted  iron 
girder  after  twenty  years'  service  in  a  railway  bridge.  Top  plate,  aver- 
age of  3  tests,  E.  L.,  26,600;  T.  S.,  40,806;  contr.,  16.1;  ext.  in  10  inches, 
7.8.  Bottom  plate,  average  of  3  tests,  E.  L.,  31,200;  T.  S.,  44,288; 
contr.,  13.3;  ext.  in  10  inches,  6.3.  Web-plate,  average  of  3  tests,  E.  L., 
28,000;  T.  S.,  45,902;  contr.,  15.9;  ext.  in  10  inches,  8.9.  Fractures 
all  fibrous.  The  results  of  30  tests  from  different  parts  of  the  girder 
prove  that  the  iron  has  undergone  no  change  during  twenty  years  of  use. 

Steel  Plates.  —  Six  plates  100  inches  long,  2  inches  wide,  thickness 
various,  0.36  to  0.97  inch.  T.  S.,  55,485  to  60,805;  E.  L.,  29,600  to  33,200; 
contr.,  52.9  to  59.5;  ext.,  17.05  to  18.57. 

Steel  Bridge  Links.  —  40  links  from  Hammersmith  Bridge,  1886. 


Fracture. 

T.S. 

E.  L. 

Contr. 

Ext.  in 
100  in. 

Silky. 

Gran- 
ular. 

70 
0 
65 
100 

Average  of  all 

67,294 
60,753 
75,936 
64,044 
63,745 
65,980 
63,980 

38,294 
36,030 
44,  1  66 
32,441 
38,118 
36,792 
39,017 

34.5% 
30.1 
31.2 
34.7 
52.8 
40.8 
6.0 

14.11% 
15.51 
12.42 
13.43 
15.46 
17.78 
6.62 

30% 

30 
100 
35 
0 

Lowest  T.  S  

Highest  T.S.  and  'E.  L..  .  . 
Lowest  E  .  L  

Greatest  Contraction 

Greatest  Extension  
Least  Contr.  and  Ext  

The  ratio  of  elastic  to  ultimate  strength  ranged  from  50.6  to  65.2  per 
cent;  average,  56.9  per  cent. 

Extension  in  lengths  of  100  inches.  At  10,000  Ibs.  per  sq.  in.,  0.018  to 
0.024;  mean,  0.020  inch;  at  20,000  Ibs.  per  sq.  in.,  0.049  to  0.063-  mean, 
0.055  inch;  at  30,000  Ibs.  per  sq.  in.,  0.083  to  0.100;  mean,  0.090;  set  at 
30,000  pounds  per  sq.  in.,  0  to  0.002;  mean,  0. 

The  mean  extension  between  10,000  to  30,000  Ibs.  per  sq.  in.  increased 
regularly  at  the  rate  of  0.007  inch  for  each  2000  Ibs.  per  sq.  in.  increment 
of  strain.  This  corresponds  to  a  modulus  of  elasticity  of  28,571,429. 
The  least  increase  of  extension  for  an  increase  of  load  of  20,000  Ibs.  per 
sq.  in.,  0.065  inch,  corresponds  to  a  modulus  of  elasticity  of  30,769,231, 
and  the  greatest,  0.076  inch,  to  a  modulus  of  26,315,789. 

Steel  Rails.  —  Bending  tests,  5  feet  between  supports,  11  tests  of  flange 
rails  72  pounds  per  yard,  4.63  inches  high, 


354  STRENGTH   OF   MATERIALS. 

Elastic  stress.  Ultimate  stress.  Deflection  at  50,000  Ultimate 

Pounds.               Pounds.  Pounds.  Deflection  i 

Hardest...   34,200                 60,960  3.24  ins.  Sins. 

Softest 32,000                  56,740  3.76    "  8    " 

Mean 32,763                 59,209  3.53    "  8    " 

All  uncracked  at  8  inches  deflection. 

Pulling  tests  of  pieces  cut  from  same  rails.     Mean  results. 

Elastic  Ultimate  Contraction  of 

Stress.  Pounds.  area  of  frac-  Extension  | 

per  sq.  in.  per  sq.  in.  ture.  in  10  ins. 

Top  of  rails 44,200             83,110  19.9%              13.5% 

Bottom  of  rails 40,900             77,820  30.9%  22.8% 

Steel  Tires.  —  Tensile  tests  of  specimens  cut  from  steel  tires. 

KRUPP  STEEL.  —  262  Tests. 

Ext.  in 

E.  L.  T.  S.  Contr.          5  inches. 

Highest 69,250  119,079  319  18.1 

Mean 52,869  104,112  29.5  19.7 

Lowest 41,700  90,523  45.5  23.7 

VICKERS,  SONS  &  Co.  —  70  Tests. 

Ext.  in 

E.  L.  T.  S.  Contr.          5  inches. 

Highest 58,600  120,789  11.8  8.4 

Mean 51,066  101,264  17.6  12.4 

Lowest 43,700  87,697  24.7  16.0 

Note  the  correspondence  between  Krupp's  and  yickers'  steels  as  to 
tensile  strength  and  elastic  limit,  and  their  great  difference  in  contrac- 
tion and  elongation.  The  fractures  of  the  Krupp  steel  averaged  22  per 
cent  silky,  78  per  cent  granular;  of  the  Vicker  steel,  7  per  cent  silky, 
93  per  cent  granular. 

Steel  Axles.  —  Tensile  tests  of  specimens  cut  from  steel  axles. 

PATENT  SHAFT  AND  AXLE  TREE  Co.  —  157  Tests. 

Ext.  in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 49,800  99,009  21.1  16.0 

Mean          36,267  72,099  33.0  23.6 

Lowest 31,800  61,382  34.8  25.3 

VICKERS,  SONS  &  Co.  —  125  Tests. 

Ext.  in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 42,600  83,701  18.9  13.2. 

Mean 37,618  70,572  41.6  27.5 

Lowest. , 30,250  56,388  49.0  37.2 

The  average  fracture  of  Patent  Shaft  and  Axle  Tree  Co.  steel  was  33 
per  cent  silky,  67  per  cent  granular. 

The  average  fracture  of  Vickers'  steel  was  88  per  cent  silky,  12  per 
cent  granular. 

Steel  Propeller  Shafts.  —  Tensile  tests  of  pieces  cut  from  two  shafts, 
mean  of  four  tests  each.  Hallow  shaft,  Whitworth,  T.  S.,  61,290:  E.  L., 
30,575;  contr.,  52.8;  ext.  in  10  inches,  28.6.  Solid  shaft,  VickersT,  T.  S., 
46,870;  E.  L.,  20,425;  contr.,  44.4;  ext.  in  10  inches,  30.7. 

Thrusting  tests,  Whitworth,  ultimate,  56,201;  elastic,  29,300;  set  at 
30,000  IDS.,  0.18  per  cent;  set  at  40,000  IDS.,  2.04  per  cent;  set  at  50,000 
IDS.,  3.82  per  cent. 

Thrusting  tests,  Vickers',  ultimate,  44,602;  elastic,  22,250;  set  at 
30,000  Ibs.,  2.29  per  cent;  set  at  40,000  Ibs.,  4.69  per  cent. 


.    .. 

115,668;"  contr.,  37.8;  ext.  in' 10  inches,  16.6.'  Spring  steel  untem- 
pered,  15  tests,  average,  E.  L.,  38,785;  T.  S.,  69,496;  contr.,  19.1;  ext. 
in  10  inches,  29.8.  These  two  lots  were  shipped  for  the  same  purpose, 
viz.,  railway  carriage  leaf  springs. 

Steel  Castings.  —44  tests,  E.  L.,  31,816  to  35,567:  T.  S.,  54,928  to 
63,840;  contr.,  1.67  to  15.8;  ext.,  1.45  to  15.1.  Note  the  great  varia- 
tion in  ductility.  The  steel  of  the  highest  strength  was  also  the  most 
ductile. 


Riveted  Joints,  Pulling  Tests  of  Riveted  Steel  Plates,  Triple  Riv- 
eted Lap  Joints,  Machine  Riveted,  Holes  Drilled. 


Plates,  width  and  thickness,  inches: 
13.50X0.25     13.00X0.51     11.75X0.78 
Plates,  gross  sectional  area  square  inches: 

3.375  6.63  9.165 

Stress,  total,  pounds: 

199,320  332,640  423,180 

Stress  per  square  inch  of  gross  area,  joint: 

59,058  50,172  46,173 

Stress  per  square  inch  of  plates,  solid: 

70,765  65,300  64,050 

Ratio  of  strength  of  joint  to  solid  plate: 

83.46  76.83  72.09 

Ratio  net  area  of  plate  to  gross: 

73.4  65.5 

Where  fractured: 

plate  at  plate  at 

holes.  holes. 


12.25  X  1.01     14.00X0.77 


62.7 

plate  at 
holes. 


Rivets,  diameter,  area  and  number: 

0.45,  0.159,  24  0.64,  0.321,  21  0.95,0.708,  12 

Rivets,  total  area: 

3.816  6.741  8.496 


12.372 
528,000 
42,696 
62,280 
68.55 
64.7 

plate  at 
holes. 


10.780 
455,210 
42,227 
68,045 
62.06 
72.9 

rivets 
sheared 


1.08,  0.916,  12  0.95,0.708, 12 
10.992  8.496 


Strength  of  Welds.  —  Tensile  tests  to  determine  ratio  of  strength  of 
weld  to  solid  bar. 

IRON  TIE  BARS.  —  28  Tests. 

Strength  of  solid  bars  varied  from 43,201  to  57,065  Ibs. 

Strength  of  welded  bars  varied  from 17,816  to  44,586  Ibs. 

Ratio  of  weld  to  solid  varied  from 37.0  to  79.1% 

IRON  PLATES.  —  7  Tests. 

Strength  of  solid  plate  from 44,851  to  47,481  Ibs. 

Strength  of  welded  plate  from 26,442  to  38,931  Ibs. 

Ratio  of  weld  to  solid 57.7  to  83.9% 

CHAIN  LINKS.  —  216  Tests. 

Strength  of  solid  bar  from 49,122  to  57,875  Ibs. 

Strength  of  welded  bar  from 39,575  to  48,824  Ibs. 

Ratio  of  weld  to  solid 72.1  to  95.4% 

IRON  BARS.  —  Hand  and  Electric  Machine  Welded. 

32  tests,  solid  iron,  average 52,444 

17  electric  welded,  average 46,836  ratio  89.1% 

19     '        hand  46,899       '     89.3% 

STEEL  BARS  AND  PLATES.  —  14  Tests. 

Strength  of  solid 54,226  to  64,580 

Strength  of  weld 28,553  to  46,019 

Ratio  weld  to  solid 52.6  to  8.2.1% 

The  ratio  of  weld  to  solid  in  all  the  tests  ranging  from  37.0  to  95.4  is 
proof  of  the  great  variation  of  workmanship  in  welding. 


356 


STRENGTH  OF  MATERIALS. 


Cast  Copper.  — 4  tests,  average,  E.  L.9  5900;  T.  S.,  24,781;  contr., 
24.5;  ext.,  21.8. 

Copper  Plates.  — As  rolled.  22  tests,  0.26  to  0.75  in.  thick;  E.  L.,  9766 
to  18,650;  T.  S.,  30,993  to  34,281;  contr.,  31.1  to  57.6;  ext.,  39.9  to 
52.2.  The  variation  in  elastic  limit  is  due  to  difference  in  the  heat  at 
which  the  plates  were  finished.  Annealing  reduces  the  T.  S.  only  about 
1000  pounds,  but  the  E.  L.  from  3000  to  7000  pounds. 

Another  series,  0.38  to  0.52  in.  thick;  148  tests,  T.  S.,  29,099  to  31,924; 
contr.,  28.7  to  56.7;  ext.  in  10  inches,  28.1  to  41.8.  Note  the  uniformity 
in  tensile  strength. 

Drawn  Copper.  —  74  tests  (0.88  to  1.08  inch  diameter);  T.  S.,  31,634 
to  40,557;  contr.,  37.5  to  64.1;  ext.  in  10  inches,  5.8  to  48.2. 

Bronze  from  a  Propeller  Blade.  —  Means  of  two  tests  each  from 
center  and  edge.  Central  portion  (sp.  gr.  8.320),  E.  L.,  7550;  T.  S., 
26,312;  contr.,  25.4;  ext.  in  10  inches,  32.8.  Edge  portion  (sp.  gr. 
8.550).  E.  L.,  8950;  T.  S.,  35,960;  contr.,  37.8;  ext.  in  10  inches,  47.9. 

Cast  German  Silver. — 10  tests:  E.  L.,  13,400  to  29,100;  T.  S., 
23,714  to  46,540;  contr.,  3.2  to  21.5;  ext.  in  10  inches,  0.6  to  10.2. 

Thin  Sheet  Metal.  —  Tensile  Strength. 

German  silver,  2  lots 75,816  to  87,129 

Bronze,  4  lots 73,380  to  92,086 

Brass,  2  lots 44,398  to  58,188 

Copper,  9  lots 30,470  to  48,450 

Iron,  13  lots,  lengthway 44,331  to  59,484 

Iron,  13  lots,  crossway 39,838  to  57,350 

Steel,  6  lots 49,253  to  78,251 

Steel,  6  lots,  crossway 55,948  to  80,799 


Wire  Ropes. 

Selected  Tests  Showing  Range  of  Variation. 


I 

t_i 

Strands. 

•si 

£% 

as 

£i 

5  § 

£M 

a  "&  . 

Description. 

f-s 

1.S 

II 

.  c 

Is 

£>•"* 

SJ 

Hemp  Core. 

||5 

o'"1 

K^&H 

o  g 

OK. 

rt  £ 

PM 

0 

r 

£ 

fig 

Galvanized       .  .  . 

7.70 

53.00 

6 

19 

0.1563 

Main 

339,780 

Ungalvanized  

7.00 

53.10 

7 

19 

0.1495 

Main  and  Strands 

314,860 

Ungalvanized  
Galvanized  

6.38 
7.10 

42.50 
37.57 

7 
6 

19 
30 

0.1347 
0.1004 

Wire  Core 
Main  and  Strands 

295,920 
272,750 

Ungalvanized  

6.18 

40.46 

7 

19 

0.1302 

Wire  Core 

268,470 

Ungalvanized  
Galvanized  

6.19 
4.92 

40.33 
20.86 

7 
6 

19 
30 

0.1316 
0.0728 

Wire  Core 
Main  and  Strands 

22  1  ,820 
1  90,890 

Galvanized   

5.36 

18.94 

6 

12 

0.1104 

Main  and  Strands 

136,550 

Galvanized  

4.82 

21.50 

6 

7 

0.  1  693 

Main 

129,710 

Ungalvanized  

3.65 

12.21 

6 

19 

0.0755 

Main 

1  1  0,  1  80 

Ungalvanized  

3.50 

12.65 

7 

7 

0.122 

Wire  Core 

101,440 

Ungalvanized  

3.82 

14.12 

6 

7 

0.135 

Main 

98,670 

Galvanized  

4.1  1 

11.35 

6 

12 

0.080 

Main  and  Strands 

75,110 

Galvanized 

3  31 

727 

6 

12 

0.068 

Main  and  Strands 

55,095 

Ungalvanized  

3.02 

8.62 

6 

7 

0.105 

Main 

49,555 

Ungalvanized  

2.68 

6.26 

6 

6 

0.0963 

Main  and  Strands 

41,205 

Galvanized  

2  87 

5.43 

6 

12 

0.0560 

Main  and  Strands 

38,555 

Galvanized 

2  46 

3  85 

6 

12 

00472 

Main  and  Strands 

28,075 

Ungalvanized  
Galvanized  

V.75 
2.04 

2.80 
.  2.72 

6 
6 

7 
12 

0.0619 
0.0378 

Main 
Main  and  Strands 

24,552 
20,415 

Galvanized  

1.76 

1.85 

6 

12 

0.0305 

Main 

14,634 

KIRKALDY'S  TESTS.  357 


Wire.  —  Tensile  Strength. 

German  silver,  5  lots <  81,735  to  92,224 

Bronze,  1  lot 78,049 

Brass,  as  drawn,  4  lots 81,114  to  98,578 

Copper,  as  drawn,  3  lots 37,607  to  46,494 

Copper  annealed,  3  lots 34,936  to  45,210 

Copper  (another  lot),  4  lots 35,052  to  62,190 

Copper  (extension  36.4  to  0.6%). 

Iron,  8  lots 59,246  to  97,908 

Iron  (extension  15.1  to  0.7%). 

Steel,  8  lots ; 103,272  to  318.823 

The  steel  of  318,823  T.  S.  was  0.047  inch  diam.,  and  had  an  extension  of 
only  0  3  per  cent;  that  of  103,272  T.  S.  was  0.107  inch  diam.,  and  had  an 
extension  of  2.2  per  cent.  One  lot_of_0.044  inch  diam.  had  267,114  T.  S., 
and  5.2  per  cent  extension. 

Hemp  Ropes,  Tin  tarred.  —  15  tests  of  ropes  from  1.53  to  6.90  inches 
circumference,  weighing  0.42  to  7.77  pounds  per  fathom,  showed  an 
ultimate  strength  of  from  1670  to  33,808  pounds,  the  strength  per  fathom 
weight  varying  from  2872  to  5534  pounds. 

Hemp  Ropes,'  Tarred.  —  15  tests  of  ropes  .from  1.44  to  7.12  inches 
circumference,  weighing  from  0.38  to  10.39  pounds  per  fathom,  showed 
an  ultimate  strength  of  from  1046  to  31,549  pounds,  the  strength  per 
fathom  weight  varying  from  1767  to  5149  pounds. 

Cotton  Ropes.  —  5  ropes,  2.48  to  6.51  inches  circumference,  1.08  to 
8.17  pounds  per  fathom.  Strength  3089  to  23,258  pounds,  or  2474  to 
3346  pounds  per  fathom  weight. 

Manila  Ropes.  —  35  tests:  1.19  to  8.90  inches  circumference,  0.20  to 
11.40  pounds  per  fathom.  Strength  1280  to  65,550  pounds,  or  3003  to 
7394  pounds  per  fathom  weight. 

Belting. 

No.  of  Tensile  strength 

lots.  per  square  inch. 

11  Leather,  single,  ordinary  tanned 3248  to  4824 

4  Leather,  single,  Helvetia 5631  to  5944 

7  Leather,  double,  ordinary  tanned 2160  to  3572 

8  Leather,  double  Helvetia 4078  to  5412 

6  Cotton,  solid  woven 5648  to  8869 

14  Cotton,  folded,  stitched 4570  to  7750 

1  Flax,  solid,  woven 9946 

1  Flax,  folded,  stitched 6389 

6  Hair,  solid,  woven 3852  to  5159 

2  Rubber,  solid,  woven 4271  to  4343 

Canvas.  —  35  lots:  Strength,  lengthwise,  113  to  408  pounds  per  inch; 
cross  ways,  191  to  468  pounds  per  inch. 

The  grades  are  numbered  1  to  6,  but  the  weights  are  not  given.  The 
strengths  vary  considerably,  even  in  the  same  number. 

Marbles.  —  Crushing  strength  of  various  marbles.  38  tests,  8  kinds. 
Specimens  were  6-inch  cubes,  or  columns  4  to  6  inches  diameter,  and  6 
and  12  inches  high.  Range  7542  to  13,720  pounds  per  square  inch. 

Granite.  —  Crushing  strength,  17  tests;  square  columns  4X4  and 
6  X  4,  4  to  24  inches  high,  3  kinds.  Crushing  strength  ranges  10,026  to 
13,271  pounds  per  square  inch.  (Very  uniform.) 

Stones.  —  (Probably  sandstone,  local  names  only  given.)  11  kinds,  42 
tests,  6X6,  columns  12,  18  and  24  inches  high.  Crushing  strength 
ranges  from  2105  to  12,122.  The  strength  of  the  column  24  inches  long 
is  generally  from  10  to  20  per  cent  less  than  that  of  the  6-inch  cube. 

Stones.  —  (Probably  sandstone)  tested  for  London  &  Northwestern 
Railway.  16  lots,  3  to  6  tests  in  a  lot.  Mean  results  of  each  lot  ranged 
from  3785  to  11,956  pounds.  The  variation  is  chiefly  due  to  the  stones 
baing  from  different  lots.  The  different  specimens  in  each  lot  gav« 
results  which  generally  agreed  within  30  per  cent. 


358 


STRENGTH   OF   MATERIALS. 


Bricks.  —  Crushing  strength,  8  lots;  6  tests  in  each  lot:  mean  results 
ranged  from  1835  to  9209  pounds  per  square  inch.  The  maximum 
variation  in  the  specimens  of  one  lot  was  over  100  per  cent  of  the 
lowest.  In  the  most  uniform  lot  the  variation  was  less  than  20  per 
cent. 

Wood.  —  Transverse  and  Thrusting  Tests. 


5- 

Thrust- 

3 

1 

Sizes  abt.  in 
.  square. 

Span, 
inches. 

Ultimate 

Stress. 

LW 
4BD2' 

ing 

Stress 

per  sq. 

in. 

45,856 

1096 

3586 

10 

lU/2to  121/2 

144 

to 

to 

to 

80,520 

1403 

5438 

37,948 

657 

2478 

Dantzic  fir  

12 

12      to  13 

144 

to 

to 

to 

54,152 

790 

3423 

32,856 

1505 

2473 

English  oak     

$ 

41/2  X  12 

120 

to' 

to 

to 

39,084 

1779 

4437 

23,624 

1190 

2656 

American  white  oak  .  .  . 

5 

41/2  X  12 

120 

to 

to 

to 

26,952 

1372 

3899 

Demerara  greenheart,  9  tests  (thrusting) 8169  to  10,785 

Oregon  pine,  2  tests 5888  and  7284 

Honduras  mahogany,  1  test 6769 

Tobasco  mahogany,  1  test 5978 

Norway  spruce,  2  tests 5259  and  5494 

American  yellow  pine,  2  tests 3875  and  3993 

English  ash,  1  test 3025 

Portland  Cement.  —  (Austrian.)  Cross-sections  of  specimens  2  X  21/2 
inches  for  pulling  tests  only;  cubes,  3X3  inches  for  thrusting  tests; 
weight,  98.8  pounds  per  imperial  bushel;  residue,  0.7  per  cent  with 
sieve  2500  meshes  per  square  inch;  38.8  per  cent  by  volume  of  water 
required  for  mixing;  time  of  setting,  7  days;  10  tests  to  each  lot.  The 
mean  results  in  Ibs.  per  sq.  in.  were  as  follows: 


Age. 
10  days 
20  days 
30  days 

Portland  Cement. 


Cement 
alone, 
Pulling. 

376 

420 

451 


Cement 
alone, 
Thrusting. 
2910 
3342 
3724 


1  Cement, 

2  Sand, 

Thrusting. 

893 

1023 

1172 


1  Cement,   1  Cement, 
3  Sand,         4  Sand, 

Thrusting.  Thrusting. 
407  228 

494  275 

594  338 


________    _________ 

cross-section,  all  aged  10  days,  180  tests; 
square  inch. 


Various   samples  pulling  tests,   2  X  21/2  inches 


, 
ranges  87  to  643  pounds  per 


TENSILE    STRENGTH   OF  WIRE. 

(From  J.  Bucknall  Smith's  Treatise  on  Wire.) 
Tons  per  i 


Black  or  annealed  iron  wire 

Bright  hard  drawn 

Bessemer,  steel  wire 

Mild  Siemens-Martin  steel  wire 

High  carbon  ditto  (or  "improved") 

Crucible  cast-steel  "improved"  wire 100 

"  Improved  "  cast-steel  "  plough  " 120 

Special  qualities  of  tempered  and  improved 

cast  steel  wire  may  attain 150  to  170  336,000  to  380,800 


in.  sectiona 
area. 
25 
35 
40 
60 
80 


Pounds  per 
sq.  in.  sec- 
tional area. 

56,000 

78,400 

89,600 
134,000 
179,200 
224,000 
268,800 


MISCELLANEOUS   TESTS    OF   MATERIALS. 


359 


MISCELLANEOUS   TESTS   OF  MATERIALS. 

Reports  of  Work  of  the  Watertown  Testing-machine  in  1883. 
TESTS    OF    RIVETED   JOINTS,    IRON    AND    STEEL   PLATES. 


''i 

w 

I\J 

^2   . 

a 

"5 
5 

Is 

A 

fc£  . 

•**3n  03 

o>  <j§ 

"S-g 
PM  2 

9 

1 
•~  SR 

jUttg 

fl-3 

1*1 

§£ 

lickness 

Is 

0> 

c3 

111 

«  |s 

is* 

s 

1 

tfj 
|I 

5 

il'P 

£fca 

^ftj 
III 

1 

H 

2 

£ 

H^-2 

HS 

1 

3/8 

H/16 

3/4 

101/2 

6 

13/4 

39,300 

47,180 

47.0  t 

3/8 

H/16 

3/4 

101/2 

6 

13/4 

41,000 

47,180 

49.0  J 

1/2 

3/4 

13/16 

10 

5 

35,650 

44,615 

45.6  t 

1/2 

3/1 

13/16 

10 

5 

2 

35,150 

44,615 

44.9  J 

3/8 

H/I6 

3/4 

10 

5 

2 

46,360 

47,180 

59.9  § 

3/8 

H/16 

3/4 

10 

5 

2 

46,875 

47,180 

60.5  § 

3/4 

'      13/16 

10 

5 

2 

46,400 

44,615 

59.4  | 

1/2 

3/4 

13/16 

10 

5 

2 

46,140 

44,615 

59.2  § 

5/8 

H/16 

101/2 

4 

25/8 

44,260 

44,635 

57.2  § 

5/8 

1 

101/2 

4 

25/8 

42,350 

44,635 

54.9  | 

3/4 

H/8 

13/11! 

11.9 

4 

2.9 

42,310 

46,590 

52.1   § 

3/4 

H/8 

13/16 

11.9 

4 

2.9 

41,920 

46,590 

51.7  § 

3'8 

3/4 

13/16 

101/2 

6 

13/4 

61,270 

53,330 

59.5  $ 

3/8 

3/4 

13/16 

10l/2 

6 

13/4 

60,830 

53,330 

59.1   I 

1/2 

15/16 

1 

10 

5 

2 

47,530 

57,215 

40.2  J 

1/2 

15/16 

1 

10 

5 

2 

49,840 

57,215 

42.3  1 

3/8 

H/16 

3/4 

10 

5 

2 

62,770 

53,330 

71.7  | 

3/8 

H/16 

3/4 

10 

5 

2 

61,210 

53,330 

69.8  | 

15/16 

1 

10 

5 

2 

68,920 

57,215 

57.1  | 

1/2 

15/16 

1 

10 

5 

2 

66,710 

57,215 

55.0  § 

5/8 

1 

H/16 

91/2 

4 

23/8 

62,180 

52,445 

63.4  | 

5/8 

1 

11/16 

91/2 

4 

23/g 

62,590 

52,445 

63.8  § 

3/4 

H/8 

13/16 

10 

4 

21/2 

54,650 

51,545 

54.0  § 

3/4 

H/8 

13/16 

10 

4 

21/2 

54,200 

51,545 

53.4  § 

*  Iron. 


t  Steel. 


Lap-joint. 


§  Butt-joint. 


The  efficiency  of  the  joints  is  found  by  dividing  the  maximum  tensile 
stress  on  the  gross  sectional  area  of  plate  by  the  tensile  strength  of  the 
material. 

COMPRESSION  TESTS  OF  3  X  3   INCH  WROUGHT-IRON  BARS. 


Length,  inches. 

Teste 
Pin  Er 
in.  Di 
pressi 
Ibs. 

d  with  Two 
ds,  Pins  U/2 
am.     Corn- 
ve  Strength, 
per  sq.  in. 

Tested  with  Two 
Flat  Ends.    Com- 
pressive  Strength, 
Ibs.  per  sq.  in. 

Tested  with  One 
Flat  and  One  Pin 
End.  Compressive 
Strength,  Ibs.  per 
sq.  in. 

30  ;... 

28,260 

^ 

3  1  ,990 
26310 

60  

26640 

90  

24,030 

(  26,780 

(25,120 

120  

25,380 
20,660 

|  25,580 
1  23,010 

1  25,190 
(  22,450 

150     . 

20,200 
16,520 

(  22,450 

1  21,870 

180  

. 

1  7,840 
13,010 

15,700 

360 


STRENGTH   OF    MATERIALS, 


Tested  with  Two  Pin 
Ends.  Length  of  Bars 
120  inches. 


Diameter 
of  Pins. 
7/8  inch  

Comp.  Str., 
per  sq.  in.,  Ibs. 
16,250 

1  1/8  inches  .  . 

....           17  740 

17/8 

"...           21,400 

21/4        " 

22.210 

COMPRESSION     OF     WROUGHT-IRON     COLUMNS, 
BOX    AND   SOLID   WEB. 

ALL  TESTED  WITH  PIN  ENDS. 


LATTICED 


Columns  made  of 

1 
H 
1 

Sectional  Area, 
square  inch. 

if 
il« 

t>"o^ 

& 

Ultimate 
Strength,  per 
square  inch, 
pounds  . 

6-inch  channel  solid  web  

100 

9831 

432 

30,220 

6     " 

15.0 
20.0 

9.977 
9.762 

592 
755 

21,050 
16,220 

8-inch  channels,  with  5/iQ-in.  continuous 
plates                   

20.0 
26.8 

26.8 

16.281 
16.141 

19.417 

1,290 
,645 

1  940 

22,540 
17,570 

25,290 

5/16-inch  continuous  plates  and  angles.. 
Width  of  plates,  12  in.,  1  in.  and  7.35  in. 
7/i6-inch  continuous  plates  and  angles.. 

26.8 
26.8 

16.168 
20.954 

1,765 
2,242 

28,020 
25,770 

8-inch  channels  latticed    ...    .  .    .    . 

13  3 

7.628 

679 

33,910 

8     "                          "       

20.0 

7.621 

924 

34,120 

8     "                           " 

268 

7  673 

1  255 

29,870 

8-inch  channels,  latticed,  swelled  sides  .  . 
8                                                                  .  . 
8     "          "                             "          "     .. 
10-inch  channels,  latticed,  swelled  sides. 
10  " 

13.4 
20.0 
26.8 
16.8 
25.0 

7.624 
7.517 
7.702 
1  1  .944 
12.175 

.   684 
921 
,280 
,470 
,926 

33,530 
33,390 
30,770 
33,740 
32,440 

10  "                           "       

16.7 

12.366 

,549 

31,130  ' 

*  10-inch  channels,  latticed  one  side;  con- 
tinuous plate  one  side    .        

25.0 
25.0 

11.932 
1  7.622 

,962 
1,848 

32,740 
26,190 

t  10-inch  channels,  latticed  one  side;  con- 
tinuous plate  one  side  

25  0 

17.721 

1,827 

17,270 

*  Pins  in  center  of  gravity  of  channel  bars  and  continuous  plate,  1.63 
inches  from  center  line  of  channel  bars. 

t  Pins  placed  in  center  of  gravity  of  channel  bars. 


TENSILE   TEST   OF   SIX   STEEL   EYE-BARS. 

COMPARED   WITH   SMALL  TEST   INGOTS. 

The  steel  was  made  by  the  Cambria  Iron  Company,  and  the  eye-bar 
heads  made  by  Keystone  Bridge  Company  by  upsetting  and  hammering. 
All  the  bars  were  made  from  one  ingot.  Two  test  pieces,  3/4-inch  round, 
rolled  from  a  test-ingot,  gave  elastic  limit  48,040  and  42,210  pounds; 
tensile  strength,  73,150  and  69,470  pounds,  and  elongation  in  8  inches, 
22.4  and  25.6  per  cent  respectively.  The  ingot  from  which  the  eye-bars 
were  made  was  14  inches  square,  rolled  to  billet,  7X6  inches.  The 
eye-bars  were  rolled  to  61/2  X  1  inch.  Chemical  tests  gave  carbon  0.27 
to  0.30;  manganese,  0.64  to  0.73;  phosphorus,  0.074  to  0.098. 


MISCELLANEOUS   TESTS    OF   IRON    AND    STEEL.       361 


Gauged  Elastic  Tensile  Elongation 

Length,  limit,  Ibs.  strength  per  per  cent,  in 

inches.  per  sq.  in.  sq.  in.,  Ibs..  Gauged  Length. 

160  37,480  67,800  15.8 

160  36,650  64,000  6.96 

160                       71,560  8.6 

200  37,600  68,720  12.3 

200  35,810  65,850  12.0 

200  33,230  64,410  16.4 

200  37,640  68,290  13.9 

The  average  tensile  strength  of  the  3/4-inch  test  pieces  was  71,310  lbs.f 
that  of  the  eye-bars  67,230  Ibs.,  a  decrease  of  5.7%.  The  average  elastic 
limit  of  the  test  pieces  was  45,150  Ibs.,  that  of  the  eye-bars  36,402  Ibs.,  a 
decrease  of  19.4%.  The  elastic  limit  of  the  test  pieces  was  63.3%  of 
the  ultimate  strength,  that  of  the  eye-bars  54.2%  of  the  ultimate  strength. 

Tests  of  11  full-sized  eye  bars,  15  X  1V4  to  21/iein.,  20.5  to  21.4  ft.  long 
between  centers  of  pins,  made  by  the  Phoenix  Iron  Co.,  are  reported  in 
Eng.  News,  Feb.  2,  1905.  The  average  T.S.  of  the  bars  was  58,300  Ibs. 
per  sq.  in.-,  E.L.,  32,800.  The  average  T.S.  of  small  specimens  was 
63,900,  E.L.,  37,000.  The  T.S.  of  the  full-sized  bars  averaged  8.8% 
and  the  E.L.  12.1%  lower  than  the  small  specimens. 

EFFECT    OF    COLD-DRAWING    ON    STEEL. 

Three  pieces  cut  from  the  same  bar  of  hot-rolled  steel: 

1.  Original  bar,  2.03  in.  diam.,  gauged  length  30  in.,  tensile  strength 

55,400  Ibs.  per  square  in.;  elongation  23.9%. 

2.  Diameter  reduced  in  compression  dies  (one  pass)  .094 in.;  T.  S.  70,420- 

el.  2.7%  in  20  in. 

3.  "      "     0.222  in.;  T.S.  81,890; 

el.  0.075%  in  20  in. 

Compression  test  of  cold-drawn  bar  (same  as  No.  3),  length  4  in.,  diam. 
1.808  in.:  Compressive  strength  per  sq.  in.,  75,000  Ibs.;  amount  of  com- 
pression 0.057  in.;  set  0.04  in.  Diameter  increased  by  compression  to 
1.821  in.  in  the  middle;  to  1.813  in.  at  the  ends. 

MISCELLANEOUS  TESTS  OF   IRON  AND    STEEL. 

Tests  of  Cold-rolled  and  Cold-drawn  Steel,  made  by  the  Cambria 
Iron  Co.  in  1897,  gave  the  following  results  (averages  of  12  tests  of  each): 

E.  L.  T.  S.  El.  in  8  in.  Red. 

Before  cold-rolling 35,390  59,980  28.3%  58.5% 

After  cold-rolling 72,530  79,830  9.6%  34.9% 

After  cold-drawing 76,350  83,860  8.9%  34.2% 

The  original  bars  were  2  in.  and  7/8  in.  diameter.  The  test  pieces  cut 
from  the  bars  were  3/4  in.  diam.,  18  in.  long.  The  reduction  in  diameter 
from  the  hot-rolled  to  the  cold-rolled  or  cold-drawn  bar  was  Vie  in.  in 
each  case. 

Cold  Rolled  Steel  Shafting  (Jones  &  Laughlins)  in/iein.  diam. — 
Torsion  tests  of  12  samples  gave  apparent  outside  fiber  stress,  calculated 
from  maximum  twisting  moment,  70,700  to  82,900  Ibs.  per  sq.in.;  fiber 
stress  at  elastic  limit,  32,500  to  38,800  Ibs.  per  sq.  in.;  shearing  modulus 
of  elasticity,  11,800,000  to  12,100,000;  number  of  turns  per  foot  before 
fracture,  1.60  to  2.06.  —  Tech.  Quar.,  vol.  xii,  Sept.,  1899. 

Torsion  Tests  on  Cold  Rolled  Shafting.  —  (Tech.  Quar.  XIII,  No.  3, 
1900,  p.  229.)  14  tests.  Diameter  about  1.69  in.  Gauged  length,  40  to 
50  in.  Outside  fiber  stress  at  elastic  limit,  28,610  to  33,590  Ibs.  per  sq. 
in.;  apparent  outside  fiber  stress  at  maximum  load,  67,980  to  77,290. 
Shearing  modulus  of  elasticity,  11,400,000  to  12,030,000  Ibs.  per  sq.  in. 
Turns  per  foot  between  jaws  at  fracture,  0.413  to  2.49. 

Torsion  Tests  on  Refined  Iron.  —  13/4  in.  diam.  14  tests.  Gauged 
length,  40  ins.  Outside  fiber  stress  at  elastic  limit,  12,790  to  19,140  Ibs. 
per  sq.  in.;  apparent  outside  fiber  stress  at  maximum  load,  45,350  to 
58,340.  Shearing  modulus  of  elasticity,  10,220,0001011,700,000.  Turns 
per  foot  between  jaws  at  fracture,  1.08  to  1.42. 


362 


STRENGTH   OF   MATERIALS. 


Tests   of   Steel    Angles  with  Riveted  End  Connections.      (F.   P. 

McKibbin,  Proc.  A.S.T.M.,  1907.)  —  The  angles  broke  through  the  rivet 
holes  in  all  cases.  The  strength  developed  ranged  from  62.5  to  79.1% 
of  the  ultimate  strength  of  the  gross  area,  or  from  73.9  to  92%  of  the 
calculated  strength  of  the  net  section  at  the  rivet  holes. 

SHEARING    STRENGTH. 

H.  V.  Loss  in  American  Engineer  and  Railroad  Journal,  March  and 
April,  1893,  describes  an  extensive  series  of  experiments  on  the  shearing 
of  iron  and  steel  bars  in  shearing  machines.  Some  of  his  results  are: 

Depth  of  penetration  at  point  of  maximum  resistance  for  soft  steel 
bars  is  independent  of  the  width,  but  varies  with  the  thickness.  If 
d  =  depth  of  penetration  and  t  =  thickness,  d_=  0.3t  for  a  flat  knife, 
d  =  0.25*  for  a  4°  bevel  knife,  and  d  =  0.16  v^a  for  an  8°  bevel  knife. 
The  ultimate  pressure  per  inch  of  width  in  flat  steel  bars  is  approxi- 
mately 50,000  Ibs.  X  t.  The  energy  consumed  in  foot-pounds  per  inch 
width  of  steel  bars  is,  approximately:  1"  thick,  1300  ft.-lbs.;  11/2", 
2500;  13/4",  3700;  17/g",  4500;  the  energy  increasing  at  a  slower  rate  than 
the  square  of  the  thickness.  Iron  angles  require  more  energy  than  steel 
angles  of  the  same  size;  steel  breaks  while  iron  has  to  be  cut  off.  For 
hot-rolled  steel  the  resistance  per  square  inch  for  rectangular  sections 
varies  from  4400  Ibs.  to  20,500  Ibs.,  depending  partly  upon  its  hardness 
and  partly  upon  the  size  of  its  cross-area,  which  latter  element  indirectly 
but  greatly  indicates  the  temperature,  as  the  smaller  dimensions  require 
a  considerably  longer  time  to  reduce  them  down  to  size,  which  time 
again  means  loss  of  heat. 

It  is  not  probable  that  the  resistance  in  practice  can  be  brought  very 
much  below  the  lowest  figures  here  given  —  viz.,  4400  Ibs.  per  square 
inch  —  as  a  decrease  of  1000  Ibs.  will  henceforth  mean  a  considerable 
increase  in  cross-section  and  temperature. 

Relation  of  Shearing  to  Tensile  Strength  of  Different  Metals. 
E.  G.  Izod,  in  a  paper  presented  to  the  British  Institution  of  Mechanical 
Engrs.  (Jan.,  1906),  describes  a  series  of  tests  on  bars  and  plates  of 
different  metals.  The  specimens  were  firmly  clamped  on  two  steel 
plates  with  opposed  shearing  edges  4  ins.  apart,  and  a  shearing  block, 
which  was  a  sliding  fit  between  these  edges-,  was  brought  down  upon 
the  specimen,  so  as  to  cut  it  in  double  shear,  by  a  testing  machine. 


a 

b 

c 

a 

6 

c 

Cast  iron.    A  
Cast  iron.    B  

9.7 
13.4 

152 

Rolled    phosphor- 
bronze  

39.5 

11.7 

61 

Cast  iron.    C  
Cast    aluminum- 
bronze.         .  .    . 

11.3 
33  1 

12  5 

122 
60 

Aluminum  
Aluminum  alloy  
Wrough  t-iron  bar 

6.4 
12.7 
26.0 

25.5 
9.6 
22  5 

70 
59 

75 

Cast    phosphor- 
bronze. 

13  4 

2  2 

178 

Mild-steel.0.14  car- 
bon 

26  9 

34  7 

78 

Cast     phosphor- 
bronze 

19  7 

8  0 

9^ 

Crucible  steel,  0.12  C 
0.48  C. 

24.9 
42  1 

43.0 
26  0 

74 

68 

Gun  metal  

12.1 

7.8 

1(K 

0.71  C.... 

56.3 

15.0 

65 

Yellow  brass 

7  5 

6  5 

1?6 

0.77  C 

61  3 

11  0 

6? 

Yellow  brass  

16.0 

35.0 

74 

a.  Tensile  strength  of  the  metal,  gross  tons  per  sq.  in.;  6.  elongation 
in  2  in.%;  c.  ratio  shearing  •*•  tensile  strength.  The  results  seem  to 
point  to  the  fact  that  there  is  no  common  law  connecting  the  ultimate 
shearing  stress  with  the  ultimate  tensile  stress,  the  ratio  varying  greatly 
with  different  materials.  The  test  figures  from  crystalline  materials, 
such  as  cast  iron  or  those  with  very  little  or  no  elongation,  seem  to  indicate 
that  the  ultimate  shear  stress  exceeds  the  ultimate  tensile  stress  by  as 
much  as  20  or  25%,  while  from' those  with  a  fairly  high  measure  of 
ductility,  the  ultimate  shear  stress  may  be  anything  from  0  to  50%  less 
than  the  ultimate  tensile  stress. 

For  shearing  strength  of  rivets,  see  pages  240,  430  and  435. 


STRENGTH    OP   IRON   AND   STEEL   PIPE. 


363 


STRENGTH  OF   IRON  AND    STEEL  PIPE. 

Tests  of  Strength  and  Threading  of  Wrought-Iron  and  Steel 
Pipe.  T.  N.  Thomson,  in  Proc.  Am.  Soc.  Heat  and  Vent.  Engineers, 
vol.  xii.,  p.  80,  describes  some  experiments  on  welded  wrought  iron  and 
steel  pipes.  Short  rings  of  6-in.  pipe  were  pulled  in  the  direction  of  a 
diameter  so  as  to  elongate  the  ring.  Four  wrought  iron  rings  broke  at 
2400,  3000,  3100  and  4100  Ibs.  and  four  steel  rings  at  5300  (defective 
weld)  18,000,  29,000  and  35,000  Ibs.  Another  series  of  9  tests  each 
were  tested  so  as  to  show  the  tensile  strength  of  the  metal  and  of  the 
weld.  The  average  strength  of  the  metal  was,  iron,  34,520,  steel,  61,850 
Ibs.  The  strength  of  the  weld  in  iron  ranged  from  49  to  84,  averaging 
71  per  cent  of  the  strength  of  the  metal,  and  in  steel  from  50  to  93, 
averaging  72%. 

A  large  number  of  iron  and  steel  pipes  of  different  sizes  were  tested  by 
twisting,  the  force  being  applied  at  the  end  of  a  three-foot  lever.  The 
average  pull  on  the  steel  pipes  was:  1/2  in.  pipe,  109  Ibs.;  1  in.,  172  Ibs.; 
11/2  in.,  300  Ibs.;  number  of  turns  in  6  ft.  length,  respectively,  15,  8  and 
51/2.  Per  cent  failed  in  weld,  0,  13  and  13  respectively.  For  different 
lots  of  iron  pipe  the  average  pull  was:  1/2  in.,  68,  81  and  65  Ibs.;  1  in., 
154,  136,  107  Ibs.;  1 1/2  in.  256,  250,  258  Ibs.  The  number  of  turns  in 
6  feet  for  the  nine  lots  were  respectively,  41/2,  53/4,  21/2;  61/4,  31/2,  21/2; 
41/2,  31/2,  21/4. '  The  failures  in  the  weld  ranged  from  33  to  100%  in  the 
different  lots. 

The  force  required  to  thread  li/4-in.  pipe  with  two  forms  of  die  was 
tested  by  pulling  on  a  lever  21  ins.  long.  The  results  were  as  follows: 

Old  form  of  die,  iron  pipe. .     83  to  87  Ibs.  pull,  steel  pipe  100  to  111  Ibs. 
Improved  die,  iron  pipe 58  to  62  Ibs.  pull,  steel  pipe,  60  to    65  Ibs. 

Mr.  Thomson  gives  the  following  table  showing  approximately  the 
steady  pull  in  pounds  required  at  the  end  of  a  16-in.  lever  to  thread 
twist  and  split  iron  and  steel  pipe  of  small  sizes: 


To  Thread  with  Oiled 
Dies. 

To 
Twist 
Lbs. 

To 

Split 
Lbs. 

Safety 
Margin 
Lbs. 

New 
Rake 
Dies. 

New 
Com- 
mon 
Dies. 

Old 
Com- 
mon 
Dies. 

1/2  in.  steel       

34 
27 
44 
44 
69 
62 

56 
33 
60 
51 
111 
106 

60 
49 
91 
73 
124 
116 

122 
102 
150 
140 
286 
273 

152 
110 
240 
176 
420 
327 

74 
46 
112 
81 
259 
173 

1/2  in.  iron 

3/4  in.  steel  

3/4  in.  iron 

1  in.  steel.  ... 

1  in.  iron 

The  margin  of  safety  is  computed  by  adding  30%  to  the  pull  required 
to  thread  with  the  old  dies  and  subtracting  the  sum  from  the  pull  re- 
quired to  split  the  pipe.  If  the  mechanic  pulls  on  the  dies  beyond  the 
limit,  due  to  imperfect  dies,  or  to  a  hard  spot  in  the  pipe,  he  will  split 
the  pipe. 

Old  Boiler  Tubes  used  as  Columns.  (Tech.  Quar.  XIII,  No.  3, 
1900,  p.  225.)  Thirteen  tests  were  made  of  old  4-in.  tubes  taken  from 
worn-out  boilers.  The  lengths  were  from  6  to  8  ft.,  ratio  l/r  53  to  71, 
and  thickness  of  metal  0.13  to  0.18  in.  It  is  not  stated  whether  the  tubes 
were  iron  or  steel.  The  maximum  load  ranged  from  34,600  to  50,000 
Ibs.,  and  the  maximum  load  per  sq.  in.  from  17,100  to  27,500  Ibs.  Six 
new  tubes  also  were  tested,  with  maximum  loads  55,600  to  64,800  Ibs., 
and  maximum  loads  per  sq.  in.  31,600  to  38,100  Ibs.  The  relati9n  of 
the  strength  per  sq.  in.  of  the  old  tubes  to  the  ratio  l/r  was  very  variable, 
being  expressed  approximately  by  the  formula  S  =  41,000  —  300  l/r 
±  5000.  That  of  the  new  tubes  is  approximately  8  =  52,000  -  300  l/r 
i  2000. 


364  STRENGTH   OF  MATERIALS. 


HOLDING-POWER  OF  BOILER-TUBES  EXPANDED  INTO 
TUBE-SHEETS. 

Experiments  by  Chief  Engineer  W.  H.  Shock,  U.  S.  N.,  on  brass  tubes, 
21/2  inches  diameter,  expanded  into  plates  s/4  inch  thick,  gave  results 
ranging  from  5850  to  46,000  Ibs.  Out  of  48  tests  5  gave  figures  under 
10,000  Ibs.,  12  between  10,000  and  20,000  Ibs.,  18  between  20,000  and 
30.000  Ibs.,  10  between  30,000  and  40,000  Ibs.,  and  3  over  40,000  Ibs. 

Experiments  by  Yarrow  &  Co.,  on  steel  tubes,  2  to  21/4  inches  diameter, 
gave  results  similarly  varying,  ranging  from  7900  to  41,715  Ibs.,  the 
majority  ranging  from  20,000  to  30,000  Ibs.  In  15  experiments  on 
4  and  5  inch  tubes  the  strain  ranged  from  20,720  to  68,040  Ibs.  Beading 
the  tube  does  not  necessarily  give  increased  resistance,  as  some  of  the 
lower  figures  were  obtained  with  beaded  tubes.  (See  paper  on  Rules 
Governing  the  Construction  of  Steam  Boilers,  Trans.  Engineering  Con- 
gress, Section  G,  Chicago,  1893.) 

The  Slipping  Point  of  Rolled  Boiler-Tube  Joints. 

(O.  P.  Hood  and  G.  L.  Christensen,  Trans.  A.  S.  M.  E.,  1908). 

When  a  tube  has  started  from  its  original  seat,  the  fit  may  be  no  longer 
continuous  at  all  points  and  a  leak  may  result,  although  the  ultimate 
holding  power  of  the  tube  may  not  be  impaired.  A  small  movement  9f 
the  tube  under  stress  is  then  the  preliminary  to  a  possible  leak,  and  it 
is  of  interest  to  know  at  what  stress  this  slipping  begins. 

As  results  of  a  series  of  experiments  with  tube  sheets  of  from  1/2  in. 
to  1  in.  in  thickness  and  with  straight  and  tapered  tube  seats,  the  authors 
found  that  the  slipping  point  of  a  3-in.  12-gage  Shelby  cold-drawn  tube 
rolled  into  a  straight,  smooth  machined  hole  in  a  1-in.  sheet  occurs  with 
a  pull  of  about  7,000  Ibs.  The  frictional  resistance  of  such  tubes  is  about 
750  Ibs.  per  sq.  in.  of  tube-bearing  area  in  sheets  5/3  in.  and  1  in.  thick. 

Various  degrees  of  rolling  do  not  greatly  affect  the  point  of  initial  slip, 
and  for  higher  resistances  to  initial  slip  other  resistance  than  friction  must 
be  depended  upon.  Cutting  a  10-pitch  square  thread  in  the  seat,  about 
0.01  in.  deep  will  raise  the  slipping  point  to  three  or  four  times  that  in  a 
smooth  hole.  In  one  test  this  thread  was  made  0.015  in.  deep  in  a  sheet 
1  in.  thick,  giving  an  abutting  area  of  about  1.4  sq.  in.,  and  a  resistance 
to  initial  slip  of  45,000  Ibs.  The  elastic  limit  of  the  tube  was  reached  at 
about  34,000  Ibs. 

Where  tubes  give  trouble  from  slipping  and  are  required  to  carry  an 
unusual  load,  the  slipping  point  can  be  easily  raised  by  serrating  the  tube 
seat  by  rolling  with  an  ordinary  flue  expander,  the  rolls  of  which  are 
grooved  about  0.007  in.  deep  and  10  grooves  to  the  inch.  One  tube 
thus  serrated  had  its  slipping  point  raised  between  three  and  four  times 
its  usual  value. 

METHODS  OF  TESTING  THE  HARDNESS  OF  METALS. 

BrinelPs  Method.  J.  A.  Brinell,  a  Swedish  engineer,  ia  1900  pub- 
lished a  method  for  determining  the  relative  hardness  of  steel  which  has 
come  into  somewhat  extensive  use.  A  hardened  steel  ball,  10  mm. 
(0.3937  in.),  is  forced  with  a  pressure  of  3000  kg.  (6614  Ibs.)  into  a  flat 
surface  on  the  sample  to  be  tested,  so  as  to  make  a  slight  spherical  in- 
dentation, the  diameter  of  which  may  be  measured  by  a  microscope  or 
the  depth  by  a  micrometer.  The  hardness  is  defined  as  the  quotient 
of  the  pressure  by  the  area  of  the  indentation.  From  the  measurement 
the  "hardness  number"  is  calculated  by  one  of  the  following  formulae: 


H  =  K  (r  +  Vr?  -&)•*•  2  x rR\     or  H  =  K  +  2  n  rd. 

K  =  load,  =  3000  kg.,  r  —  radius  of  ball,  =  5  mm.,  R  =  radius  and 
d  =  depth  of  indentation. 

The  following  table  gives  the  hardness  number  corresponding  to 
different  values  of  Li  and  d. 


STRENGTH  OP  GLASS. 


365 


R 

H 

tR 

H 

R 

H 

a 

H 

d 

H 

d 

H 

no 

945 

2.40 

156 

3.80 

54.6 

.00 

95.5 

2.20 

43.4 

3.60 

26.5 

20 

654 

2.60 

131 

4.00 

47.8 

.10 

86.8 

2.40 

39.8 

3.80 

25.1 

40 

477 

2.80 

4.20 

41.7 

.20 

79.6 

2.60 

36.7 

4.00 

23.9 

60 

363 

3.00 

95.5 

4.40 

36.4 

40 

68  2 

2.80 

34.1 

4.50 

21.2 

80 

285 

3.20 

82.5 

4.60 

31.4 

.60 

59.7 

3.00 

31.8 

5.00 

19.1 

2  00 

229 

3  40 

71.6 

4.80 

26.5 

.80 

53  0 

3.20 

29.8 

5.50 

17.4 

3.20 

187 

3.60 

62.4 

4.95 

22.2 

2.00 

48.0 

3.40 

28.1 

6.00 

15.9 

The  hardness  of  steel,  as  determined  by  the  Brinell  method,  has  a 
uirect  relation  to  the  tensile  strength,  and  is  equal  to  the  product  of  a 
coefficient,  C,  into  the  hardness  number.  Experiments  made  in  Sweden 
with  annealed  steel  showed  that  when  the  impression  was  made  trans- 
versely to  the  rolling  direction,  with  H  below  175,  C  =  0.362;  with  H 
above  175,  C  =  0.344.  When  the  impression  was  made  in  the  rolling 
direction,  with  //  below  175,  C  =  0.354;  with  H  above  175,  C  =  0.324. 
The  product,  C  X  H,  or  the  tensile  strength,  is  expressed  in  kilograms 
per  square  millimeter. 

Electro-magnetic  Method.  —  Several  instruments  have  been  de- 
vised for  testing  the  hardness  of  steel  by  electrical  methods.  According 
to  Prof.  D.  E.  Hughes  (Cass.  Mag.,  Sept.,  1908),  the  magnetic  capacity 
of  iron  and  steel  is  directly  proportional  to  the  softness,  and  the  resist- 
ance to  a  feeble  external  magnetic  force  is  directly  as  the  hardness.  The 
electric  conductivity  of  steel  decreases  with  the  increase  of  hardness. 
(See  Electric  Conductivity  of  Steel,  p.  477.) 

The  Scleroscope. — This  is  the  name  of  an  instrument  invented  by 
A.  F.  Shore  for  determining  the  hardness  of  metals.  It  consists  chiefly 
of  a  vertical  glass  tube  in  which  slides  freely  a  small  cylinder  of  very 
hard  steel,  pointed  on  the  lower  end,  called  the  hammer.  This  hammer 
is  allowed  to  fall  about  10  inches  on  to  the  sample  to  be  tested,  and  the 
distance  it  rebounds  is  taken  as  a  measure  of  the  hardness  of  the  sample. 
A  scale  on  the  tube  is  divided  into  140  equal  parts,  and  the  hardness  is 
expressed  as  the  number  on  the  scale  to  which  the  hammer  rebounds. 
Measured  in  this  way  the  hardness  of  different  substances  is  as  follows: 
Glass,  130;  porcelain,  120;  hardest  steel,  110;  tool  steel,  1%  C.,  may  be 
as  low  as  31;  mild  steel,  0.5  C,  26  to  30;  gray  castings,  39;  wrought 
iron,  18;  babbitt  metal,  4  to  10;  soft  brass,  12;  zinc,  8;  copper,  6; 
lead,  2.  (Cass.  Mag.,  Sept.,  1908.) 


STRENGTH   OF   GLASS. 

(Fairbairn's  "Useful  Information  for  Engineers,"  Second  Series.) 

Best     Common       Extra 


Flint 
Glass. 

Mean  specific  gravity 3.078 

Mean  tensile  strength,  Ibs.  per  sq.  in.,  bars     2,413 

do.  thin  plates      4,200 

Mean  crush'g  strength,  Ibs.  p.  sq.  in.,  cyl'drs  27,582 

do.  cubes    13,130 


Green  White  Crown 


Glass. 

2.528 

2,896 

4,800 

39,876 

20,206 


Glass. 
2.450 
2,546 
6,000 
31,003 
21,867 


The  bars  in  tensile  tests  were  about  1/2  inch  diameter.  The  crushing 
tests  were  made  on  cylinders  about  3/4  inch  diameter  and  from  1  to  2 
inches  high,  and  on  cubes  approximately  1  inch  on  a  side.  The  mean 
transverse  strength  of  glass,  as  calculated  by  Fairbairn  from  a  mean 
tensile  strength  of  2560  Ibs.  and  a  mean  compressive  strength  of  30,150 
Ibs.  per  sq.  in.,  is,  for  a  bar  supported  at  the  ends  and  loaded  in  the 
middle,  w  =  3140  bd2/l,  in  which  w  =  breaking  weight  in  Ibs.,  b  =- 
breadth,  d  =  depth,  and  I  =  length,  in  inches.  Actual  tests  will  prob- 
ably show  wide  variations  in  both  directions  from  the  mean  calculated 
itrength. 


366 


STRENGTH  OF  MATERIALS. 


STRENGTH  OF  ICE. 

Experiments  at  the  University  of  Illinois  in  1895  (The  Technograph, 
vol.  ix)  gave  620  IDS.  per  sq.  in.  as  the  average  crushing  strength  of  cubes  i 
of  manufactured  ice  tested  at  23°  F.,  and   906  IDS.  for  cubes  tested  at  I 
14°  F.    Natural  ice,  at  12°  F.,  tested  with  the  direction  of  pressure  parallel  I 
to  the  original  water  surface,  gave  a  mean  of  1070  Ibs.,  and  tested  with  I 
the  pressure  perpendicular  to  this  surface  1845  Ibs.     The  range  of  varia-  1 
tion  in  strength  of  individual  pieces  is  about  50%  above  and  below  the  } 
mean  figures,  the  lowest  and  highest  figures  being  respectively  318  and 
2818  Ibs.  per  sq.  in.     The  tensile  strength  of  34  samples  tested  at  19  to 
23°  F.  was  from  102  to  256  Ibs.  per  sq.  in. 

STRENGTH   OF  TIMBER. 

Strength  of  Long-leaf  Pine  (Yellow  Pine,  Pinus  Palustris)  from 
Alabama  (Bulletin  No.  8,  Forestry  Div.,  Dept.  of  Agriculture,  1893. 
Tests  by  Prof.  J.  B.  Johnson). 

The  following  is  a  condensed  table  of  the  range  of  results  of  mechani- 
cal tests  of  over  2000  specimens,  from  26  trees  from  four  different  sites 
in  Alabama;  reduced  to  15  per  cent  moisture: 


Butt  Logs. 

Middle  Logs. 

Top  Logs. 

Av'g 
of  all 
Butt 
Logs. 
0.767 

12,614 

9,460 
1,926 

2.98 
7,452 
1,598 
17,359 
866 

Specific  gravity  

0.449  to    1  .039 
4,762  to  16,200 

4,930  to  13,110 
1,119to    3,117 

0.23  to    4.69 
4,781  to    9,850 
675  to    2,094 
8,600  to  3  1,890 
464  to  1,299 

0.575  to    0.859 
7,  640  to  17,128 

5,540  to  11,790 
1,136  to    2,982 

1.34  to    4.21 
5,030  to    9,300 
656  to    1,445 
6,330  to  29,500 
539  to    1,230 

0.484  to    0.907 
4,268  to  15,554 

2,553  to  11,950 
842  to    2,697 

0.09  to    4.65 
4,  587  to    9,100 
584  to    1,766 
4,  170  to  23,280 
484  to    1,156 

Transverse  strength,  rrp- 

do.  do.  at  elast.  limit 
Mod.  of  elast.,  thous.  Ibs. 
Relative  elast.  resilience, 
inch-pounds  per  cub.  in. 
Crushing    endwise,    str. 
per  sq.  in  .-Ibs  

Crushing    across    grain, 
strength  per  sq.  in.,  Ibs. 
Tensile  strength  per  sq. 
in  

Shearing  strength  (with 
grain),  mean  persq.  in. 

Some  of  the  deductions  from  the  tests  were  as  follows: 

1.  With  the  exception  of  tensile  strength  a  reduction  of  moisture  is 
accompanied  by  an  increase  in  strength,  stiffness,  and  toughness. 

2.  Variation  in  strength  goes  generally  hand-in-hand  with  specific 
gravity. 

3.  In  the  first  20  or  30  feet  in  height  the  values  remain  constant;  then 
occurs  a  decrease  of  strength  which  amounts  at  70  feet  to  20  to  40  per 
cent  of  that  of  the  butt-log. 

4.  In  shearing  parallel  with  the  grain  and  crushing  across  and  par- 
allel with  the  grain,  practically  no  difference  was  found. 

5.  Large  beams  appear  10  to  20  per  cent  weaker  than  small  pieces. 

6.  Compression  tests  endwise  seem  to  furnish  the  best  average  state- 
ment of  the  value  of  wood,  and  if  one  test  only  can  be  made,  this  is  the 
safest,  as  was  also  recognized  by  Bauschinger. 

7.  Bled  timber  is  in  no  respect  inferior  to  unbled  timber.1 

The  figures  for  crushing  across  the  grain  represent  the  load  required  to 
cause  a  compression  of  15  per  cent.  The  relative  elastic  resilience,  in 
inch-pounds  per  cubic  inch  of  the  material,  is  obtained  by  measuring 
the  area  of  the  plotted  strain-diagram  of  the  transverse  test  from  the 
origin  to  the  point  in  the  curve  at  which  the  rate  of  deflection  is  50  per 
cent  greater  than  the  rate  in  the  earlier  part  of  the  test  where  the  dia- 
gram is  a  straight  line.  This  point  is  arbitrarily  chosen  since  there  is 
no  definite  "elastic  limit"  in  timber  as  there  is  in  iron.  The  "strength 
at  the  elastic  limit"  is  the  strength  taken  at  this  same  point.  Timber 
is  not  perfectly  elastiq  for  any  load  if  left. on  any  great. length  of  time, 

The  long-leaf  pine  is  found  in  all  the  Southern  coast  states  from  North 


STRENGTH   OF   TIMBER. 


367 


I  Carolina  to  Texas.  Prof.  Johnson  says  it  is  probably  the  strongest  timber 
I  in  large  sizes  to  be  had  in  the  United  States.  In  small  selected  speci- 
i  mens,  other  species,  as  oak  and  hickory,  may  exceed  it  in  strength  and 
(toughness.  The  other  Southern  yellow  pines,  viz.,  the  Cuban,  short- 
f  leaf  and  the  loblolly  pines  are  inferior  to  the  long-leaf  about  in  the  ratios 
(  of  their  specific  gravities;  the  long-leaf  being  the  heaviest  of  all  the 
r  pines.  It  averages  (kiln-dried)  48  pounds  per  cubic  foot,  the  Cuban  47, 
[  the  short-leaf  40,  and  the  loblolly  34  pounds. 

Strength  of  Spruce  Timber.  —  The  modulus  of  rupture  of  spruce 
f  is  given  as  follows  by  different  authors:  Hatfield,  9900  Ibs.  per  square 
i  inch;  Rankine,  11,100;  Laslett,  9045;  Trautwine,  8100;  Rodman,  6168. 
I  Trautwine  advises  for  use  to  deduct  one-third  in  the  case  of  knotty  and 
\  poor  timber. 

Prof.  Lanza,  in  25  tests  of  large  spruce  beams,  found  a  modulus  of 

Lrupture  from  2995  to  5666  Ibs.;    the  average  being  4613  Ibs.     These 

were  average  beams,  ordered  from  dealers  of  good  repute.     Two  beams 

!  of  selected  stock,  seasoned  four  years,  gave  7562  and  8748  Ibs.     The 

modulus    of   elasticity   ranged    from    897,000   to    1,588,000,    averaging 

1  1,294,000. 

Time  tests  show  much  smaller  values  for  both  modulus  of  rupture  and 
modulus  of  elasticity.  A  beam  tested  to  5800  Ibs.  in  a  screw  machine 
was  left  over  night,  and  the  resistance  was  found  next  morning  to  have 
dropped  to  about  3000,  and  it  broke  at  3500. 

Prof.  Lanza  remarks  that  while  it  was  necessary  to  use  larger  factprs 
'  of  safety,  when  the  moduli  of  rupture  were  determined  from  tests  with 
smaller  pieces,  it  will  be  sufficient  for  most  timber  constructions,  except 
in  factories,  to  use  a  factor  of  four.  For  breaking  strains  of  beams,  he 
states  that  it  is  better  engineering  to  determine  as  the  safe  load  of  a 
timber  beam  the  load  that  will  not  deflect  it  more  than  a  certain  fractior? 
of  its  span,  say  about  Vsoo  to  1/400  of  its  length. 

Expansion  of  Timber  Due  to  the  Absorption  of  Water. 

(De  Volson  Wood,  A.  S.  M.  E.,  vol.  x.) 

Pieces  36  X  5  in.,  of  pine,  oak,  and  chestnut,  were  dried  thoroughly^ 
*»nd  then  immersed  in  water  for  37  days. 

The  mean  per  cent  of  elongation  and  lateral  expansion  were: 

Pine.  Oak.  Chestnut. 

Elongation,  per  cent 0.065  0.085  0.165 

Lateral  expansion,  per  cent 2.6  3.5  3.65 


Expansion  of  Wood  by  Heat.  —  Trautwine  gives  for  the  expansion, 
of  white  pine  for  1  degree  Fahr.  1  part  in  440,530,  or  for  180  degrees 
1  part  in  2447,  or  about  one-third  of  the  expansion  of  iron. 

Shearing  Strength  of  American  Woods,  adapted  for  Pins  or 
Tree-nails. 

J.  C.  Trautwine  (Jour.  Franklin  Inst.).     (Shearing  across  the  grain.) 


per  sq.  in. 

Ash 6280 

Beech 5223 

Birch 5595 

Cedar  (white) 1 372 

"€edar  (white) 1519 

Cedar  (Central  American).  ...   3410 

Cherry 2945 

Chestnut 1536 

Dogwood 6510 

Ebony 7750 

Gum 5890 

Hemlock 2750 

Locust .7176 


per.  sq.  in. 

Hickory f 6045 

Hickory 7285 

Maple 6355 

Oak 4425 

Oak  (live) 8480 

Pine  (white) 2480 

Pine  (Northern  yellow) 4340 

Pine  (Southern  yellow) 5735 

Pine  (very  resinous  yellow) .  . .  5053 

Poplar 4418 

Spruce 3255 

Walnut  (black) 4728 

Walnut  (common) 2830 


Transverse  Tests  of  Pine  and  Spruce  Beams.  (Tech.  Quar.  XIII, 
No.  3,  1900,  p.  226.) — Tests  of  37  hard  pine  beams,  4  to  10  ins.  wide,  6  to 
12  ins.  deep,  and  8  to  1C  ft.  length  between  supports,  showed  great  varia- 


368  STRENGTH   OF  MATERIALS. 

tions  in  strength.     The  modulus  of  rupture  of  different  beams  was  as 
follows:    1,  2970;   4,  4000  to  5000;   1,  5510;   1,  6220;  9,  7000  to  8000-  8    : 
8000  to  9000;  4,  9000  to  10,000;  5,  10,000  to  11,000;  3,  11,000  to  12,000; 
1,  13,600. 

Six  tests  of  white  pine  beams  gave  moduli  of  rupture  ranging  from 
1840  to  7810;  and  eighteen  tests  of  spruce  beams  from  2750  to  7970  Ibs. 
per  sq.  in. 

.Drying  of  Wood.  —  Circular  111,  U.  S.  Forest  Service,  1907.  Sticks 
of  Southern  loblolly  pine  11  to  13  inches  diameter,  9  to  10  ft.  long,  were 
weighed  every  two  weeks  until  seasoned,  to  find  the  weight  of  water 
evaporated.  The  loss,  per  cent  of  weight,  was  as  follows: 

Weeks 2       4       6       8     10     12     14     16 

Loss  per  cent  of  green  wood 16     21     26     31     32    34     35     35 

Preservation  of  Timber.  —  U.  S.  Forest  Service,  Circular  111,  1907, 
discusses  preservative  treatment  of  timber  by  different  methods,  namely, 
brush  treatment  with  creosote  and  with  carbolinium;  open  tank  treat- 
ment with  salt  solution,  zinc  chloride  solution;  and  cylinder  treatment 
with  zinc  chloride  solution  and  creosote. 

The  increased  life  necessary  to  pay  the  cost  of  these  several  preserva- 
tive treatments  is  respectively:  6,  16,  7,  13,  41,  27,  and  55%.  The 
results  of  the  experiments  prove  that  it  will  pay  mining  companies  to 
peel  their  timber,  to  season  it  for  several  months  and  to  treat  it  with  a 


good  preservative.     Loblolly  and  pitch  pine  have  been  most  success- 
fully preserved  by  treatment  with  creosote  in  an  open  tank. 

Circular  No.  151  of  the  Forest  Service  describes  experiments  on  the 


best  method  of  treating  loblolly  pine  cross-arms  of  telegraph  poles.  The 
arms  after  being  seasoned  in  air  are  placed  in  a  closed  air-tight  cylinder, 
a  vacuum  is  applied  sufficient  to  draw  the  oil  (creosote,  dead  oil  of  coal 
tar)  from  the  storage  tank  into  the  treating  cylinder.  Sufficient  pres- 
sure is  then  applied  to  force  the  oil  into  the  heartwood  portion  of  the 
timber,  and  continued  until  the  desired  amount  of  oil  is  absorbed,  then  a 
vacuum  is  maintained  until  the  surplus  oil  is  drawn  from  the  sap  wood. 
It  is  recommended  that  heartwood  should  finally  contain  about  6  Ibs. 
of  oil  per  cubic  foot,  and  sapwood  about  10  Ibs.  The  preliminary  bath 
of  live  steam,  formerly  used,  has  been  found  unnecessary.  Much  valu- 
able information  concerning  timber  treatment  and  its  benefits  is  con- 
tained in  the  several  circulars  on  the  subject  issued  by  the  Forest 
Service. 

STRENGTH  OF   COPPER  AT  HIGH  TEMPERATURES. 

The  British  Admiralty  conducted  some  experiments  at  Portsmouth 
Dockyard  in  1877,  on  the  effect  of  increase  of  temperature  on  the  tensile 
strength  of  copper  and  various  bronzes.  The  copper  experimented  upon 
was  in  rods  0.72  in.  diameter. 

The  following  table  shows  some  of  the  results: 


Temperature, 
Fahr. 

Tensile  Strength 
in  Ibs.  per  sq.  in. 

Temperature, 
Fahr. 

Tensile  Strength 
in  Ibs.  per  sq.  in. 

Atmospheric 
100° 
200° 

23,115 
23,366 
22,110 

300° 
400° 
500° 

21,607 
21,105 
19,597 

Up  to  a  temperature  of  400°  F.  the  loss  of  strength  was  only  about 
10  per  cent,  and  at  500°  F.  the  loss  was  16  per  cent.  The  temperature  of 
steam  at  200  Ibs.  pressure  is  382°  F.,  so  that  according  to  these  experi- 
ments the  loss  of  strength  at  this  point  would  not  be  a  serious  matter. 
Above  a  temperature  of  500°  the  strength  is  seriously  affected. 

COPPER  CASTINGS  OF  HIGH  CONDUCTIVITY. 

A  method  of  making  copper  castings  of  high  electric  conductivity  is 
described  in  The  Foundry,  Sept.,  1910.  The  copper  is  melted  under 
a  coyer  of  charcoal  and  common  salt.  When  thoroughly  liquid,  2  oz. 
of  stick  magnesium  is  added  per  100  Ib.  of  copper,  being  plunged  below 
the  surface  of  the  copper  and  held  there  until  reaction  ceases.  The 
metal  should  be  stirred  for  five  minutes  with  a  plumbago  stirrer,  and 
reheated  before  pouring.  The  castings  have  a  conductivity  of  about 
85  %  if  high  grade  ingot  copper  is  used. 


TESTS   OF   AMERICAN   WOODS. 


369 


TESTS   OF   AMERICAN   WOODS.     (Watertown  Arsenal  Tests,  1883.) 

In  all  cases  a  large  number  of  tests  were  made  of  each  wood.  Mini- 
mum and  maximum  results  only  are  given.  All  of  the  test  specimens 
had  a  sectional  area  of  1.575  X  1.575  inches.  The  transverse  test  speci- 
mens were  39.37  inches,  between  supports,  and  the  compressive  test 
specimens  were  12.60  inches  long.  Modulus  of  rupture  calculated  from 

3  PI 
formula  R  =  ^-rj2  •   P  =  l°ac*  *n  Pounds  at  the  middle,  I  =  length,  in 

Inches,  b  =  breadth,  d  =  depth: 


Name  of  Wood. 

Transverse  Tests. 
Modulus  of 
Rupture. 

Compression 
Parallel  to 
Grain,  pounds 
per  square  inch. 

Min. 

Max. 

Min. 

Max. 

Cucumber  tree  (Magnolia  acuminata)  . 
Yellow  poplar  white  wood  (Lirioden- 

7,440 
6,560 
6,720 

9,680 
8,610 
12,200 
8,310 
7,470 
10,190 
9,830 
10,290 
5,950 
5,180 
10,220 
8,250 

6,720 

4,700 
8,400 
14,870 
11,560 
7,010 
9,760 
7,900 
5,950 
13,850 

11,710 
8,390 
6,310 
5,640 
9,530 
5,610 
3,780 

9,220 
9,900 
7,590 

8,220 
10,080 

12,050 
11,756 
11,530 

20,130 
13,450 
21,730 
16,800 
11,130 
14,560 
14,300 
18,500 
15,800 
10,150 
13,952 
15,070 

11,360 

11,740 
16,320 
20,710 
19,430 
18,360 
18,370 
18,420 
12,870 
18,840 

17,610 
13,430 
9,530 
15,100 
10,030 
11,530 
10,980 

21,060 
11,650 
14,680 

17,920 
16,770 

4,560 
4,150 
3,810 

7,460 
6,010 
8,330 
5,830 
5,630 
6,250 
6,240 
6,650 
4,520 
4,050 
6,980 
4,960 

4,960 

5,480 
6,940 
7,650 
7,460 
5,810 
4,960 
4,540 
3,680 
5,770 

5,770 
3,790 
2,660 
4,400 
5,060 
3,750 
2,580 

4,010 
4,150 
4,500 

4,880 
6,810 

7,410 
5,790 
6,480 

9,940 
7,500 
11,940 
9,120 
7,620 
9,400 
7,480 
8,080 
8,830 
5,970 
8,790 
8,040 

7,340 

6,810 
8,850 
10,280 
8,470 
9,070 
8,970 
8,550 
6,650 
7,840 

8,590 
6,510 
5,810 
7,040 
7,140 
5,600 
4,680 

10,600 
5,300 
7,420 

9,800 
10,700 

White  wood,  Basswood  (Tilia  Ameri- 

Sugar-maple,  Rock-maple  (Acer  sac- 

Red  maple  (Acer  rubrum) 

Wild  cherry  (Prunus  serotina)  
Sweet  gum  (Liquidambar  styraciflua)  . 
Dogwood  (Cornus  florida)    . 

Sour  gum,  Pepperidge\(Nyssasyli;atica) 
Persimmon  (Diospyros  Virginiana)  .  . 
White  ash  (Fraxunis  Americana)  .... 
Sassafras  (Sassafras  officinale) 

Slippery  elm  (Ulmus  fulva)  

\\hite  elm  (Ulmus  Americana) 

Sycamore;     Buttonwood     (Platanus 
occidentalis)  ....               . 

Butternut;     white   walnut    (Juglans 

Black  walnut  (Juglans  nigrd)  

White  oak  (Quercus  alba]  

Beech  (Fagus  ferruginea)  

Canoe-birch,  paper-birch  (Betula  pa- 

Cottonwood  (Populus  monilifera) 
White  cedar  (Thuja  occidentalis}  
Red  cedar  (Junipcrus  Virginiana)  .  .  . 
Cypress  (Saxodium  Distichum)  
White  pine  (Pinus  strobus}  

Long-leaved     pine,     Southern     pine 

White  spruce  (Picea  alba}  

Hemlock  (  Tsuga  Canadensis)  
Red  fir,  yellow  fir  (Pseudotsuga  Doug- 
Jasii)  

Tamarack  (Larix  Americana)  

370  STRENGTH   OF  MATERIALS. 

TENSILE  STRENGTH  OF  ROLLED  ZINC  PLATES. 

Herbert  F.  Moore,  in  Univ.  of  III  Bulletin,  No.  9,  1911,  gives  a 
table  from  which  the  following  averages  are  taken: 
Thickness,  Tensile  Strength,  Elongation 

In.  Lb.  per  Sq.  In.  in  8  In.,  %. 

with  across  with  across 

§rain.  grain.  grain.  grain. 

1340  23050  4.85  0.31 

0.6                                  21490                 23550                  1G.63                    3.33 
0.25                                23770                 22260                  11.90                    0.27 
0.10                               23580                33620                 20.4                    14.3 
0.018  24660  32380  

THE   STRENGTH   OF  BRICK,    STONE,   ETC. 

A  great  advance  has  recently  (1895)  been  made  in  the  manufacture 
of  brick,  in  the  direction  of  increasing  their  strength.  Chas.  P.  Chase,  in 
Engineering  News,  says:  "Taking  the  tests  as  given  in  standard  engi- 
neering books  eight  or  ten  years  ago,  we  find  in  Trautwine  the  strength  of 
brick  given  as  500  to  4200  Ibs.  per  sq.  in.  Now,  taking  recent  tests  in 
experiments  made  at  Watertown  Arsenal,  the  strength  ran  from  5000  to 
22,000  Ibs.  per  sq.  in.  In  the  tests  on  Illinois  paving-brick,  by  Prof. 
I.  O.  Baker,  we  find  an  average  strength  in  hard  paving  brick  of  over 
5000  Ibs.  per  square  inch.  The  average  crushing  strength  of  ten  varie- 
ties of  paving-brick  much  used  in  the  West,  I  find  to  be  7150  Ibs.  to  the 
square  inch." 

A  test  of  brick  made  by  the  dry-clay  process  at  Watertown  Arsenal, 
according  to  Paving,  showed  an  average  compressive  strength  of  3972  Ibs. 
per  sq.  in.  In  one  instance  it  reached  4973  Ibs.  per  sq.  in.  A  test  was 
made  at  the  same  place  on  a  "fancy  pressed  brick."  The  first  crack 
developed  at  a  pressure  of  305,000  Ibs.,  and  the  brick  crushed  at  364,300 
Ibs.,  or  11,130  Ibs.  per  sq.  in.  This  indicates  almost  as  great  compressive 
strength  as  granite  paving-blocks,  which  is  from  12,000  to  20,000  Ibs. 
per  sq.  in. 

The  three  following  notes  on  bricks  are  from  Trautwine's  Engineer's 
Pocket-book: 

Strength  of  Brick.  —  40  to  300  tons  per  sq.  ft.,  622  to  4668  Ibs.  per 
sq.  in.  A  soft  brick  will  crush  under  450  to  600  Ibs.  per  sq.  in.,  or  30  to 
40  tons  per  square  foot,  but  a  first-rate  machine-pressed  brick  will  stand 
200  to  400  tons  per  sq.  ft.  (3112  to  6224  Ibs.  per  sq.  in.). 

Weight  of  Bricks. — Per  cubic  foot,  best  pressed  brick,  150  Ibs.; 
good  pressed  brick,  131  Ibs.;  common  hard  brick,  125  Ibs.;  good  common 
brick,  118  Ibs.;  soft  inferior  brick,  100  Ibs. 

Absorption  of  Water.  —  A  brick  will  in  a  few  minutes  absorb  1/2  to 
3/4  Ib.  of  water,  the  last  being  1/7  of  the  weight  of  a  hand-molded  one, 
or  Vs  of  its  bulk. 

Strength  of  Common  Red  Brick.  —  Tests  of  67  samples  of  Hudson 
River  machine-molded  brick  were  made  by  I.  H.  Woolson,  Eng.  News, 
April  13,  1905.  The  crushing  strength,  in  Ibs.  per  sq.  in.,  of  15  pale  brick 
ranged  from  1607  to  4546,  average  3010;  44  medium,  2080  to  8944,  av. 
4080;  8  hard  brick,  2396  to  6420,  av.  4960.  Five  Philadelphia  pressed 
brick  gave  from  3524  to  9425,  av.  6361.  The  absorption  ranged  from 
8.7  to  21.4%  by  weight.  The  relation  of  absorption  to  strength  varied 
greatly,  but  on  the  average  there  was  an  increase  of  absorption  up  to 
3000  Ibs.  per  sq.  in.  crushing  strength,  and  beyond  that  a  decrease. 

The  Strongest  Brick  ever  tested  at  the  Watertown  Arsenal  was  a 
paving  brick  from  St.  Louis,  Mo.,  which  showed  a  compressive  strength 
of  38,446  Ibs.  per  sq.  in.  The  absorption  was  0.21%  by  weight  and 
0.5%  by  volume.  The  sample  was  set  on  end,  and  measured  2.45  X  3.06 
ins.  in  cross  section.  —  Eng.  News,  Mar.  14,  1907. 

Tests  of  Bricks,  full  size,  on  flat  side.  (Tests  made  at  Watertown, 
Arsenal  in  1883.)  —  The  bricks  were  tested  between  flat  steel  buttresses. 
Compressed  surfaces  (the  largest  surface)  ground  approximately  flat. 
The  bricks  were  all  about  2  to  2.1  inches  thick,  7.5  to  8.1  inches  long, 
and  3.5  to  3.76  inches  wide.  Crushing  strength  per  square  inch:  One 
lot  ranged  from  11.056  to  16,734  Ips,;  a  second,  12,995  to  22,351;  a 


STRENGTH   OF  BRICK,   STONE,   ETC. 


371 


third,  10,390  to  12,709.    Other  tests  gave  results  from  5960  to  10,250 
Ibs.  per  sq.  in. 

Tests  of  Brick.    (Tech.  Quar.,  1900.)  —  Different  brands  of  brick  tested 
on  the  broad  surfaces,  and  on  edge.^gave  results  as  follows,  Ibs.  per  sq.  in. 

(Tech.  Quar.  XII,  No.  3,  1899.)     38  tests. ' 


- 

No. 
Test. 

Aver- 
age. 

Maxi- 
mum. 

Mini- 
mum. 

Per  cent  Water 

Absorbed. 

On  broad  surface 
Bay  State,  light  hard 
Same,  tested  on  edge  .  . 
On  broad  surface 
Dover    River,     soft 
burned 

71 

67 

38 

7039 
6241 

5350 

11,240 
10,840 

8630 

3587 
3325 

3930 

15.  15  to  19.3  av.      7.5 
13.  67  to  18.2  "       7.4 

14.0    to  18.6  "     11.6 

Dover   River,    hard 
burned 

36 

8070 

10,940 

5850 

4.7    to  10.1    "      7.0 

Central  N.  Y.,  soft 
burned 

36 

2190 

3060 

1370 

17.8    to  22.0  "     19.9 

Central   N.  Y.,  me- 
dium burned  
Central  N.  Y.,  hard 
burned 

36 
36 

3600 
5360 

4950 
8810 

2080 
3310 

16.6    to  23.  4    "     18.6 
8.3    to  16.7    "     12.5 

Another     lot,*     hard 
burned      

16 

7940 

9770 

6570 

7.6    to  12.9    "     10.6 

Same,*  tested  on  edge 

16 

6430 

10,230 

3830 

6.2    to  18.7    "     11.4 

*  Brand  not  named. 

The  per  cent  water  absorbed  in  general  seemed  to  have  a  relation  to 
the  strength,  the  greatest  absorption  corresponding  to  the  lowest  strength, 
and  vice  versa,  but  there  were  many  exceptions  to  the  rule. 

Crushing  Strength  of  Masonry  Materials.  (From  Howe's  "Re- 
taining-Walls.")  — 

tons  per  sq.  ft.  tons  per  sq.  ft. 

Brick,  best  pressed  .     40  to    300     Limestones  and  marbles    250  to  1000 

Chal'c 20  to      30     Sandstone 150  to    550 

Gran  te 300  to  1200     Soapstone 400  to    800 

Strength  of  Granite.  —  The  crushing  strength  of  granite  is  commonly 
rated  at  12,000  to  15,000  Ibs.  per  sq.  in.  when  tested  in  two-inch  cubes, 
and  only  the  hardest  and  toughest  of  the  commonly  used  varieties  reach 
a  strength  above  20,000  Ibs.  Samples  of  granite  from  a  quarry  on  the 
Connecticut  River,  tested  at  the  Watertown  Arsenal,  have  shown  a 
strength  of  35,965  Ibs.  per  sq.  in.  (Engineering  News,  Jan.  12,  1893). 

Ordinary  granite  ranges  from  20,000  to  30,000  Ibs.  compressive  strength 
per  sq.  in.  A  granite  from  Asheville,  N.C.,  tested  at  the  Watertown 
Arsenal,  gave  51,900  Ibs.  —  Eng.  News,  Mar.  14,  1907. 

Strength  of  Avondale,  Pa.,  Limestone.  (Engineering  News, 
Feb.  9,  1893.)  —  Crushing  strength  of  2-in.  cubes:  light  stone  12,112, 
gray  stone  18,040,  Ibs.  per  sq.  in. 

Transverse  test  of  lintels,  tool-dressed,  42  in.  between  knife-edge  bear- 
ings, load  with  knife-edge  brought  upon  the  middle  between  bearings: 

Gray  stone,  section  6  in.  wide  X 10  in.  high,  broke  under  a  load  of  20,950  Ibs. 

Modulus  of  rupture 2,200    " 

Light  stone,  section  81/4  in.  wide  X10  in.  high,  broke  under. . .    14,720    " 

Modulus  of  rupture 1,170   " 

Absorption.  —  Gray  stone 0.051  of  1  % 

Light  stone 0.052  of  1% 

Tests  of  Sand-lime  Brick.  (I.  H.  Woolson,  Eng.  News,  June  14, 
1906).  — Eight  varieties  of  brick  in  lots  of  300  to  800  were  received  from 
different  manufacturers.  They  were  testeq*  for  transverse  strength,  on 
supports  7  in.  apart,  loaded  in  the  middle:  and  half  bricks  were  tested  by 


372 


STRENGTH  OF  MATERIALS. 


compression,  sheets  of  heavy  fibrous  paper  being  inserted  between  the 
specimen  and  the  plates  of  the  testing  machine  to  insure  an  even  bearing. 
Tests  were  made  on  the  brick  as  received,  and  on  other  samples  after 
drying  at  about  150°  F.  to  constant  weight,  requiring  from  four  to  six 
days.  The  moisture  in  two  bricks  of  each  series  was  determined,  and 
found  to  range  from  1  to  10%,  average  5.9%.  The  figures  of  results 
given  below  are  the  averages  of  10  tests  in  each  case.  Other  bricks  of 
each  lot  were  tested  for  absorption  by  being  immersed  1/2  in.  in  water  for 
48  hours,  for  resistance  to  20  repeated  freezings  and  thawings,  and  for 
resistance  to  fire  by  heating  them  in  a  fire  testing  room,  the  bricks  being 
built  in  as  8-in.  walls,  to  1700°  F.  and  maintaining  that  temperature 
three  hours,  then  cooling  them  with  a  1  Vs-in.  stream  of  cold  water  from 
a  hydrant.  Transverse  and  compressive  tests  were  made  after  these 
treatments.  The  results  given  below  are  averages  of  five  tests,  except  in 
the  case  of  the  bricks  tested  after  firing,  in  which  two  samples  are  averaged. 

EFFECT  OF  THE  FIRE  TEST.  —  Several  large  cracks  developed  in  both 
the  sand-lime  and  the  clay  brick  walls  during  the  test.     These  were  no 
worse  in  one  wall  than  in  the  other.     With  the  exception  of   surface 
deterioration  the  walls  were  solid  and  in  good  condition.     After  they 
were  cooled  the  inside  course  of  each  wall  was  cut  through  and  specimens 
of  each  series  secured  for  examination  and  test.     It  was  difficult  to 
secure  whole  bricks,  owing  to  the  extreme  brittleness. 

In  general  the  bricks  were  affected  by  fire  about  half  way  through. 
They  were  all  brittle  and  many  of  them  tender  when  removed  from  the 
wall.  With  the  sand-lime  brick,  if  a  brick  broke  the  remainder  had  t9  be 
chiseled  out  like  concrete,  whereas  a  clay  brick  under  like  conditions 
would  chip  out  easily.  The  clay  brick  were  so  brittle  and  full  of  cracks 
that  the  wall  could  be  broken  down  without  trouble.  The  sand-lime 
bricks  adhered  to  the  mortar  better,  were  cracked  less,  and  were  not  so 
brittle. 


Designation  of  Brick. 

A 

B 

C 

D 

E 

F 

G 

Modulus  of       ) 
Rupture         ) 

As  received 

272 

424 

377 

262 

190 

301 

365 

Dried 

320 

505 

406 

334 

197 

570 

494 

11 

Increase,  % 

15.0 

16.0 

7.1 

21.5 

3.5 

47.2 

26.2 

•• 

Wet 

248 

349 

345 

241 

243 

250 

485 

41 

After  fire 

17 

57 

20 

32 

24 

27 

37 

Compressive      ) 

As  received 

1875 

2300 

2871 

1923 

1610 

2460 

2669 

Strength, 

Dried 

2604 

2772 

3240 

2476 

1870 

3273 

3190 

Ibs.  per  sq.  in.    ) 

Increase,  % 
Wet 

30.2 
1611 

17.1 

2174 

20.7 
2097 

22.3 
1923 

13.5 
1108 

24.8 
2063 

16.3 
2183 

14 

After  freez- 

ing 

1596 

1619 

2265 

1174 

1167 

1851 

1739 

14 

After  fire 

1807 

2814 

2573 

2069 

1089 

2051 

4885 

%  of  lime  in  brick  

6 

10 

5 

41/9 

41/9 

5 

8 

Pressure  for  hare 
Hours  in  hardeni 

ening,  Ibs..  .  . 
ng,  Ibs  

120 
10 

135 
8 

150 

7 

125 
10 

10 

150 

7 

125 
10 

STRENGTH   OF   LIME   AND    CEMENT  MORTAR. 

(Engineering.  October  2,  1891.) 

Tests  made  at  the  University  of  Illinois  on  the  effects  of  adding  cement 
to  lime  mortar.  In  all  the  tests  a  good  quality  of  ordinary  fat  lime  was 
used,  slaked  for  two  days  in  an  earthenware  jar,  adding  two  parts  by 
weight  of  water  to  one  of  lime,  the  loss  by  evaporation  being  made  up 
by  fresh  additions  of  water.  The  cements  used  were  a  German  Port- 
land, Black  Diamond  (Louisville),  and  Rosendale.  As  regards  fineness 
of  grinding,  85  per  cent  of  the  Portland  passed  through  a  No.  100  sieve, 
as  did  72  per  cent  of  the  Rosendale.  A  fairly  sharp  sand,  thoroughly 
washed  and  dried,  passing  through  a  No.  18  sieve  and  caught  on  a  No.  30. 


CEMENT   AND   FLAGGING. 


373 


was  used.  The  mortar  in  all  cases  consisted  of  two  volumes  of  sand  to 
one  of  lime  paste.  The  following  results  were  obtained  on  adding 
various  percentages  of  cement  to  the  mortar: 


Tensile  Strength,  pounds  per  square  inch. 


Age                .    { 

4 

7 

14 

21 

28 

50 

84 

Days. 

Days. 

Days. 

Days. 

Days. 

Days. 

Days. 

Lime  mortar.  . 

4 

8 

10 

13 

18 

21 

26 

20  per  cent  Rosendale 

5 

81/2 

9l/2 

12 

17 

17 

18 

20                   Portland  . 

5 

81/2 

14 

20 

25 

24 

26 

30                  Rosendale 

7 

11 

13 

181/2 

21 

221/2 

23 

30                  Portland  . 

8 

16 

18 

22 

25 

28 

27 

40                   Rosendale 

10 

12 

161/2 

2H/-> 

221/2 

24 

36 

40                   Portland  . 

27 

39 

38 

43 

47 

59 

57 

60                  Rosendale 

9 

13 

20 

16 

22 

221/2 

23 

60                   Portland  . 

45 

58 

55 

68 

67 

102 

78 

80                  Rosendale 

12 

181/2 

22l/2 

27 

29 

3U/2 

33 

80                   Portland  . 

87 

91 

103 

124 

94 

210 

145 

1  00                   Rosendale 

18 

23 

26 

31 

34 

46 

48 

1  00                   Portland  . 

90 

120 

146 

152 

181 

205 

202 

Tests  of  Portland  Cement. 

(Tech.  Quar.  XIII.  No.  3,  1900,  p.  236.) 


IDay. 

2  Days. 

14  Days 

1  Mo. 

2Mos. 

6Mos. 

1  Year. 

Neat  cement: 
Tension,  Ibs. 

per  sq.  in... 

268-312 

454-532 

780-820 

915-920 

950-1100 

1036-  11  90 

996-1248 

Compression, 
Ibs.  per  sq.  in 

(     8650 
to 
(  10,250 

13,080 
to 
14,860 

23,640 
to 
34,820 

34,000 
to 
38,500 

36,150 
to 
50,000 

3  sand,  1  cem. 

Tens  

56-75 

79-92 

185-211 

211-230 

217-240 

300-382 

280-383 

3  sand,  1  cem. 
Comp 

(     1200 
to 
(      1585 

1750 
to 
1885 

3780 
to 
4420 

7850 
to 
8250 

8000 
to 
10,000 

TEANSVERSE  STRENGTH  OF  FLAGGING. 

(N.  J.  Steel  &  Iron  Co.'s  Book.) 
EXPERIMENTS  MADE  BY  R.  G.  HATFIELD  AND  OTHERS. 


dis- 


6  =  width  of  the  stone  in  inches;  d  =  its  thickness  in  inches;  I 
tance  between  bearings  in  inches. 

The  breaking  loads  in  tons  of  2000  Ibs.,  for  a  weight  placed  at  the  center 
of  the  space;  will  be  as  follows: 


I  I 

Bluestone  flagging 0.744  Dorchester  freestone 0.264 

Quincy  granite 0.624  Aubigny  freestone 0.216 

Little  Falls  freestone 0.576  Caen  freestone 0.144 

Belleville,  N.  J.,  freestone.  .   0.480  Glass 1.000 

Granite  (another  quarry). . .   0.432  Slate 1.2  to  2.7 

Connecticut  freestone 0.312 

Thus  a  block  of  Quincy  granite  80  inches  wide  and  6  inches  thick, 
resting  on  beams  36  inches  in  the  clear,  would  be  broken  by  a  load  resting 

midway  between  the  beams  =  80  *  36  X  0.624  =  49.92  tons. 

oo 


374  STRENGTH  OF  MATERIALS, 

MODULI  OF  ELASTICITY  OF  VARIOUS  MATERIALS. 

The  modulus  of  elasticity  determined  from  a  tensile  test  of  a  bar  of  any 
material  is  the  quotient  obtained  by  dividing  the  tensile  stress  in  pounds 
per  square  inch  at  any  point  of  the  test  by  the  elongation  per  inch  of 
length  produced  by  that  stress;  or  if  P  =  pounds  of  stress  applied, 
K  =  the  sectional  area,  I  =  length  of  the  P9rtion  of  the  bar  in  which  the 
measurement  is  made,  and  A  =  the  elongation  in  that  length,  the  modu- 

•p  \  nj 

lus  of  elasticity  E  =  j?  •*•  -  =  ~.    The  modulus  is  generally  measured 

within  the  elastic  limit  only,  in  materials  that  have  a  well-defined  elastic 
limit,  such  as  iron  and  steel,  and  when  not  otherwise  stated  the  modulus 
Is  understood  to  be  the  modulus  within  the  elastic  limit.  Within  this 
limit,  for  such  materials  the  modulus  is  practically  constant  for  any 
given  bar,  the  elongation  being  directly  proportional  to  the  stress.  In 
other  materials,  such  as  cast  iron,  which  have  no  well-defined  elastic 
limit,  the  elongations  from  the  beginning  of  a  test  increase  in  a  greater 
ratio  than  the  stresses,  and  the  modulus  is  therefore  at  its  maximum  neaf 
the  beginning  of  the  test,  and  continually  decreases.  The  moduli  of 
elasticity  of  various  materials  have  already  been  given  above  in  treating 
of  these  materials,  but  the  following  table  gives  some  additional  values 
selected  from  different  sources: 

Brass,  cast 9,170,000 

Brass  wire 14,230,000 

Copper 15,000,000  to  18,000,000 

Lead 1,000,000 

Tin,  cast 4,600,000 

Iron,  cast 12,000,000  to  27,000,000  (?) 

Iron,  wrought 22,000,000  to  29,000,000  (?) 

Steel   .  ...  28,000,000  to  32,000,000  (see  below) 

Marble  .  .  ...  25,000,000 

Slate 14,500,000 

Glass 8,000,000 

Ash.  .      1,600,000 

Beech 1,300,000 

Birch..  1,250,000  to    1,500,000 

Fir. .  869,000  to    2,191,000 

Oak. .  974,000  to    2,283,000 

Teak 2,414,000 

Walnut 306,000 

Pine,  long-leaf  (butt-logs) .      1,119,000  to    3,117,000       Avge.  1,926,000 

The  maximum  figures  given  by  some  early  writers  for  iron  and  steel, 
viz.,  40,000,000  and  42,000,000,  are  und9ubtedly  erroneous.  The  modulus 
of  elasticity  of  steel  (within  the  elastic  limit)  is  remarkably  constant, 
4  notwithstanding  great  variations  in  chemical  analysis,  temper,  etc.  It 
rarely  is  found  below  29,000,000  or  above  31,000,000.  It  is  generally 
taken  at  30,000,000  in  engineering  calculations.  Prof.  J.  B.  Johns9n, 
in  his  report  on  Long-leaf  Pine,  1893,  says:  "The  modulus  of  elasticity 
is  the  most  constant  and  reliable  property  of  all  engineering  materials. 
The  wide  range  of  value  of  the  modulus  of  elasticity  of  the  various  metals 
found  in  public  records  must  be  explained  by  erroneous  methods  of 

In  a' tensile  test  of  cast  iron  by  the  author  (Van  Nostrand's  Science 
Series,  No.  41,  page  45),  in  which  the  ultimate  strength  was  23,285  Ibs. 
per  sq.  in.,  the  measurements  of  elongation  were  made  to  0.0001  inch, 
and  the  modulus  of  elasticity  was  found  to  decrease  from  the  beginning 
of  the  test,  as  follows:  At  1000  Ibs.  per  sq.  in.,  25,000,000;  at  2000  Ibs., 
16,666,000;  at  4000  Ibs.,  15,384,000;  at  6000  Ibs.,  13,636,000;  at  8000 
Ibs.,  12,500,000;  at  12,000  Ibs.,  11,250,000;  at  15,000  Ibs.,  10,000,000; 
at  20,000  Ibs.,  8,000  000;  at  23,000  Ibs.,  6,140,000. 

FACTORS  OF  SAFETY. 

A  factor  of  safety  is  the  ratio  in  which  the  load  that  is  just  sufficient  to 
overcome  instantly  the  strength  of  a  piece  of  material  is  greater  than  the 
greatest  safe  ordinary  working  load.  (Rankine.) 

Rankine  gives  the  following  "examples  of  the  values  of  those  factors 
which  occur  in  machines": 


FACTOR   OF   SAFETY  375 

Dead  Load.           Live  Load,  Live  Load, 

Greatest.  Mean. 

Iron  and  steel 3                        6  from  6  to  40 

Timber 4  to  5               8  to  10  

Masonry 4                        8  

The  great  factor  of  safety,  40,  is  for  shafts  in  millwork  which  transmit 
very  variable  efforts. 

TJnwin  gives  the  following  "  factors  of  safety  which  have  been  adopted 
In  certain  cases  for  different  materials."  They  "include  an^allowance 
for  ordinary  contingencies." 

, A  Varying  Load  Producing % 

Stress  of  Equal  Alternate  In  Structures 

Actual       One  Kind       Stresses  of      subj.  to  vary- 

Material.  Load  only.      different  kinds,  ing  Loads  and 

Shocks 

Cast  iron 4  6  10  15 

Wrought  iron  and  steel      3  5  8  12 

Timber 7  10  15  20 

Brickwork  and  Masonry    20  30 

In  cast  iron  the  factors  are  high  to  allow  for  unknown  internal  stresses. 

Prof.  Wood  in  his  "Resistance  of  Materials"  says:  "In  regard  to  the 
margin  that  should  be  left  for  safety,  much  depends  upon  the  character 
of  the  loading.  If  the  load  is  simply  a  dead  weight,  the  margin  may  be 
comparatively  small;  but  if  the  structure  is  to  be  subjected  to  percus- 
sive forces  or  shocks,  the  margin  should  be  comparatively  large  on  account 
of  the  indeterminate  effect  produced  by  the  force.  In  machines  which 
are  subjected  to  a  constant  jar  while  in  use,  it  is  very  difficult  to  deter- 
mine the  proper  margin  which  is  consistent  with  economy  and  safety. 
Indeed,  in  such  cases,  economy  as  well  as  safety  generally  consists  in 
making  them  excessively  strong,  as  a  single  breakage  may  cost  much 
more  than  the  extra  material  necessary  to  fully  insure  safety." 

For  discussion  of  the  resistance  of  materials  to  repeated  stresses  and 
shocks,  see  pages  275  to  285. 

Instead  of  using  factors  of  safety,  it  is  becoming  customary  in  designing 
to  fix  a  certain  number  'of  pounds  per  square  inch  as  the  maximum  stress 
which  will  be  allowed  on  a  piece.  Thus,  in  designing  a  boiler,  instead  of 
naming  a  factor  of  safety  of  6  for  the  plates  and  10  for  .the  stay-bolts,  the 
ultimate  tensile  strength  9f  the  steel  being  from  50,000  t9  60,000  Ibs.  per 
sq.  in.,  an  allowable  working  stress  of  10,000  Ibs.  per  sq.  in.  on  the  plates 
and  6000  Ibs.  per  sq.  in.  on  the  stay-bolts  may  be  specified  instead.  So 
also  in  the  use  of  formulae  for  columns  (see  page  285)  the  dimensions  of  a 
column  are  calculated  after  assuming  a  maximum  allowable  compressive 
stress  per  square  inch  on  the  concave  side  of  the  column. 

The  factors  for  masonry  under  dead  load  as  given  by  Rankine  and  by 
Unwin,  viz.,  4  and  20,  show  a  remarkable  difference,  which  may  possibly 
be  explained  as  follows:  If  the  actual  crushing  strength  of  a  pier  of 
masonry  is  known  from  direct  experiment,  then  a  factor  of  safety  of  4  is 
sufficient  for  a  pier  of  the  same  size  and  quality  under  a  steady  load; 
but  if  the  crushing  strength  is  merely  assumed  from  figures  given  by  the 
authorities  (such  as  the  crushing  strength  of  pressed  brick,  quoted  above 
from  Howe's  Retaining  Walls,  40  to  300  tons  per  square  foot,  average 
170  tons),  then  a  factor  of  safety  of  20  may  be  none  too  great.  In  this 
case  the  factor  of  safety  is  really  a  "factor  of  ignorance." 

The  selection  of  the  proper  factor  of  safety  or  the  proper  maximum  unit 
stress  for  any  given  case  is  a  matter  to  be  largely  determined  by  the 
judgment  of  the  engineer  and  by  experience.  No  definite  rules  can  be 
given.  The  customary  or  advisable  factors  in  many  particular  cases  will 
be  found  where  these  cases  are  considered  throughout  this  book.  In 
general  the  following  circumstances  are  to  be  taken  into  account  m  the 
selection  of  a  factor: 

1.  When  the  ultimate  strength  of  the  material  is  known  within  narrow 
limits,  as  in  the  case  of  structural  steel  when  tests  of  samples  have  been 
made,  when  the  load  is  entirely  a  steady  one  of  a  known  amount,  and 
there  is  no  reason  to  fear  the  deterioration  of  the  metal  by  corrosion,  the 
lowest  factor  that  should  be  adopted  is  3. 

2.  When  the  circumstances  of  1  are  modified  by  a  portion  of  the  load 
being  variable,  as  in  floors  of  warehouses,  the  factor  should  be  not  less 
than  4. 


376  STRENGTH  OF  MATERIALS. 

3.  When  the  whole  load,  or  nearly  the  whole,  is  apt  to  be  alternately 
put  on  and  taken  off,  as  in  suspension  rods  of  floors  of  bridges,  the  factor 
should  be  5  or  6. 

4.  When  the  stresses  are  reversed  in  direction  from  tension  to  com- 
pression, as  in  some  bridge  diagonals  and  parts  of  machines,  the  factor 
should  be  not  less  than  6. 

5.  When  the  piece  is  subjected  to  repeated  shocks,  the  factor-should  be 
not  less  than  10. 

6.  When  the  piece  is  subject  to  deterioration  from  corrosion  the  section 
should  be  sufficiently  increased  to  allow  for  a  definite  amount  of  corrosion 
before  the  piece  be  so  far  weakened  by  it  as  to  require  removal. 

7.  When  the  strength  of  the  material,  or  the  amount  of  the  load,  or 
both  are  uncertain,  the  factor  should  be  increased  by  an  allowance  suffi- 
cient to  cover  the  amount  of  the  uncertainty. 

8.  When  the  strains  are  of  a  complex  character  and  of  uncertain 
amount,  such  as  those  in  the  crank-shaft  of  a  reversing  engine,  a  very 
high  factor  is  necessary,  possibly  even  as  high  as  40,  the  figure  given  by 
Rankine  for  shafts  in  millwork. 

Formulas  for  Factor  of  Safety.  —  (F.  E.  Cardullo,  Mach'y,  Jan,. 
1906.)     The  apparent  factor  of  safety  is  the  product  of  four  factors,  or, 
F  =  aXbXcXd. 

a  is  the  ratio  of  the  ultimate  strength  of  the  material  to  its  elastic  limit, 
not  the  yield  point,  but  the  true  elastic  limit  within  which  the  material  is, 
in  so  far  as  we  can  discover,  perfectly  elastic, and  takes  no  permanent  set. 
Two  reasons  for  keeping  the  working  stress  within  this  limit  are:  (1)  that 
the  material  will  rupture  if  strained  repeatedly  beyond  this  limit;  and 
(2)  that  the  form  and  dimensions  of  the  piece  would  be  destroyed  under 
the  same  circumstances. 

The  second  factor,  6,  is  one  depending  upon  the  character  of  the  stress 
produced  within  the  material.  The  experiments  of  Wohler  proved  that 
the  repeated  application  of  a  stress  less  than  the  ultimate  strength  of  a 
material  would  rupture  it.  Prof.  J.  B.  Johnson's  formula  for  the  relation 
between  the  ultimate  strength  and  the  "carrying  strength"  under  con- 
ditions of  variable  loads  is  as  follows: 

/  =  U  -  (2  -  Pl/p), 

where  /  is  the  "carrying  strength"  when  the  load  varies  repeatedly 
between  a  maximnm  value,  p,  and  a  minimum  value,  pi,  and  U  is  the 
ultimate  strength  of  the  material.  The  quantities  p  and  p\  have  plus 
signs  when  they  represent  loads  producing  tension,  and  minus  signs  when 
they  represent  loads  producing  compression. 

If  the  load  is  variable  the  factor  b  must  then  have  a  value, 
6  =  U/f  =  2  -  pt/p. 

Taking  a  load  varying  between  zero  and  a  maximum, 
Pi/p  =  0,     and     6  =  2-  pi/p  =  2. 

Taking  a  load  that  produces  alternately  a  tension  and  a  compression 
equal  in  amount, 

p'  =  -  p  and  pi/p  =  -  1,  and  6  =  2-  pi/p  =  2  -  (-  1)  =  3. 

The  third  factor,  c,  depends  upon  the  manner  in  which  the  load  is  applied 
to  the  piece.     When  the  load  is  suddenly  applied  c  =  2.     When  not  all 
of  the  load  is  applied  suddenly,  the  factor  2  is  reduced  accordingly.     . 
a  certain  fraction  of  the  load,  n/m,  is  suddenly  applied,  the  factor  is 
1  +  n/m. 

The  last  factor,  d,  we  may  call  the  "factor  of  ignorance."  All  the 
other  factors  have  provided  against  known  contingencies;  this  provides 
against  the  unknown.  It  commonly  varies  in  value  between  1 1/2  and  3, 
although  occasionally  it  becomes  as  great  as  10.  It  provides  against 
excessive  or  accidental  overload,  unexpectedly  severe  service,  unreliable 
or  imperfect  materials,  and  all  unforeseen  contingencies  of  manufacture 
or  operation.  When  we  know  that  the  load  will  not  be  likely  to  be 
Increased,  that  the  material  is  reliable,  that  failure  will  not  result  dis- 
astrously or  even  that  the  piece  for  some  reason  must  be  small  or  light, 
this  factor  will  be  reduced  to  its  lowest  limit,  1 1/2.  When  life  or  property 
would  be  endangered  by  thefailureof  the  piece,  this  factor  must  be  made 


THE  MECHANICAL  PROPERTIES   OF   CORK.        377 


larger.     Thus,  while  it  is  1 1/2  to  2  in  most  ordinary  steel  constructions, 
it  is  rarely  less  than  21/2  for  steel  in  a  boiler. 

The  reliability  of  the  material  in  a  great  measure  determines  the  value 
of  this  factor.  For  instance,  in  all  cases  where  it  would  be  1 1/2  for  mild 
steel,  it  is  made  2  for  cast  iron.  It  will  be  larger  for  those  materials 
subject  to  internal  strains,  for  instance  for  complicated  castings,  heavy 
forgings,  hardened  steel,  and  the  like,  also  lor  materials  subject  to  hidden 
defects,  such  as  internal  flaws  in  lorgings,  spongy  places  in  castings,  etc. 
It  will  be  smaller  for  ductile  and  larger  lor  brittle  materials.  It  will  be 
smaller  as  we  are  sure  that  the  piece  has  received  uniform  treatment,  and 
as  the  tests  we  have  give  more  uniform  results  and  more  accurate  indi- 
cations of  the  real  strength  and  quality  of  the  piece  itself.  In  fixing  the 
factor  d,  the  designer  must  depend  on  his  judgment,  guided  by  the  general 
rules  laid  down. 

Table  of  Factors  of  Safety. 

The  following  table  may  assist  in  a  proper  choice  of  the  factor  of  safety 
It  shows  the  value  of  the  four  factors  for  various  materials  and  conditions 
of  service. 

CLASS  OF  SERVICE  OR  MATERIALS.         ' 

Bpilers 

Piston  and  connecting  rods  for  double- 
acting  engines 1  1/2-2 

Piston  and  connecting  rod  for  single-acting 
engines 1 1/2-2 

Shaft  carrying  bandwheel,  fly-wheel,  or 
armature I  1/2-2 

Lathe  spindles , 

Mill  shafting 

Steel  work  in  buildings , 

Steel  work  in  bridges 

Steel  work  for  small  work 

Cast  iron  wheel  rims 

Steel  wheel"  rims 


MATERIALS. 

Cast  iron  and  other  castings 

Wrought  iron  or  mild  steel 

Oil  tempered  or  nickel  steel 

Hardened  steel 

Bronze  and  brass,  rolled  or  forged . 


i          bed 

P 

2       1      1    21/4-3 

41/2-  6 

r2       3     2    11/2 

131/2-18 

r2       2     2    11/2 

9      -12 

-2       3      1     11/2 

63/4-  9 

2        2      2     11/2 

12 

2322 

24 

2 

2 

4 

2 

21/2 

5 

2 

; 

*     H/2 

6 

2 

10 

20 

2 

4 

8 

M 

nin 

lum  Values. 

2 

2 

4 

2 

H/2 

3 

H/2 

H/2 

21/4 

H/2 

2 

3 

2 

1V2 

3 

THE  MECHANICAL  PROPERTIES   OF  CORK. 

Cork  possesses  qualities  which  distinguish  it  from  all  other  solid  or 
liquid  bodies,  namely,  its  power  of  altering  its  volume  in  a  very  marked 
degree  in  consequence  of  change  of  pressure.  It  consists,  practically, 
of  an  aggregation  of  minute  air-vessels,  having  thin,  water-tight,  and 
very  strong  walls,  and  hence,  if  compressed,  the  resistance  to  compression 
rises  in  a  manner  more  like  the  resistance  of  gases  than  the  resistance  of 
an  elastic  solid  such  as  a  spring.  In  a  spring  the  pressure  increases  in 
proportion  to  the  distance  to  which  the  spring  is  compressed,  but  with 
gases  the  pressure  increases  in  a  much  more  rapid  manner;  that  is,  in- 
versely as  the  volume  which  the  gas  is  made  to  occupy.  But  from  the 
permeability  of  cork  to  air,  it  is  evident  that,  if  subjected  to  pressure  in 
one  direction  only,  it  will  gradually  part  with  its  occluded  air  by  effusion, 
that  is,  by  its  passage  through  the  porous  walls  of  the  cells  in  which  it  is 
contained.  The  gaseous  part  of  cork  constitutes  53 %_  of  its  bulk.  Its 
elasticity  has  not  only  a  very  considerable  range,  but  it  is  very  persistent. 
Thus  in  the  better  kind  of  corks  used  in  bottling  the  corks  expand  the 
instant  they  escape  from  the  bottles.  This  expansion  may  amount  to 
an  increase  of  volume  of  75%,  even  after  the  corks  have  been  kept  in  a 
state  of  compression  in  the  bottles  for  ten  years.  If  the  cork  be  steeped 
in  hot  water,  the  volume  continues  to  increase  till  it  attains  nearly  three 
times  that  which  it  occupied  in  the  neck  of  the  bottle. 

When  cork  is  subjected  to  pressure  a  certain  amount  of  permanent 


378  STRENGTH  OF  MATERIALS. 

deformation  or  "permanent  set"  takes  place  very  quickly.  This  prop* 
erty  is  common  to  all  solid  elastic  substances  when  strained  beyond  theii 
elastic  limits,  but  with  cork  the  limits  are  comparatively  low.  Besides 
the  permanent  set,  there  is  a  certain  amount  of  sluggish  elasticity  —  that 
is,  cork  on  being  released  from  pressure  springs  back  a  certain  amount 
at  once,  but  the  complete  recovery  takes  an  appreciable  time. 

Cork  which  had  been  compressed  and  released  in  water  many  thousand 
times  had  not  changed  its  molecular  structure  in  the  least,  and  had  con- 
tinued perfectly  serviceable.  Cork  which  has  been  kept  under  a  pressure 
of  three  atmospheres  for  many  weeks  appears  to  have  shrunk  to  from 
80%  to  85%  of  its  original  volume.  —  Van  Nostrand's  Eng'g  Mag.,  1886. 
xxxv.  307. 

VULCANIZED   INDIA-RUBBER. 

The  specific  gravity  of  a  rubber  compound,  or  the  number  of  cubic 
inches  to  the  pound,  is  generally  taken  oy  buyers  as  a  correct  index  of 
the  value,  though  in  reality  such  is  often  very  far  from  being  the  case. 
In  the  rubber  works  the  qualities  of  the  rubber  made  vary  from  floating, 
the  best  quality,  to  densities  corresponding  to  11  or  12  cu.  in.  to  the 
pound,  the  latter  densities  being  in  demand  by  consumers  with  whom 
price  appears  to  be  the  main  consideration.  Such  densities  as  these  can 
only  be  obtained  by  utilizing  to  the  utmost  the  quality  that  rubber 
exhibits  of  taking  up  a  large  bulk  of  added  matters.  —  Eng'g,  1897. 

Lieutenant  X?  Vladomiroff,  a  Russian  naval  officer,  has  recently  carried 
out  a  series  of  tests  at  the  St.  Petersburg  Technical  Institute  with  view 
to  establishing  rules  for  estimating  the  quality  of  vulcanized  india- 
rubber.  The  followng,  in  brief,  are  the  conclusions  arrived  at,  recourse 
being  had  to  physical  properties,  since  chemical  analysis  did  not  give 
any  reliable  result:  1.  India-rubber  should  not  give  the  least  sign  of 
superficial  cracking  when  bent  to  an  angle  of  180  degrees  after  five  hours 
of  exposure  in  a  closed  air-bath  to  a  temperature  of  125°  C.  The 
test-pieces  should  be  2.4  inches  thick.  2.  Rubber  that  does  not  contain 
more  than  half  its  weight  of  metallic  oxides  should  stretch  to  five  times 
its  length  without  breaking.  3.  Rubber  free  from  all  foreign  matter, 
except  the  sulphur  used  in  vulcanizing  it,  should  stretch  to  at  least  seven 
times  its  length  without  rupture.  4.  The  extension  measured  immedi- 
ately after  rupture  should  not  exceed  12%  of  the  original  length,  with 
given  dimensions.  5.  Suppleness  may  be  determined  by  measuring  the 
percentage  of  ash  formed  in  incineration.  This  may  form  the  basis  for 
deciding  between  different  grades  of  rubber  for  certain  purposes.  6.  Vul- 
canized rubber  should  not  harden  under  cold.  These  rules  have  been 
adopted  for  the  Russian  navy.  —  Iron  Age,  June  15,  1893. 

Singular  Action  of  India  Rubber  under  Tension.  —  R.  H.  Thurston, 
Am.  Mack.,  Mar.  17,  1898,  gives  a  diagram  showing  the  stretch  at  dif- 
ferent loads  of  a  piece  of  partially  vulcanized  rubber.  The  results  trans- 
lated into  figures  are: 

Load,  Ibs 30        50         80      1 20        150      200        320      430 

Stretch    per    in.    of 

lengthen 0.5      1.         2.2        4  56  7       7.5 

Stretch  per  10  Ibs.  in- 
crease of  load 0.17     0.25     0.4     0.45     0.33     0.20     0.08     0.04 

Up  to  about  30%  of  the  breaking  load  the  rubber  behaves  like  a  soft 
metal  in  showing  an  increasing  rate  of  stretch  with  increase  of  load, 
then  the  rate  of  stretch  becomes  constant  for  a  while  and  later  decreases 
steadily  until  before  rupture  it  is  less  than  one-tenth  of  the  maximum. 
Even  when  stretched  almost  to  rupture  it  restores  itself  very  nearly  to 
its  original  dimensions  on  removing  the  load,  and  gradually  recovers  a 
part  of  the  loss  of  form  at  that  instant  observable.  So  far  as  known, 
no  other  substance  shows  this  curious  relation  of  stretch  to  load. 

Rubber  Goods  Analysis.   Randolph  Boiling.    (Iron  Age,  Jan.  28,  1909.) 

The  loading  of  rubber  goods  used  in  manufacturing  establishments 
with  zinc  oxide,  lead  sulphate,  calcium  sulphate,  etc.,  and  the  employ- 
ment of  the  so-called  "  rubber  substitutes  "  mixed  with  good  rubber  call  for 
close  inspection  of  the  works  chemist  in  order  to  determine  the  value  of 
the  samples  and  materials  received.  The  following  method  of  analysis  is 
recommended: 

Thin  strips  of  the  rubber  must  be  cut  into  small  bits  about  the  size  of 


PROPERTIES  OF  NICKEL.  379 

No.  7  shot.^  A  half  gram  is  heated  in  a  200  c.c.  flask  with  red  fuming 
nitric  acid  on  the  hot  plate  until  all  organic  matter  has  been  decomposed, 
and  the  total  sulphur  is  determined  by  precipitation  as  barium  sulphate. 
The  difference  between  the  total  and  combined  sulphur  gives  the  per 
cent  that  has  been  used  for  vulcanization.  Free  sulphur  indicates  either 
that  improper  methods  were  used  in  vulcanizing  or  that  an  excessive 
per  cent  of  substitutes  was  employed.  Following  is  a  scheme  for  the 
analysis  of  india-rubber  articles: 

1.  Extraction  with  acetone:    A.  Solution:    Resinous  constituents  of 
india-rubber,  fatty  oils,  mineral  oils,  resin  oils,  solid  hydrocarbons, 
resins,  free  sulphur.     B.  Residue. 

2.  Extraction  with  pyridine:    C.  Extract:    Tar,  pitch,  bituminous 
bodies,  sulphur  in  above.     D.  Residue. 

3.  Extraction  with  alcoholic  potash:  E.   Extract:   Chlorosulphide 
substitutes,   sulphide  substitutes,   oxidized   (blown)    oils,   sulphur  in 
substitutes,  chlorine  in  substitutes.     F.  Residue. 

4.  Extraction  with  nitre-naphthalene:  G.  Extract:  India-rubber,  sul- 
phur in  india-rubber,  chlorine  in  india-rubber,  the  total  of  the  above 
three  estimated  by  loss.     H.  Residue. 

5.  Extraction    with    boiling    water:    I.  Extract:  Starch    (farina), 
dextrine.     K.  Residue:  Mineral  matter,  free  carbon,  fibrous  materials, 
sulphur  in  inorganic  compounds. 

6.  Separate  estimations:  Total  sulphur,  chlorine  in  rubber. 

SPECIFICATIONS  FOR  AIR  HOSE. 

The  Bureau  of  Construction  and  Repair  of  the  U.  S.  Navy,  in  1910, 
adopted  the  following  specifications  for  air  hose: 

1.  The  hose  to  be  made  up  of  an  inner  rubber  tube,  three  or  more 
canvas  or  braided  layers,  and  an  outer  rubber  cover;  to  be  of  the  in- 
ternal diameter  required.  2.  The  tube  and  cover  shall  be  free  from 
pitting  or  other  irregularities;  the  tube  shall  not  be  less  than  I/IQ  in., 
and  the  cover  not  less  than  1/32  in.  in  thickness.  The  hose  to  be  of 
the  best  quality  rubber,  duck  and  friction,  and  to  be  capable  of  stand- 
ing a  hydrostatic  pressure  of  600  Ib.  3.  Samples  will  be  submitted  to 
the  mechanical  kinking  test.  The  samples  should  stand  the  test  for 
the  following  length  of  time  without  leakage  at  90  Ib.  air  pressure 
3/g  in 45  hours. 

7/i6  in 40  hours. 

5/8  in 30  hours. 

3/4  in 25  hours. 

1 1/4  in 3  hours. 

The  kinking  test  is  conducted  as  follows:  The  test  piece,  20  in.  in 
length,  is  fastened  to  couplings  made  up  on  45°  elbows,  the  stationary 
end  turned  up  and  the  moving  end  turned  down.  The  ends  of  the 
couplings  when  level  are  7  in.  apart.  The  moving  end  travels  vertically 
through  a  distance  of  14  in.,  and  the  speed  is  such  that  the  hose  is  • 
kinked  about  80  times  a  minute,  the  kinking  occurring  in  two  places 
about  4  in.  from  each  end.  During  this  test  an  air  pressure  of  about 
90  Ib.  per  sq.  in.  is  maintained  in  the  hose.  The  kinking  is  done  on  a 
special  machine  designed  to  kink  the  hose  at  the  speed  specified. 

NICKEL. 

Properties  of  Nickel.— (F.  L.  Sperry,  Tran.  A.I.M.E.,  1895).  Nickel 
has  similar  physical  properties  to  those  of  iron  and  copper.  It  is  less 
malleable  and  ductile  than  iron,  and  less  malleable  and  more  ductile 
than  copper.  It  alloys  with  these  metals  in  all  proportions.  It  has 
nearly  the  same  specific  gravity  as  copper,  and  is  slightly  heavier  than 
iron.  It  melts  at  a  temperature  of  about  2900°  to  3200°  F.  A  small 
percentage  of  carbon  in  metallic  nickel  lowers  its  melting-point  per- 
ceptibly. Nickel  is  harder  than  either  iron  or  copper;  is  magnetic,  but 
will  not  take  a  temper.  It  has  a  grayish-white  color,  takes  a  fine  polish, 
and  may  be  rolled  easily  into  thin  plates  or  drawn  into  wire.  It  is 
unappreciably  affected  by  atmospheric  action,  or  by  salt  water.  Com- 
mercial nickel  is  from  98  to  99  per  cent  pure.  The  impurities  are  iron, 
copper,  silicon,  sulphur,  arsenic,  carbon,  and  (in  some  nickel)  a  kernel 
of  unreduced  oxide.  It  is  not  difficult  to  cast,  and  acts  like  some  irons 


380 


STRENGTH   OF  MATERIALS. 


in  being  cold-short.  Cast  bars  are  likely  to  be  porous  or  spongy, 
but,  after  hammering  or  rolling,  are  compact  and  tough. 

The  average  results  of  several  tests  are  as  follows:  Castings,  tensile 
strength,  85,000  Ibs.  per  sq.  in.,  elongation,  12% ;  wrought  nickel,  T.  S., 
96,000,  EL,  14%;  wrought  nickel,  annealed,  T.  S.,  95,000,  EL,  23%; 
hard  rolled,  T.  S.,  78,000,  EL,  10%.  (Bee  also  page  473.) 

Nickel  readily  takes  up  carbon,  and  the  porous  nature  of  the  metaJ 
is  undoubtedly  due  to  occluded  gases.  According  to  Dr.  Wedding, 
nickel  may  take  up  as  much  as  9  %  of  carbon,  which  may  exist  either 
as  amorphous  or  as  graphitic  carbon. 

Dr.  Fleitmann,  of  Germany,  discovered  that  a  small  quantity  of  pure 
magnesium  would  free  nickel  from  occluded  gases  and  give  a  metal 
capable  of  being  drawn  or  rolled  perfectly  free  from  blow-holes,  to  such 
an  extent  that  the  metal  may  be  rolled  into  thin  sheets  3  feet  in  width. 
Aluminum  or  manganese  may  be  used  equally  as  well  as  a  purifying 
agent;  but  either,  if  used  in  excess,  serves  to  make  the  nickel  very 
much  harder.  Nickel  will  alloy  with  most  of  the  useful  metals,  and 
generally  adds  the  qualities  of  hardness,  toughness,  and  ductility. 

ALUMINUM— ITS  PROPERTIES  AND  USES. 

(Compiled  from  notes  by  Alfred  E.  Hunt,  and  from  publications 
of  the  Aluminum  Co.  of  America,  1914.) 

The  specific  gravity  of  aluminum  varies  according  to  its  treatment, 
as  follows:  Pure  cast,  2.56;  sheets,  wire,  etc.,  rolled  and  unannealed, 
2.68;  ditto,  annealed,  2.66.  The  casting  alloys  range  in  specific 
gravity  from  2.82  to  2.91.  Based  on  these  values,  an  ingot  of  cast 
aluminum  12  in.  square,  1  in.  thick,  weighs  13.3024  Ib. ;  a  rolled  sheet 
12  in.  square,  1  in.  thick,  weighs  13.9259  Ib.;  a  1-in.  cast  round  bar, 
12  in.  long,  weighs  0.8706  Ib.;  a  1-in.  rolled  bar,  12  in.  long,  weighs 
0.9114  Ib.;  a  cubic  foot  of  cast  aluminum,  159.6288  Ib.;  and  a  cubic 
foot  of  rolled  aluminum,  167.1114  Ib.  Taking  the  weight  of  rolled 
aluminum  as  1,  the  weight  of  rolled  wrought  iron  is  2.8742;  of  rolled 
steel,  2.9322;  of  rolled  copper,  3.3321;  of  rolled  brass,  3.19.  Wood 
for  structures  can  be  taken  as  about  one-third  the  weight  of  aluminum. 

Chemically,  aluminum  is  readily  soluble  in  hydrochloric  acid,  and 
in  strong  solutions  of  caustic  alkalies.  Hot  dilute  sulphuric  acid 
stowly  dissolves  it,  but  concentrated  sulphuric  acid  acts  very  slowly. 
Nitric  acid,  cold,  either  dilute  or  concentrated,  has  but  little  effect; 
hot,  it  acts  very  slowly.  Sulphur  has  no  action  at  less  than  a  red 
heat.  Chlorine,  fluorine,  bromine,  iodine,  and  fluohydric  acid  rapidly 
corrode  it.  Salt  water  has  little  effect  on  it,  and  it  resists  sea  water 
better  than  does  iron,  steel,  or  copper.  Aluminum  strips  on  the  sides 
of  a  wooden  vessel  in  sea  water  corroded  less  than  0.005  inch  in  six 
months,  about  half  the  corrosion  of  copper  strips.  Ammonium  solu- 
tions gradually  attack  the  surface  of  aluminum,  forming  a  coating 
'  which  is  more  resistant  than  the  metal,  and  which  while  rapidly  attacked 
by  concentrated  acid  or  alkali  solutions,  resists  dilute  mineral  and 
organic  acids,  and  dry  or  moist  air.  It  is  not  attacked  by  CO2,  CO,  or 
HaS,  but  will  absorb  these  gases  when  heated. 

The  presence  of  a  considerable  quantity  of  aluminum  decreases  its 
resistance  to  corrosion.  Commercial  aluminum,  such  as  is  used  for 
rolling  or  casting  alloys,  contains,  however,  only  a  negligible  quantity 
of  impurities.  Occluded  gases  in  molten  aluminum  cause  blow-holes 
in  the  ingots,  which  form  laminated  plates  when  the  metal  is  rolled 
or  hammered,  which  are  more  liable  to  corrode  than  sound  metal. 
Silicon  and  iron  are  the  impurities  usually  found,  the  former  ranging 
in  commercial  aluminum  from  0.30  to  2.0  per  cent,  and  the  latter 
from  0.15  to  2.0  per  cent.  Other  metals  are  frequently  alloyed  with 
aluminum  to  increase  the  hardness,  rigidity,  and  strength.  See 
Alloys  of  Aluminum,  page  396. 

Aluminum  is  electro  positive  as  regards  the  common  metals,  and  forms 
a  galvanic  couple  when  in  contact  with  them.  In  service  it  should  be 
insulated  from  them  by  rubber  gaskets,  or  washers,  or  by  a  liberal  coat 
of  heavy  paint. 

In  malleability  pure  aluminum  is  exceeded  only  by  gold  and  silver. 
It  is  exceeded  in  ductility  only  by  gold,  silver,  platinum,  iron,  and 


ALUMINUM — ITS  PROPERTIES  AND  USES.         381 

copper.  Sheets  of  aluminum  have  been  rolled  down  to  0.0005  in. 
thick  and  beaten  into  leaf  nearly  as  thin  as  gold  leaf.  The  metal  is 
most  malleable  at  a  temperature  of  between  400°  and  600°  F.,  and  at 
this  temperature  it  can  be  drawn  down  between  rolls  with  nearly  as 
much  draught  upon  it  as  with  heated  steel.  It  has  also  been  drawn 
into  the  finest  wire.  By  the  Mannesmann  process  aluminum  tubes 
have  been  made  in  Germany. 

The  electrical  conductivity  of  aluminum  is  61.67,  silver  being  taken 
as  100.  On  the  same  scale,  the  conductivity  of  copper  is  97.62;  of 
gold,  76.61;  of  zinc,  29.57;  of  iron,  14.57;  of  platinum,  14.42.  Alumi- 
num wire,  weight  for  weight,  has  a  conductivity  of  206,  taking  copper 
as  100  and  aluminum  as  62,  the  aluminum  wire  having  an  area  3.33 
that  of  the  copper  wire.  Pure  aluminum  is  practically  non-magnetic. 

Aluminum  melts  at  1215°  F.  It  does  not  volatilize  at  any  tem- 
perature produced  by  the  combustion  of  carbon,  but  it  is  inadvisable 
to  heat  it  much  beyond  th3  melting  point  or  to  allow  it  to  remain 
molten  for  a  great  length  of  time,  on  account  of  its  capacity  to  absorb 
gases.  It  may  be  cast  in  dry  or  green  sand  molds  or  in  metal  chills, 
and  should  be  melted  in  plumbago  crucible.  Cores  should  be  as  soft 
as  will  permit  safe  manipulation.  A  good  core  mixture  is  15  parts 
core  sand,  1  part  rosin.  The  core  should  be  sprayed  with  molasses 
water,  baked  and  washed  in  plumbago  water. 

The  mean  specific  heat  of  aluminum  is  0.2185  (water  =  1),  being 
higher  than  any  other  metal  except  magnesium  and  the  alkali  metals. 
Its  latent  heat  of  fusion  is  51.4  B.T.U.  per  Ib.  The  coefficient  of 
linear  expansion  of  aluminum  is  0.0000130  per  degree  F.  The  thermal 
conductivity,  according  to  Roberts- Austen,  is  31.33  (silver  =  100) , 
copper  being  the  only  baser  metal  which  exceeds  it.  Wiederman 
and  Franz  give  the  thermal  conductivity  for  the  metal  unannealed  as 
38.87,  and  annealed  as  37.96.  Its  shrinkage  in  cooling  is  0.2031  in. 
per  foot,  slightly  more  than  ordinary  brass.  The  shrinkage  varies 
somewhat  with  the  thickness — thicker  castings  shrinking  more  than 
thinner  ones.  The  hardness  of  aluminum  varies  with  the  purity,  the 
purest  metal  being  the  softest.  In  the  Bottone  scale  the  hardness  of 
the  diamond  is  3010,  while  that  of  aluminum  is  821. 

Aluminum  under  tension,  and  section  for  section,  is  about  as  strong 
as  cast  iron.  Its  tensile  strength  is  increased  by  cold  rolling  or  cold 
forging,  and  there  are  alloys  which  add  considerably  to  the  tensile 
strength  without  increasing  the  specific  gravity  to  over  3  or  3.25. 

The  strength  of  commercial  aluminum  is  given  in  the  following 
table  as  the  result  of  many  tests : 

Elastic  Limit  Ultimate  Strength  Percentage 

per  sq.  in.  in  per  sq.  in.  in  of  Reduction 

Form.                    Tension,  Tension,  of  Area  in 

Ibs.  Ibs.  Tension. 

Castings 8^500  12,000-14,000  15 

Sheet 12,500-25,000  24,000-40,000  20-30 

Wire 16,000-33,000  25,000-65,000  40^-60 

Bars 14,000-33,000  28,000-40,000  30-40 

The  elastic  limit  per  square  inch  under  compression  in  cast  cylin- 
dric  columns  of  length  twice  the  diameter  is  3500  Ib.  The  ultimate 
strength  per  square  inch  imder  compression  in  cylinders  of  the  same 
form  is  12,000.  The  modulus  of  elasticity  of  cast  aluminum  is  about 
9,000,000.  It  is  rather  an  open  metal  in  its  texture,  and  for  cylinders 
to  stand  pressure  an  increase  in  thickness  must  be  given  to  allow  for 
tMs  porosity.  Its  maximum  shearing  stress  in  castings  is  about 
12,000,  and  in  forgings  about  16,000,  or  about  that  of  pure  copper. 
Its  texture  and  strength  are  improved  by  forging  or  pressing  at  a 
temperature  of  about  600°  F. 

Pure  aluminum  is  too  soft  and  lacking  in  tensile  strength  and  rigidity 
for  many  purposes.  Valuable  alloys  are  now  being  made  which  seem 
to  give  great  promise  for  the  future.  They  are  alloys  containing  from 
2  %  to  7  %  or  8  %  of  copper,  manganese,  iron,  and  nickel.  See  alloys 
of  aluminum,  page  396. 

Aluminum  can  be  worked  by  any  of  the  common  mechanical  proc- 
esses, as  rolling,  stamping,  drawing,  tapping,  spinning,  forging,  ex- 


382  STRENGTH  OF  MATERIALS. 

truding  or  machining.  Owing  to  the  ductility  of  the  metal,  sheet 
aluminum  can  be  given  a  deeper  stamp  or  heavier  draw  than  most 
metals.  A  draw  of  over  one-quarter  to  one-third  more  in  depth  than 
can  be  taken  with  copper,  brass  or  steel  can  be  made  on  aluminum 
sheet  of  20  B.  &  S.  gauge  or  heavier.  The  same  sort  of  tools  and  proc- 
esses are  used  for  stamping  as  are  used  for  other  metal.  The  tools 
should  be  lubricated  with  vaseline  or  any  greasy  oil  which  is  free  from 
grit.  It  is  practically  unnecessary  to  anneal  the  work  between  re- 
draws. 

In  spinning  it  is  also  unnecessary  to  anneal  the  shells  after  they  come 
from  the  press,  when  the  first  operation  is  done  in  the  drawing  press. 
The  speed  of  the  lathe  should  range  from  2,000  to  3,000  r.  p.  m.,  and  the 
best  results  in  spinning  will  be  obtained  by  the  use  of  hard  wood 
spinning  stocks  and  metal  chucks.  For  finishing  and  burnishing,  steel 
tools  should  be  used.  The  best  lubricant  is  soap,  tallow,  or  paraffin 
candles.  In  drop  forging  aluminum,  the  castings  to  be  forged  should 
be  made  a  little  smaller  in  their  horizontal  diameter  and  a  little  greater 
in  the  vertical  diameter  than  is  desired  for  the  finished  forging.  They 
slKRild  be  heated  to  the  annealing  temperature,  about  700°  P.,  before 
being  placed  in  the  die. 

Aluminum  can  be  extruded  into  shapes  which  can  be  obtained  in  no 
other  way.  In  these  shapes,  the  metal  has  a  continuity  of  structure 
which  renders  it  easier  in  machining  than  fabricated  shapes  made  by 
other  methods.  It  is  difficult  at  the  present  time  (1914),  to  extrude  a 
shape  of  greater  diameter  than  6  inches  or  one  having  a  thickness  of 
wall  of  less  than  1/g  inch. 

In  machining,  the  tools  should  have  a  highly  whetted  edge,  such  as 
would  be  used  in  wood  working,  and  they  should  also  have  a  large 
clearance.  That  is,  the  thickness  of  the  blades  should  increase  very 
slowly  from  its  edge.  •  The  tools  should  operate  somewhat  faster  than 
for  brass,  and  the  feed  should  be  slightly  slower  in  proportion.  A  good 
lubricant  should  be  freely  used:  No.  1  grade  lard  oil,  or  lard  oil  or 
carbon  oil  mixed  with  25  per  cent  of  some  animal  oil,  give  satisfactory 
results.  Another  satisfactory  lubricant  is  a  mixture  of  lard  oil  25  per 
cent  by  volume  with  benzine  75  per  cent. 

In  sawing,  an  ordinary  circular  saw  on  a  table  may  be  used.  The 
teeth  should  have  no  "  set,"  the  saw  should  be  thinner  at  the  center  than 
at  the  periphery,  and  should  run  at  a  peripheral  speed  of  3,500  to  4,000 
feet  per  minute. 

For  drilling,  an  ordinary  twist  drill  may  be  used,  but  it  should  be 
exceedingly  sharp.  The  drill  should  rotate  about  50  per  cent  faster, 
with  a  feed  about  25  per  cent  slower,  than  would  be  used  for  brass.  In 
tapping,  a  sharp  tap  only  should  be  used  and  a  hole  drilled  with  a  drill 
from  one  to  three  sizes  larger  than  for  brass.  The  best  tap  is  one  having 
a  single  spiral  flute  with  a  lead  of  about  one  turn  in  every  three  inches. 
The  best  tapping  lubricant  is  the  lard  oil — benzine  mixture  noted 
above. 

Aluminum  may  be  finished  by  caustic  dipping  and  scratch  brushing. 
In  caustic  dipping,  the  article  is  first  dipped  into  the  benzine  and  then 
into  a  strong  solution  of  caustic  alkali,  which  is  kept  at  the  boiling 
point,  after  which  it  should  be  placed  in  a  strong  hot  solution  of  nitric 
acid.  After  draining  the  acid,  the  aluminum  should  be  dipped  in 
boiling  hot  water,  which  should  be  constantly  drained  off  and  renewed 
by  an  addition  of  fresh  water.  On  removal  from  the  water,  it  should 
be  rapidly  dried  over  a  steam  coil.  In  scratch  brushing,  the  metal  is 
carefully  cleaned  and  then  applied  to  the  scratch  brush  wheel,  which 
rotates  at  from  1500  to  2000  r.  p.  m. 

Soldering  and  Welding  Aluminum. — Aluminum  can  be  readily 
electrically  welded,  but  soldering  is  not  altogether  satisfactory.  The 
high  heat  conductivity  of  the  aluminum  withdraws  the  heat  of  the 
molten  solder  so  rapidly  that  it  "freezes"  before  it  can  flow  sufficiently. 
A  German  solder  said  to  give  good  results  is  made  of  80%  tin  to  20% 
zinc,  using  a  flux  composed  of  80  parts  stearic  acid,  10  parts  chloride  of 
zinc,  and  10  parts  of  chloride  of  tin.  Pure  tin,  fusing  at  250°  C., 
has  also  been  used  as  a  solder.  The  use  of  chloride  of  silver  as  a  flux  has 
been  patented,  and  used  with  ordinary  soft  solder  has  given  some  suc- 
cess. A  pure  nickel  soldering-bit  should  be  used,  as  it  does  not  dis- 
color aluminum  as  copper  bits  do. 


ALUMINUM — ITS    PROPERTIES    AND    USES. 


383 


The  following  table  of  aluminum  solders  which  have  been  successfully 
used  appeared  in  Machinery,  Dec.,  1914.    See  also  page  410. 


Tin. 

Alum- 
inum. 

Zinc. 

Cop- 
per. 

Bis- 
muth. 

Lead. 

Phos- 
phor- 
Tin*. 

Silver 

Anti- 
mony 

Cad- 
mium. 

Mag- 
nes- 
ium. 

95.00 

5.00 

78  50 

2  00 

19.00 

0.50 

66.70 

33.30 

20  00 

70  00 

10  00 

97.00 

3.00 

6.00 

89.50 

4.50 

71  .25 

2  25 

26.00 

0.50 

60.00 
37.50 

4.00 

8.00 
25  00 

4.00 
37  50 

12.00 

12.00 



8.00 

92.00 

30  00 

20  00 

50  00 

80.00 

2.25 

17.00 

0.75 

66  00 

15  50 

9  00 

7  00 

-j- 

2  25 

15.50 

2.50 

78.25 

2.50 

1  .25 

49.05 

20.00 

65.00 
20  '31 

15.00 
1    15 

26.06 

3  43 

30.00 

70.00 

4  00 

94  00 

2  00 

85.10 

10.80 

1.35 

2.75 

60.00 
86.00 

15.00 

5.00 
14  00 

10.00 

5.00 

.4.. 

98  00 

1   00 

1   00 

20.00 

70.00 

10  00 

48.00 

2.00 

27.00 

23.00 

90.00 

5.00 

5.00 

84.95 

.... 

15.05 

'•  10%  phosphorus.  t  This  solder  also  contains  0.25%  vanadium. 

$  This  solder  also  contains  5  %  chromium. 

Aluminum  Wire. — Tension  tests.  Diam.  0.128  in.  14  tests.  E.L. 
12,500  to  19,100;  T.  S.  25,800  to  26,900  Ibs.  per  sq.  in.;  el.  0.30  to  1.02% 
in  48  ins.;  Red.  of  area,  75.0  to  83.4%.  Mod.  of  el.  8,800,000  to 
10,700,000.— Tech.  Quar.,  xii,  1899. 

Aluminum  Rod. — Torsion  tests.  10  samples,  0.257  in.  diam.  Appar- 
ent outside  fiber  stress,  Ibs.  per  sq.  in.  15,900  to  18,300  Ibs.  per  sq.  in. 
11  samples,  0.367  in.  diam.  Apparent  outside  fiber  stress,  18,400  to 
19,200.  10  samples,  0.459  in.  diam.  Apparent  outside  ftber  stress, 
20,700  to  21,500  Ibs.  per  sq.  in.  The  average  number  of  turns  per  inch 
for  the  three  series  were  respectively,  1.58  to  3.65;  1.20  to  2.64;  0.87  to 
1.06.— Ibid. 


384 


ALLOYS. 


ALLOYS. 


ALLOYS  OF  COPPER  AND  TIN. 

(Extract  from  Report  of  U.  S.  Test  Board.*) 


Mean  Com- 

£  - 

. 

„- 

££? 

.S 

Torsion 

. 

position  by 

M.S 

.•£'"! 

«n 

H<« 

V      JO 

Tests. 

1 

Analysis. 

Is1 

.§« 

O  "g    • 

pi' 

%s 

•5? 

gil 

-  . 

1 

*®  §. 

0  ft 

'•§  g  J 

'•^sj 

.5  S^ 

§^d 

"c-i  1 

fc 

Cop- 

Tin. 

lfj§ 

11 

cfjf| 

fl  O  3 

0    03    O 

"1$^ 

'fl**^ 

OJ   *•*   WI 

per. 

EH~ 

5 

S 

1 

|«.! 

5 

1^1 

|HT! 

'  \ 

100. 

27,800 

14,000 

6.47 

29,848 

bent. 

42,000 

143 

153 

la 

100. 

12,760 

11,000 

0.47 

21,251 

2.31 

39,000 

65 

40 

2 

97.89 

1  .90 

24,580 

10,000 

13.33 

34,000 

150 

317 

3 

96.06 

3.76 

32,000 

16,000 

14.29 

33',232 

bent. 

42,048 

157 

247 

4 

94.11 

5.43 

38,659 

" 

5 

92.11 

7.80 

28,540 

19,000 

'5*53 

43,731 

" 

42,000 

J60 

126* 

6 

90.27 

9.58 

26,860 

15,750 

3.66 

49,400 

" 

38,000 

175 

114 

7 

88.41 

11.59 

60,403 

" 

8 

87.15 

12.73 

29,430 

20,000 

3'.33 

34,531 

4.00 

53,000 

182 

100* 

9 

82.70 

17.34 

67,930 

0.63 

10 

80.95 

18.84 

32,980 

*  b'.04 

56,715 

0.49 

78,000 

1'90 

16  " 

11 

77.56 

22.25 

0. 

29,926 

0.16 

12 

76.63 

23.24 

22',6io 

22,6  JO 

0. 

32,210 

0.19 

114,000 

\22 

'3'.4 

13 

72.89 

26.85 

0. 

9,512 

0.05 

14 

69.84 

29.88 

5,585 

5,585 

0. 

12,076 

0.06 

147,000 

18 

1.5 

15 

68.58 

31.26 

0. 

9,152 

0.04 

16 

67.87 

32.10 

0. 

9,477 

0.05 

17 

65.34 

34.47 

2,201 

2,201 

0. 

4,776 

0.02 

84,700 

16 

| 

18 

56.70 

43.17 

1,455 

1,455 

0. 

2,126 

0.02 

19 

44.52 

55.28 

3,010 

3,010 

0. 

4,776 

0.03 

35,800 

*23 

1 

20 

34.22 

65.80 

3,371 

3,371 

0. 

5,384 

0.04 

19,600 

17 

2 

21 

23.35 

76.29 

6,775 

6,775 

0. 

12,408 

0.27 

22 

15.08 

84.62 

9,063 

0.86 

6,'500 

*23 

25" 

23 

11.49 

88.47 

6,380 

3,  500 

4.io 

10,706 

5.85 

10,100 

23 

62 

24 

8.57 

91.39 

6,450 

3,500 

6.87 

5,305 

bent. 

9,800 

23 

132 

25 

3.72 

96.31 

4,780 

2,750 

12.32 

6,925 

" 

9,800 

23 

220 

26 

0. 

100. 

3,505 

35.51 

3,740 

" 

6400 

12 

557 

*  The  tests  of  the  alloys  of  copper  and  tin  and  of  copper  and  zinc,  the 
results  of  which  are  published  in  the  Report  of  the  U.  S.  Board  appointed 
to  test  Iron,  Steel,  and  other  Metals,  Vols.  I  and  II,  1879  and  1881,  were 
made  by  the  author  under  direction  of  Prof.  R.  H.  Thurston,  chairman  of 
the  Committee  on  Alloys.  See  preface  to  the  report  of  the  Committee, 
in  Vol.  I. 

Nos.  la  and  2  were  full  of  blow-holes. 

Tests  Nos.  1  and  la  show  the  variation  in  cast  copper  due  to  varying 
conditions  of  casting.  In  the  crushing  tests  Nos.  12  to  20,  inclusive, 
crushed  and  broke  under  the  strain,  but  all  the  others  bulged  and  flattened 
out.  In  these  cases  the  crushing  strength  is  taken  to  be  that  which 
caused  a  decrease  of  10%  in  the  length.  The  test-pieces  were  2  in.  long 
and  5'g  in.  diameter.  The  torsional  tests  were  made  in  Thurston's  torsion- 
machine,  on  pieces  5/8  in.  diameter  and  1  in.  long  between  heads. 

Specific  Gravity  of  the  Copper-tin  Alloys.  —  The  specific  gravity 
of  copper,  as  found  in  these  tests,  is  8.874  (tested  in  turnings  from  the 
Ingot,  and  reduced  to  39.1°  F.).  The  alloy  of  maximum  sp.  gr.  8.956 
contained  62.42  copper.  37,48  tin,  md  all  tUe  alloys  containing  less  taa.a 


ALLOYS  OF  COPPER  AND  TIN.          385 

37%  tin  varied  irregularly  in  sp.  gr.  between  8.65  and  8.93,  the  density 
depending  not  on  the  composition,  but  on  the  porosity  of  the  casting.  It 
is  probable  that  the  actual  sp.  gr.  of  all  these  alloys  containing  less  than 
37%  tin  is  about  8.95,  and  any  smaller  figure  indicates  porosity  in  the 
specimen. 

From  37%  to  100%  tin,  the  sp.  gr.  decreases  regularly  from  the  maxi- 
mum of  8.956  to  that  of  pure  tin,  7.293. 


Note  on  the  Strength  of  the  Copper-tin  Alloys. 

The  bars  containing  from  2%  to  24%  tin,  inclusive,  have  considerable 
strength,  and  all  the  rest  are  practically  worthless  for  purposes  in  which 
strength  is  required.  The  dividing  line  between  the  strong  and  brittle 
alloys  is  precisely  that  at  which  the  color  changes  from  golden  yellow  to 
silver-white,  viz.,  at  a  composition  containing  between  24%  and  30%  of 
tin. 

It  appears  that  the  tensile  and  compressive  strengths  of  these  alloys  are 
in  no  way  related  to  each  other,  that  the  torsional  strength  is  closely  pro- 
portional to  the  tensile  strength,  and  that  the  transverse  strength  may  de- 
pend in  some  degree  upon  the  compressive  strength,  but  it  is  much  more 
nearly  related  to  the  tensile  strength.  The  modulus  of  rupture,  as  ob- 
tained by  the  transverse  tests,  is,  in  general,  a  figure  between  those  of 
tensile  and  compressive  strengths  per  square  inch,  but  there  are  a  few 
exceptions  in  which  it  is  larger  than  either. 

The  strengths  of  the  alloys  at  the  copper  end  of  the  series  increase 
rapidly  with  the  addition  of  tin  till  about  4%,  of  tin  is  reached.  The 
transverse  strength  continues  regularly  to  increase  to  the  maximum,  till 
the  alloy  containing  about  17|%  of  tin  is  reached,  while  the  tensile  and 
torsional  strengths  also  increase,  but  irregularly,  to  the  same  point.  This 
irregularity  is  probably  due  to  porosity  of  the  metal,  and  might  possiWv 
be  removed  by  any  means  which  would  make  the  castings  more  compact. 
The  maximum  is  reached  at  the  alloy  containing  82.70  copper,  17.34  tin, 
the  transverse  strength,  however,  being  very  much  greater  at  this  point 
than  the  tensile  or  torsional  strength.  From  the  point  of  maximum 
strength  the  figures  drop  rapidly  to  the  alloys  containing  about  27.5%  of 
tin,  and  then  more  slowly  to  37.5%,  at  which  point  the  minimum  (or 
nearly  the  minimum)  strength,  by  all  three  methods  of  test,  is  reached. 
The  alloys  of  minimum  strength  are  found  from  37.5%  tin  to  52.5%  tin. 
The  absolute  minimum  is  probably  about  45%  of  tin. 

From  52.5%  of  tin  to  about  77.5%  tin  there  is  a  rather  slow  and  irregu- 
lar increase  in  strength.  From  77.5%  tin  to  the  end  of  the  series,  or  all 
tin,  the  strengths  slowly  and  somewhat  irregularly  decrease. 

The  results  of  these  tests  do  not  seem  to  corroborate  the  theory  given 
by  some  writers,  that  peculiar  properties  are  possessed  by  the  alloys 
which  are  compounded  of  simple  multiples  of  their  atomic  weights  or 
chemical  equivalents,  and  that  these  properties  are  lost  as  the  com- 
positions 'vary  more  or  less  from  this  definite  constitution.  It  does 
appear  that  a  certain  percentage  composition  gives  a  maximum  strength 
and  another  certain  percentage  a  minimum,  but  neither  of  these  com- 
positions is  represented  by  simple  multiples  of  the  atomic  weights. 

There  appears  to  be  a  regular  law  of  decrease  from  the  maximum  to 
the  minimum  strength  which  does  not  seem  to  have  any  relation  to  the 
atomic  proportions,  but  only  to  the  percentage  compositions. 

Hardness. — The  pieces  containing  less  than  24  %  of  tin  were  turned  in 
the  lathe  without  difficulty,  a  gradually  increasing  hardness  being  noticed, 
the  last  named  giving  a  very  short  chip,  and  requiring  frequent  sharpening 
of  the  tool. 

With  the  most  brittle  alloys  it  was  found  impossible  to  turn  the  test- 
pieces  in  the  lathe  to  a  smooth  surface.  No.  13  to  No.  17  (26.85  to  34.47 
tin)  could  not  be  cut  with  a  tool  at  all.  Chips  would  fly  off  in  advance 
of  the  tool  and  beneath  it,  leaving  a  rough  surface;  or  the  tool  would 
sometimes,  apparently,  crush  off  portions  of  the  metal,  grinding  it  to 
powder.  Beyond  40%  tin  the  hardness  decreased  so  that  the  bars  could 
be  easily  turned. 


386 


ALLOYS. 


ALLOTS   OF   COPPER  AND   ZINC.     (U.  S.  Test  Board.) 


Mean   Com- 

Elastic 
Limit 

*:i; 

Trans- 
verse 

"~r^     • 

Crush- 

Torsional 
Tests. 

No. 

position  by 
Analysis. 

Tensile 
Str'gth, 
Ibs.  per 
sq.  in. 

%  of 
Break- 

Ting, 
Load, 

Ibs.  per 
sq.  in. 

Elongation 
in  5  inch< 

Test 
Modu- 
lus of 
Rup- 
ture. 

I7-S. 

1^lc 

<Sd-2 

Qw 

ing 
Str'gth 
per  sq. 
in.,  Ibs. 

E-a 

£g_g 

HS«r 

^ 

Angle  of  1 
Tors.  deg.  | 

Cop- 
per. 

Zinc. 

j 

97.83 

1.88 

27,240 

130 

357 

2 

82.93 

16.98 

32,600 

26.1 

26.7 

23,197 

Bent 

155 

329 

3 

81.91 

17.99 

32,670 

30.6 

31.4 

21,193 

166 

345 

4 

77.39 

22.45 

35,630 

20.0 

35.5 

25,374 

•• 

169 

311 

5 

76.65 

23.08 

30,520 

24.6 

35.8 

22,325 

•• 

42,000 

165 

267 

6 

73.20 

26.47 

31,580 

23.7 

38.5 

25,894 

«     " 

168 

293 

7 

71.20 

28.54 

30,510 

29.5 

29.2 

24,468 

•• 

164 

269 

8 

69.74 

30.06 

28,120 

28.7 

20.7 

26,930 

" 

143 

202 

9 

66.27 

33.50 

37,800 

25.1 

37.7 

28,459 

•• 

176 

257 

10 

63.44 

36.36 

48,300 

32.8 

31.7 

43,216 

41 

202 

230 

11 

60.94 

38.65 

41,065 

40.1 

20.7 

38,968 

«• 

75,000 

194 

202 

12 

58.49 

41.10 

50,450 

54.4 

10.1 

63,304 

•• 

227 

93 

13 

55.15 

44.44 

44,280 

44.0 

15.3 

42,463 

" 

78,000 

209 

109 

14 

54.86 

44.78 

46,400 

53.9 

8.0 

47,955 

'« 

223 

72 

15 

49.66 

50.14 

30,990 

54.5 

5.0 

33,467 

1.26 

1*17,400 

172 

38 

16 

48.99 

50.82 

26,050 

100 

0.8 

40,189 

0.61 

176 

16 

17 

47.56 

52.28 

24,150 

100 

0.8 

48,471 

1.17 

12i,000 

155 

13 

18 

4336 

56.22 

9,170 

100 

17,691 

0.10 

• 

88 

2 

\9 

41.30 

58.12 

3,727 

100 

7,761 

0.04 

18 

2 

20 

32.94 

66.23 

1,774 

100 

8,296 

0.04 

.  *  • 

29 

1 

21 

29.20 

70.17 

6,414 

100 

16,579 

0.04 

40 

2 

22 

20.81 

77.63 

9,000 

100 

*0.2 

22,972 

0.13 

52J52 

65 

1 

23 

12.12 

86.67 

12,413 

100 

0.4 

35,026 

0.31 

82 

3 

24 

4.35 

94.59 

18,065 

100 

0.5 

26,162 

0.46 

81 

22 

25 

Cast. 

Zinc. 

5,400 

75 

0.7 

7,539 

0.12 

22,000 

37 

142 

Variation  in  Strength  of  Gun-bronze,  and  Means  of  Improving 
the  Strength.  — The  figures  obtained  for  alloys  of  from  7.8%  to  12.7% 
tin,  viz.,  from  26,860  to  29,430  pounds,  are  much  less  than  are  usually 
given  as  the  strength  of  gun-metal.  Bronze  guns  are  usually  cast  under 
the  pressure  of  a  head  of  metal,  which  tends  to  increase  the  strength  and 
density.  The  strength  of  the  upper  part  of  a  gun  casting,  or  sinking 
head,  is  not  greater  than  that  of  the  small  bars  which  have  been  tested 
in  these  experiments.  The  following  is  an  extract  from  the  report  of 
Major  Wade  concerning  the  strength  and  density  of  gun-bronze  (1850): 
—  Extreme  variation  of  six  samples  from  different  parts  of  the  same 
gun  (a  32-pounder  howitzer):  Specific  gravity,  8.487  to  8.835:  tenacity, 
26,428  to  52,192.  Extreme  variation  of  all  the  samples  tested:  Specific 
gravity,  8.308  to  8.850:  tenacity  23,108  to  54,531.  Extreme  variation  of 
all  the  samples  from  the  gun  heads:  Specific  gravity,  8.308  to  8,756; 
tenacity,  23,529  to  35,484. 

Major  Wade  says:  The  general  results  on  the  quality  of  bronze  as  it 
found  in  guns  are  mostly  of  a  negative  character.  They  expose  delects 
in  density  and  strength,  develop  the  heterogeneous  texture  of  the  metal 
in  different  parts  of  the  same  gun,  and  show  the  irregularity  and  un- 
certainty of  quality  which  attend  the  casting  of  all  guns,  although  made 
from  similar  materials,  treated  in  like  manner. 

Navy  ordnance  bronze  containing  9  parts  copper  and  1  part  tin,  test" 
at  Washington,   D.C.,  in  1875-6.  showed  a  variation  in  tensile  strength 
from    29  800  to   51  400    Ibs.  per  square  inch,  in  elongation  from  3%  to 
58%,  and  in  specific  gravity  from  8.39  to  8.88. 

That  a  great  improvement  may  be  made  in  the  density  and  tenacity 
of  gun-bronze  by  compression  has  been  shown  by  the  experiments 
Mr.  S.   B.    Dean  in  Boston,   Mass.,  in   1869,  and  by  those  of  General 
Uchatius  in  Austria  in  1873.     The  former  increased  the  density  of  toe 


ALLOYS    OF   COPPER,    TIN    AND    ZINC. 


387 


metal  next  the  bore  of  the  gun  from  8.321  to  8.875,  and  the  tenacity 
from  27,238  to  41,471  pounds  per  square  inch.  The  latter,  by  a  similar 
process,  obtained  the  following  figures  for  tenacity: 

Pounds  per  sq.  in. 

Bronze  with  10%  tin 72,053 

Bronze  with  8%  tin 73,958 

Bronze  with  6%  tin 77,656 


ALLOYS    OF   COPPER,   TIN,   AND    ZINC. 

(Report  of  U.  S.  Test  Board,  Vol.  II,  1881.) 


No. 
in 

Analysis, 
Original  Mixture. 

Transverse 
Strength. 

Tensile 
Strength  per 
square  inch. 

Elongation 
per  cent  in 
5  inches. 

Re- 

Mcdulus 

f 

Deflec- 

port. 

Cu. 

Sn. 

Zn. 

Ol 

Rup- 
ture. 

tion, 
.  ins. 

A. 

B. 

A. 

B. 

72 

90 

5 

5 

41,334 

2.63 

23,660 

30,740 

2.34 

9.68 

5 

88.14 

1.86 

10 

31,986 

3.67 

32,000 

33,000 

17.6 

19.5 

70 

85 

5 

10 

44,457 

2.85 

28,840 

28,560 

6.80 

5.28 

71 

85 

10 

5 

62,470 

2.56 

35,680 

36,000 

2.51 

2.25 

89 

85 

12.5 

2.5 

62,405 

2.83 

34,500 

32,800 

1.29 

2.79 

88 

82.5 

12.5 

5 

69,960 

1.61 

36,000 

34,000 

0.86 

0.92 

77 

82.5 

15 

2.5 

69,045 

1.09 

33,600 

33,800 

0.68 

67 

80 

5 

15 

42,618 

3.88 

37,560 

32,300 

11.6' 

3.59 

68 

80 

10 

10 

67,117 

2.45 

32,830 

31,950 

1.57 

1.67 

69 

80 

15 

5 

54,476 

0.44 

32,350 

30,760 

0.55 

0.44 

86 

77.5 

10 

12.5 

63,849 

1.19 

35,500 

36,000 

1.00 

1.00 

87 

77.5 

12.5 

10 

61,705 

0.71 

36,000 

32,500 

0.72 

0.59 

63 

75 

5 

20 

55,355 

2.91 

33,140 

34,960 

2.50 

3.19 

85 

75 

7.5 

17.5 

62,607 

1.39 

33,700 

39,300 

1.56 

1.33 

64 

75 

10 

15 

58,345 

0.73 

35,320 

34,000 

1.13 

1.25 

65 

75 

15 

10 

51,109 

0.31 

35,440 

28,000 

0.59 

0.54 

66 

75 

20 

5 

40,235 

0.21 

23,140 

27,660 

0.43 

83 

72.5 

7.5 

20 

51,839 

2.86 

32,700 

34,800 

3.73 

3.78 

84 

72.5 

10 

17.5 

53,230 

0.74 

30,000 

30,000 

0.48 

0.49 

59 

70 

5 

25 

57,349 

1.37 

38,000 

32,940 

2.06 

0.99 

82 

70 

7.5 

22.5 

48,836 

0.36 

38,000 

32,400 

0.84 

0.40 

60 

70 

10 

20 

36,520 

0.18 

33,140 

26,300 

0.31 

61 

70 

15 

15 

37,924 

0.20 

33,440 

27,800 

0.25 

62 

70 

20 

10 

15  126 

0.08 

17,000 

12,900 

0.03 

81 

67.5 

2.5 

30 

58,343 

2.91 

34,720 

45,850 

7.27 

3.09 

74 

67.5 

5 

27.5 

55,976 

0.49 

34,000 

34,460 

1.06 

0.43 

75 

67.5 

7.5 

25 

46,875 

0.32 

29,500 

30,000 

0.36 

0.26 

80 

65 

2.5 

32.5 

56,949 

2.36 

41,350 

38,300 

3.26 

3.02 

55 

65 

5 

30 

51,369 

0.56 

37,140 

36,000 

1.21 

0.61 

56 

65 

10 

25 

27,075 

0.14 

25,720 

22,500 

0.15 

0.19 

57 

65 

15 

20 

13,591 

0.07 

6820 

7,231 

58 

65 

20 

15 

11,932 

0.05 

3,765 

2,665 

79 

62.5 

2.5 

35 

69,255 

2.34 

44,400 

45,000 

2.  J5 

2J9 

78 

60 

2.5 

37.5 

69,508 

1.46 

57,400 

52,900 

4.87 

3.02 

52 

60 

5 

35 

46,076 

0.28 

41,160 

38,330 

0.39 

0.40 

53 

60 

10 

30 

24,699 

0.13 

21,780 

21,240 

0.15 

54 

60 

15 

25 

18,248 

0.09 

18,020 

12,400 

12 

58.22 

2.30 

39.48 

95,623 

1.99 

66,500 

67,600 

3.1  3 

3J5 

3 

58.75 

8.75 

32.5 

35,752 

0.18 

Broke 

before  te 

st;  very 

brittle 

4 

57.5 

21.25 

21.25 

2,752 

0.02 

725 

1  300 

73 

55 

0.5 

44.5 

72,308 

3.05 

68,900 

68,900 

9.43 

2.88 

50 

55 

5 

40 

38,174 

0.22 

27,400 

30,500 

0.46 

0.43 

51 

55 

10 

35 

28,258 

0.14 

25,460 

18,500 

0.29 

0.10 

49 

50 

5 

45 

20,814 

0.11 

23,000 

31,300 

0.66 

0.45 

388  ALLOYS. 

The  transverse  tests  were  made  in  bars  1  in.  square;  22  in.  between 
supports.  The  tensile  tests  were  made  on  bars  0.798  in.  diam.  turned 
from  the  two  halves  of  the  trans  verse- test  bar,  one  half  being  marked  A 
and  the  other  B. 

Ancient  Bronzes.  —  The  usual  composition  of  ancient  bronze  was 
the  same  as  that  of  modern  gun-metal  —  90  copper,  10  tin;  but  the 
proportion  of  tin  varies  from  5%  to  15%,  and  in  some  cases  lead  has 
been  found.  Some  ancient -Egyptian  tools  contained  88  copper,  12  tin. 

Strength  of  the  Copper-zinc  Alloys.  —  The  alloys  containing  less 
than  15%  of  zinc  by  original  mixture  were  generally  defective.  The 
bars  were  full  of  blow-holes,  and  the  metal  showed  signs  of  oxidation. 
To  insure  good  castings  it  appears  that  copper-zinc  alloys  should  con- 
tain more  than  15%  of  zinc. 

From  No.  2  to  No.  8  inclusive,  16.98  to  30.06%  zinc  the  bars  show  a 
remarkable  similarity  in  all  their  properties.  They  have  all  nearly  the 
same  strength  and  ductility,  the  latter  decreasing  slightly  as  zinc 
increases,  and  are  nearly  alike  in  color  and  appearance.  Between  Nos.  8 
and  10,  30.06  and  36.36%  zinc,  the  strength  by  all  methods  of  test 
rapidly  increases.  Between  No.  10  and  No.  15,  36.36  and  50.14%  zinc, 
there  is  another  group,  distinguished  by  high  strength  and  diminished 
ductility.  The  alloy  of  maximum  tensile,  transverse  and  torsional 
strength  contains  about  41%  of  zinc. 

The  alloys  containing  less  than  55%  of  zinc  are  all  yellow  metals. 
Beyond  55%  the  color  changes  to  white,  and  the  alloy  becomes  weak  and 
brittle.  Between  70%  and  pure  zinc  the  color  is  bluish  gray,  the  brit- 
tleness  decreases  and  the  strength  increases,  but  not  to  such  a  degree  as 
to  make  them  useful  for  constructive  purposes. 

Difference  between  Composition  by  Mixture  and  by  Analysis.  — 
There  is  in  every  case  a  smaller  percentage  of  zinc  in  the  average  analy- 
sis than  in  the  original  mixture,  and  a  larger  .percentage  of  copper.  The 
loss  of  zinc  is  variable,  but  in  general  averages  from  1  to  2%. 

Liquation  or  Separation  of  the  Metals.  —  In  several  of  the  bars  a 
considerable  amount  of  liquation  took  place,  analysis  showing  a  differ- 
ence in  composition  of  the  two  ends  of  the  bar.  In  such  cases  the 
change  in  composition  was  gradual  from  one  end  of  the  bar  to  the  other, 
the  upper  end  in  general  containing  the  higher  percentage  of  copper. 
A  notable  instance  was  bar  No.  13,  in  the  above  table,  turnings  from  the 
upper  end  containing  40.36%  of  zinc,  and  from  the  lower  end  48.52%. 

Specific  Gravity.  —  The  specific  gravity  follows  a  definite  law,  vary- 
ing with  the  composition,  and  decreasing  with  the  addition  of  zinc. 
From  the  plotted  curve  of  specific  gravities  the  following  mean  values 
are  taken: 

x°er  cent  zinc 0        10     20     30      40     50     60     70      80      90    100 

Specific  gravity .  .  .     8.80  8.72  8.60  8.40  8.36  8.20  8.00  7.72  7.40  7.20  7.14 

Graphic  Representation  of  the  Law  of  Variation  of  Strength  of 
Copper-Tin-Zinc  Alloys.  —  In  an  equilateral  triangle  the  sum  of  the 
perpendicular  distances  from  any  point  within  it  to  the  three  sides  is 
equal  to  the  altitude.  Such  a  triangle  can  therefore  be  used  to  show 
graphically  the  percentage  composition  of  any  compound  of  three  parts, 
such  as  a  triple  alloy.  Let  one  side  represent  0  copper,  a  second  0  tin, 
and  the  third  0  zinc,  the  vertex  opposite  each  of  these  sides  representing 
100  of  each  element  respectively.  On  points  in  a  triangle  of  wood  rep- 
resenting different  alloys  tested,  wires  were  erected  of  lengths  propor- 
tional to  the  tensile  strengths,  and  the  triangle  then  built  up  with  plaster 
to  the  height  of  the  wires.  The  surface  thus  formed  has  a  characteristic 
topography  representing  the  variations  ,of  strength  with  variations  of 
composition.  The  cut  shows  the  surface  thus  made.  The  vertical 
section  to  the  left  represents  the  law  of  tensile  strength  of  the  copper-tin 
alloys,  the  one  to  the  right  that  of  tin-zinc  alloys,  and  the  one  at  the 
rear  that  of  the  copper-zinc  alloys.  The  high  point  represents  the 
strongest  possible  alloys  of  the  three  metals.  Its  composition  is  copper 
55,  zinc  43,  tin  2,  and  its  strength  about  70,000  Ibs.  The  high  ridge  from 
this  point  to  the  point  of  maximum  height  of  the  section  on  the  left  is 
the  line  of  the  strongest  alloys,  represented  by  the  formula  zinc  +  (3  X  tin) 
=  55. 

All  alloys  lying  to  the  rear  of  the  ridge,  containing  more  copper  and 
less  tin  or  zinc  are  alloys  of  greater  ductility  than  those  on  the  line  of 


ALLOYS  OF  COPPER,   TIN   AND   ZINC. 


389 


maximum  strength,  and  are  the  valuable  commercial  alloys;  those  in 
front  on  the  declivity  toward  the  central  valley  are  brittle,  and  those  in 
the  valley  are  both  brittle  and  weak.  Passing  from  the  valley  toward  the 
section  at  the  right  the  alloys  lose  their  brittleness  and  become  soft,  the 
maximum  softness  being  at  tin=100,  but  they  remain  weak,  as  is  shown 
by  the  low  elevation  of  the  surface.  This  model  was  planned  and  con- 
structed by  Prof.  Thurston  in  1877.  (See  Trans.  A  S  C  E.,  1881. 
Report  of  the  U.  S.  Board  appointed  to  test  Iron,  Steel  etc.,  vol.  ii. 
Washington,  1881,  and  Thurston 's  Materials  of  Engineering  vol  iii.) 


FIG.  90. 

The  best  alloy  obtained  in  Thurston's  research  for  the  U.  S.  Testing 
Board  has  the  composition,  copper  55,  tin  0.5,  zinc  44.5.  The  tensile 
strength  in  a  cast  bar  was  68,900  Ibs.  per  sq.  in.,  two  specimens  giving 
the  same  result;  the  elongation  was  47  to  51  per  cent  in  5  inches. 
Thurston's  formula  for  copper-tin-zinc  alloys  of  maximum  strength 
(Trans.  A.S.C.E.,  1881)  is  z  +  3  t  =  55,  in  which  z  is  the  percentage  of 
zinc  and  t  that  of  tin.  Alloys  proportioned  according  to  this  formula 
should  have  a  strength  of  about  40,000  Ibs.  per  sq.  in.  +  500  z.  The 
formula  fails  with  alloys  containing  less  than  1  per  cent  of  tin. 
•  The  following  would  be  the  percentage  composition  of  a  number  of 
alloys  made  according  to  this  formula,  and  their  corresponding  tensile 
strength  in  castings: 


Tensile 

Tensile 

Tin. 

Zinc. 

Copper. 

Strength, 
Ibs.  per 

Tin. 

Zinc. 

Copper. 

Strength 
Ibs.  per 

sq.  in. 

sq.  in. 

1 

52 

47 

66,000 

8 

31 

61 

55,500 

2 

49 

49 

64,500 

9 

28 

63 

54,000 

3 

46 

5! 

63,000 

10 

25 

65 

52,500 

4 

43 

53 

61,500 

12 

19 

69 

49,500 

5 

40 

55 

60,000 

14 

13 

73 

46,500 

6 

37 

57 

58,500 

16 

7 

77 

43,500 

7 

34 

59 

57,000 

18 

1 

81 

40,500 

390 


ALLOYS. 


These  alloys,  while  possessing  maximum  tensile  strength,  would  In 
general  be  too  hard  for  easy  working  by  machine  tools.  Another  series 
made  on  the  formula  z  +  It  =  50  would  have  greater  ductility,  together 
With  considerable  strength,  as  follows,  the  strength  being  calculated  as 
before,  tensile  strength  in  Ibs.  per  sq.  in.  =  40,000  +  5000. 


Tensile 

Tensile 

Tin. 

Zinc. 

Copper. 

Strength, 
Ibs.  per 

Tin. 

Zinc. 

Copper. 

Strength, 
Ibs.  per 

sq.  in. 

sq.  in. 

1 

46 

53 

63,000 

7 

22 

71 

51,000 

2 

42 

56 

61,000 

8 

18 

74 

49,000 

3 

38 

59 

59,000 

9 

14 

77 

47,000 

4 

34 

62 

57,000 

10 

10 

80 

45,000 

5 

30 

65 

55,000 

11 

6 

83 

43,000 

6 

26 

68 

53,000 

12 

2 

86 

41,000 

Composition  of  Alloys  in  E very-day  Use  in  Brass  Foundries. 

(American  Machinist.) 


Cop- 
per. 

Zinc. 

Tin. 

Lead  . 

Admiralty  metal  .  . 
Bell  metal  

Ibs. 
87 

16 

Ibs. 

Ibs. 
8 

4 

Ibs. 

For    parts    of     engines     on 
board  naval  vessels. 
Bells  for  ships  and  factories 

Brass  (yellow)  
Bush  metal  

16 

64 

8 
8 

4 

1/2 
4 

For  plumbers,  ship  and  house 
brass  work. 
For  bearing  bushes  for  shaft- 

Gun metal 

32 

3 

ing. 
For  pumps  and  other  hydrau** 

Steam  metal  

Hard  gun  metal.  .  . 
Muntz  metal  

20 

16 
60 

1 

'40' 

U/2 
2V2 

1 

lie  purposes. 
Castings  subjected  to  steam 
pressure. 
For  heavy  bearings. 
Metal  from  which  bolts  and 

Phosphor  bronze  .  . 
Brazing  metal 

92 
90 

16 

3 

8pho 
10 

s.  tin 

nuts  are  forged,  valve  spin- 
dles, etc. 
For  valves,  pumps  and  gen- 
eral work. 
For   cog  and   worm  wheels, 
bushes,  axle  bearings,  slide 
valves,  etc. 
Flanges  for  copper  pipes. 

solder  

50 

50 

Solder  for  the  above  flanges'. 

Admiralty  Metal,  for  surface  condenser  tubes  where  sea  water  is  used 
for  cooling,  Cu,  70 ;  Zn,  29;  Sn,  1.  Power,  June  1,  1909. 

Gurley's  Bronze.  —  16  parts  copper,  1  tin,  1  zinc,  1/2  lead,  used  by 
W  &  L.  E.  Gurley  of  Troy  for  the  framework  of  their  engineer's  transits. 
Tensile  strength  41,114  Ibs.  per  sq.  in.,  elongation  27%  in  1  inch,  sp.  gr. 
$.696.  (W.  J.  Keep,  Trans.  A,  I.  M.  E.,  1890.) 


ALLOYS  OF  COPPER,  TIN,  AND  ZINC. 


391 


Composition  of  Various  Grades  of  Rolled  Brass,  Etc. 


Trade  Name. 

Copper. 

Zinc. 

Tin. 

Lead. 

Nickel. 

Common  high,  brass       

61  5 

38  5 

60 

40 

Cartridge  brass                    

662/Q 

331/s 

80    3 

20 

Clock  brass            .       

60 

40 

1  1/2 

Drill  rod  

60 

40 

1  1/2  to  2 

Sprin0"  brass   

662/3 

331/3 

11/2 

18  per  cent  German  silver  . 

61  1/2 

20l/-> 

18 

The  above  table  was  furnished  by  the  superintendent  of  a  mill  in  Connec- 
ticut in  1894.  He  says:  While  each  mill  has  its  own  proportions  for  various 
mixtures,  depending  upon  the  purposes  for  which  the  product  is  intended, 
the  figures  given  are  about  the  average  standard.  Thus,  between  cartridge 
brass  with  881/3  per  cent  zinc  and  common  high  brass  with  381/2  per  cent 
zinc,  there  are  any  number  of  different  mixtures  known  generally  as  "high 
brass,"  or  specifically  as. "spinning  brass,"  "drawing  brass,"  etc.,  wherein 
the  amount  of  zinc  is  dependent  upon  the  amount  of  scrap  used  in  the 
mixture,  the  degree  of  working  to  which  the  metal  is  to  be  subjected,  etc. 

Useful  Alloys  of  Copper,  Tin,  and  Zinc. 

(Selected  from  numerous  sources.) 


Copper. 

Tin. 

Zinc. 

U.  S.  Navy  Dept.  journal  boxes  )  _ 
and  guide-gibs                      .         ) 

J   6 
(82.8 
58.22 
62 
88 
(64 
(87.7 
92.5 
91 
87.75 
85 
83 
(13 
(76.5 
82 
83 
20 
87 
88 
84 
80 
81 
97 
89.5 
89 
89 
86 

^ 

79 
74 
64 

1 

13.8 
2.30 
1 
10 
8 
11.0 
5 
7 
9.75 
5 
2 
2 
11.8 
16 
15 
1 
4.4 
10 
14 
18 
17 
2 
2.1 
8 

,?* 

\iaft 

18 
91/2 

1/4  parts. 
3.4  per  cent. 
39.48    '• 
37         " 
2 
1        parts 
1  .3    per  cent 

2        " 

2.5     " 
10 
15        ** 
2       parts. 
11.7    percent. 
2  slightly  malleable. 
1.50  0.50  lead. 

4.3   4.3       M 
2 
2 
..  2.0  antimony. 
..2.0      " 
1 
5.6   2.8  lead. 
3 
8V2 
.„... 

2 
21/2      1/2  lead. 
91/2    7  lead. 
291/2    3  1/2  lead. 

Tobin  bronze  

Naval  brass 

Composition,  U.  S.  Navy  

Gun  metal                          .  . 

••        « 

«i        i> 

(C                   II 

Tough  brass  for  engines    

Bronze  for  rod-boxes  (Lafond)  
"   pieces  subject  to  shock.  . 
Red  brass     parts 

*     per  cent 

Bronze  for  pump  casings  (Lafond).. 
"   eccentric  straps. 
*'    shrill  whistles               .   . 

"   low-toned  whistles  

Art  bronze,  dull  red  fracture 

Gold  bronze  

Bearing  metal  

•«            «• 

••            «< 

«•                          «4 

««                          It 

•«                          II 

English  brass  of  A.D.  J504 

392 


ALLOYS. 


"Steam  Metal."  Alloys  of  copper  and  zinc  are  unsuitable  for  steam 
valves  and  other  like  purposes,  since  their  strength  is  greatly  reduced  at 
high  temperatures,  and  they  appear  to  undergo  a  deterioration  by  con- 
tinued heating.  Alloys  of  copper  with  from  10  to  12%  of  tin,  when  cast 
without  oxidation,  are  good  steam  metals,  and  a  favorite  alloy  is  what 
is  known  as  "government  mixture,"  88  Cu,  10  Sn,  2  Zn.  It  has  a 
tensile  strength  of  about  33,000  Ib.  per  sq.  in.,  when  cold,  and  about 
30,600  Ib.  when  heated  to  407°  F.,  corresponding  to  steam  of  250  Ib. 
pressure. 

Analyses  of  Tobin  bronze  by  Dr.  Chas.  B.  Dudley  gave  the  following: 

Pig  metal Cu,  59.00;  Zn,  38.40;  Sn,  2.16;  Fe,  0.11;  Pb,  0.31 

Boiled  bar Cu,  61.20;  Zn,  37.14;  Sn,  0.90;  Fe,  0.18;  Pb,  0.35 

The  rolled  bar  gave  78,500  Ib.  tensile  strength,  40%  elongation  in 
2  in.  and  15%  in  8  in. 

The' original  Tobin  bronze  in  1875,  as  described  by  Thurston,  Trans. 
A.  S.  C.  E.,  1881,  had  copper  58.22,  tin  2.30,  zinc  39.48.  As  cast  it 
had  a  tenacity  of  66,000  Ib.  per  sq.  in.,  and  as  rolled  79,000  Ib.;  cold 
rolled  it  gave  104,000  Ib. 

At  a  cherry-red  heat  Tobin  bronze  can  be  forged  and  stamped  as 
readily  as  steel.  Its  great  tensile  strength  and  its  resistance  to  the 
corrosive  action  of  sea  water  make  it  a  suitable  metal  for  condenser 
plates  and  other  marine  purposes. 

Miscellaneous  Alloys.  (From  a  circular  of  the  Titanium  Alloy  Mfg. 
Co.,  Niagara  Falls,  N.  Y.,  1915.) 

ANALYSES  (Approximate).    PHYSICAL  QUALITIES  (Averages). 


No. 

Cu. 

Al. 

Sn. 

Zn. 

Pb. 

T.S. 

.S 

'$* 

s~ 

»| 

<S  > 

'ga 

aO 

GG 

Brinell 
Hardness. 

Shrinkage, 
In.  per  Ft. 

I. 

-P  & 

3* 
& 

S3  . 
|s"! 

f» 

1 
3 

90 
89 
90 

10 
10 

"n 

70,000 
37,500 
77,000 

20 
8 
24.5 

7.5 
8,5 
7.5 

95 
75 

94 

0.22 
.125 
.22 

0.27 
.31 
.27 

19,500 
21,600 
25,000 

9 
10 
11 
14 
15 

90 
88 
90 
88 
80 

10 
10 
6.5 
10 
10 

"2" 
2 

Y.5 
2 
10 

37,500 
35,000 
37,000 
32,500 
30,000 

17.5 
16 
29 
6.5 
6 

8.6 
8.7 
8.8 
8.8 
9.0 

67 
72 
55 
67 
57 

.125 
.125 
.14 
.125 
.125 

.31 
.32 
.32 
.32 
.33 

'jg,50b' 

16 

18 

81 
85 

7 
5 

3 
5 

9 

5 

32,500 
30,000 

17 
18 

8.9 
8.5 

52 
55 

.125 
.14 

.33 
.31 

19 
74 

83 
70 

4 
| 

7 
77 

6 
2 

30,500 
29,500 

17.5 
25 

8.5 
8.4 

57 
52 

.125 
.186 

.31 
.30 

78 

99.75 

18,500 

10 

8.8 

35 

.25 

.32 

29 
3? 

56 
8 

0.5 
Q? 

43.5 

70,000 
18,000 

28.5 
1.5 

8.4 
2.8 

111 
52 

.25 
.186 

.30 
.10 

30,000 

33 

3 

82 

15 

23,000 

2 

3.1 

62 

.186 

.11 

Qualities  and  Uses: 

No.     1.  Strength,  toughness,  resists  corrosion. 

No.  3.  Gear  bronze;  serviceable  for  worm  wheels  running  against 
highly  finished  steel. 

No.  5.  Similar  to  No.  1,  but  more  easily  machined.  For  large,  heavy 
work. 

No.  9.  Acid  resisting;  for  mine-pump  bodies,  and  for  thrust  collars 
or  disks. 

No.  10.  "Gun  metal";  for  heavy  pressures  and  high  speeds;  for  high- 
grade  bearings. 

No.  11.  Medium  soft  bronze;  for  small  bearings  lined  with  babbitt;  for 
steam  work. 

No.  14.  Gear  bronze,  softer  than  No.  3;  machines  more  easily. 

No.  15.  Phosphor  bronze;  for  high  speed  and  heavy  pressure;  for  bear- 
ings subject  to  shock. 

No.  16.  Similar  to  No.  15,  but  somewhat  softer  and  lower  in  price. 

No.  18.  High  grade  red  brass:  a  good  steam  metal. 


COPPER-ZINC-IRON  ALLOYS. 


393 


No.  10.  Commercial  red  brass. 

No.  24.  A  good  yellow  brass;    casts  well;  takes  a  high  polish. 

No.  28.  Pure  copper,  deoxidized ;  high  electrical  conductivity. 

No.  29.  "Manganese  bronze";  for  propeller  blades,  valve  stems  and 

other  parts  requiring  high  strength;  not  good  for  bearings. 
No.  32.  Standard  aluminum  alloy;  for  crank  cases,  automobile  castings, 

No.  33.  Tougher  than  No.  32;  takes  an  extra  high  polish,  can  be  bent 
slightly  without  breaking. 

Special  Alloys.    (Engineering,  March  24,  1893.) 
JAPANESE  ALLOYS  for  art  work: 


Copper. 

Silver. 

Gold. 

Lead, 

Zinc. 

Iron. 

Shaku-do  

94.50 

1.55 

3.73 

0.11 

trace. 

trace. 

Shibu-ichi  

67.31 

32.07 

traces. 

0.52 

GILBERT'S  ALLOY  for  cera-pcrduta  process,  for  casting  in  plaster  of 
paris. 

Copper  91.4          Tin  5.7          Lead  2.9          Very  fusible. 


COPPER-ZINC-IKON  ALLOYS.* 

(F.  L.  Garrison,  Jour.  Frank.  Inst.,  June  and  July,  1891.) 

Delta  Metal.  —  This  alloy,  which  was  formerly  known  as  sterro-metal, 
is  composed  of  about  60  copper,  from  34  to  44  zinc,  2  to  4  iron,  and  1  to  2 
tin. 

The  peculiarity  of  all  these  alloys  is,  the  content  of  iron,  which  appears 
to  have  the  property  of  increasing  their  strength  to  an  unusual  degree. 
In  making  delta  metal  the  iron  is  previously  alloyed  with  zinc  in  known 
and  definite  proportions.  When  ordinary  wrought-iron  is  introduced 
into  molten  zinc,  the  latter  readily  dissolves  or  absorbs  the  former,  and 
will  take  it  up  to  the  extent  of  about  5%  or  more.  By  adding  the  zinc- 
iron  alloy  thus  obtained  to  the  requisite  amount  of  copper,  it  is  possi- 
ble to  introduce  any  definite  quantity  of  iron  up  to  5%  into  the  copper 
alloy.  Garrison  gives  the  following  as  the  range  of  composition  ot 
copper-zinc-iron,  and  copper-zinc-tin-iroa  alloys: 

I.  II. 

Per  cent.  Per  cent. 

Iron 0.1  to  5  Iron 0.1  to  5 

Copper 50  to  65  Tin 0.1  to  10 

Zinc -.49. 9  to  30  Zinc 1.8  to  45 

Copper 98  to  40 

The  advantages  claimed  for  delta  metal  are  great  strength  and  tough- 
ness. It  produces  sound  castings  of  close  grain.  It  can  be  rolled  and 
forged  hot,  and  can  stand  a  certain  amount  of  drawing  and  hammering 
when  cold.  It  takes  a  high  polish,  and  when  exposed  to  the  atmosphere 
tarnishes  less  than  brass. 

When  cast  in  sand  delta  metal  has  a  tensile  strength  of  about  45,000 
pounds  per  square  inch,  and  about  10%  elongation;  when  rolled,  ten- 
sile strength  of  60,000  to  75,000  pounds  per  square  inch,  elongation 
from  9%  to  17%  on  bars  1.128  inch  in  diameter  and  1  inch  area. 

Wallace  gives  the  ultimate  tensile  strength  33,600  to  51,520  pounds 
per  square  inch,  with  from  10%  to  20%  elongation. 

Delta  metal  can  be  forged,  stamped  and  rolled  hot.  It  must  be  forged 
at  a  dark  cherry-red  heat,  and  care  taken  to  avoid  striking  when  at  a 
black  heat. 

According  to  Lloyd's  Proving  House  tests,  made  at  Cardiff,  December 
20,  1887,  a  half-inch  delta  metal-rolled  bar  gave  a  tensile  strength  of 
88,400  pounds  per  square  inch,  with  an  elongation  of  30%  in  three 
inches. 


394 


ALLOYS. 


ALLOYS  OF  COPPER,  TIN,  AND  LEAD. 

G.  H.  Clamer,  in  Castings,  July,  1908,  describes  some  experiments  on 
the  use  of  lead  in  copper  alloys.  A  copper  and  lead  alloy  does  not  make 
what  would  be  called  good  castings;  by  the  introduction  of  tin  a  more 
homogeneous  product  is  secured.  By  the  addition  of  nickel  it  was  found 
that  more  than  15%  of  lead  could  be  used,  while  maintaining  tin  at  8  to 
10%,  and  also  that  the  tin  could  be  dispensed  with.  A  good  alloy  for 
bearings  was  then  made  without  nickel,  containing  Cu  65,  Sn  5,  Pb  30. 
This  alloy  is  largely  sold  under  the  name  of  "plastic  bronze."  If  the 
matrix  of  tin  and  copper  were  so  proportioned  that  the  tin  remained 
below  9%  then  more  than  20%  of  lead  could  be  added  with  satisfactory 
results.  As  the  tin  is  decreased  more  lead  may  be  added.  (See  Bear- 
ing Metal  Alloys,  below.) 

The  Influence  of  Lead  on  Brass.  —  E.  S.  Sperry,  Trans.  A.I.M.E., 
1897.  As  a  rule,  the  lower  the  brass  (that  is,  the  lower  in  zinc)  the 
more  difficult  it  is  to  cut.  If  the  alloy  is  made  from  pure  copper  and 
zinc,  the  chips  are  long  and  tenacious,  and  a  slow  speed  "must  be  em- 
ployed in  cutting.  For  some  classes  of  work,  such  as  spinning  or  car- 
tridge brass,  these  qualities  are  essential,  but  for  others,  such  as  clock 
brass  or  screw  rod,  they  are  almost  prohibitory.  To  make  an  alloy 
which  will  cut  easily,  giving  short  chips,  the  best  method  is  the  addition 
of  a  small  percentage  of  lead.  Experiments  were  made  on  alloys  con- 
taining different  percentages  of  lead.  The  following  is  a  condensed 
statement  of  the  chief  results: 

Cu,  60;  Zn,  30;  Pb,  10.  Difficult  to  obtain  a  homogeneous  alloy. 
Cracked  badly  on  rolling. 

Cu,  60;   Zn,  35;   Pb,  5.     Good  cutting  qualities  but  cracked  on  rolling. 

Cu,  60;  Zn,  37.5:  Pb,  2.5.  Cutting  qualities  excellent,  but  could 
only  be  hot-rolled  or  forged  with  difficulty. 

Cu,  60;  Zn,  38.75;  Pb,  1.25.  Cutting  qualities  inferor  to  those  of 
the  alloy  containing  2.5%  of  lead,  but  superior  to  those  of  pure  brass. 

Cu,  60;  Zn,  40.  Perfectly  homogeneous.  Rolls  easily  at  a  cherry 
red  heat,  and  cracks  but  slightly  in  cold  rolling.  Chips  long  and  tena- 
cious, necessitating  a  slow  speed  in  cutting. 

Tensile  tests  of  these  alloys  gave  the  following  results: 


Copper,  %  

60.0 

60.0 

60.0 

60.0 

Zinc,  %        

40  0 

37.5 

35.0 

30.0 

Lead,  %  r..;. 

None. 

2.5 

5.0 

10.0 

C 

A 

H 

C 

A 

H 

C 

A 

H 

C 

A 

H 

T.S.  per  sq.  in.*  
Elong.  in  1  in.,  %.  .  .  . 

16 
48 

60 
51 

107 

39 
28 

51 
27 

88 
0 

33 

28 

42 

26 

61 
1 

36 
36 

35 
20 

63 
2 

Elong.  in  8  in.,  %  

27 

33 

0 

27 

23 

0 

27 

22 

0 

30 

16 

3 

Red.  of  area,  %  

61 

44 

13 

30 

33 

0 

26 

33 

0 

29 

25 

4 

P.R  

92% 

65% 

61% 

38% 

*  Thousands   of  pounds.    C,   casting;     A,   annealed   sheet; 
rolled  sheet;  P.  R.,  possible  reduction  in  rolling. 


H,   hard 


The  use  of  tin,  even  in  small  amounts,  hardens  and  increases  the  ten- 
sile strength  of  brass,  which  is  detrimental  to  free  turning.  Mr.  Sperry 
gives  analyses  of  several  brasses  which  have  given  excellent  results  in 
turning,  all  included  within  the  following  range:  Cu,  60  to  66%,  Zn,  38 
to  32%,  Pb,  1.5  to  2.5%.  For  cartridge-brass  sheet,  anything  over 
0.10%  of  lead  increases  the  liability  of  cracking  in  drawing. 

PHOSPHOR-BRONZE  AND    OTHER    SPECIAL  BRONZES. 

Phosphor-bronze.  —  In  the  year  1868,  Montefiore  &  Kunzel  of  Liege. 
Belgium,  found  by  adding  small  proportions  of  phosphorus  or  "phos- 
phoret  of  tin  or  copper"  to  copper  that  the  oxides  of  that  metal,  nearly 
always  present  as  an  impurity,  more  or  less,  were  deoxidized  and  the 
copper  much  improved  in  strength  and  ductility,  the  grain  of  the  frac- 
ture became  finer,  the  color  brighter,  and  a  greater  fluidity  was  attained. 


ALLOYS  FOB  CASTING  UNDER  PRESSURE. 


395 


Three  samples  of  phosphor-bronze,  tested  by  Kirkaldy,  gave 

Elastic  limit,  Ibs.  per  sq.  in 23,800        24,700        16,100 

Tensile  strength,  IDS.  per  sq.  in. . 
Elongation,  per  cent 


52,625 
8.40 


46,100 
1.50 


44,448 
33.40 


The  strength  of  phosphor-bronze  varies  like  that  of  ordinary  bronze 
according  to  the  percentages  of  copper,  tin,  zinc,  lead,  etc.,  in  the  alloy. 

Phosphor-bronze  Rod.  —  Torsion  tests  of  20  samples,  1/4  m.  diam. 
Apparent  outside  fiber  stress,  77,500  to  86,700  Ibs.  per  sq.  in.;  average 
number  of  turns  per  inch  of  length,  0.76  to  1.50.  —  Tech.  Quar.,  vol.  xh, 
Sept.,  1899. 

Penn.  R.  R.  Co.'s  Specifications  for  Phosphor-bronze  (1902).  — 
The  metal  desired  is  a  homogeneous  alloy  of  copper,  79.70;  tin,  10.00; 
lead,  9.50-  phosphorus,  0.80.  Lots  will  not  be  accepted  if  samples  do 
not  show  tin,  between  9  and  11%;  lead,  between  8  and  11%;  phos- 
phorus, between  0.7  and  1%;  nor  if  the  metal  contains  a  sum  total  of 
other  substances  than  copper,  tin,  lead,  and  phosphorus  in  greater  quan- 
tity than  0.50  per  cent.  (See  also  p.  406.) 

Deoxidized  Bronze.  —  This  alloy  resembles  phosphor  bronze  spme- 
what  in  composition  and  also  delta  metal,  in  containing  zinc  and  iron. 
The  following  analysis  gives  its  average  composition:  Cu,  82.67;  Sn,  12.40; 
Zn,  3.23;  Pb,  2.14;  Fe,  0.10;  Ag,  0.07;  P,  0.005. 


Comparison     of    Copper,    Silicon-bronze,     and    Phosphor-bronze 
Wires.      (Engineering,  Nov.  23,  1883.) 

Description  of  Wire. 

Tensile  Strength. 

Relative  Conductivity. 

Pure  copper                              . 

39,827  Ibs.  per  sq.  in. 
41,6%  "  
108,080  "  "  "  " 

100  per  cent. 
96   " 
34    "       - 
26    "       " 

Silicon  bronze  (telegraph)  
(telephone)  
Phosphor  bronze  (telephone)  .  . 

Silicon  Bronze.     (Aluminum  World,  May,  1897.) 

The  most  useful  of  the  silicon  bronzes  are  the  3%  (97%  copper,  3% 
silicon)  and  the  5%  (95%  copper,  5%  silicon),  although  the  hardness 
and  strength  of  the  alloy  can  be  increased  or  decreased  at  will  by 
increasing  or  decreasing  silicon.  A  3%  silicon  bronze  has  a  tensile 
strength,  in  a  casting,  of  about  55,000  Ibs.  per  sq.  in.,  and  from  50%  to 
60%  elongation.  The  5%  bronze  has  a  tensile  strength  of  about  75,000 
Ibs.  and  about  8%  elongation.  More  than  5%  or  51/2%  of  silicon  in  cop- 
per makes  a  brittle  alloy.  In  using  silicon,  either  as  a  flux  or  for  making 
silicon  bronze,  the  rich  alloy  of  silicon  and  copper  which  is  now  on  the 
market  should  be  used.  It  should  be  free  from  iron  and  other  metals  if 
the  best  results  are  to  be  obtained.  Ferro-silicon  is  not  suitable  for  use 
in  copper  or  bronze  mixtures. 

Copper  and  Vanadium  Alloys.  The  Vanadium  Sales  Co.  of  America 
reports  (1908)  that  the  addition  of  vanadium  to  copper  has  given  a  tensile 
strength  of  83,000  Ibs.  per  sq.  in.;  with  an  elongation  of  over  60%. 

ALLOYS  FOR  CASTING  UNDER  PRESSURE  IN  METAL 
MOLDS.    E.  L.  Lake,  Am.  Mach.,  Feb.  13,  1908. 


No. 

Tin. 

Copper. 

Alumi- 
num. 

Zinc. 

Lead. 

Anti- 
mony. 

Iron 

j 

14.75 

5.25 

6.25 

73.75 

2 
3 

19 
12 

5 
10.6 

1. 
3.4 

72.7     - 
73.8 

2 

0.3 

6!i" 

4 

30.8 

20.4 

2.6 

46.2 

Nos.  1  and  2  suitable  for  ordinary  work,  such  as  could  be  performed  by 
average  brass  castings.    No.  3  and  4  are  harder. 


396 


ALLOYS. 


ALUMINUM  ALLOTS. 

The  useful  alloys  of  aluminum  so  far  found  have  been  chiefly  In  two 
groups,  the  one  of  aluminum  with  not  more  than  35%  of  other  metals,  and 
the  other  of  metals  containing  not  over  15%  of  aluminum;  in  the  one  case 
the  metals  impart  hardness  and  other  useful  qualities  to  the  aluminum, 
and  in  the  other  the  aluminum  gives  useful  qualities  to  the  metal  with 
which  it  is  alloyed. 

Aluminum-Copper  Alloys.  —  The  useful  aluminum-copper  alloys  can 
be  divided  into  two  classes, — the  one  containing  less  than  11%  of 
aluminum,  and  the  other  containing  less  than  15%  of  copper.  The  first 
class  is  best  known  as  Aluminum  Bronze. 

Aluminum  Bronze.  (Cowles  Electric  Smelting  and  Al.  Co.'s  circular.) 
The  standard  A  No.  2  grade  of  aluminum  bronze,  containing  10%  of 
aluminum  and  90%  of  copper,  has  many  remarkable  characteristics 
which  distinguish  it  from  all  other  metals. 

The  tenacity  of  castings  of  A  No.  2  grade  metal  varies  between  75,000 
and  90,000  Ibs.  to  the  square  inch,  with  from  4  %  to  14  %  elongation. 

Increasing  the  proportion  of  aluminum  in  bronze  beyond  11%  pro- 
duces a  brittle  alloy;  therefore  nothing  higher  than  the  A  No.  1,  which 
contains  11%,  is  made. 

The  B,  C,  D,  and  E  grades,  containing  7  H%,  5%,  2  H%,  and  11A% 
of  aluminum,  respectively,  decrease  in  tenacity  in  the  order  named,  that 
of  the  former  being  about  65,000  pounds,  while  the  latter  is  25,000 
pounds.  While  there  is  also  a  proportionate  decrease  in  transverse  and 
torsional  strengths,  elastic  limit,  and  resistance  to  compression  as  the 
percentage  of  aluminum  is  lowered  and  that  of  copper  raised,  the  ductil- 
ity, on  the  other  hand,  increases  in  the  same  proportion.  The  specific 
gravity  of  the  A  No.  1  grade  is  7.56. 

Bell  Bros.,  Newcastle,  gave  the  specific  gravity  of  the  aluminum 
bronzes  as  follows: 

3%,  8.691;         4%,  8.621;         5%,  8.369;         10%,  7.689. 

In  manufacturing  aluminum  bronze,  only  the  purest  metals  should 
be  used.  The  copper  should  be  melted  over  a  gas  or  oil  fire  in  a  plum- 
bago crucible,  being  covered  with  charcoal  to  prevent  oxidation  and 
the  absorption  of  gases.  If  a  coal  fire  is  used,  the  copper  will  absorb 
gases  from  the  coal  and  produce  an  unsatisfactory  alloy.  The  alumi- 
num is  dropped  through  the  charcoal  into  the  molten  copper.  The  alu- 
minum combines  with  the  copper  as  soon  as  its  melting  point  is  reached, 
setting  free  latent  heat  and  raising  the  temperature  of  the  mass.  The 
copper  becomes  brighter  and  more  liquid  when  the  union  takes  place, 
and  the  crucible  then  should  be  instantly  removed  from  the  fire, 
skimmed,  and  poured  into  ingot  molds  of  convenient  size.  The  liquid 
should  be  stirred  until  poured.  The  alloy  may  then  be  remelted  for 
casting.  Each  remelting  improves  the  quality  of  the  aluminum  bronze 
up  to  about  four  remeltings.  (Aluminum  Co.  of  America,  1909.) 

Tests  of  Aluminum  Bronzes. 

(John  H.  J.  Dagger,  British  Association,  1889.) 


Per  cent 
of 
Aluminum. 

Tensile  Strength. 

Elonga- 
tion, 
per  cent. 

Specific- 
Gravity. 

Tons  per 
square  inch. 

Pounds  per 
square  inch. 

11... 

40  to  45 
33  "  40 
25  "  30 
15  "   18 
13  ••   15 
11  "    13 

89,600  to  100,800 
73,920   "     89,600 
56,000  "    67,200 
33,600  "    40,320 
29,120  "    33,600 
24,640  "    29,120 

8 
14 
40 
40 
50 
55 

7.23 
7.69 
6.00 
8.37 
8.69 

10.. 

71/2                  

5-&/2:            ...... 

21/2 

11/4  

Casting. — The  melting  point  of  aluminum  bronze  varies  slightly  with 
the  amount  of  aluminum  contained,  the  higher  grades  melting  at  a 
lower  temperature  than  the  lower  grades.  The  A  No.  1  grades  melt 
at  about  1700°  FM  a  little  higher  than  ordinary  bronze  or  brass. 


ALUMINUM   ALLOYS. 


397 


Aluminum  bronze  shrinks  more  than  ordinary  brass.  As  the  metal 
solidifies  rapidly  it  is  necessary  to  pour  it  quickly  and  to  make  the 
feeders  amply  large,  so  that  there  will  be  no  "freezing"  in  them  before 
the  casting  is  properly  fed.  Baked-sand  molds  are  preferable  to  green 
sand,  except  for  small  castings,  and  when  fine  skin  colors  are  desired  in 
the  castings.  (Thos.  D.  West,  Trans.  A.  S.  M.  E.,  1886,  vol.  viii.) 

All  grades  of  aluminum  bronze  can  be  rolled,  s wedged,  spun,  or  drawn 
cold  except  A  1  and  A  2.  They  can  all  be  worked  at  a  bright  red  heat. 

In  rolling,  swedging,  or  spinning  cold,  it  should  be  annealed  very  often 
and  at  a  brighter  red  heat  than  is  used  for  annealing  brass. 

Seamless  Tubes. — Leonard  Waldo,  Trans.  A.  S.  M.  E.,  vol.  xviii, 
describes  the  manufacture  of  aluminum  bronze  seamless  tubing.  Many 
difficulties  were  met  in  all  stages  of  the  process.  A  cold  drawn  bar,  1.49 
in.  outside  diameter,  0.05  in.  thick,  showed  a  yield  point  of  68.700,  and 
a  tensile  strength  of  96,000  Ib.  per  sq.  in.  with  an  elongation  of  4.9%  in 
10  in. ;  heated  to  bright  red  and  plunged  in  water,  the  yield  point  re- 
duced to  24,200  and  the  T.  S.  to  47,600  Ib.  per  sq.  in.,  and  the  elonga- 
tion in  10  in.  increased  to  64.9%. 

Brazing. — Aluminum  bronze  will  braze  as  well  as  any  other  metal, 
using  one-quarter  brass  solder  (zinc  500,  copper  500)  and  three-quarters 
borax,  or,  better,  three-quarters  cryolite. 

Soldering. — Aluminum  bronze  can  be  soldered  by  using  a  solder  of 
pure  block  tin  .with  a  flux  of  zinc  filings  and  muriatic  acid.  It  is  advis- 
able to  "tin"  the  two  surfaces  before  putting  them  together. 

Aluminum  Brass. — (E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  vol.  xviii.) — 
Cowles  aluminum  brass  is  made  by  fusing  together  equal  weights  of  A  1 
aluminum  bronze,  copper,  and  zinc.  The  copper  and  bronze  are  first 
thoroughly  melted  and  mixed,  and  the  zinc  is  finally  added.  The 
material  is  left  in  the  furnace  until  small  test-bars  are  taken  from  it  and 
broken.  When  these  bars  show  a  tensile  strength  of  80,000  pounds  or 
over,  with  2  or  3  per  cent  ductility,  the  metal  is  ready  to  be  poured. 
Tests  of  this  brass,  on  small  bars,  have  at  times  shown  as  high  as 
100,000  pounds  tensile  strength. 

The  Aluminum  Co.  of  America  says  (1909)  that  aluminum  brass  has 
an  elastic  limit  of  about  30,000  Ib.  per  sq.  in.,  an  ultimate  strength  of 
40,000  to  50,000  Ib.  per  sq.  in.,  and  an  elongation  of  3%  to  10%  in  8  in. 
Aluminum  brass  is  used  with  aluminum  ranging  from  0.1%  to  10%. 
The  best  results  are  obtained  by  introducing  the  aluminum  in  the  form 
of  aluminized  zinc,  a  5  %  aluminized  zinc  being  used  where  less  than  1  % 
of  aluminum  is  required  and  a  10  %  aluminized  zinc  for  aluminum  per- 
centages of  over  1  %.  The  effect  of  aluminum  in  brass  in  quantities  of 
less  than  1  %  is  to  make  the  brass  flow  freely  and  to  insure  a  sounder 
casting,  and  it  enables  from  one-half  to  one-third  more  castings  to  be 
made  on  a  gate  than  is  possible  where  aluminum  is  not  used.  In  quan- 
tities over  1  %  up  to  10%  the  aluminum  increases  the  strength  of  brass, 
enabling  a  cheaper  grade  of  brass  to  be  used  vthan  wo*uld  otherwise  be 
possible.  Inasmuch  as  aluminum  lowers  the  melting  point  of  brass, 
great  care  must  be  taken  not  to  overheat  it  in  melting. 

Tests  of  Aluminum  Brass. 

(Cowles  E.  S.  &  Al.  Co.) 


Specimen  (Castings) 

Diameter 
of  Piece, 
Inch. 

Area 
sq.  in. 

Tensile 
Strength, 
Ibs.  per 
sq.  in. 

Elastic 
Limit, 
Ibs.  per 
sq.  in. 

Elonga- 
tion, 
per  et. 

Remarks. 

15%AgradeBronze  ) 

M   •  g 

1  7%  Zinc  [ 

0.465 

0.1698 

41,225 

1  7,668 

41  1/2 

S'S    $    M 

68%  Copper.             ) 

•2Jvo  £  & 

part  A  Bronze  .  .  ) 

•p-3    $•§ 

part  Zinc  > 
part  Copper  ) 

0.465 

0.1698 

78,327 

2V2 

I"     1 

part  A  Bronze.  .   ) 
part  Zinc  [ 

0.460 

0.1661 

72,246 

2i/2 

111! 

part  Copper  ) 

H 

The  first  brass  on  the  above  list  is  an  extremely  tough  metal  with  low 


398 


ALLOYS. 


elastic  limit,  made  purposely  so  as  to  "upset"  easily.  The  other,  which 
is  called  Aluminum  brass  No.  2,  is  very  hard. 

Caution  as  to  Reported  Strength  of  Alloys. — The  same  variation  in 
strength  which  has  been  found  in  tests  of  gun-metal  (copper  and 
tin)  noted  above,  must  be  expected  in  tests  of  aluminum  bronze  and  in 
fact,  of  all  alloys.  They  are  exceedingly  subject  to  variation  in  density 
and  in  grain,  caused  by  differences  hi  method  of  molding  and  casting 
temperature  of  pouring,  size  of  and  shape  casting,  depth  of  "sinking 
head,"  etc.  Chill-castings  give  higher  results  than  sand-castings,  and 
bars  cast  by  themselves  purposely  for  testing  almost  invariably  run 
higher  than  test  bars  attached  to  castings.  Bars  cut  out  from  castings 
are  generally  weaker  than  bars  cast  alone. 

Effect  of  Copper  on  Aluminum. — Tests  of  rolled  sheets  of  aluminum, 
0.04  in.  thick,  with"  varying  percentages  of  copper  are  reported  in  The 
Engineer,  Jan.  2,  1891,  as  follows: 

Aluminum,  per  cent. ........       100  98  96  94  92 

Copper,  per  cent 0  2  4  6  8 

Specific  gravity,  calculated 2.78  2.90  3.02  314 

Specific  gravity,  determined..     2.67  2.71  2.77  2.82  2.85 

Tensile  strength,  Ib.  per  sq.in.  25,535  43,563  44,130  54,773  50,374 

Tests  of  Aluminum  Alloys. 

(Engineer  Harris,  U.  S.  N.,  Trans.  A.  I.  M.  E.,  vol.  xviii.) 


Composition. 

Tensile 
Strength 
per  sq. 
in.,  Ib. 

Elastic 
Limit, 
Ib.  per 
sq.  in. 

Elonga- 
tion, 
per  ct. 

Reduc- 
tion   of 
Area, 
per  ct. 

Copper. 

Alumi- 
num. 

Silicon. 

Zinc. 

Iron. 

91.50% 
88.50 
91.50 
90.00 
63.00 
63.00 
91.50 
93.00 
88.50 
92.00 

6.50% 
9.33 
6.50 
9.00 
3.33 
3.33 
6.50 
6.50 
9.33 
6.50 

\:7d% 

1.75 
1.00 
0.33 
0.33 
1.75 
0.50 
1  .66 
0.50 

0.25% 
0.50 
0.25 

60,700 
66,000 
67,600 
72,830 
82,200 
70,400 
59,100 
53,000 
69,930 
46,530 

18,000 
27,000 
24,000 
33,000 
60,000 
55,000 
19,000 
19,000 
33,000 
1  7,000 

23.2 
3.8 
13 
2.40 
2.33 
0.4 
15.1 
6.2 
1  .33 
7.8 

30.7 
7.8 
21.62 
5.78 
9.88 
4.33 
23.59 
15.5 
3.30 
19.19 

33.'33% 
33.33 

0.25 

0.50 

For  comparison  with  the  above  6  tests  of  "Navy  Yard  Bronze," 
Cu  88,  Sn  10,  Zn  2,  are  given  in  which  the  T.  S.  ranges  from  18,000  to 
24,590,  E.  L.  from  10,000  to  13,000,  El.  2.5  to  5.8%,  Red.  4.7  to  10.89. 

Alloys  of  Aluminum,  Silicon  and  Iron. 

M.  and  E.  Bernard  have  succeeded  in  obtaining  through  electrolysis, 
by  treating  directly  and  without  previous  purification,  the  aluminum 
earths  (red  and  white  bauxites),  the  following: 

Alloys  such  as  ferro-aluminum,  ferro-silicon-aluminum,  and  silicon- 
aluminum,  where  the  proportion  of  silicon  may  exceed  10%,  which  are 
employed  in  the  metallurgy  of  iron  for  refining  steel  and  cast-iron. 

Also  silicon-aluminum,  where  the  proportion  of  silicon  does  not  exceed 
10%,  which  may %be  employed  in  mechanical  constructions  in  a  rolled  or 
hammered  condition,  in  place  of  steel,  on  account  of  their  great  resist- 
ance, especially  where  the  lightness  of  the  piece  in  construction  consti- 
tutes one  of  the  main  conditions  of  success. 

The  following  analyses  are  given: 

1.  Alloys  applied  to  the  metallurgy  of  iron,  the  refining  of  steel  and 
cast  iron:    No.  1,  Al,  70%;  Fe,  25%;  Si,  5%.     No.  2,  Al,  70;  Fe,  20; 
Si,  10.     No.  3,  Al,  70;  Fe,  15;  Si,  15.     No.  4,  Al.  70;  Fe,  10;  Si,  20. 
No.  5,  Al,  70;  Fe,  10;  Si,  10;  Mn,  10.    No.  6,  Al.  70;  Fe,  trace;  Si,  20; 
Mn,  10. 

2.  Mechanical  alloys:   No.  1,  Al,  92;  Si,  6.75;  Fe,  1.25.     No.  2,    Al, 
90;  Si,  9.25;  Fe,  0.75.    No.  3,  Al,  90;  Si,  10;  Fe,  trace.    The  best  results 
were  with  alloys  where  the  proportion  of  iron  was  very  low,  and  the 
proportion  of  silicon  in  the  neighborhood  of  10%.     Above  that  pro- 
portion the  alloy  becomes  crystalline  and  can  no  longer  be  employed. 


ALUMINUM  ALLOYS.  399 

The  density  of  the  alloys  of  silicon  is  approximately  the  same  as  that  of 
aluminum. — La  Metallurgie,  1392. 

Aluminum -Tungsten  Alloys  have  been  somewhat  used  in  Europe 
in  the  form  of  rolled  sheets  under  the  trade  name  of  Wolfranium.  An 
aluminum-tungsten  alloy  used  in  France  (1898)  for  motor-car  bodies 
has  the  following  properties:  Cast,  sp.  gr.  2.86;  T.S.,  17,000  to  24,000; 
elong.,  12  to  6%.  Rolled,  sp.  gr.,  3.09;  T.S.,  45,500  to  53,600;  elong., 
8  to  6%. 

Aluminum-Antimony  alloys  have  been  produced,  but  have  a  scien- 
tific rather  than  a  commercial  interest.  The  alloy  whose  composition 
is  Sb  Al  has  a  higher  melting  point  than  either  of  its  constituents. 

Aluminum  and  Manganese.  —  Manganese  is  one  of  the  best  harden- 
ers of  aluminum.  Professor  Carpenter  found  that  it  increased  the 
strength  when  added  in  quantities  up  to  10%. 

Undesirable  Aluminum  Alloys.  —  While  aluminum  will  combine 
with  all  the  metalloids  and  gaseous  elements,  such  as  oxygen,  nitrogen, 
sulphur,  selenium,  chlorine,  iodine,  boron,  silicon,  and  carbon,  no  useful 
result  has  been  recorded  from  the  combination  of  metallic  aluminum 
with  any  of  these  elements.  The  prevention  of  the  occlusion  of  gaseous 
metalloids  in  molten  aluminum  and  the  prevention  of  the  union  of  car- 
bon and  aluminum  are  among  the  chief  precautions  to  be  observed  in 
the  metallurgy  of  aluminum.  The  effect  of  sodium  and  potassium  on 
aluminum  is  as  undesirable  as  the  effect  of  phosphorus  and  sulphur  on 
steel.  (Aluminum  Co.  of  America.) 

Aluminum-Magnesium. — Magnalium. — A  patented  alloy  of  alumi- 
num and  magnesium,  containing  90  to  98%  Al  has  the  trade  name 
"magnalium."  It  is  lighter  than  aluminum  (sp.  gr.  2.5),  and  is  whiter, 
harder,  and  stronger.  It  can  be  forged,  rolled,  drawn,  machined,  and 
filed.  It  resists  oxidation  better  than  other  light  metals  or  alloys. 
Tensile  strength:  cast,  18,400  to  21,300  Ib.  per  sq.  in.,  with  a  reduction 
of  area-3.75%;  rolled,  52,200  Ib.  per  sq.  in.,  with  a  reduction  of  area 
of  3.7%;  annealed,  42,200  Ib.  per  sq.  in.,  reduction,  17.8%.  Al  Mg 
alloys  are  said  by  the  Aluminum  Co.  of  America  to  be  as  strong  as  Al 
Cu  alloys. 

Aluminum  and  Iron. — Aluminum  alloys  with  cast-iron  up  to  15% 
Al,  but  the  metal  decreases  in  strength  as  the  Al  increases.  Above  15  % 
Al  the  alloys  are  granular  and  have  practically  no  coherence.  (Trans. 
A.  I.  M.  E.,  vol.  xviii,  A.  S.  M.  E.,  vol.  xix.)  It  is  doubtful  if  aluminum 
has  much  effect  on  soft  gray  No.  1  foundry  iron,  except  to  keep  the 
metal  molten  a  longer  time.  With  difficult  castings,  where  loss  is 
occasioned  by  defective  castings  or  where  the  iron  does  not  flow  freely, 
the  addition  of  aluminum  will  improve  the  quality  of  the  casting,  and 
give  a  closer  grained  iron.  The  addition  of  2%  or  more  of  Al  will  de- 
crease the  shrinkag'e  of  cast  iron.  In  wrought  iron,.l%  Al  makes  the 
metal  more  fluid  at  2200°  F.  than  it  would  be  at  3500°  F.  without  Al. 
An  addition  of  0.25%  Al  to  the  bath  causes  the  charge  to  stiffen  more 
quickly.  (Aluminum  Co.  of  America,  1909.) 

Aluminum,  Copper,  and  Tin. — Prof.  R.  C.  Carpenter,  Trans. 
A.  S.  M.  E.,  vol.  xix.,  finds  the  following  alloys  of  maximum  strength  in 
a  series  in  which  two  of  the  three  metals  are  in  equal  proportions: 

Al,  85;  Cu,  7.5;  Sn,  7.5;  tensile  strength,  30,000  Ib.  per  sq.  in.; 
elongation  in  6  in.,  4%;  sp.  gr.,  3.02.  Al,  6.25;  Cu,  87.5;  Sn,  6.25; 
T.  S.,  63,000;  EL,  3.8;  sp.  gr.,  7.35.  Al,  5;  Cu,  5;  Sn,  90;  T.  S:,  11,000; 
EL,  10.1;  sp.  gr.,  6.82. 

From  85  to  95%  Cu  the  bars  have  considerable  strength,  are  close 
grained  and  of  a  golden  color.  Between  78  and  80  %  the  color  changes 
to  silver  white  and  the  bars  become  brittle.  From  78  to  20%  Cu  the 
alloys  are  very  hard  and  brittle,  and  worthless  for  practical  purposes. 
Aluminum  is  strengthened  by  the  addition  of  equal  parts  of  copper  and 
tin  up  to  7.5%  of  each,  beyond  which  the  strength  decreases.  All  the 
alloys  that  contain  between  20  and  60  %  of  either  one  of  the  three  metals 
are  very  weak. 

Aluminum  and  Zinc. — (Aluminum  Co.  of  America,  1909.)  Like  the 
copper  alloys,  the  zinc  alloys  can  be  divided  into  two  classes,  (1)  those 
containing  a  relatively  small  amount  of  aluminum,  and  (2)  those  con- 
taining less  than  35  %  of  zinc.  The  first  class  is  known  as  "  aluminized 
zinc,"  and  the  second  comprises  the  zinc  casting  alloys.  Zinc  produces 
tl  e  g-trongest  alloy  of  aluminum,  which  strength  can  be  increased  by  the 


400 


ALLOYS. 


addition  of  other  metals.  The  strongest  zinc-aluminum  alloy  may  be 
as  nigh  as  35,000  Ib.  per  sq.  in.  The  high  zinc  alloys  are  brittle  and 
more  liable  to  "draw"  in  heavy  parts  or  lugs  than  are  copper  alloys. 
This  can  often  be  overcome  by  suitable  gating,  chills,  and  risers.  There 
is  also  danger  of  burning  out  the  zinc  and  producing  a  weaker  casting. 
For  forging,  a  zinc-aluminum  alloy  of  10  to  15%  zinc  gives  excellent 
results.  It  is  tough,  flows  well  in  the  dies,  is  easily  machined  and  is 
remarkably  strong  per  unit  of  area. 

Aluminized  zinc  is  used  in  the  bath  for  galvanizing  and  in  aluminum 
brass.  It  is  made  by  melting  aluminum  in  the  crucible  and  then  grad- 
ually stirring  in  the  zinc,  after  which  it  is  cast  into  ingots.  The  5% 
alloy  is  used  in  the  galvanizing  bath  and  for  low  grade  aluminum 
brass,  and  the  10  %  alloy  for  lu'gh-grade  brass  castings.  It  is  introduced 
in  the  molten  metal  the  same  as  pure  zinc.  In  galvanizing  it  is  added 
in  such  proportions  that  the  total  amount  of  aluminum  in  the  bath 
will  be  about  1  Ib.  of  aluminum  per  ton  of  bath,  or  about  20  Ib.  of  5% 
alloy  per  ton  of  bath.  It  should  be  added  gradually,  and  as  the  bath  is 
consumed  fresh  5  %  alloy  should  be  added  about  1  Ib.  at  a  time  for  a 
5- ton  bath.  When  aluminized  zinc  is  used  it  is  unnecessary  to  use 
sal  ammoniac  to  clear  the  bath  of  oxide.  In  starting  a  new  bath,  how- 
ever, after  adding  the  aluminized  zinc,  it  is  stirred  well  until  the  alumi- 
num combines  with  the  impurities,  which  rise  to  the  surface  as  a  scum. 
This  is  removed,  some  sal  ammoniac  is  added  to  counteract  the  effects 
of  the  aluminum,  and  the  proportion  of  alloy  added  is  reduced. 

Aluminum  and  Tin.— (Aluminum  Co.  of  America,  1909.)  Tin,  al- 
loyed with  aluminum  in  proportions  of  from  1  to  15%,  gives  added 
strength  and  rigidity  to  heavy  castings,  increases  the  sharpness  of 
outline  and  decreases  shrinkage.  The  aluminum-tin  alloys  are  rather 
brittle,  and  although  small  proportions  of  tin  in  certain  casting  alloys 
have  been  advantageously  used  to  decrease  shrinkage,  they  are  com- 
paratively little  used  on  account  of  the  relative  cost  and  brittleness. 

Aluminum  and  Nickel.  —  (Aluminum  Co.  of  America,  1909.)  Al- 
uminum-nickel alloys  with  2  to  5  %  of  the  combined  alloying  metals  are 
satisfactory  for  rolling  or  hammering.  A  7  to  9  %  alloy  produces  good 
results  in  casting. 

Other  Aluminum  Alloys.  —  Al  75.7,  Cu.  3,  Zn  20,  Mn  1.3  is  an 
excellent  casting  metal,  having  a  tensile  strength  of  over  35,000  Ib. 
per  sq.  in.,  and  a  sp.  gr.  slightly  above  3.  It  has  very  little  ductility 

Al  96.5,  Cu  2,  and  chromium  1.5  is  a  little  heavier  than  pure  alumi- 
num and  has  a  tensile  strength  of  26,300  Ib.  per  sq.  in.  —  A.  S.  M.  E.t 
vol.  xix. 

With  the  exception  of  lead  and  mercury,  aluminum  unites  with  all 
metals,  though  it  unites  with  antimony  with  great  difficulty.  A  small 
percentage  of  silver  whitens  and  hardens  the  metal,  and  gives  it  added 
strength;  and  this  alloy  is  especially  applicable  to  the  manufacture  of 
fine  instruments  and  apparatus.  The  following  alloys  have  been  found 
recently  to  be  useful  in  the  arts:  Nickel-aluminum,  composed  of  20  parts 
nickel  to  80  of  aluminum;  rosine,  made  of  40  parts  nickel,  10  parts  silver, 
30  parts  aluminum,  and  20  parts  tin,  for  jewellers'  work;  mettaline,  made 
of  35  parts  cobalt,  25  parts  aluminum,  10  parts  iron,  and  30  parts  copper. 
The  aluminum-bourbouze  metal,  shown  at  the  Paris  Exposition  of  1889, 
has  a  specific  gravity  of  2.9  to  2.96,  and  can  be  cast  in  very  solid  shapes, 
as  it  has  very  little  shrinkage.  From  analysis  the  following  composi- 
tion is  deduced:  Aluminum,  85.74%;  tin,  12.94%;  silicon,  1.32%;  iron, 
none. 

Aluminum  Alloys  used  in  Automobile  Construction  (Am.  Mach., 
Aug.  22,  1907.) 

(1)  Al    2,  Zn,     1,  T.S.  35,000;  Sp.  gr.  3.1 

(2)  Al  92,  Cu,  8,  T.S.  18,000;  Sp.  gr.  2.84       Ni,  trace 

(3)  Al  83,  Zn,  15,  Cu,  2,  T.S.  23,000;  Sp.  gr.  3.1 

(1)  Unsatisfactory  on  account  of  failures  under  repeated  vibration. 
(2)  Generally  used.  Resists  vibrations  well.  (3)  Used  to  some  extent. 
Many  motor-car  makers  decline  to  use  it  because  of  uncertainty  of  its 
behavior  under  vibration. 

The  Thermit  Process.  —  When  finely  divided  aluminum  is  mixed 
with  a  metallic  oxide  and  ignited  the  aluminum  burns  with  great  rapid- 
ity and  intense  heat,  the  chemical  reaction  being  Al  +  Fe2Oa  =  A^Os 


ALLOYS  OP  MANGANESE  AND  COPPER. 


401 


+  Fe.  The  heat  thus  generated  may  be  used  to  fuse  or  weld  iron  and 
other  metals.  See  the  Thermit  Process,  under  Welding  of  Steel,  page 
488. 

Resistance  of  Aluminum  Alloys  to  Corrosion.  —  J.  W.  Richards, 
Jour.  Frank.  Inst.,  1895,  gives  the  following  table  showing  the  relative 
resistance  to  corrosion  of  aluminum  (99  %  pure)  and  alloys  of  aluminum 
with  different  metals,  when  immersed  in  the  liquids  named.  The 
figures  are  losses  per  day  in  milligrams  per  square  centimeter  of  surface: 


3% 
Caustic 
Potash. 
Cold. 

3% 
Hydro- 
chloric 
Acid. 
Cold. 

Strong 
Nitric 
Acid. 
Cold. 

Strong 
Salt 
Solu- 
tion. 
150°F. 

Strong 
Acetic 
Acid. 
140°  F. 

Car- 
bonic 
Acid. 
Water. 
77°  F. 

3  per  cent  copper  

265.0 

53.3 

36.1 

0.1 

0.4 

0.0 

3  per  cent  German  silver  . 
3  per  cent  nickel  

1534.4 
580.3 

130.6 
180.0 

97.7 
83.0 

0.05 
0.13 

0.6 
0.75 

0.01 
0.04 

2  per  cent  titanium      .    .  . 

73.4 

4.3 

18.6 

0  06 

0  20 

0.0 

99  per  cent  aluminum  .... 

35.6 

5.8 

9.6 

0.04 

0.15 

0.01 

ALLOYS   OF  MANGANESE   AND    COPPER. 

Various  Manganese  Alloys. — E.  H.  Cowles,  in  Trans.  A.  I.  M.  E., 
vol.  xviii,  p.  495,  states  that  as  the  result  of  numerous  experiments  on 
mixtures  of  the  several  metals,  copper,  zinc,  tin,  lead,  aluminum,  iron, 
and  manganese,  and  the  metalloid  silicon,  and  experiments  upon  th£ 
same  in  ascertaining  tensile  strength,  ductility,  color,  etc.,  the  most 
important  determinations  appear  to  be  about  as  follows: 

1.  That  pure  metallic  manganese  exerts  a  bleaching  effect  upon  cop- 
per more  radical  in  its  action  even  than  nickel.    In  other  words,  it  was 
found  that  18  H  %  of  manganese  present  in  copper  produces  as  white  a 
color  in  the  resulting  alloy  as  25%  of  nickel  would  do,  this  being  the 
amount  of  each  required  to  remove  the  last  trace  of  red. 

2.  That  upwards  of  20  %  or  25  %  of  manganese  may  be  added  to  cop- 
per without  reducing  its  ductility,  although  doubling  its  tensile  strength 
and  changing  its  color. 

3.  That  manganese,  copper,  and  zinc,  when  melted  together  and 
poured  into  molds  behave  very  much  like  the  most  "yeasty"  German 
silver,  producing  an  ingot  which  is  a  mass  of  blow-holes,  and  which 
swells  up  above  the  mold  before  cooling. 

4.  That  the  alloy  of  manganese  and  copper  by  itself  is  very  easily 
oxidized. 

5.  That  the  addition  of  1.25%  of  aluminum  to  a  manganese-copper 
alloy  converts  it  from  one  of  the  most  refractory  of  metals  in  the  casting 

Erocess  into  a  metal  of  superior  casting  qualities,  and  the  non-corrodi- 
ility  of  which  is  in  many  instances  greater  than  that  of  either  German 
or  nickel  silver. 

A  "silver-bronze"  alloy  especially  designed  for  rods,  sheets,  and  wire 
has  the  following  composition:  Mn,  18;  Al,  1.20;  Si,  0.5;  Zn,  13;  and  Cu, 
67.5%.  It  has  a  tensile  strength  of  about  57,000  Ibs.  on  small  bars,  and 
20%  elongation.  It  has  been  rolled  into  thin  plate  and  drawn  into  wire 
0.008  inch  in  diameter.  A  test  of  the  electrical  conductivity  of  this 
wire  (of  size  No.  32)  shows  its  resistance  to  be  41.44  times  that  of  pure 
copper.  This  is  far  lower  conductivity  than  that  of  German  silver. 

Manganese  Bronze.  (F.  L.  Garrison,  Jour.  F.  /.,  1891.)  —  This 
alloy  has  been  used  extensively  for  casting  propeller-blades.  Tests  of 
some  made  by  B.  H.  Cramp  &  Co.,  of  Philadelphia,  gave  an  average 
elastic  limit  of  30,000  Ibs.  per  sq,  in.,  tensile  strength  of  about  60,000  Ibs. 
per  sq.  in.  with  an  elongation  of  8%  to  10%  in  sand  castings.  When 
rolled,  the  E.  L.  is  about  80,000  Ibs.  per  sq.  in.,  tensile  strength  95,000  to 
106,000  Ibs.  per  sq.  in.,  with  an  elongation  of  12%  to  15%. 

Compression  tests  made  at  United  States  Na'vy  Department  from  the 
metal  in  the  pouring-gate  of  propeller-hub  of  U.  S.  S.  Maine  gave  in 
two  tests  a  crushing  stress  of  126,450  and  135,750  Ib.  per  sq.  in.  The 
specimens  were  1  inch  high  by  0.7  x  0.7  inch  in  cross-section  =  0.49 
square  inch.  Both  specimens  gave  way  by  shearing,  on  a  plane  making 
an  angle  of  nearly  456  with  the  direction  of  stress. 

A  test  on  a  specimen  1  X  1  X  1  inch  was  made  from  a  piece  of  the 


402 


ALLOYS. 


same  pouring-gate.  "  Under  stress  of  150,000  pounds  it  was  "flattened  to 
0.72  inch  high  by  about  11/4  x  11/4  inches,  but  without  rupture  or  any 
sign  of  distress. 

One  of  the  great  objections  to  the  use  of  manganese  bronze,  or  in  fact 
any  alloy  except  iron  or  steel,  for  the  propellers  of  iron  ships  is  on 
account  of  the  galvanic  action  set  up  between  the  propeller  and  the 
stern-posts.  This  difficulty  has  in  great  measure  been  overcome  by 
putting  strips  of  rolled  zinc  around  the  propeller  apertures  in  the  stern- 
frames. 

The  following  analysis  of  Parsons'  manganese  bronze  No.  2  was  made 
from  a  chip  from  the  propeller  of  Mr.  W.  K.  Vanderbilt's  yacht  Alva. 
Cu,  88.64;  Zn,  1.57;  Sn,  8.70;  Fe,  0.72;  Pb,  0.30;  P,  trace. 

It  will  be  observed  there  is  no  manganese  present  and  the  amount  of 
zinc  is  very  small. 

E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  vol.  xviii,  says:  Manganese  bronze, 
so  called,  is  in  reality  a  manganese  brass,  for  zinc  instead  of  tin  is  the 
chief  element  added  to  the  C9pper.  Mr.  P.  M.  Parsons,  the  proprietor  of 
this  brand  of  metal,  has  claimed  for  it  a  tensile  strength  of  from  24  to 
28  tons  per  sq.  in.  in  small  bars  when  cast  in  sand. 

E.  S.  Sperry,  Am.  Mach.,  Feb.  1,  1906,  gives  the  following  analyses  of 
manganese  bronze: 


Cu. 

Zn. 

Fe. 

Sn. 

Al. 

Mn. 

Pb. 

No.  1    . 

60.27 

37.52 

1.41 

0.75 

0.01 

0.01 

"     2  

56.11 

41.34 

1.30 

0.75 

0.47 

0.01 

0.02 

•••  3.:::      

60.00 

38.00 

1.25 

0.65 

0.10 

'     4  

56.00 

42.38 

1.25 

0.75 

6.50 

0.12 

No.  1  is  Parsons'  alloy  for  sheet,  No.  2  for  sand  casting.     No.  3  is  Mr. 
Sperry's  formula  for  sheet,  and  No.  4  his  formula  for  sand  castings. 


alloy  is  made  by  melting  wrought  iron,  18  Ibs.;  ferro-manganese 
(80  Fe,  20  Mn),  4  Ibs.;  tin,  10  Ibs.  The  iron  and  ferro-manganese  are 
first  melted  and  .then  the  tin  is  added.  In  making  the  bronzes  about 
15  Ibs.  of  the  copper  is  first  melted  under  charcoal,  the  steel  alloy  is 
added,  melted  and  stirred,  then  the  aluminum  is  added,  melted  and 
stirred,  then  the  rest  of  the  copper  is  added,  and  finally  the  zinc.  The 
only  function  of  the  manganese  is  to  act  as  a  carrier  to  the  i?on,  which 
is  difficult  to  alloy  with  copper  without  such  carrier.  The  iron  is 
needed  to  give  a  high  elastic  limit.  Green  sand  castings  of  No.  4  fre- 
quently give  results  as  high  as  the  following:  T.  S.,  70,000;  E.  L., 
30,000  Ibs.  per  sq.  in.;  elongation  in  6  ins.,  18%;  reduction  of  area, 
26%. 

Magnetic  Alloys  of  Non-Magnetic  Metals.  (El.  World,  April  15, 
1905;  Electrot.-Zeit.  Mar.  2,  1905.)  —  Dr.  Heusler  has  discovered  that 
alloys  of  manganese,  aluminum,  and  copper  are  strongly  magnetic.  The 
best  results  have  been  obtained  when  the  Mn  and  Al  are  in  the  proportions 
of  their  respective  atomic  weights,  55  and  27.1.  Two  such  alloys  are 
described  (1)  Mn,  26.8;  Al,  13.2;  Cu,  60.  (2)  Mn,  20.1;  Al,  9.9:  Cu,  70, 
with  1%  Pb  added.  The  first  was  too  brittle  to  be  workable.  The 
second  was  machined  without  difficulty.  These  alloys  have  as  yet  no 
commercial  importance,  as  they  are  far  inferior  magnetically  (at  most 
1  to  4)  to  iron. 

GERMAN-SILVER  AND   OTHER  NICKEL  ALLOYS. 

German  Silver.  —  The  composition  of  German  silver  is  a  very  un- 
certain thing  and  depends  largely,  on  the  honesty  of  the  manufacturer 
and  the  price  the  purchaser  is  willing  to  pay.  It  is  composed  of  copper, 
zinc,  and  nickel  in  varying  proportions.  The  best  varieties  contain 
from  18%  to  25%  of  nickel  and  from  20%  to  30%  of  zinc,  the  remainder 
being  copper.  The  more  expensive  nickel  silver  contains  from  25%  to 
33%  of  nickel  and  from  75%  to  66%  of  copper.  The  nickel  is  used  as  a 
whitening  element;  it  also  strengthens  the  alloy  and  renders  it  harder 
and  more  non-corrodible  than  the  brass  made  without  it,  of  copper  and 


ALLOYS   OF  NICKEL. 


403 


zinc.     Of  all  troublesome  alloys  to  handle  in  the  foundry  or  rolling-mill, 
German  silver  is  the  worst.      It  is  unmanageable  and  refractory  at  every 
step  in  its  transition  from  the  crude  elements  into  rods,  sheets,  or  wire. 
(E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  xviii,  p.  494.) 
The  following  list  of  copper-nickel  alloys  is  from  various  sources: 

|  Copper.  |  Nickel.    |      Tin.      |     Zinc. 


German  silver  

51  6 

25  8 

22.6 

50.2 

14.8 

3.1 

31.9 

»«           it 

51   1 

13  8 

3.2 

31.9 

it           it 

52  to  55 

18  to  25 

20  to  30 

Nickel         "                   

75  to  66 

25  to  33 

Chinese  packfong 

40  4 

31  6 

6  5  parts 

tutenag            

8 

3 

6.5     " 

German  silver 

2 

1 

1 

"      (cheaper)  

8 
8 

2 
3 

3.5     " 
3.5    " 

Nickel-copper  Alloys. — (F.  L.  Sperry,  A.  I.  M.  E.,  1895.) 

Copper.  |   Nickel.    |     Zinc.      ]     Iron.     |  Cobalt. 


Berlin  :  

52  to  63 

22  to  6 

26  to  31 

French,  tableware  

50 

18.  7  to  20 

31.3  to  30 

65.4 

16.8 

13.4 

3.4 

Christofle               

50 

50 

Austrian,  tableware  

50  to  60 

25  to  20 

25  to  20 

English,  Sheffield  

45.7  to  60 

31  6  to  15 

25.4  to  17 

0  to  2  6 

0  to  3  4 

American,  castings  

52.5 

17.7 

28  8 

bearings  

50 

25 

25 

"           one-cent  coin 

88 

12 

Nickel  coins  

75 

25 

A  refined  copper-nickel  alloy  containing  50%  copper  and  49%  nickel, 
with  very  small  amounts  of  iron,  silicon  and  carbon,  is  produced  direct 
from  Bessemer  matte  in  the  Sudbury  (Canada)  Nickel  Works.  German- 
silver  manufacturers  purchase  a  ready-made  alloy,  which  melts  at  a 
low  heat  and  requires  only  the  addition  of  zinc,  instead  of  buying  the 
nickel  and  copper  separately.  This  alloy,  "50-50"  as  it  is  called,  is 
almost  indistinguishable  from  pure  nickel.  Its  cost  is  less  than  nickel, 
its  melting-point  much  lower,  it  can  be  cast  solid  in  any  form  desired, 
and  furnishes  a  casting  which  works  easily  in  the  lathe  or  planer,  yield- 
ing a  silvery- white  surface  unchanged  by  air  or  moisture.  For  bullet 
casings  now  used  in  various  British  and  Continental  rifles,  a  special  alloy 
of  80%  copper  and  20%  nickel  is  made. 

Monel  Metal.  —  An  alloy  of  about  72%  Ni,  1.5  Fe,  26.5  Cu,  made  from 
the  Canadian  copper-nickel  ores,  is  described  in  the  Metal  Worker,  Oct.  10, 
1908.  It  has  many  valuable  properties  when  rolled  into  sheets,  making 
it  especially  suitable  for  rooting.  It  is  ductile  and  flexible,  is  easily 
soldered,  has  a  high  resistance  to  corrosion,  and  a  relatively  small  expan- 
sion and  contraction  under  temperature  changes.  The  tensile  strength 
in  castings  is  from  70,000  to  80,000  Ibs.  per  sq.  in.,  and  in  rolled  sheets  as 
high  as  108,000  Ibs. 

The  Supplee-Biddle  Hardware  Co.'s  Bulletin,  Jan.,  1915,  gives  the 
following  results  of  tests  of  bars  of  monel  metal.  The  test  pieces  were 
0.505  in.  diarn. 

Tensile 
Strength 

Bar  from  1  in.  sq.  casting 79,600 

Hot  rolled  1-in.  rod 88,150 


Elong.  Red.  o 

in  2  in.  Area 

49.2%  39.3% 

36.0  67.9 


El. 

Limit. 
31,800 
58,000 

The  strength  of  monel  metal  wire,  used  for  window  screen  cloth,  is 
given  as  90,000  Ib.  per  sq.  in.,  and  its  analysis  68%  Ni,  28%  Cu.,  2.5% 
Fe,  1.5%  Mn. 

Constantan  is  an  alloy  containing  about  60%  copper  and  40%  nickel, 
which  is  much  used  for  resistance  wire  in  electrical  instruments.  Its 
electrical  resistance  is  about  twenty-eight  to  thirty  times  that  of  copper, 
and  it  possesses  a  very  low  temperature  coefficient, --^approximately 


404 


ALLOYS. 


.00003.    This  same  material  is  also  much  used  to  form  one  element  of 
base-metal  thermo-couples. 

Manganin,  Cu  Mn  Ni,  high  resistance  alloy.  See  Electrical  Resist- 
ance under  Electrical  Engineering. 

ALLOYS   OF   BISMUTH. 

By  adding  a  small  amount  of  bismuth  to  lead  the  latter  may  be 
hardened  and  toughened.  An  alloy  consisting  of  three  parts  of  lead 
and  two  of  bismuth  has  ten  times  the  hardness  and  twenty  times  the 
tenacity  of  lead.  The  alloys  of  bismuth  with  both  tin  and  lead  are 
extremely  fusible,  and  take  fine  impressions  of  casts  and  molds.  An 
alloy  of  one  part  Bi,  two  parts  Sn,  and  one  part  Pb  is  used  by  pewter- 
workers  as  a  soft  solder,  and  by  soap-makers  for  molds.  An  alloy  of  five 
parts  Bi,  two  parts  Sn,  and  three  parts  Pb  imelts  at  199°  F.,  and  is 
S9mewhat  used  for  stereotyping,  and  for  metallic  writing-pencils.  Thorpe 
gives  the  following  proportions  for  the  better-known  fusible  metals: 


Name  of  Alloy. 

Bis- 
muth. 

Lead. 

Tin. 

Cad- 
mium. 

Mer- 
cury. 

Melting- 
point. 

Newton's  

50 

31.25 

18.75 

202°  F 

Rose's  

50 

28.10 

24  10 

203°  ' 

D'Arcet's  .  .   

50 

25.00 

25.00 

201°  ' 

D'  Arcet's  with  mercury 

50 

25.00 

25.00 

250.0 

113°  ' 

Wood's 

50 

25  00 

12  50 

12  50 

149°  ' 

Lipowitz's 

50 

26  90 

12  78 

10  40 

149°  ' 

Guthrie's  "  Eutectic  ". 

50 

20.55 

21.10 

14.03 

"Very  low.'* 

The  action  of  heat  upon  some  of  these  alloys  is  remarkable.  Thus, 
Lipowitz's  alloy,  which  solidifies  at  149°  F.,  cpntracts  very  rapidly  at 
first,  as  it  cools  from  this  point.  As  the  cooling  goes  on  the  contrac- 
tion becomes  slower  and  slower,  until  the  temperature  falls  to  101.3° 
F.  From  this  point  the  alloy  expands  as  it  cools,  until  the  temperature 
falls  to  about  77°  F.,  after  which  it  again  contracts,  so  that  at  32°  F. 
a  bar  of  the  alloy  has  the  same  length  as  at  115°  F. 

Alloys  of  bismuth  have  been  used  for  making  fusible  plugs  for  boilers, 
but  it  is  found  that  they  are  altered  by  the  continued  action  of  heat, 
so  that  one  cannot  rely  upon  them  to  melt  at  the  proper  temperature. 
Pure  Banca  tin  is  used  by  the  U.  S.  Government  for  fusible  plugs. 

FUSIBLE   ALLOYS. 

(From  various   sources.     Many   of    the    figures    are   probably   very 
inaccurate.) 

Sir  Isaac  Newton's,  bismuth  5,  lead  3,  tin  2,  melts  at 212°  F. 

Rose's,  bismuth  2,  lead  1,  tin  1,  melts  at 200  " 

Wood's,  cadmium  1,  bismuth  4,  lead  2,  tin  1,  melts  at 165  '* 

Guthrie's,  cadmium  13.29,  bismuth  47.38,  lead  19.36,  tin  19.97, 

melts  at 160  " 

Lead  1,  tin  1,  bismuth  1,  cadmium  1,  melts  at 155  '* 

Lead  3,  tin  5,  bismuth  8,  melts  at 208  " 

Lead  1,  tin  3,  bismuth  5,  melts  at 212  " 

Lead  1,  tin  4,  bismuth  5,  melts  at 240  " 

Tin  1,  bismuth  1,  melts  at 286  " 

Lead  2,  tin  3,  melts  at 334  to  367  " 

Tin  2,  bismuth  1,  melts  at 336  " 

Lead  1,  tin  2,  melts  at 340  to  360  " 

Tin  8,  bismuth  1,  melts  at 392  " 

Lead  2,  tin  1,  melts  at 440  to  475  " 

Lead  1,  tin  1,  melts  at 370  to  400  " 

Lead  1 ,  tin  3,  melts  at 356  to  383  " 

Tin  3,  bismuth  1,  melts  at 392  " 

Lead  1,  bismuth  1,  melts  at 257  " 

Lead  1,  tin  1,  bismuth  4,  melts  at 201  " 

Lead  5,  tin  3,  bismuth  8,  melts  at 202  " 

Tin  3,  Dismuth  5,  melts  at 202  M 


BEARING  METAL  ALLOYS. 


405 


BEARING-METAL   ALLOYS. 

(C.  B.  Dudley,  Jour.  F.  /.,  Feb.  and  March,  1892.) 
Alloys  are  used  as  bearings  in  place  of  wrought  iron,  cast  Iron,  or 
steel,  partly  because  wear  and  friction  are  believed  to  be  more  rapid 
when  two  metals  of  the  same  kind  work  together,  partly  because  the 
soft  metals  are  more  easily  worked  and  got  into  proper  shape,  and  partly 
because  it  is  desirable  to  use  a  soft  metal  which  will  take  the  wear 
rather  than  a  hard  metal,  which  will  wear  the  journal  more  rapidly. 

A  good  bearing-metal  must  have  five  characteristics:  (1)  It  must  be 
strong  enough  to  carry  the  load  without  distortion.  Pressures  on  car- 
journals  are  frequently  as  high  as  350  to  400  Ib.  per  square  inch. 

(2)  A  good  bearing-metal  should  not  heat  readily.     The  old  copper- 
tin  bearing,  made  of  seven  parts  copper  to  one  part  tin,  is  more  apt  to 
heat  than  some  other  alloys.     In  general,  research  seems  to  show  that 
the  harder  the  bearing-metal,  the  more  likely  it  is  to  heat. 

(3)  Good  bearing-metal  should  work  well  in  the  foundry.     Oxidation 
while  melting  causes  spongy  castings.     It  can  be  prevented  by  a  liberal 
use  of  powdered  charcoal  while  melting.     The  addition  of  1%  to  2%  of 
zinc  or  a  small  amount  of  phosphorus  greatly  aids  in  the  production  of 
sound    castings.      This   is   a  principal    element  of  value  in  phosphor- 
bronze. 

(4)  Good  bearing-metals  should  show  small  friction.     It  is  true  that 
friction  is  almost  wholly  a  question  of  the  lubricant  used ;   but  the  metal 
of  the  bearing  has  certainly  some  influence. 

(5)  Other  things  being  equal,  the  best  bearing-metal  is  that  which 
wears  slowest. 

The  principal  constituents  of  bearing-metal  alloys  are  copper,  tin, 
lead,  zinc,  antimony,  iron,  and  aluminum.  The  following  table  gives 
the  constituents  of  most  of  the  prominent  bearing-metals  as  analyzed  at 
the  Pennsylvania  Railroad  laboratory  at  Altoona. 

Analyses  of  Bearing- metal  Alloys. 


Metal. 

Copper. 

Tin. 

Lead. 

Zinc. 

Anti- 
mony. 

Iron. 

Camelia  metal          

70.20 
1.60 

4.25 
98.13 

14.75 

10.20 

0.55 
trace 

Anti-friction  metal 

White  metal             

87.92 
84.87 
1.15 
67.73 
80.69 

12  Of 

Car-brass  linintr 

trace 
9.91 
14.38 

"85J7 

15.10 

Salgee  anti-friction  
Graphite  bearing-metal  .  .  . 

4.01 

16.73 
18  83 

?    (I) 

Antimonial  lead  

75.47 
77.83 
92.39 
trace 

9.72 
9.60 
2.37 

14.57 
12.40 
5.10 
83.55 

78.44 
0.31 
15.06 
12.52 

•     (2) 

Cornish  bronze  

trace 

trace(3) 
0.07 
trace(4> 

0.65 
0.11 

Delta  metal    

*  Magnolia,  metal 

trace 

0.98 
38.40 

16.45 
19.60 

American    anti-friction 
metal  

I'obin  bronze      

59.66 
75.80 
76.41 
90.52 
81.24 

2.16 
9.20 
10.60 
9.58 
10.98 

Granev  bronze 

Damascus  bronze  

Manganese  bronze 

..   (5) 

Ajax  metal                

7.27 
88  32 

(6) 

Anti-friction  metal 

11.93 

Harrington  bronze  

55.73 

0.97 

42.67 
trace 

"J4J8" 
6.03 

0.68 
0.61 

Car-box  metal 

84.33 
94.40 

Hard  lead     

Phosphor-bronze 

79.17 
76.80 

10.22 
8.00 

9.61 
15.00 

...(7) 

Ex.  B.  metal  

<e{ 

Other  constituents: 

(1)  No  graphite. 

(2)  Possible  trace  of  carbon. 

(3)  Trace  of  phosphorus. 

(4)  Possible  trace  of  bismuth. 

*  Dr.  H.  C.  Torrey  says  this  analy; 
metal  always  contains  tin. 


(5)  No  manganese. 

[6)  Phosphorus  or  arsenic,  0.37. 
7)   Phosphorus,  0.94. 

Phosphorus,  0.20. 
is  erroneous  and  that  Magnolia 


406  ALLOYS. 

As  an  example  of  the  influence  of  minute  changes  in  an  alloy,  the  Har- 
rington bronze,  which  consists  of  a  minute  proportion  of  iron  in  a  cop- 
per-zinc alloy,  showed  after  rolling  a  tensile  strength  of  75,000  Ib.  and 
20%  elongation  in  2  inches. 

In  experimenting  on  this  subject  on  the  Pennsylvania  Railroad,  a 
certain  number  of  the  bearings  were  made  of  a  standard  bearing-metal, 
and  the  same  number  were  made  of  the  metal  to  be  tested.  These 
bearings  were  placed  on  opposite  ends  of  the  same  axle,  one  side  of  the 
car  haying  the  standard  bearings,  the  other  the  experimental.  Before 
going  into  service  the  bearings  were  carefully  weighed,  and  after  a 
sufficient  time  they  were  again  weighed.  The  standard  bearing-metal 
used  is  the  "S  bearing-metal"  of  the  Phosphor-Bronze  Smelting  Co. 
It  contains  about  79.70%  copper,  9.50%  lead,  10%  tin,  and  0.80%  phos- 
phorus. A  large  number  of  experiments  have  shown  that  the.  loss  of 
weight  of  a  bearing  of  this  metal  is  1  Jb.  to  each  18,000  to  25,000  miles 
traveled.  Besides  the  measurement  of  wear,  observations  were  made 
on  the  frequency  of  "hot  boxes"  with  the  different  metals. 

The  results  of  the  tests  for  wear,  so  far  as  given,  are  condensed  into 
the  following  table: 

Composition.  Rate 

Metal.  , * x        of 

Copper.     Tin.        Lead.     Phos.    Arsenic.  Wear. 

Standard 79.70      10.00        9.50        0.80     100 

Copper-tin 87.50      12.50       148 

Same,  second  experiment    

Same,  third  experiment 147 

Arsenic-bronze 89.20      10.00       0.80  142 

Arsenic-bronze 79.20      10.00        7.00       0.80  115 

Arsenic-bronze 79.70      10.00        9.50       0.80  101 

"K"  bronze 77.00      10.50      12.50       92 

Same,  second  experiment    92.7 

Alloy  "B" 77.00        8.00      15.00       86.5 

The  old  copper-tin  alloy  of  7  to  1  has  repeatedly  proved  its  inferiority 
to  the  phospnor-bronze  metal.  Many  more  of  the  copper-tin  bearings 
heated  than  of  the  phosphor-bronze.  The  showing  of  these  tests  was  so 
satisfactory  that  phosphor-bronze  was  adopted  as  the  standard  bearing- 
metal  of  the  Pennsylvania  R.R.,  and  was  used  for  a  long  time. 

The  experiments,  however,  were  continued.  It  was  found  that  arsenic 
practically  takes  the  place  of  phosphorus  in  a  copper-tin  alloy,  and  three 
tests  were  made  with  arsenic-bronzes  as  noted  above.  As  the  propor- 
tion to  lead  is  increased  to  correspond  with  the  standard,  the  durability 
increases  as  well.  In  view  of  these  results  the  "K"  bronze  was  tried,  in 
which  neither  phosphorus  nor  arsenic  were  used,  and  in  which  the  lead 
was  increased  above  the  proportion  in  the  standard  phosphor-bronze. 
The  result  was  that  the  metal  wore  7.30%  slower  than  the  phosphor- 
bronze.  No  trouble  from  heating  was  experienced  .with  the  "K"  bronze 
more  than  with  the  standard.  Dr.  Dudley  continues: 

At  about  this  time  we  began  to  find  evidences  that  wear  of  bearing- 
metal  alloys  variel  in  accordance  with  the  following  law:  "That  alloy 
which  has  the  greatest  power  of  distortion  without  rupture  (resilience), 
will  best  resist  wear."  It  was  now  attempted  to  design  an  alloy  in 
accordance  with  this  law,  taking  first  the  proportions  of  copper  and  tin. 
01/2  parts  copper  to  1  of  in  was  settled  on  by  experiment  as  the  standard, 
although  some  evidence  since  that  time  tends  to  show  that  12  or  possi- 
bly 15  parts  copper  to  1  of  tin  might  have  been  better.  The  influence  of 
lead  on  this  copper-tin  alloy  seems  to  be  much  the  same  as  a  still  further 
diminution  of  tin.  However,  the  tendency  9f  the  metal  to  yield  under 
pressure  increases  as  the  amount  of  tin  is  diminished,  and  the  amount 
of  the  lead  increased,  so  a  limit  is  set  to  the  use  of  lead.  A  certain 
amount  of  ti  i  is  also  necessary  to  keep  the  lead  alloyed  with  the  copper. 

Bearings  were  cast  of  the  metal  noted  in  the  table  as  alloy  "B,"  and  it 
wore  13.5%  slower  than  the  standard  phosphor-bronze.  This  metal  is 
now  the  standard  bearing-metal  of  the  Pennsylvania  Railroad,  being 
slightly  changed  in  composition  to  allow  tne  use  of  phosphor-bronze 
scrap.  The  formula  adopted  is:  Copper,  105  Ibs.:  phosphor-bronze, 
60  Ibs.:  tin.  92/4  Ibs.:  lead,  251/4  Ibs.  By  using  ordinary  care  in  the 
foundry,  keeping  the  metal  well  covered  with  charcoal  during  the  meltr 


ALLOYS   CONTAINING   ANTIMONY. 


407 


Ing,  no  trouble  Is  found  in  casting  good  bearings  with  this  metal.  The 
copper  and  the  phosphor-bronze  can  be  put  in  the  pot  before  putting  it 
in  the  melting-hole.  The  tin  and  lead  should  be  added  after  the  pot  is 
taken  from  the  fire. 

It  is  not  known  whether  the  use  of  a  little  zinc,  or  possibly  some  other 
combination,  might  not  give  still  better  results.  For  the  present,  how- 
ever, this  alloy  is  considered  to  fulfill  the  various  conditions  required  for 
good  bearing-metal  better  than  any  other  alloy.  The  phosphor-bronze 
had  an  ultimate  tensile  strength  of  30,000  lb.,  with  6%  elongation, 
whereas  the  alloy  "B"  had  24,000  lb.  T.  S.  and  11%  elongation. 

Bearing  Metal  Practice,  1907.  (G.  H.  Clamer,  Proc.  A.  S.  T.  M.,  vii, 
302,  discusses  the  history  of  bearing  metal  practice  since  the  date  o! 
Dr.  Dudley's  paper  quoted  above.  It  was  found  that  tin  could  be  dimin- 
ished and  lead  inceased  far  beyond  the  figures  formerly  used,  and  a  satis- 
factory bearing  metal  was  made  with  65%  copper,  5%  tin  and  30%  lead. 
This  alloy  is  largely  sold  under  the  name  of  "plastic  bronze."  It  has  a 
compressiye  strength  of  about  15,000  Ibs.  per  sq.  in.,  and  is  found  to 
operate  without  distortion  in  the  bearings  of  the  heaviest  Ioc9motives, 
not  only  for  driving  brasses,  but  also  for  rod  brasses  and  bushings,  and 
for  bearings  of  cars  of  100,000  Ibs.  capacity,  the  heaviest  cars  now  in 
service.  Specifications  of  different  railroads  cover  bearing  alloys  with 
tin  from  8  to  10-%  and  lead  from  10  to  15%.  There  is  also  used  a  vast 
quantity  of  bearings  made  from  scrap.  These  contain  copper,  65  to  75%, 
tin,  2  to  8%,  lead,  10  to  18%,  zinc,  5  to  20%,  and  they  constitute  from 
50  to  75  per  cent  of  the  car  bearings  now  in  use. 

White  Metal  for  Engine  Bearings.  (Report  of  a  British  Naval 
Committee,  Eng'g,  July  18,  1902.)  —  For  lining  bearings,  crankpin 
bushes,  and  other  parts  exclusive  of  cross-head  bushes:  Tin  12,  copper  1, 
antimony  1.  Melt  6  tin  1  copper,  and  6  tin  1  antimony  separately  and 
mix  the  two  together.  For  cross-head  bushes  a  harder  alloy,  viz.,  85% 
tin,  5%  copper,  10%  antimony,  has  given  good  results. 

(For  other  bearing-metals,  see  "Alloys  containing  Antimony,"  below.) 

ALLOYS    CONTAINING   ANTIMONY. 

VARIOUS  ANALYSES  OF  BABBITT  METAL  AND  OTHER  ALLOYS  CONTAIN- 
ING ANTIMONY. 


Tin. 


[Copper.[  Antimony.  ,|      Zinc.     |     Lead.     |  Bismuth. 


Babbitt  metal 
for  light  duty 
Harder  Babbitt 
for  bearings  * 
Britannia,  . 

50 
-89.3 
96 
=  88.9 
85  7 

1.8 
4 
3.7 
1.0 

5  parts 
8.9  perct. 
8  parts 
7.4per  ct. 
10.1 
16.  2 
16 
25.5 
62 
13 
7.1 
10 

2.9 
1.9 

.     81  9 

«e 

...81.0 

2 
4 
10 
1.5 
1.8 
5 



« 

70  5 

•  4            ' 

22 

6 

'"46!6" 

........ 
omotives. 

"  Babbitt  "  

...45.5 

Plate  pewter 

89.3 

White  metal  

...85 

Bearings  on  Ger.  loc 

*  It  is  mixed  as  follows:  Twelve  parts  of  copper  are  first  melted  and 
then  36  parts  of  tin  are  added;  24  parts  of  antimony  are  put  in,  and 
then  36  parts  of  tin,  the  temperature  being  lowered  as  soon  as  the 
copper  is  melted  in  order  not  to  oxidize  the  tin  and  antimony,  the  sur- 
face of  the  bath  being  protected  from  contact  with  the  air.  The  alloy 
thus  made  is  subsequently  remelted  in  the  proportion  of  50  parts  of 
alloy  to  100  tin.  (Joshua  Rose.) 

White-metal  Alloys.  — The  following  alloys  are  used  as  lining  metals 
by  the  Eastern  Railroad  of  France  (1890): 


Number. 

Lead. 

Antimony. 

Tin. 

Copper. 

1 

65 

25 

,0 

10 

2  

0 

11.12 

83.33 

5.55 

3 

70 

20 

10 

0 

4  

80 

8 

12 

0 

No.  1  is  used  for  lining  cross-head  slides,  rod-brasses  and  axle-bear- 
ings; No.  2  for  lining  axle-bearings  and  connecting-rod  brasses  of  heavy 


408 


ALLOYS. 


engines;    No.  3  for  lining  eccentric  straps  and  for  bronze  slide- valves'; 
and  No.  4  for  metallic  rod-packing. 

Some  of  the  best-known  white-metal  alloys  are  the  following  (Circular 
of  Hoveler  &  Dieckhaus,  London,  1893): 


Tin. 

Anti- 
mony. 

Lead. 

Copper. 

Zinc. 

1.   Parsons' 

86 

1 

2 

2 

27 

2.  Richards'  

70 

15 

101/2 

41/2 

0 

3.  Babbitt's                 .   . 

55 

18 

231/2 

31/2 

0 

4.   Fenton's  

16 

0 

0 

79 

5.   French  Navy  
6.  German  Navy  

^ 

0 

7V2 

7 
0 

7 

7V2 

871/3 
0 

"There  are  engineers  who  object  to  white  metal  containing  lead  or 
zinc.  This  is,  however,  a  prejudice  quite  unfounded,  inasmuch  as  lead 
and  zinc  often  have  properties  of  great  use  in  white  alloys. 

It  is  a  further  fact  that  an  "easy  liquid"  alloy  must  not  contain  more 
than  18%  of  antimony,  which  is  an  invaluable  ingredient  of  white  metal 
for  improving  its  hardness;  but  in  no  case  must  it  exceed  that  margin, 
as  this  would  reduce  the  plasticity  of  the  compound  and  make  it 
brittle. 

Hardest  tin-lead  alloy:  6  tin,  4  lead.  Hardest  of  all  tin  alloys  (?)  :  74 
tin,  18  antimony,  8  copper. 

Alloy  for  thin  open-work,  ornamental  castings:  Lead  2,  antimony  1. 
White  metal  for  patterns:  Lead  10,  bismuth  6,  antimony  2,  common 
brass  8,  tin  10. 

Type-metal  is  made  of  various  proportions  of  lead  and  antimony, 
from  17%  to  20%  antimony  according  to  the  hardness  desired. 

Babbitt  Metals.     (C.  R.  Tompkins,  Mechanical  News,  Jan.,  1891.) 

The  practice  of  lining  journal-boxes  with  a  metal  that  is  sufficiently 
fusible  to  be  melted  in  a  common  ladle  is  not  always  so  much  for  the 
purpose  ot  securing  anti-friction  properties  as  for  the  convenience  and 
cheapness  of  forming  a  perfect  bearing  in  line  with  the  shaft  without 
the  necessity  of  boring  them.  Itoxes  that  are  bored,  no  matter  how 
accurate,  require  great  care  in  fitting  and  attaching  them  to  the  frame 
or  other  parts  of  a  machine. 

It  is  not  good  practice,  however,  to  use  the  shaft  for  the  purpose  of 
casting  the  bearings,  especially  if  the  shaft  be  steel,  for  the  reason  that 
the  hot  metal   is  apt  to   spring  it;   the  better  plan  i 
of  the  same  size  or  a  trifle  larger  for  this  purpose. 


,  , 

the  hot  metal   is  apt  to   spring  it;   the  better  plan  is  to  use  a  mandrel 
of  the  same  size  or  a  trifle  larger  for  this  purpose.     For  slow-running 
journals    where  the  load  is  moderate,   almost  any  metal  that  may  be 
' 


conveniently  'melted  and  will  run  free  will  answer  the  purpose.  For 
wearing  properties,  with  a  moderate  speed,  there  is  probably  nothing 
superior  to  pure  zinc,  but  when  not  combined  with  some  other  metal  it 
shrinks  so  much  in  cooling  that  it  cannot  be  held  firmly  in  the  recess, 
and  soon  works  loose;  and  it  lacks  those  anti-friction  properties  which 
are  necessary  in  order  to  stand  high  speed. 

For  line-shafting,  and  all  work  where  the  speed  is  not  over  300  or  400 
r  p  m  an  alloy  of  8  parts  zinc  and  2  parts  block-tin  will  not  only  wear 
longer  'than  any  composition  of  this  class,  but  will  successfully  resist  a 
heavy  load  The  tin  counteracts  the  shrinkage,  so  that  the  metal,  if  not 
overheated,  will  firmly  adhere  to  the  box  until  it  is  worn  out.  But  this 
mixture  does  not  possess  sufficient  anti-friction  properties  to  warrant  its 
use  in  fast-running  journals. 

Among  all  the  soft  metals  in  use  there  are  none  that  possess  greater 
anti-friction  properties  than  pure  lead;  but  lead  alone  is  impracticable, 
for  it  is  so  soft  that  it  cannot  be  retained  in  the  recess.  But  when  by 
any  process  lead  can  be  sufficiently  hardened  to  be  retained  in  the  boxes 
without  materially  injuring  its  anti-friction  properties,  there  is  no  metal 
that  will  wear  longer  in  light  fast-running  journals.  With  most  of  the 
best  and  most  popular  anti-friction  metals  in  use  and  sold  under  the 
name  of  the  Babbitt  metal,  the  basis  is  lead. 

Lead  and  antimony  have  the  property  of  combining  with  each  other 
in  all  proportions  without  impairing  the  anti-fnction  properties  of  either. 
The  antimony  hardens  the  lead,  and  when  mixed  in  the  proportion  of  80 


SOLDERS. 


409 


parts  lead  by  weight  with  20  parts  antimony,  no  other  known  compo- 
sition of  metals  possesses  greater  anti-friction  or  wearing  properties,  or 
will  stand  a  higher  speed  without  heat  or  abrasion.  It  runs  free  in  its 
melted  state,  has  no  shrinkage,  and  is  better  adapted  to  light  high- 
speed machinery  than  any  other  known  metal.  Care,  however,  should  be 
manifested  in  using  it,  and  it  should  never  be  heated  beyond  a  temper- 
ature that  will  scorch  a  dry  pine  stick. 

Many  different  compositions  are  sold  under  the  name  of  Babbitt 
metal.  Some  are  good,  but  more  are  worthless;  while  but  very  little 
genuine  Babbitt  metal  is  sold  that  is  made  strictly  according  to  the 
original  formula.  Most  of  the  metals  sold  under  that  name  are  the 
refuse  of  type-foundries  and  other  smelting- works,  melted  and  cast  into 
fancy  ingots  with  special  brands,  and  sold  under  the  name  of  Babbitt 
metal. 

I  It  is  difficult  at  the  present  time  to  determine  the  exact  formulae 
used  by  the  original  Babbitt  the  inventor  of  the  recessed  box,  as  a  num- 
ber of  different  formulae  are  given  for  that  composition.  Tin,  copper, 
and  antimony  were  the  ingredients,  and  from  the  best  sources  of  in- 
formation the  original  proportions  were  as  follows : 

Another  writer  gives: 
83.3% 
8.3% 
8.3% 


50  parts  tin =  89.3% 

2  parts  copper =    3.6% 

4  parts  antimony =    7.1  % 


The  copper  was  first  melted,  and  the  antimony  added  first  and  then 
about  ten  or  fifteen  pounds  of  tin,  the  whole  kept  at  a  dull-red  heat  and 
constantly  stirred  until  the  metals  were  thoroughly  incorporated,  after 
which  the  balance  of  the  tin  was  added,  and  after  being  thoroughly 
stirred  again  it  was  then  cast  into  ingots.  When  the  copper  is  thoroughly 
melted,  and  before  the  antimony  is  added,  a  handful  of  powdered  char- 
coal should  be  thrown  into  the  crucible  to  form  a  flux,  in  order  to  exclude 
the  air  and  prevent  the  antimony  from  vaporizing;  otherwise  much  of  it 
will  escape  in  the  form  of  a  vapor  and  consequently  be  wasted.  This 
metal,  when  carefully  prepared,  is  probably  one  of  the  best  metals  in  use 
for  lining  boxes  that  are  subjected  to  a  heavy  weight  and  wear;  but  for 
light  fast-running  journals  the  copper  renders  it  more  susceptible  to 
friction,  and  it  is  more  liable  to  heat  than  the  metal  composed  of  lead  and 
antimony  in  the  proportions  just  given. 


SOLDERS. 

Common  solders,  equal  parts  tin  and  lead;  fine  solder,  2  tin  to  1  lead; 
cheap  solder,  2  lead,  1  tin. 

Fusing-point  of  tin-lead  alloys  (many  figures  probably  inaccurate). 


Tin   1  to  lead  25 558°  F. 


10. 
5. 
3. 
2. 
1. 


.541 
.511 
.482 
.441 
.370 


Tin    H/2  to  lead  1 334°  F. 


.340 
.356 
.365 
.378 
.381 


The  melting  point  of  the  tin-lead  alloys  decreases  almost  proportionately 
to  the  increase  of  tin,  from  619°F,  the  melting  point  of  pure  lead,  to  356°F 
*  when  the  alloy  contains  68%  of  tin,  and  then  increases  to  448°F.,  the  melt- 
ing point  of  pure  tin.  Alloys  on  either  side  of  the  68%  mixture  begin  to 
soften  materially  at  356°F,  because  at  that  temperature  the  eutectic  alloy 
melts  and  permits  the  whole  alloy  to  soften.  (Dr.  J.  A.  Mathews.) 

Common  pewter  contains  4  lead  to  1  tin. 

The  relative  hardness  of  the  various  tin  and  lead  solders  has  been 
determined  by  BrineU's  method.  The  results  are  as  follows: 


%  Tin  0  10  20  30  40 

Hardness       3.90       10.10       12.16       14.46       15.76 


70  Tin  66 

iardness     16,66 


67 
15.40 


14,58 


70 
15.84 


80 
15.20 


50 
14.90 

90 
13.25 


60 
14.58 

100 
4.14 


410 


ROPES   AND   CABLES. 


The  hardest  solder  is  the  one  composed  of  2  parts  of  tin  and  1  part  of 
lead.  It  is  the  eutectic  alloy,  or  the  one  with  the  lowest  melting  point  c* 
all  the  mixtures.  —  Mechanical  World. 

Gold  solder:  14  parts  gold,  6  silver,  4  copper.  Gold  solder  for  14-carat 
gold;  25  parts  gold,  25  silver,  121/2  brass,  1  zinc. 

Silver  solder:  Yellow  brass  70  parts,  zinc  7,  tin  111/2.  Another:  Silver 
145  parts,  brass  (3  copper,  1  zinc)  73,  zinc  4. 

German-silver  solder:  Copper  38,  zinc  54,  nickel  8. 

Novel's  solders  for  aluminum: 


Tin     100  parts,    lead  5; 
100      "        zinc  5; 


1000 
1000 


copper  10  to  15; 
nickel  10  to  15; 


melts  at  536°  to  572°  F. 

536  to  612 

662  to  842 

662  to  842 


See  also  p.  383. 

Novel's  solder  for  aluminum  bronze:  Tin,  900  parts,  copper  100.  bis- 
muth 2  to  3.  It  is  claimed  that  this  solder  is  also  suitable  for  joining 
aluminum  to  copper,  brass,  zinc,  iron  or  nickel. 


(A.  S, 


ROPES  AND  CABLES. 

STRENGTH  OF  ROPES. 

Newell  &  Co.,  Birkenhead.     Klein's  Translation  of  Welsbach, 
vol.  iii,  part  1,  sec.  2.) 


Hemp. 

Iron. 

Steel. 

TensiiG 

Girth. 

Weight 
per 

Girth. 

Weight 
per 

Girth. 

Weight 
per 

Strength, 
Gross  tons. 

Inches. 

Fathom. 

Inches. 

Fathom. 

Inches. 

Fathom. 

Pounds. 

Pounds. 

Pounds. 

23/4 

2 

1 

1 

2 

11/2 

H/2 

] 

1 

3 

33/4 

4 

l-Vs 

2 

4 

l3/4 

21/2 

H/2 

H/2 

5 

41/2 

5 

17/8 

3 

6 

2 

31/2 

1  5/8 

2 

7 

5V2 

7 

2V8 

4 

13/4 

21/2 

8 

21/4 

41/2 

9 

6 

9 

23/8 

5 

17/8 

3 

10 

21/2 

51/2 

11 

61/2 

10 

25/8 

6 

2 

31/2 

12 

23/4 

61/2 

2V8 

4 

13 

7 

12 

27/8 

7 

21/4 

41/2 

14 

3 

71/2 

15 

7V2 

14 

3V8 

8 

23/8 

5 

16 

3V4 

81/2 

17 

8 

16 

33/8 

9 

2V2 

5V2 

18 

31/2 

10 

23/8 

6 

20 

81/2 

18 

33/8 

11 

23/4 

61/2 

22 

33/4 

12 

24 

91/2 

22 

37/8 

13 

31/4 

8 

26 

10 

26 

4 

14 

28 

11 

30 

41/4 

15 

33/8 

9 

30 

43/8 

16 

32 

41/2 

18 

31/2 

10 

36 

12 

34 

45/8 

20 

33/4 

12 

40 

STRENGTH   OF   ROPES.  411 

ength  Sufficient  to    Cause    the   Maximum    Working   Stress. 

(Weisbach.) 

Hempen  rope,  dry  and  uritarred 2855  feet. 

Hempen  rope,  wet  or  tarred 1975 "   " 

Wire  rope 4590     " 

Open-link  chain 1360     " 

Stud  chain 1660     " 

Sometimes,  when  the  depths  are  very  great,  ropes  are  given  approxi- 
mately the  form  of  a  body  of  uniform  strength,  by  making  them  of  separ- 
ate pieces,  whose  diameters  diminish  towards  the  lower  end.  It  is  evi- 
dent, that  by  this  means  the  tensions  in  the  fibres  caused  by  the  rope's 
own  weight  can  be  considerably  diminished. 

Rope  for  Hoisting  or  Transmission.  Manila  Rope.  (C.  W.  Hunt 
Company,  New  York.)  —  Rope  used  for  hoisting  or  for  transmission  of 
power  is  subjected  to  a. very  severe  test.  Ordinary  rope  chafes  and  grinds 
to  powder  in  the  center,  while  the  exterior  may  look  as  though  it  was  little 
worn. 

In  bending  a  rope  over  a  sheave,  the  strands  and  the  yarns  of  these 
strands  slide  a  small  distance  upon  each  other,  causing  friction,  and  wear 
the  rooe  internally. 

The  "  Stevedore"  rope  used  by  the  C.  W.  Hunt  Company  is  made  by  lubri- 
cating the  fibres  with  plumbago,  mixed  with  sufficient  tallow  to  hold  it  in 
•  position.    This  lubricates  the  yarns  of  the  rope,  and  prevents  internal 
chafing  and  wear.     After  running  a  short  time  the  exterior  of  the  rope 
gets  compressed  and  coated  with  the  lubricant. 

In  manufacturing  rope,  the  fibres  are  first  spun  into  a  yarn,  this  yam 
being  twisted  in  a  direction  called  "right  hand."  From  20  to  80  of  these 
yarns,  depending  on  the  size  of  the  rope,  are  then  put  together  and 
twisted  in  the  opposite  direction,  or  "left  hand,"  into  a  strand.  Three  of 
these  strands,  for  a  3-strand,  or  four  for  a  4-strand  rope,  are  then  twisted 
together,  the  twist  being  again  in  the  "right  hand"  direction.  When  the 
strand  is  twisted,  it  untwists  each  of  the  threads,  and  when  the  three 
strands  are  twisted  together  into  rope,  it  untwists  the  strands,  but  again 
twists  up  the  threads.  It  is  this  opposite  twist  that  keeps  the  rope  in  its 
proper  form.  When  a  weight  is  hung  on  the  end  of  a  rope,  the  tendency 
is  for  the  rope  to  untwist,  and  become  longer.  In  untwisting  the  rope,  it 
would  twist  the  threads  up,  and  the  weight  will  revolve  until  the  strain  of 
the  untwisting  strands  just  equals  the  strain  of  the  threads  being  twisted 
tighter.  In  making  a  rope  it  is  impossible  to  make  these  strains  exactly 
balance  each  other.  It  is  this  fact  that  makes  it  necessary  to  take  out  the 
"turns"  in  a  new  rope,  that  is,  untwist  it  when  it  is  put  at  work.  The 
proper  twist  that  should  be  put  in  the  threads  has  been  ascertained  approx- 
imately by  experience. 

The  amount  of  work  that  the  rope  will  do  varies  greatly.  It  depends 
not  only  on  the  quality  of  the  fibre  and  the  method  of  laying  up  the  rope, 
but  also  on  the  kind  of  weather  when  the  rope  is  used,  the  blocks  or 
sheaves  over  which  it  is  run,  and  the  strain  in  proportion  to  the  strain  put 
upon  the  rope.  The  principal  wear  comes  in  practice  from  defective  or 
badly  set  sheaves,  from  excess  of  load  and  exposure  to  storms. 

The  loads  put  upon  the  rope  should  not  exceed  those  given  in  the 
tables,  for  the  most  economical  wear.  The  indications  of  excessive  load 
will  be  the  twist  coming  out  of  the  rope,  or  one  of  the  strands  slipping  out 
of  its  proper  position.  A  certain  amount  of  twist  comes  out  in  using  it 
the  first  day  or  two,  but  after  that  the  rope  should  remain  substantially 
the  same.  If  it  does  not,  the  load  is  too  great  for  the  durability  of  the 
rope.  If  the  rope  wears  on  the  outside,  and  is  good  on  the  inside,  it 
shows  that  it  has  been  chafed  in  running  over  the  pulleys  or  sheaves.  If 
the  blocks  are  very  small,  it  will  increase  the  sliding  of  the  strands  and 
threads,  and  result  in  a  more  rapid  internal  wear.  Rope  made  for  hoist- 
ing and  for  rope  transmission  is  usually  made  with  four  strands,  as  expe- 
rience has  shown  this  to  be  the  most  serviceable. 

The  strength  and  weight  of  "Stevedore"  rope  is  estimated  as  follows: 
Breaking  strength  in  pounds  =      720  (circumference  in  inches)  2; 
Weight  in  pounds  per  foot      =  0.032  (circumference  in  inches)  8. 

The  Technical  Words  relating  to  Cordage  most  frequently  heard 
are: 

YARN.  —  Fibres  twisted  together. 


412  ROPES  AND   CABLES/ 

THREAD.  —  Two  or  more  small  yarns  twisted  together. 

STRING.  —  The  same  as  a  thread  but  a  little  larger  yarns. 

STRAND.  —  Two  or  more  large  yarns  twisted  together* 

CORD.  —Several  threads  twisted  together. 

ROPE.  —  Several  strands  twisted  together. 

HAWSER.  —  A  rope  of  three  strands. 

SHROUD-LAID.  —  A  rope  of  four  strands. 

CABLE.  — Three  hawsers  twisted  together. 

YARNS  are  laid  up  left-handed  into  strands. 

STRANDS  are  laid  up  right-handed  into  rope. 

HAWSERS  are  laid  up  left-handed  into  a  cable. 

A  rope  is: 

LAID  by  twisting  strands  together  in  making  the  rope. 

SPLICED  by  joining  to  another  rope  by  interweaving  the  strands. 

WHIPPED.  —  By  winding  a  string  around  the  end  to  prevent  untwisting. 

SERVED.  —  When  covered  by  winding  a  yarn  continuously  and  tightly 
around  it. 

PARCELED.  —  By  wrapping  with  canvas. 

SEIZED.  —  When  two  parts  are  bound  together  by  a  yarn,  thread  or 
string. 

PAYED.  —  When  painted,  tarred  or  greased  to  resist  wet. 

HAUL.  —  To  pull  on  a  rope. 

TAUT.  —  Drawn  tight  or  strained. 

Splicing  of  Rope. — The  splice  in  a  transmission  rope  is  not  only  the 
weakest  part  of  the  rope  but  is  the  first  part  to  fail  when  the  rope  is  worn 
out.  If  the  rope  is  larger  at  the  splice,  the  projecting  part  will  wear  on 
the  pulleys  and  the  rope  fail  from  the  cutting  off  of  the  strands.  The  fol- 
lowing directions  are  given  for  splicing  a  4-strand  rope. 

The  engravings  show  each  successive  operation  in  splicing  a  13/4-inch 
manila  rope.  Each  engraving  was  made  from  a  full-size  specimen. 

Tie  a  piece  of  twine,  9  and  10,  around  the  rope  to  be  spliced,  about 
6  feet  from  each  end.  Then  unlay  the  strands  of  each  end  back  to  the 
twine. 

Butt  the  ropes  together  and  twist  each  corresponding  pair  of  strands 
loosely,  to  keep  them  from  being  tangled,  as  shown  in  Fig.  91. 

The  twine  10  is  now  cut,  and  the  strand  8  unlaid  and  strand  7  carefully 
laid  in  its  place  for  a  distance  of  four  and  a  half  feet  from  the  junction. 

The  strand  6  is  next  unlaid  about  one  and  a  half  feet  and  strand  5  laid 
in  Its  place. 

The  ends  of  the  cores  are  now  cut  off  so  they  just  meet. 

Unlay  strand  1  four  and  a  half  feet,  laying  strand  2  in  its  place. 

Unlay  strand  3  one  and  a  half  feet,  laying  in  strand  4. 

Cut  all  the  strands  off  to  a  length  of  about  twenty  inches  for  convenience 
in  manipulation. 

The  rope  now  assumes  the  form  shown  in  Fig.  92  with  the  meeting 
points  of  the  strands  three  feet  apart. 

Each  pair  of  strands  is  successively  subjected  to  the  following  operation: 

From  the  point  of  meeting  of  the  strands  8  and  7,  unlay  each  one  three 
turns;  split  both  the  strand  8  and  the  strand  7  in  halves  as  far  back  as 
they  are  now  unlaid  and  "whip"  the  end  of  each  half  strand  with  a  small 
piece  of  twine. 

The  half  of  the  strand  7  is  now  laid  in  three  turns  and  the  half  of  8  also 
laid  in  three  turns.  The  half  strands  now  meet  and  are  tied  in  a  simple 
knot,  11,  Fig.  93,  making  the  rope  at  this  point  its  original  size. 

The  rope  is  now  opened  with  a  marlin  spike  and  the  half  strand  of  7 
worked  around  the  half  strand  of  8  by  passing  the  end  of  the  half  strand  7 
through  the  rope,  as  shown  in  the  engraving,  drawn  taut,  and  again 
worked  around  this  half  strand  until  it  reaches  the  half  strand  13  that  was 
not  laid  in.  This  half  strand  13  is  now  split,  and  the  half  strand  7  drawn 
through  the  opening  thus  made,  and  then  tucked  under  the  two  adjacent 
strands,  as  shown  in  Fig.  94.  The  other  half  of  the  strand  8  is  now 
wound  around  the  other  half  strand  7  in  the  same  manner.  After  each 
pair  of  strands  has  been  treated  in  this  manner,  the  ends  are  cut  off  at  12, 
leaving  them  about  four  inches  long.  After  a  few  days  wear  they  will 
draw  into  the  body  of  the  rope  or  wear  off,  so  that  the  locality  of  the 
splice  can  scarcely  be  detected. 


FIG.  94. 
SPLICING  OF  ROPES. 


414 


ROPES  AND   CABLES. 


Cargo  Hoisting.  (C.  W.  Hunt  Company.)  —  The  amount  of  coal  that 
can  be  hoisted  with  a  rope  varies  greatly.  Under  the  ordinary  conditions 
of  use  a  rope  hoists  from  5000  to  8000  tons.  Where  the  circumstances  are 
more  ^  favorable,  the  amounts  run  up  frequently  to  12,000  or  15,000  tons 
occasionally  to  20,000  and  in  one  case  32,400  tons  to  a  single  fall 

When  a  hoisting  rope  is  first  put  in  use,  it  is  likely  from  the  strain  put 
upon  it  to  twist  up  when  the  block  is  loosened  from  the  load.  This  occurs 
in  the  first  day  or  two  only.  The  rope  should  then  be  taken  down  and 
the  *  turns'  taken  out  of  the  rope.  When  put  up  again  the  rope  should 
give  no  further  trouble  until  worn  out. 

It  is  necessary  that  the  rope  should  be  much  larger  than  is  needed  to 
bear  the  strain  from  the  load. 

Practical  experience  for  many  years  has  substantially  settled  the  most 
economical  size  of  rope  to  be  used  which  is  given  in  the  table  below 

Hoisting  ropes  are  not  spliced,  as  it  is  difficult  to  make  a  splice  that  will 
not  pull  out  while  running  over  the  sheaves,  and  the  increased  wear  to  be 
obtained  in  this  way  is  very  small. 

Coal  is  usually  hoisted  with  what  is  commonly  called  a  "double  whip-  " 
that  is,  with  a  running  block  that  is  attached  to  the  tub  which  reduces  the 
strain  on  the  rope  to  approximately  one-half  the  weight  of  the  load 
hoisted. 

Hoisting  rope  is  ordered  by  circumference,  transmission  rope  by 
diameter. 

Working  Loads  for  Manila  Eope  (C.  W.  Hunt,  Trans.]  A.  S.  M.  E., 
xxiii,  125.) 


Diameter 
of  Rope, 
Inches. 

Ultimate 
Strength, 
Pounds. 

Working  Load  in  Pounds. 

Minimum  Diameter  of 
Sheaves  in  Inches. 

Rapid. 

Medium. 

Slow. 

Rapid. 

Medium. 

Slow. 

1 

H/8 
U/4 
13/8 
H/2 
15/8 
13/4 

7,100 
9,000 
11,000 
13,400 
15,800 
18,800 
21.800 

200 
250 
300 
380 
450 
530 
620 

400 
500 
600 
750 
900 
1100 
1250 

1000 
1250 
1500 
1900 
2200 
2600 
3000 

40 
45 
50 
55 
60 
65 
70 

12 
13 
14 
15 
16 
17 
18 

8 
9 
iO 
11 
12 
13 
14 

In  this  table  the  work'required  of  the  rope  is,  for  convenience,  divided 
into  three  classes  —  "rapid,"  "medium,"  and  "slow,"  these  terms  being 
used  in  the  following  sense:  "Slow"  —  Derrick,  crane  and  quarry  work; 
speed  from  50  to  100  feet  per  minute.  "Medium"  —  Wharf  and  cargo, 
hoisting  150  to  300  feet  per  minute.  "Rapid"  —  400  to  800  feet  per 
minute. 

The  ultimate  strength  given  in  the  table  is  materially  affected  by  the 
age  and  condition  of  a  rope  in  active  service,  and  also  it  is  said  to  be 
weaker  when  it  is  wet.  Trautwine  states  that  a  few  months  of  exposed 
work  weakens  rope  20  to  50  per  cent.  The  ultimate  strength  of  a  new 
rope  given  in  the  table  is  the  result  of  tests  of  full  sized  specimens  of 
manila  rope,  purchased  in  the  open  market,  and  made  by  three  inde- 
pendent rope  walks. 

The  proper  'diameter  of  pulley-block  sheaves  for  different  classes  of 
work  given  in  the  table  is  a  compromise  of  the  various  factors  affecting 
the  case.  An  increase  in  the  diameter  of  sheave  will  materially  increase 
the  life  of  a  rope.  The  advantage,  however,  is  gained  by  increased 
difficulty  of  installation,  a  clumsiness  in  handling,  and  an  increase  in 
first  cost.  The  best  size  is  one  that  considers  the  advantages  and  the 
drawbacks  as  they  are  found  in  practical  use,  and  makes  a  fair  balance 
between  the  conflicting  elements  of  the  problem. 

Records  covering  many  years  have  been  kept  by  various  coal  dealers, 
of  the  diameter  and  cost  of  their  rope  per  tpn  of  coal  hoisted  from  ves- 
sels, using  sheaves  of  from  12  to  16  inches  in  diameter.  These  records 
show  conclusively  that,  in  hoisting  a  bucket  that  produces  900  pounds 
stress  upon  the  rope,  a  li/4-inch  diameter  rope  is  too  small  and  a  13/4- 
inch  rope  is  too  large  for  economy.  The  Pennsylvania  Railroad  Company 
uses  iy2  inch  rope,  running  over  14-inch  diameter  sheaves  for  hoisting 


STRENGTH   OF   ROPES.  415 

freight  on  lighters  in  New  York  harbor,  and  handles  on  a  single  part  of 
the  rope  loads  up  to  3,000  pounds  as  a  maximum.  Greater  weights  are 
handled  on  a  6-part  tackle. 

Life  of  Hoisting  and  Transmission  Rope.  A  rope  1  V6-in.  diam.  usu- 
ally hoists  from  a  vessel  from  7000  to  10,000  tons  of  coal,  running  with  a 
working  stress  of  850  to  950  Ibs.  over  three  sheaves,  one  12  in.,  and  two 
16  in.  diam.  In  hoisting  10,000  tons  it  makes  20,000  trips,  bending  in 
that  time  from  a  straight  line  to  the  curve  of  the  sheave  120,000  times, 
when  it  is  worn  out.  A  1000  ft.  transmission  in  a  tin-plate  mill,  with  1^ 
in.  rope,  sheaves  5  ft.,  17  ft.,  and  36  ft.  apart,  center  to  center,  runs  5000 
ft.  per  minute  making  13,900  bends  per  hour,  or  more  bends  in  9  hours 
than  the  hoisting  rope  made  in  its  entire  life,  yet  the  life  of  a  transmission 
rope  is  measured  in  years,  not  hours.  This  enormous  difference  in  the 
life  of  ropes  of  the  same  size  and  quality  is  wholly  gained  by  reducing  the 
stresses  on  the  rope  and  increasing  the  diameter  of  the  sheaves. 

Efficiency  of  Knots  as  a  percentage  of  the  full  strength  of  the  rope, 
and  the  factor  of  safety  when  used  with  the  stresses  given  in  the  5th  col" 
umn  of  the  table  of  working  loads. 

Kind  of  Knot.                                           Effy.  Fact.  9 

Eye  splice  over  an  iron  thimble 90  6.3 

Short  splice  in  the  rope 80  5.6 

Timber  hitch,  round  turn,  half-hitch 65  4.5 

Bowline  slip  knot,  clove  hitch 60  4.2 

Square  knot,  weaver's  knot  sheet  bend 50  3.5 

Flemish  loop,  overhand  knot 45  3.1 

Full  strength  of  dry  rope,  average  of  four  tests 100  7.0 

Efficiency  of  Rope  Tackles.  Robert  Grimshawin  1893  tested  a  33/4-in., 
3-strand  ordinary  dry  manila  rope  on  a  "cat  and  fish"  tackle  with  a 
6-fold  purchase.  The  sheaves  were  8-in.  diam.,  the  three  upper  ones  hav- 
ing roller  bearings  and  the  three  lower  ones  solid  bushings.  The  results 
were  as  below: 

Net  load  on  tackle,  weight  raised,  Ibs 600       800       1000         1200 

Theoretical  force  required  to  raise  the  weight  100     1333.3     166.7       200 

Actual  force  required 158       198         243  288 

Percentage  above  the  theoretical 58        48          45.8        44 

Weight  and  Strength  of  Manila  Rope.  Spencer  Miller  (Eng'g  News, 
Dec.  6,  1890)  gives  a  table  of  breaking  strength  of  manila  rope,  which  he 
considers  more  reliable  than  the  strength  computed  by  Mr.  Hunt's  formula: 
Breaking  strength  =  720  X  (circumference  in  inches)  .2  Mr.  Miller's  formula 
is:  Breaking  weight  Ibs.  =  circumference2  X  a  coefficient  which  varies 
from  900  for  1/2"  to  700  for  2"  diameter  rope,  as  below: 

Circumference  ..11/2  2  21/2  23/4  3  3l/2  33/4  41/4  4l/2  5  51/2  6 
Coefficient 900  845  820  790  780  765  760  745  735  725  712  700 

Knots. '  The  principle  of  a  knot  is  that  no  two  parts,  which  would 
move  in  the  same  direction  if  the  rope  were  to  slip,  should  lay  along  side 
of  and  touching  each  other.  (See  illustrations  on  the  next  page.) 

The  bowline  is  one  of  the  most  useful  knots,  it  will  not  slip,  and  after 
being  strained  is  easily  untied.  Commence  by  making  a  bight  in  the 
rope,  then  put  the  end  through  the  bight  and  under  the  standing  part  as 
shown  in  G,  then  pass  the  end  again  through  the  bight,  and  haul  tight. 

The  square  or  reef  knot  must  not  be  mistaken  for  the  "granny"  knot 
that  slips  under  a  strain.  Knots  H,  K  and  M  are  easily  untied  after 
being  under  strain.  The  knot  M  is  useful  when  the  rope  passes  through 
an  eye  and  is  held  by  the  knot,  as  it  will  not  slip  and  is  easily  untied 
after  being  strained. 

The  timber  hitch  S  looks  as  though  it  would  give  way,  but  it  will  not; 
the  greater  the  strain  the  tighter  it  will  hold.  The  wall  knot  looks  com- 
plicated, but  is  easily  made  by  proceeding  as  follows:  Form  a  bight  with 
strand  1  and  pass  the  strand  2  around  the  end  of  it,  and  the  strand  3 
round  the  end  of  2  and  then  through  the  bight  of  1  as  shown  in  the  cut  Z. 
Haul  the  ends  taut  when  the  appearance  is  as  shown  in  A  A.  The  end  of 
the  strand  1  is  now  laid  over  the  center  of  the  knot,  strand  2  laid  over  1 
and  3  over  2,  when  the  end  of  3  is  passed  through  the  bight  of  1  as  shown 
in  BB,  Haul  all  the  strands  taut  as  shown  in  CC. 


416 


ROPES   AND   CABLES. 


Varieties  of  Knots.  —  A  great  number  of  knots  have  been  devised  of 
which  a  few  only  are  illustrated,  but  those  selected  are  the  most  frequently 
used.  In  the  cut,  Fig.  95,  they  are  shown  open,  or  before  being  drawn 
taut,  in  order  to  show  the  position  of  the  parts.  The  names  usually 
given  to  them  are: 

Bight  of  a  rope. 

Simple  or  Overhand  knot. 

Figure  8  knot. 

Double  knot. 

Boat  knot. 

Bowline,  first  step. 

Bowline,  second  step. 

Bowline  completed. 

Square  or  reef  knot. 

Sheet  bend  or  weaver's  knot. 

Sheet  bend  with  a  toggle. 

Carrick  bend. 

Stevedore  knot  completed. 


A. 

B. 

C. 

D. 

E. 

F. 

G. 

H. 

I. 

J. 

K. 

L. 

M. 

N. 

O. 


Stevedore  knot  commenced. 
Slip  knot. 


P. 

§: 

S. 

T. 

U. 

Y. 

W. 

X. 

Y. 

Z. 

AA. 
BB. 
CO. 


Flemish  loop. 

Chain  knot  with  toggle. 

Half-hitch. 

Timber-hitch. 

Clove- hitch. 

Rolling-hitch. 

Timber-hitch  and  half-hitch. 

Black  wall-hitch. 

Fisherman's  bend. 

Round  turn  and  half-hitch 

Wall  knot  commenced. 

Wall  knot  completed. 

Wall  knot  crown  commenced. 

Wall  knot  crown  completed. 


Fia.  95.  —  KNOTS. 


SPRINGS.  417 


SPRINGS. 

Definitions.  —  A  spiral  spring  is  one  which  is  wound  around  a  fixed 
point  or  center,  and  continually  receding  from  it,  like  a  watch  spring.  A 
helical  spring  is  one  which  is  wound  around  an  arbor,  and  at  the  same  time 
advancing  like  the  thread  of  a  screw.  .  An  elliptical  or  laminated  spring  is 
made  of  nat  bars,  plaies,  or  "  leaves,"  of  regularly  varying  lengths,  super- 
posed one  upon  the  other. 

JL  •imiir.ited  Steel  Springs.  —  Clark  (Rules,  Tables  and  Data)  gives 
the  following  from  his  work  on  Railway  Machinery,  1855: 

__   1.66  LS.  U-n  .  __  1.66  L«. 


_ 
11.3  L'  AW     ' 

A  =  elasticity,  or  deflection,  in  sixteenths  of  an  inch  per  ton  of  load; 
s  =  working  strength,  or  load,  in  tons  (2240  Ibs.); 
L  —  span,  when  loaded  in  inches- 
b  =  breadth  of  p  ates,  in  inches,  taken  as  uniform; 
t  =  thickness  of  plates,  in  sixteenths  of  an  inch; 
n  —  number  o'f  plates. 

NOTE.  —  1     The  span  and  the  elasticity  are  those  due  to  the  spring 
when  weighted. 

2.  When  extra  thick  back  and  short  plates  are  used,  they  must  be 
replaced  by  an  equivalent  number  of  plates  of  the  ruling  thickness,  prior 
to  the  employment  of  the  first  two  formulae.     This  ,s  found  by  multiply- 
ing the  number  of  extra  thick  plates  by  the  cube  of  their  thickness,  and 
dividing  by  the  cube  of  the  ruling  thickness.     Conversely,  the  number 
of  plates  of  the  ruling  thickness  given  by  the  third  formula,  required  to 
be  deducted  and  replaced  by  a  given  number  of  extra  thick  plates,  are 
found  by  the  same  calculation. 

3.  It  is  assumed  that  the  plates  are  similarly  and  regularly  formed, 
and  that  they  are  of  uniform  breadth,  and  but  slightly  taper  at  the  ends. 

Reuleaux's  Constructor  gives  for  semi-elliptic  springs: 

and     .   f 


6  1 

S  =  max.  direct  fiber-strain  in  plate;  b  =  width  of  plates: 

n  —  number  of  plates  in  spring;  h  =  thickness  of  plates: 

I  —  one-half  length  of  spring;  /  =  deflection  of  end  of  spring; 

P  =  load  on  one  end  of  spring;  E  =  modulus  of  direct  elasticity 

The  above  formula  for  deflection  can  be  relied  upon  where  all  the  plates 
of  the  spring  are  regularly  shortened;  but  in  semi-elliptic  springs,  as 
used,  there  are  generally  several  plates  extending  the  full  length  of  the 
spring,  and  the  proportion  of  these  long  plates  to  the  whole  number  is 

usually  about  one-fourth.    *  In  such  cases/  =  ^rr-rp'     (G.  R.  Henderson, 

Trans   A.  S.  M.  E.,  vol.  xvi.) 

In  order  to  compare  the  formulae  of  Reuleaux  and  Clark  we  may  make 
the  following  substitutions  in  the  latter:  s  in  tons  =  P  in  Ibs.  -f-  1120; 
As  =  16/;  L  =  21;  t  =  16/i;  then 

A,  =  i  fi     _  _  1  .66  X  8  P  X  P  P/8 

""       4096  X  1120  X  nW  '  ~  5,527,  l~33nWi"« 

which  corresponds  with  Reuleaux's  formula  for  deflection  if  in  the  latter 
we  take  E  =  33,162,800. 


which  corresponds  with  Reuleaux's  formula  for  working  load  when  S  ia 
the  latter  is  taken  at  76,120. 


418 


SPRINGS. 


The  value  of  E  is  usually  taken  at  30,000,000  and  S  at  80,000,  in  which 
case  Reuleaux's  formulse  become 


13,333  nbh* 
I 


and     /  = 


PI* 


5,000,OOOn&/*3 


G.  R.  Henderson,  in  Trans.  A.  S.  M.  E.,  vol.  xvii,  gives  a  series  of 
tables  for  use  in  designing  both  elliptical  and  helical  springs. 


Helical  Steel  Springs. 

NOTATION.     Let  d  =  diam.  of  wire  or  rod  of  which  the  spring  is  made. 
D  =  outside  diameter  of  coil,  inches. 
R  =  mean  radius  9f  coil,  =  1/2  (D  —  d). 
n  =  number  of  coils. 
P  =  load  applied  to  the  spring,  Ibs. 
G  =  modulus  of  torsional  elasticity. 
S  —  stress  on  extreme  fiber  caused  by  load  P. 
F  =  extension  or  compression  of  one  coil,  in.,  for  load  P. 
Fn  =  total  extension  or  compressi9n,  for  load  P. 
W  =  safe  carrying  capacity  of  spring,  Ibs. 


Gd* 


64  PR*n , 
Gd*     ' 


W  = 


0.1 963  Sd* 
R 


16   R' 


Values  of  G  according  to  different  authorities  range  from  10,000,000  to 
14,000,000. 

The  safe  working  value  commonly  taken  for  S  =  60,000  Ibs.  per  sq.  in. 
Taking  G  at  12,000,000  and  S  at  60,000  the  above  formula  become 


PR* 
187,500  d4' 


W 


^-      If  P  =  W,  then  F  =  0.06285^-- 


For  square  steel  the  values  fpund  for  F  and  W  are  to  be  multiplied  by 
0.59  and  1.2  respectively,  d  being  the  side  of  the  square. 

The  stress  in  a  helical  spring  is  almost  wholly  one  of  torsion.  For 
method  of  deriving  the  formulae  for  springs  from  torsional  formulae  see 

rper  by  J.  W.  Cloud,  Trans.  A.  S.  M.  E.,  vol.  173.     Mr.  Cloud  takes 
=  80,000  and  G  =  12,600,000. 

Taking  from  the  Pennsylvania  Railroad  Specifications  (1891)  the 
capacity  when  closed,  Wi;  of  the  following  springs,  and  the  total  com- 
pression when  closed  H  —  h,  in  which  H  =  height  when  free  and  h 
when  closed,  and  assuming  n  =  h  •*•  d,  we  have  the  following  compari- 
son of  the  specified  values  of  capacity  and  compression  with  those  ob- 
tained from  the  formulse. 


No. 

d.in. 

D 

D-d 

TFi 

W 

H 

h 

H-h 

Fn 

n 

T. 

1/4 

U/2 

11/4 

400 

295 

9 

6 

3 

3.20 

24 

S. 

1/2 

3 

2V2 

1900 

1178 

8 

5 

3 

3.16 

10 

K. 

3/4 

53/4 

5 

2100 

1988 

7 

41/4 

23/4 

3.15 

52/s 

D. 

5 

4 

8100 

5890 

101/2 

8 

21/2 

2.76 

8 

I. 

H/4 

8 

63/4 

10000 

6788 

9 

53/4 

31/4 

3.86 

43/g 

C. 

U/8 

47/8 

33/4 

16000 

8946 

43/8 

33/8 

1 

1.05 

3 

The  value  of  Fn  in  the  table  is  calculated  from  the  formula  with  P=  Wt 
Wilson  Hartnell  (Proc.  Inst.  M.  E.,  1882,  p.  426),  says:  The  size  of  a 
spiral  spring  may  be  calculated  from  the  formula  on  page  304  of  "  Rank- 
ine's  Useful  Rules  and  Tables;"  but  the  experience  with  Salter's  springs 
has  shown  that  the  safe  limit  of  stress  is  more  than  twice  as  great  as  there 
given,  namely  60,000  to  70,000  Ibs.  per  square  inch  of  section  with  3/8-inch 
wire,  and  about  50,000  with  i/2-inch  wire.  Hence  the  work  that  can  b« 
done  by  springs  of  wire  is  four  or  five  times  as  great  as  Rankine  allows. 


SPRINGS.  419 

For  3/8-inch  wire  and  under, 

12,000  X  (diam.  of  wire)8  , 
Maximum  load  in  Ibs.  =  — =' 


Weight  in  Ibs.  to  deflect  spring  1  in.  = 


Mean  radius  of  springs 

180,000  X  (diam.)4 


Number  of  coils  X  (rad.)3 
The  work  in  foot-pounds  that  can  be  stored  up  in  a  spiral  spring  would 

lift  it  above  50  ft. 

In  a  few  rough  experiments  made  with  Salter's  springs  the  coefficient  of 

rigidity  was  noticed  to  be  12,600,000  to  13,700,000  with  i/4-inch  wire; 

11,000,000  for  11/32  inch;  and  10,600,000  to  10,900,000  for  3/8_inch  wire. 
Helical    Springs.  — J.   Begtrup,  in  the  American  Machinist  of  Aug. 

18,  1892,  gives  formulas  for  the  deflection  and  carrying  capacity  of  helical 

springs  of  round  and  square  steel,  as  follow: 

0.3927  '       F  =  8  P  (D~  d)3.  for  round  steel. 


=  0.471  FT^»         F  =  4.712  —  ^  „,.     '  ,  for  square  steel. 
L)  —  a  Hid* 

W  =  carrying  capacity  in  pounds, 

S  =  greatest  shearing  stress  per  square  inch  of  material, 
d  =  diameter  of  steel, 
D  =  outside  diameter  of  coil, 
F  =  deflection  of  one  coil, 
E  =  torsional  modulus  of  elasticity, 
P  =  load  in  pounds. 

From  these  formulas  the  following  table  has  been  calculated  by  Mr 
Begtrup.  A  spring  being  made  of  an  elastic  material,  and  of  such  shape 
as  lo  allow  a  great  amount  of  deflection,  will  not  be  affected  by  sudder. 
shocks  or  blows  to  the  same  extent  as  a  rigid  body,  and  a  factor  of  safety 
very  much  less  than  for  rigid  constructions  may  be  used. 

HOW    TO    USE   THE    TABLE. 

When  designing  a  spring  for  continuous  work,  as  a  car  spring,  use  a 
greater  factor  of  safety  than  in  the  table;  for  intermittent  working,  as  in 
a  steam-engine  governor  or  safety  valve,  use  figures  given  in  table;  for 
square  steel  multiply  line  W  by  1.2  and  line  F  by  0.59. 

Example  1. —  How  much  will  a  spring  of  3/8"  round  steel  and  3"  outside 
diameter  carry  with  safety?  In  the  line  headed  D  we  find  3,  and  right 
underneath  473,  which  is  the  weight  it  will  carry  with  safety.  How  many 
coils  must  this  spring  have  so  as  to  deflect  3"  with  a  load  of  400  pounds? 
Assuming  a  modulus  of  elasticity  of  12  millions  we  find  in  the  line  headed 
F  the  figure  0.0610;  this  is  deflection  of  one  coil  for  a  load  of  100  pounds; 
therefore  0.061  X  4  =  0.244"  is  deflection  of  one  coil  for  400  pounds  load, 
and  3  •*-  0.244  =  121/2  is  the  number  of  coils  wanted.  This  spring  will 
therefore  be  43/4"  long  when  closed,  counting  working  coils  only,  and 
stretch  to  73/4". 

Example  2. —  A  spring  31/4"  outside  diameter  of  if\^  steel  is  wound  close; 
how  much  can  it  be  extended  without  exceeding  the  limit  of  safety?  We 
find  maximum  safe  load  for  this  spring  to  be  702  pounds,  and  deflection  of 
one  coil  for  100  pounds  load  0.0405  inches;  therefore  7. 02  X  0.0405  =  0.284" 
is  the  greatest  admissible  opening  between  coils.  We  may  thus,  without 
knowing  the  load,  ascertain  whether  a  spring  is  overloaded  or  not. 

Carrying  Capacity  and  Deflection  of  Helical  Springs  of 
Round  Steel. 

d  =  diameter  of  steel.  D  =  outside  diameter  of  coil.  W=  safe,  work- 
ing load  in  pounds  —  tensile  stress  not  exceeding  60,000  pounds  per 
square  inch.  F  =  deflection  by  a  load  of  100  pounds  of  one  coil,  with  a 
modulus  of  elasticity  of  12  millions.  The  ultimate  carrying  capacity 
will  be  about  twice  the  safe  load.  (The  original  table  gives  three  values 


420 


SPRINGS. 


of  F,  corresponding  respectively  to  a  modulus  of  elasticity  of  10,  12  and 
14  millions.  To  find  values  of  F  for  10  million  modulus  increase  the  fig- 
ures here  given  by  one-fifth;  for  14  million  subtract  one-seventh.) 


d 
in. 
.065 

D 
W 
F 

0.25 
35 
0.0236 

0.50 
15 
0.3075 

0.75 

1.00 

1.25 

1.50 

1.75 

2.00 

1.228 

3.053 

6.214 

11.04 

17.87 

27.06 

.120 

D' 
W 
F 

0.50 
107 
0.0176 

0.75 
65 
0.0804 

1.00 
46 
0.2191 

1.25 
36 
0.4639 

1.50 
29 

0.8448 

1.75 
25 
1.392 

2.00 
22 
2.136 

2.25 
19 
3.107 

2.50 
17 
4.334 

.180 

D 
W 
F 

0.75 
241 
0.0118 

1.00 
167 
0.0350 

1.25 
128 
0.0778 

1.50 
104 

0.1460 

1.75 

88 
0.2457 

2.00 
75 

0.3828 

2.25 
66 
0.5632 

2.50 
59 
0.7928 

2.75 
53 
1.077 

3.00 

49 
1.423 

V4 

D 
W 
F 

1.25 
368 
0.0171 

1.50 
294 
0.0333 

1.75 
245 
0.0576 

2.00 
210 
0.0914 

2.25 
184 
0.1365 

2.50 
164 
0.  1944 

2.75 
147 
0.2665 

3.00 
134 
3.3548 

3.25 
123 
0.4607 

3.50 
113 

0.5859 

5/16 

3/8 

D 
W 
F 

D 
W 
F 

1.50 
605 
0  0117 

1.75 
500 
0.0207 

2.00 
426 
0.0336 

2.25 
371 
0  0508 

2.50 
329 
0  0732 

2.75 
295 
0  1012 

3.00 

267 
0  1357 

3.25 
245 
0  1771 

3.50 
226 
0  2263 

3.75 
209 
0  2839 

4.00 
195 
0  3505 

2.00 
765 
0.0145 

2.25 
663 
0.0222 

2.50 
589 
0.0323 

2.75 
523 
0.0452 

3.00 

473 
0.0610 

3.25 
433 
0.0801 

3.50 
398 
0.1029 

3.75 
368 
0.1297 

4.00 
343 
0.  1606 

4.25 
321 
0.1963 

4.50 
301 
0.2367 

7/16 

1/2 

D 
W 
F 

D 
W 
F 

2.00 
1263 
0  0069 

2.25 
1089 
0  0108 

2.50 

957 
0.0160 

2.75 
853 
0  0225 

3.00 
770 
0  0306 

3.25 
702 
0  0405 

3.50 

644 
0  0529 

3.75 
596 
0  0661 

4.00 
544 
0  0823 

4.50 
486 
0  1220 

5.00 

432 
0  1728 

2.00 
1963 
0.0036 

2.25 
1683 
0.0057 

2.50 

1472 
0.0085 

2.75 
1309 
0.0121 

3.00 
1178 
0.0167 

3.25 
1071 
0.0222 

3.50 
982 
0.0288 

3.75 
906 
0.0366 

4.00 
841 
0.0457 

4.50 
736 
0.0683 

5  00 

654 
0.0972 

8/18 

D 
W 
F 

2.50 
2163 
0.0048 

2.75 
1916 
O.Q070 

3  00 

1720 
0.0096 

3.25 
1560 
0.0129 

3.50 
1427 
0.0169 

3.75 
1315 
0.0216 

4.00 
1220 
0.0271 

4.25 
1137 
0.0334 

4.50 
1065 
0.0406 

5  00 
945 

0.0582 

5.50 
849 
0.0801 

5/8 

D 
W 
F 

2.50 
3068 
0.0029 

2.75 
2707 
0.0042 

3.00 

2422 
0.0058 

3.25 
2191 
0.0079 

3.50 
2001 
0.0104 

3.75 
1841 
0.0133 

4.00 
1704 
0.0168 

4.25 
1587 
0.0208 

4.50 

1484 
0.0254 

5.00 
1313 
0.0366 

5.50 
1180 
0.0506 

"/16 

D 

W 

F 

3.00 
3311 
0.0037 

3.25 
29S8 
0.0050 

3.50 

2723 
0.0066 

3.75 
2500 
0.0086 

4.00 
2311 
0.0108 

4.25 
2151 
0.0135 

4.50 
2009 
0.0165 

4.75 
1885 
0.0200 

5.00 
1776 
0.0239 

5.50 
1591 
0.0333 

6.00 
1441 
0.0447 

8/4 

D 
W 
F 

3.00 
4418 
0.0024 

3.25 
3976 
0.0033 

3.50 
3615 
0.0044 

3.75 
3313 
0.0057 

4.00 
3058 
0.0072 

4.25 
2840 
0.0090 

4.50 
2651 
0.0111 

4.75 
2485 
0.0135 

5.00 
2339 
0.0162 

5.50 
2093 
0.0226 

6.003 
1893 
0.005 

7/8 

D 
W 
F 

3.50 
6013 
0.0018 

3.75 

5490 
0.0024 

4.00 
5051 
0.0030 

4.25 
4676 
0.0038 

4.50 

4354 
0.0047 

4.75 
4073 
0.0058 

5.00 
3826 
0.0070 

5.25 
3607 
0.0083 

5.50 
3413 
0.0098 

6.00 
3080 
0.0134 

6.50 
2806 
0.0177 

1 

D 
W 
F 

3.50 
9425 
0.0010 

3.75 
8568 
0.0014 

4.00 
7854 
0.0018 

4.25 
7250 
0.0023 

4.50 
6732 
0.0028 

4.75 
6283 
0.0035 

5.00 
5890 
0.0043 

5.25 
5544 
0.0051 

5.50 

5236 
0.0061 

6.00 

4712 
0.0083 

6.50 
4284 
0.0111 

F.  D.  Howe,  Am.  Mach.  Dec.  20,  1906,  using  Begtrup's  formulae  com- 
putes a  table  for  springs  made  from  wire  of  Roebling's  or  Washburn  and 
Moen  ga-iges,  Nos.  28  to  000.  It  is  here  given  somewhat  abridged, 
values  of  F  corresponding  to  a  torsional  modulus  of  elasticity  of  12,000,000 
only  being  used. 


SPRINGS. 


421 


No.  28 
0.016" 

D 
W 
F 

0.20 
0.524 
6.32 

0.25 
0.41 
13.02 

0.3125 
0.31 
30.2 

0.375 
0.27 
47.0 

0.4375 
0.23 
76.0 

0.500 
0.20 
115 

0.5625 
0.175 
166 

0.625 
0.16 
230 

0.75 
0.13 
402 

0.875 
0.11 
695 

No.  24 
0.0225" 

D 
W 
F 

0.25 
1.18 
2.78 

0.3125 
0.92 
6.31 

0.375 
0.76 
11.35 

0.4375 
0.45 
18.57 

0.500 
0.56 
28.2 

0.5625 
0.50 
40.8 

0  625 
0.45 
56.9 

0.75 
0.37 
97.5 

0.875 
0.31 
166 

0.100 
0.28 
242 

No.  22 
0.028" 

D 
W 
F 

0.25 
2.35 
1.19 

0.3125 
1.84 
2.50 

0.375 
1  49 
4.53 

0.4375 
1.26 
7.42 

0.50 
1.095 
11.40 

0.5625 
0.96 
16.5 

0.625 
0.865 
23.1 

0.75 
0.715 
40.8 

0.875 
0.61 
66.0 

1.00 
0.53 
99.5 

No.  20 
0.035" 

D 

W 
F 

0.25 
4.7 
0.451 

0.3125 
3.64 
0.952 

0.375 
2.97 
1.75 

0.4375 
2.5 
2.90 

0.50 
2.18 
4.47 

0.5625 
1.92 
6.51 

0.625 
1.72 
9.14 

0.75 
1.42 
16.3 

0.875 
1.20 
26.4 

1.00 
1.05 
40.0 

No.  18 
0.047" 

D 

W 
F 

0.25 
12.05 
0.1158 

0.3125 
9.2 
0.294 

0.375 
7.45 
0.488 

0.4375 
6.57 
0.824 

0.50 
5.40 
1.320 

0.625 
4.23 
1.870 

0.75 
3.48 
3.96 

0.875 
2.95 
7.85 

1.00 

2.85 
12.60 

1.125 
2.27 
17.5 

No.  14 
0.08" 

D 
W 
F 

0.375 
41 
0.0418 

0.5 
28.8 
0.121 

0.625 

22.2 
0.342 

0.75 
18.1 
0.572 

0.875 
15.2 
0.82 

1.00 
13.15 
1.27 

1.125 
11.6 
1.86 

1.25 
10.35 
2.60 

1.50 
8.52 
5.48 

1.75 
7.25 
7.57 

No.  12 
0.105" 

D 
W 
F 

0.625 
52.5 
0.069 

0.75 
42.25 
0.1480 

0.875 
35.4 
0.262 

1.00 
30.4 
0.395 

1.25 
23.8 
0.830 

1.50 
19.5 
1.49 

1.75 
16.6 
2.45 

2.00 

14.4 
3.74 

2.25 
12.7 
5.45 

2.50 
11.4 
7.34 

No.  10 
0.135" 

D 

W 

F 

0.875 
77 
0.081 

1.00 
67 
0.135 

1.25 
52 
0.276 

1.50 
42.5 
0.512 

1.75 
36 

0.846 

2.00 
31 
1.295 

2.25 
27 
1.910 

2.50 
24 
2.660 

2.75 
22 
3.58 

3.00 
20 

4.75 

No.  8 
0.162" 

D 
W 
F 

1.00 
120 
0.0570 

1.25 
98.5 
0.124 

1.50 
76 
0.199 

1.75 
64 
0.554 

2.00 
55.5 
0.597 

2.25 

48.8 
0.880 

2.50 
43.5 
1.26 

2.75 
39 
1.68 

3.00 
36 
2.20 

3.25 
33 

2.85 

No.  7 
0.177" 

D 
W 
F 

1.00 
159 
0.0382 

1.25 
122 
0.0828 

1.50 
99 
0.156 

1.75 

83.5 
0.265 

2.00 
72 
0.416 

2.25 
63 
0.603 

2.50 
56.4 
0.830 

2.75 
51 
1.15 

3.00 
46.5 
1.54 

3.25 
42.5 
1.96 

No.  6 
0.192" 

D 

W 
F 

1.25 
158 
0.0572 

1.50 
128 
0.108 

1.75 
107 
0.185 

2.00 
92.5 
0.284 

2.25 
81 
0.420 

2.50 
72 
0.590 

2.75 
65 
0.802 

3.00 

59.5 
1.07 

3.25 
55.5 
1.38 

3.50 
50 
1.74 

No.  3 
0.205" 

D 
W 

F 

1.50 
155 
0.0820 

1.75 
131 
0.139 

2.00 
113 
0.218 

2.25 
99 
0.321 

2.50 

88.5 
0.412 

2.75 
80 
0.6175 

3.00 
70 
0.82 

3.25 
67 
1.60 

3.50 
61.5 
1.34 

4.00 
53.5 
2.22 

No.  4 
0.225" 

D 
W 
F 

1.50 
210 
0.0536 

1.75 
175 
0.093 

2.00 
150 
0.147 

2.25 
132 
0.220 

2.50 
118 
0.303 

2.75 
106 
0.412 

3.00 
97 
0.652 

3.25 
89 
0.715 

3.50 
82 
0.91 

4.00 
71 
1.30 

No.  2 
0.263" 

D 
W 
F 

1.50 
345 
0.0264 

1.75 
290 
0.0458 

2.00 
250 
0.0730 

2.25 
215 
0.109 

2.50 
192 
0.154 

2.75 
175 
0.214 

3.00 
156 
0.274 

3.25 
146 
0.371 

3.50 
134 
0.469 

4.00 
115 
0.720 

No.  1 
0.283" 

D 

W 
F 

1.75 
360 
0.0328 

2.00 
310 
0.0550 

2.25 
270 
0.0778 

2.50 
240 
0.112 

2.75 
215 
0.155 

3.00 
195  < 
0.208 

3.25 

,  180 
0.270 

3.50 
165 
0.344 

4.00 
145 
0.530 

4.50 
127 
0.775 

No.  0 
0.307" 

D 

W 
F 

1.75 
470 
0.0308 

2.00 
400 
0.0380 

2.25 
350 
0.0548 

2.50 
310 
0.0788 

2.75 
280 
0.109 

3.00 
250 
0.149 

3.25 
230 
0.199 

3.50 
212 
0.244 

4.00 
185 
0.327 

4.50 
162 
0.550 

No.  00 
0.331" 

D 
W 
F 

2.00 
510 
0.0289 

2.25 
445 
0.0388 

2.50 
390 
0.0564 

2.75 
350 
0.0780 

3.00 
320 
0.105 

3.25 
290 
0.137 

3.50 
270 
0.176 

4.00 
230 
0.273 

4.50 
205 
0.414 

5.00 
183 
0.562 

To  find  deflection  of  one  coil  by  one  pound,  divide  the  values  of  F  by  100. 


422 


SPRINGS. 


ELLIPTICAL  SPRINGS,   SIZES,  AND  PROOF  TESTS. 

Pennsylvania  Railroad  Specifications,  1896. 


a 

0> 
01 

£    t» 

m. 

Test 

3. 

Class. 

u£ 

XJ 

*t 

*3 

S   a) 

0Q 
1-1 

* 

ii 

Plates, 
No.  Size,  In 

Ins.  high.      Ibs. 
(a)       (6) 

Ins.     Ibs. 

(a) 

J 

oS, 
aj 

E  1  Triple  . 

40 

113/4 

5  3  x  ll/3-> 

3  3/4       9  3/8      4  800 

3         5  500 

? 

E  2,  Quadruple  .  . 
E  3  Triple  .... 

40 
36 

151/2 
113/4 

5  3  x3/8 
6  3  X  11/32 

33/4       93/4      6,650 
4             95/8      6  000 

3         8,000 
3         8000 

2 

E  4,  Singlet--. 

40 

8  3  X  11/32 

5*                     ffee 

3        2350 

E5,  "  t  

E  6  "  |..  • 

40 

4? 

7  3x3/8 
8  31/2X3/8 

1  5/16*     ....      3,000 
1  1/8*                  4  375 

0        4,970 
0        6350 

E  7.  Triple  

36 

i  i  3/4 

8  3  X  11/30 

21/2        91/2    11  800 

E  8,  Double  
E  9,        '      
E  10,  Quadruple.. 
E  11, 
E  12, 
E  13,  Double  
E  14,       "      
E  15,  Quadruple.. 
E  16, 
E  17,  Double  
E  18,  Singlet.... 
E  19,  Double  
E  20 

32 
36 
40 
40 
34 
30 
40 
36 
30 
36 
42 
22 
?? 

71/2 
91/2 
15V2 
151/2 
151/2 
91/2 
91/2 
151/2 
151/2 
91/2 

"ioi/2 

101/2 

6  3  x3/8 
5  4x11/32 
5  3  x3/8 
5  3X3/8 
5  3x3/8 
5  4x3/8 
6  4X11/32 
6  3xll/32 
6  3x11/32 
5  4x3/8 
9  31/2x3/8 
6  41/2X11/32 
7  41/2x11/32 

3             9           8,000 
31/2       87/16    5,400 
4           10           8,000 
33/4       93/4    10,600 
33/4       93/4    .13,100 
33/4        9           5,600 
33/8       9           6,840 
37/16      93/4    11,820 
41/2      101/s      8,000 
23/4       8           8,070 
1*                      5,250 
13/16    67/16  13,800 
13/16    71/8    I5  60° 

3"  6',  666 

3       10,000 
3       12,200 
3       15,780 
2       10,600 
2        8,600 
21/2  14,370 
23/415,500 
2        9,540 
0         7,300 

"2 
2 
2 

2 

E2li  
E  22,  
E  23,  

E  24,  .... 

24 
24 
36 
36 

101/2 
JO* 

10 

7  41/2X3  8 
8  41/2X3/8 
5  4x3/8 
5  4x3/8 

1             71/4    15>50 
1             81/2    18,000 
21/4       8           8,750 
21/4       8           7.500 

0       28,800 
0       32,930 
11  '4  10,750 
11/4  9,500 

(a)  Between  bands;  (&)  over  all;  a.p.t.,  auxiliary  plates  touching. 
*  Between  bottom  of  eye  and  top  of  leaf,     t  Semi-elliptical. 
Tracings  are  furnished  for  each  class  of  spring. 


SPRINGS  TO  RESIST  TORSIONAL  FORCE. 

(Reuleaux's  Constructor.) 


Flat  spiral  or  helical  spring  P  = 

o  H 


=  12 


Round  helical  spring P 


32  R' 


PIR* 

Ebh*' 

PI 

E 


Round  bar,  in  torsion F  =  •=-=  ^* 

<*  lu  /t 


Flat  bar,  in  torsion. 


'  3RV& 


P  =  force  applied  at  end  of  radius  or  lever-arm  R\  &  =  angular  motion 
at  end  of  radius  R;  S  =  permissible  maximum  stress,  =  4/5Of  permissible 
stress  in  flexure:  E  =  modulus  of  elasticity  in  tension;  G  =  torsionaJ 
modulus,  =  2/5  E;  I  =  developed  length  of  spiral,  or  length  of  bar;  d  = 
diameter  of  wire;  b  =  breadth  of  flat  bar;  h  =  thickness. 
(Compare  Elastic  Resistance  to  Torsion,  p.  334.) 


HELICAL   SPRINGS. 


423 


HELICAL   SPRINGS  — SIZES  AND   CAPACITIES. 

(Selected  from  Specifications  of  Penna.  R.  R.  Co.,  1899.) 


«+H 

Test.  Height  and 

0) 

"M 

00 

a 

^T 

co 

^ 

O 

Loads. 

.S 

»3 

f_T 

& 

.S 

•8 

a 

25 

o 

<& 

Q 

GO 

Q 

£ 

•s 

^ 

Qg 

GO 

GO 

,0 

>j  01 

• 

* 

.d 

i 

| 

"S'Z  r 

.S 

.s 

1 

? 

'S""* 

e3—  " 

fc 

5 

"M  oi 

i 

E 

1 

J2  o 

"So 
o 

of 

1 

GO 

c 

i—  i 

I 

o/o 

6s 

Ibs.     oz 

H  26 

9/64 

571/2 

59 

0      4 

i 

53/4 

3 

31/4 

no 

130 

H  18 

H/64 

75 

761/4 

0      8 

i 

8 

5 

6 

170 

270 

H  55 

3/16 

451/8 

465/16 

0      55/8 

i 

41/2 

35/16 

4 

103 

245 

H  73 

3/16 

426 

4273/4 

3      51/2 

15/16 

39 

221/2 

35 

45 

185 

H  29 

7/32 

20  !/•> 

227/16 

0      31/2 

115/32 

HI/16 

19/64 

13/8 

110 

200 

H  1 

1/4 

451/2 

47 

0     10 

U/4 

51/8 

35/8 

43/8 

250 

500 

H  5 

V4 

251/4 

281/4 

0      6 

2V4 

21/4 

H/8 

U/2 

164 

240 

H  58 

5/16 

2531/2 

2561/2 

5      7 

21/4 

23 

13 

18 

248 

495 

H  74 

5/16 

180 

1821/s 

3     141/2 

IU/16 

191/8 

13 

141/8 

587 

700 

H  681* 

3/8 

991/2 

1031/4 

3      U/2 

23/4 

9 

5 

7 

350 

700 

H  79 

3/8 

88 

903/4 

2    12 

21/8 

85/8 

6 

63/4 

676 

946 

H  802 

13/32 

1923/g 

1953/4 

7      '1/2 

29/16 

18 

119/16 

151/2 

380 

975 

H  43 

7/16 

96 

1025/i6 

4      1 

47/16 

815/ie 

33/8 

51/8 

450 

660 

H  64 

7/16 

755/8 

781/2 

3      3 

29/32 

75/8 

55/8 

53/4 

1350 

1440 

H  532 

15/32 

1695/iQ 

1729/16 

8      4 

217/32 

61/2 

21/4 

51/2 

330 

1410 

H  272 

1/2 

903/4 

951/8 

5      0 

31/4 

81/2 

51/4 

63/4 

810 

1500 

H  61 

1/2 

151/2 

213/s 

0     133/4 

41/4 

13/8 

05/8 

1 

532 

1050 

H  19 

17/32 

8U/2 

851/2 

5      2 

31/32 

8 

59/ie 

67/16 

1200 

1900 

H  863 

17/32 

1535/8 

159 

9     10 

4 

33/4 

71/2 

87/16 

1156 

1360 

H  63 

9/16 

98 

103 

6     15 

33/4 

91/8 

51/2 

7 

1050 

1800 

H  333 

9/16 

801/4 

847/s 

5     101/9 

31/4 

8 

53/8 

613/ie 

1000 

2200 

H  592 

5/8 

741/4 

773/4 

67" 

27/8 

81/4 

69/ie 

71/4 

2100 

3500 

H  8(h 

5/8 

1921/2 

1973/4 

16     11 

315/ie 

8 

19/16 

51/2 

900 

2315 

H  722 
H  152 

21/32 
U/16 

601/8 

557/8 

631/2 
593/4 

\  !i7/8 

23/4 
31/2 

75/16 
53/4 

6 

45/16 

63/8 
53/i6 

3260 
1400 

4240 
3500 

H  41 
H  40 

U/16 

3/4 

1171/2 
1771/2 

1231/2 
1865/8 

12     10 

22      21/2 

41/2 
6V2 

07/8 
6 

63/4 

73/8 

85/8 
87/8 

1500 
1900 

2720 
2300 

H  70 

3/4 

62 

66 

7     12 

33/8 

7 

55/8 

61/4 

2750 

5050 

H  172 

13/16 

100 

1063/4 

14     12 

51/8 

91/8 

6 

75/8 

1700 

3700 

H  662 

13/16 

1051/4 

1103/8 

15      7 

45/32 

07/8 

81/8 

87/8 

3670 

5040 

H  37 

27/32 

77 

817/8 

12      21/2 

315/16 

81/2 

6U/16 

71/2 

3300 

6250 

H  872 

27/32 

3013/J6 

13715/ie 

20      9 

53/8 

21/4 

73/4 

87/16 

3540 

4165 

H  122 

7/8 

85 

9U/2 

14      7 

5 

81/2 

53/: 

73/8 

2000 

5200 

H  33. 

7/8 

82 

8811/i6 

13     15 

51/8 

8 

53/8 

613/16 

2250 

5000 

H  2 

15/16 

46 

523/8 

8    151/4 

5 

45/8 

33/8 

4 

3250 

7000 

H  16 

15/16 

85 

927/s 

16     10 

> 

8 

5 

6 

3600 

5100 

H  10 

85 

92 

18     14 

51/2 

81/2 

6 

7 

4500 

7000 

H  42! 

36 

427/8 

8      0 

53/8 

35/8 

25/8 

33/8 

1795 

7180 

H  4 

1  1/16 

987/s 

105 

24    12 

| 

07/8 

81/2 

93/8 

6000 

9570 

H  861 

U/16 

535/s 

1641/2 

38      9 

8 

33/4 

71/2 

87/i6 

4624 

5440 

H  3 

U/8 

353/8 

4U/4 

9    15 

47/8 

41/8 

33/8 

33/4 

6000 

12000 

H  14! 

H/8 

51 

587/s 

14      4 

61/8 

51/8 

3H/16 

43/16 

5000 

8950 

H6! 

3/16 

991/s 

1093/4 

31       1 

8 

91/8. 

51/2 

7 

4550 

7750 

H47 

3/16 

731/2 

791/2 

23      0 

57/ie 

81/4 

69/ie 

71/4 

7400 

12500 

H  9 

1/4 

971/2 

108 

33     12 

8 

9 

53/4 

71/2 

4000 

9100 

H  72i 

1/4 

621/8 

683/4 

21      81/2 

53/8 

75/16 

6 

63/8 

0700 

14875 

H  8 

5/ie 

96 

1061/2 

36     12 

8 

91/8 

6 

71/4 

6350 

10600 

H  62 

5/16 

70 

771/ie 

26     12 

513/16 

8 

6V2 

71/4 

7900 

15800 

H  12! 

3/8 

87 

973/8 

36      7 

8 

81/2 

53/4 

73/8 

5000 

12200 

H  39i 

3/8 

755/8 

831/2 

31     11 

63/8 

83/8 

65/8 

71/2 

8150 

16300 

H  28i 

13/32 

8411/ie 

95 

37      3 

8 

81/4 

53/4 

67/8 

7325 

13250 

*  The  subscript  1  means  the  outside  coil  of  a  concentric  group  or 
cluster;  2  and  3  are  inner  coils. 


424  EIVETED   JOINTS. 

Phosphor-Bronze  Springs.    Wilfred  Lewis  (Engs'.  Club,  Phila.,  1887) 

made  some  tests  of  a  helical  spring  of  phosphor-bronze  wire,   0.12   in. 
diameter,  11/4  in.  diameter  from  center  to  center,  making  52  coils. 

Such  a  spring  of  steel,  according  to  the  practice  of  the  P.  R.  R.,  might 
be  used  for  40  Ibs.  A  load  of  30  Ibs.  gradually  applied  gave  a  permanent 
set.  With  a  load  of  21  Ibs.  in  30  hours  the  spring  lengthened  from  20 5/8 
inches  to  21 1/8  inches,  and  in  200  hours  to  21 1/4  inches.  It  was  concluded 
that  21  Ibs.  was  too  great  for  durability.  For  a  given  load  the  extension 
of  the  bronze  spring  was  just  double  the  extension  of  a  similar  steel 
spring,  that  is,  for  the  same  extension  the  steel  spring  is  twice  as  strong. 
Chromium- Vanadium  Spring  Steel.  (Proc.  Inst.  M.  E.,  1904,  pp 
1263,  1305.)  — A  spring  steel  containing  C,  0.44;  Si,  0.173;  Mn,  0.837;  Cr, 
1.044;  Va,  0.188  was  made  into  a  spring  with  dimensions  as  follows:  length 
unstretched  9.6  in.s  mean  diam.  of  coils  (D)  5.22;  No.  of  coils  (n)  4;  diam. 
of  wire,  (d)  0.561.  It  was  tempered  in  the  usual  way.  When  stretched 
it  showed  signs  of  permanent  set  at  about  1900  Ibs.  Compared  with  two 
springs  of  ordinary  steels  the  following  formulae  are  obtained: 

Load  at  which  Permanent  Set  begins.  Extension  for  a  load  W. 

Chrome- Vanadium  Spring. .  .56,300  d*/D  Ibs.  WnD*  +  1,468,000  d* 

West   Bromwich  Spring 28,400  d*/D     "     WnD*  -^-  1,575,000  d* 

Turton  &  Platt   Spring 44,200  d*/D     "     WnD*  +  1,331,600  d* 

Test  of  a  Vanadium-steel  Spring.  (Circular  of  the  American  Vana- 
dium Co.,  1908).  —  Comparative  tests  of  an  ordinary  carbon-steel  loco- 
motive flat  spring  and  of  a  vanadium-steel  spring,  made  by  the  American 
Locomotive  Co.,  showed  the  following:  The  vanadium  spring,  on  36-in. 
centers  tested  to  94,000  Ibs.,  reached  its  elastic  limit  at  85,000  Ibs.,  or 
234,000  Ibs.  per  sq.  in.  fiber  stress,  and  a  permanent  set  of  0.48  in.  The 
test  was  repeated  three  times  without  change  in  the  deflection.  The 
carbon  spring  was  tested  to  89,280  Ibs.  and  reached  an  elastic  limit  at 
65,000  Ibs.,  or  180,000  Ibs.  fiber  stress,  with  a  permanent  set  of  1.12  in. 
On  repeating  the  test  it  took  an  additional  set  of  0.25  in.,  and  on  the  next 
test  several  of  the  plates  failed. 

RIVETED  JOINTS. 

Fairbairn's  Experiments.  —  The  earliest  published  experiments  on 
riveted  joints  are  contained  in  the  memoir  by  Sir  W.  Fairbairn  in  the 
Transactions  of  the  Royal  Society.  Making  certain  empirical  allow- 
ances, he  adopted  the  following  ratios  as  expressing  the  relative  strength  • 

of  riveted  joints:        Solid  plate 100 

Double-riveted  joint 70 

Single-riveted  joint 56 

These  celebrated  ratios  appear  to  rest  on  a  very  unsatisfactory  analysis 
of  the  experiments  on  which  they  were  based. 

Loss  of  Strength  in  Punched  Plates.  (Proc.  Inst.  M.  E.t  1881.)  — 
A  report  by  Mr.  W.  Parker  and  Mr.  John,  made  in  1878  to  Lloyd's  Com- 
mittee, on  the  effect  of  punching  and  drilling,  showed  that  thin  steel 
plates  lost  comparatively  little  from  punching,  but  that  in  thick  plates 
the  loss  was  very  considerable.  The  following  table  gives  the  results  for 
plates  punched  and  not  annealed  or  reamed: 

Thickness  of  plates A'4      3/8      1/2      3/4 

Loss  of  tenacity,  per  cent 8       18       26       33 

When  7/8-in.  punched  holes  were  reamed  out  to  IVsin.  diameter,  the  loss 
of  tenacity  disappeared,  and  the  plates  carried  as  high  a  stress  as  drilled 
plates.  Annealing  also  restores  to  punched  plates  their  original  tenacity. 

The  Report  of  the  Research  Committee  of  the  Instituti9n  of  Mechanical 
Engineers,  on  Riveted  Joints  (1881),  and  records  of  investigations  by  Prof. 
A.  B.  W.  Kennedy  (1881,  1882,  and  1885),  summarize  the  existing  in- 
formation regarding  the  comparative  effects  of  punching  and  drilling 
upon  iron  and  steel  plates.  An  examination  of  the  voluminous  tables 
given  in  Professor  Unwin's  Report,  of  the  experiments  made  on  iron  and 
-  steel  plates  leads  to  the  general  conclusion  that,  while  thin  plates,  even 
of  steel,  do  not  suffer  very  much  from  punching,  yet  in  those  of  1/2  inch 
thickness  and  upwards  the  loss  of  tenacity  due  to  punching  ranges  from 
10%  to  23%  in  iron  plates,  and  from  11%  to  33%  in  the  case  of  mild 
steel.  In  drilled  plates  there  is  no  appreciable  loss  of  strength,  It  is 


RIVETED   JOINTS. 


425 


possible  to  remove  the  bad  effects  of  punching  by  subsequent  reaming  or 
annealing.  The  introduction  of  a  practicable  method  of  drilling  the 
plating  of  ships  and  other  structures,  after  it  has  been  bent  and  shaped, 
is  a  matter  of  great  importance.  In  the  modern  English  practice  (1887) 
of  the  construction  of  steam-boilers  with  steel  plates  punching  is  almost 
entirely  abolished,  and  all  rivet-holes  are  drilled  after  the  plates  have 
been  bent  to  the  desired  form. 

Strength  of  Perforated  Plates.  (P.  D.  Bennett,  Eng'g,  Feb.  12, 
1886.  p.  155.)  — Tests  were  made  to  determine  the  relative  effect  pro- 
duced upon  tensile  strength  of  a  flat  bar  of  iron  or  steel:  1.  By  a  s/4-inch 
hole  drilled  to  the  required  size;  2.  By  a  hole  punched  Vs  inch  smaller 


and  then  drilled  to  the  size  of  the  first  hole;  and,  3.    By  a  hole  punched  in 
the  bar  to  the  size  of  the  drilled  hole.    The  relative  results  in  strength 
per  square  inch  of  original  area  were  as  follows: 

1. 

2. 

3. 

4. 

Iron 
1.000 
1.029 
1.030 
0.795 

Iron. 
1.000 
1.012 
1.008 
0.894 

Steel. 
1  000 
1.068 
1.059 
0.935 

Steel. 
1.000 
1.103 
1.110 
0  927 

Perforated  by  drilling                . 

Perforated  by  punching  and  drilling 
Perforated  by  punching  only  

In  tests  2  and  4  the  holes  were  filled  with  rivets  driven  by  hydraulic 
pressure.  The  increase  of  strength  per  square  inch  caused  by  drilling  is 
a  phenomenon  of  similar  nature  to  that  of  the  increased  strength  of  a 
grooved  bar  over  that  of  a  straight  bar  of  sectional  area  equal  to  the 
smallest  section  of  the  grooved  bar.  Mr.  Bennett's  tests  on  an  iron  bar 
0.84  in.  diameter,  10  in.  long,  and  a  similar  bar  turned  to  0.84  in.  diam- 
eter at  one  point  only,  showed  that  the  relative  strength  01  the  latter  to 
the  former  was  1.323  to  1.000. 

Comparative  Efficiency  of  Riveting  done  by  Different  Methods. 

The  Reports  of  Professors  Unwin  and  Kennedy  to  the  Institution  of 
Mechanical  Engineers  (Proc.  1881,  1882,  and  1885)  tend  to  establish  the 
four  following  points: 

1.  That  the  shearing  resistance  of  rivets  is  not  highest  in  joints  riveted 
by  means  of  the  greatest  pressure; 

2.  That  the  ultimate  strength  of  joints  is  not  affected  to  an  appre- 
ciable extent  by  the  mode  of  riveting;  and,  therefore, 

3.  That  very  great  pressure  upon  the  rivets  in  riveting  is  not  the  in- 
dispensable requirement  that  it  has  been  sometimes  supposed  to  be; 

4.  That  the  most  serious  defect  of  hand-riveted  as  compared  with 
machine-riveted  work  consists  in  the  fact  that  in  hand-riveted  joints 
visible  slip  commences  at  a  comparatively  small  load,  thus  giving  such 
joints  a  low  value  as  regards  tightness,  and  possibly  also  rendering  them 
liable  to  failure  under  sudden  strains  after  slip  has  once  commenced. 

The  following  figures  of  mean  results  give  a  comparative  view  of  hand 
and  hydraulic  riveting,  as  regards  their  ultimate  strengths  in  joints,  and 
the  periods  at  which  in  both  cases  visible  slip  commenced. 


Hand  

86  01 

82  16 

149  2 

193  6 

Total  breaking  load.    Tons  .  .  .  .  | 

Hydraulic 

85  75 

82  70 

145  5 

183  1 

Hand  

21.7 

25.0 

31  7 

25  0 

Hydraulic  

47.5 

53.7 

49.7 

56.0 

Some  of  the  Conclusions  of  the  Committee  of  Research  on  Riveted 
Joints. 

(Proc.  Inst.  M.  E.,  April,  1885.) 

The  conclusions  refer  to  joints  made  in  soft  steel  plate  with  steel  rivets, 
the  holes  drilled,  and  the  plates  in  their  natural  state  (unannealed). 
The  rivet  or  shearing  area  has  been  assumed  to  be  that  of  the  holes,  not 
the  area  of  the  rivets  themselves.  The  strength  of  the  metal  in  the  joint 
has  been  compared  with  that  of  strips  cut  from  the  same  plates. 


426 


RIVETED   JOINTS. 


The  metal  between  the  rivet-holes  has  a  considerably  greater  tensile 
resistance  per  square  inch  than  the  unperf  orated  metal.  This  excess 
tenacity  amounted  to  more  than  20%,  both  in  3/8-inch  and  3/4-inch  plates, 
when  the  pitch  of  the  rivet  was  about  1.9  diameters.  In  other  cases  3/g-inch 
plate  gave  an  excess  of  15%  at  fracture  with  a  pitch  of  2  diameters,  of 
10%  with  a  pitch  of  3.6  diameters,  and  of  6.6%,  with  a  pitch  of  3.9 
diameters;  and  3/4-inch  plate  gave  7.8%  excess  with  a  pitch  of  2.8 
diameters. 

In  single-riveted  joints  it  may  be  taken  that  about  22  tons  per  square 
inch  is  the  shearing  resistance  of  rivet  steel,  when  the  pressure  on  the 
rivets  does  not  exceed  about  40  tons  per  square  inch.  In  double-riveted 
joints,  with  rivets  of  about  3/4-inch  diameter,  most  of  the  experiments 
gave  about  24  tons  per  square  inch  as  the  shearing  resistance,  but  the 
joints  in  one  series  went  at  22  tons.  [Tons  of  2240  Ibs.] 

The  ratio  of  shearing  resistance  to  tenacity  is  not  constant,  but  dimin- 
ishes very  markedly  and  not  very  irregularly  as  the  tenacity  increases. 
'  The  size  of  the  rivet  heads  and  ends  plays- a  most  important  part  in  the 
strength  of  the  joints  —  at  any  rate  in  the  case  of  single-riveted  joints. 
An  increase  of  about  one-third  in  the  weight  of  the  rivets  (all  this  increase, 
of  course,  going  to  the  heads  and  ends)  was  found  to  add  about  81/2%  to 
the  resistance  of  the  joint,  the  plates  remaining  unbroken  at  the  full 
shearing  resistance  of  22  tons  per  square  inch,  instead  of  tearing  at  a 
shearing  stress  of  only  a  little  over  20  tons.  The  additional  strength  is 
probably  due  to  the  prevention  of  the  distortion  of  the  plates  by  the 
great  tensile  stress  in  the  rivets. 

The  intensity  of  bearing  pressure  on  the  rivet  exercises,  with  joints 
proportioned  in  the  ordinary  way,  a  very  important  influence  on  their 
strength.  So  long  as  it  does  not  exceed  40  tons  per  square  inch  (meas- 
ured on  the  projected  area  of  the  rivets),  it  does  not  seem  to  affect  their 
strength;  but  pressures  of  50  to  55  tons  per  square  inch  seem  to  cause 
the  rivets  to  shear  in  most  cases  at  stresses  varying  from  16  to  18  tons 
per  square  inch.  For  ordinary  joints,  which  are  to  be  made  equally 
strong  in  plate  and  in  rivets,  the  bearing  pressure  should  therefore  prob- 
ably not  exceed  42  or  43  tons  per  square  inch.  For  double-riveted  butt- 
joints  perhaps,  as  will  be  noted  later,  a  higher  pressure  may  be  allowed, 
as  the  shearing  stress  may  probably  not  be  more  than  16  or  18  tons  per 
square  inch  when  the  plate  tears. 

A  margin  (or  net  distance  from  outside  of  holes  to  edge  of  plate)  equal 
to  the  diameter  of  the  drilled  hole  has  been  found  sufficient  in  all  cases 
hitherto  tried. 

To  attain  the  maximum  strength  of  a  joint,  the  breadth  of  lap  must  be 
such  as  to  prevent  it  from  breaking  zigzag.  It  has  been  found  that  the 
net  metal  measured  zigzag  should  be  from  30%  to  35%  in  excess  of  that 
measured  straight  across,  in  order  to  insure  a  straight  fracture.  This 
corresponds  to  a  diagonal  pitch  of  2/3  p  +  d/3,  if  p  be  the  straight  pitch 
and  d  the  diameter  of  the  rivet-hole. 

Visible  slip  or  "give"  occurs  always  in  a  riveted  joint  at  a  point  very 
much  below  its  breaking  load,  and  by  no  means  proportional  to  that  load. 
A  collation  of  the  results  obtained  in  measuring  the  slip  indicates  that  it 
depends  up9n  the  number  and  size  of  the  rivets  in  the  joint,  rather  than 
upon  anything  else;  and  that  it  is  tolerably  constant  for  a  given  size  of 
rivet  in  a  given  type  of  joint.  The  loads  per  rivet  at  which  a  joint  will 
•commence  to  slip  visibly  are  approximately  as  follows: 


Diameter  of  Rivet. 

Type  of  Joint. 

Riveting. 

Slipping  Load  per 
Rivet. 

3/4  inch 
8/4      » 
8/4      •• 
linch 
1     " 
1     " 

Single-riveted 
Double-  riveted 
Double-riveted 
Single-  riveted 
Double-  riveted 
Double-  riveted 

Hand 
Hand 
Machine 
Hand 
Hand 
Machine 

2.5  tons 
3.0  to  3.5  tons 
7  tons 
3.2  tons 
4.3  tons 
8  to  10  tons 

RIVETED   JOINTS. 


427 


To  find  the  probable  load  at  which  a  joint  of  any  breadth  will  commence 
to  slip,  multiply  the  number  of  rivets  in  the  given  breadth  by  the  proper 
figure  taken  from  the  last  column  of  the  table  above.  The  above  figures 
are  not  given  as  exact;  but  they  represent  the  results  of  the  experiments. 

The  experiments  point  to  simple  rules  for  the  proportioning  of  joints  of 
maximum  strength.  Assuming  that  a  bearing  pressure  of  43  tons  per 
square  inch  may  be  allowed  on  the  rivet,  and  that  the  excess  tenacity  of 
the  plate  is  10%  of  its  original  strength,  the  following  table  gives  the 
values  of  the  ratios  of  diameter  d  of  hole  to  thickness  t  of  plate  (d  •*-  0, 
and  of  pitch  p  to  diameter  of  hole  (p  -5-  d)  in  joints  of  maximum  strength 
in  3/8-inch  plate. 


For  Single-riveted  Plates. 


Original  Tenacity  of 
Plate. 

Shearing  Resistance 
of  Rivets. 

Ratio. 
d-r-t 

Ratio. 

Ratio. 
Plate  Area 

Tons  per 
Sq.  In. 

Lbs.  per 
Sq.  In. 

Tons  per 
Sq.  In. 

Lbs.  per 
Sq.  In. 

Rivet  Area 

30 

67,200 

22 

49,200 

2.48 

2.30 

0.667 

28 

62,720 

22 

49,200 

2.48 

2.40 

0.785 

30 

67,200 

24 

53,760 

2.28 

2.27 

0.713 

28 

62,720 

24 

53,760 

2.28 

2.36 

0.690 

This  table  shows  that  the  diameter  of  the  hole  should  be  2Vs  times  the 
thickness  of  the  plate,  and  the  pitch  of  the  rivets  23/g  times  the  diameter 
of  the  hole.  Also,  it  makes  the  mean  plate  area  71%  of  the  rivet  area. 
If  a  smaller  rivet  be  used  than  that  here  specified,  the  joint  will  not  be  of 
uniform,  and  therefore  not  of  maximum,  strength;  but  with  any  other 
size  of  rivet  the  t>est  result  will  be  got  by  use  of  the  pitch  obtained  from  the 
simple  formula  p  =  ad2/t  +  d,  where,  as  before,  d  is  the  diameter  of  the 
hole. 

The  value  of  the  constant  a  in  this  equation  is  as  follows: 
For  30-ton  plate  and  22-ton  rivets,  a  =   0.524 

"      28    "        "         "    22    "         "        "         0.558 
,.     3Q    «,        „        «    24    ..        „       „        05?0 

"     28    "        "         "    24    "        "       "         0.606 


Or,  in  the  mean,  the  pitch  p 


0.56    -  +  d. 


With  too  small  rivets  this 


gives  pitches  often  considerably  smaller  in  proportion  than  23/s  times  the 
diameter. 

For  double-riveted  lap-joints  a  similar  calculation  to  that  given 
above,  but  with  a  somewhat  smaller  allowance  for  excess  tenacity,  on 
account  of  the  large  distance  between  the  rivet-holes,  shows  that  for  joints 
of  maximum  strength  the  ratio  of  diameter  to  thickness  should  remain 
precisely  as  in  single-riveted  joints;  while  the  ratio  of  pitch  to  diameter 
of  hole  should  be  3.64  for  30-ton  plates  and  22  or  24  ton  rivets,  and  3.82 
for  28-ton  plates  with  the  same  rivets. 

Here,  still  more  than  in  the  former  case,  it  is  likely  that  the  prescribed 
size  of  rivet  may  often  be  inconveniently  large.  In  this  case  the  diameter 
of  rivet  should  be  taken  as  large  as  possible;  and  the  strongest  joint  for 
a  given  thickness  of  plate  and  diameter  of  hole  can  then  be  obtained  by 
using  the  pitch  given  by  the  equation  p  =  ad2/t  +  d,  where  the  values  of 
the  constant  a  for  different  strengths  of  plates  and  rivets  may  be  taken 
as  follows,  for  any  thickness  of  plate  from  3/8  to  3/4-inch: 


For  30-ton  plate  and  24-ton  rivets  ) 

••     28    "        "        "    22     "       "      j 

••     30    "        " 


=  1.16 

t 


••  1.06 


"  24 


p  ~  1.24 


428 


RIVETED   JOINTS. 


In  double-riveted  butt-joints  it  is  impossible  to  develop  the  full 
shearing  resistance  of  the  joint  without  getting  excessive  bearing  pressure, 
because  the  shearing  area  is  doubled  without  increasing  the  area  on  which 
the  pressure  acts.  Considering  only  the  plate  resistance  and  the  bearing 
pressure,  and  taking  this  latter  as  45  tons  per  square  inch,  the  best  pitch 
would  be  about  4  times  the  diameter  of  the  hole.  We  may  probably  say 
with  some  certainty  that  a  pressure  of  from  45  to  50  tons  per  square  inch  on 
the  rivets  will  cause  shearing  to  take  place  at  from  16  to  18  tons  per  square 
inch.  Working  out  the  equations  as  before,  but  allowing  excess  strength 
of  only  5%  on  account  of  the  large  pitch,  we  find  that  the  proportions  of 
double-riveted  butt-joints  of  maximum  strength,  under  given  conditions, 
are  those  of  the  following  table: 

Double-riveted  Butt-joints. 


Original  Ten- 
acity of  Plate, 
Tons  per  Sq. 
In. 

Shearing  Re- 
sistance of 
Rivets,  Tons 
per  Sq.  In. 

Bearing  Pres- 
sure, Tons  per 
Sq.  In. 

Ratio 
d 
t 

Ratio 
P 
d 

30 

16 

45 

1.80 

3.85 

28 

16 

45 

1.80 

4.06 

30 

18 

48 

1.70 

4.03 

28 

18 

48 

1.70 

4.27 

30 

16 

50 

2.00 

4.20 

28 

16 

50 

2.00 

4.42 

Practically,  therefore,  it  may  be  said  that  we  get  a  double-riveted  butt- 
joint  of  maximum  strength  by  making  the  diameter  of  hole  about  1.8 
times  the  thickness  of  the  plate,  and  making  the  pitch  4.1  times  the 
diameter  of  the  hole. 

The  proportions  just  given  betong  to  joints  ot  maximum  strength. 
But  in  a  boiler  the  one  part  of  the  joint,  the  plate,  is  much  more  affected 
by  time,  than  the  other  part,  the  rivets.  It  is  therefore  not  unreasonable 
to  estimate  the  percentage  by  which  the  iplates  might  be  weakened 'by 
corrosion,  etc.,  before  the  boiler  would  be  unfit  for  use  at  its  proper 
steam-pressure,  and  to  add  correspondingly  to  the  plate  area.  Probably 
the  best  thing  to  do  in  this  case  is  to  proportion  the  joint,  not  for  the 
actual  thickness  of  plate,  but  for  a  nominal  thickness  less  than  the  actual 
by  the  assumed  percentage.  In  this  case  the  joint  will  be  approximately 
one  of  uniform  strength  by  the  time  it  has  reached  its  final  workable 
condition;  up  to  which  time  the  joint  as  a  whole  will  not  really  have  been 
weakened,  the  corrosion  only  gradually  bringing  the  strength  of  the  plates 
down  to  that  of  rivets. 

Efficiencies  of  Joints. 

The  average  results  of  experiments  by  the  committee  gave:  For  double- 
riveted  lap-joints  in  3  8-inch  plates,  efficiencies  ranging  from  67.1%  to 
81.2%.  For  double-riveted  butt-joints  (in  double  shear)  61.4%  to  71.3%. 
These  low  results. were  probably  due  to  the  use  of  very  soft  steel  in  the 
rivets.  For  single-riveted  lap-joints  of  various  dimensions  the  efficiencies 
varied  from  54.8%  to  60.8%.  The  shearing  resistance  of  steel  did  not  in- 
crease nearly  so  fast  as  its  tensile  resistance.  With  very  soft' steel,  for 
instance,  of  only  26  tons  tenacity,  the  shearing  resistance  was  about  80% 
of  the  tensile  resistance,  whereas  with  very  hard  steel  of  52  tons  tenacity 
the  shearing  resistance  was  only  somewhere  about  65%  of  the  tensile 
resistance. 

Proportions  of  Pitch  and  Overlap  of  Plates  to  Diameter  of  Rivet- 
Hole  and  Thickness  of  Plate. 

(Prof.  A.  B.  W.  Kennedy,  Proc.  Inst.  M.  E.,  April,  1885.) 

t  =  thickness  of  plate: 

d  =  diameter  of  rivet  (actual)  in  parallel  hole; 

p  =  pitch  of  rivets,  center  to  center- 

s  =  space  between  lines  of  rivets; 

i  —  overlap  of  plate. 


RIVETED   JOINTS. 


429 


The  pitch  is  as  wide  as  is  allowable  without  impairing  the  tightness  ol 
the  joint  under  steam. 

For  single-riveted  lap-joints  in  the  circular  seams  of  boilers  wnich  have 
double-riveted  longitudinal  lap-joints, 

d  =  t  X  2.25;  p  =  d  X  2.25  =  t  X  5  (nearly);  I  =  t  X  6. 

For  double-riveted  lap-joints: 

d  =  2.25J;  p  =  8t;  s  =  4.5J;  I  =  10.5J. 


Single-  riveted  Joints. 

Double-riveted  Joints. 

t 

d 

P 

I 

t 

d 

P 

s 

I 

3/16 

1/4 
5/16 
3/8 
7/16 

V2 

9/16 

7/16 
9/16 
H/16 
13/16 

H/8 
U/4    - 

15/16 
U/4 
1  9/i6 
17/8 
23/ie 
21/2 
213/16 

H/8 
H/2 

17/8 
21/4 
25/8 

33/8 

3/16 
1/4 
5/16 

$k 
& 

'  7/ie 
9/16 
H/16 
13/16 

U'8 
U/4 

U/2 

2 

21/2 

31/2 
4 
41/2 

7/8 
13/16 
U/2 
13/4 

21/4 
21/2 

2 
23/4 
33/8 

45/8 

51/4 
57/8 

With  these  proportions  and  good  workmanship  there  need  be  no  fear  of 
leakage  of  steam  through  the  riveted  joint. 

The  net  diagonal  area,  or  area  of  plate,  along  a  zigzag  line  of  fracture 
should  not  be  less  than  30%  in  excess  of  the  net  area  straight  across  the 
joint,  and  35%  is  better. 

Mr.  Theodore  Cooper  (R.  R.  Gazette,  Aug.  22,  1890),  referring  to  Prof. 
Kennedy's  statement  quoted  above,  gives  as  a  sufficiently  approximate 
rule  for  the  proper  pitch  between  the  rows  in  staggered  riveting,  one-half 
of  the  pitch  of  the  rivets  in  a  row  plus  one-quarter  the  diameter  of  a 
rivet-hole. 

Test  of  Double-riveted  Lap  and  Butt  Joints. 

(Proc.  Inst.  M.  E.,  October,  1888.) 

Steel  plates  of  25  to  26  tons  per  square  inch  T.  S.,  steel  rivets  of  24.6 
tons  shearing  strength  per  square  inch. 


Kind  of  Joint. 

Thickness  of 
Plate. 

Diameter  of 
Rivet-holes. 

Ratio  of 
Pitch  to 
Diameter. 

Comparative 
Efficiency  of 
Joint. 

Lap  

3/8" 

0.8" 

3.62 

75.2 

Butt 

3/8 

0.7 

3.93 

76.5 

Lap 

3/4 

I 

2  82 

68.0 

Lap             

3/4 

.6 

3.41 

73.6 

Butt 

3/4 

1 

4  00 

72.4 

Butt  

3/4 

.6 

3.94 

76.1 

Lap 

3 

2.42 

63.0 

Lap      

| 

.75 

3.00 

70.2 

Butt 

1 

.3 

3.92 

76.1 

Diameter  of  Rivets  for  Different  Thicknesses  of  Plates. 


Thickness 
of  Plate. 

5/16 

3/8 

7/16 

1/2 

9/16 

5/8 

H/16 

3/4 

13/16 

7/8 

15/16 

1 

Diam.  (1).. 
Diam.  (2)1. 
Diam.  (3).. 
Diam.  (4).. 

5/8 

5/8 
1/2 

5/8 
5/8 
5/8 
5/8 

5/8 
3/4 
3/4 
'5/8 

3/4 
13/16 

3/4 

3/4 
13/16 
7/8 
3/4 

3/4 
7/8 

7/8 

7/8 
7/8 
13/1  « 

7/8 
15/16 

7/8 

r/s 

1 

1 
U/8 
U/8 

1 
13/16 
U/8 

1 
U/4 
U/8 

Diam  (5) 

3/4 

7/8 

15/16 

| 

Diam  (6) 

11/16 

3/4 

lrVl6 

I 

1 

Diam'.  (7)  .'  1 

3/8 

1/2 

9/16 

11/16 

3/4 

13/16 

430 


RIVETED    JOINTS. 


(1)  Lloyd's    Rules.     (2)  Liverpool    Rules. 


(4)  French  Veritas"  "  (syHartford'Stearn^Boiler'lnsirection  and  In 


(3)  English 
.      ,_,  ___________________  iler  Inspection  and  Insur- 

ance Co.,  double  riveted  lap-joints.     (6)  Ditto,  triple-riveted  butt-joints. 
(7)  F.  E.  Cardullo.    (Vie  less  than  diam.  of  hole.) 

Calculated  Efficiencies  —  Steel  Plates  and  Steel  Rivets.—  The 
following  table  has  been  calculated  by  the  author  on  the  assumptions  that 
the  excess  strength  of  the  perforated  plate  is  10%,  and  that  the  shearing 
strength  of  the  rivets  per  square  inch  is  four-fifths  of  the  tensile  strength 
of  the  plate  (or,  if  no  allowance  is  made  for  excess  strength  of  the  perfo- 
rated plate  that  the  shearing  strength  is  72.7%  of  the  tensile  strength). 
If  t  =  thickness  of  plate,  d  =  diameter  of  rivet-hole,  p  =  pitch,  and  T  = 
tensile  strength  per  square  inch,  then  for  single-riveted  plates 


(P  -  d)tX  I.IOT 


T,  whence  p 


0.  57  ly  +  d. 
-- 


For  double-riveted  lap-joints,  p  =  1.142-7-  +  d. 

The  coefficients  0.571  and  1.142  agree  closely  with  the  averages  of  those 
given  in  the  report  of  the  committee  of  the  Institution  of  Mechanical  En- 
gineers, quoted  on  page  427,  ante. 


! 

Pitch. 

Efficiency. 

1 

Pitch. 

Efficiency. 

1 

PH 
JB 

bib 

.£ 

bio 

.s 

bio 

bi 

£ 

w 
4) 

PH 
* 

bio 

a 

bio 
C 

bio 

.2 

bii 

_g 

1 

sjj 

-1 

1| 

•a! 

11 

1 

•§>! 

v'£ 

1" 

-I 

If 

H 

|S 

g 

Q* 

Is 

|5 

is 

Q* 

Is 

Q2 

I* 

1^ 

in. 
3/16 

in. 

7/16 

in. 
.020 

in. 
1.603 

fa 

7?7 

in. 

1/2 

in. 

3/4 

in. 
1.392 

in. 
2.035 

46°1 

65°  1 

3/16 

1/2 

.261 

2.023 

60.'5 

75.3 

1/2 

7/8 

1.749 

2.624 

50^0 

66.6 

1/4 

1/2 

.071 

1.642 

53.3 

69.6 

1/2 

2.142 

3.284 

53.3 

70.0 

1/4 

9/16 

.285 

2.008 

56.2 

72.0 

1/2 

U/8 

2.570 

4.016 

56.2 

72.0 

5/16 

9/16 

.137 

1.712 

50.5 

67.1 

9/16 

3/4 

1.321 

1.892 

43.2 

60.3 

5/16 

5/8 

.339 

2.053 

53.3 

69.5 

9/16 

7/8 

1.652 

2.429 

47.0 

64.0 

5/16 

H/16 

.551 

2.415 

55.7 

71.5 

9/16 

1 

2.015 

3.030 

50.4 

67.0 

3/8 

5/8 

.218 

1.810 

48.7 

65.5 

9/16 

U/8 

2.410 

3.694 

53.3 

69.5 

3/8 

3/4 

.607 

2.463 

53.3 

69.5 

9/16 

H/4 

2.836 

4.422 

55.9 

71.5 

3/8 

7/8 

.041 

3.206 

57.1 

72.7 

5/8 

3/4 

1.264 

1.778 

40.7 

57.8 

7/16 

5/8 

.136 

1.647 

45.0 

62.0 

5/8 

7/8 

1.575 

2.274 

44.4 

61.5 

7/16 

3/4 

.484 

2.218 

49.5 

66.2 

5/8 

1 

1.914 

2.827 

47.7 

64.6 

7/16- 

7/8 

.869 

2.864 

53.2 

69.4 

5/8 

U/8 

2.281 

3.438 

50.7 

67.3 

7/16 

1 

2.305 

3.610 

56.6 

72.3 

5/8 

H/4 

2.678 

4.105 

53.3 

69.5 

Apparent  Shearing  Resistance  of  Rivet  Iron  and  Steel. 

(Proc.  Inst.  M.  E.,  1879,  Engineering,  Feb.  20,  1880.) 

The  true  shearing  resistance  of  the  rivets  cannot  be  ascertained  from 
experiments  on  riveted  joints  (1)  because  the  uniform  distribution  of  the 
load  to  all  the  rivets  cannot  be  insured;  (2)  because  of  the  friction  of  the 
plates,  which  has  the  effect  of  increasing  the  apparent  resistance  to  shear- 
ing in  an  element  uncertain  in  amount.  Probably  in  the  case  of  single- 
riveted  joints  the  shearing  resistance  is  not  much  affected  by  the  friction. 

Fairbairn's  experiments  show  that  a  rivet  is  6 1/2%  weaker  in  a  drilled 
fian  in  a  punched  hole.  By  rounding  the  edge  of  the  rivet-hole,  the 
apparent  shearing  resistance  is  increased  12%.  Messrs.  Greig  and  Eyth's 
experiments  indicate  a  greater  resistance  of  the  rivets  in  punched  holes 
than  in  drilled  holes. 

If  the  apparent  shearing  resistance  is  less  for  double  than  for  single 
shear,  it  is  probably  due  to  unequal  distribution  of  the  stress  on  the  two- 
rivet  sections. 


THE   STRENGTH   OF   RIVETED   JOINTS. 


431 


; 


The  shearing  resistance  of  a  bar,  when  sheared  in  circumstances  which 
prevent  .friction,  is  usually  less  than  the  tenacity  of  the  bar.  The  fol- 
lowing results  show  the  decrease: 

Harkort,  iron Tenacity,  26.4    Shearing,  16.5         Ratio,    0.62 

Lavalley,  iron 25.4  20.2  0.79 

Greig  and  Eyth,  iron.         "         22.2  19.0  0.85 

Greig  and  Eyth,  steel  28.8  22.1  0.77 

In  Wohler's  researches  (in  1870)  the  shearing  strength  of  iron  was  found 
to  be  four-fifths  of  the  tenacity.  Later  researches  of  Bauschinger  con- 
firm this  result  generally,  but  they  show  that  for  iron  the  ratio  of  the 
shearing  resistance  and  tenacity  depends  on  the  direction  of  the  stress 
relatively  to  the  direction  of  rolling.  The  above  ratio  is  valid  only  if  the 
shear  is  in  a  plane  perpendicular  to  the  direction  of  rolling,  and  if  the 
tension  is  applied  parallel  to  the  direction  of  rolling.  If  the  plane  of  shear 
is  parallel  to  the  breadth  of  the  bar,  the  resistance  is  only  half  as  great 
as  in  a  plane  perpendicular  to  the  fibers. 

THE  STRENGTH  OF  RIVETED    JOINTS. 

Joint  of  Maximum  Efficiency.  —  (F.  E.  Cardullo.)  If  a  riveted  joint 
is  made  with  sufficient  lap,  and  a  proper  distance  between  the  rows  of 
rivets,  it  will  break  in  one  of  the  three  following  ways: 

1.  By  tearing  the  plate  along  a  line,  through  the  outer  row  of  rivets. 

2.  By  shearing  the  rivets 

3.  By  crushing  the  plate  or  the  rivets. 
Let  t  =  the  thickness  of  the  main  plates. 

d  —  the  diameter  of  the  rivet-holes. 

f  =  the  tensile  strength  of  the  plate  in  pounds  per  sq.  in. 

5  =  the  shearing  strength  of  the  rivets  in  pounds  per  sq.  in.  when 
in  single  shear. 

p  =  the  distance  between  the  centers  of  rivets  of  the  outer  row 
(see  Figs.  96  and  97)  =  the  pitch  in  single  and  double  lap  riveting  =  twice 


FIG.  96. 
TRIPLE  RIVETING. 


FIG.  97. 
QUADRUPLE  RIVETING. 


the  pitch  of  the  inner  rows  in  triple  butt  strap  riveting,  in  which  alter- 
nate rivets  in  the  outer  row  are  omitted,  =  four  times  the  pitch  in  quad- 
ruple butt  strap  riveting,  in  which  the  outer  row  has  one-fourth  of  the 
number  of  rivets  of  the  two  inner  rows. 

c  =  the  crushing  strength  of  the  rivets  or  plates  in  pounds  per 
sq.  in. 

n  =  the  number  of  rivets  in  each  group  in  single  shear.  (A  group 
is  the  number  of  rivets  on  one  side  of  a  joint  corresponding  to  the  dis- 
tance p;  =  1  rivet  in  single  riveting,  2  in  double  riveting,  5  in  triple 
butt  strap  riveting,  and  11  in  quadruple  butt  strap  riveting.) 

m  =  the  number  of  rivets  in  each  group  in  double  shear, 
s"  =  the  shearing  strength  of  rivets  in  double  shear,  in  pounds  per 
sq.  in.,  the  rivet  section  being  counted  once. 

T  —  the  strength  of  the  plate  at  the  weakest  section.  =  ft  (p  —  d).' 

S  =  the  strength  of  the  rivets  against  shearing,  =  0.7854d2  (ns  + 
ms"). 

C  =  the  strength  of  the  rivets  or  the  plates  against  crushing,  =» 


432  RIVETED   JOINTS. 

In  order  that  the  joint  shall  have  the  greatest  strength  possible,  the 
tearing,  snearing,  and  crushing  strength  must  all  be  equal.  In  order  to 
make  it  so, 

1.  Substitute  the  known  numerical  values,  equate  the  expressions  for 
shearing  and  crushing  strength,  and  find  the  value  of  d,  taking  it  to  the 
nearest  Viem. 

2.  Next  find  the  value  of  S  in  the  second  equation,  and  substitute  it 
for  T  in  the  first  equation.     Substitute  numerical  values  for  the  other 
factors  in  the  first  equation,  and  solve  for  p. 

The  efficiency  of  a  riveted  joint  in  tearing,  shearing  and  crushing,  is 
equal  to  the  tearing,  shearing  or  crushing  strength,  divided  by  the  quan- 
tity ftp,  or  the  strength  of  the  solid  plate. 

The  efficiency  in  tearing  is  also  equal  to  (p  —  d)  -5-  p. 

The  maximum  possible  efficiency  for  a  well-designed  joint  is 

-         m+n 


m  +  n  4-  (/  -H  c) 

Empirical  formula  for  the  diameter  of  the  rivet-hole  when  the  crush- 
ing strength  is  unknown.  Assuming  that  c  =  1.4/,  and  s"=  1.75s,  we  have 
by  equating  C  and  S,  and  substituting, 

f(n  4-  m) 


1.7821 


s(n+  1.75m) 


Margin.  The  distance  from  the  center  of  any  rivet-hole  to  the  edge  of 
the  plate  should  be  not  less  than  11/2(1  The  distance  between  two  adja- 
cent rivet  centers  should  be  not  less  than  2d.  It  is  better  to  increase 
each  of  these  dimensions  by  1/8  in. 

The  distance  between  the  rows  of  rivets  should  be  such  that  the  net 
section  of  plate  material  along  any  broken  diagonal  through  the  rivet- 
holes  should  be  not  less  than  30  per  cent  greater  than  the  plate  section 
along  the  outer  line  of  rivets. 

The  thickness  of  the  inner  cover  strap  of  a  butt  joint  should  be  s/4  of 
the  thickness  of  the  main  plate  or  more.  The  thickness  of  the  outer  strap 
should  be  5/8  of  the  thickness  of  the  main  plate  or  more. 

Steam  Tightness.  It  is  of  great  importance  in  boiler  riveting  that 
the  joint  be  steam  tight.  It  is  therefore  necessary  that  the  pitch  of  the 
rivets  nearest  to  the  calked  edge  be  limited  to  a  certain  function  of  the 
thickness  of  the  plate.  The  Board  of  Trade  rule  for  steam  tightness  is 

p  =  Ct  +  15/8  in. 

where  p  =  the  maximum  allowable  pitch  in  inches. 
t  =  the  thickness  of  main  plate  in  inches. 
C  =  a  constant  from  the  following  table. 

No.  of  Rivets  per  Group...  12345 

Lap  Joints  ..................  C=1.31         2.62         3.47         4.14 

Double-strapped  Joints....  C=  1.75         3.50         4.63         5.52         6.00 

The  pitch  should  not  exceed  ten  inches  under  any  circumstances. 

When  the  joint  has  been  designed  for  strength,  it  should  be  checked  by 
the  above  formula.  Should  the  pitch  for  strength  exceed  the  pitch  for 
steam  tightness,  take  the  latter,  substitute  it  in  the  formula 

ft  (p-d)  =0.7854  d2  (ns  +  ms"), 

and  solve  for  d.     If  the  value  of  d  so  obtained  is  not  the  diameter  of  some 
standard  size  rivet,  take  the  next  larger  Vie  in. 

Calculation  of  Triple-riveted  Butt  and  Strap  Joints.  —  Formulae: 
T  =  ft  (p-d),  £  =  0.7854d2  (ns  +  ms"),  C  =  dtc  (m  +  n)  (notation  on 


=  W,=  44,000;  f  =  1.75,  =  77,000,  c  .  1.4  / 
=  77,000. 
Then  T  =  55,000  t{p-d)t  S  -  276,460^,  C  -  385,000  d*. 


THE  STRENGTH   OF  RIVETED  JOINTS 


433 


For  maximum  strength,  T  =  S  =  C;  dividing  by  55,000  t,  (p  -  d)  •• 
5.027 d*/t  =  7d;  whence  d  =  1.3925  t;  p  =  Sd. 


7/16 


1/2 


9/16 


5/8 


17/32 


5/8 


H/16 


25/32 


7/8 


Thickness  of  plate  t  =  5/ie 
Diana,  rivet  hole, 

d=  1.3925  t 7/16 

Pitch  of  outer  row, 

v   =  8d.  .    3.4816    4.1776     4.8736     5.5696      6.2664     6.9624 

T  =    55,000 1  (p-d)..  52,360  75,390  102,610   134,020   169,630  209,420 

S    =  276,460  d2 52,330  75,360  102,570  133,970   169,560  209,330 

C   =  385,000  dt 52,350  75,390  102,620   134,030   169,630  209,420 

Calculations  by  logarithms,  to  nearest  10  pounds. 

Efficiency  of  all  joints  (p  -  d)    -*•  p   =  87.5  per  cent. 

Maximum  efficiency  by  Cardullo's  formula, 


139,860  178,750  207,850  229,880 

194,300  207,300  220,-200  220,200 

1171300    157,900  192,500  230,000  255,500 

.107,360    134,060    162,420  206,250  239,770  266,400 


=  87.5  per  cent. 

Diameter  of  rivet,  i/ie  in.  less  than  hole 3/8    1/2    9/16    n/16  3/4    13/16 

Diameter  of  rivet-hole,  next    largest  16th,     7/16    9/16    5/8    s/4  13/16    7/9 
For  the  same  thickness  of  plates  the  Hartford  Steam  Boiler  Inspection 
and  Insurance  Co.  gives  the  following  proportions: 

Thickness,  f,     '            5/16           3/8            7/16            i/2            9/16  5/8 

Diam.  rivet-hole,  d,     3/4             13/16          15/16          1               1 1/16  ll/16 

Pitch  of  outer  row,  p,  6 1/4          61/2          63/4          71/2          73/4  73/4 

Using  the  same  values  for  f,  s,  s"  and  c,  we  obtain: 

T  =    94,530    117,300    ' 

S  =     155,400    168,400 

C  =    90,030    - 

Strength  of  solid 

plate,  f pt  = . . . . 

Efficiency  T,  S  or 

C,  lowest  •*•  fpt, . 

per  cent    83.9          87.5          86.1          86.7        86.7  82.6 

The  5/i6  in.  plate  fails  by  crushing,  the  5/8  by  shearing,  the  others  by 
tearing. 

Calculation  of  Quadruple  Riveting.  —  In  this  case  there  are  11  rivets 
In  the  group.  If  the  upper  strap  plate  contains  all  the  rivets  except  the 
outer  row,  then  n  =  1,  m  =  10.  Using  the  same  values  for/,  s,  s"  and 
c  as  above,  we  have  ns  +  ms"  =  814,000;  T  =  55,000 £  (p  -  d);  S  =* 
639,315 d2;  C  =  847,000  dt. 

For  maximum  strength,  t  (p  —  d)  =  11.624d2  =  15. 4dt;  whence  d  = 
1. 32485 1,  p  =  16.4 d.  Efficiency  (p  -  d)+p  =  93.9  per  cent.  Check  by 

Cardullo's  formula  —  rrr—  =  93.9  per  cent. 

n  4-  m  +  f/c       114-  10/ii 
British  Board  of  Trade  and  Lloyd's  Rules  for  Riveted  Joints.— 

Board  of  Trade.  —  Tensile  strength  of  rivet  bars  between  26  and  30  tons, 
el.  in  10"  not  less  than  25%,  and  contr.  of  area  not  less  than  50%. 

The  shearing  resistance  of  the  rivet  steel  to  be  taken  at  23  tons  per 
square  inch,  5  to  be  used  for  the  factor  of  safety  independently  of  any 
addition  to  this  factor  for  the  plating.  Rivets  in  double  shear  to  have 
only  1.75  times  the  single  section  taken  in  the  calculation  instead  of  2. 
The  diameter  must  not  be  less  than  the  thickness  of  the  plate  and  the 
pitch  never  greater  than  81/2".  The  thickness  of  double  butt-straps 
(each)  not  to  be  less  than  5/8  the  thickness  of  the  plate;  single  butt-straps 
not  less  than  9/8. 

Distance  from  center  of  rivet  to  edge  of  hole  =  diameter  of  rivet  X  1V2. 

Distance  between  rows  of  rivets 

=  2  X  diam.  of  rivet  or  =  [(diam.  X  4)  4-  1]  -*•  2,  if  chain,  and 


V[(pitch  X  11)  4-  (diam.  X  4)]  X  (pitch  +  diam.  X  4) 
10 


if  zigzag. 


Diagonal  pitch  =  (pitch  X  6  4-  diam.  X  4)  4-  10. 

Lloyd's.  —  T.  S.  of  rivet  bars,  26  to  30  tons;  el.  not  less  than  20%  in  8*. 
The  material  must  stand  bending  to  a  curve,  the  inner  radius  of  which  is 


434 


RIVETED  JOINTS. 


not  greater  than  11/2  times  the  thickness  of  the  plate,  after  having  been 
uniformly  heated  to  a  low  cherry-red,  and  quenched  in  water  at  82°  F. 

Rivets  in  double  shear  to  have  only  1.75  times  the  single  section  taken 
in  the  calculation  instead  of  2.  The  shearing  strength  of  rivet  steel  to 
be  taken  at  85%  of  the  T.  S.  of  the  material  of  shell  plates.  In  any  case 
where  the  strength  of  the  longitudinal  joint  is  satisfactorily  shown  by 
experiment  to  be  greater  than  given  by  the  formula,  the  actual  strength 
may  be  taken  in  the  calculation. 


Proportions  of  Riveted  Joints.     (Hartford  S.  B.  Insp.  and  Ins.  Co.) 
Single-riveted  Girth  Seams  of  Boilers. 


Thickness. 

1/4 

5/16 

3/8 

7/16 

1/2 

Diam.  rivet-hole. 
Pitch  

3/4       H/16 
21/i6  21/i6 

13/16     3/4 
21/8      21/8 

15/16     W16 

23/8      21/8 

1              1V16 

27/16  23/8 

1  VIC   1 
21/-»   21/2 

Center  to  edge  .  . 

H/8     H/32 

17/32     U/8 

1  13/32   1  7/32 

U/2     H3/32 

19/32    U/2 

Double-riveted  Lap  Joints. 


Thickness  of  plate  

1/4 

5/16 

3/8 

7/10 

1/2 

Diam.  rivet-hole  

3/4 

13/16 

15/16 

, 

H/16 

Pitch     t 

27/8 

27/8 

31/4 

31/4 

3  32 

Dist.  bet.  rows  ...           ...... 

1  15/16 

1  15/16 

23/i6 

23/16 

2  2 

Dist.  inner  row  to  edge  :  . 

H/8 

17/32 

1  13/32 

U/2 

119/32 

Efficiency  .  . 

0  74 

0  72 

0  70 

0  70 

0  68 

Triple-riveted  Lap  Joints. 


Thickness  

1/4 

5/16 

3/8 

7/16 

1  2 

Diam.  rivet-hole 

H/16 

3/4 

13/16 

15/16 

1 

Pitch  

3 

31/8 

31/4 

33/4 

315/16 

Dist.  bet  rows 

2 

2Vl6 

23/18 

21/2 

25/8 

Inner  row  to  edge  

11/32 

H/8 

17/32 

113/32 

H/2 

Efficiency 

0  Ti 

0  76 

0  75 

0.75 

0.75 

Triple-riveted  Bull-strap  Joints. 


Thickness  

5/i6 

3/8 

7/16 

V2 

9/16 

5/8 

Diam.  rivet-hole  

3/4 

13/16 

15/16 

1 

H/16 

11/16 

Pitch,  inner  rows  

31/8 

31/4 

33/8 

33/4 

37/8 

37/8 

Dist.  bet.  inner  rows  
Dist.  outer  to  2d  row.  ..... 
Edge  to  nearest  row  
Efficiency  %  ...  

21/8 
23/8 
U/4 

88  (?) 

^ 
^ 

21/4 
23/4 

«T/32 

23/8 

U/2 
86.6 

25/8 
33/16 
1  19/32 
85.4 

25/8 
33/16 
119/32 
84(?) 

The  distance  to  the  edge  of  the  plate  is  from  the  center  of  rivet-holes. 


THE   STRENGTH   OF   RIVETED   JOINTS. 


435 


Pressure  Required   to   Drive   Hot  Rivets.  —  R.    D.   Wood  ft  Co. 
Philadelphia,  give  the  following  table  (1897): 

POWER  TO  DRIVE  RIVETS  HOT. 


Size. 

Girder- 
work. 

Tank- 
work. 

Boiler- 
work. 

Size. 

Girder- 
work. 

Tank- 
work. 

Boiler- 
work. 

in. 

tons. 

tons. 

tons. 

in. 

tons. 

tons. 

tons. 

1/2 

9 

15 

20 

U/8 

38 

60 

75 

5/8 

12 

18 

25 

U/4 

45 

70 

100 

3/4 

15 

22 

33 

U/2 

60 

85 

125 

7/8 

22 

30 

45 

13/4 

75 

100 

150 

1 

30 

45 

60 

The  above  is  based  on  the  rivet  passing  through  only  two  thicknesses  of 
plate  which  together  exceed  the  diameter  of  the  rivet  but  little,  if  any. 

As  the  plate  thickness  increases  the  power  required  increases  approxi- 
mately in  proportion  to  the  square  root  of  the  increase  of  thickness.  Thus, 
if  the  total  thickness  of  plate  is  four  times  the  diameter  of  the  rivet,  we 
should  require  twice  the  power  given  above  in  order  to  thoroughly  fill  the 
rivet-holes  and  do  good  work.  Double  the  thickness  of  plate  would 
increase  the  necessary  power  about  40%. 

It  takes  about  four  or  five  times  as  much  power  to  drive  rivets  cold  as 
to  drive  them  hot.  Thus,  a  machine  that  will  drive  3/4-in.  rivets  hot  will 
usually  drive  3/8 -in.  rivets  cold  (steel).  Baldwin  Locomotive  Worka 
drive  1/2  -in.  soft-iron  rivets  cold  with  15  tons. 

Riveting  Pressure  Required  for  Bridge  and  Boiler    Work. 

(Wilfred  Lewis,  Engineers'  Club  of  Philadelphia,  Nov.,  1893.) 

A  number  of  3'8-inch  rivets  were  subjected  to  pressures  between  10,000 
and  60,000  Ibs.  At  10,000  Ibs.  the  rivet  swelled  and  filled  the  hole  with- 
out forming  a  head.  At  20,000  Ibs.  the  head  was  formed  and  the  plates 
were  slightly  pinched.  At  30,000  Ibs.  the  rivet  was  well  set.  At  40,000 
Ibs.  the  metal  in  the  plate  surrounding  the  rivet  began  to  stretch,  and  the 
stretching  became  more  and  more  apparent  as  the  pressure  was  increased 
to  50,000  and  60,000  Ibs.  From  these  experiments  the  conclusion  might 
be  drawn  that  the  pressure  required  for  cold  riveting  was  about  300,000 
Ibs.  per  square  inch  of  rivet  section.  In  hot  riveting,  until  recently  there 
was  never  any  call  for  a 'pressure  exceeding  60,000  Ibs..  but  now  pressures 
as  high  as  150,000  Ibs.  are  not  uncommon,  and  even  300,000  Ibs.  have  been 
contemplated  as  desirable. 

Pressure  Required  for  Heading  Cold  Rivets.  —  Experiments  made 
by  the  author  in  1906  on  1/2  and  5/8  in.  soft  steel  rivets  showed  that  the 
pressure  required  to  head  a  rivet  cold,  with  a  hemispherical  heading  die, 
was  a  function  of  the  final  or  maximum  diameter  of  the  head.  The 
metal  began  to  flow  and  fill  the  hole  at  about  50,000  Ibs.  per  sq.  in.  press- 
ure, but  it  hardened  and  increased  its  resistance  as  it  flowed  until  it  reached 
a  maximum  of  about  100,000  Ibs.  per  sq.  in.  of  the  maximum  area  of  the 
head. 

Chemical  and  Physical  Tests  of  Soft  Steel  Rivets. —  Ten  rivet 
bars  and  ten  rivets  selected  from  stock  of  the  Champion  Rivet  Co.,  Cleve- 
land, O.,  were  analyzed  by  Oscar  Textor,  with  results  as  follows: 

P.  0.008  to  0.027,  av.  0.015:  Mn,  0.31  to  0.69,  av.  0.46:  S,  0.023  to 
0.044,  av.  0.033:  Si,  0.001  to  0.008,  av.  0.005-  C,  0.06  to  0.19,  av.  0.11. 
Only  four  of  the  20  samples  were  over  0.14  C,  and  these  were  made  for 
hi?h  strength.  Ten  bars  and  two  rivets  Rave  tensile  strength .  46.735  to 
55.380,  av.  52.195  Ibs.  per  sq.  in.-  elastic  limit,  31,350  to  43,150.  av. 
35,954-  elongation,  bars  only,  28  to  35,  av.  31.9%  in  8  ins.:  reduction  ot 
area.  65.6%.  Eight  bars  in  single  shear  gave  shearing  strength  35,660 
to  50  190  av.  44478  Ibs.  per  sq.  in.;  seven  bars  in  double  shear  eave 
39,170  to  53,900,  av.  45,720  Ibs.  The  shearing  strength  averaged  86.3% 
of  the  tensile  strength. 


436                                    IRON   AND   STEEL. 

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CAST  IRON. 


CAST  IRON. 


437 


The  Manufacture  of  Cast  Iron.  —  Pig  iron  is  the  name  given  to  the 
crude  form  of  iron  as  it  is  produced  in  the  blast  furnace.  This  furnace 
is  a  tall  shaft,  lined  with  fire  brick,  often  as  large  as  100  ft.  high  and  20  ft. 
in  diameter  at  its  widest  part,  called  the  "bosh."  The  furnace  is  kept 
filled  with  alternate  layers  of  fuel  (coke,  anthracite  or  charcoal),  while  a 
melting  temperature  is  maintained  at  the  bottom  by  a  strong  blast. 
The  iron  ore  as  it  travels  down  the  furnace  is  decarbonized  by  the  carbon 
monoxide  gas  produced  by  the  incomplete  combustion  of  the  fuel,  and  as 
it.  travels  farther,  into  a  zone  of  higher  temperature,  it  absorbs  carbon 
and  silicon.  The  phosphorus  originally  in  the  ore  remains  in  the  iron. 
The  sulphur  present  in  the  ore  and  in  the  fuel  may  go  into  combination 
with  the  lime  in  the  slag,  or  into  the  iron,  depending  on  the  constitution 
of  the  slag  and  on  the  temperature.  The  silica  and  alumina  in  the  ore 
unite  with  the  lime  to  form  a  fusible  slag,  which  rests  on  the  melted  iron 
in  the  hearth.  The  iron  is  tapped  from  the  furnace  several  times  a  day, 
while  in  large  furnaces  the  slag  is  usually  run  off  continuously. 

Grading  of  Pig  Iron.  —  Pig  iron  is  approximately  graded  according 
to  its  fracture,  the  number  of  grades  varying  in  different  districts.  In 
Eastern  Pennsylvania  the  principal  grades  recognized  are  known  as  No. 
1  and  2  foundry,  gray  forge  or  No.  3,  mottled  or  No.  4,  and  white  or  No. 
5.  Intermediate  grades  are  sometimes  made,  as  No.  2  X,  between  No.  1 
and  No.  2,  and  special  names  are  given  to  irons  more  highly  silidzed  than 
No.  1,  as  No.  1  X,  silver-gray,  and  soft.  Charcoal  foundry  pig  iron  is 
graded  by  numbers  1  to  5,  but  the  quality  is  very  different  from  the 
corresponding  numbers  in  anthracite  and  coke  pig.  Southern  coke  pig 
-Iron  is  graded  into  ten  or  more  grades.  Grading  by  fracture  is  a  fairly 
satisfactory  method  of  grading  irons  made  from  uniform  ore  mixtures 
and  fuel,  but  is  unreliable  as  a  means  of  determining  quality  of  irons 
produced  in  different  sections  or  from  different  ores  Grading  by  chemi- 
cal analysis,  in  the  latter  case,  is  the  only  satisfactory  method.  The 
following  analyses  of  the  five  standard  grades  of  northern  foundry  and 
mill  pig  irons  are  given  by  J.  M.  Hartman  (Bull.  1.  &  S.  A.,  Feb.,  1892): 


No.  1. 

No.  2. 

No'.  3. 

No.  4. 

No.  4B. 

No.  5. 

Iron  

92.37 

92.31 

94.66 

94  48 

94.08 

94  68 

Graphitic  ca/rbon 

3  52 

2  99 

2  50 

2  02 

2  02 

Combined  carbon  

0.13 

0.37 

1.52 

1.98 

1.43 

3  83 

2.44 

2.52 

0.72 

0.56 

0.92 

0.41 

Phosphorus  

1.25 

1.08 

0  26 

0.19 

0.04 

0  04 

0.02 

0.02 

trace 

0.08 

0.04 

0.02 

Manganese  

0.28 

0.72 

0.34 

0.67 

2.02 

0.98 

CHARACTERISTICS  OF  THESE  IRONS. 

No.  1.  Gray.  —  A  large,  dark,  open-grain  iron,  softest  of  all  the  num- 
bers and  used  exclusively  in  the  foundry.  Tensile  strength  low.  Elastic 
limit  low.  Fracture  rough.  Turns  soft  and  tough. 

No.  2.  Gray.  —  A  mixed  large  and  small  dark  grain,  harder  than  No. 
1  iron,  and  used  exclusively  in  the  foundry.  Tensile  strength  and  elastic 
limit  higher  than  No.  1.  Fracture  less  rough  than  No.  1.  Turns  harder, 
less  tough,  and  more  brittle  than  No.  1. 

No.  3.  Gray.  —  Small,  gray,  close  grain,  harder  than  No.  2  iron,  used 
either  in  the  rolling-mill  or  foundry.  Tensile  strength  and  elastic  limit 
higher  than  No.  2.  Turns  hard,  less  tough,  and  more  brittle  than  No.  2. 

No.  4.  Mottled.  —  White  background,  dotted  closely  with  small  black 
spots  of  graphitic  carbon:  little  or  no  grain.  Used  exclusively  in  the 
rolling-mill.  Tensile  strength  and  elastic  limit  lower  than  No.  3.  Turns 
with  difficulty;  less  tough  and  more  brittle  than  No.  3.  The  manganese 
In  the  B  pig  iron  replaces  part  of  the  combined  carbon,  making  the  iron 
harder  and  closing  the  grain,  notwithstanding  the  lower  combined  carbon. 


438  IRON   AND   STEEL. 

No.  5.  White.  —  Smooth,  white  fracture,  no  grain,  used  exclusively  in 
the  rolling  mill.  Tensile  strength  and  elastic  limit  much  lower  than  No.  4. 
Too  hard  to  turn  and  more  brittle  than  No.  4. 

Southern  pig  irons  are  graded  as  follows,  beginning  with  the  highest  in 
silicon:  Nos.  1  and  2  silvery,  Nos.  1  and  2  solt,  all  containing  over  3% 
of  silicon;  Nos.  1,  2,  and  3  foundry,  respectively  about  2.75%,  2.5%  and 
2%  silicon;  No.  1  mill,  or  "  foundry  forge;"  No.  2  mill,  or  gray  forge; 
mottled;  white. 

Chemistry  of  Cast  Iron.  —  Abbreviations,  TC,  total  carbon;  GC, 
graphitic  carbon;  CC,  combined  carbon.  Numerous  researches  have  been 
made  and  many  papers  written,  especially  between  the  years  1895  and 
1908,  on  the  relation  of  the  physical  properties  to  the  chemical  constitu- 
tion of  cast  iron.  Much  remains  to  be  learned  on  the  subject,  but  the 
following  is  a  brief  summary  of  prevailing  opinions. 

CARBON.  —  Carbon  exists  in  three  states  in  cast  iron:  1,  Combined 
carbon,  which  has  the  property  of  making  iron  white  and  hard ;  2,  Graphi- 
tic carbon  or  graphite,  which  is  not  alloyed  with  the  iron,  but  exists  in  it 
as  a  separate  body,  since  it  may  be  removed  from  the  fractured  surface 
of  pig  iron  by  a  brush;  3,  a  third  form,  called  by  Ledebur  "tempering 
graphite  carbon,"  into  which  combined  carbon  may  be  changed  by  pro- 
longed heating.  The  relative  percentages  in  which  GC  and  CC  may 
be  found  in  cast  iron  differ  with  the  rate  of  cooling  from  the  liquid 
state,  so  that  in  a  large  casting,  cooled  slowly,  nearly  all  the  C  may 
be  GC,  while  in  a  small  casting  from  the  same  ladle  cooled  quickly, 
it  may  be  nearly  all  CC.  Tne  total  C  in  cast  iron  usuallv  is  between 
3  and  4%. 

COMBINED  CARBON.  —  CC  increases  hardness,  brittleness  and  shrink- 
age. Up  to  about  1%  it  increases  strength,  then  decreases  it.  The 
presence  of  S  tends  to  increase  the  CC  in  a  casting,  while  Si  tends  to 
change  CC  to  GC. 

GRAPHITE.  • —  GC  in  a  casting  causes  softness  and  weakness  when 
above  3%;  softness  and  strength  when  added  to  irons  low  in  GC  and  over 
1%  in  CC.  It  increases  with  the  size  of  the  casting,  with  slow  cooling, 
or  rather  with  holding  a  long  time  in  the  mold  at  a  high  temperature. 

SILICON.  —  Si  acts  as  a  softener  by  counteracting  the  hardening  effect 
of  S,  and  by  changing  CC  into  GC,  changes  white  iron  to  gray,  increases 
fluidity  and  lessens  shrinkage.  When  added  to  hard  brittle  iron,  high  in 
CC,  it  may  increase  strength  by  removing  hard  brittleness,  but  when  it 
reduces  the  CC  to  1%  and  less  it  weakens  the  iron.  Above  3.5  or  4%  it 
changes  the  fracture  to  silvery  gray,  and  the  iron  becomes  brittle  and 
weak.  The  softening  effect  of  Si  is  modified  by  S  and  Mn. 

SULPHUR.  —  S  causes  the  C  to  take  the  form  of  CC,  increases  hardness, 
brittleness,  and  shrinkage,  and  also  has  a  weakening  effect  of  its  own. 
Above  about  0.1%  it  makes  iron  very  weak  and  brittle.  When  Si  is 
below  1%,  even  0.06  S  makes  the  iron  dangerously  brittle. 

MANGANESE.  —  Mnin  small  amount,  less  than  0.5%,  counteracts  the 
hardening  influence  of  S;  in  larger  amounts  it  changes  GC  into  CC,  and 
acts  as  a  hardener.  Above  2%  it  makes  the  iron  very  hard.  Mn  com- 
bines with  iron  in  almost  all  proportions.  When  it  is  from  10  to  30% 
the'alloyis  called  spiegeleisen,  from  the  German  word  for  mirror,  and  has 
large,  bright  crystalline  faces.  Above  50%  it  is  known  as  ferro-man- 
ganese.  Mn  has  the  property  of  increasing  the  solubility  of  iron  for 
carbon;  ordinary  pig  iron  containing  rarely  over  4.2%  C,  while  spiegel- 
eisen may  have  5%,  and  ferro-manganese  as  high  as  6%.  Cast  iron  with 
1%  Mn  is  used  in  making  chilled  rolls,  in  which  a  hard  chill  is  desired. 
When  softness  is  required  in  castings,  Mn  over  0.4%  has  to  be  avoided. 
Mn  increases  shrinkage.  It  also  decreases  the  magnetism  of  iron.  Iron 
with  25%  Mn  loses  all  its  magnetism.  It  therefore  has  to  be  avoided  in 
castings  for  dynamo  fields  and  other  pieces  of  electrical  machinery. 

PHOSPHORUS.  —  P  increases  fluidity,  and  is  therefore  valuable  for  thin 
and  ornamental  castings  in  which  strength  is  not  needed.  It  increases 
softness  and  decreases  shrinkage.  Below  0.7%  it  does  not  appear  to 
decrease  strength,  but  above  1%  it  is  a  weakener. 

COPPER.  —  Cu  is  found  in  pig  irons  made  from  ores  containing  Cu. 
From  0.1  to  1%  it  closes  the  grain  of  cast  iron,  but  does  not  appreciably 
cause  brittleness. 


g 
d 


CAST  IRON.  .  439 

LUMINUM.  —  Al  from  0.2  to  1.0%  (added  to  the  ladle  in  the  form  of 
a  FeAl  alloy)  increases  the  softness  and  strength  of  white  iron  ;  added  to 
ray  iron  it    softens  and  weakens  it.     Where  loss  is  occasioned  by 
efective  castings,  or  where  iron  does  not  flow  well,  the  addition  of  Al 
will  give  sounder,  closer  grained  castings.     In  proportions  of  2%  and 
over  Al  will  decrease  the  shrinkage  of  cast  iron. 

TITANIUM.  —  An  addition  of  2  to  3%  of  a  TiFe  alloy  containing  10% 
Ti  caused  an  increase  of  20  to  30%  in  strength  of  cast  iron.  A.  J.  Rossi, 
A.I.M.E.,  xxxiii,  194.  Ti  reacts  with  any  O  or  N  present  in  the  metal 
and  thus  purifies  it,  and  does  not  remain  in  the  metal.  After  enough 
Ti  for  deoxidation  has  been  added,  further  additions  have  no  effect. 
R.  Moldenke,  A.I.M.E.,  xxxv,  153. 

VANADIUM.  —  Va  to  the  extent  of  0.15%  added  to  the  ladle  in  the  form 
of  a  ground  FeVa  alloy  greatly  increases  the  strength  of  cast  iron.  It 
acts  as  a  deoxidizer  and  also  by  alloying. 

OXIDE  OF  IRON.  —  The  cause  of  the  difference  in  strength  of  charcoal 
and  coke  irons  of  identical  composition  is  believed  by  Dr.  Moldenke 
(A.I.M.E.,  xxxi,  988)  to  be  the  degree  of  oxidation  to  which  they  have 
been  subjected  in  making  or  temelting.  Since  Mn,  Ti,  and  Va  all  act  as 
deoxidizers,  it  should  be  possible  by  additions  to  the  ladle  of  alloys  of 
FeMn,  FeVa,  or  IfeTi,  to  make  the  two  irons  of  equal  strength. 

Temper  Carbon.  The  main  part  of  the  C  in  white  cast  iron  is  the  carbide 
Fe3C.  This  breaks  down  under  annealing  to  what  Ledebur  calls  "  temper 
carbon,"  and  in  annealing  in  oxides,  as  in  making  malleable  iron,  'it  is 
oxidized  to  CO.  The  C  remaining  in  the  casting  at  the  end  of  the  process 
is  nearly  all  GC,  since  the  latter  is  very  slowly  oxidized. 

Influence  of  Various  Elements  on  Cast  Iron.  —  W.  S.  Anderson, 
Castings,  Sept.,  1908,  gives  the  following: 

Fluidity,  increased  by      Si,  P,  G.C.      Reduced  by  S,  C.C. 
Shrinkage,  increased  by   S,  Mn,  C.C.     Reduced  by   Si,  P,  G.C. 
Strength,  increased  by      Mn,  C.C.          Reduced  by   Si,  S,  P,  G.C. 
Hardness,  inci  eased  by    S,  Mn,  C.C.     Reduced  by  Si,  G.C. 
Chill,  increased  by  S,  Mn,  C.C.     Reduced  by  Si,  P,  G.C. 

Microscopic  Constituents.     (See  also  Metaltographyj  under  Steel.) 

Ferrite,  iron  free  from  carbon.  It  is  found  in  mild  steel  in  small  amounts 
in  gray  cast  iron,  and  in  malleable  cast  iron. 

Cementite,  FesC.  Fe  with  6.67%  C.  Harder  than  hardened  steel. 
Hardness  U  on  the  mineralogical  scale.  Found  in  high  C  steel,  and  in 
white  and  mottled  pig. 

Pearlite,  a  compound  made  up  of  alternate  laminae  of  ferrite  and  cemen- 
tite,  in  the  ratio  of  7  ferrite  to  1  cementite,  and  containing  therefore 
0.83%  C.  Found  in  iron  and  steel  cooled  very  slowly  from  a  high  temper- 
ature. In  steel  of  0.83  C  it  composes  the  entire  mass.  Steels  lower  or 
higher  than  0.83  C  contain  pearlite  mixed  with  ferrite  or  with  cementite. 

Mariensite,  the  hardening  component  of  steel.  Found  in  iron  and 
steel  quenched  above  the  recalescence  point,  and  in  tempered  steel.  It 
forms  the  entire  structure  of  0.83  C  steel  quenched. 

Analyses  of  Cast  Iron.     (Notes  of  the  table  on  page  440.) 

1  to  7.  R.  Moldenke,  Pittsbg.  F'drymen's  Assn.,  1898;  1  to  5,  pig  irons; 
6,  white  iron  cast  in  chills;  7,  gray  iron  cast  in  sand  from  the  same  ladle. 
The  temperatures  were  taken  with  a  Le  Chatelier  pyrometer.  For 
comparison,  steel,  1.18  C,  melted  at  2450°  F.;  silico-spiegel,  12.30  Si, 
16.98  Mn,  at  2190°;  ferro-silicon,  12.01  Si,  2.17  CC,  at  2040°;  ferro- 
tungsten,  39.02  W,  at  2280°;  ferro-manganese,  81.4  Mn,  at  2255°;  ferro- 
chrome,  62.7  Cr,  at  2400°;  ditto,  5.4  Cr.,  at  2180°. 

8.  Gray  foundry  Swedish  pig,  very  strong.  9.  Pig  to  be  used  in  mix- 
tures of  gray  pig  and  scrap,  for  castings  requiring  a  hard  close  grain, 
machining  to  a  fine  surface,  and  resisting  wear.  8  to  15,  from  paper  by 
F.  M.  Thomas,  Castings,  July,  1908. 

16.  Specification  by  J.  E.  Johnston,  Jr.,  Am.  Mach.,  Oct.  15,  1903. 
The  results  were  excellent.  Si  might  have  been  0.75  to  1.25  if  S  had 
been  kept  below  0.035. 

17  to  22.  G.  R.  Henderson,  Trans.  A.S.M.E.,  vol.  xx.  The  chill  is  to 
be  measured  in  a  test  bar  2  X  2  X  24  in.,  the  chill  piece  being  so  placed 
as  to  form  part  of  one  side  of  the  mold.  The  actual  depth  of  white  iron 
will  be  measured, 


440 


IRON   AND   STEEL. 


Analyses  of  Cast  Iron. 

(Abbreviations,  TC,  total  carbon;  GC,  graphitic  carbon;  CC,  combined 
irbon.) 


TC 

GC 

CC 

Silicon. 

Man- 
ganese. 

Phos- 
phorus. 

Sul- 
phur. 

3.98 
3.78 
3.88 
4.03 
3.56 
4.39 
4.45 
3.30 

0.39 
1.76 
2.60 
3.47 
3.43 
0.13 
2.99 
2.80 

2  25-2  5 

3.59 
2.01 
1.28 
0.56 
0.13 
4.26 
1.46 
0.50 

06-08 

0.38 
0.69 
1.52 
2.01 
2.40 
0.65 
0.67 
2.00 

0  8-1  2 

0.13 
0.44 
0.49 
0.49 
0.90 
0.40 
0.41 
0.60 

04-08 

0.20 
0.53 
0.46 
0.39 
0.08 
0.25 
0.26 
0.08 

0  15-0  4 

0.038 
0.031 
0.035 
0.034 
0.032 
0.038 
0.039 
0.03 

Melts  at  2048°  F. 
Melts  at  2156°  F. 
Mel1sat221l°F. 
M  eh  sat  2248°  F. 
M  el  Is  at  2280°  F. 
Melts  at  2000°  F. 
Melts  at  2237°  F. 
Swedish      char- 
coal pig. 
For  engine  cylin- 

3.40 
3.40 

3.40 
3.20 
3.2-3.6 
3  0-3  2 

trace 
0.20 
0.1-0.15 
04-05 

2.90 
2.60 
2.5-2.8 
2-2  3 

0.50 
0.50 

up  to 
1.0 
up  to 

1.65 
1.58 
1.3-1.5 
1-1.3 

0.04' 
0.04 
.03-.  04 
.06-.  08 

ders. 
English,  high  P. 
No.  1. 
English,  high  P. 

For    thin    orna- 
mental work. 
For  medium  size 

2  8-3  0 

04-06 

1  2-1  5 

1.0 
06-09 

04-06 

.06-.  08 

castings. 
Heavy    machin- 

2.5-2.8 

0.6-0.8 

1.0-1.3 
1.2-1  8 

0.5-0.7 
0  4-1  0 

0.4-0.7 
0.4-0.7 

.08-.  12 
to  .06 

ery  castings. 
Cylinders      end 
hydraulic  \vork. 
For       hydraulic 

2.7-3.0 
2.6-3.1 
2  5-3  0 

0.5-0.8 
0.6-1.0 
04-09 

0.5-0.7 
0.6-0.7 
1  3-1  7 

0.3-0.5 
0.1-0.3 
0  5-1  0 

0.3-0.5 
0.3-0.5 
03-04 

.05-.  07 
.05-.  08 
03  max 

cylinders. 
For  car  wheels. 
For  car  wheels. 
Charcoal  pig.  1/4 

l'.87 

3.82 
3.84 

2.3-2.7 
2.0-2.5 
1.8-2.2 
3.44 

3.23 
3.52 
2.8-3.2 

2.3-2.4 
2  4-2  6 

0.5-1.0 
0.8-1.2 
0.9-1.4 
•   0.43 

0.59 
0.32 
0.5-0.7 

0.8-1.0 
08-1  0 

1.0-1.5 
0.8-1.2 
0.5-1.0 
1.67 

1.95 
2.04 
1.3-1.5 

1.8-2.0 
0  9-1  0 

0.5-1.0 
0.5-1.0 
0.3-0.7 
0.29 

0.39 
0.39 
0.3-0.6 

0.8-1.0 
06-07 

0.3-0.4 
0.3-0.4 
0.3-0.4 
0.095 

0.405 
0.578 
0.5-0.8 

0.6-0.8 
01-03 

.03      " 
.035    " 
.035    " 
0.032 

0.042 
0.044 
.06-.  10 

.06-.  10 
.04-.  06 

in.  chill. 
Ditto  1/2  in.  chill. 
Ditto  3/4  in.  chill. 
Ditto  1  in.  chill. 
Series     A.    Am. 
F'dmen's  Assn. 
Series   B.   ditto. 
Series    C.   ditto. 
For    locomotive 
cylinders. 
"  Semi-steel." 
"  Semi-steel." 

4.33 
3.17 

3.34 
3.5 
3.55 

3.08 

J.72 

2.57 
2.9 
3.0 

1.25 
0.45 

0.77 
0.6 
0.55 

0.73 
1.99 

1.89 
0.7 
2.75 
3.10 

0.44 
0.39 

0.39 
0.4 
2.39 
1.80 

0.43 
0.65 

0.70 
0.5 
0  86 
0.90 

0.08 
0.13 

0,09 
0.08 
0.014 

A     strong     car 
wheel,  Cu,  0.03. 
Automobile  cyl- 
inders. 
Ditto. 
Good  car  wheel. 
Scotch  irons. 
"  Am.    Scotch  ** 

0.75-1.5 

to  06 

to  0.22 

to  0.04 

Ohio  irons. 
Pig    for    malle- 

2-25 
1  2-1  5 

to  0.7 
0  5-0  8 

to  0.7 
0  35-0.6 

to  0.15 
to  0.09 

able  castings. 
Brake-shoes. 
Hard    iron     for 

1  5-2 

0  5-0  8 

0  35-0.6 

to  0.08 

heavy  work. 
Medium  iron  for 

2  2-2  8 

to  0  7 

to  0  7 

to  0.085 

general  work. 
Soft  iron  cast'ga 

23  to  25. 


CAST  IRON.  441 


„  ._  25.  Series  of  bars  tested  by  a  committee  of  the  association. 
See  results  of  tests  on  page  419.  Series  A,  soft  Bessemer  mixture;  B, 
dynamo-frame  iron;  C,  light  machinery  iron.  Samples  for  analysis  were 
taken  from  the  1-in.  square  dry  sand  bars. 

26.  Specifications  by  a  committee  of  the  Am.  Ry.  Mast.  Mechs.  Assn., 
1906.  T.S.,  25,000;  transverse  test,  3000  Ib.  on  H/4-in.  round  bar,  12  in. 
bet  ween  supports;  deflection,  0.1  in.  minimum;  shrinkage,  1/8  in.  max. 
27,  soft  "semi-steel;"  28,  harder  do.  They  approach  air-furnace  iron 
In  most  respects,  and  excel  it  in  strength;  test  bars  2  X  1  X  24  in.  of  the 
low  Si  semi-steel  showing  2800  to  3000  Ib.  transverse  strength,  with 
7/i6  in.  deflection.  M.  B.  Smith,  Eng.  Digest,  Aug.,  1908.  29.  J.  M. 
Hartman,  Bull.  I.  &  S.  Assn.,  Feb.,  1892.  The  chill  was  very  hard,  1/4  in. 
deep  at  root  of  flange,  1/2  in.  deep  on  tread.  30,  31.  Strong  and  shock- 
resisting.  T.S.,  38,000.  Castings,  June,  1908.  32.  Com.  of  A.S.T.M., 
1905,  Proc.,  v.  65.  Successful  wheels  varying  quite  considerably  from 
these  figures  may  be  made.  33,  34.  C.  A.  Meissner,  Iron  Age,  1890. 
Average  of  several.  35.  R.  Moldenke,  A.S.M.E.,  1908.  36-39.  J.  W 
Keep,  A.S.M.E.,  1907. 

A  Chilling  Iron  is  one  which  when  copied  slowly  has  a  gray  fracture, 
but  when  cast  in  a  mold  one  side  of  which  is  a  thick  mass  of  cast-iron, 
called  a  chill,  the  fractured  surface  shows  white  iron  for  some  depth  on 
the  side  that  was  rapidly  cooled  by  the  chill.  See  Table  Nos.  19-22. 

Specifications  for  Castings,  recommended  by  a  committee  of  the 
A.S.T.M.,  1908.  S  in  gray  iron  castings,  light,  not  over  0.08;  medium, 
not  over  0.10;  heavy,  not  over  0.12.  Alight  casting  is  one  having  no 
section  over  1/2  in.  thick,  a  heavy  casting  one  having  no  section  less  than 
2  in.  thick,  and  a  medium  casting  one  not  included  in  the  classification  of 
light  or  heavy.  The  transverse  strength  of  the  arbitration  bar  shall  not 
be  under  2500  Ib.  for  light,  2900  Ib.  for  medium,  and  3300  Ib.  for  heavy 
castings;  in  no  case  shall  the  deflection  be  under  0.10  in.  When  a  ten- 
sile test  is  specified  this  shall  run  not  less  than  18,000  Ib.  per  sq.  in.  for 
light,  21,000  Ib.  for  medium,  and  24,000  Ib.  for  heavy  castings. 

The  "  arbitration  bar"  is  1  1/4  in.  diam.,  15  in.  long,  cast  in  a  thoroughly 
dried  and  cold  sand  mold.  The  transverse  test  is  made  with  supports 
12  in.  apart.  The  moduli  of  rupture  corresponding  to  the  figures  for 
transverse  strength  are  respectively  39115,  45373,  and  51632,  being  the 
product  of  the  figures  given  and  the  coastant  15.646,  the  factor  for  R/P 
for  a  H/4-in.  round  bar  12  in.  between  supports.*  The  standard  form  of 
tensile  test  piece  is  0.8  in.  diam.,  1  in.  long  between  shoulders,  with  a 
fillet  7/32  in.  radius,  and  ends  1  in.  long,  11/4  in.  diam.,  cut  with  standard 
thread,  to  fit  the  holders  of  the  testing  machine. 

Specifications  bv  J.  W.  Keep,  A.S.M.E.,  1907.  See  Table  of  Analyses, 
Nos.  37-39,  page  417.  Transverse  test,  1x1  x  12-in.  bar,  hard  iron  castings. 
No.  37,  2400  to  2600  Ib.;  tensile  test  of  same  bar,  22,000  to  25,000  Ib. 
No.  38,  medium,  transverse,  2200  to  2400;  tensile,  20,000  to  23,000. 
No.  39,  soft,  transverse,  2000  to  2200;  tensile,  18,000  to  20,000. 

Specifications  for  Metal  for  Cast-iron  Pipe.  —  Proc.  A.S.T.M.,  1905, 
A.L.M.K.,  xxxv,  166.  Specimen  bars  2  in.  wide  x  1  in.  thick  x  24  in. 
between  supports,  loaded  in  the  center,  for  pipes  12  in.  or  less  in  diam. 
shall  support  1900  Ib.  and  show  a  deflection  of  not  less  than  0.30  in, 
before  breaking.  For  pipes  larger  than  12  in.,  2000  Ib.  and  0.32  in. 
The  corresponding  moduli  of  rupture  are  respectively  34,200  and  36,000 
Ib.  Four  grades  of  pig  are  specified:  No.  1,  Si,  2.75;  S,  0.035.  No  2. 
8i,  2.25;  S,  0.045.  No.  3,  Si,  1.75;  S,  0.055.  No.  4,  Si,  1.25;  S,  0.065.  A 
variation  of  10%  of  the  Si  either  way,  and  of  0.01  in  the  S  above  the 
standard,  is  allowed. 

Chemical  Standards  for  Iron  Castings.  —  The  following  analyses  are 
tentative  standards,  or  probable  best  analyses,  suggested  by  the 
Committee  on  Standards  for  Iron  Castings,  American  Foundry  men's 
Association,  June,  1910.  "Heavy"  castings  are  those  in  which  no 
section  is  less  than  2  in.  thick;  "light"  castings  are  those  having  any 
section  less  than  i/2-in.  thick;  "medium"  castings  are  those  not  in- 
cluded in  the  definition  of  light  and  heavy  castings.  The  desirable 


*  Formula,  y^Pl  =  fll/c;  see  page  299.     I  =  Vstird*;  c  =  *Ad\  d  = 
In.;?  =12  in.     /  =  0.11983;  R/P  =  MX  12  X  %  *  0.11983  =  15.646. 


442 


IRON   AND    STEEL. 


percentage  of  silicon  depends  largely  on  the  thickness  of  the  casting 
and  the  practice  followed  in  shaking  out.  These  factors,  being  in 
many  cases  undetermined,  are  allowed  for  by  giving  fairly  wide  limits 
to  this  element.  The  effect  of  purifying  alloys  and  the  use  of  steel 
scrap  have  not  been  taken  into  account.  In  many  cases  a  wide  range 
of  composition  is  compatible  with  the  best  results,  and  in  such  cases 
the  question  of  cost  will  be  the  first  element  to  be  considered. 


Si. 

S. 

P. 

Mn. 

C. 

(Comb.) 

c. 

(Total) 

Acid  -  resisting     castings 
(stills,  eggs,  etc.)  .  .  . 

1.00-2.00 
2.00-2.50 

2.25-2.75 
1.40-1.60 
1  .75-2.25 

0.05-* 
0.06-0.08 

0.06-0.08 
0.06- 
0.08- 

0.40-* 
0.60-0.80 

0.70-0.90 
0.20- 
0.40-0.50 

1.00-1.50 
0.60-0.80 

0.50-0.70 
0.60-1.00 
0.60-0.80 

3.00-3.50 

Agricultural    machinery, 
ordinary 

Agricultural     machinery, 
very  thin  
Annealing  boxes,  etc  
Automobile  castings. 

Balls  for  ball  mills  
Boiler  castings  . 

1.00-1.25 
2.00-2.50 
1.50-2.25 
0.75-1.25 
1.75-2.25 
0.80-1.00 

0.08- 
0.06- 
0.08- 
0.08-0.10 
0.07- 
0.08-0.10 

0.20- 
0.20- 
0.40-0.60 
0.20-0.40 
0.20-0.40 
0.20-0.40 

0.60-1.00 
0.60-1.00 
0.60-1.00 
0.80-1.20 
0.60-1.00 
0.80-1.20 

Car  castings,  gray  iron.  .  . 
Chilled  castings  
Chills 

Crusher  jaws 

Cutting-tools,  chilled  .... 
Cylinders: 
Air  and  ammonia  
Automobile 

1.00-1.25 

1.00-1.75 
1.75-2.00 
1.00-1.75 
0.80-1.20 
1.20-1.60 

0.08- 

0.09- 
0.08- 
0.08- 
0.10- 
0.09- 

0.20-0.40 

0.30-0.50 
0.40-0.50 
0.20-0.40 
0.20-0.40 
0.30-0.50 

0.60-0.80 

0.70-0.90 
0.60-0.80 
0.70-0.90 
0.80-1.00 
0.70-0.90 

6.55-0.65 

3.00-3.30 
3.00-3.25 
3.00-3.30 
low 
low 

low 
low 
2.97 

low 
low 

Gas  engine  . 

Hydraulic,  heavy  
Hydraulic,  medium 

Locomotive 

1.00-1.50 
1.00-1.25 
1.25-1.75 
1.25-1.50 

2.70    ' 

2.00-2.50 
2.50-3.00 

1.25-1.75 
1.50-2.25 
2.25-2.50 
1.25-2.00 

0.08-0.10 
0.10- 
0.09- 
0.07- 

0.063 

0.08- 
0.08- 

0.10- 
0.08- 
0.07- 
0.09- 

0.30-0.50 
0.20-0.40 
0.30-0.50 
0.20- 

0.30 

0.50-0.80 
0.50-0.80 

0.30-0.50 
0.40-0.60 
0.40-0.50 
0.30-0.50 

0.80-1.00 
0.80-1.00 
0.70-0.90 
0.60-0.80 

0.44 

0.30-0.40 
0.30-0.40 

0.60-0.80 
0.50-0.70 
0.50-0.70 
0.60-1.00 

1.60 

0.20-0.30 
0.20-0.30 

Steam  engine,  heavy.  .  . 
Steam  engine,  medium. 
Dies,  drop-hammer  
Diamond  polishing 
wheelsf  
Electrical  machinery 
(frames,  bases,  spiders), 
large 

Electrical  machinery, 
small  
Engine  castings: 
Bedplates  
Flywheels  
Do.,  automobile  ..... 
Frames 

Pillow  blocks  
Piston  rings  
Fire    pots    and    furnace 
castings  .... 

1.50-1.75 
1.50-2.00 

2.00-2.50 
2.00-2.50 

0.50-0.75 
1.00-1.25 
1.00-1.25 

0.08- 
0.08- 

0.06- 
0.06- 

0.15-0.20 
0.06- 
0.06- 

0.40-0.50 
0.30-0.50 

0.20- 
0.20- 

0.20-0.40 
0.20-0.30 
0.20-0.30 

0.60-0.80 
0.40-0.60 

0.60-1.00 
0.60-1.00 

1.50-2.00 
0.80-1.00 

'  b'.30-'  ' 
O.WM.OO 

low 

low 
low 

low 
low 

Grate  bars 

Grinding  machinery, 
chilled  Castings  for  .... 
Gun  carriages  

Gun  iron  .  .  . 

Hardware      (light)      and 
hollow  ware 

2.25-2.75 

1.25-2.50 
1.25-1.50 

1.25-1.50 

0.08- 

0.06- 
0.06- 

0.08- 

0.50-0.80 

0.20- 
0.20- 

0.30-0.50 

0.50-0.70 

0.60-1.00 
0.60-1.00 

0.70-0.90 

Heat  re^stant  iron   (re- 
torts) .  . 

0.30- 

low 

Ingot  molds  and  stools.  . 
Locomotive  castings, 
heavy  

*  Affixed  hyphens  indicate  that  the  percentages  present  should  be 
under  those  given. 


= 


CAST   IKON. 


443 


Si. 

S. 

P. 

Mn. 

C. 

(Comb.) 

C. 

(Total) 

Loco.  Castings,  light.  .  .  . 
Machinery  castings, 
heavy  
Do.,  medium  

1.50-2.00 

1.00-1.50 
1.50-2.00 
2.00-2.50 
1.75-2.00 
1.00-1.50 
1.50-2.00 
2.00-2.50 
1.75-2.25 
2.25-2.75 

0.08-* 

0.10- 
0.09- 
0.08- 
0.08-0.10 
0.08-0.10 
0.09- 
0.08- 
0.09- 
0.08- 

0.40-0.60 

0.30-0.50 
0.40-0.60 
0.50-0.70 
0.30- 
0.30-0.50 
0.40-0.60 
0.50-0.70 
0.50-0.70 
0.60-0.80 

0.60-0.80 

0.80-1.00 
0.60-0.80 
0.50-0.70 
0.50-0.70 
0.80-1.00 
0.70-0.90 
0.60-0.80 
0.60-0.80 
0.50-0.70 

. 

low 

Do.,  light  
Friction  clutches  

low 
low 

Gears,  heavy  
Do.,  medium 

Do.,  small  
Pulleys,  heavy  
Do.,  light  

Shaft      colla  s      and 
couplings  
Shaft  hangers  

1.75-2.00 
1.50-2.00 

0.08- 
0.08- 

0.40-0.50 
0.40-0.50 

0.60-0.80 
0.60-0.80 

Ornamental  work  
Permanent  molds  .  .  . 

2.25-2.75 
2.00-2.25 

0.08- 
0.07- 

0.60-1.00 
0.20-0.40 

0.50-0.70 
0.60-1.00 

Permanent  mold  castings. 
Piano  plates  .  . 

1.50-3.00 
2.00-2.25 

0.06- 
0.07- 

0.40- 

0.40-0.60 

0.60-0.80 

Pipe  •  
Pipe  fittings.  . 

1.50-2.00 
1.75-2.50 

1.50-1.75 
0.75-1.25 

0.10- 
0.08- 

0.08- 
0.08- 

0.50-0.80 
0.50-0.80 

0.20-0.40 
0.20-0.30 

0.60-0.80 
0.60-0.80 

0.70-0.90 
0.80-1.00 

Do.,      for      superheated 
steam  lines.  
Plow  points,  chilled  .  .  . 

low 

Propeller  wheels  
Pumps,  hand  .... 

1.00-1.75 
2.00-2.25 
2.00-2.25 

0.10- 
0.08- 
O.OS- 

0.20-0.40 
0.60-0.80 
0.60-0.80 

0.60-1.00 
0.50-0.70 
0.50-0.70 

low 

Radiators  

0.50-0.60 

Railroad  castings  
Rolling  mill  machinery: 
Housings  
Rolls,  chilled    .  . 

1.50-2.25 

1.00-1.25 
0.60-0.80 

0.75 
2.00-2.30 
1.75-2.00 
1.75-2.25 
2.25-2.75 
1.25-1.75 
1.75-2.25 

0.08- 

0.08- 
0.06-0.08 

0.03 
0.08- 
0.07- 
0.09- 
0.08- 
0.09- 
0.08- 

0.40-0.60 

0.20-0.30 
0.20-0.40 

0.25 
0.60-1.00 
0.3(V 
0.50-0.80 
0.60-0.90 
0.20-0.40 
0.30-0.50 

0.60-0.80 

0.80-1.00 
1.00-1.20 

0.66 
0.50-0.70 
0.70-0.90 
0.60-0.80 
0.60-0.80 
0.80-1.00 
0.60-0.80 

low 
3.00-3.25 

4.10 

Rolls,  unchilled  (sand- 
cast)  f    .  .  . 

1.20 

Scales  

Slag  car  castings  
Soil  pipe  and  fittings  .... 
Stove  plate  
Valves,  large 

Do.,  small  

low 

'  '2.56'  ' 

Water  heaters  
Wheels,  large  
Do.,  small  
White  iron  castings!  

2.00-2.25 
1.50-2.00 
1.75-2.00 
0.50-0.90 

0.08- 
0.09- 
0.08- 
0.15-0.25 

0.30-0.50 
0.30-0.40 
0.40-0.50 
0.20-0.70 

0.60-0.80 
0.60-0.80 
0.50-0.70 
0.17-0.50 

'  '2.96'  ' 

*  Affixed  hyphens  indicate  that  the  percentages  present  should  be 
under  those  given. 

t  But  one  or  two  analyses  available — no  suggestion  made. 

Standard  Specifications  for  Foundry  Pig  Iron. 

(American  Foundry  men's  Association,  May,  1909.) 

ANALYSIS. — It  is  recommended  that  foundry  pig  be  bought  by  analysis. 

SAMPLING.  —  Each  carload  or  its  equivalent  shall  be  considered  as  a 
unit.  One  pig  of  machine-cast,  or  one-half  pig  of  sand-cast  iron  shall  be 
taken  to  every  four  tons  in  the  car,  and  shall  be  so  chosen  from  different 
parts  9f  the  car  as  to  represent  as  nearly  as  P9.ssible  the  average  quality 
of  the  iron.  Drillings  shall  be  taken  so  as  to  fairly  represent  the  composi- 
tion of  the  pig  as  cast.  An  equal  quantity  of  the  drillings  from  each  pig 
shall  be  thoroughly  mixed  to  make  up  the  sample  for  analysis. 

PERCENTAGE  OF  ELEMENTS. — When  the  elements  are  specified  the  fol- 
lowing percentages  and  variations  shall  be  used.  Opposite  each  percent- 
age of  the  different  elements  a  syllable  has  been  affixed  so  that  buyers, 
by  combining  these  syllables,  can  form  a  code  word  to  be  used  in 
telegraphing. 


444 

SILICON 

IRON   AND   STEEL. 
SULPHUR     TOTAL  CARBON    MANGANESE 

PHOSPHORUS 

% 
1.00 
1.50 
2.00 
2.50 
3.00 

Code 
La 
Le 
Li 
Lo 
Lu 

(max.)  Code 
0.04     Sa 
0.05     Se 
0.06     Si 
0.07    So 
0.08     Su 
0.09     Sy 
0.10     Sh 

(min.) 
3.00 
3.20 
3.40 
3.60 
3.80 

Code 
Ca 

8f 

Co 

Cu 

0 
0 
0 
0 

1 
1 
1 

% 

.20 
.40 
.60 
.80 
.00 
.25 
.50 

Code 
Ma 
Me 
Mi 
Mo 
Mu 
My 
Mh 

0 
0 
0 
0 

1 
1 
1 

% 

.20 
.40 
.60 
.80 
.00 
.25 
.50 

Code 
Pa 
Pe 
Pi 
Po 
Pu 
Py 
Ph 

Percentages  of  any  element  specified  one-half  way  between  the  above 
shall  be  designated  by  the  addition  of  the  letter  x  to  the  next  lower  symbol, 
thus  Lex  means  1.75  Si. 

Allowed  variation:  Si,  0.25;  P,  0.20;  Mn,  0.20.  The  percentages  of  P 
and  Mn  may  be  used  as  maximum  or  minimum  figures  when  so  specified. 

Example:  — Le-sa-pi-me  represents  1.50  Si,  0.04  S,  0.60  P,  0.40  Mn. 

BASE  OR  QUOTING  PRICE. — For  market  quotations  an  iron  of  2.00  Si 
(with  variation  0.25  either  way)  and  S  0.05  (max.)  shall  be  taken  as  the 
base.  The  following  table  may  be  filled  out,  and  become  a  part  of  a 
contract;  "B,"  or  Base,  represents  the  price  agreed  upon  for  a  pig  of 
2.00  Si  and  under  0.05  S.  "C"  is  a  constant  differential  to  be  deter- 
mined at  the  time  the  contract  is  made. 

Sill-, Silicon > 

phur  3.25     3.00      2.75      2.50      2.25     2.00       1.75     1.50       1.25      1.00 
0.04  B  +  6C  B+5C  B+4C  B+3C  B  +  2C  B  +  C    B          B-1C  B-2C  B-3C 
0.05  B  +  5C  B+4C  B+3C  B  +  2C  B  +  1C  B          B-1C  B-2C  B-3C  B-4C 
0.03  B  +  4C  B  +  3C  B  +  2C  B  +  1C  B  B-1C  B-2C  B-3C  B-4C  B-5C 

0.07  B  +  3C  B  +  2C  B  +  1C  B  B-1C  B-2C  B-3C  B-4C  B-5C  B-CC 

0.08  B  +  2C  B  +  1C  B  B-1C  B-2C  B-3C  B-4C  B-5C  B-CC  B-7C 
0.09  B  +  1C  B  B-1C  B--2C  B-3C  B-4C  B-5C  B-6C  B-7C  B-8C 
0.10  B  B-1C  B-2C  B-3C  B-4C  B-5C  B-6C  B-7C  B-8C  B-9C 

Tensile  Tests  of  Cast-iron  Bars. 

(American  Foundrymen's  Association,  1899.) 


Square  Bars. 


Size,  in... 
(A)<7.c.. 
o  m 

0.5x0.5 
15,900 

1x1 
13,900 
15  400 

1.5x1.5 
12,100 
12900 

2x2 
10,600 
10900 

0.56 
16,000 

1.13 

13,800 
13  800 

1.69 
12,000 
13  500 

2.15 
11,000 
12  200 

"    d.  s.. 

**     d    771. 

14,600 

12,900 
13,800 

12,300 
13,400 

9,800 
12,100 

14,300 

13,700 
13,600 

11,700 
13,200 

10,500 
10,600 

(B)flr.c.. 
am. 

17,100 

15,200 
17,600 

12,900 
15,000 

11,500 
11,800 

16,500 

15,900 
19000 

13,100 
15  400 

11,400 
12500 

"    d.  c.  . 
*'    d  m. 

16,300 

15,100 
18,400 

13,300 
15  000 

11,100 
12  100 

16,700 

16,200 
16900 

13,200 
15  100 

11,000 
13  100 

(C)  ff.c.. 
"    a  m. 

17,700 

16,000 
18  500 

12,500 
15  100 

11,100 
11  700 

17,800 

15^00 
17  400 

14,200 
15  000 

12,000 
11  600 

"    d.c.. 
'*   d.  m. 

16,400 

16,000 
17,100 

12,200 
14,100 

11,300 
9,800 

16,400 

15,900 
17,700 

14,000 
15,900 

11  1600 
10,400 

av.  (7.  ... 
av.  d.  .  .  . 

av.  c.  .  .  . 

13,600 
15,800 
14,700 

16,100 
15,500 
14,800 
16,800 

13,400 
13,400 
12,500 
14,200 

11,300 
11,000 
10,900 
11,400 

13,400 
15,800 
16,300 

16,000 
15,700 
15,200 
16,400 

13,900 
13,800 
13,000 
f4,600 

11,600 
11,200 
11,200 
11,700 

Round  Bars. 


Compression  Tests  of  Cast-iron  Bars. 


Size,  i 

(A) 

n..  . 
)... 

0.5x0.5 
29,570 

Ixl 
20,010 
21,990 

1.5x1.5 
17,180 
17,920 

2x2 
13,810 
13,750 

2.5x2.5 
10,950 
12,040 

3x3 
9,830 
11,200 

3.5x3.5 
9,350 
10,770 

4x4 
9,100 
10,340 

* 

17,180 

13,880 

11,430 

10,270 

9,830 

9,950 

•• 

4 

10,950 

10,430 

9,540 

9,570 

(B) 

1  ... 
? 

38,360 

23,000 
12,440 

20,980 
24,820 

18,130 
21,640 

15,060 
18,270 

13,790 
17,000 

13,160 
15,970 

12,430 
16,140 

«< 

1 

20,980 

18,740 

15,940 

14,410 

15,200 

13,950 

4 

15,060 

13,900 

13,560 

13,760 

(C) 

... 
? 

38,360 

24,890 
27,900 

20,750 
22,060 

18,010 
21,750 

17,840 
19,800 

15,950 
18,170 

15,880 
17,100 

14,220 
16,410 

^ 

20  750 

19340 

18,050 

16,850 

16,510 

15,250 

"    ( 

4... 

,  ,  ,  

17,840 

16,040 

16,080 

14,880 

CAST  IRON. 


445 


Transverse  Tests  of  Cast-iron  Bars.     Modulus  of  Rupture. 


Bize  *... 
Diam.  f  
(A)r.d.c.... 

0.5x0.5 
0.56 
31,100 

1x1 
1.13 
33,400 
27800 

1.5x1.5 
1.69 
33,900 
38,000 

2x2 
2.15 
31,700 
32,300 

2.5x2.5 
2.82 
27,000 
28,000 

3x3 

3.38 
26,600 
28600 

3.5x3.5 
3.95 
23,400 
22400 

4x4 
4.51 

22,600 
22900 

(B)  s.  g.  c.  .  .  . 

44,400 

39,100 
37,400 

39,500 
40,300 

33,900 
34,700 

31,900 
35,800 

29,700 
33,500 

27,200 
30  100 

27,600 
27,100 

"    s.d.c  
"    s.d.m. 

35,500 

38,300 
30200 

34,000 
36,200 

32,900 
33,300 

31,900 
35,200 

30,200 
30900 

29,300 
28  100 

25,900 
25,800 

"   r.g.c  
M   r.  g.m.  .. 

"   r.  d.  m.  .  . 
(C)  s.g.c  

'      s.  g    m. 

36,400 
'37',  800  ' 
'Si',  800  ' 

46,200 
40,000 
49,000 
39,100 
39,200 

41,200 
44,800 
44,300 
37,800 
33,600 
40,200 

41,400 
38,800 
39,200 
37,700 
37,900 
37,000 

41,300 
37,100 
40,700 
33,000 
32,200 
33,700 

36,300 
32,900 
31,800 
32,800 
31,100 
33,300 

34,800 
32,700 
35,300 
32,000 
31,300 
32300 

31,000 
32,300 
31,100 
31,200 
29,200 
27,900 

s.  d,  c.  ... 

48,000 

39,100 

38,800 
38,900 

35,100 
35,400 

31,200 
33,500 

29,300 
32  700 

29,300 
29  100 

27,800 
25,500 

r.g.c  
r  g.  m.  . 

62,800 

48,500 
55,700 

39,000 
49,200 

44,500 
42900 

41,400 
41,500 

41,200 
36  500 

35,000 
34  100 

32,300 
36,000 

r.  d.  c.  .  .  . 
r.  d.  m.  .  . 
Av.  (B)  s  

(C)  s.'.  '.'.'. 

(B)&r(CJ^. 
**   d. 
Gen'l  av  
Equiv.  load.  . 

53,000 

'39;  900 
37,100 
49,900 
57,900 
48,800 
43,300 
46,100 
320 

50,400 
47,900 
36,200 
43,600 
39,100 
50,600 
43,100 
41,600 
42,400 
2356 

44,000 
51,300 
37,500 
42,000 
37,900 
45,900 
41,000 
40,700 
40,800 
7650 

40,200 
38,000 
33,700 
39,300 
36,300 
41,400 
38,800 
36,500 
37,700 
16,756 

39,500 
38,900 
33,700 
38,200 
32,600 
40,400 
36,800 
35,600 
36,200 
31,424 

37,800 
36,300 
31,100 
33,400 
31,600 
37,900 
33,900 
32,700 
33,400 
50,100 

35,200 
32,200 
28,700 
33,700 
30,500 
34,100 
32,200 
31,300 
31,700 
75,516 

32,100 
33,500 
26,600 
31,400 
27,600 
33,200 
30,400 
30,400 
29,900 
106,311 

*  Size  of  sauare  bars  as  cast,  in.       t  Diam.  of  round  bars  as  cast.  in. 

NOTES  ON  THE  TABLES  OP  TESTS. — The  machined  bars  were  cut  to 
the  next  size  smaller  than  the  size  they  were  cast.  The  transverse  bars 
were  12  in.  long  between  supports.  (A),  (B),  (C),  three  qualities  of  iron; 
for  analyses  see  page  417;  rt  round  bars;  s,  square  bars;  d,  cast  in  dry  sand; 
g,  cast  in  green  sand;  r,  bar  tested  as  cast;  m,  bar  machined  to  size.  The 
general  average  (next  to  last  line  of  the  first  table)  is  the  average  of  the  six 
lines  preceding.  The  equivalent  load  (last  line)  is  the  calculated  total 
load  that  would  break  a  square  bar  whose  modulus  of  rupture  is  that 
of  the  general  average. 

COMPRESSION  TESTS. — The  figures  given  are  the  crushing  strengths,  in 
pounds,  of  £  in.  cubes  cut  from  the  bars.  Multiply  by  4  to  obtain  Ibs. 
per  sq.  in.  (1)  Cube  cut  from  the  middle  of  the  bar;  (2)  first  £  in.  from 
edge;  (3)  second  £  in.  from  edge;  (4)  third  ^  in  from  edge. 

Some  Tests  of  Cast  Iron.  (G.  Lanza,  Trans.  A.S.M.E.,  x,  187.)  — 
The  chemical  analyses  were  as  follows:  Gun  iron:  TC,  3.51;  GC,  2.80; 
S,  0.133;  P,  0.155;  Si,  1.140.  Common  iron:  S,  0.173;  P,  0.413;  Si,  1.89. 

The  test  specimens  were  26  in.  long:  those  tested  with  the  skin  on  being 
very  nearly  1  in.  square,  and  those" tested  with  the  skin  removed  being 
cast  nearly  1 1/4  in.  square,  and  afterwards  planed  down  to  1  in.  square. 

Tensile    Elastic    Modulus 
Strength.     Limit.  '       of 

Elasticity. 

Unplaned  common. .  20,200  to  23,000  T.S.  Av.  =  22,066  6,500  13,194,233 
Planed  common.  ..  .20,300  to  20,800  "  "  =20,520  5,833  11,943,953 

Unplaned  gun 27,000  to  28,775     "      "    =28,17511,000   16,130,300 

Planed  gun 29,500  to  31,000     "     .  "   =30,500    8,500   15,932,880 

The  elastic  limit  is  not  clearly  defined  in  cast  iron,  the  elongations  increas- 
ing faster  than  the  increase  of  the  loads  from  the  beginning  of  the  test. 
The  modulus  of  elasticity  is  therefore  variable,  decreasing  as  the  loads 
increase. 

The  Strength  of  Cast  Iron  depends  on  many  other  things  besides 
its  chemical  composition.  Among  them  are  the  size  and  shape  of  the 
casting,  the  temperature  at  which  the  metal  is  poured,  and  the  rapidity  of 
cooling.  Internal  stresses  are  apt  to  be  induced  by  rapid  cooling,  and 
Blow  cooling  tends  to  cause  segregation  of  the  chemical  constituents  and 


446  IRON  AND   STEEL. 

opening  of  the  grain  of  the  metal,  making  it  weak.  The  author  recom- 
mends that  in  making  experiments  on  the  strength  of  cast  iron,  bars  of 
several  different  sizes,  such  as  1/2,  1,  11/2,  and  2  in.  square  (or  round), 
should  be  taken,  and  the  results  compared.  Tests  of  bars  of  one  size 
only  do  not  furnish  a  satisfactory  criterion  of  the  quality  of  the  iron  of 
which  they  are  made.  Trans.  A.T.M.E.,  xxvi,  1017. 

Theory  of  the  Relation  of  Strength  to  Chemical  Constitution.  — 
J.  E.  Johnston,  Jr.  (Am.  Mack.,  April  5  and  12,  1900),  and  H.  M.  Howe 
(Trans.  A.I.M.E.,  1901)  have  presented  a  theory  to  explain  the  variation 
in  strength  of  cast  iron  with  the  variation  in  combined  carbon.  It  is 
that  cast  iron  is  steel  of  CC  ranging  from  0  to  4%,  with  particles  of  graph- 
ite, which  have  no  strength,  enmeshed  with  it.  The  strength  of  the  cast 
iron  therefore  is  that  of  the'  steel  or  graphiteless  iron  containing  the  same 
percentage  of  CC,  weakened  in  some  proportion  to  the  percentage  of  GC. 
The  tensile  strength  of  steel  ranges  approximately  from  40,000  lb.  per 
sq.  in.  with  0  C  to  125,000  lb.  with  1 .20  C.  With  higher  C  it  rapidly  becomes 
weak  and  brittle.  White  cast  iron  with  3%  CC  is  about  30,000  T.S., 
and  with  4%  about  18,000.  The  amount  of  weakening  due  to  GC  is  not 
known,  but  by  making  a  few  assumptions  we  may  construct  a  table  of 
hypothetical  strengths  of  different  compositions,  with  which  results  of 
actual  tests  may  be  compared.  Suppose  the  strength  of  the  steel-white 
cast-iron  series  is  as  given  below  for  different  percentages  of  CC,  that 
6.25%  GC  entirely  destroys  the  strength,  and  that  the  weakening  effect 
of  other  percentages  is  proportional  to  the  ratio  of  the  square  root  of  that 
percentage  to  the  square  root  of  6.25,  that  the  TC.  in  two  irons  is  respec- 
tively 3%  and  4%,  then  we  have  the  following: 
Per  cent  CC..  0  0.2  0.4  0.6  0.8  1.0  1.2  1.5  2.02.5  3  3.5  4 

Steel,  T.S 40      60     80    100    110    120    125    110  60     40    30     22  18 

Cast  iron,  4% 

TC 8     13.2  19.2    26   31.2      37  41.5  40.5   26  20.7  18  15-8  18 

Cast  iron,  3% 

TC 15.419.928.5     3842.952.1      5856.1    3628.730 

The  figures  for  strength  are  in  thousands  of  pounds  per  sq.  in.  The 
table  is  calculated  as  follows:  Take  0.6  CC;  with  4%  TC.,  this  leaves 
3.4  GC,  and  with  3%  TC,  2.4  GO_The  sq.  root  of  3.4  is  1.9,  and  of  2.4  is 
1.55.  The  ratio  of  these  to  ^6.25  is  respectively  74  and  62%,  which 
subtracted  from  100  leave  26  and  38%  as  the  percentage  of  strength  of 
the  0.6  C  steel  remaining  after  the  effect  of  the  GC  is  deducted.  The 
table  indicates  that  strength  is  increased  as  total  C  is  diminished,  and  this 
agrees  with  general  experience. 

Relation  of  Strength  to  Size  of  Bar  as  Cast.  —  If  it  is  desired  that  a 
test  bar  shall  fairly  represent  a  casting  made  from  the  same  iron,  then 
the  dimensions  of  the  bar  as  cast  should  correspond  to  the  dimensions  of 
the  casting,  so  as  to  have  about  the  same  ratio  of  cooling  surface  to 
volume  that  the  casting  has.  If  the  test  bar  is  to  represent  the  strength 
of  a  plate,  it  should  be  cut  from  the  plate  itself  if  possible  or  else  cut 
from  a  cylindrical  shell  made  of  considerable  diameter  and  of  a  thickness 
equal  to  that  of  the  casting.  If  the  test  is  for  distinguishing  the  quality 
of  the  iron,  then  at  least  two  test  bars  should  be  cast,  one  say  1/2  or  5/g  in. 
and  one  say  2  or  21/2  in.  diameter,  in  order  to  show  the  effect  of  rapid 
and  slow  cooling. 

In  1904  the  author  made  some  tests  of  four  bars  of  "  semi-steel "  adver- 
tised to  have  a  strength  of  over  30,000  lb.  per  sq.  in.  The  bars  were  cast 
1/2,  1,  2,  and  3  in.  diam.,  and  turned  to  0.46,  0.69,  1.6,  and  1.85  in.  respec- 
tively. The  results  of  transverse  and  tensile  tests  were: 

Mod.  of  rupture.  .1/2  in.,  100.000;  1  in.,  61,613;  2  in.,  67,619;  3  in.,  58,543 
T.S.  per  sq.  in...  38,510;  '  37,005;  25,685;  '  20,375 

The  i/2-in.  piece  was  so  hard  that  it  could  not  be  turned  in  a  lathe  and 
had  to  be  ground. 

Influence   of  Length   of  Bar  upon   the  Modulus   of   Rupture.  — 

(R.    Moldenke,   Jour.   Am.   Foundrymen's   Assn.,   Sept.,    1899.)     Seven 
sets,  each  of  five  2-in.  square  bars,  made  of  a  heavy  machinery  mixture, 
and  cast  on  end,  were  broken  transversely,  the  distance  between  sup- 
ports ranging  from  6  to  16  ins.     The  average  results  were: 
Dist.  bet.  supports,  ins....      6  8  10  12  14  16 

Modulus  of  rupture 40,000    39,000    35,600    37,000    36,000    34,400 


CAST  IRON. 


447 


The  10-in.  bar  in  six  out  of  seven  cases  gave  a  lower  result  than  the 
12-in.  It  appears  that  the  ordinary  formulas  used  in  calculating  the 
cross  breaking"  strength  of  beams  are  not  only  incorrect  for  cast  iron,  on 
account  of  the  chemical  differences  in  the  iron  itself  when  in  different 
cross  sections,  but  that  with  the  cross  sections  identical  the  distance 
between  the  supports  must  be  specially  provided  for  by  suitable  con- 
stants in  whatever  formulae  may  be  developed.  As  seen  from  the  above 
results,  the  doubling  of  the  distance  between  supports  means  a  drop  in 
the  modulus  of  rupture  in  the  same  sized  bar  of  nearly  10  per  cent. 

Strength  in  Relation  to  Silicon  and  Cross-section. —  In  castings 
one  half-inch  square  in  section  the  strength  increases  as  silicon  increases 
from  1.00  to  3.50:  in  castings  1  in.  square  in  section  the  strength  is  practi- 
cally independent  of  silicon,  while  in  larger  castings  the  strength  decreases 
as  silicon  increases. 

The  following  table  shows  values  taken  from  Mr.  Keep's  curves  of  the 
approximate  transverse  strength  of  cast  bars  of  different  sizes  reduced  to 
the  equivalent  strength  of  a  i/2-in.  x  12-in.  bar. 


Size  of  Square  Cast  Bars. 
1/2  in.  1 1  'in~TTin.  |  3  in.  j  4  in, 


Strength  of  a  Va-in.  X  12-in. 
'  section,  Ib. 


Size  of  Square  Cast  Bars. 


1/2  in. |  1  in.  |  2  in.  |  3  in.  |  4  in. 

"^Strength  of"a~  V^in.  X  12-in." " 

section,  Ib. 


290 
324 
358 


260 
272 
278 


232 
228 
220 


222 
212 
202 


220 
208 
196 


2.50 
3.00 
3.50 


392 
426 
446 


278 
276 
264 


212 
202 
192 


190 
180 
168 


184 
172 
160 


1.00  SI. 
2.0081} 
3.50  Hfc 


Inches  Square 


FIG.  98. 

Fig.  98  shows  the  relation  of  the  strength  to  the  size  of  the  cast-iron  bar 
and  to  Si,  according  to  the  figures  in  the  above  table.  Comparing  the 
2-in.  bars  with  the  l/2-in.  bars,  we  find 

Si,  per  cent 1    1.5       2    2.5      3     3.5 

2-in.  weaker  than  l/2-in.,  per  cent. .      20     30     35     46     53      57 

The  fact  that  with  the  1-in.  bar  the  strength  is  nearly  independent  of 
Si,  shows  that  it  is  the  worst  size  of  bar  to  use  to  distinguish  the  quality 
of  the  metal.  If  two  bars  were  used,  say  l/2-in.  and  2-in.,  the  drop  in 
strength  would  be  a  better  index  to  the  quality  than  the  test  of  any 
single  bar  could  be. 

Shrinkage  of  Cast  Iron.  —  W.  J.  Keep  (A.  S.  M.  E.  xvi.,  1082)  gives  a 
series  of  curves  showing  that  shrinkage  depends  on  silicon  and  on  the 
cross-section  of  the  casting,  decreasing  as  the  silicon  and  the  section 
increase.  The  following  figures  are  obtained  by  inspection  of  the  curves: 


ij 

Size  of  Square  Bars. 

Silicon, 
Per  cent. 

Size  of  Square  Bars. 

l/2  in. 

1  in. 

2  in. 

3  in.  |  4  in. 

l/z  in.|  1  in.  |  2  in. 

3  in. 

4  in. 

Shrinkage,  In.  per  Foot. 

Shrinkage,  In.  per  Foot. 

1.00 
1.50 
2.00 

0.178 
.166 
.154 

0.158 
.145 
.133 

0.129 
.116 
.104 

0.112 
.099 
.086 

0.102 
.088 
.074 

2.50 
3.00 
3.50 

0.1421  0.121 
.130|     .109 
.118|     .097 

0.091 
.078 
.065 

0.072 
.058 
.045 

0.060 
.046 
.032 

Mr.  Keep  says:  "  The  measure  of  shrinkage  is  practically  equivalent  to 
a  chemical  analysis  of  silicon.     It  tells  whether  more  or  less  silicon  is 


448     •  IRON  AND   STEEL. 

needed  to  bring  the  quality  of  the  casting  to  an  accepted  standard  of 
excellence." 

A  shrinkage  of  l/g  in.  per  ft.  is  commonly  allowed  by  pattern  makers. 
According  to  the  table,  this  shrinkage  will  be  obtained  by  varying  the  Si 
in  relation  to  the  size  of  the  bar  as  follows:  1/2  in.,  3.25  Si;  1  in.,  2.4  Si; 
2  in.,  1.1  Si;  3  and  4,  less  than  1.0  Si. 

Shrinkage  and  Expansion  of  Cast  Iron  in  Cooling.  (T.  Turner, 
Proc.  I.  &  S.  /.,  1906.)  —  Some  irons  show  the  phenomenon  of  expanding 
immediately  after  pouring,  and  then  contracting.  Four  irons  were 
tested,,  analyzing  as  follows:  (1)  "  Washed  "  white  iron,  CC  2.73;  Si, 
0.01;  P,  0.01;  Mn  and  S,  traces.  (2)  Gray  hematite,  GC,  2.53;  CC,  0.86; 
Si,  3.47;  Mn,  0.55;  P,  0.04;  S,  0.03.  (3)  Northampton,  GC,  2.60;  CC, 
0.15;  Si,  3.98;  Mn,  0.50;  P,  1.25;  S,  0.03.  (4)  Cast  iron,  GC,  2.73;  CC, 
0.79;  Si,  1.41;  Mn,  0.43;  P,  0.96;  S,  0.07.  No.  1  was  stationary  for  5  sec- 
onds after  pouring,  shrunk  125  sec.,  stationary  10  sec.,  then  shrunk  till 
cold.  No.  2  expanded  15  sec.,  shrunk  20  sec.  to  original  size,  continued 
shrinking  90  sec.  longer,  stationary  10  sec.,  expanded  30  sec.,  then  shrunk 
till  cold.  No.  3  expanded  irregularly  with  three  expansions  and  two 
shrinkages,  until  125  sec.  after  pouring  the  total  expansion  was  0.019  in. 
in  12  in.,  then  shrunk  till  cold.  No.  4  expanded  0.08  in.  in  50  sec.,  then 
shrunk  till  cold. 

Shrinkage  Strains  Relieved  by  Uniform  Cooling.  (F.  Schumann, 
A.S.M.E.,  xvii,  433.)  —  Mr.  Jackson  in  1873  cast  a  flywheel  with  a  very 
large  rim  and  extremely  small  straight  arms.  Cast  in  the  ordinary  way, 
the  arms  broke  either  at  the  rim  or  at  the  hub.  Then  the  same  pattern 
was  molded  so  that  large  chunks  of  iron  were  cast  between  the  arms,  a 
thickness  of  sand  separating  them.  Cast  in  this  way,  all  the  arms  re- 
mained unbroken. 

Deformation  of  Castings  from  Unequal  Shrinkage.  —  (F.  Schu- 
mann, A.  S.  M.  E.,  vol.  xvii.)  A  prism  cast  in  a  sand  mold  will  main- 
tain its  alignment,  after  cooling  in  the  mold,  provided  all  parts  around 
its  center  of  gravity  of  cross  section  cool  at  the  same  rate  as  to  time  and 
temperature.  Deformation  is  due  to  unequal  contraction,  and  this  is 
due  chiefly  to  unequal  cooling. 

Modifying  causes  that  effect  contraction  are:  Imperfect  alloying  of 
two  or  more  different  irons  having  different  rates  of  contraction;  varia- 
tions in  the  thickness  of  sand  forming  the  mold;  unequal  dissipation  of 
heat,  the  upper  surface  dissipating  the  greater  amount  of  heat:  position 
and  form  of  cores,  which  tend  to  resist  the  action  of  contraction,  also 
the  difference  in  conducting  power  between  moist  sand  and  dry-baked 
cores;  differences  in  the  degree  of  moisture  of  the  sand;  unequal  expos- 
ure by  the  removal  of  the  sand  while  yet  in  the  act  of  contracting: 
flanges,  ribs,  or  gussets  that  project  from  the  side  of  the  prism,  of  suffi- 
cient area  to  cause  the  sand  to  act  as  a  buttress,  and  thus  prevent  the 
natural  longitudinal  adjustment  due  to  contraction;  in  light  castings  of 
sufficient  length  the  unyielding  sand  between  the  flanges,  etc.,  may 
cause  rupture. 

Irregular  Distribution  of  Silicon  in  Pig  Iron. —  J.  W.  Thomas 
(Iron  Age,  Nov.  12,  1891)  finds  in  analyzing  samples  taken  from  every 
other  bed  of  a  cast  of  pig  iron  that  the  silicon  varies  considerably,  the  iron 
coming  first  from  the  furnace  having  generally  the  highest  percentage.  In 
one  series  of  tests  the  silicon  decreased  from  2.040  to  1.713  from  the  first 
bed  to  the  eleventh.  In  another  case  the  third  bed  had  1.260  Si,  the 
seventh  1.718,  and  the  eleventh  1.101.  He  also  finds  that  the  silicon 
varies  in  each  pig,  being  higher  at  the  point  than  at  the  putt.  Some. of 
his  figures  are:  Point  of  pig,  2.328  Si;  butt  of  pig,  2.157;  point  of  pig, 
1.831;  butt  of  pig,  1.787. 

White  Iron  Converted  into  Gray  by  Heating.  (A.  E.  Outerbridge. 
Jr.,  Proc.  Am.  Socy.  for  Testing  MaVls,  1902,  p.  229.)  —When  white  chilled 
iron  containing  a  considerable  amount  of  Si  and  low  in  GC  is  heated  to 
about  1850°  F.  from  31/2  to  10  hours  the  CC  is  changed  into  C,  which 
differs  materially  from  graphite,  and  a  metal  is  formed  which  has  prop- 
erties midway  between  those  of  steel  and  cast  iron.  The  specific  gravity 
is  raised  from  7.2  to  about  7.8;  the  fracture  is  of  finer  grain  than  normal 
gray  iron;  and  the  metal  is  capable  of  being  forged,  hardened,  and  taking 
a  sharp  cutting  edge,  so  that  it  may  be  used  for  axes,  hatchets,  etc.  It 
differs  from  malleable  cast  iron,  since  the  latter  has  iis  carbon  removed 
by  oxidation,  while  the  converted  cast  iron  retains  its  .original  total 


CAST  -IRON.  449 

carbon,  although  in  a  changed  form.  The  tensile  strength  of  the  new 
metal  is  high,  40,000  to  50,000  Ib.  per  sq.  in.,  with  very  small  elongation. 
The  peculiar  change  from  white  to  gray  iron  does  not  take  place  if  Si 
is  low  The  analysis  of  the  original  castings  should  be  about  TO,  3.4  to 
3.8;  Si,  0.9  to  1.2;  Mn,  0.35  to  0.20;  S,  0.05  to  0.04;  P,  0.04  to  0.03.  The 
following  shows  the  change  effected  by  the  heat  treatment: 
Before  annealing,  GO,  0.72;  CO,  2.60;  Si,  0.71;  Mn,  0.11;  S,  0.045;  P,  0.04 
After  annealing.  GO,  2.75;  CC,  0.82;  Si,  0.73;  Mn,  0.11;  S,  0.040;  P,  0.04 

The  GC  after  annealing  is,  however,  not  ordinary  graphite,  but  an 
allotropic  form,  evidently  identical  with  what  Ledebur  calls  "  tempering 
graphite  carbon." 

Change  of  Combined  to  Graphitic  Carbon  by  Heating.  —  (H.  M. 
Howe,  Trans.  A.  I.  M.  E.,  1908,  p.  483.)  On  heating  white  cast  iron  to  dif- 
ferent temperatures  for  some  hours,  the  carbon  changes  from  the  com- 
bined to  the  graphitic  state  to  a  degree  which  increases  in  general  with 
the  temperature  and  with  the  silicon-content.  With  0.05  Si,  a  little 
graphite  formed  at  1832°  F.;  with  0.13  Si,  at  1652°  F. ;  with  2.12  Si,  graphite 
formed  at  a  moderate  rate  at  1112°,  and  with  3.15  Si,  it  formed  rapidly 
at  1112°  F.  In  iron  free  from  Si,  with  4.271  comb.  C.  and  0.255  graphitic, 
none  of  the  C.  was  changed  to  graphite  on  long  heating  to  from  1680°  to 
2349°  F.,  but  in  iron  with  0.75  Si  the  graphite,  originally  0.938%,  rose 
to  1.69%  on  heating  to  1787°,  and  to  2.795%  on  heating  to  2057°  F.  On 
the  other  hand,  when  carbon  enters  iron,  as  in  the  cementation  process 
in  making  blister-steel,  it  appears  chiefly  as  cementite  (combined  carbon). 
Also  on  heating  iron  containing  graphit:  to  high  temperatures  and  cooling 
quickly,  some  of  the  graphite  is  changed  to  cementite. 

Mobility  of  Molecules  of  Cast  Iron.  (A.  E.  Outerbridge,  Jr., 
A.I.M.E.,  xxvi,  176;  xxxv,  223.)  —  Within  limits,  cast  iron  is  materially 
strengthened  by  being  subjected  to  repeated  shocks  or  blows.  Six  bars 
1  in.  sq.,  15  in.  long,  subjected  for  about  4  hours  to  incessant  blows  in  a 
tumbling  barrel,  were  10  to  15%  stronger  than  companion  bars  not 
thus  treated.  Six  bars  were  struck  1000  blows  on  one  end  only  with  a 
hand  hammer,  and  they  showed  a  like  gain  in  strength.  The  increase  is 
greater  in  hard  mixtures,  or  strong  iron,  than  in  soft  mixtures,  or  weak 
iron;  greater  in  1-in.  bars  than  in  l/2-in.,  and  somewhat  greater  in  2-in. 
than  in  1-in.  bars.  Bars  were  treated  in  a  machine  by  dropping  a  14-lb. 
weight  on  the  middle  of  a  1-in.  bar,  supports  12  in.  apart.  Six  bars 
were  first  broken  by  having  the  weight  fall  a  sufficient  distance  to  break 
them  at  the  first  blow,  then  six  companion  bars  were  subjected  to  from 
10  to  50  blows  of  the  same  weight  falling  one-half  the  former  distance, 
and  then  the  weight  was  allowed  to  fall  from  the  height  at-  which  the  first 
bars  broke.  Not  one  of  the  bars  broke  at  the  first  blow;  and  from  2  to 
10,  and  in  one  case  15  blows  from  the  extreme  height  were  required  to 
break  them.  Mr.  Outerbridge  believes  that  every  casting  when  first 
made  is  under  a  condition  of  strain,  due  to  the  difference  in  the  rate  of 
cooling  at  the  surface  and  near  the  center,  and  that  it  is  practicable  to 
relieve  these  strains  by  repeatedly  tapping  the  casting,  allowing  the  parti- 
cles to  rearrange  themselves  and  assume  a  new  condition  of  molecular 
equilibrium.  The  results,  first  reported  in  1896,  were  corroborated  by 
other  experimenters.  A  report  in  Jour.  Frank.  Inst.,  1898,  gave  tests  of 
82  bars,  in  which  the  maximum  gain  in  strength  compared  with  untreated 
bars  was  40%,  and  the  maximum  increase , in  deflection  was  41%. 

In  his  second  paper,  1904,  Mr.  Outerbridge  describes  another  series  of 
tests  which  showed  that  1-in.  sq.  bars  15  in.  long  subjected  to  repeated 
heating  and  cooling  grew  longer  and  thicker  with  each  successive  oper- 
ation. One  bar  heated  about  an  hour  each  day  to  about  1450°  F.  in  a 
gas  furnace  for  27  times  increased  its  length  1  H/ie  in.  and  its  cross-section 
Vs  in.  Soft  iron  expands  more  rapidly  than  hard  iron.  White  iron  does 
not  expand  sufficiently  to  cover  the  original  shrinkage.  Wrought  iron  and 
steel  bars  similarly  treated  in  a  closed  tube  all  contracted  slightly,  the 
average  contraction  after  60  heatings  being  1/8  in.  per  foot.  The  strength 
and  deflection  of  the  cast-iron  bars  was  greatly  decreased  by  the  treatment, 
1250  as  compared  with  2150  Ib.,  and  0.1  in.  deflection  as  compared  with 
0.15  in.  The  specific  gravity  of  the  expanded  bars  was  5.49  to  6.01,  as 
compared  with  7.13  for  the  untreated  bars. 

(irate  bars  of  boiler  furnaces  grow  larger  in  use,  as  do  also  cast-iron 
pipes  in  ovens  for  heating  air. 


450  IRON   AND   STEEL. 

Castings  from  Blast  Furnace  Metal.  Castings  are  frequently  made 
from  iron  run  directly  from  the  blast  furnace,  or  from  a  ladle  filled  with 
furnace  metal.  Such  metal,  if  high  in  Si,  is  more  apt  to  throw  out  "  kish  " 
or  loose  particles  of  graphite  than  cupola  metal.  With  the  same  percen- 
tage of  Si,  it  is  softer  than  cupola  metal,  which  is  due  to  two  causes:  1, 
lower  S;  2,  higher  temperature.  T.  D.  West,  A.I.M.E.,  xxxv,  211, 
reports  an  example  of  furnace  metal  containing  Si,  0.51;  S,  0.045;  Mn, 
0.75;  P,  0.094;  which  was  easily  planed,  whereas  if  it  had  been  cupola 
metal  it  would  have  been  quite  hard.  J.  E.  Johnson,  Jr.,  ibid.,  p  213, 
says  that  furnace  metal  with  S,  0.03,  and  Si,  0.7,  makes  good  castings,  not 
too  hard  to  be  machined.  Should  the  metal  contain  over  0.9  Si,  diffi- 
culty is  experienced  in  preventing  holes  and  soft  places  in  the  castings, 
caused  by  the  deposition  of  kish  or  graphite  during  or  after  pouring. 
The  best  way  to  prevent  this  is  to  pour  the  iron  very  hot  when  making 
castings  of  small  or  moderate  size. 

Effect  of  Cupola  Melting.  (G.  R.  Henderson,  A.S.M.E.,  xx,  621.)  — 
27  car-wheels  were  analyzed  in  the  pig  and  also  after  remelting.  The 
P  remains  constant,  as  does  Si  when  under  1%.  Some  of  the  Mn  always 
disappears.  The  total  C  remains  the  same,  but  the  GO  and  CC  vary  in 
an  erratic  manner.  The  metal  charged  into  the  cupola  should  contain 
more  GO,  Si  and  Mn  than  are  desired  in  the  castings.  Fairbairn  (Manu- 
facture of  Iron,  1865)  found  that  remelting  up  to  12  times  increased  tho 
strength  and  the  deflection,  but  after  18  remeltings  the  strength  was  only 
s/s  and  the  deflection  1/3  of  the  original.  The  increase  of  strength  in  the 
first  remeltings  was  probably  due  to  the  change  .of  GC  into.  CC,  and  the 
subsequent  weakening  to  the  increase  of  S  absorbed  from  the  fuel. 

Hard  Castings  from  Soft  Pig.  (B.  F.  Fackenthal,  Jr.,  A.I.M.E., 
xxxv,  993.)  —  Samples  from  a  car  load  of  pig  gave  Si,  2.61 ;  S,  0.023.  Cast- 
ings from  the  same  iron  gave  2.33  and  2.26  Si,  and  0.26  and  0.25  S,  or 
12  times  the  S  in  the  original  pig;  probably  due  to  fuel  too  high  in  S,  but 
more  probably  to  the  use  of  too  little  fuel  in  remelting. 

The  loss  of  Si  in  remelting,  and  the  consequent  hardening,  is  affected 
by  the  amount  of  Mn,  as  shown  below: 

Mn,  per  cent 0.04      0.20      0.43      0.53 

Si  lost  in  remelting,  per  cent 34        23         12          4 

Difficult  Drilling  due  to  LowMn.— H.  Souther,  A.S.T.M.,  v,  219, 
reports  a  case  where  thin  castings  drilled  easily  while  thick  parts  on  the 
same  castings  rapidly  dulled  1/2  and  3/4-in.  drills.  The  chemical  constitu- 
tion was  normal  except  Mn;  Si,  2.5;  P,  0.7;  S  about  0.08;  C,  3.5;  Mn,  0.16. 
When  the  Mn  was  raised  to  0.5  the  trouble  disappeared. 

Addition  of  Ferro-silicon  in  the  Ladle.  (A.  E.  Outerbridge,  Proc. 
A.S.T.M.,  vi,  263.)  —Half  a  pound  of  FeSi,  containing  50%  Si,  added  to  a 
200-lb.  ladle  of  soft  cast  iron  used  for  making  pulleys  with  rims  1/4  in. 
thick,  prevented  the  chilling  of  the  surface  of  the  casting,  and  enabled 
the  pulleys  to  be  turned  more  rapidly.  Analysis  showed  that  the  actual 
increase  of  the  Si  in  the  casting  was  less  than  the  calculated  increase. 
Tests  of  the  metal  treated  with  FeSi  as  compared  with  untreated  metal 
showed  a  gain  in  strength  of  from  2  to  26%,  and  a  gain  in  deflection  of  2 
to  3%.  The  reason  assigned  for  the  increase  of  strength  with  increase  of 
softness  is  that  cupola  iron  contains  a  small  amount  of  iron  oxide,  which 
reacts  with  the  Si  added  in  the  ladle,  forming  SiO2,  which  goes  into  the 
slag. 

Additions  of  Vanadium  and  Manganese.  —  R.  Moldenke,  Am. 
*  Fdrymen's  Assn.,  1908,  Am.  Mach.,  Feb.  20,  '08.  Experiments  were 
made  by  adding  to  melted  cast  iron  in  the  ladle  a  ground  alloy  of  ferro- 
vanadium,  containing  14.67  Va,  6.36  C,  and  0.18  Si.  In  other  experi- 
ments ferro-manganese  (80%  Mn)  was  added,  together  with  the  vana- 
dium. Four  kinds  of  iron  were  used:  burnt  gray  iron  (gratebars,  stove 
iron,  etc.),  burnt  white  iron,  gray  machinery  iron  (Si,  2.72,  S,  0.065, 
P,  0.068,  Mn,  0.54)  and  remelted  car  wheels  (white,  two  samples  anal- 
yzed: Si,  0.60  and  0.53,  S,  0.122,  0.138;  P.  0.399.  0.374;  Mn,  0.38, 
0.44).  The  bars  were  11/4  in.  diam.,  12  in.  between  supports.  The 
burnt  gray  iron  was  increased  in  breaking  strength  from  1310  to  2220 
Ib.  by  the  addition  of  0.05%  Va,  and  the  burnt  white  iron  from  144O 
to  19*10  Ib.  by  the  addition  of  0.05  Va  and  0.50  Mn.  The  following  are 
average  results; 


CAST  IRON. 


451 


Gray  Machinery  Iron. 

Remelted  Car  Wheels. 

Added  Per  cent. 

Breaking 
Strength, 
Lb. 

Deflec- 
tion, In. 

Added  Per  cent. 

Breaking 
Strength, 
Lb. 

Deflec- 
tion, In. 

Va. 

Mn. 

Va. 

Mn. 

0.0 
0.0 
0.05 
0.05 
0.10 
0.10 
0.15 

Averag 

0.0 
0.50 

1980 
1970 
1980 
2130 
2372 
2530 
2360 

0.105 
0.100 
0.100 
0.100 
0.090 
0.120 
0.100 

0.0 

0.0 
0.50 

1470 
2790 
3020 
2970 
2800 
3030 
2950 
3920 
3069 

0.050 
0.070 
0.060 
0.090 
0.055 
0.090 
0.070 
0.095 

0.05 
0.05 
0.10 
0.10 
0.15 
0.15 

0.50 

0.50 

0.50 

0.50 

bars 
pe  treated 

0.50 

2224 

Mod.  of  rupture. .  .35,800 


48,020 


Experiments  with  Titanium  added  to  cast  iron  in  the  ladle  are 
reported  by  R,  Moldenke,  Proc.  Am.  Fdrymeris  Assn.,  1908.  Two 
irons  were  used:  gray,  with  2.58  Si,  0.042  S,  0.54  P,  0.74  Mn;  and  white, 
with  0.85  Si,  0.07  S,  0.42  P,  0.6  Mn.  Two  Fe  Ti  alloys  with  10%  Ti 
were  used,  one  containing  no  C,  and  the  other  5%  C.  The  latter  has 
the  lower  melting  point.  The  results  were  as  below: 


Gray  Iron. 

White  Iron.     Lb. 

Original  iron  

9  tests 
4  tests 
3  tests 
6  tests 
6  tests 
4  tests 
ted  iron, 
riginal.  . 

1  720-2260  av.  2020 
2750-3140    '     3100 
2880-3150    '     3030 
2850-3230    '     3070 
2850-3150    '     2990 
3030-3270    '     3190 
.   3070 

8  tests 
1  1  tests 

1  920-21  lOav.  2050 
2210-2660   "   2400 

Plus  0.05  Ti 

Plus  0.10  Ti.. 

Plus  0.05  Ti  and  C 
Plus  O.lOTi  and  C 
Plus  0.1  5  Ti  and  C 
Average  of  trea 
Increase  over  o 

9  tests 
10  tests 
10  tests 

2230-2720   "    2420 
2320-2460    "    2400 
2280-2620   "   2520 
2430 

18% 

52% 

Modulus  of  rupture,  treated  iron  48,030 

38.020 

The  test  bars  were  11/4  in.  diam.  12  in.  between  supports.  The  im- 
provement is  as  marked  whether  0.05,  0.10,  or  0.15%  Ti  is  used,  which 
indicates  that  if  sufficient  Ti  is  used  for  deoxidation  of  the  iron,  any 
additional  Ti  is  practically  wasted. 

Ti  lessens  the  chilling  action,  yet  whatever  chill  remains  shows  much 
harder  iron.  Test  pieces  made  with  iron  which  chilled  11/2  in.  deep 
gave  but  1  in.  chill  when  the  iron  was  treated  in  the  ladle.  The  original 
iron  crushed  at  173,000  Ibs.  per  sq.  in.  and  stood  445  in  Brinel's  test 
for  hardness,  soft  steel  running  about  105.  The  treated  piece  ran 
298,000  Ibs.  per  sq,  in.  and  showed  a  hardness  of  557.  Testing  the  soft 
metal  below  the  chilled  portion  lor  hardness  gave  332  for  the  original 
and  322  for  the  treated  piece. 

Strength  of  Cast-iron  Beams.  —  C.  H.  Benjamin,  Mach'y,  May, 
1906.  Numerous  tests  were  made  of  beams  of  different  sections  includ- 
ing hollow  rectangles  and  cylinders,  I  and  T-shapes,  etc.  All  the  sec- 
tions were  made  approximately  the  same  area,  about  4.4  sq.  in.,  and  all 
were  tested  by  transverse  loading,  with  supports  18  in.  apart.  The 
results,  when  reduced  by  the  ordinary  formula  for  stress  on  the  extreme 
fiber,  S  =  My /I,  showed  an  extraordinary  variation,  some  of  the  values 
being  as  follows:  Square  bar,  23,300;  Round  bar,  25,000.  Hollow  round, 
3.4  in.  outside  and  2.5  in.  inside  diam.,  26,450,  and  35,800.  Hollow 
ellipse,  3  in.  wide,  3.9  in.  high,  0.9  in.  thick,  36,000.  /-beam,  4  in.  high, 
web  0.44  in.  thick,  17,700.  The  holtow  cylindrical  and  elliptical  sec- 
tions are  much  stronger  than  the  solid  sections.  This  is  due  to  the 
thinner  metal,  the  greater  surface  of  hard  skin,  and  freedom  from 
shrinkage  strains.  Professor  Benjamin's  conclusions  from  these  tests  are: 

(1)  The  commonly  accepted  formulas  for  the  strength  and  stiffness 
of  beams  do  not  apply  well  to  cored  and  ribbed  sections  9f  cast  iron. 

(2)  Neither  the  strength  nor  the  stiffness  of  a  section  increases  in  pro- 
portion to  the  increase  in  the  section  modulus  or  the  moment  of  inertia. 

(3)  The  best  way  to  determine  these  qualities  for  a  cast-iron  beam  is 
by  experiment  with  the  particular  section  desired  and  not  by  reasoning 
from  any  other  section. 


452 


IRON  AND  STEEL. 


Bursting  Strength  of  Cast-Iron  Cylinders.  —  C.  IJ.  Benjamin, 
A.  S.  M.  E.,  XIX,  597;  Mach'y,  Nov.,  1905.  Four  cylinders,  20  in.  long, 
10  1/8  in.  int.  diam.,  3/4  in.  thick,  with  flanged  ends  and  bolted  covers, 
burst  at  1350,  1400,  1350,  and  1200  Ibs.  per  sq.  in.  hydraulic  pressure, 
the  corresponding  fiber  stress,  from  the  formula  S  =  pd/2  t,  being  9040, 
10,200,  9735  and  9080.  Pieces  cut  from  the  shell  had  an  average  tensile 
strength  of  14,000  Ibs.  per  sq.  in.,  and  a  modulus  of  rupture  in  trans- 
verse tests  of  30,000. 

Transverse  Strength  of  Cast-iron  Water-pipe.  (Technology  Quar- 
terly, Sept.,  1897.) — Tests  of  31  cast-iron  pipes  by  transverse  stress  gave 
a  maximum  outside  fibre  stress,  calculated  from  maximum  load,  as- 
suming each  half  of  pipe  as  a  beam  fixed  at  the  ends,  ranging  from 
12,800  Ib.  to  26,300  Ib.  per  sq.  in. 

Bars  2  in.  wide  cut  from  the  pipes  gave  moduli  of  rupture  ranging  from 
28,400  to  51,400  Ib.  per  sq.  in.     Four  of  the  tests,  bars  and  pipes: 
Moduli  of  rupture  of  bar... .   28,400          34,400          40,000          51,400 
Fibre  stress  of  pipe 18,300          12,800          14,500          26,300 

These  figures  show  a  great  variation  in  the  strength  of  both  bars  and 
pipes,  and  also  that  the  strength  of  the  bar  does  not  bear  any  definite 
relation  to  the  strength  of  the  pipe. 

Bursting  Strength  of  Flanged  Fittings.  —Power,  Feb.  4,  1908. 
The  Crane  Company,  Chicago,  published  in  the  Valve  World  records  cf 
tests  of  tees  and  ells,  standard  and  extra  heavy,  which  show  that  the 
bursting  strength  of  such  fittings  is  far  less  than  is  given  by  the  standard 
formulae  for  thick  cylinders.  As  a  result  of  the  tests  they  give  the 
following  empirical  formula:  B  =  TS/D,  in  which  B  =  bursting  pres- 
sures, Ibs.  per  sq.  in.,  T  —  thickness  of  metal,  D  =  inside  diam.,  and 
S  =  65%  of  the  tensile  strength  of  the  metal  for  pipes  up  to  12  in.  diam., 
for  larger  sizes  use  60%.  The  pipes  were  made  of  "  ferro-steel  "  of 
33,000  Ibs.  T.  S.,  and  of  cast  iron  of  22,000  Ibs.  as  tested  in  bars.  The 
following  are  the  principal  results  of  tests  of  extra  heavy  tees  and  ells 
compared  with  results  of  calculation  by  the  Crane  Company's  formula: 

BUESTINQ  STEENGTH  OF  PIPE-FITTINGS.    POUNDS  PER  SQUARE  INCH. 


Inside  Diam. 
Thickness. 

6 

3/4 

8 

13/16 

10 

15/16 

12 
I 

14 

1  1/8 

16 

13/16 

18 

1  1/4 

20 

15/16 

24 

1  1/2 

B,  Ferro-steel  
calculated    .... 

2733 
2680 

2250 
2180 

2160 
2010 

2033 
1870 

1825 
1570 

1700 
1450 

1450 
1350 

1275 
1280 

1300 
1220 

B,  Cast  iron  

1687 

1350 

1306 

1380 

1100 

1025 

600 

750 

700 

calculated  
Ells,  ferro  steel 

1790 
3266 

1450 
2725 

1340 
2350 

1190 
2133 

1060 

980 

920 

870 

820 

"     cast-iron  

2275 

1625 

1541 

1275 

1075 

1250 

Specific  Gravity  and  Strength.     (Major  Wade,  1856.) 

Third-class  guns:  Sp.  Gr.  7.087,  T.  S.  20,148.  Another  lot:  least  Sp. 
Gr.  7.163,  T.  S.  22,402. 

Second-class  guns:  Sp.  Gr.  7.154,  T.  S.  24,767.  Another  lot:  mean 
Sp.  Gr.  7.302,  T.  S.  27,232. 

First-class  guns:  Sp.  Gr.  7.204,  T.  S.  28,805.  Another  lot:  greatest 
Sp.  Gr.  7.402,  T.  S.  31,027. 

Strength  of  Charcoal  Pig  Iron.  —  Pig  iron  made  from  Salisbury 
ores,  in  furnaces  at  Wassaic  and  Millerton,  N.  Y.,  has  shown  over  40,000 
Ibs.  T.  S.  per  square  inch,  one  sample  giving  42,281  Ibs.  Muirkirk,  Md.T 
iron  tested  at  the  Washington  Navy  Yard  showed:  average  for  No.  2' 
iron,  21,601  Ibs.;  No.  3,  23,959  Ibs.;  No.  4,  41,329  Ibs.;  average  den- 
sity of  No.  4,  7.336  (J.  C.  I.  W.,  v.  p.  44). 

Nos.  3  and  4  charcoal  pig  iron  from  Chapinville,  Conn.,  showed  a 
tensile  strength  per  square  inch  of  from  34,761  Ibs.  to  41,882  Ibs.  Char- 
coal pig  iron  from  Shelby,  Ala.  (tests  made  in  August,  1891),  showed  a. 
strength  of  34,800  Ibs.  for  No.  3;  No.  4,  39,675  Ibs.;  No.  5,  46,450  Ibs.; 
and  a  mixture  of  equal  parts  of  Nos.  2,  3,  4,  and  5,  41,470  Ibs.  (Bull.. 
L  &  S.  A.) 

Variation  of  Density  and  Tenacity  of  Gun-Irons.  —  An  increase  of 
density  invariably  follows  the  rapid  cooling  of  cast  iron,  and  as  a  general 
rule  the  tenacity  is  increased  by  the  same  means.  The  tenacity  gener- 
ally increases  quite  uniformly  with  the  density,  until  the  latter  ascends 


CAST  IRON. 


453 


to  some  given  point;  after  which  an  increased  density  is  accompanied 
by  a  diminished  tenacity. 

The  turning-point  of  density  at  which  the  best  qualities  of  gun-iron 
attain  their  maximum  tenacity;  appears  to  be  about  7.30.  At  this  point 
of  density,  or  near  it,  whether  in  proof-bars  or  gun-heads,  the  tenacity  is 
greatest. 

As  the  density  of  iron  is  increased  its  liquidity  when  melted  is  dimin- 
ished. This  causes  it  to  congeal  quickly,  and  to  form  cavities  in  the 
interior  of  the  casting.  (Pamphlet  of  Builders'  Iron  Foundry,  1893.) 

"  Semi-steel "  is  a  trade  name  given  by  some  founders  to  castings  made 
from  pig  iron  melted  in  the  cupola  with  additions  of  from  20  to  30  per 
cent  of  steel  scrap.  Ferro-manganese  is  also  added  either  in  the  cupola  or 
in  the  ladle.  The  addition  of  the  steel  dilutes  the  Si  of  the  pig  iron,  and 
changes  some  of  the  C  from  GO  to  CC,  but  the  TC  is  unchanged,  for  any 
reduction  made  by  the  steel  is  balanced  by  absorption  of  C  from  the  fuel. 
Semi-steel  therefore  is  nothing  more  than  a  strong  cast  iron,  low  in  Si 
and  containing  some  Mn,  and  the  name  given  it  is  a  misnomer. 

Mixture  of  Cast  Iron  with  Steel.  —  Car  wheels  are  sometimes  made 
from  a  mixture  of  charcoal  iron,  anthracite  iron,  and  Bessemer  steel. 
The  following  shows  the  tensile  strength  of  a  number  of  tests  of  wheel 
mixtures,  the  average  tensile  strength  of  the  charcoal  iron  used  being 
22,000  Ibs.  (Jour.  C.  I.  W.,  iii,  p.  184): 

Ibs.  per  sq.  in. 

Charcoal  iron  with  2 1/2%  steel 22,467 

33/4%  steel 26,733 

61/4%  steel  and  6 1/4%  anthracite 24,400 

7V3%  steel  and  71/2%  anthracite 28,150 

21/2%  steel,  21/2%  wro't  iron,  and  61/4%  anth.  25,550 
5      %  steel,  5%  wro't  iron,  and  10%  anth 26,500 

Cast  Iron  Partially  Bessemerized.  —  Car  wheels  made  of  partially 
Bessemerized  iron  (blown  in  a  Bessemer  converter  for  3V2  minutes), 
chilled  in  a  chill  test  mold  over  an  inch  deep,  just  as  a  test  of  C9ld  blast 
charcoal  iron  for  car  wheels  would  chill.  Car  wheels  made  of  this  blown 
iron  have  run  250,000  miles.  (Jour.  C.  I.  W.,  vi,  p.  77.) 

Bad  Cast  Iron.  —  On  October  15,  1891,  the  cast-iron  fly-wheel  of  a 
large  pair  of  Corliss  engines  belonging  to  the  Amoskeag  Mfg.  Co.,  of  Man- 
chester, N.H.,  exploded  from  centrifugal  force.  The  fly-wheel  was  30 
feet  diameter  and  110  inches  face,  with  one  set  of  12  arms,  and  weighed 
116,000  Ibs.  After  the  accident,  the  rim  castings,  as  well  as  the  ends  of 
the  arms,  were  found  to  be  full  of  flaws,  caused  chiefly  by  the  drawing 
and  shrinking  of  the  metal.  Specimens  of  the  metal  were  tested  for 
tensile  strength,  and  varied  from  15,000  Ibs.  per  square  inch  in  sound 
pieces  to  1000  Ibs.  in  spongy  ones.  None  of  these  flaws  showed  on  the 
surface,  and  a  rigid  examination  of  the  parts  before  they  were  erected 
failed  to  give  any  cause  to  suspect  their  true  nature.  Experiments  were 
carried  on  for  some  time  after  the  accident  in  the  Amoskeag  Company's 
foundry  in  attempting  to  duplicate  the  flaws,  but  with  no  success  in 
approaching  the  badness  of  these  castings. 

Permanent  Expansion  of  Cast  Iron  by  Heating.  (Valve  World, 
Sept.,  1908.)  —  Cast  iron  subjected  to  continued  temperatures  of  approx- 
imately 500°  to  600°  took  a  permanent  expansion  and  did  not  return  to 
its  original  volume  when  cooled. 

As  steam  is  being  superheated  quite  commonly  to  temperatures  above 
575°,  this  fact  is  of  great  interest  inasmuch  as  it  modifies  our  ideas  about 
the  proper  material  to  be  used  in  the  construction  of  valves  and  fittings 
foT  service  under  high  temperatures.  A  permanent  volumetric  expan- 
sion is  followed  by  a  loss  of  strength,  the  loss  in  cast  iron  being  fully  40 
per  cent  in  four  years. 

Crane  Co.  made  an  attempt  to  determine  whether  cast  steel  was  affected 
in  the  same  manner  as  cast  iron.  Three  flanges  were  taken,  one  of  cast 
iron,  one  of  ferrosteel,  and  the  third  of  cast  steel.  These  flanges  were 
exposed  for  a  total  period  of  130  hours  to  temperatures  ranging  as  follows: 

Less  than  500°,  18  hours;  500°  to  700°,  97  hours;  710°  to  800°,  12  hours- 
over  800°,  3  hours.  Average  temp.,  583°. 

The  Outside  diameter  in  each  case  was  121/2  in.  and  the  bore  6  29/64  in. 

The  results  were:  Cast-steel  flange,  no  change.  Cast-iron  flange,  out- 
side diam.  increased  0.019  in.,  inside  diam.  increased  0.007  in.  Ferro-steel 
flange,  outside  diam.  increased  0.033  in.,  inside  diam.  increased  0.017  in. 


454  IRON  AND   STEEL. 

If  the  permanent  expansion  of  cast  iron  stopped  at  the  figures  given 
above,  it  would  not  be  a  serious  matter;  but  all  evidence  points  toward  a 
steady  increase  as  time  goes  on,  as  was  shown  by  one  of  Crane  Co.'s 
14-in.  valves,  which  originally  was  221/2  in.  face  to  face,  and  increased 
5/16  in.  in  length  in  four  years  under  an  average  temperature  of  about 
590°. 

MALLEABLE    CAST    IRON.* 

There  are  four  great  classes  of  work  for  whose  requirements  malleable 
cast  iron  (commonly  called  "malleable  iron"  in  America)  is  especially 
adapted.  These  are  agricultural  implements,  railway  supplies,  carriage 
and  harness  castings  and  pipe  fittings.  Besides  these  main  classes  there 
are  innumerable  other  unclassified  uses.  The  malleable  casting  is  sel- 
dom over  175  Ib.  in  weight,  or  3  ft.  in  length,  or  %  m.  thick.  The 
great  majority  of  even  the  heavier  castings  do  not  exceed  10  Ib. 

When  properly  made,  malleable  cast  iron  should  have  a  tensile 
strength  of  42,000  to  48,000  Ib.  per  sq.  in.,  with  an  elongation  of  5%  in 
2  in.  Bars  1  in.  square  and  on  supports  12  in.  apart  should  show  a 
transverse  strength  of  2500  to  3500  Ib.,  with  a  deflection  of  at  least  K  in. 

While  the  strength  of  malleable  iron  should  be  as  stated,  much  of  it 
will  fall  as  low  as  35,000  Ib.  per  sq.  in.,  and  this  will  still  be  good  for  such 
work  as  pipe  fittings,  hardware  castings  and  the  like.  On  the  other 
hand,  even  63,000  Ib.  per  sq.  in.  has  been  reached,  with  a  load  of  5000 
Ib.  and  a  deflection  of  2  y^  in.  in  the  transverse  test.  This  high  strength 
is  not  desirable,  as  the  softness  of  the  casting  is  sacrificed,  and  its  resist- 
ance to  continued  shock  is  lessened.  For  the  repeated  stresses  of  severe 
service  the  malleable  casting  ranks  ahead  of  steel,  and  only  where  a  high 
tensile  strength  is  essential  must  it  be  replaced  by  that  material. 

The  process  of  making  malleable  iron  may  be  summarized  as  follows: 
The  proper  cast  irons  are  melted  in  either  the  crucible,  the  air  furnace, 
the  open-hearth  furnace,  or  the  cupola.  The  metal  when  cast  into  the 
sand  molds  must  chill  white  or  not  more  than  just  a  little  mottled.  After 
removing  the  sand  from  the  hard  castings  they  are  packed  in  iron  scale, 
or  other  materials  containing  iron  oxide,  and  subjected  to  a  red  heat 
(1250  to  1350°  F.)  for  over  60  hours.  They  are  then  cooled  slowly, 
cleaned  from  scale,  chipped  or  ground,  and  straightened.  Much  of  the 
malleable  iron  made  to-day  (1915)  is  annealed  for  a  shorter  time  and  at 
higher  temperatures.  The  safe  method ,  however,  is  the  one  given  above. 

When  hard,  or  just  from  the  sand,  the  composition  of  the  iron  should 
be  about  as  follows:  Si,  from  0.35  up  to  1.00,  depending  upon  the  thick- 
ness and  the  purpose  the  casting  is  to  be  used  for;  P  not  over  0.225,  Mn 
not  over  0.20,  S  not  over  0.08.  The  total  carbon  can  be  from  2.75  up- 
ward, 4.15  being  about  the  highest  that  can  be  carried.  The  lower  the 
carbon  the  stronger  the  casting  subsequently.  Below  2.75  there  is  apt  to 
be  trouble  in  the  anneal,  the  black-heart  structure  may  not  appear,  and 
the  castings  remain  weak.  A  casting  1  in.  thick  would  necessitate  silicon 
at  0.35,  and  the  use  of  chills  in  the  mold  in  addition,  to  get  the  iron  white. 
For  a  casting  %  in.  thick,  Si  about  0.60  is  the  proper  limit,  except  where 
great  strength  is  desired,  when  it  can  be  dropped  to  0.45.  Above  0.60 
there  is  danger  of  getting  heavily-mottled  if  not  gray  iron  from  the  sand 
molds,  and  this  material,  when  annealed  the  long  time  required  for  the 
white  castings,  would  be  ruined.  For  very  thin  castings,  Si  can  run  up 
to  1.25  and  still  leave  the  metal  white  in  fracture. 

Pig  Iron  for  Malleable  Castings. — The  specifications  run  as  follows: 
Si,  0.75,  1.00,  1.25,  1.50,  1.75,  2.00%,  as  required;  Mn,  not  over  0.60; 
P,  not  over  0.225 ;  S,  not  over  0.05. 

Works  making  heavy  castings  almost  exclusively  specify  Si  to  include 
0.75  up  to  1.50%.  Makers  of  very  light  work  take  1.25  to  2.00%. 

The  Melting  Furnace.  —  Malleable  iron  is  melted  in  the  reverbera- 
tory  furnace,  the  open-hearth  furnace,  and  the  cupola,  the  reverberatory 
being  the  most  extensively  used.  About  85  per  cent  of  the  entire  output 
of  the  United  States  is  melted  by  this  process.  Prior  to  about  1885, 
the  standard  furnace  was  one  of  5  tons  capacity.  At  present  (1915)  we 

*  References. — R.  Moldenke,  Cass  Mag.,  1907,  and  Iron  Trade 
Review,  1908;  E.  C.  Wheeler,  Iron  Age,  Nov.  9,  1899;  C.  H.  Gale,  Indust. 
World,  April  13,  1908;  W.  H.  Hatfield,  ibid.  G.  A.  Akerlund,  Iron  Tr. 
Rev.,  Aug.  23,  J906;  C.  H.  Day,  Am.  Mach.,  April  5,  1906. 


MALLEABLE   CAST   IRON. 


455 


have  furnaces  of  25  and  30  tons  capacity,  though  furnaces  of  from  10  to 
15  tons  are  the  most  popular  and  give  more  uniform  results  than  those 
of  larger  capacity. 

The  adoption  of  the  open-hearth  furnace  for  malleable  iron  dates 
back  to  about  1893.  It  is  used  largely  in  the  Pittsburg  district. 

Cupola-melted  iron  does  not  possess  the  tensile  strength  nor  ductility 
of  iron  melted  in  the  reverberatory  or  open-hearth  furnace,  due  partly  to 
the  higher  carbon  and  sulphur  caused  by  the  metal  being  in  contact 
with  the  fuel.  This  feature  is  rather  an  advantage  than  otherwise,  as 
most  of  the  product  of  cupola-melted  iron  consists  of  pipe  fittings,  cast- 
ings that  are  not  subjected  to  any  great  stress  or  shock.  The  castings 
are  threaded,  and  a  strong,  tough  malleable  iron  does  not  cut  a  clean,  . 
smooth  thread,  but  rather  will  rough  up  under  the  cutting  tool. 

In  the  reverberatory  and  open-hearth  furnaces  the  metal  may  be 
partly  desiliconized  at  will,  by  an  oxidizing  flame  or  by  additions  of 
scrap  or  other  low-silicon  material,  while  the  total  carbon  can  be  lowered 
by  scrap  steel  additions.  Manganese  is  also  oxidized  in  the  furnace. 

The  composition  of  good  castings  in  American  practice  is :  Si,  from  0.45 
to  1.00%;  Mn  up  to  0.30%;  P,  up  to  0.225%;  S,  up  to  0.08%;  total 
carbon  in  the  hard  casting,  above  2.75%. 

In  special  cases,  especially  for  very  small  castings,  the  silicon  may  go 
up  as  high  as  1.25%,  while  for  very  heavy  work  it  may  drop  down  to 
0.35%  with  very  good  results.  In  the  case  of  charcoal  iron  this  figure 
gives  the  strongest  castings.  With  coke  irons,  however,  especially  when 
steel  scrap  additions  are  the  rule,  0.45  should  be  the  lower  limit,  and  0.65 
is  the  best  silicon  for  all-around  medium  and  heavy  work,  such  as  rail- 
road castings. 

In  American  practice  phosphorus  is  required  not  to  exceed  0.225%, 
and  is  preferred  lower.  In  European  practice  it  is  required  as  low  as 
0.10%,  but  castings  have  been  made  successfully  with  P  as  high  as 
0.40%. 

The  heat  treatment  of  metal  during  melting  has  an  important  bearing 
upon  its  tensile  strength,  elongation,  etc.  Excessive  temperatures  pro- 
mote the  chances  of  burning.  Iron  is  burnt  mainly  through  the  genera- 
tion in  melting  furnaces  of  higher  temperatures  than  those  prevailing 
during  the  initial  casting  at  blast  furnaces  and  an  excess  of  air  in  the 
flame.  The  choicest  irons  may  thus  turn  out  poor  material. 

Shrinkage  of  the  Casting.  —  The  shrinkage  of  the  hard  casting  Is 
about  1/4  in.  to  the  foot,  or  double  that  of  gray  iron.  In  annealing  about 
half  of  this  is  recovered,  and  hence  the  net  result  is  the  same  a*s  in  prdi- 
nary  foundry  pattern  practice.  The  effect  of  this  great  shrinkage  is  to 
cause  shrinkage  cracks  or  sponginess  in  the  interior  of  the  casting.  As 
soon  as  the  liquid  metal  sets  against  the  surface  of  the  mold  and  the 
source  of  supply  is  cut  off,  the  contraction  of  the  metal  in  the  interior 
as  it  cools  causes  the  particles  to  be  torn  apart  and  to  form  minute 
cracks  or  cavities.  "  Every  test  bar,  and  for  that  matter  every  casting 
may  be  regarded  as  a  shell  of  fairly  continuous  metal  with  an  interior  of 
slight  planes  of  separation  at  right  angles  to  the  surface.  This  charac- 
teristic of  malleable  iron  forms  the  basis  of  many  a  mysterious  failure." 
(Moldenke.) 

Packing  for  Annealing.  —  After  the  castings  have  been  chipped  and 
sorted  they  are  packed  in  iron  annealing  pots,  holding  about  800  pounds 
of  iron,  together  with  a  packing  composed  of  iron  ore,  hammer  and 
rolling  mill  scale,  turnings,  borings,  etc.  The  turnings,  etc.,  were  form- 
erly treated  with  a  solution  of  salammoniac  or  muriatic  acid  to  form  a 
heavy  coating  of  oxide,  but  such  treatment  is  now  considered  unnec- 
essary. Blast  furnace  slag,  coke,  sand,  and  fire  clay  have  also  been  used 
for  packing.  The  changes  in  chemical  composition  of  the_castings  when 
annealed  in  slag  and  in  coke  are  given  as  follows  by  C.  H.  Gale: 


Si. 

S. 

P. 

Mn. 

C.  C. 

G.  C. 

Hard  iron 

0  63 

0  043 

0  147 

0  21 

2  54 

Trace 

Annealed  in  slag    .  . 

0  61 

0  049 

0  145 

0  21 

0  24 

1  65 

Annealed  in  coke  

0.61 

0.065 

0.150 

0.21 

0.25 

2.00 

The  Annealing  Process. — The  effect  of  the  annealing  is  to  oxidize 
and  remove  the  carbon  from  the  surface  of  the  casting,  to  remove  it 
to  a  greater  or  less  degree  below  the  surface,  and  to  convert  the  remain- 


456  IRON  AND   STEEL. 

ing  carbon  from  the  combined  form  into  the  amorphous  form  called  a 
"temper  carbon"  by  Professor  Ledebur,  the  German  metallurgist.  It 
differs  from  the  graphite  found  in  pig  iron,  but  is  usually  reported  as 
graphitic  carbon  by  the  chemists.  In  the  original  malleable  process, 
invented  by  Reaumur,  in  1722,  the  castings  were  packed  in  iron  ore  and 
annealed  thoroughly,  so  that  most  of  the  carbon  was  probably  oxidized, 
but  in  American  practice  the  annealing  process  is  rather  a  heat  treat- 
ment than  an  oxidizing  process,  and  its  effect  is  to  precipitate  the  carbon 
rather  than  to  eliminate  it.  According  to  the  analysis  quoted  above,  the 
metal  annealed  in  slag  lost  0.65%  of  its  total  C,  while  that  annealed  in 
coke  lost  only  0.29%.  In  the  former,  S  increased  0.006%  and  in  the 
latter  0.022%.  The  Si  decreased  0.02%  in  both  cases,  while  the  P  and 
Mn  remained  constant. 

As  to  the  distribution  of  carbon  in  an  annealed  casting,  Dr.  Moldenke 
says:  "Take  a  flat  piece  of  malleable  and  plane  off  the  skin,  say  Vie  in. 
deep  and  gather  the  chips  for  analysis.  The  carbon  will  be  found,  say, 
O.lo%  perhaps  even  less.  Cut  in  another  Viein.  and  the  total  C  will  be 
nearer  0.60%.  Now  go  down  successively  by  sixteenths  and  the  total 
C  will  range  from,  say,  1.70  to  3.65%  and  will  then  remain  constant  until 
the  center  is  reached."  "The  malleable  casting  is  for  practical  purposes 
a  poor  steel  casting  with  a  lot  of  graphite,  not  crystallized,  between  the 
crystals  or  groups  of  crystals  of  the  steel." 

The  heat  in  the  annealing  process  must  be  maintained  for  from  two  to 
four  days.,  depending  upon  the  thickness  of  sections  of  the  castings  and 
the  compactness  with  which  the  castings  or  annealing  boxes  are  placed 
in  the  furnace.  An  annealing  temperature  1550°  to  1600°  Fahr.  is  often 
used,  but  it  is  not  essential,  as  the  annealing  can  be  accomplished  at 
1300°,  but  the  time  required  will  be  longer  than  that  at  the  higher  tem- 
perature. Burnt  iron  in  the  anneal  is  no  uncommon  feature,  and,  gen- 
erally speaking,  it  is  the  result  of  carelessness.  The  most  carefully  pre- 
pared metal  from  melting  furnaces  can  here  be  turned  into  worthless 
castings  by  some  slight  inattention  of  detail.  The  highest  temperature 
for  annealing  should  be  registered  in  each  foundry,  and  kept  there  by  the 
daily  and  frequent  use  of  a  thermometer  constructed  for  that  sole  pur- 
pose. Steady,  continued  heat  insures  soft  castings,  while  unequal  tem- 
peratures destroy  all  chances  for  successful  work,  although  the  initial 
metal  was  of  the  most  excellent  quality. 

After  annealing,  the  castings  are  cleaned  by  tumblers  or  the  sand 
blast;  they  are  carefully  examined  for  cracks  or  other  defects,  and  if 
sprung  out  of  shape  are  hammered  or  forced  by  hydraulic  power  to  the 
correct  shape.  Such  parts  as  are  produced  in  great  quantities  are  placed 
in  a  drop  hammer  and  one  or  two  blows  will  insure  a  correct  form.  They 
may  be  drop-forged  or  even  welded  when  the  iron  has  been  made  for  that 
purpose.  Castings  are  sometimes  dipped  into  asphaltum  diluted  with 
benzine  to  give  them  a  better  finish. 

Malleable  castings  must  never  be  straightened  hot,  especially  when 
thick.  In  the  case  of  very  thin  castings  there  is  some  latitude,  as  the 
material  is  so  decarbonized  that  it  is  nearer  a  steel  than  genuine  mal- 
leable cast  iron.  In  heating  portions  of  castings  that  were  badly  warped, 
it  seems  that  the  amorphous  carbon  in  them  was  combined  again,  and 
while  the  balance  of  the  casting  remained  black  and  sound,  the  heated 
parts  became  white  and  brittle,  as  in  the  original  hard  casting.  Hence 
the  advice  to  straighten  the  castings  cold,  preferably  with  a  drop  ham- 
mer and  suitable  dies,  or  still  better  in  the  hydraulic  press.  (R.  Moldenke. 
Proc.  A.S.T.M.,  vi,  244.) 

Physical  Characteristics.  —  The  characteristic  that  gives  malleable 
iron  its  greatest  value  as  compared  with  gray  iron  is  its  ability  to  resist 
shocks.  Malleability  in  a  light  casting  1/4  in.  thick  and  less  means  a 
soft,  pliable  condition  and  the  ability  to  withstand  considerable  distor- 
tion without  fracture,  while  in  the  heavy  sections,  1/2  in.  and  over,  it 
means  the  ability  to  resist  shocks  without  bending  or  breaking. 

For  general  purposes  it  is  not  altogether  desirable  to  have  a  metal 
very  high  in  tensile  strength,  but  rather  one  which  has  a  high  transverse 
strength,  and  especially  a  good  deflection.  It  is  not  always  that  a  strong 
and  at  the  same  time  soft  material  can  be  produced  in  a  foundry  operat- 
ing on  the  lighter  grades  of  castings.  The  purchaser,  therefore,  unless  he 
requires  very  .stiff  material,  should  rather  look  upon  the  deflection  of 


MALLEABLE   CAST  1UON.  457 

the  metal  coupled  with  the  weight  it  took  to  do  this  bending  before 
failure,  than  for  a  high  tensile  strength. 

The  ductility  of  the  malleable  casting  permits  the  driving  of  rivets, 
which  cannot  so  readily  be  done  with  gray  cast  iron;  and  for  certain 
parts  of  cars,  like  the  journal  boxes,  malleable  cast  iron  may  be  con- 
sideied  supreme,  leaving  cast  iron  and  "semi-steel  "  far  behind. 

It  was  formerly  the  general  belief  that  the  strength  of  malleable  iron 
was  largely  in  the  white  skin  always  found  on  this  material,  but  it  has 
been  demonstrated  that  the  removal  of  the  skin  does  not  proportionately 
lessen  the  strength  of  the  casting. 

Test  Bars.  —  The  rectangular  shape  is  used  for  test  bars  in  preference 
to  the  round  section,  because  the  latter  is  more  apt  to  have  serious  cracks 
in  the  center,  due  to  shrinkage,  especially  if  the  diameter  is  large.  A 
round  section,  unless  in  very  light  hardware,  is  to  be  avoided,  as  the 
shrinkage  crack  in  the  center  may  have  an  outlet  to  the  skin,  and  cause 
failure  in  service. 

It  is  customary  to  provide  for  two  sizes  of  test  bars,  the  heavy  and 
the  light.  Thus  the  1-in.  square  bar  represents  work  1/2  an  inch  thick 
and  over,  and  a  1  X  V2-in.  section  bar  cares  for  the  lighter  castings. 
Both  are  14  inches  long.  They  should  be  cast  at  the  beginning  and  at 
the  end  of  each  heat. 

Design  of  Malleable  Castings.  —  As  white  cast  iron  shrinks  a  great 
deal  more  than  gray  iron,  and  as  the  sections  of  malleable  castings  are 
lighter  than  those  of  similar  castings  of  gray  iron,  fractures  are  very 
common.  It  is  therefore  the  designer's  aim  to  distribute  the  metal  so 
as  to  meet  these  conditions.  In  long  pieces  the  stiffening  ribs  should 
extend  lengthways  so  as  to  produce  as  little  resistance  as  possible  to  the 
contraction  of  the  metal  at  the  time  of  solidification.  If  this  be  not 
possible,  the  molder  provides  a  "crush  core"  whose  interior  is  filled  with 
crushed  coke.  When  the  metal  solidifies  in  the  flask  the  core  is  crushed 
by  the  casting  and  thus  prevents  shrinkage  cracks.  At  other  times  a 
certain  corner  or  juncture  of  ribs  in  the  casting  will  be  found  cracked. 
In  order  to  prevent  this  a  small  piece  of  cast  iron  (chill)  is  embedded  in 
the  sand  at  this  critical  point,  and  the  metal  will  cool  here  more  quickly 
than  elsewhere,  and  thus  fortify  this  point,  although  it  may  happen  that 
some  other  part  of  the  casting  will  be  found  fractured  instead,  and  in 
many  cases  the  locations  and  the  shape  of  strengthening  ribs  in  the 
casting  must  be  altered  until  a  casting  is  procured  free  from  shrinkage 
cracks.  In  designing  of  malleable  cast-iron  details  the  following  rules 
should  be  observed: 

Jl)  Endeavor  to  keep  the  metal  in  different  parts  of  the  casting  at  a 
form  thickness.  In  a  small  casting,  of,  say,  10  Ibs.  weight,  l/4-in. 
metal  is  about  the  practical  thickness,  s/16  in.  for  a  casting  of  15  to  20 
Ibs.,  and  3/8  to  1/2  in.  for  castings  of  40  Ibs.  and  over.  (2)  Endeavor  to 
avoid  sharp  junctions  of  ribs  or  parts,  and  if  the  casting  is  long,  say  24 
inches  or  more,  the  ends  should  be  made  of  such  shape  as  to  offer  as 
little  resistance  as  possible  to  the  contraction  of  metal  when  cooling  in 
the  mold. 

Specifications  for  Malleable  Iron.  —  The  tensile  strength  of  malle- 
able iron  varies  with  the  thickness  of  the  metal,  the  lighter  sections  hav- 
ing a  greater  strength  per  square  inch  than  the  heavier  sections.  An 
Eastern  railroad  designates  the  tensile  strength  desired  as  follows:  Sec- 
tions 3/8  in.  thick  or  less  should  have  a  tensile  strength  of  not  less  than 
40,000  Ibs.  per  sq.  in.;  3/8to  3/4  in.  thick,  not  less  than  38,000;  and  over 
3/4  in.,  not  less  than  36,000  Ibs.  per  sq.  in.  Test  bars  5/8  and  7/8  in.  diam. 
were  made  in  the  same  mold  and  poured  from  the  same  ladle,  and  an- 
nealed together.  The  average  tensile  strength  of  five  pairs  of  bars  so 
treated,  representing  five  heats,  was,  5/8-in.  bars,  45,095;  7/g-in.  bars, 
41,316  Ibs.  per  sq.  in.  Average  elongation  in  6  in.:  5/8-in.  bars  5.3%; 
7/8-in.  bars  4.2%. 

A  very  high  tensile  strength  can  be  obtained  approaching  that  of 
cast  steel  but  at  the  expense  of  the  malleability  of  the  product.  Malle- 
able test  bars  have  been  made  with  a  tensile  strength  of  between  60,000 
and  70,000  Ibs.  per  sq.  in.,  but  the  ductility  and  ability  to  resist  shocks 
of  these  bars  was  not  equal  to  that  of  bars  breaking  at  40,000  to  45,000 
pounds  per  sq.  in. 

The  British  Admiralty  specification  is  18  tons  (40,320  Ibs.)  per 
square  inch,  a  minimum  elongation  of  4Vfc%  in  three  inches  and  a 


458 


IRON  AND   STEEL. 


bending  angle  of  at  least  90°  over  a  1-in.  radius,  the  bar  being  1  X  % 
in.  in  section. 

A  committee  of  the  American  Society  for  Testing  Materials  re- 
ported, in  1915,  a  set  of  specifications  for  malleable  castings  which  in- 
cludes the  following:  The  specimen  for  tensile  strength  is  a  round 
bar  12  in.  long,  3/4  in.  diam.  at  the  ends,  tapering  to  a  middle  portion 
4  in.  long,  5/8  in.  diam.  The  transverse  test  specimen  is  14  in.  long, 

1  in.  wide,  and  1/2,  5/8,  or  3/4  hi.  thick,  according  to  the  thickness  of 
the  casting  it  represents.     Specimens  are  to  be  cast  without  chills,  with 
the  ends  free  in  the  mold.     The  tensile  strength  shall  be  not  less  than 
38,000  Ib.  per  sq.  in.  with  an  elongation  not  less  than  5%  in  2  in.     The 
transverse  strength,  the  bar  being  tested  with  cope  side  up,  on  sup- 
ports 12  in.  apart,  pressure  being  applied  at  the  center  shall  be  respec- 
tively 900,  1400,  and  2000  Ib.  with  deflections  1.25, -1.00,  and  0.75  in 
the  1/2,  5/8,  and  8/4  in.  test  specimens.     The  specifications  are  intended 
to  cover  railroad  malleable  irons  and  the  softer  grades  only.     They  in- 
clude directions  as  to  the  casting  of  the  test  specimens  and  as  to 
inspection. 

Improvement  in  Quality  of  Castings.  (Moldenke.)  —  The  history 
of  improvement  in  the  malleable  casting  is  admirably  reflected  in  the 
test  records  of  any  works  that  has  them.  Going  back  to  the  early  90's, 
the  average  tensile  strength  9f  malleable  cast  iron  was  about  35,000  Ibs. 
per  sq.  in.,  with  an  elongation  of  about  2%  in  2  in.  The  transverse 
strength  was  perhaps  2800  Ibs.,  with  a  deflection  of  1/2  in.  Toward  the 
close  of  the  90's  a  fair  average  of  the  castings  then  made  would  run 
about  44,000  Ibs.  per  sq.  in.,  with  an  elongation  of  5%  in  2  in.,  and  the 
transverse  strength,  about  3500  Ibs.,  with  a  deflection  of  1/2  inch.  These 
average  figures  were  greatly  exceeded  in  establishments  where  special 
attention  was  given  to  the  niceties  9f  the  process.  The  tensile  strength 
here  would  run  52,000  Ibs.  per  sq.  in.  regularly,  with  7%  elongation  in 

2  in.,  and  the  transverse  strength,  50CO  and  over,  with  11/2  in.  deflection. 
Further  Progress  Desirable.    (Moldenke.)  —  We  do  not   know  at 

the  present  time  why  cupola  malleables  require  an  annealing  heat  sev- 
eral hundred  degrees  higher  than  air  or  open-hearth  furnace  iron.  The 
underlying  principles  of  the  oxidation  of  the  bath,  which  is  a  frequent 
cause  of  defective  iron,  is  practically  unknown  to  the  majority  of  those 
engaged  in  this  industry.  Heats  are  frequently  made  that  will  not 
pour  nor  anneal  properly,  but  the  causes  are  still  being  sought.  To 
produce  castings  from  successive  heats,  so  that  with  the  same  composi- 
tion they  will  have  the  same  physical  strength  regardless  of  how  they 
are  tested,  is  a  problem  partially  solved  for  steel,  but  not  yet  approached 
for  malleable  cast  iron. 

Sufficient  progress  in  the  study  of  iron  with  the  microscope  has  been 
made  to  warrant  the  belief  that  in  the  not  distant  future  we  may  be 
able  to  distinguish  the  constituents  of  the  material  by  means  of  etching 
with  various  chemicals.  When  the  sulphides  and  phosphides  of  iron, 
or  the  manganese-sulphur  compounds,  can  be  seen  directly  under  the 
microscope,  it  is  probable  that  a  method  may  be  found  by  which  the 
dangerous  ingredients  may  be  so  scattered  or  arranged  that  they  will 
do  the  least  harm. 

The  high  sulphur-  in  European  malleable  accounts  to  some  extent  for 
the  comparatively  low  strength  when  contrasted  with  our  product. 
Their  castings  being  all  very  light,  so  long  as  they  bend  and  twist  prop- 
erly, the  purpose  is  served,  and  hence  until  heavier  castings  become  the 
rule  instead  of  the  exception,  "white  heart"  and  steely-looking  frac- 
tures will  remain  the  characteristic  feature  of  European  work. 

STRENGTH  OF  MALLEABLE  CAST  IRON. 

Tests  of  Square  Bars,  1/2  in.  and  1  in.,  by  tension,  compression  and 
transverse  stress,  by  M.  H.  Miner  and  F.  E.  Blake  (Railway  Age,  Jan.  25, 
1901). 

TENSION.  Six  1/2-in.  and  six  1-in.  round  bars,  also  two  1-in.  bars 
turned  to  remove  the  skin,  from  each  of  four  makers.  Average  results: 

T.  S.,  l/2-in.  bars,  37,470-42,950,  av.  40,960;  E.  L.,  16,500-21,100,  av. 
19,176. 

T.  S.,  1-in.  bars,  35,750-40,530,  av.  38,300;  E.  L.,  14,860-19,900,  av. 
17,181. 

Tensile  strength,  turned  bars.  av.  35.090:  Elastic  limit,  av.  15.660. 


WROUGHT  IRON. 


459 


Elong.  inSin..,  y2-'m.  bars,  4.75  % ;  1-in.  bars,  4.32  % ;  turned  bars,  3.73  %. 

Modulus  of  elasticity,  y2-in.  bars,  22,289,000;  1-in.  bars,  21,677,000. 

COMPRESSION.  16  short  blocks,  2  in.  long,  1  in.  and  1/2  in.  square 
respectively. 

8  long  columns,  15  in.  long,  1  in.  sq.,  and  7.5  in.  long,  1/2  in/sq.  respec- 
tively. 

Averages  of  blocks  from  each  of  four  makers: 

Short  blocks,  l/2-in.  sq.,  93,000  to  114,500  Ibs.  per  sq.  in.  Mean, 
101,900  Ibs.  per  sq.  in. 

Short  blocks,  1  in.  sq.,  137,600  to  165,300  Ibs.  per  sq.  in.  Mean, 
152,800  Ibs.  per  sq.  in. 

Ratio  of  final  to  original  length,  1/2  in.,  61.7%;  1  in.,  52.6%.  A  small 
part  of  the  shortening  was  due  to  sliding  on  the  45°  plane  of  fracture. 

Long  columns:  1/2  in.  X  7.5  in.  Mean,  29,400  Ibs.  per  sq.  in.:  1  in. 
X  15  in.,  27,500  Ibs.  per  sq.  in.  Ratio  of  final  to  original  length,  1/2  in., 
98.5%;  1  in.,  98.8%.  The  long  columns  did  not  rupture,  but  reached 
the  maximum  stress  after  bending  into  a  permanent  curve. 

TRANSVERSE  TESTS.  Maximum  fiber  stress,  mean  of  8  tests,  l/2-in. 
bars,  34,163  Ibs.  per  sq.  in.  1-in.  bars,  36,125  Ibs.  per  sq.  in.  Length 
between  supports,  20  in.  The  bars  did  not  break,  but  failed  by  bending. 
The  l/2-in.  bars  could  be  bent  nearlv  double. 

Malleable  Bars  cast  by  Buhl  Malleable  Co.,  Detroit,  Mich.,  tested  as 
follows.  The  tests  were  reported  by  Chas.  H.  Day,  Am.  Mach.,  April  5, 
1906.  The  castings  were  all  made  at  the  same  time.  The  rectangular 
sections  were  approximately  1/4  X  3/4  in.  The  star  sections  were  square 
crosses,  1  in.  wide,  with  arms  about  1/4  in.  thick.  The  figures  here  given 
are  the  maximum  and  minimum  results  from  three  bars  of  each  section. 
TENSILE  TESTS.  COMPRESSION  TESTS. 


Section. 

Area, 
sq.  in. 

Tensile 
St'gth, 
Ibs.  per 

Elong. 
in  8  in., 

Red.  of 
Area, 

Area, 
sq.  in. 

L'gth, 
in. 

Comp. 
Str., 
Ibs.  per 

Final 
Area, 
sq.  in. 

sq.  in. 

* 

sq.  in. 

Round 

0.817 

43,000 

5.87 

4.76 

0.847 

15 

31,700 

0.901 

0.801 

43,400 

6.21 

3.98 

0.801 

15 

33,240 

0.886 

0.219 

41,130 

7.70 

3.40 

0.209 

7.5 

32,600 

0.221 

«' 

0.202 

44,700 

13.00 

3.63 

0.204 

7.5 

34,600 

0.215 

Square 

0.277 

36,700 

4.70 

2.20 

0.263 

7.5 

33,200 

0.272 

0.277 

38,100 

3.72 

3.00 

0.254 

7.5 

31,870 

0.278 

«« 

1.040 

38,460 

4.10 

3.30 

1.051 

15 

29,650 

1.070 

M 

1.Q50 

37,860 

2.38 

2.94 

1.040 

15 

30,450 

1.066 

Rect. 

0.239 

31,200* 

5.19 

1.50 

0.436 

15 

32,200 

0.448 

0.244 

37,600 

3.87 

3.80 

0.457 

15 

30,400 

0.467 

Star 

0.584 

34,600 

4.20 

3.10 

0.575 

37,200 

4.80 

3.50 

*  Broke  in  flaw. 

Tests  of  Rectangular  Cast  Bars,  made  by  a  committee  of  the  Mas- 
ter Car-builders'  Assn.  in  1891  and  1892,  gave  the  following  results 
(selected  to  show  range  of  variation) : 


Size  of 
Section, 
in. 

Tensile 
St'gth, 
Ibs.  per 
sq.  in. 

Elastic 
Limit, 
Ibs.  per 
sq.  in. 

Elonga- 
tion, % 
in  4  in. 

Size  of 
Section, 
in. 

Tensile 
St'gth, 
Ibs.  per 
sq.  in. 

Elastic 
Limit, 
Ibs.  per 
sq.  in. 

Elong. 
in  8  in.. 

%. 

0.25x1.52 
0.5  xl.53 
0.78x2 
0.88x1.54 
1.52x1.54 

34,700 
32,800 
25,100 
33,600 
28,200 

21,100 
17,000 
15,400 
19,300 

2 
2 
1.5 
1.5 
1.5 

0.29x2.78 
0.39x2.82 
0.53x2.76 
0.8  X2.76 
1.03x2.82 

28,160 
32,060 
27,875 
25,120 
28,720 

22,650 
20,595 
19,520 
18,390 
18,220 

06 
1  3 

1  1 

1  5 

WROUGHT  IRON. 

The  Manufacture  of  Wrought  Iron.  —  When  iron  ore,  which  is  an 
oxide  of  iron,  Fe2Os  or  FesCU,  containing  silica,  phosphorus,  sulphur, 
etc.,  as  impurities,  is  heated  to  a  yellow  heat  in  contact  with  charcoal  or 
other  fuel,  the  oxygen  of  the  ore  combines  with  the  carbon  of  the  fuel, 
part  of  the  iron  combines  with  silica  to  form  a  fusible  cinder  or  slag,  and 
the  remainder  of  the  iron  agglutinates  into  a  pasty  mass  which  is  inter- 
mingled with  the  cinder.  Depending  upon  the  time  and  the  tempera- 


460  IRON  AND   STEEL. 

ture  of  the  operation,  and  on  the  kind  and  quality  of  the  impurities 
present  in  the  ore  and  the  fuel,  more  or  less  of  the  sulphur  and  phos- 
phorus may  remain  in  the  iron  or  may  pass  into  the  slag ;  a  small  amount 
of  carbon  may  also  be  absorbed  by  the  iron.  By  squeezing,  hammering, 
or  rolling  the  lump  of  iron  while  it  is  highly  heated,  the  cinder  may  be 
nearly  all  expelled  from  it,  but  generally  enough  remains  to  give  a  bar 
after  being  rolled,  cooled  and  broken  across,  the  appearance  of  a  fibrous 
structure.  The  quality  of  the  finished  bar  depends  upon  the  extent  to 
which  the  chemical  impurities  and  the  intermingled  slag  have  been 
removed  from  the  iron. 

The  process  above  described  is  known  as  the  direct  process.  It  is 
now  but  little  used,  having  been  replaced  by  the  indirect  process  known 
as  puddling  or  boiling.  In  this  process  pig  iron  which  has  been  melted 
in  a  reverb  eratory  furnace  is  desilicomzed  and  decarbonized  by  the 
oxygen  derived  from  iron  ore  or  iron  scale  in  the  bottom  of  the  furnace, 
and  from  the  oxidizing  flame  of  the  furnace.  The  temperature  being  too 
low  to  maintain  the  iron,  when  low  in  carbon,  in  a  melted  C9ndition,  it 
gradually  "  comes  to  nature"  by  the  formation  of  pasty  particles  in  the 
bath,  which  adhere  to  each  other,  until  at  length  all  the  iron  is  decarbon- 
ized and  beco  Ties  of  a  pasty  condition,  and  the  lumps  so  formed  when 
gathered  together  make  the  "puddle-ball"  which  is  consolidated  int9  a 
bloom  by  the  squeezer  and  then  rolled  into  "muck-bar."  By  cutting 
the  muck-bar  into  short  lengths  and  making  a  "pile"  of  them,  heating 
the  pile  to  a  welding  heat  and  rerolling,  a  bar  is  made  which  is  freer 
from  cinder  and  more  homogeneous  than  the  original  bar,  and  it  may 
be  further  "refined"  by  another  piling  and  rerolling.  The  quality  of 
the  iron  depends  on  the  quality  of  the  pig-iron,  on  the  extent  of  the 
decarbonization,  on  the  extent  of  dephosphorization  which  has  been 
effected  in  the  furnace,  on  the  greater  or  less  contamination  of  the  iron 
by  sulphur  derived  from  the  fuel,  and  on  the  amount  of  work  done  on 
the  piles  to  free  the  iron  from  slag.  Iron  insufficiently  decarbonized  is 
irregular,  and  hard  or  "steely."  Iron  thoroughly  freed  from  impurities 
is  soft  ani  of  low  tensile  strength.  Iron  high  in  sulphur  is  "hot-short," 
liable  to  break  when  being  forged.  Iron  high  in  phosphorus  is  "cold- 
short," of  low  ductility  when  cold,  and  breaking  with  an  apparently 
crystalline  fracture. 

See  papers  on  Manufacture  and  Characteristics  of  Wrought  Iron,  by 
J.  P.  Roe,  Trans.  A.  I.  M.  E.,  xxxiii,  p.  551;  xxxvi,  pp.  203,  807. 

Electrolytic  Iron.  (L.  Guillet,  Proc.  Iron  &  Steel  Inst.,  1914,  Eng'g, 
Oct.  2,  1914.) — Using  any  pig  iron  in  solution  an  iron  can  be  obtained 
of  the  following  average  composition,  after  removal  of  the  gases  by 
annealing:  C,  0.004;  Si,  0.007;  S,  0.006;  P,  0.008.  The  metal  de- 
posited from  the  solution  is  extremely  brittle  and  hard,  due  to  occluded 
hydrogen.  The  deposition  of  the  iron  takes  place  on  a  revolving  metal 
mandrel,  making  tubes  of  from  4  to  8  in.  diam.,  12.8  ft.  long,  0.004  to 
0.24  in.  thick.  After  annealing,  the  metal  becomes  soft  and  ductile,  with 
a  tensile  strength  of  from  44,000  to  47,000  Ib.  per  sq.  in.  The  in- 
dustrial uses  of  electrolytic  iron  include  the  direct  manufacture  of 
tubes,  sheets,  rods  for  autogenous  welding,  and  the  preparation  of  raw 
material  for  the  manufacture  of  steel.  In  localities  where  cheap  electric 
current  can  be  obtained  the  cost  is  estimated  to  be  as  low  as  $30  to  $38 
per  gross  ton.  Patents  on  the  process  are  owned  by  Compagnie  Le  Fer, 
Grenoble,  France. 

Influence  of  Reduction  in  Rolling  from  Pile  to  Bar  on  the 
Strength  of  Wrought  Iron.  —  The  tensile  strength  of  the  irons  used 
in  Beardslee's  tests  ranged  from  46,000  to  62,700  Ibs.  per  sq.  in.,  brand 
L,  which  was  really  a  steel,  not  being  considered.  Some  specimens  of  L 
gave  figures  as  high  as  70,000  Ibs.  The  amount  of  reduction  of  sectional 
area  in  rolling  the  bars  has  a  notable  influence  on  the  strength  and  elastic 
limit;  the  greater  the  reduction  from  pile  to  bar,  the  higher  the  strength. 

The  following  are  a  few  figures  from  tests  of  one  of  the  brands: 
Size  of  bar,  in.  diam.:        4             3             2             1            1/2           l;4 
Area  of  pile,  sq.  in.:           80            80            72            25             9              3 
Bar  per  cent  of  pile:         15.7         8.83         4.36         3.14         2.17        1.6 
Tensile  strength,  Ib.:      46,322     47,761     48,280     51,128     52,275     59,585 
Elastic  limit.  Ib.:  23.430     26,400     31,892     36,467     39,126 

Influence  of  Chemical  Composition  on  the  Properties  of  Wrought 
Iron*  (Beardslee  on  Wrought  Iron  and  Chain  Cables.  Abridgment  by 


WROUGHT   IRON. 


461 


W.  Kent.  Wiley  &  Sons,  1879.)  —  A  series  of  2000  tests  of  specimens 
from  14  brands  of  wrought  iron,  most  of  them  of  high  repute,  was  made 
in  1877  by  Capt.  L.  A.  Beardslee,  U.S.N.,  of  the  United  States  Testing 
Board.  Forty-two  chemical  analyses  were  made  of  these  irons,  with  a 
view  to  determine  what  influence  the  chemical  composition  had  upon  the 
strength,  ductility,  and  welding  power.  From  the  report  of  these  testa 
by  A.  L.  Holley  the  following  figures  are  taken: 


Brand. 

Average 
Tensile 
Strength. 

Chemical  Composition. 

S. 

P. 

Si. 

C. 

Mn. 

Slag. 

L 

66,598 

trace 

j  0.065 
I  0.084 

0.080 
0.105 

0.212 
0.512 

0.005 
0.029 

0.192 
0.45? 

P 

54,363 

(0.009 
\  0.001 

0.250 
0.095 

0.182 
0.028 

0.033 
0.066 

0.033 
0.009 

0.848 
1.214 

B 

52  764 

0  008 

0  231 

0  156 

0  015 

0  017 

!J 

51,754 

j  0.003 
1  0.005 

0.140 
0.291 

0.182 
0.321 

0.027 
0.051 

trace 
0.053 

0.678 
1.724 

0 

51,134 

(  0.004 
\  0.005 

0.067 
0.078 

0.065 
0.073 

0.045 
0.042 

0.007 
0.005 

1.168   . 
0.974 

C 

50,765 

0.007 

0.169 

0.154 

0.042 

0.021 

Where  two  analyses  are  given,  they  are  the  extremes  of  two  or  more 
analyses  of  the  brand.  Where  one  is  given,  it  is  the  only  analysis. 
Brand  L  should  be  classed  as  a  puddled  steel. 

ORDER  OF  QUALITIES  GRADED  FROM  No.  1  TO  No.  19. 


Brand. 

Tensile 
Strength. 

Reduction  of 
Area. 

Elongation. 

Welding  Power. 

L 
P 
B 
J 
0 
C 

1 

6 
12 
16 
18 
19 

18 
6 
16 
19 
1 
12 

19 
3 
15 
18 
4 
16 

most  imperfect, 
badly, 
best, 
rather  badly, 
very-  good. 

The  reduction  of  area  varied  from  54.2  to  25.9  per  cent,  and  the  elonga* 
tion  from  29.9  to  8.3  per  cent. 

Brand  O,  the  purest  iron  of  the  series,  ranked  No.  18  in  tensile  strength 
but  was  one  of  the  most  ductile;  brand  B,  quite  impure,  was  below  tho 
average  both  in  strength  and  ductility,  but  was  the  best  in  welding 
power;  P,  also  quite  impure,  was 'one  of  the  best  in  every  respect  except 
welding,  while  L,  the  highest  in  strength,  was  not  the  most  pure,  it  ha(f 
the  least  ductility,  and  its  welding  power  was  most  imperfect.  The 
evidence  of  the  influence  of  chemical  composition  upon  quality,  there^ 
fore,  is  quite  contradictory  and  C9nfusing.  The  irons  differing  remark- 
ably in  their  mechanical  properties,  it  was  found  that  a  much  more 
marked  influence  upon  their  qualities  was  caused  by  different  treatment 
in  rolling  than  by  differences  in  composition. 

In  regard  to  slag  Mr.  Holley  says:  "It  appears  that  the  smallest  and 
most  worked  iron  often  has  the  most  slag.  It  is  hence  reasonable  to 
conclude  that  an  iron  may  be  dirty  and  yet  thoroughly  condensed." 

In  his  summary  of  "What  is  learned  from  chemical  analysis, "' he  says: 
"  So  far,  it  may  appear  that  little  of  use  to  the  makers  or  users  of  wrought 
iron  has  been  learned.  .  .  .  The  character  of  steel  can  be  surely  pred- 
icated on  the  analyses  of  the  materials ;  that  of  wrought  iron  is  altered 
by  subtle  and  unobserved  causes." 

Specifications  for  Wrought  Iron.  (F.  H.  Lewis,  Engineers'  Club  of 
Philadelphia,  1891.)  —  1.  All  wrought,  iron  must  be  tough,  ductile, 
fibrous,  and  of  uniform  quality  for  each  class,  straight,  smooth,  free  from 
cinder-pockets,  flaws,  buckles,  blisters,  and  injurious  cracks  along  the 
edges,  and  must  have  a  workmanlike  finish.  No  specific  process  or 
provision  of  manufacture  will  be  demanded,  provided  the  material  fulfills 
the  requirements  of  these  specifications. 

2.  The  tensile  strength,  limit  of  elasticity,  and  ductility  shall  be  deter- 
mined from  a  standard  test-piece  not  less  than  1/4  inch  thick  cut  from 
the  full-sized  bar,  and  planed  or  turned,  parallel.  The  area  of  cross- 


462  IRON   AND   STEEL. 

section  shall  not  bo  less  than   1/2  sq.   in.      The  elongation  shall  be 
measured  after  breaking  on  an  original  length  of  8  in. 

3.  The  tests  shall  show  not  less  than  the  following  results:         El.  in 

8  in. 

For  bar  iron  in  tension T.  S.  =  50,000;  E.  L.  =  26,000;  18% 

For  shape  iron  in  tension =  48,000;  =  26,000;  15% 

For  plates  under  36  in.  wide =  48,000;  =  26,000;  12% 

For  plates  over  36  in.  wide =  46,000;  =  25,000;  10% 

4.  When  full-sized  tension  members  are  tested  to  prove  the  strength  of 
their  connections,  a  reduction  in  their  ultimate  strength  of  (500  X  width 
of  bar)  p9unds  per  square  inch  will  be  allowed. 

5.  All  iron  shall  bend,  cpld,  180  degrees  around  a  curve  whose  diameter 
is  twice  the  thickness  of  piece  for  bar  iron,  and  three  times  the  thickness 
for  plates  and  shapes. 

6.  Iron  which  is  to  be  worked  hot  in  the  manufacture  must  be  capable 
Df  bending  sharply  to  a  right  angle  at  a  working  heat  without  sign  of 
fracture. 

7.  Specimens  of  tensile  iron  upon  being  nicked  on  one  side  and  bent 
shall  show  a  fracture  nearly  all  fibrous. 

8.  All  rivet  iron  must  be  tough  and  soft,  and  be  capable  of  bending 
cold  until  the  sides  are  in  close  contact  without  sign  of  fracture  on  the 
convex  side  of  the  curve. 

Penna.  B.  B.  Co.'s  Specifications  for  Merchant-bar  Iron  (1904). — 
One  bar  will  be  selected  for  test  from  each  100  bars  in  a  pile. 

All  the  iron  of  one  size  in  the  shipment  will  be  rejected  if  the  average 
tensile  strength  of  the  specimens  tested  full  size  as  rolled  falls  below 
47,000  Ibs.  or  exceeds  53,000  Ibs.  per  sq.  in.,  or  if  a  single  specimen  falls 
below  45,000  Ibs.  per  sq.  in.;  or  when  the  test  specimen  has  been  reduced 
by  machining  if  the  average  tensile  strength  exceeds  53,000  or  falls  below 
46,000,  or  if  a  single  specimen  falls  below  44,000  Ibs.  per  sq.  in. 

All  the  iron  of  one  size  in  the  shipment  will  be  rejected  if  the  average 
elongation  in  8  in.  falls  below  the  following  limits:  Flats  and  rounds, 
tested  as  rolled,  1/2  in.  and  over,  20%;  less  than  1/2  in.,  16%.  Flats  and 
rounds  reduced  by  machining  16%. 

Nicking  and  Bending  Tests.  —  When  necessary  to  make  nicking  and 
bending  tests,  the  iron  will  be  nicked  lightly  on  one  side  and  then  broken 
by  holding  one  end  in  a  vise,  or  steam  hammer,  and  breaking  the  iron  by 
successive  blows.  It  must  when  thus  broken  show  a  generally  fibrous 
structure,  not  more  than  25%  crystalline,  and  must  be  free  from  admix- 
,  ture  of  steel. 

Stay-bolt  Iron.  (Penna.  R.  R.  Co.'s  specifications,  1902). — Sample 
bars  must  show  a  tensile  strength  of  not  less  than  48,000  Ibs.  per  sq.  in. 
and  an  elongation  of  not  less  than  25%  in  8  in.  One  piece  from  each  lot 
will  be  threaded  in  dies  with  a  sharp  V  thread,  12  to  1  in.  and  firmly 
screwed  through  two  holders  having  a  clear  space  between  them  of  5  in. 
One  holder  will  be  rigidly  secured  to  the  bed  of  a  suitable  machine,  and  the 
other  vibrated  at  right  angles  to  the  axis  over  a  space  of  1/4  in.  or  i/s  in. 
-each  side  of  the  center  line.  Acceptable  iron  should  stand  2800  double 
vibrations  before  breakage. 

Mr.  Vauclain,  of  the  Baldwin  Locomotive  Works,  at  a  meeting  of  the 
American  Railway  Master  Mechanics'  Association,  in  1892,  says:  Many 
advocate  the  softest  iron  in  the  market  as  the  best  for  stay-bolts.  He 
believed  in  an  iron  as  hard  as  was  consistent  with  heading  the  bolt  nicely. 
The  higher  the  tensile  strength  of  the  iron,  the  more  vibrations  it  will 
stand,  for  it  is  not  so  easily  strained  beyond  the  yield-point.  The  Baldwin 
specifications  for  stay-bolt  iron  call  for  a  tensile  strength  of  50,000  to 
52,000  Ibs.  per  square  inch,  the  upper  figure  being  preferred,  and  the 
lower  being  insisted  upon  as  the  minimum. 

Specifications  for  Wrought  Iron  for  the  World's  Fair  Buildings. 
(Eng'g  News,  March  26,  1892.)  —  All  iron  to  be  used  in  the  tensile  mem- 
bers of  open  trusses,  laterals,  pins  and  bolts,  except  plate  iron  over 
8  inches  wide,  and  shaped  iron,  must  show  by  the  standard  test-pieces 
a  tensile  strength  in  Ibs.  per  square  inch  of: 

52  000  —     7000  X  area  of  original  bar  in  sq.  in. 
circumference  of  original  bar  in  inches  * 

with  an  elastic  limit  not  less  than  half  the  strength  given  by  this  formula, 
and  au  elongation  of  20%  in  8  in. 


- 


METALS  AT  VARIOUS   TEMPERATURES.  d63 

Plate  iron  8  to  24  inches  wide,  T.  S.  48,000,  E.  L.  26,000  Ibs.  per  sq.  in., 
elong.  12%.  Plates  over  24  inches  wide,  T.  S.  46,000,  E.  L.  26,000  Ibs. 
per  sq.  in.  Plates  24  4o  36  in.  wide,  elong.  10%;  36  to  48  in.,  8%;  over 
48  in.,  5%. 

All  shaped  iron,  flanges  of  beams  and  channels,  and  other  iron  not 
hereinbefore  specified,  must  show  a  T.  S.  in  Ibs.  per  sq.  in.  of: 
_     7000  X  area  of  original  bar 

circumference  of  original  bar* 

»yith  an  elastic  limit  of  not  less  than  half  the  strength  given  by  this  formula, 
and  an  elongation  of  15%  for  bars  5/8  inch  and  less  in  thickness,  and  of 
12%  for  bars  of  greater  thickness.  For  webs  of  beams  and  channels, 
specifications  for  plates  will  apply. 

All  rivet  iron  must  be  tough  and  soft,  and  pieces  of  the  full  diameter  of 
the  rivet  must  be  capable  of  bending  cold,  until  the  sides  are  in  close  con- 
tact, without  sign  of  fracture  on  the  convex  side  of  the  curve. 

TENACITY   OF  METALS   AT    VARIOUS   TEMPERATURES. 

The  British  Admiralty  made  a  series  of  experiments  to  ascertain  what 
loss  of  strength  and  ductility  takes  place  in  gun-metal  compositions  when 
raised  to  high  temperatures.  It  was  found  that  all  the  varieties  of  gun 
metal  suffer  a  gradual  but  not  serious  1933  of  strength  and  ductility  up  to 
a  certain  temperature,  at  which,  within  a  few  degrees,  a  great  change 
takes  place,  the  strength  falls  to  about-  one-half  the  original,. and  the 
ductility  is  wholly  gone.  At  temperatures  above  this  point,  up  to  500°  F., 
there  is  little,  if  any,  further  loss  of  strength;  the  temperature  at  which 
th;s  great  change  and  loss  of  strength  takes  place,  although  uniform  in 
the  specimens  cast  from  the  same  pot,  varies  about  100°  in  the  same 
comp9sition  cast  at  different  temperatures,  or  with  some  varying  condi- 
tions in  the  foundry  process.  The  temperature  at  which  the  change  took 
T, lace  in  No.  1  series  was  ascertained  to  be  about  370°,  and  in  that  of 
No.  2,  at  a  little  over  250°.  Rolled  Muntz  metal  and  copper  are  satis- 
factory up  to  500°,  and  may  be  used  as  securing-bolts  with  safety. 
Wrought  iron  increases  in  strength  up  to  500°,  but  loses  slightly  in  duc- 
tility up  to  300°,  where  an  increase  begins  and  continues  up  to  500°, 
where  it  is  still  less  than  at  the  ordinary  temperature  of  the  atmosphere. 
The  strength  of  Land  ore  steel  is  not  affected  by  temperature  up  to  500°, 
but  its  ductility  is  reduced  more  than  one-half.  (Iron,  Oct.  6,  1877.) 

Strength  of  Iron  and  Steel  Boiler-plate  at  High  Temperatures. 

(Chas.  Huston,  Jour.  F.  I.,  1877.) 

AVERAGE  OF  THREE  TESTS  OF  EACH. 

Temperature  F.  68°  575°        925° 

Charcoal  iron  plate,  tensile  strength,  Ibs 55,366  63,080  65,343 

contr.  of  area  % 26  23            21 

Soft  open-hearth  steel,  tensile  strength,  Ibs 54,600  66,083  64,350 

contr.  % 47  38            33 

1     Crucible  steel,  tensile  strength,  Ibs 64,000  69,266  68,600 

contr.  % 36  30            21 

Tensile   Strength  of  Iron   and    Steel   at  High  Temperatures.  — 

James  E.  Howard's  tests  (Iron  Age,  April  10,  1890)  show  that  the  tensile 
strength  of  steel  diminishes  as  the  temperature  increases  from  0°  until  a 
minimum  is  reached  between  200°  and  300°  F.,  the  total  decrease  being 
about  4000  Ibs.  per  square  inch  in  the  softer  steels,  and  from  6000  to 
8000  Ibs.  in  steels  of  over  80,000  Ibs.  tensile  strength.  From  this  mini- 
mum point  the  strength  increases  up  t9  a  temperature  of  400°  to  650°  F., 
the  maximum  being  reached  earlier  in  the  harder  steels,  the  increase 
amounting  to  from  10,000  to  20,000  Ibs.  per  square  inch  above  the  mini- 
mum strength  at  from  200°  to  300°.  From  this  maximum,  the  strength 
of  all  the  steel  decreases  steadily  at  a  rate  approximating  10,000  Ibs. 
decrease  per  100°  increase  of  temperature.  A  strength  of  20,000  Ibs. 
per  square  inch  is  still  shown  by  0.10  C.  steel  at  about  1000°  F.,  and  by 
0.60  to  1.00  C.  steel  at  about  1600°  F. 

The  strength  of  wrought  iron  increases  with  temperature  from  0°  up 
to  a  maximum  at  from  400  to  600°  F.,  the  increase  being  from  8000  to 
10,000  Ibs.  per  square  inch,  and  then  decreases  steadily  till  a  strength  .of 
only  6000  Ibs.  per  square  inch  is  shown  at  1500°  F. 


464 


IKON  AND   STEEL. 


Cast  iron  appears  to  maintain  its  strength,  with  a  tendency  to  In- 
crease, until  900°  is  reached,  beyond  which  temperature  the  strength 
gradually  diminishes.  Under  the  highest  temperatures,  1500°  to  1600°  F., 
numerous  cracks  on  the  cylindrical  surface  of  the  specimen  were  devel- 
oped prior  to  rupture.  It  is  remarkable  that  cast  iron,  so  much  inferior 
in  strength  to  the  steels  at  atmospheric  temperature,  under  the  highest 
temperatures  has  nearly  the  same  strength  the  high-temper  steels  then 
have. 

Strength  of  Wrought  Iron  and  Steel  at  High  Temperatures. 
(Jour.  F.  I.,  cxii,  1881,  p.  241.) — Kollmann's  experiments  at  Oberhausen 
included  tests  of  the  tensile  strength  of  iron  and  steel  at  temperatures 
ranging  between  70°  and  2000°  F.  Three  kinds  of  metal  were  tested, 
viz.,  fibrous  iron  of  52,464  Ibs.  T.  S.,  38,280  Ibs.  E.  L.,  and  17.5% 
elong.;  fine-grained  iron  of  56,892  Ibs.  T.  S.,  39,113  Ibs.  E.  L.,  and  20% 
elong.;  and  Bessemer  steel  of  84,826  Ibs.  T.  S.,  55,029  Ibs.  E.  L.,  and 
14.5%  elong.  The  mean  ultimate  tensile  strength  of  each  material 
expressed  in  per  cent  of  that  at  ordinary  atmospheric  temperature  is 
given  in  the  following  table,  the  fifth  column  of  which  exhibits,  for  pur- 
poses of  comparison,  the  results  of  experiments  by  a  committee  of  the 
Franklin  Institute  in  the  years  1832-36. 


Temperature 
Degrees  F. 

Fibrous 
Iron,  %. 

Fine-grained 
Iron,  %. 

Bessemer 
Steel,  %. 

Franklin  In- 
stitute, %. 

0 

100.0 

100.0 

100.0 

96.0 

100 

100.0 

100.0 

100.0 

102.0 

200 

100.0 

100.0 

100.0 

105.0 

300 

97.0 

100.0 

100.0 

106.0 

400 

95.5 

100.0 

100.0 

106.0 

500 

92.5 

98.5 

98.5 

104.0 

600 

88.5 

95.5 

92.0 

99.5 

700 

81.5 

90.0 

68.0 

92.5 

800 

67.5 

77.5 

44.0 

75.5 

900 

44.5 

51.5 

36.5 

53.5 

1000 

26.0 

36.0 

31.0 

36.0 

1100 

20.0 

30  5 

26  5 

1200 

18  0 

28  0 

22  0 

1400 

13  5 

19  0 

15  0 

1600 

7.0 

12.5 

10.0 

1800 

4  5 

8  5 

7  5 

2000 

3.5 

5'.0 

5.0 

Effect  of  Cold  on  the  Strength  of  Iron  and  Steel.  —  The  following 
conclusions  were  arrived  at  by  Mr.  Styffe  in  1865: 

(1)  The  absolute  strength  of  iron  and  steel  is  not  diminished  by  cold, 
even  at  the  lowest  temperature  which  ever  occurs  in  Sweden. 

(2)  Neither  in  steel  nor  in  iron  is  the  extensibility  less  in  severe  cold 
than  at  the  ordinary  temperature. 

(3)  The  limit  of  elasticity  in  both  steel  and  iron  lies  higher  in  severe 
cold. 

(4)  The  modulus  of  elasticity  in  both  steel  and  iron  is  increased  on 
reduction  of  temperature,  and  diminished  on  elevation  of  temperature; 
but  that  these  variations  never  exceed  0.05%  f9r  a  change  of  1.8°  F. 

W.  H.  Barlow  (Proc.  Inst.  C.  E.)  made  experiments  on  bars  of  wrought 
iron, "cast  iron,  malleable  cast  iron,  Bessemer  steel,  and  tool  steel.  The 
bars  were  tested  with  tensile  and  transverse  strains,  and  also  by  im- 
pact: one-half  of  them  at  a  temperature  of  50°  F.,  and  the  other  half  at 
5°  F. 

The  results  of  the  experiments  were  summarized  as  follows: 

1.  When  bars  of  wrought  iron  or  steel  were  submitted  to  a  tensile 
strain  and  broken,  their  strength  was  not  affected  by  severe  cold  (5°  F.), 
but  their  ductility  was  increased  about  1%  in  iron  and  3%  m  steel. 

2.  Whsn  bars  of  cast  iron  were  submitted  to  a  transverse  strain  at  a 
low  temperature,    their   strength  was  diminished  about  3%   and  their 
flexibility  about  16%. 

3.  When  bars  of  wrought  iron,  malleable  cast  iron,  steel,  and  ordinary 
cast  iron  were  subjected  to  impact  at  5°  F.,  the  force  required  to  break 
them,  and  their  flexibility,  were  reduced  as  follows: 


'• 


DURABILITY   OF  IKON,    COKROSION,   ETC.          465 


Reduction  of 
Force  of  Im- 
pact, %. 

Reduction  of 
Flexibility, 

%• 

Wrought  iron,  about              

3 

18 

Steel  (best  cast  tool),  about 

3  1/2 

17 

Malleable  cast  iron,  about  

41/2 

15 

Cast  iron,  about  

21 

not  taken 

The  experience  of  railways  in  Russia,  Canada,  and  other  countries 
where  the  winter  is  severe,  ie  that  the  breakages  of  rails  and  tires  are  far 
more  numerous  in  the  cold  weather  than  in  the  summer.  On  this 
account  a  softer  class  of  steel  is  employed  in  Russia  for  rails  than  is  usual 
in  more  temperate  climates. 

The  evidence  extant  in  relation  to  this  matter  leaves  no  doubt  that  the 
capability  of  wrought  iron  or  steel  to  resist  impact  is  reduced  by  cold.  On 
the  other  hand,  its  static  strength  is  not  impaired  by  low  temperatures. 

Increased  Strength  of  Steel  at  very  Low  Temperature.  —  Steel  of 
72,300  Ib.  T.  S.  and  62,800  Ib.  elastic  limit  when  tested  at  76°  F.  gave 
97,600  T.  S.  and  80,000  E.  L.  when  tested  at. the  temperature  of  liquid 
air.  —  Watertown  Arsenal  Tests,  Eng.  Rec.,  July  21,  1906. 

Prof.  R.  C.  Carpenter  (Proc.  A.  A.  A.  S.  1897)  found  that  the  strength 
of  wrought  iron  at  —  70°  F.  was  20%  greater  than  at  70°  F. 

Effect  of  Low  Temperatures  on  Strength  of  Railroad  Axles. 
(Thos.  Andrews,  Proc.  Inst.  C.  E.,  1891.)  —  Axles  6  ft.  6  in.  long  be- 
tween centers  of  journals,  total  length  7  ft.  3V2  in.,  diameter  at  middle 
41/2  in.,  at  wheel-sets  5Vs  in.,  journals  33/4  X  7  in.,  were  tested  by  impact 
at  temperatures  of  0°  and  100°  F.  Between  the  blows  each  axle  was 
half  turned  over,  and  wras  also  replaced  for  15  minutes  in  the  water-bath. 

The  mean  force  of  concussion  resulting  from  each  impact  was  ascer- 
tained as  follows: 

Let  h  =  height  of  free  fall  in  feet,  w  =  weight  of  test  ball,  hw  =  W  = 
"  energy,"  or  work  in  foot-tons,  x  =  extent  of  deflections  between  bearings 

then  F  (mean  force)  =  W/x  —  Jiw/x  . 

The  results  of  these  experiments  show  that  whereas  at  0°  F.  a  total 
average  mean  force  of  179  tons  was  sufficient  to  cause  the  breaking  of  the 
axles,  at  100°  F.  a  total  average  mean  force  of  428  tons  was  required. 
In  other  words,  the  resistance  to  concussion  of  the  axles  at  0°  F.  was  only 
about  42%  of  what  it  was  at  100°  F. 

The  average  total  deflection  at  0°  F.  was  6.48  in.,  as  against  15.06  in. 
with  the  axles  at  100°  F.  under  the  conditions  stated;  this  represents  an 
ultimate  reduction  of  flexibility,  under  the  test  of  impact,  of  about  57% 
for  the  cold  axles  at  0°  F.,  compared  with  the  warm  axles  at  100°  F. 

EXPANSION  OF  IEON  AND  STEEL  BY  HEAT. 

James  E.  Howard,  engineer  in  charge  of  the  U.  S.  test  ing- machine  at 
Watertown,  Mass.,  gives  the  following  results  of  tests  made  on  bars 
35  in.  long  (Iron  Age,  April  10,  1890) : 


Coeffi.  of 

Coeffi.  of 

C. 

Mn. 

Si. 

Expansion 
per  degree 

C. 

Mn 

Si. 

Expansion 
per  degree 

F. 

F. 

Wrought  iron 

0.0000067302 

Steel  

0  57 

0  93 

07 

0.0000063891 

Steel. 

0  09 

0  11 

0000067561 

71 

58 

08 

0000064716 

70 

45 

.0000066259 

,  •• 

81 

56 

17 

.0000062167 

«• 

31 

*7 

0000065149 

«« 

89 

57 

19 

0000062335 

it 

W 

70 

.0000066597 

97 

80 

78 

.0000061700 

«• 

.51 

.58 

02 

.0000066202 

Cast    (gun) 

iron  

.0000059261 

DURABILITY   OF   IRON,    CORROSION,   ETC. 

Crystallization  of  Iron  by  Fatigue. — Wrought  iron  of  the  best 
quality  is  very  tough,  and  breaks,  on  being  pulled  in  a  testing  machine  or 
bent  after  nicking,  with  a  fibrous  fracture.  Cold-short  iron,  however,  is 
more  brittle,  and  breaks  square  across  the  fibers  with  a  fracture  which  is 


466 


IRON  AND   STEEL. 


commonly  called  crystalline  although  no  real  crystals  are  present.  Iron 
which  has  been  repeatedly  overstrained,  and  especially  iron  subjected 
to  repeated  vibrations  and  shocks,  also  becomes  brittle,  and  breaks  with 
an  apparently  crystalline  fracture.  See  "  Resistance  of  Metals  to  Repeated 
Shocks, "  p.  276. 

Walter  H.  Finley  (Am.  Mach.,  April  27,  1905)  relates  a  case  of  fail- 
ures of  li/g-in.  wrought-iron  coupling  pins  on  a  train  of  1-ton  mine  cars, 
apparently  due  to  crystallization.  After  two  pins  were  broken  after  a 
year's  hard  service,  "several  hitchings  were  laid  on  an  anvil  and  the  pin 
broken  by  a  single  blow  from  a  sledge.  Pieces  of  the  broken  pins  were 
then  heated  to  a  bright  red,  and,  after  cooling  slowly,  were  again  put 
under  the  hammer,  which  failed  entiiely  to  break  them.  After  cutting 
with  a  cleaver,  the  pins  were  broken,  and  the  fracture  showed  a  complete 
restoration  of  the  fibrous  structure.  This  annealing  process  was  then 
applied  to  the  whole  supply  of  hitchings.  Piles  of  twenty-five  or  thirty 
were  covered  by  a  hot  wood  fire,  which  was  allowed  to  die  down  and  go 
out,  leaving  the  hitchings  in  a  bed  of  .ashes  to  cool  off  slowly..  By 
repeating  this  every  six  months  the  danger  of  brittle  pins  was  avoided.  » 

Durability  of  Cast  Iron.  —  Frederick  Gratf,  in  an  article  on  the 
Philadelphia  water-supply,  says  that  the  first  cast-iron  pipe  used  there 
was  laid  in  1820.  These  pipes  were  made  of  charcoal  iron,  and  were  in 
constant  use  for  53  years.  They  were  uncoated,  and  the  inside  was  well 
filled  with  tubercles.  In  salt  water  good  cast  iron,  even  uncoated,  will 
last  for  a  century  at  least;  but;  it  often  becomes  soft  enough  to  be  cut  by 
a  knife,  as  is  shown  in  iron  cannon  taken  up  from  the  bottom  of  harbors 
after  long  submersion.  Close-grained,  hard  white  metal  lasts  the  longest 
in  sea  water.  (Engjg  News,  April  23,  1887,  and  March  26,  1892.) 

Tests  of  Iron  after  Forty  Years'  Service.  —  A  square  link  12  inchei 
broad,  1  inch  thick  and  about  12  feet  long  was  taken  from  the  Kieff 
bridge,  then  40  years  old,  and  tested  in  comparison  with  a  similar  link 
which  had  been  preserved  in  the  stock-house  since  the  bridge  was  built. 
The  following  is  the  record  of  a  mean  of  four  longitudinal  test-pieces, 
1  X  IVsX  8  inches,  taken  from  each  link  (Stahl  und  Eisen.  1890): 
Old  Link  .  .T.  S.,  21.8  tons;  E.  L.,  11.1  tons;  Elong.,  14.05% 
New  Link.' "  22.2  11.9 

Durability  of  Iron  in  Bridges.     (G.  Lindenthal,  Eng'g,  MaY  2,  1884, 

E139.)  —  The  Old  Monongahela  suspension  bridge  in  Pittsburg,  built 
1 1845,  was  taken  down  in  1882.  The  wires  of  the  cables  were  frequently 
strained  to  half  of  their  ultimate  strength,  yet  on  testing  them  after  37 
years'  use  they  showed  a  tensile  strength  of  from  72,700  to  100,000  Ibs. 
per  sq  in.  The  elastic  limit  was  from  67,100  to  78,600  Ibs.  per  sq  in. 
Reduction  at  point  of  fracture,  35%  to  75%.  Their  diameter  was  0.13  in. 

A  new  ordinary  telegraph  wire  of  same  gauge  tested  for  comparison 
showed:  T.  S.,  of  100.000  Ibs.;  E.  L.,  81,550  Ibs.;  reduction,  57%.  Iron 
rods  used  as  stays  or  suspenders  showed:  T.  S.,  43,770  to  49,720  Ibs.  E. 
L.,  26,380  to  29,200.  Mr.  Lindenthal  draws  these  conclusions: 

"  The  above  tests  indicate  that  iron  highly  strained  for  a  long  number 
of  years,  but  still  within  the  elastic  limit,  and  exposed  to  slight  vibration, 
will  not  deteriorate  in  quality. 

"That  if  subjected  to  only  one  kind  of  strain  it  will  not  change  its 
texture,  even  if  strained  beyond  its  elastic  limit,  for  many  years.  It  will 
stretch  and  behave  much  as  in  a  testing-machine  during  a  long  test. 

"That  iron  will  change  its  texture  only  when  exposed  to  alternate 
severe  straining,  as  in  bending  in  different  directions.  If  the  bending  is 
slight  but  very  rapid,  as  in  violent  vibrations,  the  effect  is  the  same." 

Durability  of  Iron  in  Concrete.  — In  Paris  a  sewer  of  reinforced  con- 
crete 40  years  old  was  removed  and  the  metal  was  found  in  a  perfect  state 
of  preservation.  In  excavating  for  the  foundations  of  the  new  General 
Post  Office  in  London  some  old  Roman  brickwork  had  to  be  removed, 
and  the  hoop-iron  bonds  were  still  perfectly  bright  and  good.  (Eng'g, 
Aug.  16,  1907,  p.  227.) 

Corrosion  of  Iron  Bolts.  —  On  bridges  over  the  Thames  in  London, 
bolts  exposed  to  the  action  of  the  atmosphere  and  rain-water  were  eaten 
away  in  25  years  from  a  diameter  of  7/g  in.  to  1/3  in.,  and  from  5/8  in.  diam- 
eter to  5/16  inch. 

Wire  ropes  exposed  to  drip  in  colliery  shafts  are  very  liable  to  corrosion. 

Corrosive  Agents  in  the  Atmosphere.  —  The  experiments  of  F. 
Grace  Calvert  (Chemical  News,  March  3,  1871)  show  that  carbonic  acid. 


DURABILITY   OF  IRON,    CORROSION,   ETC.          467 

in  the  presence  of  moisture,  is  the  agent  which  determines  the  oxidation 
of  iron  in  the  atmosphere.  He  subjected  perfectly  cleaned  blades  of 
iron  and  steel  to  the  action  of  different  gases  for  a  period  of  four  months, 
with  results  as  follows: 

Dry  oxygen,  dry  carbonic  acid,  a  mixture  of  both  gases,  dry  and  damp 
oxygen  and  ammonia:  no  oxidation.  Damp  oxygen:  in  three  experi- 
ments one  blade  only  was  slightly  oxidized. 

Damp  carbonic  acid :  slight  appearance  of  a  white  precipitate  upon  the 
iron,  found  to  be  carbonate  of  iron.  Damp  carbonic  acid  and  oxygen: 
oxidation  very  rapid.  Iron  immersed  in  water  containing  carbonic  acid 
oxidized  rapidly. 

Iron  immersed  in  distilled  water  deprived  of  its  gases  by  boiling  rusted 
the  iron  in  spots  that  were  found  to  contain  impurities. 

Sulphurous  acid  (the  product  of  the  combustion  of  the  sulphur  in  coal) 
is  an  exceedingly  active  corrosive  agent,  especially  when  the  exposed  iron 
is  coated  with  soot.  This  accounts  for  the  rapid  corrosion  of  iron  in 
railway  bridges  exposed  to  the  smoke  from  locomotives.  (See  account  of 
experiments  by  the  author  on  action  of  sulphurous  acid  in  Jour.  Frank. 
Inst.,  June,  1875,  p.  437.)  An  analysis  of  sooty  iron  rust  from  a  railway 
bridge  showed  the  presence  of  sulphurous,  sulphuric,  and  carbonic  acids, 
chlorine,  and  ammonia.  Bloxam  states  that  ammonia  is  formed  from 
the  nitrogen  of  the  air  during  the  process  of  rusting. 

Galvanic  Action  is  a  most  active  agent  of  corrosion.  It  takes  place 
when  two  metals,  one  electro-negative  to  the  other,  are  placed  in  contact 
and  exposed  to  dampness. 

Corrosion  in  Steam-boilers.  —  Internal  corrosion  may  be  due  either 
to  the  use  of  water  containing  free  acid,  or  water  containing  sulphate 
or  cnloride  of  magnesium,  which  decompose  when  heated,  liberating  the 
acid,  or  to  water  containing  air  or  carbonic  acid  in  solution.  External 
corrosion  rarely  takes  place  when  a  boiler  is  kept  hot,  but  when  cold  it 
is  apt  to  corrode  rapidly  in  those  portions  where  it  adjoins  the  brick- 
work or  where  it  may  be  covered  by  dust  or  ashes,  or  wherever  damp- 
ness may  lodge.  (See  Impurities  of  Water,  p.  720,  and  Incrustation  and 
Corrosion,  p.  927 .) 

Corrosion  of  Iron  and  Steel.  —  Experiments  made  at  the  Riverside 
Iron  Works,  Wheeling,  W.  Va.,  on  the  comparative  liability  to  rust  of 
iron  and  soft  Bessemer  steel:  A  piece  of  iron  plate  and  a  similar  piece  of 
steel,  both  clean  and  bright,  were  placed  in  a  mixture  of  yellow  loam  and 
sand,  with  which  had  been  thoroughly  incorporated  some  carbonate  of 
soda,  nitrate  of  soda,  ammonium  chloride,  and  chloride  of  magnesium. 
The  earth  as  prepared  was  kept  moist.  At  the  end  of  33  days  the  pieces 
of  metal  were  taken  out,  cleaned,  and  weighed,  when  the  iron  was  found 
to  have  lost  0.84%  of  its  weight  and  the  steel  0.72%.  The  pieces  were 
replaced  and  after  28  days  weighed  again,  when  the  iron  was  found  to 
have  lost  2.06%  of  its  original  weight  and  the  steel  1.79%.  (Eng'g,  June 
26,  1891.) 

Internal  Corrosion  of  Iron  and  Steel  Pipes  by  Warm  Water. 
(T.  N.  Thomson,  Proc.  A.  S.  H.  V.  E.,  1908.)  —Three  short  pieces  of  iron 
and  three  of  steel  pipes,  2  in.  diam.,  were  connected  together  by  nipples 
and  made  part  of  a  pipe  line  conveying  water  at  a  temperature  varying 
from  160°  to  212°  F.  In  one  year  9 13/33  Ibs.  of  wrought  iron  lost  203/4  oz., 
and  913/32  Ibs.  of  steel  247/g  oz.  The  pipes  were  sawed  in  two  lengthwise, 
and  the  deepest  pittings  were  measured  by  a  micrometer.  Assuming  that 
the  pitting  would  have  Continued  at  a  uniform  rate  the  wrought-iron  pipes 
would  have  been  corroded  through  in  from  686  to  780  days,  and  the  steel 
pipes  from  760  to  850  days,  the  average  being  742  days  for  iron  and  797 
days  for  steel.  Two  samples  each  of  galvanized  iron  and  steel  pipe  were 
also  included  in  the  pipe  line,  and  their  calculated  life  was:  iron  770  and 
1163  days;  steel  619  and  1163  days.  Of  numerous  samples  of  corroded 
pipe  received  from  heating  engineers  ten  had  given  out  within  four  years 
of  service,  and  of  these  six  were  steel  and  four  were  iron. 

To  ascertain  whether  Pipe  is  made  of  Wrought  Iron  or  Steel,  cut 
off  a  short  piece  of  the  pipe  and  suspend  it  in  a  solution  of  9  parts  of  water, 
3  of  sulphuric  acid,  and  1  of  hydrochloric  acid  in  a  porcelain  or  glass  dish 
in  such  a  way^  that  the  end  will  not  touch  the  bottom  of  the  dish.  After 
2  to  3  hours'  immersion  remove  the  pipe  and  wash  off  the  acid.  If  the 
pipe  is  steel  the  end  will  present  a  bright,  solid,  unbroken  surface,  while 
If  made  of  iron  it  will  show  faint  ridges  or  rings,  like  the  year  rings  in  a 


468  IRON  AND  STEEL. 

tree,  showing  the  different  layers  of  iron  and  streaks  of  cinder.  In  order 
that  the  scratches  made  by  the  cutting-off  tool  may  not  be  mistaken  for 
the  cinder  marks,  file  the  end  of  the  pipe  straight  across  or  grind  on  an 
emery  wheel  until  the  marks  of  the  cutting-off  tool  have  disappeared 
before  putting  it  in  the  acid. 

Relative  Corrosion  of  Wrought  Iron  and  Steel.  (H.  M.  Howe, 
Proc.  A.  S.  T.  M.,  1906.)  —  On  one  hand  we  have  the  very  general 
opinion  that  steel  corrodes  very  much  faster  than  wrought  iron,  an  opinion 
held  so  widely  and  so  strongly  that  it  cannot  be  ignored.  On  the  other 
hand  we  have  the  results  of  direct  experiments  by  a  great  many  observers, 
in  different  countries  and  under  widely  differing  conditions;  and  these 
results  tend  to  show  that  there  is  no  very  great  difference  between  the 
corrosion  of  steel  and  wrought  iron.  Under  certain  conditions  steel  seems 
to  rust  a  little  faster  than  wrought  iron,  and  under  others  wrought  iron 
seems  to  rust  a  little  faster  than  steel.  Taking  the  tests  in  unconfin<ed 
sea  water  as  a  whole  wrought  iron  does  constantly  a  little  better  than 
steel,  and  its  advantage  seems  to  be  still  greater  in  the  case  of  boiling  sea 
water.  In  the  few  tests  in  alkaline  water  wrought  iron  seems  to  have  the 
advantage  over  steel,  whereas  in  acidulated  water  steel  seems  to  rust  more 
slowly  than  wrought  iron. 

Steel  which  in  the  first  few  months  may  rust  faster  than  wrought  iron 
may,  on  greatly  prolonging  the  experiments,  or  pushing  them  to  destruc- 
tion, actually  rust  more  slowly,  and  vice  versa. 

Carelessly  made  steel,  containing  blowholes,  may  rust  faster  than 
wrought  iron,  yet  carefully  made  steel,  free  from  blowholes,  may  rust 
more  slowly.  Any  difference  between  the  two  may  be  due  not  to  the 
inherent  and  intrinsic  nature  of  the  material,  but  to  defects  to  which  it 
is  subject  if  carelessly  made.  Care  in  manufacture,  and  special  steps  to 
lessen  the  tendency  to  rust,  might  well  make  steel  less  corrodible  than 
wrought  iron,  even  if  steel  carelessly  made  should  really  prove  more 
corrodible  than  wrought  iron. 

For  extensive  discussions  on  this  subject  see  Trans.  A.  I.  M.  E..  1905. 
Proc.  A.  S.  T.  M.,  1906  and  1908,  and  Bulletins  of  National  Tube  Co. 

Corrosion  of  Fence  Wire.  (A.  S.  Cushman,  Farmers'  Bulletin,  No. 
239,  U.  8.  Dept.  of  Agriculture,  1905.)  —  "A  large  number  of  letters  were 
received  from  all  over  the  C9untry  in  response  to  official  inquiry,  and 
all  pointed  in  the  same  direction.  As  far  as  human  testimony  is  capable 
of  establishing  a  fact,  there  need  be  not  the  slightest  question  that  modern 
eteel  does  not  serve  the  purpose  as  well  as  the  older  metal  manufactured 
twenty  or  more  years  ago." 

Electrolytic  Theory,  and  Prevention  of  Corrosion.  (A.  S.  dish- 
man,  Bulletin  No.  30,  U.  S.  Dept.  of  Agriculture,  Office  of  Public  Roads, 
1907.  The  Corrosion  of  Iron.)  —  The  various  kinds  of  merchantable  iron 
and  steel  differ,  within  wide  limits,  in  their  resistance,  not  only  to  the 
ordinary  processes  of  oxidation  known  as  rusting,  but  also  in  other  corro- 
sive influences.  Different  specimens  of  one  and  the  same  kind  of  iron  or 
steel  will  show  great  variability  in  resistance  to  corrosion  under  the  con- 
ditions of  use  and  service.  The  causes  of  this  variability  are  numerous 
and  complex,  and  the  subject  is  not  nearly  so  well  understood  at  the 
present  time  as  it  should  be.  All  investigators  are  agreed  that  iron  can- 
not rust  in  air  or  oxygen  unless  water  is  present,  and  on  the  other  hand 
it  cannot  rust  in  water  unless  oxygen  is  present. 

From  the  standpoint  of  the  modern  theory  of  solutions,  all  reactions 
which  take  place  in  the  wet  way. are  attended  with  certain  readjustments 
of  the  electrical  states  of  the  reacting  ions.  The  electrolytic  theory  of 
rusting  assumes  that  before  iron  can  oxidize  in  the  wet  way  it  must  first 
pass  into  solution  as  a  ferrous  ion. 

Dr.  Cushman  then  gives  an  account  of  his  experiments  which  he  con- 
siders demonstrate  that  iron  goes  into  solution  up  to  a  certain  maximum 
concentration  in  pure  water,  without  the  aid  of  oxygen,  carbonic  acid  or 
other  reacting  substances.  It  is  apparent  that  the  rusting  of  iron  la 
primarily  due,  not  to  attack  by  oxygen,  but  by  hydrogen  ions. 

Solutions  of  chromic  acid  and  potassium  bichromate  inhibit  the  rusting 
of  iron.  If  a  rod  or  strip  of  bright  iron  or  steel  is  immersed  for  a  few 
hours  in  a  5  to  10  per  cent  solution  of  potassium  bichromate,  and  is  then 
removed  and  thoroughly  washed,  a  certain  change  has  been  produced 
on  the  surface  of  the  metal.  The  surface  may  be  thoroughly  washed 


DURABILITY  OF  IRON,   CORROSION,   ETC.          469 

and  wiped  with  a  clean  cloth  without  disturbing  this  new  surface  condi- 
tion. No  visible  change  has  been  effected,  for  the  polished  surfaces 
examined  under  the  microscope  appear  to  be  untouched.  If,  however, 
the  polished  strips  are  immersed  in  water  it  will  be  found  that  rusting  is 
inhibited.  An  ordinary  untreated  polished  specimen  of  steel  will  show 
rusting  in  a  few  minutes  when  immersed  in  the  ordinary  distilled  water  of 
the  laboratory.  Chromated  specimens  will  stand  immersion  for  varying 
lengths  of  time  before  rust  appears.  In  some  cases  it  is  a  matter  of 
hours,  in  others  of  days  or  weeks  before  the  inhibiting  effect  is  overcome. 

It  would  follow  from  the  electrolytic  theory  that  in  order  to  have  the 
highest  resistance  to  corrosion  a  metal  should  either  be  as  free  as  possible 
from  certain  impurities,  such  as  manganese,  or  should  be  so  homogene- 
ous as  not  to  retain  localized  positive  and  negative  nodes  for  a  long  time 
without  change.  Under  the  first  condition  iron  would  seem  to  have  the 
advantage  over  steel,  but  under  the  second  much  would  depend  upon 
care  exercised  in  manufacture,  whatever  process  was  used. 

There  are  two  lines  of  advance  by  which  we  may  hope  to  meet  the 
difficulties  attendant  upon  rapid  corrosion.  One  is  by  the  manufacture 
of  better  metal,  and  the  other  is  by  the  use  of  inhibitors  and  protective 
coverings.  Although  it  is  true  that  laboratory  tests  are  frequently 
unsuccessful  in  imitating  the  conditions  in  service,  it  nevertheless  appears 
that  chromic  acid  and  its  salts  should  under  certain  circumstances  come 
into  use  to  inhibit  extremely  rapid  corrosion  by  electrolysis. 

Chrome  Paints.  — G.  B.  Heckel  (Jour.  F.  /.,  Eng.  Dig.,  Sept.,  1908) 
quotes  a  letter  from  Mr.  Cushman  as  follows:  "My  observation  that 
chromic  acid  and  certain  of  its  compounds  act  as  inhibitives  has  led  to 
many  experiments  by  other  workers  along  the  same  line.  I  have  found 
that  the  chrome  compounds  on  the  market  vary  very  much  in  their  action. 
Some  of  them  show  up  as  strong  inhibitors,  while  others  go  to  the  op- 
posite extreme  and  stimulate  corrosion.  Referring  only  to  the  labeled 
names  of  the  pigments,  I  find  among  the  good  ones,  in  the  order  cited: 
Zinc  chromate,  American  vermilion,  chrome  yellow  orange,  chrome 
yellow  dd.  Among  the  bad  ones,  also  in  the  order  given,  I  find:  Chrome 
yellow  medium,  chrome  green,  chrome  red.  Much  the  worst  of  all  is 
chrome  yellow  lemon.  I  presume  that  the  difference  is  due  to  impurities 
that  are  present  in  the  bad  pigments." 

Mr.  Heckel  suggests  the  following  formula  for  a  protective  paint:  40 
IDS.  American  vermilion,  10  Ibs.  red  lead,  5  Ibs.  Venetian  red.  Zinc 
oxide  and  lamp-black  to  produce  the  required  tint  or  shade.  Grind  in 
1  Va  gal.  of  raw  linseed  oil  —  increasing  the  quantity  as  required  for  added 
zinc  oxide  or  lamp-black  —  and  1/8  gal.  crusher's  drier.  For  use,  thin 
with  raw  oil  and  very  little  turpentine  or  benzine. 

He  states  that  the  substitution  of  zinc  chrome  for  the  American  ver- 
milion; of  any  high-grade  finely  ground  iron  oxide  for  the  Venetian  red; 
and  of  American  vermilion  for  the  red  lead,  would  probably  improve  the 
protective  value  of  the  formula;  that  the  addition  of  a  very  little  kauri 
gum  varnish,  if  zinc  oxide  is  used,  might  be  found  advantageous;  and 
that  the  substitution  of  a  certain  proportion  of  China  wood  oil  for  some 
of  the  linseed  oil  might  improve  the  wearing  qualities  of  the  paint. 

Dr.  Cushman  points  out  two  dangers  confronting  us  when  we  attempt 
to  base  an  inhibitive  formula  on  commercial  products.  The  first  is  that 
all  carbon  pigments,  excepting  pure  graphite,  may  contain  sulphur  com- 
pounds easily  oxidizable  to  sulphuric  acid  when  spread  out  as  in  a  paint 
film.  The  second  is  the  probability  of  variation  in  the  composition  of 
basic  lead  chromate  or  American  vermilion.  Because  of  these  facts,  it 
is  necessary,  before  selecting  any  particular  pigment  for  its  inhibitive 
quality,  to  ascertain  that  it  is  free  from  acids  or  acid-forming  impurities. 
As  a  result  of  his  experiments  he  recommends  the  substitution  of  Prus- 
sian blue  for  the  lamp-black  in  Mr.  Heckel's  formula,  and  lays  down  as  a 
safe  rule  in  the  formulation  of  inhibitive  paints,  a  careful  avoidance  of 
all  potential  stimulators  of  the  hydrogen  ions  and  consequently  of  any 
substance  which  might  develop  acid;  preference  being  given  to  chromate 
pigments  which  are  to  some  extent  soluble  in  water,  and  to  other  pig- 
ments which  in  undergoing  change  tend  to  develop  an  alkaline  rather 
than  an  acid  reaction.  Calcium  sulphate,  for  example,  in  any  form  (as 
a  constituent  of  Venetian  red,  for  example),  he  deems  dangerous  to  use 
because  of  the  possibility  of  its  developing  acid.  Barium  sulphate,  on 
the  other  hand,  he  regards  as  safe,  because  of  its  chemical  stability.. 


470  IRON   AND   STEEL. 

Corrosion  caused  by  Stray  Electric  Currents.  (W.  W-  Churchill, 
Science,  Sept.  28,  1906).  —  Surface  condensers  in  electric  lighting  and 
other  plants  were  abandoned  on  account  of  electrolytic  corrosion.  The 
voltage  of  the  rails  in  the  freight  yard  of  the  Long  Island  railroad  at  the 
peak  of  the  load  was  9  volts  above  the  potential  of  the  river,  decreasing 
to  2  volts  or  less  at  light  loads.  This  caused  a  destruction  of  water  pipes 
and  other  things  in  the  railroad  yards.  Experiments  with  various  metal 
plates  immersed  in  samples  of  East  River  water  showed  that  it  gave  a 
more  violent  action  than  ordinary  sea  water.  It  was  further  observed 
that  there  was  a  local  galvanic  action  going  on,  and  that  the  amount  of 
stray  currents  had  something  to  do  with  the  polarization  of  the  surfaces, 
making  the  galvanic  action  exceedingly  violent  and  destroying  thin  cop- 
per tubes  at  a  very  rapid  rate.  There  was  a  violent  local  action  between 
the  zinc  and  the  copper  of  the  brass  tubes  which  were  in  contact  with  the 
electrolyte,  and  this  increased  in  the  reaction  as  it  progressed  in  stagnant 
conditions.  By  interposing  a  counter  electromotive  force  against  the 
galvanic  couple  which  should  exceed  in  pressure  the  voltage  of  the  couple, 
the  actions  of  the  electrolytic  corrosion  ceased.  When  unconnected,  or 
electrically  separated,  plates  were  placed  in  the  electrolyte,  if  they  were 
of  composite  construction  and  had  sharp  projections  into  the  fluid,  raised 
by  cutting  and  prying  up  with  a  knife,  they  would  have  these  projections 
promptly  destroyed,  and  if  an  electric  battery  having  a  pressure  exceed- 
ing that  of  the  couple  in  the  East  River  water  was  caused  to  act  to  pro- 
duce a  counter  current,  and  having  a  pressure  exceeding  that  of  the 
galvanic  couple  (0.42  volt),  the  capacity  of  this  electrolyte  to  drive  off 
atoms  of  the  mechanically  combined  metals  in  the  alloys  used  was  ove/- 
come  and  corrosion  was  arrested. 

It,  therefore,  became  desirable  not  only  to  carefully  provide  the  bal- 
ancing quantity  of  current  to  equal  the  stray  traction  currents  arising 
from  the  ground  returns  of  railway  and  other  service,  but  to  add  to  this 
the  necessary  voltage  through  a  cathode  placed  in  the  circulating  water 
in  such  a  way  as  to  bring  to  bear  electrolytic  action  which  would  pre- 
vent the  galvanic  action  due  to  this  current  coming  into  contact  with 
alloys  of  mechanically  combined  metals  such  as  the  brass  tubes  (60% 
copper,  40%  zinc). 

In  order  to  accomplish  these  two  things,  it  was  first  necessary  to  so 
install  the  condensers  as  to  prevent  undue  amounts  of  stray  currents 
flowing  through  them,  thus  tending  to  reduce  the  amount  of  power 
required  to  prevent  injurious  action  of  these  currents  and  otherwise  to 
neutralize  them.  This  was  done  by  insulating  the  joints  in  the  piping 
and  from  ground  connections,  and  even  lining  the  large  water  connec- 
tions with  glass  melted  on  to  the  surface. 

To  furnish  electromotive  force,  a  3-K.W.  motor  generator  was  pro- 
vided. By  means  of  a  system  of  wiring,  with  ammeters  and  voltmeters, 
and  a  connection  to  an  outlying  anode  in  the  condensing  supply  intake 
at  its  harbor  end,  this  generator  was  planned  to  provide  current  to  neu- 
tralize the  stray  currents  in  the  condenser  structure  to  any  extent  that 
they  had  passed  the  insulated  joints  in  the  supports  and  connections,  as 
well  as  through  the  columns  of  water  in  the  pipe  connections,  and  then 
to  adjust  the  additional  voltage  needed  to  counteract  and  prevent  the 
galvanic  action.  All  connections  were  made  in  a  manner  to  insure  a 
uniform  voltage  of  the  various  parts  of  the  condenser  to  prevent  local 
action,  each  connection  being  so  made  and  provided  with  such  measuring 
instruments  as  to  insure  ready  adjustment  to  effect  this.  The  apparatus 
was  designed  in  accordance  with  the  above  statements.  Its  operation 
has  extended  over  fourteen  months  (to  date,  1906),  and  with  the  excep- 
tion of  about  ten  tubes  which  have  become  pitted,  the  results  have  been 
satisfactory.  The  efficiency  of  the  apparatus  amply  justifies  the  ex- 
pense of  its  installation,  while  its  operation  is  not  expensive,  and  the 
plant  described  will  be  followed  by  other  protecting  plants  of  the  same 
character. 

Electrolytic  Corrosion  due  to  Overstrain.  (C.  F.  Burgess,  El.  Rev., 
Sept.  19,  1908.)  —  Mild  steel  bars  overstrained  in  their  middle  portion 
were  subjected  to  corrosion  by  suspension  in  dilute  hydrochloric  acid 
solutions,  and  others  by  making  them  the  anode  in  neutral  solutions  of 
ammonium  chloride  and  causing  current  to  flow  under  low  current  den- 
sity. In  all  cases  a  marked  difference  was  noted  in  the  rate  at  which  the 
strained  portions  corroded  as  compared  with  the  unstrained. 


Differences 


PRESERVATIVE   COATINGS.  471 


Differences  of  potential  of  from  five  to  nine  millivolts  were  noted 
between  two  electrodes,  one  of  which  constituted  the  strained  portion 
and  one  the  unstrained. 

The  more  rapid  electrolytic  corrosion  of  the  strained  portion  appears 
to  be  due  to  the  fact  that  the  strained  metal  is  electropositive  to  the 
unstrained,  the  current  finding  the  easier  path  through  the  surface  of 
the  electropositive  metal.  That  the  strained  metal  is  the  more  electro- 
positive is  also  shown  by  a  liberation  of  hydrogen  bubbles  on  the  un- 

rained  portion. 


PRESERVATIVE    COATINGS. 


The  following  notes  have  been  furnished  to  the  author  by  Prof.  A.  H. 
Sabin.  (Revised,  1908.) 

Cement.  —  Iron-work  is  often  bedded  in  concrete;  if  free  from  cracks 
and  voids  it  is  an  efficient  protection;  The  metal  should  be  cleaned  and 
then  washed  with  neat  cement  before  embedding. 

Asphaltum.  —  This  is  applied  either  by  dipping  (as  water-pipe)  or 
by  pouring  it  9n  (as  bridge  floors).  The  asphalt  should  be  slightly  elastic 
when  cold,  with  a  high  melting-point,  not  softening  much  at  100°  F., 
applied  at  300°  to  400°;  the  surface  must  be  dry  and  should  be  hot;  the 
coating  should  be  of  considerable  thickness. 

Paint.  —  Composed  of  a  vehicle  or  binder,  usually  linseed  oil  or  some 
inferior  substitute,  or  varnish  (enamel  paints);  and  a  pigment,  which  is  a 
more  or  less  inert  solid  in  the  form  of  a  powder,  either  mixed  or  ground 
together.  Nearly  all  paint  contains  paint  drier  or  japan,  which  is  a  lead 
or  (and)  manganese  compound  soluble  in  oil,  and  acts  as  a  carrier  of 
oxygen;  as  little  should  be  used  as  possible.  Boiled  oil  contains  drier; 
no  additional  drier  is  needed.  None  should  be  used  with  varnish  paints, 
nor  with  '*  ready-mixed  paints  "  in  general. 

The  principal  pigments  are  white  lead  (carbonate  or  oxy-sulphate)  and 
white  zinc  (oxide),  red  lead  (peroxide),  oxides  of  iron,  hydrated  and 
anhydrous,  graphite,  lampblack,  bone  black,  chrome  yellow,  chrome 
green,  ultramarine  and  Prussian  blue,  and  various  tinting  colors.  White 
lead  has  the  greatest  body  or  opacity  of  white  pigments;  three  coats  of  it 
equal  five  of  white  zinc;  zinc  is  more  brilliant  and.  permanent,  but  it  is 
liable  to  peel,  and  it  is  customary  to  mix  the  two.  These  are  the  standard 
white  paints  for  all  uses,  and  the  basis  of  all  light-colored  paints.  Anhy- 
drous iron  oxides  are  brown  and  purplish  brown,  hydrated  oxides  are 
yellowish  red  to  reddish  yellow,  with  more  or  less  brown;  most  iron 
oxides  are  mixtures  of  both  sorts,  and  often  contain  a  little  manganese 
and  much  clay.  They  are  cheap,  and  are  serviceable  paints  on  wood  and 
are  often  used  on  iron,  but  for  the  latter  use  are  falling  into  disrepute. 
Graphite  used  for  painting  iron  contains  from  10  to  90%  foreign  matter, 
usually  silicates.  It  is  very  opaque,  hence  has  great  covering  power  and 
may  be  applied  in  a  very  thin  coat,  which  is  to  be  avoided.  The  best 
raphite  paints  give  very  good  results.  There  are  many  grades  of  lamp- 
lack; the  cheaper  sorts  contain  oily  matter  and  are  especially  hard  to 
dry;  all  lampblack  is  slow  to  dry  in  oil.  In  a  less  degree  this  is  true  of  all 
paints  containing  carbon,  including  graphite.  Lampblack  is  used  with 
advantage  with  red  lead;  it  is  also  an  ingredient  of  many  '*  carbon  " 
paints,  the  base  of  which  is  either  bone  black  or  artificial  graphite.  Red 
lead  dries  by  uniting  chemically  with  the  oil  to  form  a  cement;  it  is  heavy, 
ard  makes  an  expensive  paint,  and  is  often  highly  adulterated.  Pure  red 
lead  has  long  had  a  high  reputation  as  a  paint  for  iron  and  steel,  and  is 
still  used  extensively,  especially  as  a  first  coat  ;  but  of  late  years  some  of 
the  new  paints  and  varnish-like  preparations  have  displaced  it  toacon* 
siderable  extent  even,  on  the  most  important  work. 

Varnishes.  —  These  are  made  by  melting  fossil  resin,  to  which  is  then 
added  from  half  its  weight  to  three  times  its  weight  of  refined  linseed  oil, 
and  the  compound  is  thinned  with  turpentine;  they  usually  contain  a 
little  drier.  They  are  chiefly  used  on  wood,  being  more  durable  and 
more  brilliant  than  oil,  and  are  often  used  over  ptunt  to  preserve  it. 
Asphaltum  is  sometimes  substituted  in  part  or  in  whole  for  the  fossil 
resm,  and  in  this  way  are  made  black  varnishes  which  have  been  used  on 
iron  and  steel  with  good  results.  Asphaltum  and  substances  like  it  have 


g 
bl 


472  IKON    AND   STEEL. 

also  been  simply  dissolved  in  solvents,  as  benzine  or  carbon  disulphidft, 
and  used  for  the  same  purpose. 

All  these  preservative  coatings  are  supposed  to  form  impervious  films, 
keeping  out  air  and  moisture;  but  in  fact  all  are  somewhat  porous.  On 
this  account  it  is  necessary  to  have  a  film  of  appreciable  thickness,  best 
formed  by  successive  coats,  so  that  the  pores  of  one  will  be  closed  by  the 
next.  The  pigment  is  used  to  give  an  agreeable  color,  to  help  fill  the 
tiores  of  the  oil  film,  to  make  the  paint  harder,  so  that  it  will  resist  abra- 
sion, and  to  make  a  thicker  film.  In  varnishes  these  results  are  sought  to 
be  attained  by  the  resin  which  is  dissolved  in  the  oil.  There  is  no  sort  of 
agreement  among  practical  men  as  to  which  coating  is  best  for  any  par- 
ticular case;  this  is  probably  because  so  much  depends  on  the  preparation 
of  the  surface  and  the  care  with  which  the  coating  is  applied,  and  also 
because  the  conditions  of  exposure  vary  so  greatly. 

Methods  of  Application.  —  From  the  surface  of  the  rretal  mud  and 
dirt  must  be  first  removed,  then  any  rusty  spots  must  be  cleaned  thor- 
oughly; loose  scale  may  be  removed  with  wire  brushes,  but  thick  and 
closely  adherent  rust  must  be  removed  with  steel  scrapers,  or  with  hammer 
and  chisel  if  necessary.  The  sand-blast  is  used  largely  and  increasingly 
to  clean  before  painting,  and  is  the  best  method  known.  Pickling  is 
usually  done  with  10%  sulphuric  acid;  the  solution  is  made  more  active 
by  heating.  All  traces  of  acid  must  be  removed  by  washing,  and  the 
metal  must  be  immediately  dried  and  painted.  Less  than  two  coats  of 
paint  should  never  be  used,  and  three  or  four  are  better.  The  first  paint- 
ing of  metal  is  the  most  important.  Paint  is  always  thin  on  angles  and 
edges,  also  on  bolt  and  rivet  heads;  after  the  first  full  coat  apply  a  partial 
or  striping  coat,  covering  the  angles  and  edges  for  at  least  an  inch  back 
from  the  edge,  also  all  bolt  and  rivet  heads.  After  this  is  dry  apply  the 
second  full  coat.  At  least  a  week  should  elapse  between  coats. 

Cast-iron  water  pipes  are  usually  coated  by  dipping  in  a  hot  mixture  of 
coal-tar  and  coal-tar  pitch;  riveted  steel  pipes  by  dipping  in  hot  asphalt 
or  by  a  japan  enamel  which  is  baked  on  at  about  400°  F.  Ships'  bottoms 
are  coated  with  a  varnish  paint  to  prevent  rusting,  over  which  is  a  similar 
paint  containing  a  poison,  as  mercury  chloride,  or  a  copper  compound, 
or  else  for  this  second  coat  a  greasy  copper  soap  is  applied  hot;  this 
prevents  the  accumulation  of  marine  growths.  Galvanized  iron  and  tin 
surfaces  should  be  thoroughly  cleaned  with  benzine  and  scrubbed  before 
painting.  When  new  they  are  partly  covered  with  grease  and  chemicals 
used  in  coating  the  plates,  and  these  must  be  removed  or  the  paint  will 
not  adhere. 

Quantity  of  Paint  for  a  Given  Surface.  —  One  gallon  of  paint  will 
cover  250  to  400  sq.  ft.  as  a  first  coat,  depending  on  the  character  of  the 
surface,  and  from  350  to  500  sq.  ft.  as  a  second  coat. 

Qualities  of  Paints.  —  The  Railroad  and  Engineering  Journal,  vols. 
liv.  and  lv.,  1890  and  1891,  has  a  series  of  articles  on  paint  as  applied  to 
wooden  structures,  its  chemical  nature,  application,  adulteration,  etc.,  by 
Dr.  C.  B.  Dudley,  chemist,  and  F.  N.  Pease,  assistant  chemist,  of  the 
Penna.  R.  R.  They  give  the  results  of  a  long  series  of  experiments  on 
paints  as  applied  to  railway  purposes. 

Inoxydation  Processes.  (Contributed  by  Alfred  Sang,  Pittsburg, 
Pa.,  1908.)  —  The  black  oxide  of  iron  (FesO^  as  a  continuous  coating 
affords  excellent  protection  against  corrosion.  Lavoisier  (1781)  noted  its 
artificial  production  and  its  stable  qualities.  Faraday  (1858)  observed 
the  protective  properties  of  the  coating  formed  by  the  action  of  steam 
in  superheating  tubes.  Berthier  discovered  its  formation  by  the  action 
of  highly  heated  air. 

Bower-Barff  Process.  —  Dr.  Barff  s  method  was  to  heat  articles  to  be 
coated  to  about  1800°  F.  and  inject  steam  heated  to  1000°  F.  into  the 
muffle.  George  and  A.  S.  Bower  used  air  instead  of  steam,  then  carbon 
monoxide  (producer  gas)  to  reduce  the  red  oxide.  In  the  combined 
process,  the  articles  are  heated  to  1600°  F.  in  a  closed  retort;  super- 
heated steam  is  injected  for  20  min.,  then  producer  gas  for  15  to  25  min.; 
the  treatment  can  be  repeated  to  increase  the  depth  of  oxidation.  Less 
heat  is  required  for  wrought  than  for  cast  iron  or  steel.  By  a  later 
improvement,  steam  heated  above  the  temperature  of  the  articles  was 
injected  during  the  last  1  to  2  hours.  By  a  further  improvement  known 
as  the  "  Wells  Process,"  the  work  is  finished  in  one  operation,  the  steam 


PKESERVATIVE   COATINGS  473 

and  producer-gas  being  injected  together.  Articles  are  slightly  in- 
creased in  size  by  the  treatment.  The  surface  is  gray,  changing  to 
black  when  oiled;  it  will  chip  off  if  too  thin;  it  will  take  paint  or  enamel 
and  may  be  polished,  but  can  not  be  either  bent  or  machined;  the 
coating  itself  is  incorrodible  and  resists  sea- water,  mine- water  and  acid 
fumes;  the  strength  of  the  metal  is  slightly  reduced.  The  process  is 
extensively  used  for  small  hardware.  (See  F.  S.  Barff,  Jour.  I.  &  S. 
Inst.,  1877,  p.  356;  A.  S.  Bower,  Trans.  A.  I.  M.  E.,  1882,  p.  329;  B.  H. 
Thwaite,  Proc.  Inst.  C.  E.,  1883,  p.  255;  George  W.  Maynard,  Trans. 
A.  S.  M.  E.,  iv,  351.) 

Gesner  Process. — Dr.  George  W.  Gesner's  process  is  in  commercial 
operation  since  1890.  The  coating  retort  is  kept  at  1200°  F.  for  20 
minutes  after  charging,  then  steam,  partially  decomposed  by  passing 
through  a  red-hot  pipe,  is  allowed  to  act  at  intervals  during  35  min.; 
finally,  a  small  quantity  of  naphtha,  or  other  hydrocarbon,  is  intro- 
duced and  allowed  to  act  for  15  min.  The  work  is  withdrawn  when  the 
heat  has  fallen  to  800°  F.  The  articles  are  neither  increased  in  size  nor 
distorted;  the  loss  of  strength  and  reduction  of  elongation  are  only 
slight.  Large  pieces  can  be  treated.  (See  Jour.  I.  cfe  S.  Inst.,  1890  (ii), 
p.  850;  Iron  Age,  1890,  p.  544.) 

Hydraesfer  Process.-  -An  improvement  of  the  Gesner  process  pat- 
ented by  J.  J.  Bradley  and  in  commercial  operation.  As  its  name  im- 
plies, the  coating  is  thought  to  be  an  alloy  of  hydrogen,  copper,  and  iron. 
The  sulphides  and  phosphides  are  claimed  to  be  burned  out  of  the  sur- 
face of  the  metal  by  the  action  of  hydrogen  at  a  high  temperature 
giving  additional  rust-proof  qualities.  The  appearance  of  the  finished 
work  is  that  of  genuine  Bower-Barffing. 

Russia  and  Planished  Iron. — Russia  iron  is  made  by  cementation 
and  slight  oxidation.  W.  Dewees  Wood  (U.  S.  Pat.  No.  252,166  of 
1882)  treated  planished  sheets  with  hydrocarbon  vapors  or  gas  and 
superheated  steam  within  an  air-tight  and  heated  chamber. 

Niter  Process. — An  old  process  improved  by  Col.  A.  R.  Bufflngton  in 
1884.  The  articles  are  stirred  about  in  a  mixture  of  fused  potassium 
nitrate  (saltpeter)  and  manganese  dioxide,  then  suspended  in  the  vapors 
and  finally  dipped  and  washed  in  boiling  water.  Pure  chemicals  are 
essential.  Used  for  small  arms  and  pieces  which  cannot  stand  the  high 
heat  of  other  processes.  (Trans.  A.  S.  M.  E.,  vol.  vi,  p.  628.) 

Electric  Process. — A.  de  Meritens  connected  polished  articles  as 
anodes  in  a  bath  of  warm  distilled  water  and  used  a  current  as  weak  as 
Could  be  conducted.  A  black  film  of  oxide  was  formed;  too  strong  a 
current  produced  rust.  It  being  essential  that  hydrogen  be  occluded  in 
the  surface  of  the  metal,  it  was  found  necessary,  as  a  rule,  to  connect 
the  articles  as  cathodes  for  a  short  time  previous  to  inoxidation.  (Bull. 
Soc.  Intle.  des  Electr.,  1886,  p.  230.) 

Aluminum  Coatings. — Aluminum  can  be  deposited  electrically,  the 
main  difficulties  being  the  high  voltage  required  and  the  readiness  of  the 
coating  to  redissolve.  The  metal-work  of  the  tower  of  City  Hall,  Phila- 
delphia, was  coated  by  the  Tacony  Iron  &  Metal  Co.,  Tacony,  Pa.,  with 
14  oz.  per  sq.  ft.  of  copper,  on  which  was  deposited  2  Y2  oz.  of  an  alloy  of 
tin  and  aluminum.  The  Reeves  Mfg.  Co.,  Canal  Dover,  Ohio,  makes 
aluminum-coated  conductor  pipes,  etc.,  said  to  be  as  durable  as  copper 
and  as  rust-proof  as  aluminum. 

Galvanizing  is  a  method  of  coating  articles,  usually  of  iron  or  steel, 
with  zinc.  Galvanized  iron  resists  ordinary  corroding  agencies,  the 
zinc  becoming  covered  with  a  film  of  zinc  carbonate,  which  protects  the 
metal  from  further  chemical  action.  The  coating  is,  however,  quickly 
destroyed  by  mine- water,  tunnel  gases,  sea- water  and  conditions  that 
commonly  exist  in  tropical  countries.  If  the  work  is  badly  done  and  the 
coating  does  not  adhere  properly,  and  if  any  acid  from  the  pickle  or  any 
chloride  from  the  flux  remains  on  the  iron,  corrosion  takes  place  under 
the  zinc  coating.  (See  M.  P.  Wood:  Trans.  A.  S.  M.  E.,  xvi.  350.  Al- 
fred Sang:  Trans.  Am.  Foundry  men's  Assoc.,  1907,  Iron  Age,  May  23 
and  30,  1907,  and  Proc.  Eng.  Soc.  of  W.  Penna.,  Nov.,  1907.) 

The  Penna,  R.  R,  Specifications  for  galvanized  sheets  for  car  roofs 


474  IRON   AND   STEEL. 

(1907)  prescribe  that  the  black  sheets  before  galvanizing  should  weigh 
16  oz.  per  sq.  ft.,  the  galvanized  sheet  18  oz.  Sheets  will  not  be  accepted 
if  a  chemical  determination  shows  less  than  1.5  oz.  of  zinc  per  sq.  ft. 

Hot  Galvanizing.  —  The  articles  to  be  galvanized  are  first  cleaned  by 
pickling  and  then  dipped  in  a  solution  of  hydrochloric  acid  and  immersed 
in  a  bath  of  molten  zinc  at  a  temperature  of  from  800  to  900°  F.;  when 
they  have  reached  the  temperature  of  the  bath,  they  are  withdrawn  and 
the  coating  is  set  in  water;  sal-ammoniac  is  used  on  the  pot  as  a  flux, 
either  alone  or  as  an  emulsion  with  glycerine  or  some  other  fatty  medium. 
Wire,  bands  and  similar  articles  are  drawn  continuously  through  the 
bath,  and  may  be  passed  through  asbestos  wipers  to  remove  the  surplus 
metal;  in  this  case  it  is  advisable  to  use  a  very  soft  spelter  free  from  iron. 
If  wire  is  treated  slowly  and  passed  through  charcoal  dust  instead  of 
wipers  the  product  is  known  as  "double-galvanized."  Tin  can  be  added 
to  the  bath  to  help  bring  out  the  spangles,  but  it  gives  a  less  durable 
coating.  Aluminum  is  added  as  a  Zn-Al  alloy,  with  about  20%  Al,  to 
give  fluidity.  Sheets  are  galvanized  continuously,  and  except  in  the 
case  of  so-called  "flux  sheets,"  are  put  through  rolls  as  they  emerge 
from  the  bath,  to  squeeze  off  the  excess  of  zinc  and  improve  the  adherence. 

Test  for  Galvanized  Wire. — Sir  W.  Preece  devised  the  following 
standard  test  for  the  British  Post  Office:  dip  for  one  minute  in  a  saturated 
neutral,  solution  of  sulphate  of  copper,  wash  and  wipe;  to  pass,  the 
material  must  stand  3  dips. 

The  American  standard  test  is  as  follows:  prepare  a  neutral  solution  of 
sulphate  of  copper  of  sp.  gr.  1.185,  dip  for  one  minute,  wash  and  wipe  dry; 
the  wire  must  stand  4  dips  without  a  permanent  coating  of  copper  show- 
ing on  any  part  of  the  wire. 

Galvanizing  by  Cementation;  Sherardizing. — The  alloying  of  metals 
at  temperatures  below  their  melting  points  has  been  known  since  1820 
or  earlier.  Berry  (1838)  invented  a  process  of  depositing  zinc,  in  which 
the  objects  to  be  coated  were  placed  in  a  closed  retort  and  covered  with 
a  mixture  of  charcoal  and  powder  of  zinc;  the  retort  was  heated  to  cherry- 
red  for  a  longer  or  shorter  period,  according  to  the  bulk  of  the  article  and 
to  the  desired  thickness  of  the  coating.  Dumas  gave  iron  articles  a  slight 
coating  of  copper  by  dipping  them  in  a  solution  of  sulphate  of  copper  and 
then  heated  them  in  a  closed  retort  with  oxide  of  zinc  and  charcoal  dust. 
Sheet  steel  cowbells  are  coated  with  brass  by  placing  them  in  a  mixture 
of  finely  divided  brass  and  charcoal  dust  and  heating  them  to  redness  in 
an  air-tight  crucible. 

S.  Cowper-Coles's  process,  known  as  Sherardizing,  patented  in  1902, 
consists  in  packing  the  objects  which  are  to  be  coated  in  zinc  dust  or 
pulverized  zinc  to  which  zinc  oxide  with  a  small  percentage  of  charcoal 
dust  is  added,  and  heating  in  a  closed  retort  to  a  temperature  below  the 
melting  point  of  zinc.  A  large  proportion  of  sand  can  be  used  to  reduce 
the  amount  of  zinc  dust  carried  in  the  retort,  to  prevent  caking  and  give 
a  brighter  finish;  motion  of  the  retort  is  in  most  cases  necessary  to  obtain 
an  even  coating.  The  operation  lasts  from  30  minutes  to  saveral  hours, 
depending  on  the  size  of  the  drum.  Tempered  steel  is  not  affected  by 
the  process,  but  surfaces  are  hardened,  there  being  a  zinc-iron  alloy 
formed  to  a  depth  varying  with  the  time  of  treatment.  This  process  is 
suitable  for  small  work,  giving  a  superior  quality  of  zinc  coating.  (See 
Cowper-Coles,  "  Preservation  and  Ornamentatio'n  of  Iron  and  Steel  Sur- 
faces," Trans.  Soc.  Engrs.  1905,  p.  183;  "Sherardizing,"  Iron  Age, 
1904,  p.  12.  Alfred  Sang,  "Theory  and  Practice  of  Sherardizing," 
El.  Chem.  and  Metall.  Ind.,  May,  1907.) 

Lead  Coatings.  —  Lead  is  a  good  protection  for  iron  and  steel  pro- 
vided it  is  perfectly  gas-tight.  Electrically  deposited  lead  does  not 
bond  well  and  the  coating  is  porous.  Sheets  having  a  light  coating  of 
lead,  produced  by  dipping  in  the  molten  metal,  are  known  as  terne 
plates;  they  have  no  lasting  qualities.  Lead-lined  wrought  pipe,  fittings 
and  valves  are  made  for  conveying  acids  and  Qtber  corroding  liquids. 


STEEL.  475 


STEEL. 

The  Manufacture  of  Steel.  (See  Classification  of  Iron  and  Steel, 
p.  436.)  Cast  steel  is  a  malleable  alloy  of  iron,  cast  from  a  fluid  mass. 
It  is  distinguished  from  cast  iron,  which  is  not  malleable,  by  being  much 
lower  in  carbon,  and  from  wrought  iron,  which  is  welded  from  a  pasty 
mass,  by  being  free  from  intermingled  slag.  Blister  steel  is  a  highly 
carbonized  wrought  iron,  made  by  the  "cementation"  process,  which 
consists  in  keeping  wrought-iron  bars  at  a  red  heat  for  some  days  in 
contact  with  charcoal.  Not  oyer  2%  of  C  is  usually  absorbed.'  The 
surface  of  the  iron  is  covered  with  small  blisters,  supposedly  due  to  the 
action  of  carbon  on  slag.  Other  wrought  steels  were  formerly  made  by 
direct  processes  from  iron  ore,  and  by  the  puddling  process  from  wrought 
iron,  but  these  steels  are  now  replaced  by  cast  steels.  Blister  steel  is, 
however,  still  used  as  a  raw  material  in  the  manufacture  of  crucible  steel. 
Case-hardening  is  a  process  of  surface  cementation. 

Crucible  Steel  is  commonly  made  in  pots  or  crucibles  holding  about 
.  80  pounds  of  metal.  The  raw  material  may  be  steel  scrap;  blister  steel 
bars;  wrought  iron  with  charcoal;  cast  iron  with  wrought  iron  or  with 
iron  9re;  or  any  mixture  that  will  produce  a  metal  having  the  desired 
chemical  constitution.  Manganese  in  some  form  is  usually  added  to 
prevent  oxidation  of  the  iron.  Some  silicon  is  usually  absorbed  from  the 
crucible,  and  carbon  also  if  the  crucible  is  made  of  graphite  and  clay. 
The  crucible  being  covered,  the  steel  is  not  affected  by  the  oxygen  or 
sulphur  in  the  flame.  The  quality  of  crucible  steel  depends  on  the  free- 


elements  which  are  added  in  the  mixture,  or  after  melting,  to  give  par- 
ticular qualities  to  the  steel,  such  as  carbon,  manganese,  chromium, 
tungsten  and  vanadium. 

Bessemer  Steel  is  made  by  blowing  air  through  a  bath  of  melted  pig 
iron.  The  oxygen  of  the  air  first  burns  away  the  silicon,  then  the  carbon, 
and  before  the  carbon  is  entirely  burned  away,  begins  to  burn  the  iron. 
Spiegeleisen  or  ferro-manganese  is  then  added  to  deoxidize  the  metal 
and  to  give  it  the  amount  of  carbon  desired  in  the  finished  steel.  In  the 
ordinary  or  "acid"  Bessemer  process  the  lining  of  the  converter  is  a, 
silicious  material,  which  has  no  effect  on  phosphorus,  and  all  the  phos- 
phorus in  the  pig  iron  remains  in  the  steel.  In  the  "basic"  or  Thomas 
and  Gilchrist  process  the  lining  is  of  magnesian  limestone,  and  limestone- 
additions  are  made  to  the  bath,  so  as  to  keep  the  slag  basic,  and  the  phos- 
phorus enters  the  slag.  By  this  process  ores  that  were  formerly  unsuited 
to  the  manufacture  of  steel  have  been  made  available. 

Open-hearth  Steel.  —  Any  mixture  that  may  be  used  for  making 
steel  in  a  crucible  may  also  be  melted  on  the  open  hearth  of  a  Siemens 
regenerative  furnace,  and  may  be  desiliconized  and  decarbonized  by  the 
action  of  the  flame  and  by  additions  of  iron  ore,  deoxidized  by  the  addi- 
tion of  spiegeleisen  or  ferro-manganese,  and  recarbonized  by  the  same 
additions  or  by  pig  iron.  In  the  most  common  form  of  the  process  pig 
iron  and  scrap  steel  are  melted  together  on  the  hearth,  and  after  the 
manganese  has  been  added  to  the  bath  it  is  tapped  into  the  ladle.  In  the 
Talbot  process  a  large  bath  of  melted  material  is  kept  in  the  furnace, 
melted  pig  iron,  taken  from  a  blast  furnace,  is  added  to  it,  and  iron  ore 
is  added  which  contributes  its  iron  to  the  melted  metal  while  its  oxygen 
decarbonizes  the  pig  iron.  When  the  decarbonization  has  proceeded  far 
enough,  ferro-manganese  is  added  to  destroy  iron  oxide,  and  a  portion 
of  the  metal  is  tapped  out,  leaving  the  remainder  to  receive  another 
charge  of  pig  iron,  and  thus  the  process  is  continued  indefinitely.  In 
the  Duplex  Process  melted  cast  iron  is  desiliconized  in  a  Bessemer  con- 
verter, and  then  run  into  an  open  hearth,  where  the  steel-making  opera- 
tion is  finished. 

The  open -hearth  process,  like  the  Bessemer,  may  be  either  acid  or 
basic,  according  to  the  character  of  the  lining.  The  basic  process  is  a 
dephosphorizing  one,  and  is  the  one  most  generally  available,  as  it  can 
use  pig  irons  that  are  either  low  or  high  in  phosphorus. 


476 


STEEL, 


Belatioh  between  the  Chemical  Composition  and  Physical 
Character  of  Steel. 

W.  R.  Webster  (Trans.  A.  L  M.  #.,  vols.  xxi  and  xxii,  1893-4)  gives  re* 
suits  of  several  hundred  analyses  and  tensile  tests  of  basic  Bessemer  steel 
plates,  and  from  a  study  of  them  draws  conclusions  as  to  the  relation  of 
chemical  composition  to  strength,  the  chief  of  which  are  condensed  as 
follows : 

The  indications  are  that  a  pure  iron,  without  carbon,  phosphorus,  man- 
ganese, silicon,  or  sulphur,  if  it  could  be  obtained,  would  have  a  tensile 
fltrength  of  34,750  Ibs.  per  sq.  in.,  if  tested  in  a  3/8-in.  plate.    With  this  as  a 
base,  a  table  is  constructed  by  adding  the  following  hardening  effects,  as 
shown  by  increase  of  tensile  strength,  for  the  several  elements  named. 
Carbon,  a  constant  effect  of  800  Ibs.  for  each  0.01%. 
Sulphur,  "         500    "      "       "     0.01%. 
Phosphorus,  the  effect  is  higher  in  high-carbon  than  in  low-carbon  steels. 
With  carbon  hun- 
dred ths  % 9        10        11         12        13        14        15         16        17 

Each  0.01%  Phas 

an  effect  of  Ibs..  900    1000    1100    1200    1300.1400    1500    1500     1500 
Manganese,  the  effect  decreases  as  the  per  cent  of  manganese  increases. 

.00   .15  .20  .  .25  .30  .35  .40  .45  .50  .55 

to      to  to  to  to  to  to  to  to  to 

,.15   .20  .25  .30  .35  .40  .45  .50  .55  .65 
Strength  incr. 

forO.01%...  240  240  220  200  180  160  140  120  100  100  Ibs. 
Total  increase 

from  0  Mn. .  .3600  4800  5900  6900  7800  8600  9300  9900  10,400  11,400 

Silicon  is  so  low  in  this  steel  that  its  hardening  effect  has  not  been  con- 
sidered. 

With  the  above  additions  for  carbon  and  phosphorus  the  following  table 
has  been  constructed  (abridged  from  the  original  by  Mr.  Webster).  To 
the  figures  given  the  additions  for  sulphur  and  manganese  should  be  made 
as  above. 

Estimated  Ultimate  Strengths  of  Basic  Bessemer-steel  Plates. 

For  Carbon,  0.06  to  0.24;  Phosphorus,  .00  to  .10;  Manganese  and  Sulphur, 
.00  in  all  cases. 


Mn  being  per 
cent 


Carbon. 

0.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

.22 

.24 

Phos.  .005 

39,950 

41,550 

43,250 

44,950 

46,650 

48,300 

49,900 

51,500 

53,100 

54,700 

.01 

40,350 

41,950 

43,750 

.5,550 

47,350 

49,050 

50,650 

52,250 

53,850 

55,450 

.02 

41,150 

42,750 

44,750 

46,750 

48,750 

50,550 

52,150 

53,750 

55,350 

56,950 

.03 

41,950 

43,550 

45,750 

47,950 

50,150 

52,050 

53,650 

55,250 

56,850 

58,450 

.04 

42,750 

41,350 

46,750 

49,150 

51,550 

53,550 

55,150 

56,750 

58,350 

59,950 

.05 

43,550 

45,150 

47,750 

50,350 

52,950 

55,050 

56,650 

58,250 

59,850 

61,450 

.06 

44,350 

45,950 

48,750 

51,550 

54,350 

56,550 

58,150 

59,750 

61,350 

62,950 

.07 

45,150 

46,750 

49,750 

52,750 

55,750 

58,050 

59,650 

61,250 

62,850 

64,450 

.08 

45,950 

47,550 

50,750 

53,950 

57,150 

59,550 

61,150 

62,750 

64,350 

65,950 

.09 

46,750 

48,350 

51,750 

55,150 

58,550 

61,050 

62,650 

64,250 

65,850 

67,450 

.10 
0.001  P.  = 

47,550 
80  Ibs. 

49,150 
80  Ibs. 

52,750 
100  Ib. 

56,350 
I201b. 

59,950 
1401b. 

62,550 
1501b. 

64,150 
1501b. 

65,750 
1501b. 

67,350 
1501b. 

68,950 
1501b. 

In  all  rolled  steel  the  quality  depends  on  the  size  of  the  bloom  or  ingot 
from  which  it  is  rolled,  the  work  put  on  it,  and  the  temperature  at  which 
it  is  finished,  as  well  as  the  chemical  composition. 

The  above  table  is  based  on  tests  of  plates  3/8inch  thick  and  under  70 
inches  wide;  for  other  plates  Mr.  Webster  gives  the  following  corrections 
for  thickness  and  width.  They  are  made  necessary  only  by  the  effect  of 
thickness  and  width  on  the  finishing  temperature  in  ordinary  practice. 
Steel  is  frequently  spoiled  by  being  finished  at  too  high  a  temperature. 


STEEL.  477 


Thickness,  in   .    . 

3/4* 

ll/16 

5/g 

9/i6 

1/2 

7/i6    [      3/s 

5/i6 

-2000 

-1750 

-1500 

-1250 

-1000 

-500           0 

4-3000 

Correction  (2)  

-1000 

-  750 

-  500 

-  250 

0 

±500|-HOOO 

+5000 

*  And  over.     (1)  Plates  up  to  70  in.  wide.     (2)  Over  70  in.  wide. 

Comparing  the  actual  result  of  tests  of  408  plates  with  the  calculated 
results,  Mr.  Webster  found  the  variation  to  range  as  below. 

Within  Ibs.  1000     2000     3000     4000     5000 

Per  cent..  .28.4     55.1     74.7     89.9     94.9 

The  last  figure  would  indicate  that  if  specifications  were  drawn  calling 
for  steel  plates  not  to  vary  more  than  5000  Ibs.  T.  S.  from  a  specified 
figure  (equal  to  a  total  range  of  10,000  Ibs.),  there  would  be  a  probability 
of  the  rejection  of  5%  of  the  blooms  rolled,  even  if  the  whole  lot  was  made 
from  steel  of  identical  chemical  analysis. 

Campbell's  Formulae.  (H.  H.  Campbell,  The  Manufacture  and  Prop- 
erties of  Iron  and  Steel,  p.  387.)  — 

Acid  steel,    40,000  +  1000  C  4-  1000  P  4-  xMn  =  Ultimate  strength. 
Basic  steel,  41,500  4-    770  C  4-  1000  P  4-  yMn  =  Ultimate  strength. 

The  values  of  xMn  and  yMn  are  given  by  Mr.  Campbell  in  a  table, 
but  they  may  be  found  from  the  formulas  xMn  =  8  CMn  —  320  C  and 
yMn  =  90  Mn  4-  4  CMn  -  2700  -  120  C,  or,  combining  the  formulae 
we  have: 

Ult.  strength,  acid  steel,  40,000  4-  680  C  4-  1000  P  4-  8    CMn. 

basic   "      38,800  4-  650  C  4-  1000  P  +  90  Mn  +  4  CMn, 

In  these  formulae  the  unit  of  each  chemical  element  is  0.01%. 

Examples.  Required  the  tensile  strength  of  two  steels  containing 
respectively  C,  0.10,  P,  0.10,  Mn,  0.30,  and  C,  0.20,  P,  0.10,  Mn,  0.65. 

Answers,  by  Webster,  59,650  and  77,150;  by  Campbell,  57,700  and  72,850. 

Low  Tensile  Strength  of  Very  Pure  Steel .  —  Swedish  nail-rod 
open-hearth  steel,  tested  by  the  author  in  1881,  showed  a  tensile  strength  of 
only  42,591  Ibs.  per  sq.  in.  A  piece  of  American  nail-rod  steel  showed 
45,021  Ibs.  per  sq.  in.  Both  steels  contained  about  0.10  C  and  0.015  P, 
and  were  very  low  in  S,  Mn,  and  Si.  The  pieces  tested  were  bars  about 
2  x  3/8  in.  section. 

R.  A.  Hadfield  (Jour.  Iron  and  Steel  Inst.,  1894)  gives  the  strength  of 
very  pure  Swedish  iron,  remelted  and  tested  as  cast,  45,024  Ibs.  per  sq. 
in.;  remelted  and  forged,  47,040  Ibs.  The  analysis  of  the  cast  bar  was: 
C,  0.08;  Si,  0.04;  S,  0.02;  P,  0.02;  Mn,  0.01;  Fe,  99.82. 

"  Arinco  Ingot  Iron." — A  very  pure  variety  of  open-hearth  steel, 
made  by  the  American  Rolling  Mill  Co.,  Middletown,  Ohio,  has  been 
given  the  trade  name  of  Armco-American  Ingot  Iron.  It  is  claimed 
for  this  product  that  it  resists  corrosion  better  than  any  other  grade  of 
wrought  iron  or  steel.  It  is  used  chiefly  in  sheets.  The  tensile  strength 
is  given  as  38,000  to  44,000  Ib.  per  square  inch;  elastic  limit  one  half 
the  ultimate  strength;  elongation  in  8  inches,  22%.  The  following 
analyses  are  given  to  show  how  Armco  compares  in  composition  with 
other  iron  products: 

S        P        C       Mn     Si      Cu      O       H       N        Fe 

Armco 020  .003     .011   .019   .002   .025  .022   .001   .004  99.893 

Puddled  Iron.  .    .024   .155     .040  .040  .050  .025  .150  .001   .005  99.510 

^  Mild  Steel 050  .070     .115   .500  .005   .055   .023   .002   .009  99.171 

High  Carb.  Steel  .030  .030  1.000  .450  .150  .055  .025  .001  .006  98.253 

Effect  of  Oxygen  upon  Strength  of  Steel.  —  A.  Lantz,  of  the 
Peine  works,  Germany,  in  a  letter  to  Mr.  Webster,  says  that  oxygen  plays 
an  important  role  —  such  that,  given  a  like  content  of  C,  P,  and  Mn,  a 
blow  with  greater  oxygen  content  gives  a  greater  hardness  and  less  ductility 
than  a  blow  with  less  oxygen  content.  The  method  used  for  determin- 
ing oxygen  is  that  9f  Prof.  Ledebur,  given  in  Stahl  und  Eisen,  May,  1892, 
p.  193.  The  variation  in  O  may  make  a  difference  in  strength  01  nearly 
1/2  ton  per  sq.  in.  (Jour.  I.  and  S.  /.,  1894.) 

Electric  Conductivity  of  Steel. — Louis  Campredon  reports  in  Le 
Genie  Civil  [prior  to  1895]  the  results  of  experiments  on  the  electric  resist- 
ance of  steel  wires  of  different  composition,  ranging  from  0.09  to  0.14  C; 
0.21  to  0.54  Mn;  Si,  S,  and  P  low.  The  figures  show  that  the  purer  and 


478 


STEEL. 


softer  the  steel  the  better  is  its  electric  conductivity,  and,  furthermore,  that 
manganese  is  the  element  which  most  influences  the  conductivity.  The 
results  may  be  expressed  by  the  formula  R  =  5.2  +  6.2S  ±  0.3;  in  which 
R  =  relative  resistance,  copper  being  taken  as  1 ,  and  S  =  the  sum  of  the 
percentages  of  C,  P,  S,  Si,  and  Mn.  The  conclusions  are  confirmed  by 
J.  A.  Capp,  in  1903,  Trans.  A.  I.  M.  E.,  vol.  xxxiv,  who  made  forty-five 
experiments  on  steel  of  a  wide  range  of  composition.  His  results  may  be 
expressed  by  the  formula  R  =  5.5  +  4>S>  ±  1.  High  manganese  increases 
the  resistance  at  an  increasing  rate.  Mr.  Capp  proposes  the  following 
specification  for  steel  to  make  a  satisfactory  third  rail,  having  a  resistance 
eight  times  that  of  copper:  0,0.15;  Mn,  0.30;  P,  0.06;  S,  0.06;  Si,  0.05; 
none  of  these  figures  to  De  exceeded. 

Range  of  Variation  in  Strength  of  Bessemer  and  Open-Hearth 
Steels. 

The  Carnegie  Steel  Co.  in  1888  published  a  list  of  1057  tests  of  Bes- 
semer and  open-hearth  steel  from  which  the  following  figures  are  selected 


Kind  of  Steel. 

$ 

Elastic  Limit. 

Ultimate 
Strength. 

Elongation, 
Per  cent 
in  8  In. 

High't. 

Lowest. 

High't. 

Lowest. 

High't. 

Lowest. 

(a)  Bess,  structural  . 
(&)      " 
(c)             angles  .... 
(d)  O.  H.  firebox  .  .  . 
(e)  O.  H.  bridge...  . 

100 
170 
72 
25 
20 

46,570 
47,690 
41.890 

39,230 
39,970 
32,630 

71,300 
73,540 
63,450 
62,790 
69,940 

61,450 
65,200 
56,130 
50,350 
63,970 

33.00 
3.0.25 
34.30 
36.00 
30.00 

23.75 
23.15 
26.25 
25.62 
22.75 

REQUIREMENTS  OF  SPECIFICATIONS. 

a)  E.  L.,  35,000;  T.  S.,  62,000  to  70,000;  elong.,  22%  in  Sin. 

b)  E.  L.,  40,000;  T.  S.,  67,000  to  75,000. 

c)  E.  L.,  30,000;  T.  S.,  56,000  to  64,000;  elong.,  20%  in  8  in. 

d)  T.  S.,  50,000  to  62,000;  elong.,  26%  in  4  in. 

e)  T.  S.,  64,000  to  70,000;  elong.,  20%  in  8  in. 

Bending  Tests  of  Steel.  (Pencoyd  Iron  Works.)  —  Steel  below  0.10  C 
should  be  capable  of  doubling  flat  without  fracture,  after  being  chilled 
from  a  red  heat  in  cold  water.  Steel  of  0.15  C  will  occasionally  submit 
to  the  same  treatment,  but  will  usually  bend  around  a  curve  whose  radius 
is  equal  to  the  thickness  of  the  specimen;  about  90%  of  specimens  stand 
the  latter  bending  test  without  fracture.  As  the  steel  becomes  harder  its 
ability  to  endure  this  bending  test  becomes  more  exceptional,  and  when 
the  carbon  becomes  0.20  little  over  25%  of  specimens  will  stand  the  last- 
described  bending  test.  Steel  having  about  0.40%  C  will  usually  harden 
sufficiently  to  cut  soft  iron  and  maintain  an  edge. 

EFFECT  OF  HEAT  TREATMENT  AND  OF  WORK  ON  STEEL. 

Low  Strength  Due  to  Insufficient  Work.  (A.  E.  Hunt,  Trans. 
A.  I.  M.  E.,  1886.)  —  Soft  steel  ingots,  made  in  the  ordinary  way  for 
boiler  plates,  have  only  from  10,000  to  20,000  Ibs.  tensile  strength  per  sq. 
in.,  an  elongation  of  only  about  10%  in  8  in.,  and  a  reduction  of  area  of 
less  than  20%.  Such  ingots,  properly  heated  and  rolled  down  from  10  in. 
to  1/2  in.  thickness,  will  give  from  55,000  to  65,000  Ibs.  tensile  strength,  an 
elongation  in  8  in.  of  from  23%  to  33%,  and  a  reduction  of  area  of  from 
55%  to  70%.  Any  work  stopping  short  of  the  above  reduction  in  thick- 
ness ordinarily  yields  intermediate  results  in  tensile  tests. 

Effect  of  Finishing  Temperature  in  Rolling.  —  The  strength  and 
ductility  of  steel  depend  to  a  high  degree  upon  fineness  of  grain,  and 
this  may  be  obtained  by  having  the  temperature  of  the  steel  rather  low, 
say  at  a  dull  red  heat,  1300°  to  1400°  F.,  during  the  finishing  stage  of 
rolling.  In  the  manufacture  of  steel  rails  a  great  improvement  in  quality 
has  been  obtained  by  finishing  at  a  low  temperature.  An  indication  of 
the  finishing  temperature  is  the  amount  of  shrinkage  by  cooling  after 
leaving  the  rolls.  The  Phila.  &  Reading  Railway  Co.'s  specification  for 
rails  (1902)  says,  "The  temperature  of  the  ingot  or  bloom  shall  be  such 
that  with  rapid  rolling  and  without  holding  before  or  in  the  finishing 
passes  or  subsequently,  and  without  artificial  cooling  after  leaving  the 


EFFECT  OF  HEAT  TREATMENT  ON  STEEL. 


479 


last  pass,  the  distance  between  the  hot  saws  shall  not  exceed  30  ft.  6  in. 
for  a  30-ft.  rail." 

Fining  the  Grain  by  Annealing.  —  Steel  which  is  coarse-grained 
on  account  of  leaving  the  rolls  at  too  high  a  temperature  may  be  made 
fine-grained  and  have  its  ductility  greatly  increased  without  lowering  its 
tensile  strength  by  reheating  to  a  cherry-red  and  cooling  at  once  in  air. 
(See  paper  on  "Steel  Rails,"  by  Robert  Job,  Trans.  A.  I.  M.  E.t  1902.) 

Effect  of  Cold  Rolling.  —  Cold  rolling  of  iron  and  steel  increases  the 
elastic  limit  and  the  ultimate  strength,  and  decreases  the  ductility. 
Major  Wade's  experiments  on  bars  rolled  and  polished  cold  by  Lauth's 
process  showed  an  average  increase  of  load  required  to  give  a  slight  per- 
manent set  as  follows:  Transverse,  162%;  torsion,  130%;  compression, 
161%  on  short  columns  11/2  in.  long,  and  64%  on  columns  8  in.  long; 
tension,  95%.  The  hardness,  as  measured  by  the  weight  required  to 
produce  equal  indentations,  was  increased  50%;  and  it  was  found  that 
the  hardness  was  as  great  in  the  center  of  the  bars  as  elsewhere.  Sir 
W.  Fairbairn's  experiments  showed  an  increase  in  ultimate  tensile 
strength  of  50%,  and  a  reduct  on  in  the  elongation  in  10  in.  from  2  in. 
or  20 %  to  0.79  in.  or  7.9 % . 

Effect  of  Heat  Treatment  of  a  Motor-truck  Axle. — (John  Younger, 
Trans.,  A.  S.  M.  E.,  1915.) — Shafts  21/4  in.  diam.  whose  analysis  was 
approximately  C,.0.20;  Cr,  1.5;  Mn,  0.30;  Ni,  4.00;  Si,  0.20;  P  and  S 
below  0.04;  elastic  limit,  90,000;  tensile  strength,  105,000;  reduction  in 
area,  66%;  elongation  in  2  in.,  25%,  were  found  to  break  in  service. 
The  maximum  power  transmittted  was  about  33  H.P.  at  27  r.p.m 
Experiments  were  made  with  heat  treatment  to  raise  the  elastic  limit. 
The  material  selected  had  C,  0.30;  Mn,  0.50;  Cr,  1.5;  Ni,  3.5.  After 
heat  treatment  the  elastic  limit  was  175,000  Ib.  per  sq.  in.;  tensile 
strength,  185,000;  elongation  in  2  in.,  14  % ;  reduction  of  area,  53  %.  The 
shafts  are  machined  from  hot-rolled  bars  already  heat-treated  to  show 
an  elastic  limit  of  about  100,000.  They  are  then  heated  to  between 
1450°  and  1500°  F.  and  quenched  in  oil,  then  reheated  to  a  little  over 
700°  F.  and  cooled  slowly  in  air.  They  warped  slightly,  but  were 
straightened  when  hot  under  a  press.  The  Brinell  hardness  after 
treatment  was  402  to  444.  Not  one  of  the  shafts  thus  treated  has 
broken  in  service.  Other  steels,  such  as  5%  nickel  steels,  chrome- 
vanadium  steels,  and  air-hardening  steels  have  been  tried,  and  all  have 
been  standing  up  to  service.  The  success  seems  to  be  due  entirely  to 
the  high  elastic  limit.  The  Brinell  hardness  test  is  an  unfailing  indication 
of  the  success  or  non-success  of  the  heat  treatment. 

Effect  of  Annealing  on  Rolled  Bars.  (Campbell,  Mfr.  of  Iron  and 
Steel, 'p.  275.) 


Ultimate 
Strength. 

Elastic 
Limit 

Elong.  in 
8  in.,  %. 

Red.  Area, 

Elas. 
Ratio. 

Natural. 

An- 
nealed. 

Nat- 
ural. 

An- 
nealed. 

Nat- 
ural. 

An- 
nealed. 

Nat- 
ural. 

An- 
nealed. 

Nat- 
ural. 

An- 
nealed* 

d^  T58.568 
HI  I  62,187 
-^0}  70,530 
M  176,616 
co.5  (  58,130 
«  J  J  62,089 
X«  1  69,420 
<N.S  (  75,865 

54,098 
58,364 
65,500 
69,402 
51,418 
55,021 
60,850 
67,618 

40,300 
42,606 
49,000 
51,108 
40,400 
42,441 
45,090 
49,691 

31,823 
35,120 
37,685 
40,505 
30,393 
31,576- 
34,000 
39,403 

29.7 
28.0 
26.9 
24.5 
30.1 
30.1 
25.6 
24.7 

28.8 
28.6 
23.4 
23.0 
31.1 
30.4 
26.5 
26.3 

60.8 
62.2 
61.1 
53.7 
61.8 
60.9 
59.3 
54.4 

62.7 
63.5 
55.3 
56.5 
60.5 
60.0 
52.  1 
51.4 

68.8 
68.5 
69.5 
66.7 
69.5 
68.4 
65.0 
65.5 

58.8 
60.2 
57.5 
58.4 
59.1 
57.4 
55.9 
58.3 

The  bars  were  rolled  from  4  X  4-in.  billets  of  open-hearth  steel.  The 
figures  are  averages  of  from  2  to  12  tests  of  each  heat.  In  annealing  the 
bars  were  heated  in  a  muffle  and  withdrawn  when  they  had  reached  a 
dull  yellow  heat. 

Hardening  of  Soft  Steel.  —  A.  E.  Hunt  (Trans.  A.  I.  M.  E.,  1883,  vol. 
xii)  says  that  soft  steel,  no  matter  how  low  in  carbon,  will  harden  to  a  cer- 
tain extent  upon  being  heated  red-hot  and  plunged  into  water,  and  that  it 
hardens  more  when  plunged  into  brine  and  less  when  quenched  in  oil. 

A  heat  of  open-hearth  steel  of  0.15%  C  and  0.29%  Mn  gave  the  follow- 
ing results  upon  test-pieces  from  the  same  14  in.  thick  plate. 


480  STEEL. 

Unhardened T.  S.  55,000  El.  in  8  in.  27%  Red.  of  Area  62% 

Hardened  in  water 74,000  25%  50% 

Hardened  in  brine "     84,000  "          22%  43% 

Hardened  in  oil '     67,000  26%  49% 

The  greatly  increased  tenacity  after  hardening  indicates  that  there  must 
be  a  considerable  molecular  change  in  the  steel  thus  hardened,  and  that 
if  such  a  hardening  should  be  created  locally  in  a  steel  plate,  there  must 
be  very  dangerous  internal  strains  caused  thereby. 

Comparative  Tests  of  Full-sized  Eye-bars  and  Small  Samples. 
(G.  G.  S.  Morison,  A.  S.  C.  E.,  1893.)  — 17  full-sized  eye-bars,  of  the  steel 
used  in  the  Memphis  bridge,  sections  10  in.  wide  X  1  to  23/iQ  in.  thick,  and 
sample  bars  from  the  same  melts.  Average  results: 

Eye-bars:  E.  L.,  32,350;  T.  S.,  63,330;  El.  in  full  length,  13.7%;  Red. 
of  area,  36.3%. 

Small  bars:  E.  L.,  40,650;  T.  S.,  71,640;  El.  in  8  ins.,  26.2%;  Red. 
of  area,  46.7%. 

"  Kecalescence  "  of  Steel.  —  If  we  heat  a  bar  of  copper  by  a  flame 
of  constant  strength,  and  note  carefully  the  interval  of  time  occupied  in 
passing  from  each  degree  to  the  next  higher  degree,  we  find  that  these  in- 
tervals increase  regularly,  i.e.,  that  the  bar  heats  more  and  more  slowly, 
as  its  temperature  approaches  that  of  the  flame.  If  we  substitute  a  bar  of 
steel  for  one  of  copper,  we  find  that  these  intervals  increase  regularly  up 
to  a  certain  point,  when  the  rise  of  temperature  is  suddenly  and  in  most 
cases  greatly  retarded  or  even  completely  arrested.  After  this  the  regular 
rise  of  temperature  is  resumed,  though  other  like  retardations  may  recur 
as  the  temperature  rises  farther.  So  if  we  cooi  a  bar  of  steel  slowly  the 
fall  of  temperature  is  greatly  retarded  when  it  reaches  a  certain  point  in 
dull  redness.  If  the  steel  contains  much  carbon,  and  if  certain  favoring 
conditions  be  maintained,  the  temperature,  after  descending  regularly, 
suddenly  rises  spontaneously  very  abruptly,  remains  stationary  a  while 
and  then  redescends.  This  spontaneous  reheating  is  known  as  "  recales- 
cence." 

These  retardations  indicate  that  some  change  which  absorbs  or  evolves 
heat  occurs  within  the  metal.  A  retardation  while  the  temperature  is 
rising  points  to  a  change  which  absorbs  heat;  a  retardation  during  cooling 
points  to  some  change  which  evolves  heat.  (Henry  M.  Howe,  on  "Heat 
Treatment  of  Steel,"  Trans.  A.  L  M.  E.,  vol.  xxii.) 

Critical  Point.  (Campbell,  p.  287.)  —  If  a  piece  of  steel  containing  over 
0.50  C  be  allowed  to  cool  slowly  from  a  high  temperature  the  cooling  at 
first  proceeds  at  a  uniformly  retarded  rate,  but  when  about  700°  C.  is 
reached  there  is  an  interruption  of  this  regularity.  In  some  cases  the 
rate  of  cooling  may  be  very  slow,  in  other  cases  the  bar  may  not  decrease 
in  temperature  at  all,  while  in  still  other  cases  the  bar  may  actually  grow 
hotter  for  a  moment.  When  this  "  critical  point  "  is  passed,  the  bar  cools 
as  before  until  it  reaches  the  temperature  of  the  atmosphere. 

In  metallography  such  a  critical  point  is  denoted  by  the  letter  A,  and 
the  particular  one  just  described  is  known  as  Ar.  In  heating  a  piece  of 
steel  an  opposite  phenomenon  is  observed,  there  being  an  absorption  of 
heat  by  internal  molecular  actipn,  with  a  consequent  retardation  in  the 
rise  of  temperature,  and  this  point,  which  is  some  30°  C.  higher  than  Ar, 
is  called  Ac. 

In  soft  steels,  below  0.30  C,  three  critical  points  are  found  in  cooling  a 
bar  from  a  high  temperature,  called  Ar3,  Ar2,  Ari,  Art  being  the  lowest, 
and  in  heating  the  bar  there  are  also  three  points,  Aci,  Ac2,  Ac3,  the  first 
named  being  the  lowest.  At  each  of  the  points  there  is  a  change  in  the 
micro-structure  of  the  steel. 

Metallography. — This  is  a  name  given  to  a  study  of  the  micro-structure 
of  metals.  The  steel  metallographist  designates  the  different  structures 
that  are  found  in  a  polished  and  etched  section  by  the  names  austenite, 
martensite,  pearlite,  cementite,  ferrite,  troostite,  and  sorbite.  Austenite 
is  produced  by  quenching  steel  of  over  1.40  C  in  ice  water  from  above 
1050°  C.  Martensite  is  produced  by  quenching  this  steel  from  tempera- 
tures between  1050°  C.  and  Ari.  It  is  also  found  together  with  cementite 
or  ferrite  in  carbon  steels  below  1.30  C  quenched  at  any  point  above  Ar^ 
It  is  the  constituent  which  confers  hardness  on  steel.  In  steels  cooled 
slowly  to  below  Ari  the  structure  is  composed  entirely  of  ferrite,  or 
entirely  of  pearlite,  or  of  pearlite  mixed  with  ferrite  or  cementite.  Ferrite 


EFFECT  OF  HEAT  TREATMENT  ON  STEEL. 


481 


Is  iron  free  from  carbon  and  forms  almost  the  whole  of  a  low-carboiT  steel, 
while  cementite  is  considered  to  be  a  compound  of  iron  and  carbon,  FesC, 
the  C  of  this  form  being  known  as  cement  carbon.  Pearlite  is  an  inti- 
mate mixture  of  definite  proportions  of  ferrite  and  cementite,  corre- 
sponding to  a  pure  steel  of  about  0.80  C,  which,  unhardened,  consists  of 
pearlite  alone.  Steels  lower  in  C  contain  pearlite  with  ferrite,  and  steels 
higher  in  C  contain  pearlite  and  cementite.  Troostite  is  a  structure  found 
when  steel  is  quenched  while  cooling  through  the  critical  range,  and 
sorbite  when  it  is  quenched  at  the  end  of  the  critical  range.  Quenching 
in  lead  or  reheating  quenched  steel  to  a  purple  tint  may  also  produce 
sorbite.  (Campbell,  p.  296.) 

Effect  of  Work  on  the  Structure  of  Soft  and  Medium  Steel.  —  Steel 
as  usually  cast,  cooling  slowly,  forms  in  crystals  or  grains.  Rolling  tends 
to  break  up  this  grain,  but  immediately  after  the  cessation  of  work  the 
formation  of  grains  begins  and  continues  until  the  metal  has  copied  to 
the  lower  critical  point.  Hence  the  lower  the  temperature  to  which  the 
steel  is  worked,  the  more  broken  up  the  structure  will  be,  but  on  the 
other  hand  if  the  rolling  be  continued  below  the  critical  point,  the  effect 
of  cold  work  will  be  shown  and  strains  will  be  set  up  which  will  make  the 
piece  unfit  for  use  without  annealing. 

Effect  of  Heat  Treatment.  —  In  heating  steel  through  the  lowest 
critical  point  the  crystalline  structure  is  obliterated,  the  metal  assuming  the 
finest  condition  of  which  it  is  capable.  Above  this  point  the  size  of  grain 
increases  with  the  temperature. 

Effect  of  Heating  on  Crucible  Steel.  (W.  Campbell,  Proc.  A.S.T.  M., 
vi,  213.) — Six  steels,  containing  carbon  as  follows:  (1)  2.04,  (2)  1.94, 
(3)  1.72,  (4)  1.61,  (5)  1.04,  and  (6)  0.70,  were  heated  in  a  small  gas 
furnace  to  the  temperatures  given  in  the  table  and  allowed  to  cool 
slowly  in  the  furnace,  and  were  then  tested,  with  results  as  below. 


As 
Rolled 

650° 
C 

715° 
C 

760° 
C 

800° 
C 

855° 
C 

905° 
C 

950° 
C 

1070° 
C 

1200° 
C 

(1)  T.S.. 

144000 

115400 

114500 

98800 

95650 

93800 

95250 

95200 

99000 

57400 

E.L  

104200 

84600 

83900 

57700 

57800 

55500 

55350 

49350 

49600 

56000 

El.  in  2  in 

4.0 

6.0 

7.0 

11.5 

12.5 

12.0 

11.5 

6.0 

4.5 

1.0 

(2)  T.S.. 

146400 

115200 

104100 

95000 

92000 

89000 

95350 

91800 

97000 

61350 

E.L  

91000 

91500 

72600 

68650 

50500 

51000 

49450 

49800 

41750 

47000 

El.  in  2  in 

6.3 

8.0 

9.5 

15.0 

17.0 

12.5 

7.0 

9.5 

8.5 

2.0 

(3)  T.S.. 

153100 

126000 

114100 

100300 

98000 

94000 

94350 

95000 

92350 

65300 

E.L  

98100 

78300 

75700 

50500 

48750 

47900 

48600 

45200 

43100 

50600 

El.  in  2  in 

7.2 

8.0 

11.5 

16.5 

10.0 

13.5 

11.0 

7.5 

6.0 

2.0 

(4)  T.  S.  . 

157700 

128100 

117000 

98650 

97700 

95000 

97350 

96350 

94400 

69800 

E.L  

105200 

85300 

81300 

52300 

53350 

51350 

51350 

48500 

51400 

El.  in  2  in 

6  5 

14  5 

18  5 

15  0 

11  5 

7  5 

3  5 

30 

(5)  T.S.. 

141100 

105400 

97800 

86800 

96600 

111800 

115900 

111500 

106100 

112600 

EL 

75800 

57700 

55200 

44850 

46600 

47200 

50600 

46800 

56500 

89600 

El.  in  2  in. 

12.8 

18.0 

22.0 

26.5 

19.0 

13.0 

13.0 

10.5 

11.0 

11.5 

(6)  T.S... 

117000 

95200 

88700 

85600 

94300 

91350 

90300 

90500 

89500 

90000 

E.  L 

64700 

53250 

49700 

40200 

42150 

42100 

41400 

39700 

57350 

58500 

El.  in  2  in. 

17.0 

23.0 

27.5 

27.0 

19.0 

18.5 

18.0 

16.5 

18.0 

16.0 

The  critical  points  Ari  and  Aci  were  determined,  and  the  six  steels  gave 
practically  identical  results;  thus  Art  ranged  from  696  to  708,  averaging 
704°  C.,  and  Act  ranged  from  730  to  737,  averaging  733°  C. 

The  temperatures  at  which  the  finest-grained  and  a  very  coarse-grained 
fracture  were  found  are  as  follows: 

Steel  No 123  456 

Finest  fracture 800       760     715-760       760     715     715°  C 

Very  coarse  fracture 1070     1070         1070       1070     855     800°  O 

Mr.  Campbell's  paper  gives  a  list  of  fourteen  papers  by  different  authori- 
ties on  the  micro-structure  and  the  heat  treatment  of  steel. 

Burning,  Overheating,  and  Restoring  Steel.  (G.  B.  Waterhouse, 
A.  S.  T,  M.,  vi,  247.) — Burnt  metal  is  defined  as  coarsely  crystalline  and 
exceedingly  brittle  iron  or  steel,  in  consequence  of  excessive  heating, 
often  with  some  layers  of  oxide  of  iron.  It  cannot  be  effectively  restored 
by  heat  treatment  or  mechanical  work.  Overheated  metal  is  coarsely 
crystalline  from  excessive  heating,  but  with,  no  inter-crystalline  spaces. 
It  oan  be  restored  by  heat  treatment  or  mechanical  worfc.  Seven  lots  of 


'482 


STEEL: 


nickel  steel  bars,  containing  3.8%  Ni,  and  C  as  in  the  table, 
to  various  temperatures  in  a  muffle  furnace,  with  results  as 


were  heated 
below. 


%c. 

Heated  to.  .  , 

lOOOa 

lOOOb 

llOOb 

1200b 

13COb 

1200c 

1200d 

0  41 

T.  S.  .  .  . 

90245 

71800 

71700 

74000 

71320 

71487 

74989 

El.  %  in  2  in... 

26  0 

26  0 

25  5 

11  0 

7  0 

10  5 

25  0 

0.51 

T.S  

99109 

78600 

78800 

84900 

79600 

81487 

80795 

El.  %  in  2  in... 

21  0 

25  0 

24  0 

11  5 

5  0 

15  5 

22  5 

0.63 

11542! 

89000 

89400 

99600 

85200 

96040 

89842 

El.  %  in  2  in  

16  5 

20  5 

19  0 

7  0 

2  0 

10  0 

21  0 

0,79 

135194 

108960 

111840 

109600 

66800 

102705 

90214 

El.  %  in  2  in... 

14  0 

15  0 

14  0 

3  0 

0  5 

6  0 

21  0 

0.97 

T.S.... 

156827 

130336 

138112 

83117 

46648 

114107 

103476 

El.  %  in  2  in.... 

7  5 

3  5 

0  5 

0  0 

5  5 

18  0 

1,24 

T.S.....  

168697 

97510 

98183 

90729 

60600 

95103 

106304 

El.  in  2  in... 

3  5 

15  0 

1  0 

0  5 

0  0 

1  5 

3  5 

f  48 

T.  S... 

145642 

63950 

66640 

97894 

35480 

89045 

74592 

El.  in  2  in  

10.5 

23.6 

25.0 

8.0 

1.0 

17.5 

24.0 

a.  Heated  to  1000  C.,  which  took  1  hr.  25  min.,  held  tnere  25  mm.  and 
cooled  in  air.  b.  The  time  required  to  heat  to  the  temperatures  named 
was  respectively  1  h.  10  m.,  1  h.  45  m.,  2  h.  35  m.,  and  2  h.  35  m.  The 
bars  were  kept  at  the  desired  temperature  for  an  hour  and  then  cooled 
slowly  in  place,  c.  Reheated  to  700  C.  d.  Reheated  to  775  C. 

In  the  steels  below  1%  C  heating  to  1200°  is  accompanied  by  an  increase 
in  ultimate  strength  and  a  drop  in  ductility.  Heating  above  1200°  pro- 
duces a  very  coarse  crystallization  and  a  great  loss  in  strength  and 
ductility.  Reheating  the  overheated  bars  to  700°  does  not  materially 
affect  their  structure,  but  reheating  to  775°  restores  the  structure  nearly 
to  that  found  before  overheating,  and  completely  restores  the  ductility. 
Similar  results  are  found  with  carbon  steel. 

Working  Steel  at  a  Blue  Heat.  —  Not  only  are  wrought  iron  and 
Bteelmuch  more  brittle  at  a  blue  heat  (i.e.,  the  heat  that  would  produce  an 
oxide  coating  ranging  from  light  straw  to  blue  on  bright  steel,  430°  to 
600°  F.),  but  while  they  are  probably  not  seriously  affected  by  simple 
exposure  to  blueness,  even  if  prolonged,  yet  if  they  be  worked  in  this  range 
of  temperature  they  remain  extremely  brittle  after  cooling,  and  may 
Indeed  be  more  brittle  than  when  at  blueness;  this  last  point,  however, 
is  not  certain.  (Howe,  Metallurgy  of  Steel,  p.  534.) 

Tests  by  Prof.  Krohn,  for  the  German  State  Railways,  show  that  wprk- 
ing  at  blue  heat  has  a  decided  influence  on  all  materials  tested,  the  injury 
done  being  greater  on  wrought  iron  and  harder  steel  than  on  the  softer 
Bteel.  The  fact  that  wrought  iron  is  injured  by  working  at  a  blue  heat 
was  reported  by  Stromeyer.  (Engineering  News,  Jan.  9,  1892.) 

A  practice  among  boiler-makers  for  guarding  against  failures  due  to 
working  at  a  blue  heat  consists  in  the  cessation  of  work  as  soon  as  a  plate 
which  had  been  red-hot  becomes  so  cool  that  the  mark  produced  by 
rubbing  a  hammer-handle  or  other  piece  of  wood  will  not  glow.  A  plate 
which  is  not  hot  enough  to  produce  this  effect,  yet  too  hot  to  be  touched 
by  the  hand,  is  most  probably  blue  hot,  and  should  under  no  circumstances 
be  hammered  or  bent.  (C.  E.  Stromeyer,  Proc.  Inst.  C.  E.,  1886.) 

Oil-tempering  and  Annealing  of  Steel  Forcings.  —  H.  F.  J.  Porter 
says  (1897)  that  all  steel  forgings  above  0.1%  carbon  should  be  annealed, 
to  relieve  them  of  forging  and  annealing  strains,  and  that  the  process 
of  annealing  reduces  the  elastic  limit  to  47%  of  the  ultimate  strength. 
Oil-tempering  should  only  be  practiced  on  thin  sections,  and  large  forgings 
should  be  hollow  for  the  purpose.  This  process  raises  the  elastic  limit 
above  50%  of  the  ultimate  tensile  strength,  and  in  some  alloys  of  steel, 
notably  nickel  steel,  will  bring  it  up  to  60%  of  the  ultimate. 

Heat  Treatment  of  Armor  Plates.  (Hadfleld  Process,  Iron  Tr. 
Rev.,  Dec.  7,  1905.)  —  A  cast  armor  plate  of  nickel-chromium  steel  is 
heated  to  from  950°  C.  to  1100°  C.,  then  cooled,  preferably  in  air,  then 
reheated  to  about  700°  and  cooled  slowly,  preferably  in  the  furnace  m 
which  the  heating  was  previously  effected,  again  heated  to  about  700° 
and  allowed  to  cool  slowly  to  640°  C.,  whereupon  it  is  suddenly  cooled  by 
spraying  with  water  or  by  an  air  blast,  but  preferably  in  water.  It  is 
then  reheated  to  about  600°  and  again  suddenly  cooled,  preferably  by 
quenching  in  water.  Steel  treated  as  described  is  suitable  for  armor 
plates  and  other  articles  including  parts  of  safes,  Satisfactory  results 


TKEATMENT  OF  STRUCTURAL  STEEL.  483 

have  been  obtained  by  thus  treating  cast  6-in.  armor  plates  containing 
about  0.3  to  0.4  C,  0.25  Mn,  1.8  Cr,  and  3.3  Ni  cast  in  a  sand  mold. 
Such  a  6-in.  plate  attacked  by  armor-piercing  projectiles  of  4.7-in.  and 
6-in.  calibers,  stood  over  15,000  foot-tons  of  energy  without  showing  a 
crack.  Also  a  4-in.  plate  treated  as  described  and  having  a  carbonized 
or  cemented  face  has  withstood  the  attack  of  a  5.7-in.  armor-piercing  shell. 

Brittleness  Due  to  Long-continued  Heating.  If  low-carbon  steel, 
(say  under  0.15%)  is  held  for  a  very  long  time  at  temperatures  between 
500  and  750°  C.  (930  and  1380°  F.),  the  crystals  become  enormous  and 
the  steel  loses  a  large  part  of  its  strength  and  ductility.  It  takes  a  long  time, 
in  fact  days,  to  produce  this  effect  to  any  alarming  degree,  so  that  it  is 
not  liable  to  occur  during  manufacture  or  mechanical  treatment,  but 
steel  is  sometimes  placed  in  positions  where  it  may  suffer  this  injury,  for 
example,  in  the  case  of  the  tie-rods  of  furnaces,  supports  of  boilers,  etc., 
so  that  the  danger  should  be  borne  in  mind  by  all  engineers  and  users  of 
steel.  A  wrought-iron  chain  that  supported  one  side  of  a  50-ton  open- 
hearth  ladle,  which  was  heated  many  times  to  a  temperature  above  500°  C., 
finally  reached  a  condition  of  coarse  crystallization,  so  that  it  was  unable 
to  bear  the  strain  upon  it.  This  phenomenon  ol  coarse  crystallization  in 
low-carbon  steel  is  known  as  "Stead's  Brittleness,"  after  J.  E.  Stead,  who 
has  explained  its  cause.  The  effect  seems  to  begin  at  a  temperature  of 
about  500°  C.  and  proceeds  more  rapidly  with. an  increase  in  temperature 
until  we  reach  750°  C.  The  damage  may  be  repaired  completely  by  heat- 
ing the  steel  to  a  temperature  between  800  and  900°  C.  The  remedy  is 
the  same  as  that  for  coarse  crystallization,  due  to  overheating,  and  all 
steel  which  is  placed  in  positions  where  it  is  liable  to  reach  these  tempera- 
tures frequently  should  be  restored  at  intervals  of  a  week  or  a  month,  or 
as  often  as  may  be  necessary.  (Stoughton.) 

Surface  Decarburization  of  Steel  Heated  in  Melted  Salts. — A.  M. 
Portevin  (Proc.  Iron  &  Steel  Inst.,  1914.  Eng'g,  Oct.  9,  1914)  shows 
that  the  surface  layer  of  steel,  to  a  depth  which  varies  with  time  and 
temperature,  is  greatly  reduced  in  carbon  when  the  steel  is  heated  in 
a  bath  of  molten  alkaline  salts.  In  a  steel  containing  0.78  %  C  heated 
in  melted  potassium  chloride  at  900°  C.,  the  C  at  the  surface  was  re- 
duced in  1/4  hour  to  0.5,  in  2  hours  to  0.3,  and  in  5  hours  to  0.15,  the 
thickness  of  the  decarburized  layer  being  for  1/4,  2,  and  5  hours  heating, 
respectively,  0.1,  0.2,  and  0.3  mm.  When  cyanide  and  cyanate  of 
potassium  were  added  to  the  chloride  decarburization  and  recarburiza- 
tion  took  place  simultaneously,  the  percentage  of  carbon  at  the  surface 
being  0.25  at  the  end  of  both  1/4  hour  and  5  hours,  the  thickness  of  the 
decarburized  layer  increasing  from  0.06  mm.  to  0.69  mm. 

Influence  of  Annealing  upon  Magnetic  Capacity. 

Prof.  D.  E.  Hughes  (Eng'g,  Feb.  8,  1884,  p.  130)  has  invented  a  "Mag- 
netic Balance,"  for  testing  the  condition  of  iron  and  steel,  which  consists 
chiefly  of  a  delicate  magnetic  needle  suspended  over  a  graduated  circular 
index,  and  a  magnet  coil  for  magnetizing  the  bar  to  be  tested.  He  nnda 
that  the  following  laws  hold  with  every  variety  of  iron  and  steel: 

1.  The  magnetic  capacity  is  directly  proportional  to  the  softness,  or 
molecular  freedom. 

2.  The  resistance  to  a  feeble  external  magnetizing  force  is  directly  as 
the  hardness,  or  molecular  rigidity. 

The  magnetic  balance  shows  that  annealing  not  only  produces  softness 
in  iron,  and  consequent  molecular  freedom,  but  it  entirely  frees  it  from 
all  strains  previously  introduced  by  drawing  or  hammering.  Thus  a  bar 
of  iron  drawn  or  hammered  has  a  peculiar  structure,  say  a  fibrous  one, 
which  gives  a  greater  mechanical  strength  in  one  direction  than  another. 
This  bar,  if  thoroughly  annealed  at  high  temperatures,  becomes  homo- 
geneous in  all  directions,  and  has  no  longer  even  traces  of  its  previous 
strains,  provided  that  there  has  been  no  actual  separation  into  a  distinct 
series  of  fibers. 

TREATMENT  OF  STRUCTURAL  STEEL. 
(James  Christie,  Trans.  A.  S.  C.  E.,  1893.) 

Effect  of  Punching  and  Shearing.  —  The  physical  effects  of  punching 
and  shearing  as  denoted  by  tensile  test  are  for  iron  or  steel: 

Reduction  of  ductility;  elevation  of  tensile  strength  at  elastic  limit; 
reduction  of  ultimate  tensile  strength. 
*•     In  very  thin  material  the  disturbance  described  is  less  than  in  thick; 


484  STEEL. 

In  fact,  a  degree  of  thinness  is  reached  where  this  disturbance  practi- 
cally ceases.  On  the  contrary,  as  thickness  is  increased  the  injury  becomes 
more  evident. 

The  effects  described  do  not  invariably  ensue;  for  unknown  reasons  there 
are  sometimes  marked  deviations  from  what  seems  to  be  a  general  result. 

By  thoroughly  annealing  sheared  or  punched  steels  the  ductility  is  to  a 
large  extent  restored  and  the  exaggerated  elastic  limit  reduced,  the  change 
being  modified  by  the  temperature  of  reheating  and  the  method  of  cooling. 

It  is  probable  that  the  best  results  combined  with  least  expenditure  can 
be  obtained  by  punching  all  holes  where  vital  strains  are  not  transferred  by 
the  rivets,  and  by  reaming  for  important  joints  where  strains  on  riveted 
joints  are  vital,  or  wherever  perforation  may  reduce  sections  to  a  mini- 
mum. The  reaming  should  be  sufficient  to  thoroughly  remove  the  mate- 
.rial  disturbed  by  punching;  to  accomplish  this  it  is  best  to  enlarge  punched 
holes  at  least  1/8  m.  diameter  with  the  reamer. 

Riveting.  —  It  is  the  current  practice  to  perforate  holes  Vie  in.  larger 
than  the  rivet  diameter.  For  work  to  be  reamed  it  is  also  a  usual  require- 
ment to  punch  the  holes  from  l/g  to  3/16  in.  less  than  the  finished  diameter, 
the  holes  being  reamed  to  the  proper  size  after  the  various  parts  are 
assembled. 

It  is  also  excellent  practice  to  remove  the  sharp  corner  at  both  ends  of 
the  reamed  holes,  so  that  a  fillet  will  be  formed  at  the  junction  of  the  body 
and  head  of  the  finished  rivets. 

The  rivets  of  either  iron  or  mild  steel  should  be  heated  to  a  bright  red  or 
yellow  heat  and  subjected  to  a  pressure  of  not  less  than  50  tons  per  square 
inch  of  sectional  area. 

For  rivets  of  ordinary  length  this  pressure  has  been  found  sufficient  to 
completely  fill  the  hole.  If,  however,  the  holes  and  the  rivets  are  excep- 
tionally long,  a  greater  pressure  and  a  slower  movement  of  the  closing  tool 
than  is  used  for  shorter  rivets  has  been  found  advantageous. 

Welding.  —  No  welding  should  be  allowed  on  any  steel  that  enters  into 
structures.  [See  page  487.] 

Upsetting.  —  Enlarged  ends  on  tension  bars  for  screw-threads,  eye- 
bars,  etc.,  are  formed  by  upsetting  the  material.  With  proper  treatment 
and  a  sufficient  increment  of  enlarged  sectional  area  over  the  body  of 
the  bar  the  result  is  entirely  satisfactory.  The  upsetting  process  should 
be  performed  so  that  the  properly  heated  metal  is  compelled  to  flow 
without  folding  or  lapping. 

Annealing.  —  The  object  of  annealing  structural  steel  is  for  the  pur- 

Eose  of  securing  homogeneity  of  structure  that  is  supposed  to  be  impaired 
y  unequal  heating,  or  by  the  manipulation  necessarily  attendant  on 
certain  processes.  The  objects  to  be  annealed  should  be  heated  through- 
out to  a  uniform  temperature  and  uniformly  cooled. 

The  physical  effects  of  annealing,  as  indicated  by  tensile  tests,  depend 
on  the  grade  of  steel,  or  the  amount  of  hardening  elements  associated  with 
it;  also  on  the  temperature  to  which  the  steel  is  raised,  and  the  method 
or  rate  of  cooling  the  heated  material. 

The  physical  effects  of  annealing  medium-grade  steel,  as  indicated  by 
tensile  test,  are  reported  very  differently  by  different  observers,  some 
claiming  directly  opposite  results  from  others.  It  is  evident,  when  all  the 
attendant  conditions  are  considered,  that  the  obtained  results  must  vary 
both  in  kind  and  degree. 

The  temperatures  employed  will  vary  from  1000°  to  1500°  F.  In 
some  cases  the  heated  steel  is  withdrawn  at  full  temperature  from  the 
furnace  and  allowed  to  cool  in  the  atmosphere;  in  others  the  mass  is 
removed  from  the  furnace,  but  covered  under  a  muffle,  to  lessen  the  free 
radiation;  or,  again,  the  charge  is  retained  in  the  furnace,  and  the  whole 
mass  cooled  with  the  furnace,  and  more  slowly  than  by  either  of  the  other 
methods. 

The  best  general  results  from  annealing  will  probably  be  obtained  by 
introducing  the  material  into  a  uniformly  heated  oven  in  which  the  tem- 
perature is  not  so  high  as  to  cause  a  possibility  of  cracking  by  sudden  and 
unequal  changing  of  temperature,  then  gradually  raising  the  temperature 
of  the  material  until  it  is  uniformly  about  1200°  F.,  then  withdrawing  the 
material  after  the  temperature  is  somewhat  reduced  and  cooling  under 
shelter  of  a  muffle  sufficiently  to  prevent  too  free  and  unequal  cooling  on 
the  one  hand  or  excessively  slow  cooling  on  the  other. 

G.G.Mehrtens,  Trans.  A.  S.  C.  E.,  1893,  says:  "  Anuealing  is  of  advan- 


MISCELLANEOUS  NOTES   ON  STEEL.  485 

tage  to  all  steel  above  64,000  Ibs.  strength  per  square  inch,  but  it  is  ques- 
tionable whether  it  is  necessary  in  softer  steels.  The  distortions  due  to 
heating  cause  trouble  in  subsequent  straightening,  especially  of  thin  plates. 
"In  a  general  way  all  unannealed  mild  steel  for  a  strength  of  56.000  to 
64,000  Ibs.  may  be  worked  in  the  same  way  as  wrought  iron.  Rough 
treatment  or  working  at  a  blue  heat  must,  however,  be  prohibited.  Shear- 
ing is  to  be  avoided,  except  to  prepare  rough  plates,  which  should  after- 
wards be  smoothed  by  machine  tools  or  files  before  using.  Drifting  is  also 


sinking  of  the  edges  of  drilled  holes  is  all  that  is  necessary.  Working  the 
material  while  heated  should  be  avoided  as  far.  as  possible,  and  the 
engineer  should  bear  this  in  mind  when  designing  structures.  Upsetting, 
cranking,  and  bending  ought  to  be  avoided,  but  when  necessary  the 
material  should  be  annealed  after  completion. 

"The  riveting  of  a  mild-steel  rivet  should  be  finished  as  quickly  as  pos- 
sible, before  it  cools  to  the  dangerous  heat.  For  this  reason  machine  work 
is  the  best.  There  is  a  special  advantage  in  machine  work  from  the  fact 
that  the  pressure  can  be  retained  upon  the  rivet  until  it  has  cooled  suffi- 
ciently to  prevent  elongation  and  the  consequent  loosening  of  the  rivet." 

Punching  and  Drilling  of  Steel  Plates.  (Proc.  Inst.  M.  E.t  Aug., 
1887,  p.  326.)  —  In  Prof.  Unwin's  report  the  results  of  the  greater  number 
of  the  experiments  made  on  iron  and  steel  p'ates  lead  to  the  general  con- 
clusion that  while  thin  plates,  even  of  steel,  do  not  suffer  very  much  from 
punching,  yet  in  those  of  1/2  in.  thickness  and  upwards  the  loss  of  tenacity 
due  to  punching  ranges  from  10%  to  23%  iniron  plates  and  from  11%  to 
33%  in  the  case  of  mild  steel. 

MISCELLANEOUS  NOTES  ON  STEEL. 

May  Carbon  be  Burned  Out  of  Steel  ?  —  Experiments  made  at  the 
Laboratory  of  the  Penna.  Railroad  Co.  (Specifications  for  Springs,  1888) 
with  the  steel  of  spiral  springs,  show  that  the  place  from  which  the  borings 
are  taken  for  analysis  has  a  very  important  influence  on  the  amount  of 
carbon  found.  If_the  sample  is  a  piece  of  the  round  bar,  and  the  borings 
are  taken  from  the'end  of  this  piece,  the  carbon  is  always  higher  than  if  the 
borings  are  taken  from  the  side  of  the  piece.  It  is  common  to  find  a 
difference  of  0.10%  between  the  center  and  side  of  the  bar,  and  in  some 
cases  the  difference  is  as  high  as  0.23%.  Apparently  during  the  process 
of  reducing  the  metal  from  the  ingots  to  the  round  oar,  with  successive 
heatings,  the  carbon  in  the  outside  of  the  bar  is  burned  out. 

Effect  of  Nicking  a  Steel  Bar.  —  The  statement  is  sometimes  made 
that,  owing  to  the  homogeneity  of  steel,  a  bar  with  a  surface  crack  or  nick 
in  one  of  its  edges  is  liable  to  fail  by  the  gradual  spreading  of  the  nick,  and 
thus  break  under  a  very  much  smaller  load  than  a  sound  bar.  With  iron 
it  is  contended  this  does  not  occur,  as  this  metal  has  a  fibrous  structure. 
Sir  Benjamin  Baker  has,  however,  shown  that  this  theory,  at  least  so  far 
as  statical  stress  is  concerned,  is  opposed  to  the  facts,  as  'he  purposely 
made  nicks  in  specimens  of  the  mild  steel  used  at  the  Forth  Bridge,  but 
found  that  the  tensile  strength  of  the  whole  was  thus  reduced  by  only 
about  one  ton  per  square  inch  of  section.  In  an  experiment  by  the  Union 
Bridge  Company  a  full-sized  steel  counter-bar,  with  a  screw-turned 
buckle  connection,  was  tested  under  a  heavy  statical  stress,  and  at  the 
same  time  a  weight  weighing  1040  Ibs.  was  allowed  to  drop  on  it  from 
various  heights.  The  bar  was  first  broken  by  ordinary  statical  strain, 
and  showed  a  breaking  stress  of  66,800  Ibs.  per  square  inch.  The  longer 
of  the  broken  parts  was  then  placed  in  the  machine  and  put  under  the 
following  loads,  whilst  a  weight,  as  already  mentioned,  was  dropped  on  it 
from  various  heights  at  a  distance  of  five  feet  from  the  sleeve-nut  of  the 
turn-buckle,  as  shown  below: 

Stress  in  pounds  per  sq.  in 50,000     55,000     60,000     63,000     65,000 

ft.  in.      ft.  in.       ft.  in.       ft.  in.      ft.  in. 

The  weight  was  then  shifted  so  as  to  fall  directly  on  the  sleeve-nut,  and 
the  test  proceeded  as  follows: 

Stress  on  specimen  in  Ibs.  per  square  inch 65,350        65,350        68,800 

Height  of  fall,  feet 3  6  d 


486  STEEL. 

It  will  be  seen  that  under  this  trial  the  bar  carried  more  than  when 
originally  tested  statically,  showing  that  the  nicking  of  the  bar  by  screw- 
ing had  not  appreciably  weakened  its  power  of  resisting  shocks.  —  Eng'g 
News. 

Specific  Gravity  of  Soft  Steel.  (W.  Kent,  Trans.  A.  I.  M.  E.,  xiv, 
585.)  —  Five  specimens  of  boiler-plate  of  C  0.14,  P  0.03  gave  an  average 
sp.  gr.  of  7.932,  maximum  variation  0.008.  The  pieces  were  first  planed 
to  remove  all  possible  scale  indentations,  then  filed  smooth,  then  cleaned 
in  dilute  sulphuric  acid,  and  then  boiled  in  distilled  water,  to  remove  all 
traces  of  air  from  the  surface. 

The  figures  of  specific  gravity  thus  obtained  by  careful  experiment  on 
bright,  smooth  pieces  of  steel  are,  however,  too  high  for  use  in  determining 
the  weights  of  rolled  plates  for  commercial  purposes.  The  actual  average 
thickness  of  these  plates  is  always  a  little  less  than  is  shown  by  the  calipers, 
on  account  of  the  oxide  of  iron  on  the  surface,  and  because  the  surface  is 
not  perfectly  smooth  and  regular.  A  number  of  experiments  on  com- 
mercial plates,  and  comparison  of  other  authorities,  led  to  the  figure 
7.854  as  the  average  specific  gravity  of  open-hearth  boiler-plate  steel. 
This  figure  is  easily  remembered  as  being  the  same  figure  with  change  of 
position  of  the  decimal  point  (.7854)  which  expresses  the  relation  of  the 
area  of  a  circle  to  that  of  its  circumscribed  square.  Taking  the  weight 
of  a  cubic  foot  of  water  at  62°  F.  as  62.36  Ibs.  (average  of  several  authori- 
ties), this  figure  gives  489.775  Ibs.  as  the  weight  of  a  cubic  foot  of  steel, 
or  the  even  figure,  490  Ibs.,  may  be  taken  as  a  convenient  figure,  and 
accurate  within  the  limits  of  the  error  of  observation. 

A  common  method  of  approximating  the  weight  of  iron  plates  is  to  con- 
sider them  to  weigh  40  Ibs.  per  square  foot  one  inch  thick.  Taking  this 
weight  and  adding  2%  gives  almost  exactly  the  weight  of  steel  boiler- 
plate given  above  (40  X  12  X  1.02  =  489.6  Ibs.  per  cubic  foot). 

Occasional  Failures  of  Bessemer  Steel.  —  G.  H.  Clapp  and  A. 
E.  Hunt,  in  their  paper  on  "  The  Inspection  of  Materials  of  Construction  in 
the  United  States  "  (Trans.  A.  I.  M.  E.,  vol.  xix),  say:  Numerous  instances 
could  be  cited  to  show  the  unreliability  of  Bessemer  steel  for  structural 

?urposes.  One  of  the  most  marked,  however,  was  the  following:  A 
2-in.  I-beam  weighing  30  Ibs.  to  the  foot,  20  feet  long,  on  being  unloaded 
from  a  car  broke  in  two  about  6  feet  from  one  end. 

The  analyses  and  tensile  tests  made  do  not  show  any  cause  for  the  failure. 

The  cold  and  quench  bending  tests  of  both  the  original  3/4-in.  round  test- 
pieces,  and  of  pieces  cut  from  the  finished  material,  gave  satisfactory  re- 
sults; the  cold-bending  tests  closing  down  on  themselves  without  sign  of 
fracture. 

Numerous  other  cases  of  angles  and  plates  that  were  so  hard  in  places  as 
to  break  off  short  in  punching,  or,  what  was  worse,  to  break  the  punches, 
have  come  under  our  observation,  and  although  makers  of  Bessemer  steel 
claim  that  this  is  just  as  likely  to  occur  in  open-hearth  as  in  Bessemer  steel, 
we  have  as  yet  never  seen  an  instance  of  failure  of  this  kind  in  open- 
hearth  steel  having  a  composition  such  as  C  0.25%,  Mn  0.70%,  P  0.08%. 

J.  W.  Wailes,  in  a  paper  read 'before  the  Chemical  Section  of  the  British 
Association  for  the  Advancement  of  Science,  in  speaking  of  mysterious 
failures  of  steel,  states  that  investigation  shows  that  "  these  failures  occur 
in  steel  of  one  class,  viz.,  soft  steel  made  by  the  Bessemer  process." 

Dangerous  Low  Carbon  Steel. — A  remarkable  failure  of  ship-plate 
steel  is  described  in  Jour.  A.  S.  M.  E.,  Jan.,  1915  (from  Trans.  North 
East  Coast  Institution  of  Engineers  and  Shipbuilders).  In  punching 
the  plates  several  of  them  cracked,  and  on  riveting  many  of  them 
cracked  between  the  Civets;  they  also  cracked  on  being  struck  with 
an  ordinary  hammer.  The  plates  had  passed  all  the  usual  chemical 
and  physical  tests  of  Lloyd's.  A  chemical  analysis  gave  C.  0.05;  Si. 
0.08;  Mn.  0.86;  S.  0.08;  P.  0.06.  A  micrographic  examination  showed 
numerous  dove-gray  areas  of  sulphide  of  manganese.  Alternating 
stress  tests  on  bars  3/8  in.  diameter,  bent  3/g  in.  each  way  at  3  in. 
from  the  plane  of  maximum  stress,  gave  only  100  alternations  of  stress 
before  fracture,  as  compared  with  300  for  good  steel.  Prof.  J.  O. 
Arnold,  of  Sheffield,  says  the  material  appears  to  have  been  overheated 
in  manufacturing  the  plates  from  the  slab  ingots,  and  that  slow  cooling 
from  a  high  temperature  after  rolling,  the  plates  being  stacked  in  piles 
to  cool,  would  make  crystallization  more  perfect  and  hence  more 
dangerous. 


CstlVMSI 


MISCELLANEOUS   NOTES    ON   STEEL. 


487 


Segregation  in  Steel  Ingots.  (A.  Pourcel,  Trans.  A.J.  M.  E.,  1893.) 
—  H.  M.  Howe,  in  his  "  Metallurgy  of  Steel,"  gives  a  resume  of  observations, 
with  the  results  of  numerous  analyses,  bearing  upon  the  phenomena  of 

A  test-piece  taken  24  inches  from  the  head  of  an  ingot  7.5  feet  in  length 
gave  by  analysis  very  different  results  from  those  of  a  test-piece  taken 
30  inches  from  the  bottom.  '  •  Q  p 

Top                                               .     0.92        0.535        0.043        0.161         0.261 
Bottom 0.37        0.498        0.006        0.025        0.096 

Segregation  is  less  marked  in  ingots  of  extra-soft  metal  cast  in  cast-iron 
molds  of  considerable  thickness.  It  is,  however,  still  important,  and  ex- 
plains the  difference  often  shown  by  the  results  of  tests  on  pieces  taken 
from  different  portions  of  a  plate.  Two  samples,  taken  from  the  sound 
part  of  a  flat  ingot,  one  on  the  outside  and  the  other  in  the  center,  7.9 
inches  from  the  upper  edge,  gave; 

C.  S.  P.  Mn. 

Center  0.14        0.053         0.072        0.576 

Exterior 0.11        0.036         0.027       0.610 

Manganese  is  the  element  most  uniformly  disseminated  in  hard  or  soft 
steel. 

For  cannon  of  large  caliber,  if  we  reject,  in  addition  to  the  part  cast  in 
sand  and  called  the  masselotte  (sinking-head),  one-third  of  the  upper  part 
of  the  ingot,  we  can  obtain  a  tube  practically  homogeneous  in  composition, 
because  the  central  part  is  naturally  removed  by  the  boring  of  the  tube. 
With  extra-soft  steels,  destined  for  ship-  or  boiler-plates,  the  solution  for 
practically  perfect  homogeneity  lies  in  the  obtaining  of  a  metal  more 
closely  deserving  its  name  of  extra-soft  metal. 

The  injurious  consequences  of  segregation  must  be  suppressed  by  redu- 
cing, as  far  as  possible,  the  elements  subject  to  liquation. 

Segregation  in  Steel  Plates.  (C.  L.  Huston,  Proc.  A.  S.  T.  M.,  vi,  182.) 

A  plate  370  X  76  X  »/i6  in.  was  rolled  from  a  16  X  18-in.  ingot,  weighing 
2800  Ibs.,  the  ladle  test  of  which  showed  0.18  C.     Test  pieces  from  the 
plate  gave  the  Allowing: 
Top  of  Ingot: 

Tensile  Strength 56,730     67,420     67,050     66,980 

Carbon 0.13        0.25        0.27        0.25 


Bottom  of  Ingot: 

Tensile  Strength 56,120 

Carbon 0.13 

1 


67,420 
0.25 

57,720 

0.13 

2 


58,400 

0.16 

3 


58,140 

0.16 

4 


56,440 
0.13 

56,900 

0.14 

5 


Columns  1  and  5,  edge  of  plate;  3,  middle;  2  and  4,  half  way  between 
middle  and  edge. 

Other  tests  of  low-carbon  steel  showed  a  lower  degree  of  segregation. 
A  plate  from  an  ingot  of  0.23  C  gave  minimum  0.18  C  T.  S.,  64,580: 
maximum  0.38  C,  T.  S.,  70,340.  One  from  an  ingot  of  0.26  C  gave 
maximum  0.20  C,  T.  S.,  59,600;  maximum  0.50  C,  T.  S.,  78,600.  (See 
also  paper  on  this  subject  by  H.  M.  Howe  in  vol.  vii,  p.  75.) 

Endurance  of  Steel  under  Repeated  Alternate  Stresses.  (J.  E. 
Howard,  A.  S.  T  .M.,  1907,  p.  252.)  —  Small  bars  were  rapidly  rotated  in  a 
machine  while  being  subjected  to  a  transverse  strain.  Two  steels  gave 


Red.  of  area,  33.5%.  (2)  0.82  C,  T.  S.,  142,000;  E.  L.,  64,000 
7%;  Red.  of  area,  11.8%. 

Elong., 

Fiber  stress  
No.  of  rotations  be- 
fore rupture. 

60,000 
j  (1)  12,490 
1  (2)  37,250 

50,000 
33,160 
213,150 

45,000 
166,240 
605,640 

40,000 
455,000 
202,000,000 

35,000 
900.000 
Notb 

30,000 
76,326,240 
roken. 

Welding  of  Steel.  —  H.  H.  Campbell  (Manuf.  of  Iron  and  Steel, 
p.  402)  had  numerous  bars  of  steel  welded  by  different  skilled  blacksmiths. 
The  record  of  results,  he  says,  "is  extremely  unsatisfactory."  The 
worst  weld  by  each  of  four  workmen  showed  respectively  70,  54,  58,  and 
44%  of  the  strength  of  the  original  bar.  Forging  steel  showed  one  weld 
with  only  48%,  common  soft  steel  44%,  and  pure  basic  steel  59%.  In 
a  series  of  tests  by  the  Royal  Prussian  Testing  Institute,  the  average 
strength  of  welded  bars  of  medium  steel  was  58%  of  the  natural  the 
poorest  bar  showing  only  23%.  In  softer  steel  the  average  was  71%. 


488  STEEL. 

and  the  poorest  33  %,  while  in  puddled  iron  the  average  was  81  %  and  the 
poorest  62%.  Mr.  Campbell  concludes:  "A  weld  as  performed  by 
ordinary  blacksmiths,  whether  on  iron  or  steel,  is  not  nearly  as  good  as 
the  rest  of  the  bar;  and  it  is  still  more  certain  that  welds  of  large  rods  of 
common  forging  steel  are  unreliable  and  should  not  be  employed  in 
structural  work.  Electric  methods  d9  not  offer  a  solution  of  the  problem, 
for  the  metal  is  heated  beyond  the  critical  temperature  of  crystallization, 
and  only  by  heavy  reductions  under  the  hammer  or  press  can  much  be 
done  towards  restoring  the  ductility  of  the  piece." 

Welding  of  Steel.—  A.  E.  Hunt  (A-  /-  M.  E.,  1892)  says:  "I  have  never 
seen  so-called  '  welded  '  pieces  of  steel  pulled  apart  in  a  testing-machine 
or  otherwise  broken  at  the  joint  which  have  not  shown  a  smooth  cleavage 
plane,  as  it  were,  such  as  in  iron  would  be  condemned  as  an  imperfect 
weld.  My  experience  in  this  matter  leads  me  to  agree  with  the  position 
taken  by  Mr.  William  Metcalf  in  his  paper  upon  Steel  (Trans.  A.S.C.E., 
vol.  xvi,  p.  301).  Mr.  Metcalf  says,  'I  do  not  believe  steel  can  be  welded 

The  Thermit  Welding  Process.  (Goldschmidt  Thermit  Co.,  New 
York.)— When  powdered  or  finely  divided  aluminum  is  mixed  with  a 
metallic  oxide  and  ignited,  the  aluminum  burns  with  great  rapidity  and 
intense  heat,  reducing  the  oxide  to  a  metal  and  fusing  it.  It  is  said  that 
iron  oxide  and  aluminum  will  make  a  temperature  of  5400°  F.,  producing 
fused  iron  which  will  melt  any  iron  or  steel  with  which  it  comes  in  con- 
tact. The  process  is  largely  used  for  repairing  breaks  of  large  castings 
or  forgings,  such  as  the  stern  post  of  a  steamship,  a  locomotive  frame, 
etc.  In  the  operation  of  welding  a  large  fractured  piece,  the  fracture 
is  drilled  out  with  a  series  of  3/4-in.  holes  close  together,  making  a  clear 
opening.  A  mold  of  fire-clay  and  sand  is  then  made  to  fit  all  around 
the  fracture,  leaving  a  collar  or  ring  surrounding  it,  baked  in  a  furnace 
and  then  placed  in  position.  The  fractured  section  is  then  heated  by  a 
blow-torch  inserted  in  the  riser  of  the  mold.  A  conical  sheet  iron  cru- 
cible, lined  with  magnesia  tar,  is  then  inserted  in  the  riser,  and  thermit 
(the  mixture  of  aluminum  and  oxide  of  iron)  poured  into  it.  An  ignition 
powder  is  placed  on  top  of  the  thermit,  and  lighted  with  a  storm  match. 
The  mixture  begins  to  burn  with  great  agitation;  when  this  ceases  the 
crucible  is  tapped,  and  white-hot  fused  iron  or  steel  runs  into  the  mold 
and  thoroughly  fuses  with  the  pieces  to  be  joined. 

Oxy-acetylene  Welding  and  Cutting  of  Metals. — Autogenous 
Welding.  —  By  means  of  acetylene  gas  and  oxygen,  stored  in  tanks 
under  pressure,  and  a  properly  constructed  nozzle  or  torch  in  which  the 
two  gases  are  united  and  fired,  an  intense  temperature  said  to  be  6000°  F., 
is  generated,  and  it  may  be  used  to  weld  or  fuse  together  iron,  steel,  alumi- 
num, brass,  copper,  or  other  metals.  The  process  of  uniting  metals  by  heat 
without  using  either  flux  or  compression  is  called  autogenous  welding. 
The  oxy-acetylene  torch  may  also  be  used  for  cutting  metals,  such  as 
steel  plates,  beams  and  large  forgings,  and  for  repairing  flaws  or  defects, 
or  filling  cavities  by  melting  a  strip  of  metal  and  flowing  it  into  place. 
The  apparatus,  with  instruction  in  its  use,  is  furnished  by  the  Davis- 
Bournonville  Co.,  Jersey  City,  N.  J. 

Electric  Welding.  —  For  description  see  Electrical  Engineering. 

Hydraulic  Forging.  —  In  the  production  of  heavy  forgings  from 
cast  ingots  of  mild  steel  it  is  essential  that  the  mass  of  metal  should  be 
operated  on  as  equally  as  possible  throughout  its  entire  thickness.  When 
employing  a  steam-hammer  for  this  purpose  it  has  been  found  that  the  ex- 
ternal surface  of  the  ingot  absorbs  a  large  proportion  of  the  sudden  impact 
of  the  blow,  and  that  a  comparatively  small  effect  only  is  produced  on  the 
central  portions  of  the  ingot,  owing  to  the  resistance  offered  by  the  inertia 
of  the  mass  to  the  rapid  motion  of  the  falling  hammer  —  a  disadvantage 
that  is  entirely  overcome  by  the  slow,  though  powerful,  compression  of  the 
hydraulic  forging-press,  which  appears  destined  to  supersede  the  steam- 
hammer  for  the  production  of  massive  steel  forgings. 

Fluid-compressed  Steel  by  the  "  Whitworth  Process."  (Proc. 
Inst.  M.  E.,  May,  1887,  p.  167.)  —  In  this  system  a  gradually  increasing 
pressure  up  to  6  or  8  tons  per  square  inch  is  applied  to  the  fluid  ingot,  and 
within  half  an  hour  or  less  after  the  application  of  the  pressure  the  column 
of  fluid  steel  is  shortened  1 1/2  inches  per  foot  or  one-eighth  of  its  length;  the 
pressure  is  then  kept  on  for  several  hours,  the  result  being  that  the  metal 
is  compressed  into  a  perfectly  solid  and  homogeneous  material  free  from 
blow  holes. 


STEEL   CASTINGS.  489 

In  large  gun-ring  ingots  during  cooling  the  carbon  is  driven  to  the  center, 
the  center  containing  0.8  carbon  and  the  outer  ring  0.3.  The  center  is 
bored  out  until  a  test  shows  that  the  inside  of  the  ring  contains  the  same 
percentage  of  carbon  as  the  outside. 

Fluid-compressed  steel  is  made  by  the  Bethlehem  Steel  Co.  for  gun  and 
other  heavy  forcings. 

Putting  sufficient  pressure  upon  the  outside  of  the  ingot  when  the  walls 
are  solid  but  the  interior  is  still  liquid  will  prevent  the  formation  of  a 
pipe.  In  Whitworth's  system  the  ingot  is  raised  and  compressed  length- 
wise against  a  solid  ram  situated  above  it,  during  and  shortly  after  solidifi- 
cation. In  Harmet's  method  the  ingot  is  forced  upward  during  solidifi- 
cation into  its  tapered  mold.  This  causes  a  large  radial  pressure  on  its 
sides,  in  Lilienbergls  method  the  ingots  are  stripped  and  then  run  on 
their  cars  between  a  solid  and  movable  wall.  The  movable  wall  is  then 
pressed  against  one  side  of  the  ingots.  (Stoughton's  Metallurgy  of  Iron 
and  Steel.) 

For  other  methods  of  compressing  ingots  see  paper  by  A.  J.  Capron  in 
Jour.  I.  &  S.  /.,  1906,  Iron  Tr.  Rev.,  May  24, 1906. 

STEEL  CASTINGS. 

(E.  S.  Cramp,  Proc.  Eng'g  Congress,  Dept.  of  Marine  Eng'g,  Chicago,  1893.) 

In  1891  American  steel-founders  had  successfully  produced  a  consider- 
able variety  of  heavy  and  difficult  castings,  of  which  the  following  are  the 
most  noteworthy  specimens: 

Bed-plates  up  to  24,000  Ibs.;  stern-posts  up  to  54,000  Ibs.;  stems  up  to 
21,000  Ibs.;  hydraulic  cylinders  up  to  11,000  IDS.;  shaft-struts  up  to  32,000 
ibs.;  hawse-pipes  up  to  7500  Ibs.;  stern-pipes  up  to  8000  Ibs. 

The  percentage  of  success  in  these  classes  of  castings  since  1890  has 
ranged  from  65%  in  the  more  difficult  forms  to  90%  in  the  simpler  ones; 
the  tensile  strength  has  been  from  62,000  to  78,000  Ibs.,  elongation  from 
15%  to  25%. 

The  first  steel  castings  of  which  anything  is  generally  known  were 
crossing-frogs  made  for  the  Philadelphia  &  Reading  R.  R.  in  July,  1867,  by 
the  William  Butcher  Steel  Works,  now  the  Midvale  Steel  Co.  The  molds 
were  made  of  a  mixture  of  ground  fire-brick,  black-lead  crucible-pots 
ground  fine,  and  fire-clay,  and  washed  with  a  black-lead  wash.  The  steel 
was  melted  in  crucibles,  and  was  about  as  hard  as  tool  steel.  The  surface 
of  these  castings  was  very  smooth,  but  the  interior  was  very  much  honey- 
combed. This  was  before  the  days  when  the  use  of  silicon  was  known  for 
solidifying  steel.  The  sponginess,  which  was  almost  universal,  was  a  great 
obstacle  to  their  general  adoption. 

The  next  step  was  to  leave  the  ground  pots  out  of  the  molding  mixture 
and  to  wash  the  mold  with  finely  ground  fire-brick.  This  was  a  great  im- 
provement»  especially  in  very  heavy  castings;  but  this  mixture  still  clung  so 
strongly  to  the  casting  that  only  comparatively  simple  shapes  could  be 
made  with  certainty.  A  mold  made  of  such  a  mixture  became  almost  as 
hard  as  fire-brick,  and  was  such  an  obstacle  to  the  proper  shrinkage  of 
castings  that,  when  at  all  complicated  in  shape,  they  had  so  great  a 
tendency  to  crack  as  to  make  their  successful  manufacture  almost  impos- 
sible. By  this  time  the  use  of  silicon  had  been  discovered,  and  the  only 
obstacle  in  the  way  of  making  good  castings  was  a  suitable  molding 
mixture.  This  was  ultimately  found  in  mixtures  having  the  various  kinds 
of  silica  sand  as  the  principal  constituent. 

One  of  the  most  fertile  sources  of  defects  in  castings  is  a  bad  design. 
Very  intricate  shapes  can  be  cast  successfully  if  they  are  so  designed  as  to 
cool  uniformly.  Mr.  Cramp  says  while  he  is  not  yet  prepared  to  state  that 
Anything  that  can  be  cast  successfully  in  iron  can  be  cast  in  steel,  indica- 
tions seem  to  point  that  way  in  all  cases  where  it  is  possible  to  put  on  suit- 
able sinking-heads  for  feeding  the  casting. 

H.  L.  Gantt  (Trans.  A.  S.  M.  #.,xii,  710)  says:  Steel  castings  not  only 
shrink  much  more  than  iron  ones,  but  with  less  regularity.  The  amount  of 
shrinkage  varies  with  the  composition  and  the  heat  of  the  metal;  the  hotter 
the  metal  the  greater  the  shrinkage;  and,  as  we  get  smpother  castings  from 
hot  metal,  it  is  better  to  make  allowance  for  large  shrinkage  and  pour  the 
metal  as  hot  as  possible.  Allow  3/16  or  1/4  in.  per  ft.  in  length  for  shrinkage, 
and  1/4  in.  for  finish  on  machined  surfaces,  except  such  as  are  cast  "up. 
Cope  surfaces  which  are  to  be  machined  should,  in  large  or  hard  castings, 
have  an  allowance  of  from  %toy2in.  for  finish,  as  a  large  mass  of  metal 


490 


STEEL. 


slowly  rising  in  a  mold  is  apt  to  become  crusty  on  the  surface,  and  such  a 
crust  is  sure  to  be  full  of  imperfections.  On  small,  soft  castings  1/8  in.  on 
drag  side  and  1/4  in.  on  cope  side  will  be  sufficient.  No  core  should  have 
less  than  1/4  in.  finish  on  aside  and  very  large  ones  should  have  as  much  as 
1/2  in.  on  a  side.  Blow-holes  can  be  entirely  prevented  in  castings  by  the 
addition  of  manganese  and  silicon  in  sufficient  quantities;  but  both  of 
these  cause  brittleness,  and  it  is  the  object  of  the  conscientious  steel- 
maker to  put  no  more  manganese  and  silicon  in  his  steel  than  is  just  suffi- 
cient to  make  it  solid.  The  best  results  are  arrived  at  when  all  portions  of 
the  castings  are  of  a  uniform  thickness,  or  very  nearly  so. 

The  following  table  will  illustrate  the  effect  of  annealing  on  tensile 
strength  and  elongation  of  steel  castings: 


Carbon. 

Tensile  Strength. 

Elongation. 

Unannealed. 

Annealed. 

Unannealed. 

Annealed. 

0.23% 
0.37 
0.53 

68,738 
85,540 
90,121 

67,210 
82,228 
106,415 

22.40% 
8.20 
2.35 

31.40% 
21.80% 
9.80 

The  proper  annealing  of  large  castings  takes  nearly  a  week. 

The  proper  steel  for  roll  pinions,  hammer  dies,  etc.,  seems  to  be  that 
containing  about  0.60  %  of  carbon.  Such  castings,  properly  annealed,  have 
worn  weil  and  seldom  broken.  Miscellaneous  gearing  should  contain 
carbon  0.40%  to  0.60%,  gears  larger  in  diameter  being  softest.  General 
machinery  castings  should,  as  a  rule,  contain  less  than  0.40%  of  carbon, 
those  exposed  to  great  shocks  containing  as  low  as  0.20%  of  carbon.  Such 
castings  will  give  a  tensile  strength  of  from  60,000  to  80,000  Ibs.  per  sq. 
in  and  at  least  15%  extension  in  2  in.  Machinery  and  hull  castings  for 
war-vessels  for  the  United  States  Navy,  as  well  as  carriages  for  naval 
guns,  contain  from  0.20%  to  0.30%  of  carbon. 

For  description  of  methods  of  manufacture  of  steel  castings  by  the  Besse- 
mer, open-hearth,  and  crucible  processes,  see  paper  by  P.  G.  Salom,  Trans. 
A.  I.  M.  E.,  xiv.  118. 

CRUCIBLE    STEEL. 

Selection  of  Grades  by  the  Eye,  and  Effect  of  Heat  Treatment. 

(J  W.  Langley,  Amer.  Chemist,  Nov.,  1876.)  —  In  the  early  days  of  steel 
making  the  grades  were  determined  by  inspection  of  the  fractured  surfaces 
of  the  cast  ingots.  The  method  of  selection  is  described  as  follows: 

The  steel  when  thoroughly  fluid  is  poured  into  cast-iron  molds,  and 
when  cold  the  top  of  the  ingot  is  broken  off,  exposing  a  freshly  fractured 
surface.  The  appearance  presented  is  that  of  confused  groups  of  crystals, 
all  appearing  to  have  started  from  the  outside  and  to  have  met  in  the 
center;  this  general  form  is  common  to  all  ingots  of  whatever  composition, 
but  to  the  trained  eye,  and  only  to  one  long  and  critically  exercised,  a 
minute  but  indescribable  difference  is  perceived  between  varying  samples 
of  steel,  and  this  difference  is  now  known  to  be  owing  alirmst  wholly  to 
variations  in  the  amount  of  combined  carbon,  as  the  following  table  will 
show.  Twelve  samples  selected  by  the  eye  alone,  and  analyses  of  drillings 
taken  direct  from  the  ingot  before  it  had  been  heated  or  hammered,  gave 
results  as  below: 

Ingot  Nos.      1          2        3'45678        9       10       11      12 
C  0.302     .490  -.529  .649  .801  .841  .867  .871   .955  1.0051.0581.079 

Diff.  of  C  0.188  .039  .120  .152  .040  .026  .004   .084    .050    .053    .021 

The  C  is  seen  to  increase  in  quantity  in  the  order  of  the  numbers.  The 
other  elements,  with  the  exception  of  total  iron,  bear  no  relation  to  the 
number  on  the  samples.  The  mean  difference  of  Cis  0.071. 

In  mild  steels  the  discrimination  is  less  perfect. 

The  appearance  of  the  fracture  by  which  the  above  twelve  selections 
were  made  can  only  be  seen  in  the  cold  ingot  before  any  operation,  except 
the  original  one  of  casting,  has  been  performed  upon  it.  As  soon  as  it  is 
hammered,  the  structure  changes,  so  that  all  trace  of  the  primitive  con- 
dition appears  to  be  lost. 

The  specific  gravity  of  steel  is  influenced  not  only  by  its  chemical  analy- 
sis but  by  the  heat  to  which  it  is  subjected. 
The  sp.gr.  of  the  ingots  in  the  above  list  ranged  from  7.855  for  No.  1 


CRUCIBLE   STEEL.  491 

down  to  7.803  for  No.  12.  Rolling  into  bars  produced  a  very  slight  dif- 
ference, —  0.005  in  Nos.  5  and  6  and +0.020  in  No.  12,  but  overheating 
reducedthesp.gr.  of  the  bar  0.023  in  No.  3  to  0.135  in  No.  12,  the  sp.  gr.  of 
the  burnt  sample  of  No.  12  being  only  7.690. 

Effect  of  Heat  on  the  Grain  of  Steel.  (W.  Metcalf,  —  Jeans  on 
Steel,  p.  642.)  —  A  simple  experiment  will  show  the  alteration  produced 
in  a  high-carbon  steel  by  different  methods  of  hardening.  If  a  bar  of  such 
steel  be  nicked  at  about  9  or  10  places,  and  about  half  an  inch  apart,  a 
suitable  specimen  is  obtained  for  the  experiment.  Place  one  end  of  the 
bar  in  a  good  fire,  so  that  the  first  nicked  piece  is  heated  to  whiteness, 
while  the  rest  of  the  bar,  being  out  of  the  fire,  is  heated  up  less  and  less 
as  we  approach  the  other  end.  As  soon  as  the  first  piece  is  at  a  good 
white  heat,  which  of  course  burns  a  high-carbon  steel,  and  the  temperature 
of  the  rest  of  the  bar  gradually  passes  down  to  a  very  dull  red,  the  metal 
should  be  taken  out  of  the  fire  and  suddenly  plunged  in  cold  water,  in 
which  it  should  be  left  till  quite  cold.  It  should  then  be  taken  out  and 
carefully  dried.  An  examination  with  a  file  will  show  that  the  first  piece 
has  the  greatest  hardness,  while  the  last  piece  is  the  softest,  the  inter- 
mediate pieces  gradually  passing  from  one  condition  to  the  other.  On 
now  breaking  off  the  pieces  at  each  nick  it  will  be  seen  that  very  consider- 
able and  characteristic  changes  have  been  produced  in  the  appearance  of 
the  metal.  The  first  burnt  piece  is  very  open  or  crystalline  in  fracture; 
the  succeeding  pieces  become  closer  and  closer  in  the  grain  until  one  piece 
is  found  to  possess  that  perfectly  even  grain  and  velvet-like  appearance 
which  is  so  much  prized  by  experienced  steel  users.  The  first  pieces  also, 
which  have  been  too  much  hardened,  will  probably  be  cracked;  those  at 
the  other  end  will  not  be  hardened,  through.  Hence  if  it  be  desired  to 
make  the  steel  hard  and  strong,  the  temperature  used  must  be  high 
enough  to  harden  the  metal  through,  but  not  sufficient  to  open  the  grain. 

Heating  Tool  Steel.  .(Crescent  Steel  Co.,  Pittsburg,  Pa.)  — -  There  are 
three  distinct  stages  or  times  of  heating:  First,  for  forging;  second,  for 
hardening;  third,  for  tempering. 

The  first  requisite  for  a  good  heat  for  forging  is  a  clean  fire  and  plenty  of 
fuel,  so  that  jets  of  hot  air  will  not  strike  the  corners  of  the  piece;  next, 
the  fire  should  be  regular,  and  give  a  good  uniform  heat  to  the  whole  part 
to  be  forged.  It  should  be  keen  enough  to  heat. the  piece  as  rapidly  as 
may  be,  and  allow  it  to  be  thoroughly  heated  through,  without  being 
so  fierce  as  to  overheat  the  corners.  Steel  should  not  be  left  in  the  fire 
any  longer  than  is  necessary  to  heat  it  clear  through,  as  "soaking"  in 
fire  is  injurious;  on  the  other  hand,  it  is  necessary  that  it  should  be  hot 
through,  to  prevent  surface  cracks.  By  observing  these  precautions  a 
piece  of  steel  may  always  be  heated  safely,  up  to  even  a  bright  yellow 
heat,  when  there  is  much  forging  to  be  done  on  it. 

The  best  and  most  economical  of  welding  fluxes  is  clean,  crude  borax, 
which  should  be  first  thoroughly  melted  and  then  ground  to  fine  powder. 

After  the  steel  is  properly  heated,  it  should  be  forged  to  shape  as  quickly 
as  possible;  and  just  as  the  red  heat  is  leaving  the  parts  intended  for  cutting 
edges,  these  parts  should  be  refined  by  rapid,  light  blows,  continued  until 
the  red  disappears. 

For  the  second  stage  of  heating,  for  hardening,  great  care  should  be  used: 
first,  to  protect  the  cutting  edges  and  working  parts  from  heating  more 
rapidly  than  the  body  of  the  piece;  next,  that  the  whole  part  to  be  hardened 
be  heated  uniformly  through,  without  any  part  becoming  visibly  hotter 
than  the  other.  A  uniform  heat,  as  low  as  will  give  the  required  hardness, 
is  the  best  for  hardening. 

For  every  variation  of  heat  which  is  great  enough  to  be  seen  there  will 
result  a  variation  in  grain,  which  may  be  seen  by  breaking  the  piece;  and 
for  every  such  variation  in  temperature  there  is  a  very  g9od  chance  for  a 
crack  to  be  seen.  Many  a  costly  tool  is  ruined  by  inattention  to  this  point. 

The  effect  of  tpo  high  heat  is  to  open  the  grain;  to  make  the  steel  coarse. 
The  effect  of  an  irregular  heat  is  to  cause  irregular  grain,  irregular  strains, 
and  cracks. 

As  soon  as  the  piece  is  properly  heated  for  hardening,  it  should  be 
promptly  and  thoroughly  quenched  in  plenty  of  the  cooling  medium,  water, 
brine,  or  oil,  as  the  case  may  be.  An  abundance  of  cooling  bath,  to  do 
the  work  quickly  and  uniformly  all  over,  is  necessary  to  good  and  safe 
work. 

To  harden  a  large  piece  safely  a  running  stream  should  be  used. 
•    Much  uneven  hardening  is  caused_by  the.use  of  too  small  baths. 


492  STEEL. 

For  the  third  stage  of  heating,  to  temper,  the  first  important  requisite  is 
again  uniformity.  The  next  is  time;  the  more  slowly  a  piece  is  Drought 
down  to  its  temper,  the  better  and  safer  is  the  operation. 

When  expensive  tools  are  to  be  made  it  is  a  wise  precaution  to  try  small 
pieces  of  the  steel  at  different  temperatures,  so  as  to  find  out  how  low  a 
heat  will  give  the  necessary  hardness.  The  lowest  heat  is  the  best  for  any 
steel.  [This  is  true  of  carbon  steel  but  not  of  "  high  speed  "  alloy  steels.] 

Heating  in  a  Lead  Bath.  —  A  good  method  of  heating  steel  to  a 
uniform  temperature  is  by  means  of  a  bath  of  lead  kept  at  a  red  heat  by 
a  gas  furnace.  See  Heat  Treatment  by  the  Taylor-White  Process,  under 
Machine  Shop. 

Heating  Steel  in  Melted  Salts  by  Electric  Current.  —  L.  M.  Cohn 
(Electrot.  z.,  Aug.,  1906,  Mach'y,  Dec.,  1906)  describes  a  furnace  pat- 
ented by  Gebr.  Korting,  Berlin,  in  which  steel  may  be  heated  uniformly 
to  any  desired  temperature  up  to  1300°  C.  (2372°  F.)  without  danger  of 
oxidizing. 

The  furnace  consists  mainly  of  a  cast-iron  box,  lined  inside  with  fire- 
clay, a  second  lining  of  fire-bricks,  lined  again  with  asbestos,  and 
inclosing  the  crucible  made  of  one  piece  of  fireproof  material.  Two 
electrodes  lead  into  the  crucible,  through  which  alternating  current  is 
sent.  The  crucible  is  filled  with  metal  salts.  For  temperatures  above 
1000°  C.  pure  chloride  of  barium  is  used,  the  melting-point  of  which  is 
at  about  950°  C.  (1742  F.) :  for  lower  temperatures  a  mixture  of  chloride 
of  barium  and  chloride  of  potassium,  2  to  1,  is  used,  melting  at  about 
670°  C.  (1238  F.).  Any  other  suitable  salts  may  be  used.  A  regulating 
transformer  regulates  the  current,  and  thus  also  the  temperature. 

A  test  was  made  with  a  furnace,  the  bath  of  which  was  61/2  X  61/2  X  7 
in.  A  50-period  alternating  current  of  190-volt  primary  tension  was 
used.  This  tension  had  to  be  reduced  to  from  50  to  55  volts  by  the 
regulating  transformer  for  starting  the  furnace,  and  lowered  later  on. 
The  heating  lasted  about  half  an  hour.  For  temperatures  from  750  to 
1300°  C.,  the  secondary  tension  amounted  to  from  13  to  18  volts.  The 
consumption  of  energy  was  as  follows:  880°  C.,  5.4  Kw.;  1140°  C.,  8.5 
Kw. ;  1300°  C.,  12.25  Kw.  A  milling  cutter  5  in.  diam.,  11/4  in.  bore,  1  in. 
thick,  was  heated  in  62  seconds  to  1300°  C.  A  bushing  of  tool  steel  23/4 
in.  diam.,  23/4  in.  long,  5/g  in.  bore,  was  heated  in  243  seconds  to  850°C. 

Heating  to  Forge.  (Crescent  Steel  Co.)  —  The  trouble  in  the  forge 
fire  is  usually  uneven  heat,  and  not  too  high  heat.  Suppose  the  piece  to 
be  forged  has  been  put  into  a  very  hot  fire,  and  forced  as  quickly  as  possible 
to  a  high  yellow  heat,  so  that  it  is  almost  up  to  the  scintillating  point.  If 
this  be  done,  in  a  few  minutes  the  outside  will  be  quite  soft  and  in  a  nice 
condition  for  forging,  while  the  middle  parts  will  not  be  more  than  red-hot. 
Now  let  the  piece  be  placed  under  the  hammer  and  forged,  and  the  soft 
outside  will  yield  so  much  more  readily  than  the  hard  inside,  that  the 
outer  particles  will  be  torn  asunder,  while  the  inside  will  remain  sound. 

Suppose  the  case  to  be  reversed  and  the  inside  to  be  much  letter  than  the 
outside;  that  is,  that  the  inside  shall  be  in  a  state  of  semi-fusion,  while  the 
outside  is  hard  and  firm.  Now  ISt  the  piece  be  forged,  and  the  outside  will 
be  all  sound  and  the  whole  piece  will  appear  perfectly  good  until  it  is 
cropped,  and  then  it  is  found  to  be  hollow  inside. 

In  either  case,  if  the  piece  had  been  heated  soft  all  through,  or  if  it  had 
been  only  red-hot  all  through,  it  would  have  forged  perfectly  sound. 

In  some  cases  a  high  heat  is  more  desirable  to  save  heavy  labor,  but  in 
every  case  where  a  fine  steel  is  to  be  used  for  cutting  purposes  it  must  be 
borne  in  mind  that  very  heavy  forging  refines  the  bars  as  they  slowly  cool, 
and  if  the  smith  heats  such  refined  bars  until  they  are  soft,  he  raises  the 
grain,  makes  them  coarse,  and  he  cannot  get  them  fine  again  unless  he  has 
a  very  heavy  steam-hammer  at  command  and  knows  how  to  use  it  well. 

Annealing.  (Crescent  Steel  Co.)  —  Annealing  or  softening  is  accom- 
plished by  heating  steel  to  a  red  heat  and  then  cooling  it  very  slowly, 
to  prevent  it  from  getting -hard  again. 

The  higher  the  degree  of  heat,  the  more  will  steel  be  softened,  until  the 
limit  of  softness  is  reached,  when  the  steel  is  melted. 

It  does  not  follow  that  the  higher  a  piece  of  steel  is  heated  the  softer  it 
will  be  when  cooled,  no  matter  how  slowly  it  may  be  cooled;  this  is  proved 
by  the  fact  that  an  ingot  is  always  harder  than  a  rolled  or  hammered  bar 
made  from  it. 

Therefore  there  is  nothing  gained  by  heating  a  piece  of  steel  hotter  than. 


CRUCIBLE  STEEL. 


493 


a  good  bright,  cherry-red;  on  the  contrary,  a  higher  heat  has  several  dis- 
advantages: First.  If  carried  too  far,  it  may  leave  the  steel  actually 
harder  than  a  good  red  heat  would  leave  it.  Second.  If  a  scale  is  raised 
on  the  steel  this  scale  will  be  harsh,  granular  oxide  of  iron,  and  will  spoil 
the  tools  used  to  cut  it.  Third.  A  high  scaling  heat  continued  for  a  little 
time  changes  the  structure  of  the  steel,  makes  it  brittle,  liable  to  crack  m 
hardening,  and  impossible  to  refine. 

To  anneal  any  piece  of  steel,  heat  it  red-hot;  heat  it  uniformly  and  heat  it 
through,  taking  care  not  to  let  the  ends  and  corners  get  too  hot.  As 
soon  as  it  is  hot,  take  it  out  of  the  fire,  the  sooner  the  better,  and  cool  it 
as  slowly  as  possible.  A  good  rule  for  heating  is  to  heat  it  at  so  low  a  red 
that  when  the  piece  is  cold  it  will  still  show  the  blue  gloss  of  the  oxide 
that  was  put  there  by  the  hammer  or  the  rolls.  Steel  annealed  in  this 
way  will  cut  very  soft;  it  will  harden  very  hard,  without  cracking,  and 
when  tempered  it  will  be  strong,  nicely  refined,  and  will  hold  a  keen, 

Tempering. — Tempering  steel  is  the  act  of  giving  it,  after  it  has  been 
shaped,  the  hardness  necessary  for  the  work  it  has  to  do.  This  is  done  by 
first  hardening  the  piece,  generally  a  good  deal  harder  than  is  necessary, 
and  then  toughening  it  by -slow  heating  and  gradual  softening  until  it  is 
just  right  for  work. 

A  piece  of  steel  properly  tempered  should  always  be  finer  in  grain  than 
the  bar  from  which  it  is  made.  If  it  is  necessary,  in  order  to  make  the 
piece  as  hard  as  is  required,  to  heat  it  so  hot  that  after  being  hardened  the 
grain  will  be  as  coarse  as  or  coarser  than  the  grain  in  the  original  bar,  then 
the  steel  itself  is  of  too  low  carbon  for  the  desired  work. 

If  a  great  degree  of  hardness  is  n9t  desired,  as  in  the  case  of  tap?  and 
most  tools  of  complicated  form,  and  it  is  found  that  at  a  moderate  heat  the 
tools  are  too  hard  and  are  liable  to  crack,  the  smith  should  first  use  a  lower 
heat  in  order  to  save  the  tools  already  made,  and  then  notify  the  bteel- 
maker  that  his  steel  is  too  high,  so  as  to  prevent  a  recurrence  of  the 
trouble. 

)ering 
also, 

.  these 

works  Mr.  Rose  gives  a  "color  scale,"  lithographed  in  colors,  by  which  the 
following  is  a  list  of  the  tools  in  their  order  on  the  color  scale,  together 
with  the  approximate  color  and  the  temperature  at  which  the  color 
appears  on  brightened  steel  when  heated  in  the  air: 

Scrapers  for  brass;  very  pale  yellow,     Hand-plane  irons. 
430°  F.  Twist-drills. 


Steel-engraving  tools, 

Slight  turning  tools. 

Hammer  faces. 

Planer  tools  for  steel. 

Ivory-cutting  tools. 

Planer  tools  for  iron. 

Paper-cutters. 

Wood-engraving  tools. 

Bone-cutting  tools. 

Milling-cutters;  straw  yellow,  460°  F. 

Wire-drawing  dies. 

Boring-cutters. 

Leather-cutting  dies. 

Screw-cutting  dies. 

Inserted  saw-teeth. 

Taps. 

Rock-drills. 

Chasers. 

Punches  and  dies. 

Penknives. 

Reamers. 

Half-round  bits. 

Planing  and  molding  cutters. 

Stone-cutting   tools;    brown  yellow, 

500D  F. 
Gouges, 


Flat  drills  for  brass. 

Wood-boring  cutters. 

Drifts. 

Coopers'  tools. 

Edging  cutters;  light  purple,  530°  F. 

Augers. 

Dental  and  surgical  instruments 

Cold  chisels  for  steel. 

Axes;  dark  purple,  550°  F. 

Gimlets. 

Cold  chisels  for  cast  iron. 

Saws  for  bone  and  ivory. 

Needles. 

Firmer-chisels. 

Hack-saws. 

Framing-chisels. 

Cold  chisels  for  wrought  iron. 

Molding  and  planing  cutters  to  be 

filed. 

Circular  saws  for  metal. 
Screw-drivers. 


'F. 


Saws  for  wood. 

Dark  blue,  570° 
Pale  blue.  610°. 
Blue,  tinged  with  green,  630°. 


494 


STEEL. 


Uses  of  Crucible  Steel  of  Different  Carbons.    (Metcalf  on  Steel.)  — 
0.50  to  0.60  C,  for  hot  work  and  for  battering  tools. 
0.60  to  0.70  C,  ditto,  and  for  tools  of  dull  edge. 
0.70  to  0.80  C,  battering  tools,  cold-sets,  and  some  forms  of  reamers  and 

taps. 

0.80  to  0.90  C,  cold-sets,  hand-chisels,  drills,  taps,  reamers  and  dies. 
0.90  to  1.00  C,  chisels,  drills,  dies,  axes,  knives,  etc. 
1.00  to  1.10  C,  axes,  hatchets,  knives,  large  lathe-tools,  and  many  kinds 

of  dies  and  drills  if  care  be  used  in  tempering  them. 
1.10  to  1.50  C,  lathe-tools,  graving  tools,  scribers,  scrapers,  little  drills, 

and  many  similar  purposes. 

The  best  all-around  tool  steel  is  found  between  0.90  and  1.10  C;  steel 
that  can  be  adapted  safely  and  successfully  to  more  uses  than  any 
other. 

High-speed  Tool  Steel.  (A.  L.  Valentine,  Am.  Mach.,  July  2, 1908.)  — 
Eight  brands  of  high-speed  steel  were  analyzed  with  the  following 
results: 


Steel.  I 


|     W.      |      Cr. 


Mn.    |      Si.      |     Mo. 


P. 


S. 


& 

*   0  70 

14  91 

2  95 

0  01 

0  013 

0.008 

b 

C 

d 

0.25 
0.75 
0  49 

17.27 
14.83 
17  60 

2.69 
2.90 
5  11 

Trace 
0.08 

0.179 

"5J9' 

0.035 
0.02 
0.01 

Trace 
0.01 
0.007 

• 

0-65 

0.19 

0.039 

9.60 

0.016 

0.005 

f 

0  60 

13  00 

2  88 

0  019 

0.01 

0  55 

17  81 

2  48 

0  11 

0  090 

fc 

0  66 

19  03 

0  036 

0.015 

W,  Wolfram,  symbol  for  tungsten. 

Where  blanks  appear  in  the  table,  the  steel  was  not  analyzed  for  these 
ingredients. 

Many  different  brands  of  high-speed  steel  are  being  made.  Some  that 
have  been  marketed  are  almost  worthless.  From  some  of  these  steels  a 
tool  can  be  made  from  one  end  of  a  bar  that  is  easily  forged,  machined 
and  hardened,  while  the  other  end  of  the  bar  would  resist  almost  any 
cutting  tool  and  would  invariably  crack  in  hardening.  Different  bars  of 
the  same  make  also  give  very  different  results.  These  faults  are  some- 
times caused  by  non-uniform  annealing  in  the  steels  which  are  sent  out  as 
thoroughly  annealed,  and  in  many  cases  they  are  caused  by  the  use  of 
impure  ingredients.  A  good  high-speed  steel  will  stand  a  temperature 
as  high  as  1200°  F.,  or  over  double  that  of  carbon  steel,  without  losing  its 
hardness,  and  experience  has  proven  that  the  higher  the  temperature  is 
raised  over  the  white-heat  point,  the  higher  a  temperature  caused  by 
friction  the  tool  will  withstand,  before  losing  its  intense  hardness.  The 
higher  the  percentage  of  carbon  is,  the  more  brittle  and  hard  to  work  the 
steel  will  be,  especially  to  forge.  The  steel  which  has  given  the  best  all- 
around  results  has  contained  about  0.40  C.  The  analysis  of  this  same 
steel  showed  nearly  3%  of  chromium.  The  higher  the  percentage  of 
tungsten  in  the  steel,  the  better  has  been  its  cutting  qualities.  (See  Best 
High-Speed  Tool  Steel,  and  description  of  the  Taylor- White  process  of 
heat  treatment,  under  "The  Machine-Shop. " 

MANGANESE,  NICKEL,  AND  OTHER  "ALLOY"  STEELS. 

Manganese  Steel.  (H.  M.  Howe,  Trans.  A.  S.  M.  E.,  vol.  xii.)  — 
Manganese  steel  is  an  alloy  of  iron  and  manganese,  incidentally,  and 
probably  unavoidably,  containing  a  considerable  proportion  of  carbon. 

The  effect  of  small  proportions  of  manganese  on  the  hardness,  strength, 
and  ductility  of  iron  is  probably  slight.  The  point  at  which  manganese 
begins  to  have  a  predominant  effect  is  not  known;  it  may  be  somewhere 
about  2.5%. 

Manganese  steel  is  very  free  from  blow-holes;  it  welds  with  great  diffi- 
culty; its  toughness  is  increased  by  quenching  from  a  yellpw  heat;  its  elec- 
tric resistance  is  enormous,  and  very  constant  with  changing  temperature; 
it  is  low  in  thermal  conductivity.  Its  remarkable  combination  of  great 
hardness,  which  cannot  be  materially  lessened  by  annealing,  and  great 
tensile  strength,  with  astonishing  toughness  and  ductility,  at  once  creates 
and  limits  its  usefulness. 


tl  ALLOY  "    STEELS.  495 

The  hardness  of  manganese  steel  seems  to  be  of  an  anomalous  kind. 
The  alloy  is  hard,  but  under  some  conditions  not  rigid.  It  is  very  hard  in 
its  resistance  to  abrasion;  it  is  not  always  hard  in  its  resistance  to  impact. 

Manganese  steel  forges  readily  at  a  yellow  heat,  though  at  a  bright  white 
heat  it  crumbles  under  the  hammer.  But  it  offers  greater  resistance  to 
deformation,  i.e.,  it  is  harder  when  hot,  than  carbon  steel. 

The  most  important  single  use  for  manganese  steel  is  for  the  pins  which 
hold  the  buckets  of  elevator  dredges.  Here  abrasion  chiefly  is  to  be 
resisted.  Another  important  use  is  for  the  links  of  common  chain- 
elevators.  As  a  material  for  stamp-shoes,  for  horse-shoes,  for  the  knuckles 
of  an  automatic  car-coupler,  it  has  not  met  expectations. 

Manganese  steel  has  been  regularly  adopted  for  the  blades  of  the  Cyclone 
pulverizer.  Some  manganese-steel  wheels  are  reported  to  have  run  over 
300,000  miles  each  without  turning,  on  a  New  England  railroad. 

Manganese  Steel  and  its  Uses.  (E.  F.  Lake,  Am.  Mach.,  May  16, 
1907.)— When  more  than  2%  and  less  than  6%  of  Mn  is  added,  with  C 
less  than  0.5%,  it  makes  steel  very  brittle,  so  that  it  can  be  powdered 
under  a  hand  hammer.  From  6  %  Mn  up,  this  brittleness  gradually  dis- 
appears until  12%  is  reached,  when  the  former  strength  returns  and 
reaches  its  maximum  at  15%.  After  this,  a  decrease  in  toughness,  but 
not  in  transverse  strength,  takes  place  until  20%  is  reached,  after  which 
a  rapid  decrease  in  strength  again  takes  place. 

Steel  with  from  12  to  15%  Mn  and  less  than  0.5%  of  C  is  very  hard 
and  cannot  be  machined  or  drilled  in  the  ordinary  way ;  yet  it  is  so  tough 
that  it  can  be  twisted  and  bent  into  peculiar  shapes  without  breaking. 
It  is  malleable  enough  to  be  used  for  rivets  that  are  to  be  headed  cold. 

This  hardness,  toughness  and  malleability  make  manganese  steel  the 
most  durable  metal  known,  in  its  ability  to  resist  wear,  for  such  parts 
as  the  teeth  on  steam-shovel  dippers,  \vhere  they  will  outwear  about  three 
teeth  made  of  the  best  tool  steel ;  for  plow  points  on  road-building  work ; 
for  frogs,  switches  and  crossings  in  railroad  construction;  for  fluted  or 
toothed  crushing  rolls  used  on  ore,  coal  and  stone  crushers;  for  gears, 
sprockets,  link  belts,  etc.,  when  used  in  places  where  they  are  subjected 
to  the  grinding  wear  of  gritty  particles  of  dust. 

The  higher  the  percentage  of  C  in  the  steel,  the  less  percentage  of  Mn 
will  be  required  to  produce  brittleness.  Si,  however,  neutralizes  the 
injurious  tendencies  of  Mn,  and  in  Europe  the  Si-Mn  alloy  is  used  for 
automobile  springs  and  gears.  This  steel  is  not  high  in  Mn  and  can  be 
rolled,  while  the  peculiar  properties  given  to  steel  by  the  addition  of  from 
12  to  15%  of  manganese  make  such  steel  impossible  to  roll;  therefore  all 
parts  made  of  this  steel  have  to  be  cast,  after  which  it  can  be  forged  and 
rendered  tougher  by  quenching  from  a  white  heat. 

One  of  its  peculiarities  is  that  it  is  softened  by  rapid  cooling  and  can  be 
restored  to  its  former  hardness  by  heating  to  a  bright  red. 

It  is  more  difficult  to  mold  in  the  foundry  than  the  ordinary  cast  steel, 
as  it  must  be  poured  at  a  very  high  temperature,  and  in  cooling  it  shrinks 
nearly  twice  as  much.  The  shrinkage  allowed  for  patterns  to  be  cast  of 
the  ordinary  cast  steel  is  3/16  in.  per  foot,  and  for  manganese-steel  cast- 
ings 5/i6  in.  per  foot. 

This  enormous  shrinkage  makes  it  impossible  to  cast  in  any  intricate 
or  delicate  shapes,  and  as  it  is  too  hard  to  machine  or  drill  successfully, 
all  holes  must  be  cored  in  the  casting.  If  a  close  fit  is  desired  in  these 
they  must  be  ground  out  with  an  emery  wheel.  These  properties  limit 
its  use  to  a  large  extent. 

The  composition  that  seems  to  give  the  best  results  is:  Mn,  from  12 
to  15 % ;  C,  not  over  0.5 % ;  P,  not  over  0.04  % ;  S,  not  over  0.04 %. 

Manganese-steel  castings  should  be  annealed  in  order  to  remove  any 
internal  strains  which  may  be  caused  by  its  high  shrinkage  and  the  fact 
that  the  outer  surface  cools  so  much  quicker  than  the  core,  which  leaves 
the  center  of  the  casting  strained.  This  can  be  done  by  heating  to  1500° 
.  F.  and  quenching  in  water,  after  which  it  can  be  hardened  by  heating  to 
900°  and  allowed  to  cool  slowly.  Manganese-steel  castings,  when 
tested  in  a  7/8-inch  round  bar,  should  show: 

T.  S.  per  sq.  in.,  not  less  than  140,000  lb.;  E.  L.,  not  less  than  90,000 
Ib. ;  Red.  of  area,  not  less  than  50%  ;  Elong.  in  2  in.,  not  less  than  20%,. 

A  new  manganeses  steel  containing  between  5  and  9  %  of  manganese, 
with  carbon  ranging  from  about  0.7  to  about  1.3%,  is  described  in  U.  S. 
Patent  1,113,539,  Oct.  13,  1914,  assigned  to  Taylor-Wharton  Iron  & 


496 


STEEL. 


Steel  Co.     It  is  said  to  possess  the  characteristic  hardness  of  regular 
manganese  steel,  while  being  cheaper. 

Chrome  Steel.  (F.  L.  Garrison,  Jour.  F.  I.,  Sept.,  1891.) — Chromium 
increases  the  hardness  of  iron,  perhaps  also  the  tensile  strength  and 
elastic  limit,  but  it  lessens  its  weldability. 

Chromium  does  not  appear  to  give  steel  the  power  of  becoming  harder 
when  quenched  or  chilled.  Howe  states  that  chrome  steels  forge  more 
readily  than  tungsten  steels,  and  when  not  containing  over  0.5  of  chro- 
mium nearly  as  well  as  ordinary  carbon  steels  of  like  percentage  of  carbon. 
On  the  whole,  the  status  of  chrome  steel  is  not  satisfactory.  There  are 
other  steel  alloys  coming  into  use,  which  are  so  much  better  that  it  would 
seem  to  be  only  a  question  of  time  when  it  will  drop  entirely  out  of  the 
race.  Howe  states  that  many  experienced  chemists  have  found  no 
chromium,  or  but  the  merest  traces,  in  chrome  steel  sold  in  the  markets. 

J.W.  Langley  (Trans.  A.S.C.E.,  1892)  says:  Chromium,  like  manganese, 
is  a  true  hardener  of  iron  even  in  the  absence  of  carbon.  The  addition  of 
1  %  or  2  %  of  chromium  to  a  carbon  steel  will  make  a  metal  which  gets 
excessively  hard.  Hitherto  its  principal  employment  has  been  in  the 
production  of  chilled  shot  and  shell.  Powerful  molecular  stresses  result 
during  cooling,  and  the  shells  frequently  break  spontaneously  months 
after  they  are  made. 

Tungsten  Steel — Mushet  Steel.  (J.  B.  Nau,  Iron  Age,  Feb.  11, 
1892.) — By  incorporating  simultaneously  carbon  and  tungsten  in  iron, 
it  is  possible  to  obtain  a  much  harder  steel  than  with  carbon  alone,  with- 
out danger  of  an  extraordinary  brittleness  in  the  cold  metal  or  an  in- 
creased difficulty  in  the  working  of  the  heated  metal. 

When  a  special  grade  of  hardness  is  required,  it  is  frequently  the 
custom  to  use  a  high  tungsten  steel,  known  in  England  as  special  steel. 
A  specimen  from  Sheffield,  used  for  chisels,  contained  9.3  %  of  tungsten, 
0.7%  of  silver,  and  0.6%  of  carbon.  This  steel,  though  used  with  ad- 
vantage in  its  untempered  state  to  turn  chilled  rolls,  was  not  brittle; 
nevertheless  it  was  hard  enough  to  scratch  glass. 

A  sample  of  Mushet's  special  steel  contained  8.3  %  of  tungsten  and 
1.73  %  of  manganese. 

According  to  analyses  made  by  the  Due  de  Luynes  of  ten  specimens 
of  the  celebrated  Oriental  damasked  steel,  eight  contained  tungsten,  two 
of  them  in  notable  quantities  (0.518  %  to  1  %) ,  while  in  all  of  the  samples 
analyzed  nickel  was  discovered  ranging  from  traces  to  nearly  4%. 

Stein  &  Schwartz,  of  Philadelphia,  in  a  circular  say:  It  is  stated  that 
tungsten  steel  is  suitable  for  the  manufacture  of  steel  magnets,  since  it 
retains  its  magnetism  longer  than  ordinary  steel.  Cast  steel  to  which 
tungsten  has  been  added  needs  a  higher  temperature  for  tempering  than 
ordinary  steel,  and  should  be  hardened  only  between  yellow,  red,  and 
white.  Chisels  made  of  tungsten  steel  should  be  drawn  between  cherry- 
red  and  blue,  and  stand  well  on  iron  and  steel.  Tempering  is  best  done 
in  a  mixture  of  5  parts  of  yellow  rosin,  3  parts  of  tar,  and  2  parts  of 
tallow,  and  then  the  article  is  once  more  heated  and  then  tempered  as 
usual  in  water  of  about  15°  C. 

Aluminum  Steel.  (Aluminum  Co.  of  America,  1909.) — Aluminum  is 
added  to  steel:  To  increase  the  soundness  of  tops  of  ingots,  and  conse- 
quently decrease  the  scrap  losses;  to  quiet  the  ebullition  in  molten 
steel,  permitting  the  successful  pouring  of  "wild"  steel;  to  prevent 
oxidation  and  increase  the  homogeneity  of  the  steel ;  to  increase  tensile 
strength  without  decreasing  ductility;  to  remove  oxygen  or  oxides,  the 
aluminum  acting  as  a  deoxidizer;  to  reduce  the  liability  of  the  steel  to 
oxidation;  to  produce  smoother  surfaced  castings  and  ingots  than  is 
possible  without  the  use  of  aluminum. 

Aluminum  is  not  a  hardener  of  steel,  and  none  of  its  alloys  with  steel 
have  proved  advantageous.  Strictly  speaking,  there  is  no  aluminum- 
steel  in  the  sense  that  there  is  nickel-steel  or  chromium-steel.  Alumi- 
num is  the  principal  deoxidizer  of  steel ;  100  parts  by  weight  of  oxygen 
will  combine  with  114  parts  of  aluminum,  140  parts  of  silicon  or  350  parts 
of  manganese.  The  aluminum  wiU  entirely  disappear  if  there  is  any 
oxygen  present,  and  it  only  appears  in  completely  deoxidized  steel.  J 
too  much  aluminum  be  added,  the  metal  is  liable  to  form  deep  pipes  in 
the  ingots.  To  add  the  correct  quantity  requires  experience,  but  suc- 
cessful results  have  been  obtained  by  adding  from  one-eighth  to  three- 
fourth  pound  of  aluminum  to  the  ton  of  steel.  Steel  ingots  which  are 


"ALLOY"  STEELS. 


497 


to  be  hammered  or  rolled  have  been  improved  by  the  addition  of 
two  to  four  ounces  of  aluminum  per  ton  of  steel.  For  steel  castings,  to 
insure  soundness  and  absence  of  blowholes,  16  to  32  ounces  per  ton  may 
be  advantageously  added.  The  aluminum  may  be  added  by  throwing 
the  metal  in  small  pieces  into  the  ladle  as  the  metal  is  poured  into  it,  or 
by  the  use  of  ferro-aluminum  placed  in  the  ladle  before  pouring  the  steel. 
The  metal  is  more  commonly  used  in  America,  and  the  alloy  in  England. 

Nickel  Steel. — The  remarkable  tensile  strength  and  ductility  of  nickel 
steel,  as  shown  by  the  test-bars  and  the  behavior  of  nickel-steel  armor- 
plate  under  shot  tests,  are  witness  of  the  valuable  qualities  conferred 
upon  steel  by  the  addition  of  a  few  per  cent  of  nickel. 

Nickel  steel  has  shown  itself  to  be  possessed  of  some  exceedingly  valuable 
properties;  these  are,  resistance  to  cracking,  high  elastic  limit,  and  homo- 
geneity. Resistance  to  cracking,  a  property  to  which  the  name  of  non-fissi- 
bility  has  been  given  is  shown  more  remarkably  as  the  percentage  of  nickel 
increases.  Bars  of  27  %  nickel  illustrate  this  property.  A  1  J£-in.  square 
bar  was  nicked  1/4  in.  deep  and  bent  double  on  itself  without  further  fracture 
than  the  splintering  off,  as  it  were,  of  the  nicked  portion.  Sudden  failure 
or  rupture  of  this  steel  would  be  impossible;  it  seems  to  possess  the  tough- 
ness of  rawhide  with  the  strength  of  steel.  With  this  percentage  of  nickel 
the  steel  is  practically  non-corrodible  and  non-magnetic.  The  resistance 
to  cracking  shown  by  the  lower  percentages  of  nickel  is  best  illustrated  in 
the  many  trials  of  nickel-steel  armor. 

In  such  places  (shafts,  axles,  etc.)  where  failure  is  the  result  of  the  fatigue 
of  the  metal  this  higher  elastic  limit  of  nickel  steel  will  tend  to  prolong  in- 
definitely the  life  of  the  piece,  and  at  the  same  time,  through  its  superior 
toughness,  offer  greater  resistance  to  the  sudden  strains  of  shock. 

Howe  states  that  the  hardness  of  nickel  steel  depends  on  the  proportion 
of  nickel  and  carbon  jointly,  nickel  up  to  a  certain  percentage  increasing 
the  hardness,  beyond  this  lessening  it.  Thus  while  steel  with  2%  of  nickel 
and  0.90%  of  carbon  cannot  be  machined,  with  less  than  5%  nickel  it  can 
be  worked  cold  readily,  provided  the  proportion  of  carbon  be  low.  As  the 
proportion  of  nickel  rises  higher,  cold-working  becomes  less  easy.  It  forges 
easily  whether  it  contain  much  9r  little  nickel. 

The  presence  of  manganese  in  nickel  steel  is  most  important,  as  it 
appears  that  without  the  aid  of  manganese  in  proper  proportions  the 
conditions  of  treatment  would  not  be  successful. 

Properties  of  Nickel  Steel.  —  D.  H.  Browne,  in  Proc.  A.  I.  M.  E., 
1899,  gives  a  paper  of  79  pages,  entitled  "Nickel  Steel:  a  synopsis  of 
experiment  and  opinion,"  including  a  bibliography  containing  50  titles. 
Some  extracts  from  this  paper  are  here  given. 

Commercially  pure  nickel,  containing  98.13  Ni,  1.15  Co,  0.43  Fe, 
0.08  Si,  0.11  Mn,  showed  the  following  physical  properties: 


L.  P.* 

E.  L. 

T.  S. 

M.  E.* 

El.,  % 
in  2  in. 

CEst  bars 

5,119 

12,557 

40,669 

23,989,140 

18.2 

T3  (  Raw         

9,243 

21,045 

72,522 

29,506,500 

43.9 

~  <  Annealed  

17,064 

18,059 

72,806 

26,870,800 

48.6 

f§  (  Quenched  

16,921 

71,860 

45.0 

Limit  of  Proportionality.         *  Modulus  of  Elasticity. 
ANNEALED  CAST  BARS  OF  NICKEL  STEEL  WITH  C  0.15  to  0.20. 


(Had- 


field.)  The  proportion  of  Ni  used  in  soft  steels  for  armor  and  for  engine- 
forcings  is  from  3  to  3.5%.  With  0.25  C  this  produces  an  E.  L.  and  T. 
S.  equal  to  open-hearth  steel  of  0.45  C  without  Ni,  with  a  ductility 
equal  to  that  of  the  lower-carbon  steel. 

NICKEL  STEEL,  3.25  Ni,  AND  SIMPLE  STEEL  PORGINGS  COMPARED. 
(Bethlehem  Steel  Co.) 


C. 

Ni. 

T.  S. 

E.L. 

El., 

%• 

Red. 
Area, 

%• 

C. 

Ni. 

T.S. 

E.L. 

EL, 

%• 

Red. 
Area, 

%• 

0.20 
0.30 
0.40 
0.50 

0 
0 
0 
0 

55000 
75000 
85000 
95000 

28000 
37000 
43000 
48000 

34 
30 
25 
21 

60 
50 
45 
40 

0.20 
0.30 
0.40 
0.50 

3.5 
3.5 
3.5 
3.5 

85000 
95000 
110000 
125COO 

48000 
60000 
72000 
£5000 

26 
22 
18 
13 

55 

48 
40 
32 

498  STEEL, 

.As  compared  with  simple  steels  of  the  same  tensile  strength  a  3% 
nickel  steel  will  have  from  10  to  20%  higher  E.  L.  and  from  20  to  30% 
greater  elongation,  while  as  compared  with  simple  steels  of  the  same 
carbon,  the  nickel  steel,  up  to  5%  Ni,  will  have  about  40%  greater  tensile 
strength,  with  practically  the  same  elongation  and  reduction  of  area 

Cholat  and  Harmet  found  with  0.30  C  and  15%  Ni  a  T.  S.  of  213  400* Ibs 
per  sq.  in.;  when  oil-tempered  a  T.  S.  of  277,290  and  an  E.  L.  of  166  300' 

Riley  states  that  steel  of  25%  Ni  and  0.27  C  gave  a  T  S  of  102  600 
and  elong.  29%,  while  steel  of  25%  Ni  gave  94,300  T.  S.  and  40%  elong. 
Steels  high  m  Ni  are  entirely  different  in  physical  properties  from  low- 
nickel  steels. 

EFFECT  OF  Ni  ON  HARDNESS.  —  Gun  barrels  with  4.5%  Ni  and  0  30  C  are 
3!&^8r  lrry  CS1fSeiT-  S'  §°'00.°'  elon£-  25%,  red.  of  area  45%'.  Rolls 
with  5%  Ni  and  1  %  C  turned  easier  than  simple  steel  of  1  %  C.  If  a  steel 
contains  less  than  6%  Ni  the  influence  of  the  C  present  on  the  hardness 
produced  by  water  quenching  is  strongly  marked.  Above  8%  Ni  the  effect 
of  the  C  seems  to  be  masked  by  the  Ni;  steel  with  18%  Ni  is  as  hard  and 
elastic  with  0.30  as  with  0.75  C.  If  steel  with  18%  Ni  and  0.60  C  be  heated 
and  plunged  in  water  it  will  be  perceptibly  softened,  and  if  the  Ni  is 
raised  to  25%  this  softening  is  very  noticeable. 
'  COMPRESSION  TESTS  OF  LOW-CARBON  NICKEL  STEELS.  (Hadfield.) 


Carbon 

0.13 
0.95 
20 
49 

0.14 
1.92 
27 
47 

0.19 
3.82 
28 
41 

0.18 
5.81 
40 
37 

0.17 
7.65 
40 
33 

0.16 
9.51 
70 
3 

0.18 
11.39 
100 
1 

0.23 
13.48 
80 
1 

0.19 
19.64 
80 
3 

0.16 
24.51 
50 
16 

0.14 
29.07 

24 
41 

Nickel...-  
E.  L.t  tons  
Shortening*  .  .  . 

*  Shortening  by  100-ton  load,  %. 

SPECIFIC  GRAVITY. — The  sp.  gr.  of  low-carbon  nickel  steels  containing 
up  to  15%  Ni  is  about  the  same  as  that  of  carbon  steel,  from  7.86  to  7.90; 
from  19  to  39%  Ni  it  is  from  7.91  to  8.08;  one  sample  of  wire  of  29%  Ni, 
however,  being  reported  at  8.4.  A  44%  Ni  steel,  according  to  Guillaume, 
lias  a  sp.  gr.  of  8.12. 

THE  RESISTANCE  OF  CORROSION  of  nickel  steel  increases  with  the  per- 
centage of  Ni  up  to  18.  "This  alloy  is  practically  non-corrodible." 
"Tico  "  resistance  wire,  27.5%  Ni,  was  very  slightly  rusted  after  a  year's 
exposure  in  a  wet  cellar;  iron  wire  under  the  same  conditions  was  entirely 
changed  to  oxide.  With  the  ordinary  nickel  steels,  3  to  3.5%  Ni,  corrosion 
is  slightly  less  than  in  simple  steels. 

ELECTRICAL  RESISTANCE.  —  All  nickel  steels  have  a  high  electrical  resist- 
ance which  does  not  seem  to  vary  much  with  the  percentage  of  Ni.  The 
resistance  wires,  "Tico,"  "Superior,"  and  "Climax,"  containing  from  25 
to  30%  Ni,  have  about  48  times,  while  German  silver  has  about  18  times 
the  resistance  of  copper. 

MAGNETIC  PROPERTIES.  —  According  to  Guillaume  all  nickel  steels  below 
25.7%  Ni  can  be,  at  the  same  temperature,  either  magnetic  or  non- 
magnetic, according  to  their  previous  heat-treatment,  and  they  show 
different  properties  at  ascending  and  at  descending  temperatures.  The 
low-nickel  steels,  3  to  5%  Ni,  possess  a  magnetic  permeability  greater  than 
that  of  wrought  iron. 

Nickel  Steel  for  Bridges.  —  J.  A.  L.  Waddell,  Trans.  A.  S.  C.  E.,  1908, 
presents  at  length  an  argument  in  favor  of  the  use  of  nickel  steel  in  long- 
span  bridges. 

Some  Uses  of  Nickel  Steel.  (F.  L.  Sperry,  A .  I.  M.  E.,  xxv,  51.)  —  The 
propeller  shaft  of  the  U.  S.  cruiser  Brooklyn  was  made  of  hollow-forged, 
oil-tempered  nickel  steel,  17  in.  outside,  11  in.  inside  diam.,  length  38  ft.  11 
in.,  weight  per  foot,  449  Ibs.  Test  bars  cut  from  the  tube  gave  T.  S.,  90,350 
to  94,245;  E.  L.,  56,470  to  60,770;  El.  in  2  in.,  25.5  to  28.0%;  Red.  of  area, 
59.8  to  61.3%.  A  solid  shaft  of  the  same  elastic  strength  of  simple  steel, 
having  anE.L.of  3/5of  that  of  the  nickel  steel,  would  be  18.9  in.  diam.,  and 
would  have  weighed  920  Ibs.  per  foot. 

The  rotating  field  of  the  5000  H.P.  electric  generators  of  the  Niagara 
Falls  Power  Co.  is  inclosed  in  a  ring  of  forged  nickel  steel,  outside  diam. 
1393/8  in.;  inside,  130  in.;  width,  503/4  in.;  weight,  28,840  Ibs.  It  travels 
at  the  rate  of  nearly  two  miles  per  minute. 

Nickel  steel  wire  with  27.7%  Ni  and  0.40  C  used  for  torpedo  defense 
netting,  0.116  in.  diam.,  gave  a  T.  S.  of  198,700;  El.  in  2  in.,  6.25%;  Red. 
of  area,  16,5%. 


499 

Flange  plate  of  soft  nickel  steel,  Ni.  2.69;  C,  0.08;  Mn,  0.36;  P,  0.045;  S, 
0.038,  gave,  average  of  6  tests,  T.  S-,  65,760;  E.  L.,  47,080;  El.  in  8  in., 
24.8%:  Red.  of  area,  52.0%.  For  comparison:  Soft  carbon  steel,  C, 
0.10;  Mn,  0.27;  P,  0.048;  S,  0.039;  T.  S.,  54,450;  E.  L.,  35.240;  El.,  27.4%; 
Red.  of  area,  55.3%. 

Coefficients  of  Expansion  of  Nickel  Steel.  (D.  H.  Browne, 
A.L  M.  E.,  1899.)  —  Per  degree  C.  (Prefix  0.0000  to  the  figures  here  given.) 
%  Ni.  26.  28.  28.7  30.4  31.4  34.6  35.6  37.3  39.4  44.4 
Coeff.  1312  1131  1041  0458  0340  0137  0087  0356  0537  0856 

For  comparison:  Brass,  1878;  Hard  steel,  1239;  Soft  steel,  1078; 
Platinum,  0884;  Glass,  0861;  Nickel,  1252.  Ordinary  commercial  nickel 
steels,  containing  3  to  4%  Ni,  have  coefficients  about  the  same  as  carbon 
steel.  See  also  page  567. 

Invar  is  a  nickel-iron  alloy,  which  is  characterized  by  an  extraordinarily 
low  coefficient  of  expansion  at  ordinary  temperatures.  The  analysis  is 
about  as  follows:  —  carbon,  0.18;  nickel,  35.5%;  manganese,  0.42,  —  the 
other  elements  being  low.  Guillaume  gives  the  mean  coefficient  of 
expansion  for  an  alloy  containing  35.6%  nickel  as  (0.877  +  0.00117  010~6 
between  temperatures  0°  C.  and  t°  C.  where  t  does  not  exceed  200°  C. 
This  material  is  used  in  measuring  instruments  and  for  standards  of 
length,  chronometers,  etc.  Its  expansion  as  compared  with  ordinary 
steel  is  about  as  1:11.5;  with  brass,  as  1:17.2;  with  glass,  as  1  :  8.5.  Alloys 
either  richer  or  poorer  in  nickel  show  much  greater  expansion,  and  the 
alloy  containing  47.5%  nickel,  known  as  "Platinite,"  has  the  same 
coefficient  of  expansion  as  platinum  and  glass.  See  also  page  507. 

Copper  Steels.  —  Pierre  Breuil  (Jour.  I.  and  S.  /.,  1907)  gives  an  account 
of  experiments  on  four  series  of  copper  steels  containing  respectively  0.15, 
0.40,  0.65,  and  1%  of  C  with  Cu  in  each  ranging  from  0  to  34%.  An  ab- 
stract of  his  principal  conclusions  is  as  follows: 

Copper  steel  does  not  yield  a  metal  capable  of  being  rolled  in  practice, 
if  Cu  exceeds  4%. 

When  in  the  ingot  state  copper  hardens  steel  in  proportion  as  there  is 
less  C  present. 

Copper  steels  as  rolled  appear  to  be  stronger  in  proportion  as  they  con- 
tain more  Cu.  This  difference  is  the  more  manifest  in  proportion  as  the 
C  is  lower. 

Annealing  leaves  the  steels  with  the  same  characteristics,  but  greatly 
reduces  the  differences  observed  in  the  case  of  the  untreated  steeJs. 
Quenching  restores  the  differences  encountered  in  the  case  of  the  steels 
as  cast. 

Copper  steels  equal  nickel  steels  in  tensile  strength  and  would  be  less 
costly  than  the  latter.  They  are  no  more  brittle  than  nickel  steels  con- 
taining equivalent  percentages  of  Ni.  The  steel  containing  0.16%  C  and 
4%  Cu  is  remarkable  in  this  respect. 

The  presence  of  copper  makes  the  cpnstituents  of  the  steel  finer, 
approximating  them  to  classes  containing  higher  percentages  of  C. 
While  hardening  the  steel  the  presence  of  Cu  does  not  render  it  brittle. 
It  confers  upon  it  a  very  fair  degree  of  elasticity,  while  leaving  the  elon- 
gation good,  thus  conducing  to  the  production  of  a  most  valuable  metal. 

Cutting  tests  were  carried  on  with  steels  containing  C  about  1  %  and 
Cu  0%,  1%,  and  3%  respectively.  The  presence  of  Cu  in  no  wise  altered 
the  cutting  properties. 

The  presence  of  Cu  was  found  to  increase  the  electrical  resistance, 
and  a  well-defined  maximum  was  shown,  coinciding  with  2%  Cu  in  0.15  C, 
with  1.7%  in  0.35%  C,  and  with  0.5%  Cu  in  0.7  to  1%  carbon  steels. 

Nickel- Vanadium  Steels.  (Eng.  Mag.,  April,  1906.)  —  M.  Leon  Guillet 
has  investigated  the  influence  of  Ni  and  Va  when  used  jointly. 

In  steels  containing  0.20  C  and  from  2  to  12%  of  Ni,  the  tensile  strength 
and  the  elastic  limit  are  both  materially  increased  by  the  addition  of 
small  percentages  of  Va.  In  no  case  should  the  Va  exceed  1%,  the  best 
results  being  secured  by  the  use  of  0.7  to  1  %.  A  steel  containing  0.20  C, 
2%  of  Ni,  and  0.7%  Va  showed  a  tensile  strength  of  91,000  Ibs.,  an 
elastic  limit  of  70,000  Ibs.,  and  an  elongation  of  23.5%.  With  1%  Va, 
the  T.  S.  increased  to  119,500  Ibs.,  and  the  E.  L.  to  91,000  Ibs.,  the  elong. 
falling  to  22%.  A  nickel  steel  of  0.20%  C  and  12%  Ni  gave,  with 
0.7  Va,  a  T.  S.  of  over  200,000  Ibs.  and  an  E.  L.  of  172,000  Ibs.  per  sq.  in., 
the  elong.  being  Q%,  while  with,  1%  V$  theT.  S,  rose  to  220,000  Ibs. 


500  STEEL. 


and  the  E  L.  to  176,000  Ibs.,  the  elongation  remaining  unchanged. 
When  the  Va  is  increased  above  l%the  tensile  strength  falls  off,  and  the 
material  begins  to  show  evidence  of  brlttleness.  Similar  effects  are  pro; 
duced  for  steels  of  the  higher  carbon,  but  in  a  lesser  degree. 

Whpn  the  nickel-vanadium  steels  are  subjected  to  a  tempering  procsss 
th  Tbeneficial  Sets  of  theVa  are  still  further  emphasized    .The  temper- 


i 

and  an  E.  L.  of  150,000  Ibs.,  the  resistance  to  shock  and  the  h 
being  also  increased. 

Static  and  Dynamic  Properties  of  Steels.    (W.  L.  Turner,  Ira 
July  2,  1908.)  —  The  term  "crystallization"  is  a  name  given  to  designate 
Phenomena  due  to  the  influences  of  shock   and   alternating   stresses 
whether  pure  or  combined.     The  name  has  been  advantageously  altered 
to  "  intermodular  disintegration,"  but,  whatever  we  choose  to  call  it, 
there  remains  the  evidence  that  some  modification  takes  place  in  the 
structure  of  steel  when  the  above-named  forces  are  to  be  dealt  with. 
Resistance  to  fatigue  is  not  a  function  of  static  strength 
An  example  of  our  knowledge  of  the.  "life"  properties  of  ordinary  st 
is  the  case  of  the  staying  of  a  locomotive  fire-box.     Something  is 
quired    which   will   possess   considerable   strength   combined    with    the 
power  to  withstand  a  moderate  degree  of  flexure  in  all  directions.     Expe- 
rience has  shown  that  the  use  of  anything  but  the  mildest  steel  for  this 
work  is  prohibitive,  and  that  wrought  iron,  or  even  copper,  is  still  more 

The  writer  has  completed  a  preliminary  investigation  into  the  relative 
dynamic  properties  of  iron  and  the  various  ordinary  and  alloy  steels 
the  results  being  given  in  the  accompanying  table.  The  conditions  of 
the  "dynamic"  tests  were  as  follows: 

A  cylindrical  test-piece,  6  in.  long,  3/8  in.  diam.,  finished  with  emery  to 
remove  all  tool  marks,  is  clamped  at  one  end  in  a  vise.  A  tool-steel 
head,  in  which  there  is  cut  a  slot,  is  placed  over  the  other  end,  the  dis- 
tance from  the  striking  center  of  this  head  to  the  vise  line  being  4  in. 
A  crank  and  connecting  rod  furnished  the  reciprocating  motion  for  this 
head,  thereby  causing  the  test-piece  to  be  deflected  3/8  in.  each  side  of 
the  neutral  position.  In  addition  to  this  alternating  flexure,  the  test- 
piece  is  also  subjected,  at  each  reversal,  to  an  impact,  due  to  the  slot  on 
the  reciprocating  head.  The  sample  undergoes  650  alternations  per 
minute.  A  deflection  of  3/g  in.  on  each  side  has  the  effect  of  imparting  a 
permanent  set  to  the  test-piece. 

On  each  class  of  steel  a  large  number  of  dynamic  tests  were  made,  an 
average  being  taken  of  the  results  after  elimination  of  those  figures  which 
were  apparently  abnormal. 

It  is  apparent  that  the  action  of  nickel  is  twofold:  1.  It  statically 
intensifies.  2.  It  dynamically  "  poisons."  As  an  instance  of  this,  take 
tests  Nos.  13  and  15,  the  former  being  a  3.7%  nickel  steel  and  the  latter  a 
chrome-vanadium  steel.  In  the  annealed  condition,  the  elastic  limits  of 
the  two  are  almost  identical,  but  at  the  same  time  the  alternations  of 
stress  endured  by  the  latter  are  21/4  times  the  number  sustained  by  the 
nickel  steel.  Take  again  Nos.  17  and  18.  The  dynamic  figures  are  more 
than  three  to  one  in  favor  of  the  chrome-vanadium  product,  whereas  tha 
difference  in  elastic  limit  is  only  about  3%. 

It  is  manifest  that  the  static  action  of  vanadium  is  similar  to  that  of 
nickel,  but  that  its  dynamic  effects  are  the  exact  converse..  The  differ- 
ences are  markedly  brought  out  in  the  quality  figures,  which  invite 
attention  as  to  comparison  with  those  of  ordinary  carbon  steel.  Taking 
the  latter  as  standard,  the  chrome-vanadium  steels  are  as  much  above  it 
as  the  nickel  steels  are  below  it. 

Chromium,  per  se,  does  not  appear  to  exert  appreciable  influence  other 
than  statically,  but  it  is  possible  that  the  effect  of  this  metal  in  a  ternary 
steel  might  be  very  marked. 

The  dynamic  attributes  of  plain  carbon  steel  reach  a  maximum  with 
about  0.25%  C.  falling  away  on  both  sides  of  this  amount. 

The  quality  figure  in  the  case  of  the  chrome-vanadium  steel  does  not 


ALLOY       STEELS. 


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STEEL. 


appear  to  undergo  much  alteratipn  in  the  process  of  oil  tempering,  but 

there  are  considerable  variations  in  other  cases.  The  dynamic  test  may 
eventually  act  as  a  reliable  guide  to  the  correct  methods  for  the  heat 
treatment  of  individual  steels. 

Strength  for  strength,  the  chrome-vanadium  steels  also  have  the 
advantage  over  all  others  as  regards  machining  properties.  Chrome- 
vanadium  steel  may  be  forged  with  the  same  ease  as  ordinary  steel  of  simi- 
lar contents,  no  special  precaution  being  necessary  as  to  temperatures. 

Comparative  Effects  of  Cr  and  Va.  Sankey  and  J.  Kent  Smith,  Proc. 
Inst.  M.  E.,  1904. 


Cr.    Va. 

T.S.* 

E.L.* 

El.  in 
2  in. 

Red.  A. 

Cr.     Va. 

T.S.* 

E.L.* 

El.  in 
2  in. 

Red.  A. 

0.5     . 

34.0 

22.9 

33% 

60.6% 

1.0    0.15 

48.6 

36.2 

24 

56.6 

1.0     . 

38.2 

25.0 

30 

57.3 

1.0    0.15 

f52.6 

34.4 

25.0 

55.5 

...    0.1 

34.8 

28.5 

31 

60  0 

1.0    0.25 

60.4 

49.4 

18.5 

46.3 

...    0.15 

36.5 

30.4 

26 

59.0 

C-Mn 

27.0 

16.0 

35. 

60.0 

...     0.25 

39.3 

34.1 

24 

59.0 

C-Mn 

t32.2 

17.7 

34. 

52.6 

*  Tons,  of  2240  Ibs.,  per  sq.  in.  f  Open-hearth  steels;  all  the  others 
are  crucible.  The  last  two  steels  in  the  table  are  ordinary  carbon 
steels. 

Effect  of  Heat  Treatment  on  Cr-Va  Steel.  (H.  R.  Sankey  and 
J.  Kent  Smith,  Proc.  Inst.  M.  E.,  1904,  p.  1235.) — Various  kinds  of 
heat  treatment  were  given  to  several  Cr-Va  steels,  the  results  of  which 
are  recorded  at  length.  The  following  is  selected  as  a  sample  of  the 
results  obtained.  Steel  with  C,  0.297;  Si,  0.086;  Mn,  0.29;  Cr,  1.02;  Va, 
0.17.  gave: 


Tens. 

Str. 

Yield 
Point. 

El.  in 
2  in. 

Red. 
Area. 

Im- 
pact. 

Alter- 
na- 
tions. 

121,200 

82,650 

24.0% 

44.9% 

3.1 

1906 

Annealed  1/2  hr.  at  800°  C  

87360 

47260 

34  5 

H  1 

15  6 

2237 

Soaked  12  hours  at  800°  C  

86020 

68  100 

33  7 

51  5 

11.2 

Water  quenched  at  800°  C.   .  . 

167  100 

135'070 

7  5 

16  6 

1  2 

174 

Oil  quenched  at  800°  C  

122,080 

82880 

22  0 

35  2 

2.4 

296 

Oil  quenched  at  800°,  reheated  to 
350°  

132  830 

111  550 

23  0 

50  8 

9  0 

1314 

Water  quenched  at  1200°  C 

209  440 

191  520 

1  2 

1  5 

* 

* 

Oil  quenched  at  1200°  C  

140,220 

118i500 

8.5 

21.5 

3.0 

*  Too  hard  to  machine. 

The  impact  tests  were  made  on  a  machine  described  in  Eng'g,  Sept.  25, 
1903,  p.  431.  The  test-piece  was  8/4  in.  broad,  notched  so  that  0.137  in.  in 
depth  remained  to  be  broken  through.  The  figures  represent  ft  .-Ibs.  of 
energy  absorbed.  The  piece  was  broken  in  one  blow.  The  alternations- 
of-stress  tests  were  made  on  Prof.  Arnold's  machine,  described  in  The 
Engineer,  Sept.  2,  1904,  p.  227.  The  pieces  were  3/8in.  square,  one  end 
was  gripped  in  the  machine  and  the  free  end,  4  in.  long,  was  bent  forwards 
and  backwards  about  710  times  a  minute,  the  motion  of  the  free  end  being 
3/4  in.  on  each  side  of  the  center  line. 

Tests  by  torsion  of  the  same  steel  were  made.  The  test-piece  was  6  in. 
long,  3/4  in.  diam.  The  results  were: 


As  rolled 

•Shearing  Stress 

Twist 
Angle. 

No.  of 
Twists. 

~3~92~~ 
4.52 

Elastic  . 

Ulti- 
mate. 

45,700 
38,528 

99,900 
90,272 

1410° 
1628° 

Annealed  1/2  hr.  at  800°  C.    

"ALLOY"  STEELS.  503 

TTont-ttoaimont  of  Alloy  Steels.  (E.  F.  Lake,  Am.  Mach.,  Aug.  1, 
1907.)  —  In  working  the  high-grade  alloy  steels  it  is  very  important  that 
they  be  properly  heat  treated,  as  poor  workmanship  in  this  regard  will 
produce  working  parts  that  are  no  better  than  ordinary  steel,  although 
the  stock  used  be  the  highest  grade  procurable.  By  improperly  heat- 
treating  them  it  is  possible  to  make  these  high-grade  steels  more  brittle 
than  ordinary  carbon  steels. 

The  theory  of  heat  treatment  rests  upon  the  influence  of  the  rate  of 
cooling  on  certain  molecular  changes  in  structure  occurring  at  different 
temperatures.  These  changes  are  of  two  classes,  critical  and  progres- 
sive; the  former  occur  periodically  between  certain  narrow  temperature 
limits,  while  the  latter  proceed  gradually  with  the  rise  in  temperature, 
each  change  producing  alterations  in  the  physical  characteristics.  By 
controlling  the  rate  of  cooling,  these  changes  can  be  given  a  permanent 
set,  and  the  characteristics  can  thus  be  made  different  from  those  in  the 
metal  in  its  normal  state. 

The  results  obtained  are  influenced  by  certain  factors:  1.  The  original 
chemical  and  physical  properties  of  the  metal;  2.  The  composition  of 
the  gases  and  other  substances  which  come  in  contact  with  the  metal  in 
heating  and  cooling.  3.  The  time  in  which  the  temperature  is  raised 
between  certain  degrees.  4.  The  highest  temperature  attained.  5.  The 
length  of  time  the  metal  is  maintained  at  the  highest  temperature. 
6.  The  time  consumed  in  allowing  the  temperature  to  fall  to  atmos- 
pheric. 

The  highest  temperature  that  it  is  safe  to  submit  a  steel  to  for  heat- 
treating  is  governed  by  the  chemical  composition  of  the  steel.  Thus 
pure  carbon  steel  should  be  raised  to  about  1300°  F.,  while  some  of  the 
high-grade  alloy  steels  may  safely  be  raised  to  1750°.  The  alloy  steels 
must  be  handled  very  carefully  in  the  processes  of  annealing,  hardening, 
and  tempering;  for  this  reason  special  apparatus  has  been  installed  to 
aid  in  performing  these  operations  with  definite  results. 

The  baths  for  quenching  are  composed  of  a  large  variety  of  materials. 
Some  of  the  more  commonly  used  are  as  follows,  being  arranged  accord- 
ing to  their  intensity  on  0.85%  carbon  steel:  Mercury;  water  with  sulphuric 
acid  added;  nitrate  of  potassium;  sal  ammoniac;  common  salt;  carbonate 
of  lime;  carbonate  of  magnesia;  pure  water;  water  containing  soap, 
sugar,  dextrine  or  alcohol;  sweet  milk;  various  oils;  beef  suet;  tallow,- 
wax. 

With  many  of  these  alloy  steels  a  dual  quenching  gives  the  best  results, 
that  is,  the  metal  is  quenched  to  a  certain  temperature  in  one  bath  and 
then  immersed  in  the  second  one  until  completely  cooled,  or  it  may 
be  cooled  in  the  air  after  being  quenched  in  the  first  bath.  For  this  a 
lead  bath,  heated  to  the  proper  temperature,  is  sometimes  used  for  the 
first  quenching. 

With  the  exception  of  the  oils  and  some  of  the  greases,  the  quenching 
effect  increases  as  the  temperature  of  the  bath  lowers.  Sperm  ana  lin- 
seed oils,  however,  at  all  temperatures  between  32°  and  250°,  act  about 
the  same  as  distilled  water  at  160°. 

The  more  common  materials  used  for  annealing  are  powdered  char- 
coal, charred  bone,  charred  leather,  fire  clay,  magnesia  or  refractory 
earth.  The  piece  to  be  annealed  is  usually  packed  in  a  cast-iron  box 
in  some  of  these  materials  or  combinations  of  them,  the  whole  heated 
to  the  proper  temperature  and  then  set  aside,  with  the  cover  left  on,  to 
cool  gradually  to  the  atmospheric  temperature.  For  certain  grades  of 
steel  these  materials  give  good  results;  but  for  all  kinds  of  steels  and  for 
all  grades  of  annealing,  the  slow-cooling  furnace  no  doubt  gives  the 
best  satisfaction,  as  the  temperature  can  be  easily  raised  to  the  right 
point,  kept  there  as  long  as  necessary,  and  then  regulated  to  cool  down 
as  slowly  as  is  desired.  The  gas  furnace  is  the  easiest  to  handle  and 
regulate. 

A  high-grade  alloy  steel  should  be  annealed  after  every  process  in  man- 
ufacturing which  tends  to  throw  it  out  of  its  equilibrium,  such  as  forging, 
rolling  and  rough  machining,  .so  as  to  return  it  to  its  natural  state  of 
repose.  It  should  also  be  annealed  before  quenching,  case-hardening 
or  carbonizing. 

The  wide  range  of  strength  given  to  some  of  the  alloy  steels  by  heat 


504 


STEEL. 


treatment  is  shown  by  the  table  below.     The  composition  of  the 
was:  Ni,  2.43;  Cr,  0.42;  Si,  0.26;  C,  0.23;  Mn,  0.43;  P,  0.025;  S,  0.022. 


alloy 


•$* 

-g* 

•Sfc 

£^ 

'S? 

^0^' 

.r-r'. 

So 

-Sg 

Ik 

Is 

li 

|3 

Ig 

0> 

s°S 

S1^ 

s~ 

g~ 

6"" 

O1  ^ 

H  * 

H  * 

H  * 

H  * 

H^ 

H^ 

Tensile  Strength  . 
E.  L  

227,000 
208,000 

219,000 
203,500 

195,500 
150,000 

172,000 
148,500 

156,500 
125,000 

141,000 
102000 

109,500 
70,500 

Elong.,%  in  2  in. 

4 

6 

8 

11 

13 

15 

22 

VARIOUS    SPECIFICATIONS   FOR    STEEL. 

Structural  Steel.  —  There  has  been  a  change  during  the  ten  years  from 
1880  to  1890,  in  the  opinions  of  engineers,  as  to  the  requirements  in  speci- 
fications for  structural  steel,  in  the  direction  of  a  preference  for  metal  of 
low  tensile  strength  and  great  ductility.  The  following  specifications  for 
tension  members  at  different  dates  are  given  by  A.  E.  Hunt  and  G.  H. 
Clapp,  Trans.  A.  I.  M.  E.,  xix,  926: 


1879. 

Elastic  limit.. . .  50,000  40  < 
Tensile  strength  80,000  70 
Elongation  in  8  in.  12% 
Reduction  of  area  20% 


1881.        1882.     1885.         1887.  1888. 

^  45,000  40,000  40,000       40,000  38,000 

^80,000  70,000  70,000  67@75,000  63®  70,000 

18%  IS'%       18%  20%  22% 

30%  45%      42%          42%  45% 


F.  H.  Le.vis  (IronAqe,  Nov.  3,  1892)  says:  Regarding  steel  to  be  used 
under  the  same  conditions  as  wrought  iron,  that  is,  to  be  punched  without 
reaming,  there  seems  to  be  a  decided  opinion  (and  a  growing  one)  among 
engineers,  that  it  is  not  safe  to  use  steel  in  this  way,  when  the  ultimate 
tensile  strength  is  above  65,000  Ibs.  The  reason  for  this  is  not  so  much 
because  there  is  any  marked  change  in  the  material  of  this  grade,  but 
because  all  steel,  especially  Bessemer  steel,  has  a  tendency  to  segregations 
of  carbon  and  phosphorus,  producing  places  in  the  metal  which  are  harder 
than  they  normally  should  be.  As  long  as  the  percentages  of  carbon  and 
phosphorus  are  kept  low,  the  effect  of  these  segregations  is  inconsiderable' 
but  when  these  percentages  are  increased,  the  existence  of  these  hard 
spots  in  the  metal  becomes  more  marked,  and  it  is  therefore  less  adapted 
to  the  treatment  to  which  wrought  iron  is  subjected. 

There  is  a  wide  consensus  of  opinion  that  at  an  ultimate  of  64,000  to 
65,000  Ibs.  the  percentages  of  carbon  and  phosphorus  reach  a  point  where 
the  steel  has  a  tendency  to  crack  when  subjected  to  rough  treatment. 

A  grade  of  steel,  therefore,  running  in  ultimate  strength  from  54,000  to 
62,000  Ibs.,  or  in  some  cases  to  64,000  Ibs.,  is  now  generally  considered  a 
proper  material  for  this  class  of  work. 

A.  E.  Hunt,  Trans.  A.  I.  M.  E.,  1892,  says:  Why  should  the  tests  for  steel 
be  so  much  more  rigid  than  for  iron  destined  for  the  same  purpose?  Some 
of  the  reasons  are  as  follows:  Experience  shows  that  the  acceptable  quali- 
ties of  one  melt  of  steel  offer  no  absolute  guarantee  that  the  next  melt  to  it, 
even  though  made  of  the  same  stock,  will  be  equally  satisfactory. 

It  is  now  almost  universally  recognized  that  soft  steel,  if  properly  made 
and  of  good  quality,  is  for  many  purposes  a  safe  and  satisfactory  substitute 
for  wrought  iron,  being  capable  of  standing  the  same  shop-treatment  as 
wrought  iron.  But  the  conviction  is  equally  general,  that  poor  steel,  or  an 
unsuitable  grade  of  steel,  is  a  very  dangerous  substitute  for  wrought  iron 
even  under  the  same  unit  strains. 

For  this  reason  it  is  advisable  to  make  more  rigid  requirements  in  select- 
Ing  material  which  may  range  between  the  brittleness  of  glass  and  a  duc- 
tility greater  than  that  of  wrought  iron. 

Specifications  for  Structural  Steel  for  Bridges.  (Proc.  A.  S.  T.  M.( 
1905.) — Steel  shall  be  made  by  the  open-hearth  process.  The  chemi* 
cal  and  physical  properties  shall  conform  to  tUe  following  limits; 


VARIOUS   SPECIFICATIONS  FOR   STEEL-. 


Elements  Considered. 

Structural  Steel. 

Rivet  Steel. 

Steel  Castings 

Phosphorus,  f  Basic  .  .  . 
Max  \  Acid.  .  .  . 

0.04% 
0.08% 
0  05% 

0.04% 
0.04% 
0  04% 

0.05% 
0.08% 
0  05% 

Tensile  strength,  Ibs. 
per  SQ   in  .  .  . 

f   Desired 
|      60  000 

Desired 
50,000 

Not  less  than 
65,000 

Elong.:  Min.  %  in  8  in. 
Elong  •  Min  %  in  2  in 

(    1,500,000* 
(   tens.  str. 

1,500,000 
tens.  str. 

18 

Fracture  

Silky 

Silky 

Silky  or  fine 

Cold     bend     without 
fracture  

180°  flatf 

180°  flat* 

granular 
90°.  d=3t 

*  The  following  modifications  will  be  allowed  in.  the  requirements  for 
elongation  for  structural  steel:  For  each  Vie  inch  in  thickness  below 
5/16  inch,  a  deduction  of  2 1/2  will  be  allowed  from  the  specified  percent- 
age. For  each  Vs  inch  in  thickness  above  3/4  inch,  a  deduction,  of  1  will 
be  allowed  from  the  specified  percentage. 

t  Plates,  shapes  and  bars  less  than  1  in.  thick  shall  bend  as  called  for. 
Full-sized  material  for  eye-bars  and  other  steel  1  in.  thick  and  over,  tested 
as  rolled,  shall  bend  cold  180°  around  a  pin  of  a  diameter  twice  the  thick- 
ness of  the  bar,  without  fracture  on  the  outside  of  bend.  When  required 
by  the  inspector,  angles  3/4  in.  and  less  in  thickness  shall  open  flat,  and 
angles  1/2  in.  and  less  in  thickness  shall  bend  shut,  cold,  under  blows  of 
a  hammer,  without  sign  of  fracture. 

J  Rivet. steel,  when  nicked  and  bent  around  a  bar  of  the  same  diam- 
eter as  the  rivet  rod,  shall  give  a  gradual  break  and  a  fine,  silky,  uniform 
fracture. 

If  the  ultimate  strength  varies  more  than  4000  Ibs.  from  that  desired, 
a  retest  may  be  made,  at  the  discretion  of  the  inspector,  on  the  same 
gauge,  which,  to  be  acceptable,  shall  be  within  5000  ibs.  of  the  desired 
strength. 

Chemical  determinations  of  C,  P,  S,  and  Mn  shall  be  made  from  a 
test  ingot  taken  at  the  time  of  the  pouring  of  each  melt  of  steel.  Check 
analyses  shall  be  made  from  finished  material,  if  called  for  by  the  pur- 
chaser, in  which  case  an  excess  of  25%  above  the  required  limits  will  be 
allowed. 

Specimens  for  tensile  and  bending  tests  for  plates,  shapes  and  bars 
shall  be  made  by  cutting  coupons  from  the  finished  product,  which  shall 
have  both  faces  rolled  and  both  edges  milled  with  edges  parallel  for  at 
least  9  in.;  or  they  may  be  turned  3/4  in.  diam.  for  a  length  of  at  least 
9  in.,  with  enlarged  ends.  Rivet  rods  shall  be  tested  as  rolled.  Speci- 
mens shall  be  cut  from  the  finished  rolled  or  forged  bar  in  such  manner 
that  the  center  of  the  specimen  shall  be  1  in.  from  the  surface  of  the  bar. 
The  specimen  for  tensile  test  shall  be  turned  with  a  uniform  section  2  in. 
long,  with  enlarged  ends.  The  specimen  for  bending  test  shall  be  1  X  1/2 
in.  in  section. 

Specifications  for  Steel  for  the  Manhattan  Bridge.  (Eng.  News, 
Aug.  3,  1905.)  — 

MATERIAL  FOR  CABLES.  SUSPENDERS  AND  HAND  ROPES.  Open- 
hearth  steel.  (The  wire  for  serving  the  cables  shall  be  made  of  Norway 
iron  of  approved  quality.)  The  ladle  tests  of  the  steel  shall  contain  not 
more  than  :  C,  0.85;  Mn,  0.55;  Si,  0.20;  P,  0.04;  S,  0.04;  Cu,  0.02%. 
The  wire  shall  have  an  ultimate  strength  of  not  less  than  215,000  Ibs. 
per  sq.  in.  before  galvanizing,  and  an  elongation  of  not  less  than  2%  in 
12  in.  The  bright  wire  shall  be  capable  of  bending  cold  around  a  rod 
]i/2'  times  its  own  diam.  without  sign  of  fracture.  The  cable  wire  before 
galvanizing  shall  be  0.192  in.  ±  0.003  in.  in  diam.;  after  galvanizing,  the 
wire  shall  have  an  ultimate  strength  of  not  less  than  200,000  Ibs.  per  sq. 
in.  of  gross  section. 


506 


STEEI*. 


CARBON  STEEL.  The  ladle  tests  as  usually  taken  shall  contain  not 
more  than:  P,  0.04;  S,  0.04;  Mn,  0.60;  Si,  0.10%.  The  ladle  tests  of 
the  carbon  rivet  steel  shall  contain  not  more  than:  P,  0.035;  S,  0.03. 
Rivet  steel  shall  be  used  for  all  bolts  amd  threaded  rods. 

NICKEL  STEEL.  The  ladle  test  shall  contain  not  less  than  3.25  Ni, 
and  not  more  than:  P,  0.04;  S,  0.04;  Mn,  0.60;  Si,  0.10;  nickel  rivet  steel 
not  more  than:  P,  0.035;  S,  0.03%. 

Nickel  steel  for  plates  and  shapes  in  the  finished  material  must  show: 
T.  S.,  85,000  to  95,000  Ibs.  per  sq.  in.;  E.  L.,  55,000  Ibs.  min.;  elong.  in 
8  ins.,  min.,  =  1,600,000  4-  T.  S.;  min.  red.  of  area,  40%. 

Specimens  cut  from  the  finished  material  shall  show  the  following 
physical  properties: 


Material. 

T.  S.,  Ibs.  persq. 
in. 

Min.E.L. 
Ibs.  per 
sq.  in. 

Min. 
Elong., 
%  in  8  in. 

Min.  Red. 
of  Area. 

%. 

Shapes  and  universal  mill 
plates  

60,000  to  68,000 

33  000 

44 

Eye-bars,  pins  and  rollers. 
Sheared  plates  

64,000  to  72,000 
60,000  to  68  000 

35,000 
33  000 

1,500,000 

40 

44 

Rivet  rods 

50  000  to  58  000 

30  000 

~~TT'  P 

50 

High-carbon      steel      for 
trusses  

85,000  to  95,000 

45,000 

35 

Nickel  rivet  steel:  T.  S.,  70,000  to  80,000;  E.  L.,  min.,  45,000;  elong., 
min.,  1,600,000  •*•  T.  S.,  %  in  8  ins. 

STEEL  CASTINGS.  The  ladle  test  of  steel  for  castings  shall  contain 
not  more  than:  P,  0.05;  S,  0.05;  Mn,  0.80;  Si,  0.35%.  Test-pieces  taken 
from  coupons  on  the  annealed  castings  shall  show  T.  S.,  65,000;  E.  L., 
35,000;  elong.  20%  in  8  ins.  They  shall  bend  without  cracking  around  a 
rod  three  times  the  thickness  of  the  test-piece. 


Specifications  for  Steel.     (Proc.  A.  S.  T.  M.,  1905.) 


Steel  Forgings. 

Kind  of 
Steel. 

Tensile 
Strength. 

Elast. 
Limit. 

El.  in 
2  in., 

%. 

Red 
Area. 

%• 

Solid  or  hollow  forgings,  no  diam. 
or  thickness  of  section  to  exceed 

IS. 

Ic. 

|C.A. 

58,000 
75,000 
80,000 

29,000* 
37,500* 
40,000 

28 
18 
22 

35  (a) 
30  (c) 
35  (b) 

10  in. 

JN.A. 

80,000 

50,000 

25 

45  (a) 

Solid  or  hollow    forgings,    diam. 
not  to  exceed  20  in.  or  thickness 
of  section  15  in. 

)C.A. 
JN.A. 

75000 
80,000 

37,500 
45,000 

23 
25 

35  (b) 
45  (a) 

Solid  forgings  over  20  in.            .... 

C.A. 

70,000 

35,000 

24 

30  (c) 

Solid  forgings                    

N.A. 

80,000 

45,000 

24 

40  (a) 

Solid  or  hollow  forgings,  diam.  or 
thickness  not  over  3  in. 

)C.O. 

JN.O. 

90,000 
95,000 

55,000 
65,000 

20 
21 

45  (b) 
50  (b) 

Solid  rectangular  sections,  thick- 
ness  not    over  6  in.,  or   hollow 
with  walls  not  over  6  in.  thick. 

Jc.o. 

JN.O. 

85,000 
90,000 

50000 
60,000 

22 
22 

45  (b) 
50  (b) 

Solid  rect.  sections,  thickness  not 
over  10  in.,  or  hollow  with  walls 
not  over  10  in.  thick. 

Jc.o. 

JN.O. 

80,000 
85,000 

45,000 
55,000 

23 

24 

40  (b) 

45  (b) 

Locomotive  forgings             

* 

80,000 

40,000 

20 

25  (d) 

*  The  yield  point,  instead  of  the  elastic  limit,  is  specified  for  soft  steel 
and  carbon  steel  not  annealed.  It  is  determined  by  the  drop  of  the 
beam  or  halt  in  the  gauge  of  the  testing  machine.  The  elastic  limit, 
specified  for  all  other  steels,  is  determined  by  an  extensometer,  and  is 
defined  as  that  point  where  the  proportionality  changes.  The  standard 
test  specimen  is  1/2  in.  turned  diam.  with  a  gauged  length  of  3  iaches. 


VARIOUS   SPECIFICATIONS   1'OK   STJEEIi. 


507 


Kind  of  steel:  S.,  soft  or  low  carbon.  C.,  carbon  steel,  not  annealed. 
C.  A.,  carbon  steel,  annealed.  C.  O.,  carbon  steel,  oil  tempered.  N.  A., 
nickel  steel,  annealed.  N.  O.,  nickel  steel,  oil  tempered.  Bending 
tests:  A  specimen  1  X  V2  in.  shall  bend  cold  180°  without  fracture  on 
outside  of  bent  portion,  as  follows:  (a)  around  a  diam.  of  1/2  in.;  (6) 
around  a  diam.  of  1  in.;  (c)  around  a  diam.  of  1/2  in.;  (d)  no  bending 
test  required. 

Chemical  composition:  P  and  S  not  to  exceed  0.10  in  low-carbon  steel, 
0.06  in  carbon  steel  not  annealed,  0.04  in  carbon  or  nickel  steel  oil  tem- 
pered or  annealed,  0.05  in  locomotive  forgings.  Mn  not  to  exceed  0.60 
in  locomotive  forgings.  Ni  3  to  4%  in  nickel  steel. 

Specifications  for  Steel  Ship  Material.  (Amer.  Bureau  of  Shipping, 
1900.  Proc.  A.  S.  T.  M.t  1906,  p.  175.)  — 


For  Hull  Construction. 

Tens.  Strength. 

E.  L. 

El.  in 
8  in..  %. 

Plates,  angles  and  shapes 

58  000  to  60  000 

1/2  T.  S 

22*    18t 

Castings  

60  000  to  75  000 

15 

Forgings  

55  000  to  65  000 

20 

*  In  plates  18  Ibs.  per  sq.  ft.  and  over.         f  In  plates  under  18  Ibs. 

FOR  MARINE  BOILERS:  Open-hearth  steel;  Shell:  P  and  S,  each  not  over 
0.04%.  Fire-box,  not  over  0.035%.  Tensile  Strength:  Rivet  steel, 
45,000  to  55,000;  Fire-box,  52,000  to  62,000;  Shell,  55,000  to  73,000; 
Braces  and  stays,  55,000  to  65,000;  Tubes  and  all  other  steel,  52,000  to 
62,000  Ibs.  per  sq.  in. 

Elongation  in  8  in.:  Rivet  steel,  28%;  Plates  3/8  in.  and  under,  20%; 
3/8  to  3/4  in.,  22%;  3/4  in.  and  over,  25%. 

COLD  BENDING  AND  QUENCHING  TESTS.  Rivet  steel  and  all  steel  of 
52,000  to  62,000  Ibs.  T.  S.,  1/2  in.  thick  and  under,  must  bend  180°  flat  on 
itself  without  fracture  on  outside  of  bent  portion;  over  1/2  in.  thick,  180° 
around  a  mandrel  11/2  times  the  thickness  of  the  test-piece.  For  hull 
construction  a  specimen  must  stand  bending  on  a  radius  of  half  its  thick- 
ness, without  fracture  on  the  convex  side,  either  cold  or  after  being 
heated  to  cherry-red  and  quenched  in  water  at  80°  F. 

High-strength  Steel  for  Shipbuilding.  (Eng'g,  Aug.  2, 1907,  p.  137.)— 
The  average  tensile  strength  of  the  material  selected  for  the  Lusitania 
was  82,432  Ibs.  per  sq.  in.  for  normal  high-tensile  steel,  and  81,984  lbs> 
for  the  same  annealed,  as  compared  with  66,304  Ibs.  for  ordinary  mild 
steel.  The  metal  was  subjected  to  tup  tests  as  well  as  to  other  severe 
punishments,  including  the  explosion  of  heavy  charges  of  dynamite 
against  the  plates,  and  in  every  instance  the  results  were  satisfactory. 
It  was  not  deemed  prudent  to  adopt  the  high-tensile  steel  for  the  rivets, 
a  point  upon  which  there  seems  some  difference  of  opinion. 


Penna.  R.  R.  Specifications  for  Steel. 


B 

0 

fc 

OJ 

1 

C. 

Mn. 

Si. 

P. 

s. 

Cu. 

Plates  for  steel  cars  

(1) 

1899 

0.12 

0.35 

0.05 

0.04- 

0.03- 

Bar  spring  steel  

1901 

1.00 

0.25 

0.15- 

0.03- 

0.03- 

0.03- 

Steel  for  axles 

(?) 

1899 

0  40 

0  50 

0  05 

0.05- 

0.04- 

Steel  for  crank  pins  

O) 

1904 

0.45 

0.60- 

0.05- 

0.03- 

0.04- 

Billets  or  blooms  for  forging 
Boiler-shell  sheets  

(4) 

(5) 

1902 
1906 

0.45 
0  18 

0.50 
0  40- 

0.05 
0  05- 

0.03- 
0.04- 

0.02- 
0.03- 

0.03- 
0.03- 

Fire-box  sheets 

(6) 

1906 

0  18 

0  40- 

0  02- 

0  03- 

0.02- 

0.03- 

508 


StftEU 


The  minus  sign  after  a  figure  means  "or  less."  The  figures  without 
the  minus  sign  represent  the  composition  desired. 

Steel  castings.  Desired  T.  S.,  70,000  Ibs.  per  sq.  in.;  elong.  in  2  in.. 
15%.  Will  be  rejected  if  T.  S.  is  below  60,000,  or  elong.  below  12%,  or  if 
the  castings  show  blow-holes  or  shrinkage  cracks  on  machining. 

NOTES.  (1)  Tensile  strength,  52,000  Ibs.  per  sq.  in.;  elong.  in  8  ins. 
=  1,500,000  -s-  T.  S.  (2)  Axles  are  also  subjected  to  a  drop  test,  similar 
to  that  of  the  A.  S.  T.  M.  specifications.  Axles  will  be  rejected  if  they 
contain  C  below  0.35  or  above  0.50,  Mn  above  0.60,  P  above  0.07%. 
(3)  T.  S.  desired,  85,000  Ibs.  per  sq.  in.;  elong.  in  8  ins.  18%.  Pins  will 
be  rejected  if  the  T.  S.  is  below  80,003  or  above  95,000,  if  the  elongation 
is  less  than  12%,  orif  the  P  is  above  0.05%.  (4)  The  steel  will  be  re- 
jected if  the  C  is  below  0.35  or  above  0.50,  Si  above  0.25,  S  above  0.05, 
P  above  0.05,  or  Mn  above  0.60%.  (5)  T.  S.  desired,  60,000;  elong.  in 
8  ins.  26%.  Sheets  will  be  rejected  if  the  T.  S.  is  less  than  55,000  or 
over  65,000,  or  if  the  elongation  is  less  than  the  quotient  of  1,400,000 
divided  by  the  T.  S.,  or  if  P  is  over  .0.05%.  (6)  T.  S.  desired,  60,000, 
with  elong.  of  28%  in  8  in.  Sheets  will  be  rejected  if  the  T.  S.  is  less 
than  55,000  or  above  65,000  (but  if  the  elong.  is  30%  or  over  plates  will 
not  be  rejected  for  high  T.  S.),if  the  elongation  is  less  than  1,450,000  -*- 
T.  S.,  if  a  single  seam  or  cavity  more  than  1/4  in.  long  is  shown  in  either 
one  of  the  three  fractures  obtained  in  the  test  for  homogeneity,  described 
below,  or  if  on  analysis  C  is  found  below  0.15  or  over  0.25,  P  over  0.035, 
Mn  over  0.45,  Si  over  0.03,  S  over  0.045,  or  Cu  over  0.05%. 

Homogeneity  Test  for  Fire-box  Steel.  —  This  test  is  made  on  one  of  the 
broken  tensile-test  specimens,  as  follows: 

A  portion  of  the  test-piece  is  nicked  with  a  chisel,  or  grooved  on  a  ma- 
chine, transversely  about  a  sixteenth  of  an  inch  deep,  in  three  places 
about  2  in.  apart.  The  first  groove  should  be  made  on  one  side,  2  in.  from 
the  square  end  of  the  piece;  the  second,  2  in.  from  it  on  the  opposite  side; 
and  the  third,  2  in.  from  the  last,  and  on  the  opposite  side  from  it.  The 
test-piece  is  then  put  in  a  vise,  with  the  first  groove  about  1/4  in.  above 
the  jaws,  care  being  taken  to  hold  it  firmly.  The  projecting  end  of  the 
test-piece  is  then  broken  off  by  means  of  a  hammer,  a  number  of  light 
blows  being  used,  and  the  bending  being  away  from  the  groove.  The 
piece  is  broken  at  the  other  two  grooves  in  the  same  way.  The  object 
( f  this  treatment  is  to  open  and  render  visible  to  the  eye  any  seams  due 
to  failure  to  weld  up,  or  to  foreign  interposed  matter,  or  cavities  due 
to  gas  bubbles  in  the  ingot.  After  rupture,  one  side  of  each  fracture  is 
examined,  a  pocket  lens  being  used  if  necessary,  and  the  length  of  the 
seams  and  cavities  is  determined.  The  sample  shall  not  show  any  single 
seam  or  cavity  more  than  1/4  in.  long  in  either  of  the  three  fractures. 

Dr.  Chas.  B.  Dudley,  chemist  of  the  P.  R.  R.  (Trans.  A.  I.  M.  E.,  1892), 
referring  to  tests  of  crank-pins,  says:  In  testing  a  recent  shipment,  the 
piece  from  one  side  of  the  pm  showed  88,000  Ibs.  strength  and  22%  elon- 
gation, and  the  piece  from  the  opposite  side  showed  106,000  Ibs.  strength 
and  14%  elongation.  Each  piece  was  above  the  specified  strength  and 
ductility,  but  the  lack  of  uniformity  between  the  two  sides  of  the  pin  was 
so  marked  that  it  was  finally  determined  not  to  put  the  lot  of  50  pins  in 
use.  To  guard  against  trouble  of  this  sort  in  future,  the  specifications 
are  to  be  amended  to  require  that  the  difference  in  ultimate  strength  of 
the  two  specimens  shall  not  be  more  than  3000  Ibs. 

Specifications  for  Steel  Rails.     (Adopted  by  the  manufacturers  of  the 
U.  S.  and  Canada.     In  effect  Jan.  1,  1909.)—     Bessemer  rails: 
Wt.  per  yard,  Ibs.       50  to  60     61  to  70        71  to  80        81  to  90        91  to  100 
Carbon    %         ....0.35-0.45    0.35-0.45    0.40-0.50    0.43-0.53    0.45-0.55 
Manganese,  %...  .0.70-1 .00    0.70-1.00    0.75-1.05    0.80-1.10    0.84-1.14 

Phosphorus  not  over  0.10%;  silicon  not  over  0.20%.  Drop  Test:  A 
piece  of  rail  4  to  6  ft.  long,  selected  from  each  blow,  is  placed  head  up- 
wards on  supports  3  it.  apart.  The  anvil  weighs  at  least  20,000  Ibs., 
and  the  tup,  or  falling  weight,  2000  Ibs.  The  rail  should  not  break  when 
the  drop  is  as  follows: 

Weight  per  yard,  Ibs 71  to  80         81  to  90         91  to  100 

Height  of  drop,  feet 16  17 

If  any  rail  breaks  when  subjected  to  the  drop  test,  two  additional  tests 
will  be  made  of  other  rails  from  the  same  blow  of  steel,  and  if  either  of 


VARIOUS  SPECIFICATIONS  FOE  STEEL. 


509 


these  latter  tests  fail,  all  the  rails  of  the  blow  which  they  represent  will 
be  rejected;  but  if  both  of  these  additional  test-pieces  meet  the  require- 
ments, all  the  rails  of  the  blow  which  they  represent  will  be  accepted. 

Shrinkage:  The  number  of  passes  and  the  speed  of  the  roll  train  shall 
be  so  regulated  that  for  sections  75  Ibs.  per  yard  and  heavier  the  temper- 
ature on  leaving  the  rolls  will  not  exceed  that  which  requires  a  shrinkage 
allowance  at  the  hot  saws  of  611/13  inches  for  a  33-ft.  75-lb.  rail,  with  an 
increase  of  Vie  in.  for  each  increase  of  5  Ibs.  in  the  weight  of  the  section. 

Open-hearth  rails;  chemical  specifications: 

Weight  per  yard,  Ibs. . .  50  to  60  61  to  70  71  to  SO  81  to  90  93  to  100 
Carbon,  % 0.46-0.59  0.46-0.59  0.52-0.65  0.59-0.72  0.62-0.75 

Manganese,  0.60  to  0.90;  Phosphorus,  not  over  0.04;  Silicon,  not  over 
0.20.  Drop  Tests  :  50  to  60-lb.,  15  ft.;  61  to  70-lb.,  16  ft.;  heavier  sec- 
tions same  as  Bessemer. 

Specifications  for  Steel  Axles.   (Proc.  A.  S.  T.  M.,  1905   p.  56.)  — 


P.& 
B.| 

Tens. 

Str. 

Yield 
Pt. 

El.  in 
2  in. 

Red. 
Area. 

Car  and  tender  truck  

0.06 

Driving  and  engine  truck  C.  S.*  ..           .    . 

0  06 

80000 

40000 

20% 

25% 

Driving  and  engine  truck,  N.  S.'j"  

0.04 

80'N000 

50',  000 

25% 

45% 

*  Carbon  steel. 

t  Nickel  steel,  3  to  4%  Ni. 

I  Each  not  to  exceed.     Mn  in  carbon  steel  not  over  0.60  %. 

Drop  Tests.  —  One  drop  test  to  be  made  from  each  melt.  The  axle 
t.ests  on  supports  3  ft.  apart,  the  tup  weighs  1640  Ibs.,  the  anvil  supported 
on  springs,  17,500  Ibs.;  the  radius  of  the  striking  face  of  the  tup  is  5  in. 
The  axle  is  turned  over  after  the  first,  third  and  fifth  blows.  It  must 
stand  the  number  of  blows  named  below  without  rupture  and  without 
exceeding,  as  the  result  of  the  first  blow,  the  deflection  given. 


Diam.  axle  at  center,  in..  .  
Number  of  blows   .  .  . 

j% 

43/8 

47/16 

45/8 

43/4 

53/8 

r" 

Height  of  drop  ft 

24 

26 

281/2 

31 

34 

43 

43 

Deflection,  in...  ."*.  . 

81/4] 

81/4 

81/4 

8 

8 

7 

51/2 

Specifications  for  Tires.  (A.  S.  T.  M.,  1901.)  —  Physical  require- 
ments of  test-piece  1/2  in.  diam.  Tires  for  passenger  engines:  T.  S.,  100,000; 
El.  in  2  in.,  12%.  Tires  for  freight  engines  and  car  wheels:  T.  S.,  110,000; 
El.,  10%.  Tires  for  switching  engines:  T.  S.,  120,000;  El.,  8%. 

Drop  Test.  —  If  a  drop  test  is  called  for,  a  selected  tire  shall  be  placed 
vertically  under  the  drop  on  a  foundation  at  least  10  tons  in  weight  and 
subjected  to  successive  blows  from  a  tup  weighing  2240  Ibs.  falling  from 
increasing  heights  until  the  required  deflection  is  obtained,  without  break- 
ing or  cracking.  The  minimum  deflection  must  equal  D2  •»•  (40  T2  + 
27)),  D  being  internal  diameter  and  T  thickness  of  tire  at  center  of 
tread. 

Splice-bars.  (A.  S.  T.  M.t  1901.)  — Tensile  strength  of  a  specimen 
cut  from  the  head  of  the  bar,  54,000  to  64,000  Ibs.;  yield  point,  32,000 
Ibs.  Elongation  in  8  in.,  not  less  than  25  per  cent.  A  test  specimen 
cut  from  the- head  of  the  bar  shall  bend  180°  flat  on  itself  without  fracture 
on  the  outside  of  the  bent  portion.  If  preferred,  the  bending  test  may 
be  made  on  an  unpunched  splice-bar,  which  shall  be  first  flattened  and 
then  bent.  One  tensile  test  and  one  bending  test  to  be  made  from  each 
blow  or  melt  of  steel. 


510 


STEEL. 


Specifications    for    Steel    Used    in    Automobile    Construe tiouu 

(E.  F.  Lake,  Am.  Mach.,  March  14,  1907.)  — 


C. 

Mn. 

Cr. 

Ni. 

p. 

S. 

t.  S. 

E.  L. 

El.  in 
2  in. 

R.of 
A. 

(0 

0.40-0.55 

0.40- 

0.80  + 

1.50  + 

0.04- 

0.04- 

f  90000  + 
1180000  + 

65000  + 
140000  + 

18+ 

8  + 

35+a 
20  +b 

(2) 

0.20-0.35 

0.40- 

0.80  + 

1.50  + 

0.04- 

0.04- 

/  85000  + 
\  130000  + 

65000  + 
100000  + 

20  + 
12  + 

50+a 
30+b 

(3) 

0.25 

0.40 

1.50 

3.50 

0.015 

0.025 

120000 

105000 

20 

58c 

(4) 

0.25-0.35 

0.60 

1.50  + 

0.03 

0.04 

f  85000  + 
\  100000  + 

60000  + 
70000  + 

25  + 
20+ 

50+a 
50+b 

(5) 

0  45-0  55 

1  1-1  3 

0  065- 

0  06- 

85000  + 

55000  + 

15  + 

45  +  c 

6 

0.28-0.36 

0.3-0.6 

0.05- 

0.06- 

75000  + 

40000  + 

25  + 

40  +  c 

(7) 

0.85-1.00 

0.25-0.5 

0.03- 

0.03- 

H 

0.50 

1.50- 

3o!6 

0  04- 

0  06- 

The  plus  sign  means  "or  over";  the  minus  sign  "or  less.'* 
a,  fully  annealed;  b,  heat-treated,  that  is  oil-quenched  and  partly 
annealed;  c,  as  rolled. 

(1)  45%   carbon  chrome-nickel   steel,   for  gears   of   high-grade   cars. 
When  annealed  this  steel  can  be  machined  with  a  high-speed  tool  at  the 
rate  of  35  ft.  per  min./with  a  Vl6-in.  feed  and  a  3/16-in.  cut.    It  is  annealed 
at  1400°  F.  4  or  5  hours,  and  cooled  slowly.    In  heat-treating  it  is  heated 
to  1500°,  quenched  in  oil  or  water  and  drawn  at  500°  F. 

(2)  25%   carbon  chrome-nickel   steel,   for  shafts,   axles,   pivots,   etc. 
This  steel  may  be  machined  at  the  same  rate  as  (1),  and  it  forges  more 
easily. 

(3)  A  foreign  steel  used  for  forgings  that  have  to  withstand  severe 
alternating  shocks,  such  as  differential  shafts,  transmission  parts,  universal 
joints,  axles,  etc. 

(4)  Nickel  steel,  used  instead  of  (1)  in  medium  and  low-priced  cars. 

(5)  "Gun-barrel  "  steel,  used  extensively  for  rifle  barrels,  also  in  low- 
priced  automobiles,  for  shafts,  axles,  etc.     It  is  used  as  it  comes  from 
the  maker,  without  heat-treating. 

(6)  Machine  steel.     Used  for  parts  that  do  not  require  any  special 
strength. 

(7)  Spring  steel  used  in  automobiles. 

(8)  Nickel  steel  for  valves.     Used  for  its  heat-resisting  qualities  in 
valves  of  internal-combustion  engines. 

Carbonizing  or  Case-hardening.  —  Some  makers  carbonize  the  surface 
of  gears  made  from  steel  (1)  above.  They  are  packed  in  cast-iron  boxes 
with  a  mixture  of  bone  and  powdered  charcoal"  and  heated  four  hours 
at  nearly  the  melting-point  of  the  boxes,  then  cooled  slowly  in  the  boxes. 
They  are  then  taken  out,  heated  to  1400°  F.  for  four  hours  to  break  up  the 
coarse  grain  produced  by  the  carbonizing  temperature.  After  this  the 
work  is  heat-treated  as  above  described. 

The  machine  steel  (6)  case-hardens  well  by  the  use  of  this  process. 

Specifications  for  Steel  Castings.  (Proc.  A.  S.  T.  M .,  1905,. p.  53.)  — 
Open-hearth,  Bessemer,  or  crucible.  Castings  to  be  annealed  unless 
otherwise  specified.  Ordinary  castings,  in  which  no  physical  require- 
ments are  specified,  shall  contain  not  over  0.04  C  and  not  over  0.08  P. 
Castings  subject  to  physical  test  shall  contain  not  over  0.05  P  and  not 
over  0.05  S.  The  minimum  requirements  are: 


T.  S. 

Y.  P. 

El.  in  2 
in. 

Red. 
Area. 

Hard  castings   

85.000 

38,250 

15  %  * 

20% 

Medium  castings  

70000 

31,500 

18% 

25% 

Soft  castings  .                      

60,000 

27  000 

22% 

30% 

FORCE,  STATICAL    MOMENT,  EQUILIBRIUM,  ETC.       511 


For  small  or  unimportant  castings  a  test  to  destruction  may  be  sub- 
stituted. Three  samples  are  selected  from  each  melt  or  blow,  annealed 
in  the  same  furnace  charge,  and  shall  show  the  material  to  be  ductile 
and  free  from  injurious  defects,  and  suitable  for  the  purpose  intended. 
Large  castings  are  to  be  suspended  and  hammered  all  over.  -No  cracks, 
flaws,  defects  nor  weakness  shall  appear  after  such  treatment.  A  speci- 
men 1  X  V2  in.  shall  bend  cold  around  a  diam.  of  1  in.  without  fracture 
on  outside  of  bent  portion,  through  an  angle  of  120°  for  soft  and  90°  for 
medium  castings. 

Specifications  for  steel  castings  issued  by  the  U.  S.  Navy  Department, 
1889  (abridged):  Steel  for  castings  must  be  made  by  either  the  open- 
hearth  or  the  crucible  process,  and  must  not  show  more  than  0.06%  of 
phosphorus.  All  castings  must  be  annealed,  unless  otherwise  directed. 
The  tensile  strength  of  steel  castings  shall  be  at  least  60,000  Ibs.,  with  an 
elongation  of  at  least  15%  in  8  in.  for  all  castings  for  moving  parts  of 
machinery,  and  at  least  10%  in  8  in.  for  other  castings.  Bars  1  in.  sq. 
shall  be  capable  of  bending  cold,  without  fracture,  through  an  angle  of 
90°,  over  a  radius  not  greater  than  11/2  in.  All  castings  must  be  sound, 
free  from  injurious  roughness,  sponginess,  pitting,  shrinkage,  or  other 
cracks,  cavities,  etc. 

Pennsylvania  Railroad  specifications,  1888:  Steel  castings  should  have  a 
tensile  strength  of  70,000  Ibs.  per  sq.  in.  and  an  elongation  of  15%  in 
section  originally  2  in.  long.  Steel  castings  will  not  be  accepted  if  tensile 
strength  falls  below  60,000  Ibs.,  nor  if  the  elongation  is  less  than  12%,  nor 
if  castings  have  blow-holes  and  shrinkage  cracks.  Castings  weighing  80 
Ibs.  or  more  must  have  cast  with  them  a  strip  to  be  used  as  a  test-piece. 
""he  dimensions  of  this  strip  must  be  8/4  in.  sq.  by  12  in.  long. 


MECHANICS. 

FORCE,   STATICAL  MOMENT,  EQUILIBRIUM,  ETC. 


MECHANICS  is  the  science  that  treats  of  the  action  of  force  upon  bodies. 
Statics  is  the  mechanics  of  bodies  at  rest  relatively  to  the  earth's  surface. 
Dynamics  is  the  mechanics  of  bodies  in  motion.  Hydrostatics  and  hydro- 
dynamics are  the  mechanics  of  liquids,  and  Pneumatics  the  mechanics 
of  air  and  other  gases.  These  are  treated  in  other  chapters. 

There  are  four  elementary  quantities  considered  in  Mechanics:  Matter, 
Force,  Space,  Time. 

Matter.  —  Any  substance  or  material  that  can  be  weighed  or  measured. 
It  exists  in  three  forms:  solid,  liquid,  and  gaseous.  A  definite  portion 
of  matter  is  called  a  body. 

The  Quantity  of  Matter  in  a  body  may  be  determined  either  by 
measuring  its  bulk  or  by  weighing  it,  but  as  the  bulk  varies  with  temper- 
ature, with  porosity,  with  size,  shape  and  method  of  piling  its  particles, 
etc.,  weighing  is  generally  the  more  accurate  method  of  determining  its 
quantity. 

Weight.  Mass. — The  word  "weight"  is  commonly  used  in  two 
senses:  1.  As  the  measure  of  quantity  of  matter  in  a  body,  as  deter- 
mined by  weighing  it  in  an  even  balance  scale  or  on  a  lever  or  platform 
scale,  and  thus  comparing  its  quantity  with  that  of  certain  pieces  of  metal 
called  standard  weights,  such  as  the  pound  avoirdupois.  2.  As  the 
measure  of  the  force  which  the  attraction  of  gravitation  of  the  earth 
exerts  on  the  body,  as  determined  by  measuring  that  force  with  a  spring 
balance.  As  the  force  of  gravity  varies  with  the  latitude  and  elevation 
above  sea  level  of  different  parts  of  the  earth's  surface,  the  weight  deter- 
mined in  this  second  method  is  a  variable,  while  that  determined  by 
the  first  method  is  a  constant.  For  this  reason,  and  also  because  spring 
balances  are  generally  not  as  accurate  instruments  as  even  balances,  or 
lever  or  platform  scales,  the  word  "weight,"  in  engineering,  unless  other- 
wise specified,  means  the  quantity  of  matter  as  determined  by  weigh- 
ing it  by  the  first  method.  The  standard  unit  of  weight  is  the  pound. 

The  word  "mass"  is  used  in  three  senses  by  writers  on  physics  and 
engineering:  1.  As  a  general  expression  of  an  indefinite  quantity,  syn- 
onymous with  lump,  piece,  portion,  etc.,  as  in  the  expression  "a  mass 
whose  weight  is  one  pound,"  2,  As  the  quotient  of  the  weight,  aj 


512 


MECHANICS. 


determined  by  the  first  method  of  weighing  given  above,  by  32.174,  tho 
standard  value  of  g,  the  acceleration  due  to  gravity,  expressed  by 
the  formula  M  =  W/g.  This  value  is  merely  the  arithmetical  ratio  of 
the  weight  in  pounds  to  the  acceleration  in  feet  per  second  per  second, 
and  it  has  no  unit.  3.  As  a  measure  of  the  quantity  of  matter,  ex- 
actly synonymous  with  the  first  meaning  of  the  word  "weight,"  given 
above.  In  this  sense  the  word  is  used  in  many  books  on  physics  and 
theoretical  mechanics,  but  it  is  not  so  used  by  engineers.  The  state- 
ment in  such  books  that  the  engineers'  unit  of  mass  is  32.2  Ibs.  is  an 
error.  There  is  no  such  unit.  Whenever  the  term  "mass"  is  repre- 
sented by  M  in  engineering  calculations  it  is  equivalent  to  W/g,  in 
which  Wis  the  quantity  of  matter  in  pounds,  and  g  =  32.1740  (or  32.2 
approximate) . 

Local  Weight.  —  The  force,  measured  in  standard  pounds  of  force 
(see  Unit  of  Force,  below),  with  which  gravity  attracts  a  body  at  a 
locality  other  than  one  where  g  =  32.174  is  sometimes  called  the 
"local  weight"  of  the  body.  It  is  the  weight  that  would  be  indicated 
if  the  body  was  weighed  on  a  spring  balance  calibrated  for  standard 
pounds  of  force.  If  the  balance  was  calibrated  for  the  particular  lo- 
cality, it  would  indicate  not  the  local  weight,  but  the  true  or  standard 
weight,  that  is,  the  quantity  of  matter  in  pounds  or  the  force  that 
gravity  would  exert  on  the  body  at  the  standard  locality,  these  being 
numerically  identical.  The  difference  between  standard  and  local 
weight  is  rarely  large  enough  to  be  of  importance  in  engineering 
problems.  In  the  United  States  (exclusive  of  Alaska),  the  range  of 
the  value  of  g  is  only  from  0.9973  (at  lat.  25°,  10,000  ft.  above  the  sea) 
to  1.0004  (lat.  49°  at  the  sea  level)  of  the  standard  value  (lat.  45°  at 
the  sea  level)  of  32.1740. 

A  Force  is  anything  that  tends  to  change  the  state  of  a  body  with 
respect  to  rest  or  motion.  If  a  body  is  at  rest,  anything  that  tends  to 
.put  it  in  motion  is  a  fores;  if  a  body  is  in  motion,  anything  that  tends  to 
change  either  its  direction  or  its  rate  of  motion  is  a  force. 

A  force  should  always  mean  the  pull,  pressure,  rub,  attraction  (or  re- 
pulsion) of  one  body  upon  another,  and  always  implies  the  existence  of  a 
simultaneous  equal  and  ppposite  force  exerted  by  that  other  body  on  tli3 
first  body,  i.e.,  the  reaction.  In  no  case  should  we  call  anything  a  forc3 
unless  we  can  conceive  of  it  as  capable  of  measurement  by  a  spring 
balance,  and  are  able  to  say  from  what  other  body  it  comes.  (I.  P. 
Church.) 

Forces  may  be  divided  into  two  classes,  extraneous  and  molecular; 
extraneous  forces  act  on  bodies  from  without;  molecular  forces  are 
exerted  between  the  neighboring  particles  of  bodies. 

Extraneous  forces  are  of  two  kinds,  pressures  and  moving  forces:  pres- 
sures simply  tend  to  produce  motion;  moving  forces  actually  produce 
motion.  Thus,  if  gravity  act  on  a  fixed  body,  it  creates  pressure;  if  on  a 
free  body,  it  produces  motion. 

Molecular  forces  are  of  two  kinds,  attractive  and  repellent:  attractive 
forces  tend  to  bind  the  particles  of  a  body  together;  repellent  forces  tend 
to  thrust  them  asunder.  Both  kinds  of  molecular  forces  are  continu- 
ally exerted  between  the  molecules  of  bodies,  and  on  the  predominance 
of  one  or  the  other  depends  the  physical  state  of  a  body,  as  solid,  liquid, 
or  gaseous. 

The  Unit  of  Force  used  in  engineering,  by  English  writers,  is  the 
pound  avoirdupois.  Strictly,  it  is  the  force  which  would  give  to  a 
pound  of  matter  an  acceleration  of  32.1740  feet  per  sec.  per  sec.,  or  tho 
force  with  which  gravity  attracts  a  pound  of  matter  at  45°  latitude  at 
the  sea  level.  In  the  French  C.  G.  S.  or  centimeter-gram-second  system, 
the  unit  of  force  is  the  force  which  acting  on  a  mass  of  one  gram  will 
produce  in  one  second  a  velocity  of  one  centimeter  per  second.  This 
unit  is  called  a  "dyne"  =  1/980-665  gram. 

An  attempt  has  been  made  by  some  writers  on  physics  to  introduce 
the  so-called  "absolute  system"  into  English  weights  and  measures,  and 
to  define  the  "absolute  unit"  of  force  as  that  force  which  acting  on  the 
mass  whose  weight  is  one  pound  at  London  will  in  one  second  produce  a 
velocity  of  one  foot  per  second,  and  they  have  given  this  unit  the  name 
"poundal."  The  use  of  this  unit  only  makes  confusion  for  students, 
and  it  is  to  be  hoped  that  it  will  soon  be  abandoned  in  high-school  text- 
books. Professor  Perry,  in  his  "Calculus  for  Engineers,"  p.  26,  says, 


FORCE,   STATICAL   MOMENT,   EQUILIBRIUM,   ETC.    513 


"  One  might  as  well  talk  Choctaw  in  the  shops  as  to  speak  about  ...  so 
many  poundals  of  force  and  so  many  foot-poundals  of  work."* 

Inertia  is  that  property  of  a  body  by  virtue  of  which  it  tends  to  con- 
tinue in  the  state  of*rest  or  motion  in  which  it  may  be  placed,  until  acted 
on  by  some  force 

Newton's  Laws  of  Motion. —  1st  Law.  If  a  body  be  at  rest,  it  will 
remain  at  rest,  or  if  in  motion  it  will  move  uniformly  in  a  straight  line  till 
acted  on  by  some  force. 

2d  Law.  If  a  body  be  acted  on  by  several  forces,  it  will  obey  each  as 
though  the  others  did  not  exist,  and  this  whether  the  body  be  at  rest  or  in 
motion.  (This  law  is  expressed  in  different  forms  by  various  authors. 
One  of  these  forms  is:  Change  of  the  motion  of  a  body  is  proportional 
to  the  force  and  to  the  time  during  which  the  force  acts,  and  is  in  tho 
same  direction  as  the  force.) 

3d  Law.  If  a  force  act  to  change  the  state  of  a  body  with  respect  to  rest 
or  motion,  the  body  will  offer  a  resistance  equal  and  directly  opposed  to  the 
force.  Or,  to  every  action  there  is  opposed  an  equal  and  opposite  reaction. 

Graphic  Representation  of  a  force.  —  Forces  may  be  represented 
geometrically  by  straight  lines,  proportional  to  the  forces.  A  force  is 
given  when  we  know  its  intensity,  its  point  of  application,  and  the  direc- 
tion in  which  it  acts.  When  a  force  is  represented  by  a  !ine,  the  length  of 
the  line  represents  its  intensity;  one  extremity  represents  the  point  of 
application;  and  an  arrow-head  at  the  other  extremity  shows  the  direc- 
tion of  the  force.- 

Composition  of  Forces  is  the  operation  of  finding  a  single  force  whose 
effect  is  the  same  as  that  of  two  or  more  given  forces.  The  required 
force  is  called  the  resultant  of  the  given  forces. 

Resolution  of  Forces  is  the  operation  of  finding  two  or  more  forces 
whose  combined  effect  is  equivalent  to  that  of  a  given  force.  The  required 
forces  are  called  components  of  the  given  force. 

The  resultant  of  two  forces  applied  at  a  point,  and  acting  in  the  same  di- 
rection, is  equal  to  the  sum  of  the  forces.  If  two  forces  act  in  opposite 
directions,  their  resultant  is  equal  to  their  difference,  and  it  acts  in  the 
direction  of  the  greater. 

If  any  number  of  forces  be  applied  at  a  point,  some  in  one  direction  and 
others  in  a  contrary  direction,  their  resultant  is  equal  io  the  sum  of  those 
that  act  in  one  direction,  diminished  by  the  sum  of  those  that  act  in  the 
opposite  direction;  or,  the  resultant  is  equal  to  the  algebraic  sum  of  the 
components. 

Parallelogram  of  Forces.  —  If  two  forces  acting  on  a  point  be  rep- 
resented in  direction  and  intensity  by  adjacent  sides  of  a  parallelogram, 
their  resultant  will  be  represented  by  that  diagonal  of  the  parallelogram 
which  passes  through  the  point.  Thus  OR,  Fig.  99,  is  the  resultant  of 
OQ  and  OP. 

/5 


FIG.  99. 


FIG.  100. 


Polygon  of  Forces. — If  several  forces  are  applied  at  a  point  and  act 
in  a» single  plane,  their  resultant  is  found  as  follows: 

Through  the  point  draw  a  line  representing  the  first  force;  through  the 

*  Professor  Perry  himself,  however,  makes  a  slip  on  the  same  page  in 
saying :  "  Force  in  pounds  is  the  space-rate  at  which  work  in  foot-pounds 
is  done;  it  is  also  the  time-rate  at  which  momentum  is  produced  or  de- 
stroyed." He  gets  this  idea,  no  doubt,  from  the  equations  FT  =  MV, 
F  =  MV/T,  F  =  Yi  MV2  -r-  S.  Force  is  not  these  tilings:  it  is  merely 
numerically  equivalent,  when  certain  units  are  chosen,  to  these  last  two 
quotients.  We  might  as-  well  say,  since  T  =  MV/F,  that  time  is  the 
force-rate  of  momentum, 


514 


MECHANICS. 


extremity  of  this  draw  a  line  representing  the  second  force;  and  so  on, 
throughout  the  system;  finally,  draw  a  line  from  the  starting-point  to  the 
extremity  of  the  last  line  drawn,  and  this  will  be  the  resultant  required. 

Suppose  the  body  A,  Fig.  100,  to  be  urged  in  the  directions  Al.  A2,  A3, 
A4,  and  A5  by  forces  which  are  to  each  other  as  the  lengths  of  those  lines. 
Suppose  these  forces  to  act  successively  and  the  body  to  first  move  from  A 
to  1 ;  the  second  force  A2  then  acts  and  finding  the  body  at  1  would  take  it 
to  2';  the  third  force  would  then  carry  it  to  3',  the  fourth  to  4',  and  the  fifth 
to  5'.  The  line  A5'  represents  in  magnitude  and  direction  the  resultant  of 
all  the  forces  considered.  If  there  had  been  an  additional  force,  Ax,  in 
the  group,  the  body  would  be  returned  by  that  force  to  its  original  position, 
supposing  the  forces  to  act  successively,  but  if  they  had  actea  simul- 
taneously the  body  would  never  have  moved  at  all;  the  tendencies  to 
motion  balancing  each  other. 

It  follows,  therefore,  that  if  the  several  forces  which  tend  to  move  a 
body  can  be  represented  in  magnitude  and  direction  by  the  sides  of  a 
closed  polygon  taken  in  order,  the  body  will  remain  at  rest;  but  if  the 
forces  are  represented  by  the  sides  of  an  open  polygon,  the  body  will  move 
and  the  direction  will  be  represented  by  the  straight  line  which  closes  the 
polygon. 

Twisted  Polygon. — The  rule  of  the  polygon  of  forces  holds  true  even 
when  the  forces  are  not  m  one  plane.  In  this  case  the  lines  Al,  1-2',  2/-3', 
etc.,  form  a  twisted  polygon,  that  is,  one  whose  sides  are  not  in  one  plane. 

Parallelopipedon  of  Forces.  —  If  three  forces  acting  on  a  point  be 
represented  by  three  edges  of  a  parallelopipedon  which  meet  in  a  common 
point,  their  resultant  will  be  represented  by  the  diagonal  of  the  parallelo- 
pipedon that  passes  through  their  common  point. 

Thus  O#,Fig.  101, is  the  resultant  of  OQ,  OS  and  OP.  OM  is  the  result- 
ant of  OP  and  OQ,  and.  OR  is  the  resultant  of  OM  and  OS. 


FIG.  102. 

Moment  of  a  Force.  —  The  moment  of  a  force  (sometimes  called 
statical  moment),  with  respect  to  a  point,  is  the  product  of  the  force  by 
the  perpendicular  distance  from  the  point  to  the  direction  of  the  force. 
The  fixed  point  is  called  the  center  of  moments;  the  perpendicular  distance 
is  the  lever-arm  of  the  force;  and  the  moment  itself  measures  the  tendency 
of  the  force  to  produce  rotation  about  the  center  of  moments. 

If  the  force  is  expressed  in  pounds  and  the  distance  in  feet,  the  moment 
is  expressed  in  foot-pounds.  It  is  necessary  to  observe  the  distinction  be- 
tween foot-pounds  of  statical  moment  and  foot-pounds  of  work  or  energy. 
(See  Work.) 

In  the  bent  lever,  Fig.  102  (from  Trautwine),  if  the  weights  n  and  m 
represent  forces,  their  moments  about  the  point  /  are  respectively  n  X  af 
and  m  X  fc.  If  instead  of  the  weight  m  a  pulling  force  to  balance  the 
weight  n  is  applied  in  the  direction  bs,  or  by  or  bd,  s,  y,  and  d  being  the 
amounts  of  these  forces,  their  respective  moments  are  sXft,yX  fb, 

It  the  forces  acting  on  the  lever  are  in  equilibrium  it  remains  at  rest,  and 
the  moments  on  each  side  of  /  are  equal,  that  is,  n  X  af  =  m  Xfc,  or  s  X 
ft.  or  y  Xfb,  or  dX  hf. 

The  moment/  of  the  resultant  of  any  number  offerees  acting  together  in 


. 

the  sarr 


FORCE,  STATICAL  MOMENT,  EQUILIBRIUM,  ETC.     515 


e  same  plane  is  equal  to  the  algebraic  sum  of  the  moments  of  the  forces 
taken  separately. 

Statical  Moment.  Stability.  —  The  statical  moment  of  a  body  is 
the  product  of  its  weight  by  the  distance  of  its  line  of  gravity  from  some 
assumed  line  of  rotation.  The  line  of  gravity  is  a  vertical  line  drawn  from 
its  center  of  gravity  through  the  body.  The  stability  of  a  body  is  that 
resistance  which  its  weight  alone  enables  it  to  oppose  against  forces  tend- 
ing to  overturn  it  or  to  slide  it  along  its  foundation. 

To  be  safe  against  turning  on  an  edge  the  moment  of  the  forces  tending 
to  overturn  it,  taken  with  reference  to  that  edge,  must  be  less  than  the 
statical  moment.  When  a  body  rests  on  an  inclined  plane,  the  line  of 
gravity,  being  vertical,  falls  toward  the  lower  edge  of  the  body,  and  the 
condition  of  its  not  being  overturned  by  its  own  weight  is  that  the  line  of 
gravity  must  fall  within  this  ed^e.  In  the  case  of  an  inclined  tower 
resting  on  a  plane  the  same  condition  holds  —  the  line  of  gravity  must 
fall  within  the  base.  The  condition  of  stability  against  sliding  along  a 
horizontal  plane  is  that  the  horizontal  component  of  the  force  exerted 
tending  to  cause  it  to  slide  shall  be  less  than  the  product  of  the  weight  of 
the  body  into  the  coefficient  of  friction  between  the  base  of  the  body  and 
its  supporting  plane.  This  coefficient  of  friction  is  the  tangent  of  the 
angle  of  repose,  or  the  maximum  angle  at  which  the  supporting  plane 
might  be  raised  from  the  horizontal  before  the  body  would  begin  to  slide. 
(See  Friction.) 

The  Stability  of  a  Dam  against  overturning  about  its  lower  edge 
is  calculated  by  comparing  its  statical  moment  referred  to  that  edge  with 
the  resultant  pressure  of  the  water  against  its  upper  side.  The  horizontal 
pressure  on  a  square  foot  at  the  bottom  of  the  dam  is  equal  to  the  weight  of 
a  column  of  water  of  one  square  foot  in  section,  and  of  a  height  equal  to  the 
distance  of  the  bottom  below  water-level ;  or,  if  //  is  the  height,  the  pressure 
at  the  bottom  per  square  foot  =  62.4  X  H  Ibs.  At  the  water-level  the 
pressure  is  zero,  and  it  increases  uniformly  to  the  bottom,  so  that  the  sum 
of  the  pressures  on  a  vertical  strip  one  foot  in  breadth  may  be  represented 
by  the  area  of  a  triangle  whose  base  is  62.4  X  H  and  whose  altitude  is  Ht 
or  62.4  H2  -*•  2.  The  center  of  gravity  of  a  triangle  being  Va  of  its  altitude, 
the  resultant  of  all  the  horizontal  pressures  may  be  taken  as  equivalent 
to  the  sum  of  the  pressures  acting  at  1/3  H,  and  the  moment  of  the  sum  of 
the  pressures  is  therefore  62.4  X  //3  -s-  6. 

Parallel  Forces.  —  If  two  forces  are  parallel  and  act  in  the  same  direc- 
.tion.  their  resultant  is  parallel  to  both,  and  lies  between,  them,  and  the 
intensity  of  the  resultant  is  equal  to  the  sum  of  the  intensities  of  the  two 
forces.  Thus  in  Fig.  102  the  resultant  of  the  forces  n  and  m  acts  verti- 
cally downward  at  /,  and  is  equal  to  n  +  vn. 

If  two  parallel  forces  act  at  the  extremities  of  a  straight  line  and  in 
the  same  direction,  the  resultant  divides  the  line  joining  the  points  of 


CK 


FIG.  103. 


/ 


FIG.  104. 


*R 


application  of  the  components,  inversely  as  the  components.  Thus  in 
Fig.  102  m:  n::  af:  fc*  and  in  Fig.  103,  P:  Q::  SN:  SM. 

The  resultant  of  two  parallel  forces  acting  in  opposite  directions  is 
parallel  to  both,  lies  without  both,  on  the  side  and  in  the  direction  of  the 
greater,  and  its  intensity  is  equal  to  the  difference  of  the  intensities  of 
the  two  forces. 

Thus  the  resultant  of  the  two  forces  Q  and  P,  Fig.  104,  is  equal  to 
Q  —  P  =  R.  Of  any  two  parallel  forces  and  their  resultant  each  is  pro- 
portional to  the  distance  between  the  other  two:  this  in  both  Figs.  103 
and  104,  P:Q:  R::  SN:  SM:  MN. 

Couples. — If  P  and  Q  be  equal  and  act  in  opposite  directions,  R  =  0; 
that  is,  they  have  no  resultant.  Two  such  forces  constitute  a  couple. 

The  tendency  of  a  couple  is  to  produce  rotation;  the  measure  of  this 
tendency,  called  the  moment  of  the  ample-  is  the  product  of  one  of  the 
forces  by  the  distance  between  the  two. 


J 


516  MECHANICS. 

Since  a  couple  has  no  single  resultant,  no 
single  force  can  balance  a  couple.  To  prevent 
the  rotation  of  a  body  acted  on  by  a  couple  the 
application  of  two  other  forces  is  required, 
forming  a  second  couple.  Thus  in  Fig.  105, 
P  and  Q,  forming  a  couple,  may  be  balanced 

Iby  a  second  couple  formed  by  R  and  »S.     The 
point  of  application  of  either  R  or  »S  may  be  a 
fixed  pivot  or  axis. 
Moment  of  the  couple  PQ  =  P(c  +  b  +  a)  = 
moment  of  RS  =  Rb.     Also,  P  +  R  =  Q  +  S. 

The  forces  R  and  S  need  not  be  parallel  to  P 
and  Q,  but  if  not,  then  their  components  par- 
allel to  PQ  are  to  be  taken  instead  of  the  forces  themselves. 

Equilibrium  of  Forces. — A  system  of  forces  applied  at  points  of  a 
solid  body  will  be  equilibrium  when  they  have  no  tendency  to  produce 
motion,  either  of  translation  or  of  rotation. 

The  conditions  of  equilibrium  are:  1.  The  algebraic  sum  of  the  com- 
ponents of  the  forces  in  the  direction  of  any  three  rectangular  axes  must 
separately  equal  0.  2.  The  algebraic  sum  of  the  moments  of  the  forces, 
with  respect  to  any  three  rectangular  axes,  must  separately  equal  0. 

If  the  forces  lie  in  a  plane:  1.  The  algebraic  sum  of  the  components 
of  the  forces,  in  the  direction  of  any  two  rectangular  axes,  must  be 
separately  equal  to  0.  2.  The  algebraic  sum  of  the  moments  of  the 
forces,  with  respect  to  any  point  in  the  plane,  must  be  equal  to  0. 

If  a  body  is  restrained  by  a  fixed  axis,  as  in  case  of  a  pulley,  or  wheel 
and  axle,  the  forces  will  be  in  equilibrium  when  the  algebraic  sum  of 
the  moments  of  the  forces  with  respect  to  the  axis  is  equal  to  0. 

CENTER  OF  GRAVITY. 

The  center  of  gravity  of  a  body,  or  of  a  system  of  bodies  rigidly  con- 
nected together,  is  that  point  about  which,  if  suspended,  all  jthe  parts  will 
be  in  equilibrium,  that  is,  there  will  be  no  tendency  to  rotation.  It  is 
the  point  through  which  passes  the  resultant  of  the  efforts  of  gravitation 
on  each  of  the  elementary  particles  of  a  body.  In  bodies  of  equal  heavi- 
ness throughout,  the  center  of  gravity  is  the  center  of  magnitude. 

(The  center  of  magnitude  of  a  figure  is  a  point  such  that  if  the  figure 
be  divided  into  equal  parts  the  distance  of  the  center  of  magnitude  of 


the  whole  figure  from  any  given  plane  is  the  mean  of  the  distances  of 
he  centers  of  magnitude  of  the  several  equal  parts  from  that  plane.) 
A  body  suspended  at  its  center  of  gravity  is   in  equilibrium  in  all 


positions.  If  suspended  at  a  point  outside  of  its  center  of  gravity,  it 
will  take  a  position  so  that  its  center  of  gravity  is  vertically  below  its 
point  of  suspension. 

To  find  the  center  of  gravity  of  any  plane  figure  mechanically,  sus- 
pend the  figure  by  any  point  near  its  edge,  and  mark  on  it  the  direction 
of  a  plumb-line  hung  from  that  point;  then  suspend  it  from  some  other 
point,  and  again  mark  the  direction  of  the  plumb-line  in  like  manner. 
The  center  of  gravity  will  be  at  the  intersection  of  the  two  marks. 

The  Center  of  Gravity  of  Regular  Figures,  whether  plane  or  solid, 
is  the  same  as  their  geometrical  center;  for  instance,  a  straight  line, 
parallelogram,  regular  polygon,  circle,  circular  ring,  prism,,  cylinder, 
sphere,  spheroid,  middle  frustums  of  spheroid,  etc. 

Of  a  triangle:  On  a  line  drawn  from  any  angle  to  the  middle  of  the 
opposite  side,  at  a  distance  of  one-third  of  the  line  from  the  side;  or  at 
the  intersection  of  such  lines  drawn  from  any  two  angles. 

Of  a  trapezium  or  trapezoid:  Draw  a  diagonal,  dividing  it  into  two  tri- 
angles. Draw  a  line  joining  their  centers  of  gravity.  Draw  the  other 
diagonal,  making  two  other  triangles,  and  a  line  joining  their  centers 
of  gravity.  The  intersection  of  the  two  lines  is  the  center  of  gravity. 

Of  a  sector  of  a  circle:  On  the  radius  which  bisects  the  arc,  2  cr  -r  3-1 
from  the  center,  c  being  the  chord,  r  the  radius,  and  I  the  arc. 

Of  a  semicircle:     On  the  middle  radius,  0.4244  r  from  the  center. 

Of  a  Quadrant:    On  the  middle  radius,  0.600  r  from  the  center, 

Of  a  segment  of  a  circle:  c3  -j-  ]  2a  from  the  center,     c  =  chord,  a  =area. 

Of  a  paraboic  surface:   In  the  axis,  3/5  of  its  length  from  the  vertex. 

Of  a  semi-parabola  (surface):  s/5  length  of  the  axis  from  the  vertex, 
and  s/s  of  the  semi-base  from  the  axis, 


MOMENT  OF  INERTIA.     ,  517 

Of  a  cone  or  pyramid:  In  the  axis,  1/4  of  its  length  from  the  base. 

Of  a  paraboloid:  In  the  axis,  2/3  of  its  length  from  the  vertex.  . 

Of  a  cylinder,  or  regular  prism:  In  the  middle  point  of  the  axis. 

Of  a  frustum  of  a  cone  or  pyramid'  Let  a  =  length  of  a  line  drawn  from 
the  vertex  of  the  cone  when  complete  to  the  center  of  gravity  of  the  base, 
and  a'  that  portion  of  it  between  the  vertex  and  the  top  of  the  frustum; 
then  distance  of  center  of  gravity  of  the  frustum  from  center  of  gravity  of 

its  base  =  j  -  Af  2  _?a.    ,     ,2S- 
4       4(a2  +  aa    +  a 2) 

For  two  bodies,  fixed  one  at  each  end  of  a  straight  bar,  the  common 
center  of  gravity  is  in  the  bar,  at  that  point  which  divides  the  distance 
between  their  respective  centers  of  gravity  in  the  inverse  ratio  of  the 
weights.  In  this  solution  the  weight  of  the  bar  is  neglected.  But  it  may 
be  taken  as  a  third  body,  and  allowed  for  as  in  the  following  directions: 

For  more  than  two  bodies  connected  in  one  system:  Find  the  common 
center  of  gravity  of  two  of  them;  and  find  the  common  center  of  these  two 
jointly  with  a  third  body,  and  so  on  to  the  last  body  of  the  group. 

Another  method,  by  the  principle  of  moments:  To  find  the  center  of 
gravity  of  a  system  of  bodies,  or  a  body  consisting  of  several  parts,  whoso 
several  centers  are  known.  If  the  bodies  are  in  a  plane,  refer  their  several 
centers  to  two  rectangular  coordinate  axes.  Multiply  each  weight  by  its 
distance  from  one  of  the  axes,  add  the  products,  and  divide  the  sum  by  the 
eum  of  the  weights;  the  result  is  the  distance  of  the  center  of  gravity  from 
that  axis.  Do  the  same  with  regard  to  the  other  axis.  If  the  bodies  are 
not  in  a  plane,  refer  them  to  three  planes  at  right  angles  to  each  other,  and 
determine  the  mean  distance  of  the  sum  of  the  weights  from  each  plane. 
MOMENT  OF  INERTIA. 

The  moment  of  inertia  of  the  weight  of  a  body  with  respect  to  an  axis 
is  the  algebraic  sum  of  the  products  of  the  weight  of  each  elementary 
particle  by  the  square  of  its  distance  from  the  axis.  If  the  moment  of 
inertia  with  respect  to  any  axis  =  7,  the  weight  of  any  element  of  the 
body  =  w,  and  its  distance  from  the  axis  =  r,  we  have  I  =  2(wr2). 

The  moment  of  inertia  varies,  in  the  same  body,  according  to  the 
position  of  the  axis.  It  is  the  least  possible  when  the  axis  passes  through 
the  center  of  gravity.  To  find  the  moment  of  inertia  of  a  body,  referred 
to  a  given  axis,  divide  the  body  into  small  parts  of  regular  figure.  Multi- 
ply the  weight  of  each  part  by  the  square  of  the  distance  of  its  center  of 
gravity  from  the  axis.  The  sum  of  the  products  is  the  moment  of  inertia. 
The  value  of  the  moment  of  inertia  thus  obtained  will  be  more  nearly 
exact,  the  smaller  and  more  numerous  the  divisions  of  the  body. 

MOMENTS  OF  INERTIA  OF  REGULAR  SOLIDS.  —  Rod,  or  bar,  of  uniform 
thickness,  with  respect  to  an  axis  perpendicular  to  the  length  of  the  rod, 

(I2          \ 

W  =  weight  of  rod,  21  =  length,  d  =  distance  of  center  of  gravity  from 

axis. 

Thin  circular  plate,  axis  in  its  )    T=w(—-i-d2\  (2) 

own  plane,  J  \4  /' 

r  =  radius  of  plate. 
Circular  plate,  axis  perpendicular  to  )  T__  w  (^   ,    ™  \  m 

the  plate,  f*  \2  / 

Circular  ring,  axis  perpendicular  to)  J^TV  (r2  +  r'2         J 

its  own  plane,  f  \      2 

r  and  r'  are  the  exterior  and  interior  radii  of  the  ring. 


r  =  radius  of  base.  2 1  =  length  of  the  cylinder. 

By  making  d  =  0  in  any  of  the  above  formulae,  we  find  the  moment  of 
inertia  for  a  parallel  axis  through  the  center  of  gravity. 

The  moment  of  inertia,  2iur2,  numerically  equals  the  weight  of  a  body 
which,  if  concentrated  at  the  distance  unity  from  the  axis  of  rotation, 
would  require  the  same  work  to  produce  a  given  increase  of  angular 
velocity  that  the  actual  body  requires.  It  bears  the  same  relation  to 
angular  acceleration  which  weight  does  to  linear  acceleration  (Rankine). 
The  term  moment  of  inertia  is  also  used  in  regard  to  areas,  as  the  cross- 


518  MECHANICS. 

sections  of]  beams  under  strain.  In  this  case  /  =2ar2,  a  being  any  ele- 
mentary area,  and  r  its  distance  from  the  center.  (See  Strength  of  Ma- 
terials, p.  293.)  Some  writers  call  2wir2  =  ^wr^^-g  the  moment  of  inertia. 

CENTERS  OF  OSCILLATION  AND  OF  PERCUSSION. 

Center  of  Oscillation.  —  If  a  body  oscillate  about  a  fixed  horizontal 
axis,  not  passing  through  its  center  of  gravity,  there  is  a  point  in  the  line 
drawn  from  the  center  of  gravity  perpendicular  to  the  axis  whose  motion 
is  the  same  as  it  would  be  if  the  whole  mass  were  collected  at  that  point 
and  allowed  to  vibrate  as  a  pendulum  about  the  fixed  axis.  This  point  is 
called  the  center  of  oscillation. 

The  Radius  of  Oscillation,  or  distance  of  the  center  of  oscillation 
from  the  point  of  suspension  =  the  square  of  the  radius  of  gyration  -s-  dis- 
tance of  the  center  of  gravity  from  the  point  of  suspension  or  axis.  The 
centers  of  oscillation  and  suspension  are  convertible. 

If  a  straight  line,  or  uniform  thin  bar  or  cylinder,  be  suspended  at  one 
end,  oscillating  about  it  as  an  axis,  the  center  of  oscillation  is  at  2/3  the 
length  of  the  rod  from  the  axis.  If  the  point  of  suspension  is  at  1/3  the 
length  from  the  end,  the  center  of  oscillation  is  also  at  2/3  the  length  from 
the  axis,  that  is,  it  is  at  the  other  end.  In  both  cases  the  oscillation  will 
be  performed  in  the  same  time.  If  the  point  of  suspension  is  at  the 
center  of  gravity,  the  length  of  the  equivalent  simple  pendulum  is  infinite, 
and  therefore  the  time  of  vibration  is  infinite. 

F9r  a  sphere  suspended  by  a  cord,  r  —  radius,  h  =  distance  of  axis  of 
motion  from  the  center  of  the  sphere,  h'  =  distance  of  center  of  oscillation 
from  center  of  sphere,  I  =  radius  of  oscillation  =  h  +  h'  =  h  +  2/5  (r2-h  h). 

If  the  sphere  vibrate  about  an  axis  tangent  to  its  surface,  h  =  r,  and 
l  =  r+2/5r.  If  h  =  10  r,  I  =  10  r+  (r-r-25). 

Lengths  of  the  radius  of  oscillation  of  a  few  regular  plane  figures  or 
thin  plates,  suspended  by  the  vertex  or  uppermost  point. 

1st.  When  the  vibrations  are  perpendicular  t9  the  plane  of  the  figure: 

In  an  isosceles  triangle  the  radius  of  oscillation  is  equal  to  8/4  of  the 
height  of  the  triangle. 

In  a  circle,  »/8  of  the  diameter. 

In  a  parabola,  5/7  of  the  height. 

2d.  When  the  vibrations  are  edgewise,  or  in  the  plane  of  the  figure: 

In  a  circle  the  radius  of  oscillation  is  3/4  of  the  diameter. 

In  a  rectangle  suspended  by  one  angle,  2/3  of  the  diagonal. 

In  a  parabola,  suspended  -by  the  vertex,  5/7  of  the  height  plus  1/3  of 
the  parameter. 

In  a  parabola,  suspended  by  the  middle  of  the  base,  4/7  of  the  height  plus 
1/2  the  parameter. 

Center  of  Percussion.  —  The  center  of  percussion  of  a  body  oscillat- 
ing about  a  fixed  axis  is  the  point  at  which,  if  a  blow  is  struck  by  the  body, 
the  percussive  action  is  the  same  as  if  the  whole  mass  of  the  bodv  were 
concentrated  at  the  point.  It  is  identical  with  the  center  of  oscillation. 

CENTER  AND  RADIUS  OF  GYRATION. 

The  center  of  gyration,  with  reference  to  an  axis,  is  a  point  at  which,  if 
the  entire  weight  of  a  body  be  concentrated,  its  moment  of  inertia  will  re- 
main unchanged;  or,  in  a  revolving  body,  the  point  in  which  the  whole 
weight  of  the  body  may  be  conceived  to  be  concentrated,  as  if  a  pound  of 
platinum  were  substituted  for  a  pound  of  revolving  feathers,,  the  angular 
velocity  and  the  accumulated  work  remaining  the  same.  The  distance  of 
this  point  from  the  axis  is  the  radius  of  gyration.  If  W  =  the  weight  of  a 
body,  /  =  2wra  =  its  moment  of  inertia,  and  k  =  its  radius  of  gyration, 


The  moment  of  inertia  =  the  weight  X  the  square  of  the  radius  of  gyration. 
To  find  the  radius  of  gyration  divide  the  body  into  a  considerable 
number  of  equal  small  parts,  —  the  more  numerous  the  more  nearly  exact 
is  the  result,  —  then  take  the  mean  of  all  the  squares  of  the  distances  of  the 
parts  from  the  axis  of  revolution,  and  find  the  square  root  of  the  mean 
square.  Or,  if  the  moment  o.f  inertia  is  known,  divide  it  by  the  weight 
and  extract  the  square  root.  For  radius  of  gyration  of  an  area,  divide 
the  moment  of  inertia  of  the  area  by  the  area  and  extract  the  square 
root. 


CENTEK  AND  RADIUS  OF  GYRATION. 


519 


The  radius  of  gyration  is  the  least  possible  when  the  axis  passes  through 
the  center  of  gravity.  This  minimum  radius  is  called  the  principal  radius 
of  gyration.  If  we  denote  it  by  k  and  any  other  radius  of  gyration  by  k', 
we  have  for  the  five  cases  given  under  the  head  of  moment  of  inertia  above 
the  following  values: 


(1)   Rod,   axis   perpen. 
length, 


- I         ;  *.-          +  (P. 


(2)  Circular  plate,  axis  in)  /.  _  r,  ,.,  _  i/C 4.  ^2 

its  plane,  t         2:  *     "  V 4~         ' 

(3)  Circular  plate,  axis  per-  )  k  =    4 /I . 

pen.  to  plane,  J  V  2' 

(4)  Circular  ring,  axis  per-  )  *. 

pen.  to  plane,  J 


(5)  Cylinder,      axis 
pen.  to  length, 


per- 


Principal  Radii  of  Gyration  and  Squares  of  Radii  of  Gyration. 

(For  radii  of  gyration  of  sections  of  columns,  see  page  295.) 


Surface  or  Solid. 

Rad.  of  Gyration. 

Square  of  R. 
of  Gyration. 

Parallelogram:  )  axis  at  its  base  

0.5773/1 
0.2886  ft 

0.5773Z 

0.2886J 

1/3  h2 
Vl2/i2 

Vs/2 

*fo* 

(b2  +  c2)  -s-  3 
4^2  +  52 

height  h          )     "     mid-height  ..   .. 

Straight  rod:      ,    )      .      t      d 

length  J.  or  thin  S    •»    ^Sengtn 

rectang.  plate     ) 
Rectangular  prism: 
axes  2  a,  2b,  2c,  referred  to  axis  2  a  
Parallelepiped:  length  I,  base  &,  axis  at  ) 

0.577  Vb2  +  c2 
0.289  v/IF~Tl>2 

0.289\//i2  +K2 
.408  h 

Hollow  square  tube: 
out.  side  h,  inner  h't  axis  mid-length  .... 
very  thin,  side  =  h,  axis  mid-length  .... 
Thin  rectangular  tube:  sides  6,  h,  axis  ) 

12 

(W  +  h'*}  +  n 

/l2-6 

h2    h  +  3b 
12'TTft 
l/4r3  =  /i2-  16 

(fc*  +  h'2)  -s-  16 

p:    > 

12^  4 
1/2  r2 

(ft2  +  r2)  •?-  2 
;2  L  ft2  +  r» 

0.289A  J\+  \b 

Thin  circ.  plate:  rad.  r,  diam.  h,  ax.  diam. 
Flat  circ.  ring:  ciiams.  h,  ll't  axis  diam..  .  . 
Solid  circular  cylinder:  length  I,  axis  di-  ) 
ameter  at  mid-length                                ( 

»     h  +  b 
1/4  V#z  +  fc'2 

0.289  V/2  +  3r2 
0.7071r 
0.7071  VRZ  +  r2 

Circular  plate:   solid  wheel  of  uniform  j 
thickness,  or  cylinder  of  any  length,  } 
referred  to  axis  of  cyl  ) 

Hollow    circ.     cylinder,    or    flat    ring:! 
1,  length;   R,  r,  outer  and  inner  radii.  1 
Axis,  1,  longitudinal  axis;  2,  diam.  at  J 
mid-length  .  .           .       J 

.289V/2+3  (/e2+r2) 

0.289V^  +  6/^2 
r 

0.707lr 
0.6325r 
0.6325r 
0.5773r 

12  '         4 
/2      722 
12  +    2 

r3 
r2 

1/2  r2 
2/5  r2 
2/5  r2 

V«r2 
6*  +  e2 

2  ^5  -  r« 
5l5TT7i 

^ 

Same:  very  thin,  axis  its  diameter  

radius  r  ;  axis,  longitudinal  axis  .  . 
Circumf  .  of  circle,  axis  its  center  

"  diam  

Sphere:  radius  r,  axis  its  diam  

Spheroid:  equatorial  radius  r,  revolving) 
Dolar  axis  a  .                                              } 

Paraboloid:  r=rad.  of  base,  rev.  on  axis. 
Ellipsoid:  semi-axes  a,  6,  c;  revolving  on  ) 
axis  2  a  J 

0.4472V&2  +  C2 

Spherical  shell:  radii  Rt  r,  revolving  on  ) 

0.«25l/f3"rS3 

Same:  very  thin,  radius  r  

V  R3  -r3 
0  8165  r 
0.5477r 

Solid  cone:  r==rad.  of  base,  rev.  on  axis.  . 

520  MECHANICS. 

THE  PENDULUM. 

A  body  of  any  form  suspended  from  a  fixed  axis  about  which  it  oscil- 
lates by  the  force  of  gravity  is  called  a  compound  pendulum.  The  ideal 
body  concentrated  at  the  center  of  oscillation,  suspended  from  the  cen- 
ter of  suspension  by  a  string  without  weight,  is  called  a  simple  pendulum. 
This  equivalent  simple  pendulum  has  the  same  weight  as  the  given  body, 
and  also  the  same  moment  of  inertia,  referred  to  an  axis  passing  through 
the  point  of  suspension,  and  it  oscillates  in  the  same  time. 

The  ordinary  pendulum  of  a  given  length  vibrates  in  equal  times  when 
the  angle  of  the  vibrations  does  not  exceed  4  or  5  degrees,  that  is,  2°  or 
2  y?°  each  side  of  the  vertical.  This  property  of  a  pendulum  is  called  its 
isochronism. 

The  time  of  vibration  of  a  pendulum  varies  directly  as  the  square  root 
of  the  length,  and  inversely  as  the  square  root  of  the  acceleration  due  to 
gravity  at  the  given  latitude  and  elevation  above  the  earth's  surface. 

If  T  =  the  time  of  vibration,  I  —  length  of  the  simple  pendulum,  g  = 

IT  vT 

the  acceleration,  then  T  =  IT  \  _;  since  TT  is  constant  Too  — >r  .    At  a 

\0  Vg 

giyen  location  g  is  constant  and  T  oo  \/T.    If  I  be  constant,  then  for  any 

1  n*l 

location  T  oo  -7^.  If  Tbe  constant,  g  T2  =  n2 1;  I  ao  g;  g  =  -=-.  From  this 

\7g  .  T2 

equation  the  force  of  gravity  at  any  place  may  be  determined  if  the 
length  of  the  simple  pendulum,  vibrating  seconds,  at  that  plaee  is 
known.  At  New  York  this  length  is  39.1017  inches  =  3.2585  ft., 
whence  g  =  32.16  ft. 

Time  of  vibration  of  a  pendulum  of  a  given  length  at  New  York 


-H; 


I  VT 


J  39. 1017       6.253 

t  being  in  seconds  and  I  in  inches.    Length  of  a  pendulum  having  a  given 
time  of  vibration,  I  =  t*  X  39.1017  inches. 

The  time  of  vibration  of  a  pendulum  may  be  varied  by  the  addition  of 
a  weight  at  a  point  above  the  center  of  suspension,  which  counteracts 
the  lower  weight,  and  lengthens  the  period  of  vibration.  By  varying  the, 
height  of  the  upper  weight  the  time  is  varied. 

To  find  the  weight  of  the  upper  bob  of  a  compound  pendulum,  vi- 
brating seconds,  when  the  weight  of  the  lower  bob  and  the  distances  of 
the  weights  from  the  point  of  suspension  are  given: 

_        (39-1  *  D)  -  D* 


"  (39.1  X  d)   +&* 

W  =  the  weight  of  the  lower  bob,  w  =  the  weight  of  the  upper  bob; 
D  =  the  distance  of  the  lower  bob,  and  d  =  the  distance  of  the  upper 
bob  from  the  point  of  suspension,  in  inches. 

Thus,  by  means  of  a  second  bob,  short  pendulums  may  be  constructed 
to  vibrate  as  slowly  as  longer  pendulums. 

By  increasing  w  or  d  until  the  lower  weight  is  entirely  counterbalanced 
the  time  of  vibration  may  be  made  infinite. 

Conical  Pendulum. — A  weight  suspended  by  a  cord  and  revolving 
at  a  uniform  speed  in  the  circumference  of  a  circular  horizontal  plane 
whose  radius  is  r,  the  distance  of  the  plane  below  the  point  of  suspension 
being  h,  is  held  in  equilibrium  by  three  forces  —  the  tension  in  the  cord, 
the  centrifugal  force,  which  tends  to  increase  the  radius  r,  and  the  force 
of  gravity  acting  downward.  If  v  =  the  velocity  in  feet  per  second  of 
the  center  of  gravity  of  the  weight,  as  it  describes  the  circumference,  g 
=  32.16,  and  r  and  h  are  taken  in  feet,  the  time  in  seconds  of  performing 
one  revolution  is  (at  New  York  or  other  place  where  g  =  32.16) 

JL;          h  =  -¥-, :  =  0.8146  *2. 
g  4*2 

If  t  =  1  second,  h  =  0.8146  foot  =9.775  inches. 
The  principle  of  the  conical  pendulum  is  used  in  the  ordinary  fly-ball 
governor  for  steain -engines.     (See  Governors,) 


VELOCITY,  ACCELERATION,  FALLING  BODIES.       521 

CENTRIFUGAL   FORCE. 

A  body  revolving  in  a  curved  path  of  radius  =  R  in  feet  exerts  a  force, 
called  centrifugal  force,  F,  upon  the  arm  or  cord  which  restrains  it  from 
moving  in  a  straight  line,  or  "  flying  off  at  a  tangent."  If  W  =  weight  of 
the  body  in  pounds,  N  =  number  of  revolutions  per  minute,  v  =  linear 
velocity  of  the  center  of  gravity  of  the  body,  in  feet  per  second,  g  =  32.174* 
then 

,     27T/2JV    E,     W&        Wv*         W47r*RN*     WRN* 

='00034084 TF^MbS. 


If  n  =  number  of  revplutions  per  second,  F  =  1.2270  WRri*. 
(For  centrifugal  force  in  fly-wheels,  see  Fly-wheels.) 

VELOCITY,  ACCELERATION,  FALLING   BODIES. 

Velocity  is  the  rate  of  motion,  or  the  speed  of  a  body  at  any  instant. 
If  s  =  space  in  feet  passed  over  in  t  seconds,  and  v  =  velocity  in  feet  per 
~  J,  if  the  velocity  is  uniform, 

_  s     ,_**_£. 

~~  t  '  s      v  '     ~~  v 

If  the  velocity  varies  uniformly,  the  mean  velocity  vm = 1/2  («i  +  v2),  in  which 
Vi  is  the  velocity  at  the  beginning. and  v2  the  velocity  at  the  end  of  the  time  t. 
s  =  i/2  (vi  +  Vz)  t (1) 

If  vi  =  0,  then  s  =  1/2  v£.     vz  =  2  s/t. 

If  the  velocity  varies,  but  not  uniformly,  v  for  an  exceedingly  short 
interval  of  time  =  s/t,  or  in  calculus  v  =  ds/dt. 

Acceleration  is  the  change  in  velocity  which  takes  place  in  a  unit^of 
time.  The  unit  of  acceleration  is  1  foot  per  second  in  one  second.  For 
uniformly  accelerated  motion  the  acceleration  (a)  is  a  constant  quantity 

Vz  ~V\  i  V2  ~  Vi  ^rtX 

Q  —     "    ;  Vo  ==  V\  -f*  dt ',  V\  ==  V2  —  &'  I   '  ==  *      •     «     t    V<"/ 


If  the  body  start  from  rest,  Vi  =  0;  then  if  vm  =  mean  velocity 


t=        =  __=  \ 

g         32.16       \    g   ™  4.01  ~     v   ' 
u  =  space  fallen  through  in  the  rth  second  =  g  (T  —  y^). 

If  Vi    =0,5=  1/2  V2t. 

Retarded  Motion.  —  If  the  body  start  with  a  velocity  Vi  and  come  to 
rest,  v2=  0;  then  s  =  l/2Vit. 

In  any  case,  if  the  change  in  velocity  is  v, 

s  _^.  s_  _»!.  s  _  «t2 
~  2*'  S~  2a'  S  •"  2£> 

For  a  body  starting  from  or  ending  at  rest,  we  have  the  equations 
r  -at;  s  =  |f;  s  =  y;v2  =  2  as. 

Falling  Bodies.  —  In  the  case  of  falling  bodies  the  acceleration  due 
to  gravity,  at  40°  latitude,  is  32.16  feet  per  second  in  one  second,  =  g. 
Then  if  v  =  velocity  acquired  at  the  end  of  t  seconds,  or  final  velocity, 
and  h  =  height  or  space  in  feet  passed  over  in  the  same  time, 

8.02V'Ji  =*  ~; 

—         —  —    -  -• 

20  64.32  2' 


g      32.16  . 

=  space  fallen  through  in  the  rth  second  =  g  (T  -  } 


522 


MECHANICS. 


1 

2 

3 

4 

5 

6 

1 

1 

1 

1 

1 

1 

1 

2 

3 

4 

5 

6 

1 

3 

5 

7 

9 

11 

1 

4 

9 

16 

25 

36 

From  the  above  formulae  for  falling  bodies  we  obtain  the  following* 
During  the  first  second  the  body  starting  from  a  state  of  rest  (resistance 
of  the  air  neglected)  falls  g  -*•  2  =  16.08  feet;  the  acquired  velocity  is  g  = 

32.16  ft.  per  sec.;  the  distance  fallen  in  two  seconds  is  h  =  ~  =  16.08  X  4 

=  64.32  ft.;  and  the  acquired  velocity  is  v  =  gt  =  64.32  ft.  The  acceler- 
ation, or  increase  of  velocity  in  each  second,  is  constant,  and  is  32.16  ft. 
per  second.  Solving  the  equations  for  different  times,  we  find  for 

Seconds,  t 

Acceleration,  g 32.16  X 

Velocity  acquired  at  end  of  time,  v  . . . .    32.16  X 

OO    1  C 

Height  of  fall  in  each  second,  u — - —  X 

Total  height  of  fall,  h 32.16-4-2  x 

Value  of  g. — The  value  of  g  increases  with  the  latitude,  and  decreases 
with  the  elevation.  At  the  latitude  of  Philadelphia,  40°.  its  value  is 
32.16.  At  the  sea-level,  Everett  gives  g  -  32.173  -  .082  cos  2  lat.  — 
.000003  height  in  feet. 

At  lat.  45°  Everett's  formula  gives  g  =  32.173.  The  value  given  by  the 
International  Conference  on  Weights  and  Measures,  Paris,  1901,  is  32. 1740. 

Values  of  ^2g,  calculated  by  an  equation  given  by  C.  S.  Pierce,  are 
given  in  a  table  in  Smith's  Hydraulics,  from  which  we  take  the  following: 

Latitude 0°  10°          20°          30°          40°          50°          60° 

Value  of  ^2g..  8.0112  8.0118  8.0137  8.0165  8.0199  8.0235  8.0269 
Valueofp 32.090  32.094  32.105  32.132  32.160  32.189  32.216 

The  value  of  ^2g  decreases  about  .0004  for  every  1000  feet  increase  in 
elevation  above  the  sea-level. 

For  all  ordinary^  calculations  for  the  United  States,  g  is  generally  taken 
at  32.16,  and  V2g  at  8.02.  In  England  g  =  32.2.  \/2~g  =  8.025.  Practi- 
cal limiting  values  of  g  for  the  United  States,  according  to  Pierce,  are: 

Latitude  49°  at  sea-level g  =  32. 186 

25°  10,000  feet  above  the  sea g  =  32 .089 

Local  values  of  g  are  used  in  the  calculation  of  problems  that  involve 
local  gravitational  force,  such  as  those  of  falling  bodies,  lifting  loads, 
and  power  of  waterfalls.  In  all  cases  in  which  g  appears  in  an  equation 
as  a  divisor  of  w  (standard  weight  in  pounds),  as  in  the  equation  for 
centrifugal  force  on  the  preceding  page,  the  value  32.174  should  be  used. 
Fig.  106  represents  graphically  the  velocity,  space,  etc.,  of  a  body  falling 
for  six  seconds.  The  vertical  line  at  the  left  is  the  time  in  : 


horizontal  lines  represent  the  acquired 
velocities  at  the  end  of  each  second  = 
32.16 1.  The  area  of  the  small  triangle 
at  the  top  represents  the  height  fallen 
through  in  the  first  second  =  1/29=  16.08 
feet,  and  each  of  the  other  triangles  is  an 
equal  space.  The  number  of  triangles 
between  each  pair  of  horizontal  lines  rep- 
resents the  height  of  fall  in  each  second, 
and  the  number  of  triangles  between  any 
horizontal  line  and  the  top  is  the  total 
height  fallen  during  the  time.  The  figures 
under  k,  u  and  v  adjoining  the  cut  are  to 
bemultiplied  by  16.08 toobtain  the  actual 
velocities  and  heights  for  the  given  times. 
Angular  and  Linear  Velocity  of  a 
Turning  Body.  —  Let  r  =  radius  of  a 
turning  oody  in  feet,  n  =  number  of  revo- 
lutions per  minute,  v=»  linear  velocity  of 
a  point  on  the  circumference  in  feet  per 
second,  and  60  v  =  velocity  in  feet  per 
minute. 


i  seconds,  the 


h    u,  v  t 


.434   2" 


9      5     6    3" 


16     7     8  4" 


9  .10   5" 


\ 

v\ 


U  13    6- 


\\\ 


-~ 


60  v  =  2  «rrn, 


FIG.  106, 


PARALLELOGRAM   OF   VELOCITIES. 


523 


velocity  is  a  term  used  to  denote  the  angle  through  which  any 
radius  of  a  body  turns  in  a  second,  or  the  rate  at  which  any  point  in  it 
having  a  radius  equal  to  unity  is  moving,  expressed  in  feet  per  second. 
The  unit  of  angular  velocity  is  the  angle  which  at  a  distance  =  radius 
from  the  center  is  subtended  by  an  arc  equal  to  the  radius.  This  unit 

360°,  or  the  circumference. 


angle  =  ~  degrees  =  57.3°.     2irX  57.3° 


If  A 

called  a  radian, 


angular  velocity,  v  =  Ar,  A  —  - 

T 


1 80 
The  unit  angle  — —  is 


Height  Corresponding  to  a  Given  Acquired  Velocity. 


Velocity. 

,d 
bC 

"S 

w 

Velocity. 

§ 

1 

Velocity. 

1 
5 

S 

Velocity. 

^ 

M 

'£ 
« 

Velocity. 

Height. 

Velocity. 

Height.  1 

feet 

feet 

feet 

feet 

feet 

feet 

per 

feet. 

per 

feet. 

per 

feet. 

per 

feet. 

per 

feet. 

per 

foot. 

sec. 

sec. 

sec. 

sec. 

sec. 

sec 

.25 

0.0010 

13 

2.62 

34 

17.9 

55 

47.0 

76 

89.8 

97 

146 

.50 

0.0039 

14 

3.04 

35 

19.0 

56 

48.8 

77 

92.2 

98 

149 

.75 

0.0087 

15 

3.49 

36 

20.1 

57 

50.5 

78 

94.6 

99 

152 

1.00 

0.016 

16 

3.98 

37 

21.3 

58 

52.3 

79 

97.0 

100 

155 

1.25 

0.024 

17 

4.49 

38 

22.4 

59 

54.1 

80 

99  5 

105 

171 

1.50 

0.035 

18 

5.03 

39 

23.6 

60 

56.0 

81 

102.0 

110 

188 

1  75 

0  048 

1? 

5.61 

40 

24.9 

61 

57.9 

82 

104.5 

115 

205 

2 

0  062 

20 

6.22 

41 

26.1 

62 

59.8 

83 

107.1 

120 

224 

2.5 

0.097 

21 

6.85 

42 

27.4 

63 

61.7 

84 

109.7 

130 

263 

3 

0.140 

22 

7.52 

43 

28.7 

64 

63.7 

85 

112.3 

140 

304 

3  5 

0.190 

23 

8.21 

44 

30.1 

65 

65.7 

86 

115.0 

150 

330 

4 

0  248 

24 

8.94 

45 

31.4 

66 

67.7 

57 

117.7 

175 

476 

4.5 

0.314 

25 

9.71 

46 

32.9 

67 

69.8 

88 

120.4 

200 

622 

5 

0  388 

26 

10.5 

47 

34.3 

68 

71.9 

89 

123.2 

300 

1399 

6 

0  559 

27 

11.3 

48 

35.8 

69 

74.0 

90 

125.9 

400 

2488 

7 

0  761 

28 

12.2 

49 

37.3 

70 

76.2 

91 

128.7 

500 

3887 

8 

0.994 

29 

13.1 

50 

38.9 

71 

78.4 

92 

131.6 

600 

5597 

9 

1.26 

30 

14.0 

51 

40.4 

72 

80.6 

93 

134.5 

700 

7618 

10 

1.55 

31 

14.9 

52 

42.0 

73 

82.9 

94 

137.4 

800 

9952 

H 

1  88 

32 

15.9 

53 

43.7 

74 

85.1 

95 

140.3 

900 

12,593 

12 

2.24 

33 

16.9 

54 

45.3 

75 

87.5 

96 

143.3 

1000 

15,547 

3 B 


Parallelogram  of  Velocities.  —  The  principle  9f  the  composition 
and  resolution  of  forces  may  also  be  applied  to  velocities  or  to  distances 
moved  in  given  intervals  of  time.  Referring 
to  Fig.  99,  page  513,  if  a  body  at  O  has  a 
force  applied  to  it  which  acting  alone  would 
give  it  a  velocity  represented  by  OQ  per 
second,  and  at  the  same  time  it  is  acted  on 
by  another  force  which  acting  alone  would 
give  it  a  velocity  OP  per  second,  the  result 
of  the  two  forces  acting  together  for  one  sec- 
ond will  carry  it  to  R,  OR  being  the  diagonal 
of  the  parallelogram  of  OQ  and  OP,  and  the 
resultant  velocity.  If  the  two  component 
velocities  are  uniform,  the  resultant  will  be 
uniform  and  the  line  OR  will  be  a  straight 
line;  but  if  either  velocity  is  a  varying  one, 
the  line  will  be  a  curve.  Fig.  107  shows  the 

resultant  velocities,  also  the  path  traversed  linifm-m 

by  a  body  acted  on  by  two  forces,  one  of  which  would  carry  it  at  a  unit 
velocity  over  the  intervals  1,  2,  3,  B,  and  the  other  of  which  would  carry  it 
by  an  accelerated  motion  over  the  intervals  a.b.c.D  m  the  same  times.    At 


FIG.  107. 


524 


MECHANICS. 


Falling  Bodies:  Velocity  Acquired  by  a  Body  Falling  a  Given 
Height. 


>> 

>, 

>> 

>> 

fA 

;>> 

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w 

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O 

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W! 

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W 

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4 

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IS 
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H-l 

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1 

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£ 
"S  . 

>• 

4 

33 

w 

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o 
13 
>• 

feet. 

feet 
p.  sec. 

feet. 

feet 
p.sec. 

feet. 

feet 
p.sec. 

feet. 

feet 
p.sec. 

feet. 

feet 
p.sec. 

feet. 

feet 
p.sec. 

0.005 

.57 

0.39 

5.01 

.20 

8.79 

5. 

17.9 

23. 

38.5 

72 

68.1 

v.CIO 

.80 

0.40 

5.07 

.22 

8.87 

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18.3 

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38.9 

73 

68.5 

0.015 

.98 

0.41 

5.14 

.24 

8.94 

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18.7 

24. 

39.3 

74 

69.0 

0.020 

.13 

0.42 

5.20 

.26 

9.01 

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19.0 

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39.7 

75 

69.5 

0.025 

.27 

0.43 

5.26 

.28 

9.08 

.8 

19.3 

25 

40.1 

76 

69  9 

0.030 

.39 

0.44 

5.32 

.30 

9.15 

6. 

19.7 

26 

40.9 

77 

70.4 

0.035 

.50 

0.45 

5.38 

.32 

9.21 

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20.0 

27 

41.7 

78 

70.9 

0.040 

.60 

0.46 

5.44 

.34 

9.29 

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20.3 

28 

42.5 

79 

71.3 

0.045 

.70 

0.47 

5.50 

.36 

9.36 

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20.6 

29 

43.2 

80 

71.8 

0.050 

.79 

0.48 

5.56 

.38 

9.43 

.8 

20.9 

30 

43.9 

81 

72.2 

0.055 

.88 

0.49 

5.61 

.40 

9.49 

7. 

21.2 

31 

44.7 

82 

72.6 

0.060 

.97 

0.50 

5.67 

.42 

9.57 

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21.5 

32 

45.4 

83 

73.1 

0.055 

2.04 

0.51 

5.73 

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9.62 

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21.8 

33 

46.1 

84 

73.5 

0.070 

2.12 

0.52 

5.78 

.46 

9.70 

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22.1 

34 

46.8 

85 

74.0 

0.075 

2.20 

0.53 

5.84 

.48 

9.77 

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22.4 

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47.4 

86 

74.4 

0.080 

2.27 

0.54 

5.90 

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9.82 

8. 

22.7 

36 

48.1 

87 

74.8 

0.085 

2.34 

0.55 

5.95 

.52 

9.90 

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23.0 

37 

48.8 

88 

75.3 

0.090 

2.41 

0.56 

6.00 

.54 

9.96 

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23.3 

38 

49.4 

89 

75.7 

0.095 

2.47 

0.57 

6.06 

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10.0 

.6 

23.5 

39 

50.1 

90 

76.1 

0.100 

2.54 

0.58 

6/11 

.58 

10.1 

.8 

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50.7 

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76.5 

0.105 

2.60 

0.59 

6.16 

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10.2 

9. 

24.1 

41 

51.4 

92 

76.9 

0.110 

2.66 

0.60 

6.21 

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10.3 

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52.0 

93 

77.4 

0.115 

2.72 

0.62 

6.32 

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10.5 

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24.6 

43 

52.6 

94 

77.8 

0.120 

2.78 

0.64 

6.42 

.75 

10.6 

.6 

24.8 

44 

53.2 

95 

78.2 

0.125 

2.84 

0.66 

6.52 

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10.8 

.8 

25.1 

45 

53.8 

96 

78.6 

C.130 

2.89 

0.68 

6.61 

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11.1 

10. 

25.4 

46 

54.4 

97 

79.0 

C.14 

3.00 

0.70 

671 

2. 

11.4 

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26.0 

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55.0 

98 

79.4 

0.15 

3.11 

0.72 

6.81 

2.1 

11.7 

11. 

26.6 

48 

55.6 

99 

79.8 

0.16 

3.21 

0.74 

6.90 

2.2 

11.9 

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27.2 

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56.1 

100 

80.2 

0.!7 

3.31 

.0.76 

6.99 

2.3 

12.2 

12. 

27.8 

50 

56.7 

125 

89.7 

0.18 

3.40 

0.78 

7.09 

2.4 

12.4 

.5 

28.4 

51 

57.3 

150 

98.3 

0.19 

3.50 

0.80 

7.18 

2.5 

12.6 

13. 

28.9 

52 

57.8 

175 

106 

0.20 

3.59 

0.82 

7.26 

2.6 

12.0 

.5 

29.5 

53 

58.4 

200 

114 

0.21 

3.68 

0.84 

7.35 

2.7 

13.2 

14. 

30  0 

54 

59.0 

225 

120 

0.22 

3.76 

0.86 

7.44 

2.8 

13.4 

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30.5 

55 

59.5 

250 

126 

0.23 

3.85 

0.88 

7.53 

2.9 

13.7 

15. 

31.1 

56 

60.0 

275 

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0.24 

3.93 

0.90 

7.61 

3. 

13.9 

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31.6 

57 

60.6 

300 

139 

0.25 

4.01 

0.92 

7.69 

3.1 

14.1 

16. 

32.1 

58 

61.1 

350 

150 

0.26 

4.09 

0.94 

7.78 

3.2 

14.3 

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32.6 

59 

61.6 

400 

160 

0.27 

4.17 

0.96 

7.86 

3.3 

14.5 

17. 

33.1 

60 

62.1 

450 

170 

0.28 

4.25 

0.98 

7.94 

3.4 

14.8 

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33.6 

61 

62.7 

500 

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0.29 

4.32 

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8.02 

3.5 

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18. 

34.0 

62 

63.2 

550 

188 

0.30 

4.39 

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8.10 

3.6 

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34.5 

63 

63.7 

600 

197 

0.31 

4  47 

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8.18 

3.7 

15.4 

19. 

35.0 

64 

64.2 

700 

212 

0.32 

4.54 

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8.26 

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15.6 

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35.4 

65 

64.7 

800 

227 

0.33 

4.61 

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8.34 

3.9 

15.8 

20. 

35.9 

66 

65.2 

900 

241 

0  34 

4.68 

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8.41 

4. 

16.0 

.5 

36.3 

67 

65.7 

1000 

254 

0  35 

4  74 

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8.49 

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16.4 

21. 

36.8 

68 

66.1 

2000 

359 

0.36 

4.81 

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8.57 

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16.8 

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37.2 

69 

66.6 

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439 

0  37 

4.88 

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8.64 

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22. 

37.6 

70 

67.1 

4000 

507 

0.38 

4.94 

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8.72 

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17.6 

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38.1 

71 

67.6 

5000 

567 

FORCE   OF  ACCELERATION.  525 

the  end  of  the  respective  intervals  the  body  will  be  found  at  C\,  €2,  Cs,  C, 
and  the  mean  velocity  during  each  interval  is  represented  by  the  dis- 
tances between  these  points.  Such  a  curved  path  is  traversed  by  a  shot, 
the  impelling  force  from  the  gun  giving  it  a  uniform  velocity  in  the 
direction  the  gun  is  aimed,  and  gravity  giving  it  an  accelerated  velocity 
downward.  The  path  of  a  projectile  is  a  parabola.  The  distance  it  will 
travel  is  greatest  when  its  initial  direction  is  at  an  angle  45°  above  the 
horizontal. 

FUNDAMENTAL  EQUATIONS  IN  DYNAMICS. 

(Uniformly  Accelerated  Motion) 

Much  difficulty  to  students  of  Mechanics  has  resulted  from  the  use 
in  various  text-books  of  such  terms  as  "poundal"  as  a  unit  of  force 
(see  page  512),  "gee-pound,"  "slug,"  or  "engineers'  unit  of  mass" 
(  =  32.2  Ibs.  of  matter),  and  by  the  various  definitions  given  to  the 
words  "mass"  and  "weight."  The  following  elementary  treatment  of 
the  subject,  in  which  all  of  these  troublesome  words  are  avoided,  is 
taken  from  an  article  by  the  author  in  Science,  March  19,  1915.  It 
is  urgently  commended  to  the  attention  of  text-book  writers  and 
teachers,  and  constructive  criticism  of  it  is  solicited. 

The  fundamental  problem  is:  Given  a  constant  force  F  Ibs.  acting 
for  T  seconds  on  a  quantity  of  matter  W  Ibs.,  at  rest  at  the  beginning 
of  the  time,  but  free  to  move,  what  are  the  results,  assuming  that  there 
is  no  frictional  resistance? 

The  first  result  is  motion,  at  a  gradually  increasing  velocity.  The 
relati9n  between  the  elapsed  time  and  the  velocity  is  determined  by 
experiment.  The  velocity  varies  directly  as  the  time  and  as  the  force, 
and  inversely  as  the  quantity  of  matter,  and  the  equation  is  V  oo  FT/  W 
or  V  =  KFT/W,  K  being  a  constant  whose  value  is  approximately  32, 
provided  V  is  in  feet  per  second,  F  and  W  in  pounds  and  T  in  seconds. 

Accurate  determinations,  involving  precise  measurements  of  both  F 
and  W,  and  of  S,  the  distance  .traversed  during  the  time  T,  from  which 
Vis  determined,  and  precautions  to  eliminate  resistance  due  to  friction, 
give  K  =  32.1740.  This  figure  is  twice  the  number  of  feet  that  the 
body  would  fall  in  vacua  in  one  second  at  or  near  latitude  45°  at  the  sea 
level.  It  is  commonly  represented  by  g,  or  by  go,  to  distinguish  it  from 
other  values  of  g  that  may  be  obtained  by  experiments  on  falling 
bodies  (or  on  pendulums)  at  other  latitudes  and  elevations.  The 
fundamental  equation  then  is 

V  =  FTg/W    .....    ......    (1) 

The  quantity  g  is  commonly  called  the  acceleration  due  to  gravity. 
but  it  also  may  be  considered  either  as  an  abstract  figure,  the  constant 
g  in  equation  (1),  or  as  the  velocity  acquired  at  the  end  of  1  second  by 
a  falling  body,  or  as  the  distance  a  body  would  travel  in  1  second  atJ 
that  same  velocity  if  the  force  ceased  to  act  and  the  velocity  remained 
constant. 

If  the  velocity  varies  directly  as  the  time  (uniformly  accelerated 
motion),  then  the  distance  is  the  product  of  the  mean  velocity  and  the 
time.  As  the  body  starts  from  rest  when  the  velocity  is  0,  and  the 
velocity  is  V  at  the  end  of  the  time  T,  the  mean  velocity  is  1/2  V  and  the 
distance  is  1/2  VT,  whence  V=  2S/T  and  T  =  2S/V. 

The  velocity  V  in  feet  per  second,  at  the  end  of  the  time  T  is  numer- 
ically equal  to  the  number  of  feet  the  body  would  travel  in  one  second 
after  the  expiration  of  the  time  T  if  the  force  had  then  ceased  to  act 
and  the  body  continued  to  move  at  a  uniform  velocity. 

In  equation  (1)  substitute  for  V  its  value  2S/T  and  we  obtain 

S     FT2ff  •  (K 

=  ~~ 


We  have  four  elementary  quantities  F,  T,  S,  W,  one  derived  quan- 
tity V,  and  one  constant  figure  32.1740.  It  is  understood  that  F  is 
measured  in  standard  pounds  of  force,  one  pound  of  force  being  the 
force  that  gravity  exerts  on  a  pound  of  matter  at  the  standard  loca- 
tion where  g  =  32.1740. 

Each  equation  contains  four  variables,  V,  F,  T,  W,  or  S,  F,  T,  W,  and 
in  either  equation  if  values  be  given  to  any  three  the  fourth  may  be 
found.  By  transposition,  or  by  giving  new  symbols  to  the  product  or 


526  MECHANICS. 

quotient  of  two  of  the  variables,  many  different  equations  may  Toe 
derived  from  them,  the  most  important  of  which  are  given  below. 

From  (1),  let  F  =  W,  the  case  of  a  body  falling  at  latitude  45°  at  the 
sea  level;  then  V  =  gT.  If  T  also  =  1,  then  V  =  g,  that  is  the  velocity 
at  the  end  of  1  second  is  g. 

In  the  equation  V  =  gT  substitute  for  T  its  value  2S/V and  we  have 
V  =  2gS/  V,  whence  V2  =  2gS.  In  the  case  of  falling  bodies,  the  height 
of  fall  H  is  usually  substituted  for  S,  and  we  obtain 

V=V2gH (3) 

Equation  (2)  with  F  =  W  gives  V=  1/2  gT*. 
From  (1),  by  transposition  we  obtain 

FT=  WX  V/g,orFT  =  VxW/g (4) 

The  product  FT  is  sometimes  called  Impulse,  and  the  expression 
W  X  V/g  is  called  momentum.  It  is  convenient  to  use  the  letter  M 
instead  of  W/g,  so  that  the  equation  becomes 

FT  =  MV (5) 

Impulse    =  Momentum 

In  (4)  we  may  substitute  for  T  its  value  in  terms  of  S  and  V  above 
given,  viz.,  T  =  2S/V  and  obtain  F2S/V  =  MV; 

whence  FS  =  1/2  MV2, (6) 

Work  expended  =  Kinetic  energy. 

Acceleration.  —  The  quotient  V/T  is  called  the  acceleration.  It  is 
denned  as  the  rate  of  increase  of  velocity.  In  the  problem  under  con- 
sideration, the  action  of  a  force  on  a  body  free  to  move,  with  no  retarda- 
tion by  friction,  the  acceleration  is  a  constant,  V/T  =  A.  Equation 
(5)  then  may  be  written 

F  =  MA (7) 

Force  =  M  times  the  acceleration.* 

If  a  given  body  is  acted  on  at  two  different  times  by  two  forces  F 
and  FI,  and  if  A  and  A\  are  the  corresponding  accelerations,  then 

Fi  =MAi  whence  F/Fl  =^Ml (8) 

By  the  use  of  these  eight  equations  and  their  transformations  all 
problems  relating  to  uniformly  accelerated  motion  may  be  solved. 

Force  of  Acceleration.  —  Force  has  been  denned  as  that  which  causes, 
or  tends  to  cause,  or  to  destroy,  motion.  It  may  also  be  defined  as  the 
cause  of  acceleration;  and  the  unit  of  force,  the  pound,  as  the  force  re- 
quired to  produce  an  acceleration  of  32.174  ft.  per  second  per  second  of 
one  pound  of  matter  free  to  move. 

Force  equals  the  product  of  the  mass  by  the  acceleration,* or/  =  ma. 

Also,  if  v  =  the  velocity  acquired  in  the  time  t,  ft  =  mv;  *  =  mv  -r- 1; 
the  acceleration  being  uniform. 

The  force  required  to  produce  an  acceleration  of  g  (that  is,  32.174  ft. 

per  sec.  in  one  second)  is  /  =  m  g  =  —  g  =  w,  or  the  weight  of  the  body. 
Also,  /  =  ma  =  m  ***  ~  *.  in  which  vz  is  the  velocity  at  the  end,  and  vi 
the  velocity  at  the  beginning  of  the  time  t,  and  /  =  mg  = 2  = 

^  a;  —  =  -;  or,  tijie  force  required  to  give  any  acceleration  to  a  body  is 
to  the  weight  of  the  body  as  that  acceleration  is  to  the  acceleration  pro- 

*  Equation  (7)  is  sometimes  read  "force  equals  mass  times  acceler- 
ation," which  is  strictly  true  in  the  dyne-centimeter-gram-second,  or 
"absolute"  system  of  measurements,  in  which  force  is  measured  in 
dynes,  but  it  is  not  true  in  the  pound-foot-second  system,  nor  in  the 
metric  system  where  the  kilogram  is  used  as  a  unit  of  both  force  and 
quantity  of  matter,  unless  it  is  understood  that  the  word  "mass"  means 
the  quotient  of  W  divided  by  g. 


FORCE   OF  ACCELERATION.  527 

duced  by  gravity.  In  problems  in  which  the  local  attraction  of  gravity 
is  a  factor  the  local  value  of  g  must  be  used  if  great  accuracy  is  desired. 
EXAMPLE. — Tension  in  a  cord  lifting  a  weight.  A  weight  of  100  Ibs. 
is  lifted  vertically  by  a  cord  a  distance  of  80  feet  in  4  seconds,  the  velocity 
uniformly  increasing  from  0  to  the  end  of  the  time.  What  tension  must 
be  maintained  in  the  cord,  assuming  the  local  value  of  g  to  be  32.108  or 
0.998  of  the  standard  value?  Mean  velocity  =  vm  =20  ft.  per  sec.; 

final  velocity  =  vi  =  2vm  =  40;  acceleration  a  =  ~  =  -^-  =  10.     Force 

/  =  ma  =  —  =  ^  X  10  =  31.08  Ibs.      The  standard  value  of  g, 

32.174  must  be  used  here,  for  the  force  required  for  acceleration  is 
independent  of  local  gravitation.  This  is  the  force  required  to  pro- 
duce the  acceleration  only ;  to  it  must  be  added  the  force  required  to  lift 
the  weight  without  acceleration,  or  100  Ibs.  X  0.998  =  99.8  Ibs., 
making  a  total  of  130.88  Ibs.  (The  factor  0.998  is  used  here  because  the 
force  of  gravity  at  the  given  locality  is  0.002  less  than  at  the  standard 
locality) . 

The  Resistance  to  Acceleration  is  the  same  as  the  force  required  to  pro- 
duce the  acceleration  =  —  - — — <. 

Q          t 

Formulae  for  Accelerated  Motion.  —  For  cases  of  uniformity  accel- 
erated motion  other  than  those  of  falling  bodies,  we  have  the  formulae 

already  given,  /  =  —  a,  = — — .    If  the  body  starts  from  rest,  v\  = 

0,  v-2  =  v  and/  =  -  ~r\fgt  =  wv.    We  also  have  s  =  ^-.    Transforming 

0  *  £ 

id  substituting  for  g  its  value  32.174,  we  obtain 

f  _       wv~  wv  _Jf?.s_.  _  _§2_i1L^  -   64.35_/s. 

J  "    64.35  S~    32.17  t  ~  16.09  F  '  v  v* 

wv2 


" 


64.35  / 
t- 


16.09  //a       vtm  Ifs        32.17ft, 

W         __2'  \  w  w 


32.17  /        4.01     \   / 
For  any  change  in  velocity,/  =  w  (^  ~  Vl " ) . 

\  O4.OO  o   / 


(See  also  Work  of  Acceleration,  under  Work.) 

Motion  on  Inclined  Planes. — The  velocity  acquired  by  a  body  de- 
scending an  inclined  plane  by  the  force  of  gravity  (friction  neglected)  is 
equal  to  that  acquired  by  a  body  falling  freely  from  the  height  of  the 
plane. 

The  times  of  descent  down  different  inclined  planes  of  the  same  height 
vary  as  the  length  of  the  planes, 

The  rules  for  uniformly  accelerated  motion  apply  to  inclined  planes. 
If  a  is  the  angle  of  the  plane  with  the  horizontal,  sin  a  =  the  ratio  of  the 

height  to  the  length  =  j- ,  and  the  constant  accelerating  force  is  g  sin  a. 

The  final  velocity  at  the  end  of  t  seconds  is  v  =  gt  sin  a.    The  distance 
passed  over  in  t  seconds  is  I  =  1/2  gt2  sin  a.    The  time  of  descent  is 

I 


|  g  sin  a       4.01  ^/h 
Momentum,  in  many  books  erroneously  defined  as  the  quantity  of 
motion  in  a  body,  is  the  product  of  the  mass  by  the  velocity  at  any 

instant,  =  mv  =  —  v.     By  "mass"  is  "meant  the  quotient  w/g. 

Since  ft  =  mv,  the  product  of  a  constant  force  into  the  time  in  which 
it  acts  equals  numerically  the  momentum. 

Momentum  may  be  defined  as  numerically  equivalent  to  the  number 
of  pounds  of  force  that  will  stop  a  moving  body  in  1  second,  or  the  num- 
ber of  pounds  of  force  which  acting  during  1  second  will  give  it  the  given 
velocity. 


528  MECHANICS. 

Vis-viva,  or  living  force,  is  a  term  used  by  early  writers  on  Mechanics 
to  denote  the  energy  stored  in  a  moving  body.  The  term  is  now  obso- 
lete, its  place  being  taken  by  the  word  energy. 

WORK,  ENERGY,  POWER. 

The  fundamental  conceptions  in  Mechanics  are: 

Matter,  Force,  Time,  Space,  represented  by  W,  F,  T,  S. 

In  English  units  W  and  F  are  measured  in  pounds,  T  in  seconds,  5 
in  feet. 

Velocity  =  space  divided  by  time,  V  =  S  -f-  T,  if  V  be  uniform.  V 
at  end  of  time  T  (uniformly  accelerated  motion)  =  2S  -f-  T. 

Resistance  is  that  which  is  opposite  to  an  acting  force.  It  is  equal 
and  opposite  to  force. 

Work  is  the  overcoming  of  resistance  through  a  certain  distance.  It 
is  measured  by  the  product  of  the  resistance  into  the  space  through 
which  it  is  overcome.  It  is  also  measured  by  the  product  of  the  moving 
force  into  the  distance  through  which  the  force  acts  in  overcoming  the 
resistance.  Thus  in  lifting  a  body  from  the  earth  against  the  attraction 
of  gravity,  the  resistance  is  the  weight,  of  the  body,  and  the  product  of 
this  weight  into  the  height  the  body  is  lifted  is  the  work  done. 

The  Unit  of  Work,  in  British  measures,  is  the  foot-pound,  or  the 
amount  of  work  done  in  overcoming  a  pressure  or  weight  equal  to  one 
pound  through  one  foot  of  space. 

The  work  performed  by  a  piston  in  driving  a  fluid  before  it,  or  by  a 
fluid  in  driving  a  piston  before  it,  may  be  expressed  in  either  of  the  fol- 
lowing ways: 

Resistance  X  distance  traversed 

=  intensity  of  pressure  X  area  X  distance  traversed ; 
=  intensity  of  pressure  X  volume  traversed. 

By  intensity  of  pressure  is  meant  pressure  per  unit  of  area,  as  Ibs.  per 
sq.  in. 

The  work  performed  in  lifting  a  body  is  the  product  of  the  weight  of 
the  body  into  the  height  through  which  its  center  of  gravity  is  lifted. 

If  a  machine  lifts  the  centers  of  gravity  of  several  bodies  at  once  to 
heights  either  the  same  or  different,  the  whole  quantity  of  work  per- 
formed in  so  doing  is  the  sum  of  the  several  products  of  the  weights  and 
heights ;  but  that  quantity  can  also  be  computed  by  multiplying  the  sum 
of  all  the  weights  into  the  height  through  which  their  common  center  of 
gravity  is  lifted.  (Rankine.) 

Power  is  the  rate  at  which  work  is  done,  and  is  expressed  by  the  quo- 
tient of  the  work  divided  by  the  time  in  which  it  is  done,  or  by  units  of 
work  per  second,  per  minute,  etc.,  as  foot-pounds  per  second.  The  most 
common  unit  of  power  is  the  horse-power,  established  by  James  Watt  as 
the  power  of  a  strong  London  draught-horse  to  do  work  during  a  short 
interval,  and  used  by  him  to  measure  the  power  of  his  steam-engines. 
This  unit  is  33,000  foot-pounds  per  minute  =  550  foot-pounds  per  sec- 
ond =  1,980,000  foot-pounds  per  hour. 

Power  exerted  for  a  certain  time  produces  work;  PT  =  FS  =  FVT, 
if  V  be  uniform. 

Horse-power  Hours,  an  expression  for  work  measured  as  the  product 
of  a  power  into  the  time  during  which  it  acts,  =  PT.  Sometimes  it  is 
the  summation  of  a  variable  power  for  a  given  time,  or  the  average 
power  multiplied  by  the  time. 

Energy,  or  stored  work,  is  the  capacity  for  performing  work.  It  is 
measured  by  the  same  unit  as  work,  that  is,  in  foot-pounds.  It  may  be 
either  potential,  as  in  the  case  of  a  body  of  water  stored  in  a  reservoir, 
capable  of  doing  work  by  means  of  a  water-wheel,  or  actual,  sometimes 
called  kinetic,  which  is  the  energy  of  a  moving  body.  Potential  energy 
is  measured  by  the  product  of  the  weight  of  the  stored  body  into  the  dis- 
tance through  which  it  is  capable  of  acting,  or  by  the  product  of  the 
pressure  it  exerts  into  the  distance  through  which  that  pressure  is  cap- 
able of  acting.  Potential  energy  may  also  exist  as  stored  heat,  or  as 
stored  chemical  energy,  as  in  fuel,  gunpowder,  etc.,  or  as  electrical  en- 
ergy, the  measure  of  these  energies  being  the  amount  of  work  that  they 
are  capable  of  performing.  Actual  energy  of  a  moving  body  is  the  work 
which  it  is  capable  of  performing  against  a  retarding  resistance  before 
being  brought  to  rest,  and  is  equal  to  the  work  which  must  be  done 
upon  it  to  bring  it  from  a  state  of  rest  to  its  actual  velocity. 


WORK  OF  ACCELERATION,  529 

The  measure  of  actual  energy  is  the  product  of  the  weight  of  the  body 
into  the  height  from  which  it  must  fall  to  acquire  its  actual  velocity.  If 
v  =  the  velocity  in  feet  per  second,  according  to  the  principle  of  falling 

bodies,  h,  the  height  due  to  the  velocity,  =  ^—\  and  if  w  =  the  weight, 

the  energy  =  1/2  nW1  =  wv%  -i-  2g  =  wh.  Since  energy  is  the  capacity  for 
performing  work,  the  units  of  work  and  energy  are  equivalent,  or  FS  = 
1/2  mvz  =  wh.  Energy  exerted  =  work  done. 

The  actual  energy  of  a  rotating  body  whose  angular  velocity  is  A  and 

A.'2! 
moment  of  inertia  2uT2  =  I  is  —  —  ,  that  is,  the  product  of  the  moment 

of  inertia  into  the  height  due  to  the  velocity,  A,  of  a  point  whose  distance 
from  the  axis  of  rotation  is  unity  ;  or  it  is  equal  to  -jr—  ,  in  which  w  is  the 
weight  of  the  body  and  v  is  the  velocity  of  the  center  of  gyration. 

Work  of  Acceleration.—  The  work  done  in  giving  acceleration  to  a 
body  is  equal  to  the  product  of  the  force  producing  the  acceleration,  or 
of  the  resistance  to  acceleration,  into  the  distance  moved  in  a  given  time. 
This  force,  as  already  stated,  equals  product  of  the  mass  into  the  acceler- 

ation, or  /  =  ma  =~         —  .    If  the  distance  traversed  in  the  time  t  =  st 
•    Q         t         ^ 

W  V1  —  Vi 

then  work  =fs  =  --  -  --  s. 

EXAMPLE.  —  What  work  is  required  to  move  a  body  weighing  100  Ibs. 
horizontally  a  distance  of  80  ft.  in  4  seconds,  the  velocity  uniformly 
increasing,  friction  neglected? 

Mean  velocity  vm  =  20  ft.  per  second;   final  velocity  =  V2  =  2  vm  =40; 

initial  velocity  vi  =  0;  acceleration,   a  =  —  •-—  =  —  =  10;     force  = 

"  a  =  lUrr  x  10  =  3L1  lbs>;  distance  80  ffc-  work  =  fs  =  3i.i  x  so 

=  2488  foot-pounds. 

The  energy  stored  in  the  body  moving  at  the  final  velocity  of  40  ft. 
per  second  is 

1/2  ro»*  =  \  y  v2  =  Ifj^^j  =  2488  foot-pounds, 
which  equals  the  work  of  acceleration, 

_  w    V-i       _WV2V2lW 

JS~JTS~  g~t~2  *-  2  7^ 

If  a  body  of  the  weight  W  falls  from  a  height  H,  the  work  of  accelera- 
tion is  simply  WH,  or  the  same  as  the  work  required  to  raise  the  body 
to  the  same  height. 

Work  of  Accelerated  Rotation.  —  Let  A  —  angular  velocity  of  a 
solid  body  rotating  about  an  axis,  that  is,  the  velocity  of  a  particle 
whose  radius  is  unity.  Then  the  velocity  of  a  particle  whose  radius  is  r 
is  v  =  Ar.  If  the  angular  velocity  is  accelerated  from  Ai  to  Az,  the  in- 
crease of  the  velocity  of  the  particle  is  v*  —  Vi  =  r  (Ai  —  A*),  and  the 
work  of  accelerating  it  is 

w^       Vi-  —  vi2    _  wr-  A&_  —  Ai* 
_        ___     =  __          _        , 

in  which  w  is  the  weight  of  the  particle.    A  is  measured  in  radians. 
The  work  of  acceleration  of  the  whole  body  is 


The  term  Sir  r^  is  the  moment  of  inertia  of  the  body. 

"  Force  of  the  Blow  "  of  a  Steam  Hammer  or  Other  Falling 
Weight.  —  The  question  is  often  asked:  "With  what  force  does  a  fall- 
ing hammer  strike?  "  The  question  cannot  be  answered  directly,  and  it 
is  based  upon  a  misconception  or  ignorance  of  fundamental  mechanical 


530  MECHANICS. 

laws.  The  energy,  or  capacity  for  doing  work,  of  a  body  raised  to  a  given 
height  and  let  fall  cannot  be  expressed  in  pounds,  simply,  but  only  in  foot- 
pounds, which  is  the  product  of  the  weight  into  the  height  through  which 
it  falls,  or  the  product  of  its  weight  •*-  64.32  into  the  square  of  the  velocity, 
in  feet  per  second,  which  it  acquires  after  falling  through  the  given  height. 
If  F  =  weight  of  the  body,  M  its  mass,  g  the  acceleration  due  to  gravity, 
S  the  height  of  fall,  and  v  the  velocity  at  the  end  of  the  fall,  the  energy  in 
the  body  just  before  striking  is  FS  =  1/2  Mv2  =  Wv2  -*-  2  g  =  Wv2  -s-  64.32, 
which  is  the  general  equation  of  energy  of  a  moving  body.  Just  as  the 
energy  of  the  body  is  a  product  of  a  force  into  a  distance,  so  the  work  it 
does  when  it  strikes  is  not  the  manifestation  of  a  force,  which  can  be  ex- 
pressed simply  in  pounds,  but  it  is  the  overcoming  of  a  resistance  through 
a  certain  distance,  which  is  expressed  as  the  product  of  the  average  resist- 
ance into  the  distance  through  which  it  is  exerted.  If  a  hammer  weighing 
100  Ibs.  falls  10  ft.,  its  energy  is  1000  foot-pounds.  Before  being  brought 
to  rest  it  must  do  1000  foot-pounds  of  work  against  one  or  more  resistances. 
These  are  of  various  kinds,  such  as  that  due  t9  motion  imparted  to  the 
body  struck,  penetration  against  friction,  or  against  resistance  to  shearing 
pr  other  deformation,  and  crushing  and  heating  of  both  the  falling  body 
and  the  body  struck.  The  distance  through  which  these  resisting  forces 
act  is  generally  indeterminate,  and  therefore  the  average  of  the  resisting 
forces,  which  themselves  generally  vary  with  the  distance,  is  also  indeter- 
minate. 

Impact  of  Bodies.  —  If  two  inelastic  bodies  collide,  they  will  move  on 
together  as  one  mass,  with  a  common  velocity.  The  momentum  of  the 
combined  mass  is  equal  to  the  sum  of  the  momenta  of  the  two  bodies 
before  impact.  If  Wj  and  m2  are  the  masses  of  the  two  bodies  and  Vi  and  v2 
their  respective  velocities  before  impact,  and  v  their  common  velocity 
after  impact,  (mi  +  w2)v  =  miVi  +  m2v2, 


mi  +  m2 
If  the  bodies  move  in  opposite  directions,  v=  —  ^-.  —  —  ,  or  the  velocity 

mi  -f-   m2 

of  two  inelastic  bodies  after  impact  is  equal  to  the  algebraic  sum  of  their 
momenta  before  impact,  divided  by  the  sum  of  their  masses. 

If  two  inelastic  bodies  of  equal  momenta  impinge  directly  upon  one  an- 
other from  opposite  directions  they  will  be  brought  to  rest. 

Impact  of  Inelastic  Bodies  Causes  a  Loss  of  Energy,  and  this  loss 
is  equal  to  the  sum  of  the  energies  due  to  the  velocities  lost  and  gained 
by  the  bodies,  respectively. 

1/2  miVi2  +  1/2  m2V22  -  V2  (mi  +  m2)  vz  =1/2  mi  (vi  -  v)2  +  1/2  mz  (v*  -  i>)2; 
in  which  vi  —  v  is  the  velocity  lost  by  m\  and  v  —  vi  the  velocity  gained 
by  mi. 

EXAMPLE.  —  Let  mi  =  10,  m*  =  8,  Vi  =  12,  v2  =  15. 

1  Q  vy   -jo  _  O  N/  1  £J 

If  the  bodies  collide  they  will  come  to  rest,  for  v=          10  +  8    —  =  °- 

The  energy  loss  is 

1/2  10  X  144+  l/28  X  225  -1/218X  0  =  1/2  10  (12  -0)2+1/28(15-  O)2  = 
1620  ft.  -Ibs. 

What  becomes  of  the  energy  lost?  Ans.  It  is  used  doing  internal  work 
on  the  bodies  themselves,  changing  their  shape  and  heating  them. 

For  imperfectly  elastic  bodies,  let  e  =  the  elasticity,  that  is,  the  ratio 
which  the  force  of  restitution,  or  the  internal  force  tending  to  restore  the 
shape  of  a  body  after  it  has  been  compressed,  bears  to  the  force  of  com- 
pression- and  let  mi  and  m2  be  the  masses,  Vi  and  v2  their  velocities  before 
impact,  and  Vi,  vj  their  velocities  after  impact;  then 

,  _  m^i  +  7712^2  _  m2e  (vi  —  v2) 


_ 
mi  +  W2  mi  +  mt 

iVi  +  mzvz       m\e  (vi  —  ^2 
mi  +  ma  mi  +  mz 


ENERGY.  531 

If  the  bodies  are  perfectly  efastic,  their  relative  velocities  before  and 
after  impact  are  the  same.  That  is,  v\f  —  vi'  =  v2  —  vi. 

In  the  impact  of  bodies,  the  sum  of  their  momenta  after  impact  is  the 
same  as  the  sum  of  their  momenta  before  impact. 

miVi    +  m2V'2f  =  miVi  +  m2v2. 

For  demonstration  of  these  and  other  laws  of  impact,  see  Smith's  Me- 
chanics; also,  Weisbach's  Mechanics. 

Energy  of  Recoil  of  Guns.     (Eng'g,  Jan.  25,  1884,  p.  72.)  — 

Let  W  =  the  weight  of  the  gun  and  carriage; 

V  =  the  maximum  velocity  of  recoil; 

w  =  the  weight  of  the  projectile; 

v  =  the  muzzle  velocity  of  the  projectile. 

Then,  since  the  momentum  of  the  gun  and  carriage  is  equal  to  the 
rromentum  of  the  projectile  (because  both  are  acted  on  by  equal  force, 
tne  pressure  of  the  gases  in  the  gun,  for  equal  time),  we  have  WV  —  wv, 
or  V  =  wv  -f-  W. 

Taking  the  case  of  a  10-inch  gun  firing  a  400-lb.  projectile  with  a  muzzle 
velocity  of  2000  feet  per  second,  the  weight  of  the  gun  and  carriage  being 
22  tons  =  50,000  Ibs.,  we  find  the  velocity  of  recoil  = 


^-  25  -  18feet  per  a^. 

Now  the  energy  of  a  body  in  motion  is  WV2  -*-  2  g. 

5°Q®°™* 


Therefore  the  energy  of  recoil  =       '  =  198,800  foot-pounds. 

Z  X  oZ.4 

The  energy  of  the  projectile  is  4°0°*  20°o°2  =  24,844,000  foot-pounds. 

£i  X    d-Z.-Z 

Conservation  of  Energy.  —  No  form  of  energy  can  ever  be  pro- 
duced except  by  the  expenditure  of  some  other  form,  nor  annihilated  ex- 
cept by  being  reproduced  in  another  form.  '  Consequently  the  sum  total  of 
energy  in  the  universe,  like  the  sum  total  of  matter,  must  always  remain 
the  same.  (S.  Newcomb.)  Energy  can  never  be  destroyed  or  lost;  it  can 
be  transformed,  can  be  transferred  from  one  body  to  another,  but  no 
matter  what  transformations  are  undergone,  when  the  total  effects  of  the 
exertion  of  a  given  amount  of  energy  are  summed  up  the  result  will  be 
exactly  equal  to  the  amount  originally  expended  from  the  source.  This 
law  is  called  the  Conservation  of  Energy.  (Cotterill  and  Slade.) 

A  heavy  body  sustained  at  an  elevated  position  has  potential  energy. 
When  it  falls,  just  before  it  reaches  the  earth's  surface  it  has  actual  or 
-kinetic  energy,  due  to  its  velocity.  When  it  strikes,  it  may  penetrate  the 
earth  a  certain  distance  or  may  be  crushed.  In  either  case  friction  results 
by  which  the  energy  is  converted  into  heat,  which  is  gradually  radiated 
into  the  earth  or  into  the  atmosphere,  or  both.  Mechanical  energy  and 
heat  are  mutually  convertible.  Electric  energy  is  also  convertible  into 
heat  or  mechanical  energy,  and  either  kind  of  energy  may  be  converted 
into  the  other. 

Sources  of  Energy.  —  The  principal  sources  of  energy  on  the  earth's 
surface  are  the  muscular  energy  of  men  and  animals,  the  energy  of  the 
wind,  of  flowing  water,  and  of  fuel.  These  sources  derive  their  energy 
from  the  rays  of  the  sun.  Under  the  influence  of  the  sun's  rays  vegetation 
grows  and  wood  is  formed.  The  wood  may  be  used  as  fuel  under  a  steam- 
boiler,  its  carbon  being  burned  to  carbon  dioxide.  Three-tenths  of  its  heat 
energy  escapes  in  the  chimney  and  by  radiation,  and  seven-tenths  appears 
as  potential  energy  in  the  steam.  In  the  steam-engine,  of  this  seven-tenths 
six  parts  are  dissipated  in  heating  the  condensing  water  and  are  wasted; 
the  remaining  one-tenth  of  the  original  heat  energy  of  the  wood  is  con- 
verted into  mechanical  work  in  the  steam-engine,  which  may  be  used  to 
drive  machinery.  This  work  is  finally,  by  friction  of  various  kinds,  or  pos- 
sibly after  transformation  into  electric  currents,  transformed  into  neat 
which  is  radiated  into  the  atmosphere,  increasing  its  temperature.  Thus 


532 


MECHANICS. 


all  the  potential  heat  energy  of  the  wood  is,  after  various  transformations, 
converted  into  heat,  which,  mingling  with  the  store  of  heat  in  the  atmos- 

Ehere,  apparently  is  lost.  But  the  carbon  dioxide  generated  by  the  com- 
ustion  of  the  wood  is,  again,  under  the  influence  of  the  sun's  rays, 
absorbed  by  vegetation,  and  more  wood  may  thus  be  formed  having  poten- 
tial energy  equal  to  the  original. 

Perpetual  Motion.  —  The  law  of  the  conservation  of  energy,  than 
which  no  law  of  mechanics  is  more  firmly  established,  is  an  absolute  barrier 
to  all  schemes  for  obtaining  by  mechanical  means  what  is  called  "  perpetual 
motion,"  or  a  machine  which  will  do  an  amount  of  work  greater  than  the 
equivalent  of  the  energy,  whether  of  heat,  of  chemical  combination,  of  elec- 
tricity, or  mechanical  energy,  that  is  put  into  it.  Such  a  result  would  be 
the  creation  of  an  additional  store  of  energy  in  the  universe,  which  is  not 
possible  by  any  human  agency. 

The  Efficiency  of  a  Machine  is  a  fraction  expressing  the  ratio  of 
the  useful  work  to  the  whole  work  performed,  which  is  equal  to  the  energy 
expended.  The  limit  to  the  efficiency  of  a  machine  is  unity,  denoting  the 
efficiency  of  a  perfect  machine  in  which  no  work  is  lost.  The  difference 
between  the  energy  expended  and  the  useful  work  done,  or  the  loss,  is 
usually  expended  either  in  overcoming  friction  or  in  doing  work  on  bodies 
surrounding  the  machine  from  which  no  useful  work  is  received.  Thus 
in  an  engine  propelling  a  vessel  part  of  the  energy  exerted  in  the  cylinder 
does  the  useful  work  of  giving  motion  to  the  vessel,  and  the  remainder  is 
spent  in  overcoming  the  friction  of  the  machinery  and  in  making  currents 
and  eddies  in  the  surrounding  water. 

A  common  and  useful  definition  of  efficiency  is  "  output  divided  by 
input." 

ANIMAL   POWER. 

Work  of  a  Man  against  Known  Resistances.     (Rankine.) 


Kind  of  Exertion. 

R, 

Ibs. 

F, 

ft.  per 
sec. 

T" 
3600 

(hours 
per 
day). 

R  V, 
ft.-lbs. 
per  sec. 

RVT, 

ft.-lbs. 
per  day. 

1.  Raising   his    own  weight    up 
stair  or  ladder 

143 

0.5 

8 

71.5 

2,059,200 

2.  Hauling  up  weights  with  rope, 

and  lowering  the  rope  un- 

loaded                              

40 

0.75 

6 

30* 

648,000 

3.  Lifting  weights  by  hand.  ..... 
4.  Carrying     weights     up-stairs 
and  returning  unloaded  

44 
143 

0.55 
0.13 

6 
6 

24.2 
18.5 

522,720 
399,600 

5.  Shoveling     up     earth    to    a 
height  of  5  ft  3  in    

6 

1.3 

10 

7.8 

280,800 

6.  Wheeling  earth  in  barrow  up 

slope  of   1   in   12,  1/2  horiz. 

veloc.  0.9  ft.  per  sec.,  and  re- 

turning unloaded 

132 
26.5 

0.075 
2.0 

10 

8 

9.9 

53 

356,400 
1,526,400 

7.   Pushing  or  pulling  horizon- 
tally (capstan  or  oar)  

!12.5 

5.0 

62.5 

8.  Turning  a  crank  or  winch  

18.0 
20.0 

2.5 
14.4 

8 
2  rain. 

45 
288 

'1,296,666 

9    Workin0"  pump  

13.2 

2.5 

10 

33 

1,188.666 

10.  Hammering  

15 

8? 

? 

480,000 

EXPLANATION.  —  R,  resistance;  F,  effective  velocity  =  distance 
through  which  R  is  overcome  -*-  total  time  occupied,  including  the  time 
of  moving  unloaded,  if  any;  T",  time  of  working,  in  seconds  per  day; 
T"  -*•  3600,  same  time,  in  hours  per  day;  RV,  effective  power,  in  foot- 
pounds per  second;  RVT,  daily  work. 


ANIMAL  POWER. 


533 


Performance  of  a  Man  in  Transporting  Loads  Horizontally. 
(Rankine.) 


T" 

LV, 

LVT, 

Kind  of  Exertion. 

L, 
Ibs. 

y, 

ft.-sec. 

3600 
(hours 
per 

Ibs. 
con- 
veyed 

Ibs.  con- 
veyed 
1  foot. 

day). 

1  foot. 

11.  Walking     unloaded,     trans- 

porting his  own  weight.  .  . 
12.   Wheeling  load  L  in  2-whld. 

140 

5 

10 

700 

25,200,000 

barrow,  return  unloaded    . 

224 

12/3 

10 

373 

13,428,000 

13.  Ditto  in  1-wh.  barrow,  ditto.  . 

132 

12/3 

10 

220 

7  920,000 

14.   Traveling  with  burden.  ...... 

90 

21/2 

7 

225 

5.670,000 

15.  Carrying  burden,   returning 
unloaded  

140 

12/3 

6 

233 

5,032,800 

!252 

0 

0 

16.  Carrying  burden,  for  30  sec- 

126 

11.7 

1474.2 

y 

0 

23.1 

0 

EXPLANATION.  —  L,  load;  V,  effective  velocity,  computed  as  before; 
T",  time  of  working,  in  seconds  per  day;  T"  •*-  3600,  same  time  in  hours 
per  day;  LV,  transport  per  second,  in  Ibs.  conveyed  one  foot;  LVT, 
daily  transport. 

In  the  first  line  only  of  each  of  the  two  tables  above  is  the  weight  of 
the  man  taken  into  account  in  computing  the  work  done. 

Clark  says  that  the  average  net 
daily  work  of  an  ordinary  laborer 
at  a  pump,  a  winch,  or  a  crane  may 
be  taken  at  3300  foot-pounds  per 
minute,  or  one-tenth  of  a  horse- 
power, for  8  hours  a  day;  but  for 
shorter  periods  from  four  to  five 
times  this  rate  may  be  exerted. 

Mr.  Glynn  says  that  a  man  may 
exert  a  force  of  25  Ibs.  at  the 
handle  of  a  crane  for  short  periods; 
but  that  for  continuous  work  a 
force  of  15  Ibs.  is  all  that  should 
be  assumed,  moving  through  220 
feet  per  minute. 

Man-wheel. — Fig.  108  is  a  sketch 
of  a  very  efficient  man-power  hoist- 
ing-machine which  the  author  saw 


FIG.  108. 


in    Berne,    Switzerland,    in    ^o^. 

The  face  of  the  wheel  was  wide 
enough  for  three  men  to  walk  abreast,  so  that  nine  men  could  work  in  it 
at  one  time. 


Work  of  a  Horse  against  a  Known  Resistance.     (Rankine.) 


Kind  of  Exertion. 

R. 

V. 

T" 

3600 

RV. 

RVT. 

1.  Cantering  and  trotting,  draw- 
ing a  light  railway  carriage 
(thoroughbred) 

!min.   221/2 
mean  301/2 
max  50 

j  142/3 

4 

4471/2 

6,444,000 

2.  H^rse  drawing  cart  or  boat, 
walking  (draught-horse)  .  .  . 

120 

3.6 

8 

432 

12,441,600 

3.  Horse  _  drawing  a  gin  or  mill, 
walking  

100 

3.0 

8 

300 

8,640,000 

4.  Ditto   trotting  

66 

6.5 

41/9 

429 

6,950,000 

534 


MECHANICS. 


EXPLANATION.  —  R,  resistance,  in  Ibs.;  V,  velocity,  in  feet  per  second; 
T"  -f-  3600,  hours  work  per  day;  RV,  work  per  second;  RVT9  work  per 
day. 

The  average  power  of  a  draught-horse,  as  given  in  line  2  of  the  above 
table,  being  432  foot-pounds  per  second,  is  432/550  =  0.785  of  the  con- 
ventional value  assigned  by  Watt  to  the  ordinary  unit  of  the  rate  of 
work  of  prime  movers.  It  is  the  mean  of  several  results  of  experiments, 
and  may  be  considered  the  average  of  ordinary  performance  under  favor- 
able circumstances. 


Performance  of  a  Horse  in  Transporting  Loads  Horizontally. 

(Rankine.) 


Kind  of  Exertion. 

L. 

V. 

T. 

LV. 

LVT. 

5.  Walking  with  cart,  always 
loaded 

1500 

3  6 

10 

5400 

194  400  000 

6.  Trotting  ditto   .  . 

750 

7  2 

41/2 

5400 

87  480  000 

7.  Walking  with    cart,    going 
loaded,  returning  empty; 
V,  mean  velocity  

1500 

2  0 

10 

3000 

108  000  000 

8.  Carrying  burden,  walking.  . 
9.  Ditto  trotting  .. 

270 
180 

3.6 

7  2 

10 
7 

972 
1296 

34,992,000 
32  659  200 

EXPLANATION.  —  L,  load  in  Ibs. ;  F,  velocity  in  feet  per  second ;  T,  work- 
ing hours  per  day;  LV,  transport  per  second;  LVT,  transport  per  day. 

This  table  has  reference  to  conveyance  on  cpmmon  roads  only,  and 
those  evidently  in  bad  order  as  respects  the  resistance  to  traction  upon 
them. 

Horse-Gin.  —  In  this  machine  a  horse  works  less  advantageously 
than  in  drawing  a  carriage  along  a  straight  track.  In  order  that  the  best 
possible  results  may  be  realized  with  a  horse-gin,  the  diameter  of  the  cir- 
cular track  in  which  the  horse  walks  should  not  be  less  than  about  forty 
feet. 

Oxen,  Mules,  Asses.  —  Authorities  differ  considerably  as  to  the  power 
of  these  animals.  The  following  may  be  taken  as  an  approximative  com- 
parison between  them  and  draught-horses  (Rankine): 

Ox.  —  Load,  the  same  as  that  of  average  draught-horse;  best  velocity 
and  work,  two-thirds  of  horse. 

Mule.  —  Load,  one-half  of  that  of  average  draught-horse;  best  velocity, 
the  same  as  horse;  work,  one-half. 

Ass.  —  Load,  one-quarter  that  of  average  draught-horse;  best  velocity, 
the  same;  work,  one-quarter. 

Reduction  of  Draught  of  Horses  by  Increase  of  Grade  of  Roads. 
(Engineering  Record,  Prize  Essays  on  Roads,  1892.)  —  Experiments  on 
English  roads  by  GayfRer  &  Parnell: 

Calling  load  that  can  be  drawn  on  a  level  100: 

On  a  rise  of 1  in  100. 1  in  50.  1  in  40. 1  in 30. 1  in  26. 1  in  20. 1  in  10. 

A  horse  can  draw  only      90  81  72         64         54          40         25 

The  Resistance  of  Carriages  on  Roads  is  (according  to  Gen.  Morin) 
given  approximately  by  the  following  empirical  formula: 

R  =  I£  [a  +  b  (u  -  3.28)]. 

In  this  formula  R  =  total  resistance;  r  =  radius  of  wheel  in  inches; 
W  =  gross  load;  u  =  velocity  in  feet  per  second;  while  a  and  b  are 
constants,  whose  values  are:  For  good  broken-stone  road,  a  =  0.4to0.55, 
b  =  0.024  to  0.026:  for  paved  roads,  a  =  0.27,  b  =  0.0684. 

Rankine  states  that  on  gravel  the  resistance  is  about  double,  and  on 
sand  five  times,  the  resistance  on  good  broken-stone  roads. 


Ow 


ELEMENTS   OF  MACHINES.  535 


ELEMENTS   OP  MACHINES. 

The  object  of  a  machine  is  usually  to  transform  the  work  or  mechanical 
energy  exerted  at  the  point  where  the  machine  receives  its  motion  into 
work  at  the  point  where  the  final  resistance  A  r  n 

is  overcome.     The  specific  result  may  be  to        v  ;f ? 

change  the  character  or  direction  of  mo- 
tion, as  from  circular  to  rectilinear,  or  vice 
versa,  to  change  the  velocity,  or  to  overcome 
a  great  resistance  by  the  application  of  a 
moderate  force.  In  all  cases  the  total  energy  w  no 

exerted  equals  the  total  work  done,  the  latter  *IG'  •LUJ* 

including  the  overcoming  of  all  the  frictional 
resistances  of  the  machine  as  well  as  the  use- 
ful work  performed.     No  increase  of  power 
c"an  be  obtained  from  any  machine,  since  this 
is  impossible  according  to  the  law  of  conser- 
vation of  energy.  In  africtionless  machine  the       "^ 
product  of  the  force  exerted  at  the  driving- 
point  into  the  velocity  of  the  driving-point.  I 
cr  the  distance  it  moves  in  a  given  interval                                Ow 
of  time,  equals  the  product  of  the  resistance 
into  the  distance' through  which  the  resist-                    w       110 
ance  is  overcome  in  the  same  time.                                   ri(j*  11Ut 

The  most  simple  machines,  or  elementary 
machines,  are  reducible  to  three  classes,  viz., 
the  Lever,  the  C9rd,  and  the  Inclined  Plane. 

The  first  class  includes  every  machine  con- 
sisting of  a  solid  body  capable  of  revolving 
on  an  axis,  as  the  Wheel  and  Axle. 

The  second  class  includes  every  machine  in 
which  force  is  transmitted  by  means  of  flexi- 
ble threads,  ropes,  etc.,  as  the  Pulley. 

The  third  class  includes  every  machine  iri  pIQ  m 

\yhich  a  hard  surface  inclined  to  the  direc- 
tion of  ^motion  is  introduced,  as  the  Wedge  and  the  Screw. 

A  Lever  is  an  inflexible  rod  capable  of  motion  about  a  fixed  point, 
called  a  fulcrum.  The  rod  may  be  straight  or  bent  at  any  angle,  or 
curved. 

It  is  generally  regarded,  at  first,  as  without  weight,  but  its  weight  may 
be  considered  as  another  force  applied  in  a  vertical  direction  at  its  center 
of  gravity. 

The  arms  of  a  lever  are  the  portions  of  it  intercepted  between  the  force. 
P,  and  fulcrum,  C,  and  between  the  weight  or  load,  W,  and  fulcrum. 

Levers  are  divided  into  three  kinds  or  orders,  according  to  the  relative 
positions  of  the  applied  force,  load,  and  fulcrum. 

In  a  lever  of  the  first  order,  the  fulcrum  lies  between  the  points  at  which 
the  force  and  load  act.  "(Fig.  109.) 

In  a  lever  of  the  second  order,  the  load  acts  at  a  point  between  the 
fulcrum  and  the  point  of  action  of  the  force.  (Fig.  110.) 

In  a  lever  of  the  third  order,  the  point  of  action  of  the  force  is  between 
that  of  the  load  and  the  fulcrum.  (Fig.  111.) 

In  all  cases  of  levers  the  relation  between  the  force  exerted  or-  the  pull, 
P,  and  the  load  lifted,  or  resistance  overcome,  W,  is  expressed  by  the 
equation  PX  AC  =  W  X  BC,  in  which  AC  is  the  lever-arm  of  P,  and 
BC  is  the  lever-arm  of  W,  or  moment  of  the  force  =  the  moment  of  the 
resistance.  (See  Moment.) 

In  cases  in  which  the  direction  of  the  force  (or  of  the~resistance)  is  not 
at  right  angles  to  the  arm  of  the  lever  on  which  it  acts,  the  "lever-arm" 
is  the  length  of  a  perpendicular  from  the -fulcrum  to  the  line  of  direction 
of  the  force  (or  of  the  resistance).  W  :  P  :  :  AC  :  BC,  or,  the  ratio  of 
the  resistance  to  the  applied  force  is  the  inverse  ratio  of  their  lever-arms. 
Also,  if  y^is  the  velocity  of  TF,  and  Vp  is  the  velocity  of  P,  W  :  P  :  :  Vp: 
Vw,  and  P  X  Vp  =  WX  Vw. 

If  8p  is  the  distance  through  which  the  applied  force  acts,  and  Sw  is 
the  distance  the  load  is  lifted  or  through  which  the  resistance  is  over- 
come, W  ;  P  ; ;  Sp  :  Sw  :  W  X  Sw  =  P  X  Sp,  or  the  load  into  the  dis- 


536 


MECHANICS. 


tance  it  is  lifted  equals  the  force  into  the  distance  through  which  it  is 
exerted. 

These  equations  are  general  for  all  classes  of  machines  as  well  as  for 
levers,  it  being  understood  that  friction,  which  in  actual  machines  in- 
creases the  resistance,  is  not  at  present  considered. 

The  Bent  Lever.  —  In  the  bent  lever  (see  Fig.  102,  p.  514),  the  lever- 
arm  of  the  weight  m  is  cf  instead  of  bf.  The  lever  is  in  equilibrium  when 
n  X  af  =  m  X  cf,  but  it  is  to  be  observed  that  the  action  of  a  bent  lever 
may  be  very  different  from  that  of  a  straight  lever.  In  the  latter,  so 
long  as  the  i'orce  and  the  resistance  act  in  lines  parallel  to  each  other,  the 
ratio  of  the  lever-arms  remains  constant,  although  the  lever  itself  changes 
its  inclination  with  the  horizontal.  In  the  bent  lever,  however,  this 
ratio  changes:  thus,  in  the  cut,  if  the  arm  bf  is  depressed  to  a  horizontal 
direction,  the  distance  cf  lengthens  while  the  horizontal  projection  of 
af  shortens,  the  latter  becoming  zero  when  the  direction  of  af  becomes 
vertical.  As  the  arm  af  approaches  the  vertical,  the  weight  n  which 
may  be  lifted  with  a  given  force  s  is  very  great,  but  the  distance  through 
which  it  may  be  lifted  is  very  small.  In  all  cases  the  ratio  of  the  weight 
m  to  the  weight  n  is  the  inverse  ratio  of  the  horizontal  projection  of  their 
respective  lever-arms. 

The  Moving  Strut  (Fig.  112)  is  similar  to  the  bent  lever,  except  that 
one  of  the  arms  is  missing,  and  that  the  force  and  the  resistance  to  be 
overcome  act  at  the  same  end  of  the 
single  arm.  The  resistance  in  the 
case  shown  in  the  cut  is  not  the  load 
W,  but  its  resistance  to  being 
moved,  R,  which  may  be  simply 
that  due  to  its  friction  on  the  hori- 
zontal plane,  or  some  other  oppos- 
ing force.  When  the  angle  between 
the  strut  and  the  horizontal  plane 
changes,  the  ratio  of  the  resistance 
to  the  applied  force  changes.  When 
the  angle  becomes  very  small,  a 
moderate  force  will  overcome  a 
very  great  resistance,  which  tends  FIG.  112. 

to  become  infinite  as  the  angle  ap- 
proaches zero.     If  a  =the  angle,  P  X  cos  a  =  R  X  sin  a.     If  a  =  5  degrees, 
cos  a  =  0.99619,  sin  a  =  0.08716,  R  =  11.44  P. 

The  stone-crusher  (Fig.  113)  shows  a  practical  example  of  the  use  of 
two  moving  struts. 

The  Toggle-joint  is  an  elbow  or  knee-joint  consisting  of  two  bars  so 
connected  that  they;  may  be  brought  into  a  straight  line  and  made  to 
produce  great  endwise  pressure  when  a  force  is  applied  to  bring  them 
into  this  position.  It  is  a  case  of  two  moving  struts  placed  end  to  end, 


FIG.  113. 


FIG.  114. 


the  moving  force  being  applied  at  their  point  of  junction,  in  a  direction 
at  right  angles  to  the  direction  of  the  resistance,  the  other  end  of  one  of 
the  struts  resting  against  a  fixed  abutment,  and  that  of  the  other  against 
the  body  to  be  moved.  If  a —  the  angle  each  strut  makes  with  the  straight 
line  joining  the  points  about  which  their  outer  ends  rotate,  the  rati9  of 
the  resistance  to  the  applied  force  is  R  :  P  :  :  cos  a  :  2  sin  q;  2  R  sin  a 
=  P  cos  a.  The  ratio  varies  when  the  angle  varies,  becoming  infinite 
when  the  angle  becomes  zero. 


ELEMENTS    OF   MACHINES. 


537 


The  toggle-joint  is  used  where  great  resistances  are  to  be  overcome 
through  very  small  distances,  as  in  stone-crushers  (Fig.  114). 

The  Inclined  Plane,  as  a  mechanical  element,  is  supposed  perfectly 
hard  and  smooth,  unless  friction  bs  considered.  It  assists  in  sustaining 
a  heavy  body  by  its  reaction.  This  reaction,  however,  being  normal  to 
the  plane,  cannot  entirely  counteract  the  weight  of  the  body,  which  acts 
vertically  downward.  Some  other  force  must 
therefore  be  made  to  act  upon  the  body,  in  order 
that  it  may  be  sustained. 

If  the  sustaining  force  act  parallel  to  the  plane 
(Fig.  115),  the  force  is  to  the  weight  as  the  height 
of  the  plane  is  to  its  length,  measured  on  the 
incline. 

If  the  force  act  parallel  to  the  base  of  the 
plane,  the  force  is  to  the  weight  as  the  height  is 
to  the  base. 

If  the  force  act  at  any  other  angle,  let  i  —  the 
angle  of  the  plane  with. the  horizon,  and  e=  the 


FIG.  115. 


le  of  the  direction  of  the  applied  force  with  the  angle  of  the  plane. 
P  :  W  :  :  sin  i  :  cos  e;  P  X  cos  e  =  W  sin  i. 

Problems  of  the  inclined  plane  may  be  solved  by  the  parallelogram  of 
forces  thus: 

Let  the  weight  W  be  kept  at  rest  on  the  incline  by  the  force  P,  acting 
in  the  line  bP',  parallel  to  the  plane.  Draw  the  vertical  line  ba  to  repre- 
sent the  weight;  also  bb'  perpendicular  to  the  plane,  and  complete  the 
parallelogram  b'c.  Then  the  vertical  weight  bais  the  resultant  of  bb',  the 
measure  of  support  given  by  the  plane  to  the  weight,  and  be,  the  force  of 
gravity  tending  to  draw  the  weight  down  the  plane.  The  force  required 
to  maintain  the  weight  in  equilibrium  is  represented  by  this  force  be. 
Thus  the  force  and  the  weight  are  in  the  ratio  of  be  to  ba.  Since  the 
triangle  of  forces  abc  is  similar  to  the  triangle  of  the  incline  ABC,  the 
latter  may  be  substituted  for  the  former  in  determining  the  relative 
magnitude  of  the  forces,  and 

P  :  W  :  :  be  :  ab  :  :  BC  :  AB. 

The  Wedge  is  a  pair  of  inclined  planes  united  by  their  bases.  In  the 
application  of  pressure  to  the  head  or  butt  end  of  the  wedge,  to  cause  it  to 
penetrate  a  resisting  body,  the  applied  force  is  to  the  resistance  as  the 
thickness  of  the  wedge  is  to  its  length.  Let  t  be  the  thickness,  I  the  length, 
W  the  resistance,  and  P  the  applied  force  or  pressure  on  the  head  of  the 

wt  Pf 

wedge.     Then,  friction  neglected,  P:  W  :  :  t  :  I;  P  =   -^;  W  =  =^- 

I  t 

The  Screw  is  an  inclined  plane  wrapped  around  a  cylinder  in  such  a 
way  that  the  height  of  the  plane  is  parallel  to  the  axis  of  the  cylinder.  .  If 
the  screw  is  formed  upon  the  internal  surface  of  a  hollow  cylinder,  it  is 
usually  called  a  nut.  When  force  is  applied  to  raise  a  weight  or  overcome 
a  resistance  by  means  of  a  screw  and  nut,  either  the  screw  or  the  nut  may 
be  fixed,  the  other  being  movable.  The  force  is  generally  applied  at  the 
end  of  a  wrench  or  lever-arm,  or  at  the  circumference  of  a  wheel.  If  r  =» 
radius  of  the  wheel  or  lever-arm,  and  p  —  pitch 
of  the  screw,  or  distance  between  threads,  that 
is,  the  height  of  the  inclined  plane  for  one  revo- 
lution of  the  screw,  P  =  the  applied  force,  and 
W  =  the  resistance  overcome,  then,  neglecting 
resistance  due  to  friction,  2  irr  X  P  =  Wp;  W 
=  6.283  Pr  +  p.  The  ratio  of  P  to  W  is  thus 
independent  of  the  diameter  of  the  screw.  In 
actual  screws,  much  of 
A,  -----  the  power  transmitted  is 

/  x  lost  through  friction. 

The  Cam  is  a  revolv- 
ing inclined  plane.  It 
may  be  either  an  in- 
clined plane  wrapped 
around  a  cylinder  in  such 
FIG.  116.  a  way  that  the  height  of 

the  plane  is  radial  to  the 


117 


cylinder,  such  as  the  ordinary  lifting-cam,  used  in  stamp-mills  (Fig.  11G), 


538 


MECHANICS. 


or  it  may  be  an  inclined  plane  curved  edgewise,  and  rotating  in  a  plane 
parallel  to  its  base  (Fig.  117).  The  relation  of  the  weight  to  the  applied 
force  is  calculated  in  the  same  manner  as  in  the  case  of  the  screw. 

Efficiency  of  a  Screw.  —  Let  a  =  angle  of  the  thread,  that  is,  the 
angle  whose  tangent  is  the  pitch  of  the  screw  divided  by  the  circum- 
ference of  a  circle  whose  diameter  is  the  mean  of  the  diameters  at  the 
top  and  bottom  of  the  thread.     Then  for  a  square  thread 
Efficiency  =  (1  -  /tan  a)  -f-  (1  -f/cotan  a), 

in  which/  is  the  coefficient  of  friction.  (For  demonstration,  see  Cotterill 
and  Slade,  Applied  Mechanics.)  Since  cotan  =  1  -;-  tan,  we  may  sub- 
stitute for  cotan  a  the  reciprocal  of  the  tangent,  or  if  p  ==  pitch,  and 
c  =  mean  circumference  of  the  screw, 

Efficiency  =  (1  -fp/c)  -r-  (1  +fc/p). 

EXAMPLE.  —  Efficiency  of  square-threaded  screws  of  1/2  inch  pitch. 
Diameter  at  bottom  of  thread,  in.    .    .  1  2  3  4 

Diameter  at  top  of  thread,  in 11/2         21/2      3 1/2        41/2 

Mean  circumference  of  thread,  in..    .    .       3.927     7.06910.21     13.35 

Cotangent  a  =  c  *•  p =7.85414.14     20.42     26.70 

Tangenta  =  p-^c =0.1273  .0707     .0490      .0375 

Efficiency  if/ =  0.10 =55.3%  41.2%  32.7%   27.2% 

Efficiency  if /  =  0.15 =45%  •  31.7%    24.4%    19.9% 

The  efficiency  thus  increases  with  the  steepness  of  the  pitch. 

The  above  formulae  and  examples  are  for  square-threaded  screws,  and 
consider  the  friction  of  the  screw-thread  only,  and  not  the  friction  of  the 
collar  or  step  by  which  end  thrust  is  resisted,  and  which  further  reduces 
the  efficiency.  The  efficiency  is  also  further  reduced  by  giving  an  inclina- 
tion to  the  side  of  the  thread,  as  in  the  V-threaded  screw.  For  discussion 
of  this  subject,  see  paper  by  Wilfred  Lewis,  Jour.  Frank.  Inst.  1880;  also 
Trans.  A.  S.M.  E.,  vol.  xii,  784. 

Efficiency  of  Screw-bolts.  —  Mr.  Lewis  gives  the  following  approxi- 
mate formula  for  ordinary  screw-bolts  (V-threads,  with  collars):  p=  pitch 
of  screw,  d  =  outside  diameter  of  screw,  F  =  force  applied  at  circum- 
ference to  lift  a  unit  of  weight,  E  =  efficiency  of  screw.  For  an  average 
case,  in  which  the  coefficient  of  friction  may  be  assumed  at  0.15, 
F  =  (P  +  d)  ^  3d,  E  =  p  -T-  (p  +  d). 

For  bolts  of  the  dimensions  given  above,  i/2-inch  pitch,  and  outside 
diameters  11/2,  21/2,  3 1/2,  and  41/2  inches,  the  efficiencies  according  to  this 
formula  would  be,  respectively,  0.25,  0.167,  0.125,  and  0.10. 

James  McBride  (Trans.  A.  S.  M.  E.,  xii,  781)  describes  an  experiment 
with  an  ordinary  2-inch  screw-bolt,  with  a  V-thread,  41/2  threads  per  inch, 
raising  a  weight  of  7500  pounds,  the  force  being  applied  by  turning  the 
nut.  Of  the  power  applied  89.8  per  cent  was  absorbed  by  friction  of  the 
nut  on  its  supporting  washer  and  of  the  threads  of  the  bolt  in  the  nut. 
The  nut  was  not  faced,  and  had  the  flat  side  to  the  washer. 

Professor  Ball  in  his  "Experimental  Mechanics"  says:  "Experiments 
showed  in  two  cases  respectively  about  2/3  and  3/4  of  the  power  was  lost. " 
,  Weisbach  says:  "The  efficiency  is  from  19  per  cent  to  30  per  cent." 


JW 


B.          a 

FiQ.  U8, 


ELEMENTS   OF  MACHINES. 


539 


Pulleys  or  Blocks. — P  —  force  applied,  or  pull;  W '  =  load  lifted, 
or  resistance.  In  the  simple  pulley  A  (Fig.  118)  the  point  P  on  the 
pulling  rope  descends  the  same  amount  that  the"  load  is  lifted,  therefore 
P  =  W.  In  B  and  C  the  point  P  moves  twice  as  far  as  the  load  is  lifted, 
therefore  W  =  2P.  In  B  and  C  there  is  one  movable  block,  and  two 
plies  of  the  rope  engage  with  it.  In  D  there  are  three  sheaves  in  the 
movable  block,  each  with  two  plies  engaged,  or  six  in  all.  Six  plies  of 
the  rope  are  therefore  shortened  by  the  same  amount  that  the  load  is 
lifted  and  the  point  P  moves  six  times  as  far  as  the  load,  consequently 
W  =  6  P.  In  general,  the  ratio  of  W  to  P  is  equal  to  the  number  of  plies 
of  the  rope  that  are  shortened,  and  also  is  equal  to  the  number  of  plies  that 
engage  the  lower  block.  If  the  lower  block  has  2  sheaves  and  the  upper 
3,  the  end  of  the  rope  is  fastened  to  a  hook  in  the  top  of  the  lower  block, 
and  then  there  are  5  plies  shortened  instead  of  6,  and  W  =  5  P.  If  V  = 
velocity  of  W,  and  v  =  velocity  of  P,  then  in  all  cases  V  W  —  vP,  whatever 
the  number  of  sheaves  or  their  arrangement.  If  the  hauling  rope,  at  the 
pulling  end,  passes  first  around  a  sheave  in  the  upper  or  stationary  block, 
it  makes  no  difference  in  what  direction  the  rope  is  led 
from  this  block  to  the  point  at  which  the  pull  on  the 
rope  is  applied ;  but  if  it  first  passes  around  the  movable 
block,  it  is  necessary  that  the  pull  be  exerted  in  a  direc- 
tion parallel  to  the  line  of  action  of  the  resistance,  or  a 
line  joining  the. centers  of  the  two  blocks,  in  order  to 
obtain  the  maximum  effect.  If  the  rope  pulls  on 'the 
lower  block  at  an  angle,  the  block  will  be  pulled  out  of 
the  line  drawn  between  the  load  and  the  upper  block, 
and  the  effective  pull  will  be  less  than  the  actual  pull 
on  the  rope  in  the  ratio  of  the  cosine  of  the  angle  the 
pulling  rope  makes  with  the  vertical,  or  line  of  action  of 
the  resistance,  to  unity. 

Differential  Pulley.  (Fig.  119. ) — Two  pulleys,  B 
and  C,  of  different  radii,  rotate  as  one  piece  about  a 
fixed  axis,  A.  An  endless  chain,  BDECLKH,  passes 
over  both  pulleys.  The  rims  of  the  pulleys  are  shaped 
so  as  to  hold  the  chain  and  prevent  it  from  slipping. 
One  of  the  bights  or  loops  in  which  the  chain  hangs,  DE. 
passes  under  and  supports  the  running  block  F.  The 
other  loop  or  bight,  HKL,  hangs  freely,  and  is  called  the 
hauling  part.  It  is  evident  that  the  velocity  of  the  haul- 
ing part  is  equal  to  that  of  the  pitch-circle  of  the  pulley  B. 

In  order  that  the  velocity-ratio  may  be  exactly 
uniform,  the  radius  of  the  sheave  F  should  be  an  exact 
mean  between  the  radii  of  B  and  C. 

Consider  that  the  point  B  of  the  cord  BD  moves  through  an  arc  whose 
length  =  AS,  during  the  same  time  the  point  C  or  the  cord  CE  will 
move  downward  a  distance  =  AC.  The  length  of  the  bight  or  loop 
BDEC  will  be  shortened  by  AB  -  AC,  which  will  cause  the  pulley  F  to 
be  raised  half  of  this  amount.  If  P  =  the  pulling  force  on  the  cord  HK, 
and  W  the  weight  lifted  at  F,  then  P  X  AB  =  W  X  1/2  (AB  -  AC}. 

To  calculate  the  length  of  chain  required  for  a  differential  pulley,  take 
the  following  sum:  Half  the  circumference  of  A  +  half  the  circumference 
of  B  +  half  the  circumference  of  F  +  twice  the  greatest  distance  of  F 
from  A  +  the  least,  length  of  loop  HKL.  The  last  quantity  is  fixed 
according  to  convenience. 

A  Wheel  and  Axle,  or  Windlass,  resembles  two  pulleys  on  one  axis, 
having  different  diameters.  If  a  weight  be  lifted  by  means  of  a  rope 
wound  over  the  axle,  the  force  being  applied  at  the  rim  of  the  wheel, 
the  action  is  like  that  of  a  lever  of  which  the  shorter  arm  is  equal  to  the 
radius  of  the  axle  plus  half  the  thickness  of  the  rope,  and  the  longer 
arm  is  equal  to  the  radius  of  the  wheel.  A  wheel  and  axle  is  therefore 
sometimes  classed  as  a  perpetual  lever.  If  P  =  the  applied  force,  D  = 
diameter  of  the  wheel,  W  =  the  weight  lifted,  and  d  the  diameter  of  the 
axle  +  the  diameter  of  the  rope,  PD  =  Wd. 

Toothed-wheel  Gearing  is  a  combination  of  two  or  more  wheels  and 
axles  (Fig.  120 ).  If  a  series  of  wheels  and  pinions  gear  into  each  other, 
as  in  the  cut,  friction  neglected,  the  weight  lifted,  or  resistance  over- 
come, is  to  the  force  applied  inversely  as  the  distances  through  which 


FIG.  119. 


540 


MECHANICS. 


they  act  in  a  given  time.  If  R,  Ri,  R2  be  the  radii  of  the  successive  wheels, 
measured  to  the  pitch-line  of  the  teeth,  and  r,  rt,  r2  the  radii  of  the  cor- 
responding pinions,  P  the  applied  force,  and  W  the  weight  lifted,  P  X 
R  X  R\  X  #2  ==  W  X  r  X  n  X  n,  or  the  applied  force  is  to  the  weight 
as  the  product  of  the  radii  of  the  pinions  is  to  the  product  of  the  radii  of 
the  wheels;  or,  as  the  product  of  the  numbers  expressing  the  teeth  in 
each  pinion  is  to  the  product  of  the  numbers  expressing  the  teeth  in  each 
wheel. 


FIG\  120. 


FIG.  121. 


Endless  Screw,  or  Worm-gear.  (Fig.  121.)  —  This  gear  is  com- 
monly used  to  convert  motion  at  high  speed  into  motion  at  very  slow 
speed.  When  the  handle  P  describes  a  complete  circumference,  the  pitch- 
line  of  the  cog-wheel  moves  through  a  distance  equal  to  the  pitch  of  the 
screw,  and  the  weight  W  is  lifted  a  distance  equal  to  the  pitch  of  the  screw 
multiplied  by  the  ratio  of  the  diameter  of  the  axle  to  the  diameter  of  the 
pitch-circle  of  the  wheel.  The  ratio  of  the  applied  force  to  the  weight 
lifted  is  inversely  as  their  velocities,  friction  not  being  considered;  but  the 
friction  in  the  worm-gear  is  usually  very  great,  amounting  sometimes  to 
three  or  four  times  the  useful  work  done. 

If  v  «=  the  distance  through  which  the  force  P  acts  in  a  given  time,  say 
1  second,  and  V  =  distance  the  weight  W  is  lifted  in  the  same  time,  r=» 
radius  of  the  crank  or  wheel  through  which  P  acts,  t  =  pitch  of  the  screw, 
and  also  of  the  teeth  on  the  cog-wheel,  d  =  diameter  of  the  axle,  and 

D  =  diameter  of  the  pitch-line  of  the  cog-wheel,]  v  =  -^—. — -  ^  X  V; 
V  =  v  X  td  --  6.283  rD.    Pv  =  WV  +  friction. 

The  Differential  Windlass  (Fig.  122)  is  identical  in  principle  with  the 
differential  pulley,  the  difference  in  construction  being  that  in  the  dif- 
ferential windlass  the  running  block  hangs  in  the 
bight  of  a  rope  whose  two  parts  are  wound  round, 
and  have  their  ends  respectively  made  fast  to  two 
barrels  of  different  radii,  which  rotate  as  one  piece 
about  the  axis  A.  The  differential  windlass  is  • 
little  used  in  practice,  because  of  the  great  length 
of  rope  which  it  requires. 

The  Differential  Screw  (Fig.  123)  is  a  com- 
pound .screw  of  different  pitches,  in  which  the 
threads  wind  the  same  way.  Ni  and  Nz  are  the 

two     nuts;    SiSi, 

the      longer-pitched 

thread;      8282.     the 

shorter-pit  ched 

thread:  in  the  figure 

both   these    threads 

are  left-handed.  At 
each  turn  of  the  screw  the  nut  N2  advances  relatively  to  Ni  through-  a 
distance  equal  to  the  difference  of  the  pitches.  The  use  of  the  differential 
screw  is  to  combine  the  slowness  of  advance  due  to  a  fine  pitch  with 
the  .strength  of  thread  which  can  be  obtained  by  means  of  a  coarse 
pitch  only. 


FIG.  123. 


FIG.  122. 


STRESSES  IN  FRAMED  STRUCTURES. 


541 


Efficiency  of  a  Differential  Screw.  —  A  correspondent  of  tile 
American  Machinist  describes  an  experiment  with  a  differential  screw- 
punch,  consisting  of  an  outer  screw  2  inch  diameter,  3  threads  per 
inch,  and  an  inner  screw  13/8  inch  diameter,  3 1/2  threads  per  inch.  The 
pitch  of  the  outer  screw  being  1/3  inch  and  that  of  the  inner  screw  2/7  inch 
the  punch  would  advance  in  one  revolution  1/3  —  2/7  =  V2t  inch. 
Experiments  were  made  to  determine  the  force  required  to  punch  an 
ii/16-inch  hole  in  iron  1/4  inch  thick,  the  force  being  applied  at  the  end 
of  a  lever-arm  of  473/4  inch.  The  leverage  would  be  473/4x  2*  X  21  =• 
6300.  The  mean  force  applied  at  the  end  of  the  lever  was  95  pounds, 
and  the  force  at  the  punch,  if  there  was  no  friction,  would  be  6300  X 
95  =  598,500  pounds.  The  force  required  to  punch  the  iron,  assuming 
a  shearing  resistance  of  50,000  pounds  per  square  inch,  would  be  50,000  X 
n/16  XT  X  1/4  =  27,000  pounds,  and  the  efficiency  of  the  punch  would 
be  27,000  •*•  598,500  =  only  4.5  per  cent.  With  the  larger  screw  only 
used  as  a  punch  the  mean  force  at  the  end  of  the  lever  was  only  82  pounds. 
The  leverage  in  this  case  was  473/4  x  2ir  X  3  =  900,  the  total  force 
referred  to  the  punch,  including  friction,  900  X  82  =  73,800,  and  the 
efficiency  27,000  •*-  73,800  =  36.7  per  cent.  The  screws  were  of  tool- 
steel,  well  fitted,  and  lubricated  with  lard-oil  and  plumbago. 

STRESSES    IN   FRAMED    STRUCTURES. 

Framed  structures  in  general  consist  of  one  or  more  triangles,  for  the 
reason  that  the  triangle  is  the  one  polygonal  form  whose  shape  cannot  be 
changed  without  distorting  one  of  its  sides.  Problems  in  stresses  of 
simple  framed  structures  may  generally  be  solved  either  by  the  applica- 
tion of  the  triangle,  parallellogram,  or  polygon  of  forces,  by  the  principle 
of  the  lever,  or  by  the  method  of  moments.  We  shall  give  a  few  ex- 
amples, referring  the  student  to  the  works  of  Burr,  Dubois,  Johnson,  and 
others  for  more  elaborate  treatment  of  the  subject. 

1.  A  Simple  Crane.  (Figs.  124  and  125.}  —  A  is  a  fixed  mast,  B  a 
brace  or  boom,  T  a  tie,  and  P  the  load.  Required  the  strains  in  B  and  T. 
The  weight  P,  considered  as  acting  at  the  end  of  the  boom,  is  held  in 
equilibrium  by  three  forces:  first,  gravity  acting  downwards;  second,  the 
tension  in  T;  and  third,  the  thrust  of  B.  Let  the  length  of  the  line  p 
represent  the  magnitude  of  the  downward  force  exerted  by  the  load,  and 
draw  a  parallelogram  with  sides  bt  parallel,  respectively,  to  B  and  T, 
such  that  p  is  the  diagonal  of  the  parallelogram.  Then  6  and  t  are  the 
components  drawn  to  the  same  scale  as  p,  p  being  the  resultant.  Then 
if  the  length  p  represents  the  load,  t  is  the  tension  in  the  tie,  and  b  is  the 
compression  in  the  brace. 

Or,  more  simply,  T,  B,  and  that  portion  of  the  mast  included  between 
them  or  A'  may  represent  a  triangle  of  forces,  and  the  forces  are  propor- 
tional to  the  length  of  the  sides  of  the  triangle;  that  is,  if  the  height  of  the 


\ 

1 

a> 

t 

\ 
\ 

B 

— 

A 

& 

FIG.  124. 

FIG.  125. 


FIG.  126. 


triangle  A'  =  the  load,  then  B  —  the  compression  in  the  brace,  and  T  = 
the  tension  in  the  tie;  or  if  P  —  the  load  in  pounds,  the  tension  ia  T  = 

T  R 

P  X  -£*  and  the  compression  in  B  =  P  X  -p*      Als°t  it  a  =  the  angle 

the  inclined  member  makes  with  the  mast,  the  other  member  being 


542 


MECHANICS. 


horizontal,  and  the  triangle  being  right-angled,  then  the  length  of  the 
inclined  member  -=  height  of  the  triangle  X  secant  a,  and  the  strain  in  the 
inclined  member  =  P  secant  a.  Also,  the  strain  in  the  horizontal 
member  =  P  tan.  a. 

The  solution  by  the  triangle  or  parallelogram  of  forces,  and  the  equa- 
tions Tension  in  T=P  X  T/A',  and  Compression  in  B  =  PX  B/A',  hold  true 
even  if  the  triangle  is  not  right-angled,  as  in  Fig.  126 ;  but  the  trigono- 
metrical relations  ab9ve  given  do  not  hold,  except  in  the  case  of  a  right- 
angled  triangle.  It  is  evident  that  as  A'  decreases,  the  strain  in  both  T 
and  B  increases,  tending  to  become  infinite  as  A'  approaches  zero.  If 
the  tie  T  is  not  attached  to  the  mast,  but  is  extended  to  the  ground,  as 
shown  in  the  dotted  line,  the  tension  in  it  remains  the  same. 

2.  A  Guyed  Crane  or  Derrick.  (Fig.  127  )  —  The  strain  in  B  is,  as 
before,  P  X  B/A',  Af  being  that  portion  of  the  vertical  included  between 
B  and  T,  wherever  T  may  be  attached  to  A.  If,  ITowever,  the  tie  T  is 
attached  to  B  beneath  its  extremity,  there  may  be  in  addition  a  bending 
strain  in  B  due  to  a  tendency  to  turn  about  the  point  of  attachment  of  T 
as  a  fulcrum. 

The  strain  in  T  may  be  calculated  by  the  principle  of  moments.  The 
moment  of  P  is  PC,  that  is,  its  weight  X  its  perpendicular  distance  from 
the  point  of  rotation  of  B  on  the  mast.  The  moment  of  the  strain  on  T 
is  the  product  of  the  strain  into  the  perpendicular  distance  from  the  line 


FIG.  127. 

of  its  direction  to  the  same  point  of  rotation  of  B,  or  Td.  The  strain  in 
T  therefore  =  PC  •*•  d.  As  d  decreases,  the  strain  on  T  increases,  tending 
to  infinity  as  d  approaches  zero.  * 

The  strain  on  the  guy-rope  is  also  calculated  by  the  method  of  moments. 
The  moment  of  the  load  about  the  bottom  of  the  mast  O  is,  as  before,  PC. 
If  the  guy  is  horizontal,  the  strain  in  it  is  F  and  its  moment  is  Ff,  and  F  = 
PC  -^  /.  If  it  is  inclined,  the  moment  is  the  strain  G  X  the  perpendicular 
distance  of  the  line  of  its  direction  from  O,  or  Gg,  and  G  =  Pc-j-g. 

The  guy-rope  having  the  least  strain  is  the  horizontal  one  F,  and  the 
strain  in  G  =  the  strain  in  F  X  the  secant  of  the  angle  between  F  and 
G.  As  G  is  made  more  nearly  vertical  g  decreases,  and  the  strain  increases, 
becoming  infinite  when  g  =  0. 

D  3.  Shear-poles  with  Guys. 

(Fig.  128.)  —  First  assume  that 
the  two  masts  act  as  one  placed 
at  BD,  and  the  two  guys  as 
one  at  AB.  Calculate  the  strain 
in  BD  and  AB  as  in  Fig.  126. 
Multiply  half  the  strain  in  BD 
(or  AB)  by  the  secant  of  half 


the  angle  the  two  masts  (or 
guys)  make  with  each  other  to 
find  the  strain  in  each  mast  (or 
guy). 

Two  Diagonal  Braces  and 
a  Tie-rod.  (Fig.  129.)  —  Sup- 
pose  the  braces  are  used  to 
sustain  a  single  load  P.  Compressive  stress  on  AD  =  1/2  PXAD 
•*•  AB\  on  CA  =  1/2  PX  CA  -T-  AB.  This  is  true  only  if  CB  and  BD 


STRESSES    IN   FRAMED    STRUCTURES. 


543 


are  of  equal  length,  in  which  case  1/2  of  P  is  supported  by  each  abutment 
C  and  D.  If  they  are  unequal  in  length  (Fig.  130),  then,  by  the  principle 
of  the  lever,  find  the  reactions  of  the  abutments  Ri  and  R2.  If  P  is  the 
load  applied  at  the  point  B  on  the  lever  CD,  the  fulcrum  being  D, 
then  Ri  X  CD  =  P  X  BD  and  R»  X  CD  =  P  X  BC;  Ri  =  P  X  BD  -f-  C'L>; 
R2  =  PXBC  +  CD. 

The  strain  on  A(7  =  Ri  X  AC  -*-  AJS,  and  on  AD  =  R2  X  AD  -*-  AB. 

The  strain  on  the  tie  =  RiX  CB  +  AB  =  RzX  BD  +  AB. 

When  CB  =  BD,  Ri  =  Rz,  and  the  strain  on  the  tie  is  equal  to 
l/2CD  ~  AB. 


FIG.  131. 


If  the  braces  support  a  uniform  load,  as  a  pair  of  rafters,  the  strains 
caused  by  such  a  load  are  equivalent  to  that  caused  by  one-half  of  the 
load  applied  at  the  center.  The  horizontal  thrust  of  the  braces  against 
each  other  at  the  apex  equals  the  tensile  strain  in  the  tie. 

King-post  Truss  or  Bridge.  (Fig.  131. )  —  If  the  load  is  distributed 
over  the  whole  length  of  the  truss,  the  effect  is  the  same  as  if  half  the 
load  were  placed  at  the  center,  the  other 
half  being  carried  by  the  abutments.  Let 
P  =  one-half-  the  load  on  the  truss,  then 
tension  in  the  vertical  tie  AB  =  P.  Com- 
pression in  each  of  the  inclined  braces 
=  V2  P  X  AD  •*•  AB.  Tension  in  the  tie 
CD  =  1/2  P  X  BD  -T-  AB.  Horizontal 
thrust  of  inclined  brace  AD  at  D  =  the 
tension  in  the  tie.  If  W  =  the  total 
load  on  one  truss  uniformly  distributed, 
I  =  its  length  and  d  =  its  depth,  then 
the  tension  on  the  horizontal  tie  =  Wl  -*•  8  d. 

Inverted  King-post  Truss.  (Fig.  132  )  —  If  P  =  a  load  applied  at  B, 
or  one-half  of  a  uniformly  distributed  load,  then  compression  on  AB  =  P 
(the  floor-beam  CD  not  being  considered 
to  have  any  resistance  to  a  slight  bend- 
ing). Tension  on  AC  or  AD  =  1/2  P 
X  AD  -*  AB.  Compression  on  CD  = 
V2  P  X  BD  +  AB. 

Queen-post  Truss.  (Fig.  133.)  — If 
uniformly  loaded,  and  the  queen-posts 
divide  the  length  into  three  equal  bays, 
the  load  may  be  considered  to  be  divided 
into  three  equal  parts,  two  parts  of 
which,  Pi  and  Pa,  are  concentrated  at  the  panel  joints  and  the  remainder 

is  equally  divided  between  the 
abutments  and  supported  by  them 
directly.  The  two  parts  Pi  and  Pz 
only  are  considered  to  affect  the 
members  of  the  truss.  Strain  in 
the  vertical  ties  BE  and  CF  each 
equals  Pi  or  Pi.  Strain  on  AB  and 
CD  each  =  Pi  X'  CD  +  CF.  Strain 
on  the  tie  AE  or  EFoT  ED  =  Pi  X 
FD  +  CF.  Thrust  on  BC  =  tension 
FIG.  133.  on  EFf 

For  stability  to  resist  heavy  unequal  loads  the  queen-post  truss 
have  diagonal  braces  from  B  to  F  ancl  from  C  to  E, 


FIG.  132. 


544 


MECHANICS. 


Inverted  Queen-post  Truss.     (Fig.  134.)  —  Compression  on  EB  and 
FC  each  =  Pi  or  P2.     Compression  on  AB  or  BC  or  CD  =  Pi  X  AB  +  EB. 

Tension  on  AE  or  FD  =  Pi  X  AE-*- 
EB.  Tension  on  EF  =  compression 
on  BC.  For  stability  to  resist 
unequal  loads,  ties  should  be  run 
from  C  to  E  and  from  B  to  F. 

Burr  Truss  of  Five  Panels. 
(Fig.  135. )  —  Four-fifths  of  the  load 
may  betaken  as  concentrated  at  the 
points  E,  K,  L  and  F,  the  other  fifth 
being  supported  directly  by  the  two 
abutments.  For  the  strains  in  BA 
and  CD  the  truss  may  be  considered  as  a  queen-post  truss,  with  the  loads 
Pi,  P2  concentrated  at  E,  and  the  loads  P3,  P4  concentrated  at  F.  Then 
compressive  strain  on  AB  =  (Pi  +  P2)  x  AB  +  BE.  The  strain  on 
CD  is  the  same  if  the  loads  and  panel  lengths  are  equal.  The  tensile 

B 


strain  on  BE  or  CF  =  Pi  +  P2.  That  portion  of  the  truss  between  E 
and  F  may  be  considered  as  a  smaller  queen-post  truss,  supporting  the 
loads  P2,  Pa  at  K  and  L.  The  strain  on  EG  or  HF  =  P2  X  EG  -f-  GK. 
The  diagonals  GL  and  KH  receive  no  strain  unless  the  truss  is  unequally 
loaded.  The  verticals  GK  and  HL  each  receive  a  tensile  strain  equal  to 
P2  or  P3. 

For  the  strain  in  the  horizontal  members:  BG  and  CH  receive  a  thrust 
equal  to  the  horizontal  component  of  the  thrust  in  A  B  or  CD,  =  (Pi  +  P2) 
X  tan  angle  ABE,  or  (Pi  +  P2)  X  AE  -r-  BE.  GH  receives  this  thrust, 
and  also,  in  addition,  a  thrust  equal  to  the  horizontal  component  of  the 
thrust  in  EG  or  HF,  or,  in  all,  (Pi  4-  P2  +  P3)  X  AE  -^  BE. 

The  tension  in  AE  or  FD  equals  the  thrust  in  BG  or  HC,  and  the  ten* 
sion  in  EK,  KL,  and  LF  equals  the  thrust  in  GH. 

Pratt  or  Whipple  Truss.  (Fig.  136.)  —  In  this  truss  the  diagonals  are 
ties,  and  the  verticals  are  struts  or  columns.  . 

Calculation  by  the  method  of  distribution  of  strains:  Consider  first  the 
load  Pi.  The  truss  having  six  bays  or  panels,  5/6  of  the  load  is  trans- 
mitted to  the  abutment  H,  and  1/6  to  the  abutment  O,  on  the  principle 
of  the  lever.  As  the  five-sixths  must  be  transmitted  through  JA  and 
AH,  write  on  these  members  the  figure  5.  The  one-sixth  is  transmitted 
successively  through  JC,  CK,  KD,  DL,  etc.,  passing  alternately  through 
a  tie  and  a  strut.  Write  on  these  members,  up  to  the  strut  GO  inclusive, 
the  figure  1.  Then  consider  the  load  P2,  of  which  4/6  goes  to  AH  and 
2/6  to  GO.  Write  on  KB,  BJ,  JA,  and  AH  the  figure  4,  and  on  KD, 
DL,  LE,  etc.,  the  figure  2.  The  load  P3  transmits  3/6  in  each  direction; 
write  3  on  each  of  the  members  through  which  this  stress  passes,  and  so 
on  for  all  the  loads,  when  the  figures  on  the  several  members  will  appear 
as  on  the  cut.  Adding  them  up,  we  have  the  following  totals: 

TVncinn  nn  rlinc  ^nslc  J  ^  BH  BK   CJ   CL   DK   DM   EL   EN   FM    FO  GN 

L  on  diagonals  {  15     0     10      1     6       3       3      6      1       10      0    15 
**     f/     Cf     D£     E7M     ™'   ?? 

Each  of  the  figures  in  the  first  line  is  to  be  multiplied  by  Ve  P  X  secant 
of  angle  HAJ,  or  V0PX  AJ  -f-  AH,  to  obtain  the  tension,  and  each 


Compression  on  verticals  { 


STRESSES   IN   FRAMED   STRUCTURES. 


545 


figure  in  the  lower  line  is  to  be  multiplied  by  1/8  P  to  obtain  the  com- 
pression.    The  diagonals  HB  and  FO  receive  no  strain. 

It  is  common  to  build  this  truss  with  a  diagonal  strut  at  HB  instead 
of  the  post  HA  and  the  diagonal  AJ;  in  which  case  5/6  of  the  load  P  is 
carried  through  JB  and  the  strut  BH ,  which  latter  then  receives  a  strain 
=  l»/6  P  X  secant  of  HBJ. 


%H  ~]J  |K  |L  \M  N  0|| 

66666 

P!  P2  P3  P4  P5 


FIG.  136. 

The  strains  in  the  upper  and  lower  horizontal  members  or  chords  in- 
crease from  the  ends  to  the  center,  as  shown  in  the  case  of  the  Burr 
truss.  AB  receives  a  thrust  equal  to  the  horizontal  component  of  the 
tension  in  AJ,  or  15/e  P  X  tan  AJB.  BC  receives  the  same  thrust  + 
the  horizontal  component  of  the  tension  in  BK,  and  so  on.  ^The  tension 
in  the  lower  chord  of  each  panel  is  the  same  as  the  thrust  in  the  upper 
chord  of  the  same  panel.  (For  calculation  of  the  chord  strains  by  the 
method  of  moments,  see  below.) 

The  maximum  thrust  or  tension  is  at  the-  center  of  the  chords  and  is 

equal  to  .  in  which  W  is  the  total  load  supported  by  the  truss,  L  is 

the  length,  and  D  the  depth.  This  is  the  formula  for  maximum  stress  in 
the  chords  of  a  truss  of  any  form  whatever. 

The  above  calculation  is  based  on  the  assumption  that  all  the  loads 
Pi,  f*2,  etc.,  are  equal.  If  they  are  unequal,  the  value  of  each  has  to  be 
taken  into  account  in  distributing  the  strains.  Thus  the  tension  in  AJ, 
with  unequal  loads,  instead  of  being  15  X  Ve  P  secant  9  would  be  seed 
X  (5/e  Pi  +  4/6  P2  +  3/6  P3  4-  2/6  P4  +  1/6  PS).  Each  panel  load,  Pi,  etc., 
includes  its  fraction  of  the  weight  of  the  truss. 

General  Formula  for  Strains  in  Diagonals  and  Verticals.  —  Let 
n  =  total  number  of  panels,  x  =  number  of  any  vertical  considered  from 
the  nearest  end,  counting  the  end  as  1,  r  =  rolling  load  for  each  panel, 
P  =  total  load  for  each  panel, 

Strain  on  verticals  =  • '• — ^ + o~n — ' * 

For  a  uniformly  distributed  load,  leave  out  the  last  term, 

[r(x  -  1)+  (x  -  1)2J  -5-  2n. 
Strain  on  principal  diagonals   (AJ,   GN,   etc.)  =  strain  on   verticals 

X  secant  0,  that  is  secant  of  the  angle  the  diagonal  makes  with  the 

vertical. 

Strain  on  the  counterbraces  (BH,  CJ,  FO,  etc.):    The  strain  on  the 

counterbrace  in  the  first  panel  is  0,  if  the  load  is  uniform.     On  the  2d, 

1         1-4-2      i    i  o   i  o 

3d,  4th,  etc.,  it  is  P  secant  0  X  -^ »    -~  •         n       >  etc.,  P  being  the  total 

load  in  one  panel. 

Strain  in  the  Chords  —  Method  of  Moments.  —  Let  the  truss  be 
uniformly  loaded,  the  total  load  acting  on  it  =  W.  Weight  supported  at 
each  end,  or  reaction  of  the  abutment  =  W/2.  Length  of  the  truss  =  L. 
Weight  on  a  unit  of  length  =  W/L.  Horizontal  distance  from  the  nearest  ' 
abutment  to  the  point  (say  M  in  Fig.  136)  in  the  chord  where  the  strain 
is  to  be  determined  =  x.  Horizontal  strain  at  that  point  (tension  on  the 
lower  chord,  compression  in  the  upper)  =  //.  Depth  of  the  truss  =  D. 


546 


MECHANICS. 


By  the  method  of  moments  we  take  the  difference  of  the  moments,  about 
the  paint  M,  of  the  reaction  of  the  abutment  and  of  the  load  between 
M  and  the  abutments,  and  equate  that  difference  with  the  moment  of 
the  resistance,  or  of  the  strain  in  the  horizontal  chord,  considered  with 
reference  to  a  point  in  the  opposite  chord,  about  which  the  truss  would 
turn  if  the  first  chord  were  severed  at  M  . 

The  moment  of  the  reaction  of  the  abutment  is  W  x/2.   The  moment  of 
the  load  from  the  abutment  to  M  is  (W/Lx)  X  the  distance  of,  its  center  of 
gravity  from  M,  which  is  x/2,  or  moment  =  Wx*  +  2  L.    Moment  of  the 
Wx        Wx?  W    t         T-\ 

stress  in  the  chord  =  HD  =   —  —  -  •—••  whence  H  =    —  (x-  '—\» 


If  x  =  0  or  L,  H  =  0. 


-  •—•• 

W  I 
If  x  =  L/2,  H  =  •£-:-• 


which  is  the  horizontal 


strain  at  the  middle  of  the  chords,  as  before  given. 


FIG.  137. 

The  Howe  Truss.  (Fig.  137.)  —  In  the  Howe  truss  the  diagonals  are 
struts,  and  the  verticals  are  ties.  The  calculation  of  strains  may  be  made 
in  the  same  method  as  described  above  for  the  Pratt  truss. 

The  Warren  Girder.  (Fig.  138. )  —  In  the  Warren  girder,  or  triangu- 
lar truss,  there  are  no  vertical  struts,  and  the  diagonals  may  transmit  either 
tension  or  compression.  The  strains  in  the  diagonals  may  be  calculated  by 
the  method  of  distribution  of  strains  as  in  the  case  of  the  rectangular  truss. 


FIG.  138. 

.  On  the  principle  of  the  lever,  the  load  Pi  being  Vio  of  the  length  of  the 
span  from  the  line  of  the  nearest  support  a,  transmits  9/io  of  its  weight  to 
a  and  l/io  to  g.  Write  9  on  the  right  hand  of  the  strut  la,  to  represent  the 
compression,  and  1  on  the  right  hand  of  Ib,  2c,  3d,  etc.,  to  represent  com- 
pression, and  on  the  left  hand  of  62,  c3,  etc.,  to  represent  tension.  The 
load  Pz  transmits  7/i0  of  its  weight  to  a  and  3/10  to  g.  Write  7  on  each 
member  from  2  to  a,  and  3  on  each  member/ rom  2  to  g,  placing  the  figures 
representing  compression  on  the  right  hand  of  the  member,  and  those 
representing  tension  on  the  left.  Proceed  in  the  same  manner  with  all 
the  loads,  then  sum  up  the  figures  on  each  side  of  each  diagonal,  and 
write  the  difference  of  each  sum  beneath,  and  on  the  side  of  the  greater 
Bum,  to  show  whether  the  difference  represents  tension  or  compression. 
The  results  are  as  follows:  Compression,  la,  25;  26,  15;  3c.  5;  3d,  5;  4e,  15; 
&g,  25.  Tension,  U>,  15;  2c,  5;  4d,  5;  5e,  15.  Each  of  these  figures  is  to 


STRESSES  IN  FKAME0   STKUCTUKES. 


547 


6e  multiplied  by  Vio  of  one  of  the  loads  as  Pi,  and  by  the  secant  of  the 
angle  the  diagonals  make  with  a  vertical  line. 

The  strains  in  the  horizontal  chords  may  be  determined  by  the  method 
of  moments  as  in  the  case  of  rectangular  trusses. 

Roof-truss.  —  Solution  by  Method  of  Moments.  —  The  calculation  of 
strains  in  structures  by  the  method  of  statical  moments  consists  in  taking 
a  cross-section  of  the  structure  at  a  point  where  there  are  not  more  than 
three  members  (struts,  braces,  or  chords). 

To  find  the  strain  in  either  one  of  these  members  take  the  moment  about 
the  intersection  of  the  other  two  as  an  axis  of  rotation.  The  sum  of  the 
moments  of  these  members  must  be  0  if  the  structure  is  in  equilibrium. 
But  the  moments  of  the  two  members  that  pass  through  the  point  of  ref- 
erence or  axis  are  both  0,  hence  one  equation  containing  one  unknown 
quantity  can  be  found  for  each  cross-section. 


FIG.  139. 


In  the  truss  shown  in  Fig.  139  take  a  cross-section  at  ts,  and  determine 
the  strain  in  the  three  members  cut  by  it,  viz.,  CE,  ED,  and  DF.  Let 
X  =  force  exerted  in  direction  CE,  Y  =  force  exerted  in  direction  DE, 
Z  =  force  exerted  in  direction  FD. 

For  X  take  its  moment  about  the  intersection  of  Y  and  Z  at  D  =  Xx. 
For  Y  take  its  moment  about  the  intersection  of  X  and  Z  at  A  =  Yy. 
For  Z  take  its  moment  about  the  intersection  of  X  and  Y  at  E  =  Zz. 
Let  z  =  15,  x  =  18.6,  y  =  38.4,  AD  =  50,  CD  =  20  ft.  Let  PI,  P2, 
PS,  P4  be  equal  loads,  as  shown,  and  3 1/2  P  the  reaction  of  the  abutment  A. 

The  sum  of  all  the  moments  taken  about  D  or  A  or  E  will  be  0  when  the 
structure  is  at  rest.  Then  -  Xx  +  3.5  PX  50  -  P3  X  12.5  -  P2  X  25 

-  Pi  X  37.5  =  0. 

The  +  signs  are  for  moments  in  the  direction  of  the  hands  of  a  watch  or 
"  clockwise  "  and  —  signs  for  the  reverse  direction  or  anti-clockwise.    Since 
P  =  Pi  =  P2  =  P3,  -  18.6  X  +  175  P  -  75  P  =  0;  -  18.6  X  =  -  100  P; 
X  =  100  P-5-  18.6  =  5.376  P. 

-  Yy  +  P3  X  37.5  +  P2  X  25  -i-  Px  X  12.5  =  0;    38.4  Y  =  75  ;      Y  = 

75  P  +-  38.4  =  1.953  P. 

-  Zz  +  3.5  P  X  37.5  -  Pi  X  25  -  P2  X  12.5  -   P3  X  0   =  0;     15  3  = 

93.75P;Z  =  6.25  P. 

In  the  same  manner  the  forces  exerted  in  the  other  members  have  been 
found  as  follows:  EG  =  6.73  P;GJ  «=  8.07  P;JA  =  9A2P;JH  =  1.35  P; 
GF  =  1.59  P;  AH  =  8.75  P;  IIP  =  7.50  P. 

The  Fink  Roof-truss.     (Fig.    140.)  —  An  analysis  by  Prof.   P.   H. 
Philbrick  (Van  N.  Mag.,  Aug.,  1880)  gives  the  following  results: 
W=  total  load  on  roof; 
N=  No.  of  panels  on  both  rafters; 
W/N=  P  =  load  at  each  joint  b,  d,  /,  etc.; 

V=  reaction  at  A  =  l/2  W  =  1/2  NP  =  4P: 
AD=  S-,  AC  =  L\  CD  =  D; 
ti,h,ta=  tension  on  De,  eg,  gA,  respectively; 
cit  ca,  c«,  Ci=  compression  oa  C6,  bdt  df,  and/A. 


548 


MECHANICS. 


Strains  in 


1,  orDe  - 

2,  "eg   -  fe  -  3  PS  •*•  Z); 

3,  M  0A  =  k=7/2  PS 


7,or  6C==Ci=7/2 
8,  "  6cor/0=  PS 
9," 


L; 


4,  "  Af  =  c4  =7/2  PL  -s-  D;  10,  "  cd  or  dg=  V2  PS  -*-  Z); 

5,  "  fd  =  c8=7/2PL/D-PD/L;        11,"  ec  =  PS  -5-  D; 
"                                                             " 


6,  "  db  -  c2  = 


12,"  cG 


A  g  e  D  B 

FIG.  140. 

EXAMPLE.  —  Given  a  Fink  roof-truss  of  span  64  ft.,  depth  16  ft.,  with 
four  panels  on  each  side,  as  in  hecut;  total  load  32  tons,  or  4  tons 
each  at  the  points  /,  d,  b,  C,  etc.  (and  2  tons  each  at  A  and  B,  which  trans- 
mit no  strain  to  the  truss  members).  Here  W  =  32tons,  P  =  4  tons, 
S=32  ft.,  D  =  16  ft.,  L  =  V^2  +  £>2  =  2.236  X  D.  L  +  D  =  2.236, 
D  -*•  L  =  0.4472,  £-f-D  =  2,  S  -s-  L  =  -0.8944.  The  strains  on  the 
numbered  members  then  are  as  follows: 


1,  2X4X2         -16     tons; 

2,  3X4X2         =24 

3,  7/2X4X2         =28       " 

4,  7/2X4X2.236-31.3     " 

5,  31.3-4X0.447  =  29.52  " 

6,  31.3-8X0.447  =  27.72  " 


7,31.3-12X0.447   -25.94  tons. 

8,  4X0.8944=  3.58     " 

9,  8X0.8944=  7.16     " 

10,  2X2  =4  •• 

11,  4X2  =8  " 

12,  6X2          =12 


The  Economical  Angle.  —  A  structure  of  tri- 
angular form,  Fig.  141,  is  supported  at  a  and  b.  It 
sustains  any  load  L,  the  elements  cc  being  in  com- 
pression and  t  in  tension.  Required  the  angle  0  so 
that  the  total  weight  of  the  structure  shall  be  a 
minimum.  F.  R.  Honey  (Sci.  Am.  Supp.,  Jan.  17, 
1891)  gives  a  solution  of  this  problem,  with  the 


result  tan  0  = 


C+  T 


in  which  C  and  T  represent 


,-, 


the  crushing  and  the  tensile  strength  respectively  of 

the,  material   employed.      It   is   applicable   to  any 

material.     For  C  =  T,  0  =  ^43/^°.     For  C  =  0.4  T   (yellow  pine),   0  » 

493/4°.     For  C  —  0.8  T  (soft  steel),  0  =  53V*°.    For  C  =•  6  T  (cast  iron), 

*=  691/4°. 


PYROMETRY.  549 

HEAT. 

THERMOMETERS. 

The  Fahrenheit  thermometer  is  generally  used  in  English-speaking 
countries,  and  the  Centigrade,  or  Celsius,  thermometer  in  countries  that 
use  the  metric  system.  In  many  scientific  treatises  in  English,  however, 
the  Centigrade  temperatures  are  also  used,  either  with  or  without  their 
Fahrenheit  equivalents.  The  Reaumur  thermometer  is  used  to  some 
extent  on  the  Continent  of  Europe  and  in  breweries  in  this  country» 

In  the  Fahrenheit  thermometer  the  freezing-point  of  water  is  taken  at 
32°,  and  the  boiling-point  of  water  at  mean  atmospheric  pressure  at  the 
sea-level,  14.7  Ibs.  per  sq.  in.,  is  taken  at  212°,  the  distance  between  these 
two  points  being  divided  into  180°.  In  the  Centigrade  and  Re"aumur 
thermometers  the  freezing-point  is  taken  at  0°.  The  boiling-point  is 
100°  in  the  Centigrade  scale,  and  80°  in  the  Reaumur. 

1  Fahrenheit  degree  =  5/9  deg.  Centigrade  =  4/gdeg.  Reaumur. 

1  Centigrade  degree  =  9/5  deg.  Fahrenheit  =  4/5  deg.  Reaumur. 

1  Reaumur  degree  =  9/4  deg.  Fahrenheit  =5/4  deg.  Centigrade. 

Temperature  Fahrenheit     =  9/5  x  temp.  C.  +  32°       =  9/4R.  +  32°. 
Temperature  Centigrade     =  5/9  (temp.  F.  -  32°)        =5/4  R. 
Temperature  Reaumur        =  4/5  temp.  C.  =4/9  (F.  —  32°). 

HANDY  RULE  FOR  CONVERTING  CENTIGRADE  TEMPERATURE  TO  FAH- 
RENHEIT. —  Multiply  by  2,  subtract  a  tenth,  add  32. 

EXAMPLE.  —  100°  C.  X  2  =  200,  -  20  =  180,  +  32=  212°  F. 

Mercurial  Thermometer.  (Rankine,  S.  E.,  p.  234.)  — The  rate  of 
expansion  of  mercury  with  rise  of  temperature  increases  as  the  temperature 
becomes  higher;  from  which  it  follows,  that  if  a  thermometer  showing  the 
dilatation  of  mereury  simply  were  made  to  agree  with  an  air  thermometer 
at  32°  and  212°,  the  mercurial  thermometer  would  show  lower  temperatures 
than  the  air  thermometer  between  those  standard  points,  and  higher  tem- 
peratures beyond  them. 

For  example,  according  to  Regnault,  when  the  air  thermometer  marked 
350°  C.  (  =  662°  F.),  the  mercurial  thermometer  would  mark  362.16°  C. 
(=  683.89°  F.),  the  error  of  the  latter  being  in  excess  12.16°  C.  (  =  21.89° 
F.). 

Actual  mercurial  thermometers  indicate  intervals  of  temperature  pro- 
portional to  the  difference  between  the  expansion  of  mercury  and  that  of 
glass. 

The  inequalities  in  the  rate  of  expansion  of  the  glass  (which  are  very 
different  for  different  kinds  of  glass)  correct,  to  a  greater  or  less  extent,  the 
errors  arising  from  the  inequalities  in  the  rate  of  expansion  of  the  mercury. 

For  practical  purposes  connected  with  heat  engines,  the  mercurial  ther- 
mometer made  of  common  glass  may  be  considered  as  sensibly  coinciding 
with  the  air-thermometer  at  all  temperatures  not  exceeding  500°  F. 

If  the  mercury  is  not  throughout  its  whole  length  at  the  same  tempera- 
ture as  that  being  measured,  a  correction,  k,  must  be  added  to  the  tem- 
perature t  in  Fahrenheit  degrees;  k  =  95  D  (t-f)  -f-  1,000,000,  where  D  is 
the  length  of  the  mercury  column  exposed,  measured  in  Fahrenheit 
degrees,  and  t  is  the  temperature  of  the  exposed  part  of  the  thermometer. 
When  long  thermometers  are  used  in  shallow  wells  in  high-pressure  steam 
pipes  this  correction  is  often  5°  to  10°  F.  (Moyer  on  Steam  Turbines.) 

PYROMETRY. 

Principles  Used  in  Various  Pyrometers. 

Pyrometers  may  be  classified  according  to  the  principles  upon  which 
they  operate,  as  follows: 

1.  Expansion  of  mercury  in  a  glass  tube.  When  the  space  above  the 
mercury  is  filled  with  compressed  nitrogen,  and  a  specially  hard  glass  is 
used  for  the  tube,  mercury  thermometers  may  be  made  to  indicate  tem- 
peratures as  high  as  1000°  F. 


TEMPERATURES,  CENTIGRADE  AND  FAHRENHEIT. 


c. 

F 

C 

F. 

C 

F. 

r, 

F. 

C 

F 

0 

F 

C, 

F 

-40 

-40. 

26 

78.8 

92 

197.6 

158 

316.4 

224 

435.2 

290 

554 

950 

1742 

-39 

-38.2 

27 

80.6 

93 

199.4 

159 

318.2 

225 

437. 

300 

572 

960 

1760 

-38 

-36.4 

28 

82.4 

94 

201.2 

160 

320. 

226 

438.8 

310 

590 

970 

1778 

-37 

-34.6 

29 

84.2 

95 

203. 

161 

321.8 

227 

440.6 

320 

608 

980 

1796 

-36 

-32.8 

30 

86. 

96 

204.8 

162 

323.6 

228 

442.4 

330 

626 

990 

1814 

-35 

-31. 

31 

87.8 

97 

206.6 

163 

325.4 

229 

444.2 

340 

644 

1000 

1832 

-34 

-29.2 

32 

89.6 

98 

208.4 

164 

327.2 

230 

446. 

350 

662 

1010 

1850 

-33 

-27.4 

33 

91.4 

99 

210.2 

165 

329. 

231 

447.8 

360 

680 

1020 

1868 

-32 

-25.6 

34 

93.2 

100 

212. 

166 

330.8 

232 

449.6 

370 

698 

1030 

1886 

-31 

-23.8 

35 

95. 

101 

213.8 

167 

332.6 

233 

451.4 

380 

716 

1040 

1904 

-30 

-22. 

36 

96.8 

102 

215.6 

168 

334.4 

234 

453.2 

390 

734 

1050 

1922 

-29 

-20.2 

37 

98.6 

103 

217.4 

169 

336.2 

235 

455. 

400 

752 

1060 

1940 

-28 

-18.4 

38 

100.4 

104 

219.2 

170 

338. 

236 

456.8 

410 

770 

1070 

1958 

-27 

-  16.6 

39 

102.2 

105 

221. 

171 

339.8 

237 

458.6 

420 

788 

1080 

1976 

-26 

-14.8 

40 

104. 

106 

222.8 

172 

341.6 

238 

460.4 

430 

806 

1090 

1994 

-25 

-13. 

41 

105.8 

107 

224.6 

173 

343.4 

239 

462.2 

440 

824 

1100 

2012 

-24 

-11.2 

42 

107.6 

108 

226.4 

174 

345.2 

240 

464. 

450 

842 

1110 

2030 

-23 

-  9.4 

43 

109.4 

109 

228.2 

175 

347. 

241 

465.8 

460 

860 

1120 

2048 

-22 

-  7.6 

44 

111.2 

110 

230. 

176 

348.8 

242 

467.6 

470 

878 

1130 

2066 

-21 

-  5.8 

45 

113. 

1  1  1 

231.8 

177 

350.6 

243 

469.4 

480 

896 

1140 

2084 

-20 

-  4. 

46 

114.8 

112 

233.6 

178 

352.4 

244 

471.2 

490 

914 

1150 

2102 

-19 

-  2.2 

47 

116.6 

113 

235.4 

179 

354.2 

245 

473. 

500 

932 

1160 

2120 

-18 

-  0.4 

48 

118.4 

114 

237.2 

180 

356. 

246 

474.8 

510 

950 

1170 

2138 

-17 

+  1.4 

49 

120.2 

115 

239. 

181 

357.8 

247 

476.6 

520 

968 

1180 

2156 

-16 

3.2 

50 

122. 

116 

2408 

182 

359.6 

243 

478.4 

530 

986 

1190 

2174 

-15 

5. 

51 

123.8 

117 

242.6 

183 

361.4 

249 

480.2 

540 

1004 

1200 

2192 

-14 

6.8 

52 

125.6 

118 

244.4 

184 

363.2 

250 

482. 

550 

1022 

1210 

2210 

-13 

8.6 

53 

127.4 

119 

246.2 

185 

365. 

251 

483.8 

560 

1040 

1220 

2228 

-12 

10.4 

54 

129.2 

120 

248. 

186 

366.8 

252 

485.6 

570 

1058 

1230 

2246 

-11 

12.2 

55 

131. 

121 

249.8 

187 

368.6 

253 

487.4 

530 

1076 

1240 

2264 

-10 

14. 

56 

132.8 

122 

251.6 

188 

370.4 

254 

489.2 

590 

1094 

1250 

2282 

-  9 

15.8 

57 

134.6 

123 

253.4 

.189 

372.2 

255 

491. 

e»0o 

1112 

1260 

2300 

-  8 

17.6 

58 

136.4 

124 

255.2 

190 

374. 

256 

492.8 

610 

1130 

1270 

2318 

—  7 

19.4 

59 

138.2 

125 

257. 

191 

375.8 

257 

494.6 

620 

1148 

1280 

2336 

-  6 

21.2 

60 

140. 

126 

258.8 

192 

377.6 

258 

496.4 

630 

1166 

1290 

2354 

-  5 

23. 

61 

141.8 

127 

260.6 

193 

379.4 

259 

498.2 

640 

1184 

1300 

2372 

-  4 

24.8 

62 

143.6 

128 

262.4 

194 

381.2 

260 

500. 

650 

1202 

1310 

2390 

-  3 

26.6 

63 

145.4 

129 

264.2 

195 

383. 

261 

501.8 

660 

1220 

1320 

2408 

-  2 

28.4 

64 

147.2 

130 

266. 

196 

384.8 

262 

503.6 

670 

1238 

1330 

2426 

-  1 

30.2 

65 

149. 

131 

267.  £ 

197 

386.6 

263 

505.4 

680 

1256 

1340 

2444 

0 

32. 

66 

150.8 

132 

269.6 

198 

388.4 

264 

507.2 

690 

1274 

1350 

2462 

+  1 

33.8 

67 

152.6 

133 

271.4 

199 

390.2 

265 

509. 

700 

1292 

1360 

2480 

2 

35.6 

68 

154.4 

134 

273.2 

200 

392. 

266 

510.8 

710 

1310 

1370 

2498 

3 

37.4 

69 

156.2 

135 

275. 

201 

393.8 

267 

512.6 

720 

1328 

1380 

2516 

4 

39.2 

70 

153. 

136 

276.8 

202 

395.6 

268 

514.4 

730 

1346 

1390 

2534 

5 

41. 

71 

159.8 

137 

278.6 

203 

397.4 

269 

516.2 

740 

1364 

1400 

2552 

6 

42.8 

72 

161.6 

138 

280.4 

204 

399.2 

270 

518. 

750 

1382 

1410 

2570 

7 

44.6 

73 

163.4 

139 

282.2 

205 

401. 

271 

519.8 

760 

1400 

1420 

2588 

8 

46.4 

74 

165.2 

140 

284. 

206 

402.8 

272 

521.6 

770 

1418 

1430 

2606 

9 

48.2 

75 

167. 

141 

285.8 

207 

404.6 

273 

523.4 

780 

1436 

1440 

2624 

10 

50. 

76 

168.8 

142 

287.6 

208 

406.4 

274 

525.2 

790 

1454 

I4M) 

2642 

11 

51.8 

77 

170.6 

143 

289.4 

209 

408.2 

275 

527. 

800 

1472 

1460 

2660 

12 

53.6 

78 

172.4 

144 

291.2 

210 

410. 

276 

528.8 

310 

1490 

1470 

2678 

13 

55.4 

79 

174.2 

145 

293. 

211 

411.8 

277 

530.6 

320 

1508 

1480 

2696 

14 

57.2 

80 

176. 

146 

294.8 

212 

413.6 

278 

532.4 

330 

1526 

1490 

2714 

15 

59. 

81 

177.8 

147 

296.6 

213 

415.4 

279 

534.2 

840  1544 

1500 

2732 

16 

60.8 

82 

179.6 

148 

298.4 

214 

417.2 

280 

536. 

85011562 

510 

2750 

17 

62.6 

83 

181.4 

149 

300.2 

215 

419. 

281 

537.8 

360 

1580 

1520 

2768 

18 

64.4 

"84 

183.2 

150 

302. 

216 

420,8 

282 

539.6 

870 

1598 

530 

2786 

19 

66.2 

85 

185. 

151 

303.8 

217 

422.6 

283 

541.4 

330 

1616 

540 

2804 

20 

68. 

86 

186.8 

152 

305.6 

218 

424.4 

284 

543.2 

390 

1634 

550 

2822 

21 

69.8 

87 

188.6 

153 

307.4 

219 

426.2 

285 

545. 

900 

1652 

600 

2912 

22 

71.6 

88 

190.4 

154 

309.2 

220 

428. 

286 

546.8 

910 

1670 

650 

3002 

23 

73.4 

89 

192.2 

155 

311. 

221 

429.8 

287 

548.6 

920 

1688 

700  3092 

24 

75.2 

90 

194. 

156 

312.8 

222 

431.6 

288 

550.4 

930 

1706 

750  3182 

25 

77. 

91 

195.8 

157 

314.6 

223 

433.4 

289 

552.2 

940 

1724 

800  3272 

550 


TEMPERATURES,  FAHRENHEIT  AND  CENTIGRADE. 


F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

-40 

-40 

26 

-3.3 

92 

33.3 

158 

70. 

224 

106. 

290 

143. 

360 

182.2 

-39 

-39.4 

27 

-2.8 

93 

33.9 

159 

70.6 

225 

107.2 

29 

143. 

370 

187.8 

-38 

-389 

28 

—  2  2 

94 

34.4 

160 

71.1 

226 

107.8 

292 

144. 

380 

193.3 

-37 

-383 

29 

-17 

95 

35. 

16 

71.7 

227 

108.3 

293 

145. 

390 

198.9 

-36 

-378 

30 

-1.1 

96 

35.6 

162 

72.2 

228 

108.9 

294 

145.6 

400 

204.4 

-35 

-372 

31 

-0.6 

97 

36.1 

163 

72.8 

229 

109.4 

295 

146. 

410 

210. 

-34 

-36.7 

32 

0. 

98 

36.7 

164 

73.3 

230 

110. 

296 

146.7 

420 

215.6 

-33 

-36.1 

33 

+  0.6 

99 

37.2 

165 

73.9 

231 

110.6 

297 

147.2 

430 

221.1 

-32 

-35.6 

34 

1.1 

100 

37.8 

166 

74.4 

232 

111. 

298 

147.8 

440 

226.7 

-31 

-35. 

35 

1  7 

101 

38.3 

167 

75. 

233 

1117 

299 

148.3 

450 

232.2 

-30 

-34.4 

36 

2^2 

102 

38.9 

168 

75.6 

234 

112.2 

300 

148.9 

460 

237.8 

-29 

-33.9 

37 

2.8 

103 

39.4 

169 

76.1 

235 

112.8 

301 

149.4 

470 

243.3 

-28 

-33.3 

38 

3.3 

104 

40. 

170 

76.7 

236 

113.3 

302 

150. 

480 

248.9 

-27 

-32.8 

39 

3.9 

105 

40.6 

171 

77.2 

237 

113.9 

303 

150.6 

490 

254.4 

-26 

-322 

40 

4.4 

106 

41.1 

172 

77.8 

238 

114.4 

304 

151.1 

500 

260. 

-25 

-31  7 

41 

5. 

107 

41.7 

173 

78.3 

239 

115. 

305 

151.7 

510 

265.6 

-24 

-31.1 

42 

5.6 

108 

42.2 

174 

78.9 

240 

115.6 

306 

152.2 

520 

271.1 

-23 

-30.6 

43 

6.1 

109 

42.8 

175 

79.4 

241 

116.1 

307 

152.8 

530 

276.7 

-22 

-30. 

44 

6.7 

110 

43.3 

176 

80. 

242 

116.7 

308 

153.3 

540 

282.2 

-21 

-29.4 

45 

7.2 

1  1  1 

43.9 

177 

80.6 

243 

117.2 

309 

153.9 

550 

287.8 

-20 

-28.9 

46 

7.8 

112 

44.4 

178 

81.1 

244 

117.8 

310 

154.4 

560 

293.3 

-19 

-28.3 

47 

8.3 

113 

45. 

179 

81.7 

245 

118.3 

311 

155. 

570 

298.9 

-18 

-27.8 

48 

8.9 

114 

45.6 

180 

82.2 

246 

118.9 

312 

155.6 

580 

304.4 

-17 

-27.2 

49 

9.4 

115 

46.1 

181 

82.8 

247 

119.4 

313 

156.1 

590 

310. 

-16 

-26.7 

50 

10. 

116 

46.7 

182 

83.3 

248 

120. 

314 

156.7 

600 

315.6 

-15 

-26.1 

51 

10.6 

117 

47.2 

183 

83.9 

249 

120.6 

315 

157.2 

610 

321.1 

-14 

-25.6 

52 

11.1 

118 

47.8 

184 

84.4 

250 

121.1 

316 

157.8 

620 

326.7 

-13 

-25. 

53 

11.7 

119 

48.3 

185 

85. 

251 

121.7 

317 

158.3 

630 

332.2 

-12 

-24.4 

54 

12.2 

120 

48.9 

186 

85.6 

252 

122.2 

318 

158.9 

640 

337.8 

-11 

-23.9 

55 

12.8 

121 

49.4 

187 

86.1 

253 

122.8 

319 

59.4 

650 

343.3 

-10 

-23.3 

56 

13.3 

122 

50. 

188 

86.7 

254 

123.3 

320 

60. 

660 

348.9 

-  9 

-22.8 

57 

13.9 

123 

50.6 

189 

87.2 

255 

123.9 

321 

60.6 

670 

354.4 

-  8 

-22.2 

58 

14.4 

124 

51.1 

190 

87.8 

256 

124.4 

322 

61.1 

680 

360. 

-  7 

-21.7 

59 

15. 

125 

51.7 

191 

88.3 

257 

125. 

323 

61.7 

690 

365.6 

-  6 

-21.1 

60 

15.6 

126 

52.2 

192 

88.9 

258 

125.6 

324 

62.2 

700 

371.1 

-  5 

-20.6 

61 

16.1 

127 

52.8 

193 

89.4 

259 

126.1 

325 

62.8 

710 

376.7 

-  4 

-20. 

62 

16.7 

128 

53.3 

194 

90. 

260 

126.7 

326 

63.3 

720 

382.2 

-  3 

-19.4 

63 

17.2 

129 

J3.9 

195 

90.6 

261 

127.2 

327 

63.9 

730 

387.5 

-  2 

-18.9 

64 

17.8 

130 

4.4 

196 

91.1 

262 

127.8 

328 

64.4 

740 

3933 

-  1 

-18.3 

65 

18.3 

131 

55. 

197 

91.7 

263 

128.3 

329 

65. 

750 

398.9 

0 

-17.8 

66 

18.9 

132 

5.6 

198 

92.2 

264 

128.9 

330 

65.6 

760 

404.4 

+  1 

-17.2 

67 

19.4 

133 

6.1 

199 

92.8 

265 

129.4 

331 

66.1 

770 

410. 

2 

-16.7 

68 

20. 

134 

6.7 

200 

93.3 

266 

130. 

332 

66.7 

780 

415.6 

3 

-16.1 

69 

20.6 

135 

7.2 

201 

93.9 

267 

130.6 

333 

67.2 

790 

421.1 

4 

-15.6 

70 

21.1 

136 

7.8 

202 

94.4 

268 

131.1 

334 

67.8 

800 

426.7 

5 

-15. 

71 

21.7 

137 

8.3 

203 

95. 

269 

131.7 

335 

68.3 

810 

432.2 

6 

-14.4 

72 

22.2 

138 

8.9 

204 

95.6 

270 

132.2 

336 

68.9 

820 

437.8 

7 

-13.9 

73 

22.8 

139 

9.4 

205 

96.1 

271 

132.8 

337 

69.4 

830 

443.3 

8 

-13.3 

74 

23.3 

140 

60. 

206 

96.7 

272 

133.3 

338 

70. 

840 

448.9 

9 

-12.8 

75 

23.9 

141 

60.6 

207 

97.2 

273 

133.9 

339 

70.6 

850 

45^,4 

10 

-12.2 

76 

24.4 

142 

61.1 

208 

97.8 

274 

134.4 

340 

71.1 

860 

460. 

11 

-11.7 

77 

25. 

143 

61.7 

209 

98.3 

275 

135. 

341 

71.7 

870 

465.6 

12 

-  11.1 

78 

25.6 

144 

62.2 

210 

98.9 

276 

135.6 

342 

72.2 

880 

471.1 

13 

-10.6 

79 

26.1 

145 

62.8 

211 

99.4 

277 

136.1 

343 

72.8 

890 

476.7 

14 

-10. 

80 

26.7 

146 

63.3 

212 

00. 

278 

136.7 

344 

73.3 

900 

482.2 

15 

-  9.4 

81 

27.2 

147 

63.9 

213 

00.6 

279 

137.2 

345 

73.9 

910 

487.8 

16 

-  8.9 

82 

27.8 

148 

644 

214 

01.1 

280 

137.8 

346 

74.4 

920 

493.3 

17 

-  8.3 

83 

28.3 

149 

65. 

215 

01.7 

281 

138.3 

347 

75. 

930 

498.9 

18 

-  7.8 

84 

28.9 

150 

65.6 

216 

02.2 

282 

138.9 

348 

75.6 

940 

504.4 

19 

-  7.2 

85 

29.4 

151 

66.1 

217 

02.8 

283 

139.4 

349 

76.1 

950 

510. 

20 

-  6.7 

86 

30. 

152 

66.7 

218 

03.3 

284 

140. 

350 

76.7 

960 

515.6 

21 

-  6.1 

87 

30.6 

153 

67.2 

219 

03.9 

285 

140.6 

351 

77.2 

970 

521.1 

22 

-  5.6 

88 

31.1 

154 

67.8 

220 

04.4 

286 

141.1 

352 

77.8 

980 

526.7 

23 

-  5. 

89 

31.7 

155 

68.3 

221 

05. 

287 

141.7 

353 

78.3 

990 

532.2 

24 

-  4.4 

90 

32.2 

156 

68.9 

222 

05.6 

288 

142.2 

354 

78.9 

000 

537.8 

25 

-  3.9 

91 

32.8 

157)69.4 

223 

06.1 

289 

142.8 

355 

79.4 

010 

543.3 

551 


552 


HEAT. 


Temperature  Conversion  Table. 

(By  Dr.  Leonard  Waldo.) 
Reprint  from  Metallurgical  and  Chemical  Engineering* 


c° 

0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

-200 
-100 
-0 

F 

-328 
-148 

+32 

F 

-346 
-166 

+  14 

F 

-364 
-184 
-4 

F 

-382 
-202 
-22 

F 

-400 
-220 
-40 

F 

-418 
-238 
-58 

F 

-436 
-256 
-76 

F 

-454 
-274 
-94 

F 

-292 
-112 

F 

-310 
-130 

0 

32 

50 

68 

86  104 

122 

140 

158 

176 

194 

100 
200 
300 

212 
392 
572 

230 
410 
590 

248 
428 
608 

266 
446 
626 

284 
464 
644 

302 
482 
662 

320 
500 
680 

338 
518 
698 

356 
536 
716 

374 
554 
734 

400 
500 
600 

752 
932 
1112 

770 
950 
1130 

788 
968 
1148 

806 
986 
1166 

824 
1004 
1184 

842 
1022 
1202 

860 
1040 
1220 

878 
1058 
1238 

896 
1076 
1256 

914 
1094 
1274 

700 
800 
900 

1292 
1472 
1652 

1310 
1490 
1670 

1328 
1508 
1688 

1346 
1526 
1706 

1364 
1544 
1724 

1382 
1562 
1742 

1400 
1580 
1760 

1418 
1598 
1778 

1436 
1616 
1796 

1454 
1634 
1814 

1000 

1832 

1850 

1868 

1886 

1904 

1922 

1940 

1958 

1976 

1994 

1100 
1200 
1300 

2012 
2192 
2372 

2030 
2210 
2390 

2048 
2228 
2408 

2066 
2246 
2426 

2084 
2264 
2444 

2102 
2282 
2462 

2120 
2300 
2480 

2138 
2318 
2498 

2156 
2336 
2516 

2174 
2354 
2534 

1400 
1500 
1600 

2552 
2732 
2912 

2570 
2750 
2930 

2588 
2768 
2948 

2606 
2786 
2966 

2624 
2804 
2984 

2642 
2822 
3002 

2660 
2840 
3020 

2678 
2858 
3038 

2696 
2876 
3056 

2714 
2894 
3074 

1700 
1800 
1900 

3092 
3272 
3452 

3110 
3290 
3470 

3128 
3308 
3488 

3146 
3326 
3506 

3164 
3344 
3524 

3182 
3362 
3542 

3200 
3380 
3560 

3218 
3398 
3578 

3236 
3416 
3596 

3254 
3434 
3614 

2000 

3632 

3650 

3668 

3686 

3704 

3722 

3740 

3758 

3776 

3794 

2100 
2200 
2300 

3812 
3992 
4172 

3830 
4010 
4190 

3848 
4028 
4208 

3866 
4046 
4226 

3884 
4064 
4244 

3902 
4082 
4262 

3920 
4100 
4280 

3938 
4118 
4298 

3956 
4136 
4316 

3974 
4154 
4334 

2400 
2500 
2600 

4352 
4532 
4712 

4370 
4550 
4730 

4388 
4568 
4748 

4406 
4586 
4766 

4424 
4604 
4784 

4442 
4622 
4802 

4460 
4640 
4820 

4478 
4658 
4838 

4496 
4676 
4856 

4514 
4694 
4874 

2700 
2800 
2900 

4892 
5072 
5252 

4910 
5090 
5270 

4928 
5108 
5288 

4946 
5126 
5306 

4964 
5144 
5324 

4982 
5162 
5342 

5000 
5180 
5360 

5018 
5198 
5378 

5036 
5216 
5396 

5054 
5234 
5414 

3000 

5432 

5450 

5468 

5486 

5504 

5522 

5540 

5558 

5576 

5594 

3100 
3200 
3300 

5612 
5792 
5972 

5630 
5810 
5990 

5648 
5828 
6008 

5666 
5846 
6026 

5684 
5864 
6044 

5702 
5882 
6062 

5720 
5900 
6080 

5738 
5918 
6098 

5756 
5936 
6116 

5774 
5954 
6134 

3400 
3500 
3600 

6152 
6332 
6512 

6170 
6350 
6530 

6188 
6368 
6548 

6206 
6386 
6566 

6224 
6404 
6584 

6242  6260 

6422  6440 
6602|  6620 

6278 
6458 
6638 

6296 
6476 
6656 

6314 
6494 
6674 

3700 
3800 
3900 

6692 
6872 
7052 

6710 
6890 
7070 

6728 
6908 
7088 

6746 
6926 
7106 

6764 
6944 
7124 

6782 
6962 
7142 

50 

6800 
6980 
7160 

6818 
6998 
7178 

6836 
7016 
7196 

6854 
7034 
72.14 

C° 

OJ   10 

20 

30 

40 

60 

70 

80 

90 

EXAMPLES:  1347°.  C  =  2444°  F+ 12°.6F=2456°.6F:  3367°  F=  1850 
I852°.78  C.    For  other  tables  of  temperatures,  see  pages  550 and  551- 


PYEOMETRY.  553 

2.  Contraction  of  clay,  as  in  the  old  Wedgwood  pyrometer,  at  one  time 
used  by  potters.     This  instrument  was  very  inaccurate,  as  the  contraction 
of  clay  varied  with  its  nature. 

3.  Expansion  of  air,  as  in  the  air-thermometer,  Wiborgh's  pyrometer. 
Uehling  and  Steinbart's  pyrometer,  etc. 

4.  Pressure  of  vapors,  as  in  some  forms  of  Bristol's  recording  pyrometer. 

5.  Relative  expansion  of  two  metals  or  other  substances,  as  in  Brown's, 
Bulkley's  and  other  metallic  pyrometers,  consisting  of  a  copper  rod  or 
tube  inside  of  an  iron  tube,  or  vice  versa,  with  the  difference  of  expansion 
multiplied  by  gearing  and  indicated  on  a  dial. 

6.  Specific  heat  of  solids,  as  in  the  copper-ball  and  platinum-ball 
pyrometers. 

7.  Melting-points  of  metals,  alloys,  or  other  substances,  as  in  approxi- 
mate determination  of  temperature  by  melting  pieces  of  zinc,  lead,  etc., 
or  as  in  Seger's  fire-clay  pyrometer. 

8.  Time  required  to  heat  a  weighed  quantity  of  water  inclosed  in  a 
vessel,  as  in  one  form  of  water  pyrometer.    , 

9.  Increase  in  temperature  of  a  stream  of  water  or  other  liquid  flow- 
ing at  a  given  rate  through  a  tube  inserted  into  the  heated  chamber. 

10.  Changes  in  the  electric  resistance  of  platinum  or  other  metal,  as 
in  the  Siemens  pyrometer. 

11.  Measurement    of   an   electric  current   produced   by   heating  the 
junction  of  two  metals,  as  in  the  Le  Chatelier  pyrometer. 

12.  Dilution  by  cold  air  of  a  stream  of  hot  air  or  gas  flowing  from  a 
heated  chamber  and  determination  of  the  temperature  of  the  mixture  by 
a  mercury  thermometer,  as  in  Hobson's  hot-blast  pyrometer. 

13.  Polarization  and  refraction  by  prisms  and  plates  of  light  radiated 
from  heated  surfaces,  as  in  Mesure"  and  Nouel's  pyrometric  telescope  or 
optical  pyrometer,  and  Warmer's  pyrometer. 

14.  Heating  the  filament  of  an  electric  lamp  to  the  same  color  as  that 
of  an  incandescent  body,  so  that  when  the  latter  is  observed  through  a 
telescope  containing  the  lamp  the  filament  becomes  invisible,  as  in  Hoi- 
born  and   Kurlbaum's  and   Morse's    optical   pyrometers.     The   current 
required  to  heat  the  filament  is  a  measure  of  the  temperature. 

15.  The  radiation  pyrometer.     The  radiation  from  an  incandescent 
surface  is  received  in  a  telescope  containing  a  thermo-couple,  and  the 
electric  current  generated  therein  is  measured,  as  in  Fdry's  radiation 
pyrometer. 

(See  "Optical  Pyrometry  "  by  C.  W.  W.  Waidner  and  G.  K.  Burgess, 
Bulletin  No.  2.  Bureau  of  Standards,  Department  of  Commerce  and 
Labor;  also  Eng'g,  Mar.  1,  1907.) 

The  "Veritas"  Pyrometer  (called  Buller's  Rings  in  England)  is  an 
improvement  on  the  Wedge  wood  pyrometer.  It  is  based  on  the  con- 
traction of  a  flat  ring  of  a  special  clay  mixture,  which  is  made  with 
great  care  to  secure  uniformity  of  composition.  The  contraction  is 
found  to  be  directly  proportional  to  the  increase  of  temperature  above 
800°  C.  (1472°  F.)  and  its  amount  is  measured  by  a  multiplying  index. 
The  rings  are  21/2  in.  external  and  3  A  in.  internal  diam.,  5/16  in.  thick. 
They  are  made  by  Veritas  Firing  System  Co.,  Trenton,  N.  J.,  and  are 
largely  used  by  potters. 

Platinum  or  Copper  Ball  Pyrometer.  —  A  weighed  piece  of  platinum, 
copper,  or  iron  is  allowed  to  remain  in  the  furnace  or  heated  chamber  till 
it  has  attained  the  temperature  of  its  surroundings.  It  is  then  suddenly 
taken  out  and  dropped  into  a  vessel  containing  water  of  a  known  weight 
and  temperature.  The  water  is  stirred  rapidly  and  its  maximum  tem- 
perature taken.  Let  W  =  weight  of  the  water,  w  the  weight  of  the  ball, 
I  =  the  original  and  T  the  final  heat  of  the  water,  and  S  the  specific  heat  of 
the  metal;  then  the  temperature  of  fire  may  be  found  from  the  formula 


The  mean  specific  heat  of  platinum  between  32°  and  446°  F.  is  0.03333  or 
1/30  that  of  water,  and  it  increases  with  the  temperature  about  0.000305 
for  each  100°  F.  For  a  fuller  description,  by  J.  C.  Hoadley,  see  Trans. 


A.  S.  M.  E.,  vi,  702.    Compare  also  Henry  M.  Howe,  Trans.  A.  I.  M.  E.t 
"\\.  728. 
'or  accuracy  corrections  are  required  for  variations  in  the  specific  heat 


xviii.  728. 
F< 


554 


HEAT. 


of  ttie  water  and  of  the  metal  at  different  temperatures,  for  loss  of  heat  by 
radiation  from  the  metal  during  the  transfer  from  the  furnace  to  the  water, 
and  from  the  apparatus  during  the  heating  of  the  water;  also  for  the  heat- 
absorbing  capacity  of  the  vessel  containing  the  water. 

Fire-clay  or  fire-brick  may  be  used  instead  of  the  metal  ball. 

L,e  Chatelier's  Thermo-electric  Pyrometer.  —  For  a  very  full 
description,  see  paper  by  Joseph  Struthers,  School  of  Mines  Quarterly, 
vol.  xii,  1891;  also,  paper  read  by  Prof.  Roberts-  Austen  before  the  Iron 
and  Steel  Institute,  May  7,  1891. 

The  principle  upon  which  this  pyrometer  is  constructed  is  the  measure- 
ment of  a  current  of  electricity  produced  by  heating  a  couple  comp9sed  of 
two  wires,  one  platinum  and  the  other  platinum  with  10%  rhodium  — 
the  current  produced  being  measured  by  a  galvanometer. 

The  composition  of  the  gas  which  surrounds  the  couple  has  no  influence 
on  the  indications. 

When  temperatures  above  2500°  F.  are  to  be  studied,  the  wires  must 
have  an  isolating  support  and  must  be  of  good  length,  so  that  all  parts 
of  a  furnace  can  be  reached.  The  wires  are  supported  in  an  iron  tube  1/3 
inch  interior  diameter  and  held  in  place  by  a  cylinder  of  refractory  clay 
having  two  holes  bored  -through,  in  which  the  wires  are  placed.  The 
shortness  of  time  (five  seconds)  allows  the  temperature  to  be  taken  with- 
out deteriorating  the  tube. 

Tests  made  by  this  pyrometer  in  measuring  furnace  temperatures  under 
a  great  variety  of  conditions  show  that  the  readings  of  the  scale  unconnected 
are  always  within  45°  F.  of  the  correct  temperature,  and  in  the  majority 
of  industrial  measurements  this  is  sufficiently  accurate. 

Graduation  of  Le  Chatelier's  Pyrometer.  —  W.  C.  Roberts-  Austen 
in  his  Researches  on  the  Properties  of  Alloys,  Froc.  Inst.  M.  E.,  189 
says:  The  electromotive  force  produced  by  heating  the  thermo-  junction 
to  any  given  temperature  is  measured  by  the  movement  of  the  spot  01  light 
on  tne  scale  graduated  in  millimeters.  The  scale  is  calibrated  by  heating 
the  thermo-junction  to  temperatures  which  have  been  carefully  deter- 
mined by  the  aid  of  the  air-thermometer,  and  plotting  the  curve  from 
the  data  so  obtained.  Many  fusion  and  boiling-points  have  been  estab- 
lished by  concurrent  evidence  of  various  kinds,  and  are  now  generally 
accepted.  The  following  table  contains  certain  of  these: 


Deg.  F. 

Deg.  < 

•>» 

Deg.  F. 

Deg.  C 

212 
618 

100 
326 

^'Water  boils. 
Lead  melts. 

1733 
1859 

945 
1015 

Silver  melts. 
Potassium  sulphate 

676 
779 

358 
415 

Mercury  boils. 
Zinc  melts. 

1913 

1045 

melts. 
Gold  melts. 

838 
1157 

448 
625 

Sulphur  boils. 
Aluminum  melts. 

1929 
2732 

1054 
1500 

Copper  melts. 
Palladium  melts. 

1229 

665 

Selenium  boils. 

3227 

1775 

Platinum  melts. 

Chatelier  Vtates  lhat^by^eans^This"py"ometerhej  has  discovered  that 

"  .en 


The  Temperatures  Developed  in  Industrial  Furnaces.  — 

hatelier  states  that  by 
the  temperatures  whicn 


occur  in  melting  steel  and  in  other  industrial 
•      •    -      "     finds  the   melting 
•ray  cast  iron  1220° 

"Mild  steel  melts  at  1475°  (2687°  F.),  and  hard  steel  at  1410° 
(257GJ  F  )  The  furnace  for  hard  porcelain  at  the  end  of  the  baking  has  a 
heat  of  1370°  (2498°  F.).  The  heat  of  a  normal  incandescent  lamp  is 
1800°  (3272°  F.),  but  it  may  be  pushed  to  beyond  2100°  (3812°  F.). 

Prof  Roberts- Austen  (Recent  Advances  in  Pyrometry,  Trans.  A.I.M.E., 
Chicago  Meeting,  1893)  gives  an  excellent  description  of  modern  forms  of 
pyrometers.     The  following  are  some  of  his  temperature  determinations. 
TEN-TON  OPEN-HEARTH  FURNACE,  WOOLWICH  ARSENAL. 

Degrees     Degrees 
Centigrade.     Fahr. 
Temperature  of  steel,  0.3%  carbon,  pouring  into  ladle.  1645 

Steel,  0.3  %  carbon,  pouring  into  large  mold 1  ^»7b 

Reheating  furnace,  interior v 

Cupola  furnace,  No.  2  cast  iron,  pouring  into  ladle 

The  following  determinations  have  been  effected  by  M.  Le  Chatelier: 


PYBOMETKY.  555 

i 

BESSEMER  PROCESS.    SIX-TON  CONVERTER.  Deg.  O.  Deg  F,. 

A.  Bath  of  Slag 1580       2876 

B.  Metal  in  ladle , 1640       2984 

C.  Metal  in  ingot  mold 1580       2876 

D.  Ingot  in  reheating  furnace 1200       2192 

E.  Ingot  under  the  hammer 1080       1976 

OPEN-HEARTH  FURNACE  (Semi-mild  Steel). 

A.  Fuel  gas  near  gas  generator 720  1328 

B.  Fuel  gas  entering  into  bottom  of  regenerator  chamber     400  752 

C.  Fuel  gas  issuing  from  regenerator  chamber 1200  2192 

Air  issuing  from  regenerator  chamber 1000  1832 

Chimney  gases.     Furnace  in  perfect  condition 300  590 

End  of  the  melting  of  pig  charge 1420  2588 

Completion  of  conversion 1500  2732 

Molten  steel.     In  the  ladle — Commencement  of  casting.    1580  2876 

End  of  casting 1490  2714 

In  the  molds 1520  2768 

For  very  mild  (soft)  steel  the  temperatures  are  higher  by  50°  C. 
BLAST-FURNACE  (Gray-Bessemer  Pig). 

Opening  in  face  of  tuyere 1930       3506 

Molten  metal — Commencement  of  fusion 1400       2552 

End,  or  prior  to  tapping 1570       2858 

HOFFMAN  RED-BRICK  KILN 
Burning  temperatures 1100       2012 

R.  Moldenke  (The  Foundry,  Nov.,  1898)  determined  with  a  Le 
Chatelier  pyrometer  the  melting-point  of  42  samples  of  pig  iron  of 
different  grades.  The  range  was  from  2030°  F.  for  pig  containing 
3.98%  combined  carbon  to  2280  for  pig  containing  0.13  combined  car- 
bon and  3.43%  graphite.  The  results  of  the  whole  series  may  be  ex- 
pressed within  30°  F.  by  the  formula  Temp.  =  2300°  -  70  X  %  of 
combined  carbon. 

Hobson's  Hot-blast  Pyrometer  consists  of  a  brass  chamber  having 
three  hollow  arms  and  a  handle.  The  hot  blast  enters  one  of  the  arms 
and  induces  a  current  of  atmospheric  air  to  flow  into  the  second  arm. 
The  two  currents  mix  in  the  chamber  and  flow  out  through  the  third 
arm,  in  which  the  temperature  of  the  mixture  is  taken  by  a  mercury 
thermometer.  The  openings  in  the  arms  are  adjusted  so  that  the  pro- 
portion of  hot  blast  to  the  atmospheric  air  remains  the  same. 

The  Wiborgh  Air-pyrometer.  (E.  Trotz,  Trans.  A.I.M.E.,  1892.)— 
The  inventor  using  the  expansion-coefficient  of  air,  as  determined  by 
Gay-Lussac,  Dulon,  Rudberg,  and  Regnault,  bases  his  construction  on 
the  following  theory:  If  an  air- volume,  V,  inclosed  in  a  porcelain  globe 
and  connected  through  a  capillary  pipe  with  the  outside  air,  be  heated 
to  the  temperature  T  (which  is  to  be  determined)  and  thereupon  the 
connection  be  discontinued,  and  there  be  then  forced  into  the  globe 
containing  V  another  volume  of  air  V  of  known  temperature  t,  which 
was  previously  under  atmospheric  pressure  H ,  the  additional  pressure 
h,  due  to  the  addition  of  the  air- volume  V  to  the  air- volume  V,  can  be 
measured  by  a  manometer.  But  this  pressure  is  of  course  a  function 
of  the  temperature  T.  Before  the  introduction  of  V,  we  have  the  two 
separate  air-volumes,  V  at  the  temperature  T,  and  V  at  the  tempera- 
ture t,  both  under  the  atmospheric  pressure  H.  After  the  forcing  in 
of  V  into  the  globe,  we  have,  on  the  contrary,  only  the  volume  V  of 
the  temperature  T,  but  under  the  pressure  H  +  h. 

Seger  Cones.  (Stowe-Fuller  Co.,  Cleveland,  1914).  Seger  Cones 
were  developed  in  1886  in  Germany,  by  Dr.  Herman  A.  Seger.  They 
comprise  a  series  of  triangular  cones,  of  pyramidal  shape,  of  differing 
mineral  compositions,  each  one  of  which  requires  a  different  amount  of 
heat  work  to  soften  and  deform  it.  They  are  used  principally  in  the 
clay,  pottery,  and  allied  industries  to  determine  the  proper  heat  con- 
ditions of  kilns,  furnaces,  etc.  The  difference  in  softening  point 
between  any  two  adjoining  member  of  the  series,  is  kept  as  nearly 
equal  as  possible,  so  that  the  cones  form  a  sort  of  pyrometric  scale. 
The  softening  or  fusion  is  not  altogether  a  matter  of  temperature,  the 
element  of  time  entering  in  also.  A  longer  exposure  at  a  slightly  lower 
temperature  will  accomplish  the  same  amount  of  heat  work  in  clay- 
working  as  a  shorter  exposure  at  a  somewhat  higher  temperature,  pro- 


556 


HEAT. 


vided  it  is  always  above  the  critical  temperature  at  which  chemical 
reactions  take  place  in  the  clay.  Although  the  time  element  must  be 
considered,  a  melting  point  in  degrees  F.  has  been  assigned  to  each  cone 
number  for  convenience.  For  rapid  burning,  this  temperature  is 
fairly  accurate,  but  in  commercial  clay-burning,  the  cones  melt  at 
lower  temperatures  than  those  given  in  the  table.  In  extremely  long 
firings  the  difference  between  the  actual  and  assigned  temperatures 
may  be  as  much  as  100°  or  150°  C.  (212°  to  297°  F.) 

Dr.  Seger's  original  series  consisted  of  twenty  different  mixtures, 
and  covered  a  relatively  narrow  range  of  temperatures.  Several  other 
series  have  since  been  devised,  as  follows:  Hecht  series,  used  by 
china  and  glass  decorators,  consisting  of  fusible  lead-soda  borate  glass 
and  kaolin,  the  glass  alone  making  the  softest  cone,  successive  addi- 
tions of  kaolin  raising  the  fusing  point.  The  Cremer  series,  used  for 
red  burning  clays  and  for  soft  glazes,  sewer  pipe,  drain  tiles,  roof  tiles, 
etc.,  consisting  of  a  lime-soda  borate  glass,  oxide  of  iron,  feldspar, 
carbonate  of  lime,  potters  flint  and  kaolin,  it  begins  witja  a  large 
amount  of  glass  for  the  softest  cone,  and  decreasing  to  almost  none  at 
the  upper  end.  The  Seger  series,  used  for  harder  red  burning  wares  of 
vitrified  variety,  and  for  all  buff  burning  and  white  burning  clay  wares 
consisting  of  potters  flint,  feldspar,  carbonate  of  lime  and  feldspar, 
oxide  of  iron  appearing  in  the  three  lowest  temperature  cones;  no  glass 
is  used  and  the  proportion  of  kaolin  and  flint  increases  with  the  fusion 
temperature.  High  temperature  series,  used  for  testing  refractory 
materials  only,  consisting  except  in  the  two  lowest  numbers  of  kaolin 
potters  flint,  and  oxide  of  alumina;  the  highest  cone  consists  of  pure 
oxide  of  alumina.  No  temperatures  can  be  assigned  to  this  series, 
although  1850°  C.  (3362°  F.)  has  been  set  as  the  melting  point  of 
No.  36.  The  table  gives  the  approximate  fusion  points  of  the  various 
cones. 

Fusion  Points  of  Seger  Cones. 


Symbol 
or 
Cone 
No. 

Melting  Point 

Sym- 
bol 
or 
Cone 

No. 

Melting  Point 

Sym- 
bol 
or 
Cone 

No. 

Melting  Point 

Deg.C 

Deg.F 

Deg.C 

Deg.F 

Deg.C 

Deg.F 

HECHT 

SERIES 

04 

1070 

1958 

13 

1390 

2534 

022 

590 

1094 

03 

1090 

1994 

14 

1410 

2570 

021 

620 

1148 

02 

1110 

2030 

15 

1430 

2606 

020 

650 

1202 

01 

1130 

2066 

16 

1450 

2642 

019 

680 

1256 

SEGER 

17 

1470 

2678 

SERIES 

018 

710 

1310 

1 

1150 

'2102 

18 

1490 

2714 

017 

740 

1364 

2 

1170 

2138 

19 

1510 

2759 

016 

770 

1418 

3 

1190 

2174 

20 

1530 

2786 

HIGH 

015 

800 

1472 

4 

1210 

2210 

TEMP. 

012V2 

875 

1607 

5 

1230 

2246 

SERIES 

CREMER 

SERIES 

6 

1250 

2282 

26 

Lowest  Grade  for  No.  2  Refractories. 

010 

950 

1742 

7 

1270 

2318 

30 

Lowest  Grade  for  No.  1  Refractories. 

09 

970 

1778 

8 

1290 

2354 

32 

Good  Qual.  No.  1  Firebrick. 

08 
07 
06 

990 
1010 
1030 

1814 
1850 
1886 

9 
10 
11 

1310 
1330 
1350 

2390 
2476 
2462 

34 
36 

38 

Excellent  Qual.  No.  1  Firebrick. 
Melting  point  pure  Kaolin. 
Melting  point  good  qual.  Bauxite. 

05 

1050 

1922 

12 

1370 

2498 

42 

Melting  point  pure  Alumina. 

The  German  cones  are  manufactured  by  the  German  Government 
at  the  Royal  Porcelain  Factory,  Charlottenburg,  and  can  be  obtained 
in  the  United  States  through  Eimer  and  Amend,  New  York,  and  other 
chemical  supply  houses.  In  1896,  Prof.  Edw.  Orton,  Jr.,  of  the  Ohio 
State  University,  Columbus,  Ohio,  began  their  manufacture  in  Amer- 
ica. The  American  cones  agree  with  the  German  cones  in  all  re- 
pects,  and  have  come  into  general  use  in  America.  They  are  not  sold 
through  dealers,  but  must  be  obtained  direct  from  the  maker. 

Mesure  and  NouePs  Pyrometric  Telescope.  (H.  M.  Howe,  E.  and 
M.  J.,  June  7, 1890) — Mesure  and  Nouel's  telescope  gives  an  immediate 


PYROMETRY.  657 

determination  of  the  temperature  of  incandescent  bodies,  and  is  there- 
fore better  adapted  to  cases  where  a  great  number  of  observations  are 
to  be  made,  and  at  short  intervals,  than  Seger's.  The  little  telescope, 
carried  in  the  pocket  or  hung  from  the  neck,  can  be  used  by  foreman 
or  heater  at  any  moment. 

It  is  based  on  the  fact  that  a  plate  of  quartz,  cut  at  right  angles  to  the 
axis,  rotates  the  plane  of  polarization  of  polarized  light  to  a  degree  nearly 
inversely  proportional  to  the  square  of  the  length  of  the  waves;  and, 
further,  on  the  fact  that  while  a  body  at  dull  redness  merely  emits  red 
light,  as  the  temperature  rises,  the  orange,  yellow,  green,  and  blue  waves 
successively  appear. 

If,  now,  such. a  plate  of  quartz  is  placed  between  two  Nicol  prisms  at 
right  angles,  "a  ray  of  monochromatic  light  which  passes  the  first,  or 
polarizer,  and  is  watched  through  the  second,  or  analyzer,  is  not  extin- 
guished as  it  was  before  interposing  the  quartz.  Part  of  the  light  passes 
the  analyzer,  and,  to  again  extinguish  it,  we  must  turn  one  of  the  Nicols  a 
certain  angle,"  depending  on  the  length  of  the  waves  of  light,  and  hence  on 
the  temperature  of  the  incandescent  object  which  emits  this  light.  Hence 
the  angle  through  which  we  must  turn  the  analyzer  to  extinguish  the  light 
is  a  measure  of  the  temperature  of  the  object  observed. 

The  Uehling  and  Steinbart  Pyrometer.  (For  illustrated  descrip- 
tion see  Engineering,  Aug.  24,  1894.)  —  The  action  of  the  pyrometer  is 
based  on  a  principle  which  involves  the  law  of  the  flow  of  gas  through 
minute  apertures  in  the  following  manner:  If  a  closed  tube  or  chamber  be 
supplied  with  a  minute  inlet  and  a  minute  outlet  aperture,  and  air  be 
caused  by  a  constant  suction  to  flow  in  through  one  and  out  through  the 
other  of  these  apertures,  the  tension  in  the  chamber  between  the  apelrtures 
will  vary  with  the  difference  of  temperature  between  the  inflowing  and 
outflowing  air.  If  the  inflowing  air  be  made  to  vary  with  the  tem- 
perature to  be  measured,  and  the  outflowing  air  be  kept  at  a  certain  con- 
stant temperature,  then  the  tension  in  the  space  or  chamber  between  the 
two  apertures  will  be  an  exact  measure  of  the  temperature  of  the  inflow- 
ing air,  and  hence  of  the  temperature  to  be  measured. 

In  operation  it  is  necessary  that  the  air  be  sucked  into  it  through  the 
first  minute  aperture  at  the  temperature  to  be  measured,  through  the 
second  aperture  at  a  lower  but  constant  temperature,  and  that  the  suc- 
tion be  of  a  constant  tension.  The  first  aperture  is  therefore  located 
in  the  end  of  a  platinum  tube  in  the  bulb  of  a  porcelain  tube  over  which 
the  hot  blast  sweeps,  or  inserted  into  the  pipe  or  chamber  containing 
the  gas  whose  temperature  is  to  be  ascertained. 

The  second  aperture  is  located  in  a  coupling,  surrounded  by  boiling 
water,  and  the  suction  is  obtained  by  an  aspirator  and  regulated  by  a 
column  of  water  of  constant  height. 

The  tension  in  the  chamber  between  the  apertures  is  indicated  by  a 
manometer. 

The  Air-thermometer.  (Prof.  R.  C.  Carpenter,  Eng'g  News,  Jan.  5, 
1893.)  —  Air  is  a  perfect  thermometric  substance,  and  if  a  given  mass  of 
air  be  considered,  the  product  of  its  pressure  and  volume  divided  by  its 
absolute  temperature  is  in  every  case  constant.  If  the  volume  of  air 
remain  constant,  the  temperature  will  vary  with  the  pressure;  if  the 
pressure  remain  constant,  the  temperature  will  vary  with  the  volume.  As 
the  former  condition  is  more  easily  attained,  air-thermometers  are  usually 
constructed  of  constant  volume,  in  which  case  the  absolute  temperature 
will  vary  with  the  pressure. 

If  we  denote  pressures  by  p  and  p',  and  the  corresponding  absolute 
temperatures  by  T  and  T't  we  should  have 

p  :p'  ::  T  :  rand  T'  =  pf  -• 

The  absolute  temperature  T  is  to  be  considered  in  every  case  460  higher 
than  the  thermometer-reading  expressed  in  Fahrenheit  degrees.  From 
the  form  of  the  above  equation,  if  the  pressure  p  corresponding  to  a 
known  absolute  temperature  T  be  known,  T'  can  be  found.  The  quotient 
T/p  is  a  constant  which  may  be  used  in  all  determinations  with  the 
instrument.  The  pressure  on  the  instrument  can  be  expressed  in  inches 
of  mercury,  and  is  evidently  the  atmospheric  pressure  b  as  shown  by  a 
barometer,  plus  or  minus  an  additional  amount  h  shown  by  a  manometer 
attached  to  the  air-thermometer.  That  is,  in  general,  p  =  b  ±  h. 


558  HEAT. 


casr  -0+  ij*  SS***  ihe*<>™  <*  melting  ice,  in  which 

case  1  =  460  +  32  =  492°  F.  This  temperature  can~be  produced  bv  sur 
rounding  the  bulb  in  melting  ice  and  leaving  it  several  [  mfnutes^so  that  the 

\C^n  tahtUre-°f-thefC?i?f\nfd  air  sha11  acquire  that  of  the  surrounding  ice 
TV  hen  the  air  is  at  that  temperature,  note  the  reading  of  the  attached 
manometer  ft  and  that  of  a  barometer;  the  sum  will  be  the  value  of  p 
corresponding  to  the  absolute  temperature  of  492°  F  The  constant 

=  p'  °^  °btained'  can  be  «^M 


o*?1?11  TemPe?*atures  judged  by  Color.  —  The  temperature  of  a  body 
pSrilfe  ?nP%CSimateJy  Ju<J,sed  by  the  experienced  eye  unaided.  M. 
Pouillet  in  1836  constructed  a  table,  which  has  been  generally  quoted  in 
the  text-books,  giving  the  colors  and  their  corresponding  temperature, 
Whi£  H'I^W  r£Pla;ced  bv  the  tables  of  H.  M.  Howe  and  ofMaunse 
below  y  (7>ans-  A-  s-  M-  E-  18").  which  are  given 

Howe.                °C.                 °F.                White  and  Taylor.       °C.  °  F. 
Lowest  red  vis-                                           Dark    blood-red,    black- 

ible  in  dark  .  .        470                    878              red  990 
Lowest  red  vis-                                             Dark  red,'  biood-Ved,'  low 

ible    in   day-                                                 rej                                        556  j050 

n%ht-  ........        475                  887           Dark  cherry-red:'.:          '.     635  1175 

£u    r£d  ........  550,!£625     1022to1157  Medium  cherry-  red.  ..  1250 

Full  cherry....         700                 1292           Cherry,  full  red  ..........     746  1375 

feJSi  *  r.®d  ......        850  1A/        ^  1562           Light  cherry,  light  red*.      843  1550 

Full  yellow  .....  950  to  1000   1742  to  1832  Orange,  free  scalingheat     899  1650 

Light  yellow...        050                1922           Light  orange  .....    ......     941  1725 

Whlte  .........       1150                2102           Yellow.....   .                          996  1825 

Light  yellow  .............   1079  1975 

White  ...................   1205  2200 

*  Heat  at  which  scale  forms  and  adheres  on  iron  and  steel,  i.e.,  does 
not  fall  away  from  the  piece  when  allowed  to  cool  in  air. 

Skilled  observers  may  vary  100°  F.  or  more  in  their  estimation  of 
relatively  low  temperatures  by  color,  and  beyond  2200°  F.  it  is  practically 
impossible  to  make  estimations  with  any  certainty  whatever.  (Bulletin 
No.  2,  Bureau  of  Standards,  1905.) 

In  confirmation  of  the  above  paragraph  we  have  the  following,  in  a 
booklet  published  by  the  Halcomb  Steel  Co.,  1908. 
°C.     °F.  Colors.  °C.     °F.  Colors. 

400      752  Red,  visible  in  the  dark.  1000    1832    Bright  cherry-red. 

474      885   Red,  visible  in  the  twilight.         1100    2012    Orange-red. 

525      975   Red,  visible  in  the  day-         1200    2192    Orange-yellow. 
light.  1300    2372    Yellow-white. 

581     1077   Red,   visible  in   the  sun-         1400    2552    White  welding  heat. 
light.  1500    2732    Brilliant  white. 

700    1292   Dark  red.  1600    2912    Dazzling  white  (bluish 

800     1472   Dull  cherry-red.  white). 

900    1652    Cherry-red. 

Different  substances  heated  to  the  same  temperature  give  out  the 
same  color  tints.  Objects  which  emit  the  same  tint  and  intensity  of  light 
cannot  be  distinguished  from  each  other,  no  matter  how  different  their 
texture,  surface,  or  shape  may  be.  When  the  temperature  at  all  parts  of 
a  furnace  at  a  low  yellow  heat  is  the  same,  different  objects  inside  the 
furnace  (firebrick,  sand,  platinum,  iron)  become  absolutely  invisible. 
(H.  M.  Howe.) 

A  bright  bar  of  iron,  slowly  heated  in  contact  with  air,  assumes  the  fol- 
lowing tints  at  annexed  temperatures  (Claudel): 


Cent.  Fahr. 

Yellow  at 225  437 

Orange  at 243  473 

Red  at 265  509 

Violet  at 277  531 


Cent.  Fahr. 

Indigo  at 288  5  30 

Blue  at 293  559 

Green  at 332  630 

"Oxide-gray"...  400  762 


The  Halcomb  Steel  Co.  (1908)  gives  the  following  heats  and  temper 
colors  of  steel: 


MELTING    POINTS   OF   METALS.  559 

Cent.  Fahr.  Colors.  Cent.Fahr.  Colors. 

221.1  430    Very  pale  yellow.  265.6     510     Spotted  red-brown. 

226.7  440    Light  yellow.  271.1     520    Brown-purple. 

232.2  450    Pale  straw-yellow.  276.7     530     Light  purple. 

237.8  460    Straw-yellow.  282.2     540     Full  purple. 

243.3  470    Deep  straw-yellow.  287.8     550     Dark  purple. 

248.9  480    Dark  yellow.  293.3     560     Full  blue. 

254.4  490    Yellow-brown.  298.9     570    Dark  blue. 
260.0    500    Brown-yellow.                       315.6    600    Very  dark  blue. 

BOILING-POINT  AT  ATMOSPHERIC  PRESSURE. 

14.7  Ib.  per  square  inch. 

Ether,  sulphuric 100°  F.     Saturated  brine 226°  F. 

Carbon  bisulphide 118  Nitric  acid 248 

Chloroform 140  Oil  of  turpentine 315 

Bromine 145  Aniline 363 

Aqua  ammonia,  sp.gr.  0.95.  146  Naphthaline 428 

Wood  spirit 150  Phosphorus 554 

Alcohol 173  Sulphur 800 

Benzine 176  Sulphuric  acid 590 

Water 212  Linseed  oil 597 

Average  sea-water 213.2        Mercury 676 

The  boiling-points  of  liquids  increase  as  the  pressure  increases. 

3IELTING-POINTS  OF   VARIOUS  SUBSTANCES. 

The  following  figures  are  given  by  Clark  (on  the  authority  of  Pouillett 
Claudel,  and  Wilson),  except  those  marked  *,  which  are  given  by  Prof. 
Roberts- Austen,  and  those  marked  t,  which  are  given  by  Dr.  J.  A.  Marker. 
These  latter  are  probably  the  most  reliable  figures. 

Sulphurous  acid -  148°  F.       Cadmium 442°  F. 

Carbonic  acid -  108  Bismuth 504  to  507 

Mercury -  39,  -     38f  Lead 618*,  620f 

Bromine +      9.5  Zinc 779*,  786f 

Turpentine 14  Antimony 1150,  1169J 

Hyponitric  acid .  .       16  Aluminum 1157*,  1214f 

Ice 32  Magnesium 1200 

Nitro-glycerine 45  NaCl,  common  salt 1472f 

Tallow 92  -          Calcium Full  red  heat. 

Phosphorus 112  Bronze 1692 

Acetic  acid 113  Silver 17b3*,  1751" 

Stearine 109  to  120  Potassium  sulphate..   1859*,  1958" 

Spermaceti 120  Gold 1913*,  1947" 

Margaric  acid  ....      131  to  140  Copper 1929*,  1943" 

Potassium 136  to  144  Nickel 2600" 

Wax 142  to  154  Cast  iron,  white 1922,2075" 

Stearic  acid 158  "          gray  2012  to  2786, 2228* 

Sodium 194  to  208  Steel 2372  to  2532* 

Iodine.. 225  "     hard  .  . .     2570*;  mild,  2687 

Sulphur 239  Wrought  iron  2732  to  2912,  2737* 

Alloy,  1 1/2  tin,  1  lead    334,  367f  Palladium 2732* 

Tin 446,  449f  Platinum 3227*,  3110t 

Cobalt  and  manganese,  fusible  in  highest  heat  of  a  forge.  Tungsten 
and  chromium,  not  fusible  in  forge,  but  soften  and  agglomerate.  Plati- 
num and  iridium,  fusible  only  before  the  oxyhydrogen  blowpipe,  or  in  an 
electrical  furnace.  For  melting-point  of  fusible  alloys  see  Alloys.  For 
boiling  and  freezing  points  of  air  and  other  gases  see  p.  606. 

Melting  Points  of  Rare  Metals. — H.  Von  Wartenberg  has  deter- 
mined the  melting  points  of  some  rare  metals.  The  temperature  was 
measured  by  a  Wanner  pyrometer.  The  following  melting  points  were 
thus  obtained: 

Vanadium 1710°  C.  =  3110°  F. 

Rhodium 1970°  C.  =  3578°  F. 

Iridium 2360°  C.  =  4280°  F. 

Molybdenum over  2550°  C.  =  4622°  F. 

Tungsten 2900°  C.  =  5252°  F. 

The  metals  were  as  pure  as  possible.     It  is.  stated  that  the  vanadium 


560 


HEAT. 


used  was  of  97%  purity.     The  results  were  published  in  a  German 
periodical.  —  Brass  World,  June,  1910. 

QUANTITATIVE  MEASUREMENT  OF  HEAT. 

Unit  of  Heat.—  The  British  thermal  unit,  or  heat  unit  (B.T.U.),  is  the 
quantity  of  heat  required  to  raise  the  temperature  of  1  Ib.  of  pure  water 
from  62°  to  63°  F.  (Peabody>,  or  i/igo  of  the  heat  required  to  raise  the 
temperature  of  1  Ib.  of  water  from  32°  to  212°  F.  (Marks  and  Davis, 
see  Steam,  p.  867). 

The  French  thermal  unit,  or  calorie,  is  the  quantity  of  heat  required 
to  raise  the  temperature  of  1  kilogram  of  pure  water  from  15°  to  16°  C. 

1  French  calorie  =  3.968  British  thermal  units;  1  B.T.U.  =  0.252 
calorie.  The  "pound  calorie"  is  sometimes  used  by  English  writers; 
it  is  the  quantity  of  heat  required  to  raise  the  temperature  of  1  Ib.  of 
water  1°  C.  1  Ib.  calorie  =  9/5  B.T.U.  =  0.4536  calorie.  The  heat  of 
combustion  of  carbon  to  CO2  is  said  to  be  8080  calories.  This  figure  is 
used  either  for  French  calories  or  for  pound  calories,  as  it  is  the  number 
of  pounds  of  water  that  can  be  raised  1°  C.  by  the  complete  combustion 
of  1  Ib.  of  carbon,  or  the  number  of  kilograms  of  water  that  can  be 
raised  1°  C.  by  the  combustion  of  1  kilo,  of  carbon;  assuming  in  each 
case  that  all  the  heat  generated  is  transferred  to  the  water. 

The  Mechanical  Equivalent  of  Heat  is  the  number  of  foot-pounds 
of  mechanical  energy  equivalent  to  one  British  thermal  unit,  heat  and 
mechanical  energy  being  mutually  convertible.  Joule's  experiments, 
1843-50,  gave  the  figure  772,  which  is  known  as  Joule's  equivalent. 
More  recent  experiments  by  Prof.  Rowland  (1880)  and  others  give  higher 
figures;  778  is  generally  accepted,  but  777.6  is  probably  more  nearly 
correct.  (Goodenough's  "  Properties  of  Steam  and  Ammonia,"  1915.) 

1  heat-unit  is  equivalent  to  778  ft.-lbs.  of  energy.  1  ft.-lb.  =  1/778  = 
0.0012852  heat-unit.  1  horse-power  =  33,000  ft.-lbs.  per  minute  = 
2545  heat-units  per  hour  =  42.416  +  per  minute  =  0.70694  per  second. 
1  Ib.  carbon  burned  to  CO2  =  14,600  heat-units.  1  Ib.  C  per  H.P.  per 
hour  =  2545  -=-  14,600  =  17.43%  efficiency. 

Heat  of  Combustion  of  Various  Substances  in  Oxygen. 


Heat-units. 

Authority. 

Cent. 

Fahr. 

Hydrogen  to  liquid  water  at  0°  C.  . 

to  steam  at  100°  C  
Carbon  (wood  charcoal)  to  car- 
bonic acid,  CO2J  ordinary  tem- 
peratures .   .                 

I  34,462 
\  33,808 
(  34,342 
28,732 
(  8,080 
\   7,900 
(   8,137 
7,859 
7,861 
7,901 
2,473 
(  2,403 
i   2,431 
(  2,385 
5,607 
(13,120 
\  13,  108 
(  13,063 
(11,858 
h  1,942 
(11,957 
(  10,102 
1    9,915 
2,250 

62,032 
60,854 
61,816 
51,717 
14,544 
14,220 
14,647 
14,146 
14,150 
14,222 
4,451 
4,325 
4,376 
4,293 
10,093 
23,616 
23,594 
23,513 
21,344 
21,496 
21,523 
18,184 
17.847 
4,050 

Favre  and  Silbermann. 
Andrews. 
Thomsen. 
Favre  and  Silbermann. 

Andrews. 
Berthelot. 

Fay  re  and  Silbermann. 

Andrews. 
Thomsen. 
Favre  and  Silbermann. 
Thomsen. 
Andrews. 
Favre  and  Silbermana. 

Andrews. 
Thomsen. 

Favre  and  Silbermann. 
N.  W.  Lord. 

Carbon,  diamond  to  CO2  

black  diamond  to  COa  
graphite  to  CO2  . 

Carbon  to  carbonic  oxide,  CO  

Carbonic  oxide  to  CO2  per  unit  of 
CO  . 

CO  to  CO2  per  unit  of  C=21/s  x  2403 

Marsh-gas,Methane,  CH4,to  water 
and  CO2  

Olefiant  gas,  Ethylene,  C2H4,  to 
water  and  CO2  

Benzole  gas,CeH6,to  water  and  CO2 
Sulphur  to  sulphur  dioxide,  SO2.  .  . 

HEAT  OF  COMBUSTION.  561 

In  calculations  of  the  heating  value  of  mixed  fuels  the  value  for  carbon 
Is  commonly  taken  at  14,600  B.T.U.,  and  that  of  hydrogen  at  62,000. 
Taking  the  heating  value  of  C  burned  to  CO2  at  14,600,  and  that  of  C  to 
CO  at  4450,  the  difference,  10,150  B.T.U.,  is  the  heat  lost  by  the  imperfect 
combustion  of  each  Ib.  of  C  burned  to  CO  instead  of  to  CO2.  If  the  CO 
formed  by  this  imperfect  combustion  is  afterwards  burned  to  CO2  the  lost 
heat  is  regained. 

In  burning  1  pound  of  hydrogen  with  8  pounds  of  oxygen  to  form  9 
pounds  of  water,  the  units  of  heat  evolved  are  62,000;  but  if  the  resulting 
product  is  not  cooled  to  the  initial  temperature  of  the  gases,  part  of  the 
heat  is  rendered  latent  in  the  steam.  The  total  heat  of  1  Ib.  of  steam  at 
212°  F.  is  1150.0  heat-units  above  that  of  water  at  32°,  and  9  X  1150  — 
10,350  heat-units,  which  deducted  from  62,000  gives  51,650  as  the  heat 
evolved  by  the  combustion  of  1  Ib.  of  hydrogen  and  8  Ibs.  of  oxygen  at 
32°  F.  to  form  steam  at  212°  F. 

Some  writers  subtract  from  the  total  heating  value  of  hydrogen  only 
the  latent  heat  of  the  9  Ibs.  of  steam,  or  9  X  970.4  =  8734  B.T.U.,  leaving 
as  the  "  low  "  heating  value  53,266  B.T.U. 

The  use  of  heating  values  of  hydrogen  "burned  to  steam,"  in  compu- 
tations relating  to  combustion  of  fuel,  is  inconvenient,  since  it  necessi- 
tates a  statement  of  the  conditions  upon  which  the  figures  are  based ;  and 
It  is,  moreover,  misleading,  if  not  inaccurate,  since  hydrogen  in  fuel  is  not 
often  burned  in  pure  oxygen,  but  in  air;  the  temperature  of  the  gases 
before  burning  is  not  often  the  assumed  standard  temperature,  and  the 
Droducts  of  combustion  are  not  often  discharged  at  212°.  In  steam- 
boiler  practice  the  chimney  gases  are  usually  discharged  above  300°;  but 
if  economizers  are  used,  and  the  water  supplied  to  them  is  cold,  the  gases 
may  be  cooled  to  below  212°,  in  which  case  the  steam  in  the  gases  is  con- 
densed and  its  latent  heat  of  evaporation  is  utilized.  If  there  is  any  need 
at  all  of  using  figures  of  the  "available"  heating  value  of  hydrogen,  or  its 
heating  value  when  "burned  to  steam,"  the  fact  that  the  gas  is  burned  in 
air  and  not  in  pure  oxygen  should  be  taken  into  consideration.  The 
resulting  figures  will  then  be  much  lower  than  those  above  given,  and  they 
will  vary  with  different  conditions.  (Kent,  '*  Steam  Boiler  Economy," 
p.  23.) 

Suppose  that  1  Ib.  of  H  is  burned  in  twice  the  quantity  of  air  required 
for  complete  combustion,  or  2  X  (8  O  +  26.56  N)  =  69.12  Ibs.  air 
supplied  at  62°  F.,  and  that  the  products  of  combustion  escape  at  562°  F. 
The  heat  lost  in  the  products  of  combustion  will  be 

Q  Ibs.  water  heated  from  62°  to  212° 1352  B.T.U. 

Latent  heat  of  9  Ibs.  H2O  at  212°,  9  X  969.7 8727 

Superheated  steam,  9 Ibs.  X  (562°  -  212°)  X  0.48  (sp.  ht.)      1512 

Nitrogen,  26.56  X  (562°  -  62°)  X  0.2438 3238 

Excess  air,  34.56  X  (562°  -  62°)  X  0.2375 4104 

Total 18,933      " 

which  subtracted  from  62,000  gives  43,067  B.T.U.  as  the  net  available 
heating  value  under  the  conditions  named. 

Heating  Value  of  Compound  or  Mixed  Fuels.  —  The  heating  value 
of  a  solid  compound  or  mixed  fuel  is  the  sum  of  its  elementary  constituents, 
and  is  calculated  as  follows  by  Dulong's  formula: 

B.T.U.  =  i[  14,600  C  +  62,000  (H  -  Q  +  4500  SJ  ; 

in  which  C,  H,  O,  and  S  are  respectively  the  percentages  of  the  several 
elements.  The  term  H  -  1/8  O  is  called  the  "available"  or  "disposable" 
hydrogen,  or  that  which  is  not  combined  with  oxygen  in  the  fuel.  For 
all  the  common  varieties  of  coal,  cannel  coal  and  some  lignites  excepted, 
the  formula  is  accurate  within  the  limits  of  error  of  chemical  analyses  and 
calorimetric  determinations. 

Heat  Absorbed  by  Decomposition.  —  By  the  decomposition  of  a 
chemical  compound  as  much  heat  is  absorbed  or  rendered  latent  as  was 
evolved  when  the  compound  was  formed.  If  1  Ib.  of  carbon  is  burned  to 
COz,  generating  14,600  B.T.U.,  and  the  CO2  thus  formed  is  immediately 
reduced  to  CO  in  the  presence  of  glowing  carbon,  by  the  reaction  CO2  4- 
C  =  2  CO.  the  result  is  the  same  as  if  the  2  Ibs.  C  had  been  purned  directly 
to  2  CO,  generating  2X4450=8900  B.T.U.  The  2  Ibs.  C  burned  to  CO3 


562 


HEAT. 


would  generate  2  X  14,600  =  29,200  B.T.U.,  the  difference,  29  200  - 
8900  =  20,300  B.T.U.,  being  absorbed  or  rendered  latent  in  the  2  CO  'or 
10,150  B.T.U.  for  each  pound  of  carbon. 

In  like  manner  if  9  Ibs.  of  water  be  injected  into  a  large  bed  of  glowing 
coal,  it  will  be  decomposed  into  1  Ib.  H  and  8  Ibs.  O.  The  decomposition 
will  absorb  62,000  B.T.U.,  cooling  the  bed  of  coal  this  amount,  and  the 
same  quantity  of  heat  will  again  be  evolved  if  the  H  is  subsequently 
burned  with  a  fresh  supply  of  O.  The  8  Ibs.  of  O  will  combine  with  6  Ibs. 
C,  forming  14  Ibs.  CO  (since  CO  is  composed  of  12  parts  C  to  16  parts  O) 
generating  6  X  4450  =  26,700  B.T.U.  ,  and  6  X  10,150  =  60,900  B.T.U. 
will  be  latent  in  this  14  Ibs.  CO,  to  be  evolved  later  if  it  is  burned  to  CO2 
with  an  additional  supply  of  8  Ibs.  O. 

SPECIFIC   HEAT. 

Thermal  Capacity.  —  The  thermal  capacity  of  a  body  between  two 
temperatures  To  and  T\  is  the  quantity  of  heat  required  to  raise  the  tem- 
perature from  To  to  Ti.  The  ratio  of  the  heat  required  to  raise  the  temper- 
ature of  a  certain  weight  of  a  given  substance  one  degree  to  that  required 
to  raise  the  temperature  of  the  same  weight  of  water  from  62°  to  63°  F. 
is  commonly  called  the  specific  heat  of  the  substance.  Some  writers 
object  to  the  term  as  being  an  inaccurate  use  of  the  words  "  specific  " 
and  "  heat."  A  more  correct  name  would  be  "  coefficient  of  thermal 
capacity." 

Determination  of  Specific  Heat.  —  Method  by  Mixture.  —  The  body 
whose  specific  heat  is  to  be  determined  is  raised  to  a  known  temperature, 
a,nd  is  then  immersed  in  a  mass  of  liquid  of  which  the  weight,  specific 
heat,  and  temperature  are  known.  When  both  the  body  and  the  liquid 
have  attained  the  same  temperature,  this  is  carefully  ascertained. 

Now  the  quantity  of  heat  lost  by  the  body  is  the  same  as  the  quantity  of 
heat  absorbed  by  the  liquid. 

Let  c,  w,  and  t  be  the  specific  heat,  weight,  and  temperature  of  the  hot 
body,  and  c',  w',  and  tf  of  the  liquid.  Let  T  be  the  temperature  the  mix- 
ture assumes. 

Then,  by  the  definition  of  specific  heat,  c  X  w  X  (t  —  T)  =  heat-units 
lost  by  the  hot  body,  and  cf  X  w/  X  (T  —  t')  =  heat-units  gained  by  the 
cold  liquid.  If  there  is  no  heat  lost  by  radiation  or  conduction,  these 
must  be  equal,  and 


cw  (t- 


c'w*  (T-n  or    c 


Electrical  Method.  This  method  is  believed  to  be  more  accurate  in 
many  cases  than  the  method  by  mixture.  It  consists  in  measuring  the 
quantity  of  current  in  watts  required  to  heat  a  unit  weight  of  a  substance 
One  degree  in  one  minute,  and  translating  ,the  result  into  heat-units. 
i  Watt  =0.0569  B.T.U.  per  minute. 

Specific  Heats  of  Various  Substances. 

The  specific  heats  of  substances,  as  given  by  different  authorities  show 
considerable  lack  of  agreement,  especially  in  the  case  of  gases. 

The  following  tables  give  the  mean  specific  heats  of  the  substances 
named  according  to  Regnault.  (From  Rontgen's  Thermodynamics,  p. 
134.)  These  specific  heats  are  average  values,  taken  at  temperatures 
which  usually  come  under  observation  in  technical  application.  The 
actual  specific  heats  of  all  substances,  in  the  solid  or  liquid  state,  increase 
slowly  as  the  body  expands  or  as  the  temperature  rises.  It  is  probable 
that  the  specific  heat  of  a  body  when  liquid  is  greater  than  when  solid. 
For  many  bodies  this  has  been  verified  by  experiment. 


SOLIDS. 


Antimony 0 . 0508 

Copper 0 . 0951 

Gold. 0.0324 

Wrought  iron 0. 1138 

Glass 0.1937 

Cast  iron 0. 1298 

Lead 0.0314 

Platinum 0 . 0324 

Silver... 0,0570 

Hn 0.0582 


Steel  (soft) 0.1165 

Steel  (hard) 0.1175 

Zinc 0 . 0956 

Brass 0 . 0939 

Ice : 0.5040 

Sulphur 0.2026 

Charcoal 0 .  2410 

Alumina 0. 1970 

Phosphorus 0. 1887 


SPECIFIC  HEAT. 


563 


Water 1.0000 

Lead  (melted) 0.0402 

Sulphur    "      0.2340 

Bismuth  " 0 . 0308 

Tin  "      0.0637 

Sulphuric  acid 0.3350 


LIQUIDS. 


Mercury 0 . 0333 

Alcohol  (absolute) 0 . 7000 

Fusel  oil 0.5640 

Benzine 0 . 4500 

Ether 0.5034 


GASES. 
Constant  Pressure. 

Air 0.23751 

Oxygen 0.21751 

Hydrogen 3 . 40900 

Nitrogen 0. 24380 

Superheated  steam* 0. 4805 

Carbonic  acid 0 . 217 

Olefiant  gas  C2H4  (ethylene). ,    '. . .   0.404 

Carbonic  oxide. 0 . 2479 

Ammonia ".....   0 . 508 

Ether 0.4797 

Alcohol * 0.4534 

Acetic  acid 0. 4125 

Chloroform 0. 1567 

In  addition  to  the  above,  the  following  are  given  by  other  authorities. 
(Selected  from  various  sources.) 

METALS. 

Platinum,  32°  to  446°  F.. . .   0.0333 
(increased  .000305  for  each  100°  F.) 

Cadmium 0 . 0567 

Brass , 0 . 0939 

Copper,  32°  to  212°  F 0.094 

32°  to  572°  F 0.1013 

Zinc,       32°  to  21 2°  F 0.0927 

32°  to  572°  F 0.1015 

Nickel 0.1086 

Aluminum,  0°  F.  to  melting- 
point  (A.  E.  Hunt) 0..2185 

Dr.-Ing.  P.  Oberhoffer,  in  Zeit.  des  Vereines  Deutscher  Ingenieure  (Eng. 
Digest,  Sept.,  1908),  describes  some  experiments  on  the  specific  heat  of 
nearly  pure  iron.     The  following  mean  specific  heats  were  obtained: 
Temp.  F.         500  600  800  1000  1200          1300 

Sp.  Ht.          0.1228        0.1266        0.1324        0.1388        0.1462       0.1601 
Temp.  F.        1500  1800  2100  2400  2700 

Sp.  Ht.  0.1698        0.1682        0.1667        0.1662        0.1666 

The  specific  heat  increases  steadily  between  500  and  1200  F.     Then  It 
increases  rapidly  to  1400,  after  which  it  remains  nearly  constant. 
OTHER  SOLIDS. 


Constant  Volume. 
0.16847 
0.15507 
2.41226 
0.17273 
0.346 
0.171 
0.332 
0.1758 
0.299 
0.3411 
0.399 


Wrought  iron  (Petit  &  Dulong). 

32°  to  212°..  0.109S- 
32°  to  392°..  0.115 
32°  to  572°.  .  0.1218 
32°  to  662°.  .  0.1255 
Iron  at  high  temperatures. 
(Pionchon,  Comptcs  Rendus,  1887.)  > 

13823  to  1832°  F 0.213 

1749'  to  1843°  F..  .  .         .    0.218 
1922°  to  2192°  F • 0.199 


Brickwork  and  masonry,  about  0 . 20 

Marble 0.210 

Chalk 0. 215 

Quicklime 0. 217 

Magnesian  limestone 0. 217 

Silica. . % 0. 191 

Corundum 0. 198 

Stones  generally 0. 2  to  0. 22 

WOODS. 

Oven  dried,  20  varieties,  sp.  ht.  nearly  the  same  for  all,  average 
0.327.      (U.  S.  Forest  Service,  1911.) 

LIQUIDS. 


Coal    0.20  to  0.241 

Coke 0.203 

Graphite 0. 202 

Sulphate  of  lime 0. 197 

Magnesia 0. 222 

Soda 0.231 

Quartz 0. 188 

River  sand 0. 195 


Alcohol,  density  0.793 0.622 

Sulphuric  acid,  density  1.87.  .  0.335 

1.30.  .  0.661 

Hydrochloric  acid 0. 600 


Olive  oil 0. 310 

Benzine 0 . 393 

Turpentine,  density  0.872 . .  0 . 472 

Bromine I. Ill 


*  See  Superheated  Steam,  page  869. 


564 


HEAT. 


GASES. 

At  Constant  At  Constant 
Pressure.        Volume. 

Sulphurous  acid 0. 1553          0. 1246 

Light  carbureted  hydrogen,  marsh  gas  (CH4) .   0 . 5929          0 . 4683 
Blast-furnace  gases 0 . 2277  ........ 


Specific  Heat  of  Water. 


(Peabody's  Steam  Tables,  from  Barnes  and 
Regnault.) 


•C. 

•F. 

Sp.  Ht. 

°.c. 

T. 

Sp.  Ht. 

°c. 

•F. 

Sp.  Ht. 

°c. 

•F. 

Sp.  Ht. 

0 
5 

10 

20 
25 
30 

32 

41 
50 

68 
77 
86 

1.0094 
1.00530 
1.00230 
1.00030 
0.99895 
0.99806 
0.99759 

35 
40 
45 
50 
55 
60 
65 

95 

104 
113 

122 
131 

140 
149 

0.99735 
0.99735 
0.99760 
0.99800 
0.99850 
0  99940 
1.00040 

70 
75 

80 
85 
90- 
95 
100 

158 
167 
176 

188 
194 
203 
21? 

.00150 
.00275 
.00415 
.00557 
.00705 
.00855 
.01010 

120 

140 
160 
180 
200 
220 

248 
284 
320 
356 
392 
428 

.01620 
.02230 
.02850 
.03475 
.04100 
.04760 

Specific  Heat  of  Salt  Solution.     (Schuller.) 

Per  cent  salt  in  solution ....       5  10  15  20  25 

Specific  heat 0.9306     0.8909     0.8606     0.8490     0.8073 

Specific  Heat  of  Air. — Regnault  gives  for  the  mean  value  at  constant 
pressure 

Between  —  30°  C.  and  +    10°  C 0.23771 

0°  C.     '  100°  C 0.23741 

0°C.     '          200°  C 0.23751 

Hanssen  uses  0.1686  for  the  specific  heat  of  tir  it  constant  volume. 
The  value  of  this  constant  has  never  been  found  to  any  degree 'of  accuracy 
by  direct  experiment.  Prof.  Wood  gives  0.2375  -f-  1.406  =  0.1689.  The 
ratio  of  the  specific  heat  of  a  fixed  gas  at  constant  pressure  to  the  sp.  ht. 
at  constant  volume  is  given  as  follows  by  different  writers  (Eng'g,  July  12, 
1889):  Regnault,  1.3953;  Moll  and  Beck,  1.4085;  Szathmari,  1.4027;  J. 
Macfarlane  Gray,  1.4.  The  first  three  are  obtained  from  the  velocity  of 
sound  in  air.  The  fourth  is  derived  from  theory.  Prof.  Wood  says: 
The  value  of  the  ratio  for  air,  as  found  in  the  days  of  La  Place,  was  1.41, 
and  we  have  0.2377  •*-  1.41  =  0.1686,  the  value  used  by  Clausius,  Hanssen, 
and  many  others.  But  this  ratio  is  not  definitely  known.  Rankine  in 
his  later  writings  used  1.408,  and  Tait  in  a  recent  work  gives  1.404,  while 
some  experiments  give  less  than  1.4,  and  others  more  than  1.41.  Prof. 
Wood  uses  1,406. 

Specific  Heat  of  Gases.  —  Experiments  by  Mallard  and  Le  Chatelier 
indicate  a  continuous  increase  in  the  specific  heat  at  constant  volume  of 
steam,  CO2,  and  even  of  the  perfect  gases,  with  rise  of  temperature.  The 
variation  is  inappreciable  at  100°  C.,  but  increases  rapidly  at  the  high  tem- 
peratures of  the  gas-engine  cylinder.  (Robinson's  Gas  and  Petroleum 
Engines.) 

Thermal  Capacity  and  Specific  Heat  of  Gases.  (From  Damour'a 
11  Industrial  Furnaces.") — The  specific  heat  of  a  gas  at  any  temperature  is 
the  first  derivative  of  the  function  expressing  the  thermal  capacity.  It 
is  not  possible  to  derive  from  the  specific  heat  of  a  gas  at  a  given  temper- 
ature, or  even  from  the  mean  specific  heat  between  0°  and  100°  C.,  the 
thermal  capacity  at  a  temperature  above  100°  C.  The  specific  heats  of 
gases  under  constant  pressure  between  0°  and  100°  C.,  given  by  Regnault, 
are  not  sufficient  to  calculate  the  quantity  of  heat  absorbed  by  a  gas  in 
heating  or  radiated  in  cooling,  hence  all  calculations  based  on  these 
figures  are  subject  to  a  more  or  less  grave  error. 

The  thermal  capacities  of  a  molecular  volume  (22.32  liters)  of  gases 
from  absolute  0°  ( —  273°  C.)  to  a  temperature  T  ( =  273°  +  t)  may  be 
expressed  by  the  formula  Q  =  0.001  aT  +  0.000,001  bTz,  in  which  a  is  a 
constant,  6.5,  for  all  gases,  and  b  has  the  following  values  for  different 
gases:  O2,  N«,  H2,  CO,  0.6;  H2O  vapor,  2.9;  CO2,  3.7;  CH4,  6.0.  The 
tables  on  page  565  give  the  thermal  capacities  of  different  gases  under 
varying  conditions  of  pressure,  temperature  and  volume. 


EXPANSION  BY  HEAT. 


565 


SPECIFIC  HEATS  OF  GASES  PER  KILOGRAM. 


Gases. 

Under  Constant 
Pressure. 

Under  Constant 
Volume. 

Oxygen 

0  213+  38X10  ~*t 

0  150+  38X10"6* 

Nitrogen  and  Carbon  Monoxide.  . 
Hydrogen  

0.243+  42X10  -«t 
3.400+600X10  ~&t 

0.171+  42X10~6* 
2.400+600X10~6Z 

Water  Vapor               .              ... 

0  447+324X10  ~6t 

0.335+324X10  ~6t 

Carbon  Dioxide  

0.193  +  168X10  ~6t 

0.150  +  168X10-6* 

Methane  

0.608+748X10  ~6t 

0.491  +748X10  ~*t 

THERMAL  CAPACITIES  OF  GASES  PER  KILOGRAM  IN  CENTIGRADE  DEGS. 


Gases. 

Under  Constant 
Pressure. 

Under  Constant 
Volume. 

Oxygen 

0  213^+  19X10~6J2 

0  150*+  19X10~6<2 

Nitrogen  and  Carbon  Monoxide.  . 
Hydrogen  

0.243£+  21  X10-6*2 
3.400£+300X10~6Z2 

0.171  t  +  21  XlO~6t2 
2.400<+300X10~€«2 

Water  Vapor 

0  447  £  +  162XlO~6£2 

0  3352  +  162X10-6*2 

Carbon  Dioxide  
Methane  or  Marsh  Gas  

0.193J+  84X10-6*2 
0.608^+374XlO~n2 

0.150J+  84X10-6*2 
0.491  <+374XlO~6*2 

THERMAL  CAPACITIES  OF  GASES  PER  KILOGRAM. 


Temperatures. 

02 

N2,CO 

H2 

H20 

CO2 

CH4 

Degrees  Centigrade. 
200.  . 

0 
47  0 

0 

50 

0 

700 

0 
100 

0 
43  1 

0 
136.6 

400 

88  0 

100 

1400 

203 

91  0 

303  0 

600.  . 

134  0 

154 

2150 

326 

145  0 

499.0 

800 

181  0 

207 

2900 

461 

208  0 

726  0 

1000.  . 

232  0 

264 

3700 

609 

277  0 

982  0 

1200 

284  0 

325 

4550 

770 

354  0 

1269  0 

1400.  . 

334  0 

383 

5350 

943 

435  0 

1584  0 

1600 

391  0 

445 

6250 

1130 

523  0 

1931  0 

1  800  .  . 

444  0 

508 

7100 

1330 

618  0 

2307  0 

2000  .  . 

503  0 

575 

8050 

1542 

728  0 

2712  0 

2200  .  . 

558  0 

637 

8950 

1751 

840  0 

3148  0 

2400 

670  0 

708 

9900 

1985 

950  0 

3614  0 

2600  .  . 

681  0 

777 

10900 

2241 

1070  0 

4109  0 

2800  .  . 

735  0 

850 

11900 

2520 

1200  0 

4635  0 

3000  

810.0 

921 

12950 

2799 

1355.0 

5190.0 

EXPANSION  BY  HEAT. 

In  the  centigrade  scale  the  coefficient  of  expansion  of  air  per  degree 
is  0.003665  =  1/273;  that  is,  the  pressure  being  constant,  the  volume 
of  a  perfect  gas  increases  1/273  of  its  volume  at  0°  C.  for  every  in- 
crease in  temperature  of  1°  C.  In  Fahrenheit  units  it  increases  1/491.6 
=  0.002034  of  its  volume  at  32°  F.  for  every  increase  of  1°  F. 
Expansion  of  Gases  by  Heat  from  32°  to  212°  F.  (Regnault.) 


Increase  in  Volume, 
Pressure  Constant. 
Volume  at  32°  Fahr. 
=  1.0,  for 

Increase  in  Pressure, 
Volume  Constant. 
Pressure  at  32° 
Fahr.  =  1.0,  for 

100°  C. 

1°F. 

100°  C. 

1°F. 

Hydrogen.  . 

0.3661 
0.3670 
0.3670 
0.3669 
0.3710 
0.3903 

0.002034 
0.002039 
0.002039 
0.002038 
0.002061 
0.002168 

0.3667 
0.3665 
0.3668 
0.3667 
0.3688 
0.3845 

0.002037 
0.002036 
0.002039 
0.002037 
0.002039 
0.002136 

Atmospheric  air  

Nitrogen  .  .  . 

Carbon  monoxide   .  . 

Carbon  dioxide  ".  

Sulphur  dioxide  

If  the  volume  is  kept  constant,  the  pressure  varies  directly  as  the 
absolute  temperature. 


5G6 


HEAT. 


Lineal  Expansion  of  Solids  at  Ordinary  Temperature*. 

(Mostly  British  Board  of  Trade;  from  Clark.) 


For 
1°Fahr. 
Length 

For 
l°Cent. 
Length 

Cxpan- 
sion 
from 
32°  to 
212°  F. 

Accord- 
ing to 
Other 
Author- 
ities. 

Aluminum  (drawn)  .  . 

0.00001360 
0.00001234 
0.00000627 
0.00000957 
0.00001052 
0.00000306 
0.00000300 
0.00000985 
0.00000975 
0.00000594 
0.00000795 
0.00000887 
0.00004278 
0.00000451 
0.00000499 
0.00000397 
0.00000438 
0.00000498 
0.00000786 
0.00000356 
0.00000648 
0.00000556 
0.00001571 

0.00002450 
.00002221 
.00001129 
.00001722 
.00001894 
.00000550 
.00000540 
r!774 
1755 
0.00001070 
0.00001430 
0.00001596 
3.00007700 
3.00000812 
0.00000897 
0.00000714 
0  .00000789 
0.00000897 
0.00001415 
0.00000641 
0.00001166 
0.00001001 
0.00002828 

0  .  002450 
0.002221 
3.001129 
3.001722 
0.001894 
0.000550 
0.005400 
0.001774 
0.001755 
0.001070 
0.001430 
0.001596 
0.007700 
0.000812 
0.000897 
0.000714 
0.000789 
0.  000897 
0.001415, 
0.00064 
0.001166 
0.00100 
0.00282 

Aluminum,  (cast)                •   •   ••         .  ... 

1661683 
0.001868 

Antimony  (cryst.)  

Brass  plat6   

Brick  

Brick  (fire)       

Bronze  (Copper,  17;  Tin,  21/2;  Zinc,  1).  . 

0.001392 

Cement   Portland  (mixed),  pure.   . 

Concrete:  cement-mortar  and  pebbles.  . 

0.001718 

Ebonite        

Glass,  English  flint  

Glass  thermometer  ...  .       1  .  . 

Granite  red  dry  

0.001235 
0.001110 

Lead      .   .                   

0.002694 

0.00000308 
0.00000786 
0.00000256 
0.00000494 
0.00009984 
0.00000695 
0.00001129 
0.00000922 
0  00000479 
0.00000453 
0.00000200 
0.00000434 
0.00000788 
0  00001079 
0.00000577 
0.00000636 
0.00000689 
0.00000652 
0.00000417 
0.00001163 
0.00000489 
0.0000027 
0.0000140 
0.0000149 

0.00000554 
0.00001415 
0.00000460 
0.00000890 
0.0001797 
0.00001251 
0.00002033 
0.00001660 
0.00000863 
0.00000815 
0.00000360 
0.00000781 
0.00001419 
0.00001943 
0.00001038 
0.00001144 
0.00001240 
0.00001174 
0.00000750 
0.00002094 
0.00000881 
0.00000496 
0.00002532 
0.00002692 

0.00055 
0.00141 
0.00046 
0.00089 
0.01797 
0.00125 
0.00203 
0.00166 
0.00086 
0.00081 
0.00036 
0.00078 
0.00141 
0.00194 
0.00103 
0.00114 
0.00124 
0.00117 
0.00075 
0.00209 
0.00088 
0.00049 
0.00253 
0.00269 

Marbles,  various  j  to 

Masonry,  brick  j  to 

Mercury  (cubic  expansion)  

0.018018 
0.001279 

Nickel  

Pewter  

Platinum  85%    Iridium,  15%   

0.000884 

Quartz,  parallel  to  maj.  axis,  0°  to  40°  C 
Quartz,  perpend,  to  maj.  axis,  0°  to  40°C 

0.001908 

6!66io79 

Slate  

Steel,  cast  

Steel   tempered              .  .     .   .       ... 



Stone  (sandstone)  Rauville      .       . 

Tin    

0.001938 

"Wedgwood  ware 

Wood,  pine  

Zinc  ,  

0.002942 

Zinc.  8.  Tin.  1  .  . 

Invar  (see  next  page),  0 .000.000.374  to  0.000.000.44  for  1°  C. 

Cubical  expansion,  or  expansion  of  volume  =  linear  expansion  X  3. 

Expansion  of  Steel  at  High  Temperatures.  (Charpy  and  Grenet. 
Comptes  Rendut,  1902.)  —  Coefficients  of  expansion  (for  lb  C.)  of  annealed 
carbon  and  nickel  steels  at  temperatures  at  which  there  is  no  transformer 


ABSOLUTE   TEMPERATURE. 


567 


tion  of  the  sieel.     The  results  seem  to  show  that  iron  and  carbide  of  iron 
have  appreciably  the  same  coefficient  of  expansion.     [See  also  p.  449.] 


Composition 
of  Steels. 

Mean  Coefficients  of  Expansion 
from 

Coefficients  between 

C 

Mn 

Si 

P 

1.5°to  200° 

200°to500° 

500°to650c 

0.03 

0.01 

0.03 

0.013 

11.8X10-6 

14.3X10-6 

17.0X10~( 

'2475X10-6 

880°  &  950° 

0.25 

0.04 

0.05 

0.010 

11.5 

14.5 

17.5 

23.3 

800°  &  950° 

0.64 

0.12 

0.14 

0.009 

12.1 

14.1 

16.5 

23.3 

720°  &  950° 

0.93 

0.10 

0.05 

0.005 

11.6 

14.9 

16.0 

27.5 

«           « 

1.23 

0.10 

0.08 

0.005 

11.9 

14.3 

16.5 

33.8 

«           « 

1.50 

0.04 

0.09 

0.010 

11.5 

14.9 

16.5 

36.7 

«           « 

3.50 

0.03 

0.07 

0.005 

11.2 

14.2 

18.0 

33.3 

Nickel  Steels. 

Mean  Coefficients  of  Expansion  from 

Ni 

C 

Mn 

15°  to  100° 

100° 

to  200° 

200°  to  400° 

400°  to  600° 

600°  to  900° 

26.9 

0.35 

0.30 

1  1.0X10~6 

18.0X10-6 

18.7X10~6 

22.0X10-6 

23.0X10-6 

28.9 

0.35 

0.36 

10.0 

21.3 

1< 

).0 

20.0 

22.7 

30.1 

0.35 

0.34 

9.5 

14.0 

19.5 

19.0 

21.3 

34.7 

0.36 

0.36 

2.0 

2.f 

1 

.75 

19.5 

20.7 

36.1 

0.39 

0.39 

1.5 

1.5 

11.75 

17.0 

20.3. 

32.8 

0.29 

0.66 

8.0 

14.C 

I 

If 

$.0 

21.5 

22.3 

3?.  8 

0.31 

0.69 

2.5 

2.5 

12.5 

18.75 

19.3 

37.4 

0.30 

0.69 

2.5 

1.5 

8.5 

19.75 

18.3 

25.4 

1.01 

0.79 

12.5 

18.5 

1< 

>.75 

21.0 

35.0 

29.4 

0.99 

0.89 

11.0 

12.5 

19.0 

20.5 

31.7 

34.5 

0.97 

0.84 

3.0 

3.5 

13.0 

18.75 

26.7 

Invar,  an  alloy  of  iron  with  36  per  cent  of  nickel,  has  a  smaller  coeffi- 
cient of  expansion  with  the  ordinary  atmospheric  changes  of  tempera- 
ture than  any  other  metal  or  alloy  known.  This  alloy  is  sold  under  the 
name  of  "Invar,"  and  is  used  for  scientific  instruments,  pendulums  of 
clocks,  steel  tape-measures  for  survey  work,  etc.  The  Bureau  of  Stand- 
ards found  its  coefficient  of  expansion  to  range  from  0.000  000  374  to 
0.00000044  for  1°  C.,qr  about  1/28  of  that  of  steel.  For  all  surveys 
except  in  the  most  precise  geodetic  work  a  tape  of  invar  may  be  used 
without  correction  for  temperature.  (Eng.  News,  Aug.  13,  1908.) 

Platinite,  an  alloy  of  iron  with  42  per  cent  of  nickel,  has  the  same 
coefficient  of  expansion  and  contraction  at  atmospheric  temperatures  as 
has  glass.  It  can,  therefore,  be  used  for  the  manufacture  of  armored 
glass,  that  is,  a  plate  of  glass  into  which  a  network  of  steel  wire  has  toeen 
rolled,  and  which  is  used  for  fire-proofing,  etc.  It  can  also  be  used  in- 
stead of  platinum  for  the  electric  connections  passing  through  the  glass 
plugs  in  the  base  of  incandescent  electric  lights.  (Stoughton's  "Metal- 
lurgy of  Steel.") 

Expansion   of    Liquids   from   32°   to   212°   F. — Apparent   expansion 


in  glass  (Clark). 

Water 

Water  saturated  with  salt. 

Mercury 

Alcohol 


Volume  at  212° 


0466 
05 

0182 
11 


1.11 
1.08 
1.07 


volume  at  32°  being  1: 

Nitric  acid 

Olive  and  linseed  oils 

Turpentine  and  ether 

Hydrochloric  and  sulphuric 

acids .      1.06 

For  water  at  various  temperatures,  see  Water. 
For  air  at  various  temperatures,  see  Air. 

ABSOLUTE  TEMPERATURE— ABSOLUTE  ZERO. 

The  absolute  zero  of  a  gas  is  a  theoretical  consequence  of  the  law  of 
expansion  by  heat,  assuming  that  it  is  possible  to  continue  the  cooling  of 
a  perfect  gas  until  its  volume  is  diminished  to  nothing. 


568  HEAT. 

The  volume  of  a  perfect  gas  increases  1/273-1  of  its  volume  at  0°  C.  for 
every  increase  of  temperature  of  1°  C.,  and  decreases  1/273-1  of  its 
volume  at  0°  C  .  for  every  decrease  of  temperature  of  1  °  C  .  At  -  273  .  1  °  C  .  . 
the  volume  would  then  be  reduced  to  nothing.  This  point,  -  273.  1°  C.  = 
—  459.6°  F.,  or  491.6°  F.  below  the  temperature  of  melting  ice,  is  called 
the  absolute  zero,  and  absolute  temperatures  are  measured  on  either  the 
Centigrade  or  the  Fahrenheit  scale,  from  this  zero.  The  freezing-point, 
32°  F.,  corresponds  to  491.6°  F.  absolute.  If  p0  be  the  pressure  and  VQ 
the  volume  of  a  perfect  gas  at  32°  F.  =  491.6°  absolute,  =  To,  and  p  the 
pressure  and  v  the  volume  of  the  same  weight  of  gas  at  any  other 
absolute  temperature  T,  then 

pv    __T_  =  <  +  459.6.    pv       poVo  =  _ 
poVo       To~      491.6     '    T      =    To 

A  cubic  foot  of  dry  air  at  32°  F.  at  the  sea  level  (barometer  =  29.921 
in.  of  mercury)   weighs  0.080728  Ib.     The  volume  of  one  pound  is 
1/0.080728  =  12.387  cu.  ft.     The  pressure  is  2116.3  Ib.  per  sq.  ft. 
•D  -  P<®°  -  2116.3  X  12.387  _  26,214  _  KQ  ,0 
-~ZV~  491.6  ~  = 


LATENT  HEATS  OF  FUSION  AND  EVAPORATION. 

Latent  Heat  means  a  quantity  of  heat  which  has  disappeared,  having 
been  employed  to  produce  some  change  other  than  elevation  of  tempera- 
ture. By  exactly  reversing  that  change,  the  quantity  of  heat  which 
has  disappeared  is  reproduced.  Maxwell  defines  it  as  the  quantity  of 
heat  which  must  be  communicated  to  a  body  in  a  given  state  in  order  to 
convert  it  into  another  state  without  changing  its  temperature. 

Latent  Heat  of  Fusion.  —  When  a  body  passes  from  the  solid  to  the 
liquid  state,  its  temperature  remains  stationary,  or  nearly  stationary,  at 
a  certain  melting-point  during  the  whole  operation  of  melting;  and  in 
order  to  make  that  operation  go  on,  a  quantity  of  heat  must  be  trans- 
ferred to  the  substance  melted,  being  a  certain  amount  for  each  unit 
of  weight  of  the  substance.  This  quantity  is  called  the  latent  heat  of 
fusion. 

When  a  body  passes  from  the  liquid  to  the  solid  state,  its  temperature 
remains  stationary  or  nearly  stationary  during  the  whole  operation  of 
freezing;  a  quantity  of  heat  equal  to  the  latent  heat  of  fusion  is  pro- 
duced in  the  body  and  rejected  into  the  atmosphere  or  other  surround- 
ing bodies. 

The  following  are  examples  in  British  thermal  units  per  pound,  as 
given  in  Landolt  and  Bernstein's  "  Physikalische-Chemische  Tabellen" 
(Berlin,  1894). 

Miih«5tanr>p<3  Latent  Heat  Qnh«tanr»P«s      Latent  Heat 

^stances.  of  Fusion.  ubstances.       Of  Fusion. 

Bismuth  .........   22.75  Silver  ...........   37.93 

Cast  iron,  gray  ...   41.4  Beeswax  .........   76.14 

Cast  iron,  white.  .  .   59.4  Parafflne  .........    63.27 

Lead  ............      9.66  Spermaceti  .......    66.56 

Tin  ..............    25.65  Phosphorus  ......      9.06 

Zinc  .............   50.63  Sulphur  ..........    16.86 

The  latent  heat  of  fusion  of  ice  is  generally  taken  at  144  B.T.U.  per 
Ib.  The  U.  S.  Bureau  of  Standards  (1915)  gives  it  as  79.76  20°-calories 
per  gram  =  143.57  B.T.U.  per  Ib. 

Latent  Heat  of  Evaporation.  —  When  a  body  passes  from  the 
solid  or  liquid  to  the  gaseous  state,  its  temperature  during  the  operation 
remains  stationary  at  a  certain  boiling-point,  depending  on  the  pressure  of 
the  vapor  produced;  and  in  order  to  make  the  evaporation  go  on,  a 
quantity  of  heat  must  be  transferred  to  the  substance  evaporated,  whose 
amount  for  each  unit  of  weight  of  the  substance  evaporated  depends  on 
the  temperature.  That  heat  does  not  raise  the  temperature  of  the  sub- 
stance, but  disappears  in  causing  it  to  assume  the  gaseous  state,  and  it  is 
called  the  latent  heat  of  evaporation. 

When  a  body  passes  from  the  gaseous  state  to  the  liquid  or  solid  state. 
its  temperature  remains  stationary,  during  that  operation,  at  the  boiling- 
point  corresponding  to  the  pressure  of  the  vapor  :  a  quantity  of  heat 
equal  to  the  latent  heat  of  evaporation  at  that  temperature  is  produced 


EVAPORATION   AND   DRYING.  569 

in  the  body;  and  in  order  that  the  operation  of  cond'ensation  may  go  on, 
that  heat  must  be  transferred  from  the  body  condensed  to  some  other 
body. 

The  following  are  examples  of  the  latent  heat  of  evaporation  in  British 
thermal  units,  of  one  pound  of  certain  substances,  when  the  pressure  of 
the  vapor  is  one  atmosphere  of  14.7  Ibs.  on  the  square  inch: 

Boiling-point  under  Latent  Heat  in 

one  atm.  Fahr.  British  units. 

Water 212.0  965.7  (Regnault). 

Alcohol..; 172.2  364.3    (Andrews). 

Ether 95.0  162.8 

Bisulphide  of  carbon 114.8  156.0 

The  latent  heat  of  evaporation  of  water  at  a  series  of  boiling-points  ex- 
tending from  a  few  degrees  below  its  freezing-point  up  to  about  375 
degrees  Fahrenheit  has  been  determined  experimentally  by  M.  Regnault. 
The  results  of  those  experiments  are  represented  approximately  by  the 
formula,  in  British  thermal  units  per  pound, 

I  nearly  =  1091.7  -  0.7  (t  -  32°)  =  965.7  -  0.7  (t  -  212°). 

Henning  (Ann.  der  Physik,  1906)  gives  for  t  from  0°  to  100°  C. 

Forl  kg.,  1=   94.210  (365-T  C.)  0.31249. 

Forl  lb.,  1  =  141. 124  (689-2°  F.)  0.31249. 

The  last  formula  gives  for  the  latent  heat  at  212°  F.,  969.7  B.T.U. 

The  Total  Heat  of  Evaporation  is  the  sum  of  the  heat  which  dis- 
appears in  evaporating  one  pound  of  a  given  substance  at  a  given  tem- 
perature (or  latent  heat  of  evaporation)  and  of  the  heat  required  to  raise  its 
temperature,  before  evaporation,  from  some  fixed  temperature  up  to  the 
temperature  of  evaporation.  The  latter  part  of  the  total  heat  is  called  the 
sensible  heat. 

In  the  case  of  water,  the  experiments  of  M.  Regnault  show  that  the 
total  heat  of  steam  from  the  temperature  of  melting  ice  increases  at  a 
uniform  rate  as  the  temperature  of  evaporation  rises.  The  following  is 
the  formula  in  British  thermal  units  per  pound: 

h  =  1091.7  +  0.305  (t  -  32°). 

H.  N.  Davis  (Trans.  A.  S.  M.  E.,  1908)  gives,  in  British  units, 
h -1150  +0.3745  (t- 21 2) -0.000550  (J-212)*. 

For  the  total  heat,  latent  heat,  etc.,  of  steam  at  different  pressures,  see 
table  of  the  Properties  of  Saturated  Steam.  For  tables  of  total  heat, 
latent  heat,  and  other  properties  of  steams  of  ether,  alcohol,  acetone, 
chloroform,  chloride  of  carbon,  and  bisulphide  of  carbon,  see  ROntgen's 
Thermodynamics  (Dubois's  translation).  For  ammonia  and  sulphur 
dioxide,  see  Wood's  Thermodynamics;  also,  tables  under  Refrigerating 
Machinery,  in  this  book. 

EVAPORATION   AND   DRYING. 

In  evaporation,  the  formation  of  vapor  takes  place  on  the  surface;  in 
boiling,  within  the  liquid:  the  former  is  a  slow,  the  latter  a  quick,  method 
of  evaporation. 

If  we  bring  an  open  vessel  with  water  under  the  receiver  of  an  air-pump 
and  exhaust  the  air,  the  water  in  the  vessel  will  commence  to  boil,  and  if  we 
keep  up  the  vacuum  the  water  will  actually  boil  near  its  freezing-point. 
The  formation  of  steam  in  this  case  is  due  to  the  heat  which  the  water 
takes  out  of  the  surroundings. 

Steam  formed  under  pressure  has  the  same  temperature  as  the  liquid  in 
which  it  was  formed,  provided  the  steam  is  kept  under  the  same  pressure. 

By  properly  cooling  the  rising  steam  from  boiling  water,  as  in  the  mul- 
tiple-effect evaporating  systems,  we  can  regulate  the  pressure  so  that  the 
water  boils  at  low  temperatures. 

Evaporation  of  Water  in  Reservoirs.  —  Experiments  at  the  Mount 
Hope  Keservoir,  Rochester,  N.  Y.,  in  1891,  gave  the  following  results: 

July.  Aug.  Sept.  Oct. 

Mean  temperature  of  air  in  shade 70.5  70.3  68.7  53.3 

44  water  in  reservoir. ..   68.2  70.2  66.1  54.4 

"     humidity  of  air,  per  cent 67.0  74.6  75.2  74.7 

Evaporation  in  inches  during  month 5.59       4.93  4.05  3.23 

Rainfall  in  inches  during  month 3 . 44      2 , 95  1 . 44  2,16 


570  HEAT. 

Evaporation  of  Water  from  Open  Channels. — (Flynn's  Irrigation 
Canals  and  Flow  of  Water.) — Experiments  from  1881  to  1885  in  Tulare 
County,  California,  showed  an  evaporation  from  a  pan  in  the  river" 
equal  to  an  average  depth  of  i/s  in.  per  day  throughout  the  year. 

When  the  pan  was  in  the  air  the  average  evaporation  was  less  than 
3/i6  in.  per  day.  The  average  for  the  month  of  August  was  1/3  in.  per 
day,  and  for  March  and  April  1/12  in.  per  day.  Experiments  in  Colorado 
show  that  evaporation  ranges  from  0.088  to  0.16  in.  per  day  during 
the  irrigating  season. 

In  Northern  Italy  the  evaporation  was  from  1/12  to  1/9  inch  per  day 
while  in  the  south,  under  the  influence  of  hot  winds,  it  was  from  1/e 
to  l/5  inch  per  day. 

In  the  hot  season  in  Northern  India,  with  a  decidedly  hot  wind  blow- 
ing, the  average  evaporation  was  1/2'  inch  per  day.  The  evaporation 
increases  with  the  temperature  of  the  water. 

Evaporation  by  the  Multiple  System. — A  multiple  effect  is  a  series 
of  evaporating  vessels  each  having  a  steam  chamber,  so  connected  that 
the  heat  of  the  steam  or  vapor  produced  in  the  first  vessel  heats  the 
second,  the  vapor  or  steam  produced  in  the  second  heats  the  third,  and 
so  on.  The  vapor  from  the  last  vessel  is  condensed  in  a  condenser. 
Three  vessels  are  generally  used,  in  which  case  the  apparatus  is  called 
a  Triple  Effect.  In  evaporating  in  a  triple  effect  the  vacuum  is  gradu- 
ated so  that  the  liquid  is  boiled  at  a  constant  and  low  temperature. 

A  series  distilling  apparatus  of  high  efficiency  is  described  by  W.F. 
M.  Goss  in  Trans.  A.  S.  M.  E.,  1903.  It  has  seven  chambers  in  series, 
and  is  designed  to  distill  500  gallons  of  water  per  hour  with  an  effi- 
ciency of  approximately  60  Ibs.  of  water  per  pound  of  coal. 

Tests  of  Yaryan  six-effect  machines  have  shown  as  high  as  44  Ibs.  of 
water  evaporated  per  pound  of  fuel  consumed. — Mach'y,  April,  1905. 
A  description  of  a  large  distilling  apparatus,  using  three  125-H.P.  boilers 
and  a  Lillie  triple  effect,  with  record  of  tests,  is  given  in  Eng.  Ncu-s. 
Mar.  29,  1900,  and  in  Jour.  Am.  Soc'y  of  Naval  Engineers,  Feb.,  1900. . 

Tests  of  heating  and  evaporating  apparatus  used  in  sugar  houses, " 
including  calandrias,  multiple  effects,  vacuum  pans,  and  condensers, 
are  described  by  E.  W.  Kerr  in  a  178-page  pamphlet,  Bulletin  149  <f 
the  Agricultural  Experiment  Station  of  the  Louisiana  State  University, 
August,  1914. 

Resistance  to  Boiling.  —  Brine.  (Rankine.)  —  The  presence  in  a 
liquid  of  a  substance  dissolved  in  it  (as  salt  in  water)  resists  ebullition,  and 
raises  the  temperature  at  which  the  liquid  boils,  under  a  given  pressure;  but 
unless  the  dissolved  substance  enters  into  the  composition  of  the  vapor, 
the  relation  between  the  temperature  and  pressure  of  saturation  of  the 
vapor  remains  unchanged.  A  resistance  to  ebullition  is  also  offered  by  a 
vessel  of  a  material  which  attracts  the  liquid  (as  when  water  boils  in  a 
glass  vessel),  and  the  boiling  take  place  by  starts.  To  avoid  the  errors 
which  causes  of  this  kind  produce  in  the  measurement  of  boiling-points, 
it  is  advisable  to  place  the  thermometer,  not  in  the  liquid,  but  in  the 
vapor,  which  shows  the  true  boiling-point,  freed  from  the  disturbing 
effect  of  the  attractive  nature  of  the  vessel.  The  boiling-point  of  saturated 
brine  under  one  atmosphere  is  226°  F.,  and  that  of  weaker  brine  is  higher 
than  the  boiling-point  of  pure  water  by  1.2°  F.,  for  each  1/32  of  salt  that 
the  water  contains.  Average  sea-water  contains  1/32;  and  the  brine  in 
marine  boilers  is  not  suffered  to  contain  more  than  from  2/33  to  3/32. 

Methods  of  Evaporation  Employed  in  the  Manufacture  of  Salt* 
(F.  E.  Engelhardt,  Chemist  On9ndaga  Salt  Springs;  Report  for  1889.)  — 
1.  Solar  heat  —  solar  evaporation.  2.  Direct  fire,  applied  to  the  heat- 
ing surface  of  the  vessels  containing  brine  —  kettle  and  pan  methods. 
3.  The  steam-grainer  system  —  steam-pans,  steam-kettles,  etc.  4.  Use 
of  steam  and  a  reduction  of  the  atmospheric  pressure  over  the  boiling 
brine  —  vacuum  system. 

When  a  saturated  salt  solution  boils,  it  is  immaterial  whether  it  is  done 
under  ordinary  atmospheric  pressure  at  228°  F.,  or  under  four  atmospheres 
with  a  temperature  of  320°  F.,  or  in  a  vacuum  under  Vio  atmosphere,  the 
result  will  always  be  a  fine-grained  salt. 

The  fuel  consumption  is  stated  to  be  as  follows:  By  the  kettle  method, 
40  to  45  bu.  of  salt  evaporated  per  ton  of  fuel,  anthracite  dust  burned  on 
perforated  grates;  evaporation,  5.53  Ibs.  of  water  per  pound  of  coal,  By 


EVAPORATION  AND  DHYING. 


571 


the  pan  method,  70  to  75  bu.  per  ton  of  fuel.  By  vacuum  pans,  single 
effect,  86  bu.  per  ton  of  anthracite  dust  (2000  Ibs.).  With  a  double 
effect  nearly  double  that  amount  can  be  produced. 

Solubility  of  Common  Salt  in  Pure  Water.     (Andreae.) 

Temp,  of  brine,  F 32         50         86        104       140       176 

100  parts  water  dissolve  parts. .  35.63  35.69  36.03  36.32  37.06  38.00 
100  parts  brine  contain  salt 26.27  26.30  26.49  26.64  27.04  27.54 

According  to  Poggial,  100  parts  of  water  dissolve  at  229.66°  F.,  40.35 
parts  of  salt,  or  in  per  cent  of  brine,  28.749.  Gay-Lussac  found  that  at 
229.72°  F.,  100  parts  of  pure  water  would  dissolve  40.38  parts  of  salt,  in 
per  cent  of  brine,  28.764  parts. 

The  solubility  of  salt  at  229°  F.  is  only  2.5%  greater  than  at  32°.  Hence 
we  cannot,  as  in  the  case  9f  alum,  separate  the  salt  from  the  water  by 
allowing  a  saturated  solution  at  the  boiling-point  to  cool  to  a  lower 
temperature. 

Strength  of  Salt  Brines.  —  The  following  table  is  condensed  from 
one  given  in  U.  S.  Mineral  Resources  for  1888,  on  the  authority  of  Dr. 
Engelhardt. 

Relations  between   Salinometer   Strength,  Specific  Gravity,  Solid 
Contents,  etc.,  of  Brines  of  Different  Strengths. 


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Solubility  of  Sulphate  of  Lime  in  Pure  Water.     (Marignac.) 
Temperature  F.  degrees..^  32    64.5  89.6  100.4  105.8  127.4  186.8  212 

371      368       370       375       417     452 

470      466       468       474       528     572 


Parts    water   to   dissolve!, , ,- 
1  part  gypsum  410 

Parts  water  to  dissolve 
part  anhydrous  CaSO* 


s..     32 
lve}415 

3   U-or 

34  r-° 


In  salt  brine  sulphate  of  lime  is  much  more  soluble  than  in  pure  water. 
In  the  evaporation  of  salt  brine  the  accumulation  of  sulphate  of  lime  tends 


572  HEAT. 

to  stop  the  operation,  and  it  must  be  removed  from  the  pans  to  avoid 
waste  of  fuel.  The  average  strength  of  brine  in  the  New  York  salt 
districts  in  1889  was  69.38  degrees  of  the  salinometer. 

Concentration  of  Sugar  Solutions.*  ( From  "  Heating  and  Con- " 
centrating  Liquids  by  Steam,"  by  John  G.Hudson;  The  Engineer,  June  13, 
1890.)  —  In  the  early  stages  of  the  process,  when  the  liquor  is  of  low 
density,  the  evaporative  duty  will  be  high,  say  two  to  three  (British) 
gallons  per  square  foot  of  heating  surface  with  10  Ibs.  steam  pressure, 
but  will  gradually  fall  to  an  almost  nominal  amount  as  the  final  stage  is 
approached.  As  a  generally  safe  basis  for  designing,  Mr.  Hudson  takes 
an  evaporation  of  one  gallon  per  hour  for  each  square  foot  of  gross  heating 
surface,  with  steam  of  the  pressure  of  about  10  Ibs. 

As  examples  of  the  evaporative  duty  of  a  vacuum  pan  when  performing 
the  earlier  stages  of  concentration,  during  which  all  the  heating  surface 
can  be  employed,  he  gives  the  following: 

COIL  VACUUM  PAN.  — 43Ain.  copper  coils,  528  square  feet  of  surface; 
steam  in  coils,  15  Ibs.;  temperature  in  pan,  141°  to  148°;  density  of  feed, 
2o°  Baume*,  and  concentrated  to  31°  Baume*. 

First  Trial.  —  Evaporation  at  the  rate  of  2000  gallons  per  hour  =  3.8 
gallons  per  square  foot ;  transmission,  376  units  per  degree  of  difference  of 
temperature. 

Second  Trial.  —  Evaporation  at  the  rate  of  1503  gallons  per  hour  = 
2.8  gallons  per  square  foot ;  transmission,  265  units  per  degree. 

As  regards  the  total  time  needed  to  work  up  a  charge  of  massecuite  from 
liquor  of  a  given  density,  the  following  figures,  obtained  by  plotting  the 
results  from  a  large  number  of  pans,  form  a  guide  to  practical  working. 
The  pans  were  all  of  the  coil  type,  some  with  and  some  without  jackets, 
the  gross  heating  surface  probably  averaging,  and  not  greatly  differing 
from,  0.25  square  foot  per  gallon  capacity,  and  the  steam  pressure  10  Ibs. 
per  square  inch.  Both  plantation  and  refining  pans  are  included,  making 
various  grades  of  sugar: 

Density  of  feed  (degs.  Baume') 10°      15°     20°    25°     30° 

Evaporation  required  per  gallon  masse- 
cuite discharged 6.1233.62.261.5  .97 

Average  working  hours  required  per  charge  .   12.         9.      6.5    5.        4. 

Equivalent  average  evaporation  per  hour 
per  square  foot  of  gross  surface,  assum- 
ing 0.25  sq.  ft.  per  gallon  capacity 2.04  1.61.391.2  0.97 

Fastest  working  hours  required  per  charge  .     8.5      5.53.8     2. 75  2.0 

Equivalent  average  evaporation  per  hour 

per  square  foot 2.88  2.62.382.181.9 

The  quantity  of  heating  steam  needed  is  practically  the  same  in  vacuum 
as  in  open  pans.  The  advantages  proper  to  the  vacuum  system  are  pri- 
marily the  reduced  temperature  of  boiling,  and  incidentally  the  possibility 
of  using  heating  steam  of  low  pressure. 

In  a  solution  of-  sugar  in  water,  each  pound  of  sugar  adds  to  the  volume 
of  the  water  to  the  extent  of  0.061  gallon  at  a  low  density  to  0.0638  gallon 
at  high  densities. 

A  Method  of  Evaporating  by  Exhaust  Steam  is  described  by 
Albert  Stearns  in  Trans.  A.  S.  M.  E.,  vol.  viii.  A  pan  17'  6"  X  11'  X  I'  6. 
fitted  with  cast-iron  condensing  pipes  of  about  250  sq.  ft.  of  surface, 
evaporated  120  gallons  per  hour  from  clear  water,  condensing  only  about 
one-half  of  the  steam  supplied  by  a  plain  slide-valve  engine  of  14"  X  32" 
cylinder,  making  65  revs,  per  min.,  cutting  off  about  two-thirds  stroke, 
with  steam  at  75  Ibs.  boiler  pressure. 

It  was  found  that  keeping  the  pan-room  warm  and  letting  only  sufficient 
air  in  to  carry  the  vapor  up  out  of  a  ventilator  adds  to  its  efficiency,  as 
the  average  temperature  of  the  water  in  the  pan  was  only  about  165°  F. 

Experiments  were  made  with  coils  of  pipe  in  a  small  pan,  first  with  no 
agitator,  then  with  one  having  straight  blades,  and  lastly  with  troughed 
blades;  the  evaporative  results  being  about  the  proportions  of  one,  two, 
and  three  respectively. 

In  evaporating  liquors  whose  boiling-point  is  220°  F..  or  much  above 
that  of  water,  it  is  found  that  exhaust  steam  can  do  but  little  more  than 

*  For  other  sugar  data,  see  Bagasse  as  Fuel,  under  Fuel. 


EVAPORATION  AND  DRYING.  573 

bring  them  up  to  saturation  strength,  but  on  weak  liquors,  sirups,  glues, 
etc.,  it  should  be  very  useful. 

Drying  in  Vacuum. — An  apparatus  for  drying  grain  and  other  sub- 
stances in  vacuum  is  described  by  Mr.  Emil  Passburg  in  Proc.Inst.  Mech. 
Engrs.,  1889.  The  three  essential  lequirements  for  a  successful  and  eco- 
nomical process  of  drying  are:  1.  Cheap  evaporation  of  the  moisture; 
2.  Quick  drying  at  a  low  temperature;  3.  Large  capacity  of  the  apparatus, 

The  removal  of  the  moisture  can  be  effected  in  either  of  two  ways:  either 
by  slow  evaporation,  or  by  quick  evaporation  —  that  is,  by  boiling. 

Slow  Evaporation.  —  The  principal  idea  carried  into  practice  in  machines 
acting  by  slow  evaporation  is  to  bring  the  wet  substance  repeatedly  into 
contact  with  the  inner  surfaces  of  the  apparatus,  which  are  heated  by 
steam,  while  at  the  same  time  a  current  of  hot  air  is  also  passing  througk 
the  substances  for  carrying  off  the  moisture.  This  method  requires  much 
heat,  because  the  hot-air  current  has  to  move  at  a  considerable  speed  in 
order  to  shorten  the  drying  process  as  much  as  possible;  consequently  a 
great  quantity  of  heated  air  passes  through  and  escapes  unused.  As  a 
carrier  of  moisture  hot  air  cannot  in  practice  be  charged  beyond  half  its  full 
saturation;  and  it  is  in  fact  considered  a  satisfactory  result  if  even  this 
proportion  be  attained.  A  great  amount  of  heat  is  here  produced  which  is 
not  used;  while,  with  scarcely  half  the  cost  for  fuel,  a  much  quicker 
removal  of  the  water  is  obtained  by  heating  it  to  the  boiling-point. 

Quick  Evaporation  by  Boiling.  —  This  does  not  take  place  until  the 
water  is  brought  up  to  the  boiling-point  and  kept  there,  namely,  212°  F.t 
under  atmospheric  pressure.  The  vapor  generated  then  escapes  freely. 
Liquids  are  easily  evaporated  in  this  way,  because  by  their  motion  conse- 
quent on  boiling  the  heat  is  continuously  conveyed  from  the  heating  sur- 
faces through  the  liquid,  but  it  is  different  with  solid  substances,  and 
many  more  difficulties  have  to  be  overcome,  because  convection  of  the 
heat  ceases  entirely  in  solids.  The  substance  remains  motionless,  and 
consequently  a  much  greater  quantity  of  heat  is  required  than  with 
liquids  for  obtaining  the  same  results. 

Evaporation  in  Vacuum.  —  All  the  foregoing  disadvantages  are  avoided 
If  the  boiling-point  of  water  is  lowered,  that  is,  if  the  evaporation  is  carried 
out  under  vacuum. 

This  plan  has  been  successfully  applied  in  Mr.  Passburg's  vacuum  drying 
apparatus,  which  is  designed  to  evaporate  large  quantities  of  water  con- 
tained in  solid  substances. 

The  drying  apparatus  consists  of  a  top  horizontal  cylinder,  surmounted 
by  a  charging  vessel  at  one  end,  and  a  bottom  horizontal  cylinder  with  a 
discharging  vessel  beneath  it  at  the  same  end.  Both  cylinders  are 
incased  in  steam-jackets  heated  by  exhaust  steam.  In  the  top  cylinder 
works  a  revolving  cast-iron  screw  with  hollow  blades,  which  is  also  heated 
by  exhaust  steam.  .  The  bottom  cylinder  contains  a  revolving  drum  of 
tubes,  consisting  of  one  large  central  tube  surrounded  by  24  smaller  ones, 
all  fixed  in  tube-plates  at  both  ends;  this  drum  is  heated  by  live  steam 
direct  from  the  boiler.  The  substance  to  be  dried  is  fed  into  the  charg- 
ing vessel  through  two  manholes,  and  is  carried  along  the  top  cylinder 
by  the  screw  creeper  to  the  back  end,  where  it  drops  through  a  valve 
into  the  bottom  cylinder,  in  which  it  is  lifted  by  blades  attached  to  the 
drum  and  travels  forward  in  the  reverse  direction;  from  the  front  end  of 
the  bottom  cylinder  it  falls  into  a  discharging  vessel  through  another  • 
valve,  having  by  this  time  become  dried.  The  vapor  arising  during  the 
process  is  carried  off  by  an  air-pump,  through  a  dome  and  air-valve  on 
the  top  of  the  upper  cylinder,  and  also  through  a  throttle-valve  on 
the  top  of  the  lower  cylinder;  both  of  these  valves  are  supplied  with 
strainers. 

As  soon  as  the  discharging  vessel  is  filled  with  dried  material  the  valve 
connecting  it  with  the  bottom  cylinder  is  shut,  and  the  dried  charge  taken 
out  without  impairing  the  vacuum  in  the  apparatus.  When  the  charging 
vessel  requires  replenishing,  the  intermediate  valve  between  the  two  cylin- 
ders is  shut,  and  the  charging  vessel  filled  with  a  fresh  supply  of  wet  mate- 
rial; the  vacuum  still  remains  unimpaired  in  the  bottom  cylinder,  and  has 
to  be  restored  only  in  the  top  cylinder  after  the  charging  vessel  has  been 
closed  again. 

.  In  this  vacuum  the  boiling-point  of  the  water  contained  in  the  wet  mate- 
rial is  brought  down  as  low  as  110°  F.  The  difference  between  tnis  tern* 


574  HEAT. 

perature  and  that  of  the  heating  surfaces  is  ampiy  sufficient  for  obtaining 
good  results  from  the  employment  of  exhaust  steam  for  heating  all  the 
surfaces  except  the  revolving  drum  of  tubes.  The  water  contained  in 
the  solid  substance  to  be  dried  evaporates  as  soon  as  the  latter  is  heated 
to  about  110°  F.,  and  as  long  as  there  is  any  moisture  to  be  removed  the 
solid  substance  is  not  heated  above  this  temperature. 

Wet  grains  from  a  brewery  or  distillery,  containing  from  75%  to  78%  of 
water,  have  by  this  drying  process  been  converted  from  a  worthless  incum- 
brance  into  a  valuable  fo9d-stuff.  The  water  is  removed  by  evaporation 
only,  no  previous  mechanical  pressing  being  resorted  to. 

At  Guinness's  brewery  in  Dublin  two  of  these  machines  are  employed. 
In  each  of  these  the  top  cylinder  is  20  ft.  4  in.  long  and  2  ft.  8  in.  diam., 
and  the  screw  working  inside  it  makes  7  revs,  per  min.;  the  bottom 
cylinder  is  19  ft.  2  in.  long  and  5  ft.  4  in.  diam.,  and  the  drum  of  the  tubes 
inside  it  makes  5  revs,  per  min.  The  drying  surfaces  of  the  two  cylinders 
amount  together  to  a  total  area  of  about  1000  sq.  ft.,  of  which  about  40% 
is  heated  by  exhaust  steam  direct  from  the  boiler.  There  is  only  one  air- 
pump,  which  is  made  large  enough  for  three  machines;  it  is  hori- 
zontal, and  has  only  one  air-cylinder,  which  is  double-acting,  173/4  in. 
diam.  and  173/4  in.  stroke;  and  it  is  driven  at  about  45  revs,  per  min. 
As  the  result  of  about  eight  months'  experience,  the  two  machines 
have  been  drying  the  wet  grains  from  about  500  cwt.  of  malt  per  day  of 
24  hours. 

Roughly  speaking,  3  cwt.  of  malt  gave  4  cwt.  of  wet  grains,  and  the 
latter  yield  1  cwt.  of  dried  grains;  500  cwt.  of  malt  will  therefore  yield 
about  670  cwt.  of  wet  grains,  or  335  cwt.  per  machine.  The  quantity  of 
water  to  be  evaporated  from  the  wet  grains  is  from  75%  to  78%  of  their 
total  weight,  or,  say,  about  512  cwt.  altogether,  being  256  cwt.  per 
machine. 

Driers  and  Drying. 
(Contributed  by  W.  B.  Ruggles,  1909.) 

Materials  of  different  physical  and  chemical  properties  require  different 
types  of  drying  apparatus.  It  is  therefore  necessary  to  classify  mate- 
rials into  groups,  as  below,  and  design  different  machines  for  each 
grpup. 

Group  A:  Materials  which  may  be  heated  to  a  high  temperature  and 
are  not  injured  by  being  in  contact  with  products  of  combustion.  These 
include  cement  rock,  sand,  gravel,  granulated  slag,  clay,  marl,  chalk,  ore, 
graphite,  asbestos,  phosphate  rock,  slacked  lime,  etc. 

The  most  simple  machine  for  drying  these  materials  is  a  single  revolving 
shell  with  lifting  flights  on  the  inside,  the  shell  resting  on  bearing  wheels 
and  having  a  furnace  at  one  end  and  a  stack  or  fan  at  the  other.  The 
advantage  of  this  style  of  machine  is  its  low  cost  of  installation  and  the 
small  number  of  parts.  The  disadvantages  are  great  cost  of  repairs  and 
excessive  fuel  consumption,  due  to  radiation  and  high  temperature  of  the 
stack  gases.  If  the  material  is  fed  from  the  stack  and  towards  the  furnace 
end,  the  shell  near  the  furnace  gets  red-hot,  causing  excessive  radiation  and 
frequent  repairs.  Should  the  feed  be  reversed  the  exhaust  temperature 
must  be  kept  above  212°  F.t  or  recondensation  will  take  place,  wetting  the 
material. 

In  order  to  economize  fuel  the  shell  is  sometimes  supported  at  the 
ends  and  brickwork  is  erected  around  the  shell,  the  hot  gases  passing 
under  the  shell  and  back  through  it.  Although  this  method  is  more 
economical  in  the  use  of  fuel,  the  cost  of  installation  and  the  cost  of 
repairs  are  greater. 

Group  B:  Materials  such  as  will  not  be  injured  by  the  products  of  com- 
bustion but  cannot  be  raised  to  a  high  temperature  on  account  of  driving 
off  water  of  crystallizatipn,  breaking  up  chemical  combinations,  or  en 
account  of  danger  from  ignition.  Included  in  these  are  gypsum,  fluor- 
spar, iron  pyrites,  coal,. coke,  lignite,  sawdust,  leather  scraps,  cork  chips, 
tobacco  stems,  fish  scraps,  tankage,  peat,  etc.  Some  of  these  materials 
may  be  dried  in  a  single-shell  drier  and  some  in  a  bricked-in  machine, 
but  none  of  them  in  a  satisfactory  way  on  account  of  the  difficulty  of 
regulating  the  temperature  and,  in  some  cases,  the  danger  of  explosion  of 
dust. 

Group  C:  Materials  which  are  not  injured  by  a  high  temperature  but 
which  cannot  be  allowed  to  come  into  contact  with  products  of  combus- 


EVAPORATION  AND  DRYING.          575 

tion.  These  are  kaolin,  ocher  and  other  pigments,  fuller's  earth,  which  is 
to  be  used  in  filtering  vegetable  or  animal  oils,  whiting  and  similar  earthy 
materials,  a  large  proportion  of  which  would  be  lost  as  dust  in  direct-heat 
drying.  These  may  be  dried  by  passing  through  a  single-shell  drier 
incased  in  brickwork  and  allowing  heat  to  come  into  contact  with  the 
shell  only,  but  this  is  an  uneconomical  machine  to  operate,  due  to  the 
high  temperature  of  the  escaping  gases. 

Group  D:  Organic  materials  which  are  used  for  food  either  by  man  or 
the  lower  animals,  such  as  grain  which  has  been  wet,  cotton  seed,  starch 
feed,  corn  germs,  brewers'  grains,  and  breakfast  foods,  which  must  be 
dried  after  cooking.  These,  of  course,  cannot  be  brought  into  contact 
with  furnace  gases  and  must  be  kept  at  a  low  temperature.  For  these 
materials  a  drier  using  either  exhaust  or  live  steam  is  the  only  practical 
one.  This  is  generally  a  revolving  shell  in  which  are  arranged  steam 
pipes.  Care  should  be  exercised  in  selecting  a  steam  drier  which  has 
perfect  and  automatic  drainage  of  the  pipes.  The  condensed  steam 
always  amounts  to  more  than  the  water  evaporated  from  the  material. 

Group  E:  Materials  which  are  composed  wholly  or  contain  a  large  pro- 
portion of  soluble  salts,  such  as  nitrate  of  soda,  nitrate  of  potash,  car- 
bonates of  soda  or  potash,  chlorates  of  soda  or  potash,  etc.  These  in 
drying  form  a  hard  scale  which  adheres  to  the  shell,  and  a  rotary  drier 
cannot  be  profitably  used  on  account  of  frequent  stops  for  cleaning.  The 
only  practical  machine  for  such  materials  is  a  semicircular  cast-iron 
trough  having  a  shaft  through  the  center  carrying  paddles  that  C9n- 
stantl.y  stir  up  the  material  and  feed  it  through  the  drier.  This  machine 
has  brick  side  walls  and  an  exterior  furnace;  the  heat  from  the  furnace 
passing  under  the  shell  and  back  through  the  drying  material  or  out 
through  a  stack  or  fan  without  passing  through  the  material,  as  may  bo 
desired.  Should  the  material  also  require  a  low  temperature,  the  same 
type  of  drier  can  be  used  by  substituting  steam-jacketed  steel  sections 
instead  of  cast  iron. 

The  efficiency  of  a  drier  is  the  ratio  of  the  theoretical  heat  required  to 
do  the  drying  to  the  total  heat  supplied.  The  greatest  loss  is  the  heat 
carried  out  by  the  exhaust  or  waste  gases;  this  may  be  as  great  as  40% 
of  the  total  heat  from  the  fuel,  or  with  a  properly  designed  drier  may  be 
as  small  as  8%.  The  radiation  from  the  shell  or  walls  may  be  as  high  as 
25%  or  as  low  as  4%.  The  heat  carried  away  by  the  dried  material  may 
amount  under  conditions  of  careless  operation  to  as  much  as  25%  or  may 
be  as  low  as  nothing. 

A  properly  designed  drier  of  the  direct-heat  type  for  either  group  "  A  " 
or  "B"  will  give  an  efficiency  of  from  75%  to  85%;  a  bricked-in  return- 
draught  single-shell  drier,  from  60%  to  70%;  and  a  single-shell  straight- 
draught  dryer,  from  45%  to  55%.  A  properly  designed  indirect-heat 
drier  for  group  "C"  will  give  an  efficiency  of  50%  to  60%,  and  a  poorly 
designed  one  may  not  give  more  than  30%;  The  best  designed  steam 
drier  for  group  "  D,"  in  which  the  losses  in  the  boiler  producing  the 
steam  must  be  considered,  will  not  often  give  an  efficiency  of  more  than 
42%;  and,  while  a  poorly  designed  one  may  have  an  equal  efficiency, 
its  capacity  may  be  not  more  than  one-half  of  a  good  drier  of  equal  size. 
The  drier  described  for  group  "E"  will  not  give  an  efficiency  of  more 
than  55%. 

PERFORMANCE  OF  A  STEAM  DRIER. 

Material;  Starch  feed.  Moisture,  initial  39.8%,  final  0.22%. 
Dried*  material  per  hour,  831  Ibs.  Water  evaporated  per  hour,  548  Ibs. 
Steam  consumed  per  hour,  793  Ibs.  Water  evaporated  per  pound 
steam,  0.691  Ib.  Temperature  of  material,  moist,  58°,  dry,  212°. 
Steam  pressure,  98  Ibs.  gauge. 

Total  heat  to  evaporate  548  Ibs.  water  at  58°  into  steam, 
548  X  (154.2  +  969.7)  =  615,897  B.T.U. 

Heat  supplied  by  793  Ibs.  steam  condensed  to  water  at  212°, 
793  X  (1188.2  -  180.3)  =  799,265  B.T.U. 

Heat  used  to  evaporate  water, 

(615,897  -f-  799,265)  =  77.1%. 

Heat  used  to  raise  temperature  of  material, 

(831  X  154  X  0.492)  =  62,963  =  7.9%. 

Loss  by  radiation       .      .    100  -  (77.1  +  7.9)  =  15%. 

Total  efficiency    . 85.0%. 


576 


HEAT. 


Performance  of  Different  Types  of  Driers. 

(W.  B.  Ruggles.) 


.• 

s 

!l 

Type  of  drier  

l| 

Is 

^.S  g 

Hi 

t-<  ••> 

3| 

"o  6* 

V    M 

^si2 

|J| 

'5c§ 

§J 

'•£12"^ 

Q^ 

1? 

£.A| 

I* 

-u  ^q 

Material  ,,,,,,,..,,.,  

Sand 

Coal 

Cement 

Lime- 

Nitrate 

Moisture,  initial,  per  cent  ....... 

4  58 

10  2 

slurry. 
61  2 

stone. 
3  6 

of  soda. 
7  2 

Moisture,  final,  per  cent  

0 

0 

40  7 

0  5 

0  3 

Calorific  value  of  fuel,  B.T.U.  .  . 

12100 

12290 

13200 

13180 

13600 

Fuel  consumed  per  hour,  Ibs.  .  . 
Water  evaporated  per  hour,  Ibs 
Water  evap.  per  pound  fuel,  Ibs 
Material  dried  per  hour,  Ibs.  .  .  . 
Fuel  per  ton  dried  material,  Ibs. 
Heat  lost  in  exhaust  air,  per  cent 

398 
2196 
5.3 
36460 
21.8 
11.3 

213.6 
924.2 
4.3 
8300 
51.3 
42.8 

667 
4057 
6.1 
7680 
17.3 
38.4 

460 
1325 
2.3 
41400 
22.2 
38.2 

87 
349 
4.0 
4581 
38.0 
40.7 

Heat  lost  by  radiation,  etc.,  per 

cent  

7.6 

7.7 

12  5 

15  6 

13  8 

Heat  used  to  evaporate  water, 

per  cent 

52  5 

39  4 

52  0 

24  4 

33  1 

Heat  used  to  raise  temperature  of 
material,  per  cent  

28.6 

10.1 

7  1 

21  8 

12  4 

Total  efficiency,  per  cent  

81  1 

49  5 

59  1 

46  2 

45  5 

M 

3 


WATER  EVAPORATED  AND  HEAT  REQUIRED  FOR  DRYING. 
percentage  of  moisture  in  material  to  be  dried. 
Ibs.  water  evaporated  per  ton  (2000  Ibs.)  of  dry  material. 
=  British  thermal  units  required  for  drying,  per  ton  of  dry  material. 


M 

Q 

H 

M 

Q 

H 

M 

Q 

H 

1 

20.2 

85,624 

14 

325.6 

424,884 

35 

1,077 

1,269,240 

2 

40.8 

108,696 

15 

352.9 

458,248 

40 

1,333 

1,555,960 

3 

61.9 

130,424 

16 

381.0 

489,720 

45 

1,636 

1,895,320 

4 

83.3 

156,296 

17 

409.6 

521,752 

50 

2,000 

2.303,000 

5 

105.3 

180,936 

18 

439.0 

554,680 

55 

2,444 

2,800,280 

6 

127.7 

206,024 

19 

469.1 

588,392 

60 

3,000 

3,423,000 

7 

150.,? 

231,560 

20 

500.0 

623,000 

65 

3,714 

4,222,680 

8 

173.9 

257,768 

21 

531.6 

658,392 

70 

4,667 

5,290,040 

9 

197.8 

284,536 

22 

564.1 

694,792 

75 

6,000 

6,783,000 

10 

222.2 

311.864 

23 

597.4 

732.088 

80 

8,000 

9,023,000 

11 

247.2 

339,864 

24 

631.6 

770,392 

85 

11,333 

12,755.960 

12 

272.7 

368,424 

25 

666.7 

809,704 

90 

18,000 

20,223,000 

13 

298.9 

397,768 

30 

857.0 

1  .022,840 

95 

38,000 

42,623,000 

Formulae:    Q  = 


1120  Q  +  63,000. 


The  value  of  H  is  found  on  the  assumption  that  the  moisture  is  heated 
from  62°  to  212°  and  evaporated  at  that  temperature,  and  that  the 
specific  heat  of  the  material  is  0.21.  [2000  X  (212  -  62)  X  0.21]  =  63,000. 

Calculations  for  Design  of  Drying  Apparatus.  —  A  most  efficient 
system  of  drying  of  moist  materials  consists  in  a  continuous  circulation  of  a 
volume  of  warm  dry  air  over  or  through  the  moist  material,  then  passing 
the  air  charged  with  moisture  over  the  cold  surfaces  of  condenser  coils  to 
remove  the  moisture,  then  heating  the  same  air  by  steam-heating  coils 
or  other  means,  and  again  passing  it  over  the  material.  In  the  design  of 
apparatus  to  work  on  this  system  it  is  necessary  to  know  the  amount 
of  moisture  to  be  removed  in  a  given  time,  and  to  calculate  the  volume  of 
air  that  will  carry  that  moisture  at  the  temperature  at  which  it  leaves  the 
material,  making  allowanceforthefactthatthemoist,  warm  air  on  leaving 


EVAPORATION   AND   DRYING. 


577 


the  material  may  not  be  fully  saturated,  and  for  the  fact  that  the  cooled 
air  is  nearly  or  fully  saturated  at  the  temperature  at  which  it  leaves  the 
cooling  coils.  A  paper  by  Wm.  M.  Grosvenor,  read  before  the  Am.  Inst. 
of  Chemical  Engineers  (Heating  and  Ventilating  Mag.,  May,  1909)  con- 
tains a  "humidity  table"  and  a  "humidity  chart"  which  greatly  facilitate 
the  calculations  required.  The  table  is  given  in  a  condensed  form  below. 
It  is  based  on  the  following  data:  Density  of  air  4-  0.04%  CO«>  = 

0.001293052  ..      __.  _ 

1  +  0.00367  X  Temp.  C.  (m  Kg'  P6F  CU'  m')'  DenSlty  af  Water  Vapor 
=  0.62186  X  density  of  air.  Density  at  partial  pressure  •*•  density  at  760 
m.m.  =partiai  pressure  •*•  760  m.m.  Specific  heat  of  water  vapor  =  0.475; 
ep.  ht.  of  air  =  0.2373.  Kg.  per  cu.  meter  X  0.062428  =  Ibs.  per  cu.  ft. 
The  results  given  in  the  table  agree  within  1/4%  with  the  figures  of  the 
U.  S.  Weather  Bureau.  (Compare  also  the  tables  of  H.  M.  Prevost 
Murphy,  given  under  "Air,"  page  612.)  The  term  "humid  heat"  in 
the  heading  of  the  table  is  defined  as  the  B.T.U.  required  to  raise 
1°  F.  one  pound  of  air  plus  the  vapor  it  may  carry  when  saturated  at 
the  given  temperature  and  pressure;  and  "humid  volume"  is  the 
volume  of  one  pound  of  air  when  saturated  at  the  given  temperature 
and  pressure. 

Humidity  Table. 


Temp. 
F. 

Vapor 
Tension, 
Milli- 
meters of 
Mercury. 

Lbs. 
Water 
Vapor 
per  Ib. 
Air. 

Humid 
Heat, 
B.T.U. 

Humid 
Volume 
cu.ft. 

Density,  Ibs. 
per  cu.ft.  at  760 

Millimeters. 

Volume  in  cu. 
ft.  per  Ib.  of 

Dry 
Air. 

Sat'd 
Mix. 

Dry 
Air. 

Sat'd 
Mix. 

32 

4.569 

0.003761 

0.2391 

12.462 

0.080726 

0.080556 

12.388 

12.414 

35 

5.152 

.0042435 

.2393 

12.549 

.080231 

.080085 

12.464 

12.496 

40 

6.264 

.0050463 

,2398 

12.695 

.079420 

.079181 

12.590 

12.629 

45 

7.582 

.0062670 

.2403 

12.843 

.078641 

.078348 

12.718 

12.763 

50 

9.140 

.0075697 

.2409 

12.999 

.077867 

.077511 

12.842 

12.901 

55 

10.980 

.0091163 

.2416 

13.159 

.077109 

.076685 

12.968 

13.041 

60 

13.138 

.010939 

.2425 

13.326 

.076363 

.075865 

13.095 

13.180 

65 

15.660 

.013081 

.2435 

13.501 

.075635 

.075039 

13.222 

13.325 

70 

18.595 

.Oi5597 

.2447 

13.683 

.074921 

.074219 

13.348 

13.471 

75 

22.008 

.018545 

.2461 

13.876 

.074218 

.073471 

13.474 

13.624 

80 

25.965 

.021998 

.2478 

14.081 

.073531 

.072644 

13.600 

13.777 

85 

30.573 

.026026 

.2497 

14.301 

.072852 

.071744 

13.726 

13.938 

90 

35.774 

.030718 

.2519 

14.539 

.072189 

.070894 

13.852 

14.106 

95 

41.784 

.036174 

.2545 

14.793 

.071535 

.070051 

13.979 

14.275 

100 

48.679 

.042116 

.2575 

15.071 

.070894 

.069179 

14.106 

14.455 

105 

56.534 

.049973 

.2610 

15.376 

.070264 

.068288 

14.232 

14.643 

110 

65.459 

.058613 

.2651 

15.711 

.069647 

.067383 

14.358 

14.840 

115 

75.591 

.068662 

.2699 

16.084 

.069040 

.066447 

14.484 

15.050 

120 

87.010 

.080402 

.2755 

16.499 

.068443 

.065477 

14.611 

15.272 

125 

99.024 

.094147 

.2820 

16.968 

.067857 

.064480 

14.736 

15.509 

130 

114.437 

.11022 

.2896 

17.499 

.067380 

.063449 

14.863 

15.761 

135 

130.702 

.12927 

.2987 

18.103 

.066713 

.062374 

14.989 

16.032 

140 

148.885 

.15150 

.3093 

18.800 

.066156 

.061255 

15.116 

16.325 

145 

169.227 

.17816 

.3219 

19.609 

.065601 

.060104 

15.242 

16.643 

150 

191.860 

.21005 

.3371 

20.559 

.065154 

.058865 

15.368 

16.993 

155 

216.983 

.24534 

.3553 

21.687 

.064539 

.057570 

15.494 

17.370 

160 

244.803 

.29553 

.3776 

23.045 

.064016 

.056218 

15.621 

17.788 

165 

275.592 

.35286 

.4054 

24.708 

.063502 

.054795 

15.748 

18.250 

170 

309.593 

.42756 

.4405 

26.790 

.062997 

.053305 

15  874 

18.761 

175 

347.015 

.52285 

.4856 

29.454 

.062500 

.051708 

16.000 

19.339 

180 

388.121 

.64942 

.5458 

32.967 

.062015 

.050035 

16.126 

19.987 

185 

433.194 

.82430 

.6288 

37.796 

.061529 

.048265 

16.253 

20.719 

190 

482.668 

1  .00805 

.7519 

44.918 

.061053 

.046391 

16.379 

21.557 

195 

536.744 

1.4994 

.9494 

56.302 

.060588 

.044405 

16.505 

22.521 

200 

595.771 

2.2680 

1.3147 

77.304 

.060127 

.042308 

16.631 

23.638 

205 

660.116 

4.2272 

2.1562 

131.028 

.059674 

.040075 

16.758 

24.954 

210 

730.267 

15.8174 

15.9148 

562.054 

.059228 

.037323 

16.884 

26.796 

578 


HEAT. 


RADIATION   OF  HEAT0 

Radiation  of  heat  takes  place  between  bodies  at  all  distances  apart,  and 
follows  the  laws  for  the  radiation  of  light. 

The  heat  rays  proceed  in  straight  lines,  and  the  intensity  of  the  rays 
radiated  from  any  one  source  varies  inversely  as  the  square  of  their 
distance  from  the  source. 

This  statement  has  been  erroneously  interpreted  by  some  writers,  who 
have  assumed  .from  it  that  a  boiler  placed  two  feet  above  a  fire  would  re- 
ceive by  radiation  only  one-fourth  as  much  heat  as  if  it  were  only  one  foot 
above.  In  the  case  of  boiler  furnaces  the  side  walls  reflect  those  rays  that 
are  received  at  an  angle, —  following  the  law  of  optics,  that  the  angle  oj 
incidence  is  equal  to  the  angle  of  reflection,  —  with  the  result  that  the 
intensity  of  heat  two  feet  above  the  fire  is  practically  the  same  as  at  one 
foot  above,  instead  of  only  one-fourth  as  much. 

The  rate  at  which  a  hotter  body  radiates  heat,  and  a  colder  body 
absorbs  heat,  depends  upon  the  state  of  the  surfaces  of  the  bodies  as 
well  as  on  their  temperatures.  The  rate  of  radiation  and  of  absorption 
are  increased  by  darkness  and  roughness  of  the  surfaces  of  the  bodies, 
and  diminished  by  smoothness  and  polish.  For  this  reason  the  covering 


absorbing  power  under  the  same  circumstances.  When  a  polished  body 
is  struck  by  a  ray  of  heat,  it  absorbs  part  of  the  heat  and  reflects  the  rest. 

-  -  A1  -  -j  complement  of  its  absorb- 
power. 

„ ft'erent  bodies  has  been 

determined  by  experiment,  as  shown  m  the  table  below,  but  as  far  as 
quantities  of  heat  are  C9ncerned,  says  Prof.  Trowbridge  (Johnson's 
Cyclopaedia,  art.  Heat),  it  is  doubtful  whether  anything  further  than  the 
said  relative  determinations  can,  in  the  present  state  of  our  knowledge, 
be  depended  upon,  the  actual  or  absolute  quantities  for  different  tem- 
peratures being  still  uncertain.  The  authorities  do  not  even  agree  on  the 
relative  radiating  powers.  Thus,  Leslie  gives  for  tin  plate,  gold,  silver, 
and  copper  the  figure  12,  which  differs  considerably  from  the  figures  in 
the  table  below,  given  by  Clark,  stated  to  be  on  the  authority  of  Leslie, 
De  La  Provostaye  and  Desains,  and  Melloni. 

Relative  Radiating  and  Reflecting  Power  of  Different  Substances. 


Radiating  or 
Absorbing 
Power. 

Reflecting 
Power. 

Radiating  or 
Absorbing 
Power. 

Reflecting 
Power. 

100 
100 
100 
98 
93  to  98 
90 
85 
72 
27 

25 
23 

23 

0 
0 
0 
2 
7  to  2 
10 
15 
28 
73 

75 

77 

77 

Zinc,  polished  
Steel,  polished  
Platinum,  polished. 
Platinum  in  sheet  .  . 
Tin  

19 
17 
24 
17 
15 

11 

14 
7 
5 

3 
3 

81 
83 
76 

83 

85 

89 

93 
86 
93 
95 

97 
97 

Water  

Carbonate  of  lead  .  .  . 
^Vri  ting-paper 

Ivory,  jet,  marble... 
Ordinary  glass  
Ice 

Brass,  cast,  dead 

Gum  lac  

Brass,   bright  pol- 
ished   

Silver-leaf  on  glass  .  . 
Cast  iron,  bright  pol- 

Copper,  varnished.  . 
Copper,  hammered  . 
Gold  plated..  .. 

Mercury,  about  
Wrought  iron,  pol- 
ished 

Gold     on   polished 
steel                  .  . 

Silver,    polished 
bright.  

Experiments  of  Dr.  A.M.  Mayer  give  the  following:  The  relative  radi- 
ations from  a  cube  of  cast  iron,  having  faces  rough,  as  from  the  foundry, 


CONDUCTION  AND  CONVECTION  OF  HEAT.    579 


planed,  "drawfiled,"and  polished,  and  from  the  same  surfaces  oiled,  are  as 
below  (Prof.  Thurston,  in  Trans.  A.  S.  M.  E.,  vol.  xvi): 


Rough. 

Planed. 

Drawfiled. 

Polished. 

100 

60 

49 

45 

Surface  dry  

100 

32 

20 

18 

It  here  appears  that  the  oiling  of  smoothly  polished  castings,  as  of 
cylinder-heads  of  steam-engines,  more  than  doubles  the  loss  of  heat  by 
radiation,  while  it  doer-  not  seriously  affect  rough  castings. 

"  Black  Body  "  Radiation.  Stefan  and  Boltzman's  Law.  (Eng'q, 
March  1, 1907.)  —  Kirchhoff  defined  a  black  body  as  one  that  would  absorb 
all  radiations  falling  on  it,  and  would  neither  reflect  nor  transmit  any. 
The  radiation  from  such  a  body  is  a  function  of  the  temperature  alone, 
and  is  identical  with  the  radiation  inside  an  inclosure  all  parts  ol  wtncn 
have  the  same  temperature.  By  heating  the  walls  of  an  inclosure  as 
uniformly  as  possible,  and  observing  the  radiation  through  a  very  small 
opening,  a  practical  realization  of  a  black  body  is  obtained.  Stefan  and 
Boltzman's  law  is:  The  energy  radiated  by  a  black  body  is  proportional 
to  the  fourth  power  of  the  absolute  temperature,  or  E  =  K  (T4  —  T04), 
where  E  =  total  energy  radiated  by  the  body  at  T  to  the  body  at  TO,  and 
K  is  a  constant.  The  total  radiation  from  other  than  black  bodies  increases 
more  rapidly  than  the  fourth  power  of  the  absolute  temperature,  so  that 
as  the  temperature  is  raised  the  radiation  of  all  bodies  approaches  that  of 
the  black  body.  A  confirmation  of  the  Stefan  and  Boltzman  law  is  given 
in  the  results  of  experiments  by  Lummer  and  Kurlbaum,  as  below  (TQ  =» 
290  degrees  C.t  abs.  in  all  cases). 

7*=  492.          654.          795. 
108.4       109.9 
6.56         8.14 
33.1         36.6 


E      (Black  body 109.1 

— =ri  \  Polished  platinum. .      4 .28 
-  T"4  (Iron  oxide 33.1 


1108.  1481.      1761  k 

109.0         110.7      

12.18         16.69     19.64 
46.9         65.3      


The  Stefan-Boltzman  law  as  applied  to  radiation  from  a  given  body 
may  be  written  W  =  5.7  e  [(0.001T)4-  (0.001  Te  )]4;  W  =  energy  in 
watts  radiated  per  square  centimeter  of  surface,  T  =  temperature  of 
the  hot  body,  Te  •=  temperature  of  the  surrounding  space,  e  =  relative 
emissivity,  a  characteristic  of  the  radiating  body,  always  less  than 
unity.  For  clean  polished  metal  surfaces  e  ranges  from  0.02  to  0.20; 
for  non-metallic  surfaces,  from  about  0.3  to  about  0.9. 

CONDUCTION  AND  CONVECTION  OF  HEAT. 

Conduction  is  the  transfer  of  heat  between  two  bodies  or  parts  of  a 
body  which  touch  each  other.  Internal  conduction  takes  place  between 
the  parts  of  one  continuous  body,  and  external  conduction  through  the 
surface  of  contact  of  a  pair  of  distinct  bodies. 

The  rate  at  which  conduction,  whether  internal  or  external,  goes  on, 
being  proportional  to  the  area  of  the  section  or  surface  through  which  it 
takes  place,  may  be  expressed  in  thermal  units  per  square  foot  of  area  per 
hour. 

Internal  Conduction  varies  with  the  heat  conductivity,  which  depends 
upon  the  nature  of  the  substance,  and  is  directly  proportional  to  the 
difference  between  the  temperatures  of  the  two  faces  of  a  layer,  and  in- 
versely as  its  thickness.  The  reciprocal  of  the  conductivity  is  called  the 
internal  thermal  resistance  of  the  substance.  If  r  represents  this  resist- 
ance, x  the  thickness  of  the  layer  in  inches,  Tf  and  T  the  temperatures 
on  the  two  faces,  and  q  the  quantity  in  thermal  units  transmitted  per 


hour  per  square  foot  of  area,  q  —  • 
Pe"clet  gives  the  following  values  of  r: 


(Rankine.) 


Gold,  platinum,  silver 0.0016 

Copper 0.0018 

Iron 0.0043 

Zinc 0.0045 


Lead 0.0090 

Marble 0.0716 

Brick 0.1500 


680 


HEAT. 


Metals. 


Relative  Heat-conducting  Power  of  Metals. 


*C.&J.  fW.&F. 


Silver 1000    '   1000 

Gold 981         532 

Gold,  with  1  %  of  silver.  840 

Copper,  rolled 845         736 

Copper,  cast 811 

Mercury 677 

Mercury,  with  1.25%  of 

tin.... 412 

Aluminum 665         ... 

Zinc: 

cast  vertically 628 

cast  horizontally. . .  608 

rolled 641 

*  Calvert  &  Johnson. 


Metals.  *C.&J.  fW.&F. 

Cadmium 577 

Wrought  iron 436 

Tin 422 

Steel 397 

Platinum. 380 

Sodium 365 

Cast  iron 359 

Lead 287 

Antimony: 

cast  horizontally. .  215 

cast  vertically. ...  192 

Bismuth 61 


119 
145 
116 

84 


85 


18 


t  Weidemann  &  Franz. 


INFLUENCE  OF  A  NON-METALLIC  SUBSTANCE  IN  COMBINATION  ON  THE 

CONDUCTING  POWER  OF  A  METAL. 
Influence  of  carbon  on  iron: 

Wrought  iron 436 

Steel 397 

Cast  iron 359 


Cast  copper , 811 

Copper  with  1  %  of  arsenic 570 

with  0.5%  of  arsenic. .   669 
with  0.25%  of  arsenic,  771 


The  Rate  of  External  Conduction  through  the  bounding  surface 
between  a  solid  body  and  a  fluid  is  approximately  proportional  to  the 
difference  of  temperature,  when  that  is  small;  but  when  that  difference  is 
considerable,  the  rate  of  conduction  increases  faster  than  the  simple  ratio  of 
that  difference.  (Rankine.) 

If  r,  as  before,  is  the  coefficient  of  internal  thermal  resistance,  e  and  ef 
the  coefficient  of  external  resistance  of  the  two  surfaces,  x  the  thickness  of 
the  plate,  and  Tf  and  T  the  temperatures  of  the  two  fluids  in  contact 


with  the  two  surfaces,  the  rate  of  conduction  is  q 


Accord- 


ing to  Pellet,  e  +  e'  = 


e  +  e'  +  rx 
in  which  the  constants  A  and 


A  [1  -f  B  (Tf  -  T}\ 
B  have  the  following  values: 

B  for  polished  metallic  surfaces 0 . 0028 

B  for  rough  metallic  surfaces  and  for  non-metallic  surfaces  . .   0. 0037 

A  for  polished  metals,  about 0.90 

A  for  glassy  and  varnished  surfaces 1 . 34 

A  for  dull  metallic  surfaces 1 . 58 

A  for  lampblack 1 . 78 

When  a  metal  plate  has  a  liquid  at  each  side  of  it,  it  appears  from  experi- 
ments by  Pe"clet  that  B  =  0.058,  A  =  8.8; 

The  results  of  experiments  on  the  evaporative  power  of  boilers  agree 
very  well  with  the  following  approximate  formula  for  the  thermal  resist- 
ance of  boiler  plates  and  tubes: 

e+er-(T^T)' 

which  gives  for  the  rate  of  conduction,  per  square  foot  of  surface  per  hour, 

(Tr  -T7)2 


This  formula  is  proposed  by  Rankine  as  a  rough  approximation,  near 
enough  to  the  truth  for  its  purpose.  The  value  of  a  lies  between  160  and 
200.  Experiments  on  modern  boilers  usually  give  higher  values. 

Convection,  or  carrying  of  heat,  means  the  transfer  and  diffusion  of  the 
heat  in  a  fluid  mass  by  means  of  the  motion  of  the  particles  of  that  mass. 

The  conduction,  properly  so  called,  of  heat  through  a  stagnant  mass  of 
fluid  is  very  slow  in  liquids,  and  almost,  if  not  whplly,  inappreciable  in 
gases.  It  is  only  by  the  continual  circulation  and  mixture  of  the  particles 
of  the  fluid  that  uniformity  of  temperature  can  be  maintained  in  the  fluid 
mass,  or  heat  transferred  between  the  fluid  mass  and  a  solid  body. 

The  free  circulation  of  each  of  the  fluids  which  touch  the  side  of  a  solid 
plate  is  a  necessary  condition  of  the  correctness  of  Rankine's  formulae  for 
tne  conduction  of  heat  through  that  plate;  and  in  these  formulae  it  is 


CONDUCTION  AND  CONVECTION  OF  HEAT.    581 


fmplied  that  the  circulation  of  each  of  the  fluids  by  currents  and  eddies  is 
such  as  to  prevent  any  considerable  difference  of  temperature  between  the 
fluid  particles  in  contact  with  one  side  of  the  solid  plate  and  those  at  con- 
siderable distances  from  it. 

When  heat  is  to  be  transferred  by  convection  from  one  fluid  to  another, 
through  an  intervening  layer  of  metal,  the  nations  of  the  two  fluid  masses 
should,  if  possible,  be  in  opposite  directions,  in  order  that  the  hottest  par- 
ticles of  each  fluid  may  be  m  communication  with  the  hottest  particles  of 
the  other,  and  that  the  minimum  difference  of  temperature  between  the 
adjacent  particles  of  the  two  fluids  may  be  the  greatest  possible. 

Thus,  in  the  surface  condensation  of  steam,  by  passing  it  through  metal 
tubes  immersed  in  a  current  of  cold  water  or  air,  the  cooling  fluid  should 
be  made  to  move  in  the  opposite  direction  to  the  condensing  steam. 

Coefficients  of  Heat  Conduction  of  Different  Materials.  (W. 
Nusselt,  Zeit  des  Ver.  Deut.  Ing.,  June,  1908.  Eng.  Digest,  Aug.,  1908.)  — 
The  materials  were  inclosed  between  two  concentric  metal  vessels,  the 
inner  of  which  contained  an  electric  heating  device. 

It  was  found  that  the  materials  tested  all  followed  Fourier's  law,  the 
quantity  of  heat  transmitted  being  directly  proportional  to  the  extent  of 
surface,  the  duration  of  flow  and  the  temperature  difference  between  the 
inner  and  outer  surfaces;  and  inversely  proportional  to  the  thickness  of 
the  mass  of  material.  It  was  also  found  that  the  coefficient  of  conduction 
increased  as  the  temperature  increased.  The  table  gives  the  British 
equivalents  of  the  average  coefficients  obtained. 

COEFFICIENTS  OF  HEAT  CONDUCTION  AT  DIFFERENT  TEMPERATURES 

FOR  VARIOUS  INSULATING  MATERIALS. 

(B.T.U.  per  hour  =  Area  of  surface  in  square  feet  X  coefficient  -f-  thick- 
ness in  inches.) 


Lb.  per 
cu.  ft. 

Materials. 

32° 
F. 

212° 
F. 

392° 
F. 

572° 
F. 

752° 
F. 

10 

Ground  cork  

0.250 

0.387 

0.443 

8.5 

Sheep's  wool*  

0.266 

0.403 

6  3 

Silk  waste    

0.306 

0.411 

9.18 
5  06 

Silk,  tufted  
Cotton  wool                      

0.314 
0.379 

0.419 
0.476 

J1.86 

Charcoal    (carbonized     cabbage 
leaves)                               

0.403 

0.508 

13  42 

Sawdust  (0  443  at  1  12°  F  ) 

10 

Peat  refusef  (0  443  at  77°  F  ) 

2'  .85 

Kieselguhr     (infusorial      earth), 
loose         ....                     ... 

3.419 

0.532 

3.596 

0.629 

12.49 

Asphalt-cork  composition  (0.492 
at65°F.).                  .     

25.28 
12  49 

Composition,  j  loose  
Kieselguhr  stone  §                          ... 

0.484 
0.516 

0.613 
0.629 

0.653 
0.742 

J!854' 

o:%r 

12  17 

Peat  refusef  (0  564  at  68°  -F  ) 

36.2 

Kieselguhr,  dry  and  compacted 
(0  669  at  302°  F  •  0  991  at  662°  F.) 

43.07 

Composition,  §§  compacted  (0.806 
at  302°  F  •  0  967  at  428°  F.) 

22.47 

Porous  blast-furnace  slag  (0.766 
at  I12°F.)                           .... 

35  96 

Asbestos  (1  .644  at  1112°  F.)  

1.048 

1.346 

1.451 

1.499 

•1.548 

34  33 

Slag  concrete!  (1  532  at  112°  F  ) 

18.23 

Eumice    stone    gravel   (1.612   at 
112°  F  ) 

128.5 

Portland  cement,  neat   (6.287  at 
95°  F.)  

Tufted,  oily,  and  containing  foreign  matter.  Used  in  Linde's 
apparatus,  t  Hygroscopic;  measurements  made  in  moist  zones.  \  Cork, 
asbestos,  kieselguhr  and  chopped  straw,  mixed  with  a  binder  and  made 
in  sheets  for  application  to  steam  pipes  in  successive  layers,  the  whole 
being  wrapped  in  canvas  and  painted.  §  Kieselguhr,  mixed  with  a  binder 
and  burned;  very  porous  and  hygroscopic.  §§  Ingredients  of  ($)  mixed 
with  water  and  compacted.  ||  1  part  cement,  9  parts  porous  blast-furnace 
slag,  by  volume. 


582  HEAT. 

Heat  Resistance,   the  Reciprocal  of   Heat    Conductivity.     (W. 

Kent,  Trans.  A.  S.  M.  E.,  xxi-7,  278.)— The  resistance  to  the  passage  of 
heat  through  a  plate  consists  of  three  separate  resistances;  viz.,  the 
resistances  of  the  two  surfaces  and  the  resistance  of  the  body  of  the  plate 
which  latter  is  proportional  to  the  thickness  of  the  plate.  It  is  probable 
also  that  the  resistance  of  the  surface  differs  with  the  nature  of  the  body 
or  medium  with  which  it  is  in  contact. 

A  complete  set  of  experiments  on  the  heat-resisting  power  of  heat- 
insulating  substances  should  include  an  investigation  into  the  difference 
in  surface  resistance  when  a  surface  is  in  contact  with  air  and  when  it  is 
in  contact  with  another  solid  body.  Suppose  we  find  that  the  total  resist- 
ance of  a  certain  non-conductor  may  be  represented  by  the  figure  10,  and 
that  similar  pieces  all  give  the  same  figure.  Two  pieces  in  contact  give  16. 
One  piece  of  half  the  thickness  of  the  others  gives  8.  What  is  the  resist- 
ance of  the  surface  exposed  to  the  air  in  either  piece,  of  the  surface  in 
contact  with  another  surface,  and  of  the  interior  of  the  body  itself?  Let 
the  resistance  of  the  material  itself,  of  the  regular  thickness,  be  rep- 
resented by  A,  that  of  the  surface  exposed  to  the  air  by  a,  and  that  of  the 
surface  in  contact  with  another  surface  by  c. 

We  then  have  for  the  three  cases, 

Resistance  of  one  piece .4  -t-  2  a  ^  10 

of  two  pieces  in  contact ....     2A+2c+2a  =  16 
of  the  thin  piece i/2A+2a=    8 

These  three  equations  contain  three  unknown  quantities.  Solving  the 
equations  we  find  A  =  4,  a  =  3,  and  c  =  1.  Suppose  that  another 
experiment  be  made  with  the  two  pieces  separated  by  an  air  space,  and 
that  the  total  resistance  is  then  22.  If  the  resistance  of  the  air  space  be 
represented  by  s  we  have  the  two  equations:  Resistance  of  one  piece, 
A  +  2  a  =  10;  resistance  of  two  pieces  and  air  space,  2  A  +  4a  +  a  =  22, 
from  which  we  find  s  =  2.  Having  these  results  we  can  easily  estimate 
what  will  be  the  resistance  to  heat  transfer  of  any  number  of  layers  of  the 
material,  whether  in  contact  or  separated  by  air  spaces. 

The  writer  has  computed  the  figures  for  heat  resistance  of  several 
insulating  substances  from  the  figures  of  conducting  power  given  in  a  table 

Published  by  John  E.  Starr,  in  Ice  and  Refrigeration,  Nov.,  1901.  Mr. 
tarr's  figures  are  given  in  terms  of  the  B.T.U.  transmitted  per  sq.  ft.  o* 
surface  per  day  per  degree  of  difference  of  temperatures  of  the  air  adjacent 
to  each  surface.  The  writer's  figures,  th9se  in  the  last  column  of  the  table 
given  on  p.  583,  are  calculated  by  dividing  Mr.  Starr's  figures  by  24,  to 
obtain  the  hourly  rate,  and  then  taking  their  reciprocals.  They  may  be 
called  "coefficients  of  heat  resistance"  and  defined  as  the  reciprocals  of 
the  B.T.U.  per  sq.  ft.  per  hour  per  degree  of  difference  of  temperature. 

Analyzing  some  of  the  results  given  in  the  last  column  of  the  table,  we 
observe  that,  comparing  Nos.  2  and  3,  1  in.  added  thickness  of  pitch 
increased  the  coefficient  0.74;  comparing  Nos.  4  and  5,  1 1/2  in.  of  mineral 
wool  increased  the  coefficient  1.11.  If  we  assume  that  the  1  in.  of  mineral 
wool  in  No.  4  was  equal  in  heat  resistance  to  the  additional  11/2  in.  added 
in  No.  5,  or  1.11  reciprocal  units,  and  subtract  this  from  5.22,  we  get  4.11 
as  the  resistance  of  two  7/8-in.  boards  and  two  sheets  of  paper.  This 
would  indicate  that  one  7/g-in.  boaj*d  and  one  sheet  of  paper  give  nearly 
twice  as  much  resistance  as  1  in.  of  mineral  wool.  In  like  manner  any 
number  of  deductions  may  be  drawn  from  the  table,  and  some  of  them 
will  be  rather  questionable,  such  as  the  comparison  of  No.  15  and  No.  16, 
showing  that  1  in.  additional  sheet  cork  increased  the  resistance  given  by 
four  sheets  6.67  reciprocal  units,  or  one-third  the  total  resistance  of  No.  15. 
This  result  is  extraordinary,  and  indicates  that  there  must  have  been 
considerable  differences  of  conditions  during  the  two  tests.  • 

For  comparison  with  the  coefficients  of  heat  resistance  computed  from 
Mr.  Starr's  results  we  may  take  the  reciprocals  of  the  figures  given  by 
Mr.  Alfred  R.  Wolff  as  the  result  of  German  experiments  on  the  heat 
transmitted  through  various  building  materials,  as  below: 

K  =  B.T.U.  transmitted  per  hour  per  sq.  ft.  of  surface,  per  degree 
F.  difference  of  temperature. 

C  =  coefficient  of  heat  resistance  =  reciprocal  of  K. 

The  irregularity  of  the  differences  of  C  computed  from  the  original 
values  of  K  for  each  increase  of  4  inches  in  thickness  of  the  brick  walls 
inoUcates  a  difference  in  the  conditions  of  the  experiments.  The  average 


CONDUCTION  AND  CONVECTION  OF  HEAT.    583 


HEAT  CONDUCTING  AND  RESISTING  VALUES  OF  DIFFERENT  MATERIALS. 


Insulating  Material. 

Conductance, 
B.T.U.  per 
Sq.  Ft.  per 
Day  per  Deg., 
Difference  of 
Temperature. 

Coefficient 
of  Heat 
Resistance. 
C. 

1.  5/8-in.  oak  board,  1  in.  lampblacK,  7/g-in.  pine 
board  (ordinary  family  refrigerator)  
2.  7/8-in.  board,  1  in.  pitch,  7/8-in.  board  
3    7/8-in  board  2  in  pitch  7/8-in.  board.    .   .   . 

5.7 

4.89 
4.25 

4.6 
3.62 

3.38 
3.90 

2.10 
4.28 
3.71 
3.32 

1.35 

1.80 
2.10 

1.20 
0.90 
1.70 
3.30 

2.70 
2.52 
2.48 

4.21 
4.91 
5.65 

5.22 
6.63 

7.10 
6.15 

11.43 

5.61 
6.47 

7.23 

17.78 
13.33 
11.43 

20.00 
26.67 
14.12 
7.27 

8.89 
9.52 
9.68 

4.  7/s-in.  board'  paper,  1  in.  mineral  wool,  paper, 
7/8-in.  board  

5.  7/8-in.  board,  paper,  21/2  in.  mineral  wool, 
paper,  7/8-in.  board  

6.  7/8-in.  board,  paper,  21/2  in.  calcined  pumice, 
7/8-in.  board  

7    Same  as  above  when  wet   

8.  7/8-in.  board,  paper,  3  in.  sheet  cork,  7/8-in. 
board                                  .       

9.  Two  7/8-in.  boards,  paper,  solid,  no  air  space, 

10.  Two  7/8-in.  boards,  paper,  1  in.  air  space, 

11.  Two  7/8-in.  boards,   paper,   1  in.  hair  felt, 
paper  two  7/8-in  boards                      • 

12.  Two  7/8-in.  boards,  paper,  8  in.  mill  shav- 
ings paper  two  7/8-in  boards  

15.  Two  7/8-in.  boards,  paper,  3  in.  air,  4  in. 
sheet  cork  paper  two  7/8-in.  boards...  .  .  .  . 

1  7    Same  with  4  in  granulated  cork  .   

18    Same  with  1  in  sheet  cork  

19.  Four  double  7/8-in.  boards  (8  boards),  with 
paper  between,  three  8-in.  air  spaces  
20.   Four  7/8-in.  boards,  with  three  quilts  of  l/4-in 
hair  between,  papers  separating  boards  .  . 
21.   7/8-in.  board,  6  in.  patented  silicated  straw 
board,  finished  inside  with  thin  cement.  . 

difference  of  C  for  each  4  inches  of  thickness  is  about  0.80.  Using  this 
average  difference  to  even  up  the  figures  we  find  the  value  of  C  is  ex- 
pressed by  the  approximate  formula  C  =  0.70  +  0.20  t,  in  which  t  is  the 
thickness  in  inches.  The  revised  values  of  C,  computed  by  this  formula, 
and  the  corresponding  revised  values  of  K,  are  as  follows: 


Thick.,  In. 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

C 

1  50 

2  30 

3  10 

3  90 

4  70 

5  50 

6  30 

7  10 

7  90 

8  70 

K,  revised.. 
K,  original  . 
Difference.  . 

0.667 
0.68 
0.013 

0.435 
0.46 
0.025 

0.323 
0.32 
0.003 

0.256 
0.26 
0.004 

0.213 
0.23 
0.017 

0.182 
0.20 
0.018 

0.159 
0.174 
0.015 

0.141 
0.15 
0.009 

0.127 
0.129 
0.002 

0.115 
0.115 
0.0 

The  following  additional  values  of  C  are  computed  from  Mr.  Wolff's 
figures  for  K: 

Wooden  beams  planked  over,  or  ceiled :  K  C 

As  flooring 0.083  12.05 

As  ceiling 0.104  9.71 

Fireproof  construction,  floored  over: 

As  flooring 0.124  8.06 

As  ceiling 0.145  6.90 

Single  window : 1.030  0.97 

Single  skylight 1.118  0.89 

Double  window 0.518  1.93 

Double  skylight 0 . 621  1 . 61 

Poor,, , , .0.414  2,42 


584 


HEAT. 


It  should  be  noted  that  the  coefficient  of  resistance  thus  defined  will  be 
approximately  a  constant  quantity  for  a  given  substance  under  certain 
fixed  conditions,  only  when  the  difference  of  temperature  of  the  air  on  its 
two  sides  is  small  —  say  less  than  100°  F.  When  the  range  of  tem- 
perature is  great,  experiments  on  heat  transmission  indicate  that  the 
quantity  of  heat  transmitted  varies,  not  directly  as  the  difference  of  tem- 
perature, but  as  the  square  of  that  difference.  In  this  case  a  coefficient 
of  resistance  with  a  different  definition  may  be  found — viz.,  that  ob- 
tained from  the  formula  a  =  (T  —  t)2  •*•  q,  in  which  a  is  the  coefficient, 
T  —  t  the  range  of  temperature,  and  q  the  quantity  of  heat  transmitted, 
in  British  thermal  units  per  square  foot  per  hour, 

Steam-pipe  Coverings. 

Experiments  by  Prof.  Ordway,  Trans.  A.  S.  M.  E.,  vi,  168;  also  Circular 
No.  27  of  Boston  Mfrs.  Mutual  Fire  Ins.  Co.,  1890. 


Substance  1  In.  Thick.     Heat 
Applied,  310°  F. 

Pounds  of 
Water 
Heated 
10°  F.,  per 
Hour, 
Through 
1  Sq.  Ft. 

British 
Thermal 
Units  per 
Sq.  Ft.  per 
Minute. 

Solid  Mat- 
ter in  1  Sq. 
Ft.,  1  In. 
Thick, 
Parts  in 
1000. 

Air  included. 
Parts  in  100. 

8.1 

.35 

56 

944 

9.6 

60 

50 

950 

3.  Carded  cotton  wool  

10.4 

73 

20 

980 

4    Hair  felt  

10  3 

72 

185 

815 

5    Loose  lampblack.        

9  8 

63 

56 

944 

6.  Compressed  lampblack  

10.6 

77 

244 

756 

7    Cork  charcoal 

11   9 

1   98 

53 

947 

8.   White-pine  charcoal  

13  9 

2  32 

119 

881 

35.7 

5.95' 

506 

494 

10    Loose  calcined  magnesia 

12  4 

2  07 

23 

977 

1  1  .  Compressed  calcined  magnesia  .  . 
12.  Light  carbonate  of  magnesia.  .  .  . 
13.  Compressed  carb.  of  magnesia..  . 
1  4    Loose  fossil-meal 

42.6 
13  7 
15.4 
14  5 

7.10 
2.28 
2.57 
2  42 

285 
60 
15<0 
60 

715 
940 
850 
940 

1  5    Crowded  fossil-meal  ... 

15  7 

2  62 

112 

888 

16.  Ground  chalk  (Paris  white). 
1  7    Dry  plaster  of  Paris    . 

20.6 
30  9 

3.43 
5    15 

253 

368 

747 
632 

1  8    Fine  asbestos   

49  0 

8   17 

81 

919 

48.0 

8  00 

0 

1000 

20    Sand 

62   1 

10  35 

529 

471 

2  1  .  Best  slag-  wool    

13. 

2   17 

22.  Paper  

14. 

2.33 

23.  Blotting-paper  wound  tight    .  .    . 

21 

3  50 

21.7 

3.62 

25    Cork  strips  bound  on            .    .    . 

14  6 

2  43 

18. 

3. 

27    Loose  rice  chaff  . 

18  7 

3    12 

28.  Paste  of  fossil-meal  with  hair    .  . 

16.7 

2  78 

29.   Paste  of  fossil-meal  with  asbestos. 

22. 

3.67 

30.  Loose  bituminous-coal  ashes.  .  .  . 

21. 

3.50 

31.  Loose  anthracite-coal  ashes  

27. 

4.50 

32.  Paste  of  clay  and  vegetable  fiber 

30.9 

5.  15 

It  will  be  9bserved  that  several  of  the  incombustible  materials  are 
nearly  as  efficient  as  wool,  cotton,  and  feathers,  with  which  they  may  be 
compared  in  the  preceding  table.  The  materials  which  may  be  con- 
sidered wholly  free  from  the  danger  of  being  carbonized  or  ignited  by 
slow  contact  with  pipes  or  boilers  are  printed  in  Roman  type.  Those 
which  are  more  or  less  liable  to  be  carbonized  are  printed  in  italics. 

The  results  Nos.  1  to  20  inclusive  were  from  experiments  with  the 
various  non-conductors  each  used  in  a  mass  one  inch  thick,  placed  on  a 
flat  surface  of  iron  kept  headed  by  steam  to  310°  F,  The  substances 


CONDUCTION  AND  CONVECTION  OF  HEAT. 


585 


Nos.  21  to  32  were  tried  as  coverings  for  two-inch  steam-pipe;  the 
results  being  reduced  to  the  same  terms  as  the  others  for  convenience 
of  comparison. 

Experiments  on  still  air  gave  results  which  differ  little  from  those  of 
Nos.  3,  4,  and  6.  The  bulk  of  matter  in  the  best  non-conductors  is 
relatively  too  small  to  have  any  specific  effect  except  to  trap  the  air  and 
keep  it  stagnant.  These  substances  keep  the  air  still  by  virtue  of  the 
roughness  of  their  fibers  or  particles.  The  asbestos,  No.  18,  had  smooth 
fibers.  Asbestos  with  exceedingly  fine  fiber  made  a  somewhat  better 
showing,  but  asbestos  is  really  one  of  the  poorest  non-conductors.  It 
may  be  used  advantageously  to  hold  together  other  incombustible  sub- 
stances, but  the  less  of  it  the  better.  A  "magnesia"  covering,  made  of 
carbonate  of  magnesia  with  a  small  percentage  of  good  asbestos  fiber 
and  containing  0.25  of  solid  matter,  transmitted  2.5  B.T.U.  per  square 
foot  per  minute,  and  one  containing  0.396  of  solid  matter  transmitted 
3.33  B.T.U. 

Any  suitable  substance  which  is  used  to  prevent  the  escape  of  steam 
heat  should  not  be  less  than  one  inch  thick. 

Any  covering  should  be  kept  perfectly  dry,  for  not  only  is  water  a  good 
carrier  of  heat,  but  it  has  been  found  that  still  water  conducts  heat  about 
eight  times  as  rapidly  as  still  air. 

Tests  of  Commercial  Coverings  were  made  by  Mr.  Geo.  M.  Brill 
and  reported  in  Trans.  A.  S.  M.  E.,  xvi,  827.  A  length  of  60  feet  of  8-inch 
steam-pipe  was  used  in  the  tests,  and  the  heat  loss  was  determined  by  the 
condensation.  The  steam  pressure  was  from  109  to  117  Ibs.  gauge,  and 
the  temperature  of  the  air  from  58°  to  81°  F.  The  difference  between  the 
temperature  of  steam  and  air  ranged  from  263°  to  286°,  averaging 
272°. 

The  following  are  the  principal  results: 


1 

Is 

I 

fto3 

si  8 

.  i-i 

II 

1] 

*! 

3 

ss 

s1 

.  £  S 

l| 

0) 

-^2 

Kind  of  Covering. 

"8 

IU 

""-SIS  ! 

0)  d 

W  o 

03  £^ 

ft 

s  9 

03      • 

-2  • 

^  ft    *" 

-6| 

°      £x 

~£    ®    n 

£-% 

02  £ 

£1 

g||| 

IK 

•|  51 

?fl 

H  ~ 

« 

W   • 

ca 

GQ""  W 

p^W 

W  °'d 

Bare  pipe..  . 

0.846 

12.27 

2.706 

100. 

2.819 

Magnesia 

.25 

0.120 

1.74 

0.384 

0.726 

14  2 

0  400 

Rock  wool  

.60 

0.080 

1.16 

0.256 

0.766 

9.5 

0.267 

Mineral  wool       

.30 

0.089 

1.29 

0.285 

0.757 

10  5 

0  297 

Fire-felt 

30 

0  157 

2  28 

0.502 

0  689 

18  6 

0  523 

Manville  sectional  

.70 

0.109 

1.59 

0.350 

0.737 

12.9 

0.364 

Manv.  sect  and  hair-felt 

2.40 

0.066 

0.96 

0.212 

0.780 

7.8 

0.221 

Manville  wopl-cement  .  .  . 

2.20 

0.108 

1.56 

0.345 

0.738 

12.7 

0.359 

Champion  mineral  wool  . 

1.44 

0.099 

1.44 

0.317 

0.747 

11.7 

0.330 

Hair-felt  

0  H2 

0.132 

1.91 

0.422 

0.714 

15.6 

0.439 

Riley  cement 

0  75 

0  298 

4.32 

0.953 

0.548 

35  2 

0  993 

Fossil-meal            

0.75 

0.275 

3.99 

0.879 

0.571 

32  5 

0  919 

Tests  of  Pipe  Coverings  by  an  Electrical  Method.  (H.  G.  Stott, 
Power,  1902.)  —  A  length  of  about  200  ft.  of  2-in.  pipe  was  heated  to  a 
known  temperature  by  an  electrical  current.  The  pipe  was  covered  with 
different  materials,  and  the  heat  radiated  by  each  covering  was  deter- 
mined by  measuring  the  current  required  to  keep  the  pipe  at  a  constant 
temperature.  A  brief  description  of  the  various  coverings  is  given  below. 

No.  2.  Sclid  sectional  covering,  11/2  in.  thick,  of  granulated  cork 
molded  under  pressure  and  then  baked  at  a  temperature  of  500°  F.; 
1/8  in.  asbestos  paper  next  to  pipe. 

No.  3.    Solid  1-in.  molded  sectional,  85%  carbonate  of  magnesia. 


580  HEAT. 

No.  4.  Solid  1-in.  sectional,  granulated  cork  molded  under  pressure 
and  baked  at  500°  F.;  1/8  in.  asbestos  next  to  pipe. 

No.  5.  Solid  1-in.  molded  sectional,  85%  carbonate  of  magnesia;  out- 
side of  sections  covered  with  canvas  pasted  on. 

No.  6.  Laminated  1-in.  sectional,  nine  layers  of  asbestos  paper  with 
granulated  cork  between;  outside  of  sections  covered  with  canvas,  i/s  in. 
asbestos  paper  next  to  pipe. 

No.  7.  Solid  1-in.  molded  sectional,  of  85%  carbonate  of  magnesia; 
outside  of  sections  covered  with  light  canvas. 

No.  8.  Laminated  1-in.  sectional,  seven  layers  of  asbestos  paper 
indented  with  i/4-in.  square  indentations,  which  serve  to  keep  the  asbestos 
layers  from  coming  in  close  contact  with  one  another;  1/8  in.  asbestos 
paper  next  to  pipe. 

No.  9.  Laminated  1-in.  sectional,  64  layers  of  asbestos  paper,  in  which 
were  embedded  small  pieces  of  sponge;  outside  covered  with  canvas. 

No.  10.  Laminated  li/2-in.  sectional,  12  plain  layers  of  asbestos  paper 
with  corrugated  layers  between,  forming  longitudinal  air  cells;  1/8  in. 
asbestos  paper  next  to  pipe;  sections  wired  on. 

No.  11.  Laminated  1-in.  sectional,  8  layers  of  asbestos  paper  with 
corrugated  layers  between,  forming  small  air  ducts  radially  around  the 
covering. 

No.  12.  Laminated  11/4-in.  sectional,  6  layers  of  asbestos  paper 
with  corrugated  layers;  outside  of  sections  covered  with  two  layers  of 
canvas. 

No.  15.  "Remanit,"  composed  of  2  layers  wound  in  reverse  direction 
with  ropes  of  carbonized  silk.  Inner  layer  21/2  in.  wide  and  1/2  in.  thick; 
outer  layer  2  in.  wide  and  3/4  in.  thick,  over  which  was  wound  a  network 
of  fine  wire;  Vsin.  asbestos  next  to  pipe.  Made  in  Germany. 

No.  16.  2i/2-in.  covering,  85%  carbonate  of  magnesia,  1/2-in.  blocks 
about  3  in.  wide  and  18  in.  long  next  to  pipe  and  wired  on;  over  these 
blocks  were  placed  solid  2-in.  molded  sectional  covering. 

No.  17.  2i/2-in.  covering,  85%  magnesia.  Put  on  in  a  2-in.  molded 
section  wired  on;  next  to  the  pipe  and  over  this  a  i/2-in.  layer  of  magnesia 
plaster. 

No.  18.  2 i/2-in.  covering,  85%  carbonate  of  magnesia.  Put  on  in  two 
solid  1-in.  molded  sections  with  i/2-in.  layer  of  magnesia  plaster  between; 
two  1-in.  coverings  wired  on  and  placed  so  as  to  break  joints. 

No.  19.  2-in.  covering,  of  85%  carbonate  of  magnesia,  put  on  in  two 
1-in.  layers  so  as  to  break  joints. 

No.  20.     Solid  2-in.  molded  sectional,  85%  magnesia. 

No.  21.     Solid  2-in.  molded  sectional,  85%  magnesia. 

Two  samples  covered  with  the  same  thickness  of  similar  material  give 
different  results;- for  example,  Nos.  3  and  5,  and  also  Nos.  20  and  21. 
The  cause  of  this  difference  was  found  to  be  in  the  care  with  which  the 
joints  between  sections  were  made.  A  comparison  between  Nos.  19  and 
20,  having  the  same  total  thickness,  but  one  applied  in  a  solid  2-in.  section, 
and  the  other  in  two  1-in.  sections,  proved  the  desirability  of  breaking 
joints. 

An  attempt  was  made  to  determine  the  law  governing  the  effect  of 
increasing  the  thickness  of  the  insulating  material,  and  for  all  the  85% 
magnesia  coverings  the  efficiency  varied  directly  as  the  square  root  of  the 
thickness,  but  the  other  materials  tested  did  not  follow  this  simple  law 
closely,  each  one  involving  a  different  constant. 

To  determine  which  covering  is  the  most  economical  the  following 
quantities  must  be  considered:  (1)  Investment  in  covering.  (2)  Cost 
of  coal  required  to  supply  lost  heat.  (3)  Five  per  cent  interest  on 
capital  invested  in  boilers  and  stokers  rendered  idle  through  having  to 
supply  lost  heat.  (4)  Guaranteed  life  of  covering.  (5)  Thickness  of 
covering. 

The  coverings  Nos.  2  to  15  were  finished  on  the  outside  with  resin  paper 
and  8-ounce  canvas;  the  others  had  canvas  pasted  on  outside  of  the  sec- 
tions, and  an  8-oz.  canvas  finish.  The  following  is  a  condensed  statement 
of  the  results  with  the  temperature  of  the  pipe  corresponding  to  160  Ib. 
steam  pressure. 


CONDUCTION  AND  CONVECTION  OF  HEAT. 


587 


ELECTRICAL  TEST  OF  STEAM-PIPE  COVERINGS. 


No. 

Covering. 

Aver. 
Thick- 
ness. 

B.T.U. 

Loss 
per 
Min. 
persq. 
ft.  at 
160  Ib. 
Pres. 

B.T.U. 
persq. 
ft.  per 
Hr.  per 
Deg. 
Diff.  of 
Temp. 

Per 

cent 
Heat 
Saved 
by 
Cover- 
ing. 

2 
3 
4 
5 
6 
7 
8 
9 
10 
II 
12 
15 
16 

17 

J8 
(9 
20 
21 

Solid  cork  

1.68 
.13 
.20 
.19 
.48 
.12 
.26 
.24 
.70 
.22 
.29 
1.51 

2.71 

2.45 
2.50 
2.24 
2.34 
2.20 

1.672 
2.008 
2.048 
2.130 
2.123 
2.190 
2.333 
2.552 
2.750 
2.801 
2.812 
1.452 

1.381 

.387 
.412 
.465 
.555 
.568 
13. 

0.348 
0.418 
0.427 
0.444 
0.442 
0.456 
0.486 
0.532 
0.573 
0.584 
0.586 
0.302 

0.288 

0.289 
0.294 
0.305 
0.324 
0.314 
2.708 

87.1 
84.5 
84.2 
83.6 
83.7 
S3.  2 
83.1 
80.3 
78.8 
78.5 
78.4 
88.8 

89.4 

88.7 
89.0 
88.7 
88.0 
87.9 

85  %  magnesia/ 

Solid  cork  

85%  magnesia 

Laminated  asbestos  cork    .  . 

85%  magnesia  

Asbestos  air  cell  [indent! 

Asbestos  sponge  felted  '.  

Asbestos  air  cell  [long] 

"  Asbestoscel  "  [radial]  

Asbestos  air  cell  [long]  

"  Remanit"  [silk]  wrapped  

85  %  magnesia,  2"  sectional  and  1/2" 
block  

85  %  magnesia,  2!'  sectional  and  1/2" 
plaster  .  . 

85%  magnesia,  two  1"  sectional  

85%  magnesia,  two  \"  sectional  . 

85%  magnesia  2"  sectional 

85%  magnesia,  2"  sectional  .  .       .   . 

Bare  pipe  [from  outside  tests]  

Transmission  of  Heat,  through  Solid  Plates,  from  Water  to  Water. 

(Clark,  S.  E.)  —  M.  Pe"clet  found,  from  experiments  made  with  plates  of 
wrought  iron,  cast  iron,  copper,  lead,  zinc,  and  tin,  that  when  the  fluid 
in  contact  with  the  surface  of  the  plate  was  not  circulated  by  artificial 
means,  the  rate  of  conduction  was  the  same  for  different  metals  and  for 
plates  of  the  same  metal  of  different  thicknesses.  But  when  the  water 
was  thoroughly  circulated  over  the  surfaces,  and  when  these  were  perfectly 
clean,  the  quantity  of  transmitted  heat  was  inversely  proportional  to  the 
thickness,  and  directly  as  the  difference  in  temperature  of  the  two  faces 
of  the  plate.  When  the  metal  surface  became  dull,  the  rate  of  trans- 
mission of  heat  through  all  the  metals  was  very  nearly  the  same. 

It  follows,  says  Clark,  that  the  absorption  of  heat  through  metal  plates 
is  more  active  whilst  evaporation  is  in  progress  —  when  the  circulation  of 
the  water  is  more  active  —  than  while  the  water  is  being  heated  up  to  the 
boiling-point. 

Transmission  from  Steam  to  Water.  —  M.  Pellet's  principle  is 
supported  by  the  results  of  experiments  made  in  1867  by  Mr.  Isherwood  on 
the  conductivity  of  different  metals.  Cylindrical  pots,  10  inches  in 
diameter,  211/4  inches  deep  inside,  and  Vs  inch,  1/4  inch,  and  3/8  inch 
thick,  turned  and  bored,  were  formed  of  pure  copper,  brass  (60  copper 
and  40  zinc),  rolled  wrought  iron,  and  remelted  cast  iron.  They  were 
immersed  in  a  steam  bath,  which  was  varied  from  220°  to  320°  F.  Water 
at  212°  was  supplied  to  the  pots,  which  were  kept  filled.  It  was  ascer- 
tained that  the  rate  of  evaporation  was  in  the  direct  ratio  of  the  difference 
of  the  temperatures  inside  and  outside  of  the  pots;  that  is,  that  the  rate 
of  evaporation  per  degree  of  difference  of  temperatures  was  the  same  for 
all  temperatures;  and  that  the  rate  of  evaporation  was  exactly  the  same 
for  different  thicknesses  of  the  metal.  The  respective  rates  of  conductiv- 
ity of  the  several  metals  were  as  follows,  expressed  in  weight  of  water 
evaporated  from  and  at  212°  F,  per  square  foot  of  the  interior  surface  of 
the  pots  per  degree  of  difference  of  temperature  per  hour,  together  witfc 
tbe  equivalent  quantities  of  heat-units: 


588 


HEAT. 


Water  at  212°.  Heat-units.  Ratio. 

Copper 0.665  Ib.              642.5  1.00 

Brass 577    '                  556.8  0.87 

Wrought  iron .387    "                373.6  .58 

Cast  iron .327    -                315.7  .49 


Whitham,  "Steam  Engine  Design,"  p.  283,  also  Trans.  A.  S.  M.  E.,  ixf 
425,  in  using  these  data  in  deriving  a  formula  for  surface  condensers,  calls 
these  figures  those  of  perfect  conductivity,  and  multiplies  them  by  a 
coefficient  C,  which  he  takes  at  0.323,  to  obtain  the  efficiency  of  con- 
denser surface  in  ordinary  use,  i.e.,  coated  with  saline  and  greasy  deposits. 

Transmission  of  Heat  from  Steam  to  Water  through  Coils  of  Iron 
Pipe.  —  H.  G.  C.  Kopp  and  F.  J.  Meystre  (Stevens  Indicator,  Jan.,  1894) 
give  an  account  of  some  experiments  on  transmission  of  heat  through 
coils  of  pipe.  They  collate  the  results  of  earlier  experiments  as  follows, 
for  comparison: 


Steam  con- 

Heat trans- 

ID 

n 

densed  per 
square  foot 
per  degree 
difference  of 

mitted  per 
square  foot 
per  degree 
difference  of 

i 

1 

"3 

temperature 
per  hour. 

temperature 
per  hour. 

Remarks. 

d 

B 

B 

ffi 

bC  co 

.' 

bC    . 

'£ 

B 

O 

2 

If 

Rc'c 

Jfcj 

i  c^ 

ft 

X 

w 

I 

wa 

W^a 

&M 

|2« 

Laurens  . 

Copper  coils  .  . 
2  Copper  coils 

0.292 

0.981 
1  20 

315 

974 
1120 

Havrez  .  . 

Copper  coil  .  .  . 

0.268 

1.26 

280 

1200 

Perkins.  . 

Iron  coil  

0.24 

215 

(  Steam  pressure 
=  100. 

•• 

••       " 

0.22 

208.2 

(  Steam  pressure 
i      =10. 

Box  

Iron  tube  

0.235 

230 

"        " 

0.196 

207 

«« 

d        i« 

0  206 

210 

Havrez  .  . 

Cast-iron  boiler 

0.077 

0.105 

82 

"166" 

From  the  above  it  would  appear  that  the  efficiency  of  iron  surfaces  Is 
less  than  that  of  copper  coils,  plate  surfaces  being  far  inferior. 

In  all  experiments  made  up  to  the  present  time,  it  appears  that  the 
temperature  of  the  condensing  water  was  allowed  to  rise,  a  mean  between 
the  initial  and  final  temperatures  being  accepted  as  the  effective  tempera- 
ture. But  as  water  becomes  warmer  it  circulates  more  rapidly,  thereby 
causing  the  water  surrounding  the  coil  to  become  agitated  and  replaced 
by  cooler  water,  which  allows  more  heat  to  be  transmitted. 

Again,  in  accepting  the  mean  temperature  as  that  of  the  condensing 
medium,  the  assumption  is  made  that  the  rate  of  condensation  is  in  direct 
proportion  to  the  temperature  of  the  condensing  water. 

In  order  to  correct  and  avoid  any  error  arising  from  these  assumptions 
and  approximations,  experiments  were  undertaken,,  in  which  all  the  condi- 
tions were  constant  during  each  test. 

The  pressure  was  maintained  uniform  throughout  the  coil,  and  pro- 
vision was  made  for  the  free  outflow  of  the  condensed  steam,  in  order  to 
obtain  at  all  times  the  full  efficiency  of  the  condensing  surface.  The  con- 
densing water  was  continually  stirred  to  secure  uniformity  of  temperature, 
which  was  regulated  by  means  of  a  steam-pipe  and  a  cold-water  pipe 
entering  the  tank  in  which  the  coil  was  placed. 


CONDUCTION    AND   CONVECTION    OF    HEAT.         589 


The  following  is  a  condensed  statement  of  the  results. 

HEAT  TRANSMITTED  PER  SQUARE  FOOT  OF  COOLING  SURFACE,  PER  HOUR, 
PER  DEGREE  OF  DIFFERENCE  OF  TEMPERATURE.     (British  Thermal  Units.) 


Temperature 
of  Condens- 
ing Water. 

1-in.  Iron  Pipe; 
Steam  inside, 
60  Ibs.  Gauge 
Pressure. 

H/2-in.  Pipe; 
Steam  inside, 
10  Ibs. 
Pressure. 

1  1/2-m.  Pipe; 
Steam  outside, 
10  Ibs. 
Pressure. 

1  1/2-in.  Pipe; 
Steam  inside, 
60  Ibs 
Pressure. 

80" 

265 

128 

200 

100 
120 
140 
160 
180 
200 

269 
272 
277 
281 
299 
313 

130 
137 
145 
158 
174 

230 
260 
267 
271 
270 

239 
247 
276 
306 
349 
419 

The  results  indicate  that  the  heat  transmitted  per  degree  of  difference  of 
temperature  in  general  increases  as  the  temperature  of  the  condensing 
water  is  increased. 

The  amount  transmitted  is  much  larger  with  the  steam  on  the  outside  of 
the  coil  than  with  the  steam  inside  the  coil.  This  may  be  explained  in 
part  by  the  fact  that  the  condensing  water  when  inside  the  coil  flows  over 
the  surface  of  conduction  very  rapidly,  and  is  more  efficient  for  cooling 
than  when  contained  in  a  tank  outside  of  the  coil. 

This  result  is  in  accordance  with  that  found  by  Mr.  Thomas  Craddock, 
which  indicated  that  the  rate  of  cooling  by  transmission  of  heat  through 
metallic  surfaces  was  almost  wholly  dependent  on  the  rate  of  circulation  of 
the  cooling  medium  over  the  surface  to  be  cooled. 

Transmission  of  Heat  in  Condenser  Tubes.  (Eng'g,  Dec.  10,  1875, 
p.  449.)  —  In  1874  B.  C.  Nichol  made  experiments  for  determining  the 
rate  at  which  heat  was  transmitted  through  a  condenser  tube.  The 
results  went  to  show  that  the  amount  of  heat  transmitted  through  the 
walls  of  the  tube  per  estimated  degree  of  mean  difference  of  temperature 
increased  considerably  with  this  difference.  For  example: 


Estimated  mean  difference  of 
temperature  between  inside  and 
outside  of  tube,  degrees  Fahr. .  .  . 


Vertical  Tube.      Horizontal  Tube. 


128  151.9  152.9     111.6  146.2    150.4 


Heat-units  transmitted  per  hour 
per  square  foot  of  surface  per 
degree  of  mean  diff.  of  temp 422  531 


561       610       737       823 


These  results  seem  to  throw  doubt  upon  Mr.  Isherwood's  statement  that 
the  rate  of  evaporation  per  degree  of  difference  of  temperature  is  the  same 
for  all  temperatures. 

Mr.  Thomas  Craddock  found  that  water  was  enormously  more  efficient 
than  air  for  the  abstraction  of  heat  through  metallic  surfaces  in  the  process 
of  cooling.  He  proved  that  the  rate  of  cooling  by  transmission  of  heat 
through  metallic  surfaces  depends  upon  the  rate  of  circulation  of  the  cool- 
in?  medium  over  the  surface  to  be  cooled.  A  tube  filled  with  hot 'water, 
moved  by  rapid  rotation  at  the  rate  of  59  ft.  per  second,  through  air,  lost  as 
much  heat  in  one  minute  as  it  did  in  still  air  in  12  minutes.  In  water,  at  a 
velocity  of  3  ft.  per  second,  as  much  heat  was  abstracted  in  half  a  minute 
as  was  abstracted  in  one  minute  when  it  was  at  rest  in  the  water.  Mr. 
Craddock  concluded,  further,  that  the  circulation  cf  the  cooling  fluid 
became  of  greater  importance  as  the  difference  of  temperature  on  the 
two  sides  of  the  plate  became  less.  (Clark,  R.  T.  D.,  p.  461.) 

G.  A.  Orrok  (Power,  Aug.  11,  1908)  gives  a  diagram  showing  the  relation 
of  the  B.T.U.  transmitted  per  hour  per  sq.  ft.  of  surface  per  degree  of 
difference  of  temperature  to  the  velocity  of  the  water  in  the  condenser 
tubes,  in  feet  per  second,  as  obtained  by  different  experimenters.  Approx* 
Imate  figures  taken  from  the  several  curves  are  given  below. 


590 


HEAT. 


Authority. 

Tubes. 

Velocity  of  Water,  Feet  per 
Second. 

0.5 

1 

2 

3 

4 

5 

6 

B.T.U.  per  sq.  ft.  per  hr.  per 
deg.  difif. 

1.  Stanton  
2.  Stanton  
3.  Nichols  
4.  Nichols  
5.  Hepburn  
6.  Hepburn  .  .  . 
7.  Richter  
8.  Weighton.  .  . 
9.  Alien  

l/2-jn.  vert,  copper  
l/2~in-  vert,  copper  . 

325 
420 
340 
500 
365 
560 

400 
470 
370 
530 
590 

465 
525 
405 
560 

520 
560 
435 

585 

550 
585 
460 
615 

470 
650 

3/4-in.  vert,  brass  
3/4-in.  horiz.  brass  
1  i/4-in.  horiz.  copper.  .  .  . 
1  l/4-in.  horiz.  corrugated 
1  1/2-in.  horiz.  corrugated 
5/g-in.  plain  tubes.  .  .  . 

"250" 
360 
<60 

380 
225 

615 
290 

760 
365 

865 

940 

5/s-in.  horizontal  

No.  1,  water  flowing  up.     Nos.  2  and  3,  water  flowing  down. 

Transmission  of  Heat  in  Feed-water  Heaters.  (W.  R.  Billings, 
The  National  Engineer,  June,  1907.)  —  Experiments  show  that  the  rate  of 
transmission  of  heat  through  metal  surfaces  from  steam  to  water  increases 
rapidly  with  the  increased  rate  of  flow  of  the  water.  Mr.  Billings  there- 
fore recommends  the  use  of  small  tubes  in  heaters  in  which  the  water  is 
inside  of  the  tubes.  He  says:  A  high  velocity  through  the  tubes  causes 
friction  between  the  water  and  the  walls  of  the  tubes;  this  friction  is  not 
the  same  as  the  friction  between  the  particles  of  water  themselves,  and  it 
tends  to  break  up  the  column  of  water  and  bring  fresh  and  cooler  particles 
against  the  hot  walls  of  the  tubes. 

The  following  results  were  obtained  in  tests: 

li/4-m.  smooth  tubes       j  ^  II  1||'5  \}Q  67Q 

1  i/2-in.  corrugated  tubes  j  ^  II  3 ^|  4|^  ,g|  ,,§! 

V  =  velocity  of  the  water,  ft.  per  min.  U  =  B.T.U.  transmitted  per 
sq.  ft.  per  hour  per  degree  difference  of  temperature.  (See  Condensers.) 

In  calculations  of  heat  transmission  in  heaters  it  is  customary  to  take 
as  the  mean  difference  of  temperature  the  difference  between  the  tem- 
perature of  the  steam  and  the  arithmetical  mean  of  the  initial  and  final 
temperatures  of  the  water;  thus  if  S  =  steam  temperature,  /  =  initial 
and  F  =  final  temperature  of  the  water,  and  D  =  mean  difference,  then 
D  =  S  -  1/2  (/  +  F).  Mr.  Billings  shows  that  this  is  incorrect,  and  on 
the  assumption  that  the  rate  of  transmission  through  any  portion  of  the 
surface  is  directly  proportional  to  the  difference  he  finds  the  true  mean 

to  be  D  -  hyp  lQg  [(/_-f)7  +{S_pn  •     (This  formula  was  derived  by 

Cecil  P.  Poole  in  1899,  Power,  Dec.,  1906.) 

The  following  table  is  calculated  from  the  formula: 

DEGREES  OF  DIFFERENCE  BETWEEN   STEAM  TEMPERATURE  AND  ACTUAII 
AVERAGE  TEMPERATURE  OF  WATER. 


Vacuum  Heaters  Between  Engine  and  Condenser. 


Initial 
Temperature 
of  Water. 

26"  Vac.    Temp.  126°  F. 

24"  Vac.                     Temp.  141°  F. 

Final  Temp,  of  Water. 

Final  Temp,  of  Water. 

105 

110 

115 

120 

105 

110 

115 

120 

125 

130 

40.6 
37.9 
35.0 
32.2 
29.2 

40.  ,, 

46.1 
42.8 
39,3 
35.6 
31.8 

41.6 
38.4 
35.3 
31.9 
28.3 

36.9 
33.6 
30.7 
27,6 
24,3 

30.1 
27.6 
25.0 
22,4 
19.6 

62.9 
59.2 
55.5 
51.6 
47.6 

60.2 
56.6 
52.1 
48.2 
44.2 

55.3 
51.8 
48.4 
45.0 
41.2 

50.9 
47.7 
44.4 
41.0 
37.3 

46.1 
43.2 
40.1 
36,9 
33.6 

30., 

60... 

70.,, 

80  

CONDUCTION    ATSTD   CONVECTION    OF   HEAT.        591 


Initial  Temp, 
of  Water. 

Atmospheric  Heaters. 

Atmos.  Press.    Temp. 
212°  F. 

Initial  Temp,  of 
Water. 

Atmos.  Press.     Temp. 
212°  F. 

Final  Temp,  of  Water. 

Final  Temp,  of  Water. 

192 

196 

200 

204 

208 

210 

192 

196 

200 

204 

208 

210 

40 

70.6 

67.9 
65.1 
62.2 
59.4 

65.7 
63.1 
60.4 
57.7 
54.9 

60.1 
57.6 
55.2 
52.6 
50.0 

53.5 

51.2 
48.9 
46.6 
44.2 

44.8 
42.8 
40.7 
38.7 
36.6 

38.0 
36.4 
34.7 
32.9 
31.0 

105 
110 
115 
120 
125 

51.9 
50.3 
48.8 
47.2 
45.6 

47.9 
46.4 
45.0 
43.5 
41.9 

43.4 
42.1 
40.6 
39.2 
37.8 

38.2 
36.9 
35.7 
34.4 
33.1 

31.4 
30.2 
29.2 
28.0 
26.9 

26.4 
25.5 
24.5 
23.5 
22.5 

50... 

60  .. 

70... 

80  

The  error  in  using  the  arithmetic  mean  for  the  value  of  D  is  not  impor- 
tant if  F  is  very  much  lower  than  S,  but  if  it  is  within  10°  of  S  then  the 
error  may  be  a  large  one.  With  S  =  212,  7  =  40,  F  =  110,  the  arith- 
metic mean  difference  is  137,  and  the  value  by  the  logarithmic  formula 
131,  an  error  of  less  than  5%;  but  if  F  is  204,  the  arithmetic  mean  is  90, 
and  the  value  by  the  formula  53.5. 

It  should  be  observed,  however,  that  the  formula  is  based  on  an  assump- 
tion that  is  probably  greatly  in  error  for  high  temperature  differences, 
i.e.,  that  the  transmission  of  heat  is  directly  proportional  to  the  tem- 
perature difference.  It  may  be  more  nearly  proportional  to  the  square 
of  the  difference,  as  stated  by  Rankine.  This  seems  to  be  indicated  by 
the  results  of  heating  water  by  steam  coils,  given  below. 

Heating  Water  by  Steam  Coils.  —  A  catalogue  of  the  American 
Radiator  Co.  (1908)  gives  a  chart  showing  the  pounds  of  steam  condensed 
per  hour  per  sq.  ft.  of  iron,  brass  and  copper  pipe  surface,  for  different 
mean  or  average  differences  of  temperature  between  the  steam  and  the 
water.  Taking  the  latent  heat  of  the  steam  at  966  B.T.U.  per  lb.,  the  fol- 
lowing figures  are  derived  from  the  table. 


Mean 

Lb.  Steam  Condensed 
per  Hour  per  Sq.  Ft. 
of  Pipe. 

Lb.  Steam  Condensed 
per  Hour  per  Sq.  Ft. 
per  Deg.  Diff. 

B.T.U.  per  Sq. 
Ft.  per  Hour 
per  Deg.  Diff. 

Iron. 

Brass. 

Copper 

Iron. 

Brass. 

Copper 

Iron. 

Brass 

Cop. 

50 
100 
150 
200 

7.5 
18.5 
32.2 
48 

12.5 
38 
76.5 
128 

14.5 
43.5 
87.8 
144 

0.150 
0.185 
0.215 
0.240 

0.250 
0.380 
0.510 
0.640 

0.290 
0.435 
0.585 
0.720 

101 
179 
208 
232 

198 
367 
493 
618 

280 
415 
565 
696 

The  chart  is  said  to  be  plotted  from  a  large  number  of  tests  with  pipes 
placed  vertically  in  a  tank  of  water,  about  20  per  cent  being  deducted 
from  the  actual  results  as  a  margin  of  safety. 

W.  R.  Billings  (Eng.  Rec.,  Feb.,  1898)  gives  as  the  results  of  one  set  of 
experiments  with  a  closed  feed-water  heater: 

Diff.  bet.  temp,  of  steam  and  final  temp,  of 

water,  deg.  F 5      6      8      11      15      18 

B.T.U.  per  sq.  ft.  per  hr.  per  deg.  mean  diff ...  67    79    89    114    129    139 

Heat  Transmission  through  Cast-iron  Plates  Pickled  in  Nitric 
Acid.  — Experiments  by  R.  C.  Carpenter  (Trans.  A.  S.  M.  E.,  xii,  179) 
show  a  marked  change  in  the  conducting  power  of  the  plates  (from 
steam  to  water),  due  to  prolonged  treatment  with  dilute  nitric  acid. 


592 


HEAT. 


The  action  of  the  nitric  acid,  by  dissolving  the  free  iron  and  not  attack- 
ing the  carbon,  forms  a  protecting  surface  to  the  iron,  which  is  largely 
composed  of  carbon.  The  following  is  a  summary  of  results: 


Increase 

Proportionate 

in  Tem- 

Thermal Units 

Rela- 

perature 

Transmitted  for 

tive 

Character  of  Plates,  each  plate  8.4  in. 
by  5.4  in.,  exposed  surface  27  sq.  ft. 

of  3.125 

Ibs.  of 

each  Degree*  of 
Difference  of 

Trans- 
mission 

Water 

Temperature  per 

of 

each 

Square  Foot  per 

Heat. 

Minute. 

Hour. 

Cast    iron  —  untreated    skin    on,    but 

clean,  free  from  rust  

13  90 

113  2 

100  0 

Cast  iron  —  nitric  acid,  1  %  sol.,  9  days  .  . 

11.5 

97J 

86J 

1%  sol.,  18  days 

9.7 

80.08 

70.7 

1%  sol.,  40  days 

9.6 

77.8 

68.7 

5%  sol.,  9  days.. 

9.93 

87.0 

76.  8 

5%  sol.,  40  days 

10.6 

77.4 

68.  5 

Plate  of  pine  wood,  same  dimensions  as 

the  plate  of  cast  iron 

0.33 

1  .9 

J.6 

The  effect  of  covering  cast-iron  surfaces  with  varnish  has  been  investi- 
gated by  P.  M.  Chamberlain.  He  subjected  the  plate  to  the  action  of  strong 
acid  for  a  few  hours,  and  then  applied  a  non-conducting  varnish.  One 
surface  only  was  treated.  Some  of  his  results  are  as  follows: 


tfo 

<#=+-! 

o>  b  oT 


W 


170.    As  finished  — greasy. 

152.  washed  with  benzine  and  dried. 

169.    Oiled  with  lubricating  oil. 

162.    After  exposure  to  nitric  acid  sixteen  hours,  then  oiled 

(linseed  oil). 
166.    After  exposure  to  hydrochloric  acid  twelve  hours,  then 

oiled  (linseed  oil). 

113.    (After  exposure  to  sulphuric  acid  1,  water  2,  for  48 
<     hours,  then  oiled,  varnished,  and  allowed  to  dry  for 
117.    (      24  hours. 


Transmission  of  Heat  through  Solid  Plates  from  Air  or  other  Dry 
Gases  to  Water.  (From  Clark  on  the  Steam  Engine.)  —  The  law  of  the 
transmission  of  heat  from  hot  air  or  other  gases  to  water,  through  metallic 
plates,  has  not  been  exactly  determined  by  experiment.  The  general 
results  of  experiments  on  the  evaporative  action  of  different  portions  of 
the  heating  surface  of  a  steam-boiler  point  to  the  general  law  that  the 
quantity  of  heat  transmitted  per  degree  difference  of  temperature  is 
practically  uniform  for  various  differences  of  temperature. 

The  communication  of  heat  from  the  gas  to  the  plate  surface  is  much 
accelerated  by  mechanical  impingement  of  the  gaseous  products  upon  the 
surface. 

Clark  says  that  when  the  surfaces  are  perfectly  clean,  the  rate  of  trans- 
mission of  heat  through  plates  of  metal  from  air  or  gas  to  water  is  greater 
for  copper,  next  for  brass,  and  next  for  wrought  iron.  But  when  the 
surfaces  are  dimmed  or  coated,  the  rate  is  the  same  for  the  different 
metals. 

With  respect  to  the  influence  of  the  conductivity  of  metals  and  of  the 
thickness  of  the  plate  on  the  transmission  of  heat  from  burnt  gases  to 
water,  Mr.  Napier  made  experiments  with  small  boilers  of  iron  and  copper 
placed  over  a  gas-flame.  The  vessels  were  5  inches  in  diameter  and  2  1/2 
inches  deep.  From  three  vessels,  one  of  iron,  one  of  copper,  and  one 
of  iron  sides  and  copper  bottom,  each  of  them  i/so  inch  in  thickness, 


CONDUCTION  AND  CONVECTION  OF  HEAT.    593 

equal  quantities  of  water  were  evaporated  to  dryness,  in  the  times  as 
follows: 

Water.  Iron  Vessel.          Copper  Vessel.        Iron  fcdesCe?.Pper 

4  ounces  19  minutes  18.5  minutes  

11       "  33  30.75  

5J/2  "  50       •"  44  

4       "  35.7    '  36.83  minutes 

Two  other  vessels  of  iron  sides  1/30  inch  thick,  one  having  a  i/4-inch 
copper  bottom  and  the  other  a  i/4-inch  lead  bottom,  were  tested  against 
the  iron  and  copper  vessel,  Vso  inch  thick.  Equal  quantities  of  water  were 
evaporated  in  54,  55,  and  531/2  minutes  respectively.  Taken  generally, 
the  results  of  these  experiments  show  that  there  are  practically  but  slight 
differences  between  iron,  copper,  and  lead  in  evaporative  activity,  and 
that  the  activity  is  not  affected  by  the  thickness  of  the  bottom. . 

Mr.  W.  B.  Johnson  formed  a  like  conclusion  from  the  results  of  his 
observations  of  two  boilers  of  160  horse-power  each,  made  exactly  alike, 
except  that  one  had  iron  flue-tubes  and  the  other  copper  flue-tubes.  No 
difference  could  be  detected  between  the  performances  of  these  boilers. 

Divergencies  between  the  results  of  different  experimenters  are  attrib- 
utable probably  to  the  difference  of  conditions  under  which  the  heat  was 
transmitted,  as  between  water  or  steam  and  water,  and  between  gaseous 
matter  and  water.  On  one  point  the  divergence  is  extreme:  the  rate  of 
transmission  of  heat  per  degree  of  difference  of  temperature.  Whilst  from 
400  to  600  units  of  heat  are  transmitted  from  water  to  water  through  iron 
plates,  per  degree  of  difference  per  square  foot  per  hour,  the  quantity  of 
heat  transmitted  between  water  and  air,  or  other  dry  gas,  is  only  about 
from  2  to  5  units,  according  as  the  surrounding  air  is  at  rest  or  in  move- 
ment: In  a  locomotive  boiler,  where  radiant  heat  was  brought  into  play, 
17  units  of  heat  were  transmitted  through  the  plates  of  the  fire-box  per 
degree  of  difference  of  temperature  per  square  foot  per  hour. 

Transmission  of  Heat  through  Plates  from  Flame  to  Water. — 
Much  controversy  has  arisen  over  the  assertion  by  some  makers  of  live- 
steam  feed-water  heaters  that  if  the  water  fed  to  a  boiler  was  first  heated  to 
the  boiling  point  before  being  fed  into  the  boiler,  by  means  of  steam  taken 
from  the  boiler,  an  economy  of  fuel  would  result;  the  theory  being  that 
the  rate  of  transmission  through  a  plate  to  water  was  very  much  greater 
when  the  water  was  boiling  than  when  it  was  being  heated  to  the  boiling 
point,  on  account  of  the  greatly  increased  rapidity  of  circulation  of  the 
water  when  boiling.  (See  Eng'g,  Nov.  16, 1906,  and  Bnff.  Review  [London], 
Jan.,  1908.)  Two  experiments  by  Sir  Wm.  Anderson  (1872),  with  a  steam- 
jacketed  pan,  are  quoted,  one  of  which  showed  an  increased  transmission 
when  boiling  of  133%,  and  the  other  of  80%;  also  an  experiment  by 
Sir  F.  Bramwell,  with  a  steam-heated  copper  pan,  which  showed  a  gain  of 
164%  with  boiling  water.  On  the  other  hand,  experiments  by  S.  B.  Bil- 
brough  (Transvaal  Inst.  Mining  Engineers,  Feb.,  1908)  showed  in  tests 
with  a  flame-heated  pan  that  there  was  no  difference  in  the  rate  of  trans- 
mission whether  the  water  was  cold  or  boiling.  W.  M.  Sawdon  (Ptiwer, 
Jan.  12,  1909)  objects  to  Mr.  Bilbrough's  conclusions  on  the  ground  that 
no  corrections  for  radiation  were  made,  and  finds  by  a  similar  experiment, 
with  corrections,  that  the  increased  rate  of  transmission  with  boiling  water 
is  at  least  38%.  All  of  these  experiments  were  on  a  small  scale,  and  in 
view  of  their  conflict  no  conclusions  can  be  drawn  from  them  as  to  the 
value  of  live-steam  feed-water  heating  in  improving  the  economy  of  a 
steam  boiler. 

A.  Blechynden's  Tests.  —  A  series  of  steel  plates  from  0.125  in.  to 
1.187  in.  thick  were  tested  with  hot  gas  on  one  side  and  water  on  the  other 
with  differences  of  temperature  ranging  from  373°  to  1318°  F.  Trans.') 
Inst.  Naval  Architects,  1894.)  Mr.  Blechynden  found  that  the  heat 
transmitted  is  proportional  to  the  square  of  the  difference  between  the 
temperatures  at  the  two  sides  of  the  plate,  or:  Heat  transmitted  per  sq. 
ft.  -4-  (diff.  of  temp.)2  =  a  constant.  A  study  of  the  results  of  these 
tests  is  made  in  Kent's  "  Steam  Boiler  Economy,"  p.  325,  and  it  is  shown 
that  the  value  of  a  in  Rankine's  formula q  =(T\—  T)2  -5- a,  which  a  is  the 
reciprocal  of  Mr.  Blechynden's  constant  and  is  a  function  of  the  thickness 
of  the  plate.  One  of  the  plates,  A,  originally  1.187  in.  thick,  was  reduced 


594 


HEAT. 


in  four  successive  operations,  by  machining  to  0.125  in.  Another,  £,  was 
tested  in  four  thicknesses.  The  other  plates  were  tested  in  one  or  two 
thicknesses.  Each  plate  was  found  to  have  a  law  of  transmission  of  its 
own.  For  plate  A  the  value  of  a  is  represented  closely  by  the  formula 
a  =  40  4-  20  t,  in  which  t  is  the  thickness  in  inches.  The  formula  a  «= 
40  +  20  t  ±  10  covers  the  whole  range  of  the  experiments.  The  whole 
range  of  values  is  38.6  to  71.9,  which  are  very  low  when  compared  with 
values  of  a  computed  from  the  results  of  boiler  tests,  which  are  usually 
from  200  to  400,  the  low  values  obtained  by  Blechynden  no  doubt  being 
due  to  the  exceptionally  favorable  conditions  of  his  tests  as  compared 
with  those  of  boiler  tests.  Rankine  says  the  value  of  a  lies  between  160 
and  200,  but  values  below  200  are  rarely  found  in  tests  of  modern  types 
of  boilers.  (See  Steam-Boilers.) 

Cooling  of  Air.  —  H.  F.  Benson  (Am.  Mach.,  Aug.  31,  1905)  derives 
the  following  formula  for  transmission  of  heat  from  air  to  water  through 
copper  tubes.  It  is  assumed  that  the  rate  of  transmission  at  any  point  of 
the  surface  is  directly  proportional  to  the  difference  of  temperature 
between  the  air  and  water. 

Let  A  =  cooling  surface,  sq.  ft.;  K  =  Ib.  of  air  per  hour;  Sa  =  specific 
heat  of  air;  Tai  —  temp,  of  hot  inlet  air;  Ta^  =temp.  of  cooled  outlet  air; 
d  =  actual  average  diff.  of  temp,  bet  ween  "the  air  and  the  water;  17  = 
B.T.U.  absorbed  by  the  water  per  degree  of  diff.  of  temp,  per  sq.  ft.  per 
hour.  W  =  Ib.  of  water  per  hour;  TWl  =  temp,  of  inlet  water;  TW2  «=» 
temp,  of  outlet  water.  Then 


AdU  =  KSa(Tai  - 


A  =  KSa(Tai  - 


-  dU. 


KSgW 

W-KSn 


Ta,  ~  Tw 


—  T 

•         •*•  in 


TW2  -  (SaK  +  W)  (Tai -  TaJ  +  Twr 

The  more  cooling  water  used,  the  lower  is  the  temperature  Twr  Also 
the  less  TWz  is,  the  larger  d  becomes  and  the  less  surface  is  needed.  About 
10  is  the  largest  value  of  W/K  that  it  is  economical  to  use,  as  there  is  a 
saving  of  less  than  0.5%  in  increasing  it  from  10  to  15.  When  desirable 
to  save  water  it  will  be  advisable  to  make  W/K  =  5.  Values  of  U 
obtained  by  experiment  with  a  Wainwright  cooler  made  with  corrugated 
copper  tubes  are  given  in  the  following  table.  K  and  W  are  in  Ib.  per 
minute,  Ba  =  B.T.U.  from  air  per  min.,  Bw=  B.T.U.  from  water  per 
min.,  Vw  =  velocity  of  water,  ft.  per  min. 


r.i 

** 

T 

lWt 

T 

/H>2 

K 

W 

*« 

B* 

vw 

U 

221.0 

76.3 

50.0 

169.0 

125.2 

28.50 

4303 

3392 

2.20 

6.75 

217.0 

64.3 

45.8 

146.4 

122.8 

36.73 

4452 

3695 

2.84 

7.12 

224.0 

63.3 

45.7 

149.  2 

126.3 

40.30 

4819 

4171 

3.11 

7.91 

209.6 

54.0 

43.8 

125.9 

122.1 

50.00 

4511 

4105 

3.86 

8.81 

214.5 

46.3 

43.0 

106.2 

124.6 

68.95 

4976 

4357 

5.32 

10.55 

234.6 

63.6 

52.6 

120.2 

124.4 

73.25 

5051 

4852 

5.65 

8.41 

214.2 

43.5 

43.0 

94.7 

117.3 

79.84 

4753 

4128 

6.16 

14.32 

242.9 

61.7 

55.3 

114.0 

133.6 

92.72 

5649 

5443 

7.15 

10.01 

223.0 

46.0 

40.1 

79.1 

130.5 

114  80 

5484 

4477 

8.86 

7.86 

239.3 

57.5 

51.0 

95.2 

130.0 

125.70 

5612 

5556 

9.70 

9.38 

246  0 

58.0 

52.3 

95.1 

133.8 

145.90 

5977 

6244 

11.26 

10.57 

Sixteen  other  tests  were  made  besides  those  given  above,  and  their 
plotted  results  all  come  within  the  field  covered  by  those  in  the  table. 


CONDUCTION    AND    CONVECTION    OF   HEAT. 


595 


There  is  apparently  an  error  in  the  last  line  of  the  table,  for  the  heat 
gained  by  the  water  could  not  be  greater  than  that  lost  by  the  air.  The 
excess  lost  by  the  air  may  be  due  to  radiation,  but  it  shows  a  great  irregu- 
larity. It  appears  that  for  velocities  of  water  between  2.2  and  5.3  ft.  per 
min.  the  value  of  U  increases  with  the  velocity,  but  for  higher  velocities 
the  value  of  U  is  very  irregular,  and  the  cause  of  the  irregularity  is  not 
explained. 

Chas.  L.  Hubbard  (The  Engineer,  Chicago,  May  18,  1902)  made  some 
tests  by  blowing  air  through  a  tight  wooden  box  which  contained  a  nest 
of  30  li/2-in.  tin  tubes,  of  a  total  surface  of  about  20  sq.  ft.,  through 
which  cold  water  flowed.  The  results  were  as  follows: 


Cu.  ft.  of  air  per  minute  

768 

268 

469 

469 

636 

636 

Velocity  over  cooling  surface  
Initial  temperature  of  air  

638 

77° 

638 
72° 

1116 

72° 

1116 
74° 

1514 

74° 

1514 
74° 

Drop  in  temperature 

12° 

8° 

10° 

8° 

10° 

Average  temp,  of  water  
Average  temp,  of  air 

50° 
68° 

43° 
66° 

48° 
68° 

48° 
69° 

50° 

70° 

44° 
68° 

Difference  

18° 

23° 

20° 

21° 

20° 

24° 

B.T.U.  per  hour  per  sq.  ft.  per  degree 
difference  

6.5 

7.6 

10.2 

12.1 

13.8 

14.4 

Transmission  of  Heat  through  Plates  and  Tubes  from  Steam  or 
Hot  Water  to  Air.  —  The  transfer  of  heat  from  steam  or  water  through 
a  plate  or  tube  into  the  surrounding  air  is  a  complex  operation,  in  which 
the  internal  and  external  conductivity  of  the  metal,  the  radiating  power 
of  the  surface,  and  the  convection  of  heat  in  the  surrounding  air,  are  all 
concerned.  Since  the  quantity  of  heat  radiated  from  a  surface  varies  with 
the  condition  of  the  surface  and  with  the  surroundings,  according  to  laws 
not  yet  determined,  and  since  the  heat  carried  away  by  convection  varies 
with  the  rate  of  the  flow  of  the  air  over  the  surface,  it  is  evident  that  no 
general  law  can  be  laid  down  for  the  total  quantity  of  heat  emitted. 

The  following  is  condensed  from  an  article  on  "Loss  of  Heat  from 
Steampipes,"  in  The  Locomotive,  Sept.  and  Oct.,  1892. 

A  hot  steam-pipe  is  radiating  heat  constantly  off  into  space,  but  at  the 
same  time  it  is  cooling  also  by  convection.  Experimental  data  on  which 
to  base  calculations  of  the  heat  radiated  and  otherwise  lost  by  steam-pipes 
are  neither  numerous  nor  satisfactory. 

In  Box's  "  Practical  Treatise  on  Heat"  a  number  of  results  are  given  for 
the  amount  of  heat  radiated  by  different  substances  when  the  temperature 
of  the  air  is  1°  Fahr.  lower  than  the  temperature  of  the  radiating  body.  A 
portion  of  this  table  is  given  below.  It  is  said  to  be  based  on  Pellet's 
experiments. 


HEAT  UNITS  RADIATED  PER  HOUR,  PER  SQUARE  FOOT  OP  SURFACE, 
FOR  1°  FAHRENHEIT  EXCESS  IN  TEMPERATURE. 


Copper,  polished 0.0327 

Tin,  polished 0.0440 

Zinc  and  brass,  polished . . .  0.0491 

Tinned  iron,  polished 0.0858 

Sheet  iron,  polished 0.0920 

Sheet  lead 0.1329 

Sheet  iron,  ordinary 0.5662 


Glass 0.5948 

Cast  iron,  new 0.6480 

Common     steam-pipe,     in- 
ferred    0.6400 

Cast  and  sheet  iron,  rusted  . .  0.6868 
Wood,  building  stone,  and 

brick.  .                            ...  0.7358 


When  the  temperature  of  the  air  is  about  50°  or  60°  Fahr.,  and  the  radiat- 
ing body  is  not  more  than  about  30°  hotter  than  the  air,  we  may  calculate 
the  radiation  of  a  given  surface  by  assuming  the  amount  of  heat  given  off 
by  it  in  a  given  time  to  be  proportional  to  the  difference  in  temperature 
between  the  radiating  body  and  the  air.  This  is  "  Newton's  law  of  cooling. " 
But  when  the  difference  in  temperature  is  great,  Newton's  law  does  not 
hold  good;  the  radiation  is  no  longer  proportional  to  the  difference  in  tern* 
perature,  but  must  be  calculated  by  a  complex  formula  established  experi- 
mentally by  Dulong  and  Petit.  Box  has  computed  a  table  from  thit 


596 


HEAT. 


formula,  which  greatly  facilitates  its  application,  and  which  is  given 
below: 

FACTORS  FOR  REDUCTION  TO  DULONG'S  LAW  OF  RADIATION. 


Differences  in  Tem- 
perature between 
Radiating  Body 
and  the  Air. 

Temperature  of  the  Air  on  the  Fahrenheit  Scale. 

32° 

50° 

59° 

68° 

86° 

104° 

122° 

140° 

158° 

176° 

194° 

212C 

Deg.  Fahr. 
18 

.00 

.07 

.12 

.16 

.25 

.36 

.47 

.58 

1.70 

1.85 

1.99 

2.15 

36 

.03 

.11 

.16 

.21 

.30 

.40 

.52 

.68 

1.76 

1.91 

2.06 

2.23 

54 

.07 

.16 

.20 

.25 

.35 

.45 

.58 

.70 

1.83 

1.99 

2.14 

2.31 

72 

.12 

.20 

.25 

.30 

.40 

.52 

.64 

.76 

1.90 

2.07 

2.23 

2  40 

90 

.16 

.25 

.31 

.36 

.46 

.58 

.71 

.84 

1.98 

2.15 

2.33 

2.51 

108 

.21 

.31 

.36 

.42 

.52 

.65 

.78 

.92 

2.07 

2.28 

2.42 

2.62 

126 

.26 

.36 

.42 

.48 

.60 

.72 

.86 

2.00 

2.16 

2.34 

2.52 

2.72 

144 

.32 

.42 

.48 

.54 

.65 

.79 

.94 

2.08 

2.24 

2.44 

2.64 

2.83 

162 

.37 

.48 

.54 

.60 

.73 

.86 

2.02 

2.17 

2.34 

2.54 

2.74 

2.96 

180 

44 

.55 

61 

.68 

.81 

.95 

2.11 

2.27 

2.46 

2.66 

2.87 

3.10 

198 

.50 

.62 

.69!   .75ll.89l2.04 

2.21 

2.38 

2.56 

2.78 

3.  CO 

3.24 

216 

.58 

.69 

.76 

.83 

1.97 

2.13 

2.32 

2.48 

2.68 

2.91 

3.13 

3.38 

234 

.64 

.77 

.84 

.90 

2.06 

2.23 

2.43 

2.52 

2.80 

3.03 

3.28 

3.46 

252 

.71 

.85 

.92 

2.00 

2.15 

2.33 

2.52 

2.71 

2.92 

3.18 

3.43 

3.70 

270 

.79 

.93 

2.01 

2.09 

2.26 

2.44 

2.64 

2.84 

3.06 

3.32 

3.58 

3  87 

288 

.89 

2.03 

2.12 

2.20 

2.37 

2.56 

2.78 

2.99 

3.22 

3.50 

3.77 

4.07 

306 

.98 

2.13 

2.22 

2.31 

2.49 

2.69 

2.90 

3.12 

3.37 

3.66 

3  95 

4.26 

324 

2.07 

2.23 

2.33 

2.42 

2.62 

2.81 

3.04 

3.28 

3.53 

3.84 

4.14 

4.46 

342 

2.17 

2.34 

2.44 

2.54 

2.73 

2.95 

3.19 

3.44 

3.70 

4.02 

4.34 

4.68 

360 

2.27 

2.45 

2.56 

2.66 

2.86 

3.09 

3.35 

3.60 

3.88 

4,22 

4.55 

4.91 

378 

2.39 

2.57 

2.68 

2.79 

3.00 

3.24 

3.51 

3.78 

4.08 

4.42 

4.77 

5.15 

396 

2.50 

2.70 

2.81 

2.93 

3.15 

3.40 

3.68 

3.97 

4.28 

4.64 

5.01 

5.40 

414 

2.63 

2.84 

2.95 

3.07 

3.31 

3.56 

3.87 

4.12 

4.48 

4.87 

5.26 

5.67 

432 

2  76 

7  98 

3  10 

^  73 

3  47 

3  76 

4  10 

4  37, 

4  61 

5  17 

5  53 

6.04 

The  loss  of  heat  by  convection  appears  to  be  independent  of  the  nature 
of  the  surface,  that  is,  it  is  the  same  for  iron,  stone,  wood,  and  other 
materials.  It  is  different  for  bodies  of  different  shape,  however,  and  it 
varies  with  the  position  of  the  body.  Thus  a  vertical  steam-pipe  will  not 
lose  so  much  heat  by  convection  as  a  horizontal  one  will;  for  the  'air 
heated  at  the  lower  part  of  the  vertical  pipe  will  rise  along  the  surface  of 
the  pipe,  protecting  it  to  some  extent  from  the  chilling  action  of  the  sur- 
rounding cooler  air.  For  a  similar  reason  the  shape  of  a  body  has  an 
important  influence  on  the  result,  those  bodies  losing  most  heat  whose 
forms  are  such  as  to  allow  the  cool  air  free  access  to  every  part  of  their 
surface.  The  following  table  from  Box  gives  the  number  of  heat  units 
that  horizontal  cylinders  or  pipes  lose  by  convection  per  square  foot  of 
surface  per  hour,  for  one  degree  difference  in  temperature  between  the 
pipe  and  the  air. 

HEAT  UNITS  LOST  BY  CONVECTION  FROM  HORIZONTAL  PIPES,  PER  SQUARE 
FOOT  OF  SURFACE  PER  HOUR,  FOR  A  TEMPERATURE 
DIFFERENCE  OF  1°  FAHR. 


External 
Diameter 
of  Pipe 
in  Inches. 

Heat 
Units 
Lost. 

External 
Diameter 
of  Pipe 
in  Inches. 

Heat 
Units 
Lost. 

External 
Diameter 
of  Pipe 
in  Inches. 

Heat 
Units 
Lost. 

2 
3 
4 
5 
6 

0.728 
0.626 
0.574 
0.544 
0  523 

7 
8 
9 
10 
12 

0.509 
0.498 
0.489 
0  482 
0  472 

18 
24 
36 

48 

0.455 
0.447 
0  438 
0  434 

THERMODYNAMICS. 


597 


The  loss  of  heat  by  convection  is  nearly  proportional  to  the  difference 
In  temperature  between  the  hot  body  and  the  air,  but  the  experiments  of 
Dulong  and  Pficlet  show  that  this  is  not  exactly  true,  and  we  may  here  also 
resort  to  a  table  of  factors  for  correcting  the  results  obtained  by  sample 
proportion. 

FACTORS  FOR  REDUCTION  TO  DULONG'S  LAW  OF  CONVECTION. 


Difference 
in  Temp, 
between  Hot 
Body  and 
Air. 

Factor. 

Difference 
in  Temp, 
between  Hot 
Body  and 
Air. 

Factor. 

Difference 
in  Temp, 
between  Hot 
Body  and 
Air.. 

Factor. 

18°  F. 
36° 

540 

72° 
90° 
108° 
126° 
144° 
162° 

0.94 
.11 

.22 
.30 
.37 
.43 
49 
.53 
.58 

H80°F. 
198° 
216° 
234° 
252° 
270° 
288° 
306° 
324° 

1.62 
.65 
.68 
.72 
.74 
.77 
.80 
.83 
.85 

342°  F. 
360° 
378° 
396° 
414° 
432° 
450° 
468° 

.87 
.90 
.92 
.94 
.96 
.98 
2.00 
2.02 

EXAMPLE  IN  THE  USE  OF  THE  TABLES.  —  Required  the  total  loss  of  heat 
by  both  radiation  and  convection,  per  foot  of  length  of  a  steam-pipe  211/33 
in.  external  diameter,  steam  pressure  60  Ibs.,  temperature  of  the  air  in  the 
room  68°  Fahr. 

Temperature  corresponding  to  60  Ibs.  equals  307°;  temperature  dif- 
ference =  307°  -  68  =  239°. 

Area  of  one  foot  length  of  steam-pipe  =  211/32  X  3.1416  -*-  12  =» 
0.614  sq.  ft. 

Heat  radiated  per  hour  per  square  foot  per  degree  of  difference,  from 
table,  0.64. 

Radiation  loss  per  hour  by  Newton's  law  =  239°  X  0.614  ft.  X  0.64  = 
93  9  heat  units.  Same  reduced  to  conform  with  Dulong's  law  of  radiation: 
factor  from  table  for  temperature  difference  of  239°  and  temperature  of 
air  68°  =  1.93.  93.9  X  1.93  =  181.2  heat  units,  total  loss  by  radiation. 

Convection  loss  per  square  foot  per  hour  from  a  2ii/32-inch  pipe:  by 
interpolation  from  table,  2"  =  0.728,  3"  =  0.626,  211/32"  =  0.693. 

Area,  0.614  X  0.693  X  239°  =  101.7  heat  units.  Same  reduced  to 
conform  with  Dulong's  law  of  convection:  101.7  X  1.73  (from  table)  = 
175.9  heat  units  per  hour.  Total 'loss  by  radiation  and  convection  =» 
181.2  +  175.9  =  357.1  heat  units  per  hour.  Loss  per  degree  of  difference 
of  temperature  per  linear  foot  of  pipe  per  hour  =  357.1  -*•  239  =  1.494 
heat  units  =  2.433  per  sq.  ft. 

It  is  not  claimed,  says  The  Locomotive,  that  the  results  obtained  by  this 
method  of  calculation  are  strictly  accurate.  The  experimental  data  are 
not  sufficient  to  allow  us  to  compute  the  heat-loss  from  steam-pipes  with 
any  great  degree  of  refinement:  yet  it  is  believed  that  the  results  obtained 
as  indicated  above  will  be  sufficiently  near  the  truth  for  most  purposes. 
An  experiment  by  Prof.  Ordway,  in  a  pipe  211/33  in.  diam. 'under  the  above 
conditions  (Trans.  A.  S.  M.  E.t  v.  73),  showed  a  condensation  of  steam  of 
181  grams  per  hour,  which  is  equivalent  to  a  loss  of  heat  of  358.7  heat 
units  per  hour,  or  within  half  of  one  per  cent  of  that  given  by  the  above 
calculation. 

The  quantity  of  heat  given  off  by  steam  and  hot-water  radiators  in 
ordinary  practice  of  heating  buildings  by  direct  radiation  varies  from  1.25 
to  about  3.25  heat  units  per  hour  per  square  foot  per  degree  of  difference 
of  temperature.  (See  Heating  and  Ventilation.) 

THERMODYNAMICS. 

Thermodynamics,  the  science  of  heat  considered  as  a  form  of  energy, 
is  useful  in  advanced  studies  of  the  theory  of  steam,  gas,  and  air  engines, 
refrigerating  machines,  compressed  air,  etc.  The  method  of  treatment 
adopted  by  the  standard  writers  is  severely  mathematical,  involving 
constant  application  of  the  calculus.  The  student  will  find  the  subject 


598  HEAT. 

thoroughly  treated  in  the  works  by  Rontgen  (Dubois's  translation),  Wood. 
Peabody,  and  Zeuner. 

First  Law  of  Thermodynamics.  '  —  Heat  and  mechanical  energy  are 
mutually  convertible  in  the  ratio  of  about  778  foot-pounds  for  the  British 
thermal  unit.  (Wood.) 

Second  Law  of  Thermodynamics.  —  The  second  law  has  by  different 
writers  been  stated  in  a  variety  of  ways,  and  apparently  with  ideas  so 
diverse  as  not  to  cover  a  common  principle.  (Wood,  Therm.,  p.  389.) 

It  is  impossible  for  a  self-acting  machine,  unaided  by  any  external. 
agency,  to  convert  heat  from  one  body  to  another  at  a  higher  temperature. 
(Clausius.) 

If  all  the  heat  absorbed  be  at  one  temperature,  and  that  rejected  be  at 
one  lower  temperature,  then  will  the  heat  which  is  transmuted  into  work 
be  to  the  entire  heat  absorbed  in  the  same  jatio  as  the  difference  between 
the  absolute  temperature  of  the  source  and  refrigerator  is  to  the  absolute 
temperature  of  the  source.  In  other  words,  the  second  law  is  an  expression 
for  the  efficiency  of  the  perfect  elementary  engine.  (Wood.) 

The  expression       ~      •  =  —  l—^  —  2   may  be  called  the  symbolical  or 

algebraic  enunciation  of  the  second  law,  —  the  law  which  limits  the 
efficiency  of  heat  engines,  and  which  does  not  depend  on  the  nature  of  the 
working  medium  employed.  (Trowbridge.)  Qi  and  T\  =  quantity  and 
absolute  temperature  of  the  heat  received;  £2  and  Tz  =  quantity  and 
absolute  temperature  of  the  heat  rejected. 

The  expression     1  ~  —  -   represents   the  efficiency   of  a   perfect   heat 

engine  which  receives  all  its  heat  at  the  absolute  temperature  T\,  and 
rejects  heat  at  the  temperature  Tz,  converting  into  work  the  difference 
between  the  quantity  received  and  rejected. 

EXAMPLE.  —  What  is  the  efficiency  of  a  perfect  heat  engine  which 
receives  heat  at  388°  F.  (the  temperature  of  steam  of  200  Ibs.  gauge 

Pressure)  and  rejects  heat  at  100°  F.  (temperature  of  a  condenser,  pressure 
Ib.  above  vacuum)? 


pv  o 
let  it 


In  the  actual  engine  this  efficiency  can  never  be  attained,  for  the  difference 
between  the  quantity  of  heat  received  into  the  cylinder  and  that  rejected 
into  the  condenser  is  not  all  converted  into  work,  much  of  it  being  lost  by 
radiation,  leakage,  etc.  In  the  steam  engine  the  phenomenon  of  cylinder 
condensation  also  tends  to  reduce  the  efficiency. 

The  Carnot  Cycle.  —  Let  one  pound  of  gas  of  a  pressure  pit  volume  v\ 
and  absolute  temperature  T\  be  enclosed  in  an  ideal  cylinder,  having  non- 
conducting walls  but  the  bottom  a  perfect  cpn- 
ductor,  and   having  a  moving  non-conducting 
frictionless  piston.    Let  the  pressure  and  volume 
of  the  gas  be  represented  by  the  point  A  on  the 
or  pressure-  volume  diagram,  Fig.  142,  and 
it  pass  through  four  operations,  as  follows: 
1.    Apply  heat  at  a  temperature  of  T\  to  the 
bottom  of  the  cylinder  and  let  the  gas  expand, 
doing  work  against  the  piston,  at  the  constant 
temperature  Ti,  or  isothermally,  to  p*oz.  or  B. 
..,  2.    Remove  the  source  of  heat  and  put  a  non- 

X  IG.  14J.  conducting  cover  on  the  bottom,  and  let  the  gas 

expand  adiabatically,  or  without  transmission  of  heat,  to  pzvz,  or  C,  while 
its  temperature  is  being  reduced  to  7Y 

3.  Apply  to  the  bottom  of  the  cylinder  a  cold  body,  or  refrigerator,  of 
the  temperature  !T2,  and  let  the  gas  be  compressed  by  the  piston  isother- 
mally  to  the  point  D,  or  p*V4,  rejecting  heat  into  the  cold  body. 

4.  Remove  the  cold  body,  restore  the  non-conducting  bottom,  and 
compress  the  gas  adiabatically  to  A  ,  or  the  original  pm,  while  its  tempera- 
ture is  being  raised  to  the  original  T\.    The  point  D  on  the  isothermal 
line  CD  is  chosen  so  that  an  adiabatic  line  passing  through  it  will  also  pass 
through  A,  and  so  that  ft/ft'""  v*/vt. 

The  area  aABCc  represents  the  work  done  by  the  gas  on  the  piston; 


a 


THERMOD  Y  N  AMICS.  599 

the  area  CDAac  the  negative  work,  or  the  work  done  by  the  piston  on  the 
gas;  the  difference,  ABCD,  is  the  net  work. 

la.  The  area  aABb  represents  the  work  done  during  isothermal  expan- 
sion. It  is  equal  in  foot-pounds  to  Wi  =  pivi  \oge  (v<i/v\),  where  pi  =  the 
initial  absolute  pressure  in  Ibs.  per  sq.  ft.  and  vi  =  the  initial  volume  in 
cubic  feet.  It  is  also  equal  to  the  quantity  of  heat  supplied  to  the  gas,= 
Ui  =  RTi  loge  (vi/v\).  R  is  a  constant  for  a  given  gas,  =  53.35  for  air. 

2a.   The  area  bBCc  is  the  work  done  during  adiabatic  expansion,  =  Wz 

=       *   ]  1  —  (— |       } ,  y  being  the  ratio  of  the  specific  heat  at  constant 

V  —  1   I        \vz/       ' 

pressure  to  the  specific  heat  at  constant  volume.  For  air  y  =  1.406. 
The  loss  of  intrinsic  energy  =  Kv(Ti  —  Tz)  ft.-lbs.  Kv=  specific  heat 
at  constant  volume  X  778. 

3a.  CDdc  is  the  work  of  isothermal  compression,  =  Ws  =  pw\  loge 
(vsM)  =  heat  rejected  =  Uz  =  RTz\oge  (vz/vi). 

4a.   DAad  is  the  work  of  adiabatic  compression 


which  is  the  same  as  Wt  and  therefore,  being  negative,  cancels  it,  and  the 

net  work  ABCD  =  Wi  -  W-&,    The  gain  of  intrinsic  energy  is  Kv  (Ti  —  T2). 

Comparing  la  and  3a,  we  have  pivi=  p^vz;  pxvz  =  p*Vi;  vi/vz  =  vi/v*  =r. 


--  pivi  loge  r  =  RTi  loge  r\  Wz  =  pm  \oge  r  =  RTz  loge  r. 


Efficiency  _•_!  _         ^^     _  _1_J  _  j  _  _• 


Entropy. —  In  the  pv  or  pressure- volume  diagram,  energy  exerted  or 
expended  is  represented  by  an  area  the  lines  of  which  show  the  changes 
of  the  values  of  p  and  v.  In  the  Carnot  cycle  these  changes  are  shown 
by  curved  lines.  If  a  given  quantity  of  heat  Q  is  added  to  a  substance 
at  a  constant  temperature,  we  may  represent  it  by  a  rectangular  area 
in  which  the  temperature  is  represented  by  a  vertical  line,  and  the  base 
is  the  quotient  of  the  area  divided  by  the  length  of  the  vertical  line.  To 
this  quotient  is  given  the  name  entropy.  When  the  temperature  at 
which  the  heat  is  added  is  not  constant  a  ..more  general  definition  is 
needed,  viz.:  Entropy  is  length  on  a  diagram  the  area  of  which  represents 
a  quantity  of  heat,  and  the  height  at  any  point  represents  absolute  tempera- 
ture. The  value  of  the  increase  of  entropy  is  given  in  the  language  of 

calculus,  E=    |       -7p-,  which  may  be  interpreted  thus:  increase  of  entropy 

between  the  temperatures  Tz  and  T\  equals  the  summation  of  all  the 
quotients  arising  by  dividing  each  small  quantity  of  heat  added  by 
the  absolute  temperature  at  which  it  is  added.  It  is  evident  that  if 
the  several  small  quantities  of  heat  added  are  equal,  while  the  values  of 
T  constantly  increase,  the  quotients  are  not  equal,  but  are  constantly 
decreasing.  The  diagram,  called  the  temperature-entropy  diagram,  or 
the  00,  theta-phi,  diagram,  is  one  in  which  the  abscissas,  or  horizontal 
distances,  represent  ^ntropy,  and  vertical  distances  absolute  temperature. 
The  horizontal  distances  are  measured  from  an  arbitrary  vertical  line 
representing  entropy  at  32°  F.,  and  values  of  entropy  are  given  as  values 
beyond  that  point,  while  the  temperatures  are  measured  above  absolute 
zero.  Horizontal  lines  are  isothermals,  vertical  lines  adiabatics.  The  use- 
fulness of  entropy  in  thermodynamic  studies  is  due  to  the  fact  that  in 
many  cases  it  simplifies  calculations  and  makes  it  possible  to  use  alge- 
braic or  graphical  methods  instead  of  the  more  difficult  methods  of  the 
calculus. 


n 


600  HEAT. 

The  Carnot  Cycle  in  the  Temperature-Entropy  Diagram.  —  Let  a 

pound  of  gas  having  a  temperature  T\  and  entropy  E  be  subjected  to  the 
four  operations  described   above.     (1)   T\  being 
constant,  heat  (area  aABc,  Fig.  143)  is  added  and 
the  entropy  increases  from  A  to  B:   isothermal 
expansion.     (2)  No  heat  is  transferred,  as  heat, 
but  the  temperature  is  reduced  from   T\  to  TV, 
entropy  constant ;  adiabatic  expansion.    (3)  Heat 
is  rejected  at  the  constant  temperature  T2,  the 
area  CcaD  being  subtracted;  entropy  decreases 
from  C  to  D;  isothermal  compression.     (4)  En- 
tropy constant,  temperature  increases  from  D  to 
A,  or  from  T2  to  Ti;  no  heat  transferred  as  heat; 
.  adiabatic   compression.     The   area  aABc  repre- 
k         sents  the  total  heat  added  during  the  cycle,  the 
-—,     area  cCDa  the  heat  rejected ;  the  difference,  or  the 
•piTr    140  >      area  ABCD,  is  the  heat  utilized  or  converted  into 

work.     The  ratio  of  this  area  to  the  whole  area 

aABc  is  the  efficiency;  it  is  the  same  as  the  ratio  (T\—  T2) '•*•  Ti.  It 
appears  from  this  diagram  that  the  efficiency  may  be  increased  by  in- 
creasing T\  or  by  decreasing  T2;  also  that  since  T2  cannot  be  lowered  by 
any  self-acting  engine  below  the  temperature  of  the  surrounding  atmos- 
phere, say  460°+  62°  F.=  522°  F.,  it  is  not  possible  even  in  a  perfect 
engine  to  obtain  an  efficiency  of  50  per  cent  unless  the  temperature  of 
the  source  of  heat  is  above  1000°  F.  It  is  shown  also  by  this  diagram 
that  the  Carnot  cycle  gives  the  highest  possible  efficiency  of  a  heat  engine 
working  between  any  given  temperatures  T\  and  Tz,  and  that  the  admis- 
sion and  rejection  of  heat  each  at  a  constant  temperature  gives  a  higher 
efficiency  than  the  admission  or  rejection  at  any  variable  temperatures 
within  the  range  Ti  —  Tz. 

The  Reversed  Carnot  Cycle — Refrigeration. — Let  a  pound  of  cool 
gas  whose  temperature  and  entropy  are  represented  by  the  "state- 
point"  D  on  the  diagram  (1)  receive  heat  at  a  constant  temperature  Ti 
(the  temperature  of  a  refrigerating  room)  until  its  entropy  is  C;  (2)  then 
let  it  be  compressed  adiabatically  (no  heat  transmission,  CB}  to  a  high 
temperature  T\-,  (3)  then  let  it  reject  heat  into  the  atmosphere  at  this 
temperature  Ti  (isothermal  compression);  (4)  then  let  it  expand  adia- 
batically, doing  work,  as  through  a  throttled  expansion  cock,  or  by 
pushing  a  piston,  it  will  then  cool  to  a  temperature  which  may  be  far 
below  that  of  the  atmosphere  and  be  used  to  absorb  heat  from  the 
atmosphere.  (See  Refrigeration.) 

Principal  Equations  of  a  Perfect  Gas. — Notation:  P  =  pressure  in 
Ib.  per  sq.  ft.  V=  volume  in  cu.  ft.  PoVo,  pressure  and  volume  at 
32°  F.  T,  absolute  temperature  =  t°  F.  +  459.6.  Cp,  specific  heat  at 
constant  pressure.  Cv,  specific  heat  at  constant  volume.  Kp  = 
Cp  X  777. 6;  Kv  =  Cv  X  777.6;  specific  heats  taken  in  foot-pounds  of 
energy.  R,  a  constant,  =  Kp  -  Kv.  y  =  Cp/Cv.  r  =  ratio  of  iso- 
thermal expansion  or  compression  =  P2/Pi  or  Vi/V2. 

For  air;  Cp  =  0.2375;  Cv  =  0.1689;  Kp  =  184.8;  Kv  =  131.4; 
R  =  53.32;  y  =  1.406. 

Boyle's  Law,  PV  =  constant  when  T  is  constant.  PiVi  =  P2V2. 
For  1  Ib.  air  PoVo  =  2116.3  X  12.387  =  26,215  ft.-lb. 

Charles's  Law,  PiVi/Ti  =  P2V2/T2;  Pi  Vi  =  PoVo  X  Ti/To;  To  =  32 
+  459.6  =  491.6;  Pi  Vi  for  air  =  26,215  -^  491.6  =  53.32.  v 

General  Equation,  PV  =  RT.  R  is  a  constant  which  is  different  for 
different  gases.  , 

Internal  or  Intrinsic  Energy  Kv  (Ti  -  To)  =  R  (Ti  -  To)  -5-  (y  -  1) 
=  PiVi  -T-  (y  -  1)  =  amount  of  heat  in  a  body,  measured  above  abso- 
lute zero.  For  air  at  32°  F.,  Kv(Ti  -  To)  =  131.4  X  491.6  =  64,600 
ft.-lb.  When  air  is  expanded  or  compressed  isothermally,  PV  =  con- 
stant, and  the  internal  energy  remains  constant,  the  work  done  in 
expansion  =  the  heat  added,  and  the  work  done  in  compression  =  the 
heat  rejected. 


THERMODYNAMICS.  601 

Work  done  by  Adiabatic  Expansion,  no  transmission  of  heat,  from  PiFi  to 
p2F2  =  PiFi  }l  -  (Fi/VV)7"^  -*•(?-  1),  =  (PiFi  -  P2F2)  -5-  (y  -  1) 

r  —  -I 

-   Pi  Fiji    ~(P2/Pl)    Y      }   -    (y    -    1). 

Work  of  Adiabatic  Compression  from  PiFi  to  P2F2  (P2  here  being  the 
higher  pressure)  =  Pi  Fi  {(Fi/Fo)7"1  -l}  •*-  (y-  1)  =  (P2F2-PiFi)-^  y-1 

(  *=!        ) 

=  PiFi    {(Pa/Pi)  y    -IJ-J-(y-l). 

7^m  w/  Intrinsic  Energy  in  adiabatic  expansion,  or  gain  in  compression 
=  KV(T\.—  T->),  T\  being  the  higher  temperature. 

Work  of  Isothermal  Expansion,  temperature  constant,  =  heat  expended 
=  Pi  Fi  loge  Fo  /  Fi  =  Pi  Ft  loge  r  =  R  T  loge  r. 

Work  of  Isothermal  Compression  from  Pi  to  P2  =  PiFi  loge  Pi/P2 
=  RT\oger=  heat  discharged. 

Relation  between  Pressure,  Volume  and  Temperature: 


For  air,  y  =  1,406;  y  -  1  =  0.406;  1/y-  =  0.711;  l/(y  -  1)  =  2.463; 
y/(y-l)=  3.463;  (y  -  l)/y  =  0.289. 

Differential  Equations  of  a  Perfect  Gas.  Q  =  quantity  of  heat.  $  = 
entropy. 


T  (IT  f?P 

dQ  =  CpdT+  (Cv-Cp)  ±  dV.  d4>=  Cp~  +  (Cv-  Cp)  ~  . 

T  T  riP       •       f?V 

dQ=CvjjdP+Cp  |  dV.  di=  Cv  Q-f+Cp  y-  • 

fr-<j>i  =  Cv  loge  -^  +  (Cp  -  Cv)  loge  ^  • 
<h-fr  =  Cp  log,  |>  +  (Cv  -  Cp)  loge  || 
<£2  -  ^i  =  Cv  loge  ^  +  Cp  loge  £  • 

/•  F2  ,7  F  V* 

Work  of  Isothermal  Expansion,  W=  PiFi    I       ^  =PiFi  loge  ~  •  • 

•/  FI  i 

Heat  supplied  during  isothermal  expansion, 

^  -  (Cp  -  Cv)  ITi  log,  ^  • 

Heat  added  =  work  done=  ^/eT7!  loge  F2/Fi=  ^PiFi  loge  F2/Fi;  (A* 
1/778). 

Work  of  adiabatic  expansion, 


w-        pav=Vlypt  f^^^-^h-^ 
JV\  F»     Y-1  1       MV 


602 


HEAT. 


Construction  of  the  Curve  P V»  =  C.    (Am.  Mach.,  June  21,  1900.)— 
Referring  to  Fig.  144,  on  a  system  of  rectangular  coordinates  YOX  lay 

off  OB  =  pi  and  BA  «  v\. 
Draw  0.7,  extended,  at 
any  convenient  angle  a, 
say  15°,  with  OX,  and  OC 
at  an  angle  ft  with  OY.  ft 
is  found  from  the  equation 
1  +  tan  B  =[l  +  tana]n. 
Draw  AJ  parallel  to  YO. 
From  B  draw  BC  at  45° 
with  £0,  and  draw  CE 
parallel  to  OX.  From  J 
draw  J#  at  45°  with  A  J, 
and  draw  HE  and  //»/] 
parallel  to  YO.  The  inter- 
section of  CE  and  HE  is 
the  second  point  on  the 
curve,  or  pzvz.  From  J\ 
draw  JiHi  at  45°  to  HJi 
and  draw  the  vertical 
JtHiR.  Draw  D#  at  45° 
to  DOi  and  KE  parallel 
to  OX.  R  is  the  third 
point  on  the  curve,  and 
so  on. 

Conversely,  if  we  have 
a  curve  for  which  we  wish 


144. 


to  derive  an  exponent,  we  can,  by  working  backward,  locate  the  lines 
OC  and  OJ,  measure  the  angles  a  and  ft,  and  solve  for  n. 
A  The  smaller  the  angle  a  is  taken  the  more  closely  the  points  of  the 
curve  may  be  located.  If  a  =  ft  the  curve  is  the  isothermal  curve, 
pv  =  constant.  If  a  =  15°  and  ft  =  21°  30'  the  curve  is  the  adiabatic 
for  air,  n  =  1.41.  (See  Index  of  the  Curve  of  an  Air  Diagram,  p.  636.) 

Temperature-Entropy  Diagram  of  Water  .  and  Steam.  —  The  line 
OA,  Fig.  145,  is  the  origin  from  which  entropy  is  measured  on  horizontal 
tines,  and  the  line  Og  is  the  line  of  zero 
temperature,  absolute.  The  diagram 
represents  the  changes  in  the  state 
of  one  pound  of  water  due  to  the 
addition  or  subtraction  of  heat  or  to 
changes  in  temperature.  Any  point  on 
the  diagram  is  called  a  "state  point." 
A  is  the  state  of  1  Ib.  of  water  at 
32°  F.  or  492°  abs.,  B  the  state  at 
212°,  and  C  at  392°  F.,  correspond- 
ing to  about  226  Ibs.  absolute  pres- 
sure. At  212°  F.  the  area  OABb  is 
the  heat  added,  and  Ob  is  the  increase 
of  entropy.  At  392°  F.,  bBcC  is  the 
further  addition  of  heat,  and  the 
entropy,  measured  from  OA,  is  Oc. 
The  two  quantities  added  are  nearly 
the  same,  but  the  second  increase 
of  entropy  is  the  smaller,  since  the 
mean  temperature  at  which  it  is 
added  is  higher.  If  Q  =  the  quantity 
of  heat  added,  and  T\  and  Tz  are 
respectively  the  lower  and  the 
higher  temperatures,  the  addition  of 
entropy,  «£,  is  approximately  Q  -H  i/2  (7*2  4-  Ti)  =  180  •*-  1/2  (672  +  492) 
=  0.3093.  More  accurately  it  is  <j>  =  log  e  (Tz/Ti)  =  0.3119.  In  both  of 
these  expressions  it  is  assumed  that  the  specific  heat  of  water  =  1  at  all 
temperatures,  which  is  not  strictly  true.  Accurate  values  of  the  entropy 
9f  water,  taking  into  account  the  variation  in  specific  heat,  will  be  found 
in.  Marks  and  Davis  's  Steam  Tables. 

Let  the  l  Ib.  of  water  at  the  state  £  have  heat  added  to  it  at  the  eon-, 


Abs.., 

QCO 

C 

5     T2     D 

/ 

P 

/j 

X  Ti     ft 

t 

\ 

OO- 

492 

/ 

To 

\ 

•460 

0 

A 
O    & 

c        d  e 

f 

9 

K  

-  I 

Entropy  — 

—  > 

\ 

FIG.  145. 


PHYSICAL  PKOPEKTIES   OF  GASES.  603 

slant  temperature  of  212°  F.  until  it  is  evaporated.  The  quantity  of 
heat  added  will  be  the  latent  heat  of  evaporation  at  212°  (see  Steam 
Table)  or  L  =  970.4  B.T.U.,  and  it  will  be  represented  on  the  diagram  by 
the  rectangle  bBFf.  Dividing  by  T\  =  672,  the  absolute  temperature, 
gives  <J>2  -</>i  =  1.444  =  BF.  Adding  fa  =  0.312  gives  fa  =  1.756,  the 
entropy  of  1  Ib.  steam  at  212°  F.  measured  from  water  at  32°  F. 

In  like  manner  if  we  take  L  =  834.4  for  steam  at  852°  abs.,  $*  —  $\  =» 
0.980  =  CE,  and  4>i  =  entropy  of  water  at  852°  =  0.556,  the  sum  fa^ 
1.536.  =  Oe  on  the  diagram. 

E  is  the  state  point  of  dry  saturated  steam  at  852°  abs.  and  F  the 
state  point  at  672°.  The  line  EFG  is  the  line  of  saturated  steam  and  the 
line  ABC  the  water  line.  The  line  CE  represents  the  increase  of  entropy 
in  the  evaporation  of  water  at  852°  abs.  If  entropy  CD  only  is  added, 
or  cCDd  of  heat,  then  a  part  of  the  water  will  remain  unevaporated, 
viz.:  the  fraction  DE/CE  of  1  Ib.  The  state  point  D  thus  represents  wet 
steam  having  a  dry  ness  fraction  of  CD/CE. 

If  steam  having  a  state  point  E  is  expanded  adiabatically  to  672° 
abs.  its  state  point  is  then  ei,  having  the  same  entropy  as  at  E,  a  total 
heat  less  by  the  amount  represented  by  the  area  BCEei,  and  a  dryness 
fraction  Bei/BF.  If  it  is  expanded  while  remaining  saturated,  heat 
must  be  added  equal  to  eEFf,  and  the  entropy  increases  by  ef. 

If  heat  is  added  to  the  steam  at  E,  the  temperature  and  the  entropy 
both  increase,  the  line  EH  representing  the  superheating,  and  the  area 
EH,  down  to  the  line  Og,  is  the  heat  added.  If  from  the  state  point  H 
the  steam  is  expended  adiabatically,  the  state  point  follows  the  line  HJ 
until  it  cuts  the  line  JEFG,  when  the  steam  is  dry  saturated,  and  if  it 
crosses  this  line  the  steam  becomes  wet. 

If  the  state  point  follows  a  horizontal  line  to  the  left,  it  represents 
condensation  at  a  constant  temperature,  the  amount  of  heat  rejected 
being  shown  by  the  area  under  the  horizontal  line.  If  heat  is  rejected 
at  a  decreasing  temperature,  corresponding  with  the  decreasing  pressure 
at  release  in  a  steam  engine,  or  condensation  in  a  cylinder  at  a  decreasing 
pressure,  the  state  point  follows  a  curved  line  to  the  left,  as  shown  in 
the  dotted  curved  line  on  the  diagram. 

In  practical  calculations  with  the  entropy-temperature  diagram  it  is 
necessary  to  have  at  hand  tables  or  charts  of  entropy,  total  heat,  etc., 
Bucn  as  are  given  in  Peabody's  or  Marks  and  Dayis's  Steam  Tables, 
and  other  works.  The  diagram  is  of  especial  service  in  the  study  of 
steam  turbines,  and  an  excellent  chart  for  this  purpose  will  be  found  in 
Moyer's  Steam  Turbine.  It  gives  for  all  pressures  of  steam  from  0.5 
to  300  Ibs.  absolute,  and  for  different  degrees  of  dryness  up  to  300°  of 
superheating,  the  total  heat  contents  in  B.T.U.  per  pound,  the  entropy, 
and  the  velocity  of  steam  through  nozzles. 

PHYSICAL  PROPERTIES  OP  GASES. 

(Additional  matter  on  this  subject  will  be  found  under  Heat,  Air,  Gas 
and  Steam.) 

When  a  mass  of  gas  is  inclosed  in  a  vessel  it  exerts  a  pressure  against  the 
walls.  This  pressure  is  uniform  on  every  square  inch  of  the  surface  of  the 
vessel;  also,  at  any  point  in  the  fluid  mass  the  pressure  is  the  same  in  every 
direction. 

In  small  vessels  containing  gases  the  increase  of  pressure  due  to  weight 
may  be  neglected,  since  all  gases  are  very  light;  but  where  liquids  are 
concerned,  the  increase  in  pressure  due  to  their  weight  must  always  be 
taken  into  account. 

Expansion  of  Gases,  Mariotte's  L.aw.  —  The  volume  of  a  gas  dimin- 
ishes in  the  same  ratio  as  the  pressure  upon  it  is  increased,  if  the  tem- 
perature is  unchanged. 

This  law  is  by  experiment  found  to  be  very  nearly  true  for  all  gases,  and 
is  known  as  -Boyle's  or  Mariotte's  law. 

If  p  =  pressure  at  a  volume  v,  and  pi  =  pressure  at  a  volume  Vi,  pivi  = 

pv,  Pi  =  ^  P;  pv  =  a  constant. 

The  constant,  C,  varies  with  the  temperature,  everything  else  re- 
maining the  same. 


604  PHYSICAL  PROPERTIES  OF  GASES^, 

Air  compressed  by  a  pressure  of  seventy-five  atmospheres  has  a 
volume  about  2  %  less  than  that  computed  from  Boyle's  law,  but  this  is 
the  greatest  divergence  that  is  found  below  160  atmospheres  pressure. 

Law  of  Charles. — The  volume  of  a  perfect  gas  at  a  constant  pressure 
is  proportional  to  its  absolute  temperature.  If  VQ  be  the  volume  of  a 
gas  at  32°  F.,  and  vi  the  volume  at  any  other  temperature,  h,  then 

jh  +  459. 6\  /  .,    ,    ti  —  32  \ 

Vi  =  r    ' 


or  vi  =  [I  +  0.002034  (ti  -  32  )]  VQ. 
If  the  pressure  also  change  from  pa  to  pi, 


The  Densities  of  the  elementary  gases  are  simply  proportional  to 
their  atomic  weights.  The  density  of  a  compound  gas,  referred  to 
hydrogen  as  1,  is  one-half  its  molecular  weight;  thus  the  relative  den- 
sity of  CO2  is  1/2  (12  +  32)  =  22. 

Avogadro's  Law. — Equal  volumes  of  all  gases,  under  the  same  condi- 
tions of  temperature  and  pressure,  contain  the  same  number  of  molecules. 

To  find  the  weight  of  a  gas  in  pounds  per  cubic  foot  at  32°  F.,  multiply 
half  the  molecular  weight  of  the  gas  by  0.00559.  Thus  1  cu.  ft.  of  marsh- 
gas,  CH4,  =  1/2  (12  +  4)  x  0.00559  =  0>o447  Ib. 

When  a  certain  volume  of  hydrogen  combines  with  one-half  its  volume 
of  oxygen,  there  is  produced  an  amount  of  water  vapor  which  will 
occupy  the  same  volume  as  that  which  was  occupied  by  the  hydrogen 
gas  when  at  the  same  temperature  and  pressure. 

Physical  Laws  of  Methane  Gas. — (P.  F.  Walker,  Trans.  A.  S.  M.  E., 
1914.)  The  specific  heat  of  CH*  under  constant  pressure  at  tempera- 
tures from  18°  to  218°  C.  is  0.5929  according  to  Landolt  and  Bornsfcein's 
Tables.  The  same  tables,  on  the  authority  of  Lussana,  give  values  of 
0.5915  at  a  pressure  of  1  atmosphere  and  0.6919  at  30  atmospheres.  The 
ratio  of  specific  heats  at  constant  pressure  and  constant  volume  is  given 
variously  at  from  1.235  to  1.315.  The  gas  shows  a  considerable  varia- 
tion from  Boyle's  law.  PV  =  constant,  or  P V  =  P\V\.  The  variation 
amounts  to  as  much  as  4%  in  the  case  of  CH*  gas  at  300  Ib.  per  square 
inch  reduced  to  the  equivalent  volume  at  atmospheric  pressure.  The 
difference  is  of  commercial  importance  when  natural  gas  is  sold  measured 
at  high  pressures  and  the  price  based  on. the  equivalent  volume  at 
atmospheric  pressure.  The  relation  of  pressure  and  volume  is  ex- 
pressed by  PVn  =  a  constant  and  the  value  of  n  for  C7/4  ranges  from 
0.98  to  0.995,  varying  with  pressure  and  temperature,  averaging  0.99. 
Sufficient  data  are  not  yet  available  for  the  construction  of  tables 
showing  the  variation  of  the  pressure-volume  relation  from  that  given 
by  Boyle's  law. 

Saturation  Point  of  Vapors.  —  A  vapor  that  is  not  near  the  satura- 
tion point  behaves  like  a  gas  under  changes  of  temperature  and  pressure; 
but  if  it  is  sufficiently  compressed  or  cooled,  it  reaches  a  point  where  it 
begins  to  condense:  it  then  no  longer  obeys  the  same  laws  as  a  gas,  but 
its  pressure  cannot  be  increased  by  diminishing  the  size  of  the  vessel  con- 
taining it,  but  remains  constant,  except  when  the  temperature  is  changed. 
The  only  gas  that  can  prevent  a  liquid  evaporating  seems  to  be  its  own 
vapor. 

Dalton's  Law  of  Gaseous  Pressures.  —  Every  pprtion  of  a  mass  of 
gas  inclosed  in  a  vessel  contributes  to  the  pressure  against  the  sides  of  the 
vessel  the  same  amount  that  it  would  have  exerted  by  itself  had  no  other 
gas  been  present. 

Mixtures  of  Vapors  and  Gases.  —  The  pressure  exerted  against  the 
interior  of  a  vessel  by  a  given  quantity  of  a  perfect  gas  inclosed  in  it  is  the 
sum  of  the  pressures  which  any  number  of  parts  into  which  such  quan- 
tity might  be  divided  would  exert  separately,  if  each  were  inclosed  in  a 
vessel  of  the  same  bulk  alone,  at  the  same  temperature.  Although  this 
law  is  not  exactly  true  for  any  actual  gas,  it  is  very  nearly  true  for  many. 
Thus  if  0.080728  Ib.  of  air  at  32°  F.,  being  inclosed  in  a  vessel  of  one  cubic 
foot  capacity,  exerts  a  pressure  of  one  atmosphere,  or  14.7  pounds,  oji  each 


PHYSICAL  PROPERTIES   OF  GASES.  605 

square  inch  of  the  interior  of  the  vessel,  then  will  each  additional  0.080728 

Ib.  of  air  which  is  inclosed,  at  32°,  in  the  same  vessel,  produce  very  nearly 
an  additional  atmosphere  of  pressure.  The  same  law  is  applicable  to 
mixtures  of  gases  of  different  kinds.  For  example,  0.1 2344  Ib.  of  carbonic- 
acid  gas,  at  32°,  being  inclosed  in  a  vessel  of  one  cubic  foot  in  capacity, 
exerts  a  pressure  of  one  atmosphere;  consequently,  if  0.080728  Ib.  of  air 
and  0.12344  Ib.  of  carbonic  acid,  mixed,  be  inclosed  at  the  temperature 
of  32°,  in  a  vessel  of  one  cubic  foot  of  capacity,  the  mixture  will  exert  a 
pressure  of  two  atmospheres.  As  a  second  example:  Let  0.080728  Ib. 
of  air,  at  212°,  be  inclosed  in  a  vessel  of  one  cubic  foot;  it  will  exert  a 
pressure  of 

=  1.366  atmospheres. 

Let  0.03797  Ib.  of  steam,  at  212°,  be  inclosed  in  a  vessel  of  one  cubic 
foot ;  it  will  exert  a  pressure  of  one  atmosphere.  Consequently,  if  0.080728 
Ib.  of  air  and  0.03797  Ib.  of  steam  be  mixed  and  inclosed  together,  at  21 2°, 
in  a  vessel  of  one  cubic  foot,  the  mixture  will  exert  a  pressure  of  2.366 
atmospheres.  It  is  a  common  but  erroneous  practice,  in  elementary 
books  on  physics,  to  describe  this  law  as  constituting  a  difference  between 
mixed  and  homogeneous  gases;  whereas  it  is  obvious  that  for  mixed  and 
homogeneous  gases  the  law  of  pressure  is  exactly  the  same,  viz.,  that  the 
pressure  of  the  whole  of  a  gaseous  mass  is  the  sum  of  the  pressures  of  all 
its  parts.  This  is  one  of  the  laws  of  mixture  of  gases  and  vapors. 

A  second  law  is  that  the  presence  of  a  foreign  gaseous  substance  in  con- 
tact with  the  surface  of  a  solid  or  liquid  does  not  affect  the  density  of  the 
vapor  of  that  solid  or  liquid  unless  there  is  a  tendency  to  chemical  com- 
bination between  the  two  substances,  in  which  case  the  density  of  the 
vapor  is  slightly  increased.  (Rankine,  S.  E.,  p.  239.) 

If  0.0591  Ib.  of  air,  =  1  cu.  ft.  at  212°  and  atmospheric  pressure,  is  con- 
tained in  a  vessel  of  1  cu.  ft.  capacity,  and  water  at  212°  is  introduced, 
heat  at  212°  being  furnished  by  a  steam  jacket,  the  pressure  will  rise  to 
two  atmospheres. 

If  air  is  present  in  a  condenser  along  with  water  vapor,  the  pressure  is 
that  due  to  the  temperature  of  the  vapor  plus  that  due  to  the  quantity  of 
air  present. 

Flow  of  Gases.  —  By  the  principle  of  the  conservation  of  energy,  it 
may  be  shown  that  the  velocity  with  which  a  gas  under  pressure  will 
escape  into  a  vacuum  is  inversely  proportional  to  the  square  root  of  its 
density;  that  is,  oxygen,  which  is  sixteen  times  as  heavy  as  hydrogen, 
would,  under  exactly  the  same  circumstances,  escape  through  an  opening 
only  one  fourth  as  fast  as  the  latter  gas. 

Absorption  of  Gases  by  Liquids.  —  Many  gases  are  readily  absorbed 
by  water.  Other  liquids  also  possess  this  power  in  a  greater  9r  less 
degree.  Water  will,  for  example,  absorb  its  own  volume  of  carbonic-acid 
gas,  800  times  its  volume  of  ammonia,  2  Va  times  its  volume  of  chlorine, 
and  only  about  1/20  of  its  volume  of  oxygen. 

The  weight  of  gas  that  is  absorbed  by  a  given  volume  of  liquid  is  pro- 
portional to  the  pressure.  But  as  the  volume  of  a  mass  of  gas  is  less  as 
the  pressure  is  greater,  the  volume  which  a  given  amount  of  liquid  can 
absorb  at  a  certain  temperature  will  be  constant,  whatever  the  pressure. 
Water,  for  example,  can  absorb  its  own  volume  of  carbonic-acid  gas  at 
atmospheric  pressure;  it  will  also  dissolve  its  own  volume  if  the  pressure 
is  twice  as  great,  but  in  that  case  the  gas  will  be  twice  as  dense,  and  con- 
sequently twice  the  weight  of  gas  is  dissolved. 

Liquefaction  of  Gases.— Liquid  Air.  (A.  L.  Rice,  Trans.  A.S.M.  E., 
xxi,  156.)— Oxygen  was  first  liquefied  in  1877  by  Cailletet  and  Pictet, 
working  independently.  In  1884  Dewar  liquefied  air,  and  in  1898  he 
liquefied  hydrogen  at  a  temperature  of  -  396.4°  F.,  or  only  65°  above  the 
absolute  zero.  The  method  of  obtaining  the  low  temperatures  required 
for  liquefying  gases  was  suggested  by  Sir  W.  Siemens,  in  1857.  It  consists 
in  expanding  a  compressed  gas  in  a  cylinder  doing  work,  or  through  a 
small  orifice,  to  a  lower  pressure,  and  using  the  cold  gas  thereby  produced 
to  cool,  before  expansion,  the  gas  coming  to  the  apparatus.  Hampson 
claims  to  have  condensed  about  1.2  Quarts  of  liquid  air  per  hour  at  an 


606 


AIR. 


expenditure  of  3.5  H.P.  for  compression,  using  a  pressure  of  120  atmos- 
pheres expanded  to  1,  and  getting  6.6  per  cent  of  the  air  handled  as 
liquid. 

The  following  table  gives  some  physical  constants  of  the  principal  gases 
that  have  been  liquefied.  The  critical  temperature  is  that  at  which  the 
properties  of  a  liquid  and  its  vapor  are  indistinguishable,  and  above  wnich 
the  vapor  cannot  be  liquefied  by  compression.  The  critical  pressure  is 
the  pressure  of  the  vapor  at  the  critical  temperature. 


Criti- 
cal 
Temp. 
Deg.  F. 

Criti- 
cal 
Pres- 
sure  in 
Atmo- 
spheres 

Temp, 
of 
Satu- 
rated 
Vapor 
at 
Atmos. 
Pres- 
sure 
Deg.  F. 

Freez- 
ing 
Point. 
Deg.  F. 

Density  of 
Liquid  at 
Temperature 
Given. 

Water..  .»  

HjjO 

689 

200 

212 

32 

1  at  39°  F. 

Ammonia. 

NH4 

266 

115 

—  27 

—107 

0.6364  at  32°  F. 

Acotylene 

98  6 

—121 

—113  8 

Carbon  Dioxide  

EthylenC     

iV?2 

CO2 

C2H4 

88 
50 

75 
51.7 

—112 
—150 

—  69 

—272 

0.  83  at  32°  F. 

Methane        .   .   . 

CH4 

—115.2 

54.9 

—263.4 

—302.4 

l        0.415        1 

Oxygen  

C2 

—182 

50.8 

—294.5 

(  at  —  263°  F.  ) 
1         1J24 

A 

-185.8 

50.6 

—304.6 

—309.3 

\  at  —  294°  F.  I 
(     about  1.5  | 
1  of     ini0  TT    ( 

Carbon  Monoxide 

CO 

—219  1 

35.5 

—310 

—340.6 

Air          

—220 

39 

—312.6 

(         0.933       ) 

N2 

—231 

35 

—318 

—353.2 

(  at  —  313°  F.  1 
(         0.885       ) 

I  of       31R°  T?     • 

Hydrogen  

H2 

—389 

20 

-405 

AIR. 

Properties  of  Air.  —  Air  is  a  mechanical  mixture  of  the  gases  oxygen 
and  nitrogen,  with  about  1%  by  volume  of  argon.  Atmospheric  air  of 
ordinary  purity  contains  about  0.04%  of  carbon  dioxide.  The  com- 
position of  air  is  variously  given  as  follows : 


I 

>y  Volume 

. 

1 

By  Weight 

N 

0 

Ar 

N 

O 

Ar 

1.. 

79.3 

20.7 

77 

23 

2 

79  09 

20  91 

76  85 

23  15 

3  

78.122 

20  941 

0.937 

75.539 

23.024 

1  437 

4  

78.06 

21. 

0.94 

75.5 

23.2 

1.3 

(1)  Values  formerly  given  in  works  on  physics.  (2)  Average  results 
of  several  determinations,  Hempel's  Gas  Analysis.  (3)  Sir.  Wm.  Ram- 
say, Bull.  U.  S.  Geol.  Survey,  No.  330.  (4)  A.  Leduc,  Comptes  Rendus, 
1896,  Jour.  F.  I.,  Jan.,  1898.  Leduc  gives  for  the  density  of  oxygen 
relatively  to  air  1.10523;  for  nitrogen  0.9671;  for  argon,  1.376. 

The  weight  of  pure  air  at  32°  F.  and  a  barometric  pressure  of  29.92 
inches  of  mercury,  or  14.6963  Ibs.  per  sq.  in.,  or  2116.3  Ibs.  per  sq.  ft.,  is 
0.080728  Ib.  per  cubic  foot.  Volume  of  1  Ib.  =  12.387  cu.  ft.  At  any 
other  temperature  and  barometric  pressure  its  weight  in  Ibs.  per  cubic 


foot  is  W 


>  wnere  B  =  height  of  the  barometer,  T  =  tern- 


.          . 

perature  Fahr.,  and  1.3253  =  weight  in  Ib.  of  459.6  cu.  ft.  of  air  at  0°  F. 
and  one  inch  barometric  pressure.     Air  expands  1/491.6  of  its  volume  at 


AIR. 


607 


32°  F.  for  every  increase  of  1°  F.,  and  its  volume  varies  inversely  as  the 
pressure. 

Conversion  Table  for  Air  Pressures. 


le 
& 

+*% 
°1 

£& 

M 
$$ 

Ft.  of 
Water. 

o§ 
£% 

M 

& 

Ft.  of  Air 
at  62°  F. 

|&!  « 

n 

>& 

i* 

1  Ib.  per  sq.  ft  .  . 
1    in.    water    at 
62°  F 

5.196 
9 

62.355 

70.73 
144 
2116.3 

(2) 

0.19245 

1.732 
12 

13.612 
27.712 
407.27 

(3) 

V9 

0.5774 

1 

6.928 

7.859 
16 

'  (4)  ' 

.01604 

Vl2 

0.1443 

1 

1.1343 
2.3094 
33.94 

(5) 

0.01414 

0.07347 
0.1272 

0.8816 

2.036 
29.921 

(6) 

Vl44 

0.036085 

Vl6 

0.43302 

0.49117 
1 
14.6963 

(7) 

13.14 

68.30 
118.3 

819.6 

929.6 
1893 
27,815 

(8) 

29.1 

66.3 
87.2 

230 

245 
349 
1338 
(9) 

1  oz.  per  sq.  in  .  . 
1    ft.   water   at 
62°  F  
1  in.  mercury  at 
32°  F  
1  Ib.  per  sq.  in  .  . 
1  atmosphere.  .  . 
(1) 

The  figures  in  column  (8)  show  the  head  in  feet  of  air  of  uniform 
density  at  atmospheric  pressure  and  62°  F.  corresponding  to  the  pres- 
sure in  the  preceding  columns,  and  those  in  column  (9)  the  theoretical 
velocities  corresponding  to  these  heads,  or  the  velocities  of  a  jet  flowing 
from  a  frictionless  conical  orifice  whose  flow  coefficient  is  unity. 

The  Air-manometer  consists  of  a  long,  vertical  glass  tube,  closed  at 
the  upper  end,  open  at  the  lower  end,  containing  air,  provided  with  a 
scale,  and  immersed,  along  with  a  thermometer,  in  a  transparent  liquid, 
such  as  water  or  oil,  contained  in  a  strong  cylinder  of  glass,  which  com- 
municates with  the  vessel  in  which  the  pressure  is  to  be  ascertained. 
The  scale  shows  the  volume  occupied  by  the  air  in  the  tube. 

Let  vo  be  that  volume,  at  the  temperature  of  32°  Fahrenheit,  and  mean 
pressure  of  the  atmosphere,  po ;  let  vi  be  the  volume  of  the  air  at  the 
temperature  t,  and  under  the  absolute  pressure  to  be  measured  pi ;  then 
U +  459.6)  pwo 
491.6V! 

Pressure  of  the  Atmosphere  at  Different  Altitudes. 

At  the  sea  level  the  pressure  of  the  air  is  14.7  pounds  per  square  inch;  at 
1/4  of  a  mile  above  the  sea  level  it  is  14.02  pounds;  at  1/2  mile,  13.33;  at 
Simile,  12.66;  at  1  mile,  12.02;  at  li/4mile,  11.42;  at  11/2  mile,  10.88;  and 
at  2  miles,  9.80  pounds  per  square  inch.  For  a  rough  approximation  we 
may  assume  that  the  pressure  decreases  1/2  pound  per  square  inch  for 
every  1000  feet  of  ascent.  (See  table,  p.  608.) 

It  is  calculated  that  at  a  height  of  about  31/2  miles  above  the  sea  level 
the  weight  of  a  cubic  foot  of  air  is  only  one-half  what  it  is  at  the  surface  of 
the  earth,  at  seven  miles  only  one-fourth,  at  fourteen  miles  only  one- 
sixteenth,  at  twenty-one  miles  only  one  sixty-fourth,  and  at  a  height  of 
over  forty-five  miles  it  becomes  so  attenuated  as  to  have  no  appreciable 
weight. 

The  pressure  of  the  atmosphere  increases  with  the  depth  of  shafts,  equal 
to  about  one  inch  rise  in  the  barometer  for  each  900  feet  increase  in  depth: 
this  may  be  taken  as  a  rough-and-ready  rule  for  ascertaining  the  depth  of 
shafts. 

Leveling  by  the  Barometer  and  by  Boiling  Water.  (Trautwine.) 
—  Many  circumstances  combine  to  render  the  results  of  this  kind  of 
leveling  unreliable  where  great  accuracy  is  required.  It  is  difficult  to 
read  off  from  an  aneroid  (the  kind  of  barometer  usually  employed  for 
engineering  purposes)  to  within  from  two  to  five  or  six  feet,  depending  on 
its  size.  The  moisture  or  dryness  of  the  air  affects  the  results;  also  winds, 
the  vicinity  of  mountains,  and  the  daily  atmospheric  tides,  which  cause 
incessant  and  irregular  fluctuations  in  the  barometer.  A  barometer 
hanging  quietly  in  a  room  will  often  vary  Vio  of  an  inch  within  a  few 


608 


Am. 


hours,  corresponding  to  a  difference  of  elevation  of  nearly  100  feet. 
No  formula  can  be  devised  that  shall  embrace  these  sources  of  error. 
Boiling  Point  of  Water. — Temperature  in  degrees  F.,  barometer  in 
in.  of  mercury. 


In. 

0 

1 

.2 

.3 

.4 

5 

6 

7 

8 

9 

28 
29 
30 

208.7 
210.5 
212.1 

208.9 
210.6 
212.3 

209.1 
210.8 
212.4 

209.2 
210.9 
212.6 

209.4 
211.1 
212.8 

209.5 
211.3 
212.9 

209.7 
211.4 
213.1 

209.9 
211.6 
213.3 

210.1 
211.8 
213.5 

210.3 
212.0 
213.6 

To  Find  the  Difference  in  Altitude  of  Two  Places.  —  Take  from  the 
table  the  altitudes  opposite  to  the  two  boiling  temperatures,  or  to  the  two 
barometer  readings.  Subtract  the  one  opposite  the  lower  reading  from 
that  opposite  the  upper  reading.  The  remainder  will  be  the  required 
height,  as  a  rough  approximation.  To  correct  this,  add  together  the 
two  thermometer  readings,  and  divide  the  sum  by  2,  for  their  mean. 
From  table  of  corrections  for  temperature,  take  the  number  under  this 
mean.  Multiply  the  approximate  height  just  found  by  this  number 

At  70°  F.  pure  water  will  boil  at  1°  less  of  temperature  tor  an  average  of 
about  550  feet  of  elevation  above  sea  level,  up  to  a  height  of  1/2  a  mile. 
At  the  height  of  1  mile,  1°  of  boiling  temperature  will  correspond  to  aoout 
560  feet  of  elevation.  In  the  table  the  mean  of  the  temperatures  at  the 
two  stations  is  assumed  to  be  32°  F.,  at  which  no  correction- for  temperature 
is  necessary  in  using  the  table. 


&-$'•• 

a  • 

•8.1  . 

£,      . 

r 
d   . 

1  21- 

*-#c 

1 

Isl* 

tit* 

23 

1 

4  o^l 

3-S8* 

^      02 

f® 

25 
& 

tP  1 

3*8* 

^      02 

|IS 

8 

Sgjjf 

3-8  «* 

^    WJ 

184° 

16.79 

15,221 

196 

21.71 

8,481 

208 

27.73 

2,063 

185 

17.16 

14,649 

197 

22.17 

7,932 

208.5 

28.00 

1,809 

186 

17.54 

14,075 

198 

22.64 

7,381 

209 

28.29 

1,539 

187 

17.93 

13,498 

199 

23.11 

6,843 

209.5 

28.56 

1,290 

188 

18.32 

12,934 

200 

23.59 

6,304 

210 

28.85 

1,025 

189 

18.72 

12,367 

201 

24.08 

5,764 

210.5 

29.15 

754 

190 

19.13 

11,799 

202 

24.58 

5,225 

2.11 

29.42 

512 

191 

19.54 

11,243 

203 

25.08 

4,697 

211.5 

29.71 

255 

192 

19.96 

10,685 

204 

25.59 

4,169 

212 

30.00 

S.L.=  0 

193 

20.39 

10,127 

205 

26.11 

3,642 

212.5 

30.30 

—261 

194 

20.82 

9,579 

206 

26.64 

3,115 

213 

30.59 

—511 

195 

21.26 

9,031 

207 

27  18 

2589 

CORRECTIONS  FOR  TEMPERATURE. 


Mean  temp.  F.  in  shade      0 
Multiply  by                    .933 

10°l  20° 
.9541.975 

30° 
.996 

40° 
1.016 

50°  1  60° 
1.036|1.058 

70° 
1.079 

80° 
1.100 

90° 
1.121 

100° 
1.142 

Pressure  of  the  Atmosphere  per  Square  Inch  and  per  Square  Foot 
at  Various  Readings  of  the  Barometer. 

r  RULE. — Barometer  in  inches  x  0.49 16  =  pressure  per  square  inch; 
pressure  per  square  inch  X  144  =  pressure  per  square  foot. 


Barometer. 

Pressure 
per  Sq.  In. 

Pressure 
per  Sq.  Ft. 

Barometer. 

Pressure 
per  Sq.  In. 

Pressure 
per  Sq.  Ft. 

In. 
:  28.00      ' 
28.25 
28.50 
28.75 
29.00 
29.25 
29.50 

Lb. 
13.75 
13.88 
14.00 
14.12 
14.24 
14.37 
14.49 

Lb.* 
1980 
1998 
2016 
2033 
2051 
2069 
2086 

In. 
29.75 
30.00 
30.25 
30.50 
30.75 
31.00 

Lb. 

14.61 
14.73 
14.86 
14.98 
15.10 
15.23 

Lb.* 
2104 
2122 
2140 
2157 
2175 
2193 

*  Decimals  omitted. 
For  lower  pressures  see  table  of  the  Properties  of  Steam 


AIB. 


609 


Barometric  Readings  corresponding  with  Different 
Altitudes,  in  French  and  English  Measures. 


Alti- 
tude. 

Read- 
ing of 
Barom- 

Altitude. 

Reading 
of 
Barom- 

Alti- 
tude. 

Reading 
of 
Barom- 

Altitude. 

Reading 
of 
Barom- 

eter. 

eter. 

eter. 

eter. 

meters 

mm. 

feet. 

inches. 

meters. 

mm. 

feet. 

inches. 

0 

762 

0. 

30. 

1147 

660 

3763.2 

25.98 

21 

760 

68.9 

29.92 

1269 

650 

4163.3 

25.59 

127 

750 

416.7 

29.52 

1393 

640 

4568.3 

25.19 

234 

740 

767.7 

29.13 

1519 

630 

4983.1 

24.80 

342 

730 

1122.1 

28.74 

1647 

620 

5403.2 

24.41 

453 

720 

1486.2 

28.35 

1777 

610 

5830.2 

24.01 

564 

710 

1850.4 

27.95 

1909 

600 

6243. 

23.62 

678 

700 

2224.5 

27.55 

2043 

590 

6702.9 

23.22 

793 

690 

2599.7 

27.16 

2180 

580 

7152.4 

22.83 

909 

680 

2962.1 

26.77 

2318 

570 

7605.1 

22.44 

1027 

670 

3369.5 

26.38 

2460 

560 

8071. 

22.04 

Weight  of  Air  per  Cubic  Foot  at  Different  Pressures  and 
.  Temperatures. 

Formula:     W  =  0.080728  X  - 


Tempera- 
ture 

Gage. 
0 
P  = 
14.6963 

P= 
15.696 

2 

P  = 
16.696 

5 

P  = 

19.696 

10 
P  = 
24.696 

20 
P  = 
34.696 

40 
P  = 
54.696 

60 
P  = 
74.696 

80 
P  = 
94.696 

100 
P  = 
1  14.696 

120 
P  = 
134.696 

Df 

Ab. 

0 

459.6 

.086349 

.09222 

.09810 

.11573 

.14511 

.20385 

.32137 

.43S8& 

.55639 

.67391 

.79141 

32 

491.6 

.080728 

.08622 

.09171 

.10819 

.13566 

.  19059 

.30045 

.41031 

.52017 

.63004 

.73990 

42 

501.6 

.079119 

.08450 

.08989 

.10604 

13295 

.18679 

.29446 

.40213 

.50980 

.61748 

.72515 

52 

511.6 

.077572 

.08285 

.08813 

.  10396 

.13035 

.18314 

.28871 

.39427 

.49984 

.60541 

.71097 

62 

521.6 

076085 

.08126 

.08644 

.10197 

.12786 

.17963 

.28317 

.38671 

.49026 

.59380 

.69734 

70 

529.6 

.074936 

.08004 

.08513 

.  10043 

.12592 

.17691 

.27887 

.38087 

.48285 

.58483 

.68681 

80 

539.6 

073547 

07855 

08356 

.09857 

.12359 

.17364 

.27372 

.37381 

.47390 

.57399 

.67408 

90 

549.6 

072209 

07712 

08204 

.09678 

.12134 

.  17048 

.26874 

.36701 

.46528 

.56355 

.66182 

100 

559.6 

070918 

07574 

08057 

.09504 

.11937 

.16743 

.26394 

.36045 

.45697 

.55348 

.64999 

120 

579.6 

068471 

07313 

07779 

.09177 

.11506 

.16165 

.25483 

.34802 

.44120 

.53438 

.62756 

140 

599.6 

066187 

07069 

07519 

.08871 

.11122 

.15626 

.  24633 

.33641 

.42648 

.51656 

.60663 

160 

619.6 

064051 

06841 

07277 

.  08584 

.10763 

.15122 

.23838 

.32555 

.41272 

.49988 

.58705 

180 

639.6 

062048 

06627 

07049 

08316 

.10427 

.14649 

.23093 

.31537 

.39981 

.48425 

.56869 

200 

659.6 

060167 

06426 

06835 

08064 

.10111 

.14205 

.22393 

.30581 

.38769 

.46957 

.55145 

250 

709.6 

055927 

05973 

06354 

.07496 

.09398 

.13204 

.20815 

.28426 

.36037 

.43649 

.51259 

300 

759.6.052245 

05580 

05936 

.07002 

.08779 

.12335 

.  19445 

.26555 

.33665 

.40775 

.47885 

350 

809.6.049019 

05236 

05569 

.06570 

.08237 

.11573 

.18244 

.24915 

.31586 

.38257 

.44925 

400 

859.6.046163 

04931 

05245 

.06188 

.  07758 

.10900 

.17183 

.23466 

.29748 

.36032 

.42314 

450 

909.6  043630 

04660 

04957 

.05847 

.07332 

.  10301 

.16238 

.22176 

.28113 

.34051 

.39988 

500 

959.6.041357 

04417 

04699 

.05543 

.06950 

.09764 

.15392 

.21020 

.26648 

.32277 

.37905 

550 

1009.6 

.039309 

04198 

04466 

.05268 

.06606 

.09280 

.14630 

.  19979 

.25329 

.30678 

.36028 

600 

1059.6 

.037454 

04000 

04255 

.05020 

.06294 

.08842 

.13939 

.19037 

.24133 

.29230 

.34327 

650 

1109.6 

.035766 

03820 

04063 

.04793 

.06010 

.08444 

.13311 

.18179 

.23046 

.27913 

.32781 

700 

1159.6.034224 

.03655 

.03888 

.04587 

.05751 

.08080 

.12737 

.17395 

.22052 

.26710 

.31367 

800 

1259.6.031507 

.  03365 

.03579 

.04223 

.05294 

.07438 

.11726 

.16014 

.20301 

.24589 

.28877 

900 

1359.6.029190 

.03118 

.03316 

.03912 

.04905 

.06891 

.10864 

.14836 

.18808 

.22781 

.26753 

1000 

1459.  6).  0271901.02904 

.03089 

.03644 

.04569 

.06419 

.10119 

.13830 

.17519 

.21220 

.24920 

Moisture  in  the  Atmosphere.  —  Atmospheric  air  always  contains  a 
small  quantity  of  carbonic  acid  (see  Ventilation),  and  a  varying  quantity 
of  aqueous  vapor  or  moisture.  The  relative  humidity  of  the  air  at  anytime 
is  the  percentage  of  moisture  contained  in  it  as  compared  with  the  amount 
it  is  capable  of  holding  at  the  same  temperature. 

The  degree  of  saturation  or  relative  humidity  of  the  air  is  determined 
bv  the  use  of  the  dry  and  wet  bulb  thermometer.  The  degree  of  satura- 
tion for  a  number  of  different  readings  of  the  thermometer  is  given  In 


610 


AIR. 


the  following  table,  condensed  from  the  Hygrometric  Tables  of  the 
U.  S.  Weather  Bureau: 

RELATIVE  HUMIDITY,  PER  CENT. 


if* 

H  g  M 

«$!« 


Difference  between  the  Dry  and  Wet  Thermometers,  Deg.  F. 


|  2|  3|  4|  5|  6|  7|  8|  9|10|1 1|12|13|14[15|16|17118|19|20J21|22|23|24[26|28|3Q 
Relative  Humidity,  Saturation  being  100.     (Barometer  =  30  in.) 


32 
40 
50 
60 
70 
80 
90 
100 
110 
120 
140 


89  79  69|59  49  3930|20|  II    2 

92  83  75  68  60  52  45  37  29  23j  15 

93  87  80  74167161  554943  38  32  27  21  16 

94  89  83;78  73i68!63!58!53!48i43  39  34  30  26  21 


95  90|86j81  77  72  68  64  59  55  51  48;44I40  36  33  29J25  22 


96  91 187  83  7975  72;68  64J61 |57;54  50i47  44J41 


96  92,89  85  81  78  74  71  68i65|61  58  55  52  49  47  44141  39  36  34  31  29  26  22  17  13 

96  93  89  86183180  77i73  70]68:65i62  59!56  54  51  49|46|44|41  39  37  35  33  28  24  21 

97  93^90  87  84  81  78  75  73  70'67  65;62i60  57  55  52 ! 50  48  46j44  42  40J38  34,30  26 
97  94  91  88:85  82  80  77  74  72  69  67<65 \62\6Q  58i55i53  51  49147  45  43  41  ,38j34  31 
97  95  92!89i87j84l82!79l77  75!73i7Q!68;66S64l62;60i58|56l54i53  51  49|47|44|41|38 


0 
17  13 


38J35  32  29!26|23|20  18  12    7 


Mixtures  of  Air  and  Saturated  Vapor. 

(From  Goodenough's  Tables.) 


'  Pressure  of 

Weight  of 

Volume 

-Q  > 

"op 

-fi^EJ 

Saturated 

Saturated 

in  Cu.  Ft. 

(-3  o 

"csH 

^'fe  "cS 

fe 

Vapor. 

Vapor. 

fc  OJ 

o>  • 

£  h™ 

0 

ft 

In., 
Mer- 

Lb. per 

Per  Cu. 

PerLb. 

nf 

Of 

1  Lb. 

Of  one 

Ib.Dry 

^tfc 

§  ft 

^I« 

i 

cury. 

Sq.  In. 

Ft. 

OI 

Dry  Air. 

Dry 

Air. 

Air  + 
Vapor. 

£«o 

rt  * 

£Q|| 

0 

0.0375 

0.0184 

0.0000674 

0.000781 

11.58 

11.59 

0.0 

0.964 

0.964 

10 

.0628 

.0308 

.0001103. 

.001309 

11.83 

11.86 

2.411 

1.608 

4.019 

20 

.1027 

.0504 

.000177 

.002144 

12.09 

12.13 

4.823 

2.623 

7.446 

32 

.1806 

.0887 

.000303 

.003782 

12.39 

12.47 

7.716 

4.058 

11.783 

35 

.2036 

.1000 

.000340 

.004268 

12.47 

12.55 

8.44 

4.57 

13.02 

40 

.2478 

.1217 

.000410 

.005202 

12.59 

12.70 

9.65 

5.56 

15.21 

45 

.3003 

.1475 

.000492 

.00632 

12.72 

12.85 

10.86 

6.73 

17.59 

50 

.3624 

.1780 

.000588 

.00764 

12.84 

13.00 

12.07 

8.12 

20.19 

55 

.4356 

.2140 

.000699 

.00920 

12.97 

13.16 

13.28 

9.76 

23.04 

60 

.5214 

.2561 

.000829 

.01105 

13.10 

13.33 

14.48 

11.69 

26.18 

65 

.6218 

.3054 

.000979 

.01323 

13.22 

13.50 

15.69 

13.96 

29.65 

70 

.7386 

.3628 

.001153 

.01578 

13.35 

13.69 

16.90 

16.61 

33.51 

75 

.8744 

.4295 

.001352 

.01877 

13.48 

13.88 

18.11 

19.71 

37.81 

80 

1.0314 

.5066 

.001580 

.02226 

13.60 

14.09 

19.32 

23.31 

42.64 

85 

1.212 

.5955 

.001841 

.02634 

13.73 

14.31 

20.53 

27.51 

48.04 

90 

1.421 

.6977 

.002137 

.03109 

13.86 

14.55 

21.74 

32.39 

54.13 

95 

1.659 

.8148 

.002474 

.03662 

13.98 

14.80 

22.95 

38.06 

61.01 

100 

1.931 

.9486 

.002855 

.04305 

14.11 

15.08 

24.16 

44.63 

68.79 

105 

2.241 

1.1010 

.003285 

.0505 

14.24 

15.39 

25.37 

52.26 

77.63 

110 

2.594 

1.274 

.003769 

.0593 

14.36 

15.73 

26.58 

61.11 

87.69 

115 

2.994 

1.470 

.004312 

.0694 

14.49 

16.10 

27.79 

71.40 

99.10 

120 

3.444 

1.692 

.004920 

.0813 

14.62 

16.52 

29.00 

83.37 

112.37 

130 

4.523 

2.221 

.006356 

.1114 

14.88 

17.53 

31.42 

113.64 

145.06 

140 

5.878 

2.887 

.008130 

.1532 

15.13 

18.84 

33.85 

155.37 

189.22 

150 

7.566 

3.716 

.01030 

.2122 

15.39 

20.60 

36.27 

214.03 

250.3 

160 

9.649 

4.739 

.01294 

.2987 

15.64 

23.09 

38.69 

299.55 

338.2 

170 

12.20 

5.990 

.01611 

.4324 

15.90 

26.84 

41.12 

431.2 

472.3 

180 

15.29 

7.51 

.01991 

.6577 

16.16 

33.04 

43.55 

651.9 

695.5 

190 

19.01 

9.34 

.02441 

1.0985 

16.41 

45.00 

45.97 

1082.3 

1128.3 

200 

23.46 

11.53 

.02972 

2.2953 

16.67 

77.24 

48.40 

2247.5 

2296 

Below  32°  F.  the  pressure  of  saturated  vapor  in  contact  with  ice  is 
given.  Values  in  the  last  column  do  not  include  the  heat  of  the  liquid. 
Below  32°  F.  the  heat  of  sublimation  of  ice  rather  than  tue  latent  heat  of 
vaporization  is  used. 


AIR.  611 

Moisture  in  Air  at  Different  Pressures  and  Temperatures.    (H.  M. 

Prevost  Murphy,  Eng.  News,  June  18,  1908.)  —  1.  The  maximum  amount 
of  moisture  that  pure  air  can  contain  depends  only  on  its  temperature 
and  pressure,  and  has  an  unvarying  value  for  each  condition. 

2.  "The  higher  the  temperature  of  the  air,  the  greater  Is  the  amount 
of  moisture  that  it  can  contain. 

3.  The  higher  the  pressure  of  the  air,  the  smaller  is  the  amount  of 
moisture  that  it  can  contain. 

4.  When  air  is  compressed,  the  rise  of  temperature  due  to  the  com- 
pression, in  all  cases  found  in  practice,  far  more  than  offsets  the  opposite 
effect  of  the  rise  of  pressure  on  the  moisture-carrying  capacity  of  the  air. 
Water  is  deposited,  therefore,  by  compressed  air  as  it  passes  from  the  com- 
pressor to  the  various  portions  of  the  system. 

Suppose  that  a  certain  amount  of  atmospheric  air  enters  a  compressor 
and  that  it  contains  all  the  moisture  possible  at  the  existing  outside  tem- 
perature and  pressure.  As  this  air  is  compressed  its  moisture-carrying 
capacity  rapidly  increases,  consequently  all  the  moisture  is  retained  by 
the  air  and  passes  with  it  into  the  main  or  storage  reservoir.  Now  if 
this  air  is  permitted  to  pass  from  the  reservoir  into  the  various  parts  of 
the  system  before  being  cooled  to  the  outside  temperature,  it  will  carry 
more  moisture  than  it  is  capable  of  holding  when  the  temperature 
finally  drops  to  the  normal  point,  and  this  excess  quantity  will  be  de- 
posited, because,  the  pressure  being  high,  the  air  cannot  hold  as  much 
moisture  as  it  did  at  the  same  temperature  and  only  atmospheric  pressure. 
In  order  to  reduce  the  moisture  to  a  minimum,  it  is  desirable  to  cool 
the  air  to  the  outside  temperature  before  it  leaves  the  reservoir,  thereby 
causing  it  to  deposit  all  of  its  excess  moisture,  which  may  be  easily  removed 
by  drain  cocks. 

Although  compressed  air  may  be  properly  dried  before  leaving  the 
main  reservoirs,  some  moisture  may  be  temporarily  deposited  when  the 
air  is  subsequently  expanded  to  lower  pressures,  as  its  moisture-carry- 
ing capacity  is  usually  affected  more  by  the  drop  in  temperature,  result- 
ing from  the  expansion,  than  by  the  drop  in  pressure,  but  when  the  air 
again  attains  the  outside  temperature,  the  moisture  thus  deposited  will 
be  re-absorbed  if  it  is  freely  exposed  to  the  compressed  air. 

In  order  to  determine  what  percentage  of  moisture  pure  air  can  contain 
at  various  pressures  and  temperatures,  to  ascertain  how  low  the  "rela- 
tive humidity"  of  the  atmosphere  must  be  in  order  that  no  water  will  be 
deposited  in  any  part  of  a  compressed-air  system  and  also  to  find  to  what 
temperature  air  drawn  from  a  saturated  atmosphere  must  be  cooled  in 
order  to  cause  the  deposition  of  moisture  to  commence,  the  following 
formulae  and  tables  are  used,  based  on  Dalton's  law  of  gaseous  pressures, 
which  may  be  stated  as  follows: 

The  total  pressure  exerted  against  the  interior  of  a  vessel  by  a  given 

quantity  of  a  mixed  gas  enclosed  in  it  is  the  sum  ot  the  pressures  which 

each  of  the  component  gases,  or  vapors,  would  exert  separately  if  it  were 

enclosed  alone  in  a  vessel  of  the  same  bulk,  at  the  same  temperature. 

[The  derivation  of  the  formulae  is  given  at  length  in  the  original  paper.) 

Formulae  for  the  Weight,  in  Lbs.,  of  1  Cu.  Ft.  of  Dry  Air,  of  1  Cu. 

Ft.  of  Saturated  Steam  or  Water  Vapor  and  the  Maximum  Weight 

of  Water  Vapor  that  1  IJb.  of  Pure  Air  Can  Carry  at  Any  Pressure 

and  Temperature.    (Copyright,  1908,  by  H.  M.  Prevost  Murphy.) 

The  values  K  and  H  being  given  in  the  table  for  various  temperatures, 

t,  in  Fahrenheit  degrees,  the  formulae  are: 

Weight  of  1  cu.  ft.  saturated  steam  = 


77  =  elastic  force  or  tension  of  water  vapor  or  saturated  steam,  in  in.  of 
mercury  corresponding  to  the  temperature  t  (Fahr.)  =  2.036  X  (gauge  pres- 
sure -t-  atmospheric  pressure,  in  pounds  per  square  inch). 

K  =  the  ratio  of  the  weight  of  a  volume  of  saturated  steam  to  an  equal 
volume  of  pure  dry  air  at  the  same  temperature  and  pressure, 


Values  of  K  and  77  corresponding  to  the  various  temperatures  t  are 
given  in  the  table  on  p.  612, 


612 


AIB. 


Weight  of  1  cu.  ft.  pure  dry  air  = 


1.325271  M  ~_  2.698192  P 
459.2  + 1  * 


459.2  +  t 

M  =  absolute  pressure  in  inches  of  mercury. 
P  ==  absolute  pressure  in  pounds  per  square  inch. 
W  =  maximum  weight,  in  Ibs.,  of  water  vapor,  that  1  Ib.  of  pure  air 
can  contain,  when  the  temperature  of  the  mixture  is  t,  and  the  total, 
or  observed,  absolute  pressure  in  pounds  per  square  incli  is  P. 

KH 

~"  2.036  P  -  H' 

NOTE. — The  results  obtained  by  the  use  of  any  of  the  above  formulae 
agree  exactly  with  the  average  data  for  air  and  steam  weights  as  given 
by  the  most  reliable  authorities  and  careful  experiments,  for  all  pres- 
sures and  temperatures;  the  value  of  K  being  correct  for  all  tempera- 
tures up  to  the  critical  steam  temperature  of  689°  F. 

VALUES  OF  "IT"  AND  "H"  CORRESPONDING  TO  TEMPERATURES  t 
FROM  -  30°  TO  434°  P. 


t 

K 

H 

t 

K   H 

t 

K 

H 

t 

K 

H 

t 

K   H 

-30 

.6082 

.0099 

64 

.61  88'.  5962 

158 

.63239.177 

252 

.6501 

62.97 

344 

.6739  254.2 

-28 

.6084 

.0111 

66 

.6190  .6393 

160 

.63269.628 

254 

.6505 

65.21 

346 

.6745  261.0 

-26 

.6086 

.0123 

68 

.6193  .6848 

162 

.6330 

10.10 

256 

.6510 

67.49 

348 

.6751268.0 

-24 

.6088 

.0137 

70 

.6196 

.7332 

164 

.6333  10.59 

258  .6514 

69.85 

350 

.6757  275.0 

-22 

.6090 

.0152 

72 

.6198 

.7846 

166 

.6336  11.10 

260  .6518 

72.26 

352 

.6763282.2 

«-20 

.6092 

.0168 

74 

.6201 

.8391 

168 

.6340  11.63 

262  .6523 

74.75 

354 

.6770289.6 

-18 

.6094 

.0186 

76 

.6203 

.3969 

170 

.6343  12.18 

264 

.6528 

77.30 

356 

.6776297.1 

-16 

.6096 

.0206 

78 

.6206 

.9585 

172 

.6346 

12.75 

266 

.6532 

79.93 

358 

.6783304.8 

-14 

.6098 

.0227 

80 

.6209 

.024 

174 

.6350 

13.34 

268 

.6537 

82.62 

360 

.6789312.6 

-12 

.6100 

.0250 

82 

.6211 

.092 

176 

.6353 

13.96 

270 

.6541 

85.39 

362 

.6795320.6 

-10 

.6102 

.0275 

84 

.6214 

.165 

178 

.6357 

14.60 

272 

.6546 

88.26 

364 

.6803328.7 

-  8 

.6104 

.0303 

86 

.6217 

.242 

180 

.6360 

15.27 

274 

.6551 

91.18 

366 

.6809337.0 

-  6 

.6107 

.0332 

88 

.6219  .324 

182 

.6364 

15.97 

276 

.6555 

94.18 

368 

.6816345.4 

-  4 

.6109 

.0365 

90 

.6222  .410 

184 

.6367 

16.68 

278 

.6560 

97.26 

370 

.6822  354.0 

-  2 

.6111 

.0400 

92 

.6225  .501 

186 

.6371 

17.43 

280 

.6565 

100.4 

372 

.6829362.8 

0 

.6'113 

.0439 

94 

.6227  .597 

188 

.6374 

18.20 

282 

.6570 

103.7 

374 

.6836371.8 

2 

.6115 

.0481 

96 

.6230'  .698 

190 

.6377 

19.00 

284 

.6575 

107.0 

376 

.6843  380.9 

4 

.6117 

.0526 

98 

.6233  .805 

192 

.6381 

19.83 

286 

.6580 

110.4 

378 

.6850390.2 

6 

.6120 

.0576 

100 

.6236  .918 

194 

.6385 

20.69 

288 

.6584 

113.9 

380 

.6857399.6 

8 

.6122 

.0630 

102 

.62382.036 

196 

.6389 

21.58 

290 

.6590 

117.5 

382 

.6865409.3 

10 

.6124 

.0690 

104 

.6241 

2.161 

198 

.6393 

22.50 

292 

.6594 

121.2 

384 

.6871  419.1 

12 

.6126 

.0754 

106 

.62442.294 

200 

.6396 

23.46 

294 

.66CO 

125.0 

386 

.6879429.1 

14 

.6128 

.0824 

108 

.62472.432 

202 

.6400 

24.44 

296  .6604 

128.8 

388 

.6886439.3 

16 

.6131 

.0900 

110 

.6250!2.578 

204 

.6404 

25.47 

298  .6610 

132.8 

390  .6893  449.6 

181.6133 

.0983 

112 

.625312.731 

206 

.6407 

26.53 

300  .6615 

136.8 

392  .6901  460.2 

20'.6135 

.1074 

114 

.62562.892 

208 

.6411 

27.62 

302  .6620 

141.0 

394  .6908  470.9 

22-.  6137 

.1172 

116 

.62583.061 

210 

.6415 

28.75 

304 

.6625 

145.3 

396  .6915481.9 

24J.6140 

.1279 

118 

.6261 

3.239 

212 

.6419 

29.92 

306 

.6631 

149.6 

398  ,6923  493.0 

26!.6142 

.1396 

120 

.6264 

3.425 

214 

.6423 

31.14 

308 

.6636 

154.1 

400  .69311504.4 

28  .6144 

.1523 

122 

.6267 

3.621 

216 

.6426 

32.38 

310  .6641 

158.7 

402 

.6939515.9 

30  .6147 

.1661 

124 

.6270 

3.826 

218 

.6430 

33.67 

312 

.6647 

163.3 

404 

.6947527.6 

32  .6149 

.1811 

126 

.6273  4.042 

220 

.643435.01 

314 

.6652 

168.1 

406 

.6955539.5 

34 

.6151 

.1960 

128 

.62764.267 

222 

.643836.38 

316 

.6658  173.0 

408  .6962551.6 

36 

.6154 

.2120 

130 

.62794.503 

224 

.644237.80 

318 

.6663  178.0 

4101.6970564.0 

38 

..6156 

.2292 

132 

.62824.750 

226 

.644639.27 

320 

.6669i183.1 

412  .6979576.5 

40 

.6158 

.2476 

134 

.6285  5.008 

228 

.6451 

40.78 

322 

.66741  188.  3 

414 

.6987;589.3 

42 

.6161 

.2673 

136 

.62885.280 

230 

.6455 

42.34 

324 

.6680  193.7 

416 

.6995602.2 

44 

.6163 

.2883 

138 

.6291  5.563 

232 

.6458 

43.95 

326 

.6686  199.2 

418 

.7003*615.4 

46 

.6166 

.3109 

140 

.62945.859 

234 

.6463 

45.61 

328 

.6691 

204.8 

420 

.7012628.8 

48 

.6168 

.3350 

142 

.629816.167 

236 

.6467 

47.32 

330 

.6697 

210.5 

422 

.70211642.5 

50 

.6170 

.3608 

144 

.6301 

6.490 

238 

.6471 

49.08 

332 

.6703216.4 

424 

.7029656.3 

52 

.6173 

.3883 

146 

.6304 

6.827 

240 

.647550.89 

334 

.6709222.4 

426 

.7037  670.4 

54 

.6175 

.4176 

148  .630717.178 

242 

.647952.77 

336 

.6715228.5 

428 

.7046684.7 

56 

.6178 

.4490 

150  .6310  7.545 

244  .648454.69 

338 

.6721  234.7 

430 

.7055699.2 

58 

.6180 

.4824 

152!.6313  7.929 

246  .6488  56.67 

340 

.6727(241.1 

432 

.7064713.9 

60 

.6183 

.5180 

154;.  6317  8.  328 

248  .6492  58.71 

342 

.6733  i247.6 

434 

.7073728.9 

62 

.6185 

.5559 

156  .632018.744 

250 

.649660.811 

AIK. 


613 


Weights  In  Pounds,  of  Pure  Dry  Air,  Water  Vapor  and  Saturated 

Mixtures  of  Air  and  Water  Vapor  at  Various  Temperatures,  at 

Atmospheric  Pressure,  29.921  In.  of  Mercury  or  14.6963 

Lb.  per  Sq.  In.     Also  the  Elastic  Force  or  Pressure 

of  the  Air  and  Vapor  Present  in  Saturated 

Mixtures. 
(Copyright,  1908,  by  H.  M.  Prevost  Murphy.) 


Saturated  Mixtures  of  Air  and  Water  Vapor. 

,  d 

. 

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N 

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8        a  . 

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l|lii 

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ii 

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3     ^rn  ° 

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^•<'o 

H'S'S 

^>'5 

0 

0.086354 

0.0439 

29.877 

0.000077 

0.086226 

0.086303 

0.000898 

12 

0.084154 

0.0754 

29.846 

0.000130 

0.083943 

0.084073 

0.001548 

22 

0.082405 

0.1172 

29.804 

0.000198 

0.082083 

0.082281 

0.002413 

32 

0.080728 

0.1811 

29.740 

0.000300 

0.080239 

0.080539 

0.003744 

42 

0.079117 

0.2673 

29.654 

0.000435 

0.078411 

0.078846 

0.005554 

52 

0.077569 

0.3883 

29.533 

0.000621 

0.076563 

0.077184 

0.008116 

62 

0.076081 

0.5559 

29.365 

0.000874 

0.074667 

0.075541 

0.011709 

72 

0.074649 

0.7846 

29.136 

0.001213 

0.072690 

0.073903 

0.016691 

82 

0.073270 

1.092 

28.829 

0.001661 

0.070595 

0.072256 

6.023526 

92 

0.071940 

1.501 

28.420 

0.002247 

0.068331 

0.070578 

0.032877 

£02 

0.070658 

2.036 

27.885 

0.002999 

0.065850 

0.068849 

0.045546 

112 

0.069421 

2.731 

27.190 

0.003962 

0.063085 

0.067047 

0.062806 

122 

0.068227 

3.621 

26.300 

0.005175 

0.059970 

0.065145 

0.086285 

132 

0.067073 

4.750 

25.171 

0.006689 

0.056425 

0.063114 

0.118548 

142 

0.065957 

6.167 

23.754 

0.008562 

0.052363 

0.060925 

0.163508 

152 

0.064878 

7.929 

21.992 

0.010854 

0.047686 

0.058540 

0.227609 

162 

0.063834 

10.097 

19.824 

0.013636 

0.042293 

0.055929 

0.322407 

172 

0  062822 

12.749 

17.172 

0.016987 

0.036055 

0.053042 

0.471146 

182 

0.061843 

15.965 

13.956 

0.021000 

0.028845 

0.049845 

0.728012 

192   " 

0.060893 

19.826 

10.095 

0.025746 

0.020545 

0.046291 

1.25319 

202 

0.059972 

24.442 

5.479 

0.031354 

0.010982 

0.042336 

2.85507 

212 

0.059079 

29.921 

0.000 

0.037922 

0.000000 

0.037922 

Infinite- 

Applications  of  the  Formula1  and  Tables. 

EXAMPLE  1. — How  low  must  the  relative  humidity  be,  when  the  at- 
mospheric pressure  is  14.7  Ib.  per  sq.  in.  and  the  outside  temperature  is 
60°,  in  order  that  no  moisture  may  be  deposited  in  any  part  of  a  com- 
pressed air  system  carrying  a  constant  gauge  pressure  of  90  Ib.  per  sq.  in? 
A n s. — The  maximum  amount  of  moisture  that  1  Ib.  of  pure  air  can 
contain  at  90  Ib.  gauge,  =  104.7  Ib.  (absolute  pressure)  and  60°  F.,  is 
W-         KH          -          0.6183X0.5180         __ 

2.036  P-r-H~  2.036  X  104.7  -  0.5180  ~  a°° 

The  maximum  weight  of  moisture  that  1  Ib.  of  air  can  contain  at  60° 
F.  and  14.7  Ib.  (absolute  pressure)  is 

W  (at  14  7)  -         0-618  X  0.5180        _ 

14>7}  "  2.036  X  14.7  -  05180      0'01         lb* 

In  order  that  no  moisture  may  be  deposited,  the  relative  humidity 
must  not  be  above 

(0.001506  -^  0.01089)  X  100  =  13.83%. 

NOTE. — Air  is  said  to  be  saturated  with  water  vapor  when  it  contains 
the  maximum  amount  possible  at  the  existing  temperature  and  pressure. 
EXAMPLE  2. — When  compressing  air  into  a  reservoir  carrying  a  con- 
stant gauge  pressure  of  75  lb.,  from  a  saturated  atmosphere  of  14.7  lb. 
abs.  press,  and  70°  F.,  to  what  temperature  must  the  air  be  cooled  after 
compression  in  order  to  cause  the  deposition  of  moisture  to  commence? 
Ans. — First  find   the  maximum  weight  of  moisture  contained  in 
1  lb.  of  pure  air  at  14.7  lb.  pressure  and  70°  F. 


614  AIR. 

KH  0.6196  X  0.7332 

™  2.036P-#  =  2d36~X  14.7  -  0.7332  =  °'°1556  lb' 


The  temperature  to  which  the  air  must  be  cooled  in  order  to  cause 
the  deposition  of  moisture  may  be  found  by  placing  this  value  of  0.01556 
together  with  P  equal  to  75  +  14.7  in  the  equation  thus: 


_       _  •— 

2.036  X  89.7  -#    ~  182.63  -  H 

2  842 

or  H  —  .        '    —  ;  —  ~  ,  and  the  temperature  which  satisfies  this  equation 
U.Ulooo  ~r  zi. 

is  found  by  aid  of  the  table  [by  trial  and  error]  to  be  approximately 
129°  F. 

EXAMPLE  3,  —  When  the  outside  temperature  is  82°  F.,  and  the 
pressure  of  the  atmosphere  is  14.6963  Ib.  per  sq.  in.,  the  relative  humid- 
ity being  100%,  how  many  cu.  ft.  of  free  air  must  be  compressed 
and  delivered  into  a  reservoir  at  100  Ib.  gauge  in  order  to  cause  1  Ib.  of 
water  to  be  deposited  when  the  air  is  cooled  to  82°  F.? 

Ans.  —  Weight  of  moisture  mixed  with  1  Ib.  of  air  at  82°  F.t  and 
atmospheric  pressure  =  0.023526  Ib.  For  100  Ib.  gauge  pressure, 

W-  KH  0.6211  X  1.092  _o  002918  Ib 

2.036  P-H       2.036  X  114.6963  -  1.092  ~ 

Weight  of  moisture  deposited  by  each  Ib.  of  compressed  air  =  0.023526 
—  0.002918  =  0.020608  Ib.  Each  cu.  ft.  of  the  moist  atmosphere  con- 
tains 0.070595  Ib.  of  pure  air,  therefore  the  number  of  cu.  ft.  that  must 
be  delivered  to  cause  1  Ib.  of  water  to  be  deposited  is 

X  TTT;       ^=  687.37  cu.  ft. 


0.070595         0.020608 

EXAMPLE  4.  —  Under  the  same  conditions  as  stated  in  Example  3, 
what  is  the  loss  in  volumetric  efficiency  of  the  plant  when  the  excess 
moisture  is  properly  trapped  in  the  main  reservoirs? 

Ans.  —  Before  compression,  each  pound  of  air  is  mixed  with  0.023526 
Ib.  of  water  vapor  and  the  weight  of  1  cu.  ft.  of  the  mixture  is  0.072256  Ib., 
consequently  the  volume  of  the  mixture  is 

1.023526  ^  0.072256  =  14.165  cu.  ft. 

For  100  Ib.  gauge  pressure  and  82°  F.  as  shown  in  Example  3,  1  Ib. 
of  air  can  hold  0.002918  Ib.  of  water  in  suspension,  having  deposited 
0.020608  Ib.  in  the  reservoir.  The  weight  of  1  cu.  ft.  of  water  vapor  at 
82°  is  0.001661  Ib.,  consequently  by  Dalton's  law  the  volume  of  the.  mix- 
ture of  1  Ib.  of  air  and  0.002918  Ib.  of  water  vapor  at  100  Ib.  gauge  press- 
ure is  the  same  as  that  of  the  vapor  or  saturated  steam  alone;  that  is, 
0.002918  +  0.001661  =  1.757  cu.  ft. 

By  Mariotte's  law,  the  volume  of  the  1.757  cu.  ft.  of  mixed  gas  at 
114.6963  Ib.  absolute  when  expanded  to  atmospheric  pressure  will  be 

(114.6963  -^  14.6963)  X  1.757  =  13.712  cu.  ft.; 

consequently  the  decrease  of  volume,  that  is,  the  loss  of  volumetric 
efficiency,  is 
14.165  -  13.712  =  0.453  cu.  ft.,  or  (0.453  -f-  14.165)  X  100  =  3.2%. 

This  example  shows  that,  particularly  in  warm,  moist  climates,  there 
Is  a  very  appreciable  loss  in  the  efficiency  of  compressors,  due  to  the 
condensation  of  water  vapor. 

Specific  Heat  of  Air  at  Constant  Volume  and  at  Constant  Pressure. 
—  Volume  of  1  Ib.  of  air  at  32°  F.  and  pressure  of  14.7  Ibs.  per  sq.  in.  = 
12.387  cu.  ft.  =a  column  1  sq.  ft.  area  X  12.387  ft.  high.  Raising  tem- 
perature 1°  F.  expands  it  1/492,  or  to  12.4122  ft.  high,  a  rise  of  0.02522ft. 

Work  done  =  2116  Ibs.  per  sq.  ft.  X  .02522  =  53.37  foot-pounds,  or 
53.37  -i-  778  =  0.0686  heat  units. 

The  specific  heat  of  air  at  constant  pressure,  according  to  Regnault,  is 
0.2375;  but  this  includes  the  work  of  expansion,  or  0.0686  heat  units;  hence 
the  specific  heat  at  constant  volume  =  0.2375  —  0.0686  =  0.1689. 

Ratio  of  specific  heat  at  constant  pressure  to  specific  heat  at  constant 
volume  =  0.2375  -T-  0.1689  =  1.406.  (See  Specific  Heat,  p.  562.) 


FLOW  OF  AIR  THROUGH  ORIFICES.  615 

Flow  of  Air  through  Orifices.  —  Tne  tneoreticai  velocity  in  feet  per 
second  of_flow  of  any  fluid,  liquid,  or  gas  through  an  orifice  is  v  =  ^2~gh 
=  8.02  V/i,  in  which  h  —  the  "  head  "  or  height  of  the  fluid  in  feet  required 
to  produce  the  pressure  of  the  fluid  at  the  level  of  the  orifice.  (For  gases 
the  formula  holds  good  only  for  small  difference  of  pressure  on  the  two 
sides  of  the  orifice.)  The  quantity  of  flow  in  cubic  feet  per  second  is  equal 
to  the  product  of  this  velocity  by  the  area  of  the  orifice,  in  square  feet, 
multiplied  by  a  "coefficient  of  flow,"  which  takes  into  account  the  con- 
traction of  the  vein  or  flowing  stream,  the  friction  of  the  orifice,  etc. 

For  air  flowing  through  an  orifice  or  short  tube,  from  a  reservoir  of  the 
pressure  p\  into  a  reservoir  of  the  pressure  pz,  Weisbach  gives  the  following 
values  for  the  coefficient  of  flow,  obtained  from  his  experiments. 

FLOW  OP  AlR  THROUGH  AN  ORIFICE. 

Coefficient  c  in  formula  v  =  c  \/2'gh 

Diam.  1  cm.  =  0.394  in.: 

Ratio  of  pressures ...      1.05  1.09  1.43  1.65       1.89       2.15 

Coefficient 555  .589  .692  .724       .754       .788 

Diam.  2.14  cm.  '=  0.843  in.: 

Ratio  of  pressures ...      1.05  1.09  1.36  1.67       2.01        

Coefficient 558  .573  .634  .678       .723     

FLOW  OF  AlR  THROUGH  A  SHORT  TUBE. 

Diam.  1  cm.,  =  6.394  in.,  length  3  cm.  =  1.181  in. 

Ratio  of  pressures  pi  -&-p2...   1.05     1.10     1.30     

Coefficient 730      .771      .830 

Diam.  1.414  cm.  =  0.557  in.,  length  4.242  cm.  =  1.670  in.: 

Ratio  of  pressures 1.41     1 . 69     

Coefficient 813     .822 

Diam.  1  cm.  =  0.394  in.,  length  1.6  cm.  =  0.630  in.     Orifice  rounded: 

Ratio  of  pressures 1.24     1.38     1.59     1.85     2.14     

Coefficient 979     .986     .965     .971     .978.... 

Clark  (Rules,  Tables,  and  Data,  p.  891)  gives,  for  the  velocity  of  flow 
of  air  through  an  orifice  due  to  small  differences  of  pressure, 

V  -  C  i^k  X  773.2  X  (l  1  *  ~  32)  ><29-92 

in  which  V  =  Velocity  in  feet  per  second;  2  g  =  64.4;  h  «  height  of  the 
column  of  water  in  inches,  measuring  the  difference  of  pressure;  t  =  the 
temperature  Fahr.;  and  p  =  barometric  pressure  in  inches  of  mercury. 
773.2  is  the  volume  of  air  at  32°  under  a  pressure  of  29.92  inches  of  mercury 
when  that  of  an  equal  weight  of  water  is  taken  as  1. 

For  62°  F.,  the  formula  becomes  V  =  363  C  ^h/p,  and  if  p  =  29.92 
inches,  V  =  66.35  C  Vft. 

The  coefficient  of  efflux  C,  according  to  Weisbach,  is: 
For  conoidal  mouthpiece,  of  form  of  the  contracted  vein, 

with  pressures  of  from  0.23  to  1.1  atmospheres C  =  0.97  to  0.99 

Circular  orifices  in  thin  plates C  =  0.56  to  0  79 

Short  cylindrical  mouthpieces C  =  0.81  to  0.84 

The  same  rounded  at  the  inner  end C  =  0  92  to  0  93 

Conical  converging  mouthpieces C  =  0.90  to  0.99 

JR.  J.  Durley,  Trans.  A.  S.  M.  E.,  xxvii,  193,  gives  the  following: 

The  consideration  of  the  adiabatic  flow  of  a  perfect  gas  through  a 
frictionless  orifice  leads  to  the  equation 

2  7  +  1 


W  =  weight  of  gas  discharged  per  second  in  pounds. 
A  =  area  of  cross  section  of  jet  in  square  feet. 
P\  —  pressure  inside  orifice  in  pounds  per  square  foot. 
Jrt  —  pressure  outside  orifice. 

Vi  =  specific  volume  of  gas  inside  orifice  in  cu.  ft.  per  Ib. 
y  =  ratio  of  the  specific  heat  at  constant  pressure  to  that  at  constant 
volume. 


616 


AIR. 


For  air,  where  y  =  1.404,  we  have  for  a  circular  orifice  of  diameter  d 
inches,  the  initial  temperature  of  the  air  being  60°  Fahr.  (or  521°  abs.), 

W  =  0.000491  d*l 

In  practice  the  flow  is  not  frictionless,  nor  is  it  perfectly  adiabatic, 
and  the  amount  of  heat  entering  or  leaving  the  gas  is  not  known.  Hence 
the  weight  actually  discharged  is  to  be  found  from  the  formulas  by  in- 
troducing a  coefficient  of  discharge  (generally  less  than  unity)  dep'end- 
ing  on  the  conditions  of  the  experiment  and  on  the  construction  of 
the  particular  form  of  orifice  employed. 

If  we  neglect  the  changes  of  density  and  temperature  occurring  as 
the  air  passes  through  the  orifice,  we  may  obtain  a  simpler  though 
approximate  formula  for  the  ideal  discharge: 


W 


0.01369  d«-  \l~ 


(3) 


in  which  d  =  diam.  in  inches,  i  =  difference  of  pressures  measured  in 
inches  of  water,  P  =  mean  absolute  pressure  in  Ibs.  per  sq.  ft.,  and  T  = 
absolute  temperature  on  the  Fahrenheit  scale  =  degrees  F.  +  461.  In 
the  usual  case,  in  which  the  discharge  takes  place  into  the  atmosphere, 
P  is  approximately  2117  pounds  per  square  foot  and 


W  =  0.6299  d 


'V? 


(4) 


To  obtain  the  actual  discharge  the  values  found  by  the  formula  are  to  be 
multiplied  by  an  experimental  coefficient  C,  values  of  which  are  given  in 
the  table  below. 

Up  to  a  pressure  of  about  20  ins.  of  water  (or  0.722  Ibs.  per  sq.  in.)  above 
the  atmospheric  pressure,  the  results  of  formulae  (2)  and  (4)  agree  very 
closely.  At  higher  differences  of  pressure  divergence  becomes  noticeable. 

They  hold  good  only  for  orifices  of  the  particular  form  experimented 
with,  and  bored  in  plates  of  the  same  thickness,  viz.:  iron  plates  0.057  in. 
thick. 

The  experiments  and  curves  plotted  from  them  Indicate  that:  — 

(1)  The  coefficient  for  small  orifices  increases  as  the  head  increases,  but 
at  a  lesser  rate  the  larger  the  orifices,  till  for  the  2-in.  orifice  it  is  almost 
constant.     For  orifices  larger  than  2  ins.  it  decreases  as  the  head  increases, 
and  at  a  greater  rate  the  larger  the  orifice. 

(2)  The  coefficient  decreases  as  the  diameter  of  the  orifice  increases,  and 
at  a  greater  rate  the  higher  the  head. 

(3)  The   coefficient   does   not   change   appreciably   with   temperature 
(between  40°  and  100°  F.). 

(4)  The  coefficient  (at  heads  under  6  ins.)  is  not  appreciably  affected 
by  the  size  of  the  box  in  which  the  orifice  is  placed  if  the  ratio  of  the  areas 
of  the  box  and  orifice  is  at  least  20  :  1. 

MEAN  DISCHARGE  IN  POUNDS  PER  SQUARE  FOOT  OF  ORIFICE  PER  SECOND 
AS  FOUND  FROM  EXPERIMENTS. 


Diameter 
Orifice, 
Inches. 

1-inch 
Head 
Discharge 
per  Sq.  Ft. 

2-inch  Head 
Discharge 
per  Sq.  Ft. 

3-inch  Head 
Discharge 
per  Sq.  Ft. 

4-inch 
Head 
Discharge 
per  Sq.  Ft. 

5-inch 
Head 
Discharge 
per  Sq.  Ft. 

0.3125 

3.060 

4.336 

5.395 

6.188 

7.024 

0.5005 

3.012 

4.297 

5.242 

6.129 

6.821 

1.002 

3.058 

4.341 

5.348 

6.214 

6.838 

'      1.505 

3.050 

4.257 

5.222 

6.071 

6.775 

2.002 

2.983 

4.286 

5.284 

6.107 

6.788 

2.502 

3.041 

4.303 

5.224 

5.991 

6.762 

3.001 

3.078 

4.297 

5.219 

6.033 

6.802 

3.497 

3.051 

4.258 

5.202 

5.966 

6.814 

4.002 

3.046 

4.325 

5.264 

5.951 

6.774 

4.506 

3.075 

4.383 

5.508 

6.260 

7.028 

FLOW   OF  AIR  IN  PIPES. 


617 


COEFFICIENTS  OF  DISCHAEGE  FOI^VARIOUS  HEADS  AND  DIAMETERS  OF 
ORIFICE. 


Diameter 
of  Orifice, 
Inches. 

1-inch 
Head. 

2-inch 
Head. 

3-inch 
Head. 

4-inch 
Head. 

5-inch 
Head. 

5/16 

0.603  * 

0.606 

0.610 

0.613 

0.616 

V2 

0.602 

0.605 

0.608 

0.610 

0.613 

0.601 

0.603 

0.605 

0.606 

0.607 

H/2 

0.601 

0.601 

0.602 

0.603 

0.603 

2 

0.600 

0.600 

0.600 

0.600 

0.600 

21/2 

0.599 

0.599 

0.599 

0.598 

0.598 

3 

0.599 

0.598 

0.597 

0.596 

0.596 

31/2 

0.599 

0.597 

0.596 

0.595 

0.594 

4 

0.598 

0.597 

0.595 

0.594 

0.593 

41/2 

0.598 

0.596 

0.594 

0.593 

0.592 

CORRECTED  ACTUAL  DISCHARGE  IN  POUNDS  PER  SECOND  AT  60°  F.  AND 

14.7  LBS.    BAROMETRIC  PRESSURE  FOR  CIRCULAR  ORIFICES  IN 

PLATE  0.057  IN.  THICK. 


Diameter  of  Orifice  in  Inches. 


rt£ 

or 
Wo 

0.3125 

0.500  |  i.OOO 

1.500 

2.000 

2.500 

3.000 

3.500 

4.000 

4.500 

5.000 

I172 

U/2 

21/2 
31/2 
41/2 

5V2 
6 

0.00114 
0  OC162 

0.00293 
0  00416 

0.0117 
0  0166 

0.0263 
0  0373 

0.0468 
0  0663 

0.0732 
0  103 

0.105 
0  149 

0.143 
0  202 

0.187 
0  264 

0.237 
0.334 

0.292 
0  413 

0.00199 

0.00510 

0.0203 

0.0457 

0  .081  1 

0.127 

0.182 

0.248 

0.323 

0.409 

0.505 

0.00231 
0  00259 

C.  00590 
0  00662 

0.0235 
0.0263 

0.0528 
0  1591 

0.0937 
0  105 

0.146 
0.163 

0.210 
0  235 

0.285 
0  319 

0.373 
0  416 

0.471 
0.526 

0.582 
0  649 

0.00285 

0.00726 

0.0289 

0.0648 

0.115 

0.179 

0.257 

0.349 

0.455 

0.575 

0.710 

0.00308 

0.00786 

0.0312 

0.0700 

0.124 

0.193 

0.277 

0.377 

0.491 

0.621 

0.766 

0.00330 
0.00351 
0.00371 
0.00390 
0.00408 

0.00842 
0.00695 
0.00945 
0  .00993 
0.01049 

0.0334 
0.0355 
0.0375 
0.0393 
0.0411 

0.0749 
0.0794 
0.0838 
0.0879 
0.0918 

0.133 
0.141 
0.148 
0.155 
0.162 

0.206 
0.219 
0.231 
0.242 
0.252 

0.296 
0.314 
0.331 
0.347 
0.362 

0.402 
0.426 
0.449 
0.471 
0.492 

0.525 
0.556 
0.586 
0.613 
0.640 

0.663 
0.702 
0.739 
0.774 
0.808 

0.817 
0.865 
0.912 
0.953 
0.995 

Fliegner's  Equation  for  Flow  of  Air  through  an  Orifice.  —  (Peabody's 
"Thermodynamics,"  also  Trans.  A.  S.  M.  E.,  vol.  27,  p.  194.) 


- 

W  =  flow  in  pounds  per  second;  A  =  area  of  the  orifice  (or  sum  of  the 
areas  of  all  the  orifices)  in  square  inches;  P  =  absolute  pressure  in  the 
orifice  chamber  Ib.  per  sq.  in.;  T  =  absolute  temperature,  deg.  F.,  of  the 
air  in  the  chamber.  The  formula  applies  only  when  the  absolute 
pressure  in  the  reservoir  is  greater  than  twice  the  atmospheric  pressure, 
and  for  orifices  properly  made.  The  orifices  are  in  hardened  steel 
plates  3/8  in.  to  1/2  in.  thick,  accurately  ground,  with  the  inside  orifice 
rounded  to  a  radius  I/IG  in.  less  than  the  thickness  of  the  plate,  leaving 
1/16  in.  of  the  hole  straight. 

FLOW  OF  AIR  IN  PIPES. 

In  the  steady  flow  of  any  liquid  or  gas,  without  friction,  the  sum  of 
the  velocity  head,  V2  -5-  2  g,  pressure  head  p/w,  and  potential  head,  z, 
(that  is  the  distance  in  feet  above  an  assumed  datum)  at  any  section  of 

the  pipe  is  a  constant  quantity.        ~  +  —  +  z  =  a  constant.      This 

statement  is  known  as  Bernoulli's  theorem. 

V  =  velocity  in  ft.  per  sec.;  2  g  =  64.35;  p  =  absolute  pressure  in 
pounds  per  sqiiare  feet;  w  =  density,  pounds  per  cubic  feet;  z  =  height 
of  the  section  above  a  given  datum  level.  When  the  pipe  is  level  we 
may  take  its  axis  as  datum,  and  then  2=0. 

When  "fluid  friction"  or  "skin  friction"  is  taken  into  account  there 


618  AIK. 

is  a  "loss  of  head"  or  "friction  head"  between  any  two  selected  points, 

/     D2 

such  as  the  two  ends  of  the  pipe,  H  ~  fLv*  •*•  R  2  g;  or  H  =  4/  •—  —; 

H  is  the  loss  of  head,  or  head  causing  the  flow,  measured  in  feet  of  the 
fluid,  /  is  a  coefficient  of  friction  and  R  the  mean  hydraulic  radius, 
which  in  circular  pipes  =  1/4  D.  L  is  the  length  of  the  pipe  and  D  the 
diameter,  both  in  feet.  By  transposition  the  .velocity  in  feet  per 


second  is  V=^f  ^  =  4.0103  ^/y^- 

The  value  of/  in  this  formula  varies  through  a  considerable  range 
with  the  roughness  of  the  pipe,  with  the  diameter,  and  probably  to 
some  extent  with  the  velocity.  For  a  rough  approximation  its  value 
for  air  and  other  gases  may  be  taken  as  0.005. 

For  convenience  in  calculation,  the  loss  of  head  in  feet  of  H  may  be 
replaced  by  the  difference  in  pressure  in  Ib.  per  sq.  in.,  H  =  144  (p\  —  pz) 
-r  W,  and  the  diameter  d  may  be  taken  in  inches.  We  thus  obtain 

v  = 

The  quantity  of  flow  in  cubic  feet  per  minute,  Q  =  60  A  V.  A  being 
the  area  in  sq.  ft.  =60  X  0.7854  X  d2  -r-  144,  whence  we  have  (by  multi- 
plying 60  X  0.7854  X  13.89  4-  144),  Q  =  4.546  ^~  X 


i  —  P2)  —  which  is  the  common  formula  for  flow  of  any  liquid  or 


w 

gas  when  Q  is  in  cubic  feet  per  minute  measured  at  the  density  w  cor- 
responding to  the  higher  pressure  pi.     To  reduce  this  to  the  equivalent 

volume  of  "free  air"  at  atmospheric  pressure,  Qa  =  Q  X    T* 


The  weight  flowing  per  minute  is  Q  w  =  W  =  c  -  Values 

of  c  corresponding  to  different  values  of/  are  as  follows: 

/.  .  .  0  .  003  .  0035  .  004  .  0045  .  005  .  0055  .  006  .  0065  .  007  .  0075 
C...  83.0  76.9  71.9  67.8  64.3  61.3  58.7  56.4  54.7  52.4 

The  experimental  data  from  which  the  values  of  c  and  /  for  air  and 
gas  may  be  determined  are  few  in  number  and  of  doubtful  accuracy. 
Probably  the  most  reliable  are  those  obtained  by  Stockalper  at  the 
St.  Gothard  tunnel.  Unwin  found  from  these  data  that  the  value  of/ 
varied  with  the  diameter  and  that  it  might  be  expressed  by  the  formula 
/=  0.0028  (1  +  3.6/tf),  d  being  taken  in  inches. 

Ford=      I  2  3  4  6  12          24         48  In. 

/  =  0.013      .0078      .0062      .0053      .0045      .0036      .0032      .0030 
c=40.0        51.3       57.9       62.3       67.9       75.3       80.1        82.8 

Unwin  's  formula  may  be  given  the  form  Q  =  K\w  jf(I~+?3  6°d)' 

in  which  K  =  4.546  V  1  -T-  .0028  =  85.9.  This  is  practically  the 
same  as  Babcock's  formula  for  steam,  in  which  /  is  taken  at  0.0027, 
giving  K  =  87.5. 

Formulae  for  Flow  with  Large  Drop  in  Pressure.  —  The  above  for- 
mulae are  based  on  the  assumption  that  the  drop  in  pressure  is  small, 
and  that,  therefore,  the  density  remains  practically  constant  during 
the  flow.  When  the  drop  is  large  the  density  decreases  with  the  pres- 
sure and  the  velocity  increases.  Church  ("Mechanics  of  Engineering," 
p.  791)  and  Unwin  (Ency.  Brit.,  llth  ed.,  vol.  xiv.,  p.  67),  develop 
formulae  for  compressible  fluids  with  large  drop  of  pressure  and  in- 
creasing velocity.  The  temperature  is  assumed  to  be  constant,  the 
heat  generated  by  friction  balancing  the  cooling  due  to  the  work  done 
in  expansion. 


FLOW  OF  AIR  IN  PIPES.  619 

Church's  formula:  Q  =  1/4  ir  d*  -V/T77  w^  ^l*  ~"  p*^' 


Unwind  formula:   v- 


V  =  velocity,  ft.  per  sec.  ;  Q  =   volume,  cu.  ft.  per  sec.  at  the  pressure 
PI;  g  =  32.2;  R  =  the  constant  in  the  formula  PV  =  RT  (see  Thermody- 


namics) =  53.32  for  air;  d  =  diam.,  and  L  =  length,  in  feet;  pi,  pz  = 
absolute!- pressures  in  Ib.  per  sq.  ft.;  w  =  density,  Ib.  per  cu.  ft.;  2'== 
temperature  F.  +  459.6.  The  value  of  /  is  given  by  Church  as  from 


0.004  to  0.005.  Unwin  makes  it  vary  with  the  diameter  as  stated 
above. 

These  two  formulae  give  identical  results  when  the  value  of/  is  taken 
the  same  in  both,  for  RT/pi2  =1-7-  wpi. 

J.  E.  Johnson,  Jr.  (Am.  Mach.,  July  27,  1899)  gives  Church's  formula 
in  a  simpler  form  as  follows:  pi2—  pzz  =  KQ*L  -5-  d5,  in  which  pi  and 
pz  are  the  initial  and  final  pressures  in  Ib.  per  sq.  in.,  Q  the  volume  of 
free  air  (that  is  the  volume  reduced  to  atmospheric  pressure)  in  cubic 
feet  per  minute,  d  the  diameter  of  the  pipe  in  inches,  L  the  length  in  feet, 
and  K  a  numerical  coefficient  which  from  the  Mt.  Cenis  and  St.  Gothard 
experiments  has  a  value  of  about  0.0006.  E.  A.  Rix,  in  a  paper  on  the 
Compression  and  Transmission  of  Illuminating  Gas,  read  before  the 
Pacific  Coast  Gas  Ass'n,  1905,  says  he  uses  Johnson's  formula,  with  a 
coefficient  of  0.0005,  which  he  considers  more  nearly  correct  than  0.0006. 
For  gas  the  velocity  varies  inversely  as  the  square  root  of  the  density, 
and  for  gas  of  a  density  G,  relative  to  air  as  1,  Rix  gives  the  formula 
Plz  _  p22  =  0.0005  VOX  Q*L/d*. 

If  Church's  formula  is  translated  into  the  same  form  as  Johnson's, 
taking/  =  0.005,  w  =  0.07608  for  air  at  62°  F.,  and  atmospheric  pressure, 
14.7  Ibs.  per  sq.  in.,  the  value  of  K  is  0.00054.  A  more  convenient 


form  is  Qa  =  Ci         l~  in  which   Ci  =  \/^/K.     With  K  in 

Johnson's  formula  taken  at  0.0006,  Ci  =  40.8.  With  /  in  Church's 
formula  taken  at  0.005,  Ci  =  43.0. 

Note  that  Church's  formula  gives  Q  in  cubic  feet  per  second  meas- 
ured at  the  pressure  p\,  while  Johnson's  Qa  is  in  cubic  feet  per  minute 
reduced  to  atmospheric  pressure. 

Both  Church  and  Johnson  assume  that  the  flow  varies  as  \/d*,  the 
coefficients/  and  K  being  independent  of  the  diameter.  In  this  respect 
their  formulae  are  faulty,  for,  as  Unwin  shows,  the  coefficient  of  friction 
is  a  function  of  the  diameter. 

The  relation  between  the  results  given  by  these  formulae  and  those 
given  by  the  common  formula  is  the  relation  between  \/pi*  -  pz2  and 
\/pi  —  pz.  Taking  pi  (in  any  unit)  as  100,  and  different  drops  in 
pressure,  the  relative  results  are  as  follows: 

Pressure  drop  ..............       1         10        20        40        60        80 

Values  of  pz.  .  .  .......  ........      99         90         80         60         40         20 

Vpi*-pz2  +  Vpi  -  PZ    ......      14.1     13.8     13.4     12.2     11.8     10.8 

Ratio,  14.1  =  100  ...........    100         97.6     95.0     86.5     83.7     76.6 

It  thus  appears  that  the  calculated  result  by  Johnson's  formula  is 
not  more  than  5  per  cent  less  than  that  calculated  by  the  common 
formula,  when  the  same  value  of  /  is  used,  if  the  drop  in  pressure  is 
not  greater  than  20  per  cent  of  p\. 

Comparison  of  Different  Formulae.  —  We  may  compare  the  several 
formulas  given  above  by  applying  them  to  the  data  of  the  St.  Gothard 
experiments,  as  in  table  p.  620. 

The  value  of  Q  is  given  as  reduced  to  atmospheric  pressure,  14.7  Ib. 
per  sq.  in.  and  62°  F.  The  length  of  the  pipe  7.87  in.  diam.  was  15,092 
ft.,  and  that  of  the  pipe  5.91  in  diam.,  1712.6  ft.  The  mean  tempera- 
ture of  the  air  in  the  large  pipe  was  70°  F.  and  in  the  small  pipe  80°  F, 


620 


AIR. 


In  the  table,  Formula  (1)  Is  the  commonTormula,  Qi 


CAT 


(Pi   -  P2)   ( 

w  L 


Formula  (2)  is  Unwin's, 


Formula  (3)  is  Johnson's,  Q0 


}  d 


Qi  =  cubic  ft.  per  min.  at  pressure  pi. 

Qa  =  cubic  ft.  per  min.  reduced  to  atmospheric  pressure  =Q  pi  -7-14.7. 


Di- 
am- 
eter, 
In. 

Mean 
Vel. 
Ft. 
Per 
Sec. 

Cu. 

Ft. 
Per 

Min. 

Q 

Lb. 
Per 
Sec. 

Absolute 
Pressures. 
Ib.  per  sq.  in. 

Coefficient  in 
Formula. 

Ratio  of 
Coefficient  to 
Average  Value. 

(0 
c 

(l> 

& 

Pi 

P2 

(D 

(2) 

(3) 

7.87 
7.87 
7.87 
5.91 
5.91 

Av< 

19.3 
16.3 
15.6 
37.1 
29.3 

jrage. 

2105 
1401 
1169 
2105 
1169 

2.669 
1.776 

1.483 
2.669 
1.483 

82.32 
63.95 
56.45 
77.03 
53.66 

77.03 
60.71 
53.66 
73.50 
52.04 

76.0 
73.5 

70.2 
74.8 
65.5 

89.6 
86.5 
82.8 
94.9 
83.1 

51.3 

49.3 
46.0 
44.5 
43.6 

1.06 
1.02 
0.98 
1.04 
0.91 

1.03 
0.99 
0.95 
1.09 
0.95 

1.09 
1.05 
0.98 
0.95 
0.93 

72.0 

87.4 

46.9 

The  above  comparison  shows  that  no  one  of  three  formulae  fits  the 
St.  Gotnard  experiments  better  than  any  other;  each  one  when  applied 
with  the  average  value  of  its  coefficient  may  give  a  result  that  differs 
as  much  as  9  per  cent  from  the  observed  result. 

Arson's  Experiments. — Unwin  quotes  some  experiments  by  A.  Arson 
on  the  flow  of  air  through  cast-iron  pipes  which  showed  that  the  co- 
efficient of  friction  varied  with  the  velocity.  For  a  velocity  of  100  ft. 
per  sec.,  and  without  much  error  for  higher  velocities,  Unwin  finds 
that  the  values  of  /  agree  fairly  with  the  formula  /=  0.005  (1  +3.6/d). 
Translating  the  figures  given  by  him  for  the  varying  values  9f  /  into 
values  of  c  for  use  in  the  common  formula,  we  have  the  following: 

Diameter  of  pipe, inches.. .  .1.97  3.19  4.06  10  12.8  19.7 
volume  (  V  =  10  ft.  per  sec.  35 . 7  39.4  39.8  49.2  52.8  64.7 
Values  J  5Q  „  ,.  ,.  38  6  42  5  45  0  51  5  55  7  65  2 

ofc-       (         100    "    "     •'      41.3     45.5     46.0       53.6     56.4     65.4 
The  values  of  c  for  the  same  diameter  with  /  =  0.0028  (1  +3.6/d),  as 
deduced   by  Unwin  from  Stockalper's  experiments    are:    51.4,  57.9, 
62.3,  73.7,  75.9,  79.1. 

Unwin  says  that  Stockalper's  pipes  were  probably  less  rough  than 
Arson's.  The  values  of  c  according  to  Stockalper's  experiments  range 
from  21  to  37  per  cent  higher  than  those  calculated  from  the  formula 
derived  from  Arson's  experiments. 

Use  of  the  Formulae. — It  is  evident  from  the  above  comparisons 
that  any  formula  for  the  flow  of  air  or  gas  must  be  considered  as  only 
a  rough  approximation  to  the  actual  flow,  and  that  an  observed  result 
may  differ  as  much  as  40  per  cent  from  that  calculated  by  a  formula. 
Part  of  this  error  is  due  to  variations  in  the  roughness  of  pipes,  part 
due  to  error  in  measurements  of  the  actual  flow,  and  part  due  to  the 
fact  that  the  coefficients  of  the  several  formulae  are  based  on  too  few 
experiments.  In  the  light  of  our  present  knowledge,  Unwin's  formula 


for  moderate  drop,  Q  =  87 


(pi  — 


is  probably  the  best  one 


1  w  L  (I  +  3.6/rf) 

to  use  for  all  cases  in  which  the  drop  in  pressure  does  not  exceed  20 
per   cent   of    the   absolute   initial   pressure,   and    Johnson's   formula, 

Qa=  47-J(pl2~^22)  rf5  for  cases  in  which  the  drop  is  larger  and  the  pipes 


FLOW  OF  AIR  AT  LOW  PRESSURES. 


621 


are  not  less  than  12  inches  diameter.  For  smaller  pipes  the  term 
(1  +  3.6/d)  had  better  be  used  after  L  in  the  denominator.  These 
formulae  with  the  coefficients  given  apply  only  to  straight  pipes  with  a 
fairly  smooth  interior  surface.  For  crooked  or  rough  pipes  it  may  be 
well  to  use  the  common  formula  with  the  coefficients  derived  from 
Arson's  experiments,  given  above. 

Another  comparison  of  the  three  formulas  may  be  made  by  applying 
them  to  some  extreme  cases,  as  follows:  The  initial  pressure  is  taken 
at  100  Ib.  absolute  per  sq.  in.,  the  corresponding,  density  is  0.5176  Ib. 
per  cu.  ft.;  diameters  are  assumed  at  1  in.  and  48  in.,  the  drop  in  pres- 
sure 1  Ib.  and  40  Ib.  and  the  length  100  ft.  and  40,000  ft.,  making 
eight  cases  in  all.  A  ninth  case  is  taken  with  intermediate  values: 
diameter,  10  in.;  length,  1,000  ft.;  and  drop,  1  Ib.  The  results  are 
given  in  the  following  table.  The  results  obtained  by  Johnson's  for- 
mula have  been  reduced  by  dividing  them  by  the  ratio  (100  -%-  14.7) 
to  obtain  Q.  The  value  of  c  in  the  common  formula  is  taken  at  72,  the 
average  figure  from  the  St.  Gothard  experiments. 


Diarri.,  In. 

1 

48 

10 
1 
1,000 

Pi-  P2,  Ib. 

1 

40 

1 

40 

L,  f  t  

100 

40,000 

100 

40,000 

100    1  40,000 

100 

40,000 

Formula 

Cubic  feet  of  air  per  minute  at  the  pressure  p±. 

Common  .... 

10.08 
5.64 
9.75 

0.50 
0.28 
0.49 

63.3 
35.7 
55.3 

3.16 
1.78 
2.76 

1  59,800 
186,200 
155,600 

7,990 
9,310 
7,778 

1,010,000 
1,178,000 
882,300 

50,500 
58,900 
44,110 

1,008 
1,037 
974 

Unwin 

Johnson  

Ratio  of  results  to  Unwin's  =  1. 

Common  
Johnson  

1.79 
1.73 

1.79 
1.75 

1.78 
1.55 

1.78 
1.55 

0.86 
0.84 

0.86 
0.84 

0.86 
0.75 

0.86 
0.75 

0.96 
0.94 

These  figures  show  that  while  the  three  formulae  agree  fairly  well  for 
the  10-in.  pipe  with  1-lb.  drop  in  1,000  ft.,  they  show  wide  disagreements 
when  a  great  range  of  diameters,  lengths,  and  drops  in  pressure  are 
taken.  For  the  1-in.  pipe  Unwin's  figures  are  from  35  to  45  per  cent 
lower  than  those  given  by  the  common  formula  or  by  Johnson's,  but 
they  are  not  therefore  certainly  too  low.  We  have  a  check  on  them 
in  Culley  and  Sabine's  experiments  on  2  V4-in.  lead  pipes,  2000  to 
nearly  6000  ft.  long,  quoted  by  Unwin,  which  gave  a  value  of  £=  0.07. 
Unwin's  formula,  /  =  0.0028  (1  +  3.6/rf)  gives  /  =  0.0073.  The  cor- 
responding values  of  c  in  the  common  formula  are  54.7  and  53.2. 

Formula  for  Flow  of  Air  at  Low  Pressures.  —  For  ventilating  and 
similar  purposes,  air  is  usually  carried  at  pressures,  but  slightly  above 
that  of  the  atmosphere.  Pressures  are  measured  in  inches  of  wTater 
column  or  in  ounces  per  square  inch  above  atmospheric  pressure. 
For  smooth  and  straight  circular  pipes,  probably  the  best  formula  to 


use  is  Unwin's,  Q 
rived    from    the    St. 


=  87  \l 

if 


P~ 


the  coefficient  87  being  de- 


j 

f  W  Li  \L 

.  Gothard  experiments  on  compressed  air.  In 
order  to  put  the  formula  into  a  more  convenient  form  for  low  pres- 
sures, let  h  =  head  or  difference  in  pressures  measured  in  inches  of 
water  column,  =  27.712  (pi  -  p2),  and  take  w  =  0.07493  =  density 
of  air,  Ib.  per  cu.  ft.  at  70°  and  atmospheric  pressure,  then  Q  = 


87  X 


27.71    .07493  L  (1  +  3.6/d) 


60.37 


L  (I  +3.6/d)' 


or  Q   =3 


—L~'  in  which  C  is  a  coefficient  varying  with  the  diameter,  values 

for  different  diameters  being  given  in  the  table  below.  For  other 
temperatures  and  pressures,  the  flow  varying  inversely  as  the  square 
root  of  the  density,  the  figure  0.07493  in  the  above  equation  should  be 

replaced  by  0.07493  X  ~     X  in  which  p  =  absolute  pressure, 


622 


AIR. 


Ib.  per  sq.  in.;  and  T  =  degrees  F.     Q  is  the  quantity  in  cubic  feet  per 
minute  measured  at  the  given  pressure  and  temperature. 
Flow  of  Air  at  Low  Pressures. 


Q  -  cubic  feet  per  minute  =  C 


,  h  =  drop  in  pressure,  inches  of 


water  column,  d  =  diameter  in  inches,  L  =  length  of  pipe  in  feet.  C,  a 
coefficient  varying  with  the  diameter.  The  values  of  C  in  the  table 
are  based  on  air  at  atmospheric  pressure  and  70°  F.,  and  the  values  of 
Q  are  calculated  for  the  same  pressure  and  temperature  and  for  a  drop 
of  1-inch  water  column  in  100  ft. 


d. 

4 
5 
6 
7 
8 
9 

C. 

Q. 

d. 

C. 

Q. 

d. 

~22~ 
24 
26 
28 
30 
36 

C. 

Q. 

d. 

C. 

Q. 

43.9 
46.1 
47.7 
49.1 
50.1 
51.0 

140 
257 
421 
636 
908 
1,240 

10 
12 
14 
16 
18 
20 

51.8 
53.0 
53.9 
54.6 
55.1 
55.6 

1,637 
2,642 
3,950 
5,585 
7,579 
9,946 

56.0 
56.3 
56.6 
56.8 
57.1 
57.6 

12,700 
15,880 
19,500 
23,580 
28,130 
44,760 

42 
48 
54 
60 
66 
72 

57.9 
58.2 
58.4 
58.6 
58.8 
58.9 

66,240 
92,930 
125,200 
163,500 
208,000 
259,200 

For  any  other  pressure  drop  than  1-inch  water  column  per  100  ft., 
multiply  Q  by  the  square  root  of  the  drop,  or  by  the  factor  given  below: 
Drop,  h....  0.5  2  3468  10  12  14  16  18  20 
Factor 0.71  1.41  1.73  2  2.45  2.83  3.16  3.46  3.74  4  4.24  4.47 

For  drop  in  ounces  per  square  inch  (1  oz.  =  1.732  in.  of  water)  the 
factors  are: 

Drop,  oz. .    0.5        1        2        3        4        5        6        7        8       9         10        12 
Factor 0.93  1.32  1.86  2.28  2.63  2.94  3.22  3.48  3.72  3.95    4.16    4.56 

Loss  of  Pressure  in  Ounces  per  Square  Inch. — B.  F.  Sturtevant  Co. 

gives  the  following  formula:  

^25,000  dpi.  d  =  0.0000025  L& 

PI  =  loss  of  pressure,  ounces  per  sq.  in. ;  v  =  velocity,  ft.  per  sec. ; 
d  =  diameter,  inches;  L  =  length,  ft.  From  the  value  of  v  we  obtain 
the  flow  in  cubic  feet  per  minute.  Q  =  60  a  v  =  60  X  0.7854rf2  -f-  144  x 
25,000  dpi  _  K1  f?A  ^  IPI  d*  Jf  the  drop  .g  taken  ,n  inches  Qf  water 


V 


51.74 


column,  h,  then  Q  =  39.24  \l~~f~*    This  formula  gives  a  value  of  Q  9  per 

cent  less  than  that  given  in  the  above  table  for  a  4-inch  pipe,  and  33  per 
cent  less  for  a  72-inch  pipe. 

Flow  in  Rectangular  Pipes. — It  is  common  practice  to  make  air 
pipes  for  ventilating  purposes  rectangular  instead  of  circular  section 
in  order  to  economize  space.  No  records  of  experiments  on  the  flow 
of  air  in  such  pipes  are  available,  but  a  fair  estimate  of  their  capacity 
as  compared  with  that  of  circular  pipes  of  the  same  area  may  be  made 
on  the  assumption  that  they  follow  the  law  of  Chezy's  formula  for  flow 
of  water,  viz.:  that  the  flow  is  proportional  to  the  square  root  of  the 
mean  hydraulic  radius  r,  which  is  defined  as  the  quotient  of  the  area 
divided  by  the  perimeter  of  the  wetted  surface.  For  a  circular  pipe 
r  =  1/4  diameter  in  feet,  and  for  a  square  pipe  of  the  same  area,  r  = 
0.222d.  For  rectangles  of  the  same  area  r  will  decrease  as  the  ratio 
of  the  longer  to  the  shorter  side  increases.  For  different  proportions 
of  sides,  the  values  of  r  and  the  ratio  of  \/Fto  the  value  of  \XrT.  the 
hydraulic  radius  of  a  circular  pipe  having  the  same  area,  are  as  below: 

Ratio  of  sides ..  (circle)   l(sq.)      1.5        2  3  4  5  6 

r  = ^0.25     0.222  0.217  0.209  0.192  0.177  0.165  0.155 

Ratio  vT*  \/n .    1       -0.942  0.932  0.914  0.875  0.842  0.813  0.787 

That  is,  a  square  pipe  will  have  94  percent  of  the  carrying  capacity  of 
a  circular  pipe  of  the  same  area,  and  a  rectangular  pipe  whose  sides  are 
in  the  ratio  of  6  to  1  will  have  only  79  per  cent  of  thf  capacity  of  a 
circular  pipe  of  the  same  area. 


fLOW  OF  AIR. 


623 


§safl- 

o5.2^ 

«!£Q 


NO—  • 

Ooo 


GQQQQ 


coooom'f 


3TJ-COOO  — 
^©cviaNt- 
- 


^eNr^oo  — 


00  ( 


• 

poo  - 


60 

CO 


;aB* 


o 


I 

£ 


55      o 


624 


Volume  of  Air  Transmitted  in  Cubic  Feet  per  Minute  in 
Pipes  of  Various  Diameters, 


Formula  Q  = 


0.7854 
144 


Is 

Actual  Diameter  of  Pipe  in  Inches. 

ll 

1 

2 

3 

4 

5 

6 

8 

10 

12 

16 

20 

24 

1 

0.327 

1.31 

2.95 

5.24 

8.18 

11.78 

20,94 

32.73 

47.12 

83.77 

130^ 

188  5 

2 

0.655 

2.62 

5.89 

10.47 

16.36 

23.56 

41'.  89 

65.45 

94.25 

167.5 

261  8 

377  0 

3 

0.982 

3.93 

8.84 

15.7 

24.5 

35.3 

62.8 

98.2 

141.4 

251.3 

392.7 

565  .'5 

4 

1.31 

5.24 

11.78 

20.9 

32.7 

47.1 

83.8 

131 

188 

335 

523 

754 

5 

1.64 

6.54 

14.7 

26.2 

41.0 

59.0 

104 

163 

235 

419 

654 

942 

6 

1.96 

7.85 

17.7 

31.4 

49.1 

70.7 

125 

196 

283 

502 

785 

1131 

7 

2.29 

9.16 

20.6 

36.6 

57.2 

82.4 

146 

229 

330 

586 

916 

1319 

8 

2.62 

0.5 

23,5 

41.9 

65.4 

94 

167 

262  • 

377 

670 

1047 

1508 

9 

2.95 

1.78 

26.5 

47 

73 

106 

188 

294 

424 

754 

1178 

1696 

10 

3.27 

3.1 

29.4 

52 

82 

118 

209 

327 

471 

838 

1307 

1885 

12 

3.93 

5.7 

353 

63 

98 

141 

251 

393 

565 

1005 

1571 

2262 

15 

4.91 

9.6 

44.2 

78 

122 

177 

314 

491 

707 

1256 

1963 

2827 

18 

5.89 

23.5 

53 

94 

147 

212 

377 

589 

848 

1508 

2356 

3393 

20 

6.54 

26.2 

59 

105 

164 

235 

419 

654 

942 

1675 

2618 

3770 

24 

7.85 

31.4 

71 

125 

196 

283 

502 

785 

1131 

2010 

3141 

4524 

25 

8.18 

32.7 

73 

131 

204 

294 

523 

818 

1178 

2094 

3272 

4712 

28 

9.16 

36.6 

82 

146 

229 

330 

586 

916 

1319 

2346 

3665 

5278 

30 

9.8 

39.3 

88 

157- 

245 

353 

628 

982 

1414 

2513 

3927 

5655 

Effect  of  Bends  in  Pipes.    (Norwalk  Iron  Works  Co.) 
Radius  of  elbow,  in  diameter 

of  pipe  =  5321i/2li/4l         3/4       l/3 

Equivalent  lengths  of  straight 

pipe,  diams.  7.85  8.24  9.03  10.36  12.72  J  7.51  35.09  121 .2 

E.  A.  Rix  and  A.  E.  Chodzko,  in  their  treatise  on  Compressed  Air 
(189G),  give  the  following  as  the  loss  in  pressure  through  90°  bends. 
Had.    of    bend  4-  internal 

diam.  of  pipe ,  . .          1  2  3  4  5 

Loss  in  lb.  per  sq.  in O.OOSr2       .0022r2     .0016i>2     .0013r2     .0012r2 

v  is  the  velocity  of  air  at  entrance,  in  feet  per  second. 

Friction  of  Air  in  Passing  through  Valves  and  Elbows.  W.  L. 
Saunders,  Compressed  Air,  Dec.,  1902. — The  following  figures  give  the 
length  in  feet  of  straight  pipe  which  will  cause  a  reduction  in  pressure  equal 
to  that  caused  by  globe  valves,  elbows,  and  tees  in  different  diameters  of 
pipe. 
Diam.  of  pipe,  in..  1  H/2  2  2l/2  3  31/2  4  5  6  7  8  10 

Globe  Valves 24       7     10       13     16       20     28     36     44     63     70 

Elbows  and  Tees  .23       5       7        911       13     19     24     30     35     47 

Measurement  of  the  Velocity  of  Air  in  Pipes  by  an  Anemometer. 
—  Tests  were  made  by  B.  Donkin,  Jr.  (hist.  Civil  Engrs.,  1892).  to  com- 
pare the  velocity  of  air  in  pipes  from  8  in.  to  24  in.  diam.,  as  shown  by  an 
anemometer  2  3/4  in.  diam.  with  the  true  velocity  as  measured  by  the  time 
of  descent  of  a  gas-holder  holding  1622  cubic  feet.  A  table  of  the  results 
with  discussion  is  given  in  Eng'g  News,  Dec.  22,  1892.  In  pipes  from  8  in. 
to  20  in.  diam.  with  air  velocities  of  from  140  to  690  feet  per  minute  the 
anemometer  showed  errors  varying  from  14.5%  fast  to  10%  slow.  With 
a  24-inch  pipe  and  a  velocity  of  73  ft.  per  minute,  the  anemometer  gave 
from  44  to  63  feet,  or  from  13.6  to  39.6%  slow.  The  practical  conclusion 
drawn  from  these  experiments  is  that  anemometers  for  the  measurement 
of  velocities  of  air  in  pipes  of  these  diameters  should  be  used  with  great 
caution.  The  percentage  of  error  is  not  constant,  and  varies  considerably 
with  the  diameter  of  the  pipes  and  the  speeds  of  air.  The  use  of  a  baffle 
consisting  of  a  perforated  plate,  which  tended  to  equalize  the  velocity  in 
the/center  and  at  the  sides  in  some  cases  diminished  the  error. 


PLOW  OF  AIR. 


625 


The  impossibility  of  measuring  the  true  quantity  of  air  by  an  anemometer 
held  stationary  in  one  position  is  shown  by  the  following  figures,  given  by 
Win.  Daniel  (Proc.  Inst.  M.  E..  1875),  of  the  velocities  of  air  found  at 
different  points  in  the  cross-sections  of  two  different  airways  in  a  mine. 

DIFFERENCES  OF  ANEMOMETER  READINGS  IN  AIRWAYS. 

8ft.  square. 

5  x8ft. 


1712 
1622 

1795 

1859 

1329 

1685 
1344 

1782 

1091 

1477 
1262 

1524 

1049 

1356 

1293 

1333 

Average  1132. 


Average  1469. 


Equalization  of  Pipes. — It  is  frequently  desired  to  know  what  number 
of  pipes  of  a  given  size  are  equal  in  carrying  capacity  to  one  pipe  of  a 
larger  size.  At  the  same  velocity  of  flow  the  volume  delivered  by  two 
pipes  of  different  sizes  is  proportional  to  the  squares  of  their  diameters; 
thus,  one  4-inch  pipe  will  deliver  the  same  volume  as  four  2-inch  pipes, 
With  the  same  head,  however,  the  velocity  is  less  in  the  smaller  pipe,  and 
the  volume  delivered  varies  about  as  the  square  root  of  the  fifth  power 
(i.e.,  as  the  2.5  power).  The  following  table  has  been  calculated  on  this 
basis.  The  figures  opposite  the  intersection  of  any  two  sizes  is  the  num- 
ber of  the  smaller-sized  pipes  required  to  equal  one  of  the  larger.  Thus 
one  4-inch  pipe  is  equal  to  5.7  two-inch  pipes. 


|  d 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

12 

14 

16 

18 

20 

24 

2 

5.7 
15.6 

2.8 

, 

4 

32,0 

57 

2,1 

1 

5 

55.9 

9.9 

3.6 

1.7 

1 

6 

88.2 

15.6 

5.7 

2.8 

1,6 

1 

7 

130 

22.9 

8.3 

4.1 

2.3 

1.5 

1 

8 

181 

32.0 

11.7 

5.7 

3.2 

2.1 

1.4 

1 

9 

243 

43  0 

15  6 

7,6 

4.3 

2  8 

1  9 

1  3 

1 

10 

316 

55.9 

20.3 

9.9 

5.7 

3.6 

2.4 

1.7 

1.3 

1 

11 

401 

70  9 

25.7 

12  5 

7,2 

4.6 

31 

2  2 

1  7 

1  3 

12 

499 

88.2 

32.0 

15.6 

8.9 

5.7 

3.8 

2.8 

2.1 

1.6 

1 

13 

609 

108 

39,1 

19  0 

10.9 

7.1 

4.7 

3.4 

2.5 

1.9 

12 

14 

733 

130 

47.0 

22.9 

13.1 

8.3 

5.7 

4.1 

3.0 

2.3 

1.5 

15 

871 

154 

55.9 

27.2 

i5.6 

9.9 

6,7 

4.8 

3.6 

2.8 

1.7 

.2 

16 

181 

65.7 

32.0 

18.3 

11.7 

7.9 

5.7 

4.2 

3.2 

2.1 

.4 

1 

17 

711 

76  4 

37  221  3 

13  5 

9  7 

6  6 

4  9 

3  fl 

?  4 

6 

1  ? 

18 

7.43 

88  ?, 

43.024.6 

15  6 

10  6 

76 

5  7 

4  3 

2.8 

,9 

1  3 

1 

19 

778 

101 

49  1j28  1 

17  8 

17  1 

8  7 

6  5 

5  0 

3  ? 

?  1 

1  5 

1  1 

70 

316 

115 

55  Q 

37  0 

70  3 

1*  8 

9  9 

7  4 

5  7 

3  6 

2  4 

1  7 

1  3 

1 

401 

146 

70  9 

40  6 

75  7 

17  5 

1?  5 

Q  3 

7  ? 

4  6 

3  1 

1  7 

1  3 

24 

499 

181 

88  ? 

50  5 

37  0 

71  8 

15  6 

11  6 

8  9 

5  7 

3  8 

?,  8 

7  1 

1  6 

1 

?n 

609 

108 

61  7 

39  1 

26  6 

19  0 

14  7 

10  9 

4  7 

3  4 

?  5 

1  9 

1  ? 

28 

733 

266 

130 

74  2 

47  0 

37.  0 

22  9 

17  1 

13  1 

8.3 

5.7 

4.1 

3,0 

23 

1  5 

30 

871 

316 

154 

88  7 

55  Q 

38  0 

?7  7 

70  3 

15  6 

9  9 

6  7 

4  8 

3  6 

?  8 

1  7 

36 

499 

J30 

88  2 

60  0 

43  0 

32  0 

74  6 

15  6 

10  6 

7  6 

5  7 

4  3 

?  8 

42 

733 

357 

?05 

130 

88  7 

63  ? 

47  0 

36  ? 

19  0 

15  6 

11  ? 

8  3 

6  4 

4  1 

48 

499 

286 

181 

123 

88  7 

6?  7 

50  5 

3?  0 

71  8 

15  6 

11  6 

8  9 

5  7 

14 

670 

383 

?43 

165 

118 

88  ? 

67  8 

43  0 

79  2 

?rt  9 

15  6 

1?  0 

7  6 

60 

871 

499 

316 

215 

154 

115 

88.2 

55.9 

38.0 

27.2 

20.3 

15.6 

9.9 

626 


AIR. 


WIND. 

Force  of  the  Wind.  —  Smeaton  in  1759  published  a  table  of  the 
velocity  and  pressure  of  wind,  as  follows: 


VELOCITY  AND  FORCE  OP  WIND,  IN  POUNDS  PER  SQUARE  INCH 

|  Miles  per 
1  Hour. 

li 
If 

Force  per 

Sq.  Ft., 
Pounds. 

Common  Appella- 
tion of  the 
Force  of  Wind. 

I  Miles  per 
j  Hour. 

Feet  per 
Second. 

M-3 

q>"  c 

P  ~3 
&»& 

Common  Appella- 
tion of  the 
Force  of  Wind. 

1 

1.47 

0.005 

Hardly  perceptible. 

18 

26.4 

1.55 

) 

2 
3 

2.93 
4.4 

0.020 
0.044 

Just  perceptible. 

20 

25 

29.34 
36.67 

1.968 
3.075 

>  Very  brisk. 

A 
5 

5.87 
7.33 

0.079 
0.123 

Gentle,  pleasant 

30 
35 

44.00 
51.34 

4.429 
6.027 

High  wind. 

6 

8.8 

0.177 

wind. 

40 

58.68 

7.873 

7 

8 

10.25 
11.75 

0.241 
0.315 

45 
50 

66.01 
73.35 

9.963 
12.30 

•Very  high  storm. 

9 

13.2 

0.400 

55 

80.7 

14.9 

1G 

14.67 

0.492 

60 

88.00 

17.71 

12 

17.6 

0.708 

Pleasant,  brisk  gale 

65 

95.3 

20.85 

Great  storm. 

14 

20.5 

0.964 

70 

102.5 

24.1 

15 
16 

22.00 
23.45 

1.107 
1.25 

75 

80 

110.00 
117.36 

27.7 
31.49 

Hurricane. 

100 

146.67 

49.2 

Immense  hurri- 

cane. 

The  pressures  per  square  foot  in  the  above  table  correspond  to  the 
formula  P  =  0.005  F2,  in  which   V  is  the  velocity  in  miles  per  hour. 
Eng'g  News,  Feb.  9,  1893,  says  that  the  formula  was  never  well  established, 
and  has  floated  chiefly  on  Smeaton's  name  and  for  lack  of  a  better.     It 
was  put  forward  only  for  surfaces  for  use  in  windmill  practice.      The 
trend  of  modern  evidence  is  that  it  is  approximately  correct  only  for  such 
surfaces,  and  that  for  large,  solid  bodies  it  often  gives  greatly  too  large 
results.   Observations   by   others   are  thus   compared   with   Smeaton's 
formula: 

Old  Smeaton  formula  ........................  P  =  0.005    F2 

As  determined  by  Prof.  Martin  ................  P  =  0.004    F2 

'    Whipple  and  Dines  ..........  P  =  0.0029  Fa 

At  60  miles  per  hour  these  formulas  give  for  the  pressure  per  square  foot, 
18,  14.4,  and  10.44  Ibs.,  respectively,  the  pressure  varying  by  all  of  them  as 
the  square  of  the  velocity.  Lieut.  Crosby's  experiments  (Eng'g,  June  13, 
1890),  claiming  to  prove  that  P  =  fV  instead  of  P  =  /F2,  are  discredited. 

Experiments  by  M.  Eiffel  on  plates  let  fall  from  the  Eiffel  tower  in  Paris 
gave  coefficients  of  F2  ranging  from  0.0027  for  small  plates  to  0.0032  for 
plates  10  sq.  ft.  area.  For  plates  larger  than  10  sq.  ft.  the  coefficient 
remained  constant  at  0.0032.  —  Eng'g,  May  8,  1908. 

A.  R.  Wolff  ("  The  Windmill  as  a  Prime  Mover,"  p.  9)  gives  as  the  theo- 
retical pressure  per  sq.  ft.  of  surface,  P=dQv/g,  in  which  d  =  density  of 


air  in  pounds  per  cu.  ft.  = 


.  p  being  the  barometric  pres- 


sure per  square  foot  at  any  level,  and  temperature  of  32?  F.,  t  any 
absolute  temperature,  Q  =  volume  of  air  carried  along  per  square  foot  in 
one  second,  v=*  velocity  of  the  wind  in  feet  per  second,  #  =  32.  16.  Since 
Q  =  v  cu.  ft.  per  sec.,  P=dv2/g.  Multiplying  this  by  a  coefficient  0.93 
nt,  and  substituting  the  above  value  of  d,  he  obtains 


found  by  experime   ... 
p  _          0.017431  X  P 


t  X  32.16 


• ,  and  when  p  =  2116.5  Ib.  per  sq.  ft.,or  average 


atmospheric  pressure  at  the  sea-level,  P  =*  .       oo-1ft 

^ 


36  89^9 


-0.018743 


pression  in  which  the  pressure  is  shown,  to  vary  with  the  temperature; 
and  he  gives  a  table  showing  the  relation  between  velocity  and  pressure 


WINDMILLS.  627 

for  temperatures  from  0°  to  100°  F.,  and  velocities  from  1  to  80  miles  per 
hour.     For  a  temperature  of  45°  F.  the  pressures  agree  with  those  in 
Smeaton's  table,  for  0°  F.  they  are  about  10  per  cent  greater,  and  for  100°, 
x  10  per  cent  less. 

^rof.  H.  Allen  Hazen,  Eng'g  News,  July  5,  1890,  says  that  experiments 
with  whirling  arms,  by  exposing  plates  to  direct  wind,  and  on  locomotives 
with  velocities  running  up  to  40  miles  per  hour,  have  invariably  shown  the 
resistance  to  vary  with  V2.  The  coefficient  of  V2  has  been  found  in  some 
experiments  with  very  short  whirling  arms  and  low  velocities  to  vary  with 
the  perimeter  of  .the  plate,  but  this  entirely  disappears  with  longer  arms 
or  straight  line  motion,  and  the  only  question  now  to  be  determined  is 
the  value  of  the  coefficient.  Perhaps  some  of  the  best  experiments  for 
determining  this  value  were  tried  in  France  in  1886  by  carrying  flat 
boards  on  trains.  The  resulting  formula  in  this  case  was,  for  44.5  miles 
per  nour,  p  =  0.00535  SV2. 

Prof.  Kernot.  of  Melbourne  (Eng.  Rec.,  Feb.  20,  1894),  states  that 
experiments  at  the  Forth  Bridge  showed  that  the  average  pressure  on  sur- 
faces as  /arge  as  railway  carriages,  houses,  or  bridges  never  exceeded  two- 
thirds  of  that  upon  rmall  surfaces  of  one  or  two  square  feet,  and  also  that 
an  inertia  effect,  which  is  frequently  overlooked,  may  cause  some  forms 
of  anemometer  to  give  false  results  enormously  exceeding  the  correct 
indication.  Experiments  made  by  Prof.  Kernot  at  speeds  varying  from 
2  to  15  miles  per  hour  agreed  with  the  earlier  authorities.  The  pressure 
upon  one  side  of  a  cube,  or  of  a  block  proportioned  like  an  ordinary 
carriage,  was  found  to  be  0.9  of  that  upon  a  thin  plate  of  the  same  area. 
The  same  result  was  obtained  for  a  square  tower.  A  square  pyramid, 
whose  height  was  three  times  its  base,  experienced  0.8  of  the  pressure 
upon  a  thin  plate  equal  to  one  of  its  sides,  but  if  an  angle  was  turned  to 
the  wind  the  pressure  was  increased  by  fully  20%.  A  bridge  consisting 
of  two  plate-girders  connected  by  a  deck  at  the  top  was  found  to  expe- 
rience 0.9  or  the  pressure  on  a  thin  plate  equal  in  size  to  one  girder,  when 
the  distance  between  the  girders  was  equal  to  their  depth,  and  this  was 
increased  by  one-fifth  when  the  distance  between  the  girders  was  double 
the  depth.  A  lattice- work  in  which  the  area  of  the  openings  was  55%  of 
the  whole  area  experienced  a  pressure  of  80%  of  that  upon  a  plate  of  the 
same  area.  The  pressure  upon  cylinders  and  cones  was  proved  to  be  equal 
to  half  that  upon  the  diametral  planes,  and  that  upon  an  octagonal  prism 
to  be  20%  greater  than  upon  the  circumscribing  cylinder.  A  sphere  was 
subject  to  a  pressure  of  0.36  of  that  upon  a  thin  circular  plate  of  equal 
diameter.  A  hemispherical  cup  gave  the  same  result  as  the  sphere;  when 
its  concavity  was  turned  to  the  wind  the  pressure  was  1.15  of  that  on  a 
flat  plate  of  equal  diameter.  When  a  plane  surface  parallel  to  the  direc- 
tion of  the  wind  was  brought  nearly  into  contact  with  a  cylinder  or  sphere, 
the  pressure  on  the  latter  bodies  was  augmented  by  about  20%,  owing  to 
the  lateral  escape  of  the  air  being  checked.  Thus  it  is  possible  for  the 
security  of  a  tower  or  chimney  to  be  impaired  by  the  erection  of  a  building 
nearly  touching  it  on  one  side. 

Pressures  of  Wind  Registered  in  Storms.  —  Mr.  Frizell  has  examined 
the  published  records  of  Greenwich  Observatory  from  1849  to  1869,  and 
reports  that  the  highest  pressure  of  wind  he  finds  recorded  is  41  Ib.  per 
sq.  ft.,  and  there  are  numerous  instances  in  which  it  was  between  30  and 
40  Ib.  per  sq.  ft.  Prof.  Henry  says  that  on  Mount  Washington,  N.  H.,  a 
velocity  of  150  miles  per  hour  has  been  observed,  and  at  New  York  City 
60  miles  an  hour,  and  that  the  highest  winds  observed  in  1870  were  of  72 
and  63  miles  per  hour,  respectively.  Lieut.  Dunwoody,  U.  S.  A.,  says, 
in  substance,  that  the  New  England  coast  is  exposed  to  storms  which 
produce  a  pressure  of  50  Ib.  per  sq.  ft.  —  Eng.  News,  Aug.  20,  1880. 

WINDMILLS. 

Power  and  Efficiency  of  Windmills.  —  Rankine,  S.  E.,  p.  215,  gives 
the  following:  Let  Q  —  volume  of  air  which  acts  on  the  sail,  or  part  of  a 
sail,  in  cubic  feet  per  second,  v  =  velocity  of  the  wind  in  feet  per  second, 
8  =*  sectional  area  of  the  cylinder,  or  annular  cylinder  of  wind,  through 
which  the  sail,  or  part  of  the  sail,  sweeps  in  one  revolution,  &  ««  a  coeffi- 
cient to  be  found  by  experience;  then  0  =*  cvs.  Rankine,  from  experi- 
mental data  given  by  Smeaton,  and  taking  c  to  include  an  allowance  for 


628  AIR. 

friction,  gives  for  a  wheel  with  four  sails,  proportioned  in  the  best  manner, 
c  =»  0.75.  Let  A  =  weather  angle  of  the  sail  at  any  distance  from  the 
axis,  i.e.,  the  angle  the  portion  of  the  sail  considered  makes  with  its  plane 
of  revolution.  This  angle  gradually  diminishes  from  the  inner  end  of  the 
sail  to  the  tip;  u  =  the  velocity  of  the  same  portion  of  the  sail,  and  E  =• 
the  efficiency.  The  efficiency  is  the  ratio  of  the  useful  work  performed  to 
the  whole  energy  of  the  stream  of  wind  acting  on  the  surface  s  of  the  wheel, 
which  energy  is  D  s  v3  •*•  2  g,  D  being  the  weight  of  a  cubic  foot  of  air* 
Rankine's  formula  for  efficiency  is 


in  which  c  =  0.75  and  /  is  a  coefficient  of  friction  found  from  Smeaton's 
data  =»  0.016.     Rankine  gives  the  following  from  Smeaton's  data: 

A  =  weather-angle =7°  13°  19° 

V  •#•  v  *=  ratio  of  speed  of  greatest 
efficiency,  for  a  given 
weather-angle,  to  that 

ofthewind =2.63  1.86  1.41 

#-*  efficiency »=  0.24          0.29          0.31 

Rankine  gives  the  following  as  the  best  values  for  the  angle  of  weather 
at  different  distances  from  the  axis: 

Distance  in  sixths  of  total  radius       12345          6 
Weather  angle 18°     19°     18°     16°     121/2°    7° 

But  Wolff  (p.  125)  shows  that  Smeaton  did  not  term  these  the  best 
angles  but  simply  says  they  "answer  as  well  as  any,"  possibly  any  that 
were  in  existence  in  "his  time.  Wolff  says  that  they  **  cannot  in  the  nature 
of  things  be  the  most  desirable  angles."  Mathematical  considerations, 
he  says,  conclusively  show  that  the  angle  of  impulse  depends  on  the 
relative  velocity  of  each  point  of  the  sail  and  the  wind,  the  angle  growing 
larger  as  the  ratio  becomes  greater.  Smeaton's  angles  do  not  fulfil  this 
condition.  Wolff  develops  a  theoretical  formula  for  the  best  angle  of 
weather,  and  from  it  calculates  a  table  of  the  best  angles  for  different 
relative  velocities  of  the  blades  and  the  wind,  which  differ  widely  from 
those  given  by  Rankine. 

A.  R.  Wolff,  in  an  article  in  the  American  Engineer,  gives  the  following 
(see  also  his  treatise  on  Windmills) : 

Let  c  =  velocity  of  wind  in  feet  per  sec9nd; 

n  =  number  of  revolutions  of  the  windmill  per  minute; 

6ot  hi  fo,  bx  be  the  breadth  of  the  sail  or  blade  at  distances  Zo,  h,  It, 
13,  and  I,  respectively,  from  the  axis  of  the  shaft; 

Z0  =  distance  from  axis  of  shaft  to  beginning  of  sail  or  blade  proper. 

I  =  distance  from  axis  of  shaft  to  extremity  of  sail  proper; 

V0,  vi,  vz,  v3,  vx  =  the  velocity  of  the  sail  in  feet  per  second  at  dis- 
tances IQ,  li,  Iz,  h,  I,  respectively,  from  the  axis  of  the  shaft; 

do,  01,  02,  a3,  ax  =  the  angles  of  impulse  for  maximum  effect  at  dis- 
tances TO,  lit  k,  £3,  I,  respectively,  from  the  axis  of  the  shaft; 

a  =  the  angle  of  impulse  when  the  sails  or  blocks  are  plane  surfaces 
so  that  there  is  but  one  angle  to  be  considered; 

N  =  number  of  sails  or  blades  of  windmill; 

K  =  0.93; 

d  =  density  of  wind  (weight  of  a  cubic  foot  of  air  at  average  tem- 
perature and  barometric  pressure  where  mill  is  erected); 
W  =  weight  of  wind-wheel  in  pounds; 

/  =  coefficient  of  friction  of  shaft  and  bearings; 

D  =  diameter  of  bearing  of  windmill  in  feet. 

The  effective  horse-power  of  a  windmill  with  plane  sails  will  equal 
L  of  <  vQ  fsin  a cos  ajb0  cos  a 


WINDMILLS. 


629 


The  effective  horse-power  of  a  windmill  of  shape  of  sail  for  maximum 
effect  equals 


N  (I-  Ip)  Kdc3 
2200  g 


X  mean 


./2sin2 

°H— Mi 


«o  —  1  ; 


sin2  a0 


2  sin2  ai  -  1  . 
sin2  ai 


2  sin2  ax  -  1 
' 5E?aI       Z 


/TFX 0.05236  nD  g 
550 


The  mean  value  of  quantities  in  brackets  is  to  be  found  according  to 
Simpson's  rule.  Dividing  I  into  7  parts,  finding  the  angles  and  breadths 
corresponding  to  these  divisions  by  substituting  them  in  quantities  within 
brackets  will  be  found  satisfactory.  Comparison  of  these  formulae  with 
the  only  fairly  reliable  experiments  in  windmills  (Coulomb's)  showed  a 
close  agreement  of  results. 

Approximate  formulae  of  simpler  form  for  windmills  of  present  con- 
struction can  be  based  upon  the  above,  substituting  actual  average  values 
for  o,  c,  d,  and  e,  but  since  improvement  in  the  present  angles  is  possible, 
it  is  better  to  give  the  formulas  in  their  general  and  accurate  form. 

Wolff  gives  the  following  table,  based  on  the  practice  of  an  American 
manufacturer.  Since  its  preparation,  he  says,  over  1500  windmills  have 
been  sold  on  its  guaranty  (1885),  and  in  all  cases  the  results  obtained  did 
not  vary  sufficiently  from  those  presented  to  cause  any  complaint.  The 
actual  results  obtained  are  in  close  agreement  with  those  obtained  by 
theoretical  analysis/  of  the  impulse  of  wind  upon  windmill  blades. 

Capacity  of  the  Windmill. 


A 

d 

d 

~v 

* 

CO 

p 

gflf 

•s 

w 

DO   fl 

Gallons  of  Water  raised  per  Minute 
to  an  Elevation  of 

3  0) 

*     «J 

.2 

^1 

.P 

-^i'g 

jISs"! 

cj 
.1 

£$ 

^2  I 

.loo 

&Q  « 

"w 

Jl 

i 

£>  W® 

2     ® 

a* 

13 

I 

25 

50 

75 

100 

150 

200 

5"5  ® 

o>  5>I5n3 

Q 

^ 

* 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

O<«+H'^ 

^P,^? 

wheel 

81/9  ft 

16 

70  to  75 

6  162 

3.016 

0  04 

8 

10 

16 

60  to  65 

19.179 

9.563 

6.638 

4.750 

0  12 

8 

12 

16 

55  to  60 

33.941 

17.952 

11.851 

8.485 

5.680 

0.21 

8 

14 

16 

50  to  55 

45.139 

22.569 

15.304 

11.246 

7.807 

4  998 

0.28 

8 

16 

16 

45  to  50 

64.600 

31.654 

19.542 

16.150 

9.771 

8  '.075 

0.41 

8 

18 

16 

40  to  45 

97.682 

52.165 

32.513 

24.421 

17.485 

12.211 

0.61 

8 

20 

16 

35  to  40 

124.950 

63.750 

40.800 

31.248 

19.284 

15.938 

0.78 

8 

25 

16 

30  to  35 

212.381 

106.964 

71.604 

49.725 

37.349 

26.741 

1.34 

8 

These  windmills  are  made  in  regular  sizes,  as  high  as  sixty  feet  diameter 
of  wheel;  but  the  experience  with  the  larger  class  of  mills  is  too  limited  to 
enable  the  presentation  of  precise  data  as  to  their  performance. 

If  the  wind  can  be  relied  upon  in  exceptional  localities  to  average  a 
higher  velocity  for  eight  hours  a  day  than  that  stated  in  the  above  table, 
the  performance  or  horse-power  of  the  mill  will  be  increased,  and  can  be 
obtained  by  multiplying  the  figures  in  the  table  by  the  ratio  of  the  cube 
of  the  higher  average  velocity  of  wind  to  the  cube  of  the  velocity  above 
recorded. 

He  also  gives  the  following  table  showing  the  economy  of  the  windmill. 
All  the  items  of  expense,  including  both  interest  and  repairs,  are  reduced 
to  the  hour  by  dividing  tha  costs  per  annum  by  365  X  8  =  2920;  the 
Interest,  etc.,  for  the  twenty-four  hours  being  charged  to  the  eight  hours  of 
actual  work.  By  multiplying  the  figures  in  the  5th  column  by  584,  the 
first  cost  of  the  windmill,  in  dollars,  is  obtained. 


630 


AIR. 
Economy  of  the  Windmill. 


1 

J>  4 

*!! 

Expense  of  Actual  Useful  Power 
Developed,  in  Cents,  per  Hour. 

"" 

o  o 

2  a 

'1  . 

• 

t,  3  fl 

0    . 

Designa- 
tion of 
Mill. 

of  Water  r 
,  per  Hour 

jnt  Actual 
rse-power 

JJ-0J 

2     .2  cj 

31I| 

03  fl  « 
•  -  °r^ 
c3'-5^ 
ftg^^ 

tendance. 

O 
m 

*e8 

W.J2 

1$ 

!*! 

|jj| 

^4»J3^S 

g 

o 

^ 

co  ^    . 

IS| 

3 

|si 

^J 

IES&S? 

!«^ 

(2 

|&3 

wheel 

81/2  ft. 

370 

0.04 

8 

0.25 

0.25 

0.06 

0.04 

0.60 

15.0 

10 

1151 

0.12 

8 

0.30 

0.30 

0.06 

0.04 

0.70 

5.8 

12 

2036 

0.21 

8 

0.36 

0.36 

0.06 

0.04 

0.82 

5.9 

14 

2708 

0.28 

8 

0.75 

0.75 

0.06 

0.07 

1.63 

5.8 

16 

3876 

0.41 

8 

1.15 

1.15 

0.06 

0.07 

2.43 

5.9 

18 

5861 

0.61 

8 

1.35 

1.35 

0.06 

0.07 

2.83 

4.6 

20 

7497 

0.79 

8 

1.70 

1.70 

0.06 

0.10 

3.56 

4.5 

25 

12743 

1.34 

8 

2.05 

2.05 

0.06 

0.10 

4.26 

3.2 

Prof.  De  Volson  Wood  (Am.  Mach.,  Oct.  29, 1896)  quotes  some  results 
by  Thos.  O.  Perry  on  three  wheels,  each  5  ft.  diam.:  A,  a  good  "stock" 
wheel,  B  and  C,  improved  wheels.  Each  wheel  was  tested  with  a  dyna- 
mometer placed  1  ft.  from  the  axis  of  the  wheel,  and  it  registered  a 
constant  load  at  that  point  of  1.9  Ibs.  The  velocity  of  the  wind  in  each 
;est  was  8.45  miles  per  hour  =  12.4  ft.  per  second.  The  number  of  turns 
per  minute  was:  A,  30.67;  B,  38.13;  C,  56.50.  The  efficiency  was:  At 
0.142;  B,  0.176;  C,  0.261.  The  work  of  wheel  C  was  674.5  ft.  Ib.  per 
min.  =  0.020  H.P.  Assuming  that  the  power  increases  as  the  square 
of  the  diameter  and  as  the  cube  of  the  velocity,  a  wheel  of  the  quality  of 
C,  121/2  ft.  diam.,  with  a  wind  velocity  of  17  miles  per  hour,  would  be  re- 
quired for  1  H.P.;  but  wheel  C  had  an  exceptionally  high  efficiency,  and 
such  a  high  delivery  would  not  likely  be  obtained  in  practice. 

Prof.  O.  P.  Hood  (Am.  Mach.,  April  22,  1897)  quotes  the  following 
results  of  experiments  by  E.  C.  Murphy;  the  mills  were  tested  by  pumping 
water: 

Wind,  miles  per  hour 8     12.      16.      20.      25.        30 

Strokes  per  min.,  Mill  No.  1,  8-ft.  wheel  . .  10.2  19.3  25.3  28.1  25 
Strokes  per  min.,  Mill  No.  2,  8-ft.  wheel  8  20.2  26.1  28.  27.5  . . 
Strokes  per  min.,  Mill  No.  3, 12-ft.  wheel  . .  4.8  12.7  18.8  23.3  25 
Strokes  per  min.,  Mill  No.  4,  12-ft.  wheel  . .  6.2  11.9  14.7  16. 

Mill  No.  3  was  loaded  nearly  90%  heavier  than  mill  No.  4. 

In  a  25-mile  wind,  seven  12-ft.  mills  developed,  respectively,  0.379, 
0.291,  0.309,  0.6,  0.247,  0.219,  and  0.184  H.P.;  and  five  8-ft.  mills,  0.043, 
0.099,  0.059,  0.099,  and  0.005  H.P.  These  effects  include  the  effects  of 

Sumps  of  unknown  and  variable  efficiency.  The  variations  are  largely 
ue  to  the  variable  relation  of  the  fixed  load  on  the  mill  to  the  most 
favorable  load  which  that  mill  might  carry  at  each  wind  velocity.  With 
each  mill  the  efficiency  is  a  maximum  only  for  a  certain  load  and  a  certain 
velocity,  and  for  different  loads  and  velocities  the  efficiency  varies  greatly. 
The  useful  work  of  mill  No.  3  was  equal  to  0.6  H.P.  in  a  25-mile  wind, 
and  its  efficiency  was  5.8%.  In  a  16-mile  wind  the  efficiency  rose  to  12.1  %, 
and  in  a  12-mile  wind  it  fell  to  10.9%.  The  rule  of  the  power  developed, 
varying  as  the  cube  of  the  velocity,  is  far  from  true  for  a  single  wheel 
fitted  with  a  single  non-adjustable  pump,  and  can  only  be  true  when  the 
work  of  the  pump  per  stroke  is  adjusted  by  varying  the  stroke  of  the 
pump,  or  by  other  means,  for  each  change  of  velocity. 

R.  M.  Dyer  (The  Iowa  Engineer,  July,  1906;  also  Mach'y,  Aug.,  1907) 
gives  a  brief  review  of  the  history  of  windmills,  and  quotes  experiments 
by  T.  O.  Perry,  E.  C.  Murphy,  Prof.  F.  H.  King,  and  the  Aermotor  Co. 
Mr.  Perry's  experiments  are  reported  in  pamphlet  No.  20  of  the  Water 


WINDMILLS.  631 

Supply  and  Irrigation  Papers  of  the  U.  a.  Geological  Survey,  Mr.  Murphy's 
In  pamphlets  Nos.  41  and  42  of  the  same  Papers,  and  Prof.  lung's,  in 
Bulletin  No.  82  of  the  Agricultural  Experiment  Station  of  the  University 
of  Wisconsin.  The  Aermotor  Co .'s  experiments  are  described  in  catalogues 
of  that  company.  Some  of  Mr.  Dyer's  conclusions  are  as  follows: 

Experiments  showed  that  7/8  of  the  zone  of  interruption  could  be  covered 
with  sails ;  that  the  gain  in  power  in  from  3/4  to  1/3  of  the  surface  was  so  small 
that  the  use  of  the  additional  material  was  not  justifiable;  that  the  sail 
surface  should  extend  only  two-thirds  the  distance  from  the  outer  diam- 
eter to  the  center;  that  a  wheel  running  behind  the  carrying  mast  is  not 
nearly  as  efficient  as  one  running  in  front  of  the  mast;  that  there  should 
be  the  least  possible  obstruction  behind  the  wheel;  that  to  be  efficient 
the  velocity  of  the  travel  of  the  vertical  circumference  of  the  wheel 
should  be  from  1  to  U/4  times  the  velocity  of  the  wind,  hence  the 
necessity  of  back  gearing  to  reduce  the  pump  speed  to  40  strokes  per 
minute  as  a  maximum,  which  is  the  limit  of  safety  at  which  ordinary 
pumps  can  be  operated. 

I  hold  that  no  manufacturer  will  be  able  to  produce  a  marketable 
motor  which  will  absorb  and  deliver,  when  acted  upon  by  an  elastic  fluid, 
like  air,  in  which  it  is  entirely  surrounded  and  submerged,  more  than 
35%  of  the  kinetic  energy  of  the  impinging  current. 

Theoretical  demonstrations  show  that  the  kinetic  energy  of  the  air, 
impinging  on  the  intercepted  area  of  a  wheel,  varies  as  the  cube  of  the 
wind  velocity;  consequently,  the  power  of  windmills  of  the  same  type 
varies  theoretically  as  the  square  of  the  diameter,  and  as  the  cube  of  the 
wind  velocity;  but  as  a  wheel  is  designed  to  give  its  best  efficiency  in  low 
winds,  say  10  to  15  miles  per  hour,  we  cannot  expect  that  the  same 
angle  of  sail  would  obtain  the  same  percentage  of  efficiency  in  winds  of 
Considerably  higher  velocity. 

The  ordinary  wheel  works  most  efficiently  under  wind  velocities  of  from 
10  to  12  miles  per  hour;  such  wheels  will  give  reasonable  efficiency  in  from 
5-  to  6-mile  winds,  while,  if  the  wind  blows  more  than  12  miles  per  hour, 
there  will  be  power  to  spare.  Our  wheel  must  work  in  light  winds,  such 
being  nearly  always  present,  while  the  higher  velocities  only  occur  at 
intervals.  Mills  built  for  grinding  purposes,  or  geared  mills,  will  develop 
power  almost  approaching  to  the  cube  of  the  wind  velocity,  within  reason- 
able limits,  as  their  speed  need  not  be  kept  down  to  a  certain  number  of 
revolutions  per  minute,  as  in  the  case  of  the  pumping  mill. 

Should  this  theoretic  condition  hold,  the  following  table,  showing  the 
amount  of  power  for  different  sizes  of  mills  at  different  wind  velocities, 
would  apply:  Figures  show  Horse  Power,, 

5  10          15          20         25         30         35         40 

Size  mile.    mile.     mile.     mile.    mile.    mile.    mile.    mile. 

8ft 0.011    0.088    0.297    0.704    1.375    2.176      

12ft 0.025    0.20      0.675    1.6        3.125    5.4          8.57    12.8 

16ft 0.045    0.36       1.215    2.88      5.52      9.75       15.3      21.04 

These  figures  have  been  proven  by  laboratory  tests  at  velocities 
ranging  from  10  to  25  miles  per  hour  and  more  practically  by  the 
Murphy  tests  on  mills  actually  in  use,  which  show  very  close  relation 
at  the  wind  velocities  at  which  the  mills  are  best  adapted. 

The  Murphy  figures  are  as  follows: 

Size  of  mill.      10  mile.          15  mile.         20  mile. 
12  ft.          0.21  H.P.       0.58  H.P.       1.05  H.P. 
16  ft.          0.29  0.82  1.55 

For  higher  wind  velocities  the  Murphy  values  fall  much  under  the 
theoretical  values,  but  the  range  of  velocities  over  which  his  experi- 
ments extend  does  not  justify  any  change  in  the  general  law  except 
inasmuch  as  common  sense  teaches  us  that  theoretic  conditions  can 
rarely  be  attained  in  actual  practice. 

In  view  of  the  fact  that  a  windmill  does  not  work  as  efficiently  in 
high  winds  as  in  winds  under  20  miles  per  hour  my  experience  would 
lead  me  to  believe  that  the  following  figures  (H.P.)  would  be  the 
probable  extension  of  the  Murphy  tests: 

Size  of  mill.       25  mile.      30  mile.     35  mile.     40  mile. 
12  ft.  2.5  4  5  6 

16  ft.  4.  6  8  10 

A  20-ft.  mill  would  deliver  approximately  50%  greater  than  a  16-ft 


632  AIR. 

The  foregoing  table  must  be  translated  with  reasonable  allowances  for 
conditions  under  which  wind  wheels  must  work  and  which  cannot  well 
be  avoided,  e.g:  Pumping  mills  must  be  made  to  regulate  off  at  a  certain 
maximum  speed  to  prevent  damage  to  the  attached  pumping  devices. 
The  regulating  point  is  usually  between  20- and  25-mile  wind  velocities, 
so  that  no  matter  how  much  higher  the  wind  velocity  may  be  the  power 
absorbed  and  delivered  by  the  wheel  will  be  no  greater  than  that  indicated 
at  the  regulating  point. 

Electric  storage  and  lighting  from  the  power  of  a  windmill  has  been 
tested  on  a  large  scale  for  several  years  by  Charles  F.  Brush,  at  Cleveland, 
Ohio.  In  1887  he  erected  on  the  grounds  of  his  dwelling  a  windmill  56  ft. 
in  diameter,  that  operates  with  ordinary  wind  a  dynamo  at  500  revolutions 
per  minute,  with  an  output  of  12,000  watts  —  16  electric  horse-power  — 
charging  a  storage  system  that  gives  a  constant  lighting  capacity  of  100 
16  to  20  candle-power  lamps.  The  current  from  the  dynamo  is  auto- 
matically regulated  to  commence  charging  at  330  revolutions  and  70  volts, 
and  cutting  the  circuit  at  75  volts.  Thus,  by  its  24  hours'  work,  the 
storage  system  of  408  cells  in  12  parallel  series,  each  cell  having  a  capacity 
of  100  ampere-hours,  is  kept  in  constant  readiness  for  all  the  requirements 
of  the  establishment,  it  being  fitted  up  with  350  incandescent  lamps, 
about  100  being  in  use  each  evening.  The  plant  runs  at  a  mere  nominal 
expense  for  oil,  repairs,  and  attention.  (For  a  fuller  description  of  this 
plant,  and  of  a  more  recent  one  at  Marblehead  Neck,  Mass.,  see  Lieut. 
Lewis's  paper  in  Engineering  Magazine,  Dec.,  1894,  p.  475.) 

COMPRESSED  AIR. 

Heating  of  Air  by  Compression.  —  Kimball,  in  his  treatise  on  Physi- 
cal Properties  of  Gases,  says:  When  air  is  compressed,  all  the  work  which 
is  done  in  the  compression  is  converted  into  heat,  and  shows  itself  in  the 
rise  in  temperature  of  the  compressed  gas.  In  practice  many  devices  are 
employed  to  carry  off  the  heat  as  fast  as  it  is  developed,  and  keep  the  tem- 
perature down.  But  it  is  not  possible  in  any  way  to  totally  remove  this 
difficulty.  But,  it  may  be  objected,  if  all  the  work  done  in  compression  is 
converted  into  heat,  and  if  this  heat  is  got  rid  of  as  soon  as  possible,  then 
the  work  may  be  virtually  thrown  away,  and  the  compressed  air  can  have 
no  more  energy  than  it  had  before  compression.  It  is  true  that  the  com- 
pressed gas  has  no  more  energy  than  the  gas  had  before  compression,  if 
its  temperature  is  no  higher,  but  the  advantage  of  the  compression  lies  in 
bringing  its  energy  into  more  available  form. 

The  total  energy  of  the  compressed  and  uncompressed  gas  is  the  same 
at  the  same  temperature,  but  the  available  energy  is  much  greater  in  the 
former. 

When  the  compressed  air  is  used  in  driving  a  rock-drill,  or  any  other 
piece  of  machinery,  it  gives  up  energy  equal  in  amount  to  the  work  it  does, 
and  its  temperature  is  accordingly  greatly  reduced. 

Causes  of  Loss  of  Energy  in  Use  of  Compressed  Air.  (Zahner,  on 
Transmission  of  Power  by  Compressed  Air.)  —  1.  The  compression  of 
air  always  develops  heat,  and  as  the  compressed  air  always  cools  down  to 
the  temperature  of  the  surrounding  atmosphere  before  it  is  used,  the 
mechanical  equivalent  of  this  dissipated  heat  is  work  lost. 

2.  The  heat  of  compression  increases  the  volume  9f  the  air-,  and  hence 
it  is  necessary  to  carry  the  air  to  a  higher  pressure  in  the  compressor  in 
order  that  we  may  finally  have  a  given  volume  of  air  at  a  given  pressure, 
and  at  the  temperature  of  the  surrounding  atmosphere.     The  work  spent 
in  effecting  this  excess  of  pressure  is  work  lost. 

3.  Friction  of  the  air  in  the  pipes,  leakage,  dead  spaces,  the  resistance 
offered  by  the  valves,  insufficiency  of  valve-area,  inferior  workmanship, 
and  slovenly  attendance,  are  all  more  or  less  serious  causes  of  loss  of 
power. 

The  first  cause  of  loss  of  work,  namely,  the  heat  developed  by  compres- 
sion, is  entirely  unavoidable.  The  whole  of  the  mechanical  energy  which 
the  compressor-piston  spends  upon  the  air  is  converted  into  heat.  This 
heat  is  dissipated  by  conduction  and  radiation,  and  its  mechanical  equiva- 
lent is  work  lost.  The  compressed  air,  having  again  reached  thermal 


COMPRESSED-AIR.  633 

equilibrium  with  the  surrounding  atmosphere,  expands  and  does  work  in 
an  air  motor,  losing  temperature  and  intrinsic  energy  in  proportion  to 
the  work  dt>ne. 

A  large  fall  in  temperature  will  cause  any  moisture  in  the  air  to 
freeze,  and,  unless  the  air  is  pre-heated  before  use  in  the  motor,  per- 
mitting it  to  expand  to  more  than  two  volumes  will  cause  difficulties. 
It  is  for  this  reason,  and  also  because  of  the  heat-losses  in  the  compressor, 
that  the  lower  the  pressure  at  which  compressed  air  is  used  for  power 
transmission  the  more  efficient  is  the  system.  Against  the  increased 
efficiencies  of  the  lower  pressures  must  be  balanced  the  higher  cost  of 
the  mechanisms,  on  account  of  size,  to  utilize  the  lower  pressures. 

The  intrinsic  energy  of  any  gas  is  the  energy  which  it  is  capable  of 
exerting  against  a  piston  in  changing  from  a  given  state  as  to  temper- 
ature and  volume  to  a  total  privation  of  heat  and  indefinite  expansion. 
The  intrinsic  energy  of  1  Ib.  of  gas  at  any  pressure  and  volume  is  the 
product  of  its  absolute  temperature  and  its  specific  heat  .at  constant 
volume.  (See  Thermodynamics.) 

Loss  due  to  Excess  of  Pressure  caused  by  Heating  In  the  Com- 
pression-cylinder. —  If  the  air  during  compression  were  kept  at  a  con- 
stant temperature,  the  compression-curve  of  an  indicator-diagram  taken 
from  the  cylinder  would  be  an  isothermal  curve,  and  would  follow  the  law 

of  Boyle  and  Mariotte,  pv  =  a  constant,  or  pwi  =  Pov0t  or  pi  =  p0  —,povo 

being  the  pressure  and  volume  at  the  beginning  of  compression,  and 
PIVI  the  pressure  and  volume  at  the  end,  or  at  any  intermediate  point. 
But  as  the  air  is  heated  during  compression  the  pressure  increases  faster 
than  the  volume  decreases,  causing  the  work  required  for  any  given  pres- 
sure to  be  increased.  If  none  of  the  heat  were  abstracted  by  radiation  or 
by  injection  of  water,  the  curve  of  the  diagram  would  be  an  adiabatic 

/v  \  1.405 

curve,  with  the  equation  pi  =  p0  Mj  .  Cooling  the  air  during  com- 
pression, or  compressing  it  in  two  cylinders,  called  compounding,  and 
cooling  the  air  as  it  passes  from  one  cylinder  to  the  other,  reduces  the 
exponent  of  this  equation,  and  reduces  the  quantity  of  work  necessary  to 
effect  a  given  compression.  F.  T.  Cause  (Am.  Mach.,  Oct.  20,  1892), 
describing  the  operations  of  the  Popp  air-compressors  in  Paris,  says: 
The  greatest  saving  realized  in  compressing  in  a  single  cylinder  was  33  per 
cent  of  that  theoretically  possible.  In  cards  taken  from  the  2000  H.P. 
compound  compressor  at  Quai  De  La  Gare,  Paris, 'the  saving  realized  is 
85  per  cent  of  the  theoretical  amount.  Of  this  amount  only  8  per  cent  is 
due  to  cooling  during  C9rnpression,  so  that  the  increase  of  economy  in  the 
compound  compressor  is  mainly  due  to  cooling  the  air  between  the  two 
stages  of  compression.  A  compression-curve  with  exponent  1.25  is  the 
best  result  that  was  obtained  for  compression  in  a  single  cylinder  and 
cooling  with  a  very  fine  spray.  The  curve  with  exponent  1.15  is  that 
which  must  be  realized  in  a  single  cylinder  to  equal  the  present  economy 
of  the  compound  compressor  at  Quai  De  La  Gare. 

Adiabatic  and  Isothermal  Compression. —  Theoretically,  air  may 
be  compressed  adiabatically,  in  which  case  all  the  heat  of  compression 
is  retained  in  the  air,  or  isothermally,  in  which  case  the  heat  of  com- 
pression is  removed  as  rapidly  as  it  is  generated,  by  some  refrigerating 
process.  Adiabatic  compression  is  impossible  as  some  of  the  heat  will 
be  radiated  into  the  compressor  walls,  and  isothermal  compression  is 
practically  impossible,  as  the  heat  must  be  generated  before  it  can  be 
absorbed.  The  best  practical  results  that  have  been  obtained  by 
compressing  air  in  a  single  stage  compressor  make  it  possible  to  save 
approximately  one-third  of  the  loss  due  to  the  heat  generated  in  the 
compressor. 

Formulae  for  Adiabatic  Compression  or  Expansion  of  Air  (or 
Other  Sensibly  Perfect  Gas). 

Let  air  at  an  absolute  temperature  Ti,  absolute  pressure  pi,  and  volume 
vi  be  compressed  to  an  absolute  pressure  #2  and  corresponding  volume  v* 
and  absolute  temperature  Tz',  or  let  compressed  air  of  an  initial  pressure, 
volume,  and  temperature  #2,  vz,  and  Ti  be  expanded  to  pi,  vi,  and  T\,  there 
being  no  transmission  of  heat  from  or  into  the  air  during  the  operation/. 


634  AIR. 

Then  the  following  equations  express  the  relations  -between  pressure, 
volume,  and  temperature  (see  works  on  Thermodynamics): 


B  =  (&\°'n.  &  =  (vi\lmU.  vi  =  /TYv2'46. 

vt      \pj  pi       \vj  m      \Tj 

T2_M\°-»  T?      /PA0'29  P?      /?l2\3-46 

Ti~W      '  Ti~\pJ      ;  pi^VTi/ 


The  exponents  are  derived  from  the  ratio  cp  -*•  cv  =  k  of  the  specific 
heats  of  air  at  constant  pressure  and  constant  volume.  Taking  k  = 
1.406,  1  -s-  k  =  0.711;  k  -  1  =  0.406;  1  -*-  (k  -  1)  =  2.463;  k  + 
(k  -  1)  =  3.463;  (k  -  1)  •*-  k  =  0.289. 

Work  of  Adiabatic  Compression  of  Air.  —  If  air  is  compressed  in  a 
cylinder  without  clearance  from  a  volume  vi  and  pressure  pi  to  a  smaller 
volume  vz  and  higher  pressure  pz,  work  equal  to  p\vi  is  done  by  the  external 
air  on  the  piston  while  the  air  is  drawn  into  the  cylinder.  Work  is  then 
done  by  the  piston  on  the  air,  first,  in  compressing  it  to  the  pressure  pa 
and  volume  vz,  and  then  in  expelling  the  volume  vz  from  the  cylinder 

against  the  pressure  p2.     If  the  compression  is  adiabatic,  piVj.  =  Pzva  => 
constant,     k  =  1.406.  . 

The  work  of  compression  of  a  given  quantity  of  air  is,  in  foot-pounds, 


-  1 

k-l(\p 


f    /?)A"'*1  %  f  /7)o\0-29  \ 

or  2.463Pm  {(I)       -1}       -2.463  ft*  {(I)      -l}. 

The  work  of  expulsion  is  pzvi  —  Pivi  (  —  }    ~  • 

\Pi/ 

The  total  work  is  the  sum  of  the  work  of  compression  and  expulsion  less 
the  work  done  on  the  piston  during  admission,  and  it  equals 


PlVl 


The  mean  effective 'pressure  during  the  stroke  is 


Pi  and  p2  are  absolute  pressures  above  a  vacuum,  in  pounds  per  square 
foot. 

EXAMPLE.  —  Required  the  work  done  in  compressing  1  cubic  foot  of 
air  per  second  from  1  to  6  atmospheres,  including  the  work  of  expulsion 
from  the  cylinder. 

pi  -*•  pi  =  6;  60-29  -  1  =  0.681;  3.463  X  0.681  =  2.358  atmospheres 
X  14.7  =  34.66  Ib.  per  sq.  in.  mean  effective  pressure,  X  144  =  4991  Ib. 
persq.  ft.,  XI  ft.  stroke  =  4991  ft.-lb.,-*-  550  ft.-lb.  per  second  =  9.08  H.P. 

If  R  —  ratio  of  pressures  =  pz  •*•  pi,  and  if  Vi  =  1  cubic  foot,  the  work 
done  in  compressing  1  cubic  foot  from  pi  to  pz  is,  in  foot-pounds, 

3.463  pi  CRo-29_  i), 

Pi  being  taken  in  Ib.  per  sq.  ft.  For  compression  at  the  sea  level  PI  may 
be  taken  at  14  Ibs.  per  sq.  in.  =  2016  Ib.  per  sq.  ft.,  as  there  is  some  loss 
of  pressure  due  to  friction  of  valves  and  passages. 

Horse-power  required  to  compress  and  deliver  100  cubic  feet  of  free  air 
per  minute  =  1.511  Pj  (fl°'29  -  1);  Pj  being  the  pressure  of  the  free  air  in 
pounds  per  sq.  in.,  absolute. 

EXAMPLE.  To  compress  100  cu.  ft.  from  1  to  6  atmospheres.  Pj=  14.7: 
R  «  6:  1.511  X  14.7  X  0.681  =  15.13  H.P. 

Indicator-cards  from  compressors  in  good  condition  and  under  working- 
speeds  usually  follow  the  adiabatic  line  closely.  A  low  curve  indicates 
piston  leakage.  Such  cooling  as  there  may  be  from  the  cylinder- jacket 
an<1  the  re-expansion  of  the  air  in  clearance-spaces  tends  to  reduce  the 


COMPRESSED   AIR. 


635 


mean  effective  pressure,  while  the  "camel-backs"  in  the  expulsion-line, 
due  to  resistance  to  opening  of  the  discharge-valve,  tend  to  increase  it. 

Work  of  one  stroke  of  a  compressor,  with  adiabatic  compression,  in 
foot-pounds, 

W=  3.463  Pi  Vi  (R  °'29-  1). 

in  which  Pi  =  initial  absolute  pressure  in  Ib.  per  sq.  ft.  and  Vi  =  volume 
traversed  by  piston  in  cubic  feet. 

The  work  done  during  adiabatic  compression  (or  expansion)  of  1  pound 
of  air  from  a  volume  vi  and  pressure  p\  to  another  volume  vz  and  pressure 
Pz  is  equal  to  the  mechanical  equivalent  of  the  heating  (or  cooling). 
ti  is  the  higher  and  h  the  lower  temperature,  Fahr.,  the  work  done  is 
cvJ  (ti  —  fe)  foot-pounds,  cv  being  the  specific  heat  of  air  at  constant 
volume  =  0.1689,  and  J  =  778,  cvJ  =  131.4. 

The  work  during  compression  also  equals 


Ra  being  the  value  of  pv  +  absolute  temperature  for  1  Ib.  of  air  =  53.32. 
The  work  during  expansion  is 

t/Vl>\  0.29-1  r  /v.\  0.29  "I 

l-&)  J  =  2-463p2n(s)    -JJ' 

in  which  pivi  are  the  initial  and  pzVz  the  final  pressures  and  volumes. 

Compound  Compression,  with  Air  Cooled  between  the  Two  Cyl- 
inders. (Am.  Mach.,  March  10  and  31,  1898.)  —  Work  in  low-pressure 
cylinder  =  W^  in  high-pressure  cylinder  TF2.  Total  work 

Wi  +  W2  =  3.46  PxFi  [r^-29  +  #0.29  x  Ti  -0-29  _  2]. 

TI  =  ratio  of  pressures  in  1.  p.  cyl.,  r2  =  ratio  in  h.p.  cyl.,  R  =  nr2.  When 
ri  =  r'2  =  ^  R,  the  sum  Wi  +  W2is  a  minimum.  Hence  for  a  given  total 
ratio  of  pressures,  R,  the  work  of  compression,  will  be  least  when  the  ratios 
of  the  pressures  in  each  of  the  two  cylinders  are  equal. 

The  equation  may  be  simplified,  when  ri  =  **/R,  to  the  following: 

Wj.  +  W2  =  6.92  P^ffl0-^  -  1]. 

Dividing  by  TI  gives  the  mean  effective  pressure  reduced  to  the  low- 
pressure  cylinder  M.E.P.  =  6.92  PI  [RQ-^  -  1]. 

In  the  above  equati9n  the  compression  in  each  cylinder  is  supposed  to 
be  adiabatic,  but  the  intercooler  is  supposed  to  reduce  the  temperature 
of  the  air  to  that  at  which  compression  began. 

Horse-power  required  to  compress  adiabatically  100  cu.  ft.  of  free  air 
per  minute  in  two  stages  with  interceding,  and  with  equal  ratio  of  com- 
ression in  each  cylinder,  =  3.022  Pj  (R°  145-1);  PI  being  the  pressure  in 
DS.  per  sq.  in.,  absolute,  of  the  free  air,  and  Rthe  total  ratio  of  compression. 

EXAMPLE.  To  compress  100  cu.  ft.  per  min.  from  1  to  6  atmospheres 
P  =  14.7;  R  =  6;  3.022  X  14.7  X  0.2964  =  13.17  H.P. 

Mean  Effective  Pressures  of  Air  Compressed  in  Two  Stages,  assum- 
ing the  Intercooler  to  Reduce  the  Temperature  to  that  at  which 
Compression  Began.  (F.  A.  Halsey,  Am.  Mach.,  Mar.  31,  1898.) 


p 
I 


R. 

£0.145. 

M.E.P. 

from 
14  Ibs. 
Initial. 

Ultimate 
Saving 
by  Com- 
pound- 
ing^. 

R. 

£0.145. 

M.E.P. 
from 
14  Ibs. 
Initial. 

Ultimate 
Saving 
by  Com 
pound- 
ing,%. 

5.0 
5.5 
6.0 
6.5 
7.0 
7.5 
8.0 
8.5 

.263 
.280 
.296 
.312 
.326 
.336 
.352 
.364 

25.4 
27.0 
28.6 
30.1 
31.5 
32.8 
34.0 
35.2 

11.5 
12.3 

12.8 
13.2 
13.7 
14.3 
14.8 
15.3 

9.0 
9.5 
10 
11 
12 
13 
14 
15 

.375 
.386 
.396 
.416 
.434 
.451 
.466 
.481 

36.3 
37.3 
38.3 
40.2 
41.9 
43.5 
45.0 
46.4 

15.8 
16.2 
16.6 
17.2 
17.8 
18.4 
19.0 
19.4 

R  =  final  -T-  initial  absolute  pressure. 
M.E.P.  =  mean  effective  pressure,  Ib.  per  sq.  in.,  based  on  14  Ib. 
absolute  initial  pressure  reduced  to  the  low-pressure  cylinder. 


636 


AIK. 


To  find  the  Index  of   the  Curve  of  an  Air-diagram.     If  P,  Vl  be 

pressure  and  volume  at  one  point  on  the  curve,  and  P  V  the  pressure  and 

P         /Vi\x 
volume  at  another  point,  then  -p-  =  fyj  ,  in  which  x  is  the  index  to  be 

found.     Let  P  -$-_Pi  =  R,  and  Vi  +  V  «  r;  then  R  =  rx;  log  R  =x  log  r. 
whence  x  =  log  R  -r-  log  r.     (See  also  graphic  method  on  page  602.) 

Pressures,   Volumes,   Mean    Effective    Pressures,   and    Final   Temper- 
atures, in  Single-stage  Compression  from  1  Atmosphere  and  60°  Fahr. 

(Contributed  by  M.  C.  Wilkinson,  San  Pedro,  CaL,  1914.) 


Pressure. 

Volume. 

M.E.P.of 
Stroke 

Final  Tem- 
perature. 

* 

1 

i. 

,,-i 

m 

1 

| 

1 

Jr 

pi 

& 

o  II 

|2 

|ll 
f§ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0 

14.7 

1.0 

1  .0000 

1.000 

1  .000 

0.000 

o.ooo 

60.0 

60.0 

15.7 

1  .068 

0.9363 

0.948 

0.954 

0.974 

0.982 

66.3 

70.0 

2 

16.7 

.136 

.8803 

.903 

.910 

1  .896 

1  .913 

73.4 

79.6 

3 

17.7 

.204 

.8305 

.862 

.876 

2.778 

2.810 

79.7 

88.8 

4 

18.7 

.272 

.7862 

.825 

.841 

3.624 

3.681 

85.6 

97.6 

5 

19.7 

.340 

.7463 

.791 

.812 

4.432 

4:510 

91.7 

106.1 

10 

24.7 

.680 

.5952 

.660 

.692 

8.041 

8.267 

116.9 

144  5 

15 

29.7 

2.020 

.4950 

.570 

.607 

11.099 

11.515 

.138.5 

177.7 

20 

34.7 

2.360 

.4237 

.503 

.544 

13.774 

14.396 

157.5 

207.1 

25 

39.7 

2.701 

.3702 

.452 

.494 

16.155 

16.998 

174.3 

233.6 

30 

44.7 

3.041 

.3288 

.411 

.454 

18.309 

19.375 

189.5 

257.9 

35 

49.7 

3.381 

.2955 

.377 

.421 

20  259 

21.569 

203.5 

280.3 

40 

54.7 

3.721 

.2687 

.349 

.393 

22.101 

23.610 

216.3 

301.2 

45 

59.7 

4.061 

.2462 

.326 

.370 

23.777 

25.529 

228.2 

320  8 

50 

64.7 

4.401 

.2272 

.303 

.349 

25.358 

27.331 

239.4 

339.2 

55 

69.7 

4.742 

.2109 

.288 

.329 

26  842 

29.037 

249.9 

356.7 

60 

74.7 

5.082 

.1968 

.272 

.315 

28.239 

30.661 

259.8 

373.2 

65 

79.7 

5.422 

.1844 

.258 

.301 

29.562 

32.808 

269.2 

388.9 

70 

84.7 

5.762 

.1736 

.247 

.288 

30.826 

33.680 

278.1 

404.0 

75 

89.7 

6.102 

.1639 

.235 

.277 

32.031 

35.105 

286.6 

418.6 

80 

94.7 

6.442 

.1552 

.225 

.266 

33.185 

36.469 

294.8 

432.5 

85 

99.7 

6.782 

.1474 

.216 

.257 

34.288 

37.782 

302.6 

446.0 

90 

104.7 

7.122 

.1404 

.208 

.248 

35.346 

39.050 

310.1 

458.9 

95 

109.7 

7.463 

.1340 

.200 

.240 

36.368 

40.277 

317.3 

471.4 

100 

114.7 

7.803 

.1282 

.192 

.233 

37.354 

41  .463 

324.3 

483.5 

105 

119.7 

8.143 

.1228 

.186 

.226 

38.401 

42.613 

331.0 

495.3 

110 

124.7 

8.483 

.1179 

.181 

.219 

39.220 

43.728 

337.5 

506.7 

115 

129.7 

8.823 

.1133 

.175 

.213 

40.109 

44.813 

343.8 

517.8 

120 

134.7 

9.163 

.1091 

.170 

.207 

40.969 

45.866 

349.9 

528.6 

125 

139.7 

9.503 

.1052 

.165 

.202 

41  .807 

46.900 

355.8 

539.1 

130 

144.7 

9.844 

.1015 

.160 

.197 

42.623 

47.898 

361.6 

549.3 

135 

149.7 

10.184 

.0982 

.156 

.192 

43.416 

48.880 

367.2 

559.3 

140 

154.7 

10.524 

.0950 

.152 

.188 

44.189 

49.832 

372.6 

569.0 

145 

159.7 

10.864 

.0921 

.148 

.184 

44.938 

50.769 

377.9 

578.6 

150 

164.7 

11  .204 

.0893 

.145 

.180 

45.766 

51.681 

383.1 

587.9 

160 

174.7 

11  .884 

.0841 

.138 

.172 

47.084 

53.451 

393.1 

606.0 

170 

184.7 

12.565 

.0796 

.132 

.166 

48.429 

55.147 

402.7 

623.3 

180 

194.7 

13.245 

.0755 

.126 

.160 

49.723 

56.781 

411.8 

641  .0 

190 

204.7 

13.295 

.0718 

.121 

.154 

50.968 

58.359 

420.6 

656.1 

200 

214.7 

14.605 

.0685 

.117 

.147 

52.156 

59.881 

429.0 

671.7 

Columns  1,  2  and  3  give  the  relative  pressure  readings  in    gage, 
absolute  and  atmospheric  pressures. 

COMPRESSED  AIR. 


637 


Column  4  gives  the  relative  volumes  of  the  air  after  compression  and 
with  the  temperature  reduced  to  60°  F.  These  are  the  volumes  that 
are  available  for  use  in  the  operation  of  the  driven  mechanisms. 

Column  5  gives  the  relative  volumes  of  the  air  as  the  compressor 
has  to  deal  with  it. 

Column  7  gives  the  mean  effective  pressures  of  a  single  stroke  of  the 
compressor,  including  the  compression  and  expulsion  of  air  from  the 
cylinder.  In  computing  the  power  required  to  operate  the  com- 
pressor a  certain  percentage  (usually  from  5  to  20)  must  be  added 
for  mechanical  friction  and  valve  resistance  and  other  compressor 
characteristics. 

Column  9  gives  the  temperature  of  the  air  as  it  leaves  the  com- 
pressor. 

Columns  6,  8  and  10  give  the  theoretical,  final  volumes,  mean  effec- 
tive pressures  and  final  temperatures  of  air  compressed  adiabatically. 

Mean  Effective  Pressures  of  Air  Compressed  Adiabatically. 

(F.  A.  Halsey,  Am.  Mack.,  Mar.  10,  1898.) 


1_ 

R°-™. 

M.E.P.  from 
Hlbs. 
Initial. 

R. 

#0.29. 

M.E.P.  from 
I41bs. 
Initial. 

..25 

.067 

3.24 

4.75 

.570 

27.5 

1.59 

.125 

6.04 

5 

.594 

28.7 

1.75 

.176 

8.51 

5.25 

.617 

29.8 

2 

.223 

10.8 

5.5 

.639 

30.8 

2.25 

.265 

12.8 

5.75 

.660 

31.8 

2.5 

.304 

14.7 

6 

.681 

32.8 

2.75 

.341 

16.4 

6.25 

.701 

33.8 

3 

.375 

18.1 

6.5 

.720 

34.7 

3.25 

.407 

19.6 

6.75 

.739 

35  6 

3.5 

.438 

21.1 

7 

.757 

36.5 

3.75 

.467 

22.5 

7.25 

.775 

37.4 

4 

.495 

23.9 

7.5 

.793 

,.38.3 

4.25 

.521 

25.2 

8 

.827 

39.9 

4.5 

.546 

26.4 

R  —  final  -4-  initial  absolute  pressure. 

M.E.P.  =mean  effective  pressure,  Ib.  per  sq.  in.,  based  on  14  Ib.  initial. 


Horse-power  required  to  com- 
press and  deliver  One  Cubic  Foot 
of  Free  Air  per  minute  to  a  given 
pressure  with  no  cooling  of  the  air 
during  the  compression;  also  the 
horse  power  required,  supposing  the 
air  to  be  maintained  at  constant 
temperature  during  the  compression. 


H.P.  required  to  compress  and 
deliver  One  Cubic  Foot  of  Com- 
pressed Air  per  minute  at  a  given 
pressure  (the  air  being  measured  at 
the  atmospheric  temperature)  with 
no  cooling  of  the  air  during  the 
compression;  also  supposing  the  air 
to  be  maintained  at  constant  tem- 
perature during  the  compression. 


Gauge- 

Air  hot 

Air  constant 

Gauge- 

Air  not 

Air  constant 

pressure. 

cooled. 

temperature. 

pressure. 

cooled. 

temperature. 

5 

0.0196 

0.0188 

5 

0.0263 

0.0251 

10 

0.0361 

0.0333 

10 

0.0606 

0.0559 

20 

0.0628 

0.0551 

20 

0.1483 

0.1300 

30 

0.0846 

0.0713 

30 

0.2573 

0  2168 

40 

0.1032 

0.0843 

40 

0.3842 

0.3138 

50 

0.1195 

0.0946 

50 

0.5261 

0.4166 

60 

0.  1342 

0.1036 

60 

0.6818 

0.5266 

70 

0.1476 

0.1120 

70 

0.8508 

0.6456 

80 

0.1599 

0.1195 

80 

1.0302 

0.7700 

90 

0.1710 

0.1261 

90 

1.2177 

0.8979 

100 

0.1815 

0.1318 

100 

1.4171 

1.0291 

The.  horse-power  given  above  is  the  theoretical  power,  no  allowance 
being  made  for  friction  of  the  compressor  or  other  losses,  which  may 
amount  to  10  per  cent  or  more. 


638 


AIR. 


Compressed-air  Engines,  Adiabatic  Expansion.  —  Let  the  initial 
pressure  and  volume  taken  into  the  cylinder  be  pi  Ib.  per  sq.  ft.  and  Vi 
cubic  feet ;  let  expansion  take  place  to  PZ  and  vi  according  to  the  adiabatic 
law  pivi1-41  =  P2021-41;  f/hen  at  the  end  of  the  stroke  let  the  pressure  drop 
to  the  back-pressure  p3,  at  which  the  air  is  exhausted.  Assuming  no 
clearance,  the  work  done  by  one  pound  of  air  during  admission,  measured 

above  vacuum,  is  PIVI,  the  work  during  expansion  is  2.463  PiVi    I  — 

/P2v  0.29-1 

(—  J        ,  and  the  negative  or  back  pressure  work  is  —  p^vz.     The  total 

t/7)«A  0-29~| 
1  _  f  £? )         _  p3V2>  and  the  mean  effective  pres- 
va/      J 
sure  is  the  t9tal  work  divided  by  vt. 

If  the  air  is  expanded  down  to  the  back-pressure  PS  the  total  work  is 

3.463  PiVi  1 1  -  ( — \       J , 
or,  in  terms  of  the  final  pressure  and  volume, 

I  /T)i\Q'2&  ) 

I  \P3/  9 

and  the  mean  effective  pressure  is 


The  actual  work  is  reduced  by  clearance.  When  this  is  considered,  the 
product  of  the  initial  pressure  PI  by  the  clearance  volume  is  to  be  sub- 
tracted from  the  total  work  calculated  from  the  initial  volume  vi,  including 
clearance.  (See  pt  961  under  "  Steam-engine. ") 

Mean  and  Terminal  Pressures  of  Compressed  Air  used  Expansively 
for  Gauge  Pressures  from  60  to  100  Ib. 

(Frank  Richards,  Am.  Mack.,  April  13,  1893.) 


to 

Initial  Pressure. 

1 

60 

70 

80 

90 

100 

1 

.£   • 

p 

1  ,  ^ 

41 

U 

|| 

lt| 

sUi 

|,s 

flj 

"3     ® 

.s 

'o 

C  w 

Pi 

§1 

<u  ^ 

2  <?  en 
£**•  <u 
o     t-< 

il 

*£'^  M 
»     1 

|3f 

1^1 

P* 

ji  D. 

H      £< 

g  ft 

^  & 

H      ft 

a 

H      ft 

ft 

H     ft 

.25 

23.6 

1O.65 

28.74 

12.01 

33.89 

13.49 

39.04 

14.91 

44.19 

1.33 

.30 

28.9 

13.77 

34.75 

0.6 

40.61 

2.44 

46.46 

4.27 

53.32 

6.!! 

I 

32.13 

0.96 

38.41 

3.09 

44.69 

5.22 

50.98 

7.35 

57.26 

9.48 

.35 

33.66 

2.33 

40.15 

4.38 

46.64 

6.66 

53.13 

8.95 

59.62 

11.23 

35.85 

3.85 

42.63 

6.36 

49.41 

7.88 

56.2 

11.39 

62.98 

13.89 

.40 

37.93 

5.64 

44.99 

8.39 

52.05 

11.14 

59.11 

13.88 

66.16 

16.64 

.45 

41.75 

10.71 

49.31 

12.61 

56.9 

15.86 

64.45 

19.11 

72.02 

22.36 

.50 

45.14 

13.26 

53.16 

17. 

61.18 

20.81 

69.19 

24.56 

77.21 

28.33 

.60 

50.75 

21.53 

59.51 

26.4 

68.28 

31.27 

77.05 

36.14 

85.82 

41.01 

I 

51.92 
53.67 
54.93 

23.69 
27.94 
30.39 

60.84 
62.83 
64.25 

28.85 
33.03 
36.44 

69.76 
71.99 
73.57 

34.01 
38.68 
42.49 

78.69 
81.14 
82.9 

39.16 
44.33 
48.54 

87.61 
90.32 

92.22 

44.32 
49.97 
54.59 

.75 

56.52 

35.01 

66.05 

41.68 

75.59 

48.35 

85.12 

55.02 

94.66 

61.69 

.80 

57.79 

39.78 

67.5 

47.08 

77.2 

54.38 

86.91 

61.69 

96.61 

68.99 

.to 

59.15 
59.46 

47.14 
49.65 

69.03 
69.38 

55.43 
58.27 

78.92 
79.31 

63.81 
66.89 

88.81 
89.24 

72. 
75.52 

98.7 
99.17 

80.28 
87.82 

Pressures  in  italics  are  absolute;  all  others  are  gage  pressures 


AIR  COMPRESSION  AT  ALTITUDES. 


639 


AIR  COMPRESSION  AT  ALTITUDES. 

(Ingersoll-Rand  Co.     Copyright,  1906,  by  F.  M.  Hitchcock.) 
Multipliers  to  Determine   the  Volume   of  Free  Air  which,  when 
Compressed,  is  Equivalent  in  Effect  to  a  Given  Volume  of  Free 
Air  at  Sea  Level. 


Alti- 
tucle 

Barometric 
Pressure. 

Gauge  Pressure  (Pounds). 

Feet*. 

In.  of 
Mercury. 

Lb.  per 
Sq.  In. 

60 

80 

100 

125 

150 

1,000 

28.88 

14.20 

.032 

.033 

.034 

.035 

.036 

2,000 

27.80 

13.67 

.064 

.066 

.068 

.071 

.072 

3,000 

26.76 

13.16 

.097 

.102 

.105 

.107 

.109 

4,000 

25.76 

12.67 

.132 

.139 

.142 

.147 

.149 

5,000 

24.79 

12.20 

.168 

.178 

.182 

.187 

.190 

6,000 

23.86 

11.73 

.206 

.218 

.224 

.231 

.234 

7,000 

22.97 

11.30 

.245 

.258 

.267 

.274 

.278 

8,000 

22.11 

10.87 

.287 

.300 

.310 

.319 

.326 

9,000 

21.29 

10.46 

.329 

.346 

.356 

.366 

.374 

10,000 

20  49 

10.07 

.373 

.394 

.404 

416 

.424 

Horse-power  Developed  in  Compressing  One  Cubic  Foot  of  Free  Air 
at  Various  Altitudes  from  Atmospheric  to  Various  Pressures. 

Initial  Temperature  of  the  Air  in  Each  Cylinder  Taken  as  60°  F.;  Jacket 
Cooling  not  Considered ;  Allowance  made  for  usual  losses. 


Simple  Compression. 


Two  Stage  Compression. 


Altitude, 
Feet. 

Gauge  Pressure 
(Pounds). 

Gauge  Pressure  (Pounds). 

60 

80 

100 

60 

80 

100 

125 

150 

0 
1,000 
2,000 
3,000 
4,000 
5,000 
6,000 
7,000 
8,000 
9,000 
10,000 

0.1533 
0.1511 
0.1489 
0.1469 
0.1448 
0.1425 
0.1402 
0.1379 
0.1358 
0.1337 
0.1316 

0.1824 
0.1795 
0.1766 
0.1739 
0.1712 
0.1685 
0.1656 
0.1628 
0.1600 
0.1572 
0.1547 

0.2075 
0.2040 
0.2006 
0.1971 
0.1939 
0.1906 
0.1872 
0.1839 
0.1807 
0.1774 
0.1743 

0.1354 
0.1332 
0.1310 
0.1286 
0.1263 
0.1241 
0.1218 
0.1197 
0.1173 
0.1151 
0.1132 

0.1580 
0.1553 
0.1524 
0.1493 
0.  1464 
0.1438 
0.1409 
0.1383 
0.1358 
0.1329 
0.1303 

0.1765 
0.1734 
0.1700 
0.1666 
0.1635 
0.1600 
0.1566 
0.1536 
0.1504 
0.1473 
0.1442 

0.1964 
0.1926 
0.1887 
0.1848 
0.1810 
0.1772 
0.1737 
0.1700 
0.1662 
0.1627 
0.1592 

0.2138 
0.2093 
0.2048 
0.2003 
0.1963 
0.1921 
0.1879 
0.1838 
0.1797 
0.1758 
0.1717 

EXAMPLE. —  Required  the  volume  of  free  air  which  when  compressed 
to  100  Ib.  gauge  at  9,000  ft.  altitude  will  be  equivalent  to  1,000  cu.  ft. 
of  free  air  at  sea  level;  also  the  power  developed  in  compressing  this 
volume  to  100  Ib.  gauge  in  two  stage  compression  at  this  altitude. 

From  first  table  the  multiplier  is  1.356.  Equivalent  free  air  =  1,000  X 
1.356  =  1,356  cu.  ft. 

From  second  table,  power  developed  in  compressing  1  cu.  ft.  of  free  air 
is  0.1473  H.P.;  1,356  X  0.1473  =  199.73  H.P. 

The  Popp  Compressed-air  System  in  Paris.  —  A  most  extensive 
system  of  distribution  of  power  by  means  of  compressed  air  is  that  of 
M.  Popp,  in  Paris.  One  of  the  central  stations  is  laid  out  for  24,000 
horse-power.  For  a  very  complete  description  of  the  system,  see  Engineer- 
ing, Feb.  15,  June  7,  21,  and  28,  1889,  and  March  13  and  20,  April  10,  and 
May  1,  1891.  Als9  Proc.  Inst.  M.  E.,  July,  1889.  A  condensed  descrip- 
tion will  be  found  in  Modern  Mechanism,  p.  12. 

Utilization  of  Compressed  Air  in  Small  Motors.  —  In  the  earliest 
stages  of  the  Popp  system  in  Paris  it  was  recognized  that  no  good  results 


640  AIR, 

could  be  obtained  if  the  air  were  allowed  to  expand  direct  into  the  motor; 
not  only  did  the  formation  of  ice  due  to  the  expansion  of  the  air  rapidly 
accumulate  and  choke  the  exhaust,  but  the  percentage  of  useful  work 
obtained,  compared  with  that  put  into  the  air  at  the  central  station,  was 
so  small  as  to  render  commercial  results  hopeless. 

After  a  number  of  experiments  M.  Popp  adopted  a  simple  form  of 
cast-iron  stove  lined  with  fire-clay,  heated  either  by  a  gas  jet  or  by  a 
small  coke  fire.  This  apparatus  answered  the  desired  purpose  until  a 
better  arrangement  was  perfected,  and  the  type  was  accordingly  adopted 
throughout  the  whole  system.  The  economy  resulting  from  the  use  of 
the  improved  form  was  very  marked. 

It  was  found  that  more  than  70%  of  the  total  heating  value  of  the  fuel 
employed  was  absorbed  by  the  air  and  transformed  into  useful  work. 
The  efficiency  of  fuel  consumed  in  this  way  is  at  least  six  times  greater 
than  when  utilized  in  a  boiler  and  steam-engine.  According  to  Prof. 
Riedler,  from  15%  to  20%  above  the  power  at  the  central  station  can  be 
obtained  by  means  at  the  disposal  of  the  power  users.  By  heating  the 
air  to  480°  F.  an  increased  efficiency  of  30%  can  be  obtained. 

A  large  number  of  motors  in  use  among  the  subscribers  to  the  Com- 
pressed Air  Company  of  Paris  are  rotary  engines  developing  1  H.P.  and 
less,  and  these  in  the  early  times  of  the  industry  were  very  extravagant 
in  their  consumption.  Small  rotary  engines,  working  cold  air  without 
expansion,  used  as  high  as  2330  cu.  ft.  of  air  per  brake  H.P.  per  hour, 
and  with  heated  air  1624  cu.  ft.  Working  expansively,  a  1-H.P.  rotary 
engine  used  1469  cu.  ft.  of  cold  air,  or  960  cu.  ft.  of  heated  air.  and  a 
2-H.P.  rotary  engine  1059  cu.  ft.  of  cold  air,  or  847  cu.  ft.  of  air,  heated 
to  about  122°  F. 

The  efficiency  of  this  type  of  rotary  motors,  with  air  heated  to  122°  F., 
may  now  be  assumed  at  43%. 

Tests  of  a  small  Riedinger  rotary  engine,  used  for  driving  sewing- 
machines  and  indicating  about  0.1  H.P.,  showed  an  air-consumption  of 
1377  cu.  ft.  per  H.P.  per  hour  when  the  initial  pressure  of  the  air  was 
86  Ib.  per  sq.  in.  and  its  temperature  54°  F.,  and  988  cu.  ft.  when  the  air 
was  heated  to  338°  F.,  its  pressure  being  72  Ib.  With  a  1/2-H.P.  variable- 
expansion  rotary  engine  the  air-consumption  was  from  800  to  900  cu.  ft. 
per  H.P.  per  hour  for  initial  pressures  of  54  to  85  Ib.  per  sq.  in.  with  the 
air  heated  from  336°  to  388°  F.,  and  1148  cu.  ft.  with  cold  air,  46°  F.,  and 
an  initial  pressure  of  72  Ib.  The  volumes  of  air  were  all  taken  at  atmos- 
pheric pressure. 

Trials  made  with  an  old  single-cylinder  80-horse-power  Farcot  steam- 
engine,  indicating  72  H.P.,  gave  a  consumption  of  air  per  brake  H.P.  as 
low  as  465  cu.  ft.  per  hour.  The  temperature  of  admission  was  320°  F., 
and  of  exhaust  95°  F. 

Prof.  Elliott  gives  the  following  as  typical  results  of  efficiency  for 
various  systems  of  compressors  and  air-motors: 

Simple  compressor  and  simple  motor,  efficiency 39.1% 

Compound  compressor  and  simple  motor,  44.9 

"    compound  motor,  efficiency. .   50.7 
Triple  compressor  and  triple  motor,  efficiency 55.3 

The  efficiency  is  the  ratio  of  the  I. H.P.  in  the  motor  cylinders  to  the 
I.H.P.  in  the  steam-cylinders  of  the  compressor.     The  pressure  as- 
sumed is  6  atmospheres  absolute,  and  the  losses  are  equal  to  those 
found  in  Paris  over  a  distance  of  4  miles. 
Summary  of  Efficiencies  of  Compressed-air  Transmission  at  Paris, 

between  the  Central  Station  at  St.  Fargeau  and  a  10-horse-power 

Mo  tor  Working  with  Pressure  Reduced  to  4 1/2  Atmospheres. 

(The  figures  below  correspond  to  mean  results  of  two  experiments  cold  and 

two  heated.) 

One  indicated  horse-power  at  central  station  gives  0.845  I.H.P.  in  com- 
pressors, and  corresponds  to  the  compression  of  348  cu.  ft.  of  air  per  hour 
from  atmospheric  pressure  to  6  atmospheres  absolute. 

0.845  I.H.P.  in  compressors  delivers  as  much  air  as  will  do  0.52  I.H.P. 
in  adiabatic  expansion  after  it  has  fallen  to  the  normal  temperature  of  the 

The  fall  of  pressure  in  mains  between  central  station  and  Paris  (say  5 
kilometres)  reduces  the  possibility  of  work  from  0,53  to  0,51  J.H.P, 


AIR   COMPRESSORS. 


641 


The  further  fall  of  pressure  through  the  reducing  valve  to  41/2  atmos- 
pheres (absolute)  reduces  the  possibility  of  work  from  0.51  to  0.50. 

Incomplete  expansion,  wire-drawing,  and  other  such  causes  reduce  the 
actual  I.H.P.  of  the  motor  from  0.50  to  0.39. 

By  heating  the  air  before  it  enters  the  motor  to  about  320°  F.,  the 
actual  I.H.P.  at  the  motor  is,  however,  increased  to  0.54.  The  ratio  of 
gain  by  heating  the  air  is,  therefore,  0.54  -5-  0.39  =  1.38. 

In  this  process  additional  heat  is  supplied  by  the  combustion  of  about 
0.39  Ib.  of  coke  per  I.H.P.  per  hour,  and  if  this  be  taken  into  account,  the 
real  indicated  efficiency  of  the  whole  process  becomes  0.47  instead  of  0.54. 

Working  with  cold  air  the  work  spent  in  driving  the' motor  itself  reduces 
the  available  horse-power  from  0.39  to  0.26. 

Working  with  heated  air  the  work  spent  in  driving  the  motor  itself 
reduces  the  available  horse-p9wer  from  0.54  to  0.44. 

A  summary  of  the  efficiencies  is  as  follows: 

Efficiency  of  main  engines  0.845. 

Efficiency  of  compressors  0.52  -?-  0.845  =  0.61. 

Efficiency  of  transmission  through  mains  0.51  -5-  0.52  =  0.98. 

Efficiency  of  reducing  valve  0.50  -~  0.51  =  0.98. 

The  combined  efficiency  of  the  mains  and  reducing  valve  between  5  and 
41/2  atmospheres  is  thus  0.98  X  0.98  =  0.96.  If  the  reduction  had  been 
to  4,  31/2,  or  3  atmospheres,  the  corresponding  efficiencies  would  have 
been  0.93,  0.89,  and  0.85  respectively. 

Indicated  efficiency  of  motor  0.39  •*•  0.50  =  0.78. 

Indicated  efficiency  of  whole  process  with  cold  air  0.39.  Apparent 
indicated  efficiency  of  whole  process  with  heated  air  0.54. 

Real  indicated  efficiency  of  whole  process  with  heated  air  0.47. 

Mechanical  efficiency  of  motor,  cold,  0.67. 

Mechanical  efficiency  of  motor,  hot,  0.81. 


Ingersoll-Rand  Co.'s  Air  Compressors.* 

STRAIGHT  LINE  POWER-DRIVEN  COMPRESSORS,  CLASS  "ER-1." 
Air  Pressure  10  to  125  Pounds  per  sq.  in. 


Cylinders, 
Inches. 

Piston 
Dis- 
place- 
ment 
Cu.ft. 
per 
Min. 

Air 
Pres. 
De- 
signed 
for 
Lb. 
Gage. 

Braize 
H.P.  at 
Motor, 
includ- 
ing 
Belt 
Loss. 

Cylinders, 
Inches. 

Piston 
Dis- 
place- 
ment 
Cu.ft. 

Min. 

Air 
Pres. 
De- 
signed 
for 
Lb. 
Gage. 

Brake 
H.P.  at 
Motor, 
includ- 
ing 
Belt 
Loss. 

3 

1 

VI 

1 

s 

1 

w 

6 
7 
8 
9 
12 

8 
9 
10 
12 
14 

6 
6 
6 
6 
6 

52 

72 
94 
121 
215 

80-125 
50-100 
25-50 
10-  25 
10- 

8     -10 

9V2-12 
9V2-12 
10     -121/4 
15     - 

10 
12 

14 
17 

10 
10 
10 
10 

210 
304 
415 
615 

80-125 
50-100 
20-50 
10-  20 

33-38 
38-50 
32-50 
27-48 

8 
8 
8 
8 
8 

113 
145 
179 
258 
354 

80-125 
60-100 
25-60 
15-  25 
10-  15 

17     -22 
19V2-24 
18      -25 
201/2-25 
21      -25 

12 
14 
17 
20 

12 

12 
12 
12 

340 
464 
688 
955 

80-125 
45-100 
30-  45 
15-  30 

54-61 
53-73 
55-73 
35-70 

Stroke,  inches 6 

Revolutions  per  minute. .         275 
Belt  wheel 36  X  5 1/2 


8  10  12 

250  235  220 

45  X  81/2    58  X  101/2   72  X  141/2 


These  machines  are  also  built  for  steam-drive. 

*  These  tables  are  considerably  abridged  from  the  originals,  and  show 
only  the  small  and  medium-sized  machines.  Large  machines  up  to 
8,f>00  cu,  ft.  capacity  are  made,  usually  of  special  designs, 


642 


AIR. 


'IMPERIAL  XB-1"  DUPLEX  POWER-DRIVEN  COMPRESSORS. 
Air  Pressure,  15  to  100  Pounds  per  sq.  in. 


d 

X"" 

i 

,  8 

|KS 

§•§ 

•*•• 

Ig 

WTJ 

1 

tt 

ilc 

IS 
t 

<*J 

|| 

| 

I**? 

11 

W|| 

1 

|fe? 

EI! 

.^ 

oT 

Qo  ^ 

^'5? 

lovS 

s° 

I 

QO  a 

IS  '|,4a 

O  +*•£< 

S  w'aJ 

g 

.2  .fa 

! 

•P    J3<jj 

<!Q 

PQtfW 

Q^ 

GO 

w-g^ 

<!Q 

wtfpq 

Q<< 

CO 

S  a 

S  S 

7 

10 

198 

60-100 

27-37 

14 

14 

916 

35-40 

93-102 

8 

10 

258 

40-55 

29-35 

16 

14 

1198 

25-30 

99-112 

9 

10 

327 

27-35 

27-34 

18 

14 

1518 

15-20 

87-108 

10 

10 

405 

22-25 

29-33 

11 

10 

491 

15-20 

28-35 

13 

16 

826 

80-100 

135-154 

8 

12 

289 

75-100 

47-55 

14 
15 

16 
16 

959 
1103 

65-75 
45-60 

142-155 
125-155 

9 

12 

367 

55-70 

50-58 

17 

16 

1419 

30-40 

129-158 

10 

12 

454 

40-50 

51-58 

19 

16 

1775 

20-25 

123-145 

11 

12 

549 

27-35 

46-57 

21 

16 

2171 

15-20 

126-157 

12 

12 

655 

22-25 

47-54 

13 

12 

770 

15-20 

44-55 

15 

16o 

1100 

80-100 

181-206 

16 

16a 

1253 

55-75 

188-202 

9 

12a 

365 

85-100 

62-69 

18 

16fl 

1592 

35-50 

161-205 

10 

12a 

453 

60-80 

64-75 

21 

2168 

25-30 

177-202 

11 

12ft 

549 

47-55 

66-74 

24 

16a 

2836 

15-20 

162-202 

12 

12a 

654 

37-45 

67-78 

13 

12a 

769 

25-35 

63-80 

15 

20 

1254 

75-100 

197-232 

15 

12a 

1025 

15-20 

58-72 

17 

20 

1615 

50-70 

204-251 

19 

20 

2020 

35-45 

214-242 

11 

14 

563 

80-100 

94-106 

22 

20 

2714 

25-30 

223-255 

12 

14 

671 

60-75 

95-108 

25 

20 

3508 

15-20 

203-253 

13 

14 

789 

45-55 

94-106 

Stroke  of  cylinder,  in. .  10  12  I2a  14  16  16ff  20 
Revolutions  per  niin.  .  225  210  210  185  170  170  155 
Belt  wheel,  diameter  in.  54  60  72  84  96  96  108 
Belt  wheel,  face  in 8l/2  101/2  12 1/2  161/2  20.1/2  281/2  31 1/2 

"IMPERIAL  XB-2"   TWO-STAGE  POW*ER~DRIVEN  AIR  COMPRESSORS. 
For  air  pressure  of  80  to  100  pounds  per  sq.  in. — For  sea  level. 


Diameter  of  Air 
Cylinders,  Inches 

Rev. 
per 
Min. 

Piston 
Dis- 
place- 
ment, 
Cu.  Ft. 
Free   Air 
per  Min. 

Brake  H.P. 
Required  at 
Belt  Wheel. 

Belt 
Wheel. 

Low 
Press. 

High 
Press. 

Stroke. 

Air  Pressure. 

Diam., 
Inches. 

Face, 
Inches. 

80 

100 

10 
12 
14 
16 
19 
22 
23 

6V2 
7V2 

10 
12 
13 
14 

10 
12 
12 
14 
16 
16 
20 

225 
210 
210 
185 
170 
170 
155 

203 
327 
446 
599 
888 
1190 
1482 

32 
50 
68 
92 
135 
183 
226 

36 

57 
76 
104 
152 
206 
254 

54 
60 
72 
84 
96 
96 
108 

8V2 

10i/2 

121/2 

16V2 
201/2 
281/2 

31V2 

For  5,000  feet  altitude  the  low-pressure  cylinders  are  made  1  inch 
larger  diameter,  and  for  10,000  feet  altitude  2  inches  larger. 

"IMPERIAL  X-2"  DUPLEX  STEAM-DRIVEN  TWO-STAGE  AIR  COMPRESSORS. 

Air  cylinders  of  the  same  dimensions  as  the  XB-2  compressors. 
The  duplex  steam  cylinders  have  diameters  7,  8,  9,  10,  12,  and  14 
inches.  The  14  X  20-inch  cylinder  is  designed  for  150  r.  p.  m, 


TESTS   OF  AIK   COMPRESSORS. 


643 


DUPLEX  STEAM-DRIVEN  "IMPERIAL  X-l"  COMPRESSORS. 
For  air  pressures  of  15  to  100  Ib.  per  sq.  in. — Steam,  80  to  120  Ib. 


Cylinder 
Diam.,  In. 

jj 

if* 

|| 

Jti 

Cylinder 
Diam.,  In. 

ri 

|i 

|| 

it 

VI  fc 

Is 
Ij 

fa 

0) 

A* 

ill 

£,|> 

aj 

£§ 

a  as 

3  £ 

h 

1 

AH' 
tf 

111 

£.!> 

•^ 

*I 

Q 

m 

w 

Q^ 

•*-> 

-5 

7 

7 

10 

225 

198 

60-100 

28-38 

10 

14 

14 

185 

916 

35-40 

96-105 

7 

8 

10 

225 

258 

40-55 

30-36 

10 

16 

14 

185 

1198 

25-30 

103-116 

7 

9 

10 

225 

327 

27-35 

27-34 

10 

18 

1.4 

185 

1518 

15-20 

90-112 

7 

10 

10 

225 

405 

22-25 

29-34 

7 

11 

10 

225 

491 

15-20 

29-36 

12 

13 

16 

170 

826 

80-100 

141-161 

12 

14 

16 

170 

959 

65-75 

149-162 

8 

8 

12 

210 

289 

75-100 

48-57 

12 

15 

16 

170 

1103 

45-60 

135-163 

8 

9 

12 

210 

367 

55-70 

51-60 

12 

17 

16 

170 

1419 

30-40 

135-165 

8 

10 

12 

210 

454 

40-50 

53-61 

12 

19 

16 

170 

1775 

20-25 

128-151 

8 

11 

12 

210 

549 

27-35 

46-59 

12 

21 

16 

170 

2171 

15-20 

131-164 

8 

12 

12 

210 

655 

22-25 

47-56 

8 

13 

12 

210 

770 

15-20 

46-57 

14 

15 

16 

170 

1100 

80-100 

186-212 

14 

16 

16 

170 

1253 

55-75 

173-209 

9 

9 

12 

210 

365 

85-100 

65-72 

14 

18 

16 

170 

1592 

35-50 

166-212 

9 

10 

12 

210 

453 

60-80 

67-79 

14 

21 

16 

170 

2168 

25-30 

183-208 

9 

11 

12 

210 

549 

47-55 

69-78 

14 

24 

16 

170 

2836 

15-20 

168-209 

9 

12 

12 

210 

654 

37-45 

69-81 

9 

13 

12 

210 

769 

25-35 

66-84 

14 

15 

20 

150 

1213 

75-100 

196-232 

9 

15 

12 

210 

1025 

15-20 

61-76 

14 

17 

20 

150 

1562 

50-70 

204-251 

14 

19 

20 

150 

1955 

35-45 

204-242 

10 

11 

14 

185 

563 

80-100 

98-110 

14 

22 

20 

150 

2626 

25-30 

224-255 

10 

12 

14 

185 

671 

60-75 

98-112 

14 

25 

20 

150 

3395 

15-20 

203-253 

10 

13 

14 

185 

789 

45-55 

97-110 

COMPOUND  STEAM  CYLINDERS  FOR  "IMPERIAL  X"  COMPRESSORS. 

For  substituting  in  place  of  Duplex  Steam  Cylinders  in  the  "Imperial 

X-l  and  X-2"  Tables  for  Steam-Pressures  of  100  to  120  Lbs. 

Condensing  of  Non-Condensing. 


Compound  Engines  with  Plain  "D" 
Steam  Valves. 


Compound  Engines  with  Meyer 
Cut-off  Valves. 


Standard 

Standard 

Standard 

Standard 

Duplex 
Steam 

Compound 
Steam 

Stroke. 

Duplex 
Steam 

Compound 
Steam 

Stroke. 

Cylinders. 

Cylinders. 

Cylinders. 

Cylinders. 

7&  7 

7&  11 

10 

10&  10 

12&  19 

14 

8&8 

8&  13 

12 

12&  12 

14&22 

16 

9&9 

10&  16 

12 

14&  14 

16&  25 

16 

14&  14 

16&25 

20 

Tests  of  Power-driven  Air  Compressors. — R.  L.  Webb,  Portland,  Ore., 
has  furnished  the  author  with  a  copy  of  a  complete  report  of  a  test 
made  by  him  in  1912,  of  three  air  compressors,  two  of  them  18  in.  diam. 
X  12  in.  stroke,  rated  at  1000  cu.  ft.  per  min.  displacement,  and  the 
third  22  X  12  in.,  rated  at  1500  cu.  ft.  Nos.  1  and  3  were  designed  for 
35  to  45  Ib.  gage-pressure  and  No.  2  for  15  to  20  Ib.  The  compres- 
sors were  driven  by  500  volt  d.c.  shunt,  commutating  pole'  motors,  with 
a  speed  range  of  2  to  1 ,  through  Link-Belt  silent  chain  drives,  2  in.  pitch, 
9  in.  wide,  chain  speed,  1600  ft.  per  min.,  pinions  17  and  64  teeth,  chain 
gear  efficiency  about  98%;  gear  submerged  in  oil.  The  speed  control 
was  regulated  by  the  air  pressure.  The  air  delivered  was  measured 


644 


AIR. 


by  the  orifice  method,  using  Fliegner's  equation.     The  results  of  the 
tests  are  summarized  in  the  table  below: 

TESTS  OF  AIR  COMPRESSORS. 


I 

t.3 


s  l 


Volumetric 
Efficiency 
Per  cent. 


Electric 
Horse- 
pttwer. 


$ 


Compressor  No.  1,  18  X  12  in. 


71.6 

502.1 

412.3 

82.11 

45.6 

61.2 

51.75 

84.5 

44.6 

102.0 

715.3 

597.4 

83.2 

67.7 

90.7 

75.28 

83.0 

44.5 

143.0 

1002.8 

873.3 

87.1 

87.1 

133.4 

106.73 

80.0 

44.2 

Compressor  No.  2,  22  X  12  in. 


70.7 

749.8 

657.1 

85.6 

42.1 

56.4 

48.3 

85.7 

19.6 

103.8 

1100.8 

986.0 

89.5 

65.0 

87.1 

73.1 

83.0 

19.2 

141.0 

1495.3 

1333.9 

89.2 

97.6 

130.8 

106.5 

80.0 

19.5 

Compressor  No.  3,  18  X  12  in. 


70.2 
101.0 
145.0 

492.3 
708.3 
1016.9 

371.1 
567.2 
837.1 

75.4 
80.1 
82.3 

43.9 
65.8 
100.7 

58.8 
88.3 
135.0 

50.0 
73.4 
109.1 

85.0 
84.0 
80.7 

44.8 
44.7 
44.4 

Steam   Required   to  Compress   100  Cu.  Ft.  of  Free  Air.      (O.  S. 

Shantz,  Power,  Feb.  4,  1908.)  — The  following  tables  show  the  number  of 
pounds  of  steam  required  to  compress  100  cu.  ft.  of  free  air  to  different 
gauge  pressures,  by  means  of  steam  engines  using  from  12  to  40  Ibs.  of 
steam  per  I.H.P.  per  hour.  The  figures  assume  adiabatic  compression 
in  the  air  cylinders,  with  intercooling  to  atmospheric  temperature  in  the 
case  of  two-stage  compression,  and  90%  mechanical  efficiency  of  the 
compressor. 

STEAM  CONSUMPTION  OF  AIR  COMPRESSORS — SINGLE-STAGE  COMPRESSION. 


Air 
Gage 
Pres- 
sure. 

Steam  per  I.H.P.  Hour.     Lb. 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

36 

40 

20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
120 

1.36 
1  84 

1.58 
?  14 

1.82 
?  45 

2.04 
?  76 

2.26 
3.06 

[  2.49 
3  37 

2.72 
3  68 

2.94 
3.98 

3.17 
4  29 

3.40 
4.60 

3.61 
4.90 

4.08 
5  51 

4.54 
6  17. 

2.26 
2.62 
2  92 

2.64 
3.06 
3  41 

3.02 
3.50 
3  % 

3.39 
3.93 
4  38 

3.77 
4.36 
4  80 

4.15 
4.80 
5  36 

4.52 
5.25 
5  85 

4.90 
5.68 
6  32 

5.26 
6.10 

6  80 

5.65 
6.55 
7  30 

6.03 
7.00 
7  80 

6.78 
8.86 
8  76 

7.50 
8.71 
9  71 

3.22 
3.50 
3.72 
3.96 
4.18 
4.38 

3.76 
4.08 
4.34 
4.61 
4.87 
5.11 

4.30 
4.67 
4.96 
5.29 
5.58 
5.85 

4.83 
5.25 
5.58 
5.95 
6.26 
6.57 

5.36 
5.84 
6.20 
6.60 
6.96 
7.30 

5.90 
6.42 
6.82 
7.25 
7.66 
8.04 

6.45 
7.00 
7.45 
7.92 
8.36 
8.76 

6.97 
7.59 
8.05 
8.58 
9.05 
9.50 

7.50 
8.15 
8.66 
9.22 
9.75 
10.20 

8.05 
8.75 
9.30 
9.90 
10.45 
10.95 

8.60 
9.34 
9.94 
10.56 
11.15 
11.66 

9.66 
10.50 
11.15 
11.88 
12.52 
13.13 

10.70 
11.61 
12.35 
13.15 
13.90 
14.55 

TWO-STAGE  COMPRESSION. 

70 
80 
90 
100 
110 
120 
130 
140 
150 

2.82 
3.01 
3.19 
3.37 
3.54 
3.69 
3.83 
3.96 
4.10 

3.25 
3.51 
3.72 
3.93 
4.14 
4.30 
4.46 
4.62 
4.76 

3.76 
4.03 
4.26 
4.50 
4.74 
4.93 
5.11 
5.29 
5.46 

4.23 
4.52 
4.79 
5.05 
5.32 
5.54 
5.75 
5.94 
6.14 

4.69 
5.02 
5.32 
5.61 
5.91 
6.15 
6.38 
6.60 
6.81 

5.16 
5.53 
5.85 
6.19 
6.51 
6.78 
7.03 
7.26 
7.50 

5.63 
6.03 
6.38 
6.74 
7.10 
7.38 
7.66 
7.92 
6.74 

6.10 
6.53 
6.91 
7.30 
7.70 
8.00 
8.30 
8.60 
8.86 

6.56 
7.03 
7.44 
7.85 
8.27 
8.61 
8.92 
9.23 
9.55 

7.04 
7.53 
7.98 
8.42 
8.86 
9.24 
9.57 
9.90 
10.20 

7.50 
8.03 
8.50 
8.99 
9.46 
9.85 
10.20 
10.56 
10.90 

8.45 
9.05 
9.57 
10.10 
10.64 
11.05 
11.48 
11.88 
12.26 

9.35 
10.01 
10.60 
11.20 
11.80 
12.27 
12.72 
13.15 
13.60 

COMPRESSED  AIR  FOR  PUMPING. 


645 


Cubic  Feet  of  Air  Required  to  Run  Rock  Drills  at  Various  Pressures 
and  Altitudes. 

(Ingersoll-Rand  Co.,  1908.) 
TABLE  I.  —  CUBIC  FEET  OF  FREE  AIR  REQUIRED  TO  RUN  ONE  DRILL. 


Gauge  Pressure, 
Lb.  per  Sq.  In. 

Size  and  Cylinder  Diameter  of  Drill. 

A  35 

A  32 
A  86 

B 

C 

D 

D 

D 

E 

F 

F 

G 

H 

H9 

2" 

21/4* 

21/2" 

23/4* 

3" 

31/8* 

33/16* 

31/4" 

31/2* 

35/8" 

41/4* 

5" 

5V2" 

60 
70 
80 
90 
100 

50 
56 
63 
70 

77 

60 
68 
76 
84 
92 

68 
77 
86 
95 
104 

82 
93 
104 
115 
126 

90 
102 
114 
126 
138 

95 
108 
120 
133 
146 

97 
110 
123 
136 
149 

100 
113 
127 
141 
154 

108 
124 
131 
152 
166 

113 
129 
143 
159 
174 

130 
147 
164 
182 
199 

150 
170 
190 
210 
240 

164 
181 
207 
230 
252 

TABLE   II.  —  MULTIPLIERS  TO  GIVE  CAPACITY  OF   COMPRESSOR  TO  OPERATE 

•  FROM    1  TO  70   ROCK   DRILLS   AT  VARIOUS  ALTITUDES. 


Number  of  Drills. 


^g 

+2GQ 
< 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15 

20 

25 

30 

40 

50 

0 
1030 
2330 
3300 
5300 
8030 
13330 
13030 

1. 
1.03 
1.07 
1.10 
1.17 
1.26 
1.32 
1.43 

1.8 
1.85 
9? 

2.7 

2.78 
789 

3.4 
3.5 
3  64 

4.1 

4.22 
439 

4.8 
4.94 
5  14 

5.4 
5.56 

5  78 

6.0 
6.18 
64? 

6.5 
6.69 
695 

7.1 
7.3 

760 

9.5 
9.78 
10.17 

11.7 
12.05 
1252 

13.7 
14.1 
1466 

15.8 
16.3 
169 

21.4 
22.0 
22.9 
23.54 
25.04 
26.% 
28.25 
30.6 

25.5 
26.26 
27.28 
28.05 
29.84 
32.13 
33.66 
36.49 

.98 
2.10 
2.27 
2.38 
2.57 

2.97 
3.16 
3.40 
3.56 
3.86 

3.74 
3  98 

4.28 
4.49 
4.86 

4.51 
4.8 
5.17 
5.41 
5.86 

5.28 
5.62 
6.05 
6.34 
6.86 

5.94 
6.32 
6.8 
7.13 
7.72 

6.6 
7.02 
7.56 
7.92 
8.58 

7.15 
7.61 
8.19 
8.58 
9.3 

7.81 
8.31 
8.95 
9.37 
10.15 

10.45 
11.12 
11.97 
12.54 
13.58 

12.87 
13.69 
14.74 
15.44 
16.73 

15.07 
16.03 
17.26 
18.08 
19.59 

17.38 
18.49 
19.9 
20.86 
22.59 

EXAMPLE.  —  Required  the  amount  of  free  air  to  operate  thirty  5-inch 
"H"  drills  at  8,000  ft.  altitude,  using  air  at  a  gauge  pressure  of  80  Ib  per 
sq.  in.  From  Table  I,  we  find  that  one  5-inch  "  H  "  drill  operating  at  80  Ib. 

fauge  pressure  requires  190  cu.  ft.  of  free  air  per  minute.     From  Table 
I,  the  factor  for  30  drills  at  8,000  feet  altitude  is  19.9;  190  X  19.9  = 
3781  =  the  displacement  of  a  compressor  under  average  conditions,  to 
which  must  be  added  pipe  line  losses. 

The  tables  above  are  for  fair  conditions  in  ordinary  hard  rock.  In 
soft  material,  where  the  drilling  time  is  short  more  drills  can  be  run  with 
a  given  compressor  than  when  working  in  hard  material.  In  tunnel 
work,  more  rapid  progress  can  be  made  if  the  drills  are  run  at  high  air 
pressure,  and  it  is  advisable  to  have  an  excess  of  compressor  capacity 
of  about  25%.  No  allowance  has  been  made  in  the  tables  for  friction 
of  pipe  line  losses. 

Compressed-air  Table  for  Pumping  Plants* 
(Ingersoll-Rand  Co.,  1908.) 

The  following  table  shows  the  pressure  and  volume  of  air  required  for 
any  size  pump  for  pumping  by  compressed  air.  Reasonable  allowances 
have  been  made  for  loss  due  to  clearances  in  pump  and  friction  in  pipe. 

To  find  the  amount  of  air  and  pressure  required  to  pump  a  given  quan- 
tity of  water  a  given  height,  find  the  ratio  of  diameters  between  water 
and  air  cylinders,  and  multiply  the  number  of  gallons  of  water  by  the 


646 


AIR. 


figure  found  in  the  column  for  the  required  lift.  The  result  is  the  number 
of  cubic  feet  of  free  air.  The  pressure  required  on  the  pump  will  be  found 
directly  above  in  the  same  column.  For  examole:  The  ratio  between 
cylinders  being  2  to  1,  required  to  pump  100  gallons,  height  of  lift  250 
feet.  We  find  under  250  feet  at  ratio  2  to  1  the  figures  2.11 ;  2.11  X  100  = 
211  cubic  feet  of  free  air.  The  pressure  required  is  34.38  pounds  deliv- 
ered at  the  pump  piston. 


Ratio  of 
Diameters. 

Perpendicular  Height,  in  Feet,  to  which  the  Water 
is  to  be  Pumped. 

25 

50 

75 

100 

125 

150 

175 

200 

250 

300 

400 

1       to  1 
1  1/2  to  1 
1  3/4  to  1 
2      to  1 
2  1/4  to  1 
2l/2  to  1  { 

A 
B 
A 
B 
A 
B 
A 
B 
A 
B 
A 
B 

13.75 
0.21 

27.5 
0.45 
12.22 
0.65 

41.25 
0.60 
18.33 
0.80 
13.75 
0.94 

55.0 
0.75 
24.44 
0.95 
19.8 
1.14 
13.75 
1.23 

68.25 
0.89 
30.33 
1.09 
22.8 
1.24 
17.19 
1.37 
13.75 
1.53 

82.5 
1.04 
36.66 
1.24 
27.5 
1.30 
20.63 
1.52 
16.5 
1.68 
13.2 
1.79 

96.25 
1.20 
42.76 
1.39 
32.1 
1.54 
24.06 
1.66 
19.25 
1.83 
15.4 
1.98 

110.0 
1.34 
48.88 
1.53 
36.66 
1.69 
27.5 
1.81 
22.0 
1.97 
17.6 
2.06 

61.11 
1.83 
45.83 
1.99 
34.38 
2.11 
27.5 
2.26 
22.0 
2.34 

73.32 
2.12 
55.0 
2.39 
41.25 
2.40 
33.0 
2.56 
26.4 
2.62 

97.66 
2.70 
73.33 
2.88 
55.0 
2.98 
44.0 
3.15 
35.2 
3.18 

A  =  air-pressure  at  pump.     B  =  cubic  feet  of  free  air  per  gallon  of  water. 

Compressed-air  Table  for  Hoisting-engines. 

(Ingersoll-Rand  Co.,  1908.) 

The  following  table  gives  an  approximate  idea  of  the  volume  of  free  air 
required  for  operating  hoisting-engines,  the  air  being  delivered  to  the 
engine  at  60  Ibs.  gauge.  There  are  so  many  variable  conditions  to  the 
operation  of  hoisting-engines  in  common  use  that  accurate  computations 
can  only  be  offered  when  fixed  data  are  given.  In  the  table  the  engine  is 
assumed  to  actually  run  but  one-half  of  the  time  for  hoisting,  while  the 
compressor  runs  continuously.  If  the  engine  runs  less  than  one-half  the 
time,  the  volume  of  air  required  will  be  proportionately  less,  and  vice 
versa.  The  table  is  computed  for  maximum  loads,  which  also  in  practice 
may  vary  widely.  From  the  intermittent  character  of  the  work  of  a 
hoisting-engine  the  parts  are  able  to  resume  their  normal  temperature 
between  the  hoists,  and  there  is  little  probability  of  freezing  up  the 
exhaust-passages. 

Volume  of  Free  Air  Required  for  Operating  Hoisting-engines,  the 
Air  Compressed  to  6O  Pounds  Gauge  Pressure. 

SINGLE-CYLINDER  HOISTING-ENGINE. 


Diam.  of 
Cylinder, 
Inches. 

Stroke, 
Inches. 

Revolu- 
tions per 
Minute. 

Normal 
Horse- 
power. 

Actual 
Horse- 
power. 

Weight 
Lifted, 
Single 
Rope. 

Cubic  Ft. 
of  Free  Air 
Required. 

5 

61/4 
81/4 

,8oV2 

6 

8 
8. 
10 
10 
12 
12 

200 
160 
160 
125 
125 
110 
110 

3 

4 
6 
10 
.      15 
20 
25 

5.9 
6.3 
9.9 
12.1 
16.8 
18.9 
26.2 

600 
1,000 
1,500 
2,000 
3,000 
5,000 
6000 

75 

80 
125 
151 
170 

238 
330 

COMPRESSED     AIR. 


DOUBLE-CYLINDER  HOISTING-ENGINE. 


647 


Diam.  of 
Cylinder, 
Inches. 

Stroke, 
Inches. 

Revolu- 
tions per 
Minute. 

Normal 
Horse- 
power. 

Actual 
Horse- 
power. 

Weight 
Lifted, 
Single 
Rope. 

Cubic  Ft. 
of  Free  Air 
Required. 

5 

6 

200 

6 

11.8 

1  ,000 

150 

5 

8 

160 

8 

12.6 

1,650 

160 

61/4 

8 

160 

12 

19.8 

2,500 

250 

7 

10 

125 

20 

24.2 

3,500 

302 

81/4 

10 

125 

30 

33.6 

6000 

340 

81/2 

12 

110 

40 

37.8 

8000 

476 

10 

12 

110 

50 

52.4 

lO'.OOO 

660 

121/4 

15 

100 

75 

89.2 

1,125 

14 

18 

90 

100 

125. 

1,587 

Practical  Results  with  Compressed  Air.  —  Compressed-air  System 
at  the  Chapin  Mines,  Iron  Mountain,  Mich.  — These  mines  are  three  miles 
from  the  falls  which  supply  the  power.  There  are  four  turbines  at  the 
falls,  one  of  1000  horse-power  and  three  of  900  horse-power  each.  The 
pressure  is  60  pounds  at  60°  Fahr.  Each  turbine  runs  a  pair  of  compress- 
ors. The  pipe  to  the  mines  is  24  ins.  diameter.  The  power  is  applied  at 
the  mines  to  Corliss  engines,  running  pumps,  hoists,  etc.,  and  direct  to 
rock-drills. 

•  A  test  made  in  1888  gave  1430.27  H.P.  at  the  compressors,  and  390.17 
H.P.  as  the  sum  of  the  horse-power  of  the  engines  at  the  mines.  There- 
fore, only  27%  of  the  power  generated  was  recovered  at  the  mines.  This 
includes  the  loss  due  to  leakage  and  the  loss  of  energy  in  heat,  but  not  the 
friction  in  the  engines  or  compressors.  (F.  A.  Pocock,  Trans.  A.  I.  M.  E., 
1890.) 

W.  L.  Saunders  (Jour.  F.I.,  1892)  says:  "There  is  not  a  properly  designed 
compressed-air  installation  in  operation  to-day  that  loses  over  5%  by 
transmission  alone.  The  question  is  altogether  one  of  the  size  of  pipe; 
and  if  the  pipe  is  large  enough,  the  friction  loss  is  a  small  item. 

"  The  loss  of  power  in  common  practice,  where  compressed  air  is  used 
to  drive  machinery  in  mines  and  tunnels,  is  about  70% .  In  the  best  prac- 
tice, with  the  best  air-compressors,  and  without  reheating,  the  loss  is  about 
60%.  These  losses  may  be  reduced  to  a  point  as  low  as  20%  by  combin- 
ing the  best  systems  of 'reheating  with  the  best  air-compressors." 

Gain  due  to  Reheating:.  —  Prof.  Kennedy  says  compressed-air  trans- 
mission system  is  now  being  carried  on,  on  a  large  commercial  scale, 
in  such  a  fashion  that  a  small  motor  four  miles  away  from  the  central 
station  can  indicate  in  round  numbers  10  horse-power,  for  20  horse- 
power at  the  station  itaelf,  allowing  for  the  value  of  the  coke  used  in  heat- 
ing the  air. 

The  limit  to  successful  reheating  lies  in  the  fact  that  air-engines  can- 
not work  to  advantage  at  temperatures  over  350°. 

The  efficiency  pf  the  common  system  of  reheating  is  shown  by  the  re- 
sults obtained  with  the  Popp  system  in  Paris.  Air  is  admitted  to  the 
reheater  at  about  83°,  and  passes  to  the  engine  at  about  3i5°,  thus  being 
increased  in  volume  about  42%.  The  air  used  in  Paris  is  about  11  cubic 
feet  of  free  air  per  minute  per  horse-power.  The  ordinary  practice  in 
America  with  cold  air  is  from  15  to  25  cubic  feet  per  minute  per  horse- 
power. When  the  Paris  engines  were  worked  without  reheating  the  air 
consumption  was  increased  to  about  15  cubic  feet  per  horse-power  per 
minute.  The  amount  of  fuel  consumed  during  reheating  is  trifling. 

Effect  of  Temperature  of  Intake  upon  the  Discharge  of  a  Com- 
pressor. —  Air  should  be  drawn  from  outside  the  engine-room,  and 
from  as  cool  a  place  as  possible.  The  gain  in  efficiency  amounts  to  one 
per  cent  for  every  five  degrees  that  the  air  is  taken  in  lower  than  the 
temperature  of  the  engine-room.  The  inlet  conduit  should  have  an  area 
at  least  50%  of  the  area  of  the  air-piston,  and  should  be  made  of  wood, 
brick,  or  other  non-conductor  of  heat. 

Discharge  of  a  compressor  having  an  intake  capacity  of  1000  cubic  feet 
per  minute,  and  volumes  of  the  discharge  reduced  to  cubic  feet  at  atmos- 
pheric pressure  and  at  temperature  of  62  degrees  Fahrenheit: 
Temperature  of  Intake,  F.  ...     0°      32°      62°     75°    80°    90°   100°  110° 
V"Jume  discharged,  cubic  ft.  U35  1060    1000    975    966    949    932    910 


648 


AIR. 


Compressed-Air  Motors  with  a  Return  Air  Circuit. — In  the  ordinary 
use  of  motors,  such  as  rock-drills,  the  air,  after  doing  its  work  in  the 
motor,  is  allowed  to  escape  into  the  atmosphere.  In  some  systems, 
however,  notably  in  the  electric  air-drill,  the  air  exhausted  from  the 
cylinder  of  the  motor  is  returned  to  the  air  compressor.  A  marked 
increase  in  economy  is  claimed  to  have  been  effected  in  this  way  (Cass. 
Mag.,  1907). 

Intercoolers  for  Air  Compressors. — H.  V.  Haight  (Am.  Mach., 
Aug.  30,  1906).  In  multi-stage  air  compressors,  the  efficiency  is  greater 
the  more  nearly  the  temperature  of  the  air  leaving  the  intercooler  ap- 
proaches that  of  the  water  entering  it.  The  difference  of  these  tem- 
peratures for  given  temperatures  of  the  entering  water  and  air  is 
diminished  by  increasing  the  surface  of  the  intercooler  and  thereby 
decreasing  the  ratio  of  the  quantity  of  air  cooled  to  the  area  of  cooling 
surface.  Numerous  tests  of  intercoolers  with  different  ratios  of  quan- 
tity of  air  to  area  of  surface,  on  being  plotted,  approximate  to  a  straight- 
line  diagram,  from  which  the  following  figures  are  taken. 
Cu.  ft.  of  free  air  per  min.  per  sq.  ft.  of  air  cooling  surface  5  10  15 
Diff.of  temp. F°. between  water  entering  and  air  leaving  12.5°  25°  37.5° 

Centrifugal  Air  Compressors. — The  General  Electric  Company  has 
placed  on  the;  market  a  line  of  single  stage  centrifugal  air  compressors 
with  pressure  ratings  from  0.75  to  4  Ib.  per  sq.  in.,  and  capacity  from 
500  to  10,000  cu.  ft.  of  free  air  per  min.  The  compresspr  consists 
essentially  of  a  rotating  impeller  surrounded  by  a  rigid  cast-iron  casing 
and  suitable  conversion  nozzles  to  convert  velocity  of  the  air  into 
pressure.  It  is  similar  to  the  centrifugal  pump,  efficiency  depending 
entirely  upon  the  design  of  the  passages  throughout  the  machine. 

The  compressors  are  driven  by  Curtis  steam-turbines  or  by  electric 
motors  specially  designed  for  thein.  The  induction  nwtors  used  are  of 
the  squirrel-cage  type  which  do  not  permit  any  variation  in  the  speed 
and  care  must  be  taken  to  specify  a  pressure  sufficiently  high  to  coyer 
the  operating  requirements,  because  the  pressure  cannot  be  varied 
at  constant  speed  without  altering  the  design  of  the  impeller.  The 
pressure  of  the  D.  C.  motor-driven  unit  can  be  changed  by  changing 
the  speed  of  the  motor  by  means  of  the  field  rheostat. 


Standard 

Off-Standard 

Off-Standard 

Designs, 

Designs, 

Designs, 

Motor 

3450  r.p.m. 

3450  r.p.m. 

3850  r.p.m. 

Pipe 

Rating 
H.P. 

Lb. 

Cu.  Ft. 

Lb. 

Cu.  Ft. 

Lb. 

Cu.  Ft. 

Diam., 
Inches. 

per 

per 

per 

per 

per 

per 

Sq.  In. 

Min. 

Sq.  In. 

Min. 

Sq.  In. 

Min. 

5 

800 

0.75 

1,100 

.25 

600 

10 

10 

1,600 

0.75 

2,100 

.25 

1,300 

12 

20 

3,200 

0.75 

4,100 

.25 

2,600 

16 

30 

4,500 

0.75 

5,900 

.25 

3,800 

20 

50 

7,200 

0.75 

8,800 

.25 

6,000 

20 

75 

10,200 

0.75 

12,000 

.25 

8,700 

26 

10 

2 

750 

1.5 

1,000 

2.50 

500 

8 

20 

2 

1,600 

1.5 

2,103 

2.50 

1,200 

10 

30 

2 

2,500 

1.5 

3,300 

2.50 

1,900 

12 

50 

2 

4,200 

1.5 

5,400 

2.50 

3,300 

16 

75 

2 

6,200 

1.5 

8,000 

2.50 

5,000 

20 

30 

3.25 

1,250 

2.5 

1,800 

4.00 

900 

8 

50 

3.25 

2,400 

2.5 

3,200 

4.00 

1,900 

12 

75 

3.25 

3,800 

2.5 

5,000 

4.00 

3,000 

14 

Multi-stage  compressors  have  been  built  in  the  following  sizes: 

Cubic  feet  free  air 

per 'minute 4,500      9,000     16,000     25,000      40,000     50,000. 

Pressure,  pounds 

per  square  inch. .    6  to  35  6  to  25  8  to  25   12  to  30  12  to  30  12  to  30 
AS  in  the  case  of  centrifugal  pumps,  the  pressure  depends  upon  the 


HIGH  PRESSURE   CENTRIFUGAL  FANS.  649 

peripheral  velocity  of  the  impeller.  The  volume  of  free  air  delivered 
is  limited,  however,  by  the  capacity  of  the  driver.  It  must  never  be 
operated  without  being  piped  to  a  load  sufficient  to  restrict  the  flow  of 
air  to  the  rated  value,  otherwise  the  driver  will  become  seriously 
overloaded. 

The  power  required  to  drive  the  centrifugal  compressor  varies  ap- 
proximately with  the  volume  of  air  delivered  when  operating  at  a 
constant  speed,  between  the  limits  of  50  per  cent  and  125  per  cent  of 
the  rated  load.  This  gives  flexibility  and  economy  to  the  centrifugal 
type  where  variable  volumetric  loads  are  required. 

When  the  compressor  is  operating  as  an  exhauster  discharging  against 
atmospheric  pressure,  the  rated  pressure  P,  in  Ib.  per  sq.  in.,  must 
be  multiplied  by  14.7  and  then  divided  by  14.7  plus  P  to  obtain  the 
vacuum  in  Ibs.  per  sq.  in.  below  atmosphere.  The  rated  pressures  are 
?iven  for  an  atmospheric  pressure  of  14.7  Ib.  per  sq.  in.  and  a  tempera- 
ture of  60°  F.  When  the  compressors  are  operated  at  an  altitude,  the 
pressure  will  be  reduced  directly  in  proportion  to  the  barometric 
pressure.  For  other  temperatui  es,  the  pressures  will  be  inversely 
proportioned  to  the  absolute  temperature,  or  P  X  520 -r-  (460  +  T°). 
When  operated  on  gas  the  rated  pressure  is  to  be  corrected  by  multiply- 
ing it  by  the  relative  density  of  the  gas,  taking  air  =  1.  A  large 
number  of  machines  have  been  installed  to  operate  on  illuminating 
?as,  by-product  coke  oven  gas,  or  producer  gas.  Constant  suction 
governors  controlling  the  speed  of  the  turbine  drivers  are  employed 
where  close  control  of  the  suction  head  is  desired,  as  in  the  case  of  gas 
exhausters. 

Ten  large  machines  (2000  to  5000  H.P.)  for  blowing  blast  furnaces 
have  also  been  installed.  These  have  steam  turbines  for  drivers  and 
are  controlled  by  constant  volume  governors,  giving  a  constant  speed, 
so  that  a  definite  volume  of  air  per  minute  is  delivered,  regardless  of 
the  resistance  of  the  furnace. 

High-Pressure  Centrifugal  Fans.  —  (A.  Rateau,  Engg.,  Aug.  16, 1907.) 
In  1900,  a  single  wheel  fan  driven  by  a  steam  turbine  at  20,200  revs,  per 
min.  gave  an  air  pressure  of  81/4  IDS.  per  sq.  in.;  an  output  of  26.7  cu.  ft. 
free  air  per  second;  useful  work  in  H.P.  adiabatic  compression,  45.5; 
theoretical  work  in  H.P.  of  steam-flow,  162;  efficiency  of  the  set,  fan  and 
turbine,  28%.  An  efficiency  of  30.7%  was  obtained  with  an  output  of 
23  cu.  ft.  per  sec.  and  132  theoretical  H.P.  of  steam.  The  pressure 
obtained  with  a  fan  is  —  all  things  being  equal  —  proportional  to  the 
specific  weight  of  the  gas  which  flows  through  it ;  therefore,  if,  instead  of 
air  at  atmospheric  pressure,  air,  the  pressure  of  which  has  already  been 
raised,  or  a  gas  of  higher  density,  such  as  carbonic  acid,  be  used,  com- 
paratively higher  pressures  still  will  be  obtained,  or  the  engine  can.  run  at 
lower  speeds  for  the  same  increase  of  pressure. 

Multiple  Wheel  Fans.  —  The  apparatus  having  a  single  impeller  gives 
satisfaction  only  when  the  duty  and  speed  are  sufficiently  high.  The 
speed  is  limited  by  the  resistance  of  the  metal  of  which  the  impeller  is 
made,  and  also  by  the  speed  of  the  motor  driving  the  fan.  But  by  con- 
necting several  fans  in  series,  as  is  done  with  high-lift  centrifugal  pumps, 
it  is  possible  to  obtain  as  high  a  pressure  as  may  be  desired. 

Turbo-Compressor,  Bethune  Mines,  1906.  —  This  machine  compresses  air 
to  6  and  7  atmospheres  by  utilizing  the  exhaust  steam  from  the  winding- 
engines.  It  consists  of  four  sets  of  multi-cellular  fans  through  which  the 
air  flows  in  succession.  They  are  fitted  on  two  parallel  shafts,  and  each 
shaft  is  driven  by  a  low-pressure  turbine.  A  high-pressure  turbine  is 
also  mounted  on  one  of  the  shafts,  but  supplies  no  work  in  ordinary  times. 
An  automatic  device  divides  the  load  equally  between  the  two  shafts. 
Between  the  two  compressors  are  fitted  refrigerators,  in  which  cold  water 
is  made  to  circulate  by  the  action  of  a  small  centrifugal  pump  keyed  at 
the  end  of  the  shaft.  In  tests  at  a  speed  of  5000  r.p.m.,  the  volume  of 
air  drawn  per  second  was  31.7  cu.  ft.  and  the  discharge  pressure  119.5  Ib. 
per  sq.  in.  absolute.  These  conditions  of  working  correspond  to  an  effect- 
ive work  in  isothermal  compression  of  252  H.P.  The  efficiency  of  the 
compressor  has  been  as  high  as  70%.  The  results  of  two  tests  of  the 
compressor  are  given  below.  In  the  first  test  the  air  discharged,  reduced 
to  atmospheric  pressure,  was  26  cu.  Ct.  per  sec.;  in  the  second  test  it  was 
46  cu,  *W 


650 

FIRST  TEST. 

Stages.  1st.        2d.  3d.  4th. 

Abs.  pressure  at  inlet,  Ibs.  per  sq.  in.  ...     15.18  23.37  38.69       66.44 

Abs.  pressure  at  discharge    24 . 10  39 . 98  66 . 44  102 . 60 

Speed,  revs,  per  min 4660  4660  4660  4660 

Temperature  of  air  at  inlet,  deg.  F.    ...  57.2  67.8  63.  66. 

Temperature  of  air  at  discharge,  deg.  F.  171.  205.  216.  215.6 

Adiabatic  rise  in  temp.,  deg.  F 106.  122.  114.8  105.8 

Actual  rise  in  temperature;  deg.  F.     ...  113.8  137.2  153.  149.6 

Efficiency,  per  cent    60.5  60.5  54.  46.2 

SECOND  TEST. 

Stages.  1st.         2d.         3d.  4th. 

Abs.  pressure  at  inlet,  Ibs.  per  sq.  in 15.18  21.31  37.33  65.12 

Abs.  pressure  at  discharge    23.52  38 .  22     65 . 1 2  99 . 66 

Speed,  revs,  per  min 5000  5000       4840  4840 

Temp,  of  air  at  inlet,  deg.  F 55 .  69 . 8       64 . 4  68 . 5 

Temp,  of  air  at  discharge,  deg.  F 160.7  208.4  208.4  199.6 

Adiabatic  rise  in  temp.,  deg.  F 102.2  131.  123.8  100.4 

Efficiency,  per  cent    62.3  66.6       58.7  48.6 

The  Gutehoffnungshiitte  Co.  in  Germany  have  m  course  of  construc- 
tion several  centrifugal  blowing-machines  to  be  driven  by  an  electric 
motor,  and  up  to  2000  H.P.  Several  machines  are  now  being  designed 
for  Bessemer  converters,  some  of  which  will  develop  urj  to  4000  H.P. 
The  multicellular  centrifugal  compressors  are  identical  in  every  point 
with  centrifugal  pumps.  In  the  new  machines  cooling  water  is  intro- 
duced inside  the  diaphragms,  which  are  built  hollow  for  this  purpose, 
and  also  inside  the  diffuser  vanes.  By  this  means  it  is  hoped  to  reduce 
proportionally  the  heating  of  the  air:  thus  approaching  isothermal  com- 
pression much  more  nearly  than  is  done  in  the  case  of  reciprocating 
compressors. 

Test  of  a  Hydraulic  Air  Compressor.  —  (W.  O.  Webber,  Trans. 
A.  S.  M.  E.,  xxii,  599.)  The  compressor  embodies  the  principles  of 
the  old  trompe  used  in  connection  with  the  Catalan  forges  some  centuries 
ago,  modified  according  to  principles  first  described  by  J.  P.  Frizell,  in 
Jour.  F.  /.,  Sept.,  1880,  and  improved  by  Charles  H.  Taylor,  of  Montreal. 
(Patent  July  23,  1895.)  It  consists  principally  of  a  down-flow  passage 
having  an  enlarged  chamber  at  the  bottom  and  an  enlarged  tank  at 
the  top.  A  series  of  small  air  pipes  project  into  the  mouth  of  the  water 
inlet  and  the  large  chamber  at  the  upper  end  of  the  vertically  descending 
passage,  so  as  to  cause  a  number  of  small  jets  of  air  to  be  entrained  by  the 
water.  At  the  lower  end  of  the  apparatus,  deflector  plates  in  connection 
with  a  gradually  enlarging  section  of  the  lower  end  of  the  down-flow  pipe 
are  used  to  decrease  the  velocity  of  the  air  and  water,  and  cause  a  partial 
separation  to  take  place.  The  deflector  plates  change  the  direction  of 
the  flow  of  the  water  and  are  intended  to  facilitate  the  escape  of  the  air, 
the  water  then  passing  out  at  the  bottom  of  the  enlarged  chamber  into  an 
ascending  shaft,  maintaining  upon  the  air  a  pressure  due  to  the  height  of 
the  water  in  the  uptake,  the  compressed  air  being  led  on  from  the  top 
of  the  enlarged  chamber  by  means  of  a  pipe.  The  general  dimensions  of 
the  compressor  plant  are: 

Supply  penstock,  60  ins.  diam.;  supply  tank  at  top,  8  ft.  diam.  X  10  ft. 
high;  air  inlets  (feeding  numerous  small  tubes),  34  2-in.  pipes;  down  tube, 
44  ins.  diam.:  down  tube,  at  lower  end,  60  ins.  diam.;  length  of  taper  in 
down  tube,  20  ft.;  air  chamber  in  lower  end  of  shaft,  16  ft.  diam.;  total 
depth  of  shaft  below  normal  level  of  head  water,  about  150ft.;  normal 
head  and  fall,  about  22  ft.;  air  discharge  pipe,  7  ins.  diam. 

It  is  used  to  supply  power  to  engines  for  operating  the  printing  depart- 
ment of  the  Dominion  Cotton  Mills,  Magog,  P.  Q.,  Canada. 

There  were  three  series  of  tests,  viz.:  (1)  Three  tests  at  different  rates 
of  flow  of  water,  the  compressor  being  as  originally  constructed.  (2)  Four 
tests  at  different  rates  of  flow  of  water,  the  compressor  inlet  tubes  for  air 
being  increased  by  30  3/4-in.  pipes.  (3)  Four  tests  at  different  rates  of 
flow  of  water,  the  compressor  inlet  tubes  for  air  being  increased  by  153/4-m. 
pipes. 


HYDRAULIC   AIR  COMPRESSION. 


651 


The  water  used  was  measured  by  a  weir,  and  the  compressed  air  by  air 
meters.  The  table  on  p.  623  shows  the  principal  results: 

Test  1,  when  the  flow  was  about  3800  cu.  ft.  per  min.,  showed  a  decided 
advantage  by  the  use  of  30  3/4_in.  extra  air  inlet  pipes.  Test  5  shows, 
when  the  flow  of  water  is  about  4200  cu.  ft.  per  mm.,  that  the  economy 
is  highest  when  only  15  extra  air  tubes  are  employed.  Tests  8  and  9  show, 
when  the  flow  is  about  4600  cu.  ft.  per  min.,  that  there  is  no  advantage  in 
increasing  the  air-inlet  area.  Tests  10  and  11  show  that  a  flow  of  5000 
or  more  cu.  ft.  of  water  is  in  excess  of  the  capacity  of  the  plant.  These 
four  tests  may  be  summarized  as  follows: 

The  tests  show:  (1)  That  the  most  economic  rate  of  flow  of  water  with 
this  particular  installation  is  about  4300  cu.  ft.  per  min.  (2)  That  this 
plant  has  shown  an  efficiency  of  70.7  %  under  such  a  flow,  which  is  ex- 
cellent for  a  first  installation.  (3)  That  the  compressed  air  contains  only 
from  30  to  20%  as  much  moisture  as  does  the  atmosphere.  (4)  That  the 
air  is  compressed  at  the  temperature  of  the  water. 

Using  an  old  Corliss  engine  without  any  changes  in  the  valve  gear 
as  a  motor  there  was  recovered  81  H.P.  This  would  represent  a  total 
efficiency  of  work  recovered  from  the  falling  water,  of  51.2%.  When 
the  compressed  air  was  preheated  to  267°  F.  before  being  used  in  the 
engine,  111  H.P.  was  recovered,  using  115  Ibs.  coke  per  hour,  which  would 
equal  about  23  H.P.  The  efficiency  of  work  recovered  from  the  falling 
water  and  the  fuel  burned  would  be,  therefore,  about  61 1/2% .  On  the  basis 


of  Prof.  Riedler's  experiments,  which  require  only  about  425  cu.  ft.  of  air 
per  B.H.P.  per  hour,  when  preheated  to  300°  F.  and  used  in  a  hot-air 
jacketed  cylinder,  the  total  efficiency  secured  would  have  been  about 

871/2%. 

Test  No            

1 

3 

4 

5 

7 

8 

10 

Flow  of  water,  cu.  ft.  per  min..  . 
Available  head  in  ft.               .  .  . 

3772 
20.54 
146.3 

864 
51.9 

83.3 
56.8 
68.3 

66 
4.37 

61 
51.5 

3628 
20.00 
136.9 

901 
53.7 

88.2 
64.4 
57.7 

65.5 
4.03 

77.5 
44 

4066 
20.35 
156.2 

967 
53.2 

94.3 
60,3 
66.4 

66.4 
4.20 

7! 

38.5 

4292 
19.51 
158.1 

1148 
53.3 

111.74 
70.7 
65.2 

66.5 
3.74 

68 
35 

4408 
19.93 
165.8 

1091 
53.7 

107 
64.5 
59.7 

67 

4.04 

90 

29 

4700 
19.31 
171.4 

1103 
52.9 

r06.8 
62.2 
65 

66.5 
4.26 

60.5 
31.2 

5058 
18.75 
179.1 

1165 
53.3 

113.4 
63.3 
64.2 

66 
4.34 

63 
30 

Gross  water,  H.P  

Cu.  ft.  air,  at  atmos.  press.,  per 
minute    

Pressure  of  air  at  comp.,  Ibs  
Effective  work  in  compressing, 
H.P  

Efficiency  of  compressor,  %  
Temp,  of  external  air,  deg.  F..  .  . 
Temp,  of  water  and  comp.  air, 
deg.  F  

Ratio  of  water  to  air,  volumes... 
Moisture  in  external  air,  p.  c.  of 
saturation  ,  

Moisture  in  comp.  air,  p.  c.  of 
saturation  

Tests  1,  4,  and  7  were  made  with  the  original  air  inlets;  2,  5,  8  and  10 
with  the  inlets  increased  by  153/4-in.  pipes,  and  3,  6,  9  and  11  with  the 
inlets  increased  by  303/4-in.  pipes.  Tests  2,  6,9  and  11  are  omitted  here. 
They  gave,  respectively,  55.5,  61.3,  62,  and  55.4%  efficiency. 

Three  other  hydraulic  air-compressor  plants  are  mentioned  in  Mr. 
Webber's  paper,  some  of  the  principal  data  of  which  are  given  below: 


Peterboro,  Norwich, 

Ont.  Conn. 

Head  of  water 14ft.  18^  ft. 

Gauge  pressure 25  Ibs.  85  Ibs. 

Diam.  of  shaft 42  in.  24  ft. 

Diam.  of  compressor  pipe 18  ft.  13  ft. 

Depth  below  tailrace 64  ft.  215  ft. 

Horse-power 1365 


Cascade 
Range, 
Wash. 

45  ft. 

85  Ibs. 

3  ft. 
200 


In  the  Cascade  Range  plant  there  is  no  shaft,  as  the  apparatus  is  con- 
structed against  the  vertical  walls  of  a  canyon.  The  diameter  of  tne  up- 
flow  pipe  is  4  ft.  9  in. 


652  AIR. 

A  description  of  the  Norwich  plant  is  given  by  J.  Herbert  Shedd  In  a 
paper  read  before  the  New  England  Water  Works  Assn.,  1905  (Compressed 
Air,  April,  1906).  The  shaft,  24  ft.  diam.,  is  enlarged  at  the  bottom  into 
a  chamber  52  ft.  diam.,  from  which  leads  an  air  reservoir  100  ft.  long,  18  ft. 
wide  and  15  to  20  ft.  high.  Suspended  in  the  shaft  is  a  downflow  pipe 
14  ft.  diam.  connected  at  the  top  with  a  head  tank,  and  at  the  bottom  with 
the  air-chamber,  from  which  a  16-in.  main  conveys  the  air  four  miles  to 
Norwich,  where  it  is  used  in  engines  in  several  establishments. 

The  Mekarski  Compressed-air  Tramway  at  Berne,  Switzerland. 
(Eng'q  News,  April  20,  1893.) — The  Mekarski  system  has  been  intro- 
duced in  Berne,  Switzerland,  on  a  line  about  two  miles  long,  with  grades 
of  0.25%  to  3.7%  and  5.2%.  The  air  is  heated  by  passing  it  through 
superheated  water  at  330°  F.  It  thus  becomes  saturated  with  steam, 
which  subsequently  partly  condenses,  its  latent  heat  being  absorbed  by 
the  expanding  air.  The  pressure  in  the  car  reservoirs  is  440  Ib.  per  sq.  in. 

The  engine  is  constructed  like  an  ordinary  steam  tramway  locomotive, 
and  drives  two  coupled  axles,  the  wheel-base  being  5.2  ft.  It  has  a 
pair  of  outside  horizontal  cylinders,  5.1  X  8.6  in.;  four  coupled  wheels, 
27.5  in.  diameter.  The  total  weight  of  the  car,  including  compressed 
air,  is  7.25  tons,  and  with  30  passengers,  including  the  driver  and 
conductor,  about  9:5  tons.  The  authorized  speed  is  about  7  miles 
per  hour. 

The  aisad vantages  of  this  system  consist  in  the  extremely  delicate  adjust- 
ment of  the  different  parts  of  the  system,  in  the  comparatively  small 
supply  of  air  carried  by  oie  motor  car,  which  necessitates  the  ear  return- 
ing to  the  depot  for  refilling  after  a  run  of  only  four  miles  or  40  minutes, 
although  on  the  Nogent  and  Paris  lines  the  cars,  which  are,  moreover, 
larger,  and  carry  outside  passengers  on  the  top,  run  seven  miles,  and  the 
loading  pressure  is  547  Ib.  per  sq.  in.  as  against  only  440  Ib.  at  Berne. 

For  description  of  the  Mekarski  system  as  used  at  Nantes,  Franco,  see 
paper  by  Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  xix.  553. 

American  Experiments  on  Compressed  Air  for  Street  Railways. 
—  Experiments  have  been  made  in  Washington,  D.  C.,  and  in  New  York 
City  on  the  use  of  compressed  air  for  street-railway  traction.  The  air 
was  compressed  to  2000  Ib.  per  sq.  in.  and  passed  through  a  reducing- 
valve  and  a  heater  before  being  admitted  to  the  engine.  The  system  has 
since  been  abandoned.  For  an  extended  discussion  of  the  relative  merits 
of  compressed  air  and  electric  traction,  with  an  account  of  a  test  of  a 
four-stage  compressor  giving  a  pressure  of  2500  Ib.  per  sq.  in.,  see  Eng'g 
News,  Oct.  7  and  Nov.  4,  1897.  A  summarized  statement  of  the  probable 
efficiency  of  compressed-air  traction  is  given  as  follows:  Efficiency  of  com- 
pression to  2000  Ib.  per  sq.  in.  65%.  By  wire-drawing  to  100  Ibs.  57.5% 
of  theavailable  energy  of  the  air  will  be  lost,  leaving  65  X  0.425  =  27.625% 
as  the  net  efficiency  of  the  air.  This  may  be  doubled  by  heating,  making 
55.25%,  and  if  the  motor  has  an  efficiency  of  80%  the  net  efficiency  of 
traction  by  compressed  air  will  be  55.25  X  0.80  =  44.2%.  For  a  descrip- 
tion of  the  Hardie  compressed-air  locomotive,  designed  for  street-railway 
work,  see  Eng'g  News,  June  24,  1897.  For  use  of  compressed  air  in  mine 
haulage,  see  Eng'g  News,  Feb.  10,  1898. 

Operation  of  Mine  Pumps  by  Compressed  Air.  —  The  advantages 
of  compressed  air  over  steam  for  the  operation  of  mine  pumps  are:  Absence 
of  condensation  and  radiation  losses  in  pipe  lines;  high  efficiency  of  com- 
pressed-air transmission;  ease  of  disposal  of  exhaust;  absence  of  danger 
from  broken  pipes.  The  disadvantage  is  that,  at  a  given  initial  pressure 
without  reheating,  a  cylinder  full  of  air  develops  less  power  than  steam. 
The  power  end  of  the  pump  should  be  designed  for  the  use  of  air,  with 
low  clearances  and  with  proper  proportions  of  air  and  water  ends,  with 
regard  to  the  head  under  which  the  pump  is  to  operate.  Wm.  Cox  (Comp. 
Air  Mag.,  Feb.,  1899)  states  the  relations  of  simple  or  single-cylinder 
pumps  to  be  A/W  =  Vzh/p,  where  A  =  area  of  air  cylinder,  sq.  in.,  W 
=  area  of  water  cylinder,  sq.  in.,  h  =  head,  ft.,  and  p  =  air  pressure,  Ib. 
per  sq.  in.  Mr.  Cox  gives  the  volume  V  of  free  air  in  cu.  ft.  per  minute 
to  operate  a  direct-acting,  single-cylinder  pump,  working  without  cut  off, 
to  be 

V  =  0.093  W2hG/P. 

Where  W2  =  volume  of  1  cu.  ft.  of  free  air  corresponding:  to  1  cu.  ft.  of 
free  air  at  pressure  P,  G  =>  gallons  of  water  to  be  raised  per  minute,  P  => 


FANS  AND   BLOWERS.  653 

receiver-gauge  pressure  of  air  to  be  used,  and  h  =  head  in  feet  under 
which  pump  works.  This  formula  is  based  on  a  piston  speed  of  100  ft. 
per  minute  arid  15%  has  been  added  to  the  volume  ot  air  to  cover  losses. 
The  useful  work  done  in  a  pump  using  air  at  full  pressure  is  greater  at 
low  pressures  than  at  high,  and  the  efficiency  is  increased.  High  pressures 
are  not  so  economical  for  simple  pumps  as  low  pressures.  As  high-pressure 
air  is  required  for  drills,  etc.,  and  as  the  air  for  pumps  is  drawn  from  the 
same  main,  the  air  must  either  be  wire-drawn  into  the  pumps,  or  a  reducing 
valve  be  inserted  between  the  pump  and  main.  Wire-drawing  causes  a 
low  efficiency  in  the  pump.  If  a  reducing  valve  is  used,  the  increase  of 
volume  will  be  accompanied  with  a  drop  in  temperature,  so  that  the  full 
value  of  the  increase  is  not  realized.  Part  of  the  lost  heat  may  be  regained 
by  friction,  and  from  external  sources.  The  efficiency  of  the  system  may 
be  increased  by  the  use  of  underground  receivers  for  the  expanded  air 
before  it  passes  to  the  pump.  If  the  receiver  be  of  ample  size,  the  air 
will  regain  nearly  its  normal  temperature,  the  entrained  moisture  will  be 
deposited  and  freezing  troubles  avoided.  By  compounding  the  pumps, 
the  efficiency  may  be  increased  to  about  25  per  cent.  In  simple  purnps  it 
ranges  from  7  to  16  per  cent:  For  much  further  information  on  this  sub- 
ject see  Peele's  "  Compressed- Air  Plant  for  Mines,"  1908. 

FANS  AND  BLOWEES. 

Centrifugal  Fans. — The  ordinary  centrifugal  fan  consists  of  a  number 
of  blades  fixed  to  arms  revolving  at  high  speed.  The  width  of  the  blade 
is  parallel  to  the  shaft.  The  experiments  of  W.  Buckle  (Proc.  Inst.  M.  E., 
1847)  are  often  quoted  as  still  standard.  Mr.  Buckle's  conclusions, how- 
ever, do  not  agree  with  those  of  modern  experimenters,  nor  do  the  propor- 
tions of  fans  as  determined  by  him  have  any  similarity  to  those  of  modern 
fans.  The  experiments  were  made  on  fans  of  the  "  paddle-wheel" 
type,  and  have  no  bearing  on  the  more  modern  multiblade  fans  of  the 
"  Sirocco  "  type. 

The  rules  laid  down  by  Buckle  do  not  give  a  fan  the  highest  volu- 
metric efficiency  without  loss  of  mechanical  efficiency.  By  volumetric 
efficiency  is  meant  the  ratio  of  the  volume  of  air  delivered  per  revo- 
lution to  the  cubical  contents  of  the  wheel,  if  the  wheel  be  considered 
a  solid  whose  dimensions  are  those  of  the  wheel.  Inasmuch  as  the 
loss  due  to  friction  of  the  air  entering  the  fan  will  be  less  with  a  large 
inlet  than  with  a  small  one,  in  a  wheel  of  given  diameter,  more  power 
will  be  consumed  in  delivering  a  given  volume  of  air  with  a  small 
inlet  than  with  a  larger  one. 

In  the  ordinary  fan  the  number  of  blades  varies  from  4  to  8,  while 
with  multiblade  fans  it  is  from  48  to  64.  The  number  of  blades  has 
a  direct  relation  to  the  size  of  the  inlet.  This  is  made  as  large  as 
possible  for  the  reason  given  above.  Any  increase  in  the  diameter 
of  the  inlet  necessarily  decreases  the  depth  of  the  blade,  thus  di- 
minishing the  capacity  and  pressure.  To  overcome  this  decrease, 
the  number  of  blades  is  increased  to  the  limit  placed  by  construc- 
tional considerati9ns.  A  properly  proportioned  fan  is  one  in  which 
a  balance  is  obtained  between  these  two  features  of  maximum  inlet 
and  maximum  number  of  blades. 

In  some  cases  two  fans  mounted  on  one  shaft  may  be  more  useful  than 
a  single  wide  one,  as  in  such  an  arrangement -twice  the  area  of  inlet  opening 
is  obtained,  as  compared  with  a  single  wide  fan.  Such  an  arrangement 
may  be  adopted  where  occasionally  half  the  full  quantity  of  air  is  required, 
as  one  of  the  fans  may  be  put  out  of  gear  and  thus  save  power. 

Rules  for  Fan  Design.  —  It  is  impossible  to  give  any  general  rules 
or  formulse  covering  the  proportions  of  parts  of  fans  and  blowers.  There 
are  no  less  than  14  variables  involved  in  the  construction  and  operation  of 
fans,  a  slight  change  in  any  one  producing  wide  variations  in  the  perform- 
ance. The  design  of  a  new  fan  by  manufacturers  is  largely  a  matter  of 
trial  and  error,  based  on  experiments,  until  a  compromise  with  all  the 
variables  is  obtained  which  most  nearly  conforms  to  the  given  conditions. 

Pressure  Due  to  Velocity  of  the  Fan  Blades. — The  pressure  of  the 
air  due  to  the  velocity  of  the  fan  blades  .may  be  determined  by  the  formula 

<y2 

H  =  — '  deduced  from  the  law  of  falling  bodies,  in  which  H  is  the  "  head  " 
or  height  of  a  homogeneous  column  of  air  one  inch  square  whose  weight  is 


654 


AIR. 


equai  to  the  pressure  per  square  inch  of  the  air  leaving  the  fan,  v  is  the 
velocity  of  the  air  leaving  the  fan  in  feet  per  second,  and  g  the  acceleration 


,       .      , 

-*•  2  g,  the  formula  according  to  him  being  H  =  v2  -*-  g  See  also  Trow- 
bridge  (Trans.  A.  S.  M.  E.,  vii.,  536).  This  law  is  analogous  to  that  of 
the  pressure  of  a  fluid  jet  striking  a  plane  surface  perpendicularly  and 
escaping  at  right  angles  to  its  original  path,  this  pressure  beins:  twice  that 
due  the  height  calculated  from  the  formula  h  =  v2  -s-  2  g.  (See  HawksTey, 
Proc.  Inst.  M.  E.,  1882.)  Buckle  says:  "  From  the  experiments 
it  appears  that  the  velocity  of  the  tips  of  the  fan  is  equal  to  nine- 
tenths  of  the  velocity  a  body  would  acquire  in  falling  the  height  of  a 
homogeneous  column  of  air  equivalent  to  the  density." 

To  convert  the  head  H  expressed  in  feet  to  pressure  in  Ib.  per  sq.  in. 
multiply  it  by  the  weight  of  a  cubic  foot  of  air  at  the  pressure  and  tem- 
perature of  the  air  expelled  from  the  fan  (about  0.08  Ib.  usually) 
and  divide  by  144.  Multiply  this  by  16  to  obtain  pressure  in  ounces 
per  sq.  in.  or  by  2.035  to  obtain  inches  of  mercury,  or  by  27.71  to 
obtain  pressure  in  inches  of  water_column.  Taking  0.08  as  the  weight 
of  1  cu.  ft.  of  air,  and  v  =0.9  ^YgH, 

=0.00001066  v2;  v  =310  ^p_  nearly; 
=0.0001706  v*;    v  =  80  ^p\      " 
=0.00002169  v-;  v  =220  Vp2      « 
=0.0002954  v2;    v  =   60  ^ps      " 
in  which  v  =  velocity  of  tips  of  blades  in  feet  per  second. 

Testing  the  above  formula  by  one  of  Buckle's  experiments  with  a 
vane  14  inches  long,  we  have  p  =0.00001066  v2  =9.56  oz.  The  experi- 
ment gave  9.4  oz. 

Taking  the  formula  v  =80  v^,  we  have  for  different  pressures  in 
ounces  per  square  inch  the  following  velocities  of  the  tips  of  the  blades 
in  feet  per  second: 

Pi  =  ounces  per  square  inch  2  3  4  5  6  7  8  10  12  14 
v  =feet  per  second  ______  113  139  160  179  196  212  226  253  277  299 

Commenting  on  the  statements  and  formulae  given  above,  the 
B.  F.  Sturtevant  Co.,  in  a  letter  to  the  author,  says:  "  Let  us  assume 
that  the  fan  considered  is  of  the  centrifugal  type,  which  is  a  wheel 
in  a  spiral  casing.  In  any  case  of  centrifugal  fan  the  pressure  at  the 


p  Ib.  per  sq.  in. 
pi  ounces  per  sq.  in. 
P2  inches  of  mercury 
ps  inches  of  water 


Straight-  /Forward  Backward 

FIG.  146.    TYPES  OF  FAN  BLOWERS. 

fan  outlet  is  wholly  dependent  upon  the  load  on  the  fan,  and,  there- 
fore, the  pressure  cannot  well  be  expressed  by  a  formula,  unless  it 
includes  some  term  which  is  an  expression  in  some  way  of  the  load 
upon  the  fan.  The  actual  pressure  depends  upon  the  design  of  both 
wheel  and  housing,  upon  the  blade  area  and  also  upon  the  form  of  the 
blades.  With  a  curved  blade  running  with  the  concave  side  forward 
it  is  possible  to  obtain  a  much  higher  pressure  than  if  the  blade  is  run- 
ning with  the  convex  side  forward.  This  can  only  be  shown  by  tests, 
and  can  be  figured  out  by  blade-velocity  diagrams." 

It  should  be  noted,  however,  that  while  the  fan  with  a  blade  con- 
caved in  the  direction  of  rotation  has  the  highest  efficiency,  all  other 


PRESSURE  CHARACTERISTICS  OF  FANS.     655* 

things  being  equal,  the  noise  of  operation  is  increased.  A  blade  con- 
vex in  the  direction  of  retain  runs  more  quietly,  and  in  most  situa- 
tions it  is  necessary  to  sacrifice  efficiency  in  order  to  obtain  quiet 
operation. 

Fig.  146  shows  the  relation  of  the  velocity  of  air  leaving  a  fan  to 
the  velocity  of  the  tips  of  the  blades  for  radial,  bent  forward,  and 
bent  backward  blades.  V  represents  the  direction  and  amount  of 
the  velocity  relative  to  the  blade  as  the  air  leaves  the  blade,  U  the 
tangential  velocity  of  the  tip  of  the  blade,  and  R  the  component  of 
U  and  V,  the  velocity  of  the  air  relative  to  the  fan  casing. 

The  kinetic  energy  of  the  air  due  to  its  velocity  as  it  leaves  the 
blades  is  partially  converted  into  pressure  energy  as  the  velocity 
is  reduced  in  the  expanding  scroll  casing  of  the  fan,  and  in  the 
diverging  outlet  of  the  fan  if  such  an  outlet  is  used.  The  total  or 
dynamic  pressure  is  the  sum  of  the  static  pressure  and  the  velocity 
pressure. 

QUANTITY  OF  Am  OF  A  GIVEN  DENSITY  DELIVERED  BY  A  FAN. 

Total  area  of  nozzles  in  square  feet  X  velocity  in  feet  per  minute  corre- 
sponding to  density  (see  table)  =  air  delivered  in  cubic  feet  per  minute, 
discharging  freely  into  the  atmosphere  (approximate).  See  p.  670. 


Density, 

Velocity, 

Density, 

Velocity, 

Density, 

Velocity, 

ounces 

feet.  per 

ounces 

feet  per 

ounces 

feet  per 

per  sq.  in. 

minute. 

per  sq.  in. 

minute. 

per  sq.  in. 

minute. 

1 

5,000 

5 

11,000 

9 

15,000 

2 

7,000 

6 

12,250 

10 

15,800 

3 

8,600 

7 

13,200 

11 

16,500 

4 

10,000 

8 

14,150 

12 

17,300 

M  Blast  Area,"  or  "  Capacity  Area."  When  the  fan  outlet  is  small 
the  velocity  of  the  outflow  is  equal  to  the  peripheral  velocity  of  the  fan. 

Start  with  the  outlet  closed;  then  if  the  opening  be  slowly  increased 
while  the  speed  of  the  fan  remains  constant  the  air  will  continue  to  flow 
with  the  same  velocity  as  the  fan  tips  until  a  certain  size  of  outlet  is 
reached.  If  the  outlet  is  still  further  increased  the  pressure  within  the 
casing  will  drop,  and  the  velocity  of  outflow  will  become  less  than  the 
tip  velocity.  The  size  of  the  outlet  at  which  this  change  takes  place  is 
called  the  blast  area,  or  capacity  area,  of  the  fan.  This  varies  somewhat 
with  different  types  and  makes  of  fans,  but  for  the  common  form  of 
blower  it  is  approximately,  DW  -s-  3,  in  which  D  is  the  diameter  of  the 
fan  wheel  and  W  its  width  at  the  circumference.  —  (C.  L.  Hubbard.) 

•.This  established  capacity  area  has  no  relation  to  the  area  of  the  outlet 
in  the  casing,  which  may  be  of  any  size,  but  is  usually  about  twice  the 
capacity  area.  The  velocity  of  the  air  discharged  through  this  latter 
area  is  practically  that  of  the  circumference  of  the  wheel,  and  the  pressure 
created  is  that  corresponding  thereto.  —  W.'B.  Sno_w. 

Pressure  Characteristics  of  Fans. — Figs.  147  and  148  show 
the  relation  of  the  static  and  total  pressures,  the  efficiency  and  the 
horse-power,  to  the  capacity  of  two  fans,  one  a  radial  blade  fan,  and 
the  other  a  multi-blade  (conoidal)  as  determined  by  tests  by  the 
Buffalo  Forge  Co.  In  the  test  the  fan  was  run  at  a  uniform  speed 
and  the  capacity  was  varied  by  varying  the  area  of  outlet.  The 
characteristics  of  the  two  fans  differ  greatly.  In  the  case  of  the 
radial  fan  the  highest  pressure  corresponds  to  zero  capacity,  while 
with  the  multi-blade  fan  the  static  pressure  increases  as  the  capacity 
increases  up  to  100  per  cent,  or  rated  capacity,  which  is  the  point  of 
maximum  efficiency. 

If  a  forward-curved  blade  fan  is  intended  to  operate  at  a  certain 
pressure  and  capacity,  and  if  for  any  reason,  such  as  resistance  greater 
than  expected,  the  quantity  of  air  handled  is  less  than  the  fan's 
rating  for  the  speed  maintained,  the  total  pressure  will  also  be  less 
than  that  specified.  With  the  straight-blade  fan  the  opposite  holds 
true,  for  as  the  capacity  is  reduced  the  pressure  will  increase,  at  con- 
stant speed. 

Care  should  be  taken  in  the  selection  of  a  fan  with  forward-curved 
blades  in  case  it  is  to  be  driven  by  a  motor.  If  for  any  reason  there 


056 


AIR. 


should  be  a  tendency  to  operate  above  rated  capacity,  both  the  air 
quantity  and  the  pressure  will  increase,  which  may  overload  the 
motor  in  case  sufficient  margin  of  motor  capacity  has  not  been  pro- 
vided. (Buffalo  Forge  Co.) 

For  a  given  fan  area  of  outlet,  piping  system,  and  air  density,  the 


0  20  40  60  80  100 

Per  Cent  of  Rated  Capacity 
FIG.  147.    CHARACTERISTICS  OF  A  RADIAL  BLADE  FAN. 

relations  of  volume  delivered,  pressure  at  the  fan  outlet,  speed  and 
horse-power  theoretically  vary  as  follows: 

Volume  delivered  varies  directly  as  speed  of  the  fan. 

Pressure  varies  as  the  square  of  the  speed. 

Horse-power  varies  as  the  cube  of  the  speed. 

For  a  given  volume  the  horse-power  varies  as  the  square  of  the 
speed,  showing  the  great  advantage  of  large  fans  at  slow  speeds  over 


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Per  Cent  of  Rated  Capacity 
FIG.  148.    CHARACTERISTICS  OF  A  MULTI-BLADE  FAN. 

small  fans  at  high  speeds  delivering  the  same  volume,  the  type  of  fan 
being  the  same.  The  theoretical  values  are  greatly  modified  by  vari- 
ations in  practical  conditions.  For  every  fan  running  at  constant  speed 
there  is  a  pressure  and  corresponding  volume  at  which  a  fan  will 
operate  at  its  maximum  efficiency  (see  characteristic  curves),  and  a 


FANS  AND  BLOWERS. 


C57 


wide  variation  in  these  conditions  will  give  a  great  drop  in  efficiency. 
In  selecting  a  fan  for  any  purpose  the  catalogues  and  bulletins  issued 
by  manufacturers  should  be  examined,  and  a  tabular  comparison 
made  of  the  sizes,  speed,  etc.,  of  different  fans  which  may  be  used  for 
the  given  purpose  and  conditions.  The  following  is  an  example  of 
such  a  comparison  of  three  multi-blade  fans  (Sturtevant)  which  may  be 
used  to  deliver  approximately  15,000  cu.  ft.  of  air  against  a  resistance, 
of  5  in.  of  water  column.  . 


Wheel 

Resistance,  5  in. 

Size 

R  P  M 

H  P 

Inches. 

Vol. 

R.P.M. 

H.P. 

Turbovane.. 

221/2 

15,500 

2210 

25 

Smallest 

Highest 

Medium 

Supervane.  . 
Multivane.  . 

25 
26 

15,400 
15,900 

1033 
1103 

23.5 
26 

Medium 
Largest 

Lowest 
Medium 

Lowest 
Highest 

Experiments  on  a  Fan  with  Constant  Discharge-opening  and 
Varying  Speed. — The  first  four  columns  are  given  by  Mr.  Snell,  the 
others  are  calculated  by  the  author. 


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i 

0 

13 

-is 

III 

a»    g  2 

«2  ®" 

o---ft 
13  S5 

11 

1 

£ 

w 

> 

o     *". 

t>  .. 

H 

8 

600 

0.50 

1336 

0.25 

60.2 

56.6 

85.1 

3,630 

0.182 

73 

800 

0.88 

1787 

0.70 

80.3 

75.0 

85.6 

4,856 

0.429 

61 

1000 

1.38 

2245 

1.35 

100.4 

94 

85.4 

6,100 

0.845 

63 

1200 

2.00 

2712 

2.20 

120.4 

113 

85.1 

7,370 

1.479 

67 

1400 

2.75 

3177 

3.45 

140.5 

133 

84.8 

8,633 

2.283 

66 

1600 

3.80 

3670 

5.10 

160.6 

156 

82.4 

9,973 

3.803 

74 

1800 

4.80 

4172 

8.00 

180.6 

175 

82.4 

11,337 

5.462 

68 

2000 

5.95 

4674 

11.40 

200.7 

195 

85.6 

12,701 

7.586 

67 

Mr.  Snell  has  not  found  any  practical  difference  between  the  mechanical 
efficiencies  of  blowers  with  curved  blades  and  those  with  straight  radial 
ones.  From  these  experiments,  says  Mr.  Snell,  it  appears  that  we  may 
expect  to  receive  back  65%  to  75%  of  the  power  expended,  and  no  more. 
The  great  amount  of  power  often  used  to  run  a  fan  is  not  due  to  the  fan 
itself,  but  to  the  method  of  selecting,  erecting,  and  piping  it.  (For  opin- 
ions on  the  relative  merits  of  fans  and  positive  rotary  blowers,  see  discus- 
sion of  Mr.  Snell's  paper,  Trans.  A.  S.  M.  E.,  ix.  66,  etc.) 

Comparative  Efficiency  of  Fans  and  Positive  Blowers.  (H.  M. 
Howe,  Trans.  A.  I.  M.  E.,  x.  482.)  —  Experiments  with  fans  and  positive 
(Baker)  blowers  working  at  moderately  low  pressures,  under  20  ounces, 
.show  that  they  work  more  efficiently  at  a  given  pressure  when  delivering 
large  volumes  (i.e.,  when  working  nearly  up  to  their  maximum  capacity) 
than  when  delivering  comparatively  small  volumes.  Therefore,  when 
great  variations  in  the  quantity  and"^  pressure  of  blast  required  are  liable 
to  arise,  the  highest  efficiency  would  be  obtained  by  having  a  number  of 
blowers,  always  driving  them  up  to  their  full  capacity,  ana  regulating  the 
amount  of  blast  by  altering  the  number  of  blowers  at  work,  instead  of 
having  one  or  two  very  large  blowers  and  regulating  the  amount  of  blast 
by  the  speed  of  the  blowers. 

There  appears  to  be  little  difference  between  the  efficiency  of  fans  and 
of  Baker  blowers  when  each  works  under  favorable  conditions  as  regards 
quantity  of  work,  and  when  each  is  in  good  order. 

For  a  given  speed  of  fan,  any  diminution  in  the  size  of  the  blast-orifice 
decreases  the  consumption  of  power  and  at  the  same  time  raises  the  pros- 


658 


AIR. 


sure  of  tlie  blast;  but  it  increases  the  consumption  of  power  per  unit  of 
prince  for  a  given  pressure  of  blast.  When  the  orifice  has  been  reduced  to 
the  normal  size  for  any  given  fan,  further  diminishing  it  causes  but  slight 
elevation  of  the  blast  pressure;  and,  when  the  orifice  becomes  compara- 
tively small,  further  diminishing  it  causes  no  sensible  elevation  of  the 
blast  pressure,  which  remains  practically  constant,  even  when  the  orifice  is 
entirely  closed. 

Many  of  the  failures  of  fans  have  been  due  to  too  low  speed,  to  too  small 
pulleys,  to  improper  fastening  of  belts,  or  to  the  belts  being  too  nearly  ver- 
tical; m  brief,  to  bad  mechanical  arrangement,  rather  than  to  inherent 
defects  in  the  principles  of  the  machine. 

If  several  fans  are  used,  it  is  probably  essential  to  high  efficiency  to  pro- 
vide a  separate  blast  pipe  for  each  (at  least  if  the  fans  are  of  different  size 
or  speed),  while  any  number  of  positive  blowers  may  deliver  into  the  same 
pipe  without  lowering  their  efficiency. 

The  Sturtevant  Multi-blade  Fans.— The  B.  F.  Sturteyant  Co. 
has  developed  three  styles  of  fans  with  numerous  blades  which  have 
been  given  the  trade  names  Multivane,  Supervane,  and  Turbovane. 
The  Multivane  and  Supervane  fans  are  used  for  the  same  kind  of 
service,  that  is,  mostly  for  heating,  ventilating,  and  mechanical 
draught.  For  a  given  diameter,  the  Supervane  operates  at  lower  speed 
and  requires  less  power  than  the  Multivane.  The  Turbovane  fan 
is  designed  for  high-speed  direct-connected  drives,  such  as  steam 
turbines.  It  is  a  very  wide  fan,  made  double  inlet,  and  for  a  given 
volume  and  pressure  will  be  smaller  in  diameter  and  operate  at  about 
twice  the  speed  of  the  Multivane  and  require  about  the  same  power. 
The  Turbovane  and  Supervane  fans  have  blades  considerably  deeper 
than  the  Multivane.  The  curvature  is  also  radically  different  in 
all  three  types.  The  spiral  or  housing  is  considerably  different  in  the 
three  types. 


Sturtevant  Multivane  Fan. 


Resistance  1/2  in. 

Resistance  2  in. 

Resistance  5  in. 

|ll 

s|. 

g 

£L 

% 

gsrf 

g 

«!•§ 

N 

'SnJ 

•34*  g 

PH' 

04 

o^d'S 

W 

PH 

^s's 

PH' 

PH' 

-^55 

S3 

W 

t> 

gj 

g 

^ 

gj 

w 

> 

ti 

g 

fe 

2 

21 

1,300 

705 

0.220 

2,850 

1471 

2.15 

3,980 

2205 

6.6 

13 

3 

26l'2 

2,030 

565 

0.345 

4,440 

1178 

3.3 

6,210 

1764 

10.0 

161/2 

4 

31  1/2 

2,920 

470 

0.495 

6,400 

980 

4.8 

8,940 

1471 

14.5 

191/2 

5 

37 

3,980 

404 

0.67 

8,720 

840 

6.5 

12,200 

1260 

20 

23 

6 

42 

5,200 

353 

0.88 

11,400 

735 

8.5 

15,900 

1103 

26 

26 

61/2 

47 

6,570     314 

1.10 

14,400 

654 

11.0 

20,100 

980 

33 

291/2 

7 

521/2 

8,110 

282 

1.40 

17/800 

588 

13.5 

24,800 

882 

41 

32  1/2 

8 

63 

11,700 

235 

2.00 

25,600 

490 

19 

35,800 

735 

60 

39 

9 

73V2 

15,900 

202 

2.70 

34,800 

420 

26 

48,700 

631 

80 

451/2 

10 

831/2 

20,800 

176 

3.50 

45,500 

368 

34 

63,600 

552 

105 

52 

11 

94 

26,300 

157 

4.45 

57,600 

327 

43 

80,500 

490 

135 

581/2 

12 

1041/2 

32,500 

141 

5.5 

71,000 

294 

54 

99,400 

441 

165 

65 

13 

115 

39,400 

128 

6.7 

86,100 

268  j  64 

121,000 

401 

200 

71  1/2 

14 

1251/2 

46,800 

118 

7.9 

102,000 

245    76 

143,000 

368 

235 

78 

15  . 

136 

54,800 

109 

9.3 

120,000 

226    90 

168,000 

340 

275 

841/2 

16 

1461/2 

63,500 

101 

11.0 

139,000 

210  105 

195.000 

315 

320 

91 

17 

157 

73,000 

94 

12.5 

160,000 

196  120 

224,000 

294 

370 

971/2 

18 

167 

83,100 

88 

14 

182,000 

184  135 

255,000 

276 

420 

104 

20 

188 

105,000 

78 

18 

230,000 

163  170 

322,000 

245 

530 

117 

22 

209 

130,000 

71 

22 

285,000 

147:215 

398.000 

221 

655 

130 

24 

230 

157,000 

64 

27 

344,000 

134  260 

481,000 

200 

795 

143 

26 

2501/2 

187,000 

55 

32 

410,000 

115305 

573.000 

173 

945 

156 

FANS   AND   BLOWERS. 


659' 


Sturtevant  Supervane  Fan. 


Resistance  1/2  in. 

Resistance  2  in. 

Resistance  5  in. 

°b£<»- 

7  oj 

§&  • 

g 

g  a  • 

^ 

Sft  . 

^' 

«l-2 

N 

'Soli 

-oVe 

PH 

P^ 

oV§ 

P^ 

PH 

'oVl 

P^ 

PH' 

£33 

OQ 

£ 

PJ 

W 

> 

tf 

W 

> 

PJ 

W 

^ 

A 

26 

1,470 

645 

0.235 

2,940 

1290 

1.90 

4,160 

1980 

6.4 

13 

B 

32 

2,230 

525 

0.355 

4,460 

1051 

2.90 

6,320 

1610 

9.7 

16 

C 

38 

3,150 

442 

0.50 

6,300 

885 

4.05 

8,910 

1358 

13.5 

19 

D 

44 

4,200 

382 

0.67 

8,420 

764 

5.4 

11,900 

1171 

18.0 

22 

E 

491/2 

5,450 

337 

0.87 

10,900 

673 

7.0 

15,400 

1033 

23.5 

25 

F 

55V2 

6,820 

300 

1.10 

13,600 

600 

8.8 

19,300 

921 

30 

28 

G 

631/2 

8,900 

262 

1.40 

17,800 

525 

11.5 

25,200 

805 

38 

32 

H 

73V2 

11,300 

233 

1.80 

22,600 

467 

14.5 

32,000 

716 

49 

36 

J 

791/2 

13,900 

210 

2.20 

27,800 

420 

18 

39,400 

645 

60 

40 

K 

9H/2 

18,500 

183 

2.90 

36,900 

365 

24 

52,300 

560 

80 

46 

L 

103 

23,500 

162 

3.75 

47,000 

323 

30 

66,600 

496 

100 

52 

M 

115 

29,300 

145 

4.65 

58,500 

290 

38 

83,000 

444 

125 

58 

N 

127 

35,600 

131 

5.7 

71,200 

263 

46 

101,000 

403 

155 

64 

P 

139 

42,700 

120 

6.8 

85,400 

240 

56 

121,000 

368 

185 

70 

1501/2 

50,300 

111 

8.0 

101,000 

221 

66 

143,000 

339 

220 

76 

R 

166V2 

61,400 

100 

9.8 

123,000 

200 

80 

174,000 

307 

265 

84 

S 

1821/2 

73,500 

91 

11.5 

147,000 

183 

96 

208,000 

280 

320 

92 

T 

I98V2 

86,900 

84 

14.0 

174,000 

168 

110 

246,000 

258 

375 

100 

U 

2141/2 

102,000 

78 

16.0 

204,000 

156  130" 

288,000 

239    440 

108 

V 

230 

117,000 

72 

18.5 

234,000 

145 

150 

332,000 

222    505 

116 

W 

254 

143,000 

66 

23 

285,000 

131 

185 

404,000 

202 

615 

128 

X 

2771/2 

171,000 

6027 

341,000 

120 

220 

483,000 

184 

740 

140 

Y 

301  1/2 

201,000 

5532 

401,000 

111  260 

569,000 

170 

870 

152 

Sturtevant  Turbovane  Fan. 


Resistance  1  in. 

Resistance  3  in. 

Resistance  6  in. 

o  -^ 

Too 

all 

3£d 

g 

gY. 

,a 

8£  . 

g 

•3  11 

N 

£rl£ 

J+rg 

PH' 

PH 

^c's 

pj 

PH 

'o'd's 

PH' 

PH 

j55S 

33 

W 

>. 

tf 

W 

!*_ 

PH' 

W 

>*" 

P4 

W 

^ 

40 

28 

1,670 

1958 

0.53 

2,930 

3400 

2.85 

4,010 

47oO 

7.8 

IH/2 

45 

35 

2,610 

1563 

0.83 

4,560 

2720 

4.4 

6,250 

3800 

12.0 

141/2 

50 

42 

3,770 

1300 

1.20 

6,600 

2260 

6.5 

9,050 

3161 

17.5 

17 

55 

49 

5,100 

1118 

1.65 

8,950 

1940 

8.8 

12,300 

2719 

23.5 

20' 

60 

56 

6,700 

978 

2.15 

11,700 

1700 

11.0 

16,100 

2380 

31 

221/2 

65 

63 

8,500 

868 

2.75 

14,900 

1510 

14.5 

20,400 

2115 

39 

251/2 

70 

70 

10,500 

781 

3.35 

18,300 

1358 

17.5 

25,100 

1900 

48 

281/2 

80 

84 

15,100 

651 

4.85 

26,300 

1131 

26 

36,100 

1582 

70 

34 

90 

97 

20,500 

558 

6.5 

35,800 

971 

35 

49,100 

1360 

92 

39  1/2 

100 

112 

26,800 

490 

8.5 

46,800 

851 

45 

64,000 

1192 

120 

45 

110 

126 

34,000 

435 

11.0 

59,500 

755 

58 

81,500 

1058 

155 

51 

120 

140 

41,800 

391 

13.5 

73,000 

679 

70 

101,000 

950 

190 

561/2 

130 

154 

50,500 

353 

16.5 

88,500 

617 

86 

122,000 

865 

230 

62 

140 

168 

60,500 

326 

19.5 

106,000 

566 

100 

145,000 

792 

280 

67  1/2 

150 

182 

71,000 

300 

22.5 

124,000 

521 

120 

170,000 

729 

325 

73  1/2 

160 

196 

82,000 

279 

26 

144,000 

485 

140 

197,000 

680      380 

79 

660 


AIR. 


Capacity  of  Fans  and  Blowers. — The  folio  wing  .tables  supplied  (1909) 
by  the  American  Blower  Co.,  Detroit,  show  the  capacities  of  exhaust  fans 
and  volume  and  pressure  blowers.  The  tables  are  all  based  on  curves 
established  by  experiment.  The  pressures,  volumes  and  horse-powers 
were  all  actually  measured  with  the  apparatus  working  against  maintained 
resistances  formed  by  restrictions  equivalent  to  those  found  in  actual  prac- 
tice, and  which  experience  shows  will  produce  the  best  results. 


Speed,  Capacity  and  Horse-power  of  Steel  Plate  Exhaust  Fans. 

(American  Blower  Co.,  Type  E,  1908.) 


Diameter  of 
wheel,  in. 

i 

'5 

fts 

9 

15  .g 

1/2  oz.  pres- 
sure. 

3/4  oz.  pres- 
sure. 

1  oz.  pres- 
sure. 

2  oz.  pres- 
sure. 

fc 
ft    . 

| 

b 

0) 
ft    . 

ft 

1. 

1 

ft. 

1 

^£ 

II 
w 

si 

cTC- 

5 

aj 

t«  3 

o  fl 

11 

O 

11 

P^ 
tf 

o  £ 
O 

%  1 
« 

PH 

P3 

"  C 

11 

O 

-o  % 

si 

|a 

PS 

<+"  3. 
1S 

16 
19 
22 
25 
28 
31 
34 
38 
44 
50 

61/8 
71/8 
81/8 
93/8 
107/s 
123/g 
131/2 

151/8 
161/2 

10 
12 
14 
16 
18 
20 
22 
24 
27 
29 

985 
830 

715 
630 
563 

508 
464 
415 
375 

328 

1,09 
1  580 
2,155 
2,820 
3  560 
4,400 
5,330 
6,350 
7,440 
10,050 

0.30 
0.43 
0.59 
0.77 
0.97 
1.20 
1.45 
1.73 
2.02 
2.75 

1200 
1012 
876 
772 
689 
622 
567 
509 
459 
402 

1,345 
1,940 
2,635 
3,450 
4,360 
5,390 
6,525 
7,775 
9,120 
12,100 

0.56 
0.80 
1.08 
1.41 
1.78 
2.20 
2.66 
3.18 
3.72 
4.94 

1390 
1170 
1010 
890 
795 
719 
655 
587 
530 
464 

1  555 
2,240 
3,040 
3.980 
5030 
6,220 
7,530 
8,960 
10.500 
13,980 

0.85 
1.22 
1.66 
2.17 
2.74 
3.39 
4.10 
4.89 
5.72 
7.62 

1966 
1655 
1430 
1260 
1125 
1015 
927 
830 
750 
656 

2.200 
3,175 
4,310 
5.646 
7,140 
8,820 
10,650 
12700 
14,875 
19,800 

2.40 
3.46 
4.70 
0.15 
7.79 
9.63 
11.60 
13.85 
16.20 
21.60 

Speed,  Capacity  and  Horse-power  of  Volume  Blowers. 

(American  Blower  Co.,  Type  V,  1909.) 


1/2  oz.  pres- 

3/4 oz.  pres- 

1 oz.  pres- 

1 1/2  oz.  pres- 

sure. 

sure. 

sure. 

sure. 

ft 

~.s 

(_ 

JLi 

«-, 

i> 

t_ 

"o.d 

o> 

•~    .. 

ft. 

cc 

ft. 

g 

ft. 

ft. 

» 

»_r 

^c 

*-§ 

O  j/ 

o  ^ 

^^ 

o  ^ 

•  « 

Ji  ^ 

1  * 

fi  < 

<D'S 

2e 

^ 

t>  c 

s  1 

a 

*«    § 

<u  | 

g 

Cf  g 

?£ 

JEJ 

0  C3 

2  S 

i*i 

72  £ 

PH 

"°  S 

B3    ^ 

PH 

&    g 

2  ft 

PH 

"°  S 

^ 

PH 

^a 

2  ft 

Q 

£ 

Q 

P^ 

o 

PQ 

tf 

O 

PJ 

0 

P^ 

-6 

P3 

81/2 

? 

41/o 

1850 

223 

0  06 

7.270 

273 

0  11 

2620 

315 

0.17 

3210 

386 

0.32 

101/4 

73/8 

5  1/2 

1535 

332 

0  09 

1880 

407 

0,17 

2170 

469 

0.26 

2660 

576 

0.48 

17, 

61/2 

1310 

464 

0  13 

1600 

569 

0.23 

1850 

656 

0.36 

2275 

805 

0.66 

!^1/2 

43/2 
51/8 

81/2 

1015 
830 

795 
1185 

0.22 
0  32 

1240 
1013 

975 
1450 

0.40 
0.59 

1435 
1170 

1122 
1675 

0.61 
0.92 

1760 
1435 

1377 
2055 

1.13 
1.68 

iV2 

6V2 
7l/o 

123/8 

700 
606 

1686 

7735 

0.46 
0  61 

858 
742 

2065 
2740 

0.84 
1.12 

990 
858 

2385 
3160 

1.30 
1.72 

1215 
1050 

2930 
3880 

2.40 
3.18 

291/2 

8i/2 
91/2 

161/4 
181/4 

534 
477 

2910 
3660 

0.79 
1.00 

654 
585 

3560 
4490 

1  45 
1.83 

755 
675 

4110 
5175 

2.24 
2.82 

928 
825 

5040 
6350 

4.13 
5.20 

NOTE:  This  table  also  applies  to  Type  V,  cast-iron  exhaust  fans. 


FANS   AND    BLOWERS. 


661 


Steel  Pressure  Blowers  for  Cupolas  (Average  Application). 

(American  Blower  Co.,  1909.) 


_  1  JSo.  of  blower.  | 

Dia.  of  wheel, 
in. 

Width  periph'y. 
in. 

^  £ 

P 

il 

o 

|.s 

3  cp 

°£ 

OS'S, 

Q 

53/4 

Area  of  outlet, 
sq.ft. 

Oz. 

2 

3 

4 

5 

6 

7 

8 

9 

In. 

3.46 

5.19 

6.92 

8.65 

10.38 

12.12 

13.83 

15.56 

H.P. 

const, 
at  1000 
cu.  ft. 

1.242 

1960 
361 
0.45 

1.86 

2400 
434 
0.81 

2.48 

3.10 

3095 
560 
1.74 

3.73 

4.35 

3666 
665 
2.89 

4.95 

3915 
708 
3.51 

5.58 

4150 

752 
4.20 

41,2 

3/8 

3.80 

0.18 

R.P.M. 
C.F. 
H.P. 

2770 
500 
1.24 

3390 
610 

2.28 

2895 
843 
3.15 

2 

7 

15/8 

4.45 

63/4 
73/4 

0.2485 

R.P.M. 
C.F. 
H.P. 

1675 

498 
0.62 

2050 
600 
1.12 

2362 
691 
1.72 

2645 
774 
2.40 

3130 
916 
3.99 

3340 
978 
4.84 

3540 
1038 
5.79 

3 

4 

9V2 

17/8 

5.11 

0.327 

R.P.M. 
C.F. 
H.P. 

1460 
655 
0.82 

1785 
789 
1.47 

2060 
910 
2.26 

2300 
1018 
3.16 

2520 
1110 
4.15 

2730 
1207 
5.25 

2910 
1286 
6.36 

3085 
1365 
7.62 

22 

21/8 

5.76 

83/4 

0.4176 

R.P.M. 
C.F. 
H.P. 

1292 
838 
1.04 

1582 
1006 
1.87 

1825 
1162 

2.88 

2040 
1300 
4.03 

2235 
1415 
5.28 

2420 
1540 
6.70 

2585 
1643 
8.14 

2740 
1746 
9.74 

5 

241/2 

23/8 

6.41 

93/4 

0.519 

R.P.M. 
C.F. 
H.P. 

1162 
1040 
1.30 

1422 
1250 
2.33 

1640 
1442 
3.58 

1835 
1612 
5.00 

2010 
1760 
6.57 

2175 
1915 
8.34 

2320 
2040 
10.10 

2460 
2166 
12.10 

6 

27 

27/8 

7.06 

103/4 

0.63 

R.P.M. 
C.F. 
H.P. 

1055 
1262 
1.57 

1290 
1520 
2.83 

1490 
1750 
4.34 

1665 
1960 
6.08 

1825 
2135 
7.96 

1975 
2375 
10.10 

2105 
2475 
12.25 

2233 
2630 
14,12 

7 

32 

33/8 

8.39 

121/2 

0.852 

R.P.M. 
C.F. 
H.P. 

889 
1705 
2.12 

1087 
2055 
3.83 

1255 
2366 
5.86 

1405 
2650 
8.23 

1535 
2890 
10.78 

1660 
3140 
13.66 

1775 
3350 
16.60 

1880 
3555 
19.83 

8 

37 

37/8 

9.70 

14 

1.069 

R.P.M. 
C.F. 
H.P. 

769 
2140 
2.66 

940 
2575 
4.79 

1085 
2970 
7.36 

1212 
3325 
10.3 

1328 
3620 
13.5 

1446 
3940 
17.15 

1533 
4200 
20.80 

1625 
4460 
24.90 

9 

10 

42 

43/8 

10.98 

16 

1.396 

R.P.M. 
C.F. 
H.P. 

679 
2800 
3.48 

830 
3370 
6.27 

958 
3880 
9.63 

1072 
4340 
13.46 

1172 
4730 
17.65 

1270 
5150 
22.40 

1355 
5500 
27.25 

1435 
5825 
32.50 

47 

47/8 

12.30 

171/2 

1.67 

R.P.M. 
C.F. 
H.P. 

606 
3350 
4.17 

742 
4025 
7.5 

855 
4640 
11.5 

956 
5200 
16.12 

1048 
5660 
21.12 

1133 
6160 
26.80 

1210 
6570 
32.55 

1280 
6970 
38.90 

11 
12 

52 

33/8 

13.6 

191/4 
21 

2.02 

R.P.M. 
C.F. 
H.P. 

548 
4050 
5.03 

670 
4870 
9.06 

774 
5610 
13.9 

865 
6290 
'19.5 

947 
6850 
25.55 

1025 
7450 
32.40 

1093 
7950 
39.33 

1160 
8440 
47.10 

57 

57/8 

14.92 

2.405 

R.P.M. 
C.F. 
H.P. 

500 
4820 
6.00 

611 
5800 
10.78 

705 
6700 
16.62 

789 
7490 
23.25 

863 
8160 
30.45 

934 
8870 
38.60 

996 
9460 
46.85 

1056 
10040 
56.10 

662 


AIR. 


Steel  Pressure  Blowers  for  Cupolas  (Average  Application).— 

Continued. 


to  |  No.  of  blower. 

"o3 
1 

•s-3 

cS 

Q 

>. 

Xs 

*'~ 

T3 

£ 

15/8 

o  '*"' 

«.s 

is 

.S'ft 
Q 

63/4 

Area  of  outlet, 
sq.ft. 

Oz. 

10 

17.28 

11 
19.02 

12 

13 

14 

15 

16 

In. 

20.75 

22.5 

24.22 

25.95 

27.66 

Circum 
whee 

H.P. 

const, 
at  1000 
cu.ft. 

6.20 

6.82 

7.44 

8.07 

8.69 

9.30 

9.9.. 

17 

4.45 

0.2485 

R.P.M. 
C.F. 
H.P. 

3740 
1093 
6.78 

3920 
1148 
7.83 

4090 
1196 
8.9 

3 

191/2 

17/8 

5.11 

73/4 

0.327 

R.P.M. 
C.F. 
H.P. 

3255 
1440 
8.93 

3415 
1510 
10.3 

3570 
1575 
11.72 

3710 
1642 
13.26 

3955 
1700 
14.75 

3985 
1762 
16.4 

4120 
1820 
18.05 

4 
5 

6 

22 
241/2 

2V8 

5.76 

83/4 
93/4 

0.4176 

R.P.M. 
C.F. 
H.P. 

2890 
1840 
11.40 

3030 
1930 
13.16 

3163 
2012 
14.96 

3290 
2095 
16.9 

3420 
2175 
18.9 

3535 

2250 
20.9 

3650 
2325 
23.1 

23/8 

6.41 

0.519 

R.P.M. 
C.F. 
H.P. 

2595 
2280 
14.13 

2720 
2395 
16.33 

2845 
2500 
18.6 

2960 
2605 
21.05 

3075 
2700 
23.45 

3180 
2800 
26.05 

3280 
2885 
28.66 

27 

27/8 

7.06 

103/4 

0.63 

R.P.M. 
C.F. 
H.P. 

2355 
2770 
17.18 

2470 
2910 
19.85 

2580 
3033 
22.6 

2685 
3165 
25.55 

2790 
3280 
28.50 

2885 
3395 
31.55 

2980 
3500 
34.7 

7 
8 

32 

33/8 

8.39 

121/2 

0.852 

R.P.M. 
C.F. 
H.P. 

1983 
3750 
23.25 

2080 
3930 
26.80 

2170 
4110 
30.6 

2260 
4276 
34.5 

2345 
4430 
33.  5 

2430 
4590 
42.7 

251C 
4730 
47. 

37 

37/8 

9.70 

14 

1.069 

R.P.M. 
C.F. 
H.P. 

1715 
4700 
29.15 

1800 
4930 
33.66 

1880 
5150 
38.33 

1955 
5360 
43.25 

2030 
5560 
48.30 

2100 
5760 
53.55 

2170 
5940 
59. 

9 

42 

43/8 

10.98 

16 

1.396 

R.P.M. 
C.F. 
H.P. 

1515 
6150 
38.15 

1590 
6450 
44.00 

1660 
6730 
50.15 

1728 
7010 
56.60 

1792 
7270 
63.2 

1855 
7525 
70. 

1916 
7760 
77. 

10 
11 

47 

47/8 

12.30 

171/2 

1.67 

R.P.M. 
C.F. 
H.P. 

1352 
7350 
45.60 

1418 
7715 
52.66 

1480 
8055 
60, 

1540 
8390 
67.66 

1600 
8700 
75.6 

1655 
9010 
83.9 

1710 
9300 
92.25 

52 

53/8 
57/8 

3.6 

91/4 

2.02 

R.P.M. 
C.F. 
H.P. 

1222 
8900 
55.20 

1282 
9330 
63.6 

1340 
9750 
72.5 

1393 
10140 
82. 

1447 
10520 
91.5 

1498 
10890 
101.2 

1546 
H220 
111.33 

12 

57 

4.92 

2, 

2.405 

R.P.M. 
C.F. 
H.P. 

1113 
10580 
65.5 

1168 
11100 
75.70 

1220 
11600 
86.33 

1270 
12080 
97.5 

1318 
12520 
10? 

1363 
12960 
120.5 

1410 
13380 
132.75 

Caution  in  Regard  to  Use  of  Fan  and  Blower  Tables.  —  Many  en- 
gineers report  that  some  manufacturers'  tables  overrate  the  capacity  of 
their  fans  and  underestimate  the  horse-power  required  to  drive  them.  In 
some  cases  the  complaints  may  be  due  to  restricted  air  outlets,  long  and 
crooked  pipes,  slipping  of  belts,  too  small  engines,  etc.  It  may  also  be 
due  to  the  fact  that  the  volumes  are  stated  without  being  accompanied 
by  information  as  to  the  maintained  resistance,  and  the  volumes  givea 


FANS   AND    BLOWERS. 


663 


may  be  those  delivered  with  an  unrestricted  inlet  and  outlet.  As  this 
condition  is  not  a  practical  one,  the  volume  delivered  in  an  installation 
is  much  smaller  than  that  given  in  the  tables.  The  underestimating  of 
horse-power  required  may  be  due  to  the  fact  that  the  volumes  given  in 
tables  are  for  operation  against  a  practical  resistance,  and  in  an  installa- 
tion it  might  be  that  the  resistance  was  low,  consequently  the  volume 
and  also  the  horse-powei  required  would  be  greater. 

Capacity  of  Sturtevant  High-Pressure  Blowers  (1908). 


Number  of 
blower. 

Capacity  in  cubic  feet 
per  minute,  1/2  lb.  pres- 
sure. 

Revolutions  per 
minute. 

Inside  dia. 
of  inlet 
and  outbt, 
inches. 

Approx. 
weight, 
pounds.* 

000 

1  to          5 

200  to  1000 

13  '8 

40 

00 

5  to        25 

375  to    800 

11/3 

80 

0 

25  to        45 

370  to    800 

21/2 

140 

] 

45  to       130 

240  to    600 

3 

330 

2 

130  to       225 

300  to    500 

4 

550 

3 

•  225  to       325 

380  to    525 

4 

760 

4 

325  to       560 

350  to    565 

6 

1,080 

5 

560  to    1  ,030 

300  to    475 

8 

1,670 

6 

1,030  to    1,540 

290  to    415 

10 

2,500 

7 

1,540  to    2,300 

280  to    410 

10 

3,200 

8 

2,300  to   3,300 

265  to    375 

12 

4,700 

9 

3,300  to    4,700 

250  to    350 

16 

6,100 

10 

4,700  to    6,000 

260  to    330 

16 

8,000 

11 

6,000  to    8,500 

220  to    310 

20 

12,100 

12 

8500  to  11,300 

190  to    250 

24 

18,700 

13 

11,  300  to  15,500 

190  to    260 

30 

22,700 

*  Of  blower  for  1/2  lb.  pressure. 

Performance  of  a  No.    7  Steel    Pressure    Blower    under    Varying 

Conditions   of  Outlet. 

Per  cent  of 
Rated  Ca- 
pacity      0     20     40     60     80     100  120  140  160  180  200  220  240 

Per  cent  of 

Rated  H.P.  28     42     57     72     86     100  116  130  144  159  173  187  202 

Total  pres- 
sure, oz 10.211.411.912.011.911.410.910.39.7    9.1    8.5    7.9    7.2 

Static  pres- 
sure, oz     ..10.211.211.611.411.0   10.29.2    8.0    6.6    5.0    3.5    1.9    0.3 

Efficiency,  per 

cent 0     26     40     50     56      60     62     61     59     56     52     48     45 

The  above  figures  are  taken  from  a  plotted  curve  of  the  results  of 
a  test  by  the  Buffalo  Forge  Co.  in  1905.  A  letter  describing  the  test 
eavs  : 

The  object  was  to  determine  the  variation  of  pressure,  power  and 
efficiency  obtained  at  a  constant  speed  with  capacities  varying  from  zero 
discharge  to  free  delivery.  A  series  of  capacity  conditions  were  secured 
by  restricting  the  outlet  of  the  blower  by  a  series  of  converging  cones, 
so  arranged  as  to  make  the  convergence  in  each  case  very  slight,  and  of 
sufficient  length  to  avoid  any  noticeable  inequality  in  velocities  at  the 
discharge  orifice.  The  fan  was  operated  as  nearly  at  constant  speed  as 
possible.  The  velocity  of  the  air  at  the  point  of  discharge  was  measured 
by  a  Pitot  tube  and  draft  gauge  of  usual  construction.  Readings  were 
taken  over  several  points  of  the  outlet  and  the  average  taken,  although 


664 


AlE. 


the  variation  under  nearly  all  conditions  was  scarcely  perceptible.  A 
coefficient  of  93%  was  assumed  for  the  discharge  orifice.  The  pressure 
was  taken  as  the  reading  given  by  the  Pitot  tube  and  draft  gauge  at 
outlet.  The  agreement  of  this  reading  with  the  static  pressure  in  a 
chamber  from  which  a  nozzle  was  conducted  had  been  checked  by  a 
previous  test  in  which  the  two  readings,  i.e.,  velocity  and  static  pressure, 
were  found  to  agree  exactly  within  the  limit  of  accuracy  of  the  draft 
gauge,  which  was  about  0.01  in.,  or,  in  this  case,  within  1%  The  horse- 
power was  determined  by  means  of  a  motor  which  had  been  previously 
calibrated  by  a  series  of  brake  tests.  Variations  in  speed  were  assumed 
to  produce  variation  in  capacity  in  proportion  to  the  speed,  variation  in 
pressure  to  the  square  of  the  speed,  and  variation  in  H.P.  in  proportion  to 
the  cube  of  the  speed.  These  relations  had  been  previously  shown  to 
hold  true  for  fans  in  other  tests.  They  were  also  checked  up  by  oper- 
ating the  fan  at  various  speeds  and  plotting  the  capacities  directly  with 
the  speed  as  abscissa,  the  pressure  with  the  square  of  the  speed  as  abscissa, 
and  the  horse  power  with  the  cube  of  the  speed  as  abscissa.  These  were 
found,  as  in  previous  cases,  to  have  a  practically  straight-line  relation,  in 
which  the  line  passed  through  the  origin. 

Effect  of  Resistance  upon  the  Capacity  of  a  Fan.  —  A  study  of  the 
figures  in  the  above  table  shows  the  importance  of  having  ample  capacity 
in  the  air  mains  and  delivery  pipes,  an.i  of  the  absence  of  sharp  bends 
or  other  obstructions  to  the  flow  which  may  increase  the  resistance  or 
pressure  against  which  the  fan  operates.  The  fan  delivering  its  rated 
capacity  against  a  static  pressure  of  10.2  ounces  delivers  only  40  % 
of  that  capacity,  with  the  same  number  of  revolutions,  if  the  pressure  is 
increased  to  11.6  ounces;  the  power  is  reduced  only  to  57%,  instead  of 
40%,  and  the  efficiency  drops  from  60%  to  40%. 


Dimensions  of  Sirocco  Fans. 

(American  Blower  Co.,  1909.) 


•s  • 

i 

i 

.2 

^d 

<3£ 

± 

Ov<n   <* 

0) 

d 

«-."*. 

°7R 

-tj  » 

C3   >> 

1 

1% 

"S.si 

•£.S 

*°.S 

^ 

t,  to 

W    93 

^ 

U          m 
^   >  *? 

^S 

tsj 

"  E? 

•3.8 

"o 

5g 

lit 

3j 

£| 

•  JH 

^j? 

o§5 

-oW| 

•5  n 

c3££ 

-S 

Q 

-g<jj 

•swi 

•2  35 

^  w 

c3i5 

BM 

0>,£jO 

S_^Q  *i 

^  W 

s 

s  "" 

H 

H 

& 

^ 

^ 

s 

< 

^                ** 

^ 

6 

3 

48 

56 

ii" 

4 

10" 

.23 

.123 

.11 

.12 

3" 

9 

41/2 

48 

127 

r  4" 

6 

r  3" 

.49* 

.349 

.25 

.35 

41/4" 

12 

6 

64 

226 

r  9" 

8 

,/     7// 

.85 

.616 

.44 

.60 

53/4" 

15 

71/2 

64 

353 

2'     4" 

10 

2'    0" 

1.46 

.957 

.69 

.92 

71/4;; 

18 

9 

64 

509 

2'   10" 

12 

2'     5" 

1.87 

1.37 

1.00 

1.40 

21 

101/2 

64 

693 

3/     4// 

14 

2'   10" 

2.40 

1.87 

1.34 

1.87 

10"  2 

24 

12 

64 

904 

y   8" 

16 

y  3" 

3.14 

2.46 

1.78 

2.40 

1  1  1/2" 

27 

131/2 

64 

1144 

4/    3" 

18 

3'     7" 

4.59 

3.11 

2.25 

3.14 

13" 

30 

15 

64 

1413 

4'     7" 

20 

4'    0" 

5.58 

3.83 

2.78 

3.83 

1  4  1/2" 

36 

18 

64 

2036 

5'     6" 

24 

4'   10" 

7.87 

5.50 

4.00 

5.58 

17" 

42 

21 

64 

2770 

6'     5" 

23 

5'     7" 

10.56 

7.47 

5.44 

7.47 

20" 

48 

24 

64 

3617 

7'     3" 

32 

6'     5" 

13.6 

9.79 

7.11 

9.85 

23" 

54 

27 

64 

4578 

8'     2" 

36 

7'     3" 

17.0 

12.3 

9.00 

12.3 

26" 

60 

30 

64 

5652 

y      ,// 

40 

S'     0" 

20.9 

15.2 

11.11 

15.3 

281/2" 

66 

33 

64 

6839 

y   ||// 

44 

8'   10'J 

25.2 

18.4 

13.41 

18.3 

311/2" 

72 

36 

64 

8144 

lO'   10" 

43 

9,     r 

29.8 

22.2 

16.00 

22.3 

341/2" 

Sirocco  or  Multtvane  Fans.  —  There  has  recently  (1909)  come  into  use 
a  fan  of  radically  different  proportions  and  characteristics  from  the  ordi- 
nary centrifugal  fan.  This  fan  is  composed  of  a  great  number  of  shallow 
vanes,  ranging  from  48  to  64,  set  close  together  around  the  periphery  of 
the  fan  wheel.  Over  a  large  range  of  sizes,  64  vanes  appear  to  give  the 


Speed,  Capacities  and  Horse-power  of  Sirocco  Fans.     (American 

Blower  Co.,  1909.) 

The  figures  given  represent  dynamic  pressures  in  oz.  per  sq.  in.      For 
static  pressure,  deduct  28.8%;  for  velocity  pressure,  deduct  71.2%. 


£  4, 

.£•£ 

N 

P 

N 

0 

0 
eo~ 

o 

1  1/4  OZ. 

N 

O 

o 

0 

o 

N 

O 

6 
9 
\2 
15 
18 
21 
24 
27 
30 
36 
42 
48 

Cu.ft. 
R.P.M. 
B.H.P. 

155 
1,145 
.0185 

220 
1,615 
.052 

270 
1,980 
.095 

310 
2,290 
.147 

350 
2,560 
.205 

380 
2,800 
.270 

410 
3,025 
.34 

440 

3,230 
.42 

490 
3,616 
.58 

540 
3,960 
.76 

Cu.ft, 
R.P.M. 
B.H.P. 

350 
762 
.042 

500 
1,076 
.118 

610 
1,320 
.216 

700 
1,524 
.333 

790 
1,700 
.463 

860 
1,866 
.610 

930 
2,020 
.77 

1,000 
2,152 
.95 

1,110 
2,408 
1.32 

1,220 
2,640 
1.73 

Cu.ft, 
R.P.M. 
B.H.P. 

625 
572 
.074 

880 
808 
.208 

1,080 
990 
.381 

1,250 
1,145 
.588 

1,400 

1,280 
.82 

1,530 
1,400 
1.08 

1,650 
1,512 
1.36 

1,770 
1,615 
1.66 

1,970 
1,808 
2.32 

2,170 
1,980 
3.05 

Cu.ft. 
R.P.M. 
B.H.P. 

975 
456 
.115 

1,380 
645 
.326 

1,690 
790 
.600 

1,950 
912 
.923 

2,180 
1,020 
1.29 

2,400 
1,120 
1.69 

2,590 
1,210 
2.14 

2,760 
1,290 
2.61 

3,090 
1,444 
3.65 

3,390 
1,580 
4.8 
"4^880 
1,320 
6.9 

Cu.  ft, 
R.P.M. 
B.H.P. 

1,410 
381 
.167 

1,990 
538 
.470 

2,440 
660 
.862 

2,820 
762 
1.33 

3,160 
850 

1.85 

3,450 
933 
2.43 

3,720 
1,010 
3.07 

3,980 
1,076 
3.75 

4,450 
1,204 
5.25 

Cu.  ft, 
R.P.M. 
B.H.P. 

1,925 
326 

.227 

2,710 
•  462 
.640 

3,310 
565 
1.17 

3,850 
652 
1.81 

4,290 
730 
2.53 

4,700 
800 
3.33 

5,070 
864 
4.18 

5,420 
924 
5.11 

6,060 
1,032 
7.15 

6,620 
1,130 
9.4 

Cu.  ft. 
R.P.M. 
B.H.P. 

2,500 
286 
.296 

3,540 
404 
.832 

4,340 
495 
1.53 

5,000 
572 
2.35 

5,600 
640 
3.28 

6,120 
700 

4.32 

6,620 
756 

5.44 

7,080 
807 
6.64 

7.900 
904 
9.3 

8,680 
990 
12.2 

Cu.  ft. 
R.P.M. 
B.H.P. 

3,175 
254 
.373 

4,490 
359 
1.05 

5,500 
440 
1.94 

6,350 
508 
2.98 

7,100 
568 
4.16 

7,780 
622 
5.48 

8,400 
672 
6.90 

8,980 
718 
8.44 

10,050 
804 
11.8 

11,000 
880 
15.5 

Cu.  ft, 
R.P.M. 
B.H.P. 

3,910 
228 
.460 

5,520 
322 
1.30 

6,770 
395 
2.40 

7,820 
456 
3.68 

8,750 
510 
5.15 

9,600 
560 
6.75 

10,350 
604 
8.53 

11,050 
645 
10.4 

12,350 
722 
14.5 

13,550 
790 
19.1 

Cu.ft. 
R.P.M. 
B.H.P. 

5,650 
190 
.665 

7,950 
269 
1.87 

9,750 
330 
3.44 

11,300 
381 
5.30 

12,640 
425 
7.40 

13,800 
466 
9.72 

14,900 
504 
12.25 

15,900 
538 
15.0 

17,800 
602 
20.9 

19,500 
660 
27.5 

Cu.  ft. 
R.P.M. 
B.H.P. 

7,700 
163 
.903 

10,850 
231 
2.55 

13,300 
283 
4.69 

15,400 
326 
7.24 
"207)00 
286 
9.40 

17,170 
365 
10.1 

18,800 
400 
13.3 

20,300 
432 
16.7 

21,700 
462 
20.4 

24,250 
516 
28.5 

26,600 
566 
37.5 

Cu.ft. 
R.P.M. 
B.H.P. 

10,000 
143 
1.18 

14,150 
202 
3.32 

17,350 
248 
6.10 

22,400 
320 
13.1 

24,500 
350 
17.2 

26,500 
378 
21.75 

28,300 
403 
26.6 

31,600 
452 
37.1 

34,700 
495 
48.8 

54 
60 
66 
72 
78 
84 

Cu.  ft. 
R.P.M. 
B.H.P. 

12,700 
127 
1.49 

17,950 
179 
4.20 

22,000 
220 
7.75 

25,400 
254 
11.9 

28,400 
284 
16.6 

31,100 
311 
21.9 

33,600 
336 
27.6 

35,900 
359 
33.7 

40,200 
402 
47.1 

44,000 
440 
62. 

Cu.  ft. 
R.P.M. 
B.H.P. 

15,650 
114 
1.84 

22,100 
161 
5.20 
2MOO 
147 
6.30 

27,100 
198 
9.58 

31,300 

228 
14.7 

35,000 
255 
20.6 

38,400 
280 
27.0 

41,400 
302 
34.1 

44,200 
322 
41.6 

49,400 
361 
58.2 

54,200 
396 
76.5 

Cu.  ft. 
R.P.M. 
B.H.P. 

18,950 
104 
2.23 

32,850 
180 
11.6 

37,900 
208 
17.8 

42,300 
232 
24.9 

46,400 
254 
32.7 

50,100 
275 
41.2 

53,600 
294 
50.4 

60,000 
328 
70.4 

65,700 
360 
92.6 
78,000 
330 
110. 

Cu.  ft. 
R.P.M. 
B.II.P. 

22,600 
95 
2.66 

31,800 
134 
7.48 

39,000 
165 
13.7 

45,200 
190 
21.2 

50,600 
212 
29.6 

55,200 
233 
38.9 

59,600 
252 
49.0 

63,600 
269 
59.8 

71,200 
301 
83.6 

Cu.  ft. 
R.P.M 
B.H.P. 

26,400 
88 
3.10 

37,350 
124 
8.77 

45,800 
153 
16.1 

52,800 
176 
24.8 

59,100 
197 
34.7 

64,700 
215 
45.6 

70,000 
233 
57.5 

74,700 
248 
70.2 

83,500 
278 
98. 

91,600 
305 
129. 

Cu.  ft. 
R.P.M. 
B.H.P 

30,800 
81 
3.61 

43,400 
115 
10.2 

53,200 
142 
18.7 

61,600 
163 
28.9 

68,700 
182 
40.4 

75,200 
200 
53.0 

81,200 
216 
66.8 

86,800 
231 
81.7 

97,100 
258 
114. 

106,400 
283 
150. 

90 

Cu.  ft 
R.P.M 
B.H.P 

35,250 
76 
4  14 

49,800 
107 
1  11.7 

61.000 
132 
21.5 

70,500 
152 
33.1 

78,800 
170 
46.2 

86,400 
186 
60.7 

93,300 
201 
76.7 

99,600 
214 
93  6 

111,200 
241 
131. 

122.000 
264 
172. 

665 


666 


AIR. 


best  results.  The  vanes,  measured  radially,  have  a  depth  l/ie  the  fan 
diameter.  Axialiy,  they  are  much  longer  than  those  of  the  ordinary  fan, 
being  3/5  the  fan  diameter.  The  fan  occupies  about  1/2  the  space,  and  is 
about  2/3  the  weight  of  the  ordinary  fan.  The  vanes  are  concaved  in  the 
direction  of  rotation  and  the  outer  edge  is  set  forward  of  the  inner  edge. 
The  inlet  area  is  of  the  same  diameter  as  the  inner  edge  of  the  blades. 
Usually  the  inlet  is  on  one  side  of  the  fan  only,  and  is  unobstructed,  the 
wheel  being  overhung  from  a  bearing  at  the  opposite  end.  A  peculiarity 
of  this  type  of  fan  is  that  the  air  leaves  it  at  a  velocity  about  80  per 
cent  in  excess  of  the  peripheral  speed  of  the  blades.  The  velocity  of 
the  air  through  the  inlet  is  practically  uniform  over  the  entire  inlet 
area.  The  power  consumption  is  relatively  low.  This  type  of  fan  was 
invented  by  S.  C.  Davidson  of  Belfast,  Ireland,  and  is  known  at  the 
"Sirocco"  fan.  It  is  made  under  that  name  in  this  country  by  the 
American  Blower  Co.,  to  which  the  author  in  indebted  for  the  preceding 
tables. 

A  Test  of  a  "  Sirocco  "  Mine  Fan  at  Llwnypia,  Wales,  is  reported  in 
Eng'g.,  April  16,  1909.    The  fan  is  11  ft.  Sin.  diam.,  double  inlet,  direct- 
coupled  to  a  3-phase  motor.    Average  of  three  tests:  Revs,  per  min.,  184; 
Seripheral  speed,  6,705  ft.  per  min.;  water-gauge  in  fan  drift  and  in  main 
rift,  each  6  in.;  area  of  drift,  184.6  sq.  ft.;  av.  velocity  of  air,  1842 
ft.  per  min;  volume  of  air,  340,033  cu.  ft.  per  min.;  H.P.  input  at  motor, 
420;  Brake  H.P.  on  fan  shaft,  390;  Indicated  H.P.  in  air,  321.5;  efficiency 
of  motor,  93%;  mechanical  efficiency  of  fan,  82.43%;  combined  mechan- 
ical efficiency  of  fan  and  motor,  76.6%. 

High-Pressure  Centrifugal  Fans.  (See  page  648.) 
The  Conoidal  Fan. — A  multiblade  fan  in  which  the  blades  are 
not  parallel  to  the  shaft,  but  inclined  to  it,  so  that  their  tips  form 
the  shape  of  a  cone,  the  inlet  being  the  large  diameter,  is  made  by  the 
Buffalo  Forge  Co.  It  is  known  as  the  Buffalo  Niagara  Conoidal 
Fan.  A  table  of  the  regular  sizes  of  these  fans  is  given  below. 

Capacities  of  Buffalo  Niagara  Conoidal  Fans. 

Under  Average  Working  Conditions  at  70°  F.  and  30  in.  Barometer. 
Static  Pressure  is  77.5%  of  Total  Pressure.  Volumes  in  cu.  ft.  per  min. 


J 

<x> 
P 

1-in.  Total 
Pressure,  or 
0.577  oz. 

2-in.  Total 
Pressure,  or 
1.154  oz. 

4-in.  Total 
Pressure,  or 
2.307  oz. 

6 

ll 

O 

a 

Uj 

a 

d 

cuS 

<l>J/2 

PH 

,_; 

p* 

PH 

,_; 

PH* 

PH 

• 

PH 

c3 

E 

ii  • 

tf 

O 

w 

A 

{> 

w 

P4 

> 

H 

~3~ 

155/8 

1.31 

675 

2,440 

0.54 

955 

3,450 

1.54 

1350 

4,480 

4.35 

31/2 

181/8 

1.79 

579 

3,320 

0.74 

818 

4,690 

2.09 

1157 

6,640 

5.92 

201/2 

2.33 

506 

4,340 

0.97 

716 

6,130 

2.73 

1013 

8,670 

7.73 

41/2 

231/2 

2.95 

450 

5,490 

1.22 

636 

7,760 

3.46 

900 

10,970 

9.78 

5 

261,8 

3.64 

405 

6,770 

1.51 

573 

9,580 

4.27 

810 

13,550 

12.1 

51/2 

283/4 

4.41 

368 

8,200 

1.83 

521 

11,590 

5.17 

736 

16,390 

14.6 

6 

313/8 

5.25 

338 

9,750 

2.17 

477 

13,790 

6.15 

675 

19,510 

17.4 

7 

361/2 

7.14 

289 

13,280 

2.96 

409 

18,770 

8.37 

579 

26,550 

23.7 

8 

42 

9.33 

253 

17,340 

3.87 

358 

24,520 

10.9 

506 

34,680 

30.9 

9 

47 

11.81 

225 

21,950 

4.89 

318 

31,020 

13.8 

450 

43.890 

39.1 

10 

52 

14.58 

203 

27,090 

6.04 

286 

38,310 

17.1 

405 

54,180 

48.3 

11 

58 

17.64 

184 

32,780 

7.31 

260 

46,360 

20.7 

368 

65,560 

58.5 

12 

63 

21.00 

169 

39,010 

8.70 

239 

55,170 

24.6 

338 

78,020 

69.6 

13 

68 

24.65 

156 

45,780 

10.2 

220 

64,730 

28.9 

312 

91,560 

81.6 

14 

73 

28.68 

145 

53,100 

11.8 

205 

75,090 

33.5 

289 

106,200 

94.7 

15 

78 

32.80 

135 

60,960 

13.6 

191 

86,200 

38.4 

270 

121,920 

108.7 

16 

84 

37.32 

127 

69,360 

15.5 

179 

98,060 

43.7 

253 

138,700 

123.7   . 

17 

89 

42.14 

119 

78,300 

17.5 

169 

110,720 

49.4 

238 

156,600 

139.6 

18 

94 

47.24 

113 

87,780 

19.6 

159 

124,110 

55.3 

225 

175,550 

156.5 

19 

99 

52.63 

107 

97,800 

21.8 

151 

138,280 

61.7 

213 

195,600 

174.4 

20      1105 

58.32 

101 

108,370 

24.2 

143 

153,250 

68.3 

202 

216,720 

193.2 

FANS   AND   BLOWERS.     '  667 

METHODS  OF  TESTING  FANS. 

Anemometer  Method. — Measurements  by  anemometers  are  liable  to 
be  very  inaccurate  (see  page  625)  and  results  obtained  by  them  should 
be  considered  only  as  rough  approximations. 

Water  Gauge  Readings  at  End  of  Tapered  Cone. — This  method  is 
also  far  from  accurate  on  account  of  variable  eddies  in  the  air  column. 

Pitot  Tube  Readings  in  Center  of  Discharge  Pipe. — This  method 
gives  fairly  accurate  results  when  the  discharge  pipe  is  the  same  size 
as  the  fan  outlet,  when  the  Pitot  tube  is  placed  at  a  distance  equal  to 
at  least  15  diameters  of  the  pipe  from  the  fan  outlet,  when  the  tube  is 
so  made  that  it  will  give  correct  readings  of  the  static  pressure,  and 
when  the  velocities  computed  from  the  readings  are  corrected  by  a 
coefficient  (0.87  to  0.92  in  different  experiments)  for  the  ratio  between 
the  average  velocity  and  the  velocity  at  the  center  of  the  tube. 

Pitot  Tube  Readings  in  Zones  of  Equal  Area. — More  accurate  results 
may  be  obtained  if  the  tube  is  traversed  across  two  diameters  of  the 
tube  at  right  angles  to  each  other,  placing  the  nozzle  successively  at 
points  which  will  divide  the  cross-sectional  area  into  equal  annular 
areas  (with  one  central  circular  area).  If  ten  such  points  are  taken 
on  each  diameter,  the  radial  distances  of  the  points  from  the  center .  of 
the  pipe  will  be  31,  55,  71,  84,  and  95%  of  the  radius  of  the  pipe  from 
the  center.  Since  the  velocity  at  any  point  is  proportional  to  the 
square  root  of  the  velocity  head,  it  is  necessary  for  accurate  results 
to  take  the  average  of  the  square  root  of  the  readings,  and  square  this 
average  to  obtain  the  mean  velocity  head  of  the  whole  area  of  the  pipe. 
For  low  pressures  an  inclined  manometer  should  be  used  with  the  Pitot 
tube,  and  it  should  contain  gasoline  instead  of  water,  as  it  keeps  the 
tubes  clean,  has  a  definite  meniscus  and  almost  no  capillary  attraction 
for  the  glass.  The  readings  of  the  tube  are  to  be  corrected  for  the 
inclination  and  for  the  specific  gravity  of  the  gasoline  to  reduce  them 
to  equivalent  inches  of  water  column. 

The  best  form  of  Pitot  tube  is  one  made  of  two  thin  brass  tubes,  the 
outer  one  i/4-in.  and  the  inner  one  i/s-in.  external  diameter,  each  about 
4  or  5  in.  long,  the  two  being  soldered  together  at  one  end  and  the  end 
then  tapered  down  to  a  sharp  edged  nozzle.  Each  tube  is  connected 
near  the  rear  end  to  tubes  at  right  angles  to  the  double  tube,  leading 
to  two  manometers,  one  for  reading  the  total,  or  dynamic  or  impact 
pressure,  the  other  the  static  pressure.  The  difference  between  these 
two  readings  is  the  velocity  head.  It  may  be  obtained  in  one  reading 
by  connecting  both  parts  of  the  tube  to  a  single  manometer.  The 
outer,  or  static,  tube  has  two  or  more  smooth  holes  drilled  in  it,  diamet- 
rically opposite,  at  right  angles  to  the  axis,  to  receive  the  static  pressure. 
The  exact  form  of  the  nozzle  of  the  impact  tube  is  not  of  importance, 
as  different  forms  give  identical  readings,  but  care  must  be  taken  with 
the  holes  of  the  static  tube  or  errors  will  be  made  in  the  readings  due 
to  action  of  the  dynamic  pressure  on  these  holes  if  they  are  not  properly 
made.  A  thin  slot  instead  of  the  holes  has  been  found  to  give  in- 
accurate readings.  (See  papers  by  Chas.  S.  Treat,  Trans.  A.  S.  M.  E., 
vol.  34,  and  W.  C.  Rowse,  Jour.  A.  S.  M.  E.,  Sept.,  1913.) 

For  accurate  scientific  work  it  is  well  to  check  the  static  tube  read- 
ings by  manometer  readings  from  a  piezometer  ring,  which  is  a  narrow 
annular  channel  encircling  the  pipe  and  soldered  to  it  to  make  it  air- 
tight. Six  or  more  smooth  holes  are  bored  into  the  pipe  at  right  angles 
to  its  axis,  to  connect  the  interior  of  the  pipe  with  the  ring.  The  Pitot 
tube  may  also  be  calibrated  by  means  of  a  Thomas  electric  gas  meter. 

The  Thomas  Electric  Meter  for  air  and  gas  consists  of  an  enlargement 
of  section  of  the  flow  pipe  into  a  chamber  of  a  diameter  equal  to  about 
two  diameters  of  the  pipe,  with  conical  ends  connecting  it  with  the 
pipe.  In  the  interior  is  placed  an  electric  heater  made  of  bare  resistance 
wire  mounted  on  a  fiber  frame  and  equally  distributed  over  the  section 
of  the  chamber,  and  also  two  electric  resistance  thermometers,  one  in 
front  of  and  the  other  behind  the  heater.  An  electric  current,  meas- 
ured by  a  wattmeter,  is  passed  through  the  heater  and  the  temperatures 
before  and  after  the  heating  are  measured  by  the  thermometers.  If 
Ti  and  T*  are  the  temperatures  before  and  after  the  heating,  H  the 
heat  units  corresponding  to  the  watts  delivered  to  the  heater  (1  watt  » 


668 


AIK. 


3.415  B.T.TJ.  per  hour),  .and  S  the  Specific  heat  of  the  air,  then  the 
weight  of  air  heated  in  Ib.  per  min.  is  W  =  f.nfsfrr ™-r- 

OUO  \2  2  —  JL  I). 

When  the  Pitot  tube  is  correctly  made  and  used  its  formula  is 
v  =  \/2gh,  in  which  h  is  the  mean  velocity  head,  measured  as  the  height 
in  feet  of  a  column  of  air  which  would  produce  the  observed  velocity 
and  v  the  velocity  in  ft.  per  sec. 

To  convert  the  velocity  head  as  measured  in  the  Pitot  tube  in  inches 
of  water  column  into  velocity  of  the  air  in  feet  per  min.  we  have  the 
following  formulae: 

p  =  velocity  pressure  in  inches  of  water  gage. 

h  =  corresponding  heat  in  feet  of  a  column  of  air. 

v  =  velocity  of  air  in  ft.  per  sec.      V  =  velocity  in  ft.  per  min. 

w  =  weight  of  1  cu.  ft.  of  air  under  existing  conditions. 

,  =  62-3*>.  „  =  .  /  64.32X62.3  p.  „  =  1R  97  ^  fi> 

I  to" 


12  w 


V  =  18.27 


V,  ft.  per  min.  =  1096.2  *I!L 
\tc 

The  average  weight  of  1  cu.  ft.  of  air  was  found  by  the  American 
Blower  Co.  in  a  large  number  of  tests  to  be  0.0715  Ib.  per  cu.  ft.,  whence 
V 


The  velocity  of  flow  of  air  at  a  given  density  produced  by  a  pres- 
sure of  1  in.  of  water  is  called  the  "velocity  constant"  of  air  at  that 
density.  A  table  of  such  constants  is  given  by  the  American  Blower 
Co.,  from  which  the  following  table  is  condensed: 

AIR  CONSTANTS  FOR  DRY  AIR  AT  SEA  LEVEL,  BAR.  29.92  IN. 


o.  . 
Sfe 

H° 

K. 

6 
33 

& 

d  . 

Sfe 

EH° 

K. 

.2 

3 

d  . 
Sfc 
£° 

K. 

0 

a 

i 

tf 

d 
6fe 
H° 

K. 

_o 

3 

-40 
-20 
0 
10 
20 
30 
40 
50 

3567 
3651 
3733 
3773 
3813 
3852 
3891 
3930 

0.890 
.911 
.932 
.942 
.952 
.961 
.971 
.981 

60 
70 
80 
90 
100 
HO 
120 
140 

3968 
4006 
4044 
4081 
4118 
4155 
4191 
4263 

0.990 
.000 
.009 
.018 
.028 
.037 
.046 
.064 

160 
180 
200 
250 
300 
350 
400 
450 

4333 
4402 
4470 
4636 
4796 
4890 
5101 
5246 

.082 
.098 
.114 
.157 
.197 
.236 
.273 
.310 

500 
600 
700 
800 
900 
1000 
1100 
1200 

5389 
5663 
5925 
6177 
6418 
6650 
6873 
7090 

.345 
.413 
.478 
.542 
.602 
.660 
.715 
.770 

Constant  K  — 


weight  of  1  cu"  ft'  water  at  62°  F' 


12  X  weight  of  1  cu.  ft.  air  at  temp,  stated. 

The  values  under  Ratio  give  ratios  of  fan  speeds  necessary  at  the 
various  temperatures  to  produce  the  same  water  gage  indication. 

Horse-power  of  a  Fan. — If  C  =  cu.  ft.  of  air  delivered  per  minute, 
W  =  weight  of  1  cu.  ft.  of  air  under  existing  conditions,  H  the  height 
in  feet  of  an  air  column  equivalent  to  the  total  pressure,  D  the  dynamic 
pressure  in  inches  of  water  column  =  WH  -h  5.2,  the  horse-power 
developed  by  the  delivery  of  the  air  is  A  =  CWH  -r-  33,000  =  CD  -f-  6356. 
One  inch  water  gage  =  5.2  Ib.  per  sq.  ft.  The  total  pressure  D  with 
which  the  fan  should  be  credited  is  the  difference  between  the  total 
pressure  in  the  discharge  pipe  and  that  in  the  inlet  pipe. 

The  air  horse-power  divided  by  the  power  required  to  drive  the  fan, 
as  measured  by  a  dynamometer,  gives  the  mechanical  efficiency  of  the 
fan. 

From  the  above  formulae  the  air  horse-power  is  a  function  of  two 
variables,  volume  and  pressure.  To  obtain  what  is  called  the  "  static 
efficiency,"  the  fan  should  be  credited  with  the  difference  between 
the  static  pressure  in  the  medium  from  which  the  fan  is  drawing 
air  and  the  static  pressure  in  the  discharge  pipe.  To  obtain  the 


FANS  AND  BLOWERS.  669 

Impact  or  total  efficiency  the  fan  should  be  credited  with  the  kinetic 
energy  in  the  air  in  the  discharge  pipe  or  with  the  difference  between 
the  static  pressure  in  the  medium  from  which  the  fan  is  drawing 
air  and  the  total  or  impact  pressure  in  the  discharge  pipe. 

The  work  of  compression  is  negligible,  as  these  methods  have  to  do 
with  air  under  low  pressure.  When  readings  are  taken  on  the  suction 
side  of  the  fan,  for  the  purpose  of  determining  static  efficiency,  the 
fan  should  be  credited  only  with  the  difference  between  the  static 
pressure  in  the  discharging  medium  and  the  impact  pressure  in  the 
inlet  pipe.  If  the  object  is  to  determine  the  impact  efficiency  where 
readings  are  taken  at  the  suction  side  of  the  fan,  the  pressure  with 
which  the  fan  should  be  credited  is  the  difference  between  the  impact 
reading  at  the  fan  discharge  and  the  impact  reading  obtained  in  the 
inlet  pipe.  This  total  pressure  with  which  the  fan  is  credited  may 
also  be  expressed  as  the  difference  between  the  static  pressure  in  the 
discharge  pipe  and  the  static  suction  in  the  inlet  pipe,  plus  the  increase 
of  the  velocity  pressure  in  the  outlet  pipe  over  the  velocity  pressure 
in  the  inlet  pipe. 

Accuracy  of  Pitot  Tube  Measurements. — To  obtain  even  approx- 
imately accurate  results  v/ith  Pitot  tubes  it  is  necessary  both  to  have 
the  tube  properly  made  and  to  take  great  precautions  in  using  it. 
W.  C.  Rowse,  Trans.  A.  S.  M.  E.,  vol.  35  (1913),  p.  633,  tested  several 
forms  of  tube,  comparing  their  readings  with  those  of  a  Thomas 
electric  gas  meter.  He  found  the  best  tube  to  be  one  made  of  a 
i/4-in.  outer  and  a  Vs-in.  inner  thin  brass  tube,  4  or  5  in.  long,  soldered 
together  at  one  end,  which  was  tapered  for  3/4  in.  down  to  the  internal 
diameter  of  the  inner  tube,  which  was  thus  given  a  sharp  edge.  The 
outer  tube  was  perforated  with  a  small  smooth  hole  0.02  in.  diameter 
on  each  side  at  the  middle  of  its  length.  The  rear  end  of  the  small 
tube  and  the  annular  space  between  the  two  tubes  were  each  con- 
nected to  1/4  in.  upright  tubes,  from  which  rubber  tubes  led  to  two 
manometers.  The  inner  tube  received  the  impact  pressure  and  the 
annular  space  the  static  pressure.  The  difference  between  the  two 
is  the  velocity  pressure,  a  direct  reading  of  which  could  be  made  by 
connecting  the  two  rubber  tubes,  or  branches  from  them,  to  the  two 
legs  of  a  single  manometer.  The  manometers  were  U  tubes,  of  glass 
about  1/2  in.  internal  diameter,  containing  gasoline,  and  were  inclined 
at  an  angle  of  1  vertical  to  10  horizontal  in  order  to  magnify  the 
readings.  The  scale  was  graduated  so  as  to  read  in  hundredths  of 
ari  inch  of  water  column.  To  obtain  mean  velocities  and  pressures 
the  tube  was  traversed  across  two  diameters  of  the  pipe,  vertical  and 
horizontal,  ten  readings  being  taken  on  each  diameter,  at  points 
located  at  the  center  of  five  annular  areas  into  which  the  total  area 
of  the  pipe  was  divided.  The  radial  distances  of  these  points  from  the 
center  of  the  pipe  were  32,  55,  71,  84  and  95  per  cent,  respectively, 
of  the  radius  of  the  pipe.  (See  Appendix  No.  6  of  the  report  of  the 
Power  Test  Committee  of  the  A.  S.  M.  E.,  1915.)  The  results  of  these 
tests  showed  that  accuracy  within  1  %  could  be  obtained  when  all 
readings  were  obtained  with  a  sufficient  degree  of  refinement  and 
when  the  Pitot  tube  was  preceded  by  a  length  of  pipe  20  to  38  times 
the  pipe  diameter  in  order  to  make  the  flow  as  nearly  uniform  across 
the  section  of  the  pipe  as  possible. 

When  readings  were  taken  at  the  center  of  a  12-in.  galvanized  iron 
pipe  the  mean  pressure  was  0.80  of  the  pressure  at  the  center,  corre- 
sponding to  a  mean  velocity  of  "^0.80  or  0.894  of  the  velocity  at  the 
center,  within  a  limit  of  error  of  2%.  The  mean  velocity  head  was 
obtained  by  taking  the  square  of  the  average  of  the  square  roots  of 
each  of  the  20  readings.  Tests  of  Pitot  tubes  with  long  narrow  slots 
in  the  outer  tube,  instead  of  the  small  holes,  gave  results  which  were 
in  error  from  3.5  to  10%. 

The  Thomas  Electric  Gas  Meter,  referred  to  above,  is. described 
in  Trans.  A.  S.  M.  E.,  vol.  31,  p.  655.  It  consists  in  an  enlarged 
section  of  the  gas  or  air  pipe  containing  an  electric  heating  device 
with  electric  instruments  for  determining  both  the  increase  of  tem- 
perature and  the  energy  absorbed  in  heating.  Given  the  specific 
neat,  the  rise  in  temperature,  and  the  watts  of  energy  absorbed,  the 
weight  of  gas  flowing  in  a  given  time  may  be  computed. 


670 


AIR. 


Flow  of  Air  through  an  Orifice. 

VELOCITY,  VOLUME,  AND  H.P.  REQUIRED  WHEN  AIR  UNDER  GIVEN  PRESSURE 
IN  OUNCES  PER  SQ.  IN.  IS  ALLOWED  TO  ESCAPE  INTO  THE  ATMOSPHERE. 

(B.  F.  Sturtevant  Co.) 


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1/8 

0.216 

1.828 

12.69 

0.00043 

0.0340 

2 

7.284 

50.59 

0.02759 

0.5454 

1/4 

0.432 

2,585 

17.95 

0.00122 

0.0680 

21/8 

7.507 

52.13 

0.03021 

0.5795 

3/8 

0.648 

3,165 

21.98 

0.00225 

0.1022 

21/4 

7.722 

53.63 

0.03291 

0.6136 

1/2 

0.864 

3.654 

25.37 

0.00346 

0.1363 

23/8 

7.932 

55.08 

0.03568 

0.6476 

5/8 

.080 

4.084 

28.36 

0.00483 

0.1703 

21  2 

8.136 

56.50 

0.03852 

0.6818 

3/4 

.296 

4.473 

31.06 

0.00635 

0.2044 

25/8 

8,334 

57.88 

0.04144 

0.7160 

7/8 

.512 

4.830 

33.54 

0.00800 

0.2385 

23/4 

8.528 

59.22 

0.04442 

0.7500 

.728 

5.162 

35.85 

0.00978 

0.2728 

27/8 

8,718 

60.54 

0.04747 

0.7841 

H/8 

.944 

5.473 

38.01 

0.01166 

0.3068 

3 

8.903 

61.83 

0.05058 

0.8180 

2.160 

5.768 

40.06 

0.01366 

0.3410 

31/8 

9.084 

63.08 

0.05376 

0.8522 

13/8 

2.376 

6.048 

42.00 

0.01575 

0.3750 

31/4 

9.262 

64.32 

0.05701 

0.8863 

U/2 

2.59? 

6.315 

43.86 

0.01794 

0.4090 

33/8 

9.435 

65.52 

0.06031 

0.9205 

15/8 

2.808 

6.571 

45.63 

0.02022 

0.4431 

31/2 

9.606 

66.71 

0.06368 

0.9546 

13/4 

3.024 

6.818 

47.34 

0.02260 

0.4772 

35/8 

9,773 

67.87 

0.06740 

0.9887 

17/8 

3.240 

7,055 

49.00 

0.02505 

0.5112 

33/4 

9.938 

69.01 

0.07058 

1.0227 

37/8 

10.100 

70.14 

0.07412 

1  .0567 

(0 

(2) 

(3) 

(4) 

(5) 

(6) 

d) 

(3) 

(4) 

(5) 

(6) 

The  headings  of  the  3d  and  4th  columns  in  the  above  table  have  been 
abridged  from  the  original,  which  read  as  follows:  Velocity  of  dry  air, 
50°  F.,  escaping  into  the  atmosphere  through  any  shaped  orifice  in  any 
pipe  or  reservoir  in  which  the  given  pressure  is  maintained.  Volume  of 
air  in  cubic  feet  which  may  be  discharged  in  one  minute  through  an  orifice 
having  an  effective  area  of  discharge  of  one  square  inch.  The  6th  column, 
not  in  the  original,  has  been  calculated  by  the  author.  The  figures  repre- 
sent the  horse-power  theoretically  required  to  move  1000  cu.  ft.  of  air  of 
the  given  pressures  through  an  orifice,  without  allowance  for  the  work  of 
compression  or  for  friction  or  other  losses  of  the  fan.  These  losses  may 
amount  to  60%  or  more  of  the  given  horse-power. 

The  change  in  density  which  results  from  a  change  in  pressure  has  been 
.  taken  into  account  in  the  calculations  of  the  table.  The  volume  of  air  at 
a  given  velocity  discharged  through  an  orifice  depends  upon  its  shape,  and 
is  always  less  than  that  measured  by  its  full  area.  For  a  given  effective 
area  the  volume  is  proportional  to  the  velocity.  The  power  required  to 
move  air  through  an  orifice  is  measured  by  the  product  of  the  velocity  and 
the  total  resisting  pressure.  This  power  for  a  given  orifice  varies  as  the 
cube  of  the  velocity.  For  a  given  volume  it  varies  as  the  square  of  the 
velocity.  In  the  movement  of  air  by  means  of  a  fan  there  are  unavoidable 
resistances  which,  in  proportion  to  their  amount,  increase  the  actual  power 
considerably  above  the  amount  here  given. 

Pipe  Lines  for  Fans  and  Blowers.  —  In  installing  fane  and  blowers 
careful  consideration  should  be  given  to  the  pipe  line  conducting  the  air 
from  the  fan  or  blower.  Bends  and  turns  in  the  pipe,  even  of  long  radii, 
will  cause  considerable  drop  in  pressure,  and  in  straight  pipe  the  friction  of 
the  moving  air  is  a  source  of  considerable  loss.  The  friction  increases  with 
the  length  of  the  pipe  and  is  inversely  as  the  diameter.  It  also  varies  as  the 
square  of  the  velocity.  In  long  runs  of  pipe,  the  increased  cost  of  a  larger 
pipe  can  often  be  compensated  by  the  decreased  cost  of  the  motor  and 
power  for  operating  the  blower. 

The  advisability  of  using  a  large  pipe  for  conveying  the  air  is  shown  by 


FANS   AND   BLOWERS. 


671 


the  following  table  which  gives  the  size  of  pipe  which  should  be  used  for 
pressure  losses  not  exceeding  one-fourth  and  one-half  ounce  per  square 
inch,  for  various  lengths  of  pipe. 

Diameters  of  Blast  Pipes. 

(B.  F.  Sturtevant  Co.,  1908.) 


(H 

H 

Length  of  Pipe  in  Feet. 

ft 

o 

'3 

°.A 

"1 

20 

40 

60 

80 

100 

120 

140 

*L 

41 

«1 

Diameter  of  Pipe  with  Drop  of 

|l 

fa 

1* 

1/4 
Oz. 

1/2 
Oz. 

1/4 
Oz. 

1/2 
Oz. 

1/4 
Oz. 

1/2 
Oz. 

1/4 
Oz. 

1/2 
Oz. 

1/4 
Oz. 

1/2 
Oz. 

£ 

ol 

1/4 
Oz 

1/2 
Oz. 

1 

23 

500 

6 

5 

7 

6 

7 

6 

8 

7 

9 

8 

9 

8 

9 

8 

2 

27 

1,000 

8 

7 

9 

8 

10 

9 

11 

9 

11 

10 

12 

11 

12 

11 

3 

30 

1,500 

10 

8 

11 

10 

11 

10 

12 

11 

13 

11 

13 

12 

14 

12 

4 

32 

2,000 

11 

9 

12 

11 

13 

12 

14 

12 

15 

.13 

15 

14 

16 

14 

5 

36 

2,500 

12 

10 

14 

12 

15 

13 

15 

14 

16 

14 

17 

15 

17 

15 

6 

39 

3,000 

13 

11 

15 

13 

16 

14 

17 

15 

18 

15 

18 

16 

18 

16 

7 

42 

3,500 

13 

12 

15 

13 

17 

15 

17 

15 

18 

16 

19 

17 

20 

18 

8 

45 

4,000 

15 

12 

16 

15 

18 

15 

18 

16 

19 

17 

20 

18 

21 

18 

9 

48 

4,500 

15 

13 

17 

15 

18 

16 

19 

17 

20 

18 

21 

19 

22 

19 

10 

54 

5,000 

15 

13 

18 

15 

19 

17 

20 

18 

21 

18 

22 

19 

23 

20 

11 

54 

5,500 

16 

14 

18 

16 

20 

17 

21 

18 

22 

19 

23 

20 

23 

20 

12 

60 

6,000 

17 

14 

19 

17 

20 

17 

21 

19 

22 

20 

23 

21 

24 

21 

13 

60 

6,500 

17 

14 

19 

17 

21 

18 

23 

19 

23 

20 

24 

21 

25 

22 

14 

60 

7,000 

18 

15 

20 

18 

22 

19 

23 

20 

24 

21 

25 

22 

26 

23 

15 

66 

7,500 

18 

16 

21 

18 

22 

19 

24 

21 

25 

22 

26 

22 

27 

23 

16 

66 

8,000 

18 

16 

22 

18 

23 

20 

24 

22 

26 

22 

26 

23 

27 

24 

17 

66 

8.500 

18 

16 

22 

18 

23 

20 

24 

22 

26 

22 

27 

24 

28 

24 

18 

72 

9,000 

18 

17 

22 

18 

24 

21 

25 

22 

27 

23 

27 

24 

28 

25 

19 

72 

9,500 

20 

17 

-23 

20 

24 

22 

26 

23 

28 

23 

28 

25 

29 

26 

20 

72 

10,000 

20 

18 

23 

20 

25 

22 

27 

23 

28 

24 

29 

25 

30 

26 

21 

78 

10,500 

21 

18 

24 

21 

26 

23 

27 

23 

29 

25 

30 

26 

30 

26 

22 

78 

11,000 

21 

18 

24 

21 

27 

23 

28 

24 

29 

26 

30 

27 

31 

27 

23 

78 

11,500 

21 

19 

25 

21 

27 

24 

28 

25 

30 

26 

30 

27 

31 

27 

24 

84 

12,000 

22 

19 

25 

22 

28 

24 

28 

25 

31 

26 

31 

27 

32 

28 

25 

84 

12,500 

22 

19 

26 

22 

28 

24 

29 

26 

31 

27 

32 

28 

33 

28 

26 

84 

13,000 

22 

19 

26 

22 

28 

24 

29 

26 

31 

27 

32 

28 

33 

28 

27 

90 

13.500 

23 

20 

26 

23 

28 

24 

30 

26 

31 

27 

32 

28 

34 

28 

28 

90 

14,000 

23 

20 

27 

23 

29 

25 

30 

27 

32 

28 

33 

29 

34 

29 

29 

90 

14,500 

23 

20 

27 

23 

29 

26 

31 

27 

32 

28 

33 

29 

34 

30 

30 

90 

15.000 

24 

21 

27 

24 

29 

26 

31 

27 

32 

28 

34 

30 

35 

30 

The  minimum  radius  of  each  turn  should  be  equal  to  the  diameter  of  the 
pipe.  For  each  turn  thus  made  add  three  feet  in  length,  when  using  this 
table.  If  the  turns  are  of  less  radius,  the  length  added  should  be  increased 
proportionately. 

The  above  table  has  been  constructed  on  the  following  basis:  A  loss  of, 
say,  1/2  oz.  pressure  was  allowed  as  a  standard  for  the  transmission  of  a 
given  quantity  of  air  through  a  given  length  of  pipe  of  any  diameter.  The 
increased  loss  due  to  increasing  the  length  of  pipe  was  compensated  for  by 
increasing  the  diameter  sufficiently  to  keep  the  loss  still  at  1/2  oz.  Thus, 
if  2500  cu.  ft.  of  air  is  to  be  delivered  per  minute  through  100  ft  of  pipe 
with  a  loss  of  not  more  than  i/2  oz.,  a  H-in.  pipe  will  be  required,  If  it  is 


672  AIR. 

necessary  to  increase  the  length  of  pipe  to  140  ft.,  a  pipe  15  in.  diameter 
will  be  required  if  the  loss  in  pressure  is  not  to  exceed  1/2  oz.  In  deciding 
the  size  of  pipe  the  loss  in  pressure  in  the  pipe  must  be  added  to  the  pres- 
sure to  be  maintained  at  the  fan  or  blower,  if  the  tabulated  efficiency  of 
the  latter  is  to  be  secured  at  the  delivery  end  of  the  pipe. 

Centrifugal  Ventilators  for  Mines.  —  Of  different  appliances  for  ven- 
tilating mines  various  forms  of  centrifugal  machines  having  proved  their 
efficiency  have  now  almost  completely  replaced  all  others.  Most  if  not  all 
of  the  machines  in  use  in  this  country  are  of  this  class,  being  either  open- 
periphery  fans,  or  closed,  with  chimney  and  spiral  casing,  of  a  more  or  less 
modified  Guibal  type.  The  theory  of  such  machines  has  been  demonstrated 
by  Mr.  Daniel  Murgue  in  "  Theories  and  Practices  of  Centrifugal  Ventilating 
Machines,"  translated  by  A.  L.  Stevenson,  and  is  discussed  in  a  paper  by  R. 
Van  A.  Norris,  Trans.  A.  I.  M.  E.,  xx.  637.  From  this  paper  the  following 
formula  are  taken: 

Let  a  =  area  in  sq.  ft.  of  an  orifice  in  a  thin  plate,  of  such  area  that  its 
resistance  to  the  passage  of  a  given  quantity  of  air  equals  the 
resistance  of  the  mine; 
o  =  orifice  in  a  thin  plate  of  such  area  that  its  resistance  to  the  pas- 

sage of  a  given  quantity  of  air  equals  that  of  the  machine; 
Q^=  quantity  of  air  passing  in  cubic  feet  per  minute; 
V  =  velocity  of  air  passing  through  a  in  feet  per  second; 
V0  =  velocity  of  air  passing  through  o  in  feet  per  second  ; 
h,  =  head  in  feet  air-column  to  produce  velocity  V; 
ho  =  head  in  feet  air-column  to  produce  velocity  VQ. 


, 

feet  per  minute 

0.403  Q 
= 


Q  =  0.65 aV;    V  =  ^Tgh;  Q  =  Q.65a^2gh't 

a  =    ,         =  equivalent  orifice  of  mine; 

0.65  v  2  gh 

or,  reducing  to  water-gauge  in  inches  and  quantity  in  thousands  of  cubic 
fpftt,  npr  minute. 

=  0.65  oF0;     Fo  =  ^2  ^0;    (?  =  0.65  o  ^/2gh0-l 


v/ 


O2 

—  equivalent  orifice  of  machine. 


0.65%2  g 

The  theoretical  depression  which  can  be  produced  by  any  centrifugal 
ventilator  is  double  that  due  to  its  tangential  speed.  The  formula 

T»        y2 
H  -2~g-  2~g' 

in  which  Tis  the  tangential  speed,  V  the  velocity  of  exit  of  the  air  from  the 
space  between  the  blades,  and  H  the  depression  measured  in  feet  of  air- 
column,  is  an  expression  for  the  theoretical  depression  which  can  be  pro- 
duced by  an  uncovered  ventilator:  this  reaches  a  maximum  when  the  air 
leaves  the  blades  without  speed,  that  is,  V  =  0,  and  H  =  Tz  *•  2  g. 

Hence  the  theoretical  depression  which  can  be  produced  by  any  uncov- 
ered ventilator  is  equal  to  the  height  due  to  its  tangential  speed,  and  one- 
half  tnat  which  can  be  produced  by  a  covered  ventilator  with  expanding 
chimney.  Practical  considerations  in  the  design  of  the  fan  wheel  and 
casing  will  probably  cause  the  actual  results  obtained  with  fans  to  vary 
considerably  from  these  formulae. 

So  long  as  the  condition  of  the  mine  remains  constant: 

(1)  The  volume  produced  by  any  ventilator  varies  directly  as  the  speed 
of  rotation. 

(2)  The  depression  produced  by  any  ventilator  varies  as  the  square  of 
the  speed  of  rotation. 

(3)  For  the  same  tangential  speed  with  decreased  resistance  the  quantity 
of  air  increases  and  the  depression  diminishes, 


MINE   VENTILATING   FANS. 


673 


The  following  table  shows  a  few  results,  selected  from  Mr.  Norris's 
paper,  giving  the  range  of  efficiency  which  may  be  expected  under  dif- 
ferent circumstances.  Details  of  these  and  other  fans,  with  diagrams 
of  the  results,  are  given  in  the  paper. 


Experiments  on  Mine-Ventilating  Fans. 


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O 

p 

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ffl 

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84 

5517 

236,684 

2818 

3040 

4290 

1  80 

67.13 

88.40 

75.9 

^  S 

100 

6282 

336,862 

3369 

3040 

5393 

2.50 

132.70 

155.43 

85.4 

11 

1  1  1 

6973 

347,396 

3130 

3040 

5002 

3.20 

175.17 

209.64 

83.6 

rS 

123 

7727 

394,100 

3204 

3040 

5100 

3.60 

223.56 

295.21 

75.7 

)> 

100 

6282 

188,888 

1889 

1520 

3007 

1.40 

41.67 

97.99 

42.5 

130 

8167 

274,876 

2114 

1520 

3366 

2.00 

86.63 

194.95 

44.6 

22 

CJ 

59 

3702 

59,587 

1010 

1520 

1610 

1.20 

11.27 

16.76 

67.83 

< 

83 

5208 

82,969 

1000 

1520 

1593 

2.15 

27.86 

48.54 

57.38 

n  J 

40 

3140 

49,611 

1240 

3096 

1580 

0.87 

6.80 

13.82 

49.2 

32 

Dl 

70 

5495 

137,760 

1825 

3096 

2507 

2.55 

55.35 

67.44 

82.07 

50 

2749 

147,232 

2944 

1522 

5356 

0.50 

11.60 

28.55 

40.63 

E  •s 

69 

3793 

205,761 

2982 

1522 

5451 

1.00 

32.42 

45.98 

70.50 

83 

( 

96 

5278 

299,600 

3121 

1522 

5676 

2.15 

101.50 

120.64 

84.10 

200 

7540 

133,198 

666 

746 

1767 

3.35 

70.30 

102.79 

68.40 

26.9 

200 

7540 

180,809 

904 

746 

2398 

3.05 

86.89 

129.07 

67.30 

38.3 

200 

7540 

209,150 

1046 

746 

2774 

2.80 

92.50 

150.08 

61.70 

46.3 

10 

785 

28,896 

2890 

3022 

3680 

0.10 

0.45 

1.30 

35. 

20 

1570 

57,120 

2856 

3022 

3637 

0.20 

1.80 

3.70 

49. 

25 

1962 

66,640 

2665 

3022 

3399 

0.29 

2.90 

6.10 

48. 

30 

2355 

73,080 

2436 

3022 

3103 

0.40 

4.60 

9.70 

47. 

52 

G,^ 

35 

2747 

94,080 

2688 

3022 

3425 

0.50 

7.40 

15.00 

48. 

^ 

40 

3140 

112,000 

2800 

3022 

3567 

0.70 

12.30 

24.90 

49. 

50 

3925 

132,700 

2654 

3022 

3381 

0.90 

18.80 

38.80 

48. 

60 

4710 

173,600 

2893 

3022 

3686 

1.35 

36.90 

66.40 

55. 

70 

5495 

203,280 

2904 

3022 

3718 

1.80 

57.70 

107.10 

54. 

m 

6280 

222,320 

2779 

3022 

3540 

2.25 

78.80 

152.60 

52. 

Type  of  fan. 

Diam. 

Width. 

No.  inlets. 

Diam. 
inlets. 

A.  Guibal,  double    .                ... 

20ft. 

6ft. 

4 

8ft.  10  in. 

B.  Same,  only  left  hand  running 
C   Guibal 

20 
20 

6 
6 

4 
2 

8       10 
8       10 

D.  Guibal             

25 

8 

1 

11         6 

E.  Guibal  double 

171/o 

4 

4 

8 

F.  Capell...... 

12 

10 

2 

7 

G.  Guibal 

25 

8 

12 

An  examination  of  the  detailed  results  of  each  test  in  Mr.  Norris's  table 
shows  a  mass  of  contradictions  from  which  it  is  exceedingly  diffiault  to 
draw  any  satisfactory  conclusions.  The  following,  he  states,  appear  to  be 
more  or  less  warranted  by  some  of  the  figures: 

1.  Influence  of  the  Condition  of  the  Airways  on  the  Fan.  —  Mines  with 
varying  equivalent  orifices  give  air  per  100  ft.  speed  of  tip  of  fan,  within 
limits  as  follows,  the  quantity  depending  on  the  resistance  of  the  mine; 


674 


AIR. 


E  quivalent 
orifice, 
sq.  ft. 

Cu.ft.air 
per  100  ft. 
speed  of  fan. 

Average. 

Equivalent 
orifice, 
sq.  ft. 

Cu.ft.  air 
per  100  ft. 
speed  of  fan. 

Average. 

Under  20 
20  to  30 
30  to  40 
40  to  50 

1100  to  1700 
1300  to  1800 
1500  to  2500 
2300  to  3500 

13QO 
1600 
2100 
2700 

60  to  70 
70  to  80 
80  to  90 
90  to  100 

3300  to  5100 
4000  to  4700 
3000  to  5600 

4000 
4400 
4800 

50  to  60 

2700  to  4800 

3500 

100  to  114 

5200  to  6200 

5700 

The  influence  of  the  mine  on  the  efficiency  of  the  fan  does  not  seem  to  be 
very  clear.  Eight  fans,  with  equivalent  orifices  over  50  square  feet,  give 
efficiencies  over  70%;  four,  with  smaller  equivalent  mine-orifices,  give 
about  the  same  figures;  while,  on  the  contrary,  six  fans,  with  equivalent 
orifices  of  over  50  square  feet,  give  lower  efficiencies,  as  do  ten  fans,  all 
drawing  from  mines  with  small  equivalent  orifices.  It  would  seem  that, 
on  the  whole,  large  airways  tend  to  assist  somewhat  in  attaining  high 
efficiency. 

2.  Influence  of  the  Diameter  of  the  Fan.  —  This  seems  to  be  practically  nil, 
the  only  advantage  of  large  fans  being  in  their  greater  width  and  the  lower 
speed  required  of  the  engines. 

3.  Influence  of  the  Width  of  a  Fan.  —  This  appears  to  be  small  as  regards 
the  efficiency  of  the  machine;  but  the  wider  fans  are,  as  a  rule,  exhausting 
more  air.     However,  increasing  the  width  of  the  fan  of  a  given  diameter 
causes  an  increase  in  the  velocity  of  the  air  through  the  wheel  inlet,  and 
this  increased  velocity  will  become  at  a  certain  point  a  serious  loss  and 
will  decrease  the  mechanical  efficiency. 

4.  Influence  of  Shape  of  Blades.  —  This  appears,  within  reasonable  limits, 
to  be  practically  nil.     Thus,  six  fans  with  tips  of  blades  curved  forward, 
three  fans  with  flat  blades,  and  one  with  blades  curved  back  to  a  tangent 
with  the  circumference,  all  give  very  high  efficiencies  —  over  70  per  cent. 
A  prominent  manufacturer  claims,  however,  that  his  tests  show  a  higher 
efficiency  with  vanes  curved  forward  as  compared  with  straight  or  back- 
wardiy  curved  vanes. 

5.  Influence  of  the  Shape  of  the  Spiral  Casing.  —  This  appears  to  be 
considerable.     The  shapes  of  spiral  casing  in  use  fall  into  two  classes, 
the  first  presenting  a  large  spiral,  beginning  at  or  near  the  point  of  cut-off, 
and  the  second  a  circular  casing  reaching  around  three-quarters  of  the 
circumference  of  the  fan,  with  a  short  spiral   reaching  to  the  evasee 
chimney.     Fans  having  the  first  form  of  casing  appear  to  give  in 
almost  every  case  high  efficiencies. 

Fans  that  have  a  spiral  belonging  to  the  first  class,  but  very  much  con- 
tracted, give  only  medium  efficiencies.  It  seems  probable  that  the  proper 
shape  of  spiral  casing  would  be  one  of  such  form  that  the  air  between  each 
pair  of  blades  could  constantly  and  freely  discharge  into  the  space  between 
the  fan  and  casing,  the  whole  being  swept  along  to  the  evasee  chimney. 
This  would  require  a  spiral  beginning  near  the  point  of  cut-off,  enlarging  by 
gradually  increasing  increments,  to  allow  for  the  slowing  of  the  air  caused 
by  its  friction  against  the  casing,  and  reaching  the  chimney  with  an  area 
such  that  the  air  could  make  its  exit  with  its  then  existing  speed  —  some- 
what less  than  the  periphery-speed  of  the  fan. 

6.  Influence  of  the  Shutter.  —  The  shutter  certainly  appears. to  be  an  ad- 
vantage, as  by  it  the  exit  area  can  be  regulated  to  suit  the  varying  quantity 
of  air  given  by  the  fan,  and  in  this  way  re-entries  can  be  prevented      J 
not  uncommon  to  find  shutterless  fans,  into  the  chimneys  of  which  bits  of 
paper  may  be  dropped,  which  are  drawn  into  the  fan,  make  the  circuit,  and 
are  again  thrown  out.     This  peculiarity  has  not  been  noticed  with  fans 
provided  with  shutters. 

7.  Influence  of  the  Speed  at  which  a  Fan  is  Run.  —  It  is  noticeable  that 
most  of  the  fans  giving  high  efficiency  were  running  at  a  rather  high 
periphery  velocity.     The  best  speed  seems  to  be  between  5000  and  6000 
feet  per  minute.     The  fans  appear  to  reach  a  maximum  efficiency  at  some- 
where about  the  speed  given,  and  to  decrease  rapidly  in  efficiency  when 
this  maximum  point  is  passed.     The  same  manufacturer  mentioned  in 
note  4  states  that  the  efficiency  is  not  affected  by  the  tip  speed,  providing 
that  the  comparison  is  always  made  at  the  same  point  in  the  efficiency 
curve.   ' 


DISK  FANS. 


675 


In  discussion,  of  Mr.  JN orris's  paper,  Mr.  A.  H.  Starrs  says:  From  the  "  cu- 
bic feet  per  revolution"  and  "cubical  contents  of  fan-blades,"  as  given  in 
the  table,  we  find  that  the  enclosed  fans  empty  themselves  from  one-half  to 
twice  per *re volution,  while  the  open  fans  are  emptied  from  one  and  three- 
quarters  to  nearly  three  times ;  this  for  fans  of  both  types,  on  mines  covering 
the  same  range  of  equivalent  orifices.  One  open  fan,  on  a  very  large 
orifice,  was  emptied  nearly  four  times,  while  a  closed  fan,  on  a  still 
larger  orifice,  only  shows  one  and  one-half  times.  For  the  open  fans  the 
"cubic  feet  per  100  ft.  motion"  is  greater,  in  proportion  to  the  fan 
width  and  equivalent  orifice,  than  for  the  enclosed  type.  Notwithstand- 
ing this  apparently  free  discharge  of  the  open  fans,  they  show  very  low 
efficiencies. 

As  illustrating  the  very  large  capacity  of  centrifugal  fans  to  pass  air,  if 
the  conditions  of  the  mine  are  made  favorable,  a  16-ft.  diam.  fan,  4  ft.  6  in. 
wide,  at  130  revolutions,  passed  360,000  cu.  ft.  per  min.,  and  another,  of 
same  diameter,  but  slightly  wider  and  with  larger  intake  circles,  passed 
500,000  cu.  ft.,  the  water-gauge  in  both  instances  being  about  1/2  in. 

T.  D.  Jones  says:  The  efficiency  reported  in  some  cases  by  Mr.  Norris  is 
larger  than  I  have  ever  been  able  to  determine  by  experiment.  My  own 
experiments,  recorded  in  the  Pennsylvania  Mine  Inspectors'  Reports  from 
1875  to  1881,  did  not  show  more  than  60%  to  65%. 


DISK  FANS. 

Efficiency  of  Disk  Fans.  —  Prof.  A.  B.  W.  Kennedy  (Industries,  Jan. 
17,  1890)  made  a  series  of  tests  on  two  disk  fans,  2  and  3  ft.  diameter, 
known  as  the  Verity  Silent  Air-propeller.  The  principal  results  and 
conclusions  are  condense'd  as  below. 


Propeller, 
2ft.  diam. 
i 

Propeller, 
3  ft.  diam. 

Speed  of  fan,  revolutions  per  minute.  . 
Net  H  P  to  drive  fan  and  belt 

750 
0  42 

676 
0.32 

577 
0.227 

576 
1.02 

459 
0.575 

373 

0.324 

Cubic  feet  of  air  per  minute 

4,183 

3,830 

3,410 

7,400 

5,800 

4,470 

Mean  velocity  of  air  in  3-ft.  flue,  feet 

593 

5'43 

482 

1,046 

820 

632 

Mean  velocity  of  air  in  flue,  same 

diameter  as  fan/  

1,330 

1,220 

1,085 

Cu.  ft.  of  air  per  min.  per  effective  H.P 
Motion  given  to  air  per  rev.  of  fan,  ft.. 
Cubic  feet  of  air  per  rev.  of  fan  

9,980 
1.77 
5.58 

11,970 
1.81 
5.66 

15,000 
1.88 
5.90 

7,250 
1.82 
12.8 

10,070 
1.79 
12.6 

13,800 
1.70 
12.0 

In  each  case  the  efficiency  of  the  fan,  that  is,  the  quantity  of  air  delivered 
per  effective  horse-power,  increases  very  rapidly  as  the  speed  diminishes, 
so  that  lower  speeds  are  much  m9re  economical  than  higher  pnes.  On  the 
other  hand,  as  the  quantity  of  air  delivered  per  revolution  is  very  nearly 
constant,  the  actual  useful  work  done  by  the  fan  increases  almost  directly 
with  its  speed.  Comparing  the  large  and  small  fans  with  about  the 
same  air  delivery,  the  former  (running  at  a  much  lower  speed,  of  course) 
is  much  the  more  economical.  Comparing  the  two  fans  running  at  the 
same  speed,  however,  the  smaller  fan  is  very  much  the  more  economical. 
The  delivery  of  air  per  revolution  of  fan  is  very  nearly  directly  propor- 
tional to  the  area  of  the  fan's  diameter. 

The  air  delivered  per  minute  by  the  3-ft.  fan  is  nearly  12.5  R  cubic  feet 
(R  being  the  number  of  revolutions  made  by  the  fan  per  minute).  For 
the  2-ft.  fan  the  quantity  is  5.7R  cubic  feet.  For  either  of  these  or  any 
other  similar  fans  of  which  the  area  is  A  square  feet,  the  delivery  will  be 
about  1.8  A  R  cubic  feet.  Of  course  any  change  in  the  pitch  of  the  blades 
might  entirely  change  these  figures. 

The  net  H.P.  taken  up  is  not  far  from  proportional  to  the  square  of  the 
number  of  revolutions  above  100  per  minute.  Thus  for  the  3-ft.  fan  the 


net 


'  while  for  the  2-ft-  fan  the  net  H-  p  is 


. 

The  denominators  of  these  two  fractions  are  very  nearly  proportional 
inversely  to  ,the  square  of  the  fan  areas  or  the  fourth  power  of  the  fan 


676 


AIR. 


diameters.     The  net  H.P.  required  to  drive  a  fan  of  diameter  D  feet  or 
area  A  square  feet,  at  a  speed  of  R  revolutions  per  minute,  will  therefore 


The  3-ft.  fan  was  also  noiseless 


The  2-ft.  fan  was  noiseless  at  all  speeds. 
up  to  over  450  revolutions  per  minute. 

Experiments  made  with  a  Blackmail  Disk  Fan,  4  ft.  diam.  by  Geo. 
A.  Suter,  to  determine  the  volumes  of  air  delivered  under  various  con- 
ditions, and  the  power  required;  with  calculations  of  efficiency  and  ratio 
of  increase  of  power  to  increase  of  velocity,  by  G.  H.  Babcock.  (Trans. 
A.S.M.E.,vii.54,7): 


gj 

a 
1 

> 

i 

Cu.  ft.  of  Air 
delivered 
per  min., 

j_T 
o 

jgj 

O 

i.S 

«   . 

,«Sr* 
^  s 
r~  d 
p 

id 

Wts  • 

*o  vj& 

•|fc& 
| 

Ratio  of  In- 
crease of 
Delivery 

Ratio  of  In- 
crease of 
Power. 

Exponent  x, 
HP*  Vx. 

Exponent  y, 

fcoo  yy. 

Efficiency 
of  Fan. 

350 

25  797 

0  65 

1  682 

440 

32575 

2  29 

257 

262 

3  523 

5  4 

9553 

534 

41,929 

4  42 

.186 

.287 

1.843 

2.4 

1.062 

612 

47  756 

7  41 

146 

139 

1  677 

3  97 

9358 

For 

series 

.749 

.851 

11.140 

4. 

340 

20372 

0  76 

7110 

453 

26660 

1  99 

.332 

.308 

2.6J8 

3.55 

.6063 

536 

31  649 

3  86 

183 

187 

1  940 

3  86 

5205 

627 

36543 

'6  47 

.167 

.155 

1.676 

3  59 

.4802 

For 

series 

.761 

.794 

8.513 

3.63 

340 

9  983 

1  12 

0  28 

3939 

430 
534 
570 

n;oi7 

17,018 
18,649 
For 

3.17 
6.07 
8.46 
series 

0.47 
0.75 
0.87 

.265 
.242 
.068 
.676 

.304 
.307 
.096 
.704 

2.837 
1.915 
1.394 
7.554 

3.93 
2.25 
3.63 
3.24 

1.95 
1.74 
1.60 
1.81 

.3046 
.3319 
.3027 

330 

8399 

1  31 

0  26 

2631 

437 
516 

10,071 
11,157 
For 

3.27 
6.00 
series 

0.45 
0.75 

.324 
.181 
563 

.199 
.103 
329 

3.J42 
1.457 
4  580 

6.31 

3.66 
5  35 

3.06 
4.96 
3  72 

.2188 
.2202 

Nature  of  the  Experiments.  —  First  Series:  Drawing  air  through  30  ft. 
of  48-in.  diam.  pipe  on  inlet  side  of  the  fan. 

Second  Series:  Forcing  air  through  30  ft.  of  48-in.  diam.  pipe  on  outlet 
side  of  the  fan. 

Third  Series:  Drawing  air  through  30  ft.  of  48-in.  pipe  on  inlet  side  of 
the  fan  —  the  pipe  being  obstructed  by  a  diaphragm  of  cheese-cloth. 

Fourth  Series:  Forcing  air  through  30  ft.  of  48-in.  pipe  on  outlet  side 
of  fan  —  the  pipe  being  obstructed  by  a  diaphragm  of  cheese-cloth. 

Mr.  Babcock  says  concerning  these  experiments:  The  first  four  experi- 
ments are  evidently  the  subject  of  some  error,  because  the  efficiency  is 
such  as  to  prove  on  an  average  that  the  fan  was  a  source  of  power  sufficient 
to  overcome  all  losses  and  help  drive  the  engine  besides.  The  second 
series  is  less  questionable,  but  still  the  efficiency  in  the  first  two  experi- 
ments is  larger  than  might  be  expected.  In  the  third  and  fourth  series 
the  resistance  of  the  cheese-cloth  in  the  pipe  reduces  the  efficiency  largely, 
as  would  be  expected.  In  this  case  the  value  has  been  calculated  from 
the  height  equivalent  to  the  water-pressure,  rather  than  the  actual  veloc- 
ity of  the  air. 

This  record  of  experiments  made  with  the  disk  fan  shows  that  this  kind 
of  fan  is  not  adapted  for  use  where  there  is  any  material  resistance  to  the 
flow  of  the  air.  In  the  centrifugal  fan  the  power  used  is  nearly  propor- 
tioned to  the  amount  of  air  moved  under  a  given  head,  while  in  this  fan 
the  power  required  for  the  same  number  of  revolutions  of  the  fan  increases 
very  materially  with  the  resistance,  notwithstanding  the  quantity  of  air 
moved  is  at  the  same  time  considerably  reduced.  In  fact  from  the  inspec- 


POSITIVE   ROTARY   BLOWERS.  677 

tion  of  the  third  and  lourth  series  of  tests,  it  would  appear  that  the  power 
required  is  very  nearly  the  same  for  a  given  pressure,  whether  more  or 
less  air  be  in  motion.  It  would  seem  that  the  main  advantage,  if  any, 
of  the  disk  fan  over  the  centrifugal  fan  for  slight  resistances  consists  in  the 
fact  that  the  delivery  is  the  full  area  of  the  disk,  while  with  centrifugal 
fans  intended  to  move  the  same  quantity  of  air  the  opening  is  much 
smaller. 

It  will  be  seen  by  columns  8  and  9  of  the  table  that  the  power  used  in- 
creased much  more  rapidly  than  the  cube  of  the  velocity,  as  in  centrifugal 
fans.  The  different  experiments  do  not  agree  with  each  other,  but  a 
general  average  may  be  assumed  as  about  the  cube  root  of  the  eleventh 
power. 

Capacity  of  Disk  Fans.  (C.  L.  Hubbard,  The  Metal  Worker,  Sept.  5, 
1908.) — The  rated  capacities  given  in  catalogues  are  for  fans  revolving 
in  free  air  —  that  is,  mounted  in  an  opening  without  being  connected  with 
ducts  or  subject  to  other  frictional  resistance. 

The  following  data,  based  upon  tests,  apply  to  fans  working  against  a 
resistance  equivalent  to  that  of  a  shallow  heater  of  open  pattern,  and 
connecting  with  ducts  of  medium  length  through  which  the  air  flows  at  a 
velocity  not  greater  than  600  or  800  ft.  per  minute.  Under  these  con- 
ditions a  good  type  of  fan  will  propel  the  air  in  a  direction  parallel  to  the 
shaft,  a  distance  equal  to  about  0.7  of  its  diameter  at  each  revolution. 
From  this  we  have  the  equation  Q  =  0.7  D  X  R  X  A,  in  which  Q  =  cu. 
ft.  of  air  discharged  per  minute;  D  =  diam.  of  fan,  in  ft.;  R  =  revs,  per 
min.;  A  =  area  of  fan,  in  sq.  ft.  The  following  table  is  calculated  on  this 
basis. 
Diam.  of  fan,  in. 

18      24       30       36       42      48       54      60       72       84       96 
Cu.  ft  per  rev. 

1.85    4.40   8.59    14.8    23.6  35.2    50.1    68.7    118.7188.6  281.5 

Revolutions  per  min.  for  velocity  of  air  through  fan  =  1000  ft.  per  min. 
952     714     571     476     408     357     317     286     238     204     179 

The  velocity  of  the  air  through  the  fan  is  proportional  to  the  number 
of  revolutions.  For  the  conditions  stated  the  H.P.  required  per  1000  cu. 
ft  of  air  moved  will  be  about  0.16  when  the  velocity  through  the  fan  is 
1000  ft.  per  min.,  0.14  for  a  velocity  of  800  ft.,  and  0.18  for  1200  ft.  For 
a  fan  moving  in  free  air  the  required  speed  for  moving  a  given  volume  of 
air  will  be  about  0.6  of  the  number  of  revolutions  given  above  and  the 
H.P.  about  0.3  of  that  required  when  moving  against  the  resistance  stated. 

POSITIVE   ROTARY  BLOWERS. 

Rotary  Blowers,  Centrifugal  Fans,  and  Piston  Blowers.  (Cata- 
logue of  the  Connersville  Blower  Co.)  — In  ordinary  work  the  advantage 
of  a  positive  blower  9ver  a  fan  begins  at  about  8  oz.  pressure,  and  the 
efficiency  of  the  positive  blower  increases  from  8  oz.  as  the  pressure  goes 
up  to  a  point  where  the  ordinary  centrifugal  fan  fails  entirely.  The 
highest  efficiency  of  rotary  blowers  is  when  they  are  working  against 
pressures  ranging  between  1  and  8  Ibs. 

Fans,  when  run  at  constant  speed,  cannot  be  made  to  handle  a  constant 
volume  of  fluid  when  the  pressure  is  variable;  and  they  cannot  give  a  high 
efficiency  except  for  low  and  uniform  pressures. 

When  a  fan  blower  is  used  to  furnish  blast  for  a  cup9la  it  is  driven  at  a 
constant  speed,  and  the  amount  of  air  discharged  by  it  varies  according 
to  the  resistance  met  with  in  the  cupola.  With  a  positive  blower  running 
at  a  constant  speed,  however,  there  is  a  constant  volume  of  air  forced 
into  the  cupola,  regardless  of  changing  resistance. 

A  rotary  blower  of  the  two-impeller  type  is  not  an  economical  com- 
pressor, because  the  impellers  are  working  against  the  full  pressure  c.t  all 
times,  while  in  an  ideal  blowing  engine  the  theoretical  mean  -effective 
pressure  on  the  piston,  when  discharging  air  at  15  Ibs.  pressure,  is  111/2  Ibs. 
For  high  pressures,  on  account  of  the  increase  of  leakage  and  the  increase 
of  power  required  because  it  does  not  compress  gradually,  the  rotary 
blower  must  give  way  to  the  piston  type  of  machine.  Commercially,  the 
line  is  crossed  at  about  8  Ibs.  pressure. 

1.  A  fan  is  the  cheapest  in  first  cost,  and  if  properly  applied  may  be 
used  economically  for  pressures  up  to  8  oz. 


678 


AIR. 


2.  A  rotary  blower  costs  more  than  a  fan,  but  much  less  than  a  blowing 
engine;  is  more  economical  than  either  between  8  oz..and  8  Ibs.  pressure, 
and  can  be  arranged  to  give  a  constant  pressure  or  a  constant  volume. 

3.  Piston  machines  cost  much  more  than  rotary  blowers,  but  should 
be  used  for  continuous  duty  for  pressures  above  8  Ibs.,  and  may  be  econom- 
ical if  they  are  properly  constructed  and  not  run  at  too  high  a  piston  speed. 

The  horse-power  required  to  operate  rotary  blowers  is  prop9rtional  to 
the  volume  and  pressure  of  air  discharged.  In  making  estimates  for 
power  it  is  safe  to  assume  that  for  each  1000  cu.  ft.  of  free  air  discharged, 
at  one  pound  pressure,  5  H.P.  should  be  provided. 

Test  of  a  Rotary  Blower.  (Connersville  Blower  Co.)  —  The  test  was 
made  in  1904  on  two  39  X  84  in.  blowers  coupled  direct  to  two  12  and  24  X 
36  in.  compound  Corliss  engines.  The  results  given  below  are  for  the 
combined  units. 


Air  pressure,  Ibs  
Engine,  I.H.P  

0 
19.30 

0.05 
23.76 

0.5 

52.83 

1.0 

100.91 

1.5 

132.67 

2. 
176.11 

2.5 
223.20 

3. 

256.87 

3.5 

287.56 

Displacement,  cu.ft. 

19,212 

18,727 

18,508 

18,344 

18,200 

18,028 

17,966 

17,863 

Efficiency  

68.5 

79 

84 

85.6 

86 

86 

85.9 

In  calculating  the  efficiency  the  theoretical  horse-power  was  taken  as 
the  power  required  to  compress  adiabatically  and  to  discharge  the  net 
amount  of  air  at  the  different  pressures  and  at  the  same  altitude.  The 
test  was  made  up  to  3.5  Ibs.  only.  Estimated  efficiencies  for  higher 
pressures  from  an  extension  of  the  plotted  curve  are:  6  Ibs.  84%,  8  Ibs. 
82%,  10  Ibs.  79.5%.  The  theoretical  discharge  of  the  blower  was  19,250 
cu.  ft. 

CAPACITY  OF  ROTAIIY  BLOWERS  FOR  CUPOLAS. 


Cu.ft 
per 
rev. 

Revs, 
per 
min. 

Tons 
per 
hour. 

Suitable 
for  cupola 
in.  diam.* 

Cu.  ft. 
per 
rev. 

Revs, 
per 
min. 

Tons 
per 
hour. 

Suitable 
for  cupola 
in.  diam. 

1.5 

(  200 
i   400 

2 

|  18  to  20 

45 

(  135 
\  165 

12 
15 

i  54  to  66 

3.3 

i   175 
{  335 

2 

|  24  to  27 

(  200 
(  130 

18 
15 

1 

6 

j   185 
i  275 

2 
3 

}  28  to  32 

57 

1  155 
(  185 

18 
21 

60  to  72 

10 

\  200 
\  250 

4 

5 

j  32  to  38 

65 

(  140 
<  160 

18 
21 

[  66  to  84 

(   150 

4 

!• 

I  185 

24 

) 

13 

t    190 
(   175 

5 
61/2 

32  to  40 

84 

(  125 
]  145 

21 
24 

[  72  to  90 

(   150 

5 

) 

I  160 

27 

) 

17 

<  205 
(   250 

61/2 
81/2 

j-  36  to  45 

100 

(  120 
1  135 

24 
27 

\  84  to  96 

(   166 

8 

) 

(  160 

30 

) 

24 

<  200 
(  240 
(    150 

10 
12 
10 

>  42  to  54 
) 

118 

(  115 
<  130 
(  140 

27 
30 
33 

)  Two 
(  cupolas 
)  60  to  66 

33 

<    180 

12 

>  48  to  60 

(   210 

14 

) 

*  Inside  diam.     The  capacity  in  tons  per  hour  is  based  on  30,000  cu.  ft. 
of  air  Der  ton  of  iron  melted. 

For  smith  fires:  an  ordinary  fire  requires  about  60  cu.  ft.  per  min. 

For  oil  furnaces :  an  ordinary  furnace  burns  about  2  gallons  of  oil  per 
hour  and  1800  cu.  ft.  of  air  should  be  provided  for  each  gallon  of  oil.    For 
each  100  cu.  ft.  of  air  discharged  per  minute  at  16  oz.  pressure,  1/2  H.P. 
should  be  provided. 
Sizes  of  small  blowers.        173  288  576  cu.  in.  per  rev. 

Revs,  per  min 800  to  1500     500  to  900        300  to  600 

Diam.  of  outlet,  in 21/2  21/2  3 


STEAM   JET   BLOWER   AND   EXHAUSTER. 


G79 


ROTARY  GAS  EXHAUSTERS. 


Cu.  ft.  per  rev  

2ft 

H/2 

3.3 

6 

10 

13 

17 

24 

33 

Rev.  per  min.  . 

200 

180 

170 

160 

150 

150 

140 

130 

120 

Diam.  of  pipe  open- 

ing .   .        . 

4 

6 

8 

10 

12 

12 

16 

16 

20 

Cu.  ft.  per  rev  

45 

57 

65 

84 

100 

118 

155 

200 

300 

Rev.  per  min  

110 

100 

95 

90 

85 

82 

80 

80 

75 

Diam.  pipe  opening 

20 

24 

24 

30 

30 

30 

36 

36 

42 

There  is  no  gradual  compressing  of  air  in  a  rotary  machine,  and  the 
unbalanced  areas  of  the  impellers  are  working  against  the  full  difference 
of  pressure  at  all  times.  The  possible  efficiency  of  such  a  machine  under 
ordinary  temperature  and  conditions  of  atmosphere,  assuming  no  me- 
chanical friction,  leakage,  nor  radiation  of  heat  of  compression,  would  be 
as  follows: 

Gauge  pres.  Ib 1  2  3  4  5     10    -   15 

Efficiency  % 97.5     95.5     93.3     91.7     90     82.7     76.7 

The  proper  application  of  rotary  positive  machines  when  operating  in 
air  or  gas  under  differences  of  pressures  from  8  oz.  to  5  Ibs.  is  where  con- 
stant quantities  of -fluid  are  required  to  be  delivered  against  a  variable 
resistance,  or  where  a  constant  pressure  is  required  and  the  volume  is 
variable.  These  are  the  requirements  of  gas  works,  pneumatic-tube 
transmission  (both  the  vacuum  and  pressure  systems),  foundry  cupolas, 
smelting  furnaces,  knobbling  fires,  sand  blast,  burning  of  fuel  oil,  con- 
veying granular  substances,  the  operation  of  many  kinds  of  metallurgical 
furnaces,  etc.  —  J.  T.  Wilkin,  Trans.  A.  S.  M.  E.,  Vol.  xxiv. 

STEAM-JET  BLOWER  AND  EXHAUSTER 

The  Steam-jet  as  a  Means  for  Ventilation.  —  Between  1810  and 
1850  the  steam-jet  was  employed  to  a  considerable  extent  for  ventilating 
English  collieries,  and  in  1852  a  committee  of  the  House  of  Commons 
reported  that  it  was  the  most  powerful  and  at  the  same  time  the  cheapest 
method  for  the  ventilation  of  mines;  but  experiments  made  shortly  after- 
wards proved  that  this  opinion  was  erroneous,  and  that  furnace  ventila- 
tion was  less  than  half  as  expensive,  and  in  consequence  the  jet  was  soon 
abandoned  as  a  permanent  method  of  ventilation. 

For  an  account  of  these  experiments  see  Colliery  Engineer,  Feb.,  1890. 
The  jet,  however,  is  sometimes  advantageously  used  as  a  substitute,  for 
instance,  in  the  case  of  a  fan  standing  for  repairs,  or  after  an  explosion, 
when  the  furnace  may  not  be  kept  going,  or  in  the  case  of  the  fan  having 
been  rendered  useless. 

A  Blower  and  Exhauster  is  made  by  Schutte  &  Koerting  Co.,  Phil- 
adelphia, on  the  principle  of  the  steam-jet  ejector.  The  following  is  a 
table  of  capacities. 


Diameter  of 
Pipes,  Inches. 

Capacity 
per 

Diameter  of 
Pipes,  Inches. 

Capacity 
Per 

Diameter  of 
Pipes,  Inches. 

Capacity 

TT/vni« 

_A:- 

Steam. 

Cu.  ft. 

Air. 

Steam. 

H-.,,- 
Cu.  ft. 

Air. 

Steam. 

Cu.  ft. 

V. 

l/4 

300 

2 

3/4 

4,000 

5 

2 

27,000 

a/4 

3/8 

600 

2V'2 

6,000 

6 

2 

35,000 

1 

3/8 

1,000 

3 

M/4 

12,000 

7 

2V2 

48,000 

IVa 

Va 

2,000 

4 

n/2 

18,000 

8 

3 

60,000 

When  used  as  exhausters  with  a  steam  pressure  of  45  Ib.,  these 
machines  will  produce  a  vacuum  of  20  in.  mercury  (23.3  ft.  water 
column),  but  they  can  be  specially  constructed  to  produce  a  vacuum 
of  25  in.  mercury  (29.3  ft.  water  column). 


G80 


AIR. 


When  used  as  compressors,  they  will  operate  against  a  counter-pres- 
sure equal  to  1/7  of  the  steam  pressure. 

Another  steam-jet  blower  is  used  for  boiler-firing,  ventilation,  and 
similar  purposes  where  a  low  counter-pressure  or  rarefaction  meets  the 
requirements. 

The  y9lumes  as  given  in  the  following  table  of  capacities  are  under  the 
supposition  of  a  steam-pressure  of  60  Ibs.  and  a  counter-pressure  of, 
say,  from  0.5  to  2  inches  of  water: 


Diameter 
in  Inches. 

Capacity 
per 
Hour, 
Cubic 
Feet. 

Diameter 
in  Inches. 

Capacity 
per 
Hour, 
Cubic 
Feet. 

Diameter 
in  Inches. 

Capacity 
per 
Hour, 
Cubic 
Feet. 

4 

4 

if 

M 

4 

|| 

4 

^5 

6  cJ 

4 

8 
9 

3 

4 

6 

J/8 

V2 
V2 
3/4 

10,000 
20,000 
30,000 
45,000 

11 

12 
14 
16 

7 
8 
10 
12 

V4 

1 
1 

60,000 
90,000 
120,000 
180,000 

18 
24 
32 
42 

14 
18 
24 
32 

2 

2V2 

240,000 
500,000 
1,000,000 
2,000,000 

Maximum  coal  burning  capacity  per  hour  =  cu.  ft.  air  per  hr.  -:-  200. 

BLOWING-ENGINES. 

Blowing-  engines.  —  The  following  table  showing  dimensions, 
capacity,  etc.,  of  Corliss  horizontal  cross-compound  condensing 
blowing  engines  is  condensed  from  a  table  published  about  1901  by 
the  Philadelphia  Engineering  Works.  Similar  engines  are  built  by 
William  Tod  &  Co.,  Youngstown,  Ohio,  and  other  builders. 

Corliss      Horizontal      Cross-compound      Condensing      Blowing- 
engines. 


Indicated 
Horse-power. 

d 

a 
I 

CO 

k 

o> 
tf 

*££ 
££ 

53.J3 

o< 

1   - 

1-3 
ad4 

J»  02 

CG   M 

-ft-0' 
s0^ 

g 

|J9 

§l 

»Q 
a 

o>   • 

-OC 

i 

4S 

Blast  Cylinders, 
Diam.,  in. 

StrokeofAllCyl- 
inders,  in. 

£s 

,C  bO 

tc'£ 

| 

P,G  . 

^•5S 

i  °£ 

ft£   . 

&$% 

/* 
&%$ 
$*> 

15  Exp. 
125  Ib. 
Steam. 

1,596 

13  Exp. 
100  Ib. 

Steam. 

2,280 
2,060 

"i.980" 
1,702 
1,386 
1,175 
822 

60 
60 
60 
60 
60 
60 
60 
60 

45,600 
45,600 
45,600 
39,600 
39,600 
39,600 
23,500 
23,500 

15 

12 
10 
15 
12 
10 
15 
10 

44 
42 
32 
40 
38 
36 
34 
28 

78 
72 
60 
72 
70 
66 
60 
50 

(2)  84 
(2)  84 
(2)  84 
(2)  78 
(2)  78 
(2)  78 
(2)  72 
(2)  72 

60 
60 
60 
60 
60 
60 
60 
60 

505,000 
475,000 
355,000 
445,000 
425,000 
415,000 
340,000 
270,000 

605,000 
550,000 
436,000 
545,000 
491,000 
450,000 
430,000 
300,000 

Vertical  engines  are  built  of  the  same  dimensions  as  above,  except 
that  the  stroke  is  48  in.  instead  of  60,  and  they  are  run  at  a  higher 
number  of  revolutions  to  give  the  same  piston-speed  and  the  same 
I.H.P. 

The  calculations  of  power,  capacity,  etc.,  of  blowing-engines  are  the 
same  as  those  for  air-compressors.  They  are  built  without  any  provision 
for  cooling  the  air  during  compression.  About  400  feet  per  minute  is  the 
usual  piston-speed  for  recent  forms  of  engines,  but  with  positive  air-valves, 
which  have  been  introduced  to  some  extent,  this  speed  may  be  increased. 
The  efficiency  of  the  engine,  that  is,  the  ratio  of  the  I.H.P.  of  the  air- 
cylinder  to  that  of  the  steam-cylinder,  is  usually  taken  at  90  per  cent,  the 
losses  by  friction,  leakage,  etc.,  being  taken  at  10  per  cent. 

Horse-power  of  Steam  Cylinders  of  Blowing-engines. — (Wm. 
Tod  &  Co.,  1914.)  To  find  the  indicated  horse-power  to  be  developed 
in  the  steam  cylinders  of  a  blowing-engine,  multiply  the  number  of 


HEATING   AND   VENTILATION.  681 

cubic  feet  of  free  air  to  be  compressed  per  minute  by  the  figures  given 
below  for  the  respective  pressures  named. 

Gage  press.  Ib. 

persq.  in. ...       5  10          15         20         25         30         35         40 

Factor... 0.0226    .0415    .0577    .0722    .0853    .0973    .1084  .1187 

These  factors  are  based  on  the  theoretical  horse-power  required 
to  compress  and  deliver  1  cu.  ft.  of  air  to  the  pressure  stated,  plus 
an  allowance  of  15%,  which  is  stated  to  be  about  right  for  mechanically- 
operated  air  valves.  With  poppet  air  valves  the  loss  may  be  about 
10%. 

HEATING  AND  VENTILATION. 

Ventilation.  (A.  R.  Wolff,  Stevens  Indicator,  April,  1890.)  —  The 
popular  impression  that  the  impure  air  falls  to  the  bottom  of  a  crowded 
room  is  erroneous.  There  is  a  constant  mingling  of  the  fresh  air  admitted 
with  the  impure  air  due  to  the  law  of  diffusion  of  gases,  to  difference  of 
temperature,  etc.  The  process  of  ventilation  is  one  of  dilution  of  the 
impure  air  by  the  fresh,  and  a  room  is  properly  ventilated  in  the  opinion 
of  the  hygienists  when  the  dilution  is  such  that  the  carbonic  acid  in  the 
air  does  not  exceed  from  6  to  8  parts  by  volume  in  10,000.  Pure  country 
air  contains  about  4  parts  CO2  in  10,000,  and  badly-ventilated  quarters 
as  high  as  80  parts. 

An  ordinary  man  exhales  0.6  of  a  cubic  foot  of  CO2  per  hour.  New 
York  gas  gives  9ut  0.75  of  a  cubic  feet  of  CO2  for  each  cubic  foot  of  gas 
burnt.  An  ordinary  lamp  gives  out  1  cu.  ft.  of  CO2  per  hour.  An 
ordinary  candle  gives  out  0.3  cu.  ft.  per  hour.  [The  use  of  gaslight  for 
interior  lighting  does  not  affect  the  atmosphere  deleteriously.  See 
pamphlet  issued  by  National  Commercial  Gas  Assn.,  1914. 1 

To  determine  the  quantity  of  air  to  be  supplied  to  the  inmates  of  an 
unlighted  room,  to  dilute  the  air  to  a  desired  standard  of  purity,  we 
can  establish  equations  as  follows: 

Let  v  =  cubic  feet  of  fresh  air  to  be  supplied  per  hour. 

r  =  cubic  feet  of  CO2  in  each  10,000  cu.  ft.  of  the  entering  air; 
R  =  cubic  feet  of  CO2  which  each  10,000  cu.  ft.  9f  the  air  in  the 

room  may  contain  for  proper  health  conditions ; 
n  =  number  of  persons  in  the  room ; 
0.6  =  cubic  feet  of  COz  exhaled  by  one  man  per  hour. 

Tnen  in  nrm  +°-6 n equals  cubic  feet  of  CO2  communicated  to  the  room 

1U,UUU 

during  one  hour. 

This  value  divided  by  v  and  multiplied  by  10,000  gives  the  proportion 
of  COa  in  10,000  parts  of  the  air  in  the  room,  and  this  should  equal  R,  the 
standard  of  purity  desired.  Therefore 


c 
'°TV 


R-r 


If  we  place  r  at  4  and  R  at  6,  v  =  6000  n  -f-  (6  -  4)  =  3000  n,  or  the 
quantity  of  air  to  be  supplied  per  person  is  3000  cubic  feet  per  hour. 

If  the  original  air  in  the  room  is  of  the  purity  of  external  air,  and  the 
cubic  contents  of  the  room  is  equal  to  100  cu.  ft.  per  inmate,  only  3000  — 
100  =  2900  cu.  ft.  of  fresh  air  from  without  will  have  to  be  supplied  the 
first  hour  to  keep  the  air  within  the  standard  purity  of  6  parts  of  CCh  in 
10,000.  If  the  cubic  contents  of  the  room  equals  200  cu.  ft.  per  inmate, 
only  3000  —  200  =  2800  cu.  ft.  will  have  to  be  supplied  the  first  hour  to 
keep  the  air  within  the  standard  purity,  and  so  on. 

Again,  if  we  only  desire  to  maintain  a  standard  of  purity  of  8  parts 
Of  carbonic  acid  in  10,000,  the  equation  gives  as  the  required  air-supply 
per  hour 

v=-  8_4-  n  — 1500  n,  or  1500  cu.  ft.  of  fresh  air  per  inmate  per  hour. 


682 


HEATING    AND   VENTILATION. 


Cubic  feet  of  air  containing  4  parts  of  carbonic  acid  in  10,000  necessary 
per  person  per  hour  to  keep  the  air  in  room  at  the  composition  of 

6  7  8  9          10         15         20      parts  of  CO2  in  10,000. 

3000      2000     1500     1200     1000      545       375     cubic  feet. 

If  the  original  air  in  the  room  is  of  purity  of  external  atmosphere  (4  parts 
of  carbonic  acid  in  10,000),  the  amount  of  air  to  be  supplied  the  first  hour, 
for  given  cubic  spaces  per  inmate,  to  have  given  standards  of  purity  not 
exceeded  at  the  end  of  the  hour,  is  obtained  from  the  following  table: 


Cubic 
Feet  of 
f  Space 
in  Room 
per 
Individ- 
ual. 

Proportion  of  Carbonic  Acid  in  10,000  Parts  of  the  Air,  not  to 
be  Exceeded  at  End  of  Hour. 

a      |      7 

8 

9 

10 

15 

20 

Cubic  Feet  of  Air,  of  Composition  4  Parts  of  Carbonic  Acid  in 
10,000,  to  be  Supplied  the  First  Hour. 

100 
200 
300 
400 
500 
600 
700 
800 
900 
1000 
1500 
2000 
2500 

2900 
2800 
2700 
2600 
2500 
2400 
2300 
2200 
2100 
2000 
1500 
1000 
500 

1900 
1800 
1700 
1600 
1500 
1400 
1300 
1200 
1100 
1000 
500 
None 

1400 
1300 
1200 
1100 
1000 
900 
800 
700 
600 
500 
None 

1100 
1000 
900 
800 
700 
600 
500 
400 
300 
200 
None 

900 
800 
700 
600 
500 
400 
300 
200 
100 
None 

445 
345 
245 
145 
45 
None 

275 
175 
75 
None 

It  is  exceptional  that  systematic  ventilation  supplies  the  3000  cubic 
feet  per  inmate  per  lumr,  which  adequate  health  considerations  demand. 
For  large  auditoriums  in  which  the  cubic  space  perindividual  is  great,  and  in 
which  the  atmosphere  is  thoroughly  fresh  before  the  rooms  are  occupied, 
and  the  occupancy  is  of  two  or  three  hours'  duration,  the  systematic  air- 
supply  may  be  reduced,  and  2000  to  2500  cubic  feet  per  inmate  per  hour 
is  a  satisfactory  allowance. 

In  hospitals  where,  on  account  of  unhealthy  excretions  of  various  kinds, 
the  air-dilution  must  be  largest,  an  air-supply  of  from  4000  to  6000  cubic 
feet  per  inmate  per  hour  should  be  provided,  and  this  is  actually  secured 
in  some  hospitals.  A  report  dated  March  15,  1882,  by  a  commission  ap- 
pointed to  examine  the  public  schools  of  the  District  of  Columbia,  says: 

"  In  each  class-room  not  less  than  15  square  feet  of  floor-space  should  be 
allotted  to  each  pupil.  In  each  class-room  the  window-space  should  not 
be  less  than  one-fourth  the  floor-space,  and  the  distance  of  desk  most 
remote  from  the  window  should  not  be  more  than  one  and  a  half  times  the 
height  of  the  top  of  the  window  from  the  floor.  The  height  of  the  class- 
room should  never  exceed  14  feet.  The  provisions  for  ventilation  should 
be  such  as  to  provide  for  each  person  in  a  class-room  not  less  than  30  cubic 
feet  of  fresh  air  per  minute  (1800  per  hour),  which  amount  must  be  intro- 
duced and  thoroughly  distributed  without  creating  unpleasant  draughts, 
or  causing  any  two  parts  of  the  room  to  differ  in  temperature  more  than 
2°  Fahr.,  or  the  maximum  temperature  to  exceed  70°  Fahr."  [The  provi- 
sion of  30  cu.  ft.  p_T  minute  for  each  person  in  a  class-room  is  now  (1909) 
required  by  law  in  several  states.] 

When  the  air  enters  at  or  near  the  floor,  it  is  desirable  that  the  velocity 
of  inlet  should  not  exceed  2  feet  per  second,  which  means  larger  sizes  of 
register  openings  and  flues  than  are  usually  obtainable,  and  much  higher 
velocities  of  inlet  than  two  feet  per  second  are  the  rule  in  practice. 
The  velocity  of  current  into  vent-flues  can  safely  be  as  high  as  6  or  even 
10  feet  per  second,  without  being  disagreeably  perceptible. 

The  entrance  of  fresh  air  into  a  room  is  coincident  with,  or  dependent 
on,  the  removal  of  an  equal  amount  of  air  from  the  room.  The  ordinary 
means  of  removal  is  the  vertical  vent-duct,  rising  to  the  top  of  the  build- 


HEATING    AND    VENTILATION. 


683 


Ing.  Sometimes  reliance  for  the  production  of  the  current  in  this  vent- 
duct  is  placed  solely  on  the  difference  of  temperature  of  the  air  in  the 
room  and  that  of  the  external  atmosphere;  sometimes  a  steam  coil  is 
placed  within  the  flue  near  its  bottom  to  heat  the  air  within  the  duct 
sometimes  steam  pipes  (risers  and  returns)  run  up  the  duct  performing 
the  same  functions:  or  steam  jets  within  the  flue,  or  exhaust  fans,  driven 
by  steam  or  electric  power,  act  directly  as  exhausters;  sometimes  the 
heating  of  the  air  in  the  flue  is  accomplished  by  gas-jets. 

The  draft  of  such  a  duct  is  caused  by  the  difference  of  weight  of  the 
heated  air  in  the  duct,  and  of  a  column  of  equal  height  and  cross-sectional 
area  of  the  external  air. 

Let  d  —  density,  or  weight  in  pounds,  of  a  cubic  foot  of  the  external  air. 

Let  d\  =  density,  or  weight  in  pounds,  of  a  cubic  foot  of  the  heated  air 
within  the  duct. 

Let  h  =  vertical  height,  in  feet,  of  the  vent-duct. 

h  (d  —  di)  =  the  pressure,  in  pounds  per  square  foot,  with  which  the 
air  is  forced  into  and  out  of  the  vent-duct. 

This  pressure  expressed  in  height  of  a  column  of  air  of  density  within 
the  vent-duct  is  h  (d  —  di)  -r-  d\. 

Or,  if  t  =  absolute  temperature  of  external  air,  and  ti  =  absolute  tem- 
perature of  the  air  in  the  vent-duct,  then  the  pressure  =  h  (t\  -  t)  •*-  t. 

The  theoretical  velocity,  in  feet  per  second,  with  which  the  air  would 
travel  through  the  vent-duct  under  this  pressure  is 


2gh(tl-t) 
t 


=  8.02 


The  actual  velocity  will  be  considerably  less  than  this,  on  account  of  loss 
due  to  friction.  This  friction  will  vary  with  the  form  and  cross-sectional 
area  of  the  vent-duct  and  its  connections,  and  with  the  degree  of  smooth- 
ness of  its  interior  surface.  On  this  account,  as  well  as  to  prevent  leakage 
of  air  through  crevices  in  the  wall,  tin  lining  of  vent-flues  is  desirable. 

The  loss  by  friction  may  be  estimated  at  approximately  50%,  and  the 
actual  velocity  of  the  air  as  it  flows  through  the  vent-duct  is 


ii, 


it/  2gh  y- 


-,  or,  approximately,  v=4 


y  h 


V  =  velocity  of  air  in  vent-duct,  in  feet  per  minute,  and  the  external 
_-r  be  at  32°  Fahr.,  since  the  absolute  temperature  on  Fahrenheit  scale 
equals  thermometric  temperature  plus  459.4, 


fro 


=  240^ 


491.4 
>m  which  has  been  computed  the  following  table: 


Quantity  of  Air,  in  Cubic  Feet,  Discharged  per  3Iinute  through  a 
Ventilating  Duct,  of  which  the  Cross-sectional  'Area  is  One 
Square  Foot  (the  External  Temperature  of  Air  being  32°  Fahr.). 


Height  of 


Excess  of  Temperature  of  Air  in  Vent-duct  above 
that  of  External  Air. 


feet. 

5° 

10° 

15° 

20° 

25° 

30° 

50° 

100° 

150° 

10 

77 

108 

133 

153 

171 

188 

242 

342 

419 

15  

94 

133 

162 

188 

210 

230 

297 

419 

514 

20 

108 

153 

188 

217 

242 

265 

342 

484 

593 

25  . 

121 

171 

210 

242 

271 

297 

383 

541 

663 

30 

133 

188 

230 

265 

297 

325 

419 

593 

726 

35  .       

143 

203 

248 

286 

320 

351 

453 

640 

784 

40          

153 

217 

265 

306 

342 

375 

484 

683 

838 

43 

162 

230 

282 

325 

363 

398 

514 

723 

889 

50... 

171 

242 

297 

342 

383 

419 

541 

760 

937 

684  HEATING    AND   VENTILATION. 

Multiplying  the  figures  in  preceding  table  by  60  gives  the  cubic  feet 
of  air  discharged  per  hour  per  square  foot  of  cross-section  of  vent-duct. 
Knowing  the  cross-sectional  area  of  vent-ducts  we  can  find  the  total  dis- 
charge; or  for  a  desired  air-removal,  we  can  proportion  the  cross-sectional 
area  of  vent-ducts  required. 

Heating  and  Ventilating  of  L.arge  Buildings.  (A.  R.  Wolff,  Jour. 
Frank.  Inst.,  1893.)  —  The  transmission  of  heat  from  the  interior  to  the 
exterior  of  a  room  or  building,  through  the  walls,  ceilings,  windows,  etc., 
is  calculated  as  follows: 

S  =  amount  of  transmitting  surface  in  square  feet ; 
t  =  temperature  F.  inside,  £0  =  temperature  outside; 

K  =  a  coefficient  representing,  for  various  materials  composing  build- 
ings, the  loss  by  transmission  per  square  foot  of  surface  in  British 
thermal  units  per  hour,  for  each  degree  of  difference  of  tempera- 
ture on  the  two  sides  of  the  material; 

Q  —  total  heat  transmission  =  SK  (t—  £o). 

This  quantity  of  heat  is  also  the  amount  that  must  be  conveyed  to  the 
room  in  order  to  make  good  the  loss  by  transmission,  but  it  does  not 
cover  the  additional  heat  to  be  conveyed  on  -account  of  the  change  of 
air  for  purposes  of  ventilation.  (See  Wolff's  coefficients  below,  page 
688.) 

These  coefficients  are  to  be  increased  respectively  as  follows:  10%  when 
the  exposure  is  a  northerly  one,  and  winds  are  to  be  counted  on  as  impor- 
tant factors;  10%  when  the  building  is  heated  during  the  daytime  only, 
and  the  location  of  the  building  is  not  an  exposed  one:  30%  when  the 
building  is  heated  during  the  daytime  only,  and  the  location  of  the  build- 
ing is  exposed;  50%  when  the  building  is  heated  during  the  winter  months 
intermittently,  with  long  intervals  (say  days  or  weeks)  of  non-heating. 

The  value  of  the  radiating-surface  is  about  as  follows:  Ordinary  bronzed 
cast-iron  radiating-surfaces,  in  American  radiators  (of  Bundy  or  similar 
type),  located  in  rooms,  give  out  about  250  heat-units  per  hour  for  each 
square  foot  of  surface,  with  ordinary  steam-pressure,  say  3  to  5  Ibs,  per 
sq.  in.,  and  about  0.6  this  amount  with  ordinary  hot-water  heating. 

Non-painted  radiating-surfaces,  of  the  ordinary  "indirect"  type 
(Climax  or  pin  surfaces),  give  out  about  400  heat-units  per  hour  for  each 
square  foot  of  heating-surface,  with  ordinary  steam-pressure,  say  3  to 
5  Ibs.  per  sq.  in.;  and  about  0.6  this  amount  with  ordinary  hot-water 
heating. 

A  person  gives  out  about  400  heat-units  per  hour;  an  ordinary  gas- 
burner,  about  4800  heat-units  per  hour;  an  incandescent  electric  (16 
candle-power)  light,  about  200  heat-units  per  hour. 

The  following  example  is  given  by  Mr.  Wolff  to  show  the  application  of 
the  formula  and  coefficients : 

Lecture-room  40  X  60  ft.,  20  ft.  high,  48,000  cubic  feet,  to  be  heated 
to  69°  F.;  exposures  as  follows:  North  wall,  60  X  20  ft.,  with  four  windows, 
each  14  X  8  feet,  outside  temperature  0°  F.  Room  beyond  west  wall  and 
room  overhead  heated  to  69°,  except  a  double  skylight  in  ceiling,  14  X  24 
ft.,  exposed  to  the  outside  temperature  of  0°.  Store-room  beyond  east 
wall  at  36°.  Door  6X12  ft.  in  wall.  Corridor  beyond  south  wall  heated 
to  59°.  Two  doors,  6  X  12,  in  wall.  Cellar  below,  temperature  36°. 

If  we  assume  that  the  lecture-room  must  be  heated  to  69°  F.  in  the 
daytime  when  unoccupied,  so  as  to  be  at  this  temperature  when  first 
persons  arrive,  there  will  be  required,  ventilation  not  being  considered, 
and  bronzed  direct  low-pressure  steam-radiators  being  the  heating  media, 
about  113,550  -s-  250  =  455  sq.  ft.  of  radiating-surface. 

If  we  assume  that  there  are  160  persons  in  the  lecture-room,  and  we 
provide  2500  cubic  feet  of  fresh  air  per  person  per  hour,  we  will  supply 
160  X  2500  =  400,000  cubic  feet  of  air  per  hour  (i.e.,  over  eight  changes 
of  contents  of  room  per  hour). 

To  heat  this  air  from  0°  F.  to  69°  F.  will  require  400,000  X  0.01785  X 
69  =  492.660  thermal  units  per  hour  (0.01785  being  the  product  of  the 
weight  of  a  cubic  foot,  0.075,  by  the  specific  heat  of  air,  0.238).  Accord- 
ingly there  must  be  provided  492,660  •*•  400  =  1232  sq.  ft.  of  indirect 


HEATING  AND   VENTILATION. 


685 


surface,  to  heat  the  air  required  for  ventilation,  in  zero  weather.  If  the 
room  were  to  be  warmed  entirely  indirectly,  that  is,  by  the  air  supplied 
to  room  (including  the  heat  to  be  conveyed  to  cover  loss  by  transmission 
through  walls,  etc.),  there  would  have  to  be  conveyed  to  the  fresh-air 
supply  492,660  +  118,443  =  611,103  heat-units.  This  would  imply  the 
provision  of  an  amount  of  indirect  heating-surface  of  the  "Climax"  type 
of  611,103  •+•  400  =  1527  sq.  ft.,  and  the  fresh  air  entering  the  room 
would  have  to  b?  at  a  temperature  of  about  86°  F.,  viz., 

The  above  calculations  do  not,  however,  take  into  account  that  160 
persons  in  the  lecture-room  give  out  160  X  400  =  64,000  thermal  units 
per  hour;  and  that,  say,  50  electric  lights  give  out  50  X  200  =  10,000 
thermal  units  per  hour;  or,  say,  50  gaslights,  50  X  4800  =  240,000 
thermal  units  per  hour.  The  presence  of  160  people  and  the  gaslighting 
would  diminish  considerably  the  amount  of  heat  required.  If  the  50 
gaslights  give  out  240,000  thermal  units  per  hour,  the  air  supplied  for 
ventilation  must  enter  considerably  below  69°  Fahr.,  or  the  room  will  be 
heated  to  an  unbearably  high  temperature.  If  400,000  cubic  feet  of  fresh 
air  per  hour  are  supplied,  and  240,000  thermal  units  per  hour  generated 
by  the  gas  must  be  abstracted,  it  means  that  the  air  must,  under  these 

240  000 
conditions,  enter  .^^  ^  OM785  -  about  34°  less  than  86°.  or  at 

about  52°  Fahr.  Recent  researches  show  that  the  increase  of  CO2  in 
air  due  to  gas  lighting  is  not  detrimental  to  health. 

The  following  table  shows  the  calculation  of  heat  transmission  (some 
figures  changed  from  the  original) : 


*•«    . 

.g~ 

fe  * 

n!^ 

Kind  of  Transmitting 
Surface. 

Thickness 
of  Wall  in 
inches. 

Calculation 
of  Area  of 
Transmit- 
ting Sur- 
face. 

Square  feet 
of  Surface. 

3 
t 

uj 

Thermal 

Units. 

69° 
69 
33 
33 
10 
10 
10 
10 
69 
69 
33 

Outside  wall                 

36" 
36* 
24" 
36" 

63x22-448 
4x  8X   14 
42x22-  72 
6x12 
45x22-  72 
6x12 
17x22-  72 
6x12 
32x42-336 
14x24 
62x42 

wall,  10%.. 

938 
448 
852 
72 
918 
72 
302 
72 
1,008 
336 
2,604 

10 
83 
4 
19 
2 
5 

5 
10 
35 
4 

9,380 
37,186 
3,408 
1,368 
1,836 
360 
302 
360 
10,080 
11,760 
10,416 

Four  windows  (single)    .  •  .  .  . 

Inside  wall  (store-room)  
Door                               

Inside  wall  (corridor)  

Inside  wall  (corridor)  

Door  

Roof                         

Double  skylight 

Floor  I 

Supplementary  allowance,  north  outside 
Supplementary  allowance,  north  outside 

Exposed  location  and  intermittent  day  c 
Total  thermal  units  

86,456 
^938 
3,718 

windows,  1C 
r  night  use,  '. 

%  

M)%.r..... 

91,112 
27,333 

118,445 

Comfortable  Temperatures  and  Humidities. — A.  G.  Woodman  and 
J.  F.  Norton,  in  a  work  on  Air,  Water,  and  Food  (1914),  give,  on  the 
authority  of  Hill's  Recent  Advances  in  Physiology  and  Biochemistry, 
a  "curve  of  comfort,"  practically  a  straight  line,  which  runs  from  20% 
relative  humidity  at  87°  F.  to  75%  at  55°  F.  It  approximates  40,  50 
and  60%  respectively  at  75°,  70°  and  65°  F,  showing  that  to  secure 
comfort  as  temperature  rises,  the  humidity  must  be  decreased.  The 
most  comfortable  conditions  for  indoor  workers  are  given  at  40% 
humidity  at  68°  and  60  %  at  64°  F. 

Carbon  Dioxide  Allowable  in  Factories. — Haldane  and  Osborne 
(London,  1902)  recommend  that  the  COa  in  the  air  at  the  breathing 


686  HEATING   AND   VENTILATION. 

line  in  factories,  and  away  from  the  immediate  influence  of  special 
sources  of  contamination,  such  as  persons  or  gas  lights,  should  not 
rise  during  daylight,  or  after  dark  when  electric  lights  only  are  used, 
beyond  12  volumes  in  10,000  of  air,  and  when  gas  or  oil  is  used  for 
lighting  not  over  20  volumes  after  dark. 

A  pamphlet  issued  by  the  National  Commercial  Gas  Association 
(1914)  states  that  the  use  of  gas  for  interior  lighting  does  not  affect  the 
atmosphere  of  interiors  deleteriously. 

Heat  Produced  by  Human  Beings. — According  to  Landry  and 
Roseman,  the  average  man  produces  every  24  hours  per  kilogram  of 
body  32  to  38  calories  when  at  rest,  35  to  45  when  in  easy  action,  and 
50  to  70  when  at  hard  work.  Translating  this  into  British  thermal 
units  per  hour,  and  taking  the  weight  of  an  average  man  at  140  lb., 
these  figures  are  equivalent,  approximately,  to  a  man  giving  off  336  to 
400  B.  T.  U.  per  hour  when  at  rest,  368  to  473  when  in  easy  action, 
and  525  to  735  when  at  hard  work. 

Atwater  and  Rosa,  average  of  13  experiments,  found  that  a  man  gave 
off  2200  cal.  per  24  hours  at  rest  and  3400  at  work,  equivalent  to  364 
and  562  B.  T.  U.  per  hour,  respectively. 

Standards  of  Ventilation. —  (C-E.A.  Winslow,  N.  Y.  State  Com- 
mission on  Ventilation, 'Science,  April  30,  1915.)  Pettenkoffer  in  1863 
showed  that  CO2  in  itself  is  without  effect  in  the  highest  concentrations 
which  it  ever  attains  in  occupied  rooms.  During  the  last  fifteen  years 
the  researches  of  Fliigge,  Haldane,  Hill,  Benedict  and  others  indicate 
that  the  effects  experienced  in  a  badly  ventilated  room  are  due  to  the 
heat  and  moisture  produced  by  the  bodies  of  the  occupants  rather  than 
to  CO2  or  other  substances  from  the  breath.  Subjects  immured  in 
close  chambers  are  not  at  all  relieved  by  breathing  pure  outdoor  air 
through  a  tube,  but  are  relieved  completely  by  keeping  the  chamber 
artificially  cool,  and  to  a  considerable  extent  by  the  mere  circulating  of 
the  air  by  an  electric  fan. 

The  experiments  of  the  N.  Y.  State  Commission  show  that  the  work- 
ing of  the  circulatory  and  heat  regulating  machinery  of  the  body  was 
markedly  influenced  by  a  slight  increase  in  room  temperature,  as  from 
68°  to  75°  with  50%  relative  humidity  in  both  cases.  Psychological 
tests  failed  to  show  that  86°  and  80  %  relative  humidity  had  any  effect 
on  the  power  to  dp  mental  work,  but  with  physical  work  (lifting 
dumb  bells  and  riding  a  stationary  bicycle),  when  the  subjects  had 
a  choice  they  accomplished  15  %  less  work  at  75°,  and  37  %  less  at 
86°,  than  they  did  at  68°.  As  to  the  effect  of  stagnant  breathed  air 
contaminated  so  as  to  show  from  20  to  60  parts  CO2  per  10,000,  the  re- 
sults are  entirely  negative  so  far  as  mental  and  physical  tests  are  con- 
cerned. 

In  practice,  an  unventilated  room  is  an  overheated  room.  Ventila- 
tion is  just  as  essential  to  remove  the  heat  produced  by  human  bodies  as 
it  was  once  thought  to  be  to  remove  the  CO2  produced  by  the  lungs. 
The  quantitative  standards  of  air  change  established  on  the  old  chemical 
basis  serve  very  well  in  the  new,  or  heat  change,  basis.  An  average 
adult  producing  400  B.T.U.  per  hour  will  require  2000  cubic  feet  of 
air  per  hour  at  60°  to  prevent  the  temperature  rising  above  70°.  An 
ordinary  gas  burner  produces  300  B.T.U.  per  candle-power  hour,  and 
requires  1500  cubic  feet  of  air  per  hour  per  candle  power.  In  crowded 
auditoria  every  bit  of  the  2000  cubic  feet  of  air  per  hour  per  person  is 
needed,  and  in  many  industrial  processes,  where  the  heat  from  human 
beings  is  reinforced  by  friction  and  other  sources,  even  more  will  be 
required. 

Recent  research  has  on  the  whole  strengthened  the  arguments  for 
ventilation.  The  thermometer  is  the  first  essential;  a  rise  above  70° 
must  be  recognized  as  a  sign  of  discomfort,  of  decreased  efficiency  and 
lowered  vitality.  The  standard  of  30  cubic  feet  of  air  per  minute  per 
capita  remains  as  the  amount  necessary  to  supply  if  an  occupied  room 
is  to  be  kept  cool  and  fresh. 

The  question  of  humidity  remains  to  be  solved.  A  lack  of  humidity 
makes  hot  air  feel  cooler  and  cold  air  feel  warmer.  Extreme  dryness, 
at  high  or  moderate  temperatures,  is  believed  by  many  to  be  in  itself 
harmful,  but  there  is  no  solid  experimental  evidence  on  this  point. 

Air  Washing.— (D  D.  Kimball,  N.  Y.  State  Commission  on  Ventila- 
tion, Science,  April  30,  1915.)  An  air  washer  consists  of  a  sheet-metal 


HEATING  AND   VENTILATING   PROBLEMS. 


687 


chamber  in  which  the  air  is  passed  through  a  heavy  mist  and  then 
through  baffles  or  eliminator  plates  by  which  the  entrained  moisture  is 
remoTed.  The  base  of  the  washer  is  a  tank  into  which  the  spray  falls 
and  from  which  it  is  drawn  by  a  centrifugal  pump.  The  pump  forces 
the  water  through  spray  nozzles  in  the  spray  chamber  of  the  washer. 
Manufacturers  customarily  guarantee  the  removal  of  98%  of  the  dust 
in  the  air.  Practically  all  the  larger  particles  are  removed,  but  there  is 
always  a  residue  of  fine  dust  which  no  washer  will  remove.  When  there 
is  very  little  dust  in  the  air,  as  after  a  heavy  rain,  the  percentage  of  the 
remaining  dust  that  can  be  removed  is  quite  small.  M.  C.  Whipple's 
tests  showed  that  the  dust  removed  varied  from  64  %  down  to  7%. 

The  best  results  in  artificial  humidification  have  been  obtained  by 
means  of  the  air  washer.  The  degree  of  humidification  is  controlled  by 
thermostatic  devices.  The  air  washer  may  also  be  used  for  air  cooling. 
The  evaporation  in  the  spray  chamber  will  lower  the  temperature  to 
the  extent  of  75%  or  more  of  the  difference  between  the  wet  and  dry 
bulb  temperatures,  equivalent  to  a  temperature  reduction  often 
amounting  to  10  to  15  degrees.  Unfortunately  cooling  by  means  of  an 
air  washer  is  expensive.  Roughly,  the  cost  of  cooling  10  degrees  equals 
the  cost  of  heating  70  degrees. 

Contamination  of  Air. — The  following  data  are  found  in  "The  Air 
and  Ventilation  of  Subways,"  by  G.  A.  Soper  (1908). 

Carbon  dioxide  in  air  in  streets  of  European  cities,  3.01  to  5.02  parts 
in  10,000.  Center  of  Paris  annual  average  varied  from  3.06  to  3.44 
parts.  Average 'of  309  analyses  in  New  York,  3.67  parts. 

An  average  adult  inhales  about  396  cubic  inches  per  minute.  Analysis 
of  inspired  air:  O,  20.81;  N,  79.15;  CO2,  0.04.  Expired  air:  O,  16.00; 
N,  79.59;  CO-2,  4.38.  Air  highly  charged  with  CO2  is  not  dangerous  to 
breathe  for  a  considerable  time.  CCh  must  be  present  to  40  times  the 
amount  present  when  the  room  begins  to  smell  "stuffy"  before  it  in- 
creases the  rate  of  breathing.  Neither  does  a  decrease  of  2  or  3  per  cent 
in  the  oxygen  produce  any  immediate  effect.  Long  before  the  air  be- 
comes so  vitiated  as  this  other  impurities  from  the  lungs  make  the  air 
extremely  unpleasant. 

The  CO2  in  badly  vitiated  places  seldom  rises  above  50  parts  in 
10,000. 

The  air  becomes  uncomfortably  close  and  musty  when  CCh  exceeds 
8  parts  in  10,000. 

Amount  of  CO2  exhaled  by  a  man,  average  per  hour:  at  rest,  16.11 
grams,  or  8198  cu.  cm.;  at  work,  30.71  grams,  or  15,628  cu.  cm. 

STANDARD  VALUES  FOR  USE  IN  CALCULATION  OF  HEATING 
AND  VENTILATING  PROBLEMS. 

Heating  Value  of  Coal. 


Volatile 
Matter  in 
the  Com- 
bustible, 
Per  Cent. 

Heating  Value 
per  Ib. 
Combustible, 
B.T.U. 

Aver- 
age. 

Moisture, 
in 
Air-dried 
Coal, 
Per  Cent. 

Ash  in 
Air-dried 
Coal, 
Per  Cent. 

Anthracite  
Semi-anthracite  .  . 
Semi-bituminous  . 
Bit.  eastern  
Bit  western  
Lignite  

3     to    7.5 
7.5  to  12.5 
12.5  to  25 
25  to  40 
35  to  50 
Over  50 

14,700  to  14,900 
14,900  to  15,500 
15,500  to  16,000 
14,800  to  15,000 
13,500  to  14,800 
11,  000  to  13,500 

14,800 
15,200 
15,750 
15,150 
14,150 
12,250 

0.5  to  1.0 
0.5  to  1.0 
0.5  to  1.0 
1.  to  4. 
4.  to  14. 
10.  to  18. 

10.  to  18. 
10.  to  18. 
5.  to  10. 
5.  to  15. 
10.  to  25. 
5.  to  25. 

Average  Heating  Value  of  Air-Dried  Coal. — Anthracite,  12,600;  semi- 
anthracite,  12,950;  semi-bituminous,  14,450;  bituminous  eastern,  13,250; 
bituminous  western,  10,400;  lignite,  9,700. 

Eastern  bituminous  coal  is  that  of  the  Appalachian  coal  field  extending 
from  Pennsylvania  and  Ohio  to  Alabama.  Western  bituminous  coal 
is  that  of  the  great  coal  fields  west  of  Ohio. 

Steam  Boiler  Efficiency.  —  The  maximum  efficiency  obtainable  with 
anthracite  in  low-pressure  steam  b9ilers,  water  heaters  or  hot-air  furnaces 
is  about  80  per  cent,  when  the  thickness  of. the  coal  bed  and  the  draft 
are  such  as  to  cause  enough  air  to  be  supplied  to  effect  complete  combus- 
tion of  the  carbon  to  CO2.  With  coals  high  in  volatile  matter  the  max- 


688 


HEATING   AND   VENTILATION. 


imum  efficiency  is  probably  not  over  70  per  cent.  Very  much  lower 
efficiencies  than  these  figures  are  obtained  when*  the  air  supply  is  either 
deficient  or  greatly  in  excess,  or  when  the  furnace  is  not  adapted  to  burn 
the  volatile  matter  in  the  coal.  D.  T.  Randall,  in  tests  made  in  1908 
for  the  U.  S.  Geological  Survey,  with  house-heating  boilers,  obtained 
efficiencies  ranging  from  0.62  with  coke,  0.61  with  anthracite,  and  0.58 
with  semi-bituminous,  down  to  0.39  with  Illinois  coal. 

Available  Heating  Value  of  the  Coal. — Using  the  figures  given  above  as 
the  average  heating  value  of  coal  stored  in  a  dry  cellar,  the  following  are 
the  probable  maximum  values  in  B.  T.U.,  of  the  heat  available  for  fur- 
nishing steam  or  heating  water  or  air,  for  the  several  efficiencies  stated : 


Anthracite. 

Semi-An. 

Semi-Bit. 

Bit.  East. 

Bit.  West. 

Lignite. 

Eff'y  0.80 

0.77 

0.75 

0.70 

0.65 

0.60 

B.T.U...  10,080 

9,933 

10,837 

9,275 

6,760 

5.820 

For  average  values  in  practice,  about  10  per  cent  may  be  deducted  from 
these  figures.  (It  is  possible  that  an  efficiency  higher  than  80%  may  be 
obtained  with  anthracite  in  some  forms  of  air-heating  furnaces  in  which 
the  escaping  chimney  gases  are  cooled,  by  contact  with  the  cold  air  inlet 
pipes,  to  comparatively  low  temperatures.) 

The  value  10,000  B.T.U.  is  usually  taken  as  the  figure  to  be  used  in 
calculation  for  design  of  heating  and  ventilating  apparatus.  For  coals 
with  lower  available  heating  values  proper  reductions  must  be  made. 

Heat  Transmission  through  Walls,  Windows,  etc.,  in  B.T.U.  per 
Sq.  Ft.  per  Hour  per  Degree  of  Difference  of  Temperature. 


Wolff. 
B.T.U. 

Hauss. 
B.T.U. 

Wolff. 
B.T.U. 

Hauss  . 
B.T.U. 

GLASS  SURFACES. 
Vault  light  

1.42 

FLOORS. 
Toists    with    double 

0.10 
0.31 

0.07 

Single  window  
Double  window  
Single  skylight 

1.20 
0.56 
1.03 
0.50 

0  40 

1.00 
0.46 
1.06 
0.48 

0.40 

Concrete  floor  

Fireproof    construc- 
tion, planked  over. 
Wooden    beam   con- 
struction, planked 
over   

0.124 
0  083 



Double  skylight  

DOORS. 
Door  
l-in.  pine...-  

Concrete     floor     on 
brick  arch  

0.22 
0.20 
0.16 

0.20 
0.09 
0.08 

0.10 
0.14 

2-in.  pine  

PARTITIONS. 

Solid  plaster, 
1  3/4  to  2  1/4  in 

0.28 

0.60 
0.48 

Stone  floor  on  arches 
Planks  laid  on  earth. 
Planks    laid    on    as- 
phalt   

Arch  with  air  space 

Stones  laid  on  earth. 

CEILINGS. 
Joists     with     single 
floor 

2  1/2  to  3  1/4  in.... 

Fireproof 

0.30 
0.28 

2-in.  pine  board 

A.rches  with  air  space 

BRICK  WALLS. 


Thickness  , 
In. 

Wolff. 

Hauss. 

Average  . 
B.T.U.* 

Thickness, 
In. 

Wolff. 

Hauss. 

Average, 
B.T.U.* 

4 

0.66 

0.537 

25 

0  18 

0  188 

43/4 

0.48 

0  508 

28 

0  18 

017? 

8 

0.45 

0  397 

30 

0  16 

0  163 

10 

0.34 

0.351 

32 

0.16 

0  154 

12 

6.33 

0  313 

35 

Oil 

01  A\ 

15 

0.26 

0.272 

36 

0  145 

0  140 

16 

0.27 

0  260 

40 

0  13 

01? 

01  ?fl 

20 

0.23 

0.22 

0.222 

45 

0.11 

0  116 

24 

0.20 

0  194 

fure  for  brick  walls  was  obtained  by  plotting  the 
's  and  Hauss 's  figures  and  drawing  a  straight  line 


*  The  average  _ 
reciprocals  of  Wo] 


RESIDENCE  HEATING. 


689 


SOLID  SANDSTONE  WALLS.     (Hauss.) 

Thickness,  in. .  .     12       16       20      24       28       32       36       40       44       48 

B.T.U 0.45    0.39    0.35    0.32    0.29    0.26    0.24    0.22    0.20    0.19 

For  limestone  walls,  add  10  per  cent. 

Allowances  for  Exposures.  —  Wolff  adds  25%  for  north  and  west  ex- 
posures, 15%  for  east,  and  5%  for  south  exposures,  also  10%  additional 
for  reheating,  and  10%  to  the  transmission  through  floor  and  ceilings. 
The  allowance  for  reheating  Mr.  Wolff  explains  as  follows  in  a  letter  to 
the  author,  Mar.  10,  1905.  The  allowance  is  made  on  the  basis  that  the 
apparatus  will  not  be  run  continuously;  in  other  words,  that  it  will  not  be 
run  at  all,  or  only  lightly,  overnight.  The  rooms  will  cool  off  below  the 
required  temperature  of  70°,  and  to  be  able  to  heat  up  quickly  in  the 
morning  an  allowance  of  10%  is  made  to  the  transmission  figures  to  meet 
this  condition.  Hauss  makes  allowances  as  follows:  5%  for  rooms  with 
unusual  exposure;  10%  where  exposures  are  north,  east,  northeast, 
northwest  and  west;  81/3%  where  the  height  of  ceiling  is  more  than  13  ft.; 
62/3%  where  it  is  more  than  15  ft.;  10%  where  it  is  more  than  18  ft.  For 
rooms  heated  daily,  but  where  heating  is  interrupted  at  night,  add 

A  =  0.0025  [(N  -  1)  Wi]  -  Z. 

For  rooms  not  heated  daily,  add  B  =  [0.1  W  (8  —  Z)]  •*•  Z. 
In  these  formulas  W\  =  B.T.U.  transmitted  per  hour  by  exposed  sur- 
faces; W  =  total  B.T.U.  necessary,  including  that  for  ventilation  or 
changes  of  air;  AT  =  time  from  cessation  of  heating  to  time  of  starting 
fire  again,  hours;  Z  —  time  necessary  after  fire  is  started  until  required 
room  temperature  is  reached,  hours. 

Allowance  for  Exposure  and  for  Leakage.  —  In  calculations  of  the 
quantity  of  neat  required  by  ordinary  residences,  the  formula  total  heat 

(Ti-  To)  (~+  G  +  —}    is    commonly  used.      Ti  =  temp,  of  room, 

To  =  outside  temp.,  W  =  exposed  wall  surface  less  window  surface, 
O  =  glass  surface,  C  =  cubic  C9ntents  of  room,  n  =  number  of  changes 
of  air  per  hour.  The  factor  n  is  usually  assumed  arbitrarily  or  guessed 
at;  some  writers  take  its  value  at  1,  others  1  for  the  rooms,  2  for  the  halls, 
etc.;  others  object  to  the  use  of  C  as  a  factor,  saying  that  the  allowance  for 
exposure  and  leakage  should  be  made  proportional  to  the  exposed  wall 
and  glass  surface  since  it  is  on  these  surfaces  that  the  leakage  occurs, 
and  omitting  the  term  nC/56  they  multiply  the  remainder  of  the  ex- 
pression by  a  factor  for  exposure,  c  =  1.1  to  1.3,  depending  on  toe  direc- 
ion  of  the  exposure.  To  show  what  different  results  may  be  obtained 
by  the  use  of  the  two  methods,  the  following  table  is  calculated,  apply- 
ing both  to  six  rooms  of  widely  differing  sizes.  Two  sides  of  each  room, 
north  and  east,  are  exposed.  Ti  =  70;  TQ  =  0;  G  =  1/5  (W  +  G). 


O 

s 

«*-. 

Total  Wall, 

<5 

0  + 

+ 

CD* 

g 

Size,  ft. 

0 
o 

(W  +  G) 

•£U 

1 

§ 

• 

. 

II 

sq.  ft. 

1 

£  + 

5 

«] 

&J 

& 

O 

0 

0 

is* 

^t^. 

o 

l>. 

<N 

0 

CO 

6 

A 

10x10x10 

1,000 

20x10=  200 

40 

5 

5,600 

1,250 

1,120 

1,680 

B 

10x20x10 

2,000 

30x10=  300 

60 

62/3 

8,400 

2,500 

1,680 

2,520 

C 
D 

20x20x12 
20x40x14 

4,800 
11,200 

40x12=  480 
60x14=  840 

96 

168 

10 
171/3 

13,440 
23,520 

6,000 
14.000 

2,688 
4,704 

4,032 
7,056 

E 

40x40x13 

24.000 

80x15=1200 

240 

20 

33.600 

30.000 

6,720 

10.0^0 

F 

40x80x16 

51.200 

120x16=1920 

384 

262/3 

54.460 

64.000 

10.892 

16.33d 

The  figures  in  the  column  headed  H  =  70  (TF/4  +  G)  represent  the 
heat  transmitted  through  the  walls,  those  in  the  column  70  C756  are  the 

between  them,  representing  the  average  heat  resistances,  and  then  taking 
the  reciprocals  of  the  resistances  for  different  thicknesses.  The  resist- 
ance corresponds  to  the  straight  line  formula  R  =  0.12  +  0.165  t,  where 
t  =  thickness  in  inches.  (Hauss's  figures  are  from  a  paper  by  Chas. 
F.  Hauss,  of  Antwerp,  Belgium,  in  Trans.  A.  S.  H.  V.  E.,  1904.) 


690  HEATING  AND   VENTILATION. 

heat  required  for  one  change  of  air  per  hour ;  0.2  H  is  the  heat  correspond- 
ing to  an  allowance  ol  20%  lor  exposure  and  leakage,  and  0.3  H  corre- 
sponds to  an  allowance  of  30%.  For  the  small  rooms  A  and  B  the 
difference  between  70  C/56  and  0.2  H  or  0.3  H  is  not  of  great  importance, 
but  it  becomes  very  important  in  the  largest  rooms;  in  room  F  the  differ- 
ence between  70  C/56  and  0.2  H  is  nearly  equal  to  the  total  heat  trans- 
mitted through  the  walls,  indicating  that  the  use  of  the  cubic  contents 
as  a  factor  in  calculations  of  large  rooms  is  likely  to  lead  to  great  errors. 
This  is  due  to  the  fact  that  the  ratio  C  •*•  (W  +  G)  varies  greatly  with 
different  sizes  of  rooms. 

With  forced  ventilation,  the  quantity  of  heat  needed  depends  chiefly 
upon  the  number  of  persons  to  be  provided  for.     Assuming  2000  cu.  ft. 
per  hour  per  person,  heated  from  0°  to  70°,  and  1,  2  and  4  persons  per 
100  sq.  ft.  of  floor  surface,  the  heat  required  for  the  air  is  as  follows: 
Room A          B  C  D  E  F 

1  person  per  100  sq.  ft.      2,500      5,000    10,000    20,000      40,000      80.000 

2  persons  per  100  sq.ft.      5,000    10,000    20,000    40,000      80,000    160,000 
4  persons  per  100  sq.  ft.    10,000    20,000    40,000    80,000    160,000    320,000 
Ratio  of  last  line  to  H..         1.8         2.4         3.0         3.4  4.8  5.9 

Heating  by  Hot-air  Furnaces.  —  A  simple  formula  for  calculating  the 
total  heat  in  British  Thermal  Units  required  for  heating  and  ventilating 

by  any  system  is  H  =  Fc  (  G  +  — )  +  ^~\  ( Ti  -  T0) .    (See  notation  above.) 

The  formula  is  derived  as  follows:  The  heat  transmitted  through  1  sq.  ft. 
of  single  glass  window  is  approximately  1  B.T.U.  per  hour  per  degree  of 
difference  of  temperature,  and  that  through  1  sq.  ft.  of  16-in.  brick  wall 
about  0.25  B.T.U.  (For  more  accurate  calculations  figures  taken  from 
the  tables  (p.  688)  should  be  used.)  The  specific  heat  of  air  is  taken  at 
0.238,  and  the  weight  of  1  cu.  ft.  air  at  70°  F.  at  0.075  Ib.  per  cu.  ft. 
The  product  of  these  figures  is  0.01785,  and  its  reciprocal  is  56. 

For  a  difference  T\  -  T0  =  70°,  0.01785  X  70  =  1.2495,  we  may. 
therefore,  write  the  formula 


Total  heat  =  70  [C(G  +  2^1  +  1.25  A 
«»•.    L  V       i4  /  J 


-    -       .    - 

=  heat  conducted  through  walls  +  heat  exhausted  in 
ventilation. 

A  is  the  cubic  feet  of  air  (measured  at  70°)  supplied  to  and  exhausted 
from  the  building.  This  formula  neglects  the  heat  conducted  through 
the  roof,  for  which  a  proper  addition  should  be  made. 

There  are  two  methods  of  heating  by  hot-air  furnaces;  one  in  which 
all  the  air  for  both  heating  and  ventilation  is  taken  from  outdoors  and 
exhausted  from  the  building,  and  the  other  in  which  only  the  air  for 
ventilation  is  taken  from  outdoors,  and  additional  air  is  recirculated 
through  the  furnace  from  the  building  itself.  The  first  method  is  an 
exceedingly  wasteful  one  in  cold  weather.  By  the  second  it  is  possible 
to  heat  a  building  with  no  greater  expenditure  of  fuel  than  is  required 
for  steam  or  hot-water  heating. 

EXAMPLE.  —  Required  the  amount  of  heat  and  the  quantity  of  air  to  be 
circulated  by  the  two  methods  named  for  a  building  which  has  G  =  400, 
W  =  2000,  C  =  16,000,  n  =  2,  Ti  =  70°,  To  =  0°,  T2,  the  temperature 
at  which  the  air  leaves  the  furnace,  being  taken  for  three  cases  as  100°, 
120°,  and  140°.     Assume  c,  the  coefficient  for  exposure,  including  heat 
lost  through  roof,  =  1.2.     When  only  enough  air  for  ventilation  is  taken 
into  and  exhausted  from  the  building,  the  formula  gives 
70  X  1.2  (500  +  400)  +1.25  X  32,000  =  115,600  B.T.U.  =  75,600  for 
heat  +  40,000  for  ventilation. 

Suppose  all  the  air  required  for  heating  is  taken  from  outdoors  at  0°  F., 
and  all  exhausted  at  70°,  the  quantity,  A,  then,  instead  of  being  32,000 
cu.  ft.,  has  to  be  calculated  as  follows: 

Total  heat  =  c  (G  +  ^\  (Ti-  TO)  +  A  X  0.01785  X  (Ti  -   T0) 

=  0.01785  A  (T2  -  To). 
Heat  supplied  by  furnace  =  heat  for  conduction  +  heat  for  ventilation 


CARRYING   CAPACITY   OF  AIR   PIPES. 


691 


from  which  we  find    A  =  c     <3+          (Ti  -  To)   *  0.01785  (T2  -  Ti) 

=  75,600  ^  0.01785  (T2  -  70°). 

For  the  value  of  Ti T2  =  100  T2  =  120  !T2  =  140 

A  =  cu.  ft 141,117  84,706  60,504 

Heat  lost  by  exhausting  this  air  at  70° ...    176,396  105,882  75,630 

Adding  75,600  loss  by  walls  gives  total .  . .    251,996  181,482  152,230 
Excess   above   115,600   actually   required 

for  heating  and  ventilating,  %  .-. 118.0  57.0  31.7 

British  Thermal  Units  Absorbed  in  Heating  1  Cu.  Ft.  of  Air,  or  given 

up  in  cooling  it.  —  (The  air  is  measured  at  70°  F.) 

Ti  -  Ti  = 

10°    20      30     40     50  56    60     70     80     90     100    110    120  126  130  140 
0.18  0.36  0.54  0.71  0.89  1.  1.07  1.25  1.43  1.61  1.78  1.96  2.14  2.25  2.32  2.5 


Area  in  Square  Inches  of  Pipe  required  to  Deliver  10O  Cu.  Ft.  of 
Air  per  Minute,  at  Different  Velocities.  —  The  air  is  measured  at  the 
temperature  of  the  air  in  the  pipe. 


Velocity  per  second 2       3 

Area,  sq.  in 120    80 


4 
60 


5 

48 


6 
40 


7 
34.3 


8        9     10 
30    26.7  24 


The  quantity  of  air  required  for  ventilation  or  heating  should  be 
figured  at  a  standard  temperature,  say  70°  F.,  but  when  warmer  air  is 
to  be  delivered  into  the  room  through  pipes,  the  area  of  the  pipes  should 
be  calculated  on  the  basis  of  the  temperature  of  the  warm  air,  and  not  on 
that  of  the  room. 

EXAMPLE.  —  A  room  requires  to  be  supplied  with  1000  cu.  ft.  per  min. 
at  70°  F.  for  ventilation,  but  the  air  is  also  used  for  heating  and  is  delivered 
into  the  room  at  120°  F.  Required,  the  area  of  the  delivery  pipe,  if  the 
velocity  of  the  heated  ai;  In  the  pipe  is  6  ft.  per  second. 

From  the  table  of  volumes,  given  on  the  next  page,  1000  cu.  ft.  at  70° 

'  1094  cu.  ft.  at  120°.  From  the  above  table  of  areas,  at  6  ft.  velocity 
40  sq.  in.  area  is  required  for  100  cu.  ft.,  therefore  1094  cu.  ft.  will  require 
10.94  X  40  =  437.6  sq.  in.  or  about  3  sq.  ft. 

Carrying  Capacity  of  Air  Pipes. 


Diam. 

Area  in 
Sq.  In. 

Area, 
Sq.  Ft. 

Velocity,  Feet  per  Second. 

3 

4 

5 

6 

7 

8 

Cu.  Ft.  per  Min. 

5 

19.63 

.1364 

24.6 

32.7 

40.9 

49.1 

57.3 

65.5 

6 

28.27 

.1963 

35.3 

47.1 

58.9 

70.7 

82.4 

94.2 

7 

38.48 

.2673 

48.1 

64.2 

80.2 

96.2 

112. 

128. 

8 

50.27 

.3491 

62.8 

83.8 

105. 

126. 

147. 

168. 

9 

63.62 

.4418 

80.0 

106. 

133. 

159. 

186. 

212. 

10 

78.54 

.5454 

98.2 

131. 

164. 

196. 

229. 

262. 

11 

95.03 

.6600 

119. 

158. 

198. 

238. 

277. 

317. 

12 

113.1 

.7854 

141. 

188. 

236. 

283. 

330. 

377. 

13 

132.7 

.9218 

166. 

221. 

277. 

332. 

-  387. 

442. 

14 

153.9 

1.069 

192. 

257. 

321. 

385. 

449. 

513. 

15 

176.7 

1.227 

221. 

294. 

368. 

442. 

515. 

589. 

11.3 

100. 

0.694 

125. 

167. 

208. 

250. 

292. 

333. 

13.6 

144. 

1. 

180. 

240. 

300. 

360. 

420. 

480. 

The  figures  in  the  table  give  the  carrying  capacity  of  pipes  in  cu.  ft. 
of  air  at  the  temperature  of  the  air  flowing  in  the  pipes.  To  reduce  the 
figures  to  cu.  ft.  at  a  standard  temperature  (such  as  70°  F.)  divide  by 
the  ratio  of  the  volume  per  cu.  ft.  of  the  air  in  the  pipe  to  that  of  the  ftfr 
of  the  standard  temperature,  as  in  the  following  table; 


692 


HEATING   AND   VENTILATION. 


Volume  of  Air  at  Different  Temperatures. 

(Atmospheric  pressure.) 


Fahr. 
Deg. 

Cu.  Ft. 
in  1  Ib. 

Compar- 
ative 
Volume. 

Fahr. 
Deg. 

Cu.  Ft. 
in  1  Ib. 

Compar- 
ative 
Volume. 

Fahr. 
Deg. 

Cu.Ft. 
in  1  Ib. 

Compar- 
ative 
Volume 

0 

11.583 

0.867 

90 

13.845 

.038 

160 

15.603 

.169 

32 

12.387 

0.928 

100 

14.096 

.056 

170 

15.854 

.188 

40 

12.586 

0.943 

110 

14.346 

.075 

180 

16.106 

.207 

50 

12.840 

0.962 

120 

14.596 

.094 

190 

16.357 

.226 

62 

13.141 

0.985 

130 

14.848 

.113 

200 

16.608 

.245 

70 

13.342 

1.000 

140 

15.100 

.132 

210 

16.860 

.264 

80 

13.593 

1.019 

150 

15.351 

.151 

212 

16.910 

.267 

Sizes  of  Air  Pipes  Used  in  Furnace  Heating.     (W.  G.  Snow,  Eng. 
News,  April  12,  1900.) 


W'th. 
of 
Room 
Ft. 

8... 
10.... 
12 

Length  of  Room,  Ft. 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

Diameter  of  Pipe,  Ins. 

8,7 
8,7 

8,7 
9,  8 
9,8 

9,  8 
9,  8 
10,  8 

9,  8 
10,  8 
10,  8 

10,    8 
10,    9 

10,    9 
11,    9 

11,    9 

12,  10 

14  . 

10,  8 

10,9 
11,9 

11,    9 
11,    9 

12,  10 

11,    9 
12,  10 
12,  10 
13,  11 

12,  10 
12,  10 
13,  11 
13,  11 

12,  10 
13,  10 
13,  11 
13,  11 

13,  10 
13,  10 
13,  11 
14,  12 

13,  10 
13,  11 
14,  12 
14,  12 

13,  11 
14,  12 
14,  12 

16 

18 

20.. 

The  first  figure  in  each  column  shows  the  size  of  pipe  for  the  first  floor 
and  the  second  figure  the  size  for  the  second  floor.  Temperature  at  regis- 
ter, 140°;  room,  70°;  outside,  0°.  Rooms  8  to  16  ft.  in  width  assumed  to 
.be  9  ft.  high;  18  to  20  ft.  width,  10  ft.  high.  When  first-floor  pipes  are 
longer  than  15  ft.  use  one  size  larger  than  that  stated.  For  third  floor, 
use  one  size  smaller  than  for  second  floor.  For  rooms  with  three  expo- 
sures, increase  the  area  of  pipe  in  proportion  to  the  exposure. 

The  table  was  calculated  on  the  following  basis: 

The  loss  of  heat  is  calculated  by  first  reducing  the  total  exposure  to 
equivalent  glass  surface.  This  is  done  by  adding  to  the  actual  glass 
surface  one-quarter  the  area  of  exposed  wood  and  plaster  or  brick  walls 
and  1/20  the  area  of  floor  or  ceiling.  Ten  per  cent  is  added  where  the 
exposure  is  severe.  The  window  area  assumed  is  20%  of  the  entire  ex- 
posure of  the  room. 

Multiply  the  equivalent  of  glass  surface  by  85.  The  product  will  be 
the  total  loss  of  heat  by  transmission  per  hour. 

Assuming  the  temperature  of  the  entering  air  to  be  140°  and  that  of 
the  room  to  be  70°,  the  air  escaping  at  approximately  the  latter  tempera- 
ture will  carry  away  one-half  the  heat  brought  in.  The  9ther  half,  corre- 
sponding to  the  drop  in  temperature  from  140°  to  70°,  is  lost  by  trans- 
mission. With  outside  temperature  zero,  each  cubic  foot  of  air  at  140° 
brings  into  the  room  2.2  heat  units.  Since  one-half  of  this,  or  1.1  heat 
units,  can  be  utilized  to  offset  the  loss  by  transmission,  to  ascertain  the 
volume  of  air  per  hour  at  140°  required  to  heat  a  given  room,  divide  the 
loss  of  heat  by  transmission  by  1.1.  This  result  divided  by  60  gives  the 
number  of  cubic  feet  per  minute.  In  calculating  the  table,  maximum 
velocities  of  280  and  400  ft.  were  used  for  pipes  leading  t6  the  first  and 
second  floors  respectively.  The  size  of  the  smaller  pipes  was  based  on 
lower  velocities,  according  to  their  size,  to  allow  for  their  greater  resist* 
ance  and  loss  of  temperature. 


BOILERS   FOR   HOUSE   HEATING. 


693 


Furnace-Heating  with  Forced  Air  Supply.  (The  Metal  Worker, 
April  8,  1905.)  —Tests  were  made  of  a  Kelsey  furnace  with  the  air  supply 
furnished  by  a  48-in.  Sturtevant  disk  fan  driven  by  a  5  H.P.  electric 
motor.  A  connection  was  made  from  the  air  intake,  between  the  fan  and 
the  furnace,  to  the  ash  pit  so  that  the  rate  of  combustion  could  be  regu- 
lated independently  of  the  chimney-draft  condition.  The  furnace  had 
4.91  sq.  ft.  of  grate  surface  and  238  sq.  ft.  of  heating  surface.  The  volume 
of  air  was  determined  by  anemometer  readings  at  24  points  in  a  cross- 
section  of  a  rectangular  intake  of  11.88  sq.  ft.  area.  The  principal 
results  obtained  in  two  tests  of  8  hours  each  are  as  follows: 


Av.  temp,  of  the  cold  air 

Per  cent  humidity  of  the  cold  air. 
Ay.  temp,  of  the  warm  air. 


39° 

71 

135° 

Air  delivered  to  heater,  cu.  ft.  per  hour.  . . .  250,896 
B.T.U.  absorbed  by  the  dry  air  per  hour. . .  451,872 
B.T.U.  absorbed  by  the  vapor  per  hour ....  2,016 
Avge.  no.  of  pounds  of  coal  burned  per  hour  36 

B.T.U.  given  by  the  coal  per  hour 529,200 


Per  cent  efficiency  of  the  furnace. 


85.7 


58° 

56 

152° 

249,195 

421,496 

3,102 

33.5 

492,450 

86.2 


Grate  Surface  and  Bate  of  Burning  Coal. 

In  steam  boilers  for  power  plants,  which  are  constantly  attended  by 
firemen,  coal  is  generally  burned  at  between  10  and  30  Ibs.  per  sq.  ft. 
of  grate  per  hour.  In  small  boilers,  house  heaters  and  furnaces,  which 
.  even  in  the  C9ldest  weather  are  supplied  with  fresh  coal  only  once  in 
several  hours,  it  is  necessary  to.  burn  the  coal  at  very  much  slower  rates. 
Taking  a  cubic  foot  of  coal  as  weighing  60  Ibs.,  in  a  bed  12  inches  deep, 
and  1  sq.  ft.  of  grate  area,  it  would  be  one-half  burned  away  in  71/2  hours 
at  a  rate  of  burning  of  4  Ibs.  per  sq.  ft.  of  grate  per  hour.  This  figure, 
4  Ibs.,  is  commonly  taken  in  designing  grate  surface  for  house-heating 
boilers  and  furnaces.  Using  this  figure  we  have  the  following  as  the 
rated  capacity  of  different  areas  of  grate  surface. 

Rated  Capacity  of  Furnaces  and  Boilers  for  House  Heating. 


fYml 

Equiv. 

Equiv. 

Equiv. 

Diam. 
of 
Round 
Grate. 

Area  in  — 

^oai- 
burning 
Capacity 
per 

TT_,1T, 

Capacity, 
B.T.U. 
per 
Hour. 

Ibs. 
Steam 
Evap. 
2  12°  per 

Ibs. 
Air  per 
Hour 
Heated 

cu.  ft. 
Air  at 
70° 
Heated 

.clour. 

Hour. 

100°. 

100°. 

ins. 
12 

sq.in. 
113.1 

sq.ft. 
.785 

Ibs. 
3.142 

(a) 
31,420 

(b) 
32.5 

(c) 
1,320 

(d) 
17,610 

14 

153.9 

1.069 

4.276 

42,760 

44.3 

1,797 

23,970 

16 

201.1 

1.396 

5.585 

55,850 

57.8 

2,347 

31,300 

18 

254.5 

1.767 

7.069 

70,690 

73.2 

2,970 

39,620 

20 

314.2 

2.182 

8.728 

87,280 

90.4 

3,667 

48,920 

22 

380.1 

2.640 

10.560 

105,600 

109.4 

4,437 

59,190 

24 

452.4 

3.142 

12.566 

125,660 

130.1 

5,280 

70,430 

26 

530.9 

3.687 

14.748 

147,480 

152.7 

6,197 

82,670 

28 

615.8 

4.276 

17.104 

171,040 

177.1 

7,187 

95,870 

30 

706.9 

4.909 

19.636 

196,360 

203.3 

8,260 

110,190 

32 

804.2 

5.585 

22.340 

223,400 

231.3 

9,387 

125,220 

34 

907.9 

6.305 

25.220 

252,200 

261.2 

10,597 

141  360 

36 

1017.9 

7.069 

28.276 

282,760 

292.8 

11,881 

158,490 

Figures  in  column  (b)  =  (a)  -*•  965.7. 

Figures  in  column  (c)  =  (a)  -4-  (100  X  0.238). 

Figures  in-column  (d)  =  (c)  X  13.34. 

Latent  heat  of  steam  at  212°  =  965.7  B.T.U.  [new  steam  tables  give 
970.4]. 

Specific  heat  of  air  =  0.238. 

Note  that  the  figures  in  the  last  three  columns  are  all  based  on  the  rate 
of  combustion  of  4  Ibs.  of  coal  per  sq.  ft.  of  grate  per  hour,  which  is  taken 
as  the  standard  for  house  heating.  For  heating  schoolhouses  and  other 
large  buildings  where  th3  furnace  is  fed  with  coal  more  frequently  a 


694  HEATING   AND   VENTILATION. 

much  higher  actual  capacity  may  be  obtained  from  the  grate  surface 
named.     A  committee  of  the  Am.  Soc.  H.  and  V.  Engrs.  in  1909  says: 

The  grate  surface  to  be  provided  depends  on  the  rate  of  combustion, 
and  this  in  turn  depends  on  the  attendance  and  draft,  and  on  the  size  or 
the  boiler.  Small  boilers  are  usually  adapted  for  intermittent  attention 
and  a  slow  rate  of  combustion.  The  larger  the  boiler,  the  more  attention 
Is  given  to  it,  and  the  more  heating  surface  is  provided  per  square  foot 
of  grate.  The  following  rates  of  combustion  are  common  for  internally 
fired  heating  boilers: 

Sq.  ft.  of  grate 4  to  8       10  to  18       20  to  30 

Lbs.  coal  per  sq.  ft.  grate  per  hr.  not  over         4  -6  10 

Capacity  of  1  sq.  ft.  and  of  10O  sq.  in.  of  Grate  Surface,  for  Steam, 
Hot-water,  or  Furnace  Heating. 

(Based  on  burning  4  Ibs.  of  coal  per  sq.  ft.  of  grate  per  hour  and  10,000 

B.T.U.  available  heating  value  of  1  Ib.  of  coal.) 
1  sq.  ft.          100  sq.  ins. 
grate  equals       grate  equals 

4  2.775      Ibs.  of  coal  per  hour. 

40,000  27,750  B.T.U.  per  hour. 

41.25  28.61        Ibs.  of  steam  evap.  from  and  at  212°  per  hr. 

156.5  108.7          sq.  ft.  of  steam  radiating  surface  =-  B.T.U. 

-i-  255.6*. 
261.4  181.5          sq.    ft.   of    hot-water    radiating  surface  =» 

B.T.U. -153  f. 
22,420.  15,570.  cu.  ft.  of  air  (measured  at  70°  F.)  per  hour 

heated  100°. 

*  Steam  temperature  212°,  room  temperature  70°,  radiator  coefficient, 
that  is  the  B.T.U,  transmitted  per  sq.  ft.  of  surface  per  hour  per  degree  of 
difference  of  temperature,  1.8. 

t  Water  temperature  160°,  room  temperature  70°,  radiator  co- 
efficient 1.7. 

For  any  other  rate  of  combustion  than  4  Ibs.,  multiply  the  figures  In  the 
table  by  that  rate  and  divide  by  4. 

STEAM-HEATING. 

The  Rating  of  House-heating  Boilers. 

(W.  Kent,  Trans.  A.  S.  H.  V.  E.,  1909.) 

The  rating  of  a  steam-boiler  for  house-heating  may  be  based  upon  one 
or  more  of  several  data:  1,  square  feet  of  grate-surface;  2,  square  feet  of 
heating-surface;  3,  coal-burning  capacity;  4,  steam-making  capacity; 
5,  square  feet  of  steam-radiating-surface,  including  mains,  that  it  will 
supply.  In  establishing  such  a  rating  the  following  considerations  should 
be  taken  into  account: 

1.  One  sq.  ft.  of  cast-iron  radiator  surface  will  give  off  about  250  B.T.U. 
per  hour  under  ordinary  conditions  of  temperature  of  steam  212°,  and 
temperature  of  room  70°. 

2.  One  pound  of  good  anthracite  or  semi-bituminous  coal  under  the 
best    conditions  of    air-supply,  in  a  boiler   properly  proportioned,  will 
transmit  about  10,000  B.T.U.  to  the  boiler. 

3.  In  order  to  obtain  this  economical  result  from  trie  coal  the  boilers 
should  be  driven  at  a  rate  not  greatly  exceeding  2  Ibs.  of  water  evaporated 
from   and  at  212°  per  sq.  ft.  of  heating-surface  per  hour,  corresponding 
to  a  heat  transmission  of  2  X  970  =  1940,  or,  say,  approximately  2000 
B.T.U.  per  hour  per  sq.  ft.  of  heating-surface. 

4.  A    satisfactory   boiler  or  furnace   for  house-heating  should   not 
require  coal  to  be  fed  oftener  than  once  in  8  hours:  this  requires  a  rate 
of  burning  of  only  3  to  5  pounds  of  coal  per  sq.  ft.  of  grate  per  hour. 

5.  For  commercial  and  constructive  reasons,  it  Is  not  convenient  to 
establish  a  fixed  ratio  of  heating-  to  grate-surface  for  all  sizes  of  boilers. 
The  grate-surface  is  limited  by  the  available  area  in  which  it  may  be 
placed,  but  on  a  given  grate  more  heating-surface  may  be  piled  in  one 
form  of  boiler  than  in  another,  and  in  boilers  of  one  general  form  one 
boiler  may  be  built  higher  than  another,  Urns  obtaining  a  greater  amount 
of  heating-surface. 


STEAM- HEATING. 


695 


6.   The  rate  of  burning  coal  and  the  ratio  of  heating-  to  grate-surface 
both  being  variable,  the  coal-burning  rate  and  the  ratio  may  be  so  related 
to  each  other  as  to  establish  condition  3,  viz.,  a  rate  of  evaporation  of 
2  Ibs.  of  water  from  and  at  212°  per  sq.  ft.  of  heating-surface  per  hour. 
These  general  considerations  lead  to  the  following  calculations: 
1  Ib.  of  coal,  10,000  B.T.U.  utilized  in  the  boiler,  will  supply  10,000  + 
250  =  40   sq.    ft.   radiating-surface,   and    will   require   10,000  •*-  2000  = 
5  sq.  ft.  boiler  heating-surface.     1  sq.  ft.  of  boiler-surface  will   supply 
2000  •*•  250  or  40  •*•  5  =  8  sq.  ft.  radiating-surface. 


Low 
Boiler. 

Medi- 
um. 

High  Boiler. 

1  sq.  ft.  of  grate  should  burn  

3 

4 

5  Ib.  coal  per  hour. 

1  sq.  ft.  of  grate  should  develop. 

30,000 

40,000 

50,000  B.T.U.  per  hour. 

1  sq.  ft.  of  grate  will  require  
1  sq.  ft.  of  grate  will  supply  

15 
120 

20 
160 

25  sq.  ft.  heating-surf. 
200  sq.ft.  radiating-sur 

Type  of   boiler,   depending  on 

ratio  heating-  -r-  grate-surface. 

A. 

B. 

C. 

TABLE  OF  RATINGS. 


Type  and  No. 

6 
O 

£ 

£  " 
'  !tJj 

Coal  Burned 
per  Hour,  Ibs. 

J-,  O 

i^  • 

Type  and  No. 

O 

£ 

IS 

-^  m 
^W 

Coal  Burned 
per  Hour,  Ibs. 

^  o 

i,  . 

tf00 

A  1... 
A  2... 
A  3... 
A  4... 
A  5... 
B  4... 
F  5... 
B»  6 
B  7... 

1 
2 
3 
4 
5 
4 
5 
6 

15 
30 
45 
60 
75 
80 
100 
120 
140 

3 
6 
9 
12 
15 
16 
20 
24 
28 

30 
60 
90 
120 
150 
160 
200 
240 
280 

120 
240 
360 
480 
600 
640 
800 
960 
1,120 

B  8... 
C  6... 
C  7... 
C  8... 
C  10... 
C  12... 
C  14... 
C  16... 

8 
6 
7 
8 
10 
12 
14 
16 

160 
150 
175 
200 
250 
300 
350 
400 

32 
30 
35 
40 
50 
60 
70 
80 

320 
300 
350 
400 
500 
600 
700 
800 

1,280 
1,200 
1,400 
1,600 
2,000 
2,400 
2,800 
3,200 

The  table  is  based  on  the  utilization- in  the  boiler  of  10,000  B.T.U.  per 
pound  of  good  coal.  For  poorer  coal  the  same  figures  will  hold  good 
except  the  pounds  coal  burned  per  hour,  which  should  be  increased  in 
the  ratio  of  the  B.T.U.  of  the  good  to  that  of  the  poor  coal.  Thus  for 
coal  from  which  8000  B.T.U.  can  be  utilized  the  coal  burned  per  hour 
will  be  25  per  cent  greater. 

For  comparison  with  the  above  table  the  following  figures  are  taken 
and  calculated  from  the  catalogue  of  a  prominent  maker  of  cast-iron 
boilers: 


Coal 

H 
Heat- 

R 
Radiat- 

// 

5 

R 

B.T.U. 

P'N, 

per 
Hour 

Height. 

Q 

mg- 

ing-sur- 

per Hour 

H  I* 

per 

Grate. 

sur- 

face. 

0 

G 

H 

=  flx250 

« 

sq.ft. 

face. 

Grate 

* 

Low  

i   2.1 
«    4.7 

45 
90 

210 
600 

21.5 
19.1 

100 
128 

4.7 
6.7 

52,500 
150,000 

,167 
,667 

2.5 
3.2 

Medium.. 

]    4.2 
\    8.2 

103 
195 

600 
1,500 

24.5 
23.8 

143 
183 

5.8 
7.7 

150,000 
375,000 

,456 
,923 

3.6 
4.6 

High  

(   6.7 
1147 

210 
420 

1,200 
3,300 

31.3 
28.6 

179 
225 

5.7 
7.9 

300,000 
825,000 

,476 
,964 

4.5 
5.6 

*  Equals  B.T.U.  per  hour  4-  10,000  O. 


696  HEATING   AND   VENTILATION. 


TESTING  CAST-IRON  HOUSE-HEATING  BOILERS. 

The  testing  of  the  evaporating  power  and  the  economy  of  small-sized 
boilers  is  more  difficult  than  the  testing  of  large  steam-boilers  for  the 
reason  that  the  small  quantity  of  coal  burned  in  a  day  makes  it  impossible 
to  procure  a  uniform  condition  of  the  coal  on  the  grate  throughout  the 
test,  and  large  errors  are  apt  to  be  made  in  the  calculation  on  account  of 
the  difference  of  condition  at  the  beginning  and  end  of  a  test.  The 
following  is  suggested  as  a  method  of  test  which  will  avoid  these  errors. 

(a)  Measure  the  grate-surface  and  weigh  out  an  amount  of  coal  equal 
to  30,  40,  or  50  Ibs.  per  sq.  ft.  of  grate,  according  to  the  type  A,  B,  or  C, 
or  the  ratio  of  heating-  to  grate-surface. 

(&)  Disconnect  the  steam-pipe,  so  that  the  steam  may  be  wasted  at 
atmospheric  pressure.  Fill  the  boiler  with  cold  water  to  a  marked  level, 
and  take  the  weight  of  this  water  and  its  temperature. 

(c)  Start  a  brisk  fire  with  plenty  of  wood,  so  as  to  cause  the  coal  to 
ignite  rapidly;  feed  the  coal  as  needed,  and  gradually  increase  the  thick- 
ness of  the  bed  of  coal  as  it  burns  brightly  on  top,  getting  the  fire-pot  full 
as  the  last  of  the  coal  is  fired.     Then  burn  away  all  the  coal  until  it  ceases 
to  make  steam,  when  the  test  may  be  considered  as  at  an  end. 

(d)  Record  the  temperature  of  the  gases  of  combustion  in  the  flue  every 
half-hour. 

(e)  Periodically,  as  needed,  feed  cold  water,  which  has  been  weighed, 
to  bring  the  water  level  to  the  original  mark.     Record  the  time  and  the 
weight. 

CALCULATIONS. 

Total  water  fed  to  the  boiler,  including  original  cold 
water,  pounds  X  (212°  —  original  cold-water  tem- 
perature) = B.T.U. 

Water  apparently  evaporated,  pounds  X  970  = B.T.U. 

Add  correction  for  increased  bulk  of  hot  water: 
Original  water,  pounds  x(62'3 L~  59'8)  X  970  = B.T.U. 

O^J.o  

Total B.T.U. 

Divide  by  970  to  obtain  equivalent  water  evaporation  from  and  at 
212°  F. 

Divide  by  the  number  of  pounds  of  coal  to  obtain  equivalent  water  per 
pound  of  coal. 

The  last  result  may  be  considerably  less  than  10  pounds  on  account  of 
imperfect  combustion  at  the  beginning  of  the  test,  excessive  air-supply 
when  the  coal  bed  is  thin  in  the  latter  half  of  the  test,  and  loss  by  radiation, 
but  the  results  will  be  fairly  comparable  with  results  from  other  boilers 
of  the  same  size  and  run  under  the  same  conditions.  The  records  of  water 
fed  and  of  temperature  of  gases  should  be  plotted,  with  time  as  the  base, 
for  comparison  with  other  tests. 

Proportions  of  House-heating  Boilers.  —  A  committee  of  the  Am. 
Soc.  Heating  and  Ventilating  Engineers,  reporting  in  1909  on  the  method 
of  rating  small  house-heating  boilers,  shows  the  following  ratings,  in  square 
feet  of  radiating  surface  supplied  by  certain  boilers  of  nearly  the  same 
nominal  capacity,  as  given  in  makers'  catalogues. 

Boiler....                                                      .    A.  B.       C.       D.  E.       F. 

Rated  capacity 800  800  775     750  750     750 

Square  inches  of  grate 616  740  648     528  630     648 

Ratio  of  grate  to  100  sq.  ft.  of  capacity  77  92.5  83.6    70.4  84     86.2 

Estimated  rate  of  combustion 5.1  4.2  4.65    5.63  4.4%    4.5 

The  figures  in  the  last  line  are  Ibs.  of  coal  per  sq.  ft.  of  grate  surface  per 
hour,  and  are  based  on  the  assumptions  of  10,000  B.T.U.  utilized  per 
Ib.  of  coal  and  270  B.T.U.  transmitted  by  each  sq.  ft.  of  radiating  sur- 
face per  hour. 


STEAM- HEATING. 


697 


"  The  question  of  heating  surface  in  a  boiler  seems  to  be  an  unknown 
quantity,  and  inquiry  among  the  manufacturers  does  not  produce  much 
information  on  the  subject." 

Folio  wing  is  the  list  of  sizes  and  ratings  of  the  "Manhattan"  sectional 
steam  boiler.  The  figures  for  sq.  ft.  of  grate  surface  and  for  the  ratio  of 
heating  to  grate  surface  (approx.)  have  been  computed  from  the  sizes 
given  in  the  catalogue  (1909). 


"S.A 

•*>  0 
0>—i 

bib- 

"S.S      • 

^.s 

tii 

^  c 

0}  O 

i||j 

Size  of 

0>  <u 

^Jj 

?5g 

OB 
JH    C 
QJ  O 

|«l| 

Size  of 

a  flj 

S®  . 

<3g8 

e  tj 

§  £  c~ 

Grate. 

08  cc^ 

oO<g 

JS'S 

S  w 

lid— 

Grate. 

§5^ 

.20-g 

1* 

s.i  0^2 

t°« 

S** 

S  o> 
1^ 

ls-il 

J** 

|s<2 

ins. 

sq.ft. 

ins. 

sq.ft. 

4 

450 

18x19 

2.37 

68 

29 

10 

2250 

24x63 

10.5 

212 

20 

5 

600 

18x25 

3.75 

84 

23 

6 

2200 

36x36 

9 

256 

28 

6 

750 

18x31 

3.87 

100 

26 

7 

2700 

36x43 

11.74 

298 

26 

7 

900 

18x37 

4.65 

116 

25 

8 

3200 

36x50 

13.33 

340 

26 

8 

1050 

18x43 

5.37 

132 

25 

9 

3700 

36x57 

14.25 

382 

26 

5 

1000 

24x30 

5 

111 

22 

10 

4200 

36x64 

16 

424 

26 

6 

1250 

24x36 

6 

128 

21 

11 

4700 

36x71 

17.5 

466 

27 

7 

1500 

24x43 

7.16 

149 

21 

12 

5200 

36x78 

19.5 

508 

26 

8 

1750 

24x50 

8.33 

170 

20 

13 

5700 

36x84 

21 

550 

26 

9 

2000 

24x57 

9.5 

191 

20 

14 

6200 

36x90 

22.5 

592 

26 

It  appears  from  this  list  that  there  are  three  sets  of  proportions,  corre- 
sponding to  the  three  widths  of  grate  surface.  The  average  ratio  of 
heating  to  grate  surface  in  the  three  sets  is  respectively  25.0,  20.7,  and 
25.8;  the  rated  sq.  ft.  of  radiating  surface  per  sq.  ft.  of  grate  is  185,  208, 
and  259,  and  the  sq.  ft.  of  radiating  surface  per  sq.  ft.  of  boiler  heating 
surface  is  7.4,  10.1,  and  9.8.  Taking  10,000  B.T.U.  utilized  per  Ib.  of 
coal,  and  250  B.T.U.  emitted  per  sq.  ft.  of  radiating  surface  per  hour, 
the  rate  of  combustion  required  to  supply  the  radiating  surface  is  respec- 
tively 4.62,  5.22,  and  6.40  Ibs.  per  sq.  ft.  of  grate  per  hour. 

Coefficient  of  Heat  Transmission  in  Direct  Radiation.  —  The  value 
of  K,  or  the  B.T.U.  transmitted  per  sq.  ft.  of  radiating  surface  per  hour 
per  degree  of  difference  of  temperature  between  the  steam  (or  hot  water) 
and  the  air  in  the  room,  is  commonly  taken  at  1.8  in  steam  heating, 
with  a  temperature  difference  of  about  142°,  and  1.6  in  hot-water  heat- 
ing, with  a  temperature  difference  averaging  80°.  Its  value  as  found  by 
test  varies  with  the  conditions;  thus  the  total  heat  transmitted  is  not 
directly  proportional  to  the  temperature  difference,  but  increases  at  a 
faster  rate;  single  pipes  exposed  on  all  sides  transmit  more  heat  than 
pipes  in  a  group;  low  radiators  more  than  high  ones;  radiators  exposed 
to  currents  of  cool  air  more  than  those  in  relatively  quiet  air;  radiators 
with  a  free  circulation  of  steam  throughout  more  than  those  that  are 
partly  filled  with  water  or  air,  etc.  The  total  range  of  the  value  of  K, 
for  ordinary  conditions  of  practice,  is  probably  between  1.5  and  2.0  for 
steam-heating  with  a  temperature  difference  of  140°,  averaging  1.8,  and 
between  1.2  and  1.7,  averaging  1.6,  for  hot-water  heating,  with  a  tem- 
perature difference  of  80°. 

C.  F.  Hauss,  Trans.  A.  S.  H.  V.  E.,  1904,  gives  as  a  basis  for  calcula- 
tion, for  a  room  heated  to  70°  with  steam  at  11/2  Ibs.  gauge  pressure 
(temperature  difference  146°  F.)  1  sq.  ft.  of  single  column  radiator  gives 
off  300  B.T.U.  per  hour;  2-column,  275;  3-column,  250;  4-column,  225. 

Value  of  K  in  Cast-iron  Direct  Radiators.  (J.  R.  Allen,  Trans. 
A.  S.  H.  V.  E.,  1908.)  Ts  =  temp,  of  steam;  Tj_=  temp,  of  room. 


Ts  -  T!  = 

110 

120 

130 

140 

150 

160 

2-col. 

rad  .... 

.1.71 

1 

.745 

1.76 

1. 

82 

1, 

,855 

1 

.895 

3-col. 

rad  

.1.65 

1 

.695 

1.745 

1. 

79 

1. 

835 

1. 

,885 

Ts 

-5Ti  = 

170 

180 

200 

220 

240 

260 

2-col. 

rad  

.1.93 

1 

.965 

2.04 

2. 

11 

2. 

,185 

2 

,265 

3-col. 

rad.... 

.1.93 

1 

.98 

2.075 

2 

.165 

2. 

260 

2. 

36 

698  HEATING   AND   VENTILATION. 

B.T.U.  Transmitted  per  Hour  per  Sq.  Ft.  of  Heating  Surface  in 
Indirect  Radiators.  (W.  S.  Munroe,  Eng.  Rec.,  Nov.  18,  1899.) 

Cu.  ft.  of  air  per  hour  per  sq.  ft.  of  surface. 
100     200     300     400       500       600     700     800       900 

B.T.U.  per  hour  per  sq.  ft.  of  heating  surface. 
"Gold  Pin  ")(a).  ..  200     325     450     560       370       780     870     950     1030 

radiator     ((&)••.  300     550     760     950     1130     1300 
"Whittier"      (6)...  250     400     520     620       710 

B.T.U.  per  hr.  per  sq.  ft.  per  deg.  diff.  of  temp.* 

Gold  Pin  (a) 1.3     2.2     3.0     3.7       4.5       5.2     5.8     6.3       6.9 

Gold  Pin  (6) 2.0     3.7     5.1     6.3       7.7       8.7 

Whittier  (6) 1.7     2.7     3.5     4.1       4.7 

Temperature  difference  between  steam  and  entering  air,  (a)  150; 
(6)  215. 

*  Between  steam  and  entering  air. 

Short  Rules  for  Computing  Radiating-Surfaces.  —  In  the  early  days 
of  steam-heating,  when  little  was  known  about  "  British  Thermal  Units," 
it  was  customary  to  estimate  the  amount  of  radiating-surface  by  dividing 
the  cubic  contents  of  the  room  to  be  heated  by  a  certain  factor  supposed 
to  be  derived  from  "experience."  Two  of  these  rules  are  as  follows: 

One  square  foot  of  surface  will  heat  from  40  to  100  cu.  ft.  of  space  to 
75°  in  —  10°  latitudes.  This  range  is  intended  to  meet  conditions  of 
exposed  or  corner  rooms  of  buildings,  and  those  less  so,  as  intermediate 
ones  of  a  block.  As  a  general  rule,  1  sq.  ft.  of  surface  will  heat  70  cu.  ft. 
of  air  in  outer  or  front  rooms  and  100  cu.  ft.  in  inner  rooms.  In  large 
stores  in  cities,  with  buildings  on  each  side,  1  to  100  is  ample.  The 
following  are  approximate  proportions: 

One  square  foot  radiating-surface  will  heat: 

In  Dwellings,  In  Hall,  Stores,  In  Churches, 
Schoolrooms,  Lofts,  Factories,  Large  Audito- 
Offices,  etc.  etc.  riums,  etc. 

By  direct  radiation.. . .        60  to  80  ft.  75  to  100  ft.         150  to  200  ft. 

By  indirect  radiation..        40  to  50  ft.  50  to    70  ft.         100  to  140  ft. 

Isolated  buildings  exposed  to  prevailing  north  or  west  winds  should 
have  a  generous  addition  made  to  the  heating-surface  on  their  exposed 
sides. 

1  sq.  ft.  of  boiler-surface  will  supply  from  7  to  10  sq.  ft.  of  radiating- 
surface,  depending  upon  the  size  of  boiler  and  the  efficiency  of  its  surface, 
as  well  as  that  of  the  radiating-surface.  Small  boilers  for  house  use 
should  be  much  larger  proportionately  than  large  plants.  Each  horse- 
power of  boiler  will  supply  from  240  to  360  ft.  of  1-in.  steam-pipe,  or 
80  to  120  sq.  ft.  of  radiating-surface.  Under  ordinary  conditions  1 
horse-power  will  heat,  approximately,  in  — 

Brick  dwellings,  in  blocks,  as  in  cities 15,000  to  20,000  cu.  ft. 

Brick  stores,  in  blocks 10,000  15,000 

Brick  dwellings,  exposed  all  round 10,000  15,000 

Brick  mills,  shops,  factories,  etc 7,000  10,000 

Wooden  dwellings,  exposed 7,000  10,000 

Foundries  and  wooden  shops 6,000  10,000 

Exhibition  buildings,  largely  glass,  etc 4,000  15,000 

Such  "rules  of  thumb,"  as  they  are  called,  are  generally  supplanted  by 
the  modern  "heat-unit"  methods. 

Carrying  Capacity  of  Pipes  in  Low -Pressure  Steam  Heating.    (W. 

Kent,  Trans.  A.  S.  II.  V.  E.,  1907.)  — The  following  table  is  based  on  an 
assumed  drop  of  1  pound  pressure  per  1000  feet,  not  because  that  is 
the  drop  which  should  always  be  used — in  fact  the  writer  believes  that 
in  large  installations  a  far  greater  drop  is  permissible  —  but  because  it 
gives  a  basis  upon  which  the  flow  for  any  other  drop  may  be  calculated, 


FLOW  OF  STEAM  IN  PIPES. 


699 


merely  by  multiplying  the  figures  in  the  tables  by  the  square  root  9f  the 
assigned  drop.    The  formula  from  which  the  tables  are  calculated  is  the 

in  which  W=  weight  of  steam 


well  known  one,  W 
in  Ibs.  per  hour; 


weight  of  steam  in  pounds  per  cubic  foot,  at 


eng       n    ee.          e  coecens  c  are    erve      rom     acocs    o 

(see  page  618)  which  is  believed  to  be  as  accurate  as  any  that  has  been 

derived  from  the  very  few  recorded  experiments  on  steam. 


Nominal  diam.  of 
pipe 

1/2 

3/4 

1 

U/4 

11/2 

2 

21/2 

3 

31/2 

Value  of  c  —  

334 

37.5 

41  .3 

45.8 

48.4 

52.5 

55.5 

59.0 

61  3 

Nominal  diam.  of 
pipe  

4 

41/2 

5 

6 

7 

8 

9 

10 

1?. 

Value  of  c  —  

63.2 

64.8 

66.5 

68.7 

70.7 

72.2 

73.4 

74.5 

76.3 

Flow  of  Steam  in  Pipes  for  a  Drop  of  1  Ifo.  per  1000  Ft.  Length. 

(Pounds  per  Hour.) 


i  • 

£.2 

fi 

IH 

Pi  =0.3 

pi=1.3 

Pi=2.3 

Pi=3.3 

pi=4.3 

pi=5.3 

Pi  =  6.3 

pi  =  8.3 

pi=10.3 

•3.0. 

3  s 

W  — 

w  — 

W  — 

w~ 

w= 

W  — 

w  = 

w= 

W  — 

'SvH 

11 

.03732 

.04042 

.04277 

.04512 

.04746 

.04980 

.05213 

.05676 

.0614 

0  ° 

T~~ 

H/4 

1.049 
1.380 

17.1 
37.6 

17.8 
39.4 

18.3 
40.2 

18.8 
41.3 

19.2 

42.4 

19.7 
43.4 

20.2 
44.4 

21.0 
46.3 

21.9 

48.2 

H/2 

1.610 

58.4 

60.7 

62.5 

64.1 

65.8 

67.4 

68.9 

71.9 

74.8 

2 

2.067 

118.2 

123.0 

126.6 

130.0 

133.3 

136.6 

139.7 

145.8 

151.6 

21/2 

2.469 

194.9 

202.8 

208.7 

214.3 

219.7 

225.1 

230.3 

240.3 

250.0 

3 

3.068 

356.6 

371.0 

381.8 

392.0 

402.1 

411.9 

421.4 

439.7 

457.3 

31/2 

3.548 

532.7 

554.5 

570.5 

585.8 

600.8 

615.4 

629.8 

481.5 

683.8 

4 

4.026 

753.6 

784.2 

807.0 

828.6 

849.6 

870.6 

890.4 

929.4 

966.6 

41/2 

4.506 

1025. 

1066. 

1096. 

1126. 

1154. 

1184. 

1210. 

1262. 

1315. 

5 

5.047 

1395. 

1451. 

1494. 

1534. 

1573. 

1611. 

1649. 

1720. 

1789. 

6 

6.065 

2281. 

2374. 

2443. 

2509. 

2573. 

2635. 

2696. 

2813. 

2926. 

7 

7.023 

3387. 

3525. 

3628. 

3725. 

3820. 

3913. 

4003. 

4177. 

4345. 

8 

7.981 

4776. 

4970. 

5114. 

5250. 

5385. 

5518. 

5644. 

5889. 

6123. 

9 

8.941 

6429. 

6693. 

6885. 

7070. 

7250. 

7430. 

7604. 

7934. 

8251. 

10 

10.020 

8676 

9030. 

9294. 

9545. 

9785. 

10025. 

10259. 

10702. 

11123. 

It 

11.000 

11106. 

11556. 

11892. 

12210. 

12522. 

12828. 

13128. 

13698. 

14244. 

12  112.000 

13950. 

14520. 

14940. 

15342. 

15732. 

16116. 

16488. 

17202. 

17892. 

Pi  =  initial  pressure,   by  gauge,    Ib.   per   sq.  in.    w  =  density,  Ib. 
per  cu.  ft. 

For  any  other  drop  of  pressure  per  1000  feet  length,  multiply  the  fig- 
ures in  the  table  by  the  square  root  of  that  drop,  or  by  the  factor  below. 

Drop  Ib.  per 

1000  ft....      14        1/2         2          3  4 

Factor 0.5     0.71    1.41    1.73       2.0 


6          8         10        15        20 
2.45    2.83    3.16   3.87   4.47 


In  all  cases  the  judgment  of  the  engineer  must  be  used  in  the  assump- 
tion of  the  drop  to  be  allowed.  For  small  distributing  pipes  it  will  gen- 
erally be  desirable  to  assume  a  drop  of  not  more  than  one  pound  per 
1000  feet  to  insure  that  each  single  radiator  shall  always  have  an  ample 
supply  for  the  worst  conditions,  and  in  that  case  the  size  of  piping  given 
in  the  table  up  to  two  inches  may  be  used;  but  for  main  pipes  supplying 
totals  of  more  than  500  square  feet,  greater  drops  may  be  allowed. 


'700 


HEATING   AND   VENTILATION. 


Proportioning  Pipes  to  Radiating  Surface. 

FIGURES   USED  IN  CALCULATION  OF  RADIATING  SURFA.CE. 

P  =  Pressure  by  gauge,  Ibs.  per  sq.  in. 
0.          0.3        1.3        2.3        3.3        4.3        5.3        6.3        8.3 

L  =  latent  heat  of  evaporation,  B.T.U.  per  lb.* 
965.7    965.0    962.6    960.4    958.3    956.3    954.4    952.6    949.1     945.8 


10.3 


212. 


Temperature  Fahrenheit,  T\. 
213.       216.3    219.4    222.4    225.2    227.9 


142.       143. 
Hi  =  Tt  X  1.8 


230.5    2.35.4    240.0 
!T2=  TI—  70°,  difference  of  temperature. 
146.3    149.4    152.4    155.2    157.9    160.5     165.4    170.0 


heat  transmission  per  sq.  ft.  radiating  surface,  B.T.U. 

per  hour. 
255.6    257.4    263.3    268.9    274.3    279.2    284.2    288.9    297.7    306.0 

Ht+  L  =  steam  condensed  per  sq.  ft.  radiating  surface,  Ibs.  per  hour. 
0.2647    0.267    0.274    0.280    0.286    0.292    0.298    0.303    0.314    0.324 

Heciprocal  of  above  =  radiating  surface  per  lb.  of  steam  condensed  per 

hour. 

3.42      3.36 


3.78        3.75      3.65      3.57      3.50 


3.30      3.18      3.09 


The  last  three  lines  of  figures  are  based  on  the  empirical  constant  1.8 
for  the  average  British  thermal  units  transmitted  per  square  foot  of  radi- 
ating surface  per  hour  per  degree  of  difference  of  temperature.  This 
figure  is  approximately  correct  for  several  forms  of  both  cast-iron  radia- 
tors and  pipe  coils,  not  over  30  inches  high  and  not  over  two  pipes  in 
width. 


RADIATING  SURFACE  SUPPIJED  BY  DIFFERENT  SIZES  OF  PIPE. 

On  basis  of  steam  in  pipe  at  0.3  and  10.3  Ibs.  gauge  pressure,  tempera- 
ture of  room  70°,  heat  transmitted  per  square  foot  radiating  surface  257.4 
and  306  British  thermal  units  per  hour,  and  drop  of  pressure  in  pipe  at 
the  rate  of  1  lb.  per  1000  feet  length;  =  pounds  of  steam  per  hour  in  the 
table  on  the  preceding  page,  1st  column,  X  3.75,  and  last  column,  X  3.09. 


Size  of 
Pipe. 

Radiating 
Surface, 
Sq.  Ft. 

Size  of 
Pipe, 

Radiating 
Surface, 
Sq.Ft. 

Size  of 
Pipe. 

Radiating 
Surface, 
Sq.  Ft. 

In. 

0.3  lb. 

10.3  lb. 

In, 

0.3  lb. 

10.3  lb. 

In. 

0.3  lb. 

10.31b. 

1/2 

16 

16 

21/2 

734 

769 

6 

7,541 

7,90! 

3/4 

36 

38 

3 

1,296 

1,357 

7 

11,010 

11,535 

1 

71 

75 

31/2 

1,895 

1,986 

8 

15,307 

16,040 

11/4 

150 

157 

2,630 

2,755 

9 

20,482 

21,451 

H/2 

230 

241 

41/2 

3,520 

3,686 

10 

27,427 

28,718 

2 

453 

475 

5 

4,695 

4,919 

12 

43,312 

45,423 

For  greater  drops  than  1  lb.  per  1000  ft.  length  of  pipe,  multiply  the 
figures  by  the  square  root  of  the  drop. 

*  The  latest  steam  tables  (1909)  give  somewhat  higher  figures,  but  the 
difference  is  unimportant  here. 


SIZES   OF   STEAM   PIPES   FOB   HEATING, 


701 


Sizes  of  Steam  Pipes  in  Heating  Plants.  —  G.  W.  Stanton,  in  HeatinQ 
and  Ventilating  Mag.,  April,  1908,  gives  tables  for  proportioning  pipes  to 
radiating  surface,  from  which  the  following  tablets  condensed: 


Sup- 
ply 

Pipe. 
Ins. 

Radiating  Surface  Sq.  Ft. 

Returns. 

Drips. 

Connections. 

A 

B 

C 

D 

B 

CxD 

A 

BAD 

At 

A2BA 

1 

H/4 
H/2 

BjA 

U'4 

H/2 

2l/2 
31/2 

h 

6 
7 
8 
9 
10 
12 
14 
16 

24 
60 
125 
250 
600 
800 
1,000 
1,600 
1,900 
2,300 
4,100 
6,500 
9,600 
13,600 

60 
100 
200 
400 
700 
1,000 
1,600 
2,300 
3,200 
4  100 
6,500 
9,600 
13,600 

36 
72 
120 
280 
528 
900 
1,320 
1,920 
2,760 
3,720 
6,000 
9,000 
12,800 
17,800 
23,200 
37,000 
54,000 
76,000 

60 
120 
240 
480 
880 
1,500 
2,200 
3,200 
4,600 
6,200 
10,000 
15,000 
21,600 
30,000 
39,000 
62,000 
92,000 
130,000 

1 
1 

11/4 

I  V2 

2 
21/2 
21/2 
21/2 

3 

31/2 
4 

1 
1 
U/4 
U/2 

21/2 
21/2 

3 

31/2 
3V, 

4 
41/2 

6 

7 
8 

3/4 

13/4 

H/4 
U/4 
11/2 

U/2 
U/2 

3/4 
3/4 

1 

U/4 
U/4 
U/4 
11/4 

U/4 

u/2 

2V, 
31/2 
41/2 

U/4 
U/2 

Supply  mains  and  risers 
are   of    the   same   size. 
Riser     connections     on 
the  two-pipe  system  to 
be  the  same  size  as  the 
riser. 

A.  For  single-pipe  steam-heating  system   0  to 
riser  connections.     A 2,  radiator  connections. 


Ib.   pressure.     A\, 


B.  Two-pipe  system  0  to  5  Ib.  pressure;  Bi,  Ci,  radiator  connections, 
supply;  B%,  Ci,  radiator  connections,  return. 

C,  D.  Two-pipe  system  2  and  5  Ibs.  respectively,  mains  and  risers  not 
over  100  ft.  length.     For  other  lengths,  multiply  the  given  radiating 
surface  by  factors,  as  below: 


Length,  ft...  .      200 
Factor  ......   0.71 


300 
0.58 


400 
0.5 


500 
0.45 


600 
0.41 


700 
0.38 


800 
0.35 


900 
0.33 


1000 
0.32 


Mr.  Stanton  says:  Theoretically  both  supply  and  return  mains  could 
be  much  smaller,  but  in  practice  it  has  been  found  that  while -smaller 
pipes  can  be  used  if  a  job  is  properly  and  carefully  figured  and  propor- 
tioned and  installed,  for  work  as  ordinarily  installed  it  is  far  safer  to  use 
the  sizes  that  have  been  tried  and  proven.  By  using  the  sizes  given  a 
job  will  circulate  throughout  with  1  Ib.  steam  pressure  at  the  boiler. 

Resistance  of  Fittings.  — Where  the  pipe  supplying  the  radiation  con- 
tains a  large  number  of  fittings,  or  other  conditions  make  such  a  refine- 
ment necessary,  it  is  advisable  to  add  to  the  actual  distance  of  the  radia- 
tion from  the  source  of  supply  a  distance  equivalent  to  the  resistance 
offered  by  the  fittings,  and  by  the  entrance  to  the  radiator,  the  value  of 
which,  expressed  in  feet  of  pipe  of  the  same  diameter  as  the  fitting,  will 
be  found  in  the  accompanying  table.  Power,  Dec.,  1907. 

FEET  OF  PIPE  TO  BE  ADDED  FOR  EACH  FITTING. 


Size  Pipe. 

' 

U/4 

11/2 

2 

21/2 

3 

31/2 

4 

41/2 

5 

6 

7 

8 

9 

10 

Elbows... 

3 

4 

5 

7 

8 

10 

12 

13 

15 

17 

20 

23 

27 

30 

33 

Globe  V.. 

7 

8 

10 

13 

17 

20 

23 

27 

30 

33 

40 

47 

53 

60 

67 

Entrance 

5 

6 

8 

10 

12 

15 

18 

20 

23 

25 

30 

35 

40 

45 

50 

702  HEATING   AND   VENTILATION. 

Overhead  Steam-pipes.  (A.  R.  Wolff,  Stevens  Indicator,  1887.)  — 
When  the  overhead  system  of  steam-heating  is  employed,  in  which  sys- 
tem direct  radiating-pipes,  usually  1 1/4  in.  in  diam.,  are  placed  in  rows 
overhead,  suspended  upon  horizontal  racks,  the  pipes  running  horizon- 
tally, and  side  by  side,  around  the  whole  interior  of  the  building  from  2 
to  3  ft.  from  the  walls,  and  from  2  to  4  ft.  from  the  ceiling,  the  amount 
of  li/4-in.  pipe  required,  according  to  Mr.  C.  J.  H.  Woodbury,  for  heating 
mills  (for  which  use  this  system  is  deservedly  much  in  vogue),  is  about 
1  ft.  in  length  for  every  90  cu.  ft.  of  space.  Of  course  a  great  range  of 
difference  exists,  due  to  the  special  character  of  the  operating  machinery 
in  the  mill,  both  in  respect  to  the  amount  of  air  circulated  by  the  ma- 
chinery, and  also  the  aid  to  warming  the  room  by  the  friction  of  the 
journals. 

Removal  of  Air  from  Radiators.  Vacuum  Systems.  —  In  order 
that  a  steam  radiator  may  work  at  its  highest  capacity  it  is  necessary 
that  it  be  neither  water-bound  nor  air-bound.  Proper  drainage  must 
therefore  be  provided,  and  also  means  for  continuously,  or  frequently, 
removing  air  from  the  system,  such  as  automatic  air-valves  on  each 
radiator,  an  air-pump  or  an  air-ejector  on  a  chamber  or  receiver  into 
which  the  returns  are  carried,  or  separate  air-pipes  connecting  each 
radiator  with  a  vacuum  chamber.  When  a  vacuum  system  is  used, 
especially  with  a  high  vacuum,  much  lower  temperatures  than  usual  may 
be  used  in  the  radiators,  which  is  an  advantage  in  moderate  weather. 

Steam-consumption  in  Car-heating. 

C.,  M.  &  ST.  PAUL  RAILWAY  TESTS.     (Engineering,  June  27,  1890,  p.  764.) 

Outside  Temperature.         Inside  Temperature.        ^^rte^THw^ 

40  70  70  Ibs. 

30  70  85 

10  70  100 

Heating  a  Greenhouse  by  Steam. — Wm.  J.  Baldwin  answers .  a 
question  in  the  American  Machinist  as  below:  With  five  pounds  steam- 
pressure,  how  many  square  feet  or  inches  of  heating-surface  is  necessary 
to  heat  100  square  feet  of  glass  on  the  roof,  ends,  and  sides  of  a  green- 
house  in  order  to  maintain  a  night  heat  of  55°  to  65°,  while  the  thermom- 
eter outside  ranges  at  from  15°  to  20°  below  zero:  also,  what  boiler- 
surface  is  necessary?  Which  is  the  best  for  the  purpose  to  use  —  2"  pipe 
or  1 1/4"  pipe? 

Ans.  —  Reliable  authorities  agree  that  1.25  to  1.50  cubic  feet  of  air  in 
an  enclosed  space  will  be  cooled  per  minute  per  sq.  ft.  of  glass  as  many 
degrees  as  the  internal  temperature  of  the  house  exceeds  that  of  the  air 
outside.  Between  +  65°  and  —20°  there  will  be  a  difference  of  85°,  or, 
say,  one  cubic  foot  9f  air  cooled  127.5°  F.  for  each  sq.  ft.  of  glass  for  the 
most  extreme  condition  mentioned.  Multiply  this  by  the  number  of 
square  feet  of  glass  and  by  60,  and  we  have  the  number  of  cubic  feet  of 
air  cooled  1°  per  hour  within  the  building  or  house.  Divide  the  number 
thus  found  by  48,  and  it  gives  the  units  of  heat  required,  approximately. 
Divide  again  by  953,  and  it  will  give  the  number  of  pounds  of  steam  that 
must  be  condensed  from  a  pressure  and  temperature  of  five  pounds 
above  atmosphere  to  water  at  the  same  temperature  in  an  hour  to  main- 
tain the  heat.  Each  square  foot  of  surface  of  pipe  will  condense  from 
1/4  to  nearly  1/2  lb.  of  steam  per  hour,  according  as  the  coils  are  exposed 
or  well  or  poorly  arranged,  for  which  an  average  of  1/3  lb.  may  .be  taken. 
According  to  this,  it  will  require  3  sq.  ft.  of  pipe  surface  per  lb.  of  steam 
to  be  condensed.  Proportion  the  heating-surface  of  the  boiler  to  have 
about  one  fifth  the  actual  radiating-surface,  if  you  wish  to  keep  steam 
over  night,  and  proportion  the  grate  to  burn  not  more  than  six  pounds 
of  coal  per  sq.  ft.  of  grate  per  hour.  With  very  slow  combustion,  such 
as  takes  place  in  base-burning  boilers,  the  grate  might  be  proportioned 
for  four  to  five  pounds  of  coal  per  hour.  It  is  cheaper  to  make  coils  of 
H/4"  pipe  than  of  2",  and  there  is  nothing  to  be  gained  by  using  2"  pipe 
unless  the  coils  are  very  long.  The  pipes  in  a  greenhouse  should  be 
under  or  in  front  of  the  benches,  with  every  chance  for  a  good  circulation 


HOT-WATER   HEATING.  703 

of  air.     "Header"  coils  are  better  than  "return-bend"  coils  for  this 
purpose. 

Mr.  Baldwin's  rule  may  be  given  the  following  form:  Let  H  =  heat- 
units  transferred  per  hour,  T  =  temperature  inside  the  greenhouse,  t  = 
temperature  outside,  S  =  sq.  ft.  of  glass  surface;  then  H  =  1.5  S  (T  —  t) 
X  60  -*-  48  =  1.875  S  (T  —  t).  Mr.  Wolff's  coefficient  K  for  single  sky- 
lights gives  H  =  1.03  S  (T -  0,  and  for  single  windows,  1.20  S  (T  -  t). 

Heating  a  Greenhouse  by  Hot  Water.  —  W.  M.  Mackay,  of  the 
Richardson  &  Boynton  Co.,  in  a  lecture  before  the  Master  Plumbers' 
Association,  N.  Y.,  1889,  says:  I  find  that  while  greenhouses  were  for- 
merly heated  by  4-inch  and  3-inch  cast-iron  pipe,  ,on  account  of  the  large 
body  of  water  which  they  contained,  and  the  supposition  that  they  gave 
better  satisfaction  and  a  more  even  temperature,  florists  of  long  experi- 
ence who  have  tried  4 -inch  and  3-inch  cast-iron  pipe,  and  also  2-inch 
wrought-iron  pipe  for  a  number  of  years  in  heating  their  greenhouses 
by  hot  water,  and  who  have  also  tried  steam-heat,  tell  me  that  they  get 
better  satisfaction,  greater  economy,  and  are  able  to  maintain  a  more 
even  temperature  with  2-inch  wrought-iron  pipe  and  hot  water  than  by 
any  other  system  they  have  used.  They  attribute  this  result  principally 
to 'the  fact  that  this  size  pipe  contains  less  water  and  on  this  account  the 
heat  can  be  raised  and  lowered  quicker  than,  by  any  other  arrangement 
of  pipes,  and  a  more  uniform  temperature  maintained  than  by  steam  or 
any  other  system. 

HOT- WATER  HEATING. 

The  following  notes  are  from  the  catalogue  of  the  Nason  Mfg.  Co.: 

There  are  two  distinct  forms  or  modifications  of  hot-water  apparatus, 
depending  upon  the  temperature  of  the  water. 

In  the  first  or  open-tank  system  the  water  is  never  above  212°  tempera- 
ture, arfd  rarely  above  200°.  This  method  always  gives  satisfaction 
where  the  surface  is  sufficiently  liberal,  but  in  making  it  so  its  cost  is 
considerably  greater  than  that  for  a  steam-heating  apparatus. 

In  the  second  method,  sometimes  called  (erroneously)  high-pressure 
hot-water  heating,  or  the  closed -system  apparatus,  the  tank  is  closed. 
If  it  is  provided  with  a  safety-valve  set  at  10  Ibs.  it  is  practically  as  safe 
as  the  open-tank  system. 

Law  of  Velocity  of  Flow.  —  The  motive  power  of  the  circulation  in  a 
hot-water  apparatus  is  the  difference  between  the  specific  gravities  of 
the  water  in  the  ascending  and  the  descending  pipes.  This  effective 
pressure  is  very  small,  and  is  equal  to  about  one  grain  for  each  foot  in 
height  for  each  degree  difference  between  the  pipes;  thus,  with  a  height 
of  1  ft.  "  up  "  pipe,  and  a  difference  between  the  temperatures  of  the 
up  and  down  pipes  of  8°,  the  difference  in  their  specific  gravities  is  equal 
to  8.16  grains  (0.001166  Ib.)  on  each  square  inch  of  the  section  of  return- 
pipe,  and  the  velocity  of  the  circulation  is  proportioned  to  these  differ- 
ences in  temperature  and  height. 

Main  flow-pipes  from  the  heater,  from  which  branches  may  be  taken, 
are  to  be  preferred  to  the  practice  of  taking  off  nearly  as  many  pipes  from 
the  heater  as  there  are  radiators  to  supply. 

It  is  not  necessary  that  the  main  flow  and  return  pipes  should  equal  in 
capacity  that  of  all  their  branches.  The  hottest  water  will  seek  the 
highest  level,  while  gravity  will  cause  an  even  distribution  of  the  heated 
water  if  the  surface  is  properly  proportioned. 

It  is  good  practice  to  reduce  the  size  of  the  vertical  mains  as  they  ascend, 
say  at  the  rate  of  one  size  for  each  floor. 

As  with  steam,  so  with  hot  water,  the  pipes  must  be  unconfined  to  allow 
for  expansion  of  the  pipes  consequent  on  having  their  temperatures  in- 
creased. 

An  expansion  tank  is  required  to  keep  the  apparatus  filled  with  water, 
which  latter  expands  1/24  of  its  bulk  on  being  heated  from  40°  to  212°, 
and  the  cistern  must  have  capacity  to  hold  certainly  this  increased  bulk. 
It  is  recommended  that  the  supply  cistern  be  placed  on  level  with  or 
above  the  highest  pipes  of  the  apparatus,  in  order  to  receive  the  air  which 
collects  in  the  mains  and  radiators,  and  capable  of  holding  at  least  1/30  of 
the  water  in  the  entire  apparatus. 

Arrangement  of  Mains  for  Hot-water  Heating.  (W.  M.  Mackay, 
Lecture  before  Master  Plumbers'  Assoc.,  N.  Y.,  1889).  — There  are  two 
different  systems  of  mains  in  general  use,  either  of  which,  if  properly 


704  HEATING   AND   VENTILATION. 

placed,  will  give  good  satisfaction.  One  is  the  taking  of  a  single  large- 
flow  main  from  the  heater  to  supply  all  the  radiators  on  the  several  floors, 
with  a  corresponding  return  mam  of  the  same  size.  The  other  is  the  tak- 
ing of  a  number  of  2-inch  wrought-iron  mains  from  the  heater,  with  the 
same  number  of  return  mains  of  the  same  size,  branching  off  to  the  several 
radiators  or  coils  with  li/4-inch  or  1-inch  pipe,  according  to  the  size  of 
the  radiator  or  coil.  A  2-inch  main  will  supply  three  U/4-inch  or  four 
1-inch  branches,  and  these  branches  should  be  taken  from  the  top  of  the 
horizontal  main  with  a  nipple  and  elbow,  except  in  special  cases  where  it 
it  is  found  necessary  to  retard  the  flow  of  water  to  the  near  radiator,  for 
the  purpose  of  assisting  the  circulation  in  the  far  radiator;  in  this  case 
the  branch  is  taken  from  the  side  of  the  horizontal  main.  The  flow  and 
return  mains  are  usually  run  side  by  side,  suspended  from  the  basement 
ceiling,  and  should  have  a  gradual  ascent  from  the  heater  to  the  radiators 
of  at  least  1  inch  in  10  feet.  It  is  customary,  and  an  advantage  where 
2-inch  mains  are  used,  to  reduce  the  size  of  the  main  at  every  point  where 
a  branch  is  taken  off. 

The  single  or  large  main  system  is  best  adapted  for  large  buildings ;  but 
there  is  a  limit  as  to  size  of  main  which  it  is  not  wise  to  go  beyond  — 
generally  6-inch,  except  in  special  cases. 

The  proper  area  of  cold-air  pipe  necessary  for  100  square  feet  of  indi- 
rect radiation  in  hot-water  heating  is  75  square  inches,  while  the  hot-air 
pipe  should  have  at  least  100  square  inches  of  area.  There  should  be  a 
damper  in  the  cold-air  pipe  for  the  purpose  of  controlling  the  amount  of 
air  admitted  to  the  radiator,  depending  on  the  severity  of  the  weather. 

Sizes  of  Pipe  for  Hot-water  Heating.  —  A  theoretical  calculation  of 
the  required  size  of  pipe  in  hot-water  heating  may  be  made  in  the  follow- 
ing manner.  Having  given  the  amount  of  heat,  in  B.T.U.  to  be  emitted 
by  a  radiator  per  minute,  assume  the  temperatures  of  the  water  entering 
and  leaving,  say  160°  and  140°.  Dividing  the  B.T.U.  by  the  difference 
in  temperatures  gives  the  number  of  pounds  of  water  to  be  circulated, 
and  this  divided  by  the  weight  of  water  per  cubic  foot  gives  the  number 
of  cubic  feet  per  minute.  The  motive  force  to  move  this  water,  per 
square  inch  of  the  area  of  the  riser,  is  the  difference  in  weight  per  cu.  ft. 
of  water  at  the  two  temperatures,  divided  by  144,  and  multiplied  by  H, 
the  height  of  the  riser,  or  for  Ti  =  160  and  T2  =  140,  (61.37  -  60.98) 
+  144  =  q.00271  Ib.  per  sq.  in.  for  each  foot  of  the  riser.  Dividing  144 
by  61.37  gives  2.34,  the  ft.  head  of  water  corresponding  to  1  Ib.  per  sq. 
in.,  and  0.00271  X  2.34  =  0.0066  ft.  head,  or  if  the  riser  is  20  ft.  high, 
20  X  0.0066  =  0.132  ft.  head,  which  is  the  motive  force  to  move  the  water 
over  the  whole  length  of  the  circuit,  overcoming  the  friction  of  the  riser, 
the  return  pipe,  the  radiator  and  its  connections.  If  the  circuit  has  a 
resistance  equal  to  that  of  a  50-ft.  pipe,  then  50  -*-  0.132  =  380  is  the 
ratio  of  length  of  pipe  to  the  head,  which  ratio  is  to  be  taken  with  the 
number  of  cubic  feet  to  be  circulated,  and  by  means  of  formulae  for  flow 
of  water,  such  as  Darcy's,  or  hydraulic  tables,  the  diameter  of  pipe  re- 
quired to  convey  the  given  quantity  of  water  with  this  ratio  of  length  of 
pipe  to  head  is  found.  This  tedious  calculation  is  made  more  complicated 
by  the  fact  that  estimates  have  to  be  made  of  the  frictional  resistance  of 
the  radiator  and  its  connections,  elbows,  valves,  etc.,  so  that  in  practice 
it  is  almost  never  used,  and  "rules  of  thumb"  and  tables  derived  from 
experience  are  used  instead. 

On  this  subject  a  committee  of  the  Am.  Soc.  Heating  and  Ventilating 
Engineers  reported  in  1909  as  follows: 

The  amount  of  water  of  a  certain  temperature  required  per  hour  by 
radiation  may  be  determined  by  the  following  formula: 

g)-x*eo/xeo  -  cu- ft- ot  water  per  minute- 

R  =  square  feet  of  radiation;  X  =  B.T.U.  given  off  per  hour  by  1  sq. 
ft.  of  radiation  (150  for  direct  and  230  for  indirect)  with  water  at  170*. 
Twenty  is  the  drop  in  temperature  in  degrees  between  the  water  entering- 
the  radiation  and  that  leaving  it;  60.8  is  the  weight  of  a  cubic  foot  of 
water  at  170  degrees;  60  is  to  reduce  the  result  from  hours  to  minutes. 

The  average  sizes  of  mains,  as  used  by  seven  prominent  engineers  in 
regular  practice  for  1800  square  feet  of  radiation,  are  given  below: 


HOT- WATER    HEATING. 


705 


2-pipe  open-tank  system,  100  ft.  mains,  5-in.  pipe  =  26.6  ft.  per  min. 

1-pipe  open-tank  system,  100  ft.  mains,  6-in.  pipe  =  18.4  ft.  per  min. 

Overhead  open-tank  system,  100  ft.  mains,  4-in.  pipe  =  41.8  ft.  per  min. 

Overhead  open-tank  system,  100  ft.  mains,  3-in.  pipe  =  72.1  ft.  per 
min. 

For  1200  sq;  ft.  indirect  radiation  with  separate  main,  100  ft.  long, 
direct  from  boiler,  open  system,  the  bottom  of  the  radiator  being  1  ft. 
above  the  top  of  the  boiler  —  5-in.  pipe  =  22.4  ft.  per  min. 

CAPACITY  OF  MAINS  100  FT.  LONG. 

Expressed  in  the  number  of  square  feet  of  hot-water  radiating  sur- 
face they  will  supply,  the  radiators  being  placed  in  rooms  at  70°  F.,  and 
20°  drop  assumed. 


Diameter  of 
Pipes,  Ins. 

Two-Pipe 
up  Feed 
Open  Tank. 

One-Pipe 
up  Feed 
Open  Tank. 

Overhead 
Open 
Tank. 

Overhead 
Closed 
Tank. 

Two-Pipe 
Open 
Tank. 

H/4 

75 

45 

127 

250 

48 

I  1/2 

107 

65 

181 

335 

69 

2 

200 

121 

339 

667 

129 

21/2... 

•   314 

190 

533 

1,060 

202 

3 

540 

328 

916 

1,800 

348 

31/2  

780 

474 

1,334 

2,600 

502 

4. 

1  060 

645 

1,800 

3,350 

684 

5 

1  860 

1  130 

3  150 

6200 

1  200 

6 

2960 

1,800 

5,000 

9]  800 

1,910 

7  ... 

4,280 

2,700 

7,200 

13,900 

2,760 

8 

5,850 

3,500 

9,900 

19500 

3,778 

The  figures  are  for  direct  radiation  except  the  last  column  which  is  for 
indirect,  12  in.  above  boiler. 

CAPACITY  OF  RISERS. 

Expressed  in  the  number  of  sq.  ft.  of  direct  lK)t-water  radiating  sur- 
face they  will  supply,  the  radiators  being  placed  in  rooms  at  70°  F.,  and 
20°  drop-assumed.  The  figures  in  the  last  column  are  for  the  closed-tank 
overhead  system  the  others  are  for  the  open-tank  system. 


Diameter 
of  Riser. 
Inches. 

1st  Floor. 

2d  Floor. 

3d  Floor. 

4th  Floor. 

Drop 
Risers,  not 
exceeding 
4  floors. 

1 

33 

46 

57 

64 

48 

1  1/4.  .  . 

71 

104 

124 

142 

112 

11/2     . 

100 

140     - 

175 

200 

160 

2.  ........ 

187 

262 

325 

375 

300 

21/7     . 

292 

410 

492 

580 

471 

3/2:.  :.:::::::.. 

500 

755 

875 

1,000 

810 

All  horizontal  branches  from  mains  to  risers  or  from  risers  to  radiators, 
more  than  10  ft.  long  (unless  within  15  ft.  of  the  boiler),  should  be  in- 
creased one  size  over  that  indicated  for  risers  in  the  above  table. 

For  indirect  radiation,  the  amount  of  surface  may  be  computed  as 
follows : 

Temperature  of  the  air  entering  the  room,  110°  =  T. 

Average  temperature  of  the  air  passing  through  the  radiator,  55°. 

Temperature  of  the  air  leaving  the  room,  70°  =  t. 

Velocity  of  the  air  passing  through  the  radiator,  240  ft.  per  min. 

Cubic  feet  of  air  to  be  conveyed  per  hour,  =  C  =  (H  X  55)  +•  (T  -  f). 

H  =  exposure  loss  in  B.T.U.  per  hour. 

Heat  necessary  to  raise  this  air  to  the  entering  temperature  from 
0°  F.,  T  X  C  +  55  =-  JJ . 


706 


HEATING   AND   VENTILATION. 


The  amount  of  radiation  is  found  by  dividing  the  total  heat  by  the 
emission  of  heat  by  indirect  radiators  per  square  foot  per  hour  per  degree 
difference  in  temperature.  This  varies  with  the  velocity,  as  shown  below: 
Velocity,  ft.  per  min...  .  174  246  300  342  378  400  428  450  474  492 
B.T.U 1.70  2.00  2.22  2.38  2.52  2.60  2.67  2.72  2.76  2.80 

The  difference  between  170  degrees  (average  temperature  of  the  water 
in  the  radiator)  and  55  degrees  (average  temperature  of  the  air  in  the 
radiator)  being  115,  the  emission  at  240  ft.  per  min.  is  2.  per  degree  differ- 
ence or  230  B.T.U. 

Ordinarily  the  amount  of  indirect  radiation  required  is  computed  by 
adding  a  percentage  to  the  amount  of  direct  radiation  [computed  by  the 
usual  rules],  and  an  addition  of  50%  has  been  found  sufficient  in  many 
cases;  but  in  buildings  where  a  standard  of  ventilation  is  to  be  maintained, 
the  formula  mentioned  seems  more  likely  to  give  satisfactory  results. 
Free  area  between  the  sections  of  radiation  to  allow  passage  of  the  re- 
quired volume  of  air  at  the  assumed  velocity  must  be  maintained.  The 
cold-air  supply  duct,  on  account  of  less  frictional  resistance,  may  ordi- 
narily have  80%  of  the  area  between  the  radiator  sections.  The  hot-air 
flues  may  safely  be  proportioned  for  the  following  air  velocities  per  min- 
ute: First  floor,  200  feet;  second  floor,  300  feet;  third  floor,  400  feet. 

PIPE  SIZES  FOR  HOT- WATER  HEATING. 

Based  on  20°  difference  in  temperature  between  flow  and  return  water. 
(C.  L.  Hubbard,  The  Engineer  July  1,  1902.) 


Diam.  of  )     i 
-Pipe,      f     ' 

U/4 

H/2 

2 

21/2 

3 

31/2 

4 

5    ' 

6 

7 

Length  of 
Run. 

Square  Feet  of  Direct  Radiating  Surface. 

Feet. 
100 
200 
300 
400 
500 
600 
700 
800 
1000 

100 
200 

1st  story 
2d 

3d 
4th 
5th 
6th 

30 

60 
50 

100 
75 
50 

200 
150 
125 
100 
75 

350 
250 
200 
175 
150 
125 

550 
400 
300 
275 
250 
225 
200 
175 
150 

850 
600 
450 
400 
350 
325 
300 
250 
225 

1,200 
850 
700 
600 
525 
475 
450 
400 
350 

1,400 
1,150 
1.000 
900 
850 
775 
725 
650 

,600 
,400 
,300 
,200 
,150 
,000 

1,700 
1,600 
1,500 

Square  Feet  of  Indirect  Radiation. 

15 

30 
20 

50 
30 

100 
70 

200 
120 

300 
200 

400 
300 

600 
400 

1,000 
700 

Square  Feet  of  Direct  Radiating  Surface. 

30 
55 
65 
75 
85 
95 

60 
90 
110 
125 
140 
160 

100 
140 
165 
185 
210 
240 

200 
275 
375 
425 
500 

350 
275 

550 

850 

The  size  of  pipe  required  to  supply  any  given  amount  of  hot-water 
radiating  surface  depends  upon  (1)  The  square  feet  of  radiation;  (2)  its 
elevation  above  the  boiler;  (3)  the  difference  in  temperature  of  the  water 
in  the  supply  and  return  pipes;  (4)  the  length  of  the  pipe  connecting  the 
radiator  with  the  boiler. 

In  estimating  the  length  of  a  pipe  the  number  of  bends  and  valves  must 
be  taken  into  account.  It  is  customary  to  consider  an  elbow  as  equivalent 
to  a  pipe  60  diameters  in  length,  and  a  return  bend  to  120  diameters.  A 
globe  valve  may  be  taken  about  the  same  as  an  elbow. 

A  series  of  articles  on  The  Determination  of  the  Sizes  of  Pipe  for  Hot 
Water  Heating,  by  F.  E.  Geisecke,  is  printed  in  Domestic  Engineering, 
beginning  in  May,  1909. 


HOT -WATER  HEATING. 


707 


Sizes  of  Flow  and  Return  Pipes  Approximately  Proportioned  to 
Surface  of  Direct  Radiators  for  Gravity  Hot-Water  Heating. 

(G.  W.  Stanton,  Heat.  &  Ventg.  Mag.,  April,  1908.) 


Mains. 

Branches  of  Mains. 

Size 
of 
Mains. 

In  Cellar 
or 
Basement. 

On  One 
or  More 
Floors. 
Average. 

First 
Floor 
10'-15'. 

Second 
Floor 
15'-25'. 

Third 
Floor 
25'-35'. 

Fourth 
or  Fifth 
Floor 
35'-45'. 

Square  Feet  of  Radiating  Surface. 

,«, 

H/4 

u/2 

21/2 

3V2 
41/2 

6 
7 
8 
9 
10 
11 
12 

40 
75 
120 
195 
320 
490 
650 
870 
1,120 
1,400 

45 
80 
135 
210 
350 
525 
690 
920 
1,185 
1,485 

50 
85 
150 
230 
370 
550 
730 
970 
1,250 
1,560 

50 
110 
180 
290 
400 
620 
820 
1,050 
1,325 

100 
135 
225 
320 
500 
650 
850 
1,050 
1,350 
2,900 
3,900 
5,000 
6,300 
7,900 
9,500 
11,400 

135 

220 
350 
460 
675 
850 
1,100 
1,350 
1,700 
3,600 
4,800 
6,200 
7,700 
9,800 
11,800 
14.000 

Note.  —  The  heights  of  the  several 
floors  are  taken  as: 
1st.    10  to  15ft.;  2d.    15  to  25  ft. 
3d.    25  to  35  ft.;    4th.    35  to  45  ft. 

Sizes  of  Pipe  for  Gravity  Hot-Water  Heating.  (John  Jaeger,  Heating 
and  Ventilating  Mag.,  Feb.,  1912.) — The  assumed  temperature  of  the 
water  supplied  to  the  radiators  is  185°,  and  the  drop  36°,  giving  a  mean 
temperature  of  170°.  The  temperature  difference  creates  a  water 
pressure  of  0.148  in.  of  water  per  foot  of  height.  With  the  assumed 
heights,  H,  between  the  center  of  the  boiler  and  the  center  of  the 
radiator  on  the  several  floors,  and  the  assumed  lengths,  L,  of  the 
circuit,  making  allowance  for  resistance  of  connections,  as  given  in  the 
table,  and  using  the  ordinary  tables  for  flow  of  water  in  pipes,  the 
figures  for  number  of  square  feet  of  radiating  surface  that  will  be 
supplied  by  different  sizes  of  pipe  are  obtained,  assuming  that  each 
square  foot  emits  170  B.  T.  U.  per  hour. 

L.  Size  of  Pipe,  In. 

Ft.  1/2  3/4  1  11/4         11/2 

Sq.  Ft.  of  Radiating  Surface. 


Floor 


H. 

Ft. 


Basement. .  .  . 
First  floor .  .  . 
Second  floor .  . 
Third  floor. .  . 
Fourth  floor .  , 


3.5 

6 
19 
31 

42 


80 
100 
125 
150 
175 


11 

13 

22 

26.5 

29 


32 
39 

62 
74 
81 


57 
70 
130 
160 
175 


127  180 

156  221 

238  377 

290  450 

314  490 


Heating  by  Hot  Water,  with  Forced  Circulation.  — The  principal 
defect  of  gravity  hot-water  systems,  that  the  motive  force  is  only  the 
difference  in  weight  of  two  columns  of  water  of  different  temperatures,  is 
overcome  by  giving  the  water  a  forced  circulation,  either  by  means  of  a 
pump  or  by  a  steam  ejector.  For  large  installations  a  pump  gives  facili- 
ties for  forcing  the  hot  water  to  any  distance  required.  The  design  of 
such  a  system  is  chiefly  a  problem  in  hydraulics.  After  determining  the 
quantity  of  heat  to  be  given  out  by  each  radiator,  a  certain  drop  in 
temperature  is  assumed,  andjrom  that  the  volume  of  water  required  by 
each  radiator  is  calculated.  The  piping  system  then  has  to  be  designed 
so  that  it  will  carry  the  proper  supply  of  water  to  each  radiator  without 
short-circuiting,  and  with  a  minimum  total  cost  for  power  to  force  the 
water,  for  loss  by  radiation,  and  for  interest,  etc.,  on  cost  of  plant.  No 
short  rules  or  formulae  have  been  established  for  designing  a  forced  hot- 
water  system,  and  each  case  has  to  be  studied  as  an  original  problem  to 


708  pEATTNG  AND  VENTILATION. 

be  solved  by  application  or  tne  laws  of  heat  transmission  and  hydraulics. 
Forced  systems  using  steam  ejectors  have  come  into  use  to  some  dtent 
in  Europe  in  small  installations,  and  some  of  them  are  described  in  the 
Transactions  of  the  Amer.  Soc'y  of  Heating  and  Ventilating  Engineers. 

A  system  of  distributing  heat  and  power  to  customers  by  means  of  hot 
water  pumped  from  a  central  station  was  adopted  by  the  Boston  Heating 
Co.  in  1888.  It  was  not  commercially  successful.  A  description  of  the 
plant  is  given  by  A.  V.  Abbott  in  Trans.  A.  I.  M.  E.,  1888. 

Corrosion  of  Pipe  in  Hot-Water  Heating  .Systems. — The  chief  agent 
of  internal  corrosion  in  hot- water  pipes  appears  to  be  oxygen  dissolved 
in  the  water.  If  this  is  removed  corrosion  is  prevented.  Buildings 
equipped  with  closed  heating  systems  have  suffered  serious  damage  in 
six  or  eight  years,  while  no  such  damage  has  been  found  in  open  or 
vented  systems,  in  which  the  air  dissolved  in  the  water  is  allowed  to 
escape  in  an  open  tank  placed  at  the  top  of  the  system.  (F.  N.  Speller, 
Eng.  News,  Feb.  13,  1913.) 

THE  BLOWER  SYSTEM  OF  HEATING. 

The  system  provides  for  the  use  of  a  fan  or  blower  which  takes  its  sup- 
ply of  fresh  air  from  the  outside  of  the  building  to  be  heated,  forces  it 
over  steam  coils,  located  either  centrally  or  divided  up  into  a  number  oi 
independent  groups,  and  then  into  the  several  ducts  or  flues  leading  to  the 
various  rooms.  The  movement  of  the  warmed  air  is  positive,  and  the 
delivery  of  the  air  to  the  various  points  of  supply  is  certain  and  entirely 
independent  of  atmospheric  conditions. 

Advantages  and  Disadvantages  of  the  Plenum  System.  (Prof. 
W.  F.  Barrett,  Brit.  Inst.  H.  &  V.  Engrs.,  1905.)— Advantages:  (1)  The 
evenness  of  temperature  produced;  (2)  the  ventilation  of  the  building 
is  concurrent  with  its  warming;  (3)  the  air  can  be  drawn  from  sources 
free  from  contamination  and  can  be  filtered  from  suspended  impurities, 
warmed  and  brought  to  the  proper  hygrometric  state  before  its  intro- 
duction to  the  different  rooms  or  wards;  (4)  the  degree  of  temperature 
and  of  ventilation  can  be  easily  controlled  in  any  part  of  the  building, 
and  (5)  the  removal  of  ugly  pipes  running  through  the  rooms  has  a  great 
architectural  and  esthetic  advantage. 

Disadvantages:  (1)  The  most  obvious  is  that  no  windows  can  be 
opened  nor  doors  left  open;  double  doors  with  an  air  lock  between  must 
also  be  provided  if  the  doors  are  frequently  opened  and  closed;  (2)  the 
mechanical  arrangements  are  elaborate  and  the  system  requires  to  be 
used  with  intelligent  care;  (3)  the  whole  elaborate  system  needs  to  be 
set  going  even  if  only  one  or  two  rooms  in  a  large  building  require  to 
be  warmed,  as  often  happens  in  the  winter  vacation  of  a  college;  (4)  the 
temporary  failure  of  the  system,  through  the  breakdown  of  the  engines 
or  other  cause,  throws  the  whole  system  into  confusion,  and  if,  as  in  the 
Royal  Victoria  Hospital,  the  windows  are  not  made  to  open,  imminent 
danger  results;  (5)  then,  also,  in  the  case  of  hospital  wards  and  asylums 
it  is  possible  that  the  outlet  ducts  may  become  coated  with  disease  germs, 
and  unless  periodically  cleansed,  a  back  current,  through  a  high  wind  or 
temporary  failure  of  the  system  may  bring  a  cloud  of  these  disease  germs 
back  into  the  wards. 

Heat  Radiated  from  Coils  in  the  Blower  System.  —  The  committee 
on  Fan-blast  Heating,  of  the  A.  S.  H.  V.  E.,  in  1909,  gives  the  following 
formula  for  amount  of  heat  radiated  from  hot-blast  coils  with  different 
velocities  of  air  passing  through  the  heater:  #  =  B.T.U.  per  sq.  ft.  of  sur- 
face per  hour  per  degree  of  difference  between  the  average  temperature  of 
the  air  and  the  steam  temperature,  =  V4  v,  in  which  V=  velocity  of  the 
air  through  the  free  area  of  the  coil  in  feet  per  second.  A  plotted  curve 
of  20  tests  of  different  heaters  shows  that  the  formula  represents  the  aver- 
age results,  but  individual  tests  show  a  wide  variation  from  the  average, 
thus:  For  velocity  1000  ft.  per  min.,  average  9  B.T.U.,  range  7.5  to  11; 
1600  ft.  per  min.,  average  10.4,  range  9.5  to  12. 

The  committee  also  gives  the  following  formula  for  the  rise  in  tem- 
perature of  each  two-row  section  of  a  coil: 


'     A  X   Vm  X  W  X  60  X  0.2377 
In  which  R  =  degrees  F.  rise  for  each  two-row  section ;  Ts  =  tern- 


THE  BLOWER  SYSTEM  OF  HEATING. 


709' 


perature  of  steam;  Ta= temperature  of  air;  H  **  square  feet  of  sur- 
face in  two-row  section-,  B  =  B.T.U.  per  degree  difference  between  air 
and  steam;  E  »  >/4  Fs,  in  which  Vs  —  air  velocity  in  ft.  per  sec.; 
A  =  area  through  heater  in  sq.  ft.;  Vm  =  velocity  of  air  in  ft.  per  min.; 
TF  =  weight  of  1  cu.  ft.  of  air,  Ibs. 

The  value  of  R  is  computed  for  each  two-row  section  in  a  coil,  and  the 
results  added.  From  a  set  of  curves  plotted  from  the  formula  the  follow- 
ing figures  are  taken. 


Number  of  Rows. 

4 

8 

12 

16 

20 

24 

28 

Temperature  Rise,  Degrees. 

Steam,  80  Ibs:  Vm  =  1,200.  .  . 

43 
36 
31 
25 

83 
68 
53 
48 

115 
96 
80 
68 

144 
122 
100 
85 

167 
145 
118 
101 

189 
165 
133 
115 

209 
182 
146 
128 

Steam,  80  Ibs.  Vm  =  1,800  
Steam,    5  Ibs.  Vm  =  1,200.  .  . 

Steam,    5  Ibs.  V  m  =  1,800  

A  formula  for  the  rise  in  temperature  of  air  in  passing  through  the 
coils  of  a  hot-blast  heater  is  given  by  Perry  West,  Trans.  A.  S.  H.  V.  E., 

1909,  page  57,  as  follows:  R=  KDZmN  -r-  %/V,  in  which  #=rise  in 
temperature  of  the  air;  K  =  a  constant  depending  on  the  kind  of  heat- 
ing surface;  D  =  an  average  of  the  summation  of  temperature  differ- 
ences between  the  air  and  the  steam  =  -(Ti-TD)  •*•  loge  [(Ts  -  To)  -*• 
(Ts  -  Ti)];  Z  =  number  of  sq.  ft.  of  heating  surface  per  sq.  ft.  of  clear 
area  per  unit  depth  of  heater,  m  —  a  power  applicable  to  Z  and  depend- 
ing on  the  type  of  heating  surface;  N  =  number  of  units  in  depth  of 
heater-  V  =  velocity  of  the  air  at  70°  F.  in  ft.  per  min.  through  the  clear 
area-  n  =  a  root  applicable  to  F  and  depending  on  experiment. 

For  practical  purposes  and  within  the  range  of  present  knowledge  on 
the  subject  the  formula  may  be  written  #«=  0.085  DZN  -*-  %Jv,  and  from 
this  formula  with  Ts  =  227°  and  T0  =  0°,  with  different  values  of  Ti,  the 
temperature  of  the  air  leaving  the  coils,  a  set  of  curves  is  plotted,  from 
which  the  figures  in  the  following  table  are  taken. 


Sq.  ft.  of  heating  surface  •*•  sq.  ft.  free  area  through  heater. 


Velocity, 
Ft.  per  Min. 

20 

30 

40 

50 

60 

70 

CO 

90 

100  |  120 

Rise  in  Temperature,  Degrees  F. 

500 

43 
38 
36 
34 
29 

63 
55 
52 
49 
42 

79 
70 
66 
63 
55 

95 
84 
79 
75 
66 

108 
97 
92 
87 
76 

120 
108 
102 
98 
86 

131 
118 
112 
108 
95 

141 
128 
121 
117 
104 

151 
138 
130 
125 
112 

170 
157 
147 
140 
127 

800  

1000  .. 

1200 

2000  

Burt-S.  Harrison  (Htg,  and  Ventg.  Mag.,  Oct.  and  Nov.,  1907)  gives  the 


folio  wing  for 


24' 


'  in  which  2^  =  temp,  of  steam 


in  coils,  i  =  temp.  of  air  entering  coils,  V  =  velocity  of  air  through  coils  in 
ft.  per  sec.,  N=  no.  of  rows  of  1-in.  pipe  in  depth  of  heater.  Charts  are 
given  by  means  of  which  heaters  may  be  designed  for  any  set  of  con- 
ditions. 

Tests  of  Cast-iron  Heaters  for  Hot-blast  Work.  —  An  extensive 
series  of  tests  of  the  Amer.  Radiator  Go's,  "Vento"  cast-iron  heater  is 
described  by  Theo.  Weinshank  in  Trans.  A.  S.  H.  V.  E.,  1908.  The  tests 
were  made  under  the  supervision  of  Prof,  J.  H.  Kinealy.  The  principal 
results  are  given  in  the  table  on  page  710. 


710 


HEATING  AND   VENTILATION. 


TESTS  OF  A  "VENTO"  CAST-IRON  HEATER. 


Velocity, 
Ft.  per 
Min. 

Number  of  sections  heater  is 
deep. 

Number  of  sections  heater  is 
deep. 

1 

2 

3 

4 

5    1    6 

1 

2 

3    1     4 

5    |    6 

Rise  of  temperature,  K,  per  de- 
gree difference  between  tem- 
perature of  steam  and  mean 
temperature  of  air  for  differ- 
ent velocities  of  air. 

Heat     units     transmitted     per 
square  foot  of  heating  surface 
per  hour  per  degree  difference 
between    the    temperature    of 
the  steam  and  the  mean  tem- 
perature of  the  air. 

1600... 
1500     

0.124 
0.132 
0.139 
0.147 
0.154 
0.162 
0.170 
0.177 
0.185 

0.253 
0.261 
0.268 
0.276 
0  283 

0.395 
0.403 
0.410 
0.418 
0  425 

0.527 
0.535 
0.542 
0.550 
0  557 

0.649 
0.657 
0.664 
0.672 
0  679 

0.761 
0.769 
0.776 
0.784 
0  791 

11.94 
11.91 
11.70 
11.50 
11  11 

12.17 
11.76 
11.28 
10.79 
10  21 

12.67 
12.11 
11.50 
10.89 
10.22 

12.67 
12.06 
11.41 
10.75 
10  05 

12.50 
11.86 
11.18 
10.51 
9  81 

12.20 
11.56 
10.89 
10.22 
9.52 

1400  

1300 

1200  
1100  

0.291 
0.299 
0.306 
0.314 

0.433 
0.441 
0.448 
0.456 

0.565 
0.573 
0.580 
0.588 

0.687 
0.695 
0.702 
0.710 

0.799 
0.807 
0.814 
0.822 

10.72 
10.23 
9.59 
8.90 

9.63 
8.99 
8.28 
7.56 

9.55 
8.84 
8.08 
7.31 

9.34 
8.61 
7.85 
7.08 

9.09 
8.36 
7.60 
6.48 

8.82 
8.10 
7.35 
6.60 

1000  
900     

800  

Velocity, 
Ft.  per 
Min. 

Final    temperature,    T,    of    air 
when  entering  heater  at  0°  F. 
Temperature     of    steam     in 
heater,  227°. 

Friction  loss  in  inches  of  water 
due  to  the  sections. 

1600... 

?6  5 

51  0 

74  9 

94  7 

111  3 

17<>  7 

0  236 

0  288 

0  416 

0  543 

0.672 
0.590 
0.514 
0.443 
0.378 
0.318 
0.262 
0  212 

0.800 
0.703 
0.613 
0.528 
0.450 
0.378 
0.312 
0  253 

1500  
1400  
1300... 

28.1 
29.5 
31.1 
32.4 
34.0 
35.6 
36  9 

52.4 
53.8 
55.0 
56.4 
57.7 
59.1 
60.1 

76.3 
77.2 
77.6 
79.6 
80.5 
82.0 
83  0 

95.8 
96.7 
97.9 
99.0 
100.0 
100.1 
102.1 

112.4 
113.3 
114.3 
115.3 
116.2 
117.2 
118  0 

126.0 
126.8 
127.7 
128.7 
1  29/6 
130.5 
131.3 

0.207 
0.180 
0.156 
0.133 
0.111 
0.092 
0  074 

0.253 
0.220 
0.190 
0.162 
0.136 
0.112 
0  091 

0.366 
0.318 
0.274 
0.234 
0.197 
0.162 
0  132 

0.477 
0.415 
0.358 
0.306 
0.257 
0.212 
0  172 

1200 

1100  .. 

1000 

900  

800  

38.5 

61.6 

84.3 

103.1 

119.0 

132.3 

0.059 

0.072 

0.104 

0.136 

0.167 

0.200 

Formulae. — s  =  no.  of  sections;  V=  velocity,  ft.  per  min.,  air  meas- 
ured afc70°;  k  =  rise  of  temp,  per  degree  difference;  t  =  final  tempera- 
ture. /  =  friction  loss  in  in.  of  water,  t  =  454  k  -t-  (2  +  k) .  k  = 

s   (0.167  -  0.005  s)  -  0.061    (^  g0Q°°)  •      /=   (°-8s  +  0.2)    (V/4000)2. 
Values  of  k  and/  when  s  =  2  or  more. 

Factory  Heating  by  the  Fan  System. 

In  factories  where  the  space  provided  per  operative  is  large,  warm  air 
is  recirculated,  sufficient  air  for  ventilation  being  provided  by  leakage 
through  the  walls  and  windows.  The  air  is  commonly  heated  by  steam 
coils  furnished  with  exhaust  steam  from  the  factory  engine.  When  the 
engine  is  not  running,  or  when  it  does  not  supply  enough  exhaust  steam 
for  the  purpose,  steam  from  the  boilers  is  admitted  to  the  coils  through 
a  reducing  valve.  The  following  proportions  are  commonly  used  in  de- 
signing. Coils,  pipes  1-in.,  set  2i/s  in.  centers;  free  area  through  coils, 
40%  of  cross  area.  Velocity  of  air  through  free  area,  1200  to  1800  ft. 
per  min. ;  number  of  coils  in  series  8  to  20 ;  circumferential  speed  of  fan, 
4000  to  6000  ft.  per  min.;  temperature  of  air  leaving  coils,  120°  to  160° 
F.;  velocity  of  air  at  outlet  of  coil  stack,  3000  to  4000  ft.  per  min.;  veloc- 
ity in  branch  pipes,  2000  to  2800  ft.,  the  lower  velocities  in  the  longest 
pipes. 

In  factories  in  which  mechanical  ventilation  as  well  as  heating  is  re- 
quired, outlet  flues  at  proper  points  must  be  provided,  to  avoid  the  neces- 
sity of  opening  windows,  and  the  outflow  of  air  in  them  may  be  assisted 
either  by  exhaust  fans  or  by  steam  coils  in  the  flues. 

Cooling  Air  for  Ventilation. 

The  chief  difficulty  in  the  artificial  cooling  of  air  is  due  to  the  moisture 
it  contains,  and  the  great  quantity  of  heat  that  has  to  be  absorbed  or 
abstracted  from  the  air  in  order  to  condense  this  moisture.  The  cooled 


THE   BLOWER   SYSTEM   OF   HEATING. 


711 


and  moisture-laden  air  also  needs  to  be  partially  reheated  in  order  to 
bring  it  to  a  degree  of  relative  humidity  that  will  make  it  suitable  for  ven- 
tilation. To  cool  1  Ib.  of  dry  air  from  82°  to  72°  requires  the  abstracting 


of  10  X  0.2375  B.T.U.  (0.2375  being  the  specific  heat  at  constant  pres- 
sure).    If  thejdr  at  82°  is    saturated,  or   100%  ^relative  humidity,   it 


__   .  -_,  —    100%   relative  humidity 

contains  0.0235  Ib.  of  water  vapor,  while  1  Ib.  at  72°  contains  0.0167 
BO  that  0.0068  Ib.  will  be  condensed  in  cooling  from  vapor  at  82°  to 
water  at  72°.  The  total  heat  (above  32°)  in  1  Ib.  vapor  at  82°  is  1095.6 
B.T.U.  and  that  in  1  Ib.  of  water  at  72°  is  40  B.T.U.  The  difference, 
1055.6  X  0.0068  =  7.178  B.T.U.,  is  the  amount  of  heat  abstracted  in 
condensing  the  moisture.  The  B.T.U.  in  1  Ib.  vapor  at  72°  is  1091.2. 
and  the  B.T.U.  abstracted  in  cooling  the  remaining  vapor  from  82°  to 
72°  is  0.0167  X  (1095.6  -  1091.2)  =  0.073  B.T.U.  The  sum,  7.251 
B.T.U.,  is  more  than  three  times  that  required  to  cool  the  dry  air  from 
82°  to  72°.  Expressing  these  principles  in  formulae  we  have: 

Let  Ti  =  original  and  Tz  the  final  temperature  of  the  air, 
a  =  vapor  in  1  Ib.  saturated  air  at  Ti;  b  =  do.  at  Tz, 
H  =  relative  humidity  of  the  air  at  Ti\h  —  desired  do.  at  Tz, 
U  =  total  heat,  in  B.T.U.,  in  1  Ib.  vapor  at  Ti;  u  =  do.  at  Tz, 
w  =  total  heat  in  water  at  Ti. 

Then  total  heat  abstracted  in  cooling  air  from  T\  to  Tz  =  (aH  —  bh)  X 
(U  _  W)  -|-  bh  (u  -  u)  +  0.2375  (Ti  -  Tz),  or  aHU  -  bhu  -  (aH  -  bh)  w 
+  0.2375  (Ti  -  Tz),  or  aH  (U-  w)  -  bh  (u  -  w)  +  0.2375  (Ti  -  Tz). 

EXAMPLE. — Required  the  amount  of  heat  to  be  abstracted  per  hour 
in  cooling  the  air  for  an  audience  chamber  containing  1000  persons, 
1500  cu.  ft.  (measured  at  70°  P.),  being  supplied  per  person  per  hour, 
the  temperature  of  the  air  before  cooling  being  82°,  with  relative 
humidity  80%,  and  after  cooling  72°,  with  humidity  70%. 
1000  X  1500  =  1,500,000  cu.  ft.,  at  0.075  Ib.  per  cu.  ft. 

=  112,500  Ibs. 
For  1  Ib.  aH  (U  -  w)  -  bh  (u  -  w)  +  0.2375  (Ti  -  Tz). 

0.0235  X  0.8  X  (1095.6  -  40)   -  0.0167  X  0.7  X  (1091.2  -  40) 
+  2.375  =  9.932  B.T.U. 

112,500  X  9.932  =  1,061,100  B.T.U. 

Taking  142  B.T.U.  as  the  latent  heat  of  melting  ice,  this  amount  is 
equivalent  to  the  heat  that  would  melt  7472  Ibs.  of  ice  per  hour. 

See  also  paper  by  W.  W.  Macon,  Trans.  A.  S.  H.  V.  E.,  1909,  and 
Air-cooling  of  the  New  York  Stock  Exchange,  Eng.  Rec.,  April,  1905, 
and  The  Metal  Worker,  Aug.  5,  1905. 

Capacities  of  Fans  or  Blowers  for  Hot-Blast  or  Plenum  Heating. 

(Computed  by  F.  R.  Still,  American  Blower  Co.,  Detroit,  Mich.) 


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8,500 

415,200 
510,000 

1,021,000 
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9.45 

1760 

580 

714 

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10,500 

630,000 

1,550,000 

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11.66 

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100 

60 

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12,500 

750,000 

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1050 

110 

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15,800 

948,000 

2,335,000 

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72 

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19,800 

1,118,000 

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22. 

1650 

140 

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26,200 

1,572,000 

3,870,000 

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29.1 

2200 

160 

96 

160 

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33,000 

1,980,000 

4,870,000 

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36.7 

2770 

180 

108 

140 

15 

41,600 

2,496,000 

6,130,000 

" 

46.3 

3490 

200 

120 

125 

18 

50,000 

3,000,000 

7.375,000 

" 

55.5 

4140 

712 


HEATING   AND   VENTILATION. 


Capacities  of  Fans  or  Blowers  for  Hot-blast  or  Plenum  Heating  — 

Continued. 


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23,800 

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33,100 

36.80 

31,400 

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8,310 

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41,700 

46  30 

39,600 

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10,470 

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211 

3165 

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52,500 

58.40 

50,000 

200 

12,420 

7560 

10 

5 

252 

3780 

108 

63,200 

70.25 

60,000 

Temperature  of  fresh  air,  0°;  of  air  from  coils,  120°;  of  steam,  227°; 
Pressure  of  steam,  5  Ibs. 

Pe  ipheral  velocity  of  fan-tips,  4000  ft.;  number  of  pipes  deep  in  coil, 
24;  depth  of  coil,  60  inches;  area  of  coils  approximately  twice  free  area. 

Relative  Efficiency  of  Fans  and  Heated  Chimneys  for  Ventila- 
tion. —  W.  P.  Trowbridge,  Trans.  A.S.  M.  E.  vii.  531,  gives  a  theoretical 
solution  of  the  relative  amounts  of  heat  expended  to  remove  a  given 
volume  of  impure  air  by  a  fan  and  by  a  chimney.  Assuming  the  total 
efficiency  of  a  fan  to  be  only  1/25,  which  is  made  up  of  an  efficiency  of  l/io 
for  the  engine,  5/10  for  the  fan  itself,  and  8/10  for  efficiency  as  regards 
friction,  the  fan  requires  an  expenditure  of  heat  to  drive  it  of  only  Vss  of 
the  amount  that  would  be  required  to  produce  the  same  ventilation  by 
a  chimney  100  ft.  high.  For  a  chimney  500  ft.  high  the  fan  will  be  7.6 
times  more  efficient. 

The  following  figures  are  given  by  Atkinson  (Coll.  Engr.,  1889),  show- 
ing the  minimum  depth  at  which  a  furnace  would  be  equal  to  a  ventilating. 
machine,  assuming  that  the  sources  of  loss  are  the  same  in  each  case,  i.e., 
that  the  loss  of  fuel  in  a  furnace  from  the  cooling  in  the  upcast  is  equiva- 
lent to  the  power  expended  in  overcoming  the  friction  in  the  machine, 
and  also  assuming  that  the  ventilating-rnachine  utilizes  60  per  cent  of  the 
engine-power.  The  coal  consumption  of  the  engine  per  I.H.P.  is  taken 
at  8  Ibs.  per  hour. 

Average  temperature  in  upcast 100°  F.        150°  F.     '    200°  F. 

Minimum  depth  for  equal  economy..   960  yards.  1040  yards.  1130  yards. 

PERFORMANCE  OF  HEATING  GUARANTEE. 

Heating  a  Building  to  70°  F.  Inside  when  the  Outside  Tempera- 
ture is  Zero.  —  It  is  customary  in  some  contracts  for  heating  to  guaran- 
tee that  the  apparatus  will  heat  the  interior  of  the  building  to  70°  in  zero 
weather.  As  it  may  not  be  practicable  to  obtain  zero  weather  for  the 
purpose  of  a  test,  it  may  be  difficult  to  prove  the  performance  of  the 
guarantee  unless  an  equivalent  test  may  be  made  when  the  outside  tem- 
perature is  above  zero,  heating  the  building  to  a  higher  temperature 
than  70°,  The  following  method  was  proposed  by  the  author  (Eng.  Rectt 


ELECTRICAL  HEATING.  713 

Aug.  11,  1894)  for  determining  to  what  temperature  the  rooms  should 
be  heated  for  various  temperatures  of  the  outside  atmosphere  and  of  the 
steam  or  hot  water  in  the  radiators. 

Let    S  =  sq.  ft.  of  surface  of  the  steam  or  hot-water  radiator; 
W  =  sq.  ft.  of  surface  of  exposed  walls,  windows,  etc.; 
Ts  =  temp,  of  the  steam  or  hot  water,   7\=  temp,  of  inside  of 
building  or  room,  TO  =  temp,  of  outside  of  building  or  room  ; 
a  =  heat-units  transmitted  per  sq.  ft.  of  surface  of  radiator  per 

hour  per  degree  of  difference  of  temperature; 
6  =  average  heat-units  transmitted  per  sq.  ft.  of  wails  per  hour 
per  degree  of  difference  of  temperature,  including  allow- 
ance for  ventilation. 

Tt  is  assumed  that  within  the  range  of  temperatures  considered  New- 
ton's law  of  cooling  holds  good,  viz.,  that  it  is  proportional  to  the  differ- 
ence of  temperature  between  the  two  sides  of  the  radiating-surface, 

hW 

Then  aS  (Ts  -  7\)  =  bW  (^  -  T0~).    Let  -^  =  C;  then 

T\-     r  -  TS  +  CT°  •  r  -  T*  ~  Tl 

-L  Q)  i        •*•  1  —         i     •     fi        t    W    — 
- 


- 

i     •     fi        t    W    —   Tfi  Tfi  * 

1-rU  ./I  —   1  o 

Ts  -  70 
If  T7!  =  70,  and  TQ  =  0,  C  =  -^  — 

Let    Ts  =  140°        160°        180°       200°        212°        220°  250°  300° 

Then  C  =     1        1.286     1.571     1.857     2.029     2.143     2.571.  3.286 

and   from  the  formula   TI=  (Ts+  CTo)  --s-  (1  +  C)   we  find  the  inside 

temperatures  corresponding  to  the  given   values  of   Ts  and    T0  which 

should  be  produced  by  an  apparatus  capable  of  heating  the  building  to 
70°  in  zero  weather. 

For             TQ=         -20       -  10        0          10          20  30  40°  F. 

Inside  Temperatures  TV 

For  Ts  =  140°  F.     60           65           70       75          .80  85  90 

160            58.7       64.3       70       75.6       81.3  86.9  92.5 

180            57.8       63.9       70       76.1       82.2  88.4  94.5 

200            57.0       63.5       70       76.5       83.0  89.5  96.0 

212            56.6       63.3       70       76.7       83.4  90.1  96.8 

220            56.4       63.2       70       76.8       83.6  90.5  97.3 

250            55.6       62.8       70       77.2       84.4  91.6  98.8 

300            54.7       62.4       70       77.7       85.3  93.0  100.7 

J.  R.  Allen  (Trans.  A.  S.  H.  V.  E.,  1908)  develops  a  complex  formula 
for  the  inside  temperature  which  takes  into  consideration  the  fact  that 
the  coefficient  of  transmission  of  the  radiator  is  not  constant  but  in- 
creases with  the  temperature.  With  Ts  =  227  and  a  two-column  cast-iron 
radiator  he  finds  for  T0  =  -20  -10  0  10  20  30  40 
Tj.  =  58  64  70  77.5  83  90  97 

For  all  values  of  Tn  between  —  10  and  40  these  figures  are  within  one 
ree  of  those  computed  by  the  author's  method. 

ELECTRICAL  HEATING. 

Heating  by  Electricity.  —  If  the  electric  currents  are  generated  by  a 
dynamo  driven  by  a  steam-engine,  electric  heating  will  prove  very  ex- 
pensive, since  the  steam-engine  wastes  in  the  exhaust-steam  and  by 
radiation  about  90%  of  the  heat-units  supplied  to  it.  In  direct  steam- 
heating,  with  a  good  boiler  and  properly  covered  supply-pipes,  we  can 
utilize  about  60%  of  the  total  heat  value  of  the  fuel.  One  pound  of  coal, 
with  a  heating  value  of  13,000  heat-units,  would  supply  to  the  radiators 
about  13,000  X  0.60  =  7800  heat-units.  In  electric  heating,  suppose  we 
have  a  first-class  condensing-engine  developing  1  H.P.  for  every  2  Ibs.  of 
coal  burned  per  hour.  This  would  be  equivalent  to  1,980,000  ft.-lbs.  -t- 


714  HEATING  AND   VENTILATION. 

778  =  2545  heat-units,  or  1272  heat-units  for  1  Ib.  of  coal.  The  friction 
of  the  engine  and  of  the  dynamo  and  the  loss  by  electric  leakage  and 
by  heat  radiation  from  the  conducting  wires  might  reduce  the  heat- 
units  delivered  as  electric  current  to  the  electric  radiator,  and  there  con- 
verted into  heat,  to  50%  of  this,  or  only  636  heat-units,  or  less  than  one 
twelfth  of  that  delivered  to  the  steam-radiators  in  direct  steam-heating. 
Electric  heating,  therefore,  will  prove  uneconomical  unless  the  electric 
current  is  derived  from  water  or  wind  power  which  would  otherwise  be 
wasted.  (See  Electrical  Engineering.) 

MINE-VENTILATION. 

Friction  of  Air  in  Underground  Passages.  —  In  ventilating  a  mine  or 
other  underground  passage  the  resistance  to  be  overcome  is,  according 
to  most  writers  on  the  subject,  proportional  to  the  extent  of  the  fric- 
tional  surface  exposed;  that  is,  to  the  product  lo  of  the  length  of  the  ganr- 
way  by  its  perimeter,  to  the  density  of  the  air  in  circulation,  to  the 
square  of  its  average  speed,  v,  and  lastly  to  a  coefficient  k,  whose  numer- 
ical value  varies  according  to  the  nature  of  the  sides  of  the  gangway  and 
the  irregularities  of  its  course. 

The  formula  for  the  loss  of  head,  neglecting  the  variation  in  density  as 

ks  v2 
unimportant,  is  p  = ,  in  which  p  =  loss  of  pressure  in  pounds  per 

square  foot,  s  =  square  feet  of  rubbing-surface  exposed  to  the  air,  v  the 
velocity  of  the  air  in  feet  per  minute,  a  the  area  of  the  passage  in  square 
feet,  and  k  the  coefficient  of  friction.  W.  Fairley,  in  Colliery  Engineer, 
Oct.  and  Nov.,  1893,  gives  the  following  formulae  for  all  the  quantities 
involved,  using  the  same  notation  as  the  above,  with  these  additions: 
h  =  horse-power  of  ventilation;  I  =  length  of  air-channel;  o  =  perimeter 
of  air-channel;  q  =  quantity  of  air  circulating  in  cubic  feet  per  minute 
u  =  units  of  work,  in  foot-pounds,  applied  to  circulate  the  air ;  w  =  water^ 
gauge  in  inches.  Then, 

_  ksv2  _  ksv2q  _  ksv3  _  _w   _  g 
"    p    "       u      ~   pv   ~  pv  ~  v  ' 
—       u  gj>       _  5.2  qw 

~  33,000  ~"  33,000  ~~  33,000  * 

3      fc  =  pa  =    u    =   -     P         =     5>2  w 
sv2       sv3      sv2  •*•  a      sv2  •*-  a' 

''  kv*o' 

5     o  =  -  =   pa  - 
I       kvH ' 


ks  j    a         q         av' 

I  »A£Y       «'      C 

7.  pa  =  ksv2  =     i  /  r-  )  ks  =  -  ;  pa3  =  ksq2. 

W  r/       v_         __ 

i  /£%  =  4  /*LO 

y   ks  y  ks    ' 


u       ksv3 
8.    «  -  «.  -  -  -  — 


pa_        u_  _  qp_       vpa       , 
kv*       kv*       kv*        kv* 


10.    u  =  qp  =  vpa  =  ^2-  =  ksv3  =  5.2  qw  =  33,000  h. 

U         v    _     M.     _    ff    _    //^    _    t3/^    =    4    /P*m 

~  pa  ~  a  ~        ks  ks  ks 


MINE  -VENTILATION. 


715 


«*•— fi 


5.2  a 


To  find  the  quantity  of  air  with  a  given  horse-power  and  efficiency  (e) 
of  engine: 

h  X  33,000  X  e 
"- 


The  value  of  fc,  the  coefficient  of  friction,  as  stated,  varies  according  to 
the  nature  of  the  sides  of  the  gangway.  Widely  divergent  values  have 
been  given  by  different  authorities  (see  Colliery  Engineer,  Nov.,  1893),  the 
most  generally  accepted  one  until  recently  being  probably  that  of  J.  J. 
Atkinson,  .0000000217,  which  is  the  pressure  per  square  foot  in  decimals 
of  a  pound  for  each  square  foot  of  rubbing-surface  and  a  velocity  of  one 
foot  per  minute.  Mr.  Fairley,  in  his  "Theory  and  Practice  of  Ventilating 
Coal-mines,"  gives  a  value  less  than  half  of  Atkinson's  or  .00000001;  and 
recent  experiments  by  D.  Murgue  show  that  even  this  value  is  high  under 
most  conditions.  Murgue's  results  are  given  in  his  paper  on  Experi- 
mental Investigations  in  the  Loss  of  Head  of  Air-currents  in  Under- 
ground Workings,  Trans.  A.  I.  M.  E.,  1893,  vol.  xxiii.  63.  His  coefficients 
are  given  in  the  following  table,  as  determined  in  twelve  experiments: 

Coefficient  of  Loss  of 

Head  by  Friction. 
French.  British. 

(Straight,  normal  section  .........  00092     .000,000,00486 
Straight,  normal  section  .........  00094 
Straight,  large  section  ...........  00104 


Brick-lined 

arched 
gangways. 

Timbered 
gangways. 


I  Straight,  normal  section 00122 

Straight,  normal  section 00030 

Straight,  normal  section 00036 

Continuous  curve,  normal  section      .  00062 

Sinuous,  intermediate  section 00051 

Sinuous,  small  section 00055 

!  Straight,  normal  section 00168 
Straight,  normal  section 00144 
Slightly  sinuous,  small  section. . .  .  00238 


.000,000,00497. 

.000,000,00549 

.000,000,00645 

.000,000,00158 

.000,000,00190 

.000,000,00328 

.000,000,00269 

.000,000,00291 

.000,000,00888 

.000,000,00761 

.000,000,01257 


The  French  coefficients  which  are  given  by  Murgue  represent  the  height 
of  water-gauge  in  millimeters  for  each  square  meter  of  rubbing-surface 
and  a  velocity  of  one  meter  per  second.  To  convert  them  to  the  British 
measure  of  pounds  per  square  foot  for  each  square  foot  of  rubbing-surface 
and  a  velocity  of  one  foot  per  minute  they  have  been  multiplied  by  the 
factor  of  conversion,  .000005283.  For  a  velocity  of  1000  feet  per  minute, 
since  the  loss  of  head  varies  as  -y2,  move  the  decimal  point  in  the  coefficients 
six  places  to  the  right. 

Equivalent  Orifice.  —  The  head  absorbed  by  the  working-chambers 
of  a  mine  cannot  be  computed  a  priori,  because  the  openings,  cross- 
passages,  irregular-shaped  gob-piles,  and  daily  changes  in  the  size  and 
shape  of  the  chambers  present  much  too  complicated  a  network  for  accu- 
rate analysis.     In  order  to  overcome  this  difficulty  Murgue  proposed  in 
1872  the  method  of  equivalent  orifice.     This  method  consists  in  substitut- 
ing for  the  mine  to  be  considered  the  equivalent  thin-lipped  orifice, 
requiring  the  same  height  of  head  for  the  discharge  of  an  equal  volume 
of  air.     The  area  of  this  orifice  is  obtained  when  the  head  and  the  dis- 
charge are  known,  by  means  of  the  following  formulae,  as  given  by  Fairley: 
Let  Q  =  quantity  of  air  in  thousands  of  cubic  feet  per  minute; 
w  =  inches  of  water-gauge; 
A  =  area  in  square  feet  of  equivalent  orifice. 

Then 


0.37 


*  Murgue  gives  A  « 


and  Norris  A 


^  0.403^ 

V'U 


See  page  072,  ante. 


716 


WATER. 


Motive  Column  or  the  Head  of  Air  Due  to  Differences  of  Tem- 
perature, etc.     (Fairley.) 

Let  M  =  motive  column  in  feet; 

T  =  temperature  of  upcast; 

/  =  weight  of  one  cubic  foot  of  the  flowing  air; 

t  —  temperature  of  downcast; 

D  =  depth  of  downcast. 
Then 

T-t     _5.2Xt»       _,y  M.w_  /XM_    P   . 
-JXM,W  -    52      -  — 


M  =  D- 


T+459"1        / 

To  find  diameter  of  a  round  airway  to  pass  the  same  amount  of  air  as  a 
square  airway,  the  length  and  power  remaining  the  same: 

Let  D  ~  diameter  of  round  airway,  A  =  area  of  square  airway;  O  = 

perimeter  of  square  airway.     Then  D3  =  t  /  A*  X  3.1416 

y  0.78543X  O 

If  two  fans  are  employed  to  ventilate  a  mine,  each  of  which  when 
worked  separately  produces  a  certain  quantity,  which  may  be  indicated 
by  A  and  B,  then  the  quantity  of  air  that  will  pass  when  the  two  fans  are 
worked  together  will  be  <\/A*+B*.  (For  mine-ventilating  fans,  see 
page  672.) 

WATER. 

Expansion  of  Water.  —  The  following  table  gives  the  relative  vol- 
umes of  water  at  different  temperatures,  compared  with  its  volume  at 
•  4°  C.  according  to  Kopp,  as  corrected  by  Porter. 


Cent. 

Fahr. 

Volume. 

Cent. 

Fahr. 

Volume. 

Cent. 

Fahr. 

Volume. 

4° 
5 
10 
15 
20 
25 
30 

39.1° 
41 
50 
59 
68 
77 
86 

.09000 
.00001 
.00025 
.00083 
.00171 
.00286 
.00425 

35° 
40 
45 
50 
55 
60 
65 

95° 
104 
113 
122 
131 
140 
149 

.00586 
.00767 
.00967 
.01186 
.01423 
.01678 
.01951 

70° 
75 
80 
85 
90 
95 
100 

158° 
167 
176 
185 
194 
203 
212 

.02241 
.02548 
.02872 
.03213 
.03570 
.03943 
.04332 

Weight  of  1  cu.  ft.  at  39.1°  F.  =  62.4245  Ib.  -4-  1.04332  =  59.833. 
weight  of  1  cu.  ft.  at  212°  F. 

Weight  of  Water  at  Different  Temperatures.  —  The  weight  of 
water  at  maximum  density,  39.1°,  is  generally  taken  at  the  figure  given 
by  Rankine,  62.425  Ibs.  per  cubic  foot.  Some  authorities  give  as  low  as 
62.379.  The  figure  62.5  commonly  given  is  approximate.  The  highest 
authoritative  figure  is  62.428.  At  62°  F.  the  figures  range  from  62.291  to 
62.360.  The  figure  62.355  is  generally  accepted  as  the  most  accurate. 

At  32°  F.  figures  given  by  different  writers  range  from  62.379  to  62.418. 
Hamilton  Smith,  Jr.  (from  Rosetti)  gives  62.416. 


Weight  of  Water  at  Temperatures   above   200°  F. 

BOrnstein's  Tables,  1905.) 


(Landolt  and 


Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Deg. 

Per 

Deg. 

Per 

Deg. 

Per 

Deg. 

Per 

Deg. 

Per 

Deg. 

Per 

.  F. 

Cu. 

F. 

Cu. 

F. 

Cu. 

F. 

Cu. 

F. 

Cu. 

F 

Cu. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

200 

60.12 

270 

58.26 

340 

55.94 

410 

53.0 

480 

49.7 

550 

45.6 

210 

59.88 

280 

57.96 

350 

55.57 

420 

52.6 

490 

49.2 

560 

44.9 

220 

59.63 

290 

57.65 

360 

55.18 

430 

52.2 

500 

48.7 

570 

44.1 

239 

59.37 

300 

57.33 

370 

54.78 

440 

51.7 

510 

48.1 

580 

43.3 

240 

59.11 

310 

57.00 

380 

54.36 

450 

51.2 

520 

47.6 

590 

42.6 

250 

58.83 

320 

56  66 

390 

53.94 

460 

50.7 

530 

47.0 

600 

41.8 

260 

58.55 

330 

56.30 

400 

53.5 

470 

50.2 

540 

46.3 

WATER. 


717 


Weight  of  Water  per  Cubic  Foot,  from  32°  to  212°  F.,  and  heat* 
units  per  pound,  reckoned  above  32°  F.:  The  figures  for  weight  of  water 
in  following  table,  made  by  interpolating  the  table  given  by  Clark  as  cal- 
culated from  Rankine's  formula,  with  corrections  for  apparent  errors,  was 
published  by  the  author  in  1884,  Trans.  A.  S.  M.  E.,  vi.  90.  The  figures 
tor  heat  units  are  from  Marks  and  Da  vis's  Steam  Tables,  1909. 


& 

&M 

g  0> 

&H3 

H 

As 

—  ',0 

It0 

.2?  o>  2 

>  ft£ 

Heat-units. 

L* 

l^fcc 

j5-§ 

Jo 

~~3 

A  °+: 
.^£2 
2&2 

Heat-units. 

h  fa- 
is* 

fl   3  0> 

£  +-~ 

-S.2 

""•-Q 

ill 

^  a£ 
& 

Heat-units. 

Tempera- 
ture, 
deg.  F. 

J° 
"~1'Q 

A0*.1 

|fc! 

Heat-units. 

32 

62.42 

0. 

78 

62.25 

46.04 

123 

61.68 

90.90 

168 

60.81 

135.86 

33 

62.42 

1.01 

79 

62.24 

47.04 

124 

61.67 

91.90 

169 

60.79 

136.86 

34 

62.42 

2.02 

80 

62.23 

48.03 

125 

61.65 

92.90 

170 

60.77 

137.87 

35 

62.42 

3.02 

81 

62.22 

49.03 

126 

61.63 

93.90 

171 

60.75 

138.87 

36 

62.42 

4.03 

82 

62.21 

50.03 

127 

61.61 

94.89 

172 

60.73 

139.87 

37 

62.42 

5.04 

83 

62.20 

51.02 

128 

61.60 

95.89 

173 

60.70 

140.87 

38 

62.42 

6.04 

84 

62.19 

52.02 

129 

61.58 

96.89 

174 

60.68 

141.87 

39 

62.42 

7.05 

85 

62.18 

53.02 

130 

61.56 

97.89 

175 

60.66 

142.87 

40 

62.42 

8.05 

86 

62.17 

54.01 

131 

61.54 

98.89 

176 

60.64 

143.87 

41 

62.42 

9.05 

87 

62.16 

55.01 

132 

61.52 

99.88 

177 

60.62 

144.88 

42 

62.42 

10.06 

88 

62.15 

56.01 

133 

61.51 

100.88 

178 

60.59 

145.88 

43 

62.42 

11.06 

89 

62.14 

57.00 

134 

61.49 

101.88 

179 

60.57 

146.88 

44 

62.42 

12.06 

90 

62.13 

58.00 

135 

61.47 

102.88 

180 

60.55 

147.88 

45 

62.42 

13.07 

91 

62.12 

59.00 

136 

61.45 

103.88 

181 

60.53 

148.88 

46 

62.42 

14.07 

92 

62.11 

60.00 

137 

61.43 

104.87 

182 

60.50 

149.89 

47 

62.42 

15.07 

93 

62.10 

60.99 

138 

61.41 

105.87 

183 

60.48 

150.89 

48 

62.41 

16.07 

94 

62.09 

61.99 

139 

61.39 

106.87 

184 

60.46 

151  89 

49 

62.41 

17.08 

95 

62.08 

62.99 

140 

61.37 

107.87 

185 

60.44 

152.89 

50 

62.41 

18.08 

96 

62.07 

63  98 

141 

61.36 

108  87 

186 

60.41 

153.89 

51 

62.41 

19.08 

97 

62.06 

64.98 

142 

61.34 

109.87 

187 

60.39 

154.90 

52 

62.40 

20.08 

98 

62.05 

65.98 

143 

61.32 

110.87 

188 

60.37 

155.90 

53 

62.40 

21.08 

99 

62.03 

66.97 

144 

61.30 

111.87 

189 

60.34 

156.90 

54 

62.40 

22.08 

100 

62.02 

67.97 

145 

61.28 

112.86 

190 

60.32 

157.91 

55 

62.39 

23.08 

101 

62.01 

68.97 

146 

61.26 

113.86 

191 

60.29 

158.91 

56 

62.39 

24.08 

102 

62.00 

69.96 

147 

61.24 

114.86 

192 

60.27 

159.91 

57 

62.39 

25.08 

103 

61.99 

70.96 

148 

61.22 

115.86 

193 

60.25 

160.91 

58 

62.38 

26.08 

104 

61.97 

71.96 

149 

61.20 

116.86 

194 

60.22 

161.92 

59 

62.38 

27.08 

105 

61.96 

72.95 

150 

61.18 

117.86 

195 

60.20 

162.92 

60 

62.37 

28.08 

106 

61.95 

73.95 

151 

61.16 

118.86 

196 

60.17 

163.92 

61 

62.37 

29.08 

107 

61.93 

74.95 

152 

61.14 

119.86 

197 

60.15 

164.93 

62 

62.36 

30.08 

108 

61.92 

75.95 

153 

61.12 

120.86 

198 

60.12 

165.93 

63 

62.36 

31.07 

109 

61.91 

76.94 

154 

61.10 

121.86 

199 

60.10 

166.94 

64 

62.35 

32.07 

110 

61.89 

77.94 

155 

61.08 

122.86 

200 

60.07 

167.94 

65 

62.34 

33.07 

1  1  1 

61.88 

78.94 

156 

61.06 

123.86 

201 

60.05 

168.94 

66 

62.34 

34.07 

112 

61.86 

79.93 

157 

61.04 

124.86 

202 

60.02 

169.95 

67 

62.33 

35.07 

113 

61.85 

80.93 

158 

61.02 

125.86 

203 

60.00 

170.95 

68 

62.33 

36.07 

114 

61.83 

81.93 

159 

61.00 

126.86 

204 

59.97 

171.96 

69 

62.32 

37.06 

115 

61.82 

82.92 

160 

60.98 

127.86 

205 

59.95 

172.96 

70 

62.31 

38.06 

116 

61.80 

83.92 

161 

60.96 

128.86 

206 

59.92 

173.97 

71 

62.31 

39.06 

117 

61.78 

84.92 

162 

60.94 

129.86 

207 

59.89 

174.97 

72 

62.30 

40.05 

118 

61.77 

85.92 

163 

60.92 

130.86 

208 

59.87 

175.98 

73 

62.29 

41.05 

119 

61.75 

86.91 

164 

60.90 

131.86 

209 

59.84 

176.98 

74 

62.28 

42.05 

120 

61.74 

87.91 

165 

60.87 

132.86 

210 

59.82 

177.99 

75 

62.28 

43.05 

121 

61.72 

88.91 

166 

60.85 

133.86 

211 

59.79 

178.99 

76 

62.27 

43.04 

122 

61.70 

89.91 

167 

60.83 

134.86 

212 

59.76 

180.00 

77 

62.261  45.04 

Later  authorities  give  figures  for  the  weight  of  water  which  differ  in  the 
second  decimal  place  only  from  those  given  above,  as  follows: 

Temp.  F 40  50  60  70  80  90 

Lbs.  per  cu.  ft 62.43     62.42     62.37     62.30     62.22     62.11 

110 


Temp.  F 100 

Lbs.  per  cu.  ft...    62.00 

Temp.  F 160         170 

Lbs.  per  qu.  ft. . .   61 . 00     60 . 80 


120 

61.86  61.71 
180 
60.50 


130  140  150 
61.55  61.38  61.18 

190  200  210 
60.36  60.12  59.88 


718 


WATER. 


Comparison  of  Heads  of  Water  in  Feet  with  Pressures  in  Various 

Units. 

One  foot  of  water  at  39.1°  Fahr.  =  62.425  Ibs.  on  the  square  foot; 

=    0.4335  Ibs.  on  the  square  inch; 

=    0.0295  atmosphere; 

=    0.8826  inch  of  mercury  at  32°; 

=  77o  o  (  feet  of  air  at  32°  and 

\     atmospheric  pressure; 

One  Ib.  on  the  square  foot,  at  39.1°  Fahr..    =    0.01602  foot  of  water- 
One  Ib.  on  the  square  inch,  at  39.1°  Fahr  . 
One  atmosphere  of  29 . 922  in.  of  mercury  . 

One  inch  of  mercury  at  32° 

One  foot  of  air  at  32°,  and  1  atmosphere. 

One  foot  of  average  sea-water 

One  foot  of  water  at  62°  F . . 

One  foot  of  water  at  62°  F 

One  inch  of  water  at  62°  F.  =  0  .5774  ounce 
One  Ib.  of  water  on  the  square  inch  at  62°  F 
One  ounce  of  water  on  the  square  inch  at 

62°  F =     1 . 732  inches  of  water. 


2.307      feet  of  water; 

=  33.9  feet  of  water; 

=     1.133      feet  of  water; 

=    0.001293  feet  of  water; 

=     1 . 026  foot  of  pure  water; 

=  62.355  Ibs.  per  sq.  foot; 

=  0.43302  Ib.  per  sq.  inch; 
0.036085  Ib.  per  sq.  inch 
2.3094  feet  of  water. 


Pressure  in  Pounds  per  Square  Inch  for  Different  Heads  of  Water. 

At  62°  F.  1  foot  head  =  0.433  Ib.  per  square  inch,  0.433  X  144  =  62.352 
Ibs.  per  cubic  foot. 


Head,  feet. 

0 

' 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0.433 

0.866 

1.299 

1.732 

2.165 

2.598 

3.031 

3.464 

3.897 

10 

4.330 

4.763 

5.196 

5.629 

6.062 

6.495 

6.928 

7.361 

7.794 

8.227 

20 

8.660 

9.093 

9.526 

9.959 

10.392 

10.825 

11.258 

11.691 

12.124 

12.557 

30 

12.990 

13.423 

13.856 

14.289 

14.722 

15.155 

15.588 

16.021 

16.454 

16.887 

40 

17.320 

17.753 

18.186 

18.619 

19.052 

19.485 

19.918 

20.351 

20.784 

21.217 

50 

21.650 

22.083 

22.516 

22.949 

23.  382123.815 

24.248 

24.681 

25.114 

25.547 

60 

25.980 

26.413 

26.846 

27.279 

27.712 

28.145 

28.578 

29.011 

29.444 

29.877 

70 

30.310 

30.743 

31.176 

31.609 

32.042 

32.475 

32.908 

33.341 

33.774 

34.207 

80 

34.640 

35.073 

35.506 

35.939 

36.372 

36.805 

37.238 

37.671 

38.104 

38.537 

90 

38.970 

39.403 

39.836 

40.269 

40.702 

41.135 

41.568 

42.001 

42.436 

42.867 

Head  in  Feet  of  Water,  Corresponding  to  Pressures  in  Pounds  per 
Square  Inch. 

1  Ib.  per  square  inch  =  2.30947  feet  head,  1  atmosphere  =  14.7  Ibs. 
per  sq.  inch  =  33.94  ft.  head. 


Pressure. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

2.309 

4.619 

6.928 

9.238 

11.547 

13.857 

16.166 

18.476 

20.785 

10 

23.0947 

25.404 

27.714 

30.023 

32.333 

34.642 

36.952 

39.261 

41.570 

43.880 

20 

46.1894 

48.499 

50.808 

53.118 

55.427 

57.737 

60.046 

62.356 

64.665 

66.975 

30 

69.2841 

71.594 

73.903 

76.213 

78.522 

80.831 

83.141 

85.450 

87.760 

90.069 

40 

92.3788 

94.688 

96.998 

99.307 

101.62 

103.93 

106.24 

108.55 

110.85 

113.16 

50 

115.4735 

117.78 

120.09 

122.40 

124.71 

127.02  129.33 

131.64 

133.95 

136.26 

60 

138.5682 

140.88 

143.19 

145.50 

147.81 

150.12  152.42 

154.73 

157.04 

159.35 

70 

161.6629 

163.97 

166.28 

168.59 

170.90 

173.  211175.  52 

177.83 

180.14 

182.45 

80 

184.7576 

187.07 

189.38 

191.69 

194.00 

196.31 

198.61 

200.92 

203.23 

205.54 

96 

207,8523 

210.16 

212.47 

214.78 

217,09 

219.40221.71 

224.02 

226.33 

228.64 

WATER.  719 

Pressure  of  Water  due  to  its  Weight.  —  The  pressure  of  still  water 
in  pounds  per  square  inch  against  the  sides  of  any  pipe,  channel,  or  vessel 
of  any  shape  whatever  is  due  solely  to  the  "  head,"  or  height  of  the 
level  surface  of  the  water  above  the  point  at  which  the  pressure  is  con- 
sidered, and  is  equal  to  0.43302  Ib.  per  square  inch  for  every  foot  of  head, 
or  62.355  Ibs.  per  square  foot  for  every  foot  of  head  (at  62°  F.).  ' 

The  pressure  per  square  inch  is  equal  in  all  directions,  downwards, 
upwards,  or  sideways,  and  is  independent  of  the  shape  or  size  of  the 
containing  vessel. 

The  pressure  against  a  vertical  surface,  as  a  retaining-wall,  at  any 
point  is  in  direct  ratio  to  the  head  above  that  point,  increasing  from  0  at 
the  level  surface  to  a  maximum  at  the  bottom.  The  total  pressure 
against  a  vertical  strip  of  a  unit's  breadth  increases  as  the  area  of  a 
right-angled  triangle  whose  perpendicular  represents  the  height  of  the 
strip  and  whose  base  represents  the  pressure  on  a  unit  of  surface  at  the 
bottom;  that  is,  it  increases  as  the  square  of  the  depth.  The  sum  of  all 
the  horizontal  pressures  is  represented  by  the  area  of  the  triangle,  and 
the  resultant  of  this  sum  is  equal  to  this  sum  exerted  at  a  point  one  third 
of  the  height  from  the  bottom.  (The  center  of  gravity  of  the  area  of  a 
triangle  is  one  third  of  its  height.) 

The  horizontal  pressure  is  the  same  if  the  surface  is  inclined  instead 
of  vertical. 

(For  an  elaboration  of  these  principles  see  Trautwine's  Pocket-Book, 
or  the  chapter  on  Hydrostatics  in  any  work  on  Physics.  For  dams, 
retaining-walls,  etc.,  see  Trautwine.) 

The  amount  of  pressure  on  the  interior  walls  of  a  pipe  has  no  appreci- 
able effect  upon  the  amount  of  flow. 

Buoyancy.  —  When  a  body  is  immersed  in  a  liquid,  whether  it  float  or 
sink,  it  is  buoyed  up  by  a  force  equal  to  the  weight  of  the  bulk  of  the 
liquid  displaced  by  the  body.  The  weight  of  a  floating  body -is  equal  to 
the  weight  of  the  bulk  of  the  liquid  that  it  displaces.  The  upward 
pressure  or  buoyancy  of  the  liquid  may  be  regarded  as  exerted  at  the 
center  of  gravity  of  the  displaced  water,  which  is  called  the  center  of 
pressure  or  of  buoyancy.  A  vertical  line  drawn  through  it  is  called  the 
axis  of  buoyancy  or  of  flotation.  In  a  floating  body  at  rest  a  line  joining 
the  center  of  gravity  and  the  center  of  buoyancy  is  vertical,  and  is  called 
the  axis  of  equilibrium.  When  an  external  force  causes  the  axis  of 
equilibrium  to  lean,  if  a  vertical  line  be  drawn  upward  from  the  center 
of  buoyancy  to  this  axis,  the  point  where  it  cuts  the  axis  is  called  the 
metacenter.  If  the  metacenter  is  above  the  center  of  gravity  the  distance 
between  them  is  called  the  metacentric  height,  and  the  body  is  then  said 
to  be  in  stable  equilibrium,  tending  to  return  to  its  original  position 
when  the  external  force  is  removed. 

Boiling-point.  —  Water  boils  at  212°  F.  (100°  C.)  at  mean  atmos- 
pheric pressure  at  the  sea-level,  14.696  Ibs.  per  square  inch.  The  tem- 
perature at  which  water  boils  at  any  given  pressure  is  the  same  as  the 
temperature  of  saturated  steam  at  the  same  pressure.  For  boiling-point 
of  water  at  other  pressure  than  14.696  Ibs.  per  square  inch,  see  table  of 
the  Properties  of  Saturated  Steam. 

The  Boiling-point  of  Water  may  be  Raised.  —  When  water  is 
entirely  freed  of  air,  which  may  be  accomplished  by  freezing  or  boiling, 
the  cohe  ion  of  its  atoms  is  greatly  increased,  so  that  its  temperature 
may  be  raised  over  50°  above  the.  ordinary  bailing-point  before  ebullition 
takes  place.  It  was  found  by  Faraday  that  when  such  air-freed  water 
did  boil  the  rupture  of  the  liquid  was  like  an  explosion.  When  water 
is  surrounded  by  a  film  of  oil,  its  boiling  temperature  may  be  raised 
considerably  above  its  normal  standard.  This  has  been  applied  as  a 
theoretical  explanation  in  the  instance  of  boiler  explosions. 

The  freezing-point  also  may  be  lowered,  if  the  water  is  perfectly  quiet, 
to  — 10°  C.,  or  18°  Fahrenheit  below  the  normal  freezing-point.  (Hamilton 
Smith,  Jr.,  on  Hydraulics,  p.  13.) 

Kreezing-point.  —  Water  freezes  at  32°  F.  at  the  ordinary  atmos- 
pheric pressure,  and  ice  melts  at  the  same  temperature.  In  the  melting 
of  1  pound  of  ice  into  water  at  32°  F.  about '142  heat-units  are  absorbed, 
or  become  latent;  and  in  freezing  1  Ib.  of  water  into  ice  a  like  quantity 
of  heat  is  given  out  to  the  surrounding  medium. 

Sea-water  freezes  at  27°  F.    The  ice  is  fresh,     (Trautwine.) 


720 


WATER. 


^Sf  innd 

67.50  Ibs.; 


(£rom  Cla?°  —  1  cubic  foot  of  ice  at  32°  F.  weighs 
pound  of  ice  at  32°  F.  has  a  volume  of  0.0174  cu.  ft.  =  30.067 


Relative  volume  of  ice  to  water  at  32°  F.,  1.0855,  the  expansion  in 
passing  into  the  solid  state  being  8.55%.  Specific  gravity  of  ice  =  0.922, 
water  at  02  .r  .  being  1  . 


,  melting-point  of  ice  is  lower  than  32°  F.,  being  at 
F.  for  each  additional  atmosphere  of  pressure. 
The  specific  heat  of  ice  "s  0.504,  that  of  water  being  1. 
1  cubic  foot  of  fresh  snow,  according  to  humidity  of  atmosphere: 

£  •      i£V12  *lbsrrt  Jucubl,£,foot  of  snow  moistened  and  compacted  by 
rain:  15  Ibs.  to  50  Ibs.     (Trautwine.) 

The  latent  heat  of  fusion  of  ice  is  143.6  B.T.U.  per  Ib. 

Specific  Heat  of  Water.     (From  Davis  and  Marks's  Steam  Tables.) 


Deg.   Sp. 
F.    Ht. 

Deg.   Sp. 
F.    Ht. 

Deg.  Sp. 
F.   Ht. 

Deg.  Sp. 
F.   Ht. 

Deg.  Sp. 
F.   Ht. 

Deg.  Sp. 
F.   Ht. 

20  1.0168 

120  0.9974 

220   .007 

320   .035 

420   .072 

520   .123 

30  1.0098 

130  0.9974 

230   .009 

330   .038 

430   .077 

530   .128 

40  1.0045 

140  0.9986 

240   .012 

340   .041 

440   .082 

540   .134 

50  1.0012 

150  0.9994 

250   .015 

350   .045 

450   .086 

550   .140 

60  0.9990 

160   .0002 

260   .018 

360   .048 

460   .091 

560   .146 

70  0.9977 

170   .0010 

270   .021 

370   .052 

470   .096 

570   .152 

80  0.9970 

180   .0019 

280   .023 

380   .056 

480   .101 

580   .158 

90  0.9967 

190   .0029 

290   .026 

390   .060 

490   .106 

590   .165 

100  0.9967 

200   .0039 

300   .029 

400   .064 

500   .112 

600   .172 

110  0.9970 

210   .0050 

310   .032 

410   .068 

510   .117 

These  figures  are  based  on  the  mean  value  of  the  heat  unit,  that  is, 
Viso  of  the  heat  needed  to  raise  1  Ib.  of  water  from  32°  to  212°. 

Compressibility  of  Water.  —  Water  is  very  slightly  compressible. 
Its  compressibility  is  from  0.000040  to  0.000051  for  one  atmosphere, 
decreasing  with  increase  of  temperature.  For  each  foot  of  pressure  dis- 
tilled water  will  be  diminished  in  volume  0.0000015  to  0.0000013.  Water 
is  so  incompressible  that  even  at  a  depth  of  a  mile  a  cubic  foot  of  water 
will  weigh  only  about  half  a  pound  more  than  at  the  surface. 


THE   IMPURITIES   OF   WATER. 

(A.  E.  Hunt  and  G.  H.  Clapp,  Trans.  A.  I.  M.  E.,  xvii.  338.) 

Commercial  analyses  are  made  to  determine  concerning  a  given  water*. 
(1)  its  applicability  for  making  steam;  (2)  its  hardness,  or  the  facility 
with  which  it  will  "form  a  lather"  necessary  for  washing;  or  (3)  its 
adaptation  to  other  manufacturing  purposes. 

At  the  Buffalo  meeting  of  the  Chemical  Section  of  the  A.  A.  A.  S.  it 
was  decided  to  report  all  water  analyses  in  parts  per  thousand,  hundred- 
thousand,  and  million. 

To  convert  grains  per  imperial  (British)  gallon  into  parts  per  100,000, 
divide  by  0.7.  To  convert  parts  per  100,000  into  grains  per  IT.  S.  gallon, 
multiply  by  0.5835.-  To  convert  grains  per  U.  S.  gallon  into  parts  per 
million  multiply  by  17.14. 

The  most  common  commercial  analysis  of  water  is  made  to  determine 
its  fitness  for  making  steam.  Water  containing  more  than  5  parts  per 
100,000  of  free  sulphuric  or  nitric  acid  is  liable  to  cause  serious  corrosion, 
not  only  of  the  metal  of  the  boiler  itself,  but  of  the  pipes,  cylinders,  pistons, 
and  valves  with  which  the  steam  comes  in  contact. 

The  total  residue  in  water  used  for  making  steam  causes  the  interior 
linings  of  boilers  to  become  coated,  and  often  produces  a  dangerous  hard 


THE  IMPURITIES   OF  WATEB.  721 

scale,  which  prevents  the  cooling  action  of  the  water  from  protecting 
the  metal  against  burning. 

Lime  and  magnesia  bicarbonates  in  water  lose  their  excess  of  carbonic  acid 
on  boiling,  and  often,  especially  when  the  water  contains  sulphuric  acid, 
produce,  with  the  other  solid  residues  constantly  being  formed  by  the 
evaporation,  a  very  hard  and  insoluble  scale.  A  larger  amount  than  100 
parts  per  100,000  of  total  solid  residue  will  ordinarily  cause  troublesome 
scale,  and  should  condemn  the  water  for  use  in  steam-boilers,  unless  a 
better  supply  cannot  be  obtained. 

The  following  is  a  tabulated  form  of  the  causes  of  trouble  with  water 
for  steam  purposes,  and  the  proposed  remedies,  given  by  Prof.  L.  M. 
Norton. 

CAUSES  OF  INCRUSTATION. 

1.  Deposition  of  suspended  matter. 

2.  Deposition  of  deposed  salts  from  concentration. 

3.  Deposition   of   carbonates   of   lime   and   magnesia   by   boiling   off 
carbonic  acid,  which  holds  them  in  solution. 

4.  Deposition  of  sulphates  of  lime,  because  sulphate  of  lime  is  but 
slightly  soluble  in  cold  water,  less  soluble  in  hot  water,  insoluble  above 
270°  F. 

5.  Deposition  of  magnesia,  because  magnesium  salts  decompose  at  high 
temperature. 

6.  Deposition  of  lime  soap,  iron  soap,  etc.,  formed  by  saponification  of 
grease. 

MEANS  FOR  PREVENTING  INCRUSTATION. 

1.  Filtration. 

2.  Blowing  off. 

3.  Use  of  internal  collecting  apparatus  or  devices  for  directing  the 
circulation. 

4.  Heating  feed-water. 

5.  Chemical  or  other  treatment  of  water  in  boiler. 

6.  Introduction  of  zinc  into  boiler. 

7.  Chemical  treatment  of  -water  outside  of  boiler. 

TABULAR  VIEW. 

Troublesome  Substance.  Trouble.  Remedy  or  Palliation. 

Sediment,  mud,  clay,  etc.  Incrustation.   Filtration;  blowing  off. 

Readily  soluble  salts.  Blowing  off. 

Bicarbonates  of  lime,  magnesia, )  .< 


(     magnesia,  etc". 
Quir^oto  r,f  li™  "  f  Addition     of    carb.     soda, 

1      barium  hydrate,  etc. 
Chloride  and  sulphate  of  mag-)  prtrrrt0:nn     j  Addi  ion   of   caibonate    of 

nesium.  f  u<          on-    (     soda,  etc. 

Carbonate    of    soda    in    large)     T>_:  .„.•„„      (Addition   of   barium   chlo- 

amounts.  J     J          ng-     {     ride,  etc. 

Acid  (in  mine  waters).  Corrosion.     Alkali. 

Dinl°v!jpn    carbonic    acid    and}  Corrosion,   j    toiler!  to  formTthhi  in- 
ternal coating. 

G rease  (from  condensed  water).  l[?rr°s^R  ^Different  cases  require  dif- 

Primine      !•     ferent  remedies.    Consult 

Organic  matter  (sewage).  )  corrosion   or  I     a  specialist  on  the  sub- 

(incrustation/     Jeci< 

The  mineral  matters  causing  the  most  troublesome  boiler-scales  are 
bicarbonates  and  sulphates  of  lime  and  magnesia,  oxides  of  iron  and 
alumina,  and  silica.  The  analyses  of  some  of  the  most  common  and 
troublesome  boiler-scales  are  given  in  the  following  table: 


722 


WATER. 


Analyses  of  Boiler-scale.     (Chandler.) 


Sul- 

Per- 

Car- 

X-" 

phate 
of 

Mag- 
nesia. 

Silica. 

oxide 
of 

Water. 

bonate 
of 

Lime. 

Iron. 

Lime. 

N.Y.C.&H.R.Ry.,No.    1 

74.07 

9.19 

0.65 

0.08 

1.14 

14.78 

No.    2 

71.37 

1.76 

No.  3 

62.86 

J8.  95 

2.60 

0.92 

1.28 

12.62 

No.   4 

53.05 

4.79 

No.   5 

46.83 

5.32 

No.  6 

30.80 

31.17 

7.75 

1.08 

2.44 

26.93 

No.   7 

4.95 

2.61 

2.07 

1.03 

0.63 

86.25 

No.  8 

0.88 

2.84 

0.65 

0.36 

0.15 

93.19 

No.  9 

4.81 

2.92 

No.  10 

30.07 

8.24 

Analyses  in  parts  per  100,000  of  Water  giving  Bad  Results  in 
Steam-boilers.     (A.  E.  Hunt.) 


. 

.5 

'<8  bio 

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U 

c3  O 

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$ 

1 

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S 

t 

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O°ce 

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B 

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PQ 

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H 

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o 

' 

Coal-mine  water 

110 

25 

119 

39 

890 

5QO 

780 

30 

640 

Salt-well 

151 

38 

190 

48 

360 

Q90 

38 

21 

30 

1310 

Spring  

75 

89 

95 

PO 

310 

75 

10 

80 

36 

Moriongahela  River  

no 

161 

710 

38 

70 

80 

70 

94 

81 

719 

710 

90 

it                 « 

37 

87 

61 

104 

78 

190 

38 

Allegheny  R.,  near  Oil-works.  . 

30 

50 

41 

68 

890 

47 

Many  substances  have  been  added  with  the  idea  of  causing  chemical 
action  which  will  prevent  boiler-scale.  As  a  general  rule,  these  do  more 
harm  than  good,  for  a  boiler  is  one  of  the  worst  possible  places  in  which 
to  carry  on  chemical  reaction,  where  it  nearly  always  causes  more  or  less 
corrosion  of  the  metal,  and  is  liable  to  cause  dangerous  explosions. 

In  cases  where  water  containing  large  amounts  of  total  solid  residue  is 
necessarily  used,  a  heavy  petroleum  oil,  free  from  tar  or  wax,  which  is  not 
acted  upon  by  acids  or  alkalies,  not  having  sufficient  wax  in  it  to  cause 
saponification,  and  which  has  a  vaporizing-point  at  nearly  600°  F.,  will 
give  the  best  results  in  preventing  boiler-scale.  Its  action  is  to  form  a 
thin  greasy  film  over  the  boiler  linings,  protecting  them  largely  from  the 
action  of  acids  in  the  water  and  greasing  the  sediment  which  is  formed, 
thus  preventing  the  formation  of  scale  and  keeping  the  solid  residue 
from  the  evaporation  of  the  water  in  such  a  plastic  suspended  condition 
that  it  can  be  easily  ejected  from  the  boiler  by  the  process  of  "blowing 
off."  If  the  water  is  not  blown  off  sufficiently  often,  this  sediment 
forms  into  a  "putty"  that  will  necessitate  cleaning  the  boilers.  Any 
boiler  using  bad  water  should  be  blown  off  every  twelve  hours. 


PURIFYING  WATER. 


723 


Hardness  of  Water.  —  The  hardness  of  water,  or  its  opposite  quality, 
Indicated  by  the  ease  with  which  it  will  form  a  lather  with  soap,  depends 
almost  altogether  upon  the  presence  of  compounds  of  lime  and  magnesia. 
Almost  all  soaps  consist,  chemically,  of  oleate,  stearate,  and  palmitate  of 
an  alkaline  base,  usually  soda  and  potash.  The  more  lime  and  magnesia 
in  a  sample  of  water,  the  more  soap  a  given  volume  of  the  water  will 
decompose,  so  as  to  give  insoluble  oleate,  palmitate,  and  stearate  of 
lime  and  magnesia,  and  consequently  the  more  soap  must  be  added  in 
order  that  the  necessary  quantity  of  soap  may  remain  in  solution  to 
form  the  lather.  The  relative  hardness  of  samples  of  water  is  generally 
expressed  in  terms  of  the  number  of  standard  soap-measures  consumed 
by  a  gallon  of  water  in  yielding  a  permanent  lather. 

In  Great  Britain  the  standard  soap-measure  is  the  quantity  required  to 
precipitate  one  grain  of  carbonate  of  lime:  in  the  U.  S.  it  is  the  quantity 
required  to  precipitate  one  milligramme. 

If  a  water  charged  with  a  bicarbonate  of  lime,  magnesia,  or  iron 
is  boiled,  it  will,  on  the  excess  of  the  carbonic  acid  being  expelled, 
deposit  a  considerable  quantity  of  the  lime,  magnesia,  or  iron,  and  con- 
sequently the  water  will  be  softer.  The  hardness  of  the  water  after 
this  deposit  of  lime,  after  long  boiling,  is  called  the  permanent  hardness 
and  the  difference  between  it  and  the  total  hardness  is  called  temporary 
hardness. 

Lime  salts  in  water  react  immediately  on  soap-solutions,  precipitating 
the  oleate,  palmitate,  or  stearate  of  lime  at  once.  Magnesia  salts,  on  the 
contrary,  require  some  considerable  time  for  reaction.  They  are,  how- 
ever, more  powerful  hardeners;  one  equivalent  of  magnesia  salts  con- 
suming as  much  soap  as  one  and  one-half  equivalents  of  lime. 

The  presence  of  soda  and  potash  salts  softens  rather  than  hardens 
water.  Each  grain  of  carbonate  of  lime  per  gallon  of  water  causes  an 
increased  expenditure  for  soap  of  about  2  ounces  per  100  gallons  of  water. 
(Eng'g  News,  Jan.  31,  1885.) 

Low  degrees  of  hardness  (down  to  200  parts  of  calcium  carbonate 
(CaCOs)  per  million)  are  usually  determined  by  means  of  a  standard 
solution  of  soap.  To  50  c.c.  of  the  water  is  added  alcoholic  soap  solu- 
tion from  a  burette,  shaking  well  after  each  addition,  until  a  lather  is 
obtained  which  covers  the  entire  surface  of  the  liquid  when  the  bottle  is 
laid  on  its  side  and  which  lasts  five  minutes.  From  the  number  of  c.c. 
of  soap  solution  used,  the  hardness  of  the  water  may  be  calculated  by 
the  use  of  Clark's  table,  given  below,  in  parts  of  CaCOs  per  million. 


c.c.  Soap 
Sol. 

Pts. 
CaCOs. 

c.e.  Soap 
.Sol. 

Pts. 
CaCO3. 

c.c.  Soap 
Sol. 

Pts. 

CaCOs. 

c.c.  Soap 
Sol. 

Pts. 
CaCOa. 

0  7 

0 

4  0 

46 

8  0  . 

103 

12  0 

164 

1  0  . 

..  5 

50.. 

...60 

9.0... 

...118 

13.0.    . 

.180 

2  0 

19 

6  0 

74 

10  0 

133 

14  0 

196 

3.0. 

32 

7.0  

89 

11.0  

....148 

15.0  

.   ...212 

For  waters  which  are  harder  than  200  parts  per  million,  a  solution  of 
soap  ten  times  as  strong  may  be  used,  the  end  or  determining  point  being 
reached  when  sufficient  soap  has  been  added  to  deaden  the  harsh  sound 
produced  on  shaking  the  bottle  containing  the  water.  —  A.  H.  Gill,  En- 
gine-Room Chemistry. 

Purifying  Feed-water  for  Steam-boilers.  (See  also  Incrustation 
and  Corrosion,  p.  927.)  —  When  the  water  used  for  steam-boilers  con- 
tains a  large  amount  of  scale-forming  material  it  is  usually  advisable  to 
purify  it  before  allowing  it  to  enter  the  boiler  rather  than  to  attempt  the 
prevention  of  scale  by  the  introduction  of  chemicals  into  the  boiler. 
Carbonates  of  lime  and  magnesia  may  be  removed  to  a  considerable 
extent  by  simple  heating  of  the  water  in  an  exhaust-steam  feed-water 
heater  or,  still  better,  by  a  live-steam  heater.  (See  circular  of  the  Hoppes 
Mfg.  Co.,  Springfield,  O.)  When  the  water  is  very  bad  it  is  best  treated 


724 


WATER. 


with  chemicals  —  lime,  soda-ash,  caustic  soda,  etc.  --in  tanks,  the  pre- 
cipitates being  separated  by  settling  or  filtering.  For  a  description  of 
several  systems  of  water  purification  see  a  series  of  articles  on  the  sub- 
ject by  Albert  A.  Gary  in  Eng'g  Mag.,  1897. 

Mr.  H.  E.  Smith,  chemist  of  the  Chicago,  Milwaukee  &  St.  Paul  Ry. 
Co.,  in  a  letter  to  the  author,  June,  1902,  writes  as  follows  concerning 
the  chemical  action  of  soda-ash  on  the  scale-forming  substances  in  boiler 
waters: 

Soda-ash  acts  on  carbonates  of  lime  and  magnesia  in  boiler  water  in  the 
following  manner:  —  The  carbonates  are  held  in  solution  by  means  of 
the  carbonic  acid  gas  also  present  which  probably  forms  bicarbonates  of 
lime  and  magnesia.  Any  means  which  will  expel  or  absorb  this  carbonic 
acid  will  cause  the  precipitation  of  the  carbonates.  One  of  these  means 
is  soda  ash  (carbonate  of  soda),  which  absorbs  the  gas  with  the  forma- 
tion of  bicarbonate  of  soda.  This  method  would  not  be  practicable  for 
softening  cold  water,  but  it  serves  in  a  boiler.  The  carbonates  precipi- 
tated in  this  manner  are  in  flocculent  condition  instead  of  semi-crystalline 
as  when  thrown  down  by  heat.  In  practice  it  is  desirable  and  sufficient 
to  precipitate  only  a  portion  of  the  lime  and  magnesia  in  flocculent 
condition.  As  to  equations,  the  following  represent  what  occurs:  — 

Ca  (HCOa)j  4-  Na2CO3  =  CaCO3  +  2  NaHCOs. 
Mg  (HCO«)i  4-  Na2CO3  =  MgCO3  +  2  NaHCOs. 
(free)  CO2  +  Na2CO3  +  H2O  =  2  NaHCO3. 

Chemical  equivalents:  —  106  pounds  of  pure  carbonate  of  soda  — 
equal  to  about  109  pounds  of  commercial  58  degree  soda-ash  —  are 
chemically  equivalent  to  — i.e.,  react  exactly  with  —  the  following 
weights  of  the  substances  named:  Calcium  sulphate,  136  Ibs.;  magnesium 
sulphate,  120  Ibs.;  calcium  carbonate,  100  Ibs.;  magnesium  carbonate, 
84  Ibs.;  calcium  chloride,  111  Ibs.;  magnesium  chloride,  95  Ibs. 

Such  numbers  are  simply  the  molecular  weights  of  the  substances 
reduced  to  a  common  basis  with  regard  to  the  valence  of  the  component 
atoms. 

Important  work  in  this  line  should  not  be  undertaken  by  an  amateur. 
"  Recipes"  have  a  certain  field  of  usefulness,  but  will  not  coyer  the  whole 
subject.  In  water  purification,  as  in  a  problem  of  mechanical  engineer- 
ing, methods  and  apparatus  must  be  adapted  to  the  conditions  presented. 
Not  only  must  the  character  of  the  raw  water  be  considered  but  also  the 
conditions  of  purification  and  use. 

Water-softening  Apparatus.  (From  the  Report  of  the  Committee 
on  Water  Service,  of  the  Am.  Railway  Eng'g  and  Maintenance  of  Way 
Assn.,  Eng.  Rec.,  April  20,  1907).  —  Between  three  and  four  hours  is  nec- 
essary for  reaction  and  precipitation.  Water  taken  from  running  streams 
in  winter  should  have  at  least  four  hours'  time.  At  least  three  feet  of 
the  bottom  of  each  settling  tank  should  be  reserved  for  the  accumulation 
of  the  precipitates. 

The  proper  capacities  for  settling  tanks,  measured  above  the  space 
reserved  for  sludge,  can  be  determined  as  follows:  a  =  capacity  of  soft- 
ener in  gallons  per  hour;  b  =  hours  required  for  reaction  and  precipitation; 
c  =  number  of  settling  tanks  (never  less  than  two);  x  =  number  of 
hours  required  to  fill  the  portion  of  settling  tank  above  the  sludge  portion; 
y  =  number  of  hours  required  to  transfer  treated  water  from  one  settling 
tank  to  the  storage  tank  (y  should  never  be  greater  than  x). 

Where  one  pump  alternates  between  filling  and  emptying  settling 
tanks,  x  —  y.  Settling  capacity  in  each  tank=  2  ax  =  ab  -s-  (c  —  1). 

For  plants  where  the  quantity  of  water  supplied  to  the  softener  and  the 
capacity  of  the  plant  are  equal,  the  settling  capacity  of  each  tank  is  equal 
to  ax.  The  number  of  hours  required  to  fill  all  the  settling  tanks  should 
equal  the  number  of  hours  required  to  fill,  precipitate  and  empty  one 
tank,  as  expressed  by  the  following  equation:  ex  =  x  +  b  4-  y. 

If  y  =*  xt  ax  =  ab  -*•  (c  —  2). 

If  y  -  1/2  *,  oz  -  06  -*•  (c  -  1.5). 


PURIFYING   WATER. 


725 


An  article  on  "The  Present  Status  of  Water  Softening,"  by  G.  C. 
Whipple,  in  Cass.  Mag.,  Mar.,  1907,  illustrates  several  different  forms  of 
water-purifying  apparatus.  A  classification  of  degrees  of  hardness  cor- 
responding to  parts  of  carbonates  and  sulphates  of  lime  and  magnesia 
per  million  parts  of  water  is  given  as  follows:  Very  soft,  0  to  10  parts; 
soft,  10  to  20;  slightly  hard,  25  to  50;  hard,  50  to  100;  very  hard,  100  to 
200;  excessively  hard,  200  to  500;  mineral  water,  500  or  more.  The 
same  article  gives  the  following  figures  showing  the  quantity  of  chemicals 
required  for  the  various  constituents  of  hard  water.  For  each  part  per 
million  of  the  substances  mentioned  it  is  necessary  to  add  the  stated 
number  of  pounds  per  million  gallons  of  lime  and  soda. 


For  Each  Part  per  Million  of 

Pounds  per  Million 
Gallons. 

Lime. 

Soda. 

Free  CC>2 

10.62 
4.77 
4.67 
0.00 
19.48 

0 
9.03 
0 

8.85 
0 

Free  acid  (calculated  as  112804)  

Alkalinity 

Incrustants  

Magnesium 

The  above  figures  do  not  take  into  account  any  impurities  in  the 
chemicals.  These  have  to  be  considered  in  actual  operation. 

An  illustrated  description  of  a  water-purifying  plant  on  the  Chicago 
&  Northwestern  Ry.  by  G.  M.  Davidson  is  found  in  Eng.  News,  April  2, 
1903.  Two  precipitation  tanks  are  used,  each  30  ft.  diarn.,  16  ft.  high, 
or  70,000  gallons  each.  As  some  water  is  left  with  the  sludge  in  the 
bottom  after  each  emptying,  their  net  capacity  is  about  60,000  gallons 
each.  The  time  required  for  filling,  precipitating,  settling  and  trans- 
ferring the  clear  water  to  supply  tanks  is  12  hours.  Once  a  month  the 
sludge  is  removed,  and  it  is  found  to  make  a  good  whitewash.  Lime  and 
soda-ash,  in  predetermined  quantity,  as  found  by  analysis  of  the  water, 
are  used  as  precipitants.  The  following  table  shows  the  effect  of  treat- 
ment of  well  water  at  Council  Bluffs,  Iowa. 


Before 
Treatment. 

After 
Treatment. 

Total  solid  matter,  grains  per  gallon  

53.67 

31.35 

Carbonates  of  lime  and  magnesia  

25  57 

3  14 

Sulphates  of  lime  and  magnesia 

19  55 

Silica  and  oxides  of  iron  and  aluminum  

1.76 

0  40 

Total  incrusting  solids   •       •   • 

46  88 

3  54 

Alkali  chlorides.  

1.21 

1  27 

Alkali  sulphates                                  ...   .       

5  58 

26  32 

Total  non-incrusting  solids  

6.79 

27.81 

Pounds  scale-forming  matter  in  1000  gals  

6.69 

0.51 

The  minimum  amount  of  scaling  matter  which  will  justify  treatment 
cannot  be  stated  in  terms  of  analysis  alone,  but  should  be  stated  in  terms 
of  pounds  incrusting  matter  held  in  solution  in  a  day's  supply.  Besides 
the  scale-forming  solids,  nearly  all  water  contains  more  or  less  free  car- 
bonic acid.  Sulphuric  acid  is  also  foifnd,  particularly  in  streams  adjacent 
to  coal  mines.  Serious  trouble  from  corrosion  will  result  from  a  small 
amount  of  this  acid.  In  treating  waters,  the  acids  can  be  neutralized, 
and  the  incrusting  matter  can  be  reduced  to  at  least  5  grains  per  gallon  in 
most  cases. 


726 


HYDRAULICS. 


QUANTITY  OF  PURE  REAGENTS  REQUIRED  TO  REMOVE  ONE  POUND  OF 
INCRUSTING  OR  CORROSIVE  MATTER  FROM  THE  WATER. 


Incrusting  or  Corrosive 
Substance  Held  in 
Solution. 

Amount  of  Reagent.     (Pure.) 

Foaming  Mat- 
ter Increased. 

Sulphuric  acid  

0  .  57  Ib  .  lime  plus  1  .  08  Ibs  .  soda  ash 

1  45  Ibs 

Free  carbonic  acid  .... 

1.27  Ibs.  lime  

None 

Calcium,  carbonate 

0  56  Ib.  lime 

Calcium  sulphate 

0  78  Ib.  soda  ash  

04  Ibs 

Calcium  chloride. 

0  96  Ib.  soda  ash  

05  Ibs 

Calcium  nitrate 

0  65  Ib    soda  ash 

04  Ibs 

Magnesium  carbonate 

1  33  Ibs.  lirne 

Magnesium  sulphate.  .  .  . 
Magnesium  chloride  
Magnesium  nitrate  

Calcium  carbonate 

0.47lb.lime  plus  0.88  Ib.  soda  ash. 
0.59  Ib.  lime  plus  1.11  Ibs.  soda  ash 
0.38  Ib.  lime  plus  0.72  Ib.  soda  ash. 

1  71  Ibs   barium  hydrate 

.18  Ibs. 
.22  Ibs. 
.15  Ibs. 

Magnesium  carbonate 

4  05  Ibs  barium  hydrate.  . 

None 

Magnesium  sulphate 

1  42  Ibs.  barium  hydrate.  .  .  . 

None 

*Calcium  sulphate  

1  .26  Ibs.  barium  hydrate  

None 

*  In  precipitating  the  calcium  sulphate,  there  would  also  be  precipi- 
tated 0.74  Ib.  of  calcium  carbonate  or  0.31  Ib.  of  magnesium  carbonate, 
the  1.26  Ibs.  of  barium  hydrate  performing  the  work  of  0.41  Ib.  of  lime 
and  0.78  Ib.  of  soda-ash,  or  for  reacting  on  either  magnesium  or  calcium 
sulphate,  1  Ib.  of  barium  hydrate  performs  the  work  of  0.33  Ib.  of  lime 
plus  0.62  Ib.  of  soda-ash,  and  the  lime  treatment  can  be  correspondingly 
reduced. 

Barium  hydrate  has  no  advantage  over  lime  as  a  reagent  to  precipitate 
the  carbonates  of  lime  and  magnesia  and  should  not  be  considered  except 
in  connection  with  the  treating  of  water  containing  calcium  sulphate. 


HYDRAULICS  -FLOW  OF  WATER. 

Formulae  for  Discharge  of  Water  through  Orifices  and  Weirs.  — 

For  rectangular  or  circular  orifices,  with  the  head  measured  from  center 
of  the  orifice  to  the  surface  of  the  still  water  in  the  feeding  reservoir: 

Q  =  c  ^2gHX  a (1) 

For  weirs  with  no  allowance  for  increased  head  due  to  velocity  of 
approach: 

Q  =  C2/sV2gHXLH (2) 

For  rectangular  and  circular  or  other  shaped  vertical  or  inclined  orifices: 
formula  based  on  the  proposition  that  each  successive  horizontal  layer  of 
water  passing  through  the  orifice  has  a  velocity  due  to  its  respective 
head: 

Q 
For  rectangular  vertical  weirsj 

Q  =  C2/3V20#XZ,/? (4) 

Q  =  quantity  of  water  discharged  in  cubic  feet  per  second;  C  =  ap- 
proximate coefficient  for  formulas  (1)  and  (2):  c  =  correct  coefficient 
for  (3)  and  (4). 

Values  of  the  coefficients  c  and  C  are  given  below. 

g  =  32.16;  *^2g  =  8.02;  H  =»  head  in  feet  measured  from  center  of 
orifice  to  level  of  still  water;  #5  =  head  measured  from  bottom  of 
orifice;  HI  =»  head  measured  from  top  of  orifice;  h  =  H,  corrected  for 
velocity  of  approach,  Va  «  H  +  1.33  Vaz/2  g  for  weirs  with  no  end  con- 
traction, and  H  +  1.4  V02/2  g  for  weirs  with  end  contraction;  a*  area  in 
square  feet;  L -length  in  feet, 


HYDRAULICS. 


727 


Flow  of  Water  from  Orifices.  —  The  theoretical  velocity  of  water 
flowing  from  an  orifice  is  the  same  as  the  velocity  of  a  falling  body  which 
has  fallen  from  a  height  equal  to  the  head  of  water,  =  */2  gll.  The 
actual  velocity  at  the  smaller  section  of  the  vena  contracta  is  substan- 
tially the  same  as  the  theoretical,  but  the  velocity  at  the  plane  of  the 
orifice  is  C  ^2  gH,  in  which  the  coefficient  C  has  the  nearly  constant 
value  of  0.62.  The  smallest  diameter  of  the  vena  contracta  is  therefore 
about  0.79  of  that  of  the  orifice.  If  C  be  the  approximate  coefficient 
=  0.62,  and  c  the  correct  coefficient,  the  ratio  C/c  varies  with  different 
ratios  of  the  head  to  the  diameter  of  the  vertical  orifice,  or  toH/D.  Ham- 
ilton Smith,  Jr.,  gives  the  following: 

H/D  =  0.5          0.875  1.  1.5  2.  2.5  5.         10. 

C/c    =0.9604    0.9849     0.9918     0.9965     0.9980     0.9987     0.9997     1. 

For  vertical  rectangular  orifices  of  ratio  of  head  to  width  W; 
ForH/W=     0.5       0.6        0.8       1         1.5       2.          3.        4.         5.       8. 
C/c  =  .9428  .9657  .9823  .9890  .9953  .9974  .9988  .9993  .9996  .9998 

For  H  •*•  D  or  H  -f-  W  over  8,  C  =  c,  practically. 

For  great  heads,  312  ft.  to  336  ft.,  with  converging  mouthpieces,  c 
has  a  value  of  about  one,  and  for  small  circular  orifices  in  thin  plates, 
with  full  contraction,  c  =  about  0.60. 

Mr.  Smith  as  the  result  of  the  collation  of  many  experimental  data  of 
others  as  well  as  hi's  own,  gives  tables  of  the  value  of  c  for  vertical  orifices, 
with  full  contraction,  with  a  free  discharge  into  the  air,  with  the  inner 
face  of  the  plate,  in  which  the  orifice  is  pierced,  plane,  and  with  sharp 
inner  corners,  so  that  the  escaping  vein  only  touches  these  inner  edges. 
These  tables  are  abridged  below.  The  coefficient  c  is  to  be  used  in  the 
formulae  (3)  and  (4)  above.  For  formulae  (1)  and  (2)  use  the  coefficient 
C  found  from  the  values  of  the  ratios  C/c  above. 


Values  of  Coefficient  c  for  Vertical  Orifices  with  Sharp  Edges, 
Full  Contraction,  and  Free  Discharge  into  Air.  (Hamilton 
Smith,  Jr.) 


Head  from 
Center  of 
Orifice  H. 

Square  Orifices.    Length  of  the  Side  of  the  Square,  in  feet. 

07 

03 

04 

05 

07 

.10 

.12 

.15 

.20 

.40 

.60 

.80 

1.0 

0.4 
0.6 
1.0 
3.0 
6.0 
10 

643 

637 

628 

621 

616 

.611 

.660 
.648 
.632 
.623 
616 

.645 
.636 
.622 
.616 
611 

.636 
.628 
.616 

.630 
.622 
.612 

.623 
.618 
.609 

.617 
.613 
607 

.613 
.610 
606 

.610 
.608 
.606 

.605 
.605 
.605 

.601 
.603 
605 

.598 
.601 
604 

.596 
.600 
.603 

'!599 
60^ 

.612 
608 

.609 
.606 

.607 
605 

.605 
604 

.605 
.604 

.605 
.603 

.604 
.603 

.604 
.603 

.603 
.602 

.602 
.602 

.602 
601 

20. 
100.  (?) 

.606 
.599 

.605 
.598 

.604 
.598 

.603 
.598 

.602 
.598 

.602 
.598 

.602 
.598 

.602 
.598 

.602 
.598 

.601 
.598 

.601 
.598 

.601 
.598 

.600 
.598 

Circular  Orifices.    Diameters,  in  feet. 


H. 

0? 

03 

04 

05 

07 

10 

1? 

15 

70 

40 

60 

.80 

1.0 

0.4 

637 

67.8 

618 

,612 

.606 

0.6 

.655 

.640 

.630 

.624 

.618 

.613 

.609 

.605 

.601 

.596 

.593 

.590 

1.0 

644 

,631 

67.3 

617 

617. 

,608 

,605 

603 

600 

.598 

.595 

.593 

.591 

2. 

.632 

.621 

.614 

.610 

.607 

.604 

.601 

.600 

.599 

.599 

.597 

.596 

.595 

4. 

67.3 

614 

609 

605 

603 

607, 

600 

,599 

.599 

.598 

.597 

.597 

.596 

6. 

.618 

.611 

.607 

.604 

607. 

.600 

.599 

.599 

.598 

.598 

.597 

.596 

.596 

10. 

611 

606 

603 

601 

.599 

598 

.598 

.597 

.597 

.597 

.596 

,596 

.595 

20. 

601 

600 

599 

598 

597 

596 

596 

596 

596 

596 

,596 

.595 

.594 

50.(?) 

,596 

596 

595 

,595 

594 

.594 

.594 

.594 

.594 

.594 

.594 

.593 

.593 

100.  (?) 

.593 

.593 

.592 

.592 

.592 

.592 

.592 

.592 

.592 

.592 

.592 

.592 

.592 

728  HYDRAULICS, 


HYDRAULIC  FORMULA.  —  FLOW  OF  WATER  IN  OPEN  AND 
CLOSED    CHANNELS. 

Flow  of  Water  in  Pipes.  —  The  quantity  of  water  discharged 
through  a  pipe  depends  on  the  "head";  that  is,  the  vertical  distance 
between  the  level  surface  of  still  water  in  the  chamber  at  the  entrance 
end  of  the  pipe  and  the  level  of  the  center  of  the  discharge  end  of  the 
pipe;  also  upon  the  length  of  the  pipe,  upon  the  character  of  its  interior 
surface  as  to  smoothness,  and  upon  the  number  and  sharpness  of  the 
bends;  but  it  is  independent  of  the  position  of  the  pipe,  as  horizontal, 
or  inclined  upwards  or  downwards. 

The  head,  instead  of  being  an  actual  distance  between  levels,  may  be 
caused  by  pressure,  as  by  a  pump,  in  which  case  the  head  is  calculated 
as  a  vertical  distance  corresponding  to  the  pressure,  1  Ib.  per  sq.  in. 
=  2.309  ft.  head,  or  1  ft.  head  =  0.433  Ib.  per  sq.  in. 

The  total  head  operating  to  cause  flow  is  divided  into  three  parts: 

1.  The  velocity-head,  which  is  the  height  through  which  a  body  must 
fall  in  vacuo  to  acquire  the  velocity  with  which  the  water  flows  into  the 
pipe  =  vz  -f-  2  g,  in  which  v  is  the  velocity  in  ft.  per  sec.  and  2  g  =  64.32; 

2.  the  entry-head,  that  required  to  overcome  the  resistance  to  entrance 
to  the  pipe.     With  sharp-edged  entrance  the  entry-head  =  about  1/2  the 
velocity-head;    with  smooth  rounded  entrance  the  entry-head  is  inap- 
preciable;   3.   the  friction-head,  due  to  the  frictional  resistance  to  flow 
within  the  pipe. 

In  ordinary  cases  of  pipes  of  considerable  length  the  sum  of  the  entry 
and  velocity  heads  required  scarcely  exceeds  1  foot.  In  the  case  of 
long  pipes  with  low  heads  the  sum  of  the  velocity  and  entry  heads  is 
generally  so  small  that  it  may  be  neglected. 

General  Formula  for  Flow  of  Water  in  Pipes  or  Conduits. 

Mean  velocity  in  ft.  per  sec.  =  c  v'mean  hydraulic  radius  X  slope 


Do.  for  pipes  running  full  -  c  ydlameter  x  slope, 

in  which  c  is  a  coefficient  determined  by  experiment.  (See  pages  following.) 

area  of  wet  cross-section 


The  mean  hydraulic-  radius 


wet  perimeter 


In  pipes  running  full,  or  exactly  half  full,  and  in  semicircular  open 
channels,  running  full  it  is  equal  to  1/4  diameter. 

The  slope  =  the  head  (or  pressure  expressed  as  a  head,  in  feet) 

•*•  length  of  pipe  measured  in  a  straight  line  from  end  to  end. 

In  open  channels  the  slope  is  the  actual  slope  of  the  surface,  or  its 
fall  per  unit  of  length,  or  the  sine  of  the  angle  of  the  slope  with  the  horizon. 


Chezy's     Formula:      v  =  c  *^r  V    =  c  ^rs;     r  =  mean     hydraulic 
idius,  s  =  slope  =  '       *       * 
dimensions  in  feet. 


radius,  s  =  slope  =  head  -s-  length,  v  =  velocity  in  feet  per  second,  all 
-'--i  fee" 


Quantity  of  Water  Discharged.  —  If  Q  —  discharge  in  cubic  feet 
per  second  and  a  =  area  of  channel,  Q  =  av  =  ac  v'rs. 


mu 
and 
one  completely  filled. 

Values  of  the  Coefficient  c.     (Chiefly  condensed  from  P.  J.  Flynn 
in  Flow  of  Water.)  —  Almost  all  the  old  hydraulic  formulae  for  finding  the 


HYDRAULIC   FORMULAE. 


729 


mean  velocity  in  open  and  closed  channels  have  constant  coefficients, 
and  are  therefore  correct  for  only  a  small  range  of  channels.  They 
have  often  been  found  to  give  incorrect  results  with  disastrous  effects. 
Ganguillet  and  Kutter  thoroughly  investigated  the  American,  French, 
and  other  experiments,  and  they  gave  as  the  result  of  their  labors  the 
formula  now  generally  known  as  Kutter's  formula.  There  are  so  many 
varying  conditions  affecting  the  flow  of  water,  that  all  hydraulic  for- 
mulae are  only  approximations  to  the  correct  result. 

When  the  surface-slope  measurement  is  good,  Kutter's  formula  will 
give  results  seldom  exceeding  71/2%  error,  provided  the  rugosity  co- 
efficient of  the  formula  is  known  for  the  site.  For  small  open  channels 
Darcy's  and  Bazin's  formulae,  and  for  cast-iron  pipes  Darcy's  formulas, 
are  generally  accepted  as  being  approximately  correct. 

Table  giving  Fall  in  Feet  per  Mile,  the  Distance  on  Slope  corresponding 
to  1  Ft.  Fall,  the  Fall  in  1000  Ft.,  the  Equivalent  Loss  in  Pressure 
in  Pipes  per  1000_Ft.  Length;  also  Values  of  VTfor  Use  in  the 
Formula  v  =  c  \/rs~. ' 

s  =  H  -5-  L  =  sine  of  angle  of  slope  =  fall  of  water  surface  (Jf)     • 
in  any  distance  (L)  divided  by  that  distance. 


Loss  of 

Loss  of 

Fall 

Slope, 

Pres- 

Fall 

Slope, 

Pres- 

in 
Feet 
per 

S,0Fpe, 
In 

Feet 
per 
1000. 

sure  per 
1000 
Feet. 

VT 

in 
Feet 
per 

Slope, 
IFt. 
In 

Feet 
1000. 

sure  per 
1000 
Feet. 

vT 

Mile. 

Lb.   per 

Mile. 

Lb.  per 

sq.  in. 

sq.  in. 

0.25 

21120ft. 

0.0473 

0.02048 

0.00688 

20 

264  ft. 

3.7879 

1.640 

0.06155 

.30 

17600 

.0568 

.02459 

.00754 

21.12 

250 

4.0000 

1.732 

.06325 

.40 

13200 

.0758 

.03282 

.00870 

22 

1240 

4.1667 

1.804 

.06455 

.50 

10560 

.0947 

.04101 

.00973 

24 

220 

4.5455 

1.968 

.06742 

.60 

8800 

.1136 

.04919 

.01066 

26.4 

200 

5.0000 

2.165 

.07071 

.80 

6600 

.1515 

.06560 

.01231 

28 

188.6 

5.3030 

2.296 

.07282 

1 

5280 

.1894 

.08201 

.01376 

31.68 

166.7 

6.0000 

2.598 

.07746 

1.056 

5000 

.2000 

.08660 

.01414 

35.20 

150 

6.6667 

2.887 

.08165 

1.25 

4224 

.2367 

.1025 

.01539 

42.24 

125 

8.0000 

3.464 

.08944 

1.5 

3520 

.2841 

.1230 

.01685 

44 

120 

8.3333 

3.608 

.09129 

1.75 

3017 

.3314 

.1435 

.01821 

48 

110 

9.0909 

3.936 

.09535 

2 

2640 

.3788 

.1640 

.01946 

52.8 

100    . 

10.000 

4.330 

.10000 

2.5 

2112 

.4735 

.2050 

.02176 

60 

88 

11.364 

4.913 

.10660 

2.64 

2000 

.5000 

.2165 

.02236 

63.36 

83.3 

12.000 

5.196 

.10954 

3 

1760 

.5632 

.2460 

.02384 

66 

83 

12.500 

5.413 

.11180 

3.5 

1508 

.6631 

.2871 

.02575 

70.4 

75 

13.333 

5.773 

.11547 

4 

1320 

.7576 

.3280 

.02752 

79.20 

66.7 

15.000 

6.495 

.12247 

5 

1056 

.9470 

.4101 

.03077 

88 

60 

16.667 

7.217 

.12910 

5.28 

1000 

.0000 

.4330 

.03162 

105.6 

50 

20.000 

8.660 

.14142 

6 

880 

.1364 

.4921 

.03371 

120 

44 

22.727 

9.841 

.15076 

7 

754.3 

.3257 

.5740 

.03642 

132 

40 

25.000 

10.83 

.15811 

8 

660 

.5152 

.6561 

.03893 

160 

33 

30.303 

13.12 

.17408 

9 

586.6 

.7044 

.7380 

.04129 

220 

24 

41.667 

18.04 

.20412 

10 

528 

.8939 

.8201 

.04352 

264 

20 

50.000 

21.65 

.22361 

10.56 

500 

2.0000 

.8660 

.04472 

330 

16 

62.500 

27.06 

.25000 

12 

440 

2.2727 

.9841 

.04767 

440 

12 

83.333 

36.08 

.28868 

13 

406.1 

2.4621 

1.066 

.04962 

528 

10 

100.00 

43.30 

.31623 

14 

377.1 

2.6515 

1.148 

.05149 

660 

8 

125.00 

54.13 

.35355 

15 

352 

2.8409 

1.230 

.05330 

880 

6 

166.67 

72.17 

.40825 

16 

330 

3.0303 

1.312 

.05505 

1056 

5 

200 

86.60 

.44721 

18 

293.3 

3.4091 

1.476 

.05839 

1320 

4 

250 

108.25 

.50000 

730 


HYDRAULICS. 


Values  of  Vr"  for  Circular  Pipes,  Sewers,  and  Conduits  of  Different 
Diameters. 


r  =  mean  hydraulic  depth  = 
funning  full  or  exactly  half  full. 


p^Hmeter 


=  1/4  diam*  for  circular 


Diam., 
ft.  in. 

V7 

In  Feet. 

Diam., 
ft.  in. 

Vr 
in  Feet. 

Diam., 
ft.  in. 

V7 

in  Feet. 

Diam., 
ft.  in. 

v; 

in  Feet. 

3/8 

0.088 

2 

0.707 

4      6 

.061 

9 

.500 

1/2 

.102 

2      1 

.722 

4      7 

.070 

9    3 

.521 

3/4 

.125 

2      2 

.736 

4      8 

.080 

9    6 

.541 

1 

.144 

2      3 

.750 

4      9 

.089 

9    9 

.561 

H/4 

.161 

2      4 

.764 

4    10 

.099 

10 

.581 

U/2 

.177 

2      5 

.777 

4    11 

.109 

10    3 

.601 

13/4 

.191 

2      6 

.790 

5 

.118 

10    6 

.620 

•  2 

.204 

2      7 

.804 

5      1 

.127 

10    9 

.639 

21/2 

.228 

2      8 

.817 

5     2 

.137 

11 

.658 

3 

.251 

2      9 

.829 

5      3 

.146 

11     3 

.677 

4 

.290 

2    10 

.842 

5      4 

.155 

11     6 

.696 

5 

.323 

2    11 

.854 

5      5 

.164 

11     9 

.714 

6 

.354 

3 

.866 

5      6 

.173 

12 

.732 

7 

.382 

3      1 

.878 

5      7 

.181 

12    3 

.750 

8 

.408 

3      2 

.890 

5      8 

.190 

12    6 

.768 

9 

.433 

3      3 

.901 

5      9 

.199 

12    9 

.785 

10 

.456 

3      4 

.913 

5    10 

.208 

13 

,803 

11 

.479 

3      5 

.924 

5    11 

.216 

13    3 

.820 

.500 

3      6 

.935 

6 

.225 

13    6 

.837 

| 

.520 

3      7 

.946 

6      3 

.250 

14 

.871 

2 

.540 

3      8 

.957 

6      6 

.275 

14    6 

.904 

3 

.559 

3      9 

.968 

6     9 

.299 

15 

.936 

4 

.577 

3    10 

.979 

7 

.323 

15    6 

.968 

5 

.595 

3    11 

.990 

7     3 

.346 

16 

2. 

6 

.612 

4 

7     6 

.369 

16    6 

2  031 

7 

.629 

4      1 

!oio 

7     9 

.392 

17 

2.061 

8 

.646 

4     2 

.021 

8 

.414 

17    6 

2.091 

9 

.661 

4     3 

.031 

8     3 

.436 

18 

2.121 

1   10 

.677 

4     4 

.041 

8     6 

.458 

19 

2.180 

1  11 

.692 

4     5 

.051 

8     9 

.479 

20 

2.236 

Kutter's  Formula  for  measures  in  feet  is 


1.811 


+  41.6  + 


0.00281 


1+(41.6+M0281)X    « 
\  S        /       Vi 


a 


in  which  v  =  mean  velocity  in  feet  per  second ;  r  =  -  =  hydraulic  mean 

depth  in  feet  =  area  of  cross-section  in  square  feet  divided  by  wetted 
perimeter  in  lineal  feet ;  s  =  fall  of  water-surface  (/i)  in  any  distance  (I) 

divided  by  that  distance,  =  r»=  sine  of  slope;  n  =  the  coefficient  of 

rugosity,  depending  on  the  nature  of  the  lining  or  surface  of  the  channel. 
If  we  let  the  first  term  of  the  right-hand  side  of  the  equation  equal  c,  we 
have  Chezy's  formula,  v  —  c  vVs  =  c  X  ^/rX  Vs. 

Values  of  n  in  Kutter's  Formula.  —  The  accuracy  of  Kutter's  for- 
mula depends,  in  a  great  measure,  on  the  proper  selection  of  the  coefficient 


HYDRAULIC   FORMULAE.  731 

of  roughness  n.  Experience  is  required  in  order  to  give  the  right  value  to 
this  coefficient,  and  to  this  end  great  assistance  can  be  obtained,  in  making 
this  selection,  by  consulting  and  comparing  the  results  obtained  from 
experiments  on  the  flow  of  water  already  made  in  different  channels. 

In  some  cases  it  would  be  well  to  provide  for  the  contingency  of  future 
deterioration  of  channel,  by  selecting  a  high  value  of  rc,  as,  for  instance, 
where  a  dense  growth  of  weeds  is  likely  to  occur  in  small  channels,  and 
also  where  channels  are  likely  not  to  be  kept  in  a  state  of  good  repair. 

The  following  table,  giving  the  value  of  n  for  different  materials,  is 
compiled  from  Kutter,  Jackson,  and  Hering,  and  this  value  of  n  applies 
also  in  each  instance  to  the  surfaces  of  other  materials  equally  rough. 

VALUE  OP  n  IN  KUTTER'S  FORMULA  FOR  DIFFERENT  CHANNELS. 

n  —  .009,  well-planed  timber,  in  perfect  order  and  alignment;  otherwise, 
perhaps  .01  would  be  suitable. 

n  =  .010,  plaster  in  pure  cement;  planed  timber;  glazed,  coated,  or 
enameled  stoneware  and  iron  pipes;  glazed  surfaces  of  every  sort  in 
perfect  order. 

n  =  .011,  plaster  in  cement  with  one-third  sand,  in  good  condition; 
also  for  iron,  cement,  and  terra-cotta  pipes,  well  joined,  and  in  best  order. 

n  =  .012,  unplaned  timber,  when  perfectly  continuous  on  the  inside; 
flumes. 

n  =  .013,  ashlar  and  well-laid  brickwork;  ordinary  metal;  earthen  and 
stoneware  pipe  in  good  condition,  but  not  new;  cement  and  terra-cotta 
pipe  not  well  jointed  nor  in  perfect  order,  plaster  and  planed  wood  in  • 
imperfect  or  inferior  condition;  and,  generally,  the  materials  mentioned 
with  n  =  .010,  when  in  imperfect  or  inferior  condition. 

n  =  .015,  second  class  or  rough-faced  brickwork;  well-dressed  stone- 
work; foul  and  slightly  tuberculated  iron;  cement  and  terra-cotta  pipes, 
with  imperfect  joints  and  in  bad  order;  and  canvas  lining  on  wooden 
frames. 

n  —  .017,  brickwork,  ashlar,  and  stoneware  in  an  inferior  condition; 
tuberculated  iron  pipes;  rubble  in  cement  or  plaster  in  good  order;  tine 
gravel,  well  rammed,  Vs  to  2/3  inch  diameter;  and,  generally,  the  materials 
mentioned  with  n  =  .013  when  in  bad  order  and  condition. 

n  =  .020,  rubble  in  cement  in  an  inferior  condition;  coarse  rubble, 
rough  set  in  a  normal  condition;  coarse  rubble  set  dry:  ruined  brickwork 
and  masonry;  coarse  gravel  well  rammed,  from  1  to  11/3  inch  diameter; 
canals  with  beds  and  banks  of  very  firm,  regular  gravel,  carefully  trimmed 
and  rammed  in  defective  places;  rough  rubble  with  bed*partially  covered 
with  silt  and  mud;  rectangular  wooden  troughs  with  battens  on  the 
inside  two  inches  apart;  trimmed  earth  in  perfect  order. 

n  =  .0225,  canals  in  earth  above  the  average  in  order  and  regimen. 

n  =  .025,  canals  and  rivers  in  earth  of  tolerably  uniform  cross-section; 
slope  and  direction,  in  moderately  good  order  and  regimen,  and  free  from 
stones  and  weeds. 

n  =  .0275,  canals  and  rivers  in  earth  below  the  average  in  order  and 
regimen. 

n  =  .030,  canals  and  rivers  in  earth  in  rather  bad  order  and  regimen, 
having  stones  and  weeds  occasionally,  and  obstructed  by  detritus. 

n  =  .035,  suitable  for  rivers  and  canals  with  earthen  beds  in  bad  order 
and  regimen,  and  having  stones  and  weeds  in  great  quantities. 

n  =  .05,  torrents  encumbered  with  detritus. 

Kutter's  formula  has  the  advantage  of  being  easily  adapted  to  a  change 
in  the  surface  of  the  pipe  exposed  to  the  flow  of  water,  by  a  change  in 
the  value  of  n.  For  cast-iron  pipes  it  is  usual  to  use  n  =  .013  to  provide 
for  the  future  deterioration  of  the  surface.  _  __ 

Reducing  Kutter's  formula  to  the  form  v  =  c  X  **r  X  ^s,  and  taking 
n,  the  coefficient  of  roughness  in  the  formula,  =  .011,  .012,  and  .013,  and 
a  =  .001,  we  have  the  following  values  of  the  coefficient  c  of  different 
diameters  of  conduit. 


732 


HYDRAULICS. 


Values  of  c  in  Formula  *  =  e  X  vVx  ^s~toT  Metal  Pipes  and 
Moderately  Smooth  Conduits  Generally. 

By  KUTTER'S  FORMULA,     (s  =0.001  or  greater.) 


Diameter. 

n  =  .OI1 

n=.0l2 

n  =  .013 

Diameter. 

n  =  .011 

n  =  .0)2 

n  =.013 

ft.     in. 

c  = 

c  = 

c  = 

ft. 

c  = 

c  = 

c  = 

0       6 

87.4 

77.5 

69.5 

8 

155.4 

141.9 

130.4 

1 

105.7 

94.6 

85.3 

9 

157.7 

144.1 

132.7 

1        6 

116.1 

104.3 

94.4 

10 

159.7 

146 

134.5 

2 

123.6 

111.3 

101.1 

11 

161.5 

147.8 

136.2 

3 

133.6 

120.8 

110.1 

12 

163 

149.3 

137.7 

4 

140.4 

127.4 

116.5 

14 

165.8 

152 

140.4 

5 

145.4 

132.3 

121.1 

16 

168 

154.2 

142.1 

6 

149.4 

136.1 

124.8 

18 

169.9 

156.1 

144.4 

7 

152.7 

139.2 

127.9 

20 

171.6 

157.7 

146 

For  circular  pipes  the  hydraulic  mean  depth  r  equals  1/4  of  the 
diameter. 

According  to  Kutter's  formula  the  value  of  c,  the  coefficient  of 
discharge,  is  the  same  for  all  slopes  greater  than  1  in  1000.  At  a 
slope  of  1  in  5000  the  value  of  c  is  slightly  lower,  and  it  further 
decreases  as  the  slope  becomes  flatter. 

The  reliability  of  the  values  of  the  coefficient  of  Kutter's  formula  for 
pipes  of  less  than  6  in.  diameter  is  considered  doubtful. 

Values  of  c  ror  Earthen  Channels,  by  Kutter's  Formula,  for  Use 
in  Formula  v  =  c  vV*. 


Coefficient  of  Roughness, 

Coefficient  of  Roughness, 

n=.0225. 

n=.035. 

>/r  in  feet. 

V^  in  feet. 

0.4 

1.0 

1.8 

2.5 

4.0 

0.4 

1  .0 

1.8 

2.5    I   4.0 

Slope,  1  in 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c 

1,000 

35.7 

62.5 

80.3 

89.2 

99.9 

19.7 

37.6 

51.6 

59.3 

69  2 

1,250 

35.5 

62.3 

80.3 

89.3 

100.2 

19.6 

37.6 

51.6 

59.4 

69  4 

1,667 

35.2 

62.1 

80.3 

89.5 

100.6 

19.4 

37.4 

51.6 

59.5 

69  8 

2,500 

34.6 

61.7 

80.3 

89.8 

101.4 

19.1 

37.1 

51.6 

59.7 

70  4 

3333 

34. 

61.2 

80.3 

90.1 

102.2 

18.8 

36.9 

51.6 

59.9 

71.0 

5,000 

33. 

60.5 

80.3 

90.7 

103.7 

18.3 

36.4 

51.6 

60.4 

7?  ? 

7,500 

31.6 

59.4 

80.3 

91.5 

106.0 

17.6 

35.8 

51.6 

60.9 

73  9 

10,000 

30.5 

58.5 

80.3 

92.3 

107.9 

17.1 

35.3 

51.6 

60.5 

75  4 

15,840 

28.5 

56.7 

80.2 

93.9 

112.2 

16.2 

34.3 

51.6 

62.5 

78  6 

20,000 

27.4 

55.7 

80.2 

94.8 

115.0 

15.6 

33.8 

51.5 

63.1 

80.6 

Darcy's  Formula   for  clean  iron  pipes  under  pressure  is 

rs )  1/2 

v=  )     '  ,  ,  0.00000162 


0.00007726  + 

According  to  Unwin  and  other  authors   Darcy's  experiments  are 
represented  approximately  by  the  formula 


in  which/,  called  the  "coefficient  of  friction,"  =0.006  I  1  +~[2d ) '  ^ 

being  the  loss  of  head,  I  the  length  of  the  pipe,  h/l  the  slope  s,  and 
d/4  the  mean  hydraulic  radius  r,  of  the  Chezy  formula.  All  the  dimen- 
sions are  in  feet. 

Darcy's  formula,  as  given  by  J.  B.  Francis,  for  old  cast-iron  pipe, 
lined  with  deposit  and  under  pressure  is 

/          144d2s  \l/2 

=1 . .  .  .          I     . 


in  which  d 


V0,00082(12«f+l)/ 

= diameter  in  feet. 


HYDRAULIC  FORMULA. 


733 


.s 

•d 


i 


E    . 


P^ 


ffi 


t  —  fno*  —  CO  —  c 


or^sO^  —  o 

~ 


O  O  o  o  O  o  O  O  —  —  '  —  '  —  '  ~  —  '  < 


~ 


500 r 


—  ~ * 

8OOOO  —  —  (NC^ro, 
OOOOOOOOO 


-o^rris 
OON^O'OO^<^rOOvO<N<NQ^IsN  —  '^J-O'^-^ 


—  i fS 


50000 — — — r 


qqq 
2606 


734 


HYDRAULICS. 


The  relation  of  the  value  of  c  in  Chezy's  formula  V  •• 
value  of  the  coefficient  of  friction /is  c  •• 


to  the 


/  = 

.0035 

.0040 

.0045 

.0050 

.0055 

.0060 

.0065 

135.5 

127.8 

119.6 

113.4 

108.1 

,  103.5 

99.4 

/  = 

.0070 

.0075 

.0080 

.0090 

.010 

.011 

.012 

C  = 

95.8 

92.6 

89.7 

84.5 

80.2 

76.5 

73.2 

c  = 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

/7r 

.018 

,^,T;^ 

.013 

rl  K*~l-r-r^r 

.010  . 

*  -4-V,^  -P^l 

008  .0064 

.0053 

.0045 

^»^  4.V,«  1 

.0038  . 

0033  .002 

.  .  _____     ._„     ._     ., 

Unwin  derives  the  following  equations  from  the  Darcy  formula: 

Velocity,  ft.  per  sec  ......    v  =  4.012  ^dh/(fl)  =  1.273  _£/d2=  c 

Diameter,  ft  .............    d=  Q.QG22fvl/h  =  1.128  ^Q/v. 

Quantity,  cu.  ft.  per  sec.  Q=  3.149  ^/htf/fl. 
Head,  ft  .................  h  =  O.WQ8fQH/d&. 

Rough  preliminary  calculations  may  be  made  by  the  following  approx- 
imate formulae.    They  are  least  accurate  for  small  pipes,    s  =  slope,  =  h/l. 
New  and  clean  pipes.  Old  and  incrusted  pipes. 

v  =  56 
Q  =  44     rfss.  Q  =  31.4 


d  =  0. 


d  =  0. 


Weisbach  gives/ =0.00644,  which  Unwin  says  is  possibly  too  small 
for  tubes  of  small  bore,  and  he  gives/ =0.006  to  0.01  for  4-in.  tubes 
and/  =0.0084  to  0.012  for  2-in.  tubes.  Another  formula  by  Weisbach  is 

,  0.01716W  j?2 
}d  2g 

William  Cox  (Amer.  Mach.,  Dec.  28,  1893)  gives  a  simpler  formula 
which  gives  almost  identical  results: 


h=  (0.0144  +- 


H  =  friction-head  in  feet  =  -v-  - 
d 

4V2_j_  5V_  2 


(!) 


V  in 


(2) 
feet 


Hd  : 
L  1200 

In  this  formula  H  and  L  are  in  feet,  d  in  inches,  and 
per  second. 

Values  of  the  Coefficient  of  Friction.  Un  win's  "Hydraulics"  gives 
values  of/,  based  on  Darcy  's  experiments,  as  follows:  Clean  and  smooth 
pipes,  /=  0.005  [1  +  l/(12d)].  Incrusted  pipes,  /=  O.Oiqi  +  l/(12d)]. 
In  1886  Unwin  examined  all  the  more  carefully  made  experiments  on 
flow  in  pipes,  including  those  of  Darcy,  classifying  them  according  to 
the  quality  and  condition  of  their  surfaces,  and  showing  the  relation 
of  the  value  of  /  to  both  diameter  and  velocity.  The  results  agree 
fairly  closely  with  the  following  values,  /=  a  (1  +  P/d).  (d  is  in  feet.) 


Kind  of  Pipe. 

Values  of  a  for  Velocities  in  ft.  per  Second. 

Values 
of  /3 

Drawn  wought  iron  
Asphalted  cast  iron  
Clean  cast  iron  
Incrusted  cast  iron  at  all  ^ 

1-2 
.00375 
.00492 
.00405 
velocities  a 

2-3 

.00322 
.00455 
.00395 
=  0.0085* 

3-4 
.00297 
.00432 
.00387 

4-5 
.00275 
.00415 
.00382 

0.37 
0.20 
0.28 
0.26 

From  the  experiments  of  Clemens  Herschel,  1892-6,  on  clean  steel 

riveted  pipes,   Unwin  derives  the  following  values  of  /  for  different 
velocities. 

2  34  5  6 

OOGO      .0057      .0055  .0055      .0055 

0058      .0054      .0054  .0054      .0054 

.0071      .0060      .0053  .0047      .0042 


Ft.  per  sec 1 

48-in.  pipe,  av.  of  2 0066 

42-in.  pipe,  av.  of  2 0067 

36-in.  pipe 0087 


Unwin  attributes  the  anomalies  in  this  table  to  errors  of  observation. 
In  comparing  the  results  with  those  on  cast-iron  pipes,  the  roughness  of 
the  rivet  heads  and  joints  must  be  considered,  and  the  resistance  can 
only  be  determined  by  direct  experiment  on  riveted  pipes. 


HYDRAULIC   FORMULA. 


735 


Two  portions  of  the  48-in.  main  were  tested  after  being  four  years  in 
i  use,  and  the  coefficients  derived  from  them  differ  remarkably. 

Ft.  per  sec 1  2  3  4  5  6 

Upper  part 0106       .0080       .0075       .0073       .0072          .0072 

Lower  part 0068       .0060       .0058       .0060       .0060         .0060 

Marx,  Wing,  and  Hopkins  in  1897  and  1899  made  gaugings  on  a  6-ft. 
main,  part  of  which  was  of  riveted  steel  and  part  of  wood  staves.  (Trans. 
A.  S.  C.  E.,  xl,  471,  and  xliv,  34.)  From  these  tests  Unwin  derives  the 
following  values  of/. 

Ft.  per  sec.      1  1.5  2  2.5  3  4  5  5.5 

Steel  pipe: 

1897... /  =  .0053      .0052      .0053      .0055      .0055      .0052      

1899... /==  .0097      .0076      .0067      .0063      .0061      .0060      .0058      .0058 

Wood  staves: 

1897.  ../=  .0064      .0053      .0048      ......      .0043      .0041      ... 

1899..  ./=  .0048      .0046      .0045      0044      .0043      .0043      .0043 

Freeman's  experiments  on  fire  hose  pipes  (Trans.  A.  S.  C.  Ef,  xxi,  303) 
give  the  following  values  of/. 

Velocity,  ft.  per  sec 4  6  10  15  20 

Unlined  canvas 0095     .0095     .0093     .0088     .0085 

Rough  rubber-lined  cotton 0078      .0078     .0078     .0075      .0073 

Smooth  rubber-lined  cotton 0060     .0058     .0055     .0048     .0045 

The  Resistance  at  the  Inlet  of  a  Pipe  is  equal  to  the  frictional  resist- 
ance of  a  straight  pipe  whose  length  is  10  =  (1  +/o)  d  •*•  4  /.  Values  of /0  are: 
(A)  for  end  of  pipe  flush  with  reservoir  wall,  0.5;  (B)  pipe  entering  wall, 
straight  edges,  0.56;  (C)  pipe  entering  wall,  sharp  edges,  1.30;  (D)  bell- 
mouthed  inlet,  0.02  to  0.05.  Values  of  lQ/d  are  for 

/=  0.005  4,53  £,75  C,  78  D,  115 

0.010  26  38  39  58 

Multiplying  these  figures  by  d  gives  the  length  of  straight  pipe  to  be 
added  to  the  actual  length  to  allow  for  the  inlet  resistance.  In  long 
lengths  of  pipe  the  relative  value  of  this  length  is  so  small  that  it  may  be 
neglected  in  practical  calculations.  —  (Unwin.) 

Loss  of  Head  in  Pipe  by  Friction.  —  Loss  of  head  by  friction  in 
each  100  feet  in  length  of  riveted  pipe  when  discharging  the  following 
quantities  of  water  per  minute  (Pelton  Water-wheel  Co.). 

V  =  velocity  in  feet  per  second;  h  =  loss  of  head  in  feet;  Q  =  dis- 
charge in  cubic  feet  per  minute. 


Inside  Diameter  of  Pipe  in  Inches. 


V 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 

7 

8 

9 

10 

11 

12 

h  \  Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

0.338 
0.698 
1.175 
1.76 

2.46 
3.26 

32.0 
48.1 
64.1 
80.2 
96.2 
112.0 

0.296 
0.611 
1.027 
1.54 
2.15 
2.85 

41.9 

62.8 
83.7 
105 
125 
146 

0.264 
0.544 
0.913 
1.37 
1.92 
2.52 

53 
79.5 

106 
132 
159 
185 

0.237 

0.488 
0.822 
1.23 
1.71 
2.28 

65.4 
98.2 
131 
163 
196 
229 

0.216 
0.444 
0.747 
1.122 
1.56 
2.07 

79.2 
119 
158 
198 
237 
277 

0.198 
0.407 
0.685 
1.028 
1.43 
1.91 

94.2 
141 
188 
235 
283 
330 

V 

13  in. 

14  in. 

15  in. 

16  in. 

18  in. 

20  in. 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

167 
251 
335 
419 
502 
586 

h 

Q 

h 

Q 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 

0.183 
.375 
.632 
.949 
1.325 
1.75 

110 
166 
221 
276 
332 
387 

0.169 
.349 
.587 
.881 
1.229 
1.63 

128 
192 
256 
321 
385 
449 

0.158 
.325 
.548 
.822 
1.H8 
1.52 

147 
221 
294 
368 
442 
515 

0.147 
.306 
.513 
.770 
1.076 
1.43 

0.132 
.271 
.456 
.685 
.957 
1.27 

212 
318 
424 
530 
636 
742 

0.119 
.245 
.410 
.617 
.861 
1.143 

262 
393 
523 
654 
785 
916 

736 


HYDRAULICS. 


Loss  of  Head  (Continued). 


Diameter  of  Pipe  in  Inches. 

22  in. 

24  in. 

26  in. 

28  in. 

30  in. 

36  in. 

V 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

848 
1273 
1697 
2121 

2545 
2868 

0.108 
.222 
.373 
.561 
.782 
1.040 

316 
475 
633 
792 
950 
1109 

0.098 
.204 
.342 
.513 
.717 
.953 

377 
565 
754 
942 
1131 
1319 

0.091 
.188 
.315 
.474 
.662 
.879 

442 
663 
885 
1106 
1327 
1548 

0.084 
.174 
.293 
.440 
.615 
.817 

513 
770 
1026 
1283 
1539 
1796 

0.079 
.163 
.273 
.411 
.574 
.762 

589 
883 
1178 
1472 
1767 
2061 

0.066 
.135 
.228 
.342 
.479 
.636 

This  table  is  based  on  Cox's  reconstruction  of  Weisbach's  formula, 
using  the  denominator  1000  instead  of  1200,  to  be  on  the  safe  side,  allow- 
ing 20%  for  the  loss  of  head  due  to  the  laps  and  rivet-heads  in  the  pipe. 

EXAMPLE.  — Given  200  ft.  head  and  600  ft.  of  11-inch  pipe,  carrying 
119  cubic  feet  of  water  per  minute.  To  find  effective  head:  In  right- 
hand  column,  under  11-inch  pipe,  find  119  cubic  ft.;  opposite  this  will 
be  found  the  loss  by  friction  in  100  ft.  of  length  for  this  amount  of  water, 
which  is  0.444.  Multiply  this  by  the  number  of  hundred  feet  of  pipe, 
which  is  6,  and  we  have  2.66  ft.,  which  is  the  loss  of  head.  Therefore 
the  effective  head  is  200  -  2.66  =  197.34. 

EXPLANATION.  —  The  loss  of  head  by  friction  in  a  pipe  depends  not 
only  upon  diameter  and  length,  but  upon  the  quantity  of  water  passed 
through  it.  The  head  or  pressure  is  what  would  be  indicated  by  a 
pressure-gauge  attached  to  the  pipe  near  the  wheel.  Readings  of  gauge 
should  be  taken  while  the  water  is  flowing  from  the  nozzle. 

To  reduce  heads  in  feet  to  pressure  in  pounds  multiply  by  0.433.  Ta 
reduce  pounds  pressure  to  feet  multiply  by  2.309. 

Exponential  Formulae.  Williams  and  Hazen's  Tables.  —  From 
Chezy's  formula,  v  =  c  vVs,  it  would  appear  that  the  velocity  varies  as 
the  square  root  of  the  head,  or  that  the  head  varies  as  the  square  of  the 
velocity;  this  is  not  true,  however,  for  c  is  not  a  constant,  but  a  variable, 
depending  on  both  r  and  s.  Hazen  and  Williams,  as  a  result  of  a  study 
of  the  best  records  of  experiments  and  plotting  them  on  logarithmic  ruled 
paper,  found  an  exponential  formula  v  =  cr°'W  s°'54,  in  which  the  coefficient 
c  is  practically  independent  of  the  diameter  and  the  slope,  and  varies  only 
with  the  condition  of  the  surface.  In  order  to  equalize  the  numerical 
value  of  c  to  that  of  the  c  in  the  Chezy  formula,  at  a  slope  of  0.001,  they 
added  the  factor  q.OOl-o-04  to  the  formula,  so  that  the  working  formula 
of  Hazen  and  Williams  is 

v  =  cr0-63  s0-54  O.OOl-o-04  =  1.318  crO-63  s*&. 

APPROXIMATE  VALUES  OF  C  IN  THE  HAZEN  &  WILLIAMS  FORMULA. 
(a)     140  for  the  very  best  cast-iron  pipe,  laid  straight  and  when  new; 
for  very  smooth  and  clean  masonry  conduits; 
for  straight  lead,  copper,  brass,  tin,  and  glass  pipes. 
(6)     130  for  good  new  cast-iron  pipe,  and  other  pipes  under  (a)  when 
not  quite  smooth.* 

(c)  120  for  cast-iron  pipe  5  years  old,  for  smooth  new  iron  pipes, 

smooth  wooden  stave  pipes  and  ordinary  masonry  conduits. 

(d)  110  for  new  riveted  steel  pipe,  for  vitrified  pipe,  and  for  cast-iron 

pipe  10  years  old. 

(e)  100  for  ordinary  iron  pipes,  14  to  20  years  old,  for  riveted  steel 

pipe  10  years  old,  and  for  brick  sewers. 
(/)       80  for  old  iron  pipes,  and  for  very  rough  cast-iron  pipes  over 

60  inches  diameter. 
(g)      60  down  to  40,  for  very  rough  pipes,  the  lower  figure  for  the 

smaller  diameters. 

*  130  may  also  be  used  for  straight  lead,  tin,  and  drawn  copper  pipes. 
Computations  of  the  exponential  formula  are  made  by  logarithms,  or  by 
the  Hazen- Williams  hydraulic  slide  rule.  On  logarithmic  ruled  paper 
values  of  v  for  different  values  of  c,  r  and  s  may  be  plotted  in  straight 
lines.  (See  "Hydraulic  Tables,"  by  Williams  and  Hazen,  John  Wiley  & 
Sons.) 


FLOW  OF  WATER. 


737 


Values  of  Coefficient  K  for  Reducing  the  Hazen  and_Williams 
Formula  to  the  Style  of  Chezy's  Formula  v  =  c  \/r  \/s~ 


Diam., 
Ft.In. 

Slope  =  Head  -v-  Length  of  Pipe. 

0  0005 

0  001 

0  002 

0.003 

0.005 

0.01 

0.02 

0.04 

0.06 

0.10 

0.20 

ri2 

0  2 
0  4 
0  8 
0  12 
2 

8 
12 
16 
20 

0  5374 

0  5525 

0  5680 

0  5773 

0.5892 

0  6058 

0  6228 

0  6403 

0  6508 

0  6642 

0  6829 

.5880 
.6435 
7042 

.6046 
.6616 
7240 

.6216 
.6802 
7443 

.6317 
.6913 
.7565 

.6448 
.7056 
.7721 

.6629 
.7254 
.7938 

.6815 
.7458 
8161 

.7007 
.7667 
8390 

.7122 
.7793 
8528 

.7269 
.7954 
8704 

.7473 
.8177 
8949 

.7706 
.8123 
.8889 
.9727 
1.064 
1.122 
1.165 
1.199 

.7922 
.8351 
.9138 
.000 
.094 
.154 
.197 
.233 

.8145 
.8586 
.9395 
.028 
.125 
.186 
.231 
.267 

.8278 
.8726 
.9549 
1.045 
1.143 
1.205 
1.251 
1.288 

.8449 
.8906 
.9746 
.067 
.167 
.230 
.277 
.315 

.8686 
.9157 
.002 
.096 
.200 
.265 
.313 
.352 

.8931 
.9414 
.030 
.127 
.234 
.300 
.350 
.390 

.9182 
.9679 
.059 
.159 
.268 
.337 
.388 
.429 

.9332 
.9837 
.076 
.178 
.289 
.359 
.411 
.452 

.9525 
.004 
.099 
.202 
.316 
.387 
.440 
1.482 

.9792 
.032 
.130 
.236 
.353 
.426 
.480 
.524 

H.  &  W.  Formula:  V=  1.318  cr°-63  s°-54  = 


Short  Formulae.       E.  Sherman 


§0.50 

Gould, 


(T)  '  a0-04 

Eng.  News,  Sept.  6,  1900, 


8  in.  to  48  in.  diam. 


( Rough, 
( Smooth, 


v  =  1> 
;  v  =  1.80 


3  to  6  in,  diam. 


(  Rough,    Q2  =0.785  M*;  v 


1.1 

t  Smooth,  Qz  =  1 .57  M5 ;     v  =  1 .6 
FLOW  OF  WATER— EXPERIMENTS  AND  TABLES. 

The  Flow  of  Water  through  New  Cast-iron  Pipe  was  measured  by 
S.  Bent  Russell,  of  the  St.  Louis,  Mo.,  Water-works.  The  pipe  was  12 
inches  in  diameter,  1631  feet  long,  and  laid  on  a  uniform  grade  from 
end  to  end.  Under  an  average  total  head  of  3.36  feet  the  flow  was 
43,200  cubic  feet  in  seven  hours;  under  an  average  head  of  3.37  feet  the 
flow  was  the  same;  under  an  average  total  head  of  3.41  feet  the  flow 
was  46,700  cubic  feet  in  8  hours  and  35  minutes.  Making  allowance  for 
loss  of  head  due  to  entrance__and  to  curves,  it  was  found  that  the  value 
of  c  in  the  formula  v  =  c  Vrs  was  from  88  to  93.  (Eng'g  Record,  April 

Flow  of  Water  in  a  20-inch  Pipe  75,000  Feet  Long.  —  A  com- 
parison of  experimental  data  with  calculations  by  different  formulae  is 
given  by  Chas.  B.  Brush,  Trans.  A.  S.  C.  E.,  1888.  The  pipe  experi- 
mented with  was  that  supplying  the  city  of  Hoboken,  N.  J. 

RESULTS  OBTAINED  BY  THE  HACKENSACK  WATER  Co.,  FROM  1882-1887, 
IN  PUMPING  THROUGH  A  20-iN.  CAST-IRON  MAIN  75,000  FEET  LONG. 

Pressure  in  Ibs.  per  sq.  in.  at  pumping-station: 

95  100  105  110  115  120  125  130 

Total  effective  head  in  feet: 

55  66  77  89          100          112          123          135 

Discharge  in  U.  S.  gallons  in  24  hours,  1  =  1000: 

2,848       3,165       3,354       3,566       3,804       3,904       4,116       4,255 
Theoretical  discharge  by  Darcy's  formula: 

2,743       3,004       3,244       3,488       3,699       3,915       4,102       4,297 
Actual  velocity  in  main  in  feet  per  second: 

2,00         2,24        2,36        2.52        2,63        2,70        2,92        3,00 


738 


HYDRAULICS. 


Flow  of  Water  In  Circular  Pipes,  Sewers,  etc.,  Flowing  Full. 
Based  on  Kutter's  Formula,  with  n    -  0.013. 

Discharge  in  cubic  feet  per  second. 


Diam- 
eter. 

Slope,  or  Head  Divided  by  Length  of  Pipe. 

1  in  40 

1  in  70     1  in  100|  1  in  200|  1  in  300|  1  in  400|  1  in  500[  1  in  600 

5  in. 
6  " 
7  " 
8  " 
9  " 

0.456 
0.762 
1.17 

1.70 
2.37 

0.344 
0.576 

0.889 
1.29 
1.79 

0.288 
0.482 
0.744 
1.08 
1.50 

0.204 
0.341 
0.526 
0.765 
1.06 

0.166 
0.278 
0.430 
0.624 
0.868 

0.144 
0.241 
0.372 
0.54 
0.75 

0.137 
0.230 
0.355 
0.516 
0.717 

0.118 
0.197 
0.304 
0.441 
0.613 

10  in.  S 

It  " 
12  " 
13  " 
14  " 

1  in  60 
2.59 
3.39 
4.32 
5.38 
6.60 

1  in  80 
2.24 
2.94 
3.74 
4.66 
5.72 

1  in  100 
2.01 
2.63 
3.35 
4.16 
5.15 

1  in  200 
1.42 
1.86 
2.37 
2.95 
3.62 

1  in  300 
1.16 
1.52 
1.93 
2.40 
2.95 

1  in  400 
1.00 
1.31 
1.67 
2.08 
2.57 

1  in  500 
0.90 
1.17 
1.5 
1.86 
2.29 

1  in  600 
0.82 
1.07 
1.37 
1.70 
2.09 

s  = 
15  in. 
16  " 

18  " 
20  " 
22  " 

1  in  100 
6.18 
7.38 
10.2! 
13.65 
17.71 

1  in  200 
4.37 
5.22 
7.22 
9.65 
12.52 

1  in  300 
3.57 
4.26 
5.89 
7.88 
10.22 

1  in  400 
3.09 
3.69 
5.10 
6.82 
8.85 

1  in  500 
2.77 
3.30 
4.56 
6.10 
7.92 

1  in  600 
2.52 
3.01 
4.17 
5.57 
7.23 

1  in  700 
2.34 
2.79 
3.86 
5.16 
6.69 

1  in  800 
2.19 
2.61 
3.61 
4.83 
6.26 

,  s  = 

2ft. 
2ft.2in. 
2  "  4" 
2  "  6  " 
2  "  8  " 

1  in  200 
15.88 
19.73 
24.15 
29.08 
34.71 

1  in  400 
11.23 
13.96 
17.07 
20.56 
24.54 

1  in  600 
9.13 

11.39 
13.94 
16.79 
20.04 

1  in  800 
7.94 
9.87 
12.07 
14.54 
17.35 

1  in  1000 
7.10 
8.82 
10.80 
13.00 
15.52 

1  in  1250 
6.35 
7.89 
9.66 
11.63 
13.88 

1  in  1500 
5.80 
7.20 
8.82 
10.62 
12.67 

1  in  1800 
5.29 
6.58 
8.05 
9  69 
11.57 

2ft.lofnT 

3  " 
3  "  2in. 
3  "  4  " 
3  "  6  " 

1  in  500 
25.84 
30.14 
34.90 
40.08 
45.66 

1  in  750 
21.10 
24.61 
28.50 
32.72 
37.28 

1  in  1000 
18.27 
21.31 
24.68 
28.34 
32.28 

1  in  1250 
16.34 
19.06 
22.07 
25.35 
28.87 

1  in  1500 
14.92 
17.40 
20.15 
23.14 
26.36 

1  in  1750 
13.81 
16.11 
18.66 
21.42 
24.40 

1  in  2000 
12.92 
15.07 
17.45 
20.04 
22.83 

1  in  2000 
25.87 
29.18 
32.74 
44.88 
59.46 

1  in  2500 
11.55 
13.48 
15.61 
17.93 
20.41 

1  in  2500 
23.14 
26.10 
29.28 
40.14 
53.18 

3ft.   8in. 
3  "  10  " 
4  " 
4  "    6in. 

5  " 

1  in  500 
51.74 
58.36 
65.47 
89.75 
118.9 

1  in  750 
42.52 
47.65 
53.46 
73.28 
97.09 

1  in  1000 
36.59 
41.27 
46.30 
63.47 
84.08 

1  in  1250 
32.72 
36.91 
41.41 
56.76 
75.21 

1  in  1500 
29.87 
33.69 
37.80 
51.82 
68.65 

lin  1750 
27.66 
31.20 
34.50 
47.97 
63.56 

5ft.6in7 
6  " 
6  "  6  " 
7  " 
7  "  6  " 

1  in  750 
125.2 

157.8 
195.0 
237.7 
285.3 

1  in  1000 
108.4 
136.7 
168.8 
205.9 
247.1 

1  in  1  500 
88.54 
111.6 
137.9 
168.1 
201.7 

1  in  2000 
76.67 
96.66 
119.4 
145.6 
174.7 

1  in  2500 
68.58 
86.45 
106.8 
130.2 
156.3 

1  in  3000 
62.60 
78.92 
97.49 
118.8 
142.6 

1  in  3500 
57.96 
73.07 
90.26 
110.00 
132.1 

1  in  4000 
54.21 
68.35 
84.43 
102.9 
123.5 

s  = 

8ft. 
8  "  6in. 

9  " 
9  "  6  " 
10  " 

1  in  1500 
239.4 
281.1 
327.0 
376.9 
431.4 

1  in  2000 
207.3 
243.5 
283.1 
326.4 
373.6 

1  in  2500 
195.4 
217.8 
253.3 
291.9 
334.  1 

1  in  3000 
169.3 
198.8 
231.2 
266.5 
305.0 

1  in  3500 
156.7 
184.0 
214.0 
246.7 
282.4 

1  in  4000 
146.6 
172.2 
200.2 
230.8 
264.2 

1  in  4500 
138.2 
162.3 
188.7 
217.6 
249.1 

1  in  5000 
131.1 
154.0 
179.1 
206.4 
236.3 

For  U.  S.  gallons  multiply  the  figures  in  the  table  by  7.4805. 

For  a  given  diameter  the  quantity  of  flow  varies  as  the  square  root  of 
the  sine  of  the  slope.  From  this  principle  the  flow  for  other  slopes  than 
those  given  in  the  table  may  be  found.  Thus,  what  is  the  flow  for  a 


FLOW  OF  WATER  IN  PIPES. 


739 


pipe  8  feet  diameter,  slope  1  in  125?  From  the  table  take  Q  =  207.3 
for  slope  1  in  2000.  The  given  slope  1  in  125  is  to  1  in  2000  as  16  to 
1,  and  the  square  root  of  this  ratio  is  4  to  1.  Therefore  the  flow  required 
is  207.3  X  4  =  829.2  cu.  ft. 

Circular  Pipes,  Conduits,  etc.,  Flowing  FulL 

Values  of  the  factor  ac  \/r  in  the  formula  Q  =  ac  \/r  X  \/s  corre- 
sponding to  different  values  of  the  coefficient  of  roughness,  n.  (Based 
on  Kutter's  formula.) 


Diam., 
Ft.  In. 

Value  of  ac  \A. 

w=.010. 

n=.011. 

n=.012. 

n=.013. 

n=.015. 

n=.017. 

2 

307.6 

274.50 

247.33 

224.63 

188.77 

164 

2  3 

421.9 

377.07 

340.10 

309.23 

260.47 

223.9 

2  6 

559.6 

500.78 

452.07 

411.27 

347.28 

299.3 

2  9 

722.4 

647.18 

584.90 

532.76 

451.23 

388.8 

3 

911.8 

817.50 

739.59 

674.09 

570.90 

493.3 

3  3 

1128.9 

1013.1 

917.41 

836.69 

709.56 

613.9 

3  6 

1374.7 

1234.4 

1118.6 

1021.1 

866.91 

750.8 

3  9 

1652.1 

1484.2 

1345.9 

1229.7 

1045 

906 

4 

1962.8 

1764.3 

1600.9 

1463.9 

1245.3 

1080.7 

4  6 

2682.1 

2413.3 

2193 

2007 

1711.4 

1487.3 

5 

3543 

3191.8 

2903.6 

2659 

2272.7 

1977 

5  6 

4557.8 

4111.9 

3742.7 

3429 

2934.  8 

2557.2 

6 

5731.5 

5176.3 

4713.9 

4322 

3702.3 

3232.5 

6  6 

7075.2 

6394.9 

5825.9 

5339 

4588.3 

4010 

7 

8595.1 

7774.3 

7087 

6510 

5591.6 

4893.2 

7  6 

10296 

9318.3 

8501.8 

7814 

6717 

5884.3 

6 

12196 

11044 

10083 

9272 

7978.3 

"6995.3 

8  6 

14298 

12954 

11832 

10889 

9377.9 

8226.7 

9 

16604 

15049 

13751 

12663 

10917 

9580 

9  6 

19118 

17338 

15847 

14597 

12594 

11061 

10 

21858 

19834 

18134 

16709 

14426 

12678 

10  6 

24823 

22534 

20612 

18996 

16412 

14434 

11 

28020 

25444 

23285 

21464 

18555 

16333 

11  6 

31482 

28593 

26179 

24139 

20879 

18395 

12 

35156 

31937 

29254 

26981 

23352 

20584 

12  6 

39104 

35529 

32558 

30041 

26012 

22938 

13 

43307 

39358 

36077 

33301 

28850 

25451 

13  6 

47751 

43412 

39802 

36752 

31860 

28117 

14 

52491 

47739 

43773 

40432 

35073 

30965 

14  6 

57496 

52308 

47969 

44322 

38454 

33973 

15 

62748 

57103 

52382 

48413 

42040 

37147 

16 

74191 

67557 

62008 

57343 

49823 

44073 

17 

86769 

79050  . 

72594   . 

67140 

58387 

51669 

18 

00617 

91711 

84247 

77932 

67839 

60067 

19 

115769 

105570 

96991 

89759 

78201 

69301 

20 

32133 

120570 

110905 

102559 

89423 

79259 

Flow  of  Water  in  Pipes  from  3/g  Inch  to  13  Inches  Diameter  for  a 
Uniform  Velocity  of  100  Ft.  per  Min. 


Diam. 
ID  In. 

Area 
Sq.  Ft. 

Cu.  Ft. 
per.  Min. 

U.  S. 
Gallons 
per  Min. 

Diam. 
in  In. 

Area 
Sq.  Ft. 

Cu.  Ft. 
per  Min. 

U.S. 
Gallons 
per  Min. 

3/8 

.00077 

0.077 

.57 

4 

.0873 

8.73 

65.28 

!/2 

.00136 

0.136 

1.02 

5 

.136 

13.6 

102.00 

3/4 

.00307 

0.307 

2.30 

6 

.196 

19.6 

146.88 

.00545 

0.545 

4.08 

7 

.267 

26.7 

199.92 

n/4 

.00852 

0.852 

6.38 

8 

.349 

34.9 

261.12 

11/2 

.01227 

1.227 

9.18 

9 

.442 

44.2 

330.48 

13/4 

.01670 

1.670 

•    12.50 

10 

.545 

54.5 

408.00 

.02182 

2.182 

16.32 

11 

.660 

66.0 

493.68 

21/2 

.0341 

3.41 

25.50 

12 

.785 

78.5 

587.52 

3 

.0491 

4.91 

36.72 

740 


HYDRAULICS. 


Flow  of  Water  in  Circular  Pipes,  Conduits,  etc.,  Flowing;  under 
Pressure. 

Based  on  Darcy's  formulae  for  the  flow  of  water  through  cast-iron 
pipes.  With  comparison  of  results  obtained  by  Kutter's  formula,  with 
ft  =  0.013.  (Condensed  from  Flynn  on  Water  Power.)  _ 

Values  of  a,  and  also  the  values  of  the  factors  c  Vr  and  ac  vV  for  use 

In  the  formulae  Q  =  av;  v  =  c  \/r  X  Vs,  and  Q  =  ac  V7x  ^s. 

Q  =  discharge  in  cubic  feet  per  second,  a  =  area  in  square  feet,  v  = 
velocity  in  feet  per  second,  r  =  mean  hydraulic  depth,  1/4  diam.  for 
pipes  running  full,  s,  =  sine  of  slope. 

(For  values  of  V?  see  page  729.) 


Size  of  Pipe. 

Clean  Cast-iron 
Pipes. 

Value  of 
ac  Vrby 
Kutter's 
Formula, 
when 
n=.OI3. 

Old  Cast-iron  Pipes 
Lined  with  Deposit. 

d—diam. 
in 
ft.  in. 

a  =  area  in 
square 
feet. 

For 
Velocity, 

For  Dis- 
charge, 

For 
Velocity, 

For 
Discharge, 

2 

3.142 

78.80 

247.57 

224.63 

52.961 

166.41 

2      2 

3.687 

28.15 

302.90 

55.258 

203.74 

2      4 

4.276 

85.39 

365.14 

57.436 

245.60 

2      6 

4.909 

88.39 

433.92 

411.37 

59.455 

291.87 

2      8 

5.585 

91.51 

511.10 

61.55 

343.8 

2     10 

6.305 

94.40 

595.17 

63.49 

400.3 

3 

7  068 

97.17 

686.76 

674.09 

65.35 

461.9 

3      2 

7.875 

99.93 

786.94 

67.21 

529.3 

3      4 

8.726 

102.6 

895.7 

69 

602 

3      6 

9.621 

105.1 

1011.2 

1021.1 

70.70 

680.2 

3      8 

10.559 

107.6 

1136.5 

72.40 

764.5 

3     10 

11.541 

110.2 

1271.4 

74.10 

855.2 

4 

12.566 

112.6 

1414.7 

1463.9 

75.73 

951.6 

4      3 

14.186 

116.1 

1647.6 

78.12 

1108.2 

4      6 

15.904 

119.6 

1901.9 

2007 

80.43 

1279.2 

4      9 

17.721 

122.8 

2176.1 

82.20 

1456.8 

5 

19.635 

126.1 

2476.4 

2659 

84.83 

1665.7 

5      3 

21.648 

129.3 

2799.7 

86.99 

1883.2 

5      6 

23.758 

132.4 

3146.3 

3429 

89.07 

2116.2 

5      9 

25  967 

135.4 

3516 

91.08 

2365 

5 

28.274 

138.4 

3912.8 

4322 

93.08 

2631.7 

6      6 

33  183 

144.1 

4728.1 

5339 

96.93 

3216.4 

7 

38  485 

149.6 

5757.5 

6510 

100.61 

3872.5 

7      6 

44  179 

154.9 

6841.6 

7814 

104.11 

4601.9 

g 

50  266 

160 

8043 

9272 

107.61 

5409.9 

8      6 

56.745 

165 

9463.7 

10889 

111 

6299.1 

9 

63.617 

169.8 

10804 

12663 

114.2 

7267.3 

9      6 

70  882 

174.5 

12370 

14597 

117.4 

8329.6 

10 

78.540 

179.1 

14066 

16709 

120.4 

9460.9 

10      6 

68.590 

183.6 

15893 

18996 

123.4 

10690 

11 

95  033 

187.9 

17855 

21464 

126.3 

12010 

11       6 

103  869 

192.2 

19966 

24139 

129.3 

13429 

12 

113.098 

196.3 

22204 

26981 

132 

14935 

12      6 

122  719 

200.4 

24598 

30041 

134.8 

16545 

13 

132.733 

204.4 

27134 

33301 

137.5 

18252 

13      6 

143  139 

208.3 

29818 

36752 

140.1 

20056 

14 

153  938 

212.2 

32664 

40432 

142.7 

21971 

14      6 
15 

165.130 
176  715 

216.0 
219.6 

35660 
38807 

44322 
48413 

145.2 
147.7 

23986 
26103 

15      6 
16 

188.692 
201  062 

223.3 
226.9 

42125 
45621 

52753 
57343 

150.1 
152.6 

28335 
30686 

16      6 

213  825 

230.4 

49273 

62132 

155 

33144 

17 

226  981 

233.9 

53082 

67140 

157.3 

35704 

17      i 

240  529 

237.3 

57074 

72409 

159.6 

38389 

18 

254  170 

240.7 

61249 

77932 

161.9 

41199 

19 

283  529 

247.3 

70154 

89759 

166.4 

47186 

20 

314.159 

253.8 

79736 

102559 

170.7 

53633 

FLOW   OP   WATEB  IN   PIPES. 


741 


Flow  of  Water  in  Circular  Pipes  from  3/s  Inch  to  12  Inches 
Diameter. 

Based  on  Darcy's  formula  for  clean  cast-iron  pipes.     Q  =  ac  v'r  VJ. 


Value 

Dia. 

Slope,  or  Jlead  Divided  by  Length  of  Pipe. 

ofocVr. 

in. 

1  in  10 

1in20 

1  in  40 

1  in  60 

1  in  80 

1  in  100 

1  in  150 

1  in  200 

Quan 

tityin 

cubic 

feet  per 

second. 

.00403 

s/8 

.00127 

.00090 

.00064 

.00052 

.00045 

.00040 

.00033 

.00028 

.00914 

1/2 

.00289 

.00204 

.00145 

.00118 

.00102 

.00091 

.00075 

.00065 

.02855 

3/4 

.00903 

.00638 

.00451 

.00369 

.00319 

.00286 

.00233 

.00202 

.06334 

.02003 

.01416 

.01001 

.00818 

.00708 

.00633 

.00517 

.00448 

.11659 

11/4 

.03687 

.02607 

.01843 

.01505 

.01303 

.01166 

.00952 

.00824 

.19115 

U/9 

.06044 

.04274 

.03022 

.02468 

.02137 

.01912 

.01561 

.01352 

.28936 

13/4 

.09140 

.06470 

.04575 

.03736 

.03235 

.02894 

.02363 

.02046 

.41357 

.13077 

.09247 

.06539 

.05339 

.04624 

.04136 

.03377 

.02927 

.74786 

21/2 

.23647 

.16722 

.11824 

.09655 

.08361 

.07479 

.06106 

.05288 

1.2089 

3 

.38225 

.27031 

.19113 

.15607 

.13515 

.12089 

.09871 

.08548 

2.5630 

4 

.81042 

.57309 

.40521 

.33088 

.28654 

.25630 

.20927 

.18123 

4.5610 

5 

1.4422 

1.0198 

.72109 

.58882 

.50992 

.45610 

.37241 

.32251 

'7.3068 

6 

2.3104 

1  .6338 

1.1552 

.94331 

.81690 

.73068 

.59660 

.51666 

10.852 

7 

3.4314 

2.4265 

1.7157 

1.4110 

1.2132 

1.0852 

.88607 

.76734 

15.270 

8 

4.8284 

3.4143 

2.4141 

1.9713 

1.7072 

1.5270 

1.2468 

1  .0797 

20.652 

9 

6.5302 

4.6178 

3.2651 

2.6662 

2.3089 

2.0652 

1.6862 

1.4603 

26.952 

10 

8.5222 

6.0265 

4.2611 

3.4795 

3.0132 

2.6952 

2.2006 

1.9058 

34.428 

11 

10.886 

7.6981 

5.4431 

4.4447 

3.8491 

3.4428. 

2.8110 

2.4344 

42.918 

12 

13.571 

9.5965 

6.7853 

5.5407 

4.7982 

4.2918 

3.5043 

3.0347 

Value  of  Vs^ 

0.3162 

0.2236 

0.1581 

0.1291 

0.1118 

0.1 

0.08165 

0.07071 

Value 

f            A  / 

Dia 

1  in  250 

1  in  300 

1  in  350 

1  in  400 

1  in  450 

1  in  500 

1  in  550 

1  in  600 

of  ocv  r. 

in. 

.00403 

3/8 

.00025 

.00023 

.00022 

.00020 

.00019 

.00018 

.00017 

.00016 

.00914 

1/2 

.00058 

.00033 

.00049 

.00046 

.00043 

.00041 

.00039 

.00037 

.02855 

3/4 

.00181 

.00165 

.00153 

.00143 

.00134 

.00128 

.00122 

.00117 

.06334 

1 

.00400 

.00366 

.00339 

.00317 

.00298 

.00283 

.00270 

.00259 

.11659 

H/4 

.00737 

.00673 

.00623 

.00583 

.00549 

.00521 

.00497 

.00476 

.19115 

H/2 

.01209 

.01104 

.01022 

.00956 

.00901 

.00855 

.00815 

.00780 

.28936 

13/4 

.01830 

.01671 

.01547 

.01447 

.01363 

.01294 

.01234 

.01181 

.41357 

2 

.02615 

.02388 

.02211 

.02068 

.01948 

.01849 

.01763 

.01688 

.74786 

21/2 

.04730 

.04318 

.03997 

.03739 

.03523 

.03344 

.03189 

.03053 

1.2089 

3 

.07645 

.06980 

.06462 

.06045 

.05695 

.05406 

.05155 

.04935 

2.5630 

4 

.16208 

.14799 

.  13699 

.12815 

.12074 

.11461 

.10929 

.  10463 

4.5610 

5 

.28843 

.26335 

.24379 

.22805 

.21487 

.20397 

.19448 

.19620 

7.3068 

6 

.46208 

.42189 

.39055 

.36534 

.34422 

.32676 

.31156 

.29830 

10.852 

7 

.68628 

.62660 

.58005 

.54260 

.51124 

.48530 

.46273 

.44303 

15.270 

8 

.96567 

.88158 

.81617 

.76350 

.71936 

.68286 

.65111 

.62340 

20.652 

9 

1  3060 

1.1924 

1.1038 

1.0326 

.97292 

.92356 

.88060 

.84310 

26.952 

10 

1.7044 

1.5562 

1.4405 

1  .3476 

1.2697 

1.2053 

1.1492 

1.1003 

34.428 

11 

2.1772 

1.9878 

1.8402 

1.7214 

1.6219 

1.5396 

1.4680 

1.4055 

42.918 

12 

2.7141 

2.4781 

2.2940 

2.1459 

2.0219 

1.9193 

1.8300 

1.7521 

Value  of  VJ= 

.06324 

.05774 

.05345 

.05 

.04711 

.04472 

.04264 

.04082 

For  U.  S.  gals,  per  sec.,    multiply  the  figures  in  the  table  by 7.4805 

"  min.,        "  "       ...       448.83 

"       "  hour,        "  "  26929.8 

"       "  24hrs.t     "  "       ...646315. 

'or  any  other  slope  the  flow  is  proportional  to  the  square  root  of  the 
thus,  flow  in  slope  of  1  in  100  is  double  that  in  slope  of  1  in  400. 


742 


HYDRAULICS. 


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FLOW   OF   WATER. 


743 


Flow  or  Water  in  Cubic  Feet  per  Second. 
Pipes  1  Ft.  to  20  Ft.  Diameter. 

Calculated  from  the  Hazen  and  Williams  formula  with  C  = 


100. 


Fall,  Feet  per  1  000 

Actual 
Internal 

1   1  2  1  3 

4 

6 

8  |  10  |  15 

20 

40 

Diam., 
In. 

Drop  in  Pressure,  Lb.  per  Sq.  In.  per  1000  Ft.  Length. 

0.433 

0.866 

1.299 

1.732 

2.598 

5.464 

4.330 

6.495 

8.660 

17.32 

12 

1.037 

1.508 

1.877 

2.192 

2.729 

3.188 

3.596 

4.475 

5.228 

8.335 

13 

1.280 

1.861 

2.317 

2.706 

3.368 

3.934 

4.438 

5.524 

.6.453 

10.29 

14 

1.555 

2.262 

2.815 

3.288 

4.093 

4.781 

5.393 

6.713 

7.842 

12.50 

15 

1.865 

2.712 

3.375 

3.943 

4.908 

5.732 

6.466 

8.048 

9.402 

14.99 

16 

2.210 

3.213 

4.000 

4.672 

5.815 

6.793 

7.663 

9.537 

11.14 

17.76 

18 

3.012 

4.380 

5.452 

6.368 

7.927 

9.259 

10.45 

13.00 

15.19 

24.21 

20 

3.974 

5.778 

7.193 

8.402 

10.46 

12.22 

13.78 

17.15 

20.04 

31.94 

22 

5.100 

7.415 

9.231 

10.78 

13.42 

15.68 

17.68 

22.01 

25.71 

40.99 

Diam.,  Ft. 

2 

6.420 

9.334 

11.62 

13.57 

16.89 

19.73 

22.26 

27.70 

32.36 

51.60 

21/2 

11.54 

16.79 

20.89 

24.41 

30.38 

35.48 

40.03 

49.80 

58.20 

92.79 

3 

18.65 

27.11 

33.75 

39.42 

49.07 

57.32 

64.66 

80.48 

94.01 

149.9 

31/2 

27.97 

40.67 

50.62 

59.13 

73.60 

85.97 

96.98 

120.7 

141.0 

224.8 

39.74 

57.78 

71.92 

84.01 

104.6 

122.1 

137.8 

171.5 

200.3 

319.4 

41/2 

54.17 

78.76 

98.04 

114.5 

142.5 

166.5 

187.8 

233.8 

273.1 

435.4 

71.46 

103.9 

129.3 

151.1 

188.1 

219.7 

247.8 

308.4 

360.3 

574.4 

51/2 

91.82 

133.5 

166.2 

194.1 

241.7 

282.2 

318.4 

396.3 

462.9 

738.0 

6 

115.4 

167.8 

208.9 

244.0 

303.8 

354.8 

400.2 

498.2 

581.9 

927.8 

61/2 

142.5 

207.2 

257.9 

301.2 

374.9 

437.9 

494.0 

614.9 

718.3 

1145' 

7 

173.1 

251.7 

313.4 

366.0 

455.6 

532.2 

600.3 

747.2 

872.9 

1392 

71/2 

207.6 

301.8 

375.7 

438.8 

546.3 

638.1 

719.8 

859.9 

1047 

1668 

8 

246.0 

357.7 

445.2 

520.0 

647.3 

756.1 

852.9 

1062 

1240 

1977 

81/2 

288.5 

419.5 

522.2 

609.9 

759.2 

886.8 

1000 

1245 

1455 

2319 

9 

335.3 

487.5 

606.9 

708.9 

882.4 

1031 

1163 

1447 

1690 

2695 

10 

442.4 

643.2 

800.6 

935.2 

1164 

1360 

1534 

1909 

2230 

3556 

11 

568.4 

826.4 

1029 

1202 

1496 

1747 

1971 

2453 

2866 

4568 

12 

714.6 

1015 

1293 

1511 

1880 

2196 

2478 

3084 

3602 

5743 

13 

882.0 

1282 

1596 

1865 

2321 

2711 

3058 

3807 

4447 

7089 

14 

1072 

1558 

1940 

2266 

2820 

3294 

3716 

4625 

5403 

8614 

15 

1285 

1868 

2326 

2717 

3381 

3950 

4456 

5546 

6478 

10328 

16 

1223 

2214 

2756 

3219 

4007 

4681 

5280 

6572 

7677 

12239 

17 

1786 

2597 

3232 

3776 

4700 

5490 

6193 

7708 

9004 

14354 

18 

2076 

3018 

3757 

4388 

5462 

6380 

7197 

8958 

10464 

16683 

19 

2393 

3479 

4331 

5059 

6297 

7355 

8297 

10327 

12063 

19232 

20 

2738 

3982 

4956 

5789 

7206 

8417 

9495 

11818 

13806 

22010 

4.5  ft.  per  mile,  discharged  15  million  gallons  per  day;  velocity,  2.892  ft. 
per  sec.,  /  =  0.00574. 

(2)  East  Jersey  riveted  steel  pipe  line,  Newark,  N.  J.,  21  miles  long,  48 
in.  diam.,  50  million  U.  S.  gals,  per  day;  velocity  about  6  ft.  per  sec. 

(3)  Perth  to  Coolgarlie,  Western  Australia,  351  miles,  30  in.  steel  pipe 
with  lock-bar  joints.     Eight  pumping  stations  in  the  line.     Two  tests 
showed  delivery  of  5  and  5.6  million  gals,  per  day;  hydraulic  gradient 
2.25  and  2.8  ft.  per  mile;  velocity,  1.889  and  2.115  ft.  per  sec.;/=  0.00480 
and  0.00486. 

Flow  of  Water  in  Riveted  Steel  Pipes.  —  The  laps  and  rivets  tend 
to  decrease  the  carrying  capacity  of  the  pipe.  See  paper  on  "New 
Formulas  for  Calculating  the  Flow  of  Water  in  Pipes  and  Channels,"  by 
W.  E.  Foss,  Jour.  Assoc.  Eng.  Soc.,  xiii,  295.  Also  Clemens  Herschel's 
book  on  "115  Experiments  on  the  Carrying  Capacity  of  Large  Riveted 
Metal  Conduits,"  John  Wiley  &  Sons,  1897. 


744 


HYDRAULICS. 


Flow  of  Water  in  House-service  Pipes. 

Mr.  E.  Kuichling,  C.  E.,  furnished  the  following  table  to  the  Thomson 
Meter  Co.: 


Condition  of 
Discharge. 

Pressure  in  Main, 
pounds  per 
square  inch. 

Discharge,  or  Quantity  capable  of  being  delivered,  in 
Cubic  Feet  per  Minute,  from  the  Pipe,  under  the 
conditions  specified  in  the  first  column. 

Nominal  Diameters  of  Iron  or  Lead  Service-pipe  in 
Inches. 

1/2 

5/8 

3/4 

1 

H/2 

2 

3 

4 

6 

Through  35 
feet  of  ser- 
vice-pipe, 
no  back 
pressure. 

30 
40 
50 
60 
75 
100 
130 

.10 
.27 
.42 
.56 
.74 
2.01 
2.29 

1.92 
2.22 
2.48 
2.71 
3.03 
3.50 
3.99 

3.01 
3.48 
3.89 
4.26 
4.77 
5.50 
6.28 

6.13 
7.08 
7.92 
8.67 
9.70 
11.20 
12.77 

16.58 
19.14 
21.40 
23.44 
26.21 
30.27 
34.51 

33.34 

33.50 
43.04 
47.15 
52.71 
60  87 
69.40 

88.16 
101.80 
113.82 
124.68 
139.39 
160.96 
183.52 

173.85 
200.75 
224.44 
245.87 
274.89 
317.41 
361.91 

444.63 
513.42 
574.02 
628.81 
703.03 
811.79 
925.58 

Through  100 
feet  of  ser- 
vice-pipe, 
no  back 
pressure. 

30 
40 
50 
60 
75 
100 
130 

0.66 
0.77 
0.86 
0.94 
1.05 
1.22 
1.39 

.16 
.34 
.50 
.65 
.84 
2.13 
2.42 

1.84 
2.12 
2.37 
2.60 
2.91 
3.36 
3.83 

3.78 
4.36 
4.88 
5.34 
5.97 
6.90 
7.86 

10.40 
12.01 
13.43 
14.71 
16.45 
18.99 
21.66 

21.30 
24.59 
27.50 
30.12 
33.68 
38.89 
44.34 

58.19 
67.19 
75.13 
82.30 
92.01 
106.24 
121.14 

118.13 
136.41 
152.51 
167.06 
186.78 
215.68 
245.91 

317.23 
366.30 
409.54 
448.63 
501.58 
579.18 
660.36 

Through  100 
feet  of  ser- 
vice-pipe, 
and  15  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.55 
0.66 
0.75 
0.83 
0.94 
.10 
1.26 

0.96 
.15 
.31 
.45 
.64 
.92 
2.20 

1.52 
1.81 
2.06 
2.29 
2.59 
3.02 
3.48 

3.11 
3.72 
4.24 
4.70 
5.32 
6.21 
7.14 

8.57 
10.24 
11.67 
12.94 
14.64 
17.10 
19.66 

17.55 
20.95 
23.87 
26.48 
29.96 
35.00 
40.23 

47.90 
57.20 
65.18 
72.28 
81.79 
95.55 
109.82 

97.17 
116.01 
132.20 
146.61 
165.90 
193.82 
222.75 

260.56 
311.09 
354.49 
393.13 
444.85 
519.72 
597.31 

Through  100 
feet  of  ser- 
vice-pipe, 
and  30  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.44 
0.55 
0  65 
0.73 
JO.  84 
1.00 
1.15 

0.77 
0.97 
1.14 
1.28 
1.47 
1.74 
2.02 

1.22 
1.53 
1.79 
2.02 
2.32 
2.75 
3.19 

2.50 
3.15 
3.69 
4.15 
4.77 
5.65 
6.55 

6.80 
8  68 
10.16 
11.45 
13.15 
15.58 
18.07 

14.11 
17.79 
20.82 
23.47 
26.95 
31.93 
37.02 

38.63 
48.68 
56.98 
64.22 
73.76 
87.38 
101.33 

78.54 
98  98 
115.87 
130.59 
149.99 
177.67 
206.04 

211.54 
266.59 
312.08 
351.73 
403.98 
478.55 
554.96 

In  this  table  it  is  assumed  that  the  pipe  is  straight  and  smooth  inside; 
that  the  friction  of  the  main  and  meter  are  disregarded;  that  the  inlet 
from  the  main  is  of  ordinary  character,  sharp,  not  flaring  or  rounded,  and 
that  the  outlet  is  the  full  diameter  of  pipe.  The  deliveries  given  will  be 
increased  if,  first,  the  pipe  between  the  meter  and  the  main  is  of  larger 
diameter  than  the  outlet;  second,  if  the  main  is  tapped,  say  for  1-inch 
pipe,  but  is  enlarged  from  the  tap  to  1 1/4  or  1 1/2  inch;  or,  third,  if  pipe  on 
the  outlet  is  larger  than  that  on  the  inlet  side  of  the  meter.  The  exact 
details  of  the  conditions  given  are  rarely  met  in  practice;  consequently 
the  quantities  of  the  table  may  be  expected  to  be  decreased,  because  the 
pipe  is  liable  to  be  throttled  at  the  joints,  additional  bends  may  inter- 
pose, or  stop-cocks  may  be  used,  or  the  back-pressure  may  be  increased. 


LOSS    OF    HEAD. 


745 


Friction  Loss  iu  Clean  Cast-iron  Pipe. 

Compiled  from  Weston's  "Friction  of  Water  in  Pipes"  as  computed  from 

formulas  of  Henry  Darcy. 

Pounds  loss  per  1000  feet  in  pipe  of  given  diameter.     (Small   lower 
figures  give  Velocity  in  Feet  per  Second.) 


U.  S.Gals   per 
Mill,  and  (Cu. 
Ft.  per  Sec.) 

Diameter  of  Pipe  in  Inches. 

3 

4 

5 

6 

8 

10 

12 

14 

16 

20 

24 

30 

0.66 

0.23 

0~01 
0.45 

Q.03 

0  fi8 

250 

(0.56) 
500 
(1.11) 
750 
(1.67) 
1,000 
(2.23) 

60 
11 
220 
23 
477 
34 

20 
6.4 
82 
13.0 
184 
19.0 
328 
26.0 

6.4 
4.0 
25.8 
8.2 
58.0 
12.2 
103.0 
16.3 

2.5 

2.8 
10.0 
6.0 
23.0 
8.0 
40.0 
11.0 

0.6 
1.6 
2.3 
3.2 
5.0 
4.8 
9.0 
6.4 

0.2 
1.2 
0.7 
2.4 
1.6 
3.1 
2.9 
4.1 

0.07 
0.7 
0.29 
1.4 
0.66 
2.1 
1.20 
2.8 

0.03 
0.52 
0.13 
1.04 
0.30 
1.56 
0.53 
2.08 

0.83 
2.60 
1.10 
?  1? 

0.02 
0.4 
0.07 
0.8 
0.15 
1.2 
0.27 
1.6 

0.01 

0.26 
0.02 
0.51 
0.05 
0.77 
0.09 
1.0 

0.00 
0.18 
0.01 
0.35 
0.02 
0.53 
0.03 
0.71 

1,250 

(2.79) 
1,500 
(3.34) 
1,750 
(3.90) 
2,000 
(4.46) 

..*.. 

161.0 
20.4 
231.9 
24.5 

63.0 
14.0 
91.0 
17.0 
123.0 
20.0 
160.0 
23.0 

14.0 
8.0 
21.0 
10.0 
28.0 
11.0 
37.0 
13.0 

4.6 
5.1 
6.6 
6.1 

1.80 
3.6 
2.60 
4  3 

0.42 
2.0 
0.61 
2  4 

0.14 
1.3 
0.20 
1  5 

0.06 
0.89 
0.08 
1   06 

9.0 

7.1 
12.0 

8.2 

3.60 
5.0 
4.70 
5.7 

1.64 
3.65 
2.14 
4.17 

0.83 
2.8 
1.10 
3.2 

0.27 
1.8 
0.35 
2.0 

0.11 
1.24 
0.14 
1.42 

6:65 
0.91 

2,500 

(5.57) 
3,000 
(6.68) 
4,000 
(8.91) 
5,000 
(11.14) 

Diam.  of 
Pipeinln. 

58.0 
16.0 

18.0 
10.2 
26.0 
12.0 

7.30 
7.1 
10.00 

8.5 

3.34 
5.21 
4.81 
6.25 
8.55 
8.34 

1.70 
4.0 
2.40 
4.8 
4.30 
6.4 
6.80 
8.0 

0.55 
2.6 
0.79 
3.1 
.40 
4.1 
2.20 
5.1 

0.22 
1.80 
0.32 
2.10 
0.56 
2.80 
1.00 
3  .-60 

0.07 
1.13 
0.10 
1.40 
0.18 
l.SO 
0.29 
2.30 

0.41 
2.70 
0.56 
3.20 
0.73 
3  fiO 

36 

48 

0.11 
1.6 

0.03 

0.89 

_ 

6,000 

(13.37) 
7,000 
(15.60) 
8,000 
(17.82) 
9,000 
(20.05) 
10,000 
(22.28) 

0.16 
1.9 
0.23 
2.2 
0.29 
2.5 
0.37 
2.8 
0.45 
3.1 

0.04 
1.06 
0.05 
1.2 
0.07 
1.4 
0.09 
1.6 
0.11 
1.8 

3.20 
6.1 
4.30 
7.1 

1.30 
4.30 
1.70 
5.00 
2.20 
">  70 

2.80 
6.40 

0.92 
4.10 
1.13 
4.50 

Vel.ft.persec.. 
Hd.duevel.ft  . 

0.016 

2 
0.062 

3 
0.14 

4 
0.25 

5 

0.39 

6 
0.56 

7 
0.76 

8 
1.0 

9 
1.3 

10 
1.6 

It 
1.9 

12 
2.2 

Vel.ft.persec.. 
Hd.duevel.ft.. 

13 
2.6 

14 
3.1 

15 
3.5 

16 
4.0 

17 

4.5 

18 
5.0 

19 
5.6 

20 
6.2 

25 
9.3 

30 
14.0 

40 
24.8 

50 

38.8 

These  losses  are  for  new,  clean,  straight,  tar-coated,  cast-iron  pipes.     For 
pipes  that  have  been  in  service  a  number  of  years  the  losses 
will  be  larger  on  account  of  corrosion  and  incrustation,  and     10  years  1.3 
the  losses  in  the  tables  should  be  multiplied  under  average     20  1.6 

conditions  by  the  factors  opposite;  but  they  must  be  used     30  2.0 

with  much  discretion,  for  some  waters  corrode  pipes  much     50  2.6 

more  rapiclly  than  others.  75  3.4 

The  same  figures  may  be  used  for  wrought-iron  pipes  which  are  not 
subject  to  a  frequent  change  of  water. 


746  HYDRAULIC   FORMULAE  „ 


Hydraulic  Formulae.      (The  Lombard  Governor  Co., 

Head  (#)  in  feet.  Pressure  (P).  in  Ibs.  per  sq.  in.  Diameter  (£>)  in 
feet  Area  (A)  m  sq.  ft.  Quantity  (Q)  in  cubic  ft.  per  second.  Time 
(T)  in  seconds. 

Spouting  velocity  =  8.02  \/~H. 

Time  (TJ  to  acquire  spouting  velocity  in  a  vertical  pipe,  or  (Ti)  in  a 
pipe  on  an  angle  (0)  from  horizontal: 

T!=  8.02  *SH  +  32.17,     T2=  8.02  V#  +  32.17  sin  Q. 

Head  (H)  or  pressure  (P)  which  will  vent  any  quantity  (Q)  through  a 
round  orifice  of  any  diameter  (Z>)  or  area  (A): 
H  =  Q2  .=-  14.1  £>4   =  QZ  +  23.75  A2;  P  =  Q*  -*-  34.1  £M   =  £2  -j-  55.3  A\ 

Quantity  (Q)  discharged  through  a  round  orifice  of  any  diameter  (D)  or 
area  (A)  under  any  pressure  (P)  or  under  any  head  (H}  : 


Q  =  VP  X  55.3  X  A2      =Vpx  34.1  X  Z>4; 
=  V#  x  23.75  X  A2    =V#X  14.71  X  Z>4. 

Diameter  (D)  or  area  (A)  of  a  round  orifice  to  vent  any  quantity  (Q) 
under  any  head  (H)  or  under  any  pressure  (P): 


Time  (T)  of  emptying  a  vessel  of  any  area  (A)  through  an  orifice  of  any 
area  (a)  anywhere  in  its  side:  T  =  0.416  A  VH  •*•  a. 
;  Time  (T)  of  lowering  a  water  level  from  (H)  to  (ft)  in  a  tank  of  area  A 
through  an  orifice  of  any  area  (a)  in  its  side.     27=0.416A(V/^  —  \/&)  -=-a. 

Kinetic  energy  (K)  or  foot-pounds  in  water  in  a  round  pipe  of  any 
diameter  (Z>)  when  moving  at  velocity  (F):  K  =  0.76  X  D2  X  L  X  V2. 

Area  (a)  of  an  orifice  to  empty  a  tank  of  any  area  (A)  in  any  time  (T) 
from  any  head  (H):  a  =  T  •*•  0.409  A  V#. 

Area  (a)  of  an  orifice  to  lower  water  in  a  tank  of  area  (A)  from  head  (//) 
to  (ft)  in  time  (T7):  a  =  T  •*•  0.409  X  AX  (^H  -  Vft). 

Compound  Pipes  and  Pipes  with  Branches.  (Unwin.)  —  Loss  of 
head  in  a  main  consisting  of  different  diameters.  (1)  Constant  discharge. 
Total  loss  of  head  H  =  hi  +  ft2  +  ft3  =  0.1008/Q2  (li/dj  +  h/dv>  +  h/d^}. 

(2)  Constant  velocity  in  the  main,  the  discharge  Diminishing  from  sec- 
tion to  section.  H  =  0.0551  /y  5/2(Z1/x/Q1+  12/VQ2  +  13/VQS),  Equiv- 
alent main  of  uniform  diameter.  Length  of  equivalent  main 


Loss  of  head  in  a  main  of  uniform  diameter  in  which  the  discharge  de- 
creases uniformly  along  its  length,  such  as  a  main  with  numerous  branch 
pipes  uniformly  spaced  and  delivering  equal  quantities:  ft  =  0.0336 
fQH/d*,  Q  being  the  quantity  entering  the  pipe.  The  loss  of  head  is  just 
one-third  of  the  loss  in  a  pipe  carrying  the  uniform  quantity  Q  through- 
out its  length. 

Loss  of  head  in  a  pipe  that  receives  Q  cu.  ft.  per  sec.  at  the  inlet,  and 
delivers  Qx  cu.  ft.  at  x  ft.  from  the  inlet,  having  distributed  qx  cu.  ft. 
uniformly  in  that  distance,  hx—  0.1008/z  (Qx+  0.55  qx)/d5. 

Delivery  by  two  or  more  mains,  in  parallel.  Total  discharge  =  Qt  +  Q 
4-Qa  =  3.149  ^h/f  (V^s/k+Vd^H- VdsVfc) .  Diameter ofan equivalent 
main  to  discharge  the  same  total  quantity,  d=(v^+v/(/25+\/^5)2/5. 

Rifled  Pipes  for  Conveying  Heavy  Oils.  (Eng.  Rec.,  May  23,  1908.)— 
The  oil  from  the  California  fields  is  a  heavy,  viscous  fluid.  Attempts 
to  handle  it  in  long  pipe  lines  of  the  ordinary  type  have  not  been  practi- 
cally successful.  High  pumping  pressures  are  required,  resulting  in  large 
expense  for  pipe  and  for  pumping  equipment. 


LOSS  OF  HEAD. 


747 


The  method  of  pumping  in  the  rifled-pipe  line  is  to  inject  about  10  per 
cent  of  water  with  the  oil  and  to  give  the  cil  and  water  a  centrifugal 
motion,  by  means  of  the  rifled  pipe,  sufficient  to  throw  the  water  to  the 
outside,  where  it  forms  a  thin  film  of 'lubrication  between  the  oil  and  the 
sides  of  the  pipe  that  greatly  reduces  the  friction.  The  rifled  pipe  de- 
livers at  ordinary  temperatures  eight  t9  ten  times  as  much  oil,  through  a 
long  line,  as  does  a  line  of  ordinary  pipe  under  similar  conditions.  An 
8-in.  rifled  pipe  line  282  miles  in  length  has  been  built  from  the  Kern  oil 
fields  to  Porta  Costa,  on  tidewater  near  San  Francisco.  The  pipe  is 
rifled  with  six  helical  grooves  to  the  circumference,  these  grooves  making 
a  complete  turn  through  360  deg.  in  10  ft.  of  length. 

Loss  of  Pressure  Caused  by  Valves  and  Fittings  — The  data  given 
below  are  condensed  from  the  results  of  experiments  by  John  R.  Freeman 
for  the  Inspection  Department  of  the  Assoc.  Facty.  Mut.  Ins.  Cos.  The 
friction  losses  in  ells  and  tees  are  approximate.  Fittings  of  the  same  nom- 
inal size  with  the  different  curvatures  and  different  smoothness  as  made 
by  different  manufacturers  will  cause  materially  different  friction  losses. 
The  figures  are  the  number  of  feet  of  clean,  straight  pipe  of  same  size 
which  would  cause  the  same  loss  as  the  fitting.  Grinnell  dry-pipe  valve. 
6-in.,  80  ft.;  4-in.,  47  ft.  Grinnell  alarm  check,  6-in.,  100  ft.;  4-in.,  47  ft. 
Pratt  &  Cady  check  valve,  6-in.,  50  ft.;  4-in.,  25  ft.  4-in.  Walworth  globe 
check  valve,  6-in.,  200  ft.;  4-in.,  130' ft.  21/2  in.  to  8-in.  ells,  long-turn, 
4  ft.;  short-turn  9  ft.  3-in.  to  8-in,  tees,  long-turn,  9  ft.;  short-turn,  17  ft. 
One-eighth  bend,  5  ft. 

Effect  of  Bends  and  Curves  in  Pipes.  —  Weisbach's  rule  for  bends: 
Loss  of  head  in  feet  =  [0.131  +  1.847  (^)7/2J  X  ~  X  ^~,  in  which  r 

«*  internal  radius  of  pipe  in  feet,  R-  =  radius  of  curvature  of  axis  of  pipe, 
v  •=  velocity  in  feet  per  second,  and  a  =  the  central  angle,  or  angle  sub- 
tended by  the  bend. 

Hamilton  Smith,  Jr.,  in  his  work  on  Hydraulics,  says:  The  experimental 
data  at  hand  are  entirely  insufficient  to  permit  a  satisfactory  analysis  of 
this  quite  complicated  subject;  in  fact,  about  the  only  experiments  of 
value  are  those  made  by  Bossut  and  Dubuat  with  small  pipes. 

Curves.  —  If  the  pipe  has  easy  curves,  say  with  radius  not  less  than  5 
diameters  of  the  pipe,  the  flow  will  not  be  materially  diminished,  provided 
the  tops  of  all  curves  are  kept  below  the  hydraulic  grade-line  and  provision 
be  made  for  escape  of  air  from  the  tops  of  all  curves.  (Trautwine.) 

Williams,  Hubbell  and  Fenkel  (Trans.  A.  S.  C.  E.,  1901)  C9nclude  from 
an  extensive  series  of  experiments  that  curves  of  short  radius,  down  to 
about  21/2  diameters,  offer  less  resistance  to  the  flow  of  water  than  do 
those  of  longer  radius,  and  that  earlier  theories  and  practices  regarding 
curve  resistance  are  incorrect.  For  a  90°  curve  in  30  in.  cast-iron  pipe, 
6  ft.  radius,  they  found  the  loss  of  head  15.7%  greater  than  that  of  a 
straight  pipe  of  equal  length;  with  10  ft.  radius.  17.3%  greater:  with  25 ft. 
radius,  52.7%  greater;  and  with  60  ft.  radius,  90.2%  greater. 

Friction  Heads  for  Elbows.    Heads  Required  to  Overcome  the 
Resistance  of  Circular  90°  Bends. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.) 


Velocity 

Radius  of  Bend  in  Diameters  of  Pipe. 

in  Feet 
Per 

0.5 

0.75 

1.00 

1.25 

1.5     |      2.0 

3.0 

5.0 

Second. 

Head,  in  Feet. 

1 

0.016 

0.005 

0.002 

0.002 

0.001 

0.001 

0.001 

0.001 

2 

.062 

.018 

.009 

.007 

.005 

.005 

.004 

.004 

3 

.140 

.041 

.020 

.015 

.012 

.011 

.010 

.009 

4 

.245 

.072 

.036 

.026 

.021 

.019 

.017 

.016 

5 

.388 

.113 

.056 

.041 

.033 

.029 

.027 

.025 

6 

.559 

.162 

.081 

.059 

.048 

.042 

.038 

.036 

7 

.761 

.221 

.110 

.080' 

.066 

.057 

.052 

.050 

8 

.994 

.288 

.144 

.104 

.086 

.074 

.069 

.065 

9 

1.260 

.365 

.182 

.132 

.108 

.094 

.086 

.082 

10 

1.550 

.450 

.225 

.163 

.134 

.116 

.106 

.101 

12 

2.340 

.649 

.324 

.236 

.192 

.167 

.153 

.145 

748 


HYDRAULICS. 


Loss  of  Head  In  Pipes,  Tees  and  Elbows. — Results  of  tests  made 
on  locomotive  water  columns  by  Arthur  N.  Talbot  and  Melvin  L. 
Enger  (Bulletin  No.  48,  Univ.  of  111.  Engineering  Experiment  Station) 
may  be  expressed  by  the  following  formula:  Loss  of  head  in  100  ft.  of 
new  cast-iron  pipe  for  sizes  above  6  in.  diam.  =  0.044  v1*  •*•  d1-25,  in 
which  v  =  velocity  of  flow  in  feet  per  sec.,  and  d  =  internal  diameter  of 
pipe,  in  ft.  The  results  for  pipes  from  8  to  24  in.  in  diameter  agree 
closely  with  those  obtained  by  Williams  and  Hazen  for  pipes  after 
about  three  years  of  service,  with  the  diagram  given  in  Turneaure  and 
Russell's  "Public  Water  Supplies,"  and  with  the  formula  of  Unwin; 
they  are,  however,  generally  smaller  than  those  given  by  the  Ellis  and 
Howland  tables  and  by  Darcy's  formula. 

The  following  tables  are  taken  from  diagrams  included  in  the  Bulle- 
tin; they  give  the  values  selected  by  the  Committee  on  Water  Service, 
Am.  Ry.  Eng'g  and  Maintenance  of  Way  Association,  as  representing 
the  maximum  results  of  numerous  tests. 

LOSS  OF  HEAD  IN  TEES,  IN  FEET. 


Discharge, 
Gal  per 

Cu.  Ft. 

Sizes  o 

f  Tees. 

Min. 

Sec. 

8  In. 

10  In. 

12  In. 

14  In. 

16  In. 

18  In. 

1000.  ., 

20.5 

1.1 

0.4 

0.25 

2000.  ., 

41 

4 

1  7 

0  95 

0  40 

0  25 

0  13 

3000 

61  5 

8  7 

3  9 

1  95 

1  00 

0  60 

0  35 

4000 

82 

6  7 

3  35 

1  75 

1.10 

0  65 

5000.  . 

102  5 

10  3 

5  20 

2  70 

1  60 

1  00 

6000.  ., 

123 

7  30 

3  90 

2  30 

1  45 

7000  

143.5 

5  30 

3  10 

2  00 

8000  

164 

6.80 

3.90 

2.60 

LOSS  OF  HEAD  IN  ELBOWS,  IN  FEET. 

(Radius  of  curvature  of  elbow  axis  =  1.5  X  diameter  of  elbow.) 


Discharge, 
Gal  per 

Cu.  Ft. 
Der 

Sizes  of 

Elbows. 

Min. 

Sec. 

8  In. 

10  In. 

12  In. 

14  In. 

16  In. 

18  In. 

1000.  . 

20.5 

0.2 

2000  

41 

1.2 

0.5 

0.20 

0.10 

3000.  ., 

61.5 

2.8 

]   1 

0  50 

0  25 

0  15 

4000 

82 

1  9 

0  95 

0  50 

0  25 

0  10 

5000  
6000.  . 

102.5 
123 

3.2 

1.50 
2  20 

0.75 
1   15 

0.40 
0  60 

0.15 
0  25 

7000  '   ! 
8000.., 

143.5 
164 

3.00 

1.65 
2.10 

0.87 
1.15 

0.50 
0.70 

(Radius  of  curvature  =  3  X  diameter.) 


1000  
2000.  .. 

20.5 
41 

0.25 
0.75 

0.35 

0  10 





3000  

61.5 

2.00 

0.80 

0.40 

0.15 

4000.  ., 

82 

4  00 

1  45 

0  70 

0  33 

0  12 

5000  
6000. 

102.5 
123 

2.25 

1.10 
1  60 

0.50 
0  70 

0.20 
0  40 

0.07 
0  10 

7000.  . 

143  5 

2  20 

1  00 

0  58 

0  25 

8000  

164 

3.00 

1.45 

0.85 

0.45 

Hydraulic  Grade-line.  —  In  a  straight  tube  of  uniform  diameter 
throughout,  running  full  and  discharging  freely  into  the  air,  the  hydraulic 
grade-line  is  a  straight  line  drawn  from  the  discharge  end  to  a  point  imme- 
diately over  the  entry  end  of  the  pipe  and  at  a  depth  below  the  surface 
equal  to  the  entry  and  velocity  heads.  (Trautwine.) 

In  a  pipe  leading  from  a  reservoir,  no  part  of  its  length  should  be  above 
the  hydraulic  grade-line. 

Air-bound  Pipes.  —  A  pipe  is  said  to  be  air-bound  when,  In  conse- 
quence of  air  being  entrapped  at  the  high  points  of  vertical  curves  in  the 
line,  water  will  not  flow  out  of  the  pipe,  although  the  supply  is  higher  than 
the  outlet.  The  remedy  is  to  provide  cocks  or  valves  at  the  high  points, 


FIRE-STREAMS.  .  749 

through  which  the  air  may  be  discharged.  The  valve  may  be  made 
automatic  by  means  of  a  float. 

Water-Hammer. — When  selecting  valves  and  fittings,  the  possibility 
of  shock  or  strain  due  to  water-hammer,  in  excess  of  the  average  work- 
ing pressure  of  the  line  or  system,  should  be  considered.  Many  valves 
and  fittings,  installed  where  the  working  pressure  under  nomal  con- 
ditions would  be  low,  have  failed  because  of  pressure  due  to  water- 
hammer.  This  danger  can  be  avoided  by  proper  cushioning  of  the 
line  by  air  chambers,  or  by  relief  valves. 

When  a  valve  in  a  pipe  is  closed  while  the  water  is  flowing,  the  velocity 
of  the  water  behind  the  valve  is  retarded  and  a  dynamic  pressure  is 
produced.  When  the  valve  is  closed  quickly  this  dynamic  pressure 
may  be  very  great.  It  is  then  called  "water-hammer"  or  "water- 
ram,"  and  it  causes  in  many  cases  fracture  of  the  pipe.  It  is  provided 
against  by  arrangements  which  prevent  the  rapid  closing  of  the  valve. 
Formulae  for  the  pressure  produced  by  this  shock  are  (see  Merriman's 
Hydraulics) 

p  =  0.027  £H_po  +  pi.    .    .     (1)  P=63v-Po+Pi (2) 

where  po  =  the  static  pressure,  Ib.  per  sq.  in.,  when  there  is  no  flow, 
Pi  =  the  static  pressure  when  the  flow  is  in  progress,  p  =  the  maximum 
dynamic  pressure  due  to  the  water-hammer  in  excess  over  the  pressure 
p*  v  =  the  velocity  in  feet  per  second,  L  =  length  of  pipe  back  from 
the  valve  in  feet,  and  t  =  time  of  closing  the  valve  in  seconds.  Formula 
(1)  is  to  be  used  when  t  is  greater  than  0.000428L  and  (2)  when  t  is 
equal  to  or  less  than  this. 

From  the  first  of  these  formulae  the  value  of  t  when  p  —  0  is  found 
to  be  t  =  0.027  Lv  -±  (PO-PI),  which  is  the  time  required  for  the 
valve  closing  in  order  that  there  may  be  no  water-hammer. 

Vertical  Jets.  (Molesworth.)  —  H  =  head  of  water,  h  =  height  of 
jet,  d  =  diameter  of  jet,  K  =  coefficient,  varying  with  ratio  of  diameter 
of  jet  to  head;'  then  h  =  KH. 

If  H  =  d  X  300       600       1000       1500       1800       2800       3500       4500 
K  =        0.96       0.9       O.S5         0.8        0.7          0.6         0.5      0.25 

Water   Delivered    through  Meters.     (Thomson  Meter  Co.)  —  The 
best  modern  practice  limits  the  velocity  in  water-pipes  to  10  lineal  feet 
per  second.     Assume  this  as  a  basis  of  delivery,  and  we  find,  for  the  sev- 
eral sizes  of  pipes  usually  metered,  the  following  approximate  results: 
Nominal  diameter  of  pipe  in  inches: 

3/8        5/8        3/4  1        11/2         2  3  4  6 

Quantity  delivered,  in  cubic  feet  per  minute,  due  to  said  velocity: 
0.46     1.28     1.85     3.28     7.36     13.1     29.5     52.4     117.9 

Prices  Charged  for  Water  in  Different  Cities.     (National  Meter  Co.) 

Average  minimum  price  for  1000  gallons  in  163  places .9.4  cents. 

Average  maximum  price  for  1000  gallons  in  163  places 28 

Extremes,  21/2  cents  to 100 

FIRE-STREAMS. 

Fire-Stream  Tables. — The  tables  on  pages  750  and  751  are  con- 
densed from  one  contained  in  the  pamphlet  of  "Fire-Stream  Tables" 
of  the  Associated  Factory  Mutual  Fire  Ins.  Cos.,  based  on  the  experi- 
ments of  John  K.  Freeman,  Trans.  A.  S.  C.  E.,  vol.  xxi,  1889. 

The  pressure  in  the  first  column  is  that  indicated  by  a  gauge  attached 
at  the  base  of  the  play  pipe  and  set  level  with  the  end  of  the  nozzle.  The 
vertical  and  horizontal  distances,  in  2d  and  3d  cols.,  are  those  of  effective 
fire-streams  with  moderate  wind.  The  maximum  limit  of  a  "  fair  stream  " 
is  about  10%  greater  for  a  vertical  stream;  12%  for  a  horizontal  stream. 
In  still  air  much  greater  distances  are  reached  by  the  extreme  drops. 
The  pressures  given  are  for  the  best  quality  of  rubber-lined  hose,  smooth 
inside.  The  hose  friction  varies  greatly  in  different  kinds  of  hose,  accord- 
ing to  smoothness  of  inside  surface,  and  pressures  as  much  as  50% 
greater  are  required  for  the  same  delivery  in  long  lengths  of  inferior 
rubber-lined  or  linen  hose.  The  pressures  at  the  hydrant  are  those  while 
the  stream  is  flowing,  and  are  those  required  with  smooth  nozzles.  Ring 


750 


HYDRAULICS. 


nozzles  require  greater  pressures.     With  the  same  pressures  at  the  base 
01  tne  play  pipe,  the  discharge  of  a3/4-in.  smooth  nozzle  is  the  same  as  that 
or  a  7/8-m.  ring  nozzle;  of  a  7/g-in.  smooth  nozzle,  the  same  as  that  of  a ' 
1-in.  ring  nozzle. 

The  figures  for  hydrant  pressure  in  the  body  of  the  table  are  derived 
py  adding  to  the  nozzle  or  play-pipe  pressure  the  friction  loss  in  the 
nose,  and  also  the  friction  loss  of  a  Chapman  4-way  independent  gate 
hydrant  ranging  from  0.86  Ib.  for  200  gals,  per  min.  flowing  to  2.31  Ibs. 
for  600  gals. 

The  following  notes  are  taken  from  the  pamphlet  referred  to.  The 
discharge  as  stated  in  Ellis's  tables  and  in  their  numerous  copies  in  trade 
catalogues  is  from  15  to  20%  in  error. 

In  the  best  rubber-lined  hose,  2i/2-in.  diam.,  the  loss  of  head  due  to 
friction,  for  a  discharge  of  240  gallons  per  minute,  is  14.1  Ibs.  per  100  ft. 
length;  in  inferior  rubber-lined  mill  hose,  25.5  Ibs.,  and  in  unlined  linen 
hose,  33.2  Ibs. 

Less  than  a  ll/s-in.  smooth-nozzle  stream  with  40  Ibs.  pressure  at  the 
base  of  the  play  pipe,  discharging  about  240  gals,  per  min.,  cannot  be 
called  a  first-class  stream  for  a  factory  fire.  80  Ibs.  per  sq.  in.  is  con- 
sidered the  best  hydrant  pressure  for  general  use;  100  Ibs.  should  not  be 
exceeded,  except  for  very  high  buildings,  or  lengths  of  hose  over  300  ft. 

Hydrant  Pressures  Required  with  Different  Sizes  and  Lengths  of 
Hose.     (J.  R.  Freeman,  Trans.  A.  S.  C.  E.,  1889.) 

3/4-inch  smooth  nozzle.  * 


J 

r 

1 

Fire- 
steam 
Distance. 

Gal.  per  Min. 

Hydrant  Pressure  with  Different  Lengths  of 
Hose  to  Maintain  Pressure  at  Base  of  Play  Pipe. 

Vert. 

Hor. 

50ft. 

100ft. 

200ft. 

300ft. 

400ft. 

500ft. 

600ft. 

800ft. 

1000 
ft. 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 

17 
33 

48 
60 
67 
72 
76 
79 
81 
83 

19 
29 
37 
44 
50 
54 
58 
62 
65 
68 

52 
73 
90 
104 
116 
127 
137 
147 
156 
164 

10 
21 
31 
42 
52 
63 
73 
84 
94 
105 

11 

22 
32 
43 
54 
65 
75 
86 
97 
108 

11 
23 
34 
46 
57 
68 
80 
91 
102 
114 

12 
24 
36 
48 
60 
72 
84 
96 
108 
120 

13 
25 
38 
50 
63 
76 
88 
101 
113 
126 

13 
26 
40 
53 
66 
79 
92 
106 
119 
132 

14 
28 
41 
55 
69 
83 
97 
111 
124 
138 

15 
30 
45 
60 
75 
90 
105 
120 
135 
150 

16 
32 
49 
65 
81 
97 
114 
130 
146 
163 

7/8-inch  smooth  nozzle. 


10 

18 

21 

71 

11 

11 

13 

14 

15 

16 

17 

19 

22 

20 

34 

33 

100 

22 

23 

25 

27 

30 

32 

34 

39 

43 

30 

49 

42 

123 

33 

34 

38 

41 

45 

48 

51 

58 

65 

40 

62 

49 

142 

43 

46 

50 

55 

59 

64 

68 

78 

87 

50 

71 

55 

159 

54 

57 

63 

69 

74 

80 

86 

97 

108 

60 

77 

61 

174 

65 

69 

75 

82 

89 

96 

103 

116 

130 

70 

81 

66 

188 

76 

80 

88 

96 

104 

112 

120 

136 

152 

80 

85 

70 

201 

87 

91 

101 

110 

119 

128 

137 

155 

173 

90 

88 

74 

213 

98 

103 

113 

123 

134 

144 

154 

174 

195 

100 

90 

76 

224 

109 

114 

126 

137 

148 

160 

171 

194 

216 

1-inch  smooth  nozzle. 

10 

18 

21 

93 

12 

12 

14 

16 

18 

20 

22 

26 

30 

20 

35 

37 

132 

23 

25 

29 

33 

37 

41 

45 

52 

60 

30 

51 

47 

161 

34 

37 

43 

49 

55 

61 

67 

79 

90 

40 

64 

55 

186 

46 

50 

58 

66 

73 

81 

89 

105 

120 

50 

73 

61 

208 

57 

62 

72 

82 

92 

102 

111 

131 

151 

60 

79 

67 

228 

69 

75 

87 

98 

110 

122 

134 

157 

181 

70 

85 

72 

246 

80 

87 

101 

115 

128 

142 

156 

183 

211 

80 

89 

76 

263 

92 

100 

115 

131 

147 

162 

178 

209 

241 

90 

92 

80 

279 

103 

112 

130 

147 

165 

183 

200 

236 

.... 

100 

96 

83 

295 

115 

125 

144 

164 

183 

203 

223 

FIBE-STREAMS. 


751 


Hydrant  Pressures  Required  with  Different  Sizes  and  Lengths  of 

Hose. — Continued. 
1  i/8-inch  smooth  nozzle. 


A 

Fire- 
Steam 
Distance. 

a 

1. 

h 

0 

a 

"08 

o 

Hydrant  Pressure  with  Different  Lengths  of 
Hose  to  Maintain  Pressure  at  Base  of  Play  Pipe. 

Vert. 

Hor. 

50ft. 

100ft. 

200ft. 

300ft. 

400ft. 

500ft. 

600ft. 

800ft. 

1000 
ft. 

10 

20 
30 
40 
50 
60 
70 
80 
90 
100 

18 
36 
52 
65 
75 
83 
88 
92 
96 
99 

22 
38 
50 
59 
66 
72 
77 
81 
85 
89 

119 
168 
206 
238 
266 
291 
314 
336 
356 
376 

12 
25 
37 
50 
62 
74 
87 
99 
112 
124 

14 

28 
42 
56 
70 
84 
98 
112 
126 
140 

17 
34 
52 
69 
86 
103 
120 
138 
155 
172 

20 
41 
61 
81 
102 
122 
143 
163 
183 
204 

24 
47 
71 
94 
118 
141 
165 
188 
212 
236 

27 
54 
80 
107 
134 
160 
187 
214 
241 

30 
60 
90^ 
120 
150 
180 
209 
239 

36 
73 
109 
145 
181 
218 
254 

43 
85 
128 
171 
213 
256 

1  i/4-inch  smooth  nozzle. 


10 
20 
30 
40 
50 
60 

19 
37 
53 
67 
77 
85 

22 
40 
54 
63 
70 
76 

1-48 
209 
256 
296 
331 
363 

14 
27 
41 
55 
68 
82 

16 
32 
49 
65 
81 
97 

21 
42 
63 
84 
106 
127 

26 
52 
78 
104 
130 
156 

31 
62 
93 
124 
155 
186 

36 
72 
108 
144 
180 
216 

41 

82 
123 
164 
204 
245 

51 

101 

152 
203 

254 

61 

121 

182 
243 

70 

91 

81 

39? 

96 

113 

148 

182 

217 

252 

80 

95 

85 

410 

110 

129 

169 

208 

248 

90 

99 

90 

444 

123 

145 

190 

234 

100 

101 

93 

468 

137 

162 

211 

261 

1 3/8-inch  smooth  nozzle. 


10 

20 
30 
40 

20 
38 
55 
69 

23 
42 
56 
66 

182 
257 
315 
363 

16 
31 
47 
62 

19 
39 

58 
77 

27 
53 
80 
107 

34 
68 
103 
137 

42 
83 
125 
166 

49 
98 
147 
196 

56 
113 
169 
226 

71 
143 
214 

86 
173 
259 

50 

79 

73 

405 

78 

96 

134 

171 

208 

245 

60 

87 

79 

445 

93 

116 

160 

205 

250 

70 

92 

84 

480 

109 

135 

187 

239 



80 

97 

88 

514 

\?A 

154 

214 

90 

100 

92 

•M1) 

140 

173 

240 

too 

103 

96 

574 

156 

193 

Pump  Inspection  Table. 

Discharge  of  nozzles  attached  to  50  ft.  of  2 1  ,/2-in.  best  quality  rubber- 
lined  hose,  inside  smooth.      (J.  R.  Freeman.) 


d  3 

Size  of  Smooth  Nozzle. 

Ring  Nozzle. 

Wftj 

1  3/4 

1  1/2 

1  3/8 

1  V4 

1  VS. 

1 

7/8 

3/4 

1  3/8 

1  V4 

1  1/8 

10 

193 

163 

146 

127 

107 

87 

68 

5? 

118 

101 

84 

20 

274 

232 

206 

179 

151 

123 

96 

72 

167 

143 

119 

30 

335 

283 

251 

219 

184 

150 

118 

88 

205 

175 

145 

40 

387 

327 

291 

253 

213 

173 

136 

101 

237 

202 

168 

50 

432 

366 

323 

283 

238 

194 

152 

113 

264 

226 

188 

60 

473 

400 

357 

309 

261 

213 

167 

124 

289 

247 

205 

70 

510 

432 

385 

334 

281 

230 

180 

134 

313 

267 

222 

80 

546 

461 

412 

357 

301 

246 

192 

144 

334 

285 

237 

90 

579 

490 

437 

379 

319 

261 

204 

152 

355 

303 

252 

100 

610 

515 

461 

400 

337 

275 

215 

161 

374 

319 

266 

752 


HYDRAULICS. 


Pipe  Sizes  for  Ordinary  Fire-Streams. 

(U.  S.  Cast  Iron  Pipe  &  Foundry  Co.,  1914.) 


No. 

40  Lb. 

50  Lb. 

60  Lb. 

70  Lb. 

80  Lb. 

90  Lb. 

of 

1  l/o 

Pressure. 

Pressure. 

Pressure. 

Pressure. 

Pressure. 

Pressure. 

/  8 

In. 

a 

£ 

a 

d 

^a 

3 

Hose 
Noz- 

|| 

1 

II 

o 

.11 

o 

it 

o 

li 

o 

|i 

! 

zles. 

£*'& 

E 

£c/] 

| 

Pn03 

E 

fig 

g 

f^'m 

g 

ftai 

E 

1 

4 

20 

6 

23 

6 

25 

6 

27 

6 

29 

6 

30 

2 

6 

40 

8 

45 

8 

50 

8 

53 

8 

57 

8 

61 

3 

8 

61 

8 

68 

10 

74 

10 

80 

10 

86 

10 

91 

4 

10 

81 

10 

90 

10 

99 

10 

107 

12 

114 

12 

121 

5 

10 

101 

12 

113 

12 

124 

12 

134 

12 

143 

12 

152 

6 

12 

121 

12 

135 

12 

149 

14 

160 

14 

172 

14 

182 

7 

12 

141 

14 

158 

14 

174 

14 

187 

14 

200 

16 

212 

8 

12 

162 

14 

181 

14 

199 

16 

214 

16 

229 

16 

242 

9 

14 

182 

14 

203 

16 

223 

16 

241 

16 

257 

18 

273 

10 

14 

202 

16 

226 

16 

248 

16 

267 

18 

286 

18 

303 

11 

16 

222 

16 

248 

18 

273 

18 

294 

18 

314 

18 

333 

12 

16 

243 

18 

271 

18 

298 

18 

321 

20 

343 

20 

364 

13 

16 

263 

18 

293 

18 

323 

20 

348 

20 

372 

20 

394 

14 

18 

283 

18 

316 

20 

348 

20 

374 

20 

400 

20 

424 

15 

18 

303 

20 

339 

20 

372 

20 

401 

20 

429 

24 

455 

Flow  given  in  cubic  feet  per  minute.  Figures  are  based  on  1  %-in. 
smooth-bore  nozzles,  playing  simultaneously  and  attached  to  200  ft. 
of  best  quality  rubber-lined  hose;  pressures  measured  at  hose  connec- 
tions. Velocity  of  water  in  pipe,  approximately  3  ft.  per  second. 

Friction  Loss  in  Rubber-Lined  Cotton  Hose  with  Smoothest  Lining. 


03 

1 
"o 

a 

c3 

3 

2 
21/8 
21/4 
23/8 

21/2 

18 

fa 

»* 

Gallons  per  Minute  Flowing. 

dj 

|l 

>& 

Velocity 
Head 
72  -  20. 

100 

200 

300 

400 

500 

600 

700 

800 

1000 

Friction  Loss,  Pounds  per  100ft.  Length. 

Ft. 

Lbs. 

0.17 
0.69 
1.5 
2.7 
4.2 
6.1 
8.2 
10.7 
13.6 
16.7 

6.836 
5.170 
3.790 
2.895 
2.240 
1.748 
1.391 
1.097 
0.900 
0:416 
0.214 

27.3 
20.7 
15.2 
11.6 
9.0 
7.0 
5.6 
4.4 
3.6 
1.7 
0.9 

61.5 
46.5 
34.1 
26.1 
20.2 
15.7 
12.5 
9.9 
8.1 
3.7 
1.9 

109 
82.7 
60.6 
46.3 
35.8 
23.0 
22.3 
17.6 
14.4 
6.7 
3.4 

171 
129 
94.7 
72.4 
56.0 
43.7 
34.8 
27.4 
22.5 
10.4 
5.4 

5 

10 
15 
20 
25 
30 
35 
40 
45 
50 

0.39 
1.6 
3.5 
6.2 
9.7 
14.0 
19.0 
24.8 
31.4 
38.8 

189 
136 
104 
80.6 
62.9 
50.1 
39.5 
32.4 
15.0 
7.7 

186 
138 
110 
85.7 
68.2 
53.8 
44.1 
20.4 
10.5 

185 
143 
112 
89.0 
70.2 
57.6 
26.6 
13.7 

224 
175 
139 
110 
90 
41.6 
21.4 

The  above  table  is  computed  on  the  basis  of  14  Ibs.  per  100  ft.  length 
of  2i/2-in.  hose  with  250  gals,  per  min.  flowing,  as  found  in  Freeman's 
tests,  assuming  that  the  loss  varies  as  the  square  of  the  quantity,  and 
for  different  diameters  and  the  same  quantity  inversely  as  the  5th  power 
of  the  diameter. 

Rated  Capacities  of  Steam  Fire-engines,  which  is  perhaps  one  third 
greater  than  their  ordinary  rate  of  work  at  fires,  are  substantially  as 
follows : 

3d  size,     550  gals,  per  min.,  or     792,000  gals,  per  24  hours. 

2d    "         700     "  1,008,000 

1st    "         900     "  "  1,296,000 

1  ext..    1,100    •"  !'  1.584,000        !! 


FLOW  OF  WATER  THROUGH  NOZZLES. 


753 


p.b 


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754  HYDRAULICS. 


THE    SIPHON. 

The  Siphon  is  a  bent  tube  of  unequal  branches,  open  at  both  ends,  and 
is  used  to  convey  a  liquid  from  a  higher  to  a  lower  level,  over  an  interme- 
diate point  higher  than  either.  Its  parallel  branches  being  in  a  vertical 
plane  and  plunged  into  two  bodies  of  liquid  whose  upper  surfaces  are  at 
different  levels,  the  fluid  will  stand  at  the  same  level  both  within  and 
without  each  branch  of  the  tube  when  a  vent  or  small  opening  is  made 
at  the  bend.  If  the  air  be  withdrawn  from  the  siphon  through  this  vent, 
the  water  will  rise  in  the  branches  by  the  atmospheric  pressure  without, 
and  when  the  two  columns  unite  and  the  vent  is  closed,  the  liquid  will 
flow  from  the  upper  reservoir  as  long  as  the  end  of  the  shorter  branch 
of  the  siphon  is  below  the  surface  of  the  liquid  in  the  reservoir. 

If  the  water  was  free  from  air  the  height  of  the  bend  above  the  supply 
level  might  be  as  great  as  33  feet. 

If  A  =  area  of  cross-section  of  the  tube  in  square  feet,  H  =  the  differ- 
ence in  level  between  the  two  reservoirs  in  feet,  D  the  density  of  the 
liquid  in  pounds  per  cubic  foot,  then  ADH  measures  the  intensity  of  the 
force  which  causes  the  movement  of  the  fluid,  and  V  =  ^2gH=  8.02 
"*/H  is  the  theoretical  velocity,  in  feet  per  second,  which  is  reduced  by 
the  loss  of  head  for  entry  and  friction,  as  in  other  cases  of  flow  of  liquids 
through  pipes.  In  the  case  of  the  difference  of  level  being  greater  than 
33  feet,  however,  the  velocity  of  the  water  in  the  shorter  leg  is  limited 
to  that  due  to  a  height  of  33  feet,  or  that  due  to  the  difference  between 
the  atmospheric  pressure  at  the  entrance  and  the  vacuum  at  the  bend. 

Long  Siphons.  —  Prof.  Joseph  Torrey,  in  the  Amer.  Machinist,  de- 
scribes a  long  siphon  which  was  a  partial  failure. 

The  length  of  the  pipe  was  1792  feet.  The  pipe  was  3  inches  diameter, 
and  rose  at  one  point  9  feet  above  the  initial  level.  The  final  level  was 
20  feet  below  the  initial  level.  No  automatic  air  valve  was  provided. 
The  highest  point  in  the  siphon  was  about  one  third  the  total  distance 
from  the  pond  and  nearest  the  pond.  At  this  point  a  pump  was  placed, 
whose  mission  was  to  fill  the  pipe  when  necessary.  This  siphon  would 
flow  for  about  two  hours  and  then  cease,  owing  to  accumulation  of  air  in 
the  pipe.  When  in  full  operation  it  discharged  431/2  gallons  per  minute. 
The  theoretical  discharge  from  such  a  sized  pipe  with  the  specified  head 
is  551/2  gallons  per  minute. 

Siphon  on  the  Water-supply  of  Mount  Vernon,  X,  T.  (Eng'g 
News,  May  4,  1893.)  —  A  12-inch  siphon,  925  feet  long,  with  a  maximum 
lift  of  22.12  feet  and  a  45°  change  in  alignment,  was  put  in  use  in  1892  „ 
by  the  New  York  City  Suburban  Water  Co.  At  its  summit  the  siphon 
crosses  a  supply  main,  which  is  tapped  to  charge  the  siphon.  The  air- 
chamber  at  the  siphon  is  12  inches  by  16  feet  long.  A  i/2-inch  tap  and 
cock  at  the  top  of  the  chamber  provide  an  outlet  for  the  collected  air. 

It  was  found  that  the  siphon  with  air-chamber  as  described  would  run 
until  125  cubic  feet  of  air  had  gathered,  and  that  this  took  place  only 
half  as  soon  with  a  14-foot  lift  as  with  the  full  lift  of  22.12  feet.  The 
siphon  will  operate  about  12  hours  without  being  recharged,  but  more 
water  can  be  gotten  over  by  charging  every  six  hours.  It  can  be  kept 
running  23  hours  out  of  24  with  only  one  man  in  attendance.  With  the 
siphon  as  described  above  it  is  necessary  to  close  the  valves  at  each  end 
of  the  siphon  to  recharge  it.  It  has  been  found  by  weir  measurements 
that  the  discharge  of  the  siphon  before  air  accumulates  at  the  summit  is 
practically  the  same  as  through  a  straight  pipe. 

A  successful  siphon  is  described  by  R.  S.  Hale  in  Jour.  Assoc.  Eng. 
Soc.,  1900.  A  2-in.  galvanized  pipe  had  been  used,  and  it  had  been  nec- 
essary to  open  a  waste-pipe  and  thus  secure  a  continuous  flow  in  order 
to  keep  the  siphon  in  operation.  The  trouble  seemed  to  be  due  to  very 
small  air  leaks  in  the  joints.  When  the  2-in.  iron  pipe  was  replaced  by  a 
1-in  lead  pipe,  the  siphon  was  entirely  successful.  The  maximum  rise 
of  the  pipe  above  the  level  of  the  pond  was  12  ft.,  the  discharge  about 
850  ft.  below  the  level,  and  the  length  500  ft. 


VELOCITY  OF  ^ATER  IN  OPEN   CHANNELS.       755 


VELOCITY  OF  WATER  IN  OPEN  CHANNELS. 

Irrigation  Canals.  —  The  minimum  mean  velocity  required  to  pre- 
vent the  deposit  of  silt  or  the  growth  of  aquatic  plants  is  in  Northern 
India  taken  at  1 1/2  feet  per  second.  It  is  stated  that  in  America  a  higher 
velocity  is  required  for  this  purpose,  and  it  varies  from  2  to  3 1/2  feet  per 
second.  The  maximum  allowable  velocity  will  vary  with  the  nature  of 
the  soil  of  the  bed.  A  sandy  bed  will  be  disturbed  if  the  velocity  exceeds 
3  feet  per  second.  Good  loam  with  not  too  much  sand  will  bear  a  velocity 
of  4  feet  per  second.  The  Cavour  Canal  in  Italy,  over  a  gravel  bed,  has  a 
velocity  of  about  5  per  second.  (Flynn's  "Irrigation  Canals.") 

Mean  Surface  and  Bottom  Velocities.  —  According  to  the  formula 

of  Bazin.  

v=  1W^-  25-4  Vrs;  v  =  Vb  +  10.87  \/rs. 

.*.  vj)  =*  v  —  10.87  Vrs,  in  which  v  =  mean  velocity  in  feet  per  second, 
vmax=  maximum  surface  velocity  in  feet  per  second,  v&=  bottom  velocity 
in  feet  per  second,  r  =  hydraulic  mean  depth  in  feet  =  area  of  cross-section 
in  square  feet  divided  by  wetted  perimeter  in  feet,  s  =  sine  of  slope. 

The  least  velocity,  or  that  of  the  particles  in  contact  with  the  bed,  is 
almost  as  much  less  than  the  mean  velocity  as  the  greatest  velocity  is 
greater  than  the  mean. 

Rankine  states  that  in  ordinary  cases  the  velocities  may  be  taken  as 
bearing  to  each  other  nearly  the  proportions  of  3,  4,  and  5.  In  very  slow 
currents  they  are  nearly  as  2,  3,  and  4. 

Safe  Bottom  and  Mean  Velocities. — Ganguillet  &  Kutter  give  the 
following  table  of.  safe  bottom  and  mean  velocities  in  channels,  calculated 
from  the  formula  v  =  Vb  + 


Material  of  Channel. 

Safe  Bottom  Velocity 
Vfr,  in  Feet  per  Second. 

Mean  Velocity  v,  in 
Feet  per  Second. 

Soft  brown  earth 

0  249 

0  328 

0  499 

0  656 

Sar  d    

1  000 

1  312 

Gravel  

1.998 

2.625 

Pebbles 

2  999 

3  938 

Broken  stone,  flint  .    

4  003 

5  579 

Conglomerate,  soft  slate.  .  .  . 
Stratified  rock  

4.988 
6  006 

6.564 
8  204 

Hard  rock  

10.009 

13.127 

Ganguillet  &  Kutter  state  that  they  are  unable  for  want  of  observations 
to  judge  how  far  these  figures  are  trustworthy.  They  consider  them  to  be 
rather  disproportionately  small  than  too  large,  and  therefore  recommend 
them  more  confidently. 

Water  flowing  at  a  high  velocity  and  carrying  large  quantities  of  silt  is 

very  destructive  to  channels,  even  when  constructed  of  the  best  masonry. 

Resistance  of  Soils  to  Erosion  by  Water.  —  W.  A.    Burr,    En&g 

News,  Feb.  8,  1894,  gives  a  diagram  showing  the  resistance  of  various  soils 

to  erosion  by  flowing  water. 

Experiments  show  that  a  velocity  greater  than  1.1  feet  per  second  will 
erode  sand,  while  pure  clay  will  stand  a  velocity  of  7.35  feet  per  second. 
The  greater  the  proportion  of  clay  carried  by  any  soil,  the  higher  the  per- 
missible velocity.  Mr.  Burr  states  that  experiments  have  shown  that  the 
line  describing  the  power  of  soils  to  resist  erosion  is  parabolic.  From  his 
diagram  the  following  figures  are  selected  as  representing  different  classes 
of  soils: 

Pure  sand  resists  erosion  by  flow  of 1.1    feet  per  second. 

Sandy  soil,  15%  clay 1.2  '  " 

Sandy  loam,  40%  clay 1.8 

Loamy  soil,  65%  clay 3.0 

Clay  loam,  85%  clay 4.8 

Agricultural  clay,  95%  clay 6.2 

Clay. ! 7.35 

Abrading  and  Transporting  Power  of  Water. — Prof.  J.  LeConte, 
in  his  "Elements  of  Geology,"  states: 

The  erosive  power  of  water,  or  its  power  of  overcoming  cohesion, 
5.  varies  as  the  square  of  the  velocity  of  the  current, 


756 


HYDFAULTCS. 


The  transporting  power* of  a  current  varies  as  "the  sixth  power  of  the 
velocity.  *  *  *  If  the  velocity  therefore  be  increased  ten  times,  the 
transporting  power  is  increased  1,000,000  times.  A  current  running 
three  feet  per  second,  or  about  two  miles  per  hour,  will  bear  fragments 
of  stone  of  the  size  of  a  hen's  egg,  or  about  three  ounces  weight.  A 
current  of  ten  miles  an  hour  will  bear  fragments  of  one  and  a  half  tons, 
and  a  torrent  of  twenty  miles  an  hour  will  carry  fragments  of  100  tons. 

The  transporting  power  of  water  must  not  be  confounded  with  its 
erosive  power.  The  resistance  to  be  overcome  in  the  one  case  is  weight, 
in  the  other,  cohesion;  the  latter  varies  as  the  square:  the  former  as  the 
sixth  power  of  the  velocity. 

In  many  cases  of  removal  of  slightly  cohering  material,  the  resistance 
is  a  mixture  of  these  two  resistances,  and  the  power  of  removing  mate- 
rial will  vary  at  some  rate  between  v2  and  v6. 

Baldwin  Latham  has  found  that  in  order  to  prevent  deposits  of  sewage 
silt  in  small  sewers  or  drains,  such  as  those  from  6  inches  to  9  inches 
diameter,  a  mean  velocity  of  not  less  than  3  feet  per  second  should  be 
produced.  Sewers  from  12  to  24  inches  diameter  should  have  a  velocity 
of  not  less  than  21/2  feet  per  second,  and  in  sewers  of  larger  dimensions 
in  no  case  should  the  velocity  be  less  than  2  feet  per  second. 

The  specific  gravity  of  the  materials  has  a  marked  effect  upon  the 
mean  velocities  necessary  to  move  them.  T.  E.  Blackwell  found  that 
coal  of  a  sp.  gr.  of  1.26  was  moved  by  a  current  of  from  1.25  to  1.50  ft. 
per  second,  while  stones  of  a  sp.  gr.  of  2.32  to  3.00  required  a  velocity  of 
2.5  to  2.75  ft.  per  second. 

Chailly  gives  the  following  formula  for  finding  the  velocity  required  to 
move  rounded  stones  or  shingle: 

v  =  5.67  ^ag, 

in  which  v  =  velocity  of  water  in  feet  per  second,  a  =  average  diameter 
in  feet  of  the  body  to  be  moved,  g  =  its  specific  gravity. 

Geo.  Y.  Wisner,  Eng'g  News,  Jan.  10,  1895,  doubts  the  general  accuracy 
of  statements  made  by  many  authorities  concerning  the  rate  of  flow  of 
a  current  and  the  size  of  particles  which  different  velocities  will  move. 
He  says: 

The  scouring  action  of  any  river,  for  any  given  rate  of  current,  must 
be  an  inverse  function  of  the  depth.  The  fact  that  some  engineer  has 
found  that  a  given  velocity  of  current  on  some  stream  of  unknown  depth 
will  move  sand  or  gravel  has  no  bearing  whatever  on  what  may  be  ex- 
pected of  currents  of  the  same  velocity  in  streams  of  greater  depths.  In 
channels  3  to  5  ft.  deep  a  mean  velocity  of  3  to  5  ft.  per  second  may 
produce  rapid  scouring,  while  in  depths  of  18  ft.  and  upwards  current 
velocities  of  6  to  8  ft.  per  second  often  have  no  effect  whatever  on  the 
Channel  bed. 

Frictional  Resistance  of  Surfaces  Moved  in  Water.  (Ency.  Brit., 
llth  ed.  Vol.  xiv,  p.  58.) — Froude's  experiments  were  made  by  pulling 
boards  19  in.  wide,  3/8  in.  thick,  finely  sharpened  at  both  ends,  set  edge- 
wise in  water.  The  following  table  gives:  A,  the  power  of  the  speed 
to  which  the  resistance  is  proportional;  B,  the  mean  resistance  in 
pounds  per  sq.  ft.  of  the  whole  surface  of  a  board  of  the  lengths  stated 
In  the  table,  at  the  standard  speed  of  10  ft.  per  second. 


Surface. 

Length  of  Surface,  in  Feet. 

2ft. 

8ft. 

20ft. 

50ft. 

Varnish      ..... 

A 
2.00 

B 
0.41 
0.38 
0.30 
0.87 
0.81 
0.90 
1.10 

A 
1.85 
1  .94 
1.99 
1.92 
2.00 
2.00 
2.00 

B 
0.325 
0.314 
0.278 
0.626 
0.583 
0.625 
0.714 

A 
1.85 
1.93 
1.90 
1.89 
2.00 
2.00 
2.00 

B 
0.278 
0.271 
0.262 
0.531 
0.480 
0.534 
0.588 

A 
1.83 

B 
0.226 

Paraffin 

Tinfoil  

2.J6 
1.93 
2.00 
2.00 
2.00 

1.83 
1  .87 
2.06 
2.00 

0.232 
0.423 
0.337 
0.456 

Calico        .... 

Fine  Sand  
Medium  Sand.  . 
Coarse  Sand  .  .  . 

Unwin's  experiments  (Proc.  Inst.  Civ.  Engrs.,  Ixxx)  were  made  with 
disks  10,  15,  and  20  in.  diam.  rotated  in  water  by  a  vertical  shaft,  in 
Chambers  22  in.  diam.,  and  3,  6,  and  12  in.  deepr  In  all  cases  the  fric- 


MEASUREMENT   OF  FLOWING  WATER,  757 

tional  resistances  increased  a  little  as  the  chamber  was  made  larger. 
The  friction  depends  not  only  on  the  surface  of  the  disk,  but  to  some 
extent  on  the  surface  of  the  chamber  in  which  it  rotates.  For  the 
smoother  surface  the  friction  varied  as  the  1.85  power  of  the  velocity. 
For  rougher  surfaces  it  varied  as  the  1.9  to  the  2.1  power.  The  friction 
decreased  18  per  cent  with  increase  of  temperature  from  41°  to  130°  P. 
The  resistances  in  pounds  per  sq.  ft.  at  10  ft.  per  second  were  as 
follows  for  different  surfaces:  Bright  brass,  0.202  to  0.229;  Varnish, 
0.220  to  0.233;  Fine  sand,  0.339;  Very  cparse  sand,  0.587  to  0.715. 
The  results  agree  fairly  well  with  those  obtained  by  Froude  with  planks 
50  ft.  long. 

Grade  of  Sewers.  — The  following  empirical  formula  is  given  in  Bau- 
meister's  "Cleaning  and  Sewerage  of  Cities,"  for  the  minimum  grade 
for  a  sewer  of  clear  diameter  equal  to  d  inches,  and  either  circular  or 
oval  in  section: 

'  Minimum  grade,  in  per  cent    —  •  • 

As  the  lowest  limit  of  grades  which  can  be  flushed,  0.1  to  0.2  per  cent 
may  be  assumed  for  sewers  which  are  sometimes  dry,  while  0.3  per  cent 
is  allowable  for  the  trunk  sewers  in  large  cities.  The  sewers  should  run 
dry  as  rarely  as  possible. 

MEASUREMENT   OF   FLOWING    WATER. 

Piezometer.  —  If  a  vertical  or  oblique  tube  be  inserted  into  a  pipe 
containing  water  under  pressure,  the  water  will  rise  in  the  former,  and  the 
vertical  height  to  which  it  rises  will  be  the  head  producing  the  pressure 
at  the  point  where  the  tube  is  attached.  Such  a  tube  is  called  a  piezom- 
eter or  pressure  measure.  If  the  water  in  the  piezometer  falls  below 
its  proper  level  it  shows  that  the  pressure  in  the  main  pipe  has  been 
reduced  by  an  obstruction  between  the  piezometer  and  the  reservoir.  If 
the  water  rises  above  its  proper  level,  it  indicates  that  the  pressure  there 
has  been  increased  by  an  obstruction  beyond  the  piezometer. 

If  we  imagine  a  pipe  full  of  water  to  be  provided  with  a  number  of  pie- 
zometers, then  a  line  joining  the  tops  of  the  columns  of  water  in  them  la 
the  hydraulic  grade-line. 

Pitot  Tub6  Gauge.  — The  Pitot  tube  is  used  for  measuring  the  veloc- 
ity of  fluids  in  motion.  It  has  been  used  with  great  success  in  measuring 
the  flow  of  natural  gas.  (S.  W.  Robinson,  Report  Ohio  Geol.  Survey,  1890.) 
(See  also  Van  Nostrand's  Mag.,  vol.  xxxv.)  It  is  simply  a  tube  so  bent 
that  a  short  leg  extends  into  the  current  of  fluid  flowing  from  a  tube,  with 
the  plane  of  the  entering  orifice  opposed  at  right  angles  to  the  direction  of 
the  current.  The  pressure  caused  by  the  impact  of  the  current  is  trans- 
mitted through  the  tube  to  a  pressure-gauge  of  any  kind,  such  as  a  column 
of  water  or  of  mercury,  or  a  Bourdon  spring-gauge.  From  the  pressure 
thus  indicated  and  the  known  density  and  temperature  of  the  flowing  gas 
is  obtained  the  head  corresponding  to  the  pressure,  and  from  this  the 
velocity.  In  a  modification  of  the  Pitot  tube  described  by  Prof  Robinson, 
there  are  two  tubes  inserted  into  the  pipe  conveying  the  gas,  one  of  which 
has  the  plane  of  the  orifice  at  right  angles  to  the  current,  to  receive  the 
static  pressure  plus  the  pressure  due  to  impact;  the  other  has  the  plane  of 
its  orifice  parallel  to  the  current,  so  as  to  receive  the  static  pressure  only. 
These  tubes  are  connected  to  the  legs  of  a  t/tube  partly  filled  with  mercury, 
which  then  registers  the  difference  in  pressure  in  the  two  tubes,  from  which, 
the  velocity  may  be  calculated.  Comparative  tests  of  Pitot  tubes  with 
gas-meters,  for  measurement  of  the  flow  of  natural  gas,  have  shown  an 
agreement  within  3%. 

It  appears  from  experiments  made  by  W.  M.  White,  described  in  a 
paper  before  the  Louisiana  Eng'g  Socy.,  1901,  by  Williams,  Hubbell  and 
Fenkel  (Trans.  A.  S.  C.  E.,  1901),  and  by  W.  B.  Gregory  (Trans.  A.  8. 
M.  E.,  1903),  that  in  the  formula,  for  the  Pitot  tube,  V=cV2gHtln 
which  V  is  the  velocity  of  the  current  in  feet  per  second,  //  the  head  in 
feet  cf  the  fluid  corresponding  to  the  pressure  measured  by  the  tube, 
and  c  an  experimental  coefficient,  c  =  1  when  the  plane  at  the  point  of 


758  HYDRAULICS. 

the  tube  is  /exactly  at  right  angles  with  the  direction  of  the  current 
and  when  the  static  pressure  is  correctly  measured.  The  total  pressure 
produced  by  a  jet  striking  an  extended  plane  surface  at  right  angles  to 
it,  and  escaping  parallel  to  the  plate,  equals  twice  the  product  of  the 
area  of  the  jet  into  the  pressure  calculated  from  the  "  head  due  the  veloc- 

Ufc'I  a>nd  for  ^1S  case  H  =  2  *  V2/2  9  instead  of  V*/2  g;  but  as  found  in 
Whites  experiments  the  maximum  pressure  at  a  point  on  the  plate 
exactly  opposite  the  jet  corresponds  to  h=  V*/2  g.  Experiments  made 
with  four  different  shapes  of  nozzles  placed  under  the  center  of  a  falling 
stream  of  water  showed  that  the  pressure  produced  was  capable  of  sus- 

l  t0  the  height  *  the 


Tests  by  J.  A.  Knesche  (Indust.  Eng'g,  Nov.,  1909),  in  which  a  Pitot 
tube  was  inserted  ma  4-m.  water  pipe,  gave  C  =  about  0.77  for  velocities 
°f  2.5  to  8  ft.  per  sec.,  and  smaller  values  for  lower  velocities.  He  holds 
that  the  coefficient  of  a  tube  should  be  determined  by  experiment  before 
its  readings  can  be  considered  accurate. 

For  a  brief  discussion  of  various  theories  of  the  Pitot  tube  see  Eng'g 
News,  April  17,  June  5,  and  July  31,  1913. 

Maximum  and  Mean  Velocities  in  Pipes.—  Williams,  Hubbell  and 
Fenkel  (Trans.  A.  S.  C.  E.,  1901)  found  a  ratio  of  0.84  between  the  mean 
and  the  maximum  velocities  of  water  flowing  in  closed  circular  conduits, 
under  normal  conditions,  at  ordinary  velocities;  whereby  observations  of 
velocity  taken  at  the  center  under  such  conditions,  with  a  properly  rated 
Pitot  tube,  may  be  relied  on  to  give  results  within  3  %  of  correctness. 
The  Venturi  Meter,  invented  by  Clemens  Herschel,  and  described  in 
a  pamphlet  issued  by  the  Builders'  Iron  Foundry  of  Providence,  R.I.  ,  la 
named  from  Venturi,  who  first  called  attention,  in  1796,  to  the  relation  be- 
tween the  velocities  and  pressures  of  fluids  when  flowing  through  converg- 
ing and  diverging  tubes.  It  consists  of  two  parts  —  the  tube,  through 
which  the  water  flows,  and  the  recorder,  which  registers  the  quantity  of 
water  that  passes  through  the  tube.  The  tube  takes  the  shape  of  two  trun- 
cated cones  joined  in  their  smallest  diameters  by  a  short  throat-piece.  At 
the  up-stream  end  and  at  the  throat  there  are  pressure-chambers,  at 
which  points  the  pressures  are  taken. 

The  action  of  the  tube  is  based  on  that  property  which  causes  the  small 
section  of  a  gently  expanding  frustum  of  a  cone  to  receive,  without  material 
resultant  loss  of  head,  as  much  water  at  the  smallest  diameter  as  is  dis- 
charged at  the  large  end,  and  on  that  further  property  which  causes  the 
pressure  of  the  water  flowing  through  the  throat  to  be  less,  by  virtue  of  its 
greater  velocity,  than  the  pressure  at  the  up-stream  end  of  the  tube,  each 
pressure  being  at  the  same  time  a  function  of  the  velocity  at  that  point  and 
of  the  hydrostatic  pressure  which  would  obtain  were  the  water  motionless 
within  the  pipe. 

Tne  recorder  is  connected  with  the  tube  by  pressure-pipes  which  lead  to 
it  from  the  chambers  surrounding  the  up-stream  end  and  the  throat  of  the 
tube.  It  may  be  placed  in  any  convenient  position  within  1000  feet  of  the 
meter.  It  is  operated  by  a  weight  and  clockwork.  The  difference  of  pres- 
sure or  head  at  the  entrance  and  at  the  throat  of  the  meter  is  balanced  in 
the  recorder  by  the  difference  of  level  in  two  columns  of  mercury  in 
cylindrical  receivers,  one  within  the  other.  The  inner  carries  a  float,  the 
position  of  which  is  indicative  of  the  quantity  of  water  flowing  through 
the  tube.  By  its  rise  and  fall  the  float  varies  the  time  of  contact  between 
an  integrating  drum  and  the  counters  by  which  the  successive  readings 
are  registered. 

There  is  no  limit  to  the  sizes  of  the  meters  nor  the  quantity  of  water 
that  may  be  measured.  Meters  with  24-inch,  36-inch,  48-inch,  and  even 
20-foot  tubes  can  be  readily  made. 

Measurement  by  Venturi  Tubes.  (Trans.  A.  S.  C.  E.,  Npv.,  1887, 
and  Jan.,  1888.)  —  Mr.  Herschel  recommends  the  use  of  a  Venturi  tube,  in- 
serted in  the  force-main  of  the  pumping  engine,  for  determining  the 
quantity  of  water  discharged.  Such  a  tube  applied  to  a  24-inch  main  has 
a  total  length  of  about  20  feet.  At  a  distance  of  4  feet  from  the  end 
nearest  the  engine  the  inside  diameter  of  the  tube  is  contracted  to  a  throat 
having  a  diameter  of  about  8  inches.  A  pressure-gauge  is  attached  to  each 
of  two  chambers,  the  onesurroundingand  communicating  with.the  entrance 
or  main  pipe,  the  other  with  the  throat.  According  to  experiments  made 


tir»r»n  f.wn  f. 


MEASUREMENT  OF  FLOWING  WATER,  759 


upon  two  tubes  of  this  kind,  one  4  in.  in  diameter  at  the  throat  and  12  in. 
at  the  entrance,  and  the  other  about  36  in.  in  diameter  at  the  throat  and 
9  feet  at  its  entrance,  the  quantity  of  water  which  passes  through  the  tube 
is  very  nearly  the  theoretical  discharge  through  an  opening  having  an  area 
equal  to  that  of  the  throat,  and  a  velocity  which  is  that  due  to  the  difference 
in  head  shown  by  the  two  gauges.  Mr.  Herschel  states  that  the  coefficient 
for  these  two  widely-varying  sizes  of  tubes  and  for  a  wide  range  of  velocity 
through  the  pipe,  was  found  to  be  within  two  per  cent,  either  way,  of  98%. 
In  other  words,  the  quantity  of  water  flowing  through  the  tube  per  second 
is  expressed  within  two  per  cent  by  the  formula  W=  0.98  X  A  X  ^2  gh, 
in  which  A  is  the  area  of  the  throat  of  the  tube,  h  the  head,  in  feet,  corre- 
sponding to  the  difference  in  the  pressure  of  the  water  entering  the  tube  and 
that  found  at  the  throat,  and  g  =  32.16. 

Coefficient  of  Flow  in  Venturi  Meters. — (Allen  Hazen,   Eng.   News, 
July  31,  1913.)       The    formula    for    flow    in    a  Venturi    meter    is 


d  and  D  respectively  are  diameters  of  the  throat  and  entrance,  in  inches, 
h  is  the  head  on  the  meter,  C  a  coefficient  which  depends  on  the  fractional 
resistance  and  has  an  average  value  of  very  close  to  0.99  for  ordinary 
waterworks  conditions.  K  =  28",276  if  Q  is  the  quantity  in  U.  S.  gal- 
lons per  24  hours  and  h  is  measured  in  feet  of  water.  If  C  =  0.99  then 
KC  =  27,993  for  h  in  feet  of  water,  8081  if  h  is  in  inches  of  water  and 
28,684  if  h  is  in  inches  of  mercury.  For  Q  in  cubic  feet  per  second,  di- 
vide these  figures  by  646,315  giving  respectively  KC  =  0.04331,  0.01250 
and  0.04438. 

Measurement  of  Discharge  of  Pumping-engines  by  means  of 
Nozzles.  (Trans.  A.  S.  M.  E.,  xii,  575.) — The  measurement  of  water 
by  computation  from  its  discharge  through  orifices,  or  through  the  nozzles 
of  fire-hose,  furnishes  a  means  of  determining  the  quantity  of  water  de- 
livered by  a  pumping-engine  which  can  be  applied  without  much  difficulty. 
John  R.  Freeman,  Trans.  A.  S.  C.  E.,  Nov.,  1889,  describes  a  series  of  ex- 
periments covering  a  wide  range  of  pressures  and  sizes,  and  the  results 
showed  that  the  coefficient  of  discharge  for  a  smooth  nozzle  of  ordinary 
good  form  was  within  one-half  of  one  per  cent,  either  way,  of  0.977;  the 
diameter  of  the  nozzle  being  accurately  calipered,  and  the  pressures  being 
determined  by  means  of  an  accurate  gauge  attached  to  a  suitable  piezom- 
eter at  the  base  of  the  play-pipe. 

In  order  to  use  this  method  for  determining  the  quantity  of  water  dis- 
charged by  a  pumping-engine,  it  would  be  necessary  to  provide  a  pressure- 
box,  to  which  the  water  would  be  conducted,  and  attach  to  the  box  as 
many  nozzles  as  would  be  required  to  carry  off  the  water.  According  to 
Mr.  Freeman's  estimate,  four  1  1/4-inch  nozzles,  thus  connected,  with  a 
pressure  of  80  Ibs.  per  square  inch,  would  discharge  the  full  capacity  of  a 
two-and-a-half-million  engine.  He  also  suggests  the  use  of  a  portable 
apparatus  with  a  single  opening  for  discharge,  consisting  essentially  of  a 
Siamese  nozzle,  so-called,  the  water  being  carried  to  it  by  three  or  more 
lines  of  fire-hose. 

To  insure  reliability  for  these  measurements,  it  is  necessary  that  the 
ehut-off  valve  in  the  force-main,  or  the  several  shut-off  valves,  should  be 
tight,  so  that  all  the  water  discharged  by  the  engine  may  pass  through  the 
nozzles. 

The  Lea  V-Notch  Recording  Water  Meter  is  described  by  D.  Robert 
YarnaU  in  Trans.  A.  S.  M.  E.,  1912.  It  is  extensively  used  in  large 
power  plants  for  recording  the  flow  of  boiler  feed  water.  It  consists 
of  a  metering  tank  or  flume  from  which  the  water  passes  over  a  90° 
V-notch  into  a  catch  basin  below,  the  height  of  the  water  above  the 
notch  being  recorded  on  a  clock-driven  paper  chart  which  revolves 
once  in  24  jiours.  The  formula  for  the  90°  V-notch  is  cu.  ft.  per  min.  = 
Q.3Q5H2\/H,  in  which  H  is  the  height  in  inches  of  the  still  water  behind 
the  notch  measured  above  the  level  of  the  bottom  of  the  notch.  Tests 
by  Mr.  YarnaU  of  a  recording  meter  made  on  this  principle  showed  an 


760 


HYDEAULICS. 


average  error  of  0.5%.  The  Yarnall- Waring  Co.,  Philadelphia,  makers 
•of  the  meter  give  the  following  figures  for  the  flow  of  water  in  pounds 
per  hour  corresponding  to  different  heights  of  water  in  inches  above 
the  notch: 


Height,  in.: 
1234 
Flow,  Ib.  per  hour: 
1,140      6,480      17,830      36,610 

Height,  in.: 
9                 10                11 
Flow,  Ib.  per  hour: 
277,960       361,740       459,030 

5 
63,940 

12 
568,720 

6 

100,860 

13 
694,710 

7 
148,290 

14 
836,110 

8 
207,060 

15 
993,510 

Flow  through  Rectangular  Orifices.     (Approximate.     See  p.  727.) 

CUBIC  FEET  OF  WATER  DISCHARGED  PER  MINUTE  THROUGH  AN  ORIFICE 
ONE  INCH  SQUARE,  UNDER  ANY  HEAD  OF  WATER  FROM  3  TO  72  INCHES. 

For  any  other  orifice  multiply  by  its  area  in  square  inches. 
Formula,  Q'  =  0.624  *Sh"  X  a.     Q'*=  cu.  ft.  per  min.;  a  =  area  in  sq.  in. 


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4.78 

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2.28 

24 

2.97 

34 

3.52 

44 

4.00 

54 

4.42 

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4.81 

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3.03 

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4.05 

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4.27 

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4.65 

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5.03 

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4.30 

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5.07 

12 

2.12 

22 

2.84 

32 

3.41 

42 

3.91 

52 

4.34 

62 

4.74 

72 

5.09 

Measurement  of  an  Open  Stream  by  Velocity  and  Cross-section.  — 

Measure  the  depth  of  the  water  at  from  6  to  12  points  across  the  stream  at 
equal  distances  between.  Add  all  the  depths  in  feet  together  and  divide 
by  the  number  of  measurements  made;  this  will  be  the  average  depth  of 
the  stream,  which  multiplied  by  its  width  will  give  its  area  or  cross-section. 
Multiply  this  by  the  velocity  of  the  stream  in  feet  per  minute,  and  the 
result  will  be  the  discharge  in  cubic  feet  per  minute  of  the  stream. 

The  velocity  of  the  stream  can  be  found  by  laying  off  100  feet  of  the  bank 
and  throwing  a  float  into  the  middle,  noting  the  time  taken  in  passing  over 
the  100  ft.  Do  this  a  number  of  times  and  take  the  average;  then,  divid- 
ing this  distance  by  the  time  gives  the  velocity  at  the  surface.  As  the  top 
of  the  stream  flows  faster  than  the  bottom  or  sides  —  the  average  velocity 
being  about  83%  of  the  surface  velocity  at  the  middle  —  it  is  convenient  to 
measure  a  distance  of  120  feet  for  the  float  and  reckon  it  as  100 


MEASUREMENT   OF   FLOWING   WATER. 


761 


Miner's  Inch  Measurements.     (Pelton  Water  Wheel  Co.) 

The  cut,  Fig. 149,  shows  the  form  of  measuring-box  ordinarily  used,  and 
the  following  table  gives  the  discharge  in  cubic  feet  per  minute  of  a  miner's 
inch  of  water,  as  measured  under  the  various  heads  and  different  lengths 
and  heights  of  apertures  used  in  California. 


FIG.  149. 


Length 

Openings  2  Inches  High. 

Openings  4  Inches  High. 

of 

Opening 
in 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

inches. 

Center, 
5  inches. 

Center, 
6  inches. 

Center, 
7  inches. 

Center, 
5  inches. 

Center, 
6  inches. 

Center, 
7  inches. 

Cu.  ft. 

Cu.  ft. 

Cu.ft. 

c 

j.ft. 

Cu.  ft. 

Cu.  ft. 

4 

.348 

.473 

.589 

.320 

.450 

1.570 

6 

.355 

.480 

.596 

.336 

.470 

1.595 

8 

.359 

.484 

.600 

.344 

.481 

.608 

10 

.361 

.485 

.602 

.349 

.487 

.615 

12 

.363 

.487 

.604 

.352 

.491 

.620 

14 

.364 

.488 

.604 

.354 

.494 

.623 

16 

.365 

.489 

.605 

.356 

.496 

.626 

18 

.365 

.489 

.606 

.357 

.498 

.628 

20 

.365 

.490 

.606 

.359 

.499 

.630 

22 

.366 

.490 

.607 

.359 

.500 

.631 

24 

.366 

.490 

.607 

.360 

.501 

.632 

26 

.366 

.490 

.607 

.361 

.502 

.633 

28 

.367 

.491 

.607 

.361 

.503 

.634 

30 

.367 

.491 

.608 

.362 

.505 

.635 

40 

.367 

.492 

.608 

.363 

.505 

.637 

50 

.368 

.493 

.609 

.364 

.507 

.639 

60 

.368 

.493 

.609 

.365 

.508 

.640 

70 

.368 

.493 

.609 

.365 

.508 

.641 

80 

.368 

.493 

.609 

.366 

.509 

.641 

90 

.369 

.493 

1.610 

.366 

.509 

.641 

100 

.369 

.494 

1.610 

.366 

.509 

.642 

NOTE.  —  The  apertures  from  which  the  above  measurements  were  ob- 
tained were  through  material  1 1/4  inches  thick,  and  the  lower  edge  2  inches 
above  the  bottom  of  the  measuring-box,  thus  giving  full  contraction,. 


762 


HYDRAULICS. 


Flow  of  Water  Over  Weirs.  Weir  Dam  Measurement.  "  (Pelton 
Water  Wheel  Co.)  —  Place  a  board  or  plank  in  the  stream,  as  shown  in 
the  sketch,  at  some  point  where  a  pond  will  form  above.  The  length  of 
the  notch  in  the  dam  should  be  from  two  to  four  times  its  depth  for  small 
quantities  and  longer  for  large  quantities.  The  edges  of  the  notch  should 
be  beveled -to  ward  the  intake  side,  as  shown.  The  overfall  below  the  notch 
should  not  be  less  than  twice  its  depth.  Francis  says  a  fall  below  the 
crest  equal  to  one-half  the  head  is  sufficient,  but  there  must  be  a  free  access 
of  air  under  the  sheet. 


FIG.  150. 

In  the  pond,  about  6  ft.  above  the  dam,  drive  a  stake,  and  then  obstruct 
the  water  until  it  rises  precisely  to  the  bottom  of  the  notch  and  mark  the 
stake  at  this  level.  Then  complete  the  dam  so  as  to  cause  all  the  water  to 
flow  through  the  notch,  and,  after  time  for  the  water  to  settle,  mark  the 
stake  again  for  this  new  level.  If  preferred  the  stake  can  be  driven  with 
its  top  precisely  level  with  the  bottom  of  the  notch  and  the  depth  of  the 
water  be  measured  with  a  rule  after  the  water  is  flowing  free,  but  the  marks 
are  preferable  in  most  cases.  The  stake  can  then  be  withdrawn;  and  the 
distance  between  the  marks  is  the  theoretical  depth  of  flow  corresponding 
to  the  quantities  in  the  weir  table  on  the  following  page. 

Francis's  Formulae  for  Weirs. 

Q  =  discharge  in  cubic  feet  per  second,  L  =  length  of  the  weir, 
H  =  depth  of  water  on  the  weir,  h  =  head  due  the  velocity  of  ap- 
proach =  V2  ~-  64.3;  dimensions  in  feet,  velocity  in  feet  per  second. 

Francis's  formula,  Q  =  3.33  (L  -  0.2H)  X  H  *h. 

This  formula  applies  to  weirs  having  perfect  contraction  at  each  end 
and  the  velocity  of  approach  negligible.  When  the  velocity  of  approach 
is  considered  the  formula  is  Q  =  3.33  (L  -  0.2  H}  X  [(H  +  h)  3/2  -  h  3/2]. 
The  Francis  formula  is  not  applicable  when  the  depth  on  the  weir 
exceeds  one- third  of  the  length  nor  to  very  small  depths.  The  distance 
from  the  side  of  the  canal  to  the  end  of  the  weir  should  not  be  less  than 
three  times  the  .depth  on  the  weir, 


MEASUREMENT  OP  FLOWING  WATER. 


763 


With  both  end  contractions  suppressed  the  term  0.2  H  is  omitted  from 
the  formula,  and  with  one  end  contraction  suppressed  it  becomes 
0.1  tf. 

If  Q'  -  discharge  in  cubic  feet  per  minute,  and  I'  and  h'  are  taken  in 
inches,  the  first  of  the  above  formulae  reduces  to  Q'  =  0.4  I'  h'  3/2-  From  this 
formula  the  following  table  is  calculated.  The  values  are  sufficiently 
accurate  for  ordinary  computations  of  water-power  for  weirs  without  end 
contraction,  that  is,  for  a  weir  the  full  width  of  the  channel  of  approach. 
For  weirs  with  full  end  contraction  multiply  the  values  taken  from  the 
table  by  the  length  of  the  weir  crest  in  inches  less  0.2  times  the  head  in 
inches,  to  obtain  the  discharge. 

Weir  Table. 

GIVING  CUBIC  FEET  OF  WATER  PER  MINUTE  THAT  WILL  FLOW  OVER"  A.  WEIR 
ONE  INCH  WIDE  AND  FROM  1/3  TO  207/8  INCHES  DEEP. 

For  other  widths  multiply  by  the  width  in  inches. 


Depth. 

1/8  in. 

1/4  in. 

3/8  in. 

1/2  in. 

5/8  in. 

3/4  in. 

7/8  in. 

In. 

cu.  ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

•cu.ft. 

cu.ft. 

cu.ft. 

0 

.00 

.01 

.05 

.09 

.14 

.19 

.26 

.32 

1 

.40 

.47 

.55 

.64 

.73 

.82 

.92 

1.02 

2 

1.13 

1.23 

1.35 

1.46 

1.58 

1.70 

1.82 

1.95 

3 

2.07 

2.21 

2.34 

2.48 

2.61 

2.76 

2.90 

3.05 

4 

3.20 

,3.35 

3.50 

3.66 

3.81 

3.97 

4.14 

4.30 

5 

4.47 

4.64 

4.81 

4.98 

5.15 

5.33 

3.51 

5.69 

6 

5.87 

6.06 

6.25 

6.44 

6.62 

6.82 

7.01 

7.21 

7 

7.40 

7.60 

7.80 

8.01 

8.21 

8.42 

8.63 

8.83 

8 

9.05 

9.26 

9.47 

9.69 

9.91 

10.13 

10.35 

10.57 

9 

10.80 

11.02 

11.25 

11.48 

11.71 

11.94 

12.17 

12.41 

10 

12.64 

12.88 

13.12 

13.36 

13.60 

13.85 

14.09 

14.34 

11 

14.59 

14.84 

15.09 

15.34 

.    15.59 

15.85 

16.11 

16.36 

12 

16.62 

16.88 

17.15 

17.41 

17.67 

17.94 

18.21 

18.47 

13 

18.74 

19.01 

19.29 

19.56 

19.84 

20.11 

20.39 

20.67 

14 

20.95 

21.23 

21.51 

21.80 

22.08 

22.37 

22.65 

22.94 

15 

23.23 

23.52 

23.82 

24.11 

24.40 

24.70 

25.00 

25.30 

16 

25.60 

25.90 

26.20 

26.50 

26.80 

27.11 

27.42 

27.72 

17 

28.03 

28.34 

28.65 

28.97 

29.28 

29.59 

29.91 

30.22 

18 

30.54 

30.86 

31.18 

31  .50 

31.82 

32.15 

32.47 

32.80 

19 

33.12 

33.45 

33.78 

34.11 

34.44 

34.77 

35.10 

35.44 

20 

35.77 

36.11 

36.45 

36.78 

37.12 

37.46 

37.80 

38.15 

When  the  velocity  of  the  approaching  water  is  less  than  1/2  foot  per 
second,  the  result  obtained  by  the  table  is  fairly  accurate.  When  the  vel- 
ocity of  approach  is  greater  than  1/2  foot  per  second,  a  correction  should  be 
applied,  see  page  727. 

For  more  accurate  computations,  the  coefficients  of  flow  of  Hamilton 
Smith,  Jr.,  or  of  Bazin  should  be  used.  In  Smith's  Hydraulics  will  be  found 
a  collection  of  results  of  experiments  on  orifices  and  weirs  of  various  shapes 
made  by  many  different  authorities,  together  with  a  discussion  of  their 
several  formula.  (See  also  Trautwine's  Pocket  Book,  Unwin's  Hydrau- 
lics, Church's  Mechanics  of  Engineering,  Merriman's  Hydraulics, 
Williams  and  Hazen's  Hydraulic  Tables,  Hughes  and  Safford's  Hydrau- 
lics, and  Weir  Experiments,  Coefficients  and  Formulas,  by  R.  E. 
Horton,  Water  Supply  and  Irrigation  paper  No.  200  of  the  U.  S. 
Geological  Survey.) 

Bazin's  Experiments. — M.  Bazin  (Annales  des  Fonts  et  Chaussees, 
Oct.,  1888,  translated  by  Marichal  and  Trautwine,  Proc.  Engrs.  Club  of 
Phila.,  Jan.,  1890)  made  an  extensive  series  of  experiments  with  a  sharp- 
crested  weir  without  lateral  contraction,  the  air  being  admitted  freely  be- 
hind the  falling  sheet,  and  found  values  of  m  varying  from  0.42  to  0.50, 
with  variations  of  the  length  of  the  weir  from  19  3/4  to  78  3/4  in.,  of  the 
height  of  the  crest  above  the  bottom  of  the  channel  from  0.79  to  2.46  ft., 


764 


HYDRAULICS. 


and  of  the  head  from  1.97  to  23.62  In. 
the  following  formula: 


From  these  experiments  he  deduces 


0.425+  0.21  (-5-^-77) 


In  which  P  is  the  height  in  feet  of  the  crest  of  the  weir  above  the  bottom  of 
the  chanriel  of  approach,  L  the  length  of  the  weir,  H  the  head,  both  in  feet, 
and  Q  the  discharge  in  cu.  ft.  per  sec.  This  formula,  says  M.  Bazin,  is 
entirely  practical  where  errors  of  2%  to  3%  are  admissible.  The  following 
table  is  condensed  from  M.  Bazin's  paper: 


VALUES  .OF  THE  COEFFICIENT  m  IN  THE  FORMULA  Q-  =  mLH  V2  gH,  FOR  A 
SHARP-CRESTED  WEIR  WITHOUT  LATERAL  CONTRACTION;  THE  Am 
BEING  ADMITTED  FREELY  BEHIND  THE  FALLING  SHEET. 


Head,  H. 

Height  of  Crest  of  Weir  Above  Bed  of  Channel. 

Feet...  0.66 
Inches  7.87 

0.98 
11.81 

1.31 
15.75 

1.64|  1.97 
19.69|23.62 

2.62 
31.50 

3.28 
39.38 

4.92 
59.07 

6.56 
78.76 

00 
00 

Ft. 
0.164 
0.230 
0.295 
0.394 
0.525 
0.656 
0.787 
0  919 
.050 
.181 
.312 
.444 
.575 
.706 
.837 
.969 

In. 
1.97 
2.76 
3.54 
4.72 
6.30 
7.87 
9.45 
11.02 
12.60 
14.17 
15.75 
17.32 
18.90 
20.47 
22.05 
23.62 

m 
0.458 
0.455 
0.457 
0.462 
0.471 
0.480 
0.488 
0.496 

m 
0.453 
0.448 
0.447 
0.448 
0.453 
0.459 
0.465 
0.472 
0.478 
0.483 
0.489 
0.494 

m 
0.451 
0.445 
0.442 
0.442 
0.444 
0.447 
0.452 
0.457 
0.462 
0.467 
0.472 
0.476 
0.480 
0.483 
0.487 
0.490 

m 
0.450 
0.443 
0.440 
0.438 
0.438 
0.440 
0.444 
0.448 
0.452 
0.456 
0.459 
0.463 
0.467 
0.470 
0.473 
0.476 

m 
0.449 
0.442 
0.438 
0.436 
0.435 
0.436 
0.438 
0.441 
0.444 
0.448 
0.451 
0.454 
0.457 
0.460 
0.463 
0.466 

m 
0.449 
0.441 
0.436 
0.433 
0.431 
0.431 
0.432 
0.433 
0.436 
0.438 
0.440 
0.442 
0.444 
0.446 
0.448 
0.451 

m 
0.449 
0.440 
0.436 
0.432 
0.429 
0.428 
0.428 
0.429 
'0.430 
0.432 
0.433 
0.435 
0.436 
0.438 
0.439 
0.441 

m 
0.448 
0.440 
0.435 
0.430 
0.427 
0.425 
0.424 
0.424 
0.424 
0.424 
0.424 
0.425 
0.425 
0.426 
0.427 
0.427 

m 
0.448 
0.439 
0.434 
0.430 
0.426 
0.423 
0.422 
0.422 
0.421 
0.421 
0.421 
0.421 
0.421 
0.421 
0.421 
0.421 

m 
0.4481 
0.4391 
0.4340 
0.4291 
0.4246 
0.4215 
0.4194 
0.4181 
0.4J68 
0.4156 
0.4144 
0.4134 
0.4122 
0.4112 
0.4101 
0.4092 

A  comparison  of  the  results  of  this  formula  with  those  of  experiments, 
says  M.  Bazin,  justifies  us  in  believing  that,  except  in  the  unusual  case  of  a 
very  low  weir  (which  should  always  be  avoided),  the  preceding  table  will 
give  the  coefficient  m  in  all  cases  within  1% ;  provided,  however,  that  the 
arrangements  of  the  standard  weir  are  exactly  reproduced.  It  is  especially 
important  that  the  admission  of  the  air  behind  the  falling  sheet  be  perfectly 
assured.  If  this  condition  is  not  complied  with,  m  may  vary  within  much 
wider  limits.  The  type  adopted  gives  the  least  possible  variation  in  the 
coefficient. 

Triangular  Weir. — For  the  formula  of  the  triangular  or  V-notch 
weir,  see  the  Lea  Recorder,  page  759. 

The  Cippoleti,  or  Trapezoidal  Weir.  —  Cippoleti  found  that  by  using 
a  trapezoidal  weir  with  the  sides  inclined  1  horizontal  to  4  vertical,  with 
end  contraction,  the  discharge  is  equal  to  that  of  a  rectangular  weir 
without  end  contraction  (that  is  with  the  width  of  the  weir  equal  to  the 
width  of  the  channel)  and  is  represented  by  the  simple  formula  Q  =  3.367 
L#3/2.  A.  D.  Flinn  and  C.  W.  D.  Dyer  (Trans.  A.  S.  C.  E.t  1894),  in 
experiments  with  a  trapezoidal  weir,  with  values  of  L  from  3  to  9  ft. 
and  .of  H  from  0.24  to  1.40  ft.,  found  the  value  of  the  coefficient  to  aver- 
age 3.334,  the  water  being  measured  by  a  rectangular  weir  and  the  results 
being  computed  by  Francis's  formula,  and  3.354  when  Smith's  formula 
was  used.  They  conclude  that  Cippoleti's  formula  when  applied  to  a 
properly  constructed  trapezoidal  weir  will  give  the  discharge  with  an 
error  due  to  combined  inaccuracies,  not  greater  than  1%. 


WATEK-POWEfU  765 


WATER-POWER, 

Power  of  a  Fall  of  Water  —  Efficiency.  —  The  gross  power  of  a  fall 

Kf  water  is  the  produc*  of  the  weight  of  water  discharged  in  a  unit  of  time 
ito  the  total  head,  i.e.,  the  difference  of  vertical  elevation  of  the  upper 
surface  of  the  water  at  the  points  where  the  fall  in  question  begins  and 
ends.  The  term  "head"  used  in  connection  with  water-wheels  is  the 
difference  in  height  from  the  surface  of  the  water  in  the  wheel-pit  to  the 
surface  in  the  pen-stock  when  the  wheel  is  running. 

If  Q  =  cubic  feet  of  water  discharged  per  second,  D  =  weight  of  a  cubic 
foot  of  water  =  62.36  Ibs.  at  60°  F.,  H  =  total  head  in  feet;  then 

DQH  =  gross  power  in  foot-pounds  per  second, 
and  DQH  -*•  550  =  0.1134  QH  =  gross  horse-power. 

If  Qf  is  taken  in  cubic  feet  per  minute,  H.P.=  Q'X'36  =  .00189Q'g. 


A  water-wheel  or  motor  of  any  kind  cannot  utilize  the  whole  of  the  head 
H,  since  there  are  losses  of  head  at  both  the  entrance  to  and  the  exit  from 
the  wheel.  There  are  also  losses  of  energy  due  to  friction  of  the  water  in 
its  passage  through  the  wheel.  The  ratio  of  the  power  developed  by  the 
wheel  to  the  gross'  power  of  the  fall  is  the  efficiency  of  the  wheel.  For  75  % 

efficiency,  net  horse-power  =  0.00142  Q'H  =  —  -g 

A  head  of  water  can  be  made  use  of  in  one  or  other  of  the  following  ways, 
viz.: 

1st.   By  its  weight,  as  in  the  water-balance  and  in  the  overshot-wheel. 

2d.  By  its  pressure,  as  in  turbines  and  in  the  hydraulic  engine,  hydraulic 
press,  crane,  etc. 

3d.   By  its  impulse,  as  in  the  undershot-wheel,  and  in  the  Pelton  wheel. 

4th.   By  a  combination  of  the  above. 

Horse-power  of  a  Running  Stream.  —  The  gross  horse-power  is 
H.P.  =  QH  X  62.36  •*-  550  =  0.1134  QH,  in  which  Q  is  the  discharge  in 
cubic  feet  per  second  actually  impinging  on  the  float  or  bucket,  and  H  = 

1)2  <y2 

theoretical  head  due  to  the  velocity  of  the  stream  =  ^-—  =  ^—.  .  in  which 

2  g       o4.4 

v  is  the  velocity  in  feet  per  second.   If  Q'  be  taken  in  cubic  feet  per  minute, 
H.P.  =  0.00189  Q'H. 

Thus,  if  the  floats  of  an  undershot-wheel  driven  by  a  current  alone  be  5 
feet  X  1  foot,  and  the  velocity  of  stream  =  210  ft.  per  minute,  or  31/2  ft. 
per  sec.,  of  which  the  theoretical  head  is  0.19  ft.,  Q  =  5  sq.  ft.  X  210  =  1050 
cu.  ft.  per  minute;  H.P.  =  1050  X  0.19  X  0.00189  =.  0.377  H.P. 

The  wheels  would  realize  only  about  0.4  of  this  power,  on  account  of 
friction  and  slip,  or  0.151  H.P.,  or  about  0.03  H.P.  per  square  foot  of 
float,  which  is  equivalent  to  33  sq.  ft,  of  float  per  H.P. 

Current  Motors.  —  A  current  motor  could  only  utilize  the  whole 
power  of  a  running  stream  if  it  could  take  all  the  velocity  out  of  the  water, 
so  that  it  would  leave  the  floats  or  buckets  with  no  velocity  at  all;  or  in 
other  words,  it  would  require  the  backing  up  of  the  whole  volume  of  the 
stream  until  the  actual  head  was  equivalent  to  the  theoretical  head  due  to 
the  velocity  of  the  stream.  As  but  a  small  fraction  of  the  velocity  of  the 
stream  can  be  taken  up  by  a  current  motor,  its  efficiency  is  very  small. 
Current  motors  may  be  used  to  obtain  small  amounts  of  power  from  large 
streams,  but  for  large  powers  they  are  not  practicable. 

Bernoulli's  Theorem.  —  Energy  of  Water  Flowing  in  a  Tube.  — 

tfi  f 

The  head  due  to  the  velocity  is  —  ;  the  head  due  to  the  pressure  is—  ;  the 

head  due  to  actual  height  above  the  datum  plane  is  h  feet.  The  total  head 

v^  f 

is  the  sum  of  these  =  -  --  \-h+  —  ,  in  feet,  in  which  v  =  velocity  in  feet  per 

second,  f  »  pressure  in  Ibs.  per  sq.  ft.,  w  =  weight  of  1  cu.  ft.  of  water  ** 


766  WATER-  POWER. 

62.36  Ibs.    If  p  =  pressure  in  Ibs.  per  sq.  in.,  ^  =  2.309  p.     If  a  constant 

quantity  of  water  is  flowing  through  a  tube  in  a  given  time,  the  velocity 
varying  at  different  points  on  account  of  changes  in  the  diameter,  the 
energy  remains  constant  (loss  by  friction  excepted)  and  the  sum  of  the 
three  heads  is  constant,  the  pressure  head  increasing  as  the  velocity  de- 
creases, and  vice-versa.  This  principle  is  known  as  "  Bernoulli's  Theo- 
rem." 

In  hydraulic  transmission  the  velocity  and  the  height  above  datum  are 
usually  small  compared  with  the  pressure-head.  The  work  or  energy  of  a 
given  quantity  of  water  under  pressure  =  its  volume  in  cubic  feet  X  its 
pressure  in  Ibs.  per  sq.  ft.;  or  if  Q  =  quantity  in  cubic  feet  per  second, 
and  p  =  pressure  in  Ibs.  per  square  inch,  W  =  144  pQ,  and  the  H.P. 


Maximum  Efficiency  of  a  Long  Conduit.  —  A.  L.  Adams  and  R.  C. 
Gemmell  (Eng'g  News,  May  4,  1893)  show  by  mathematical  analysis  that 
the  conditions  for  securing  the  maximum  amount  of  power  through  a  long 
conduit  of  fixed  diameter,  without  regard  to  the  economy  of  water,  is  that 
the  draught  from  the  pipe  should  be  such  that  the  frictional  loss  in  the  pipe 
will  be  equal  to  one-third  of  the  entire  static  head. 

Mill-Power.  —  A  "mill-power"  is  a  unit  used  to  rate  a  water-power 
for  the  purpose  of  renting  it.  The  value  of  the  unit  is  different  in  different 
localities.  The  following  are  examples  (from  Emerson): 

Holyoke,  Mass.  —  Each  mill-power  at  the  respective  falls  is  declared  to 
be  the  right  during  16  hours  in  a  day  to  draw  38  cu.  ft.  of  water  per  second 
at  the  upper  fall  when  the  head  there  is  20  feet,  or  a  quantity  proportionate 
to  the  height  at  the  falls.  This  is  equal  to  86.2  horse-power  as  a  maximum. 

Lowell,  Mass.  —  The  right  to  draw  during  15  hours  in  the  day  so  much 
water  as  shall  give  a  power  equal  to  25  cu.  ft.  a  second  at  the  great  fall, 
when  the  fall  there  is  30  feet.  Equal  to  85  H.P.  maximum. 

Lawrence,  Mass.  —  The  right  to  draw  during  16  hours  in  a  day  so  much 
water  as  shall  give  a  power  equal  to  30  cu.  ft.  per  second  when  the  head  is 
25  feet.  Equal  to  85  H.P.  maximum. 

Minneapolis,  Minn.  —  30  cu.  ft.  of  water  per  second  with  head  of  22  feet. 
Equal  to  74.8  H.P. 

Manchester,  N.H.  —  Divide  725  by  the  number  of  feet  of  fall  minus  1, 
and  the  quotient  will  be  the  number  of  cubic  feet  per  second  in  that  fall. 
For  20  feet  fall  this  equals  38.1  cu.  ft.,  equal  to  86.4  H.P.  maximum. 

Cohoes,  N.Y.  —  "  Mill-power"  equivalent  to  the  power  given  by  6  cu.  ft. 
per  second,  when  the  fall  is  20  feet.  Equal  to  13.6  H.P.,  maximum. 

Passaic,  N.J.  —  Mill-power:  The  right  to  draw  81/2  cu.  ft.  of  water  per 
sec.,  fall  of  22  feet,  equal  to  21.2  horse-power.  Maximum  rental  $700  per 
year  for  each  mill-power  =  $33.00  per  H.P. 

The  horse-power  maximum  above  given  is  that  due  theoretically  to  the 
weight  of  water  and  the  height  of  the  fall,  assuming  the  water-wheel  to 
have  perfect  efficiency.  It  should  be  multiplied  by  the  efficiency  of  the 
wheel,  say  75%  for  good  turbines,  to  obtain  the  H.P.  delivered  by  the 
wheel. 

Value  of  a  Water-power.  —  In  estimating  the  value  of  a  water- 
power,  especially  where  such  value  is  used  as  testimony  for  a  plaintiff 
whose  water-power  has  been  diminished  or  confiscated,  it  is  a  common 
custom  for  the  person  making  such  estimate  to  say  that  the  value  is  repre- 
sented by  a  sum  of  money  which,  when  put  at  interest,  would  maintain  a 
steam-plant  of  the  same  power  in  the  same  place. 

Mr.  Charles  T.  Main  (Trans.  A.  S.  M.  E.,  xiii.  140)  points  out  that  this 
system  of  estimating  is  erroneous;  that  the  value  of  a  power  depends  upon 
a  great  number  of  conditions,  such  as  location,  quantity  of  water,  fall  or 
head,  uniformity  of  flow,  conditions  which  fix  the  expense  of  dams,  canals, 
foundations  of  buildings,  freight  charges  for  fuel,  raw  materials  and  finished 
product,  etc.  He  gives  an  estimate  of  relative  cost  of  steam  and  water- 
power  for  a  500  H.P.  plant  from  which  the  following  is  condensed: 

The  amount  of  heat  required  per  H.P.  varies  with  different  kinds  of 
business,  but  in  an  average  plain  cotton-mill,  the  steam  required  for  heat- 
ing and  slashing  is  equivalent  to  about  25%  of  steam  exhausted  from  the 
high-pressure  cylinder  of  a  compound  engine  of  the  power  required  to  run 
that  mill,  the  steam  to  be  taken  from  the  receiver. 


WATER-POWER.  767 

The  coal  consumption  per  H.P.  per  hour  for  a  compound  engine  is  taken 
at  1 3/4  ibs.  per  hour,  when  no  steam  is  taken  from  the  receiver  for  heating 
purposes.  The  gross  consumption  when  25%  is  taken  from  the  receiver  is 
about  2.06  Ibs. 

75%  of  the  steam  is  used  as  in  a  compound  engine  at  1.75  Ibs.  =  1.31  Ibs. 
25%  of  the  steam  is  used  as  in  a  high-pressure  engine  at  3.00  Ibs.  =  .75  Ib. 

2.06  Ibs. 

The  running  expenses  per  H.  P.  per  year  are  as  follows: 
2.06  Ibs.  coal  per  hour  =  21.115  Ibs.  for  101/4  hours  or  one  day  = 

6503.42  Ibs.  for  308  days,  which,  at  $3.00  per  long  ton  =  $8.71 

Atendance  of  boilers,  one  man  @  $2.00,  and  one  man  @  $1.25  =  2.00 
Attendance  of  engine,  one  man  @  $3.50.  2.16 

Oil,  waste,  and  supplies.  .80 

The  cost  of  such  a  steam-plant  in  New  England  and  vicinity  of  500 
H.  P.  is  about  $65  per  H.  P.  Taking  the  fixed  expenses  as  4% 
on  engine,  5%  on  boilers,  and  2%  on  other  portions,  repairs  at 
2%,  interest  at  5%,  taxes  at  U/2%  on  8/4  cost,  and  insurance  at 
1/2%  on  exposed  portion,  the  total  average  per  cent  is  about 
121/2%,  or  $65  X  0.121/2  =  8.13 

Gross  cost  of  power  and  low-pressure  steam  per  H.  P.  $21.80 

Comparing  this  with  water-power,  Mr.  Main  says:  "At  Lawrence  the 
cost  of  dam  and  canals  was  about  $650,000,  or  $65  per  H.  P  The  cost 
per  H.  P.  of  wheel-plant  from  canal  to  river  is  about  $45  per  H.  P.  of 
plant,  or  about  $65  per  H.  P.  used,  the  additional  $20  being  caused  by 
making  the  plant  large  enough  to  compensate  for  fluctuation  of  power 
due  to  rise  and  fall  of  river.  The  total  cost  per  H.  P.  of  developed  plant 
is  then  about  $130  per  H.  P.  Placing  the  depreciation  on  the  whole 
plant  at  2%,  repairs  at  1%,  interest  at  5%,  taxes  and  insurance  at  1%, 
or  a  total  of  9%,  gives: 

Fixed  expenses  per  H.  P.  $130  x   .09  =  $11.70 
Running  expenses  per  H.  P.  (Estimated)      2.00 

$13.70 

"To  this  has  to  be  added  the  amount  of  steam  required  for  heating 
purposes,  said  to  be  about  25%  of  the  total  amount  used,  but  in  winter 
months  the  consumption  is  at  least  371/2%.  It  is  therefore  necessary  to 
have  a  boiler  plant  of  about  37  1/2%  of  the  size  of  the  one  considered  with 
the  steam-plant,  costing  about  $20  X  0.375  =  $7.50  per  H.P  of  total 
power  used.  The  expense  of  running  this  boiler-plant  is,  per  H.  P  of 
the  total  plant  per  year: 

Fixed  expenses  121/2%  on  $7.50 .   $0.94 

Coal 3  20 

Labor ? . .     i .  23 

Total $<T43 

Making  a  total  cost  per  year  for  water-power  with  the  auxiliary  boiler 
plant  $13.70  +  $5.43  =  $19.13  which  deducted  from  $21.80  makes  a 
difference  in  favor  of  water-power  of  $2.67,  or  for  10,000  H  P  a  savinsr 
of  $26,700  per  year. 

"It  is  fair  to  say,"  says  Mr.  Main,  "that  the  value  of  this  constant 
power  is  a  sum  of  money  which  when  put  at  interest  will  produce  the 
saying;  or  if  6%  is  a  fair  interest  to  receive  on  money  thus  invested  the 
value  would  be  $26,700  -4-  0.06  =  $445,000." 

Mr.  Main  makes  the  following  general  statements  as  to  the  value  of  a 
water-power:  "The  value  of  an  undeveloped  variable  power  is  usually 
nothing  if  its  variation  is  great,  unless  it  is  to  be  supplemented  by  a 
steam-plant.  It  is  of  value  then  only  when  the  cost  per  horse-power  for 

le  double-plant  is  less  than  the  cost  of  steam-power  under  the  same 
conditions  as  mentioned  for  a  permanent  power,  and  its  value  can  be 
represented  m  the  same  manner  as  the  value  of  a  permanent  power  lias 


7G8 


WATER-POWER. 


"The  value  of  a  developed  power  is  as  follows:  If  the  power  can  be 
run  cheaper  than  steam,  the  value  is  that  of  the  power,  plus  the  cost  of 
plant,  less  depreciation.  If  it  cannot  be  run  as  cheaply  as  steam,  con- 
sidering its  cost,  etc.,  the  value  of  the  power  itself  is  nothing,  but  the 
value  of  the  plant  is  such  as  could  be  paid  for  it  new,  which  would  bring 
the  total  cost  of  running  down  to  the  cost  of  steam-power,  less  de- 
preciation." 

Mr.  Samuel  Webber,  Iron  Age,  Feb.  and  March,  1893,  writes  a  series 
of  articles  showing  the  development  of  American  turbine  wheels,  and 
incidentally  criticises  the  statements  of  Mr.  Main  and  others  who  have 
made  comparisons  of  costs  of  steam  and  of  water-power  unfavorable  to 
the  latter.  He  says :  ' '  They  have  based  their  calculations  on  the  cost 
of  steam,  on  large  compound  engines  of  1000  or  more  H.  P.  and  120 
pounds  pressure  of  steam  in  their  boilers,  and  by  careful  10-hour  trials 
succeeded  in  figuring  down  steam  to  a  cost  of  about  $20  per  H.  P.,  ignor- 
ing the  well-known  fact  that  its  average  cost  in  practical  use,  except 
near  the  coal  mines,  is  from  $40  to  $50.  In  many  instances,  dams, 
canals,  and  modern  turbines  can  be  all  completed  for  a  cost  of  $100  per 
H.  P. ;  and  the  interest  on  that,  and  the  cost  of  attendance  and  oil,  will 
bring  water-power  up  to  about  $10  or  $12  per  annum;  and  with  a  man 
competent  to  attend  the  dynamo  in  attendance,  it  can  probably  be 
safely  estimated  at  not  over  $15  per  H.  P." 

WATER-WHEELS. 

Water-wheels  are  classified  as  vertical  wheels  (including  current 
motors,  undershot,  breast,  and  overshot  wheels),  turbine  wheels,  and 
impulse  wheels.  Undershot  and  breast  wheels  give  very  low  efficiency, 
and  are  now  no  longer  built.  The  overshot  wheels  when  made  of  large 
diameter  (wheels  as  high  as  72  ft.  diameter  have  been  made)  and  prop- 
erly designed  have  given  efficiencies  of  over  80%,  but  they  have  been 
almost  entirely  supplanted  by  turbines,  on  account  of  their  cumbersome- 
ness,  high  cost,  leakage,  and  inability  to  work  in  back  water. 

Turbines  are  generally  classified  according  to  the  direction  in  which 
the  water  flows  through  them,  as  follows: 

Tangential  flow :  Barker's  mill.  Parallel  flow:  Jonval.  Radial  out- 
ward flow:  Fourneyron.  Radial  inward  flow:  Thompson  vortex; 
Francis.  Inward  and  downward  flow:  Central  discharge  scroll  wheels 
and  earlier  American  type  of  wheels;  Swain  turbine. 

HYDRAULIC   TURBINES 

Theory  and  Proportions. — For  the  theory  of  water  turbines  consult 
Prof.  De  Volson  Wood's  paper  on  Hydraulic  Reaction  Motors,  Trans. 
A.  S.  M.  E.,  xiv,  266;  also  Prof.  Unwin's  paper  on  Hydraulics,  Ency. 
Brit.,  llth  ed.,  vol.  14;  Merriman's  and  Bovey's  books  on  Hydraulics, 
Church's  Hydraulic  Motors,  and  Daugherty's  Hydraulic  Turbines. 
The  following  formulae  and  example  are  condensed  from  Church's 
theoretical  discussion  of  the  subject. 

Fig.  151  represents  a  simple  Fourneyron  or  radial  outward  flow 
turbine  placed  at  the  bottom  of  an  open  wheel-pit.  PP  is  a  short 
penstock  through  which  the  water  descends  into  a  cylindrical  gate  CC, 
which  is  movable  vertically.  The  water  passes  through  the  guides 
G  into  the  wheel  or  runner  W.  Rf  represents  the  resistance  overcome 
by  the  turbine  acting  through  the  pulley  M  at  a  velocity  of  vl  ft.  per 
second.  The  turbine  itself  is  shown  in  black  shading.  EE  and  DD 
are  the  two  crowns  or  rings  between  which  are  inserted  the  curved 
vertical  buckets  W. 

Notation. — Referring  to  Figs.  152  and  152a. 

wn  =  absolute  velocity  of  the  water    leaving  the  wheel  at  N, 
being  represented  by  the  diagonal  of  the  parallelogram 

Gn  %• 

cn  =  relative  velocity  of  the  water  at  N. 
%  =  velocity  of  the  outer  rim  of  the  wheel, 


HYDRAULIC   TURBINES 


768A 


L  =  absolute   velocity   of  the  water  entering  the  wheel  channel  at 
the  point   1   on  inner  rim  of  the  runner,  represented  by  the 
diagonal  of  the  parallelogram  ci  vi. 
=  relative  velocity  of  the  water  at  the  point  1. 

=  velocity  of  the  inner 
rim  of  the  wheel,  tan- 
gent to  the  vane  curve 
at  1." 

:  angle  between  the  tan- 
gent to  the  inner  rim 
Vi  and  a  tangent  to 
the  direction  of  the 
water  at  1. 

=  angle  between  tangent 
i>i  and  the  tangent  to 

Pthe  vane  at  1. 
fj.  =  angle  between  vn  and 
wn. 

5  =  angle  between  cn  and 
the  tangent  to  the 
outer  rim. 

h  =  height,  in  feet,  from  the 
surface  of  head- water 
to  that  of  tail-water. 
h  hn  =  h  e  i  g  h  t  respectively 
from  a  point  halfway 
between  the  crowns 
(top  and  bottom  of 
the  vanes)  and  the 
head-water  and  tail- 
water. 

e  =  height  or  vertical  dis- 
tance between  crowns. 
•h  7*2  —  radii  of  inner  and  outer 

edges  of  the  wheel. 
Q  =  cubic  feet  of  water  used 
per  second,  in  steady 
flow. 
7  =  weight  of  1  cubic  foot 


Wheel  or 
Runner 


Horizontal  Section  N  A  X. 
FIG.  151. — Fourneyron  Turbine* 


of  water,  Ib. 

Pi»  Pn  ~  internal     pressure     of 
the  water  at  entrance 
and  exit  of  the  wheel. 
pa  =  pressure  of  atmosphere,  Ib  per  sq.  ft. 

b  =  height   of  the  water  barometer  in  feet. 

If  the  wheel  is  run  at  the  proper  speed  and  the  angle  ft  has  been 
given  a  value  such  that  the  tangent  to  the  vane  curve  at  1  coincides 
in  direction  with  the  relative  velocity  CL  there  will  be  no  "elbow" 
or  sharp  turn  in  the  absolute  path  of  the  water  as  it  enters  the  wheel, 
but  the  path  will  be  a  smooth  curve,  GIN,  Fig.  1520.  In  this  way 
impact  or  shock  and  the  corresponding  loss  of  energy  are  avoided. 

The  quantities,  Q,  hi  hn,  7,  r\,  TZ,  a,  and  5  being  given,  it  is  required 
to  determine  the  best  value  for  the  velocity  vn  of  the  outer  wheel-rim 
and  the  proper  height  e  between  crowns  so  that  the  whole  available 
flow  Q  may  be  utilized.  Nine  unknown  quantities  are  involved,  viz.: 
Vi,  vn,  Wi,  wn,  e,  GI,  cn,  PI,  and  pn,  and  nine  independent  and  simul- 
taneous equations  are  needed. 

Disregarding  friction  for  the  present,  the  following  are  the  equations: 

(1)  d2    =  Wi*  +  Vi2  —  2  Wi  vi  cos  a. 

(2)  Wrf  =  Cn2  +  Vn2  -2CnVn  COS  g. 


768s 


WATER-POWER 


2g 

(5)  Vn*=  cn,  when  tne  angle  5  is  small. 

(6)  [27rri  e  sin  a]  wl  =  [2wrn  e  sin  5]  cn. 

(7)  Q  =  [27rrn  e  sin  5]  cn. 

(9)  pn  =  7^  +  Pa- 

From  these  equations  the  following  are  derived: 

(10)  Velocity  of  outer  rim  for  max.  efficiency,  vn  =  . 


gh  (tan  a) 
sin  5 


(11)  Power,  ft.-lbs.  per  sec.  exerted  by  the  water  on  the  turbine, 
L  =  Q7h  —  —  — ~.     This  power  L  equals  the  whole  theoretic  power 

of  the  mill-site  less  the  kinetic  energy  carried  away  per  second  by  the 
water  leaving  the  wheel  at  N. 

•-  ~  (Wi  vi  cos  a  -  [wn  cos  M]  %). 


(12)  L 

Efficiency,  i\  =  1  -  (2  tan 


a  sin2— --T-  sin  6). 


FIG.  152.— Path  of  Water. 
•ft. 


FIG.  152a.  —Velocity  Diagrams. 

From  (17) 
vn  =  0.92 


From  this  expression  we  see 
that  the  smaller  the  angles  a 
and  5  can  be  made  the  greater 
the  efficiency.  In  practice  a  is 
taken  from  20°  to  30°  and  5  from 
15°  to  20°. 

With  a  =  25°  and  5  =  15°  we 
obtain  t]  =  0.92,  but  in  actual 
practice  this  figure  is  reduced  to 
80  per  cent  or  less  (unless  in  ex- 
ceptional cases)  on  account  of 
fluid  friction  and  imperfect 
guidance  of  the  water;  75  per 
cent  is  a  fairly  good  perform- 
ance. When  a  turbine  (fric- 
tionless)  is  running  with  the 
speed  of  maximum  efficiency, 
the  following  formula  holds 
good  for  an  kinds  of  turbines: 

(13)  Wi  Vi  cos  a  =  gh. 

EXAMPLE. — Given  7i  =  60  ft., 
Q  =  150  cu.  ft.  per  sec.,  n  =  2 
ft.,  rn  =  2.5  ft.,  angle  a  =  20°, 
5  =  15°,  it  is  required  to  de- 
sign an  outward  radial  dis- 
charge turbine  having  parallel 
crowns,  to  find  the  outer  rim 
velocity  vn  for  the  best  effect, 
the  vane  tangent  angle  p  at 
entrance  and  the  proper  dis- 
tance e  between  crowns,  that  all 
the  water  available  may  be  used 
at  full  gate. 

=  48  ft.  per  sec, 


HYDRAULIC   TURBINES.  769 

48  X  60 
With  rn  =  2.5  ft.  this  is  equivalent  to  2^  ^2  5  =  183  revs,  permin. 

From  (6)     taking  cn  =  vn, 

vn  rn  sin  5      43  x  2.5  X  0.259 

5.4  ft.  per  sec. 


2.0X0.342 
From  (8)  Vi  =  n  %  •*-  rn  =  (2-5-  2.5)  48  =  38.4  ft.  per  sec. 

From  (14)  tan  USO*  -  ft  -    - 


Whence  180°  -  ft  =  105°  19';  /3  =  74°  41'. 

From  (15)  e  =  Q  -f-  2irrn  sin  5  vn  =  150  -f-  (2?r  x  2.5  X  0.259  X  48)  = 
0.768  ft.,  or,  adding  10  per  cent  for  thickness  of  vanes,  0.845  ft. 

Assuming  75  per  cent  efficiency,  the  power  of  this  wheel  is 
0.75  X  Qjh  =  0.75  X  150X  62.4  X  60  =  421,200  ft.-lbs.  per  sec.  =  766  H.P. 

The  formulae  above  given  apply  to  inward  flow  as  well  as  to  outward 
ial 


flow  turbines.     For  axial  flow  turbines  r\  =  r^  =  r,  which  is  measured 

ining  the  wheel  vanes. 
vn  for  the  best  effect,  assuming 


to  the  middle  point  of  the  ring  containing  the  wheel  vanes. 
Another  formula  for  the  value  of  vn  for  the  best 


8  per  cent  friction  losses,  is 


%  =  0.92        o   rn 


Fn  being  the  aggregate  sectional  area  of  the  exit  passages  of  the 
turbine,  that  of  each  passage  being  taken  at  right  angles  to  the  relative 
velocity  cn,  and  Fo  the  aggregate  sectional  areas  of  the  guide  passages 
at  the  entrance  point,  1. 

To  find  j8,  the  vane  tangent  angle  at  the  point  1, 

(14)  tan  (180°  -  0 


. 
i  -  Wi  cos  a 

To  find  e,  the  distance  between  crowns  (the  common  height  of  all 
the  wheel  passages  at  full  gate), 
(15)  e  =  Q  -r  2wrn  (sin  6)  %. 

This  value  should  be  increased  somewhat  (perhaps  10  per  cent  in 
some  cases)  to  allow  for  the  thickness  of  the  vanes. 

When  friction  is  taken  into  account,  the  value  of  vn  (the  velocity  of 
the  outer  rim)  for  best  effect  is 

}  l 

f0  and  fn  are  coefficients  of  resistance  due  to  friction,  respectively,  of 
the  passages  between  the  head  water  surface  and  the  guide  outlets 
and  the  passages  through  the  vanes.  According  to  Weisbach,  each  of 
these  coefficients  may  be  taken  at  from  0.05  to  0.10.  Taking  the 
larger  value  the  equation  reduces  to 

(17)   vn  =  0.92 

Besides  the  loss  due  to  friction  of  the  passages  there  are  other  losses, 
such  as  those  due  to  the  friction  of  the  wheel  in  the  tail-water,  to  axle 
friction,  and  to  leakage  between  the  edges  of  the  wheel-crowns  and 
the  guides.  Refined  analysis  of  these  losses  is  impracticable,  and  the 
efficiency  of  any  given  wheel  can  be  determined  only  by  actual  test. 

The  formulae  given  above  may  be  used  for  approximate  computations 
in  the  preliminary  design  of  a  turbine,  but  in  practical  design  many 


769A 


WATER-POWER 


considerations  enter  which  the  formulas  do  not  cover,   such  as  the 
number  of  vanes  and  guides,  their  shape  and  proportions. 
Determination  of  the  Dimensions  of  Water  Turbine  Runners. —  S.  J. 

Zowski  (Eng.  News,  Jan.  6,  1910)  developed  a  series  of  empirical 
formulae  for  the  design  of  water  turbine  runners.  The  starting  point 
of  the  theory  upon  which  the  formulae  are  built  is  the  formula  for  the 
peripheral  velocity  of  the  mean  circumference  of  the  runner; 


Transformations  of  this  equation  and  the  application  of  certain 
constants  result  in  the  empirical  formulae  given  in  the  accompanying 
table: 

Comparison  of  Formulae  for  Dimensions  of  Hydraulic  Turbines 

(Zowski). 


Bucket 
Angle  ft 
deg. 

Vane 
Angle  a 
deg. 

Speed 
Constant 

Entrance 
Diameter 
D 

No.  of 

Buckets 
n 

No.  of 
Guide 
Vanes 
n' 

Low  speed  

60-90 

20  or  less 

5  4.588  to 

87  to  99    /— 

3.7  V^~ 

2.5  VoT 

N      NH 

Medium  speed. 

901 

25-32 

5.198 

99      _ 

3.0Vd~ 

3.0  Vd" 

High  speed.  .  .  . 

90-135 

30-40 

5  5.  198  to 
\  7.006 

99  to  134 

2.2Vd~ 

3.5  V<T 

N       VH 

NOTES:  Efficiency. — In  the  calculations  leading  to  the  figures  in 
the  above  table,  a  hydraulic  efficiency  of  84  per  cent  has  been  assumed 
for  medium-speed  runners,  and  of  83  per  cent  for  other  types.  These 
efficiencies  are  not  unusual  for  runners  of  fair  design  and  construction, 
and  with  them  the  values  of  Kv  above  are  obtained. 

Values  of  (3  and  a — For  high  heads,  requiring  low-speed  runners,  it 
Will  be  advisable  to  keep  #  in  the  neighborhood  of  90°,  since  the  smaller 
the  ratio  /3/a  the  smaller  is  the  pressure  head  under  which  the  water 
passes  from  the  guide  case  into  the  runner  buckets. 

Number  of  Buckets  and  Guide  Vanes  n  and  n'. — Some  turbine  builders 
use  in  every  case  as  many  buckets  as  possible,  but  the  majority  use 
less  in  a  high-speed  than  in  a  low-speed  runner.  A  few  more  guide 
vanes  than  buckets  should  be  used.  It  is  advisable  to  use  an  even 
number  of  guide  vanes,  and  often,  for  manufacturing  reasons,  to  make 
this  number  divisible  by  4.  The  number  of  buckets  should  be  un- 
even to  avoid  haying  more  than  one  bucket  edge  coincide  with  a  vane 
tip  at  the  same  time. 

Prof.  Zowski  classifies  turbines  with  respect  to  speed  as  low  speed, 
medium  speed,  and  high  speed.  High-speed  runners  are  those  in 
which  the  angle  0  is  greater  than  90°,  medium  speed,  those  in  which 
0  is  90°,  and  low  speed,  those  in  which  P  is  less  than  90°.  High-speed 
runners  are  frequently  known  as  the  "American"  type.  He  also 
classifies  them  with  respect  to  capacity,  as  low  capacity,  medium 
capacity,  and  high  capacity,  based  on  the  proportions  of  the  runner 
profile  or  the  ratios  of  (a)  diameter,  D,  at  entrance  point  of  buckets; 
(&)  diameter  at  exit  point  of  buckets,  D'\  (c)  diameter  at  neck  of  draft 
tube,  D".  See  Fig.  153. 

The  capacity  depends  on  the  relation  of  B/D  and  varies  between 
the  limits  of  Vso  D  and  1/2  -D.  The  minimum  value  depends  on  the 
purity  of  the  water.  Low  capacity  runners  are  stated  to  be  those 
in  which  the  diameter  of  the  draft  tube  is  equal  to  or  less  than  the 
bucket  exit  diameter,  and  B/D  will  lie  between  1/30  and  Vs.  In 
medium  capacity  runners,  the  draft  tube  diameter  is  larger  than  the 


HYDRAULIC  TURBINES. 


769s 


bucket  exit  diameter,  but  less  than  the  mean  diameter  of  the  runner; 
B/D  lies  between  i/g  and  1/4.  In  high  capacity  runners,  the  draft 
tube  diameter  is  greater  than  the  mean  exit  diameter  of  the  runner, 
and  B/D  lies  between  1/4  and  1/2. 


D"  >  D" 

FIG.  153. — Limiting  Profiles  of  Three  Types  of  Radial  Inward 
Flow  Turbine. 


The  capacity  of  runners  may  be  characterized  by  the  capacity 
constant 


If  a  series  of  values,  as  in  the  table  below,  be  assigned  to  Kq  and 
these  values  substituted  in  the  above  equation,  we  may  obtain  the 
diameter  of  the  runner  in  terms  of  the  discharge  per  foot  of  head. 
The  constants  and  resulting  formulae  for  diameter  are  as  follows: 


Type  of 
Turbine. 

Range  of 

Kv. 

Diam.  in 
Terms  of  Qi. 

Discharge  Loss 
in  Terms  of 
Total  Head. 

Low   speed,  low  capa- 
city   

0  21  to  0  89 

(2.20  to  1.06)  V(?i 

(0.04  to  0.06)  H 

Medium    speed,    medi- 
um capacity  

0.89  to  2.  19 

(1.06  to  0.67)  V5i 

(00.5  to  0.08)H 

High  speed,  high  capa- 
city   

2.  19  to  4.66 

(0.67  to  0.46)  V<?I 

(0.08  to  O.I5)H 

The  discharge  loss  represents  the  flow  velocity  at  the  neck  of  the 
draft  tube.  With  properly  designed  runners  it  is  about  the  same  as 
the  ftow  velocity  in  the  discharge  area  of  the  runner.  This  velocity 
is  a  direct  loss,  which,  however,  is  partly  recovered  by  the  conical  lower 
part  of  the  draft  tube.  In  low  capacity  runners  it  is  not  difficult  to 
reduce  the  discharge  loss  to  a  minimum  in  the  runner  itself,  while 
in  high  capacity  runners  large  discharge  losses  must  be  allowed.  The 
values  given  for  discharge  losses  in  the  above  table  represent  good 
practice. 

The  speed  and  capacity  constants  have  been  combined  by  Prof. 
Zowski  to  form  a  type -characteristic  Kj,  described  below.  The  range 
of  KI  is  as  follows: 


Low  Speed,  Low 
Capacity. 
12  to  28 


Medium  Speed,  Medium 
Capacity 
28  to  44 


High  Speed,  High 
Capacity 
44  to  87 


Compare  the  above  ranges  with  those  given  by  Baashuus  on  page.  771. 


770 


WATER-POWEB. 


ft: 


Comparison  of  American  High-Speed  Runners—  Type  Characteristic. 

—  S.  J.  Zowski   (Eng.  News,  Jan.  28,   1909)  compares  the  runners  of 
standard  American  high-speed  turbines  by  means  of  speed  and  capa- 
city criteria.     Referring  to  Fig.  154,  he  uses  the  notation: 
H.P.  =  effective  power  of  the  runner. 
N  =  speed  of  runner,  r.  p.  m. 
Q  =  discharge  of  runner,  cu.  ft.  per  sec. 
i  =  specific  discharge  of  runner  =  Q  -4-  V  H  . 
[  =  net  head  acting  on  turbine  =  gross  head  minus  all  losses  in 

head  race  conduit  and  tail  race,  in  feet. 
e^  =  hydraulic  efficiency  of  the  turbine  ;   (1  —  e^)  H  =  head  lost 

inside  of  turbine  due  to  friction,  eddies  and  shocks. 
D  =  mean  entrance  diameter  of  runner,  feet. 
d  =  mean  entrance  diameter  of  runner,  inches. 
B  =  height  of  guide  case,  feet. 
a  =  angle  between  entrance  speed  and  peripheral  speed  at  D 

(see  Fig.  154). 
P  =  bucket  angle  at  D 
c  =  real  entrance  speed  at  D. 
w  =  relative  entrance  speed  at  D. 
v  =  peripheral  speed  at  D. 
n  =  number  of  buckets. 
nf  —  number  of  guide  vanes. 
cr  =  radial    entrance    speed  at    D  = 
radial  component  of  c   (see  Fig. 
154). 

Kv  =  sPeed  constant. 
Kq  =  capacity  constant. 
KI  =  type  constant. 

-      V 


For  a  value  of  e^  =  0.83, 


=  5.167 


\ 


sin  (3  cos  a 

For  the  conditions,  /3  =  135°,  a  =  40°,  and 
e^  =  0.83;  the  value  of  Kv  is  about  7.0. 

The  constant  Kv  can  also  be  used  to  de- 
termine whether  a  further  increase  of  speed 
is  possible.  If  K^  be  considerably  larger 
than  7,  either  the  guaranteed  speed  is  higher 
than  the  speed  at  which  the  runner  gives 
maximum  efficiency,  or  the  nominal  diam- 
eter of  the  runner  is  larger  than  the  mean 
diameter  D. 

K   =        Q        =  -2-1 
q      Z>2  V  H       D* 

Kq  is  the  specific  discharge  of  a  runner 
with  its  diameter  reduced  to  1  ft.  Kq  will 
have  nearly  the  same  value  for  all  runners 
of  the  same  type  and  is  a  criterion  for  ca- 
pacities of  different  runner  types. 


FIG.  154.  —  Horizontal 
and  Vertical  Sections  of 
High-speed  Turbine. 


The  speed  and  capacity  criteria,  however, 
fail  to  give  the  information  as  to  what  ex- 
tent each  type  of  runner  meets  the  require- 
ment of  highest  possible  speed  with  highest  capacity  in  cubic  feet  per 
second.  Two  runners  with  different  values  of  Kv  and  Kq  may  be  equiv- 
alent when  the  speed  and  capacity  are  considered  together.  A  third 
criterion  K>.  known  as  the  type  characteristic  or  specific  speed,  which 


HYDRAULIC   TURBINES. 


770A 


combines  Kv  and  Kq  must  be  introduced  to  give  this  information. 
A  convenient  method  of  combination  has  been  indicated  by  Professor 

Camerer,  of  Munich,  and  gives  a  value  of  K^  •- 
Values  of  HI>M  for  different  heads  are  given  below. 
VALUES  OP 


H 

#1.25 

H 

Hl-25 

H 

Hi.25 

H 

Hi.25 

H 

Hi.25 

2 

2.38 

35 

85.13 

140 

841.6 

400 

1789 

900 

4930 

4 

5.66 

40 

100.6 

160 

569.0 

450 

2073 

950 

5274 

6 

9.39 

45 

116.6 

180 

659.3 

500 

2364 

1000 

5623 

8 

13.45 

50 

133.0 

200 

752.2 

550 

2663 

1200 

7079 

10 

17.78 

60 

167.0 

220 

847.3 

600 

2970 

1400 

8564 

12 

22.33 

70 

202.5 

240 

944.6 

650 

3282 

1600 

10120 

15 

29.52 

80 

239.3 

260 

1044 

700 

3601 

1800 

11724 

20 

42.29 

90 

277.2 

280 

1145 

750 

3925 

2000 

13375 

25 

55.90 

100 

316.2 

300 

1249 

800 

4255 

2500 

17678 

30 

70.21 

120 

397.2 

350 

1514 

850 

4590 

3000 

22202 

The  value  of  K^  is  an  absolute  criterion  for  turbines  in  reference  to 
the  combination  of  highest  speed,  highest  capacity  and  good  efficiency. 
Its  meaning  can  be  found  by  assuming  H.P.  =  1  and  H  =  1,  when 
KI  =  N  in  r.  p.  m.  The  following  table  compares  the  capacity  and 
speed  constants  and  type  characteristics  of  the  standard  American 
turbines  by  means  of  this  criterion: 

Mean  Values  of  Capacity  Constants,  Speed  Constants  and  Type  Char- 
acteristics of  American  High-Speed  Runners. 

Values  in  Foot  and  Pound  System. 


Capa- 

Speed 

Type 

Velocity 
Coefficient, 

K>              V 

Name  of  Runner  Type. 

Maker 

city 
Con- 
stant, 
JCfl 

Con- 
stant, 
Kv 

Charac- 
teristic, 

*t 

V       V17H 
Kv 

(2 

VT5 

Smith  

, 

3.68 

7.26 

80.6 

0.905 

Improved  New  American  .  . 
Leviathan  

2 
3 

3.43 
2.96 

7!47 

79 
74.1 

0.885 
0.931 

Improved  Samson 

4 

3.18 

7.07 

73.1 

0  881 

Victor  Increased  Capacity.. 
Victor  Standard  Capacity.  . 
Trump  

5 
5 

6 

3.59 
3.26 
3.52 

6.1 
6.1 
5.87 

66.6 
63.5 
63.4 

0.761 
0.761 
0.729 

New  Success 

1 

2  75 

5.88 

55 

0  733 

New  American  

2 

2.8 

5.6 

54.1 

0.69 

McCormick* 

1    ) 

Jolly  McCormick*  

7   } 

2.8 

5.35 

51.4 

0.667 

Alcott  High  Duty  Special.  . 
Risdon  Double  Capacity.  .  . 

3   X 
3 

2.25 
1.7 

5.46 
5.9 

46.7 
43.8 

0.681 
0.735 

*These  two  runners  are  identical  and  have  the  same  characteristics. 
The  makers  of  the  above  turbines  are  as  follows:    1.  S.  Morgan  Smith  Co. 
2.  Dayton  Globe  Iron  Works  Co.   3.  Risdon-Alcott  Turbine  Co.    4.  The  James 
Leffel  &  Co.       5.  Platt  Iron  Works  Co.       6.  Trump  Mfg.  Co.       7.  Wellman- 
Seaver-Morgan  Co. 

The  data  were  gathered  from  catalogs  of  the  different  concerns  and 
the  values  of  power  and  speed  tabulated  in  the  catalogs  were  based 
on  tests  made  in  the  Holyoke  flume.  The  values  of  the  discharge  are 
based  on  tfoe  assumption  of  80  per  cent  efficiency, 


770s 


WATER-POWER . 


Specific  Discharge. — Prof.  Merriman  (Hydraulics,  10th  ed.,  p.  476) 
uses  a  coefficient  or  efficiency  which  he  calls  the  specific  discharge. 
It  is  the  discharge  of  a  1-H.P.  turbine  under  a  head  of  1  foot.  If  Q  is 
the  discharge  of  a  turbine,  in  cubic  feet  per  second,  //  the  head  in  feet 
and  H.P.  the  horsepower,  then  the  specific  discharge  Qs  =QH/H.P. 
The  specific  discharge  is  characteristic  of  the  efficiency  of  a  given  type, 
and  is  the  greater  the  lower  the  efficiency.  For  high,  medium  and 
low  efficiency,  respectively,  the  specific  discharge  is  less  than  10,  from 
10.5  to  11.5  and  greater  than  12. 

The  specific  diameter  of  a  given  type  is  the  diameter  D  correspond- 
ing to  a  head  of  1  foot  and  the  specific  speed  N8  (or  type  characteristic 
KI).  By  means  of  a  test  on  one  size  of  a  given  type  the  quantities 
Ns,  Qs  and  a  constant,  k\,  can  be  computed.  For  any  other  size  of 
that  type  under  any  head  H 

N  =  NS  ft1'25  +  V  HJF         Q  =Qo  H.P.  -  H         D  =  ki  V1F-*-  N 


N  VHJP? 


Qs- 


ND 


H.P. 


The  following  values  of  these  constants  have  been  obtained  in  tests 
of  the  turbines  named : 


Manufacturer. 
Allis-Chalmers  Co 

Type. 

(           A 
j           B 

Specific 
Speed 

^s 
13.4 
20.4 
29.4 
40.6 
47 
47.5 
74.1 
53 
57 
81 

etermine 

March  2, 

Specific       Specific 
Dis-            Con- 
charge,         stant 

Qs              *i 
11.6           1078 
11.6           1149 
11.6           1224 
11.1           1280 
11.1           1250 
10.4           1350 
11.0           1714 
11.0           1260 
11.0           1350 
10.9           1660 

the  Size  and  Type 

1911)  discusses  the 

Risdon-Alcott  Co.  .  . 

•••••)         c 

(            D 

(        Alcott 
I        Risdon 

(     Leviathan 
1    McCormick 
S.  Morgan  Smith  Co.  .  .  .  •<  New  Success 
(         Smith 

The  Use  of  Type  Characteristics  to  DI 
of  Turbines.  —  N.  Baashuus   (Eng.  News, 

use  of  type  characteristics  as  developed  by  Zowski  for  determining 
the  size  and  type  of  turbine  to  be  used  in  power  plants.  If  H.P.  be 
the  horsepower  capacity  of  a  single  turbine  unit,  N  the  speed  of 
the  turbine  in  r.  p  m.,  H  effective  head  at  the  turbine  casing  in 

N    /H  P 
feet,  KV  =  T?A/—  —  •     The  value  of  KV  for  radial  inward   flow   tur- 

H\  Vtf 

bines  will  lie  between  10  and  100,  while  for  impulse  wheels  it  will  lie 
between  5  and  1,  or  even  a  lower  figure.  The  practical  type  char- 
acteristics will  always  be  within  these  limits  irrespective  of  the  capacity, 
speed,  head,  size  or  design  of  the  turbine.  Where  an  inward  flow 
turbine  has  more  than  one  runner,  or  the  impulse  wheel  more  than 
one  nozzle,  the  H.P.  to  be  applied  in  the  above  formula  is  the  power 
developed  by  one  runner  or  one  nozzle  only. 

EXAMPLE.  —  Assuming  an  available  effective  head  of  324  feet  and  an 
available  flow  of  about  310  cu.  ft.  per  sec.  at  the  power-plant  site, 

=  9,100.     Of  this,  103  H.P.  will  be 


the  total  capacity  is  H.P.i  = 

required  for  exciters  and  lighting  purposes,  calling  for  two  100-H.P. 
exciter  units  running  at  550  r.  p.  m.,  one  being  in  reserve.  The  remain- 
ing 9,000  H.P.  would  be  generated  by  three  3,000-H.P.  units  run- 
ning at  500  r.  p.  m.  with  a  fourth  unit  as  a  reserve.  From  these 

data  we  find  the  type  characteristic  of  the  main  unit  Kt  =  ^  - 


5=  2J  calling  for  a  radial  inward  flow  turbine,    Likewise  for  an  exciter 


HYDRAULIC  TURBINES. 


771 


unit,  KI  =  4.25,  calling  for  an  impulse  wheel.     This  characteristic  is 
not  only  intended  to  give  information  as  to  the  class  of  wheel  to  be 
used,  but  it  will  also  indicate  the  particular  variety  in  each  class. 
The  accompanying  table  shows  the  values  of  K^  and  the  efficiency 


Classes  of  Radial  Inward  Flow  Turbines 


Type  of  Turbine. 

*t* 

Efficiency! 

Maximum. 

Power. 

Efficiency 
at  Half 
Power. 

Low  speed.                 .    .        . 

10  to  20 
30  to  50 
60  to  80 
90  to  100 

82 
82 
80 
73 

3/4 
3/4 
8/10 
9/10 

76 
75 
70 
53 

Medium  speed  

High  speed 

Very  high  speed  

of  various  classes  of  radial  inward  flow  types.  The  figures  are  only 
approximate  and  there  are  turbine  tests  on  record  showing  better 
results.  The  table,  however,  is  a  guide  as  to  the  particular  type  of 
machine  to  be  installed.  Similarly  the  relation  of  type  characteristic 
to  efficiency  in  impulse  wheels  is  as  follows: 


Ktl 

Efficiency  at  about 


=    12345 

powert =80     79     78     77     76 

In  selecting  a  type  for  a  proposed  turbine  plant,  the  speed  in  revolu- 
tions can  be  chosen  so  that  turbines  of  high  efficiency  are  secured. 
In  cases  of  low  head,  the  turbines  would  run  too  slowly  for  most  pur- 
poses, which  disadvantage  can  be  overcome  by  keying  several  runners 
to  one  shaft.  For  instance:  A  750-H.P.  dynamo  is  to  be  driven  at 
257  r.  p.  m.  under  36  ft.  head.  We  may  use  one,  two  or  four  turbines 
to  develop  the  power,  the  values  of  K^  being  80,  56.5  and  40  respec- 
tively. The  first  corresponds  to  the  high-speed  turbine  which  would 
be  unsuitable  if  water  were  scarce  in  dry  seasons.  The  second  would 
utilize  water  in  a  more  economical  way,  while  the  third  combination 
represents  the  most  favorable  type  as  to  efficiency.  Similarly,  the 
number  of  runners  or  nozzles  on  impulse  wheel  installations  may  be 
determined. 

With  a  400-ft.  head,  and  1300  H.P.  to  be  developed  at  an  efficiency 
of  not  less  than  78  per  cent,  a  turbine  whose  value  of  K^  is  about  3 

Lould  be  used.     The  revolutions  with  a  single  turbine  wheel  will  be 

N  =  KtXHX  T/H7N  =  150. 

If  this  is  too  slow,  two  nozzles  can  be  arranged  to  supply  water  to 
the  runner,  each  supplying  one-half  of  the  1300  H.P.,  and  the  cor- 
responding r.  p.  m.  would  be  212.  Likewise,  with  four  nozzles  N  = 
300,  and  with  six  N  =  357,  giving  the  same  efficiency  in  each  case. 

The  characteristic  K^  also  can  be  used  to  determine  the  principal 
dimensions  of  turbines  for  any  given  installation.  The  various  di- 
mensions of  a  given  type  of  standard  turbine  can  usually  be  expressed 
as  functions  of  the  diameter  of  the  runner,  which  functions  are  prac- 
tically the  same  for  all  sizes  of  the  same  type.  If  a  turbine  plant  of 
a  certain  type  characteristic  K^  is  proposed,  it  may  be  compared  with 

*KI  refers  to  the  maximum  power  of  one  runner  only.  In  some 
cases  where  K^  exceeds  100,  multiplex  turbines  must  be  used. 

fAt  maximum  power  the  efficiencies  are  a  few  per  cent  lower  than 
at  maximum  efficiency. 

%K£  refers  to  maximum  power  of  one  nozzle  only.  In  cases  where  the 
type  characteristic  is  between  5  and  10,  turbines  with  more  than  one 
nozzle  must  be  used. 

IfAt  maximum  and  half  power,  the  efficiencies  are  a  few  per  cent  lower. 


77U 


WATER-POWER. 


any  existing  plant  of  the  same  type  characteristic  built  in  the  same  way 
as  the  natural  conditions  dictate  that  the  new  one  should  be  built. 
Standardized  turbines  of  the  same  type  will  have  runner  diameters  in 
the  ratio  of  ^N/H,  and  this  ratio  may  be  applied  to  the  dimensions  of 
the  existing  plant,  to  determine  those  of  the  new  one. 

EXAMPLE.  —  A  proposed  power  house  is  to  have  three  turbines  on 
horizontal  shafts,  two  runners  per  turbine,  developing  625  H.P.  per 
runner  at  257  r.  p.  m.  under  an  effective  head  of  39  ft.     The  type 
characteristic  for  a  twin  turbine  is  __ 
257          1250 


Assume  that  the  dimensions  of  an  existing  plant  of  similar  type 
to  the  proposed  are  available,  and  that  this  plant  operates  under  an 
effective  head  of  53  ft.,  and  develops  650  H.P.  per  runner  in  twin  tur- 
bines, at  360  r.  p.  m.  Its  type  characteristic  would  be  64,  which  would 
be  close  enough  to  that  of  the  proposed  plant  for  our  purpose.  The 
ratio  between  the  sizes  of  the  turbines  would  be 


a. 

IV 


— 
257  = 


1.2 


and  all  dimensions  of  turbines  in  the  new  plant  would  be  1.2  times 
those  of  the  old.  This  method  is,  of  course,  approximate,  and  it  may 
be  sometimes  advisable  to  increase  somewhat  the  obtained  results. 

Estimating  the  Weight  of  a  Turbine.  —  A  preliminary  approximate 
estimate  of  the  weight  of  a  turbine  may  be  determined  in  the  same 
manner  from  the  known  weights  of  existing  plants.  If  designed  for 
the  same  head,  turbines  of  different  sizes  of  a  standardized  series  will 
have  weights  approximately  proportional  to  a  function  of  the  ratio  of 
diameters: 


The  first  value  should  be  used  with  D^/Di  less  than  1,  and  the  second 
with  DZ/DI  greater  than  1.  For  different  heads  the  weights  of  turbines 
of  the  same  size  are  approximately  in  the  proportion: 


The  first  value  should  be  used  with  H2/Hi  less  than  1,  and  the 
second  with  HZ  /Hi  greater  than  1. 

Wit  DI  and  if  i  always  refer  to  the  installation  whose  weight  is  known. 

Selecting  a  Turbine.  —  In  selecting  a  turbine  for  a  given  location 
manufacturers'  catalogs  should  be  consulted,  and  the  characteristics 
of  the  several  designs  that  seem  to  fit  the  conditions  should  be  com- 
pared before  making  a  decision.  Considerations  of  first  cost,  space 
occupied,  number  of  revolutions,  regulation,  etc.,  tend  to  complicate 
the  problem.  The  type  of  wheel  that  is  best  suited  for  different  heads 
is  roughly  indicated  in  the  following  table: 


Head. 

Type. 

Remarks. 

Under  30  ft. 

Open  flume. 

Except  single  units  of  less  than  100  H.P. 

when  the  encased  type  may  be  preferable. 

30  to    50ft. 

Open    flume    or 

The  latter  most  economical  for  units  of  less 

steel  encased. 

than  500  H.P. 

50  to  100  ft. 

Steel-plate     en- 

Except small  units,  when  cast-iron  casings 

cased. 

may  be  lower  in  cost. 

100  to  600  ft. 

Cast-iron     cas- 

Cast steel  for  large  units  under  high  heads. 

ings. 

300  to  600  ft. 

Impulse  wheels. 

For  wheels  under  about  500  H.P. 

600  to  3000  ft. 

Impulse  wheels. 

Reaction  wheels  for  special  conditions,  where 
little  or  no  regulation  is  required. 

Limits  to  type  characteristics  K^  may  be  imposed  by  runner  strength, 
tendency  to  erosion  or  pitting,  or  limits  in  the  generator  construction. 


HYDRAULIC   TURBINES 


771s 


The  approximate  relation  of  the  characteristic  ,to  the  head,  in  general 
use,  is  as  follows: 

Head  in  feet  20     50     100    200     300     400     500        600 

Type  characteristic 90    70      50      37      31      28      26.5      25 

The  relation  of  type  characteristic  K^  to  other  ^variables  is  about  as 
below : 
Kt 10      20        30       40      50        60        70      80        90     100 


0.64    0.68     0.71     0.74    0.76     0.78     0.80    0.82   0.83 


5.1       5.4       5.7 


11       18 


25 


89      100 


6 

33 

110 


6.2       6.4       6.5      6.6     6.7 


42 
120 


48        53        57       60 
130    140      149      157 


Speed  coeff.*  ____  4.8 
Width  of  runner, 

per  cent  of  I>i..  7 
Runner  discharge 

diam.%ofZ>i..    48        72 

*Runner  inlet  peripheral  velocity,  ft.  per  sec.,  for  1  ft.  head. 

Dit  inlet  diameter. 

Efficiency  of  Turbine  Wheels.  —  Up  to  about  1910,  the  opinion  was 
commonly  held  that  high  efficiencies  were  unobtainable  with  wheels  of 
high  type  characteristics  (Kt).  Tests  of  turbines  at  the  Holyoke 
flume  of  wheels  designed  since  that  time,  show  that  this  opinion  is 
erroneous.  S.  J.  Zowski  (Eng.  Rec.,  Nov.  28,  1914,  Dec.  26,  1914) 
presents  curves  of  several  tests  wherein  remarkably  high  efficiencies 
have  been  obtained  with  high  type  characteristic  wheels.  The  follow- 
ing table  gives  the  principal  data  and  best  efficiency  of  the  several 
wheels. 

Efficiency  of  Turbine  Wheels. 


Holyoke 
Test 
No. 

Diam., 
In. 

Best 
Efficiency, 
Per  Cent. 

Normal 
Speed, 
R.P.M.* 

Normal 
Power, 
H.P.i* 

Type 
Charac- 
teristic, 

*f 

B'lder. 
See 
note. 

1900 
2060 
2068 
2121 
2122 
2208 
2359 
2363 

35 
30 
30 
30 
30 
30 
35 
30 

90 
87.2 
83.2 
89.2 
89.3 
90.1 
93.07 
90.7 

45.3 
49.0 
51.8 
48.0 
49.9 
47.8 
47.2 
50 

2.48 
3.19 
3.20 
2.65 
3.25 
3.60 
2.7 
4.17 

71.3 
87.4 
92.8 
78.0 
90.0 
91.0 
77.6 
102 

A 
B 
B 
B 
B 
C 
A 
A 

*The  normal  power  and  normal  speed  are  the  speed  jmd  power  of 
thejurbine  reduced  to  1  ft.  head.  H.P.],  =  H.P.  -^  H  V-ff.  N!  =  N  + 
V  H  where  H.P.  is  the  actual  horsepower  developed,  N  the  actual 
r.p.m.  and  H  the  head  in  feet. 

NOTE. — The  builders  of  the  above  turbines  are:  A — The  James  Leffel 
&  Co. ;  B— Allis-Chalmers  Co. ;  C — I.  P.  Morris  Co. 

Further  details  of  the  tests  of  the  last  two  turbines  are  reported 
by  the  maker  as  follows. 

Holyoke  Test  No.  3359,  Vertical  35,  Type  F  Turbines 


Rev. 
per 

Min. 

Propor- 
tional 
Gateage. 

1  1  Ft.  Head. 

14  Ft.  Head. 

17  Ft.  Head. 

20  Ft.  Head. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

175 
175 
175 
175 
175 
175 

1.000 
.889 
.833 
,778 
.667 
.556 

88.00 
89.30 
86.45 
84.85 
81.25 
76.00 

108.5 
99.6 
87.0 
80.1 
66.9 
49.5 

87.47 
91.08 
93.00 
90.80 
87.45 
83.45 

154.5 
147.6 
141.4 
127.5 
103.2 
80.1 

86.00 
88.60 
90.15 
90.10 
88.00 
84.83 

202.4 
190.6 
182.2 
172.4 
141.6 
112.2 

84.25 
86.30 
86.65 
86.70 
86.60 
84.35 

251.5 
234.5 
222.5 
210.0 
180.2 
142.3 

772 


WATER-POWER , 


Holyoke  Test  No.  2362,  Vertical  30,  Type  Z  Turbines 


Rev. 
per 
Min. 

Propor- 
tional 
Gateage  . 

1  1  Ft.  Head. 

14  Ft.  Head. 

17  Ft.  Head. 

20  Ft.  Head. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

Effi- 
ciency. 

Horse- 
Power. 

175 
175 
175 
175 
175 
175 
175 

1.000 
.891 
.796 
.749 
.700 
.600 
.500 

83.50 
87.30 
88.35 
86.65 
84.20 
77.20 
70.90 

162.3 
160.0 
148.7 
137.8 
127.0 
100.4 
77.8 

83.35 
87.30 
90.00 
90.50 
89.55 
83.90 
77.20 

227.5 
223.5 
215.5 
206.5 
192.5 
155.2 
121.0 

81.40 
85.35 
87.90 
89.07 
89.28 
87.23 
80.65 

288.0 
285.0 

273  ;o 

265.0 
252.0 
215.5 
168.0 

79.30 
83.30 
85.85 
86.75 
87.00 
85.90 
81.60 

348.0 
344.0 
330.5 
320.8 
305.0 
269.5 
217.5 

Relation  of  Gate  Opening  to  Efficiency. — The  per  cent  of  gate  opening 
corresponding  to  different  efficiencies  and  different  type  characteristics 
are  approximately  as  follows  in  modern  types  of  turbines: 


Effi- 
ciency. 
85 
90 
85 
80 
75 
70 


20       30 


40 


-Type  Characteristics. — 
50  60  70 


80      90     100 


Gate  Openings  Corresponding  to  the  Stated  Efficiencies. 


95 

57 
45' 
36 
27 


96 
75 
56 
44 
35 
26 


97 

65-82 
55 
44 
35 
25 


98 

65-82 
55 
45 
36 
26 


68-80 
57 
47 
37 

28 


98 

72-78 
60 
50 
39 
32 


97 
77 
64 
55 
46 
38 


96       94 


70 
60 
55 

48 


82 
70 
64 
60 


Relation  of  Efficiency  and  of  Water  Consumption  to  Speed.— Fig.  155 

(from  Church)  shows  graphically  the  results  of  tests  of  a  160-H.P. 


0.2, 


0.4, 


0.6         0.8         1.0         1.2 
.  Keys,  per  Second 


1.6 


FIG.  155. — Test  Results  of  a  160-H.P.  Fourneyron  Turbine. 

Fourneyron  turbine.  It  will  be  seen  that  there  is  a  certain  speed  at 
which  the  turbine  gives  its  maximum  efficiency,  and  that  the  efficiency 
decreases  rapidly  as  the  speed  is  either  decreased  or  increased. 

Tests  at  the  Philadelphia  Exhibition,  1876  (R.  H.  Thurston,  Trans. 
A.  S.  M.  E.,  viii,  359). — Twenty  wheels  were  tested,  of  which  thirteen 

fave  efficiencies  ranging  from  75.15  to  87.68  at  full  gate,  averaging 
8.66  per  cent.     The  other  seven  gave  results  between  65  and  75  per 


_  .  HYDRAULIC  TURBINES.  773 

cent.     At  less  than  full  gate  the  following  average  results  were  ob- 
tained from  the  thirteen  wheels : 

Per    cent    of    full    discharge, 

about 9/10           7/8  3/4  5/8  l/2              1 

Number  of  wheels  tested 4           6  8  6  4           1 

Efficiencies,  average 73.5  74.6  70.8  65.1  70.7  55.0 

Rating  and  Efficiency  of  Turbines. — The  following  notes  and  tables 
are  condensed  from  a  pamphlet  entitled  "Turbine  Water-wheel  Tests 
and  Power  Tables,"  by  it.  E.  Horton.  Water-supply  and  Irrigation 
Paper  No.  ISO,  U.  S.  Geol.  Survey,  1906. 

Theory  does  not  indicate  the  numbers  of  guides  of  buckets  most  de- 
sirable. If,  however,  they  are  too  few,  the  stream  will  not  properly 
follow  the  flow  lines  indicated  by  theory.  If  the  buckets  are  too  small 
and  too  numerous,  the  surface-friction  factor  will  be  large. 

It  is  customary  to  make  the  number  of  guide  chutes  greater  than  the 
number  of  buckets,  so  that  any  object  passing  through  the  chutes  will 
be  likely  to  pass  through  the  buckets  also. 

With  most  forms  of  gates  the  size  of  the  jet  is  decreased  as  the  gate  is 
closed,  the  bucket  area  remaining  unchanged,  so  that  the  wheel  operates 
mostly  by  reaction  at  full  gate  and  by  impulse  to  an  increasing  extent  as 
the  gate  is  closed.  Hence,  the  speed  of  maximum  efficiency  varies  as 
the  gate  is  closed.  The  ratio  peripheral  velocity  -5-  velocity  due  head 
for  maximum  efficiency  for  a  36-inch  Hercules  turbine  is  given  below: 

Proportional  gate  opening.       Full         0.806       0.647       0.489       0.379 

Maximum  efficiency 85 . 6         87 . 1         86 . 3  80          73 . 1 

Periph.  vel.   +  vel.due  head  0.677       0.648       0.641       0.603       0.585 

The  double  Fourneyron  turbine  used  in  the  first  installation  of  the 
Niagara  Falls  Power  Co.  is  operated  under  a  head  of  about  135  ft.  Two 
wheels  are  used,  one  being  placed  at  the  top  and  the  other  at  the  bottom 
of  the  globe  penstock.  The  runner  and  buckets  are  attached  to  the  ver- 
tical shaft.  Holes  are  provided  in  the  upper  penstock  drum  to  allow 
water  under  full  pressure  of  the  head  to  pass  through  and  act  vertically 
against  the  upper  runner.  In  this  way  the  vertical  pressure  of  the  great 
column  of  water  is  neutralized  and  a  means  is  provided  to  counter- 
balance the  weight  of  the  long  vertical  shaft  and  the  armature  of  the 
dynamo  at  its  upper  end.  These  turbines  discharge  430  cu.  ft.  per 
second,  make  250  rev.  per  min.,  and  are  rated  at  5000  H.P. 

A  Fourneyron  turbine  at  Trenton  Falls,  N.  Y.,  operates  under  265  ft. 
gross  head  and  has  37  buckets,  each  5y2  in.  deep  and  is/ieinch  wide  at  the 
least  section.  The  total  area  of  outflow  at  the  minimum  section  is  165 
sq.  in.  The  wheel  develops  950  H.P. 

The  theoretical  horse-power  of  a  given  quantity  of  water  Q,  in  cu.  ft. 
per  min.,  falling  through  a  height  H,  in  ft.,  is  H.P.  =  0.00189  QH. 

In  practice  the  theoretical  power  is  multiplied  by  an  efficiency  factor 
E  to  obtain  the  net  power  available  on  the  turbine  shaft  as  determin- 
able  by  dynamometer  test. 

Manufacturers'  rating  tables  are  usually  based  on.efficiencies  of  about 
80%.  In  selecting  turbines  from  a  maker's  list  the  rated  efficiency 
may  be  obtained  by  the  following  formula: 

E  =  tabled  efficiency.  H.P.  =  tabled  horse-power.  Q  =  tabled  dis- 
charge (cu.ft.per  min.)  for  any  head  H.  E  =  -3f;°°°  *!*  J*-  =  528.8  5i 

b^ .  4  X  Q  fi  Q  a. 

Relations  of  Power,  Speed  and  Discharge. — Nearly  all  American  tur- 
bine builders  publish  rating  tables  showing  the  discharge  in  cu.  ft.  per 
min.,  rev.  per  min.,  and  H.P.  for  each  size  pattern  under  heads  varying 
from  3  or  4  ft.  to  40  ft.  or  more. 

Examples  of  each  size  of  a  number  of  the  leading  types  of  turbines 
have  been  tested  in  the  Holyoke  flume.  For  such  turbines  the  rating 
tables  have  usually  been  prepared  directly  from  the  tests. 

Let  M,  R,  and  Q  denote,  respectively,  the  H.P.,  r.p.m.,  and  discharge 
in  cu.  ft.  per  min.  of  a  turbine,  as  expressed  in  the  tables,  for  any  head 
H  in  feet.  The  subscripts  1  and  16  added  signify  the  power,  speed,  and 
discharge  for  the  particular  heads  1  and  16  ft.,  respectively. 

Let  P,  N,  and  F  denote  coefficients  of  power,  speed,  and  discharge^ 


774  WATER-POWER. 

which  represent,  respectively,  the  H.P.,  r.p.m.,  and  discharge  in  cu.  ft. 
per  sec.  under  a  head  of  1  ft. 

The  speed  of  a  turbine  or  the  number  of  rev.  per  min.  and  the  dis- 
charge are  proportional  to  the  square  root  of  the  head.  The  H.P. 
varies  with  the  product  of  the  head  and  discharge,  and  is  consequently 
proportional  to  the  three-halves  power  of  the  head. 

Given  the  values  of  M,  R,  and  Q  from  the  tables  for  any  head  H,  these 
quantities  for  any  other  head  h  are: 

MH:Mh::  H3/2  :  7i3/2;  RH  :  Eh  :  :  H^  :  fti/2;  QH  :  Qh  :  :  H1'*'  :  tf/2. 

If  H  and  h  are  taken  at  16  ft.  and  1  ft.,  respectively,  the  values  of 
the  coefficients  P,  N,  and  F  are: 

P  =  Mi6/H3/2  =  Mi6/64  =  0.01562  Mw 
N  =  #i6/H1/2  =  #16/4  =  0.25  #16 
F  =  #16/60  HJ/2  =  Che/240  =  0.00417  Qie. 

P,  N,  and  F,  when  derived  for  a  given  wheel,  enable  the  power,  speed, 
and  discharge  to  be  calculated  without  the  aid  of  the  tables,  and  for 
any  head  H,  by  means  of  the  following  formula  : 
M 


R  = 
Q  = 

Since  at  a  head  of  1  ft^andMi,  Ri,  and  Q\  equal  P,  N,  and  60  F,  re- 
spectively, JJi3/2  and  \/H\  each  equals  1.  Calculations  involving  .72^2 
may  be  facilitated  by  the  use  of  the  appended  table  of  three-halves 
powers.  Rating  tables  for  sizes  other  than  those  tested  are  computed 
usually  on  the  following  basis: 

1.  The  efficiency  and  coefficients  of  gate  and  bucket  discharge  for  the 
sizes  tested  are  assumed  to  apply  to  the  other  sizes  also. 

2.  The  discharge  for  additional  sizes  is  computed  in  proportion  to 
the  measured  area  of  the  vent  or  discharge  orifices. 

Having  these  data,  together  with  the  efficiency,  the  tables  of  dis- 
charge and  horse-power  can  be  prepared.  The  peripheral  speed  cor- 
responding to  maximum  efficiency  determined  from  tests  of  one  size 
of  turbine  may  be  assumed  to  apply  to  the  other  sizes  also.  From  this 
datum  the  revolutions  per  minute  can  be  computed,  the  number  of 
revolutions  required  to  give  a  constant  peripheral  speed  being  inversely 
proportional  to  the  diameter  of  the  turbine. 

In  point  of  discharge,  the  writer's  observation  has  been  that  the  rat- 
ing tables  are  usually  fairly  accurate.  In  the  matter  of  efficiency  there 
are  undoubtedly  much  larger  discrepancies. 

The  discharge  of  turbines  is  nearly  always  expressed  in  cubic  feet  per 
minute.  The  "vent"  in  square  inches  is  also  used  by  millwrights  and 
manufacturers,  although  to  a  decreasing  extent.  The  vent  of  a  turbine 
is^the  area  of  van  orifice  which  would,  under  any  given  head,  theoretically 
discharge  the  same  quantity  of  water  that  is  vented  or  passed  through  a 
turbine  under  that  same  head  when  the  wheel  is  so  loaded  as  to  be 


running  at  maximum  efficiency. 

If  V  =  vent  in  sq.  in.,  Q  =  disc 
H ,  F  =  discharge  in  cu.  ft.  per  sec.  under  a  head  of  1  foot,  then  Q  = 


If  y  =  vent  in  sq.  in.,  Q  =  discharge  in  cu.  ft.  per  min.  under  a  head 


60  V/144\/2  gH  =  3.344  V\/H,  and  V=  0.3  Q/VH;  also  V=  17.94  F 
and  F  =  0.0557  V. 

The  vent  of  a  turbine  should  not  be  confused  with  the  area  of  the 
outlet  orifice  of  the  buckets.  The  actual  discharge  through  a  turbine 
is  commonly  from  40  to  60%  of  the  theoretical  discharge  of  an  orifice 
whose  area  equals  the  combined  cross-sectional  areas  of  the  outlet 
ports  measured  in  the  narrowest  section. 

Tests  of  Turbine  Discharge  by  Salt  Solution.  —  Abraham  Streiflf 
(Eng.  Rec.,  Jan.  31,  1914)  describes  a  method  of  determining  the  dis- 
charge of  a  turbine  by  means  of  a  concentrated  salt  solution  injected 
in  the  head  or  tail  race.  The  degree  of  dilution  of  the  salt  in  the 
tail  race  after  a  certain  period  of  time  is  an  index  of  the  discharge  of 
the  turbine.  The  ratio  of  the  discharge  of  the  initial  solution  to  the 
discharge  of  tiie  turbine  varies  inversely  as  their  concentrations. 

(Continued  on  page  778) 


HYDBAULIC  TURBINES.'  775' 

TABLE  OP  H3/2  FOB  CALCULATING  HORSE-POWER  OF  TURBINES. 


«o 

*£ 
wfe 

0.0 

0.2 

0.4 

0.6 

0.8 

T3 

|e 

0.0 

0.2 

0.4 

0.6 

0.8 

0 

0.00 

0.09 

0.25 

0.46 

0.72 

1 

1.00 

1.32 

1.66 

2.02 

2.42 

51 

364.21 

366.36 

368.50 

370.66 

372.82 

2 

2.83 

3.26 

3.72 

4.19 

4.69 

52 

374.98 

377.14 

379.31 

381.48 

383.66 

3 

5.20 

5.72 

6.27 

6.83 

7.41 

53 

385.85 

388.03 

390.22 

392.42 

394.61 

4 

8.00 

8.61 

9.23 

9.87 

10.52 

54 

396.81 

399.02 

401.23 

403.45 

405.67 

11.18 

11.86 

12.55 

13.25 

13.97 

55 

407.89 

410.11 

412.35 

414.58 

416.82 

6 

14.70 

15.44 

16.19 

16.96 

17.73 

56 

419.07 

421.31 

423.56 

425.81 

428.07 

18.52 

19.32 

20.13 

20.95 

21.78 

57 

430.34 

432.60 

434.87 

437.15 

439.43 

8 

22.63 

23.48 

24.35 

25.22 

26.11 

58 

441.71 

444.00 

446.29 

448.58 

450.88 

9 

27.00 

27.91 

28.82 

29.75 

30.68 

59 

453.09 

455.49 

457.80 

460.12 

462.43 

10 

31.62 

32.58 

33.54 

34.51 

35.49 

60 

464.75 

467.08 

469.41 

471.75 

474.08 

11 

36.48 

37.48 

38.49 

39.51 

40.53 

61 

476.42 

478.77 

481.12 

483.47 

485.82 

12 

41.57 

42.61 

43.66 

44.73 

45.79 

62 

488.19 

490.55 

492.92 

495.29 

497.67 

13 

46.87 

47.96 

49.05 

50.15 

51.26 

63 

500.04 

502.43 

504.82 

507.20 

509.60 

14 

52.38 

53.51 

54.64 

55.79 

56.94 

64 

512.00 

514.40 

516.80 

519.22 

521.63 

15 

58.09 

59.26 

60.43 

61.61 

62.80 

65 

524.04 

526.46 

528.89 

531.31 

533.75 

16 

64.00 

65.20 

66.41 

67.63 

68.85 

66 

536.18 

538.62 

541.07 

543.51 

545.96 

17 

70.09 

71.33 

75.58 

73.84 

75.10 

67 

548.42 

550.87 

553.33 

555.80 

558.27 

18 

76.37 

77.64 

78.93 

80.22 

81.52 

68 

560.74 

563.22 

565.70 

568.18 

570.66 

19 

82.82 

84.13 

85.45 

86.77 

88.10 

69 

573.16 

575.65 

578.14 

580.65 

583.15 

20 

89.44 

90.79 

92.14 

93.50 

94.86 

70 

585.66 

588.17 

590.68 

593.20 

595.73 

21 

96.23 

97.61 

99.00 

100.39 

101.79 

71 

598.25 

600.79 

603.32 

605.85 

608.39 

22 

103.19 

104.60 

106.02 

107.44 

108.87 

72 

610.93 

613.48 

616.04 

618.59 

621.15 

23 

110.30 

111.74 

113.19 

114.65 

116.11 

73 

623.71 

626.27 

628.84 

631.41 

633.99 

24 

117.58 

119.05 

120.53 

122.01 

123.50 

74 

636.57 

639.15 

641.74 

644.33 

646.92 

25 

125.00 

126.50 

128.01 

129.53 

131.05 

75 

649.52 

652.11 

654.72 

657.33 

659.94 

26 

132.57 

134.11 

135.65 

137.19 

138.74 

76 

662.55 

665,17 

667.79 

670.41 

673.04 

27 

140.30 

141.86 

143.43 

145.00 

146.58 

77 

675.67 

678.20 

680.94 

683.58 

686.23 

28 

148.16 

149.75 

151.35 

152.95 

154.56 

78 

688.87 

691.52 

694.18 

696.84 

699.50 

29 

156.17 

157.79 

159.41 

161.04 

162.68 

79 

702.16 

704.83 

707.50 

710.18 

712.85 

30 

164.32 

165.96 

167.61 

169.27 

170.93 

80 

715.54 

718.22 

720.92 

723.60 

726.30 

i 

31 

172.60 

174.27 

175.95 

177.64 

179.33 

81 

729.00 

731.70 

734.40 

737.11 

739.82 

32 

181.02 

182.72 

184.42 

186.13 

187.85 

82 

742.54 

745.26 

747.98 

750.70 

753.43 

33 

189.57 

191.30 

193.03 

194.76 

196.51 

83 

756.16 

758.90 

761.63 

764.38 

767.12 

34 

198.25 

200.00 

201.76 

203.52 

205.29 

84 

769.87 

772.62 

775.37 

778.13 

780.89 

35 

207.06 

208.84 

210.62 

212.41 

214.20 

85 

783.66 

786.42 

789.20 

791.97 

794.75 

36 

216.00 

217.80 

219.61 

221.42 

223.24 

86 

797.53 

800.31 

803.10 

805.89 

808.68 

37 

225.06 

226.89228.72 

230.56 

232.40 

87 

811.48 

814.27 

817.08 

819.88 

822.70 

38 

234.25 

236.10237.96 

239.82 

241.68 

88 

825.51 

828.32 

831.15 

833.97 

836.79 

39 

243.56 

245.43247.31 

249.20 

251.09 

89 

839.62 

842.45 

845.29 

848.13 

850.96 

40 

252.98 

254.88'256.79 

258.70 

260.61 

90 

853.81 

856.66 

859.51 

848.37 

865.22 

41 

262.53 

264.45266.38 

268.31 

270.25 

91 

868.08 

870.94 

873.81 

876.68 

879.55 

42 

272.19 

274.14 

276.09 

278.05 

280.01 

92 

882.43 

885.30 

888.19 

891.07 

893.96 

43 

281.97 

283.94 

285.91 

287.89 

289.88 

93 

896.86 

899.  75  1902.65 

905.55 

908.45 

44 

291.86 

293.86 

295.85 

297.85 

299.86 

94 

911.36 

914.27 

917.18 

920.10 

923.02 

45 

301.87 

303.88 

305.90 

307.93 

309.95 

95 

925.94 

928.87 

931.79 

934.73 

937.66 

46 

311.99 

314.02 

316.07 

318.11 

330.16 

96 

940.60 

943.54 

946.48 

949.43 

952  38 

47 

322.22 

324.27 

326.34 

328.41 

330.48 

97 

955.33 

958.29 

961.25 

964.21 

967.17 

48 

332.55 

334.63 

336.72 

338.81 

340.90 

98 

970.14 

973.11 

976.09 

979.07 

982.05 

49 

343.00 

345.10 

347.21 

349.32 

351.43 

99 

985.03 

988.02 

991.01 

994.00 

996.99 

50 

353.55 

355.67 

357.80359.93 

362.07 

100 

1000.00 

776 


WATER-POWER. 


Power  Table  for  Turbines — LEFPEL  VERTICAL  STANDARD  SAMSON  TYPE  (1916) 
P  =  horsepower;    W  =  quantity  of  water,  cu.  ft.  per  sec.;   S  =  speed,  r.p.m. 


Size. 

Head,  Feet. 

3 

5 

10 

15 

20 

25 

30 

35 

40 

50 

p 

1.1 

2.5 

7.0 

12.9 

19.9 

27.8 

36.5 

46.2 

56.  3- 

78.0 

W 

252 

325 

460 

553 

650 

727 

796 

860 

919 

1026 

S 

161 

208 

294 

360 

416 

464 

510 

550 

588 

657 

p 

1.5 

3.2 

9.2 

16.9 

25.9 

36.2 

47.6 

60.3 

73.5 

102.0 

W 

328 

423 

601 

734 

848 

948 

1039 

1121 

1199 

1338 

S 

161 

208 

294 

360 

416 

464 

510 

550 

588 

657 

( 

p 

2.0 

4.3 

12.1 

22.2 

34.1 

47.7 

62.6 

79.4 

96.7 

135.0 

17C-< 

W 

433 

558 

791 

967 

1116 

1248 

1367 

1476 

1579 

1763 

1 

S 

161 

208 

294 

360 

416 

464 

510 

550 

588 

657 

I 

p 

2.4 

5.3 

14.9 

27.4 

42.1 

58.9 

77.3 

97.9 

119.0 

167.0 

17B^ 

W 

533 

689 

975 

1193 

1377 

1540 

1687 

1821 

1948 

2179 

1 

S 

161 

208 

294 

360 

416 

464 

510 

550 

588 

657 

( 

p 

3.2 

6.9 

19.5 

35.6 

55.0 

77.0 

101.0 

128.0 

156.0 

218.0 

17A-J 

W 

697 

900 

1275 

1559 

1800 

2013 

2205 

2381 

2546 

2846 

S 

161 

208 

294 

360 

416 

464 

510 

550 

588 

657 

( 

p 

4.2 

9.0 

25.5 

46.9 

72.2 

101.  0 

133.0 

167.0 

204.0 

285.0 

20  4 

W 

914 

1180 

1669 

2044 

2360 

2639 

2891 

3127 

3338 

3731 

( 

S 

140 

182 

257 

315 

364 

407 

445 

481 

514 

575 

( 

p 

5.5 

11.9 

33.8 

62.0 

95.5 

133.0 

175.0 

221.0 

270.0 

377.0 

23  \ 

W 

1209 

1561 

2207 

2703 

3122 

3489 

3823 

4130 

4415 

4935 

1 

S 

127 

158 

224 

274 

316 

354 

387 

418 

447 

500 

p 

7.10 

15.2 

43.2 

79.3 

121.0 

171.0 

224.0 

283.0 

345.0 

482.0 

W 

1545 

1995 

2821 

3455 

3919 

4460 

4886 

5278 

5642 

6306 

S 

108 

140 

198 

242 

280 

313 

343 

370 

396 

442 

p 

9.44 

20.3 

57.5 

106.0 

162.0 

227.0 

299.0 

376.0 

460.0 

642.0 

W 

2057 

2656 

3756 

4600 

5312 

5938 

6505 

7026 

7512 

8400 

S 

94 

121 

171 

210 

242 

271 

297 

321 

343 

381 

I 

p 

12.8 

27.5 

77.9 

143.0 

220.0 

308.0 

405.0 

510.0 

623.0 

871.0 

35  \ 

W 

2789 

3600 

5091 

6236 

7200 

8050 

8818 

9525 

10183 

11385 

I 

S 

81 

104 

147 

180 

208 

232 

255 

275 

294 

329 

( 

p 

16.8 

36.1 

102.0 

188.0 

289.0 

404.0 

531.0 

668.0 

817.0 

1143.0 

40 

W 

3657 

4722 

6677 

8178 

9443 

10558  11565 

12472 

13354 

14930 

1 

S 

70 

91 

129 

157 

182 

203 

223 

240 

257 

288 

( 

p 

21.2 

45.7 

129.0 

238.0 

366.0 

511.0 

672.0 

847.0 

1034.0 

1448.0 

45 

W 

4629 

5975 

8450 

10350 

11951 

13361 

14636 

15809 

16901 

18900 

/ 

S 

63 

81 

114 

140 

162 

181 

198 

214 

229 

256 

( 

p 

26.2 

56.4 

160.0 

293.0 

451.0 

631.0 

829.0 

1045.0 

1280.0 

1789.0 

50  - 

W 

5714 

7377 

10433 

12777 

14754 

16496 

18070 

19518 

20870 

23330 

1 

S 

56 

73 

103 

126 

145 

162 

178 

192 

205 

230 

\ 

p 

32.9 

70.8 

200.0 

368.0 

566.0 

791.0 

1040.0 

1314.0 

1602.0 

2239.0 

56 

W 

7168 

9254 

13087 

16028 

18508 

20692 

22667 

24506 

26200 

29260 

) 

S 

50 

65 

92 

112 

130 

145 

159 

172 

183 

205 

I 

p 

40.3 

86.8 

245.0 

451.0 

694.0 

970.0 

1275.0 

1608.0 

1963.0 

2743.0 

63  \ 

W 

8787 

11344 

16042 

19648 

22688 

25365 

27786 

30092 

32100 

35900 

I 

S 

'  45 

59 

83 

102 

117 

131 

144 

155 

166 

186 

( 

p 

48.5 

104.0 

295.0 

542.0 

835.0 

1167.0 

1534.0 

1932.0 

2361.0 

3300.0 

68  \ 

W 

10570 

13645 

19297 

23634 

27290 

30511 

33450 

36120 

38620 

43200 

i 

S 

41 

53 

76 

93 

107 

120 

131 

142 

152 

170 

( 

p 

57.5 

124.0 

350.0 

642.0 

992.0 

1382.0 

1818.0 

2292.0 

2800.0 

3912.0 

74  1 

W 

12517 

16159 

22852 

27988 

32318 

36132 

39560 

42750 

45700 

51100 

1 

S 

38 

49 

70 

85 

99 

110 

120 

130 

139 

156 

HYDRAULIC  TURBINES. 


777 


Power  Table  for  Turbines. — LEFPEL  VERTICAL  Z-TYPE  (1916). 
=  horsepower;     W  =  quantity  of  water,  cu.  ft.  per  sec.;  S  =  speed,  r.p.m. 


Size. 

Head,  Feet 

6 

7 

8 

10 

15 

W 

25 

30 

35 

40 

I 

p 

9.05 

11.53 

14.30 

20.40 

38.15 

58.90 

82.30 

108.2 

136.2 

166.5 

13  J 

W 

1035 

1120 

1202 

1352 

1670 

1933 

2160 

2368 

2557 

2730 

1 

s 

306.0 

331.0 

354.0 

395.0 

484.0 

559.0 

625.0 

685.0 

740.0 

790.0 

( 

p 

14.47 

18.24 

22.50 

31.85 

60.20 

93.00 

130.0 

171.0 

215.5 

263.0 

15  J 

W 

1625 

1755 

1885 

2115 

2620 

3030 

3390 

3710 

4015 

4280 

1 

s 

245.0 

265.0 

283.0 

316.0 

387.0 

447.0 

500.0 

548.0 

592.0 

632.0 

p 

21.08 

26.70 

32.80 

46.40 

87.50 

135.0 

189.5 

249.0 

314.0 

383.0 

W 

2350 

2550 

2725 

3060 

3785 

4385 

4910 

5375 

5805 

6200 

s 

204.0 

221.0 

236.0 

263.0 

323.0 

372.0 

417.0 

456.0 

493.0 

526.0 

( 

p 

29.05 

36.72 

45.30 

63.90 

121.0 

187.0 

261.5 

343.0 

433.0 

528.0 

31  J 

W 

3225 

3485 

3740 

4190 

5200 

6015 

6730 

7370 

7965 

8505 

1 

s 

175.0 

189.1 

202.0 

225.5 

277.0 

319.0 

357.0 

391.0 

423.0 

452.0 

p 

38.35 

48.50 

60.00 

84.50 

160.0 

247.0 

345.0 

454.0 

571.5 

698.0 

W 

4230 

4580 

4920 

5510 

6835 

7900 

8840 

9680 

10460 

11170 

s 

153.0 

165.5 

177.0 

197.5 

242.0 

279.0 

312.5 

342.0 

370.0 

395.0 

p 

49.25 

62.00 

76.60 

108.1 

204.5 

316.0 

442.2 

580.0 

732.0 

893.0 

W 

5375 

•5825 

6250 

7000 

8700 

10040 

•11225 

12300 

13300 

14200 

s 

136.0 

147.0 

157.0 

175.6 

215.0 

248.5 

278.0 

304.5 

329.0 

351.0 

( 

p 

61.40 

77.50 

95.70 

135.0 

255.5 

395.4 

551.5 

725.0 

912.5 

1116.0 

30  -1 

W 

6680 

7230 

7760 

8700 

10790 

12500 

13960 

15295 

16500 

17640 

1 

s 

122.5 

132.2 

141.4 

158.1 

193.6 

223.5 

250.0 

274.0 

296.0 

316.0 

( 

p 

74.25 

93.55 

115.2 

163.2 

308.0 

479.0 

670.0 

879.0 

1108.0 

1355.0 

33  - 

W 

8050 

8720 

9350 

10500 

13000 

15110 

16900 

18500 

19950 

21340 

1 

s 

111.3 

120.5 

128.5 

143.5 

176.0 

203.0 

227.0 

249.0 

269.0 

287.0 

( 

p 

88.15 

111.9 

138.0 

195.0 

367.5 

570.0 

796.0 

1045.0 

1318.0 

1613.0 

36  I 

W 

9610 

10420 

11180 

12560 

15510 

18000 

20100 

22000 

23750 

25400 

1 

s 

102.0 

110.5 

118.0 

131.5 

161.0 

186.0 

208.0 

228.0 

247.0 

263.0 

{• 

p 

103.7 

131.0 

162.0 

228.3 

431.5 

669.0 

935.0 

1229.0 

1548.0 

1892.0 

W 

11290 

12210 

13110 

14700 

18200 

21110 

23600 

25820 

27900 

29800 

s 

94.0 

102.0 

109.0 

121.5 

148.9 

172.0 

192.2 

211.0 

227.5 

243.0 

t 

p 

120.1 

152.0 

187.7 

265.0 

500.0 

776.0 

1085.0 

1423.0 

1703.0 

2188.0 

&  \ 

W 

13100 

14170 

15210 

17050 

21130 

24500 

27350 

29990 

32340 

34590 

I 

s 

87.5 

94.5 

101.0 

113.0 

138.5 

159.5 

178.5 

195.5 

211.0 

226.0 

p 

138.0 

174.5 

215.3 

304.0 

575.0 

890.0 

1245.0 

1634.0 

2060.0 

2512.0 

W 

15030 

16270 

17450 

19570 

24270 

28100 

31400 

34400 

37100 

39700 

s 

81.5 

88.3 

94.2 

105.4 

129.0 

149.0 

166.5 

182.5 

197.2 

211.0 

\ 

p 

157.0 

199.2 

245.0 

346.0 

654.0 

1013.0 

1417.0 

1858.0 

2342.0 

2855.0 

48  \ 

W 

17100 

18515 

19860 

22300 

27600 

32000 

35720 

39150 

42250 

45120 

1 

s 

76.5 

82.7 

88.4 

98.7 

121.0 

139.5 

156.0 

171.0 

185.0 

197.5 

( 

p 

176.5 

224.0 

276.5 

391.0 

738.0 

1144.0 

1600.0 

2100.0 

2645.0 

3225.0 

51  1 

W 

19300 

20900 

22410 

25150 

31160 

36100 

40290 

44120 

47600 

51000 

I 

s 

72.0 

78.0 

83.2 

93.0 

114.0 

131.5 

147.0 

161.0 

174.0 

186.0 

p 

198.0 

251.3 

310.0 

438.0 

827.5 

1283.0 

1792.0 

2353.0 

2950.0 

3610.0* 

W 

21640 

23430 

25120 

28200 

34930 

40450 

45250 

49550 

53400 

57100" 

s 

68.0 

73.6 

78.5 

87.8 

107.5 

124.0 

139.0 

152.0 

164.5 

176.5 

( 

p 

220.6 

280.0 

345.2 

488.0 

921.0 

1430.0 

1998.0 

2623.0 

3290.0 

4027.0 

57  \ 

W 

24120 

26120 

28000 

31400 

38900 

45150 

50360 

55150 

59500 

63650 

( 

s 

64.5 

69.6 

74.5 

83.0 

101.7 

117.6 

131.5 

144.0 

156.0 

166.5 

( 

p 

244.5 

310.0 

383.0 

541.0 

1020.0 

1584.0 

2212.0 

2904.0 

3640.0 

4465.0 

60  i 

W 

26730 

28920 

31040 

34800 

43125 

50000 

55840 

61180 

65950 

70550 

} 

s 

61.2 

66.2 

70.7 

79.0 

96.7 

111.7 

125.0 

137.0 

148.0 

158.0 

778 


WATER-POWER. 


Three  conditions  must  be  fulfilled  to  obtain  accuracy!  (1)  Constant 
initial  discharge  of  solution;  (2)  perfect  mix;  (3)  precise  titration  of 
the  salt  solutions.  The  solution  should  be  clear  and  free  from  im- 
purities. The  amount  of  initial  solution  injected  should  be  about 
0.0001  of  the  approximate  discharge  of  the  turbine,  and  a  volumetric 
analysis  of  the  salt  solution  can  measure  the  discharge  with  an  ac- 
curacy of  0.1  per  cent.  To  make  the  analysis,  three  solutions  are 
needed:  Silver  nitrate,  salt  and  potassium  chromate. 

If  D  is  the  discharge  of  the  turbine  in  liters  per  second,  NI  the  cubic 
centimeters  of  silver  nitrate  solution  required  to  titrate  one  liter  of 
initial  salt  solution,  n  the  cubic  centimeters  of  silver  nitrate  required  to 
titrate  one  liter  of  turbine  discharge  before  the  test,  N2  the  cubic 
centimeters  of  silver  nitrate  solution  to  titrate  one  liter  of  turbine  dis- 
charge after  the  test,  and  d  the  cubic  centimeters  discharge  of  initial 
solution 


The  value  of  D  may  be  expressed  in  cu.  ft.  by  multiplying  the  result 
by  0.03531. 

Results  of  a  comparison  of  this  method  of  measuring  the  discharge 
of  a  5500  H.P.  turbine  at  500  r.  p.  m.  under  a  head  of  2300  ft.,  with 
a  weir,  a  current  meter  and  a  moving  screen,  are  as  follows: 

Salt      Current  Moving      Weir. 
Solution.  Meter.    Screen. 
Discharge,  cu.  ft.  per  sec  .......    =  46  .  086     45  .  585     45  .  867     46  .  326 

Mr.  Streifl  describes  (Eng.  Rec.,  Sept.  5,  1914)  the  application  of 
this  method  to  the  testing  of  the  low-head  turbines  of  the  Grand 
Rapids-Muskegon  Power  Co.  The  plant  comprised  two  7200-H.P. 
horizontal,  8-runner  units  operating  at  225  r.  p.  m.  under  39^  ft. 
head.  The  water  consumption  was  found  to  be  2140  cu.  ft.  per  sec. 
The  results  were  within  1.3  per  cent  of  the  results  as  obtained  by 
Ott  current  meters. 

Draft  Tubes.  —  Conical  draft  tubes  are  commonly  used  with  inward 
flow  turbines  for  the  purpose  of  enabling  the  turbine  to  be  set  high  above 
the  tail-  water  and  also  of  reducing  the  loss  of  power  due  to  the  velocity 
of  the  discharge.  The  maximum  height  of  these  tubes  should  not  be 
over  20  ft.,  and  the  angle  of  flare  should  not  be  greater  than  7°  with 
the  vertical.  For  the  best  results  a  parabolic  cone  should  be  used, 
so  as  to  decrease  the  velocity  in  direct  proportion  to  the  height  above 
the  tail  water,  and  in  that  case  the  angle  of  flare  at  the  bottom  may 
be  increased,  so  that  the  velocity  of  the  water  at  the  exit  does  not 
exceed  6  ft.  per  second  or  0.1  V2  gH. 

Recent  Turbine  Practice  (H.  Birchard  Taylor,  Gen.  Elec.  Rev., 
June,  1914).  —  The  single  runner  vertical  unit  has  (1914)  almost  dis- 
placed the  multi-runner,  horizontal  type  of  turbine  in  large  first-class, 
low-head  installations.  It  has  had  increasing  application  in  moderate 
and  high-head  plants.  Present  practice  favors  molding  of  the  volute 
casing  directly  in  the  substructure  of  the  power  house  for  all  low-head 
turbines.  For  heads  exceeding  100  ft.,  the  amount  of  concrete  rein- 
forcement required  is  usually  sufficiently  great  to  warrant  the  use  of 
cast-iron  casings,  which  must  be  increased  in  thickness  with  increase 
of  head,  until  at  250  ft.  head,  cast  steel  becomes  the  standard  material. 

The  thrust  bearing  of  vertical  wheels  is  almost  universally  located 
above  the  generator  on  a  cast-iron  supporting  truss  which  forms  at 
the  same  time  a  generator  head  cover.  This  truss  must  be  rigid  and 
the  upper  face  on  which  the  bearing  is  mounted  must  be  level.  Up 
to  about  1909,  the  thrust  bearing  comprised  an  annular  chamber  be- 
tween a  revolving  and  stationary  disk,  into  which  oil  under  pressure 
was  pumped.  The  disadvantage  of  the  oil  pressure  bearing  is  that 
an  excessive  drop  in  pressure;  or  a  momentary  failure  of  the  oil  supply 
to  the  bearing  will  result  in  its  immediate  destruction.  This  bearing 
has  now  (1914)  been  generally  superseded  by  roller  bearings  or  a  com- 
bination of  roller  and  pressure  bearing. 

Lignum  vitse  guide  bearings  have  recently  come  into  general  use 
with  vertical  turbines  for  both  high-  and  low-head  installations.  These 


[HYDRAULIC  TURBINES. 


779 


bearings  are  now  so  designed  as  to  present  a  somewhat  greater  projected 

area  to  the  shaft  than  is  called  for  by  a  babbitted  bearing.    The  lignum 

vitae  is  dovetailed  into  the  bearing  boxes  in  the  form  of  strips  running 

parallel  to  the  axis  of  the  shaft,  and 

with  the  end  grain  of  the  wood  pre- 

sented normally  to  the  surface  of  the 

shaft.       Twenty    or    more    of  these 

strips  are  used,  evenly  spaced  in  a 

liberal  length  and  separated  by  spaces 

for  cooling   water   circulation.     The 

resultant    bearing    pressure  may  be 

made  so   light   as   to   eliminate  the 

necessity  of  making   adjustment   to 

take  up  wear.     Clear  water  is  piped 

to  these  bearings  in  the  same  manner 

as  oil.     A  bronze  sleeve   is  used   on 

the  shaft  where  it  passes  through  the 

bearing  and  stuffing  box. 

A  10,000  H.P.  Turbine  at  Sno- 
qualmie,  Wash.  (Arthur  Giesler, 
Enq.  News,  Mar.  20,  1906).  —  The  fall 
is  about  270  ft.  high.  The  wheel  was 
designed  by  the  Platt  Iron  Works  Co., 
Dayton,  O.,  for  an  effective  head  of 
260  ft.  and  300  r.p.m.,  the  latter 
being  fixed  by  the  limitations  of 
dynamo  design.  The  turbine  is  a 
horizontal  shaft  machine,  of  the 


Francis  Turbine  Runner. 


Francis  type,  radial  inward  flow  with 
central  axial  discharge.  The  turbine  proper  has  only  one  bearing,  8% 
X  26  in.,  the  generator  having  three  bearings.  The  wheel  is  66  in.  out- 
side diam.  by  9  in.  wide  through  the  vanes.  It  has  34  vanes  which  ex- 
tend a  short  distance  beyond  the  end  plate  of  the  wheel  on  the  dis- 
charge side.  There  are  32  guide  vanes,  of  the  swivel  type,  connected 
to  a  rotatable  ring  which  is  actuated  by  a  Lombard  governor.  The  tur- 
bine wheel  or  runner  is  an  annular  steel  casting.  It  is  bolted  to  a 
disk  46  in.  diam.,  which  is  an  enlargement  of  the  13  Ms  in.  hollow 
nickel-steel  shaft.  A  test  for  efficiency  was  made,  in  which  the  output 
was  measured  on  the  electrical  side,  and  the  input  by  the  drop  of  head 
across  the  head  gate.  At  10,000  H.P.  the  efficiency  shown  was  84%, 
the  figure  being  subject  to  the  inaccuracy  of  the  water  measurement. 
The  maximum  capacity  registered  was  8250  K.W.  or  11,000  H.P. 
With  the  generator  and  the  governor  disconnected,  with  full  gates 
and  no  load,  the  wheel  ran  at  505  r.p.m. 

Turbines  of  13,500  H.P.  —  Four  Francis  turbines,  with  vertical  shafts, 
rated  at  13,500  H.P.  each,  have  been  built  by  Allis-Chalmers  Co.,  for  the 
Great  Northern  Power  Co.,  Duluth,  Minn.  The  available  head  is 
365  ft.,  and  the  wheels  run  at  375  r.p.m.;  discharging,  at  full  load, 
about  400  cu.  ft.  per  second,  each.  The  runners  are  62  in.  diameter. 
The  penstock  for  each  wheel  is  84  in.  diameter,  reduced  gradually  to 
66  in.  at  the  wheel. 

Some  Large  Turbines.  —  Much  larger  turbines  than  those  above 
noted  have  been  built  in  the  years  1910^-1915.  From  a  long  list  of 
turbines  constructed  by  I.  P.  Morris  Co.  in  these  years,  the  following 
are  selected: 

Capacity 

No.       Each        Head     Rev. 

Location.  Date       of       Unit,  in         per 

Units.     H.P.          Ft.       Min. 

McCall  Ferry,  Penna  ..  1910  5  13,500  53  94 

Holtwood,  Pa.,  Susquehanna  R.  1913  2  17,000  62  116 

Grandmere,  P.  Q.,  Canada  .....  1915  6  20,000  76  120 

Shawinigan  Falls,  P.  Q  ........  1913  2  18,500  145  225 

Long  Lake,  Washington  .......  1912  2  22,500  168  200 

Grace  Station,  Idaho  ..........  1913  2  16,500  482  514 

Feather  River,  Cal  ............  19H  2  18,500  465  400 


780  WATER-POWER. 

The  "  Fall-increaser"  for  Turbines. — A  circular  issued  Nov.;  1908, 
by  Clemens  Herschel,  the  inventor  of  the  Venturi  meter,  illustrates  a 
device,  based  on  the  principle  of  the  meter,  for  diminishing  the  back- 
water head  which  acts  against  the  turbine.  The  surplus  water,  which 
would  otherwise  run  to  waste,  is  caused  to  flow  into  a  tube  of  the 
Venturi  shape,  and  the  pressure  in  the  narrow  section,  or  throat  of  this 
tube,  is  less  than  that  due  to  the  head  of  the  back-water  into  which  the 
tube  discharges.  The  throat  is  perforated  with  a  great  number  of 
6-in.  holes,  through  which  the  discharge-water  of  the  turbine  is  caused 
to  flow,  the  velocity  through  the  holes  being  never  over  4  ft.  per  second. 
The  circular  says,  that  fall-increasers  add  about  10%  to  the  annual 
output  of  power  with  no  appreciable  increase  in  operating  expenses. 

For  half  the  days  of  the  year  the  fall-increasers  are  shut  down  be- 
cause there  is  not  enough,  or  only  enough,  water  to  supply  the  plain 
turbines ;  but  for  the  other  half  of  the  year  the  f all-increasers  keep  the 
output  of  power  practically  constant,  and  at  the  full  output,  where  this 
power  output  would  fall  to  half  the  full  output  or  less  if  the  fall-increases 
had  not  been  built.  An  illustrated  description  of  the  fall-increaser, 
with  results  of  tests,  is  given  in  the  Harvard  Eng'g  Journal,  June,  1908. 
See  also  U.  S.  Pat.  No.  873,435  and  Eng.  News,  June  11,  1908. 

TANGENTIAL  OE  IMPULSE  WATER-WHEELS. 

The  Pelton  Water-wheel. — Mr.  Ross  E.  Browne  (Eng'g  News,  Feb. 
20,  1892)  thus  outlines  the  principles  upon  which  this  water-wheel  is 
constructed : 

The  function  of  a  water-wheel,  operated  by  a  jet  of  water  escaping 
from  a  nozzle,  is  to  convert  the  energy  of  the  jet,  due  to  its  velocity, 
into  useful  work.  In  order  to  utilize  this  energy  fully  the  wheel-bucket, 
after  catching  the  jet,  must  bring  it  to  rest  before  discharging  it,  with- 
out inducing  turbulence  or  agitation  of  the  particles. 

This  cannot  be  fully  effected,  and  unavoidable  difficulties  necessitate 
the  loss  of  a  portion  of  the  energy.  The  principal  losses  occur  as 
follows:  First,  in  sharp  or  angular  diversion  of  the  jet  in  entering,  or 
in  its  course  through  the  bucket,  causing  impact,  or  the  conversion  of  a 
portion  of  the  energy  into  heat  instead  of  useful  work.  Second,  in  the 


FIG.  155a.  FIG.  156&.  FIG.  i5bc. 


so-called  frictional  resistance  offered  to  the  motion  of  the  water  by  the 
wetted  surfaces  of  the  buckets.  Third,  in  the  velocity  of  the  water,  as 
it  leaves  the  bucket,  representing  energy  which  has  not  been  con- 
verted into  work. 

Hence,  in  seeking  a  high  efficiency:  1.  The  bucket-surface  at  the  en- 
trance will  be  approximately  parallel  to  the  relative  course  of  the  jet, 
and  the  bucket  should  be  curved  in  such  a  manner  as  to  avoid  sharp 
angular  deflection  of  the  stream. 

2.  The  path  of  the  jet  in  the  bucket  should  be  short;  in  other  words, 
the  total  wetted  surface  of  the  bucket  should  be  small. 

3.  The  discharge  end  of  the  bucket  should  be  as  nearly  tangential  to 
the  wheel  periphery  as   compatible  with  the  clearance  of  the  bucket 
which  follows;    and  great  differences  of  velocity  in  the  parts  of  the 
escaping  water  should  be  avoided.     In  order  to  bring  the  water  to  rest 
at  the  discharge  end  of  the  bucket,  it  is  shown,  mathematically,  that 
the  velocity  of  the  bucket  should  be  one-half  the  velocity  of  the  jet. 

A  bucket,  such  as  shown  in  Fig.  156a,  will  cause  the  heaping  of  more 
or  less  dead  or  turbulent  water  at  the  point  indicated  by  dark  shading. 
This  dead  water  is  subsequently  thrown  from  the  wheel  with  con- 
siderable velocity,  and  represents  a  large  loss  of  energy.  The  intro- 
duction of  the  wedge  in  the  Pelton  bucket  (see  Fig.  156&)  avoids  this 
loss. 


TANGENTIAL   OR   IMPULSE   WATER-WHEELS.         781 

A  wheel  of  the  form  of  the  Pelton  (Fig.  156c)  conforms  closely  in  con- 
struction to  each  of  these  requirements.  [In  wheels  as  now  made 
(1916)  the  sharp  corners  shown  in  this  bucket  are  eliminated. 1 

Considerations  in  the  Choice  of  a  Tangential  Wheel  (Joshua 
Hendy  Iron  Works). — The  horse-power  that  can  be  developed  by  a  tan- 
gential wheel  does  not  depend  upon  the  size  of  the  wheel  but  solely  upon 
the  head  and  volume  of  water  available.  The  number  of  revolutions  per 
minute  that  a  wheel  makes  (running  under  normal  conditions)  depends 
solely  upon  two  factors,  viz.,  its  diameter  and  the  head  of  water. 

The  choice  of  the  diameter  of  a  wheel  is  not  therefore  controlled  by  tho 
power  required  but  by  the  speed  required  when  working  under  a  given 
head.  If  a  wheel  has  no  load,  and  is  not  governed,  it  will  speed  up  until 
the  periphery  is  revolving  at  approximately  the  same  velocity  as  tho 
spouting  velocity  of  the  jet,  but  as  soon  as  the  wheel  commences  to 


The  diameter  of  pulley  wheels  on  wheel  shaft  and  countershafts  of 
machinery  should  be  so  proportioned  that  the  water-wheel  shall  run  at 
the  speed  given  in  the  table.  The  width,  area  and  curvature  of  buckets 
are  designed  to  meet  conditions  of  volume  of  flow  under  given  heads. 
The  higher  the  peripheral  velocity  of  the  wheel,  the  greater  the  volume 
of  water  that  the  buckets  can  handle,  and  consequently  the  same 
standard  wheel  can  handle  more  water,  the  higher  the  head. 

Wheels  designed  for  a  given  horse-power  can  be  used  for  smaller 
powers  (within  reasonable  limits)  with  very  little  loss  of  efficiency,  but 
an  increase  in  the  volume  to  be  used  requires  a  larger  bucket.  If,  for 
the  purpose  of  maintaining  the  same  speed  conditions,  the  same  diam- 
eter of  wheel  is  to  be  adhered  to,  then  a  special  wheel  must  be  built 
with  either  very  large  buckets  or  with  two  or  more  nozzles,  or  else  a 
double  or  multiple  unit  must  be  adopted. 

It  is  advised  to  subdivide  large  streams  between  two,  three  or  more 
runners,  as  this  insures  a  greater  freedom  from  breakdown  and  is  often 
cheapest  in  the  end.  Single-nozzle,  multiple  runner  units  are  easier  to 
govern  than  multiple-nozzle,  single  runner  units.  When  two  or  more 
nozzles  are  used  in  combination  on  one  runner,  the  increased  volume 
to  be  dealt  with  is  divided  between  the  different  nozzles,  which  ar.3 
so  arranged  that  their  respective  jets  impinge  on  different  buckets  at 
different  parts  of  the  periphery. 

Combined  Heads. — When  two  or  moue  water  powers  are  available  at 
the  same  site,  but  under  different  heads,  it  is  possible  to  utilize  them  by 
mounting  wheels  of  different  diameters  in  parallel,  or,  when  the  differ- 
ence of  head  and  volume  is  very  great,  it  would  even  be  possible  to 
arrange  for  a  turbine  for  the  low  head  and  a  tangential  wheel  for  the 
high  head,  although,  in  the  latter  case,  it  would  probably  be  best  to 
mount  them  independently  and  connect  to  the  machinery  through  the 
medium  of  belts  and  countershafts.  In  either  case,  separate  pipe  lines 
must  be  employed. 

Reversible  Wheels. — In  the  case  of  reversible  wheels  desired  for  use 
with  hoists,  cableways,  etc.,  two  wheels  of  proper  dimensions  and  the 
same  type  may  be  mounted  parallel  on  the  same  shaft,  one  of  the  wheels 
having  the  buckets  and  nozzles  arranged  to  run  in  the  opposite  direction 
to  the  other.  Suitable  valves,  levers  and  pipe  connections,  can  be  ar- 
ranged to  cut  the  water  off  one  wheel  and  turn  it  on  to  the  other. 

Control  of  Tangential  Water-wheels. — The  methods  of  regulating 
tangential  water-wheels  may  be  classified  under  ftve  heads: 

1.  Permanently  or  semi-permanently  altering  the  area  of  efflux  of  the 
nozzles,  with  water  economy  and  without  loss  of  efficiency. 

2.  Reducing  the  volume  of  flow  without  altering  the  area  of  efflux, 
with  water  economy  but  with  loss  of  efficiency. 

3.  Variable  alteration  of  the  area  of  efflux  without  loss  of  efficiency 
and  with  water  economy. 

4.  Deflection  of  the  jet,  so  that  only  a  portion  of  its  energy  is  trans- 
mitted to  the  wheel,  without  water  economy. 

5.  Combined  regulation  of  3  and  4,  producing  an  effect  whereby  the 
energy  of  the  jet  is  reduced  rapidly  without  water  ram  and  the  area  of 
efflux  reduced  slowly  to  effect  water  economy,  or  by  a  combination  of 
3  with  some  form  of  by-pass. 


782  WATER-POWER. 

Governors.*— Of  the  five  methods  of  control  enumerated  above,  the 
first  cannot  be  done  automatically ;  the  other  four,  however,  are  suscep- 
tible to  either  hand  regulation  or  automatic  regulation  by  means  of  gov- 
ernors, the  function  of  the  governor  being  merely  to  automatically  bring 
into  action  the  particular  controlling  device  with  which  the  wheel  has 
been  equipped.  There  are  two  leading  types  of  governors,  the  hydraulic 
and  the  mechanical.  In  the  first,  the  mechanism  of  the  water-wheel 
regulator  is  actuated  by  a  hydraulically  operated  piston,  the  motive 
power  being  taken  from  a  small  branch  pipe  from  the  main  water  supply, 
or  from  an  independent  high-pressure  oil-pumping  system,  the  position 
of  the  piston  in  the  cylinder  and  consequent  relative  position  ef  the 
controlling  mechanism  being  dependent  upon  the  amount  of  fluid  under 
pressure  admitted  to  the  cylinder  at  either  end.  This  is  controlled  by  a 
main  valve,  operated  by  a  very  sensitive  relay  valve  which,  in  turn,  is 
directly  controlled  by  the  centrifugal  balls  of  the  governor. 

The  second  type,  or  mechanically  operated  governor,  consists  of  a 
device  for  automatically  controlling  and  directing  the  transmission  of 
the  requisite  amount  of  energy  taken  from  the  wheel  shaft,  to  operate 
the  water-regulating  mechanism.  The  Lombard  governor  represents 
the  first  type,  and  the  Lombard-Replogle  governor  the  second. 

The  close  regulation  that  can  be  obtained  with  the  latter  is  remark- 
able. Any  size  will  go  into  operation  and  make  correction  at  so  slight 
a  deviation  as  one-tenth  of  one  per  cent  from  normal,  and  in  installa- 
tions which  have  been  made  they  will  not  permit  of  a  departure  of  more 
than  five  to  eight  per  cent  temporarily  where  there  is  an  instantaneous 
drop  from  full  load  to  practically  no  load.  When  there  is  sufficient 
fly-wheel  effect,  the  deviation  will  not  be  over  two  per  cent.  The 
adoption  of  fly  wheels  greatly  facilitates  many  problems  of  governing. 

Efficiency  of  the  Doble  Nozzle. — The  nozzle  tip  is  of  brass,  highly 
polished  in  the  interior,  with  concave  curves  near  the  end.  It  contains 
a  conical  regulating  needle,  which  is  set  at  any  desired  distance  from  the 
opening  to  regulate  the  size  of  the  opening  and  the  diameter  of  the  jet. 
A  jet  flowing  from  the  nozzle  has  a  clear,  glassy  appearance.  Tests 
by  H.  C.  Crowell  and  G.  C.  D.  Lenth,  at  Mass.  Inst.  of  Tech.,  1903,  gave 
efficiencies  under  constant  head  from  96.4  to  99.3  %  for  different  settings 
of  the  needle,  the  coefficient  of  velocity  being  from  0.982  to  0.997.  The 
efficiency  of  a  jet  is  equal  to  the  ratio  of  the  velocity  head  in  the  jet  to 
the  total  head  at  the  entrance  to  the  nozzle,  and  equal  to  the  square  of 
the  coefficient  of  velocity. — Bulletin  of  the  Abner  Doble  Co.,  No.  6, 1904. 

Tests  of  a  12-in.  Doble  Laboratory  Motor  (Bulletin  No.  12,  1908. 
Abner  Doble  Co.). — The  tests  were  made  by  students  at  the  University 
of  Missouri.  The  available  head  was  46  ft.  The  needle  valve  was 
opened  two,  four,  six  and  eight  turns  in  the  four  series  of  tests,  and  with 
each  opening  different  loads  were  applied  by  a  Prony  brake.  The 
results  were  recorded  and  plotted  in  curves  showing  the  relation  of 
speed,  load  and  efficiency,  and  from  these  curves  the  following  approxi- 
mate figures  are  taken: 

Speed,  Revolutions  per  Minute. 


Valve  open                          200 

300 

400 

500 

600 

700 

800 

Two  turns 

B.H.P.. 

Effy.  % 

0.20 
62 

0.26 
75 

0.27 
80 

0.26 

77 

0.22 
64 

0.14 
41 

0.03 
13 

Four  turns 

B.H.P.. 

Effy.  % 

0.36 
57 

0.45 
75 

0.51 

85 

0.50 

85 

0.42 
71 

0.30 
50 

0.12 
19 

B.H.P.! 

0.41 

0.55 

0.63 

0.66 

0.60 

0.41 

0.20 

oix  turns 
Eight  turns 

Effy.  % 
B.H.P.? 

Effy.  % 

48 
0.48 
53 

64 
0.62 
70 

73 
0.70 
79 

76 
0.71 
81 

74 
0.64 

72 

66 
0.43 
50 

51 
0.  19 
23 

Water-power   Plants  Operating  under  High  Pressures.  —  The 

fol- 

lowing  notes  are  contributed  by  the  Pel  ton  Water  Wheel  Co.: 

The  Consolidated  Virginia  &  Col.  Mining  Co.,  Virginia,  Nev.,  has  a 
3-ft.  steel-disk  Pelton  wheel  operating  under  2100  ft.  fall,  equal  to 
911  Ib.  per  sq.  in.  It  runs  at  a  peripheral  velocity  of  10,804  ft.  per 
minute  and  has  a  capacity  of  over  100  H.  P;  The  rigidity  with  which 
water  under  such  a  high  pressure  as  this  leaves  the  nozzle  is  shown  in 
the  fact  that  it  is  impossible  to  cut  the  stream  with  an  axe,  however 
heavy  the  blow,  as  it  will  rebound  just  as  it  would  from  a  steel  rod 
traveling  at  a  high  rate  of  speed. 


TANGENTIAL  OK  IMPULSE  WATER-WHEELS. 


783 


In  the  hydraulic  power-hoist  of  the  Milwaukee  Mining  Co.,  Idaho,  one 
cage  travels  up  as  the  other  descends ;  the  maximum  load  of  5500  Ibs.  at 
a  speed  of  400  ft.  per  min.  is  carried  by  one  of  a  pair  of  Pelton  wheels  (one 
for  each  cage).  Wheels  are  started  and  stopped  by  opening  and  closing 
a  small  hydraulic  valve  at  the  engineer's  stand  which  operates  the  larger 
valves  by  hydraulic  pressure.  An  air-chamber  takes  up  the  shock 
that  would  otherwise  occur  on  the  pipe  line  under  the  pressure  due  to 
the  850  ft.  fall. 

The  Mannesmann  Cycle  Tube  Works,  North  Adams,  Mass.,  are  using 
four  Pelton  wheels,  having  a  fly-wheel  rim,  under  a  pump  pressure  of 
600  Ibs.  per  sq.  in.  These  wheels  are  direct-connected  to  the  rolls 
through  which  the  ingots  are  passed  for  drawing  out  seamless  tubing. 

The  Alaska  Gold  Mining  Co.,  Douglass  Island,  Alaska,  has  a  |22-ft 
Pelton  wheel  on  the  shaft  of  a  Riedler  duplex  compressor.  It  is  used  as 
a  fly-wheel  as  well,  weighing  25,000  lb.,  and  develops  500  H.P.  at  75 
revolutions.  A  valve  connected  to  the  pressure-chamber  starts  and 
stops  the  wheel  automatically,  thus  maintaining  the  pressure  in  the 
air-receiver. 
At  Pachuca  in  Mexico  five  Pelton  wheels  having  a  capacity  of  600 

Amount  of  Water  Required  to  Develop  a  Given  Horse-Power,  with  a 
Given  Available  Effective  Head. 


Effective 
Head  in 
Feet. 

Horse-Power  Based  on  85%  Efficiency  of  the  Water  "Wheel. 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

Flow  in  Cubic  Feet  of  Water  per  Minute  Required  to 
Develop  Power. 

50 

125 
104 
88 
77 
70 
63 
59 
52 
48 
45 
42 
39 
37 
35 
33 
31 
30 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
19 
19 
18 
18 
18 
17 
17 
16 
16 

250 
208 
177 
155 
140 
125 
118 
104 
96 
89 
83 
78 
73 
69 
65 
62 
59 
57 
54 
52 
50 
48 
46 
45 
43 
42 
41 
40 
38 
37 
36 
35 
34 
33 
32 
31 

375 
312 
266 
232 
210 
186 
176 
156 
143 
133 
125 
117 
110 
104 
98 
93 
89 
85 
81 
78 
75 
72 
69 
67 
65 
62 
60 
59 
57 
55 
53 
52 
50 
49 
48 
47 

500 
416 
355 
311 
280 
248 
234 
208 
192 
178 
166 
155 
146 
138 
132 
124 
118 
113 
108 
104 
100 
96 
92 
89 
86 
83 
80 
78 
76 
74 
71 
69 
67 
66 
64 
63 

625 
520 
444 
388 
350 
312 
293 
260 
240 
222 
208 
195 
183 
172 
164 
155 
148 
141 
135 
130 
125 
120 
115 
111 
107 
104 
100 
97 
94 
92 
89 
86 
84 
82 
80 
77 

750 
624 
532 
466 
420 
372 
350 
312 
287 
266 
250 
233 
220 
207 
198 
186 
177 
169 
162 
155 
149 
144 
138 
133 
129 
124 
120 
117 
113 
110 
106 
102 
100 
98 
96 
94 

875 
726 
621 
544 
490 
435 
410 
364 
335 
310 
292, 
272 
256 
242 
230 
218 
206 
198 
190 
181 
174 
167 
161 
156 
150 
145 
140 
136 
132 
128 
124 
121 
117 
114 
111 
105 

1000 
830 
709 
622 
560 
498 
467 
415 
385 
355 
332 
312 
293 
276 
262 
248 
236 
225 
216 
207 
199 
191 
184 
178 
172 
166 
160 
156 
151 
146 
142 
138 
134 
130 
127 
124 

1125 
934 
798 
699 
630 
558 
525 
467 
430 
400 
375 
350 
330 
310 
295 
280  . 
266 
255 
243 
233 
224 
215 
207 
200 
193 
187 
180 
175 
170 
165 
160 
155 
151 
147 
144 
140 

1250 
1038 
886 
876 
700 
622 
585 
520 
478 
443 
416 
388 
365 
345 
326 
310 
295 
283 
270 
258 
248 
238 
230 
222 
215 
208 
200 
194 
.  188 
183 
178 
172 
168 
164 
160 
156 

60..  . 

70  
80.  .  . 

90 

100. 

110..  . 

120  
130 

140 

150..  . 

160  . 

170..  . 

180 

190..  . 

200  
210.  .  . 

22*0  
230.  .  . 

240  
250..  . 

260 

270..  . 

280 

29"0..  . 

300.  . 

310 

320..  . 

330  
340.  .. 

350 

360.  .  . 

370.  .  . 

380... 

390..  . 

400  

784  POWER  OF  OCEAN  WAVES. 

H.P.  each  under  800  ft.  head  are  driving  an  electric  transmission  plant. 
These  wheels  weigh  less  than  500  Ib.  each,  showing  over  a  horse-power 
per  pound  of  metal. 

Formulae  for  Calculating  the  Power  of  Jet  Water-wheels,  such  as 
the  Pelton  (F.  K.  Blue). — H.P.  =  horse-power  delivered;  d  =  62.36  Ib. 
per  cu.  ft.;  E  =  efficiency  of  turbine;  q  =  quantity  of  water,  cubic  feet 
per  minute;  h  =  feet  effective  head:  d  =  inches  diameter  of  jet;  p  = 
pounds  per  square  inch  effective  head ;  c  =  coefficient  of  discharge  from 
nozzle  which  may  be  ordinarily  taken  at  0.9. 

H.P.= 


d2=  201.6  

.Ec  Vft3  J^C  VpS  c  Y//i  c  >y^ 

Tangential  Water-wheel  Tables. — The  tables  on  pages  785  and  786  are 
compiled  on  the  following  basis : 

The  head  (h)  is  the  net  effective  head  at  the  nozzle.  Proper  allow- 
ance must  be  made  for  all  losses  in  the  pipe  line. 

The  velocity  of  efflux  ( V)  is  the  approximate  spouting  velocity  of  the  , 
jet  in  ft.  per  min.  as  it  issues  from  the  nozzle  =  \/2  gh  X  60  =  481.2  \/hl 

The  discharge  in  cubic  feet  per  minute  =  Q  =  V  X  a,  where  a  equals 
the  cross-section  area  of  nozzle  opening  in  sq.  ft.,  no  allowance  being 
made  for  friction  in  the  nozzle. 

The  weight  of  a  cubic  foot  of  water  is  taken  at  39.2°  Fahr.  =  62.425  Ib. 

The  theoretical  horse-power  =  Q  X  62.425  X  h  ~  33,000  =  0.00189£ft. 

The  horse-power  in  the  tables  is  based  on  85  %  mechanical  efficiency 
for  the  wheels. 

The  diameter  is  the  effective  diameter  at  the  line  of  the  nozzle  center, 
where  the  jet  impinges  on  the  center  of  the  bucket. 

The  number  of  revolutions  is  based  on  a  peripheral  speed  for  the 
effective  diameter,  of  half  the  velocity  of  efflux  of  the  jet,  and  equals 
V  -T-  2  C,  where  C  =  the  circumference  (in  feet)  of  the  effective  diameter. 

Small  wheels,  up  to  24-in.  diam.,  are  commonly  called  motors. 

THE  POWER  OF  OCEAN  WAVES. 

Albert  W.  Stahl,  U.  S.  N.  (Trans.  A.  S.  M.  E.,  xiii,  438),  gives  the 
following  formulae  and  table,  based  upon  a  theoretical  discussion  of 
wave  motion : 

The  total  energy  of  one  whole  wave-length  of  a  wave  H  feet  high, 
L  feet  long,  and  one  foot  in  breadth,  the  length  being  the  distance 
between  successive  crests,  and  the  height  the  vertical  distance  between 

the\ crest  and  the  trough,  is  E  =  8  LH%  t  I  —  4.935—  j  foot-pounds. 

The  time  required  for  each  wave  to  travel  through  a  distance  equal  to 
its  own  length  is  P  <=  -%/•  seconds,  and  the  number  of  waves  passing 

60  /5  1^3 

any  given  point  in  0110  minute  is  N  =  -p  =  60^   ' •*"  ••     Hence  the  total 

energy  of  an  indefinite  series  of  such  waves,  expressed  in  horse-power  per 
foot*of  breadth,  is 


By  substituting  various  values  for  H  -*-  L,  within  the  limits  of  such 
values  actually  occurring  in  nature,  we  obtain  the  table  on  page  787. 
The  figures  are  correct  for  trochoidal  deep-sea  waves  only,  but  they 

(Continued  on  pag*  786) 


TANGENTIAL   OR   IMPULSE   WATER   WHEELS.       785 


Tangential  Water- Wheel  Table.     (Joshua  Hendy  Iron  Works.) 

P  =  horse-power,  Q  =  cubic  feet  per  minute,  R  =  revs,  per  min.  The 
smaller  figures  in  the  first  column  give  the  spouting  velocity  of  the  jet 
in  feet  per  minute.  (The  table  is  greatly  condensed  from  the  original; 
6-in.,  15-in.,  and  30-in.  wheels  are  also  listed.  P  and  Q  are  the  same, 
with  any  given  head,  for  a  30  as  for  a  36-in.  wheel,  but  R  is  20%  greater.)  - 


f£ 

K.S 

12 

Inch. 

18 

Inch. 

24 

Inch. 

36 

Inch. 

48 

Inch. 

60 

Inch. 

72 

Inch. 

8 

Feet. 

10 

Feet. 

12 

Feet. 

20  ' 

P 

.12 

.37 

.66 

1.50 

2.64 

4.18 

6.00 

10.64 

16.48 

23.80 

91')'?  J 

3.91 

11.72 

20.83 

46.93 

83.32 

130.36 

187.72 

332.70 

515.04 

748.95 

L\  JL  1 

R 

342 

228 

171 

114 

85 

70 

57 

43 

34 

29 

*A( 

P 

.23 

.69 

1.22 

2.76 

4.88 

7.69 

11.04 

19.53 

30.00 

43.80 

30  ) 

?f\if\  i 

4.79 

14.36 

25.51 

57.44 

102.04 

159.66 

229.76 

407.03 

630.00 

916.4? 

iOJO  1 

R 

418 

279 

209 

139 

104 

83 

69 

52 

41 

35 

**( 

P 

.35 

U)6 

1.89 

4.24 

7.58 

11.85 

16.96 

30.08 

46.60 

67.60 

40) 

5.53 

16.59 

29.46 

66.36 

107.84 

184.36 

265.44 

470.27 

728.16 

1058.86 

3043  ( 

R 

484 

323 

242 

161 

121 

96 

80 

62 

49 

40 

...  ( 

P 

.49 

1.49 

2.65 

5.98 

10.60 

16.63 

23.93 

42.05 

65.00 

94.50 

50  ) 

6.18 

18.54 

32.93 

74.17 

131.72 

206.13 

296.70 

525.90 

814.32 

1184.15 

3403  ( 

R 

541 

361 

270 

180 

135 

108 

90 

69 

55 

46 

CA    ( 

P 

.65 

1.96 

3.48 

7.84 

13.94 

21.77 

31.36 

55.20 

85.62 

124.50 

60  V 

6.77 

20.31 

36.08 

81.25 

144.32 

225.80 

325.00 

576.00 

892.00 

1297.00 

3727  ) 

R 

592 

395 

296 

197 

148 

118 

98 

75 

60 

50 

( 

P 

.82 

2.47 

4.39 

9.88 

17.58 

27.51 

39.52 

70.00 

107.80 

157.50 

70 

Q 

7.31 

21.94 

38.97 

87.76 

155.88 

243.89 

351.04 

624.00 

966.24 

1405.17 

4026  ( 

R 

640 

427 

320 

2.13 

160 

130 

106 

81 

64 

54 

/ 

P 

1.00 

3.01 

5.36 

12.04 

21.44 

33.54 

48.16 

85.76 

134.16 

192.64 

80 

Q 

7.82 

23.46 

41.66 

93.84 

166.64 

260.73 

375.36 

666.56 

1042.92 

1501.44 

4304  ( 

R 

684 

456 

342 

228 

171 

137 

114 

87 

69 

58 

( 

P 

1.20 

3.60 

6.39 

14.40 

25.59 

40.04 

57.60 

102.36 

160.16 

230.40 

90 

Q 

8.29 

24.88 

44.19 

99.52 

176.75 

276.55 

398.08 

707.00 

1106.20 

1592.32 

4565  ( 

R 

726 

484 

363 

242 

181 

145 

121 

93 

73 

62 

( 

P 

1.40 

4.21 

7.49 

16.84 

29.93 

46  85 

67.36 

119.72 

187.40 

269.44 

100  ) 

Q 

8.74 

26.22 

46.58 

104.88 

186.32 

291.51 

419.52 

745.28 

1166.04 

1678.08 

4812  ( 

R 

765 

510 

382 

255 

191 

152 

127 

96 

77 

64 

( 

P 

1.84 

5.54 

9.85 

22.18 

39.41 

61.66 

88.75 

157.64 

246.64 

355.00 

120) 

Q 

9.57 

28.72 

51.02 

114.91 

204.10 

319.33 

459.64 

816.40 

1277.32 

1838  56 

5271  ( 

R 

838 

559 

419 

279 

209 

167 

139 

105 

83 

70 

1>IA  ( 

P 

2.33 

6.99 

12.41 

27.96 

49.64 

77.71 

111.85 

198.56 

310.84 

447.40 

140  ) 

10.34 

31.03 

55.11 

124.12 

220.44 

344.92 

496.48 

881.76 

1379.68 

1985.92 

5694  ) 

R 

906 

604 

453 

302 

226 

181 

151 

114 

90 

75 

( 

P 

2.84 

8.54 

15.17 

34.16 

60.68 

94.94 

136.65 

242.72 

377.76 

546.60 

160 

11.05 

33.17 

58.92 

132.68 

235.68 

368.73 

530.75 

942.72 

1474.92 

2123.00 

6087  ( 

R 

969 

646 

484 

323 

242 

193 

161 

121 

97 

81 

t 

P 

3.39 

10.19 

18.10 

40.77 

72.41 

113.30 

163.08 

289.64 

453.20 

652.32 

183  ) 

11.72 

35.18 

62  49 

140.74 

249.97 

391.10 

562.96 

999.83 

1564.40 

2251.84 

6455  ) 

1024 

683 

513 

342 

256 

206 

171 

128 

103 

86 

( 

P 

3.97 

11.93 

21.20 

47.75 

84.81 

132.70 

191.00 

339.24 

530.80 

764.00 

200  ) 

Q 

12.36 

37.08 

65.87 

148.35 

263.49 

412.25 

593.40 

1053.96 

1649.00 

2373.60 

6805  ) 

R 

1080 

720 

540 

360 

270 

216 

180 

135 

108 

90 

Q«C   ( 

P 

56  99 

101.20 

158  38 

227  96 

404  80 

633  52 

911  84 

4/0  \ 

7215  \ 

Q 

157  J3 

279^44 

437.23 

629  '.32 

1117^76 

1748  92 

2517.28 

R 

382 

287 

229 

191 

144 

115 

96 

250  ( 

P 

5.56 

16.68 

29.63 

66.74 

118.54 

185.47 

266.96 

474.16 

741.88 

1067.84 

7608  j 

3 

13.82 

41.46 

73.64 

165.86 

294.59 

460.91 

663.45 

1178.36 

1843.64 

2653.80 

H 

1209 

806 

605 

403 

302 

241 

202 

151 

n\ 

101 

786 


WATER-POWER. 


Tangential  Water- Wheel  Table.— Continued. 


•d^ 
g* 

W.2 

12 

Inch. 

18 
Inch. 

24 

Inch. 

36 

Inch. 

48 

Inch. 

60 

Inch. 

72 

Inch. 

8 

Feet. 

10 

Feet. 

12 

Feet. 

O7  C    { 

P 

77  00 

136.76 

214  00 

308  00 

547.04 

856  00 

173?  nn 

•f  9  1 

7O7R  < 

173  94 

308.92 

483  39 

695  !  76 

1235  68 

1  933  56 

1  /,->£.  UU 

7783   (\A 

S7/J    1 

-o 

423 

317 

253 

211 

J59 

127 

£/OJ  .  lH 
IflA 

300  ( 

P 

7.31 

21.93 

38.95 

87.73 

155.83 

243.82 

350.94 

623.32 

975.28 

IUO 

1403  76 

8335  ) 

Q 

15.13 

45.42 

80.67 

181.59 

322.71 

504.91 

726.76 

1290.84 

2019.64 

2907  .  04 

( 

R 

1326 

884 

663 

442 

331 

265 

221 

166 

133 

QOK   ( 

P 

98  93 

175  68 

274  94 

395  72 

702  72 

1099  76 

1582  88 

325  ) 

8A77  i 

189'  10 

335  '84 

525  '50 

756  '.  40 

1343  36 

2102  00 

3025  60 

OO/Z  i 

R 

460 

344 

276 

230 

J72 

J38 

J15 

350  ( 

P 

9.21 

27.64 

49.09 

110.56 

196.38 

307.25 

442.27 

785.52 

1229  00 

1769  08 

9002  i 

Q 

16.35 

49.06 

87.14 

196.25 

348.57 

545.36 

785.00 

1394.28 

2181.44 

3140.00 

R 

1432 

955 

716 

477 

358 

275 

238 

179 

143 

119 

400  ( 

P 

11.25 

33.77 

59.98 

135.08 

239.94 

375.40 

540.35 

959.76 

1501.60 

2161.40 

9624  / 

Q 

17.48 

52.45 

93.16 

209.80 

372.64 

583.02 

839.20 

1490.56 

2332.08 

3356.80 

R 

1531 

1021 

765 

510 

382 

306 

255 

101 

153 

128 

450  ( 

P 

13.43 

40.79 

71.57 

161.19 

286.31 

447.95 

644.78 

1145.24 

1791.80 

2579.12 

10208  j 

Q 

18.54 

55.63 

98.81 

222.52 

395.24 

618.38 

890.11 

1580.96 

2473.52 

35,60.44 

R 

1624 

1083 

812 

541 

406 

324 

270 

203 

162 

135 

500  ( 

P 

15.73 

47.20 

83.83 

188.80 

335.34 

524.66 

755.20 

1341.36 

2098.64 

3020.80 

10760  / 

Q 

19.54 

58.64 

104.15 

234.56 

416.62 

651.83 

938.25 

1666.48 

2607.02 

3753.00 

R 

1713 

1142 

856 

571 

428 

342 

285 

214 

171 

143 

-      f 

p 

217  82 

386  84 

605  31 

871  28 

1547  36 

2421.24 

3485  12 

550  ) 
1  1*770  \ 

Q 

246.00 

436.92 

683  62 

984.00 

1747  '68 

2734  48 

3936  00 

1  IZ/y  || 

R 

599 

449 

359 

299 

225 

J79 

150 

600  ( 

P 

24.26 

62.04 

110.19 

248.16 

440.77 

689.63 

992.65 

1763.08 

2758.52 

3970.60 

1  1  787  ) 

Q 

25.12 

64.24 

114.09 

256.95 

456.38 

714.05 

1027.80 

1825.52 

2856.20 

4111.20 

R 

1876 

1251 

938 

625 

469 

375 

312 

235 

188 

156 

f 

p 

270  97 

484.16 

748  80 

1083  88 

1936.64 

2995  20 

4335  52 

640  } 

Q 

264  '63 

466  12 

73l'59 

1058  '52 

1864  48 

292636 

4234^08 

12169  ) 

R 

644 

483 

387 

322 

242 

194 

161 

7Afl  ( 

p 

30.57 

78.18 

138.86 

312.73 

555.46 

869.06 

1250.92 

2221.84 

3476.24 

5003  68 

1  UU  • 
17731   ) 

Q 

27.13 

69.38 

123.23 

277.54 

492.95 

771.26 

1110.16 

1971.80 

3085.04 

4440.64 

l£/j>l   1 

R 

2026 

1351 

1013 

675 

506 

405 

337 

253 

203 

169 

7CA   ( 

P 

33.91 

86.70 

154.00 

346.83 

616.03 

963.82 

1387.34 

2464.12 

3855.28 

5549.36 

f  OIF  I 

13178  i 

Q 

28.08 

71.82 

127.56 

287.28 

510.25 

798.33 

1149.13 

2041.00 

3193.32 

4596.52 

R 

2098 

1309 

1049 

699 

524 

419 

349 

262 

210 

175 

Qf\f\   \ 

P 

37.35 

95.52 

169.66 

382.09 

678.66 

1061.81 

1528.36 

2714.64 

4247.24 

6113.44 

oUU  ) 

13610  ) 

Q 

29.00 

74.17 

131.74 

296.70 

526.99 

824.51 

1186.81 

2107.96 

3298.04 

4747.24 

R 

2166 

1444 

1083 

722 

542 

433 

361 

271 

217 

181 

QAA   ( 

p 

44.57 

113.98 

202.45 

455.94 

809.82 

1267.02 

1823.76 

3239.28 

5068.08 

7295.04 

i/UU     I 

IXXIA  S 

Q 

30.76 

78.67  139.74 

314.70 

558.96 

874.53 

1258.81 

2235.84 

3498.12 

5035.24 

1  *HjO  i 

R 

.2298 

15321     1149 

766 

574 

459 

383 

287 

229 

192 

i  ftftft  ( 

P 

52.20 

133.50 

237.12 

534.01 

948.48 

1483.97 

2136.04 

3793  92 

5935.88 

8544.16 

1UUU  1 

Q 

32.42 

82.93 

147.30 

331.72 

589.19 

921.83 

1326.91 

2356.76 

3687.32 

5287.64 

15217  ) 

11 

2420 

1615 

1210 

807 

605 

484 

403  |        303 

242 

202 

give  a  close  approximation  for  any  nearly  regular  series  of  waves  in  deep 
water  and  a  fair  approximation  for  waves  in  shallow  water. 
The  utilization  of  the  energy  in  ocean  waves  divides  itself  into: 

1.  The  various  motions  of  the  water  which  may  be  utilized  for  power. 

2.  The  wave-motor  proper.     That  is,  the  portion  of  the  apparatus 
in  direct  contact  with  the  water,  and  receiving  and  transmitting  the 
energy  thereof;    together  with  the  mechanism  for  transmitting  this 
energy  to  the  machinery  for  utilizing  the  same. 

3.  Regulating  devices,  for  obtaining  a  uniform  motion,  from  the 


TIDAL  POWER. 


787 


irregular  and  more  or  less  spasmodic  action  of  the  waves,  as  well  as  for 
adjusting  the  apparatus  to  the  state  of  the  tide  and  condition  of  the  sea. 

4.  Storage  arrangements  for  insuring  a  continuous  and  uniform  out- 
put of  power  during  a  calm,  or  when  the  waves  are  comparatively  small. 

The  motions  that  may  be  utilized  for  power  purposes  are  the  following : 
1.  Vertical  rise  and  fall  of  particles  at  and  near  the  surface.  2.  Hori- 
zontal to-and-fro  motion  of  particles  at  and  near  the  surface.  3.  Vary- 
ing slope  of  surface  of  wave.  4.  Impetus  of  waves  rolling  up  the  beach 
in  the  form  of  breakers.  5.  Motion  of  distorted  verticals.  All  of 
these  motions,  except  the  last  one  mentioned,  have  at  various  times 
been  proposed  to  be  utilized  for  power  purposes ;  and  the  last  is  proposed 
to  be  used  in  apparatus  described  by  Mr.  Stahl. 

The  motion  of  distorted  verticals  is  thus  denned:  A  set  of  particles, 
originally  in  the  same  vertical  straight  line  when  the  water  is  at  rest, 
does  not  remain  in  a  vertical  line  during  the  passage  9f  the  wave;  so 
that  the  line  connecting  a  set  of  such  particles,  while  vertical  and 
straight  in  still  water,  becomes  distorted,  as  well  as  displaced,  during 
the  passage  of  the  wave,  its  upper  portion  moving  farther  and  more 
rapidly  than  its  lower  portion. 

Mr.  Stahl's  paper  contains  illustrations  of  several  wave-motors  de- 
signed upon  various  principles.  His  conclusion  as  to  their  practicability 
is  as  follows :  ' '  Possibly  none  of  the  methods  described  in  this  paper  may 
ever  prove  commerically  successful;  indeed  the  problem  may  not  be 
susceptible  of  a  financially  successful  solution.  My  own  investigations, 
however,  so  far  as  I  have  yet  been  able  to  carry  them,  incline  me  to  the 
belief  that  wave-power  can  and  will  be  utilized  on  a  paying  basis." 

TOTAL  ENERGY  OF  DEEP-SEA  WAVES  IN  TERMS  OP  HORSE-POWER  PER 
FOOT  OP  BREADTH 


Ratio  of 
Length  to 
Height  of 
Waves. 

Length  of  Waves  in  Feet. 

25 

50 

75 

100 

150     |     200 

300     |     400 

50 
40 
30 
20 
15 
10 
5 

0.04 
0.06 
0.12 
0.25 
0.42 
0.98 
3.30 

0.23 
0.36 
0.64 
1.44 
2.83 
5.53 
18.68 

0.64 
1.00 
1.77 
3.96 
6.97 
15.24 
51.48 

1.31 
2.05 
3.64 
8.13 
14.31 
31.29 
105.68 

3.62 
5.65 
10.02 
21.79 
39.43 
86.22 
291.20 

7.43 
11.59 
20.57 
45.98 
80.94 
177.00 
597.78 

20.46 
31.95 
56.70 
120.70 
223.06 
487.75 
1647.31 

42.01 
65.58 
116.38 
260.08 
457.89 
1001.25 
3381.60 

Continuous  Utilization  of  Tidal  Power  (P.  Decceur,  Proc.  Inst. 
C,  E.  1890). — In  cpnnection  with  the  training- walls  to  be  constructed  in 
the  estuary  of  the  Seine,  it  is  proposed  to  construct  large  basins,  by 
means  of  which  the  power  available  from  the  rise  and  fall  of  the  tide 
could  be  utilized.  The  method  proposed  is  to  have  two  basins  separ- 
ated by  a  bank  rising  above  high  water,  within  which  turbines  would 
be  placed.  The  upper  basin  would  be  in  communication  with  the  sea 
during  the  higher  one-third  of  the  tidal  range,  rising,  and  the  lower 
basin  during  the  lower  one- third  of  the  tidal  range,  falling.  The  tur- 
bine proposed  is  of  an  improved  model  designed  to  utilize  a  large  flow 
with  a  moderate  diameter.  One  has  been  designed  to  produce  300 
horse-power,  with  a  minimum  head  of  5  ft.  3  in.  at  a  speed  of  15  revo- 
lutions per  minute,  the  vanes  having  13  ft.  internal  diameter.  The 
speed  would  be  maintained  constant  by  regulating  sluices. 


788 


PUMPS  AND   PUMPING   ENGINES. 


PUMPS  AND  PUMPING  ENGINES. 

Theoretical  Capacity  of  a  Pump.  —  Let  Q'*=  cu.  ft.  per  min., 
C'  »  U.  S.  gals,  per  min.  =  7.4805  Q*  \  d  =  diam.  of  pump  in  inches; 
*/  =  stroke  in  inches ;  N  ==  number  of  single  strokes  per  rain. 

Capacity  in  cu.  ft.  per  min. 


I'iarn  =  °-°004545^: 


4     231 


Capacity  in  U.  S.  gals,  per  min.  i 
Capacity  in  gals,  per  hour 

Diameter    required    for    a  )          d  =  46  Q 
given  capacity  per  min.   ) 

If  v  =  piston  speed  in  feet  per  min.,  d 
If  the  piston  speed  is  100  feet  per  min.: 


'  0.0034  AW; 
=  0.204  Nd*l. 


^  =  17.15  -v/-t7% 


V7T,  /7S7 

^  =4.95\y. 


Nl  =  1200,  and  d  =  1.354 


,  0.495 


G'  =  4.08  dz  per  min. 
The  actual  capacity  will  be  from  60%  to  95%  of  the  theoretical,  accord- 
ing to  the  tightness  of  the  piston,  valves,  suction-pipe,  etc. 

Theoretical  Horse-power  .Required  to   Raise  Water  to  a  Given 
Height.  —  Horse-power  = 
Volume  in  cu.  ft.  per  min.  X  pressure  per  sq.  ft.    _  Weight  X  height  of  lift 

33,000  33,000 

Q'  =  cu.  ft.  per  min.;  G'  =  gals,  per  min.;  W  =  wt.  in  Ibs.;  P  =* 
pressure  in  Ibs.  per  sq.  ft.;  p  =  pressure  in  Ibs.  per  sq.  in.;  //  =  height  of 
lift  in  ft.;  W  =  62.355  Q',  P  -  144  p,  p  =  0.433  H,  H  =  2.3094  p,  G'  = 
7.4805  Q'. 

=     Q'P    ^  Q'H  X  144  X  0.433  =     Q'H    _      G'H    =  1.0104  G'H 
33,000  33,000  529,23       3958.9  4000 


HP.  = 


WH 


Q'  X  62.355  X  2.3094  p  =     Q'p  G'p 

33,000  229.17     "  1714.3' 


33,000 

For  the  actual  horse-power  required  an  allowance  must  be  made  for 
the  friction,  slips,  etc.,  of  engine,  pump,  valves,  and  passages. 

Depth  of  Suction. — Theoretically  a  perfect  pump  will  draw  water 
to  a  height  of  nearly  34  feet,  or  the  height  corresponding  to  a  perfect 
vacuum  (14.7  Ibs.  X  2.309  =  33.95  feet);  but  since  a  perfect  vacuum 
cannot  be  obtained  on  account  of  valve-leakage,  air  contained  in  the 
water,  and  the  vapor  of  the  water  itself,  the  actual  height  is  generally 
(ess  than  30  feet.  When  the  water  is  warm  the  height  to  which  it  can  be 
lifted  by  suction  decreases,  on  account  of  the  increased  pressure  of  the 
vapor.  In  pumping  hot  water,  therefore,  the  water  must  flow  into  the 
pump  by  gravity.  The  following  table  shows  the  theoretical  maximum 
depth  of  suction  for  different  temperatures,  leakage  not  considered: 


Temp. 
Fahr. 

Absolute 
Pressure 
of  Vapor, 
Ibs.  per 
sq.  in. 

Vacuum 
in 
Inches  of 
Mercury. 

Max. 

Depth 
(of 
Suc- 
tion, 
feet. 

Temp. 
Fahr. 

Absolute 
Pressure 
of  Vapor, 
Ibs.  per 
sq.  in. 

Vacuum 
in 
Inches  of 
Mercury. 

Max. 
Depth 
of 

Suc- 
tion, 
feet. 

102  1 

1 

27.88 

31.6 

182.9 

8 

13.63 

15.4 

126.3 

2 

25.85 

29.3 

188.3 

9 

11.60 

13.1 

141.6 

3 

23.83 

27.0 

193.2 

10 

9.56 

10.8 

153.1 

4 

21.78 

24.7 

197.8 

11 

7.52 

8.5 

162.3 

5 

19.74 

22.3 

202.0 

12 

5.49 

6.2 

170.1 

6 

17.70 

20.0 

205.9 

13 

3.45 

3.9 

176.9 

7 

15.67 

17.7 

209.6 

14 

1.41 

1.6 

PUMPS  AND  PUMPING  ENGINES. 


789 


The  Deane  Single  Boiler-feed  or  Pressure  Pump. 

pumping  clear  liquids  at  a  pressure  not  exceeding  150  Ibs. 


Suitable  for 


Sizes. 

Capacity 

Sizes  of  Pipes. 

per  min. 

at  Given 

0> 

Speed. 

•8 

.s 

1 

. 

j. 

-7-« 

«*H 

o> 

.s 

& 

• 

1 

1       t-4 

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3 

1 

to 

| 

i 

3 

fl 

1 

3 

|1 
02 

|| 

SOQ 

1" 

| 

3 

1 

1 

1 

A 

o 

1 

0 

3 

2 

5 

.07 

150 

10 

291/2 

7 

1/2 

3/4 

U/4 

1 

31/2 

21/4 

5 

.09 

150 

13 

331/2 

71/2 

1/2 

3/4 

U/4 

U/2 

4 

23/8 

5' 

.10 

150 

15 

331/2 

71/2 

1/2 

3/4 

U/4 

2 

4 

21/2 

5 

.11 

150 

16 

331/2 

71/2 

1/2 

3/4 

U/4 

21/2 

43/4 

3 

5 

.15 

150 

22 

34 

81/2 

1/2 

3/4 

H/2 

1/4 

3 

5 

31/4 

7 

.25 

125 

31 

431/2 

91/4 

3/4 

1 

2 

1/2 

4 

51/2 

33/4 

7 

.33 

125 

42 

43l/2 

91/4 

3/4 

1 

2 

U/2 

41/2 

7 

41/4 

8 

.49 

120 

58 

511/o 

12 

1 

U/2 

3 

2 

5 

7 

41/2 

10 

.69 

100 

69 

55 

12 

1 

U/2 

3 

2 

6 

71/2 

5 

10 

.85 

100 

85 

55 

12 

1 

U/2 

3 

2 

61/2 

8 

5 

12 

1.02 

100 

102 

63 

14 

1 

U/2 

3 

2V2 

7 

10 

6 

12 

1.47 

100 

147 

69 

19 

1  1/2 

2 

4 

4 

8 

12 

7 

12 

2.00 

100 

200 

69 

19 

2 

21/2 

5 

4 

9 

14 

8 

12 

2.61 

100 

261 

69 

21 

2 

21/2 

5 

5 

The  Deane  Single  Tank  or  Light-service  Pump.  —  These  pumps 
will  all  stand  a  constant  .working  pressure  of  75  Ibs.  on  the  water-cylinders. 


Sizes. 

Capacity 
per  min. 

Sizes  of  Pipes. 

03 

\ 

"Speed0 

o 

• 

0 

* 

J, 

o    . 

£  . 

*o  4; 

a^ 

M 

d 

.S 

-^ 

g 

g 

fijj 

£   QJ 

•£  o 

11 

B 

fl 

JO 

tc 

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1 

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§02 

^^ 

2 

9 

72 

i 

jd 

w 

m 

^ 

^ 

O 

OQ 

O 

^ 

m 

S 

03 

Q 

4 

4 

5 

.27 

130 

35 

33 

91/2 

1/2 

3/4 

2 

H/2 

3 

4 

7 

.38 

125 

48 

451/2 

15 

3/4 

1 

3 

2V2 

5V2 

51/2 

7 

.72 

125 

90 

451/2 

15 

3/4 

] 

3 

21/2 

7V2 

71/2 

10 

1.91 

110 

210 

58 

17 

1 

1V2 

5 

4 

8 

6 

12 

1.46 

100 

146 

67 

201/2 

1 

11/2 

4 

4 

6 

7 

12 

2.00 

100 

200 

66 

17 

3/4 

4 

4 

8 

7 

12 

2.00 

100 

200 

67 

201/2 

1 

U/2 

5 

4 

8 

8 

12 

2.61 

100 

261 

68 

30 

1 

1  V2 

5 

5 

10 

8 

12 

2.61 

100 

261 

681/2 

30 

11.2 

5 

5 

8 

10 

12 

4.08 

100 

408 

68 

20i/2 

U/2 

8 

8 

10 

10 

12 

4.08 

100 

408 

681/2 

30 

U/2 

2 

8 

8 

'12 

10 

12 

4.08 

100 

408 

64 

24 

2 

2V2 

8 

8 

10 

12 

12 

5.87 

100 

587 

681/2 

30 

U/2 

2 

8 

8 

12 

12 

12 

5.87 

100 

587 

64 

281/2 

2 

21/2 

8 

8 

10 

12 

18 

8.79 

70 

616 

95 

25 

H/2 

2 

8 

8 

12 

12 

18 

8.79 

70 

616 

95 

281/2 

2 

21/2 

8 

8 

12 

14 

18 

12.00 

70 

840 

95 

281/2 

2 

21/2 

8 

8 

14 

16 

18 

15.66 

70 

1096 

95 

34 

2 

21/2 

12 

10 

16 

16 

18 

15.66 

70 

1096 

95 

34 

2 

21/2 

12 

10 

18 

16 

18 

15  66 

70 

1096 

97 

34 

3 

3V2 

12 

10 

16 

18 

24 

26.42 

50 

1321 

115 

40 

2 

21/2 

14 

12 

18 

18 

24 

26.42 

50 

1321 

135 

40 

3 

3V2 

14 

12 

790  PUMPS  AND  PUMPING  ENGINES. 

Amount  of  Water  raised  by  a  Single-acting  Lift-pump.  —  It  Is 

common  to  estimate  that  the  quantity  of  water  raised  by  a  single-acting 
bucket-valve  pump  per  minute  is  equal  to  the  number  of  strokes  in  one 
direction  per  minute,  multiplied  by  the  volume  traversed  by  the  piston 
in  a  single  stroke,  on  the  theory  that  the  water  rises  in  the  pump  only 
when  the  piston  or  bucket  ascends;  but  the  fact  is  that  the  column  of 
water  does  not  cease  flowing  when  the  bucket  descends,  but  flows  on 
continuously  through  the  valve  in  the  bucket,  so  that  the  discharge  of 
the  pump,  if  it  is  operated  at  a  high  speed,  may  amount  to  considerably 
more  than  that  calculated  from  the  displacement  multiplied  by  the  num- 
ber of  single  strokes  in  one  direction. 

Proportioning  the  Steam-cylinder  of  a  Direct-acting  Pump,  — 

Let 

A  =  area  of  steam-cylinder;  a  =  area  of  pump-cylinder; 

D  =  diameter  of  steam-cylinder;  d  =  diameter  of  pump-cylinder; 

P  =  steam-pressure,  Ibs.  per  sq.  in.;  p  =  resistance  per  sq.  in.  on  pumps; 

H  =  head  =  2.309  p;  p  =  0.433  H\ 

work  done  in  pump-cylinder 
E  -  efficiency  of  the  pump  =  work  done  by  ' 


.-  - 

EP'  p     *  \EP' 


-  =  ^  =  OA**H',  #  =  2.309  #P  —  .  If  #=75%,  H  =  1.732P-- 
d        JbJr  MiP  d  O> 

E  is  commonly  taken  at  0.7  to  0.8  for  ordinary  direct-acting  pumps. 
For  the  highest  class  of  pumping-engines  it  may  amount  to  0.9.  The 
steam-pressure  P  is  the  mean  effective  pressure,  according  to  the  indi- 
cator-diagram; the  water-pressure  p  is  the  mean  total  pressure  acting 
on  the  pump  plunger  or  piston,  including  the  suction,  as  could  be  shown 
by  an  indicator-diagram  of  the  water-cylinder.  The  pressure  on  the 
pump-piston  is  frequently  much  greater  than  that  due  to  the  height  of 
the  lift  *  on  account  of  the  friction  of  the  valves  and  passages,  which 
increases  rapidly  with  velocity  of  flow. 

Speed  of  Water  through  Pipes  and  Pump-passages.  —  The  speed 
of  the  water  is  commonly  from  100  to  200  feet  per  minute.  If  200  feel 
per  minute  is  exceeded,  the  loss  from  friction  may  be  considerable. 


„  gallons  per  minute 

The  diameter  of  pipe  required  is  *.95^vd^ty  in  f^t  per 


For  a  velocity  of  200  feet  per  minute,  diam.  =  0.35  X  ^gallons  per  min. 

Sizes  of  Direct-acting  Pumps.  —The  tables  on  pages  789  and  791 
are  selected  from  catalogues  of  manufacturers,  as  representing  the  two 
common  types  of  direct-acting  pump,  viz.,  the  single-cylinder  and  the 
duplex.  Both  types  are  made  by  most  of  the  leading  manufacturers. 

Efficiency  of  Small  Direct-acting  Pumps.  —  Chas.  E.  Emery,  in 
Reports  of  Judges  of  Philadelphia  Exhibition,  1876,  Group  xx.,  says: 
"  Experiments  made  with  steam-pumps  at  the  American  Institute  Exhibi- 
tion of  1867  showed  that  average-sized  steam-pumps  do  not,  on  the  aver- 
age utilize  more  than  50  per  cent  of  the  indicated  power  in  the  steam- 
cylinders,  the  remainder  being  absorbed  in  the  friction  of  the  engine,  but 
more  particularly  in  the  passage  of  the  water  through  the  pump  It 
may  be  safely  stated  that  ordinary  steam-pumps  rarely  require  less  than 
120  pounds  of  steam  per  hour  for  each  horse-power  utilized  m  raising 
water,  equivalent  to  a  duty  of  only  15,000,000  foot-pounds  per  100 
pounds  of  coal.  With  larger  steam-pumps,  particularly  when  they  are 
proportioned  for  the  work  to  be  done,  the  duty  will  be  materially  in- 
creased," 


PUMPS  AND  PUMPING  ENGINES. 

The  Worthington  Duplex  Pump. 

STANDARD  SIZES  FOR  ORDINARY  SERVICE. 


791 


03 
& 

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&  £ 

.£  °  ' 
US  ® 

Sizes  of  Pipes  for 
Short  Lengths. 

(j 

e 

03 

3        2 

'i'2' 

To  be  increased  as 

1 

03 

fl 

o  tl 

•£  flw 

c^ 

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length  increases. 

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1 

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5 

3 

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£ 

o 

Q    - 

w 

H 

02 

3 

3 

2 

3 

.04 

100  to  250 

8  to      20 

27/8 

3/8 

1/2 

H/4 

i 

41/2 

23/4 

4 

.10 

100  to  200 

20  to      40 

4 

1/2 

3/4 

2 

n/2 

51/4 

31/2 

5 

.20 

100  to  200 

40  to      80 

5 

3,4 

U/4 

21/2 

n/2 

6 

4 

6 

.33 

100  to  150 

70  to    100 

55/8 

1 

U/2 

3 

2 

71/2 

41/2 

6 

.42 

100  to  150 

85  to     125 

63  8 

U/2 

2 

4 

3 

71/2 

5 

6 

.51 

100  to  150 

100  to    150 

7 

U/2 

2 

4 

3 

7l/2 

41/2 

10 

.69 

75  to  125 

100  to    170 

63/8 

U/2 

2 

4 

3 

9 

51/4 

10 

.93 

75  to  125 

135  to    230 

71/2 

2 

21/2 

4 

3 

10 

6 

10 

1.22 

75  to  125 

180  to    300 

81/2 

2 

21/2 

5 

4 

10 

7 

10 

1.66 

75  to  125 

245  to    410 

97/8 

2 

21/2 

6 

5 

12 

7 

10 

1.66 

75  to  125 

245  to    410 

97/8 

21/2 

3 

6 

5 

14 

7 

10 

1.66 

75  to  125 

245  to    410 

97/8 

21/2 

3 

6 

5 

12 

81/2 

10 

2.45 

75  to  125 

365  to    610 

12 

21/2 

3 

6 

5 

14 

81/2 

10 

2.45 

75  to  125 

365  co    610 

12 

21,2 

3 

6 

5 

16 

81/2 

10 

2.45 

75  to  125 

365  to    610 

12 

21/2 

3 

6 

5 

181/2 

81/2 

10 

2.45 

75  to  125 

365  to    610 

12 

3 

31/2 

6 

5 

20 

81/2 

10 

2.45 

75  to  125 

365  to    610 

12 

4 

5 

6 

5 

12 

101/4 

10 

3.57 

75  to  125 

530  to    890 

141/4 

21/2 

3 

8 

7 

14 

101/4 

10 

3.57 

75  to  125 

530  to    890 

141/4 

21/2 

3 

8 

7 

16 

101/4 

10 

3.57 

75  to  125 

530  to    890 

141/4 

21/2 

3 

8 

7 

181/2 

101/4 

10 

3.57 

75  to  125 

530  to    890 

141/4 

3 

31/2 

8 

7 

20 

101/4 

10 

3.57 

75  to  125 

530  to    890 

141/4 

4 

5 

8 

7 

14 

12 

10 

4.89 

75  to  125 

730  to  1220 

17 

21/2 

3 

10 

8 

16 

12 

10 

4.89 

75  to  125 

730  to  1220 

17 

21/2 

3 

10 

8 

181/2 

12 

10 

4.89 

75  to  125 

730  to  1220 

17 

3 

31/2 

10 

8 

20 

12 

10 

4.89 

75  to  125 

730  to  1220 

17 

4 

5 

10 

8 

181/2 

14 

10 

6.66 

75  to  125 

990  to  1660 

193/4 

3 

31/2 

12 

10 

20 

14 

10 

6.66 

75  to  125 

990  to  1660 

193/4 

4 

5 

12 

10 

17 

10 

15 

5.10 

50  to  100 

510  to  1020 

14 

3 

31/2 

8 

7 

20 

12 

15 

7.34 

50  to  100 

730  to  1460 

17 

4 

5 

12 

10 

20 

15 

15 

11  47 

50  to  100 

1145  to  2290 

21 

25 

15 

15 

11.47 

50  to  100 

1145  to  2290 

21 

Speed  of  Piston.  —  A  piston  speed  of  100  feet  per  minute  is  commonly 
assumed  as  correct  in  practice,  but  for  short-stroke  pumps  this  gives  too 
high  a  speed  of  rotation,  requiring  too  frequent  a  reversal  of  the  valves. 
For  long-stroke  pumps,  2  feet  and  upward,  this  speed  may  be  consider- 
ably exceeded,  if  valves  and  passages  are  of  ample  area. 


792 


PUMPS  AND   PUMPING  ENGINES. 


Number  of  Strokes  Required  to  Attain  a  Piston  Speed  from  50  to 

125  Feet  per  Minute  for  Pumps  Having  Strokes 

from  3  to  18  Inches  in  Length. 


Speed  of 
Piston,  in 
Feet  per 
Min. 

Length  of  Stroke  in  Inches. 

3 

4 

5 

6 

7 

8 

10  |  12 

15 

18 

Number  of  Strokes  per  Minute. 

50 

200 

150 

120 

100 

86 

75 

60 

50 

40 

33 

55 

220 

165 

132 

110 

94 

82.5 

66 

55 

44 

37 

60 

240 

180 

144 

120 

103 

90 

72 

60 

48 

40 

65 

260 

195 

156 

130 

111 

97.5 

78 

65 

52 

43 

70 

280 

210 

168 

140 

120 

105 

84 

70 

56 

47 

75 

300 

225 

180 

150 

128 

112.5 

90 

75 

60 

50 

80 

320 

1  240 

192 

160 

137 

120 

96 

80 

64 

53 

85 

340 

255 

204 

170 

146 

127.5 

102 

85 

68 

57 

90 

360 

270 

216 

180 

154 

135 

108 

90 

72 

60 

95 

380 

285 

228 

190 

163 

142.5 

114 

95 

76 

63 

100 

400 

300 

240 

200 

171 

150 

120 

100 

80 

67 

105 

420 

315 

252 

210 

180 

157.5 

126 

105 

84 

70 

110 

440 

330 

264 

220 

188 

165 

132 

110 

88 

73 

115 

460 

345 

276 

230 

197 

172.5 

138 

115 

92 

77 

120 

480 

360 

288 

240 

206 

180 

144 

120 

96 

80 

125 

500 

375 

300 

250 

214 

187.5 

150 

125 

100 

83 

Underwriters'  Pumps  —  Standard  Sizes. 

(National  Board  of  Fire  Underwriters,  1908.) 


Pump  Sizes,  In. 

Capacity  at  100  Lb. 
at  Pump. 

Boiler  Power 
Required. 

Full  Speed. 

Steam 

No.  of 

Nomi- 
nal 

Actual 

Pfllc 

Horse- 

Pres- 
sure 

Revs. 

Piston 
Speed, 

s        &       J* 

1  V2-In. 

Gals. 

Power. 

at 

per 

Ft. 

J         g        2 

Streams  . 

per 

Min 

Pump, 

Min. 

per 

CO                ^              CO 

Min. 

Lb. 

Min. 

14       X  7       XI2 
14       X  71/4X12 

[TWO] 

500 

j    483! 
1    520  \ 

100 

40 

70 

140 

16       X  9       X12 

Three 

750 

806 

115 

45 

70 

140 

18       X20       X12 
18V2X101/4X12 
20       X12       X16 

|  Four  | 
Six 

1000 
1500 

j    999) 
1  1050  f 
1655 

150 
200 

45 

50 

70 
60 

140 
160 

The  standard  allowance  for  a  good  1 1/8-in.  (smooth  nozzle)  fire- 
stream  is  250  gal.  per  minute. 

FIston  Speed  of  Pumping-engines.  —  (John  Birkinbine,  Trans.  A.  7. 
M.  E.,  v.  459.)  —  In  dealing  with  such  a  ponderous  and  unyielding  sub- 
stance  as  water  there  are  many  difficulties  to  overcome  in  making  a  pump 
work  with  a  high  piston  speed.  The  attainment  of  moderately  high  speed 
is,  however,  easily  accomplished.  Well-proportioned  pumping-engines  of 
large  capacity,  provided  with  ample  water-ways  and  properly  constructed 
valves,  are  operated  successfully  against  heavy  pressures  at  a  speed  of 
250  ft.  per  minute,  without  "thug,"  concussion,  or  injury  to  the  appara- 
tus, and  there  is  no  doubt  that  the  speed  can  be  still  further  increased. 

Speed  of  Water  through  Valves.  —  If  areas  through  valves  and 
water  passages  are  sufficient  to  give  a  velocity  of  250  ft.  per  min.  or  less, 
they  are  ample.  The  water  should  be  carefully  guided  and  not  too 
abruptly  deflected.  (F.  W.  Dean,  Eng.  News,  Aug.  10,  1893  ) 

Boiler-feed  Pumps.  —  Practice  has  shown  that  100  ft.  of  piston  speed 
per  minute  is  the  limit,  if  excessive  wear  and  tear  is  to  be  avoided. 

The  velocity  of  water  through  the  suction-pipe  must  not  exceed  200  ft. 
per  minute,  else  the  resistance  of  the  Suction  is  too  great, 


PUMPS  AND   PUMPING   ENGINES.  793 

""  Trie  approximate  size  of  suction-pipe,  where  the  length  does  not  exceed 
25  ft.  and  there  are  not  more  than  two  elbows,  may  be  found  as  follows: 

7/io  of  the  diameter  of  the  cylinder  multiplied  by  1/100  of  the  piston 
speed  in  feet.  For  duplex  pumps  of  small  size,  a  pipe  one  size  larger  is 
usually  employed.  The  velocity  of  flow  in  the  discharge-pipe  should  not 
exceed  500  ft.  per  minute.  The  volume  of  discharge  and  length  of  pipe 
vary  so  greatly  in  different  installations  that  where  the  water  is  to  be 
forced  more  than  50  ft.  the  size  of  discharge-pipe  should  be  calculated 
for  the  particular  conditions,  allowing  no  greater  velocity  than  500  ft. 
per  minute.  The  size  of  discharge-pipe  is  calculated  in  single-cylinder 
pumps  from  250  to  400  ft.  per  minute.  Greater  velocity  is  permitted  in 
the  larger  pipes. 

In  determining  the  proper  size  of  pump  for  a  steam-boiler,  allowance 
must  be  made  for  a  supply  of  water  sufficient  for  the  maximum  capacity 
of  the  boiler  when  over  driven,  with  an  additional  allowance  for  feeding 
water  beyond  this  maximum  capacity  when  the  water  level  in  the  boiler 
becomes  low.  The  average  run  of  horizontal  tubular  boilers  will  evapor- 
ate from  2  to  3  Ibs.  of  water  per  sq.  ft.  of  heating-surface  per  hour,  but 
may  be  driven  up  to  6  Ibs.  if  the  grate-surface  is  too  large  or  the  draught 
too  great  for  economical  working. 

Pump- Valves.  —  A.  F.  Nagle  (Trans.  A.  S.  M.  E.,  x.  521)  gives  a 
number  of  designs  with  dimensions  of  double-beat  or  Cornish  valves 
used  in  large  pumping-engines,  with  a  discussion  of  the  theory  of  their 
proportions.  Mr.  Nagle  says:  There  is  one  feature  in  which  the  Cornish 
valves  are  necessarily  defective,  namely,  the  lift  must  always  be  quite 
large,  unless  great  power  is  sacrificed  to  reduce  it.  A  small  valve  pre- 
sents proportionately  a  larger  surface  of  discharge  with  the  same  lift  than 
a  larger  valve,  so  that  whatever  the  total  area  of  valve-seat  opening,  its 
full  contents  can  be  discharged  with  less  lift  through  numerous  small  valves 
than  with  one  large  one.  See  also  Mr..Nagle's  paper  on  Punip  Valves  and 
Valve  Areas,  Trans.  A.  S.  M.  E.,  1909. 

Henry  R.  Worthington  was  the  first  to  use  numerous  small  rubber 
valves  in  preference  to  the  larger  metal  valves.  These  valves  work  well 
under  all  the  conditions  of  a  city  pumping-engine.  A  volute  spring  is 
generally  used  to  limit  the  rise  of  the  valve. 

In  the  Leavitt  high-duty  sewerage-engine  at  Boston  (Am.  Machinist, 
May  31,  1884),  the  valves  are  of  rubber,  3/4  inch  thick,  the  opening  in 
valve-seat  being  13 1/2X4 1/2  inches.  The  valves  have  iron  face  and 
back-plates,  and  form  their  own  hinges. 

The  large  pumping  engines  at  the  St.  Louis  water  works  have  rub* 
ber  valves  3V2  in.  outside  diam.  There  are  seven  valve  cages  in  each 
of  the  suction  and  discharge  diaphragms,  each  cage  having  28  valves. 
The  aggregate  free  area  of  196  valves  is  7.26  sq.  ft.,  the  area  of  one 
plunger  being  6.26  sq.  ft.  The  suction  and  discharge  pipes  are  each 
36  in.  diam.,  =  7.07  sq.  ft.  area.  (Bull.  No.  1609,  Allis-Chalmers  Co. 
Such  liberal  proportions  of  valves  are  found  usually  only  in  the  highest 
grade  of  large  high-duty  engines.  In  small  and  medium  sized  pumps 
a  valve  area  equal  to  one-third  the  plunger  area  is  commonly  used.) 

The  Worthington  "High-Duty"  Pumping  Engine  dispenses  with  a 
fly-wheel,  and  substitutes  for  it  a  pair  of  oscillating  hydraulic  cylinders, 
which  receive  part  of  the  energy  exerted  by  the  steam  during  the  first 
half  of  the  stroke,  and  give  it  out  in  the  latter  half.  For  description  see 
catalogue  of  H.  R.  Worthington,  New  York.  A  test  of  a  triple  expan- 
sion condensing  engine  of  this  type  is  reported  in  Eng.  News,  Nov.  29, 

1904.  Steam  cylinders  13,  21,  34  ins.;  plungers  30  in.,  stroke  25  in. 
Steam  pressure,  124  Ibs.     Total  head,  79  ft.;  capacity,  14,267,000  gal. 
in  24  hrs.     Duty  per  million  B.T.U.,  102,224,000  ft.-lbs. 

The  d'Auria  Pumping  Engine  substitutes  for  a  fly-wheel  a  compen- 
sating cylinder  in  line  with  the  plunger,  with  a  piston  which  pushes  water 
to  and  fro  through  a  pipe  connecting  the  ends  of  the  cylinder.  It  is  built 
by  the  Builders'  Iron  Foundry,  Providence,  R.  I. 

A  72,000,000-gallon  Pumping  Engine  at  the  Calf  Pasture  Station  of 
the  Boston  Main  Drainage  Works  is  described  in  Eng.  News,  July  6. 

1905.  It  has  three  cylinders,  18V2,  33  and  523/4  ins.,  and  two  plungers, 
60-in.  diam.;  stroke  of  all,  10  ft.     The  piston-rods  of  the  two  smaller 
cylinders  connect  to  one  end  of  a  walking  beam  and  the  rod  of  the  third 
cylinder  to  the  other.     Steam  pressure  185  Ibs.  gauge;  revolutions  per 
niin.  17:  static  head  37  to  43  ft.    Suction  valves  128;  ports,  4  X  161/4  in.; 


794 


PUMPS   AND    PUMPING   ENGINES. 


total  port  area  8576  sq.  in.  Delivery  valves,  96;  ports,  4  X 1G3/4  to  203/4 
in.;  total  port  area  7215  sq.  in.  The  valves  are  rectangular,  rubber  flaps, 
backed  and  faced  with  bronze  and  weighted  with  lead.  They  are  set  with 
their  longest  dimension  horizontal,  on  ports  which  incline  about  45°  to  the 
horizontal.  At  17  r.p.m.  the  displacement  is  72,000,000  gallons  in  24  hours. 
The  Screw  Pumping  Engine  of  the  Kinnickinick  Flushing  Tunnel, 
Milwaukee,  has  a  capacity  of  30,000  cubic  feet  per  minute  (=  323,000,000 
gal.  in  24  hrs.)  at  55  r.p.m.  The  head  is  31/2  ft.  The  wheel  12.5  ft. 
diam.,  made  of  six  blades,  revolves  in  a  casing  set  in  the  tunnel  lining. 
A  cone,  6  ft.  diam.  at  the  base,  placed  concentric  with  the  wheel  on 
the  approach  side  diverts  the  water  to  the  blades.  A  casing  beyond 
the  wheel  contains  stationary  deflector  blades  which  reduce  the  swirling 
motion  of  the  water  (Allis-Chalmers  Co.,  Bulletin  No.  1610).  The  two 
screw  pumping  engines  of  the  Chicago  sewerage  system  have  wheels 
143/4  ft.  diam.,  consisting  of  a  hexagonal  hub  surmounted  by  six  blades, 
and  revolving  in  cylindrical  casings  16  ft.  long,  allowing  1/4  in.  clearance 
at  the  sides.  The  pumps  are  driven  by  vertical  triple-expansion  engines 
with  cylinders  22,  38  and  62  in.  diam.,  and  42  in.  stroke. 

Finance  of  Pumping  Engine  Economy. — A  critical  discussion  of 
the  results  obtained  by  the  Nordberg  and  other  high-duty  engines  is 
printed  in  Eng.  News,  Sept.  27,  1900.  It  is  shown  that  the  practical 
question  in  most  cases  is  not  how  great  fuel  economy  can  be  reached, 
but  how  economical  an  engine  it  will  pay  to  install,  taking  into  consid- 
eration interest,  depreciation,  repairs,  cost  of  labor  and  of  fuel,  etc. 
The  following  table  is  given,  showing  that  with  low  cost  of  fuel  and 
labor  it  does  not  pay  to  put  in  a  very  high  duty  engine.  Accuracy  is 
not  claimed  for  the  figures;  they  are  given  only  to  show  the  method 
of  computation  that  should  be  used,  and  to  show  the  influence  of  different 
factors  on  the  final  result. 


TABULAR  STATEMENT  OP  TOTAL  ANNUAL  COST  OF   PUMPING  WITH  AN 

800-H. P.  ENGINE,  AS  INFLUENCED  BY  VARYING  DUTY  OF  ENGINE, 

VARYING  PRICE  OF  FUEL,  AND  VARYING  TIME  OF  OPERATION. 


Duty  per  million  B.T.U. 

First  cost: 
Engine               .       

50. 
$24,000 
30.00 
27,000 
51,000 

1,440 
2,160 
3,600 
6,022 

17,280 
23,040 
28,800 

25,920 
34,560 
43,200 

26,902 
32,662 
38,422 

35,522 

44.IH2 

J2$l 

100. 
$48,000 
60.00 
13,500 
61,500 

2,880 
1,080 
3,960 
6,022 

8,640 
11,520 
14,400 

12,960 
17,280 
21,600 

18,622 
21,502 
24,382 

22,942 
27,262 
31,382 

120. 
$68,000 
85.00 
11,250 
79,250 

4,080 
900 
4,980 
7,655 

7,200 
9,600 
12,400 

10,800 
14,400 
18,600 

19,835 
22,235 
25,035 

23,435 
27,033 
31,235 

150. 
$118,000 
147.50 
9,000 
127,000 

7,080 
720 
7,800 
9,307 

5,760 
7,680 
9,600 

8,640 
11,520 
14,400 

22,867 
24,787 
26,707 

25,747 
28,627 
31,507 

180. 
$148,000 
185.00 
7,500 
155,500 

8,880 
600 
9,480 
10,220 

4,800 
6,400 
8,000 

7,200 
9,600 
12,000 

24,500 
25,100 
27,700 

26,900 
29,300 
31,700 

Engine  per  H  P 

Boilers  economizers     .... 

Engine  and  boilers  .%.  .  . 
Int.  and  depreciation: 
On  engine  at  6%  

Boilers  8% 

Total               ..   

Labor  per  annum 

Fuel  cost: 
4,000  hrs.  per  yr.: 
$3  00  per  ton  

4  00  per  ton    .       .   .   ....... 

5  00  per  ton  

6,000  hrs.  per  yr.: 
$3  00  per  ton      

4  00  per  ton 

5  00  per  ton    

Total  annual  cost: 
4,000  hrs.  per  yr.: 
Coal  $3  per  ton,  

4  per  ton 

5  per  ton  ,  

6.000  hrs,  per  yr. 
CoaJi  $3  per  ton.  ,.,,.,,,,.,,. 

4  per  ton,,,  ,,,,,,,».,. 

5  per  ton  

PUMPS  AND   PUMPING   ENGINES. 


795 


Cost  of  Electric  Current  for  Pumping  1000  Gallons  per  Minute 

100  ft.  High.     (Theoretical  H.P.  with  100%  efficiency  = 

100,000  -3-  3958.9  =  25.259  H.P.) 

Assume  cost  of  current  =  1  cent  per  K.W.  hour  delivered  to  the  motor- 
efficiency  of  motor  =  90%;  mechanical   efficiency  of  triplex  pumps  =' 
SJ%;  of  centrifugal  pumps  =  72%;  combined  efficiency,  triplex  pumps, 
72%;  centrifugal,  64.8%.     1  K.W.  =  1.34  electrical  H.P.  on  wire 

Triplex,  1.34  X  0.72  =  0.9648  pump  H.P.;    X  33,000=  31  ,'838  ft  -Ibs 
per  mm. 

Centrifugal,   1.34  X  0.648  =  0.86382  pump  H.P.;    X  33,000  =  28654 
ft  .-Ibs.  per  min. 

1000  gallons  100  ft.  high  =  833,400  ft  .-Ibs.  per  min 

31'838  =  26-!763    K.W.  X  8760    hours   per   year 


x, 

X 


, 

$2293.04. 


"  28'655  =  29-0840 


x  876°  hours 


For  100%  efficiency,  $2293.04  X  0.72  =  $1650.00.  For  any  other  effi- 
ciency, divide  $1650.00  by  the  efficiency.  For  any  other  cost  per  K  W 
hour,  in  cents,  multiply  by  that  cost. 


Cost  of  Fuel  per  Year 
100  Ft. 


for  Pumping  1,000  Gallons  per  Minute 
High  by  Steam  Pumps. 


0, 

100%  Effy.        90% 

(3) 

(4) 

(5) 

(6) 

(7) 

10. 

198. 

178.2 

142.56 

0.5846 

0.42090 

153.63 

460.89 

11.88 

166.667 

150. 

120. 

0.6945 

0.50004 

182.51 

547.53 

14. 

141.433 

127.87 

101.83 

0.8184 

0.58926 

215.08 

645.24 

14.256 

138.889 

125. 

100. 

0.8334 

0.60005 

219.02 

657.06 

15. 

132. 

118.8 

95.04 

0.8769 

0.63125 

230.44 

691.32 

16. 

123.75 

111.375 

89.10 

0.9354 

0.67344 

245.80 

737.40 

17.82 

111.111 

100. 

80. 

1.0417 

0.75006 

273.77 

821.31 

20. 

99. 

89.1 

71.28 

1.1692 

0.84180 

307.26 

921.78 

23.76 

83.333 

75. 

60. 

1.3890 

1  .00008 

365.03 

1095.09 

30. 

66. 

59.4 

47.52 

1.7538 

1.26270 

460.89 

1382.67 

35.64 

55.556 

50. 

40. 

2.0835 

1.50012 

547.54 

1642.62 

40. 

49.5 

44.5 

35.64 

2.3384 

1.68360 

614.52 

1843.56 

47.52 

41.667 

37.5 

30. 

2.7780 

2.00016 

.   730.06 

2190.18 

50. 

39.6 

35.64 

28.51 

2.9230 

2.10450 

768.15 

2304.45 

a 

b 

c 

d 

e 

f 

g 

h 

(1)  Lbs.  steam  per  I. H.P.  per  hour. 

(2)  Duty  million  ft.-lbs.  per  1000  Ibs.  steam,  &,.  100%  effy.,  c,  90%. 

(3)  Duty  per  100  Ibs.  coal,  90%  effy.,  8  Ibs.  steam  per  Ib.  coai. 

(4)  Lbs.  coal  per  min.  for  1000  gals.,  100  ft.  high. 

(5)  Tons,  2000  Ibs.  in  24  hours. 

(6)  Tons  per  year,  365  days. 

(7)  Cost  of  fuel  per  year  at  $3.00  per  ton. 

Factors  for  calculation:  fr  =  1980  •*•  a;  c  =  b  X  0.9;  d  =»  c  X  0.8, 
e  =  8334  -^  100  d;  /  =  e  X  0.72;  g  =  f  X  365;  h  =  g  X  3. 

For  any  other  cost  of  coal  per  ton,  multiply  the  figures  in  the  last 
column  by  the  ratio  of  that  cost  to  $3.00. 

Cost  of  Pumping   1000  Gallons  per  Minute  100  ft.  High  by 
Gas  Engines. 

Assume  a  gas  engine  supplied  by  an  anthracite  gas  producer  using  1.5 
Ibs.  of  coal  per  brake  H.P.  hour,  coal  costing  $3.00  per  ton  of  2000  Ibs. 

Efficiency  of  triplex  pump  80%,  of  centrifugal  pump,  72%. 

1*000  gals,  per  min.  100  ft.  high  =  833,400  ft.-lbs.  per  min.  -f.  33,000 
=  25.2545  H.P. 

Fuel  cost  per  brake  H.P.  hour  1 .5  Ibs.  X  300  cents  -f-  2000  =  0.225 
centX  8760  hours  per  year-  $19.71  per  H.P.  X  25.2545=  $497.766  for 
100%  efficiency. 

For  80%  effy.,  $622.21 ;  for  72%  effy.,  $691.34;  or  the  same  as  the  cost 
with  a  steam  pumping  engine  of  95,000,000  foot-pounds  duty  per  100 
Ibs.  of  coal. 


796 


PUMPS   AND    PUMPING 


Cost  of  Fuel  for  Electric  Current. 

Based  on  10  Ibs.  steam  per  T.H.P.  hour,  8  Ibs.  steam  per  Ib.  coal  or 
1.25  Ibs.  coal  per  I.H.P.  per  hour.  (Electric  line  loss  not  included.) 

Efficiency  o^  engine  0.90,  of  generator  0.90,  combined  effv.  0.81 

I.H.P.  =  0.746  K.W.,  0.746  X  0.81  =  0.6426  K.W.  on  wire  for'lO  Ibs 
steam.  Reciprocal  =  16.5492  Ibs.  steam  per  K.W.  hour.  8  Ibs.  steam 
per  Ib.  coal  =  2.06865  Ibs.  coal,  at  $3.00  per  ton  of  2,000  Ibs.  =  0.3103 
cents  per  K.W.  hour. 

Lbs.  steam  per  I.H.P.  hr.  — 

12  14  16  18  20  30  40 

Fuel  cost,  cents  per  K.W.  hr.  — 

0.3724      0.4344       0.4965     0.5585       0.6206       0.9309        1.2412 

CENTRIFUGAL,  PUMPS. 

Theory  of  Centrifugal  Pumps. — Bulletin  No.  173  of  the  TJniv.  of 
Wisconsin,  1907,  contains  an  investigation  by  C.  B.  Stewart  of  a  6-in. 
centrifugal  pump  which  gave  a  maximum  efficiency,  under  the  best 
conditions  of  load,  of  only  32%,  together  with  a  discussion  of  the  general 
theory  of  M.  Combe,  1840,  which  has  been  followed  by  Weisbach,  Ran- 
kine,  and  Unwin.  Mr.  Stewart  says  that  the  theory  of  the  centrifugal 
pump,  at  the  times  of  these  writers,  seemed  practically  settled,  but  it 
was  found  later  that  the  pump  did  not  follow  the  theoretical  laws  de-^ 
rived,  and  the  subject  is  still  open  for  investigation.  The  theoretical 
head  developed  by  the  impeller  can  be  stated  for  the  condition  of  impend- 
ing delivery,  but  as  soon  as  flow  begins  the  ordinary  theory  does  not 
seem  to  apply/  Experiment  shows  that  the  main  difficulty  to  be  over- 
come in  order  to  secure  high  efficiency  with  the  centrifugal  pump  is  in 
providing  some  means  of  transforming  the  portion  of  the  energy  which 
exists  in  the  kinetic  form,  at  the  outlet  of  the  impeller,  to  the  pressure 
form,  or  of  reducing  the  loss  of  head  in  the  pump  casing  to  a  minimum. 
The  theoretical  head  for  impending  delivery  is  V2+g,  while  experiment 
shows  that  the  maximum  actual  head  approaches  V2-*-  2g  as  a  limit. 
As  the  flow  commences  each  pound  of  water  discharged  will  possess  the 
kinetic  energy  Vz+2g  in  addition  to  its  pressure  energy.  To  secure 
high  efficiency  some  means  must  be  found  of  utilizing  this  kinetic  energy. 
The  use  of  a  free  vortex  or  whirlpool,  surrounding  the  impeller,  and  this 
surrounded  by  a  suitable  spiral  discharge  chamber,  is  practically  accepted 
as  one  means  of  utilizing  the  energy  of  the  velocity  head.  Guide  vanes 
surrounding  the  impeller  also  provide  a  means  of  changing  velocity  head 
to  pressure  head,  but  the  comparative  advantage  of  these  two  means 
cannot  be  stated  until  more  experimental  data  are  obtained. 

The  catalogue  of  the  Alberger  Pump  Co.,  1908,  contains  the  following: 

It  was  not  until  the  year  1901  that  the  centrifugal  pump  was  shown  to 
be  nothing  more  or  less  than  a  water  turbine  reversed,  and  when  designed 
on  similar  lines  was  capable  of  dealing  with  heads  as  great,  and  with 
efficiencies  as  good,  as  could  be  obtained  with  the  turbines  themselves. 
Since  this  date  great  progress  has  been  made  in  both  the  theory  and 
design,  until  now  it  is  quite  possible  to  build  a  pump  for  any  reasonable 
conditions  and  to  accurately  estimate  the  efficiency  and  other  charac- 
teristics to  be  expected  during  actual  operation. 

The  mechanical  power  delivered  to  the  shaft  of  a  centrifugal  pump  by 
the  prime  mover  is  transmitted  to  the  water  by  means  of  a  series  of 
radial  vanes  mounted  together  to  form  a  single  member  called  the  im- 
peller, and  revolved  by  the  shaft.  The  water  is  led  to  the  inner  ends  of 
the  impeller  vanes,  which  gently  pick  it  up  and  with  a  rapidly  accelerat- 
ing motion  cause  it  to  flow  radially  between  them  so  that  upon  reaching 
the  outer  circumference  of  the  impeller  the  water,  owing  to  the  velocity 
and  pressure  acquired,  has  absorbed  all  the  power  transmitted  to  the 
pump  shaft.  The  problem  to  be  solved  in  impeller  design  is  to  obtain 
the  required  velocity  and  pressure  with  the  minimum  loss  in  shock  and 
friction.  Since  the  energy  of  the  water  on  leaving  the  pump  is  required  to 
be  mostly  in  the  form  of  pressure,  the  next  problem  is  to  transform  into 
pressure  the  kinetic  energy  of  the  water  due  to  its  velocity  on  leaving  the 
impeller  and  furthermore  to  accomplish  this  with  the  least  possible  loss. 

The  next  consideration  in  impeller  design  is  the  proportions  of  the 
vanes  and  the  water  passages,  and  to  properly  solve  this  problem  an 


CENTRIFUGAL  PUMPS.  797 

extensive  use  of  intricate  mathematical  formulse  is  necessary  in  addition 
to  a  wide  knowledge  of  the  practical  side  of  the  question.  It  is  possible 
to  obtain  the  same  results  as  to  capacity  and  head  with  practically  an 
infinite  number  of  different  shapes,  each  of  which  gives  a  different  effi- 
ciency as  well  as  other  varied  characteristics.  The  change  from  velocity 
to  pressure  is  accomplished  by  slowing  down  the  speed  of  the  water  in  an 
annular  diffusion  space  extending  from  the  impeller  to  the  volute  casing 
itself  and  so  designed  that  there  is  the  least  loss  from  eddies  or  shock. 
It  is  necessary  that  this  change  shall  take  place  gradually  and  uniformly, 
as  otherwise  most  of  the  velocity  would  be  consumed  in  producing  eddies. 
With  a  proper  design  of  the  diffusion  space  and  volute  it  is  possible  to 
transform  practically  the  whole  of  the  velocity  into  pressure  so  that  the 
loss  from  this  source  may  be  very  small. 

It  is  necessary  also  to  furnish  a  uniform  supply  of  water  to  all  parts  of 
the  inlet  or  suction  opening  of  the  impeller,  for  unless  all  the  impeller 
vanes  receive  the  same  quantity  of  water  at  their  inner  edges,  they 
cannot  deliver  an  equal  quantity  at  their  outer  edges,  and  this  would 
seriously  interfere  with  the  continuity  of  the  flow  of  water  and  the  sue-  . 
cessful  operation  of  the  pump. 

Relation  of  the  Peripheral  Speed  to  the  Head. —  For  constant  speed 
the  discharge  of  a  centrifugal  pump  for  any  lift  varies  with  the  square 
root  of  the  difference  between  the  actual  lift  and  the  hydrostatic  head 
created  by  the  pump  without  discharge.  If  any  centrifugal  pump  con- 
nected to  a  source  of  supply  and  to  a  discharge  pipe  of  considerable 
height  is  put  in  revolution,  it  will  be  found  that  it  is  necessary  to  main- 
tain a  certain  peripheral  runner  speed  to  hold  the  water  1  ft.  high  without 
discharge,  and  that  for  any  other  height  the  requisite  speed  will  be  very 
nearly  proportional  to  the  square  root  of  the  height. 

Experiments  prove  that  the  peripheral  speed  in  ft.  per  min.  neces- 
sary to  lift  water  to  a  given  height  with_yanes  of  different  forms  is  approx; 
Imately  as  follows:  a,  481  \/h\  b,  554  \/h;  c,  610  ^h\  d,  780  Vh ;  e,  394  Vft. 
a  is  a  straight  radial  vane,  b  is  a  straight  vane  bent  backward,  c  is  a  curved 
vane,  its  extremity  making  an  angle  of  27°  with  a  tangent  to  the  impeller, 
d  is  a  curved  vane  with  an  angle  of  18°,  e  is  a  vane  curved  in  the  reverse 
direction  so  that  outer  end  is  radial.  ^ 

Applying  the  above  formula,  speed  ft.  per  min.  ^coeff.  X  */h,  to  the 
design  of  Mr.  Clifford,  gives  60  X  75.05  =  C  X  ^85,  whence  C  =  488. 
The  vane  angle  was  12°.  It  is  evident  that  the  value  of  C  depends  on 
other  things  than  the  shape  or  angle  of  the  vanes,  such  as  smoothness  of 
the  vanes  and  other  surfaces,  shape  and  area  of  the  diffusion  vanes,  and 
resistance  due  to  eddies  in  the  pump  passages. 

The  coefficient  varies  with  the  shape  of  the  vanes;  this  means  that 
different  speeds  are  necessary  to  hold  water  to  the  same  heights  witli 
these  different  forms  of  vanes,  and  for  any  constant  speed  or  lift  there 
must  be  a  form  of  vane  more  suitable  than  any  other.  It  would  seem  at 
first  glance  that  the  runner  which  creates  a  given  hydrostatic  head  with 
the  least  peripheral  velocity  must  be  the  most  efficient,  but  practically 
it  is  apparent  from  tests  that  the  curvature  of  the  vanes  can  be  designed 
to  suit  the  speed  and  lift  without  materially  lowering  the  efficiency. 
(L.  A.  Hicks,  Eng.  News,  Aug.  9,  1900.) 

The  quotient  of  the  radial  velocity  of  flow  in  a  centrifugal  pump 
divided  by  the  peripheral  velocity  is  a  constant  C.  By  plotting  effi- 
ciency curves  for  various  speeds  in  the  discharge-efficiency  diagram, 
it  is  found  that  the  points  of  maximum  efficiency  of  the  various  curves 
lie  nearly  in  a  straight  line,  hence  the  constant  C  varies  but  little  with 
the  speed.  Examination  of  the  data  from  a  large  number  of  pumps 
of  various  designs  shows  that  high  speeds  are  consistent  with  good 
efficiency,  and  that  the  best  values  for  C  lie  between  the  limits  of  0.12 
and  0.15.  There  is  no  advantage  in  the  use  of  excessively  wide  im- 
pellers.— (N.  W.  Akimoff,  Jour.  Franklin  Institute,  May,  1911.) 

Design  of  a  Four-stage  Turbine  Pump.  —  C.  W.  Clifford,  in  Am. 
Mach.,  Oct.  17,  1907,  describes  the  design  of  a  four-stage  pump  of  a 
capacity  of  2300  gallons  per  minute  =  5.124  cu.  ft.  per  sec.  Following 
is  an  abstract  of  the  method  adopted.  The  total  head  was  1000  ft. 
Three  sets  of  four-stage  pumps  were  used  at  elevations  of  16,  332,  and 
666  ft.,  the  discharge  of  the  first  being  the  suction  of  the  second,  and  so  on. 


798  PUMPS  AND   PUMPING  ENGINES. 

The  speed  of  the  motor  shaft  is  850  r.p.m.  This  gives,  for  the  diameter 
of  the  impeller,  d  =  12  X  60  X  75.05  -f-  850  TT  =  20.24  in.  Circumfer- 
ence C  =  63.6  in;  h  =  head  for  each  impeller,  in  ft. 

V  =  peripheral  speed  =  1.015  ^2  gh  =  75.05  ft.  per  sec.,  1.015  being 
an  assumed  coefficient.  The  velocity  V  is  divided  into  two  parts  by  the 
formula  V\=V  —  Vz;  Vz  =  2 gh  •*•  2  V;  whence  Vi  =  38.65  ft.  per  sec. 
This  is  the  tangential  component  of  the  actual  velocity  of  the  water  as  it 
leaves  the  vane  of  the  impeller.  The  radial  component,  or  the  radial 
velocity,  was  taken  approximately  at  8  ft.  per  sec.;  8  •*•  38.65  =  tang,  of 
11°  42',  the  calculated  angle  between  the  vane  and  a  tangent  at  the 
periphery.  Taking  this  at  12°  gives  tang.  12°  X  38.65  =  8/215  ft.  per  sec. 
=»  radial  velocity  V.  The  outflow  area  at  the  impeller  then  is  5.124  X 
144  •+•  (8.215  X  0.85)  =  105  sq.  in.;  the  0.85  is  an  allowance  for  contrac- 
tion of  area  in  the  impeller.  The  thickness  of  the  vane  measured  on  the 
periphery  is  approximately  13/4  in.;  taking  this  into  account  the  width 
of  the  impeller  was  made  17/8in.  [105  •*•  (63.6  -  6  X  13/4)  =  1.98  in.]. 
The  Vanes  were  then  plotted  as  shown  in  Fig.  156,  keeping  the  distance 
between  them  nearly  constant  and  of  uniform  section.  Care  was  taken 
to  increase  the  velocity  as  gradually  as  possible. 

The  suction  velocity  was  9.37  ft.  per  sec.,  the  diam.  of  the  opening  being 
10  in.  This  was  increased  to  11  ft.  per  sec.  at  the  opening  of  the  im- 
peller, from  which,  after  deducting  the  area  of  the  shaft,  the  diameter,  d, 
of  the  impeller  inlet  was  found.  Three  long  and  three  short  vanes  were 
used  to  reduce  the  shock. 

The  diffusive  vanes,  Fig.  157,  were  then  designed,  the  object  being  to 
change  the  direction  of  the  water  to  a  radial  one,  and  to  reduce  the 
velocity  gradually  to  2  ft.  per  sec.  at  the  discharge  through  the  ports. 

Fig.  158  shows  a  cross-section  of  the  pump.  The  pumps  were  thor- 
oughly tested,  and  the  following  figures  are  derived  from  a  mean  curve 
of  the  results: 

Gals,  per  min..  500     1000     1500     2000     2200     2400     2500     3000     3500 

Efficiency,  %      30         51         68        78        79        78        76        61         31 

A  Combination   Single-stage  and  Two-stage  Pump,  for  low  and 

high  heads,  designed  by  Rateau,  is  described  by  J.  B.  Sperry  in  Power, 
July  13,  1909.  It  has  two  runners,  one  carried  on  the  main  driving- 
shaft,  and  the  other  on  a  hollow  shaft,  driven  from  the  main  shaft  by  a 
clutch.  It  has  two  discharge  pipes,  either  one  of  which  may  be  closed. 
When  the  hollow  shaft  is  uncoupled,  one  runner  only  is  used,  and  the 
pump  is  then  a  single-stage  pump  for  low  heads.  When  the  shafts  are 
coupled,  the  water  passes  through  both  runners,  and  may  then  be  deliv- 
ered against  a  high  head. 

Tests  of  De  Laval  Centrifugal  Pumps.— The  tables  on  pp.  800, 801  con- 
tain a  condensed  record  of  tests  of  three  De  Laval  pumps  made  by  Prof. 
J.  E.  Denton  and  the  author  in  April,  1904.  Two  of  the  pumps  were 
driven  by  De  Laval  steam  turbines,  and  the  other  one  by  an  electric 
motor.  In  the  two-stage  pump  the  small  wheel  was  coupled  direct  to 
the  high-speed  shaft  of  the  turbine,  running  at  about  20,500  r.p.m.,  and 
the  large  wheel  was  coupled  to  the  low-speed  shaft,  which  is  driven  by  the 
first  through  gears  of  a  ratio  of  1  to  10.  The  water  delivery  and  the 
duty  were  computed  from  weir  measurements,  Francis's  formula  being 
used,  and  this  was  checked  by  calibration  of  the  weir  at  different  heads 
by  a  tank,  the  error  of  the  formula  for  the  weir  used  being  less  than  1%. 
Pitot  tube  measurements  of  the  water  delivered  through  a  nozzle  were 
also  made. 

One  inch  below  the  center  of  the  nozzle  was  located  one  end  of  a  thin 
half-inch  brass  tube,  tapered  so  as  to  make  an  orifice  of  3/32  inch  diameter. 
The  other  end  of  this  tube  was  connected  to  a  vertical  glass  tube,  fastened 
to  the  wall  of  the  testing  room,  graduated  in  inches  over  a  height  of  about 
30  ft.  The  stream  of  water  issuing  from  the  nozzle  impinged  upon  the 
orifice  of  the  brass  tube,  and  thereby  maintained  a  height  of  water  In 
the  glass  tube.  This  height  afforded  a  "Pitot  Tube  Basis"  of  measure- 
ment of  the  quantity  of  water  flowing,  the  reliability  of  which  was  tested 
by  the  flow  as  determined  from  the  weir.  The  Pitot  tube  gave  the 
same  result  as  the  weir  from  the  formula  Qi  —  C  X  Area  of  Nozzle  X 
^2gh  with  a  value  of  C  varying  only  between  0.953  and  0.977  for  the 
large  nozzle,  and  between  0.942  and  0.960  for  the  small  nozzle. 


CENTRIFUGAL    PUMPS. 


799 


800 


PUMPS   AND   PUMPING   ENGINES. 


TEST  OP  STEAM  TURBINE  CENTRIFUGAL  PUMP,  RATED  AT  1700  GALS. 
PER  MIN.,  100  FT.  HEAD. 


Steam 

S 

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u 

bC 

a 

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No.  of 
Test. 

Press,  at 
the  Gover- 
nor Valve. 
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s 

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olutions 
Minute. 

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6 

190 

126 

251/4 

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47.7 

25.45 

37.43 

22.95 

45.97 

1,978 

0.481 

10 

190 

148 

251/2 

,536 

56.65 

24.42 

50.44 

34.95 

70.75 

1,958 

0617 

| 

188 

155.2 

25 

,553 

59.6 

24.06 

61.50 

44.54 

94.9 

,860 

0.747 

2 

188 

153.5 

251/4 

,547 

58.9 

24.21 

61.86 

44.55 

100.37 

,759 

0.756 

3 

188 

150.7 

251/4 

,540 

57.7 

24.33 

61.47 

43.59 

106.94 

,615 

0.755 

4 

188 

143.5 

251/2 

,549 

54.8 

24.53 

60.00 

40.72 

115.46 

,398 

0.743 

188 

161 

253/s 

,540 

47.5 

24.5 

54.47 

31.80 

125.85 

,001 

0.676 

6A 

189  5 

170 

251/2 

565 

24  9 

Shut- 

offT 

142  15 

t? 

189' 

169.5 

1  537 



45.15 

43.85 

95.14 

,87.6 

1 

189 
189 

169 
169.7 

535 

45  12 

43.82 

99.05 

753 

,538 

44.62 

42.93 

104.42 

,629 

*  The  brake  H.P.  and  the  steam  per  B.H.P.  hour  were  calculated  by  a 
formula  derived  from  Prony  brake  tests  of  the  turbine, 
t  Non-condensing. 

TEST  OF  ELECTRIC  MOTOR  CENTRIFUGAL  PUMP.     DIAM.  OF  PUMP  WHEE& 
89/32  IN.     RATED  AT  1200  GALS.  PER  MIN.  —  45  FT.  HEAD. 
2000  REVS.  PER  MIN. 


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242.5 

55.2 

17.94 

15.07 

2,006 

3.158 

10.25 

28.52 

,417 

0.680 

2.. 

242.3 

54.8 

17.80 

14.94 

1,996 

3.126 

10.67 

30.12 

,403 

0.714 

3.. 

242 

59 

19.14 

16.22 

1,996 

2.885 

11.80 

36.1 

,295 

0.728 

4.. 

242 

62.4 

20.24 

17.27 

2,005 

2.826 

12.18 

38.05 

,268 

0  706f 

5.. 

241.8 

62.9 

20.39 

17.41 

2,000 

2.525 

13.06 

45.66 

,133 

0.750 

6.. 

240.8 

66 

21.30 

18.28 

2,005 

2.504 

13.40 

47.25 

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0.733f 

7.. 

241.4 

64 

20.71 

17.71 

2,003 

2.197 

13.12 

52.7 

986 

0.742 

8.. 

239.7 

66.3 

21.30 

18.28 

1,997 

2.179 

13.15 

53.28 

978 

0.720t 

9.. 

240.9 

63.2 

20.41 

17.43 

2,007 

1.735 

11.42 

58.10 

779 

0.665f 

10.. 

242 

62 

20.11 

17.14 

2,003 

1.760 

11.71 

58.76 

790 

0.683 

11.. 

248 

34 

11.30     8.74 

2,040 

Shut-off 

68.39 

*  Brake  H.P.  calculated  from  a  formula  derived  from  a  brake  test  of 
the  motor. 

f  Tests  marked  t  were  made  with  the  pump  suction  throttled  so  as  to 
make  the  suction  equal  to  about  22  ft.  of  water  column.  In  the  other 
tests  the  suction  was  from  5,6  to  10.9  ft. 


CENTRIFUGAL  PUMPS. 


801 


TEST  OF  STEAM  TURBINE  TWO-STAGE  CENTRIFUGAL  PUMP.     RATED  AT 

250  GALS.  PER  MIN.     700  FT.  HEAD.    LARGE  PUMP  WHEEL, 

2050  R.P.M.;  SMALL  WHEEL,  20,500  R.P.M. 


Steam 

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25.25 

341 

2,104 

0.830 

135.76 

12.83 

373 

18.63 

106.2 

175 

138.3 

27.5 

24.4 

2,092 

0.799 

193.85 

17  54 

359 

181 

162.3 

27.05 

25.5 

'385 

2,074 

0.790 

288 

25.78 

354 

28.73 

68.9 

178 

173.7 

26.2 

25.5 

316 

2,056 

0.775 

358.78 

31.50 

347 

32.9 

60.2 

180 

180.3 

26 

25.3 

326 

2,027 

0.750 

420.5 

35.60 

336 

36.00 

54.9 

181 

182 

25.3 

25.25 

325 

2,001 

0.731 

494.35 

40.92 

328 

41.55 

47.7 

180 

182 

24.9 

25.35 

1,962 

0.697 

585.06 

46.19 

312 

186 

188.3 

25.5 

26.3 

'iii 

2,014 

0.664 

632.6 

47.58 

299 

47.43 

41.77 

185 

185 

30 

25.3 

331 

2,012 

0.558 

756.38 

47.81 

251 

47.67 

41.5 

185 

184 

29     ' 

26.5 

325 

2,029 

0.544 

781.4 

48.15 

244 

48.88 

40.50 

.    A  Test  of  a  Lea-Deagan  Two-Stage  Pump,  by  Prof.  J.  E.  Denton, 

is  reported  in  Eng.  Rec.,  Sept.  29,  1906.     The  pump  had  a  10-in.  suction 

and  discharge  line,  and  impellers  24  in.  diam.,  each  with  8  blades.     The 

following  table  shows  the  principal  results,  as  taken  from  plotted  curves 

of  the  tests.    The  pump  w"as  designed  to  give  equal  efficiency  at  different 

speeds. 

Gal.  per  min. 

400  800  1200  1600  2000  2400  2800  3000  3200  3400  3600  3800 
Efficiency. 
400  r.p.m.  42     61     69       75      77       77      70 

39     56     65       71      75       77    77.6     77      74*  *70'  ' 
35     50     62       68      71       74      76       77      78      78 


500 

600 

Head. 

400  r.p.m.  55 
500       "      63 


76     54 


55 


600 


53 

84 


126  127  125 


87     55 


51      47       42  34     ... 

82      78       73  67       63      58      51 

122    118     115  107     104    101      97 

The  following  results  were  obtained  under  conditions  of  maximum 
efficiency: 

400  r.p.m.         77.7%  effy.        2296  gals,  per  min. 

500       "  77.6        "  2794  "  " 

600       "  77.97      "  3235  " 


43.6  ft.  lift 
67.4 
100.7 


np 


A  High-Duty  Centrifugal  Pump. — A  45,000,000  gal.  centrifugal  punr 
at  the  Deer  Island  sewage  pumping  station,  Boston,  Mass.,  was  testea 
in  1896  and  showed  a  duty  of  95,867,476  ft.-lbs.,  based  on  coal  fired  to 
the  boilers*.  —  (Allis-Chalmers  Co.,  Bulletin  No.  1062.) 

Rotary  Pumps.  —  Pumps  with  two  parallel  geared  shafts  carrying 
vanes  or  impellers  which  mesh  with  each  other,  and  other  forms  of  posi- 
tive driven  apparatus,  in  which  the  water  is  pushed  at  a  nwderate  veloc- 
ity, instead  of  being  rotated  at  a  high  velocity  as  in  centrifugal  pumps, 
are  known  as  rotary  pumps.  They  have  an  advantage  over  recipro- 
cating pumps  in  being  valveless,  and  over  centrifugal  pumps  in  working 
under  variable  heads.  They  are  usually  not  economical,  but  when  care- 
fully designed  with  the  impellers  of  the  correct  cycloidal  shape,  like 
those  used  in  positive  rotary  blowers,  they  give  a  high  efficiency. 
They  are  especially  useful  in  handling  large  volumes  of  water  at 
beads  from  JO  to  50  feet  arid  also  as  vacuum  pumps  for  condenser^. 


802 


PUMPS   AND   PUMPING  ENGINES. 


They  are  not  well  adapted  for  lifting  small  quantities  of  water  at 
high  pressure. 

By  calibrating  the  discharge  per  revolution  and  attaching  a  revolu- 
tion counter  a  rotary  pump  may  be  used  as  a  water  meter. 

An  improvement  in  rotary  pumps  is  to  drive  the  two  impellers 
by  a  cross-compound  engine,  the  two  cylinders  of  which  are  so  set  that 
the  high-pressure  pistpn  drives  one  impeller  and  the  low-pressure  pis- 
ton the  other.  In  this  arrangement  the  transmission  of  power  from 
one  impeller  shaft  to  the  other  through  gearing  is  avoided.  (Conners- 
ville  Blower  Co.,  1915.) 

Tests  of  Centrifugal  and  Rotary  Pumps.  (W.  B.  Gregory,  Bull. 
183  U.  S.  Dept.  of  Agriculture,  1907.)  —  These  pumps  are  used  for  irri- 
gation and  drainage  in  Louisiana.  A  few  records  of  small  pumps,  giving 
very  low  efficiencies,  are  omitted.  Oil  was  used  as  fuel  in  the  boilers, 
except  in  the  pump  of  the  New  Orleans  drainage  station  No.  7  (figures  in 
the  last  column),  which  was  driven  by  a  gas-engine. 


Actual  lift  

15.5 

72.6 
127.5 
155.6 

81.7 
72  1 

16.2 
157.0 
287.4 
671.2 

42.9 
34  3 

11.2 
116.0 
147.1 
229.8 

64.2 
40  7 

30.2 
93.2 
318.0 
648.0 

49.0 
33  8 

9.5 

71.4 
76.5 
137.7 

55.6 

23.7 
68.7 
222.8 
503.9 

44.3 
33  9 

31.7 
85.6 
306.8 
452.3 

67.9 
78  ? 

6.8 
1-30.5 
98.8 
193.6 

51.0 
31  4 

31.6 
152.9 
547.9 
657.7 

83.3 
75  4 

13.4 
30.5 
46.2 
90.6 

51.0 

Disch.  cu.  ft.  per  sec..  . 
Water  horse-power  
I.H.P  

Effy.,  engine,  gearing 
and  pumps. 

Duty,  per  1000  Ibs.  stea. 

Duty,       per      million 
B.T.U.  in  fuel  

37.8 
8.16 

a,f 

18.3 
4.23 

b,g 

20.7 
4.68 

b,g 

24.2 
4.16 

b,g 

22.1 
c,  g 

17.3 
4.09 

b,g 

51.1 
9.70 

a,  g 

16.7 
3.93 

d,g 

50.1 
9.61 

a,  g 

82.4 
e.g 

Therm,  effy.  f  ronxstea. 
Kind  of  engine,   and 
pump  

.a,  Tandem  compound  condensing  Corliss;  6,  Simple  condensing  Cor- 
liss; c,  Simple  non-condensing  Corliss;  d,  Triple-expansion  condensing, 
vertical;  e,  Three-cylinder  vertical  gas-engine,  with  gas-producer,  0.85  Ib. 
coal  per  I.H.P.  per  hour;  /,  Rotary  pump;  g,  Cycloidal  rotary. 

The  relatively  low  duty  per  million  B.T.U.  is  due  to  the  low  efficiency 
of  the  boilers.  The  test  whose  figures  are  given  in  the  next  to  the  last 
column  is  reported  by  Prof.  Gregory  in  Trans.  A.  S.  M.  E.,  to  vol.  xxviii. 

DUTY  TRIALS  OF  PUMPING-ENGINES. 

A  committee  of  the  A.  S.  M.  E.  (Trans.,  xii.  530)  reported  in  1891  on  a 
standard  method  of  conducting  duty  trials.  Instead  of  the  old  unit  of 
duty  of  foot-pounds  of  work  per  1 00  Ibs.  of  coal  used,  the  committee  recom- 
mend a  new  unit,  foot-pounds  of  work  per  million  heat-units  furnished  by 
the  boiler.  The  variations  in  quantity  of  coal  make  the  old  standard  unfit 
as  a  basis  of  duty  ratings.  The  new  unit  is  the  precise  equivalent  of  100 
Ibs.  of  coal  in  cases  where  each  pound  of  coal  imparts  10,000  heat-units  to 
the  water  in  the  boiler,  or  where  the  evaporation  is  10,000  +  970.4  =  10.305 
Ibs.  of  water  from  and  at  2 1 2  °  per  pound  of  fuel.  This  evaporative  result 
is  readily  obtained  from  all  grades  of  Cumberland  or  other  semi-bitumi- 
nous coal  used  in  horizontal  return  tubular  boilers,  and,  in  many  cases, 
from  the  best  grades  of  anthracite  coal. 

The  committee  on  Power  Tests  (1915)  reaffirmed  the  new  unit,  de- 
fining it  as  follows: 

The  duty  per  million  heat-units  is  found  by  dividing  the  number  of 
foot-pounds  of  work  done  during  the  trial  by  the  total  number  of  heat- 
units  consumed,  and  multiplying  the  quotient  by  1,000,000.  The 
amount  of  work  is  found  in  the  case  of  reciprocating  pumps  by  mul- 
tiplying the  net  area  of  the  plunger  in  sq.  in.,  the  total  head  expressed 
in  pounds  per  square  inch  *  by  the  length  of  the  stroke  in  feet,  and 
the  total  number  of  single  strokes  during  the  trial ;  finally  correcting 

*  The  total  head  is  determined  by  adding  together  the  pressure 
shown  by  the  gage  on  the  force  main,  the  vacuum  shown  by  the  gage 
on -the  suction  main,  and  the  vertical  distance  between  the  center  of 
the  force-main  gage  and  the  point  where  |the  suction-gage  pipe  con- 
nects to  the  suction  main,  all  expressed  in  the  same  units  (pounds  per 
nch  or  foot).  A  pet-cock  should  l?e  attacfiec}  to  the  gage  pipe 


DUTY  TRIALS   OF  PUMPING  ENGINES.  803 

for  the  percentage  of  leakage  of  the  pump.  In  cases  where  the  water 
delivered  is  determined  by  weir  or  other  measurement,  the  work  done  is 
found  by  multiplying  the  weight  of  water  discharged  during  the  trial  by 
the  total  head  in  feet. 

The  water  noise-power  of  a  pump  is  found  by  dividing  the  num- 
ber of  foot-pounds  of  work  done  per  minute  by  33,000. 

Capacity. — The  capacity  in  gallons  per  24  hours  for  reciprocating 
pumps  in  cases  where  the  water  delivered  is  not  measured,  is  found 
by  multiplying  the  net  area  of  the  plunger  in  square  inches  by  the 
length  of  the  stroke  in  feet  (in  direct-connected  engines  the  average 
length  of  stroke);  then  by  the  number  of  single  strokes  per  minute; 
and  the  product  of  these  three  by  the  constant  74.8;  finally  correcting 
for  the  percentage  of  leakage  of  the  pump. 

Leakage  of  Pump. — The  percentage  of  leakage  is  the  percentage 
borne  by  the  quantity  of  leakage,  found  on  the  leakage  trial,  to  the 
quantity  of  water  discharged  on  the  duty  run  determined  from  plunger 
displacement. 

Leakage  Test  of  Pump. — The  leakage  of  an  inside  plunger  (the  only 
type  which  requires  testing)  is  most  satisfactorily  determined  by  making 
the  test  with  the  cylinder-head  removed.  A  wide  board  or  plank  may  be 
temporarily  bolted  to  the  lower  part  of  the  end  of  the  cylinder,  so  as  to 
hold  back  the  water  in  the  manner  of  a  dam,  and  an  opening  made  in  the 
temporary  head  thus  provided  for  the  reception  of  an  overflow-pipe. 
The  plunger  is  blocked  at  some  intermediate  point  in  the  stroke  (or,  if 
this  position  is  not  practicable,  at  the  end  of  the  stroke),  and  the  water 
from  the  force  main  is  admitted  at  full  pressure  behind  it.  The  leakage 
escapes  through  the  overflow-pipe,  and  it  is  collected  in  barrels  and 
measured.  The  test  should  be  made,  if  possible,  with  the  plunger  in 
various  positions. 

In  the  case  of  a  pump  so  planned  that  it  is  difficult  to  remove  the 
cylinder-head,  it  may  be  desirable  to  take  the  leakage  from  one  of  the 
openings  which  are  provided  for  the  inspection  of  the  suction- valves, 
the  head  being  allowed  to  remain  in  place. 

It  is  assumed  that  there  is  a  practical  absence  of  valve  leakage.  Exami- 
nation for  such  leakage  should  be  made,  and  if  it  occurs,  and  it  is  found  to 
be  due  to  disordered  valves,  it  should  be  remedied  before  making  the 
plunger  test.  Leakage  of  the  discharge  valves  will  be  shown  by  water 
passing  down  into  the  empty  cylinder  at  either  end  when  they  are  under 
pressure.  Leakage  of  the  suction-valves  will  be  shown  by  the  disappear- 
ance of  water  which  covers  them. 

If  valve  leakage  is  found  which  cannot  be  remedied  the  quantity  of 
water  thus  lost  should  also  be  tested.  One  method  is  to  measure  the 
amount  of  water  required  to  maintain  a  certain  pressure  in  the  pump 
cylinder  when  this  is  introduced  through  a  pipe  temporarily  erected,  no 
water  being  allowed  to  enter  through  the  discharge  valves  of  the  pump. 
>  Friction. — The  percentage  of  total  friction  in  a  reciprocating 

Eurnp  is  the  percentage  of  the  friction  horse-power  to  the  indicated 
orse-power  of  the  steam  cylinders. 

Data  and  Results. — The  data  and  results  should  be  reported  In 
accordance  with  the  form  given  herewith,  adding  lines  for  data  not 

below  each  gage  cock,  and  opened  occasionally  so  as  to  free  the  pipe 
of  air  in  the  case  of  the  force-main  gage  and  of  water  in  the  case  of 
the  suction  gage.  If  the  suction  main  is  under  a  pressure  instead  of 
a  vacuum  the  suction  gage  should  be  attached  at  such  a  level  that  the 
connecting  pipe  may  be  filled  with  water  when  the  pet-cock  is  opened, 
in  which  case  the  correction  for  difference  in  elevation  of  gages  is 
the  vertical  distance  between  the  centers  of  the  gages,  and  the  reading 
of  the  suction  gage  is  to  be  subtracted  from  that  of  the  force-main 
gage. 

If  the  water  is  drawn  from  an  open  well  beneath  the  pump,  the 
total  head  is  that  shown  by  the  force-main  gage  corrected  for  the 
elevation  of  the  center  of  the  gage  above  the  level  of  water  in  the 
pump  well. 

If  there  is  a  material  difference  in  velocity  of  the  water  at  *,he 
points  where  the  two  gages  are  attached,  a  correction  should  be  made 
for  tne  corresponding  difference  in  "velocity-head."  1 


804  PUMPS  AND   PUMPING  ENGINES. 

provided  for,  or  omitting  those  not  required,  as  may  conform  to  the 
object  in  view. 

In  the  case  of  a  pumping  engine  of  the  reciprocating  class  for  which 
a  record  of  the  complete  performance  is  desired,  the  additional  engine 
data  and  results  given  in  the  Steam  Engine  Code  may  supplement 
those  here  given. 

DATA  AND   RESULTS   OF  STEAM   PUMPING   MACHINERY 

TEST. 

Code  of  1915. 

1.  Test  of pump  located  at 

To  determine 

Test  conducted  by 


DIMENSIONS,    ETC. 

2.  Type  of  machinery 

3.  Rated  capacity  in  gallons  per  24  hrs gals. 

4.  Size  of  engine  or  turbine 

5.  Size  of  pump 

6.  Auxiliaries  (steam  or  electric  driven) 

7.  Date 

8.  Duration hrs. 

AVERAGE    PRESSURES    AND    TEMPERATURES. 

9.  Pressure  in  steam  pipe  near  throttle  by  gage Ibs. 

10.  Vacuum  in  condenser ins. 

11.  Temperature  of  steam,  if  superheated,  at  throttle degs. 

12.  Temperature  corresponding  to  pressure  in  exhaust  pipe 

near  engine  or  turbine degs. 

13.  Pressure  in  force  main  by  gage Ibs. 

14.  Vacuum  or  pressure  in  suction  main  by  gage ins.  or  Ibs. 

(a)  Correction  for  difference  in  elevation  of  the  two 

gages Ibs. 

15.  Total  head  expressed  in  Ibs.  perssure  per  sq.  in Ibs. 

(a)  Total  head  expressed  in  feet ft. 

QUALITY  OF  STEAM- 

1 6.  Percentage  of  moisture  in  steam,  degrees  superheating,  %  or  degs. 

TOTAL    QUANTITIES, 

17.  Total  water  fed  to  boilers Ibs. 

18.  Total  condensed  steam  from  surface  condenser  (corrected 

i     for  condenser  leakage) Ibs. 

19.  Total  dry  steam  consumed  (Item  19  or  20  less  moisture 

in  steam) Ibs. 

20.  Total  gals,  of  water  discharged,  by  measurement gals. 

(a)  Total  gals,  of  water  discharged,  by  plunger  dis- 
placement, uncorrected gals. 

(6)  Percentage  of  slip  ("^f^"  £""  2°)  X  100.   percent. 

(c)  Leakage  of  pump gals. 

(d)  Total  gals,  of  water  discharged,  by  calculation 

from     plunger     displacement,     corrected     for 


leakage gals. 

(e)  Total  weight  of  water  discharged,  as  measured  . .  Ibs. 
(/)    Total  weight  of  water  discharged,  by  calculation 


from     plunger     displacement,     corrected     for 
leakage Ibs, 

HOURLY    QUANTITIES. 

21.  Total  water  fed  to  boilers  or  drawn  from  surface  con- 

denser per  hr Ibs. 

22.  Total  dry  steam  consumed  for  all  purposes  per  hour, 

(Item  19  -5-  Item  8) Ibs. 


- 


DUTY  TRIALS   OF  PUMPING  ENGINES.  805 

23.  Steam  consumed  per  hour  for  all  purposes  foreign  to 

main  engine Ibs. 

24.  Dry  steam  consumed  by  engine  or  turbine  per  hour 

(Item  23  -  Item  24) Ibs. 

25.  Weight  of  water  discharged  per  hour,  by  measurement.  .   Ibs. 

(a)  Weight  of  water  discharged  per  hour,  calculated 
from  plunger  displacement,  corrected Ibs. 

HOURLY  HEAT  DATA. 

26.  Heat-units   consumed   by   engine   or   turbine   per  hour 

(Item  24  X  total  heat  of  one  Ib.  of  steam  above  exhaust 
temperature  of  Item  12) B.T.U. 

INDICATOR  DIAGRAMS. 

Mean  effective  pressure,  each  steam  cylinder Ibs.  per  sq.  in. 

(a)  Mean  effective  pressure,  each  water  cylinder.  Ibs.  per  sq.  in 

SPEED  AND  STROKE. 

28.  Revolutions  per  minute R.P.M . 

(a)  Number  of  single  strokes  per  minute strokes 

(b)  Average  length  of  stroke feet.  . 

POWER. 

29.  Indicated  horse-power  developed I.H.P. 

30.  Water  horse-power H.P. 

31.  Friction  horse-power  (Item  29  -  Item  30) H.P. 

32.  Percentage  of  I.H.P.  lost  in  friction per  cent* 

CAPACITY. 

Gallons  of  water  pumped  in  24  hrs.,  as  measured gals. 

(a)  Gals,  of  water  pumped  in  24  hrs.,  calculated  from 
plunger  displacement,  corrected gals. 

(b)  Gals,  of  water  pumped  per  minute,  as  measured . .  gals. 

(c)  Gals,  of  water  pumped  per  minute,  calculated  from 
plunger  displacement,  corrected gals. 

ECONOMY  RESULTS. 

34.  Heat-units  consumed  per  I.H.P.-hr , B.T.U. 

EFFICIENCY  RESULTS. 

35.  Thermal  efficiency  referred  to  I.H.P.  (2546.5  +  Item  34) 

X  100 per  cent. 

DUTY. 

36.  Duty  per  1,000,000  heat-units ft.-lbs. 

WORK  DONE  PER  HEAT-UNIT. 

37.  Ft.-lbs.  of  work  per  B.T.U.  (1,980,000  -T-  Item  34) ft.-lbs. 

The  Nordberg  Pumping  Engine  at  Wildwood,  Pa.  —  Eng.  News 
May  4,  1899,  Aug.  23,  1900,  Trans.  A.  S.  M.  E.,  1899.  The  peculiar 
feature  of  this  engine  is  the  method  used  in  heating  the  feed-water.  The 
engine  is  quadruple  expansion,  with  four  cylinders  and  three  receivers. 
There  are  five  feed-water  heaters  in  series,  a,  b,  c,  d,  e.  The  water  is 
taken,  from  the  hot-well  and  passed  in  succession  through  a  which  is 
heated  by  the  exhaust  steam  on  its  passage  to  the  condenser;  b  receives 
its  heat  from  the  fourth  cylinder,  and  c,  d  and  e  respectively  from  the 
third,  second  and  first  receivers.  An  approach  is  made  to  the  requirement 
of  the  Carnot  thermodynamic  cycle,  i.e.,  that  heat  entering  the  system 
should  be  entered  at  the  highest  temperature;  in  this  case  the  water 
receives  the  heat  from  the  receivers  at  gradually  increasing  temperatures. 
The  temperatures  of  the  water  leaving  the  several  heaters  were,  on  the 
test,  105°,  136°,  193°,  260°,  and  311°  F.  The  economy  obtained  with  this 
engine  was  the  highest  on  record  at  the  date  (1900)  viz.,  162,948,824  ft. 
Ibs.  per  million  B,T.UM  and  it  has  not  yet  been  exceeded  (1909), 


806 


PUMPS   AND   PUMPING   ENGINES. 


Notable  High-duty  Pumping  Engine  Records. 


Date  of  test  

,& 
Wildwood, 
Pa. 

(2) 
1900 
St. 
Louis 
(10). 

(3) 
1900 
Boston, 
Chest- 
nut Hill 

& 

Boston, 
Spot 
Pond. 

(5) 
1906 
St. 
Louis 
(3) 
Bissell's 
Point. 

Locality*  •  • 

Capacity,  mil.  gal.,  24  hrs.  .  . 
Diam.  of  steam  cylinders,  in. 
Stroke  in 

6 
.19.5,29,49.5 
57.5x42 
(2,14^ 

504 
200 
712 
6.95 
93.05 
12.26,  11.4 
186* 
162.9*147.5f 
150.2* 
22.81 

15 
34,  62,92 
X42 

«»,$ 

292 
126 
801 
3.16 
96.84 
10.68 
202 
158.07 
179.45 
21.00 

30 
30,  56,87 
x66 

m& 

140 
185 
801 
6.71 
93.29 
10.34 
196 
156.8 
178.49 
21.63 

30 
22,41.5,62 
x60 
(3)  30.5 
244 
125 
151 
464 
3.47 
96.53 
11.09 
203 
156.59 
172.40 
20.84 

20 
34,  62,94 

(3)%! 

238 
146 
859 
2.27 
97.73 

No.  and  diam.  of  plungers.  .  . 
Piston  speed,  ft.  per  min  
Total  head,  ft  

Steam  pressure  .... 

Indicated  Horse-power  
Friction  %  

Mechanical  efficiency,  %  
Dry  steam  per  I.H.P.  hr  
B.T.U.  per  J.H.P.  per  min..  . 
Duty,  B.T.U.  basis..  
Duty  per  1000  Ibs.  steam  
Thermal  efficiency.  %..., 

202.8 
158.85 
181.30 
20.92 

*  With  reheaters. 


t  Without  reheaters. 


(1),  (2).  From  Eng.  Alews,  Sept.  27,  1900.  (3)  Do.  Aug.  23,  1900. 
(4)  Do.  Nov.  4,  1901.  (5)  Allis-Chalmers  Co.,  Bulletin  No.  1609.  The 
Wildwood  engine  has  double-acting  plungers. 

The  coal  consumption  of  the  Chestnut  Hill  engine  was  1.062  Ibs.  per 
I.H.P.  per  hour,  the  lowest  figure  on  record  at  that  date,  1901. 

VACUUM   PUMPS. 

.  The  Pulsometer.  —  In  the  pulsometer  the  water  is  raised  bv  suction 
into  the  pump-chamber  by  the  condensation  of  steam  within  it,  and  is 
then  forced  into  the  delivery-pipe  by  the  pressure  of  a  new  quantity  of 
steam  on  the  surface  of  the  water.  Two  chambers  are  used  which  work 
alternately,  one  raising  while  the  other  is  discharging. 

Test  of  a  Pulsometer.  —  A  test  of  a  pulsometer  is  described  by  De  Volson 
Wood  in  Trans.  A.  S.  M.  E.,  xiii.  It  had  a  SVz-inch  suction-pipe,  stood 
40  in.  high,  and  weighed  695  Ibs. 

The  steam-pipe  was  1  inch  in  diameter.  A  throttle  was  placed  about 
2  feet  from  the  pump,  and  pressure  gauges  placed  on  both  sides  of  the 
throttle,  and  a  mercury  well  and  thermometer  placed  beyond  the  throttle 
The  wire  drawing  due  to  throttling  caused  superheating. 

The  pounds  of  steam  used  were  computed  from  the  increase  of  the 
temperature  of  the  water  in  passing  through  the  pump. 

Pounds  of  steam  X  loss  of  heat  =  Ibs.  of  water  sucked  in  X  increase  of 
temp. 

The  loss  of  heat  in  a  pound  of  steam  is  the  total  heat  in  a  pound  of 
saturated  steam  as  found  from  "steam  tables"  for  the  given  pressure 
plus  the  heat  of  superheating,  minus  the  temperature  of  the  discharged 
water;  or 


Pounds  of  steam  = 


.  water  X  increase  of  temp.  . 


The  results  for  the  four  tests  are  given  in  the  table  on  p.  807. 

Of  the  two  tests  having  the  highest  lift  (54.05  ft.),  that  was  more 
efficient  which  had  the  smaller  suction  (12.26  ft.),  and  this  was  also  the 
most  efficient  of  the  four  tests.  But,  on  the  other  hand,  the  other  two 
tests  having  the  same  lift  (29.9  ft.),  that  was  the  more  efficient  which  had 
the  greater  suction  (19.67),  so  that  no  law  in  this  regard  was  established. 
The  pressures  used,  19,  30,  43.8,  26.1,  follow  the  order  of  magnitude  of 
the  total  heads,  but  are  not  proportional  thereto.  No  attempt  was  made 
to  determine  what  pressure  would  give  the  best  efficiency  for  any  par- 


THE   JET   PUMP. 
Test  of  a  Pulso meter. 


807 


Data  and  Results. 

1 

2 

3 

4 

Strokes  per  minute  

71 

60 

57 

64 

Steam  pressure  in  pipe  before 

114 

110 

127 

104.3 

Steam  pressure  after  throttling.. 
Steam  temp,  after  throttling,  °F.  . 
Steam  superheating  °F  •  •  

19 
270.4 
3.1 

30 
277 
3.4 

43.8 
309.0 
17.4 

26.1 
270.1 
1.4 

1617 

931 

1518 

1019.9 

\Vater  pumped  Ibs  . 

404,786 

186,362 

228,425 

248,053 

Water  temp,  before  entering  pump 
"Water  temperature  ris©  of 

75.15 
4.47 

80.6 
5.5 

76.3 

7.49 

70.25 
4.55 

Water  head  by  gauge  on  lift,  ft..  .  . 
Water  head  by  gauge  on  suction.  . 
Water  head  by  gauge,  total  (//) 
Water  head  by  measure,  total  (/i) 
Coeffi.  of  friction  of  plant,  h/H  .... 
Efficiency  of  pulsometer 

29.90 
12.26 
42.16 
32.8 
0.777 
0  012 

54.05 
12.26 
66.31 
57.80 
0.877 
0.0155 

54.05 
19.67 
73.72 
66.6 
0.911 
0.0126 

29.90 
19.67 
49.57 
41.60 
0.839 
0.0138 

Eff'y  of  plant  exclusive  of  boiler 
Eff'y  of  plant  if  that  of  boiler  be  0.7 
Duty,  if  1  Ib.  evaporates  10  Ibs. 
water  

0.0093 
0.0065 

10,511,400 

0.0136 
0.0095 

13,391,000 

0.0115 
0.0080 

11,059,000 

O'.OI  16 
0.0081 

12,036,300 

ticular  head.  The  'pressure  used  was  intrusted  to  a  practical  runner, 
and  he  judged  that  when  the  pump  was  running  regularly  and  well,  the 
pressure  then  existing  was  the  proper  one.  It  is  peculiar  that,  in  the  first 
test,  a  pressure  of  19  Ibs.  of  steam  should  produce  a  greater  number  of 
strokes  and  pump  over  50%  more  water  than  26.1  Ibs.,  the  lift  being  the 
same  as  in  the  fourth  experiment. 

Chas.  E.  Emery  in  discussion  of  Prof.  Wood's  paper  says,  referring  to 
tests  made  by  himself  and  others  at  the  Centennial  Exhibition  in  1876 
(see  Report  of  the  Judges,  Group  xx.),  that  a  vacuum-pump  tested  by 
him  in  1871  gave  a  duty  of  4.7  millions;  one  tested  by  J.  F.  Flagg,  at  the 
Cincinnati  Exposition  in  1875,  gave  a  maximum  duty  of  3.25  millions. 
Several  vacuum  and  small  steam-pumps,  compared  later  on  the  same 
basis,  were  reported  to  have  given  duties  of  10  to  11  millions,  the  steam- 
pumps  doing  no  better  than  the  vacuum-pumps.  Injectors,  when  used 
for  lifting  water  not  required  to  be  heated,  have  an  efficiency  of  2  to  5 
millions;  vacuum-pumps  vary  generally  between  3  and  10;  small  steam- 
pumps  between  8  and  15;  larger  steam-pumps,  between  15  and  30,  and 
pumping-engines  between  30  and  140  millions. 


1893 


A  very  high  record  of  test  of  a  pulsometer  is  given  in  Eng'g,  Nov.  24, 
,  p.  639,  viz.:  Height  of  suction  11.27  ft.;   total  height  of  lift,  102.6 


ft.;  horizontal  length  of  delivery-pipe,  118  ft.;  quantity  delivered  per 
hour,  26,188  British  gallons.  Weight  of  steam  used  per  H.  P.  per  hour, 
92.76  Ibs.;  work  done  per  pound  of  steam  21,345  foot-pounds,  equal  to  a 
duty  of  21,345,000  foot-pounds  per  100  Ibs.  of  coal,  if  10  Ibs.  of  steam 
were  generated  per  pound  of  coal. 

The  Jet-pump.  —  This  machine  works  by  means  of  the  tendency  of  a 
stream  or  jet  of  fluid  to  drive  or  carry  contiguous  particles  of  fluid  along 
with  it.  The  water-jet  pump,  in  its  present  form,  was  invented  by  Prof. 
James  Thomson,  and  first  described  in  1852.  In  some  experiments  on  a 
small  scale  as  to  the  efficiency  of  the  jet-pump,  the  greatest  efficiency  was 
found  to  take  place  when  the  depth  from  which  the  water  was  drawn  by 
the  suction-pipe  was  about  nine  tenths  of  the  height  from  which  the 
water  fell  to  form  the  jet;  the  flow  up  the  suction-pipe  being  in  that  case 
about  one  fifth  of  that  of  the  jet,  and  the  efficiency,  consequently,  9/io  X 
1/5  =  0.18.  This  is  but  a  low  efficiency;  but  it  is  probable  that  it  may  be 
increased  by  improvements  in  proportions  of  the  machine.  (Rankine, 
S.  E.) 

The  Injector  when  used  as  a  pump  has  a  very  low  efficiency.  (See 
Injectors,  under  Steam-boilers.) 


808  PUMPS  AND  PUMPING  ENGINES. 

GAS-ENGINE  PUMPS. 

The  Humphrey  Gas  Pump  is  a  single-acting  reciprocating  pumping 
engine,  the  motive  power  of  which  is  furnished  by  the  explosion  of  a 
mixture  of  gas  and  air,  as  in  a  gas  engine,  the  force  of  the  explosion 
acting  directly  on  the  surface  of  a  column  of  water  in  the  vertical 
cylindrical  part  of  a  J  or  V-shaped  pipe  instead  of  on  a  reciprocating 
piston.  The  upper  part  of  the  cylinder  contains  the  combustion 
chamber  and  valves  similar  to  those  of  an  Otto  cycle  gas  engine.  The 
lower  part  contains  a  suction  valve  box  through  which  water  enters 
into  the  "play  pipe"  and  through  which  it  passes  to  a  surge  tank  and 
thence  to  the  delivery  pipe  or  reservoir.  The  charge  of  gas  and  air 
for  starting  is  forced  into  the  combustion  chamber  by  a  2-cylinder 
air-compressor.  When  the  explosion  takes  place  the  water  is  forced 
into  the  surge  tank  while  the  products  of  combustion  expand  to  a 
low  pressure,  the  inertia  of  the  moving  column  of  water  in  the  play 
pipe  causing  it  to  continue  in  motion  after  the  pressure  upon  it  has 
decreased  to  atmospheric  pressure.  The  scavenging  valves  of  the  gas 
cylinder  and  the  suction  valves  of  the  water  pump  then  open,  admitting 
air  and  water.  Most  of  the  water  follows  the  moving  column  in  the 
play  pipe  while  the  rest  rises  in  the  explosion  cylinder.  After  the 
kinetic  energy  in  the  moving  column  is  expended  in  forcing  water  into 
the  surge  tank  the  column  comes  to  rest  and  starts  to  flow  back  into 
the  cylinder,  the  suction  valves  closing.  When  the  surface  reaches 
the  level  of  the  exhaust  valves  of  the  gas  cylinder  these  are  closed 
and  the  kinetic  energy  of  the  backward  moving  column  is  expended  in 
compressing  the  imprisoned  mixture  of  gases  and  scavenging  air  to  a 
pressure  higher  than  that  of  the  surge  tank,  which  starts  the  water 
moving  downward  again  until  the  pressure  is  again  reduced  below 
that  of  the  atmosphere.  A  fresh  charge  of  gas  and  air  is  then  drawn 
into  the  explosion  chamber,  compressed  by  the  next  return  of  the 
to-and-fro  moving  water  column  and  then  ignited.  The  motion  of 
the  water  is  similar  to  the  swing  of  the  pendulum  of  a  clock,  the  time 
of  vibration  being  nearly  proportional  to  the  square  root  of  the  length 
of  the  moving  column.  The  pump  was  invented  in  1906  by  Mr.  H.  A. 
Humphrey.  For  illustrated  descriptions  see  Eng'g,  Nov.  26  and  Dec. 
3,  1909,  and  circulars  of  the  Humphrey  Gas  Pump  Co.,  Syracuse, 
N.  Y...  makers  under  the  Humphrey  and  Smyth  patents. 

Tests  of  five  pumps  at  Chingford,  England,  gave  the  following 
figures:  Four  pumps,  capacity  each  47,000  to  48,000  U.  S.  gal.  per 
min.;  lift  30  to  32  ft.;  water  H.P.  developed,  301  to  323;  gas  used  per 
min.,  390  to  400  cu.  ft.  (at  60°  F.  and  30  in.  bar.);  heating  value  of 
gas  (lower  value)  B.T.U.  per  cu.  ft.,  142  to  146;  thermal  efficiency, 
22.19  to  24.07%;  anthracite  per  water  H.P.-hour,  0.881  to  0.957  Ib. 
A  smaller  pump,  capacity  26,000  U.  S.  gal.  per  min.,  gave  a  thermal 
efficiency  of  26.63%  and  a  coal  consumption  of  0.796  Ib.  per  water 
H.P.-hour.  The  cylinders  of  the  larger  engine  are  7  ft.  diam.,  the  play 
pipe,  6  ft.  (Eng'g,  Feb.  14,  1913). 

A  Humphrey  gas  pump  of  26,000  gal.  capacity  per  min.  at  37  ft.  head 
has  been  installed  for  irrigation  purposes  at  Del  Rio,  Texas.  It  is  guar- 
anteed to  deliver  not  less  than  26,000  gal.  per  min.  with  a  thermal 
efficiency  of  20%  when  using  producer  gas  of  a  heating  value  of  not 
less  than  100  B.T.U.  per  cu.  ft.  The  principal  dimensions  are:  Ex- 
plosion cylinder,  66  in.  diam.  X  41  in.;  water  cylinder,  66  in.  X  89  in. 
long;  valve  boxes,  66  in.  X  73  in.  long;  number  of  5-in.  valves,  400; 
lift,  1  in.;  total  discharge  area  of  valves,  4160  sq.  in.;  play  pipe  diam., 
66  in.,  length,  including  135°  bend,  106  ft.  Number  of  explosions,  12 
to  20  per  min. 

Humphrey  pumps  without  discharge  valves  are  limited  to  heads  of 
about  15  to  40  ft.,  but  a  pump  with  an  intensifier  and  discharge  valves 
is  made  for  heads  up  to  150  ft. 

PUMPING  BY  COMPRESSED  AIR— THE  AIR-LIFT   PUMP. 

Air-lift  Pump. — The  air-lift  pump  consists  of  a  vertical  water-pipe 
with  its  lower  end  submerged  in  a  well,  and  a  smaller  pipe  delivering  air 
into  it  at  the  bottom.  The  rising  column  in  the  pipe  consists  of  air 
mingled  with  water,  the  air  being  in  bubbles  of  various  sizes,  and  is  there- 
fore lighter  than  a  column  of  water  of  the  same  height;  consequently  the 


PtJMPING  BY  COMPRESSED  AIE.  809 

water  in  the  pipe  is  raised  above  the  level  of  the  surrounding  water. 
This  method  of  raising  water  was  proposed  as  early  as  1797,  by  Loescher, 
of  Freiberg,  and  was  mentioned  by  Collon  in  lectures  in  Paris  in  1876, 
but  its  first  practical  application  probably  was  by  Werner  Siemens  in 
Berlin  in  1885.  Dr.  J.  G.  Pohle  experimented  on  the  principle  in  Cali- 
fornia in  1886,  and  U.  S.  patents  on  apparatus  involving  it  were  granted 
to  Pohle  and  Hill  in  the  same  year.  A  paper  describing  tests  of  the  air- 
lift pump  made  by  Randall,  Browne  and  Behr  was  read  before  the  Tech- 
nical Society  of  the  Pacific  Coast  in  Feb.,  1890. 

The  diameter  of  the  pump-column  was  3  in.,  of  the  air-pipe  0.9  in.,  and 
of  the  air-discharge  nozzle  5/s  in.  The  air-pipe  had  four  sharp  bends  and  a 
length  of  35  ft.  plus  the  depth  of  submersion. 

The  water  was  pumped  from  a  closed  pipe-well  (55  ft.  deep  and  10  in. 
in  diameter).  The  efficiency  of  the  pump  was  based  on  the  least  work 
theoretically  required  to  compress  the  air  and  deliver  it  to  the  receiver. 
If  the  efficiency  of  the  compressor  be  taken  at  70%,  the  efficiency  of  the 
pump  and  compressor  together  would  be  70%  of  the  efficiency  found  for 
the  pump  alone. 

For  a  given  submersion  (ft)  and  lift  (#),  the  ratio  of  the  two  being  kept 
within  reasonable  limits,  (#)  being  not  much  greater  than  (ft),  the  effi- 
ciency was  greatest  when  the  pressure  in  the  receiver  did  not  greatly 
exceed  the  head  'due  to  the  submersion.  The  smaller  the  ratio  H  •*•  ft, 
the  higher  was  the  efficiency. 

The  pump,  as  erected,  showed  the  following  efficiencies: 

For  H  •*-  ft  =       0.5  1.0  1.5  2.0 

Efficiency    =50%  40%  30%  25% 

The  fact  that  there  are  absolutely  no  moving  parts  makes  the  pump 
especially  fitted  for  handling  dirty  or  gritty  water,  sewage,  mine  water, 
and  acid  or  alkali  solutions  in  chemical  or  metallurgical  works. 

In  Newark,  N.  J.,  pumps  of  this  type  are  at  work  having  a  total  capacity 
of  1,000,000  gallons  daily,  lifting  water  from  three  8-in.  artesian  wells. 
The  Newark  Chemical  Works  use  an  air-lift  pump  to  raise  sulphuric  acid 
of  1.72°  gravity.  The  Colorado  Central  Consolidated  Mining  Co.,  in  one 
of  its  mines  at  Georgetown,  Colo.,  lifts  water  in  one  case  250  ft.,  using  a 
series  of  lifts. 

For  a  full  account  of  the  theory  of  the  pump,  and  details  of  the  tests 
above  referred  to,  see  Eng'g  News,  June  8,  1893. 

Numerous  tests  of  air-lift  pumps  are  described  in  Greene's  "Pumping 
Machinery."  Greene  says  that  the  air  pipe  should  be  introduced  near 
the  bottom  of  the  discharge  pipe  and  should  be  immersed  so  that  the 
ratio  hi fh  is  3  to  1  at  the  start  and  2.2  to  1  in  operation,  hi  is  the 
depth  of  immersion  below  the  water  level  and  h  the  height  of  the  dis- 
charge at  the  top  of  the  well  measured  above  the  water  level.  Different 
tests  give  the  following  efficiencies  for  various  ratios  hi/h. 
h/hi  = 

3.1  to  2.2        0.6  1  1.4  2.4        3.91.5    1    0.660.50.43 

Efficiency,  % : 

36         16  to  43  19  to  42  34  to  41   15  to  24     2     50    40    30      25     20 

The  efficiency  is  the  ratio  of  the  work  done  in  raising  the  water  to 
the  work  of  compressing  the  air. 

The  amount  of  free  air  required  varies  according  to  different  manu- 
facturers. One  gives  cu.  ft.  air  per  min.  =  LW  +  19;  another  L W  H-15; 
L  =  lift  of  water  above  the  water  level,  in  ft.,  W  =  cu.  ft.  of  water  per 
min. 

Air-Lifts  for  Deep  Oil- Wells  are  described  by  E.  M.  Ivens,  in  Trans. 
A.  S.  M .  E.  1909,  p.  341.  The  following  are  some  results  obtained  in  wells 
in  Evangeline,  La.: 

Cu.  ft.  free  air  per  minute,  displacement  of 

compressor 650  442  702  536 

Cu.  ft.  oil  pumped  per  minute 4.35  4.87  13.7  5.54 

Air  pressure  at  well,  Ibs.  per  sq.  in 155  200  202  252 

Pumping  head,  from  oil  level  while  pumping,  ft.  1155  1081  1076  917 

Submergence,  from  oil  level  to  air  entrance,  ft.  358  412  419  583 

Submergence  -s-  total  ft.  of  vertical  pipe,  %. . .  23.6  27.6  28  39 

Pumping  efficiency,  % 9.3  13.4  19.5  10.3 


810  PUMPS  AND   PUMPING  ENGINES. 

Artesian  Well  Pumping  by  Compressed  Air.  — H.  Tipper,  Eng.  News, 
Jan.  16,  1908,  mentions  cases  where  1-in.  air  lines  supplied  air  for  6-in. 
Wells,  with  the  inside  air-pipe  system;  the  length  of  the  pipe  was  300  ft. 
from  the  well  top,  and  another  350  ft.  to  the  compressor.  The  wells 
pumped  75  gals,  per  min.,  using  200  cu.  ft.  of  air,  the  efficiency  being  61/2%. 
Changing  the  pipes  to  21/2  in.  above  the  well,  and  2  in.  in  the  well,  and 
putting  an  air  receiver  near  the  compressor,  raised  the  delivery  to  180 
gals,  per  min.,  with  a  little  less  air,  and  the  efficiency  to  23%.  A  large 
receiver  capacity,  a  large  pipe  above  ground,  a  submergence  of  55%, 
well  piping  proportioned  for  a  friction  loss  of  not  over  5%,  with  lifts  not 
over  200  ft.,  gave  the  best  results,  1  gal.  of  water  being  raised  per  cu.  ft. 
of  air.  The  utmost  net  efficiency  of  the  air-lift  is  not  over  25  to  30%. 

Eng.  News,  June  18,  1908,  contains  an  account  of  tests  of  eleven  wells 
at  Atlantic  City.  The  Atlantic  City  wells  were  10  in.  diam.,  water  pipes, 
4  to  51/4  in.,  air  pipes,  3/4  to  11/4  in.  The  maximum  lift  of  the  several 
wells  ranged  from  26  to  40  ft.,  the  submergence,  37  to  49  ft.,  ratio  of  sub- 
mergence to  lift,  0.9  to  1.8,  submergence  %  of  length  of  pipe,  53  to  64. 
Capacity  test,  3,544,900  gals,  in  24  hrs.,  mean  lift,  26.88  ft.,  air  pressure, 
31  Ibs.,  duty  of  whole  plant,  19,900,000  ft.  Ibs.  per  1000  Ibs.  of  steam  used 
by  the  compressors.  Two-thirds  capacity  test,  delivery,  2,642,900  gals., 
mean  lift,  25.43  ft.,  air  pressure,  26  Ibs.,  duty,  24,207,000. 

An  article  in  The  Engineer  (Chicago),  Aug.  15,  1904,  gives  the  following 
formulae  and  rules  for  the  design  of  air-lifts  of  maximum  efficiency.  The 
authority  is  not  given. 

Ratio  of  area  of  air  pipe  to  area  of  water  pipe,  0.16. 

Submerged  portion  =  65%  of  total  length  of  pipe. 

Economical  range  of  submersion  ratio,  55  to  80%. 

Velocity  of  air  in  air  pipe,  not  over  4000  ft.  per  min. 

Volume  of  air  to  raise  1  cu.  ft.  of  water,  3.9  to  4.5  cu.  ft. 

C  —  cu.  ft.  of  water  raised  per  min.,  A  =  cu.  ft.  of  air  used,  L  =*  lift 
above  water  level,  D  =  submergence,  in  feet. 

A  =  LC  •*•  16.824;  C  =  8.24  AD  -r-  L*. 

Where  L  exceeds  180  ft.  it  will  be  more  economical  to  use  two  or  more 
air-lifts  in  series. 

THE  HYDRAULIC   RAM. 

Efficiency.  —  The  hydraulic  ram  is  used  where  a  considerable  flow  of 
water  with  a  moderate  fall  is  available,  to  raise  a  small  portion  of  that  flow 
to  a  height  exceeding  that  of  the  fall.  The  following  are  rules  given  by 
Eytelwem  Us  the  results  of  his  experiments  (from  Rankine)  • 
.  £et  Q  be  the  whole  supply  of  water  in  cubic  feet  per  second,  of  which  q 
is  lifted  to  the  height  h  above  the  pond,  and  Q  —  q  runs  to  waste  at  the 
depth  //  below  the  pond;  L,  the  length  of  the  supply-pipe,  from  the  pond 
to  the  waste-clack;  D,  its  diameter  in  feet;  then 

Efficiency,  ^J^      -  =  1.12-0.2  T^JJ  ,  when  ^does  not  exceed  20; 
or 

1-4-  (1  4-  ft/10  H)  nearly,  when  h/H  does  not  exceed  12. 


D'Aubuisson  gives      Q^      =1.42-0.28  -%/—  - 

.  Clark,  using  five  sixths  of  the  values  given  by  D'Aubuisson's  formula, 
gives: 

Ratio  of  lift  to  fall.      4       6       8     10     12     14     16     18     20     22     24 
Efficiency  per  cent.   72     61     52     44     37     31     25     19     14       9       4 

The  efficiency  as  calculated  by  the  two  formulas  given  above  is  nearly 
the  same  for  high  ratios  of  lift,  but  for  low  ratios  there  is  considerable 
difference.  For  example: 

Let  Q  =  100,  H  =  10,  II  +  li  =  '  20  40  100  200 
Efficiency,  D'Aubuisson's  formula,  %  80  72  44  14 
q  =  effy.  X  QH  -J-  (H  +  h)=  40  18  4.4  0.7 

Efficiency  by  Rankine's  formula,  %      662/3     65.9     41.4     13.4 
D'Aubuisson's  formula  is  that  of  the  machine  itself,  on  the  basis  that 


THE  HYDBAXJLIC  RAM. 


811 


the  energy  put  into  the  machine  is  that  of  the  whole"  column  of  water, 
Q,  falling  through  the  height  h  and  that  the  energy  delivered  is  that  of  q 
raised  through  the  whole  height  above  the  ram,  H  +  h;  while  Rankine's 
efficiency  is  that  of  the  whole  plant,  assuming  that  the  energy  put  in  is 

and  that  the  work  done  is 
j  ram  but  only  from  that  of 

rr-s   *- the  one  in  harmony  with 

the  usual  definition  of  efficiency.  It  also  is  applicable  (as  Rankine's  is 
not)  to  the  case  of  a  ram  which  uses  the  quantity  Q  from  one  source  of 
supply  to  pump  water  of  different  quality  from  a  source  at  the  level  of 
the  ram. 

An  extensive  mathematical  investigation  of  the  hydraulic  ram,  by 
L.  F.  Harza,  is  contained  in  Bulletin  No.  205  of  the  University  of  Wiscon- 
sin, 1908,  together  with  results  of  tests  of  a  Rife  "hydraulic  engine," 
which  appear  to  verify  the  theory.  It  was  found  both  by  theory  and  by 
experiment  that  the  efficiency  bears  a  relation  to  the  velocity  in  the 
drive  pipe.  From  plotted  diagrams  of  the  results  the  following  figures 
(roughly  approximate)  are  taken:  Length  of  2-in.  drive  pipe,  85.4  ft.; 
supply  head,  8.2  ft. 

Max.  vel.  in  drive  pipe,  ft.  per  sec 1.5       2       3       4       56 

Efficiency  of  machine,  %. 


Pumping  head,  ft 2.6 

12.3 
23.2 
43.5 
63.1 


60 
60 
55 


30 
60 
65 
60 
60 

20 
45 
53 
53 
55 

15 
33 
40 
42 
50 

18 
20 
30 

28 

0 
0 
0 
0 
0 

The  author  of  the  paper  concludes  that  the  comparison  of  experiment 
and  theory  has  demonstrated  the  practicability  of  the  logical  design  of 
a  hydraulic  ram  for  any  given  working  conditions. 

An  interesting  historical  account,  with  illustrations,  of  the  develop- 
ment of  the  hydraulic  ram,  with  a  description  of  PearsaH's  hydraulic 
engine,  is  given  by  J.  Richards  in  Jour.  Assn.  Eng'g  Societies,  Jan.,  1898. 
For  a  description  of  the  Rife  hydraulic  engine  see  Eng.  News,  Dec.  31. 
1896. 

The  Columbia  Steel  Co.,  Portland,  Ore.,  furnished  the  author  in  July, 
1908,  records  of  tests  of  four  hydraulic  rams,  from  which  the  following 
is  condensed,  the  efficiency,  by  D'Aubuisson's  formula,  being  calculated 
from  the  data  given.  L  =  length  in  ft.  and  D  =  diam.  in  ins.  of  the 
drive  pipe,  I  and  d,  length  and  diameter  of  the  discharge  pipe. 


Size  of  Ram. 

H 

h  + 
H 

Q* 

<Z* 

L 

D 

I 

d 

Effy. 
% 

Ins. 
3                 

Ft. 
4 

F.t. 
28 

35 

3.5 

Ft. 
28 

Ins. 
3 

Ft. 
1008 

Ins. 
U/2 

58.9 

41/9              

5 

45 

100 

8 

40 

•41/2 

325 

72.0 

6               

12 

36.4 

200 

50.5 

60 

41/2 

945 

21/2 

76.6 

6                          

37.6 

144.1 

6.26 

1.15 

192.5 

6 

1785, 

lot 

70.4 

*  Q  and  q  are  in  gallons  per  min.,  except  the  last  line,  which  is  In  cu. 
ft.  per  sec. 

f  Eleven  rams  discharge  into  one  10-in.  jointed  wood  pipe.  The  loss 
of  head  in  the  drive  pipe  was  0.7  ft.,  and  in  the  discharge  pipe,  2.7  ft.  On 
another  test  1  cu.  ft.  per  sec.  was  deliyered  with  less  than  5  cu.  ft.  enter- 
ing the  drive  pipe.  Taking  5  cu.  ft.  gives  76.6%  efficiency. 

A  description  and  record  of  test  of  the  Foster  "impact  engine"  is  given 
in  Eng'g  News,  Aug.  3,  1905.  Two  engines  are  connected  into  one  8-in. 
delivery  pipe.  Using  the  same  notation  as  before,  the  data  of  the  tests 
of  the  two  engines  are  as  follows:  Q,  gal.  per  min.,  582,  578;  q,  232,  228; 
H,  36.75,  37.25;  H  +  h,  84,  84;  strokes  per  min.,  130,  130;  Effy.  (D'Aubu- 
isson),  91.23,  89.06%. 

Prof.  R.  C.  Carpenter  (Eng'g  Mechanics,  1894)  reports  the  results  of 
four  tests  of  a  ram  constructed  by  Rumsey  &  Co.,  Seneca  Falls.  The 
supply-pipe  used  was  11/2  inches  in  diameter,  about  50  feet  long,  with  3 
elbows.  Each  run  was  made  with  a  different  stroke  for  the  waste-valve, 
the  supply  and  .delivery  head  being  constant;. the  obje.ct  of  the  expert- 


812 


HYDRAULIC-PRESSURE  TRANSMISSION. 


ment  was  to  find  that  stroke  of  clack-valve  which  would  give  the  highest 
efficiency. 


Length  of  stroke,  per  cent  

100 
52 
5.67 
19.75 
297 
1615 
64.1 

80 
56 
5.77 
19.75 
296 
1567 
64.7 

60 
61 
5.58 
19.75 
301 
1518 
70.2 

46 
66 
5.65 
19.75 
297.5 
1455.5 
71.4 

Number  of  strokes  per  minute  

Delivery  liead.  feet  of  water     .   . 

Total  water  pumped  poimds  

Total  water  supplied,  pounds  
Efficiency  per  cent               .  • 

The  highest  efficiency  realized  was  obtained  when  the  clack-valve  trav- 
eled 60%  of  its  full  stroke,  the  full  travel  being  15/16  in. 

HYDRAULIC-PRESSURE  TRANSMISSION. 

Water  under  high  pressure  (700  to  2000  Ibs.  per  sq.  in.  and  upwards^ 
affords  a  satisfactory  method  of  transmitting  power  to  a  distance,  espe- 
cially for  the  movement  of  heavy  loads  at  small  velocities,  as  by  cranes 
and  elevators.  The  system  consists  usually  of  one  or  more  pumps  ca- 
pable of  developing  the  required  pressure;  accumulators,  which  are  vertical 
cylinders  with  heavily-weighted  plungers  passing  through  stuffing-boxes 
in  the  upper  end,  by  which  a  quantity  of  water  may  be  accumulated  at  the 
pressure  to  which  the  plunger  is  weighted;  the  distributing-pipes;  and  the 
presses,  cranes,  or  other  machinery  to  be  operated. 

The  earliest  important  use  of  hydraulic  pressure  probably  was  in  the 
Bramah  hydraulic  press,  patented  in  1796.  Sir.  W.  G.  Armstrong  in 
1846  was  one  of  the  pioneers  in  the  adaptation  of  the  hydraulic  system 
to  cranes.  The  use  of  the  accumulator  by  Armstrong  led  to  the  extended 
use  of  hydraulic  machinery.  Recent  developments  and  applications  of 
the  system  are  largely  due  to  Ralph  Tweddell,  of  London,  and  Sir  Joseph 
Whitworth.  Sir  Henry  Bessemer,  in  his  patent  of  May  13,  1856,  No. 
1292,  first  suggested  the  use  of  hydraulic  pressure  for  compressing  steel 
ingots  while  in  the  fluid  state. 

The  Gross  Amount  of  Energy  of  the  water  under  pressure  stored  in 
the  accumulator,  measured  in  foot-pounds,  is  its  volume  in  cubic  feet  X 
its  pressure  in  pounds  per  square  foot.  The  horse-power  of  a  given 
quantity  steadily  flowing  is  H.P.  =  144  pQ/550  =0.2618  pQ,  in  which  Q  is 
the  quantity  flowing  in  cubic  feet  per  second  and  p  the  pressure  in  pounds 
per  square  inch. 

The  loss  of  energy  due  to  velocity  of  flow  in  the  pipe  is  calculated  as 
follows  (R.  G.  Blaine,  Eng'g,  May  22  and  June  5,  1891): 

According  to  Darcy,  every  pound  of  water  loses  A4L/D  times  its  kinetic 
energy,  or  energy  due  to  its  velocity,  in  passing  along  a  straight  pipe  L 
feet  in  length  and  D  feet  diameter,  where  A  is  a  variable  coefficient.  For 

clean  cast-iron  pipes  it  may  be  taken  as  A =0.005  ( 1  +7^7)) »  or  f°r  ^i- 

ameter  in  inches  =  d. 

d  =  1/2      1      2         3          4          5         6          7  8          9         10        12 

A  =  .015 .01 .0075  .00667  .00625  .006  .00583 .00571 .00563 .00556 .0055  .00542 

The  loss  of  energy  per  minute  is  60  X  62.36  Q  X  -jj   ~ ,  and  the 

horse-power  wasted   in  the  pipe  is   W  =  —     - — ^j~ — -  — ,  in  which  A 

varies  with  the  diameter  as  above,     p  =  pressure  at  entrance  in  pounds 
per  square  inch.     Values  of  0.6363  A  for  different  diameters  of  pipe  in 
inches  are: 
d  =  1/2  12  3  4  5  6  7  8 

.00954    .00636    .00477    .00424    .00398    .00382    .00371    .00363    .00358 
9  10  12 

.00353  .00350    .00345 

Efficiency  of  Hydraulic  Apparatus.  —  The  useful  effect  of  a  direct 
hydraulic  plunger  or  ram  is  usually  taken  at  93%.  The  following  is 
given  as  the  efficiency  of  a  ram  with  chain-and-pulley  multiplying  gear 
properly  proportioned  and  well  lubricated: 

Gear     2  to  1     4  to  1     6  to  1     8  to  1     10  to  1     12  to  1     14  to  1     16  to  1 
Eff'y      0.80        0.76       0.72        0.67         0.63          0.59          0.54         0,50 


HYDRAULIC-PRESSURE   TRANSMISSION.  813 

With  large  sheaves,  small  steel  pins,  and  wire  rope  for  multiplying 
pear  the  efficiency  has  been  found  as  high  as  66%  for  a  multiplication  of 
20  to  1. 

Henry  Adams  gives  the  following  formula  for  effective  pressure  in 
cranes  and  hoists:  P  —  accumulator  pressure  in  pounds  per  square  inch; 
m  =  ratio  of  multiplying  power;  E  =  effective  pressure  in  pounds  per 
square  inch,  including  all  allowances  for  friction; 
E=  P  (0.84 -0.02m). 

J.  E.  Tuit  (Eng'g,  June  15,  1888)  describes  some  experiments  on  the 
friction  of  hydraulic  jacks  from  31/4  to  135/g-mch  'diameter,  fitted  with 
cupped  leather  packings.  The  friction  'loss  varied  from  5.6%  to  18.8% 
according  to  the  condition  of  the  leather,  the  distribution  of  the  load  on 
the  ram,  etc.  The  friction  increased  considerably  with  eccentric  loads. 
With  hemp  packing  a  plunger,  14-inch  diameter,  showed  a  friction  loss 
of  from  11.4%  to  3.4%,  the  load  being  central,  and  from  15.0%  to  7.6% 
with  eccentric  load,  the  percentage  of  loss  decreasing  in  both  cases  with 
increase  of  load. 

Thickness  of  Hydraulic  Cylinders.  —  Sir  W.  G.  Armstrong  gives  the 
following,  for  cast-iron  cylinders,  for  a  pressure  of  1000  Ibs.  per  sq.  in.: 
Diam.  of  cylinder,  inches  — 

2  4  6  8  10  12         16         20         24 

Thickness,  inches  — 

0.832     1.146     1.552     1.875     2.222     2.578     3.19     3.69     4.11 

For  any  other  pressure  multiply  by  the  ratio  of  that  pressure  to  1000. 
These  figures  correspond  nearly  to  the  formula  t  =  0.175  d  +  0.48,  in 
which  t  =  thickness  and  d  =  diameter  in  inches,  up  to  16  inches  diam- 
eter, but  for  20  inches  diameter  the  addition  0.48  is  reduced  to  0.19  and 
at  24  inches  it  disappears.  For  formulae  for  thick  cylinders  see  page  339. 

Cast  iron  should  not  be  used  for  pressures  exceeding  2000  Ibs.  per 
square  inch.  For  higher  pressures  steel  castings  or  forged  steel  should 
be  used.  For  working  pressures  of  750  Ibs.  per  square  inch  the  test 
pressure  should  be  2500  Ibs.  per  square  inch,  and  for  1500  Ibs.  the  test 
pressure  should  not  be  less  than  3500  Ibs. 

Speed  of  Hoisting  by  Hydraulic  Pressure.  —  The  maximum  allow- 
able speed  for  warehouse  cranes  is  6  feet  per  second ;  for  platform  cranes 
4  feet  per  second;  for  passenger  and  wagon  hoists,  heavy  loads,  2  feet  per 
second.  The  maximum  speed  under  any  circumstances  should  never 
exceed  10  feet  per  second. 

The  Speed  of  Water  Through  Valves  should  never  be  greater  than 
100  feet  per  second. 

Speed  of  Water  Through  Pipes.  —  Experiments  on  water  at  1600 
Ibs.  pressure  per  square  inch  flowing  into  a  flanging-machine  ram,  20- 
inch  diameter,  through  a  i/2-inch  pipe  contracted  at  one  point  to  i/4-inch, 
gave  a  velocity  of  114  feet  per  second  in  the  pipe,  and  456  feet  at  the 
reduced  section.  Through  a  i/2-mch  pipe  reduced  to  3/8_inch  at  one 
point  the  velocity  was  213  feet  per  second  in  the  pips  and  381  feet  at  the 
reduced  section.  In  a  i/2-inch  pipe  without  contraction  the  velocity 
was  355  feet  per  second. 

For  many  of  the  above  notes  the  author  is  indebted  to  Mr.  John  Platt, 
consulting  engineer,  of  New  York. 

High-pressure  Hydraulic  Presses  in  Iron-works  are  described  by 
R.  M.  Daelen,  of  Germany,  in  Trans.  A.  I  M.  E.,  1892.  The  following 
distinct  arrangements  used  in  different  systems  of  high-pressure  hydrau- 
lic work  are  discussed  and  illustrated: 

1.  Steam-pump,  with  fly-wheel  and  accumulator. 

2.  Steam-pump,  without  fly-wheel  and  with  accumulator. 

3.  Steam-pump,  without  fly-wheel  and  without  accumulator. 

In  these  three  systems  the  valve-motion  of  the  working  press  is  oper- 
ated in  the  high-pressure  column.  This  is  avoided  in  the  following: 

4.  Single-acting  steam-intensifier  without  accumulator. 

5.  Steam-pump  with  fly-wheel,  without  accumulator  and  with  DiDe- 
circuit. 

6.  Steam-pump   with   fly-wheel,    without    accumulator   and    without 
pipe-circuit. 

The  disadvantages  of  accumulators  are  thus  stated:  The  weighted 


814  HYDRAULIC-PRESSURE  TRANSMISSION. 

plungers  which  formerly  served  in  most  cases  as  accumulators,  cause 
violent  shocks  in  the  pipe-line  when  changes  take  place  in  the  move- 
ment of  the  water,  so  that  in  many  places,  in  order  to  avoid  bursting 
from  this  cause,  the  pipes  are  made  exclusively  of  forged  and  bored  steel. 
The  seats  and  cones  of  the  metallic  valves  are  cut  by  the  water  (at  high 
speed),  and  in  such  cases  only  the  most  careful  maintenance  can  prevent 
great  losses  of  power. 

Hydraulic  Power  in  Ixmdon.  —  The  general  principle  involved  is 
pumping  water  into  mains  laid  in  the  streets,  from  which  service-pipes 
are  carried  into  the  houses  to  work  lifts  or  three-cylinder  motors  when 
rotary  power  is  required.  In  some  cases  a  small  Pelton  wheel  has  been 
tried,  working  under  a  pressure  of  over  '700  Ibs.  on  the  square  inch. 
Over  55  miles  of  hydraulic  mains  are  at  present  laid  (1892). 

The  reservoir  of  power  consists  of  capacious  accumulators,  loaded  to 
800  Ibs.  per  sq.  in. 

The  engine-house  contains  six  sets  of  triple-expansion  pumping  en- 
gines. Each  pump  will  deliver  300  gallons  of  water  per  minute. 

The  water  delivered  from  the  main  pumps  passes  into  the  accumu- 
lators. The  rams  are  20  inches  in  diameter,  and  have  a  stroke  of  23 
feet.  They  are  each  loaded  with  110  tons  of  slag,  contained  in  a  wrought- 
iron  cylindrical  box  suspended  from  a  cross-head  on  the  top  of  the  ram. 
One  of  the  accumulators  is  loaded  a  little  more  heavily  than  the  other, 
so  that  they  rise  and  fall  successively;  the  more  heavily  loaded  actuates  a 
stop-valve  on  the  main  steam-pipe. 

The  mains  in  the  public  streets  are  so  constructed  and  laid  as  to  be  per- 
fectly trustworthy  and  free  from  leakage.  Every  pipe  and  valve  used 
throughout  the  system  is  tested  to  2500  Ibs.  per  sq.  in.  before  being  placed 
on  the  ground  and  again  tested  to  a  reduced  pressure  in  the  trenches  to 
insure  the  perfect  tightness  of  the  joints.  The  jointing  material  used  is 
gutta-percha. 

The  average  rate  obtained  by  the  company  is  about  3  shillings  per 
thousand  gallons.  The  principal  use  of  the  power  is  for  intermittent 
work  in  cases  where  direct  pressure  can  be  employed,  as,  for  instance, 
passenger  elevators,  cranes,  presses,  warehouse  hoists,  etc. 

An  important  use  of  the  hydraulic  power  is  its  application  to  the 
extinguishing  of  fire  by  means  of  Greathead's  injector  hydrant.  By  the 
use  of  these  hydrants  a  continuous  fire-engine  is  available. 

Hydraulic  Riveting-machines.  —  Hydraulic  riveting  was  introduced 
in  England  by  Mr.  R.  H.  Tweddell.  Fixed  riveters  were  first  used  about 
1868.  Portable  riveting-machines  were  introduced  in  1872. 

The  riveting  of  the  large  steel  plates  in  the  Forth  Bridge  was  done  by 
small  portable  machines  working  with  a  pressure  of  1000  Ibs.  per  square 
inch.  In  exceptional  cases  3  tons  per  inch  were  used.  (Proc.  Inst.  M.  E.. 
May,  1889.) 

An  application  of  hydraulic  pressure  invented  by  Andrew  Higginson, 
of  Liverpool,  dispenses  with  the  necessity  of  accumulators.  It  consists 
of  a  three-throw  pump  driven  by  shafting  or  worked  by  steam  and 
depends  partially  upon  the  work  accumulated  in  a  heavy  fly-wheel. 
The  water  in  its  passage  from  the  pumps  and  back  to  them  is  in  con- 
stant circulation  at  a  very  feeble  pressure,  requiring  a  minimum  of 
power  to  preserve  the  tube  of  water  ready  for  action  at  the  desired 
moment,  when  by  the  use  of  a  tap  the  current  is  stopped  from  going 
back  to  the  pumps,  and  is  thrown  upon  the  piston  9f  the  tool  to  be  set 
in  motion.  The  water  is  now  confined,  and  the  driving-belt  or  steam- 
engine,  supplemented  by  the  momentum  of  the  heavy  fly-wheel,  is 
employed  in  closing  up  the  rivet,  or  bending  or  forging  the  object  sub- 
jected to  its  operation. 

Hydraulic  Forging-press. 

For  a  very  complete  illustrated  account  of  the  development  of  the 
hydraulic  forging-press,  see  a  paper  by  R.  H.  Tweddell  in  Proc.  Inst. 
C.  E.,  vol.  cxvii.  1893-4. 

In  the  Allen  forging-press  the  force-pump  and  the  large  or  main  cylinder 
of  the  press  are  in  direct  and  constant  communication.  There  are  no 
intermediate  valves  of  any  kind,  nor  has  the  pump  any  clack-valves, 
but  it  simply  forces  its  cylinder  full  of  water  direct  into  the  cylinder  of 
the  press,  and  receives  the  same  water,  as  it  were,  back  again  on  the  return 


HYDRAULIC-PRESSURE  TRANSMISSION.  815 

stroke.  Thus,  when  both  cylinders  and  the  pipe  connecting  them  are 
full,  the  large  ram  of  the  press  rises  and  falls  simultaneously  with  each 
stroke  of  the  pump,  keeping  up  a  continuous  oscillating  motion,  the  ram, 
of  course,  traveling  the  shorter  distance,  owing  to  the  larger  capacity  of 
the  press  cylinder.  (Journal  Iron  and  Steel  Institute,  1891.  See  also 
illustrated  article  in  "Modern  Mechanism,"  page  668.) 

A  2000-ton  forging-press  erected  at  the  Couillet  forges  in  Belgium  is 
described  in  Eng.  and  M.  Jour.,  Nov.  25,  1893.  The  press  is  composed 
essentially  of  two  parts  —  the  press  itself  and  the  compressor.  The  com- 
pressor is  formed  of  a  vertical  steam-cylinder  and  a  hydraulic  cylinder. 
The  piston-rod  of  the  former  forms  the  piston  of  the  latter.  The  hy- 
draulic piston  discharges  the  water  into  the  press  proper.  The  distribu- 
tion is  made  by  a  cylindrical  balanced  valve;  as  soon  as  the  pressure  is 
released  the  steam-piston  falls  automatically  under  the  action  of  gravity. 
During  its  descent  the  steam  passes  to  the  other  face  of  the  piston  to 
reheat  the  cylinder,  and  finally  escapes  from  the  upper  end. 

When  steam  enters  under  the  piston  of  the  compressor-cylinder  the 
piston  rises,  and  its  rod  forces  the  water  into  the  press  proper.  The 
pressure  thus  exerted  on  the  piston  of  the  latter  is  transmitted  through  a 
cross-head  to  the  forging  which  is  upon  the  anvil.  To  raise  the  cross- 
head  two  small  single-acting  steam-cylinders  are  used,  their  piston-rods 
being  connected  to  the  cross-head:  steam  acts  only  on  the  pistons  of  these 
cylinders  from  below.  The  admission  of  steam  to  the  cylinders,  which 
stand  on  top  of  the  press  frame,  is  regulated  by  the  same  lever  which 
directs  the  motions  of  the  compressor.  The  movement  given  to  the  dies 
is  sufficient  for  all  the  ordinary  purposes  of  forging. 

A  speed  of  30  blows  per  minute  has  been  attained.  A  double  press  on 
the  same  system,  having  two  compressors  and  giving  a  maximum  pressure 
of  6000  tons,  has  been  erected  in  .the  Krupp  works,  at  Essen. 

Hydraulic  Engine  driving  an  Air-compressor  and  a  Forging- 
hammer.  ( Iron  Age,  May  12,  1892.) — The  great  hammer  in  Terni, 
near  Rome,  is  one  of  the  largest  in  existence.  Its  falling  weight  amounts 
to  100  tons,  and  the  foundation  belonging  to  it  consists  of  a  block  of  cast 
iron  of  1000  tons.  The  stroke  is  16  feet  43/4  inches;  the  diameter  of  the 
cylinder  6  feet  31/2  inches;  diameter  of  piston-rod  133/4  inches;  total 
height  of  the  hammer,  62  feet  4  inches.  The  power  to  work  the  hammer, 
as  well  as  the  two  cranes  of  100  and  150  tons  respectively,  and  other 
auxiliary  appliances  belonging  to  it,  is  furnished  by  four  air-compressors 
coupled  together  and  driven  directly  by  water-pressure  engines,  by 
means  of  which  the  air  is  compressed  to  73.5  pounds  per  square  inch. 
The  cylinders  of  the  water-pressure  engines,  which  are  provided  with  a 
bronze  lining,  have  a  133/4-inch  bore.  The  stroke  is  473/4  inches,  with  a 
pressure  of  water  on  the  piston  amounting  to  264.6  pounds  per  square 
inch.  f  The  compressors  are  bored  out  to  31 1/2  inches  diameter,  and  have 
473/4-inch  stroke.  Each  of  the  four  cylinders  requires  a  power  equal  to 
280  horse-power.  The  compressed  air  is  delivered  into  huge  reservoirs, 
where  a  uniform  pressure  is  kept  up  by  means  of  a  suitable  water-column. 

The  Hydraulic  Forging  Plant  at  Bethlehem,  Pa.,  is  described  in  a 
paper  by  R.  W.  Davenport,  read  before  the  Society  of  Naval  Engineers 
and  Marine  Architects,  1893.  It  includes  two  hydraulic  forging-presses 
complete,  with  engines  and  pumps,  one  of  1500  and  one  of  4500  tons 
capacity,  together  with  two  Whitworth  hydraulic  traveling  forging- 
cranes  and  other  necessary  appliances  for  each  press;  and  a  complete 
fluid-compression  plant,  including  a  press  of  7000  tons  capacity  and  a 
125-ton,  hydraulic  traveling  crane  for.  serving  it  _(the.  upper  and  lower 
heads  of  this  press  weighing  respectively  about  135  and  120  tons). 

A  later  forging-press  designed  by  John  Fritz,  for  the  Bethlehem 
Works,  of  14,000  tons  capacity,  is  run  by  engines  and  pumps  of  15,000 
horse-power.  The  plant  is  served  by  four  open-hearth  steel  furnaces  of 
a  united  capacity  of  120  tons  of  steel  per  heat. 

The  Davy  High-speed  Steam-hydraulic  Forging  Press  is  described 
in  the  Iron  Age,  April  15,  1909.  It  is  built  in  sizes  ranging  from  150  to 
12,000  tons  capacity.  In  the  four-column  type,  in  which  all  but  the 
smaller  sizes  are  built,  there  is  a  central  press  operated  by  hydraulic 
pressure  from  a  steam  intensifier,  and  two  steam  balance  cylinders 
carried  on  top  of  the  entablature.  A  single  lever  controls  the  press. 
The  operator  admits  steam  to  the  balance  cylinders,  lifting  the  cross- 


816  FUEL. 

head  and  the  main  plunger,  and  forcing  the  water  from  the  press  cylinder 
into  the  water  cylinder  of  the  intensifier.  Exhausting  the  steam  from 
the  balance  cylinders,  allows  the  plunger  to  descend  and  rest  on  the 
forging.  To  and  fro  motions  of  the  lever,  slow  or  fast  as  the  operator 
desires,  up  to  120  a  minute,  then  are  made  to  reduce  the  forging.  The 
smaller,  or  single  frame,  type  has  only  one  balance  cylinder,  immediately 
above  the  press  cylinder.  The  Davy  press  is  made  in  the  United  States 
by  the  United  Engineering  &  Foundry  Co.,  Pittsburgh. 

Some  References  on  Hydraulic  Transmission.  —  Reuleaux's  "  Con- 
structor;" "Hydraulic  Motors,  Turbines,  and  Pressure-engines,"  G. 
Bodmer,  London,  1889;  Robinson's  "Hydraulic  Power  and  Hydraulic 
Machinery,"  London,  1888;  Colyer's  "Hydraulic  Steam,  and  Hand-power 
Lifting  and  Pressing  Machinery  "  London,  1881,  See  also  Engineering 
(London),  Aug.  1,  1884,  p.  99;  March  13,  1885,  p.  262;  May  22  and  June 
5,  1891,  pp.  612,  665;  Feb.  19,  1892,  p.  25;  Feb.  10,  1893,  p.  170. 


FUEL. 

Theory  of  Combustion  of  Solid  Fuel.  (From  Rankine,  somewhat 
altered.)  —  The  ingredients  of  every  kind  of  fuel  commonly  used  may  be 
thus  classed:  (1)  Fixed  or  free  carbon,  which  is  left  in  the  form  of  char- 
coal or  coke  after  the  volatile  ingredients  of  the  fuel  have  been  distilled 
away.  These  ingredients  burn  either  wholly  in  the  solid  state  (C  to  COs), 
or  part  in  the  solid  state  and  part  in  the  gaseous  state  (CO  +  O  =  CO2), 
the  latter  part  being  first  dissolved  by  previously  formed  carbon  dioxide 
by  the  reaction  CO2  +  C  =  2  CO.  Carbon  monoxide,  CO,  is  produced 
when  the  supply  of  air  to  the  fire  is  insufficient. 

(2)  Hydrocarbons,  such  as  olefiant  gas,  pitch,  tar,  naphtha,  etc.,  all  of 
which  must  pass  into  the  gaseous  state  before  being  burned. 

If  mixed  on  their  first  issuing  from  amongst  the  burning  carbon  with  a 
large  quantity  of  hot  air,  these  inflammable  gases  are  completely  burned 
with  a  transparent  blue  flame,  producing  carbon  dioxide  and  steam. 
When  mixed  with  cold  air  they  are  apt  to  be  chilled  and  pass  off  unburned. 
When  raised  to  a  red  heat,  or  thereabouts,  before  being  mixed  with  a 
sufficient  quantity  of  air  for  perfect  combustion,  they  disengage  carbon 
in  fine  powder,  arid  pass  to  the  condition  partly  of  marsh  gas,  CH4  and 
partly  of  free  hydrogen;  and  the  higher  the  temperature,  the  greater  is 
the  proportion  of  carbon  thus  disengaged. 

If  the  disengaged  carbon  is  cooled  below  the  temperature  of  ignition 
before  coming  in  contact  with  oxygen,  it  constitutes,  while  floating  in  the 
gas,  smoke,  and  when  deposited  on  solid  bodies,  soot. 

But  if  the  disengaged  carbon  is  maintained  at  the  temperature  of  igni- 
tion and  supplied  with  oxygen  sufficient  for  its  combustion,  it  burns 
while  floating  in  the  inflammable  gas,  and  forms  red,  yellow,  or  white 
flame.  The  flame  from  fuel  is  the  larger  the  more  slowly  its  combustion 
is  effected.  The  flame  itself  is  apt  to  be  chilled  by  radiation,  as  into  the 
heating  surface  of  a  steam-boiler,  so  that  the  combustion  is  not  completed, 
and  part  of  the  gas  and  smoke  pass  off  unburned. 

(3)  Oxygen  or  hydrogen  either  actually  forming  water,  or  existing  in 
combination  with  the  other  constituents  in  the  proportions  which  form 
water.     Such  quantities  of  oxygen  and  hydrogen  are  to  be  left  out  of 
account  in  determining  the  heat  generated  by  the  combustion.     If  the 
quantity  of  water  actually  or  virtually  present  in  each  pound  of  fuel  is  so 
great  as  to  make  its  latent  heat  of  evaporation  worth  considering,  that 
heat  is  deducted  from,  the  total  available  heat  of  combustion  of  the  fuel. 

(4)  Nitrogen,  either  free  or  in  combination  with  other  constituents. 
This  substance  is  simply  inert. 

(5)  Sulphide  of  iron,  which  exists  in  coal  and  is  detrimental,  as 
tending  to  cause  spontaneous  combustion. 

(6)  Other  inert  mineral  compounds  of  various  kinds  form  the  ash 
left  after  complete  combustion  of  the  fuel,  and  also  the  clinker  or  glassy 
material  produced  by  fusion  of  the  ash,  which  tends  to  choke  the  grate. 

The  imperfect  combustion  of  carbon,  making  carbon  monoxide, 
produces  less  than  one-third  of  the  heat  which  is  yielded  by  the  com- 
plete combustion,  making  carbon  dioxide, 


FUEL. 


817 


The  total  heat  of  combustion  of  any  compound  of  hydrogen  and  carbon 
is  nearly  the  sum  of  the  quantities  of  heat  which  the  constituents  would 
produce  separately  by  their  combustion.  (Marsh-gas  is  an  exception.) 

In  computing  the  total  heat  of  combustion  of  compounds  containing 
oxygen  as  well  as  hydrogen  and  carbon,  the  following  principle  is  to  be 
observed :  When  hydrogen  and  oxygen  exist  in  a  compound  in  the  proper 
proportion  to  form  water  (that  is,  by  weight  one  part  of  hydrogen  to 
eight  of  oxygen),  these  constituents  have  no  effect  on  the  total  heat  of 
combustion.  If  hydrogen  exists  in  a  greater  proportion,  only  the  surplus 
of  hydrogen  above  that  which  is  required  by  the  oxygen  is  to  be  taken 
into  account. 

The  following  is  a  general  formula  (Dulong's)  for  the  total  heat  of  com- 
bustion of  any  compound  of  carbon,  hydrogen,  and  oxygen: 

Let  <7,  //,  and  O  be  the  fractions  of  one  pound  of'the  compound,  which 
consists  respectively  of  carbon,  hydrogen,  and  oxygen,  the  remaindei 
being  nitrogen,  ash,  and  other  impurities.  Let  h  be  the  total  heat  of 
combustion  of  one  pound  of  the  compound  in  British  thermal  units. 

Then  h  =  14,600  C  -H  62,000  (H  -  Vs  0). 

Oxygen  and  Air  Required  for  the  Combustion  of  Carbon,  Hydro* 
gen,  etc. 


Chemical  Reaction. 

Lbs.   0 
perlb. 
Fuel. 

Lbs.N, 
=3.32  O 

Air  per 
lb.= 
4.32  O. 

Gase- 
ous 
Prod- 
ucts 
per  Ib. 

Heat  of 
Combus- 
tion. 
B.T.U. 
per  Ib. 

CtoCCfe              C+2O=CO2 
C  to  CO               C  +  O  =  CO 
CO  to  CO2        CO  +  0  =  CO2 
H  to  H2O         2  H  +  O  =  H2O 
CH4toCO2)     CH4  +  4O 
andH20  |            =CO2  +  2H2O 
StoSO2            S  +  2O  =  SO2 
CO  to  COa,  per  Ib.  of  C  or  pe 

i% 

84/? 

4 

1 
r  2  1/3  11 

8.85 
4.43 
1.90 
26.56 

13.28 
3.32 

5.  Of  CO 

11.52 
5.76 
2.47 
34.56 

17.28 
4.32 

,  14,600 

12.52 
6.76 
3.47 
35.56 

18.28 
5.32 

-4450 

14,600 
4,450 
4,350 
62,000 

23,600 
4,050 
=  10,150. 

For  heat  of  combustion  of  various  fuels  see  Heat,  page  560. 

Analyses  of  Gases  of  Combustion. — The  following  are  selected 
from  a  large  number  of  analyses  of  gases  from  locomotive  boilers,  to 
show  the  range  of  composition  under  different  circumstances  (P.  H. 
Dudley,  Trans.  A.  I.  M.  E.,  iv,  250): 


Test. 

CO2 

CO 

O 

N 

1 

13.8 

2.5 

2.5 

81.6 

No  smoke  visible. 

2 

11.5 



6 

82.5 

Old  fire,  escaping  gas  white,  engine  working 
hard. 

3 

8.5 

8 

83 

Fresh  fire,  much  black  gas,  engine  working 
hard. 

4 
5 

2.3 
5.7 

17.2 
14.7 

80.5 
79.6 

Old  fire,damper  closed,  engine  standing  still. 
'*    smoke  white,  engine  working  hard. 

6 

8 

8.4 
12 
3.4 

1.2 

1 

8.4 
4.4 
16.8 

82 
82.6 
76.8 

New  fire,  engine  not  workingjhard. 
Smoke  black,  engine  not  working  hard, 
dark,  blower  on,  engine  standing  still. 

9 

6 

13.5 

81.5 

"       white,  engine  working  hard. 

In  analyses  on  the  Cleveland  and  Pittsburgh  road,  in  every  instance 
when  the  smoke  was  the  blackest,  there  was  found  the  greatest  percent- 
age of  unconsumed  oxygen  in  the  product,  showing  that  something 
besides  the  mere  presence  of  oxygen  is  required  to  effect  the  combustion 
of  the  volatile  carbon  of  fuels.  (What  is  needed  is  thorough  mixture  of 
the  oxygen  with  the  volatile  gases  in  a  hot  combustion  chamber.) 

Temperature  of  the  Fire.  (Rankine,  S.  E.,  p.  283.)  —  By  temper- 
ature of  the  fire  is  meant  the  temperature  of  the  products  of  combustion 
at  the  instant  that  the  combustion  is  complete.  The  elevation  of  that 
temperature  above  the  temperature  at  which  the  air  and  the  fuel  are 
supplied  to  the  furnace  may  be  computed  by  dividing  the  total  heat  of 


818 


FUEL. 


combustion  of  one  Ib.  of  fuel  by  the  weight  and  by  the  nicaii  specific 
heat  of  the  whole  products  of  combustion,  and  of  the  air  employed  for 
their  dilution  under  constant  pressure. 

Temperature  of  the  Fire,  the  Fuel  Containing  Hydrogen  and 
Water.  —  The  following  formula  is  developed  in  the  author's  "  Steam- 
boiler  Economy"  on  the  assumptions  that  all  the  hydrogen  and  the 
water  exist  in  the  combustion  chamber  as  superheated  steam  at  the  tem- 
perature of  the  fire,  and  that  the  specific  heat  of  the  gases  is  a  constant, 
=  0,237.  The  last  assumption  is  probably  largely  in  error,  since  it  is 
now  known  that  the  specific  heat  of  gases  increases  with  the  tempera- 
ture. (See  page  564. )  The  formula  will  give  approximate  results,  how- 
ever, and  is  sufficiently  accurate  when  relative  figures  only  are  desired. 

Let  C,  H,  O,  and  JV  represent  respectively  the  percentages  of  carbon, 
hydrogen,  oxygen,  and  water  in  a  fuel,  and  /  the  pounds  of  dry  gas  per 
pound  of  fuel,  =  COz+  N  +  excess  air,  then  the  theoretical  elevation  ol 
the  temperature  of  the  fire  above  the  temperature  of  the  atmosphere, 
=  616  (7  +  2220  H  -  327  O  -  44  W 
/+0.02  W  +  O.IS  H 

EXAMPLE.  —  Required  the  maximum  temperature  obtainable  by  burn- 
ing moist  wood  of  the  composition  C,  38;  //,  5;  O,  32;  ash,  1;  moisture  24; 
the  dry  gas  being  15  Ibs.  per  pound  of  wood,  and  the  temperature  of  the 
atmosphere  62°. 

T  _616  X38  +2220  X5  -327  X  32  -  44  X  24  _  _ 

15+0.02X24+0.18X5 

Rise  of  Temperature  in  Combustion  of  Gases.  (Eng'g,  March 
12  and  April  2,  1886.)  —  It  is  found  that  the  temperatures  obtained  by 
experiment  fall  short  of  those  obtained  by  calculation.  Three  theories 
have  been  given  to  account  for  this:  1.  The  cooling  effect  of  the  sides  of 
the  containing  vessel;  2.  The  retardation  of  the  evolution  of  heat  caused 
by  dissociation;  3.  The  increase  of  the  .specific  heat  of  the  gases  at  very 
high  temperatures.  The  calculated  temperatures  are  obtainable  9nly  on 
the  condition  that  the  gases  shall  combine  instantaneously  and  simulta- 
neously throughout  their  whole  mass.  This  condition  is  practically  im- 
possible in  experiments.  The  gases  formed  at  the  beginning  of  an  explo- 
sion dilute  the  remaining  combustible  gases  and  tend  to  retard  or  check 
the  combustion  of  the  remainder. 

CLASSIFICATION   OF   SOLID   FUELS. 

Gruner  classifies  solid  fuels  as  follows  (Eng'g  and  M'g  Jour.,  July,  1874). 


Name  of  Fuel. 

Ratio  TPJ. 
O+N* 

Proportion  of  Coke  of 
Charcoal  yielded  by 
the  Dry  Pure  Fuel. 

H     • 

Pure  cellulose  

8 

0.28@  0.30 

Wood  (cellulose  and  encasing  matter)  .  . 
Peat  and  fossil  fuel  

7 
6@  5 

.30®    .35 
.35  @     40 

5 

.40@    .50 

Bituminous  coals        

4  @  1 

50  @     90 

Anthracite  

1  @0.75 

.90  @    .92 

*  The  nitrogen  rarely  exceeds  1  per  cent  of  the  weight  of  the  fuel. 

Progressive  Change  from  Wood  to  Graphite. 

(J.  S.  Newberry  in  Johnson's  Cyclopedia,.) 


1 

. 

J 

- 

IN 

t 

|| 

. 

o.  . 

£ 

.tJ  SQ 

£'3 

fr 

H! 

A 

M 

«C> 

^ 

V 

w 

O  ~ 

Carbon  

49.1 

18.65 

30.45 

12.35 

18.10 

3.57 

14.53 

1.42 

13.11 

Hydrogen.              .  . 

6  3 

3  25 

3.05 

1.85 

1.20 

0.93 

0  71 

0.14 

0.13 

Oxygen  

44.6 

24.40 

20.20 

18.13 

2.07 

1.32 

0.65 

0.65 

0.00 

100.0 

46.30 

53.70 

32.33 

21.37 

5.82 

15.45 

2.21 

13.24 

CLASSIFICATION  OF  SOLID  FUELS. 


819 


Classification  of  Coals. 

It  is  convenient  to  classify  the  several  varieties  of  coal  according  to 
the  relative  percentages  of  carbon  and  volatile  matter  contained  in  their 
combustible  portion  as  determined  by  proximate  analysis.  The  follow- 
ing is  the  classification  given  in  the  author's  " Steam-boiler  Economy": 


Heating 

Relative 

Fixed 
Carbon. 

Volatile 
Matter. 

Value 
per  Ib.  of 
Combustible 

Value  of 
Combus- 
tible. Semi- 

B.T.U. 

bit.  =  100 

Anthracite  

97  to  90 

3  to  10 

14800  to  15400 

93 

Semi-anthracite  

90  to  85 

10  to  15 

15400  to  15500 

97 

Semi-bituminous 

85  to  70 

15  to  30 

15400  to  16000 

100 

Bituminous,  Eastern.  . 

70  to  55 

30  to  45 

14800  to  15600 

96 

Bituminous,  Western  . 

65  to  50 

35  to  50 

12500  to  14800 

90 

Lignite  

under  50 

over  50 

11000  to  13500 

77 

The  anthracites,  with  some  unimportant  exceptions,  are  confined  to 
three  small  fields  in  eastern  Pennsylvania.  The  semi-anthracites  are 
found  in  a  few  small  areas  in  the  western  part  of  the  anthracite  field. 
The  semi-bituminous  coals  are  found  on  the  eastern  border  of  the  great 
Appalachian  coal  field,  extending  from  north  central  Pennsylvania  across 
the  southern  boundary  of  Virginia  into  Tennessee,  a  distance  of  over  300 
miles.  They  include  the  coals  of  Clearfield,  Cambria,  and  Somerset 
counties,  Pennsylvania,  and  the  Cumberland,  Md.,  the  Pocahontas,  Va 
and  the  New  River,  W.  Va.,  coals. 

It  is  a  peculiarity  of  the  semi-bituminous  coals  that  their  combustible 
portion  is  of  remarkably  uniform  composition,  the  volatile  matter  usually 
ranging  between  18  and  22%  of  the  combustible,  and  approaching  in  its 
analysis  marsh  gas,  CH4,  with  very  little  oxygen.  They  are  usually  low 
also  in  moisture,  ash,  and  sulphur,  and  rank  among  the  best  steaming 
coals  in  the  world. 

The  eastern  bituminous  coals  occupy  the  remainder  of  the  Appala- 
chian coal  field,  from  Pennsylvania  and  eastern  Ohio  to  Alabama  They 
are  higher  in  volatile  matter,  ranging  from  30  to  over  40%,  the  higher 
figures  in  the  western  portion  of  the  field.  The  volatile  matter  is  of 
lower  heating  value,  being  .higher  in  oxygen.  The  western  bituminous 
coals  are  found  in  most  of  the  states  west  of  Ohio.  They  are  higher  in 
volatile  matter  and  in  oxygen  and  moisture  than  the  bituminous  coals 
of  the  Appalachian  field,  and  usually  give  off  a  denser  smoke  when 
burned  in  ordinary  furnaces. 

A  later  classification  by  the  author  (Trans.  A.  S.  M.  E.,  1914; 
"  Steam-boiler  Economy,"  2d  edition,  1915)  is  given  in  the  table  below. 
It  divides  the  bituminous  coals  into  three  grades,  high,  medium  and 
low,  the  chief  distinction  between  them  being  the  percentage  of 
moisture  found  in  the  coal  after  it  is  air-dried.  The  coals  highest 
in  inherent  moisture  are  also  highest  in  oxygen. 

Classes:  I.  Anthracite.  II.  Semi-anthracite.  III.  Semi-bitumi- 
nous. IV.  Cannel.  V.  Bituminous,  high  grade.  VI.  Bituminous,  me- 
dium grade.  VII.  Bituminous,  low  grade.  VIII.  Sub-bituminous  and 
lignite. 


Class. 

Volatile 
Matter,  % 
of  Com- 
bustible. 

Oxygen 
in  Com- 
bustible 
Per  Cent. 

Moisture 
in  Air-dry, 
Ash-free 
Coal,  % 

B.T.U. 

per  Ib. 
Combustible. 

B.T.U.  per 
Ib.  Air-dry, 
Ash-free 
Coal 

J 

IV* 
V 
VI 
VII 
VIII 

less  than  10 
10  to  15 
15  to  30 
45  to  60 
30  to  45 
32  to  50 
32  to  50 
27  to  60 

1  to   4 
Ito   5 
1  to   6 
5  to   8 
5  to  14 
6  to  14 
7  to  14 
10  to  33 

less  than  1.8 
less  than  1.8 
less  than  1.8 
less  than  1.8 
1     to  4 
2.5  to  6.5 
5    to  12 
7     to  26 

14,800  to  15,400 
15,400  to  15,500 
15,400  to  16,050 
15,700  to  16,200 
14,800  to  15,600 
13,800  to  15,100 
12,400  to  14,600 
9,600  to  13,250 

14,600  to  15,400 
15,200  to  15,500 
15,300  to  16,000 
15,500  to  16,050 
14,350  to  14,400 
11,  300  to  14,400 
11,  300  to  13,400 
7,400  to  11,650 

*  Eastern  cannel.    The  Utah  caonel  is  much  lower  in  heating  value.     - 


820 


FUEL. 


The  U.  S.  Geological  Survey  classifies  coals  into  six  groups,  as  follows: 
(1)  anthracite;  (2)  semi-anthracite;  (3)  semi-bituminous;  (4)  bitu- 
minous; (5)  sub-bituminous,  or  black  lignite;  and  (6)  lignite. 

Classes  5  and  6  are  described  as  follows: 

Sub-bituminous  coal  is  commonly  known  as  "lignite,"  "lignitic  coal," 
"black  lignite,"  "brown  coal,"  etc.  It  is  generally  black  and  shining, 
closely  resembling  bituminous  coal,  but  it  weathers  more  rapidly  on 
exposure  and  lacks  the  prismatic  structure  of  bituminous  coal.  Its 
calorific  value  is  generally  less  than  that  of  bituminous  coal.  The  local- 
ities in  which  this  sub-bituminous  coal  is  found  include  Montana,  Idaho, 
Washington,  Oregon,  California,  Wyoming,  Utah,  Colorado,  New  Mexico, 
and  Texas. 

Lignite  is  commonly  known  as  "lignite,"  "brown  lignite,"  or  "brown 
coal."  It  usually  has  a  woody  structure  and  is  distinctly  brown  in  color, 
even  on  a  fresh  fracture.  It  carries  a  higher  percentage  of  moisture  than 
any  other  class  of  coals,  its  mine  samples  showing  from  30  to  40%  of 
moisture.  The  localities  in  which  lignite  is  found  are  chiefly  North 
Dakota,  South  Dakota,  Texas,  Arkansas,  Louisiana,  Mississippi,  and 
Alabama. 

The  following  analyses  of  representative  coals  of  the  six  classes  are 
given  by  Prof.  N.  W.  "Lord: 

Class  1  —  Anthracite  Culm.     Penna. 

Class  2  —  Semi-anthracite.     Arkansas. 

Class  3  —  Semi-bituminous.     W.  Va. 

Class  4(a)  —  Bituminous  coking.    Connellsville,  Pa. 

Class  4(ft)  —  Bituminous  non-coking.    Hocking  Valley,  Ohio. 

Class  5  —  Sub-bituminous.    Wyoming,  black  lignite. 

Class  6  —  Lignite.    Texas. 

COMPOSITION  OF  ILLUSTRATIVE  COALS — CAR-LOAD  SAMPLES. 
Proximate  Analysis  of  "Air-dried"  Sample. 

Class ,      1  2  3  4a         4b  5  6 

Moisture 2.08        1.28       0.65       0.97       7.55       8.68       9.88 

Vol.  comb 7.27      12.82     18.80     29.09     34.03     41.31     36.17 

Fixed  carbon 74.32     73.69     75.92     60.85     52.57     46.49     43.65 

Ash 16.33     12.21       4.63       9.09       5.85       3.52     10.30 

Loss  on  air-drying  .     3.40       1.10       1.10       4.20  Undet.     11.30     23.50 

Ultimate  Analysis  of  Coal  Dried  at  105°  C. 

Hydrogen 2.63  3.63  4.54  4.57  5.06  5.31  4.47 

Carbon 76.86  78.32  86.47  77.10  75.82  73.31  64.84 

Oxygen 2.27  2.25  2.68  6.67  10.47  15.72  16.52 

Nitrogen 0.82  1.41  1.08  1.58  1.50  1.21  1.30 

Sulphur 0.78  2.03  0.57  0.90  0.82  0.60  1.44 

Ash 16.64  12.36  4.66  9.18  6.33  3.85  11.43 

Results  Calculated  to  an  Ash  and  Moisture-Free  Basis. 

Volatile  comb 8.91      14.82     19.85     32.34     39.30     47.05     45.31 

Fixed  carbon 91.09     85.18     80.15     67.66     60.70     52.95     54.69 

Ultimate  Analysis. 

Hydrogen 3.16       4.14       4.76       5.03  5.41  5.50  5.05 

Carbon 92.20     89.36     90.70     84.89  80.93  76.35  73.21 

Oxygen 2.72       2.57       2.81       7.34  11.18  16.28  18.65 

Nitrogen 0.98       1.61        1.13       1.74  1.61  1.25  1.47 

Sulphur 0.94       2.32       0.60        1.00  0.87  0.62  1.62 

Calorific  Value  in  B.T.U.  per  lb.,  by  Dulong's  formula. 
Air-dried  coal.  12,472     13,406     15,190     13,951     12,510     11,620     10,288 
Combustible  ..  15,286     15,496     16,037     15,511     14,446     13,235     12,889 

Caking  and  Non-caking  Coals.  —  Bituminous  coals  are  sometimes 
classified  as  caking  and  non-caking  coals,  according  to  their  behavior 
when  subjected  to  the  process  of  coking.  The  former  undergo  an  incipi- 
ent fusion  or  softening  when  heated,  so  that  the  fragments  coalesce  and 
yield  a  compact  coke,  while  the  latter  (also  called  free-burning)  preserve 
their  form,  producing  a  coke  which  is  only  serviceable  when  made  from 


CLASSIFICATION   OF   SOLID   FUELS. 


821 


large  pieces  of  coal,  the  smaller  pieces  being  incoherent.  The  reason  of 
this  difference  is  not  clearly  understood,  as  non-caking  coals  are  often  of 
similar  ultimate  chemical  composition  to  caking  coals.  Some  coals 
which  cannot  be  made  into  coke  in  a  bee-hive  oven  are  easily  coked  in 
gas-heated  ovens. 

Cannel  Coals  are  coals  that  are  higher  in  hydrogen  than  ordinary 
coals.  They  are  valuable  as  enrichers  in  gas-making.  The  following  are 
gome  ultimate  analyses: 


C. 

H. 

O+N. 

S. 

Ash. 

Combustible. 

C. 

H. 

O+N. 

Boghead,  Scotland  
Albertite,  Nova  Scotia  .  . 
Tasmanite,  Tasmania  .  .  . 

63.10 
82.67 
79.34 

8.91 
9.14 
10.41 

7.25 
8.19 
4.93 

0.96 

19.78 

79.61 
82.67 
83.80 

11.24 
9.14 
10.99 

9.15 
8.19 
5.21 

5.32 

Rhode  Island  Graphitic  Anthracite.  —  A  peculiar  variety  of  coal  is 
found  in  the  central  part  of  Rhode  Island  and  in  Eastern  Massachusetts. 
It  resembles  both  graphite  and  anthracite  coal,  and  has  about  the  follow- 
ing composition  (A.  E.  Hunt,  Trans.  A.  I.  M.  E.,  xvii.  678:  Graphitic 
carbon,  78%;  volatile  matter,  2.60%;  silica,  15.06%;  phosphorus,  .045%. 
It  burns  with  extreme  difficulty. 

ANALYSIS  AND  HEATING  VALUE  OF  COALS. 

Coal  is  composed  of  four  different  things,  which  may  be  separated  by 
proximate  analysis,  viz.:  fixed  carbon,  volatile  hydrocarbon,  ash  and 
moisture.  In  making  a  proximate  analysis  of  a  weighed  quantity,  such 
as  a  gram  of  coal,  the  moisture  is  first  driven  off  by  heating  it  to  about 
250°  F.  then  the  volatile  matter  is  driven  off  by  heating  it  in  a  closed 
crucible  to  a  red  heat,  then  the  carbon  is  burned  out  of  the  remaining 
coke  at  a  white  heat,  with  sufficient  air  supplied,  until  nothing  is  left 
but  the  ash. 

The  fixed  carbon  has  a  constant  heating  value  of  about  14,600  B.T.U. 
per  Ib.  The  value  of  the  volatile  hydrocarbon  depends  on  its  composi- 
tion, and  that  depends  chiefly  on  the  district  in  which  the  coal  is  mined. 
It  may  be  as  high  as  21,000  B.T.U.  per  Ib.,  or  about  the  heating  value  of 
marsh  gas,  in  the  best  semi-bituminous  coals,  which  contain  very  small 
percentages  of  oxygen,  or  as  low  as  12,000  B.T.U.  per  Ib.,  as  in  those 
from  some  of  the  western  states,  which  are  high  in  oxygen.  The  ash  has 
no  heating  value,  and  the  moisture  has  in  effect  less  than  none,  for  its 
evaporation  and  the  superheating  of  the  steam  made  from  it  to  the  tem- 
perature of  the  chimney  gases,  absorb  some  of  the  heat  generated  by  the 
combustion  of  the  fixed  carbon  and  volatile  matter. 

The  analysis  of  a  coal  may  be  reported  in  three  different  forms,  as  per- 
centages of  the  moist  coal,  of  the  dry  coal  or  of  the  combustible,  as  in  the 
following  table.  By  "combustible"  is  always  meant  the  sum  of  the 
fixed  carbon  and  volatile  matter,  the  moisture  and  ash  being  excluded, 
By  some  writers  it  is  called  "coal  dry  and  free  from  ash"  and  by  others 
"pure  coal." 


Moist  Coal. 

Dry  Coal. 

Combus- 
tible. 

Moisture  
Volatile  matter  

10 
30 

33.33 

37.50 

50 

55.56 

62.50 

Ash....  

10 

11.11 

100 

100.00 

100.00 

The  sulphur,  commonly  reported  with  a  proximate  analysis,  is  deter- 
mined separately.  In  the  proximate  analysis  part  of  it  escapes  with  the 
volatile  matter  and  the  rest  of  it  is  found  in  the  ash  as  sulphide  of  iron. 
The  sulphur  should  be  given  separately,  in  the  report  of  the  analysis. 

The  relation  of  the  volatile  matter  and  of  the  fixed  carbon  in  the  com- 
bustible portion  of  the  coal  enables  us  to  judge  the  class  to  which  the 
coal  belongs,  as  anthracite,  semi-anthracite,  semi-bituminous,  bituminous 


822 


FUEL. 


or  lignite.  Coals  containing  less  than  10  per  cent  volatile  matter  in  the 
combustible  would  be  classed  as  anthracite,  between  10  and  15  per 
cent  as  semi-anthracite,  between  15  and  30  per  cent  as  semi- bituminous, 
between  30  and  50  per  cent  as  bituminous,  and  over  50  per  cent  as  lig- 
nitic  coals  or  lignites.  In  the  classification  of  the  U.S.  Geological  Sur- 
vey the  sub-bituminous  coals  and  lignites  are  distinguished  by  their 
structure  and  color  rather  than  by  analysis. 

The  figures  in  the  second  column,  representing  the  percentages  in  the 
dry  coal,  are  useful  in  comparing  different  lots  of  coal  of  one  class,  and 
they  are  better  for  this  purpose  than  the  figures  in  the  first  column,  for 
the  moisture  is  a  variable  constituent,  depending  to  a  large  extent  on  the 
weather  to  which  the  coal  has  been  subjected  since  it  was  mined,  on  the 
amount  of  moisture  in  the  atmosphere  at  the  time  when  it  is  analyzed , 
and  on  the  extent  to  which  it  may  have  accidentally  been  dried  during 
the  process  of  sampling. 

The  heating  value  of  a  coal  depends  on  its  percentage  of  total  combus- 
tible matter,  and  on  the  heating  value  per  pound  of  that  combustible. 
The  latter  differs  in  different  districts  and  bears  a  relation  to  the  per- 
centage of  volatile  matter.  It  is  highest  in  the  semi-bituminous  coals, 
being  nearly  constant  at  about  15,750  B.T.U.  per  pound.  It  is  between 
14,800  and  15,500  B.T.U.  in  anthracite,  and  ranges  from  15,500  down  to 
13,000  in  the  bituminous  coals,  decreasing  usually  as  we  go  westward, 
and  as  the  volatile  matter  contains  an  increasing  percentage  of  oxygen. 
In  some  lignites  it  is  as  low  as  10,000. 

In  reporting  the  heating  value  of  a  coal,  the  B.T.U.  per  pound  of  com- 
bustible should  always  be  stated,  for  convenient  comparison  with  other 
reports. 

In  1892  the  author  deduced  from  Mahler's  tests  on  European  coals 
the  following  table  of  the  approximate  heating  value  of  coals  of  differ- 
ent composition. 

APPROXIMATE  HEATING  VALUES  OF  COALS. 


Equivalent 

Equivalent 

Per  Cent 
Volatile 
Matter  in 

Heating 
Value,  B.T.U. 

Water 
Evapora- 
tion from 

Per  Cent 
Volatile 
Matter  in 

Heating 
Value,  B.T.U. 

Water 
Evapora- 
tion from 

Coal  Dry 
and  Free 
from  Ash. 

per  Ib. 
Combus- 
tible. 

and  at  212° 
per  Ib. 
Combus- 

Coal Dry 
and  Free 
from  Ash. 

per  Ib. 
Combus- 
tible. 

andat212c 
per  Ib. 
Combus- 

tible. 

tible. 

0 

14,580 

15.09 

32 

15.480 

16.03 

3 

14,940 

15.47 

37 

15,120 

15.65 

6 

15,210 

15.75 

40 

14,760 

15.28 

10 

15,480 

16.03 

43 

14,220 

14.72 

13 

15,660 

16.21 

45 

13.860 

14.35 

20 

15.840 

16.40 

47 

13.320 

13.79 

28 

15.660 

16.21 

49 

12.420 

12.86 

The  experiments  of  Lord  and  Haas  on  American  coals  (Trans. 
A.I.M.E.,  1897)  practically  confirm  these  figures  for  all  coals  in  which 
the  percentage  of  fixed  carbon  is  60%  and  over  of  the  combustible,  but 
for  coals  containing  less  than  60  %  fixed  carbon  or  more  than  40  %  volatile 
matter  in  the  combustible,  they  are  liable  to  an  error  in  either  direction 
of  about  4%.  It  appears  from  these  experiments  that  the  coal  of  one 
seam  in  a  given  district  has  the  same  heating  value  per  pound  of  com- 
bustible within  one  or  two  per  cent  [true  only  of  some  districts],  but  coals 
of  the  same  proximate  analysis,  and  containing  over  40  %  volatile  matter, 
but  mined  in  different  districts,  may  vary  6  or  8  %  in  heating  value. 

The  coals  containing  from  72  to  87  per  cent  of  fixed  carbon  in  the  com- 
bustible have  practically  the  same  heating  value.  This  is  confirmed  by 
Lord  and  Haas's  tests  of  Pocahontas  coal.  A  study  of  these  tests  and  of 
Mahler's  indicates  that  the  heating  value  of  all  the  semi-bituminous  coals, 
75  to  87.5%  fixed  carbon,  is  within  1  H%  of  15,750  B.T.U.  per  pound. 

The  heating  value  of  any  coal  may  also  be  calculated  from  its  ultimate 
analysis,  with  a  probable  error  not  exceeding  2%,  by  Dulong's  formula: 


ANALYSES  AND  HEATING  VALUE  OF  COALS.         823 


Heating  value  per  Ib.  =  146  C  -f  620/H  -  ^-l  +  40  S 


in  which  C,  H,  S,  and  O  are  respectively  the  percentages  of  carbon, 
hydrogen,  sulphur  and  oxygen.  Its  approximate  accuracy  is  proved  by 
both  Mahler's  and  Lord  and  Haas's  experiments,  and  any  deviation  of 
the  calorimetric  determination  of  any  coals  (cannel  coals  and  lignites 
excepted)  more  than  2  %  from  that  calculated  by  the  formula,  is  more 
likely  to  proceed  from  an  error  in  either  the  calorimetric  test  or  the 
analysis,  than  from  an  error  in  the  formula. 

Average  Results  of  Lord  and  Haas's  Tests. — ("  Steam  Boiler 
Economy,"  p.  156.) 


Name  of  Coal. 

C. 

H. 

O. 

N. 

S. 

,d 

$ 

'o 

ri 

O 

1 

l,f 

tf 

H 

03 

% 

> 

ft 
fi 

>^° 

ft 

Pocahontas,  Va. 

84.87 

4.20 

2.84 

0.85 

0.59 

5.89 

0.76 

18.51 

74.84 

19.82 

15766 

Thacker,  W.  Va. 

78.65 

5.00 

6.01 

1.41 

1.28 

6.27 

1.38135.68 

56.67 

38.62 

15237 

Pittsburg,  Pa..  . 

75.24 

5.01 

7.04 

1.51 

1.79 

8.02 

1.3736.80 

53.81 

40.61 

14963 

Middle  Kittan- 

ing,  Pa  

75,.  19 

4.91 

7.47 

1.46 

1.98 

7.18 

1.81 

36.32 

54.69 

39.91 

14800 

Upper  Freeport, 

Pa.  and  O  . 

72.65 

4.82 

7.26 

1.34 

2.89 

9.10 

1.93 

37.35 

51.63 

41.98 

14755 

Mahoning,  O  .  .  . 

71.13 

4.56 

7.17 

1.23 

1.86 

10.90 

3.15 

35.00 

50.95 

40.72 

14728 

Jackson  Co.,  O.  . 

70.72 

4.45 

10.82 

1.47 

1.13 

3.25 

8.17 

35.79 

52.78 

40.41 

14141 

Hocking  Val- 

ley, O  

68.03 

4.97 

9.87 

1.44 

1.59 

8.00 

6.59 

35.77 

49.64 

41.84 

14040 

*  Per  Ib.  of  combustible,  by  the  Mahler  calorimeter.  The  average 
figures  calculated  from  the  ultimate  analyses  agreed  within  0.5  %,  except 
in  the  case  of  the  Jackson  Co.  coal,  in  which  the  calorimetric  result  was 
1.6%  higher  than  that  computed  from  the  analysis. 

Sizes  of  Anthracite  Coal. — When  anthracite  is  mined  it  is  crushed 
in  a  "  breaker,"  and  passed  over  screens  separating  it  into  different  sizes, 
which  are  named  as  follows: 

Lump,  passes  over  bars  set  3  1/2  to  5  in.  apart;  steamboat,  over  3  1/2 
in.  and  out  of  screen;  broken,  through  4 1/2  in.,  over  3  1/4  in.;  egg,  3  1/4 
to  2  s/16  in. ;  stove,  2  5/i6  to  1 5/g  in. ;  chestnut,  1 5/8  to  7/8  in. ;  pea,  7/8  to 
9/16  in.;  buckwheat,  No.  1,  9/16  to5/i6in.;  No.  2,  5/i6  to3/16;  No.  3,  3/16 
to  3/32  in.;  culm,  through  3/32  in. 

The  terms  "buckwheat,"  "rice"  and  "barley"  are  used  in  some 
localities  instead  of  No.  1,  No.  2  and  No.  3  buckwheat. 

When  coal  is  screened  into  sizes  for  shipment  the  purity  of  the  dif- 
ferent sizes  as  regards  ash  varies  greatly.  Samples  from  one  mine  gave 
results  as  follows: 


LName  of  Coal. 

Screened. 

Analyses. 

Through 
Inches. 

Over 
Inches. 

Fixed 
Carbon. 

Ash. 

2.5 
1.75 
1.25 
0.75 
0.50 

1.75 
1.25 
0.75 
0.50 
0.25 

88.49 
83.67 
80.72 
79.05 
76.92 

5.66 
10.17 
12.67 
14.66 
16.62 


omve   .  . 

Chestnut.  . 

Pea  

Buckwheat   .... 

Space  Occupied  by  Anthracite  Coal.  (J.  C.  I.  W.,  vol.  iii.)— The 
cubic  contents  of  2240  Ib.  of  hard  Lehigh  coal  is  a  little  over  36  feet;  an 
average  Schuylkill  white-ash,  37  to  38  feet;  Shamokin,  38  to  39  feet; 
Lorberry,  nearly  41. 

According  to  measurements  made  with  Wilkes-Barre  anthracite  coal 
from  the  Wyoming  Valley,  it  requires  32.2  cu.  ft.  of  lump,  33.9  cu.  ft. 


824 


FUEL. 


broken,  34. 5  cu.  ft.  egg,  34.8  cu.  ft.  of  stove,  35.7  cu.  ft.  of  chestnut,  and 

36.7  cu.  ft.  of  pea,  to  make  one  ton  Of  coal  of  2240  Ib. ;  while  it  requires 

28.8  cu.  ft.  of  lump,  30.3  cu.  ft.  of  broken,  30.8  cu.  ft.  of  egg,  31.1  cu.  ft. 
of  stove,  31.9  cu.  ft.  of  chestnut,  or  32.8  cu.  ft.  of  pea,  for  one  ton  (2000  Ib.) 

Bernice  Basin,  Pa.,  Coals. 

Water    Vol.  H.C.  Fixed  C.     Ash.  Sulphur. 
Bernice  Basin,  Sullivan^       0.96         3.56         82.52         3.27     0.24 

and   Lycoming   Cos!;  >        to  to  to  to         to 

range  of  8 J       1.97         8.56         89.39         9.34     1:04 

This  coal  is  on  the  dividing-line  between  the  anthracites  and  semi- 
anthracites,  and  is  similar  to  the  coal  of  the  Lykens  Valley  district. 

More  recent  analyses  (Trans.  A.  I.  M.  E.,  xiv.  721)  give: 

Water    VoL  H.C.  Fixed  C.      Ash.  Sulphur 

Working  seam 0.65         9.40         83.69         5.34     0.91 

60  ft.  below  seam 3.67       15.42         71.34         8.97     0.59 

The  first  is  a  semi-anthracite,  the  second  a  semi-bituminous. 

Connellsville  Coal  and  Coke.  (Trans.  A.  I.  M.  E.,  xiii.  332.) — The 
Connellsville  coal-field,  in  the  southwestern  part  of  Pennsylvania,  is  a 
strip  about  3  miles  wide  and  60  miles  in  length.  The  mine  workings  are 
confined  to  the  Pittsburgh  seam,  which  here  has  its  best  development  as 
to  size,  and  its  quality  best  adapted  to  coke-making.  It  generally  af- 
fords from  7  to  8  feet  of  coal. 

The  following  analyses  by  T.  T.  Morrell  show  about  its  range  of  com- 
position: 

Moisture.  Vol.  Mat.  Fixed  C.     Ash.     Sulphur.  Phosph's. 
HeroldMine     1.26         28.83         60.79         8.44         0.67         0.013 
KintzMine.      0.79         31.91         56.46         9.52         1.32         0.02 

In  comparing  the  composition  of  coals  across  the  Appalachian  field, 
in  the  western  section  of  Pennsylvania,  it  will  be  noted  that  'the  Con- 
nellsville variety  occupies  a  peculiar  position  between  the  rather  dry 
semi-bituminous  coals  eastward  of  it  and  the  fat  bituminous  coals  flank- 
ing it  on  the  west. 

Indiana  Coals.  (J.  S.  Alexander,  Trans.  A.  I.  M.  E.,  iv.  100.) — The 
typical  block  coal  of  the  Brazil  (Indiana)  district  differs  in  chemical 
composition  but  little  from  the  coking  coals  of  Western  Pennyslvania. 
The  physical  difference,  however,  is  quite  marked;  the  latter  has  a 
cuboid  structure  made  up  of  bituminous  particles  lying  against  each 
other,  so  that  under  the  action  of  heat  fusion  throughout  the  mass 
readily  takes  place,  while  block  coal  is  formed  of  alternate  layers  of  rich 
bituminous  matter  and  a  charcoal-like  substance,  which  is  not  only  very 
slow  of  combustion,  but  so  retards  the  transmission  of  heat  that  agglu- 
tination is  prevented,  and  the  coal  burns  away  layer  by  layer,  retaining 
its  form  until  consumed. 

Illinois  Coals.  The  Illinois  coals  are  generally  high  in  moisture, 
volatile  matter,  ash  and  sulphur,  and  the  volatile  matter  is  high  in 
oxygen;  consequently  the  coals  are  low  in  heating  value.  The  range  of 
quality  is  a  wide  one.  The  Big  Muddy  coal  of  Jackson  Co.,  which  has  a 
high  reputation  as  a  steam  coal  in  the  St.  Louis  market,  has  about  36% 
of  volatile  matter  in  the  combustible,  while  a.  coal  from  Staunton, 
Macoupin  Co.,  tested  by  the  author  in  1883  (Trans.  A.  S.  M.  E.,  v.  266) 
had  68%.  A  boiler,  test  with  this  coal  gave  only  6.19  Ibs.  of  water 
evaporated  from  and  at  212°  per  Ib.  of  combustible,  in  the  same  boiler 
that  had  given  9.88  Ibs.  with  Jackson,  O.,  nut. 

Prof.  S.  W.  Parr,  in  Bulletin  No.  3  of  the  111.  State  Geol.  Survey,  1906, 
reports  the  analyses  and  calorimetric  tests  of  150  Illinois  coals.  The 
two  having  the  lowest  and  the  highest  value  per  pound  of  combustible 
have  the  following  analysis: 


Air-dried  Coal. 

Pure  Coal. 

Moist. 

Ash. 

Vol. 

Fixed 
C. 

S. 

Vol. 

Fixed 
C. 

B.T.U. 
per  Ib. 

Lowest.  . 
Highest  . 

9.90 
5.68 

5.02 
8.90 

40.75 
33.32 

44.33 
52.10 

2.00 
1.18 

47.90 
39.02 

52.10 
60.98 

12,162 
14,830 

The  poorest  coal  of  the  series  had  a  heating  value  of  only  8645  B.T.U. 


ANALYSES  AND  HEATING  VALUE  OF  COALS.    825 


per  lb.,  air  dry;  it  contained  9.70  moisture  and  31.18  ash, -and  the  B.T.U. 
per  lb.  combustible  was  14,623.  The  best  coal  had  a  heating  value  of 
13,303  per  lb.;  moistures  4.20,  ash  5.50,  B.T.U.  per  lb.  combustible, 
14,734. 

Of  the  150  coals,  28  gave  between  14,500  and  14,830  B.T.U.  per  lb. 
combustible;  82  between  14,000  and  14,500;  32  between  13,500  and 
14,000;  6  between  13,000  and  13,500;  one  12,535  and  one  12,162.  The 
average  is  about  14,200.  The  volatile  matter  ranged  from  36.24%  to 
53.80%  of  the  combustible;  the  sulphur  from  0-.62  to  4.96%;  the  ash 
from  2.32  to  31.18%,  and  the  moisture  from  3.28  to  12.74%,  all  calcu- 
lated from  the  air-dried  samples.  The  moisture  in  the  coal  as  mined  is 
not  stated,  but  was  no  doubt  considerably  higher.  The  author  has 
found  over  14%  moisture  in  a  lump  of  Illinois  coal  that  was  apparently 
dry,  having  been  exposed  to  air,  under  cover,  for  more  than  a  month. 

Colorado  Coals. — The  Colorado  coals  are  of  extremely  variable  com- 
position, ranging  all  the  way  from  lignite  to  anthracite.  G.  C.  Hewitt 
(Trans.  A.  I.  M.  E.,  xvii.  377)  says:  The  coal  seams,  where  unchanged 
by  heat  and  flexure,  carry  a  lignite  containing  from  5  %  to  20  %  of  water. 
In  the  southeastern  corner  of  the  field  the  seams  have  been  metamor- 
phosed so  that  in  four  miles  the  same  seams  are  an  anthracite,  coking, 
and  dry  coal.  The  dry  seams  also  present  wide  chemical  and  physical 
changes  in  short  distances.  A  soft  and  loosely  bedded  coal  has  in  a 
hundred  feet  become  compact  and  hard  without  the  interventi9n  of  a 
faul( .  A  couple  of  hundred  feet  has  reduced  the  water  of  combination 
from  12%  to  5%. 

Western  Arkansas  and  Oklahoma  (formerly  Indian  Territory). 
(H.  M.  Chance,  Trans.  A.  I.  M.  E.,  1890.) — The  western  Arkansas  coals 
are  dry  semi-bituminous  or  semi-ant hracitic  coals,  mostly  non-coking, 
or  with  quite  feeble  coking  properties,  ranging  from  14%  to  16%  in 
volatile  matter,  the  highest  percentage  yet  found,  according  to  Mr. 
Winslow's  Arkansas  report,  being  17.65. 

In  the  Mitchell  basin,  about  10  miles  west  from  the  Arkansas  line,  the 
coal  shows  19  %  volatile  matter;  the  Mayberry  coal,  about  8  miles  farther 
west,  contains  23  % ;  and  the  Bryan  Mine  coal,  about  the  same  distance 
west,  shows  26%.  About  30  miles  farther  west,  the  coal  shows  from 
38%  to  41.5  %  volatile  matter,  which  is  also  about  the  percentage  in 
coals  of  the  McAlester  and  Lehigh  districts. 

Analyses  of  Foreign  Coals.     (Selected  from  D.  L.  Barnes's  paper  on 
American  Locomotive  Practice,  Trans.  A.  S.  C.  E.,  1893.) 


Volatile 
Matter. 

Fixed 
Carbon. 

1 

Volatile 
Matter. 

Fixed 
Carbon. 

1 

Great  Britain: 
South-  Wales  
South-  Wales  
Lancashire,  Eng. 
Derbyshire,    " 
Durham, 
Staffordshire,  " 
Scotlandf  
Scotlandj 

8.5 
6.2 
17.2 
17.7 
15.05 
20.4 
17.1 
17.5 

21.93 

88.3 
92.3 
80.1 
79.9 
86.8 
78.6 
63.1 
80.1 

70.55 

3.2 
1.5 
2.7 
2.4 
1  .1 
1.0 
19.8 
2.4 

7.52 

South  America: 
Chili,  Chiroqui.  . 
Patagonia 

24.11 
24.35 
40.5 

26.8 
26.9 

15.8 
14.98 
26.5 
6.16 

38.98 
62.25 
57.9 

60.7 
67.6 

64.3 
82.39 
70.3 
63.4 

36.91 
13.4 
1.6 

12.5 
5.5 

10.0 
2.04 
14.2 
30.45 

Brazil  

Canada: 
Nova  Scotia  .... 
Cape  Breton.  .  .. 
Australia: 
Lignite. 

South  America: 
Chili  

Sydney,  N.S.W.. 
Borneo  
Tasmania  

*  Semi-bit,  coking  coal.  t  Boghead  cannel  gas  coal. 

J  Semi-bit,  steam-coal. 

An  analysis  of  Pictou,  N.  S.,  coal,  in  Trans.  A.  I.  M.  E.,  xiv.  560,  is: 
vol.,  29.63;  carbon,  56.98;  ash,  13.39;  and  one  of  Sydney,  Cape  Breton, 
coal  is:  vol.,  34.07;  carbon,  61.43;  ash,  4.50. 

Sampling  'Coal  for  Analysis. — J.  P.  Kimball,  Trans.  A.  I.  M.  E., 
xii.  317,  says:  The  unsuitable  sampling  of  a  coal-seam,  or  the  improper 
preparation  of  the  sample  in  the  laboratory,  often  gives  rise  to  errors  in 


826  FUEL. 

determinations  of  the  ash  so  wide  in  range  as  to  vitiate  the  analysis  for 
all  practical  purposes;  every  other  single  determination,  excepting  mois- 
ture, showing  its  relative  part  of  the  error.  The  determinations  of  sul- 
phur and  ash  are  especially  liable  to  error,  as  they  are  intimately  asso- 
ciated in  the  slates. 

Wm.  JForsyth,  in  his  paper  on  The  Heating  Value  of  Western  Coals 
(Eng'g  News,  Jan.  17, 1895) ,  says:  This  trouble  in  getting  a  fairly  average 
sample  of  anthracite  coal  has  compelled  the  Reading  R.  R.  Co.,  in  get- 
ting its  samples,  to  take  as  much  as  300  Ib.  for  one  sample,  drawn  direct 
from  the  chutes,  as  it  stands  ready  for  shipment. 

The  directions  for  collecting  samples  of  coal  for  analysis  at  the  C.,  B. 
&  Q.  laboratory  are  as  follows: 

Two  samples  should  be  taken,  one  marked  "average,"  the  other 
"select."  Each  sample  should  contain  about  10  Ib.,  made  up  of  lumps 
about  the  size  of  an  orange  taken  from  different  parts  of  the  dump  or 
car,  and  so  selected  that  they  shall  represent  as  nearly  as  possible,  first, 
the  average  lot;  second,  the  best  coal. 

An  example  ol  the  difference  between  an  "average"  and  a  "select" 
sample,  taken  from  Mr.  Forsyth's  paper,  is  the  following  of  an  Illinois 
coal: 

Moisture.    Vol.  Mat.    Fixed  Carbon.   Ash. 

Average 1.36  27.69  35.41  35.54 

Select 1.90  34.70  48.23  15.17 

The  theoretical  evaporative  power  of  the  former  was  9.13  Ibs.  of  water 
from  and  at  212°  per  Ib.  of  coal,  and  that  of  the  latter  11.44  Ibs. 

For  methods  of  sampling  see  Kent's  "Steam  Boiler  Economy,"  2d 
edition  (1915),  also  Report  of  the  Power  Test  Committee,  A.  S.  M.  E., 
1915,  and  Technical  Paper  No.  8  of  the  U.  S.  Bureau  of  Mines,  1913. 

RELATIVE  VALUE  OF  STEAM  COALS. 

The  heating  value  of  a  coal  may  be  determined,  with  more  or  less 
approximation  to  accuracy,  by  three  different  methods. 

1st,  by  chemical  analysis;  2d,  by  combustion  in  a  coal  calorimeter; 
3d,  by  actual  trial  in  a  steam-boiler. 

The  accuracy  of  the  first  two  methods  depends  on  the  precision  of  the 
method  of  analysis  or  calorimetry  adopted,  and  upon  the  care  and  skill 
of  the  operator.  The  results  of  the  third  method  are  subject  to  numer- 
ous sources  of  variation  and  error,  and  may  be  taken  as  approximately 
true  only  for  the  particular  conditions  under  which  the  test  is  made. 
Analysis  and  calorimetry  give  with  considerable  accuracy  the  heating 
value  which  may  be  obtained  under  the  conditions  of  perfect  combus- 
tion and  complete  absorption  of  the  heat  produced.  A  boiler  test  gives 
the  actual  result  under  conditions  of  more  or  less  imperfect  combustion., 
and  of  numerous  and  variable  wastes.  It  may  give  the  highest  practical 
heating  value,  if  the  conditions  of  grate-bars,  draft,  extent  of  heating 
surface,  method  of  firing,  etc.,  are  the  best  possible  for  the  particular 
C9al  tested,  and  it  may  give  results  far  beneath  the  highest  if  these  con- 
ditions are  adverse  or  unsuitable  to  the  coal. 

In  a  paper  entitled  Proposed  Apparatus  for  Determining  the  Heating 
Power  of  Different  Coals  (Trans.  A.  I.  M.  E.,  xiv.  727)  the  author  de- 
scribed and  illustrated  an  apparatus  designed  to  test  fuel  on  a  large 
scale,  avoiding  the  errors  of  a  steam-boiler  test.  It  consists  of  a  fire- 
brick furnace  enclosed  in  a  water  casing,  and  two  cylindrical  shells  con- 
taining a  great  number  of  tubes,  which  are  surrounded  by  cooling  water 
and  through  which  the  gases  of  combustion  pass  while  being  cooled. 
No  steam  is  generated  in  the  apparatus,  but  water  is  passed  through  it 
and  allowed  to  escape  at  a  temperature  below  200°  F.  The  product  of 
the  weight  of  the  water  passed  through  the  apparatus  by  its  increase  in 
temperature  is  the  measure  of  the  heating  value  of  the  fuel. 

A  study  of  M.  Mahler's  calorimetric  tests  shows  that  the  maximum 
difference  between  the  results  of  these  tests  and  the  calculated  heating 
power  by  Dulong's  law  in  any  single  case  is  only  a  little  over  3%, 
and  the  results  of  31  tests  show  that  Dulong's  formula  gives  an  aver- 
age of  only  47  thermal  units  less  than  the  calorimetric  tests,  the 


RELATIVE  VALUE  OF  oTEAM  COALS.      827 

average  total  heating  value  being  over  14.000  B.T.U.,  a  difference  of 
less  than  0.4%.* 

The  close  agreement  of  the  results  of  calorimetric  tests  when  properly 
conducted,  and  of  the  heating  power  calculated  from  the  ultimate  chemi- 
cal analysis  indicates  that  either  the  chemical  or  the  calorimetric  method 
may  be  accepted  as  correct  enough  for  all  practical  purposes  for  deter- 
mining the  total  heating  power  of  coal.  The  results  obtained  by  either 
method  may  be  taken  as  a  standard  by  which  the  results  of  a  boiler  test 
are  to  be  compared,  and  the  difference  between  the  total  heating  power 
and  the  result  of  the  boiler  test  is  a  measure  of  the  inefficiency  of  the 
boiler  under  the  conditions  of  any  particular  test. 

The  heating  value  that  can  be  obtained  in  boiler  practice  from  any 
given  coal  depends  upon  the  efficiency  of  the  boiler,  and  this  largely 
upon  the  difficulty  of  thoroughly  burning  the  volatile  combustible 
matter  in  the  boiler  furnace. 

With  the  best  anthracite  coal,  in  which  the  combustible  portion  is, 
say,  97%  fixed  carbon  and  3%  volatile  matter,  the  highest  result  that 
can  be  expected  in  a  boiler-test  with  all  conditions  favorable  is  12.2  Ib. 
of  water  evaporated  from  and  at  212°  per  Ib.  of  combustible,  which  is 
79%  of  15.47  Ib.,  the  theoretical  heating-power.  With  the  best  semi- 
bituminous  coals,  such  as  Cumberland  and  Pocahontas,  in  which  the 
fixed  carbon  is  80%  of  the  total  combustible,  12.5  Ib.,  or  76%  of  the 
theoretical  16.4  Ib.,  may  be  obtained.  For  Pittsburgh  coal,  with  a 
fixed  carbon  ratio  of  68%,  11  Ib.,  or  69%  of  the  theoretical  16.03  Ib.,  is 
about  the  best  practically  obtainable  with  the  best  boilers  when  hand- 
fired,  with  ordinary  furnaces.  (The  author  has  obtained  78%  with  an 
automatic  stoker  set  in  a  "Dutch  oven"  furnace.)  With  some  good 
Ohio  coals,  witli  a  fixed  carbon  ratio  of  60%,  10  Ib.,  or  66%  of  the  the- 
oretical 15.28  Ib.,  has  been  obtained,  under  favorable  conditions,  with  a 
fire-brick  arch  over  the  furnace.  With  coals  mined  west  of  Ohio,  with 
lower  carbon  ratios,  the  boiler  efficiency  is  not  apt  to  be  as  high  as  60% 
unless  a  special  furnace,  adapted  to  the  coal,  is  used. 

From  these  figures  a  table  of  probable  maximum  boiler-test  results 
with  ordinary  furnaces  from  coals  of  different  fixed  carbon  ratios  may 
be  constructed  as  follows: 

Fixed  carbon  ratio 97         80         68         60         54         50 

Evap.  from  and  at  212°  per  Ib.  combustible,  maximum  in  boiler-tests: 

12.2     12.5     11          10  8.3       7.0 

Boiler  efficiency,  per  cent 80         76         69         66         60         55 

Loss,  chimney,  radiation,  imperfect  combustion,  etc.: 

20         24         31         34         40         45 

The  difference  between  the  loss  of  20%  with  anthracite  and  the  great- 
er losses  with  the  other  coals  is  chiefly  due  to  imperfect  combustion  of 
the  bituminous  coals,  the  more  highly  volatile  coals  sending  up  the 
chimney  the  greater  quantity  of  smoke  and  unburned  hydrocarbon 
gases.  It  is  a  measure  of  the  inefficiency  of  the  boiler  furnace  and  of  the 
inefficiency  of  heating-surface  caused  by  the  deposition  of  soot,  the 
latter  being  primarily  caused  by  the  imperfection  of  the  ordinary 
furnace  and  its  unsuitability  to  the  proper  burning  of  bituminous  coal. 
If  in  a  boiler-test  with  an  ordinary  furnace  lower  results  are  obtained 
than  those  in  the  above  table,  it  is  an  indication  of  unfavorable  condi- 
tions, such  as  bad  firing,  wrong  proportions  of  boiler,  defective  draft,  a 
rate  of  driving  beyond  the  capacity  of  the  furnace,  or  beyond  the 
capacity  of  the  boiler  to  absorb  the  heat  produced  in  the  furnace.  It  is 
quite  possible,  however,  with  automatic  stokers  and  fire-brick  com- 
bustion chambers  to  obtain  an  efficiency  of  70%  with  the  highly 
volatile  western  coals. 

Under  exceptionally  good  conditions,  with  mechanical  stokers,  very 
large  combustion  chambers,  and  the  air  supply  controlled  according  to 
the  indications  of  gas  analyses,  as  high  as  81  %  efficiency  has  been 
obtained.  See  under  Steam- Boilers,  page  898. 

*  The  formula  commonly  used  in  the  United  States  is  14,600  C  + 
62,000  (H  -  l/gO)  +  4050  S.  F9r  a  description  of  the  Mahler  catori- 
meter  and  its  method  of  operation  see  the  author's  "Steam  Boiler 
Economy."  Prof.  S.  W.  Parr,  of  the  University  of  Illinois,  has  put  a 
calorimeter  on  the  market  which  gives  results  practically  equal  to  those 
obtained  with  Mahler's  instrument. 


Classified  List  of  Coals. 


As  Received. 

Combustible.  ' 

Air-dry,  Ash-free 

Moist.      Ash. 

B.T.U. 

Vol. 

S. 

0. 

B.T.U. 

Moist. 

B.T.U. 

I.  ANTHRACITE. 


Alaska. 

7.43 

14.36 

11,891 

8.8 

0.73 

4.04 

15,203 

1.55 

14,968 

Colo... 

2.70 

5.83 

14,099 

3.6 

0.87 

1.32 

15,413 

1.08 

15,247 

Pa  

2.80 

7.83 

13,298 

1.3 

1.00 

2.13 

14,882 

1.43 

14,666 

Pa 

330 

9.12 

13,351 

3.7 

0.68 

2.41 

15,248 

0.83 

15,123 

Wash 

8.5 

0.72 

2.67 

15.410 

0.80 

15.367 

II.  SEMI-ANTHRACITE. 

Ark....|     2.36 

12.08 

13,259 

14.8 

2.33 

2.57 

15,496 

1.45 

15,272 

Pa  3.38 

11.50 

13,156 

10.0 

D.74 

2.17 

15,457 

0.91 

15,398 

Va  |    4.80 

18.03 

11,961 

13.1 

0.82 

4.18 

15,500 

0.90 

15.439 

III.  SEMI-BITUMINOUS. 

Ala.... 

3.08 

3.75 

14,681 

28.8 

0.59 

4.45 

15,757 

1.15 

15,577 

Ala.... 

2.38 

4.88 

14,487 

27.9 

1.58 

3.42 

15,620 

0.94 

15,475 

Alaska  . 

5.14 

5.00 

14,065 

15.5 

1.29 

3.02 

15.651 

0.60 

15,559 

Ark.  .  .  . 

2.77 

9.07 

13,774 

16.7 

3.16 

1.69 

15,624 

0.86 

15.525 

Ark.... 

3.21 

9.29 

13,588 

17.0 

3.57 

1.25 

15,530 

0.92 

15,387 

Colo.  .  . 

0.96 

8.62 

14,330 

23.8 

0.58 

4.34 

15,849 

0.83 

15.716 

Colo... 

3.07 

9.16 

13,990 

25.8 

0.72 

2.29 

15,939 

1.43 

15.712 

Ga  

3.80 

14.49 

12,791 

19.4 

1.55 

5.96 

15,653 

0.74 

15,540 

Md... 

3.20 

6.70 

14,100 

16.0 

1.02 

2.54 

15,640 

1.10 

15,478 

Md.... 

2.60 

6.80 

14,360 

17.5 

0.98 

2.47 

15,856 

0.66 

15,746 

Mont.  . 

2.05 

8.31 

14,092 

18.3 

0.96 

2.93 

15,721 

0.61 

15,625 

Okla... 

2.37 

8.83 

13,840 

21.7 

1.15 

2.87 

15.586 

0.53 

15,504 

Okla... 

5.11 

8.03 

13,662 

15.7 

1.36 

1.87 

15,728 

0.70 

15,619 

Pa 

425 

7.87 

13,513 

24.8 

1.81 

5.50 

15,376 

0.40 

15,316 

Pa 

1.10 

7.41 

14,499 

17.3 

1.63 

2.82 

15,847 

0.65 

15,744 

Va  

4.00 

4.31 

14,520 

19.0 

0.68 

3.42 

15,840 

0.54 

15,750 

Va  

4.10 

3.18 

14,740 

17.5 

0.68 

2.23 

15,910 

0.64 

15,795 

Wash.. 

5.81 

17.04 

11,776 

16.3 

0.48 

3.97 

15,264 

1.67 

15,013 

W.Va.. 

3.71 

3.39 

14,306 

25.3 

0.86 

4.13 

15,399 

1.18 

15,218 

W.Va.. 

1.75 

4.58 

15,023 

19.9 

0.60 

2.80 

16,038 

0.69 

15.998 

IV.  CANNEL.* 

Ky.... 

2.36 

10.49 

13,770 

55.5 

1.38 

7.57 

15,800 

0.92 

15,646 

Ky.... 

1.70 

9.31 

14,251 

57.0 

1.15 

7.61 

16,013 

1.44 

15784 

W.Va.. 

1.80 

3.44 

15,330 

47.4 

0.92 

5.34 

16,176 

0.84 

16,042 

Utah... 

7.35 

23.24 

10,355 

67.6 

2.32 

13.68 

14,918 

8.26 

13,686 

V.  BITUMINOUS,  HIGH-GRADE. 

Ala.... 

2.18 

2.79 

14,816 

33.4 

1.13 

6.99 

15,590 

1.23 

15,400 

Ala  

3.83 

5.48 

13,799 

35.3 

1.07 

7.00 

15,214 

1.77 

14,947 

Colo... 

2.64 

5.21 

13,529 

31.3 

0.72 

9.38 

14,681 

1.01 

14,533 

Colo.  .  . 

2.28 

9.16 

13,781 

33.7 

0.56 

8.77 

15,559 

0.87 

15,423 

Ill 

7.81 

8.38 

12,418 

40.0 

2.82 

9.74 

14,818 

2.34 

14,470 

Kan... 

2.50 

12.45 

12,900 

39.8 

6.68 

5.26 

15,167 

2.86 

14,734 

Kan... 

9.04 

15.72 

11,142 

39.5 

4.93 

7.27 

14,809 

2.49 

14,436 

Ky  

3.41 

5.73 

13,928 

35.3 

0.58 

8.05 

15,328 

1.64 

15,095 

N.Mex. 

2.78 

14.57 

12,294 

41.5 

0.74 

8.79 

14,875 

1.64 

14,630 

N.Mex. 

2.45 

17.40 

12,200 

34.4 

0.96 

6.93 

15,221 

0.80 

15,099 

Ohio... 

3.53 

9.12 

13,072 

42.9 

3.97 

7.04 

14,965 

2.38 

14,642 

Ohio... 

5.59 

8.29 

12,773 

42.8 

3.66 

9.01 

14,832 

3.83 

14,431 

Okla... 

2.09 

20.07 

11,695 

35.5 

7.36 

3.71 

15,025 

1.38 

14,814 

Okla... 

2.81 

8.75 

13,320 

40.8 

2.06 

7.35 

15,061 

1.57 

14,825 

Pa.  .... 

2.61 

6.17 

13,997 

38.3 

1.38 

6.94 

15,345 

1.42 

15,127 

Pa  

5.13 

8.71 

13,365 

32.4 

1.00 

7.35 

15,511 

1.07 

15,346 

Tenn.  .  . 

6.39 

9.53 

12,578 

38.4 

1.17 

7.94 

1  4,960 

1.97 

14,665 

Tenn... 

3.89 

14  .43 

12,514 

33.8 

0.95 

6.70 

15,320 

1.08 

15,137 

Va  

4.44 

5.98 

13,363 

40.2 

0.85 

12.18 

14.918 

2.52 

14,381 

Va  

3.31 

3.76 

14,209 

35.3 

0.97 

5.65 

15,291 

1.49 

15,069 

Wash.. 

2.32 

13.58 

12,443 

44.0 

5.23 

13.93 

14,796 

1.55 

14,569 

W.Va.. 

4.21 

7.22 

13,379 

40.0 

0.72 

10.10 

15,107 

2.11 

14,787 

W.Va.  . 

2.86 

5.83 

14,105 

36.4 

0.73 

5.14 

15,448 

1.36 

15,237 

Wyo... 

5.49 

3.12 

13,570 

39.3 

0.99 

11.40 

14,848 

2.13 

14,552 

*  H  in  combustible:    Ky.,  7.13,  and  7.40;   W.  Va.,  7.13;    Utah,  7.73 
The  highest  II  in  the  other  coals  is  5.78,  a  Missouri  bituminous. 


ANALYSIS  AND   HEATING   VALUE   OF  COALS.       829 


Classified  List  of  Coals. — Continued. 


As  Received. 

Combustible. 

Air-dry,Ash-free 

Moist. 

Ash. 

B.T.U. 

Vol. 

S. 

o. 

B.T.U. 

Moist. 

B.T.U. 

VI.  BITUMINOUS  MEDIUM  GRADE 

Ala.... 

3.95 

14.59 

11,785 

37.7 

1.37 

10.45 

14,467 

2.69 

14,078 

Alaska  . 

7.06 

21.78 

9,846 

44.2 

1.83 

14.11 

13,838 

2.55 

13,484 

Cal.... 

6.95 

6.23 

12,447 

53.8 

4.80 

11.47 

14,336 

5.19 

13,593 

Ill 

8.12 

8.63 

1  2,064 

41.4 

1.36 

12.02 

14,492 

5.15 

13,745 

111 

8.86 

11.66 

1  1  ,702 

39.3 

3.10 

9.03 

14,724 

3.71 

14,177 

Ind.... 

16.91 

17.37 

9,524 

40.9 

2.88 

9.50 

14,492 

5.48 

13,698 

Ind.... 

7.88 

14.20 

11,146 

47.3 

6.60 

9.96 

14,305 

5.01 

13,576 

Iowa.  .  . 

13.88 

14.01 

10,244 

51.2 

8.53 

8.96 

14,206 

5.35 

13,445 

Iowa.  .  . 

8.24 

16.00 

11,027 

40.6 

6.64 

8.03 

14,555 

6.24 

13,647 

Kan  .  .  . 

6.95 

12.19 

1  1  ,905 

44.2 

9.94 

5.64 

14,724 

4.09 

14,121 

Kan... 

2.50 

12.45 

1  2,900 

39.8 

5.22 

5.98 

14,922 

4.30 

14,269 

Ky.... 

7.92 

10.06 

12.022 

44.0 

4.29 

8.90 

14,657 

6.52 

13.702 

Ky.... 

5.27 

14.18 

11,950 

43.5 

5.64 

7.46 

14,836 

2.98 

14,394 

Mich... 

11.91 

6.84 

11,781 

38.8 

1.53 

9.54 

14,499 

4.70 

13,818 

Mich... 

11.55 

3.25 

12,442 

37.1 

1.11 

10.51 

14,603 

5.59 

13,786 

Mo.... 

17.30 

23.38 

8,240 

44.6 

4.96 

11.83 

13,892 

3.42 

13,416 

Mo.... 

12.67 

4.83 

12,487 

50.2 

6.21 

6.12 

15,134 

5.68 

14.276 

Mont.  . 

3.51 

19.50 

10,881 

34.3 

4.86 

9.50 

14,134 

2.42 

13.791 

Mont  .  . 

5.77 

10.57 

12,281 

39.6 

0.60 

9.77 

14,681 

2.30 

14,342 

N.Mex. 

5.02 

12.00 

12,064 

44.3 

0.68 

12.70 

14,539 

3.06 

14,093 

Ohio... 

4.14 

9.38 

12,874 

37.8 

0.63 

11.58 

14,269 

4.69 

14,152 

Ohio... 

7.71 

11.95 

11,515 

47.7 

5.74 

9.44 

1  4,332 

3.30 

13,523 

Okla... 

7.04 

10.01 

12,202 

41.7 

2.31 

9.26 

14,711 

4.31 

14,075 

Utah... 

5.58 

8.99 

12,170 

45.6 

0.60 

13.30 

14,245 

4.98 

13,536 

Utah... 

6.05 

4.87 

13,151 

47.2 

0.62 

10.93 

14,764 

2.47 

14,399 

Wash.. 

6.02 

19.35 

10,708 

41.8 

0.57 

12.38 

14,348 

3.26 

13,879 

Wyo... 

3.96 

4.77 

13,502 

39.6 

0.84 

9.25 

14,793 

2.73 

14,391 

VTI.  BITUMINOUS  Low  GRADE. 

Alaska. 

10.77 

14.87 

9,641 

40.8 

0.94 

18.83 

12,964 

5.42 

12,261 

Ill 

11.35 

13.40 

10,733 

46.0 

6.33 

10.53 

14,263 

6.75 

13.300 

111 

14.43 

13.28 

1  0,064 

40.8 

5.55 

12.02 

13,921 

6.02 

13,084 

Ind.... 

12.11 

6.83 

11,952 

42.2 

1.78 

10.55 

14,746 

9.60 

13,329 

Ind.... 

13.18 

15.63 

10,030 

44.8 

6.73 

9.69 

14,089 

6.17 

13,220 

Iowa.  .  . 

14.08 

10.96 

10,723 

47.5 

5.69 

9.73 

14,305 

11.33 

12.684 

Mo  

15.36 

10.99 

10,460 

47.3 

4.85 

10.68 

14,202 

7.37 

13,156 

Mont  .  . 

9.76 

16.42 

10,235 

37.5 

0.86 

16.21 

13,865 

7.58 

12,813 

Mont.  . 

10.88 

26.88 

7.742 

32.6 

2.88 

16.14 

12,438 

8.09 

11,432 

N.Mex. 

12.29 

6.99 

11,252 

42.8 

0.78 

14.00 

13,939 

11.70 

12,309* 

N.Mex. 

15.79 

9.37 

9,970 

46.8 

2.38 

15.69 

13,322 

7.87 

12,008* 

Okla... 

8.29 

25.05 

9,110 

45.9 

5.93 

10.62 

13,667 

7.74 

12,609 

Ore 

48  1 

1  65 

14618 

11.88 

1  2,882 

Utah... 

10.35 

9.62 

10,874 

45.4 

7.27 

16.05 

13,586 

9.65 

12,276 

Utah... 

14.19 

9.92 

9.927 

44.0 

7.10 

14.18 

13,081 

11.47 

11,374 

Wash.. 

12.05 

10.41 

10,414 

47.5 

0.44 

17.11 

13.423 

6.56 

12,548 

VIII.  SUB-BITUMINOUS  AND  LIGNITE. 

Ark.... 

39.43 

9.71 

6,356 

52.1 

0.96 

21.17 

12,497 

22.00 

9,750 

Cal.... 

18.51 

15.49 

8,507 

53.5 

4.62 

16.79 

12,890 

10.95 

11.478 

Colo... 

19.65 

6.00 

8,638 

41.4 

0.44 

16.97 

11,619 

8.21 

10,664 

Colo.  .  . 

19.28 

4.70 

9,064 

45.5 

0.51 

16.52 

13,239 

15.35 

10,094 

Mont.  . 

30.00 

11.90 

6,914 

69.0 

1.86 

23.47 

11,900 

15.55 

10.143 

Mont.  . 

24.59 

14.01 

6,208 

54.1 

0.67 

26.64 

10,211 

25.02 

7.656 

N.Dak. 

35.96 

7.75 

7,069 

56.7 

2.04 

17.69 

12,557 

26.20 

8,886 

N.Dak. 

38.92 

5.39 

6,739 

45.9 

0.86 

22.67 

12,101 

11.66 

10,885 

Ore  

16.10 

13.17 

9.031 

44.0 

1.15 

19.68 

12,769 

10.16 

11,471 

Ore.... 

13.77 

7.46 

9,054 

47.0 

5.52 

11,493 

7.05 

10,684 

S.  Dak. 

30.45 

12.15 

6,944 

40.0 

0.68 

12,098 

15.77 

10,189 

Tex.... 

34.70 

11.20 

7,056 

59.6 

1.46 

J8.99 

13,043 

15.73 

11,077 

Tex  

33.71 

7.28 

7,348 

49.6 

0.90 

20.54 

12.452 

11.82 

11.036 

(Table  continued  on  p.  830.) 


830 


FUEL. 


Classified  List  of  Coals. — Continued. 


As  Received. 

Combustible. 

Air-dry,  Ash-free 

Moist. 

Ash. 

B.T.U. 

Vol. 

S. 

o. 

B.T.U. 

Moist.  |  B.T.U. 

VIII.  SUB-BITUMINOUS  AND  LIGNITE. — Continued. 


Utah... 

16.59 

13.44 

7,882 

46.6 

4.88 

22.14 

1  1  ,264 

15.35 

9*535 

Wash.. 

27  .17 

10.92 

7,569 

54.6 

0.53 

22.06 

12,226 

17.21 

10,122 

Wyo... 

10.26 

9.83 

10,354 

27.8 

1.09 

10.94 

12,956 

9.56 

11,573 

Wyo... 

31.37 

10.12 

5,634 

50.6 

2.17 

29.86 

9.630 

22.69 

7,458t 

NOT   CLASSIFIED^ 

R.  I... 

23.68 

30.77 

5,976 

6.6 

0.05 

5.59 

13,120 

1.26 

12,955 

R.  I  .  .  . 

2.41 

19.06 

10,996 

6.3 

0.09 

3.27 

14,002 

0.52 

13,930 

Alaska  . 

5.71 

34.15 

8,386 

21.7 

10.76 

5.28 

13,945 

4.77 

13,279 

Ark.  .  .  . 

5.26 

24.81 

10,451 

21.0 

1.43 

6.44 

14,945 

1.77 

14,722 

Idaho.. 

34.28 

13.38 

8,613 

50.9 

4.77 

16,457 

16.42 

13,757 

*  These  two  samples  are  classed  as  sub-bituminous  by  the  Bureau  of 
Mines. 

t  Sample  from  surface  exposure;  coal  badly  weathered. 

t  The  Rhode  Island  coals  are  graphitic  and  are  not  used  as  fuel.  The 
two  samples  from  Alaska  and  Arkansas  may  be  classed  as  semi-bitumi- 
nous by  their  percentage  of  volatile  matter,  but  they  are  higher  in 
oxygen  and  in  moisture,  and  lower  in  heating  value  than  other  semi- 
bituminous  coals.  The  Idaho  coal  is  apparently  a  cannel  coal  very 
high  in  moisture,  but  the  ultimate  analysis  is  lacking. 

Purchase  of  Coal  under  Specifications. — It  is  customary  for  large 
users  of  coal  to  purchase  it  under  specifications  of  its  analysis  or  heating 
value  with  a  penalty  attached  for  failure  to  meet  the  specifications.  The 
following  standards  for  a  specification  were  given  by  the  author  in  his 
"Steam  Boiler  Economy,"  1901.  (Revised  in  2d  edition,  1915): 

Anthracite  and  Semi-anthracite. — The  standard  is  a  coal  containing 
5  %  volatile  matter,  not  over  2  %  moisture,  and  not  over  10  %  ash.  A 
premium  of  0.5%  on  the  price  will  be  given  for  each  per  cent  of  volatile 
matter  above  5%  up  to  and  including  15%,  and  a  reduction  of  2%  on 
the  price  will  be  made  for  each  1%  of  moisture  and  ash  above  the 
standard. 

Semi-bituminous  and  Bituminous. — The  standard  is  a  semi-bitumi- 
nous  coal  containing  not  over  20%  volatile  matter,  2  %  moisture,  6  %  ash. 
A  reduction  of  1  %  in  the  price  will  be  made  for  each  1  %  of  volatile  mat- 
ter in  excess  of  25  % ,  and  of  2  %  for  each  1  %  of  ash  and  moisture  in  excess 
of  the  standard. 

For  western  coals  in  which  the  volatile  matter  differs  greatly  in  its 
percentage  of  oxygen,  the  above  specification  based  on  proximate  analy- 
sis may  not  be  sufficiently  accurate,  and  it  is  well  to  introduce  either  the 
heating  value  asdetermined  by  a  calorimeter  or  the  percentage  of  oxygen. 
The  author  has  proposed  the  following  for  Illinois  coal: 

The  standard  is  a  coal  containing  not  over  6%  moisture  and  10%  ash 
in  an  air-dried  sample,  and  whose  heating  value  is  14,500  B.T.U.  per 
pound  of  combustible.  For  lower  heating  value  per  Ib.  of  the  com- 
bustible, the  "price  shall  be  reduced  proportionately,  and  for  each  1% 
increase  in  ash  or  moisture  above  the  specified  figures,  2%  of  the  price 
shall  be  deducted. 

Several  departments  of  the  U.  S.  government  now  purchase  coal  under 
specifications.  See  paper  on  the  subject  by  D.  T.  Randall,  Bulletin  No. 
339,  U.  S.  Geological  Survey,  1908,  also  "Steam  Boiler  Economy,' 
2d  edition. 

Weathering  of  Coal.  (I.  P.  Kimball,  Trans.  A.  I.  M.  E.,  viii,  204.)— 
The  effect  of  the  weathering  of  coal,  while  sometimes  increasing  it 
weight,  is  to  diminish  the  carbon  ana  disposable  hydrogen  and  to  increase 
the  oxygen  and  indisposable  hydrogen.  Hence  a  reduction  in  the  cal- 
orific value.  An  excess  of  pyrites  in  coal  tends  to  produce  rapid  oxida- 
tion and  mechanical  disintegration  of  the  mass,  with  development  of 
heat,  loss  of  coking  power,  and  spontaneous  ignition. 

The  only  appreciable  results  of  the  weathering  of  anthracite  are  con- 


PRESSED   FUEL.  831 

fined  to  the  oxidation  of  its  accessory  pyrites.  In  coking  coals,  however, 
weathering  reduces  and  finally  destroys  the  coking  power. 

Richters  found  that  at  a  temperature  of  158°  to  180°  Fahr.,  three  coals 
lost  in  fourteen  days  an  average  of  3.6%  of  calorific  power.  It  appears 
from  the  experiments  of  Richters  and  Reder  that  when  there  is  no  rise 
of  temperature  of  coal  piled  in  heaps  and  exposed  to  the  air  for  nine  to 
twelve  months,  it  undergoes  no  sensible  change,  but  when  the  coal 
becomes  heated  it  suffers  loss  of  C  and  H  by  oxidation  and  increases  in 
weight  by  the  fixation  of  oxygen.  (See  also  paper  by  R.  P.  Rothwell, 
Trans.  A.  I.  M.  E.,  iv.  55.) 

Experiments  by  S.  W.  Parr  and  N.  D.  Hamilton  (Bull.  No.  17  of 
Univ'y  of  111.  Eng'g  Experiment  Station,  1907)  on  samples  of  about 
100  Ib.  each,  show  that  no  appreciable  change  takes  place  in  coal  sub- 
merged in  water.  Their  conclusions  are: 

(a)  Submerged  coal  does  not  lose  appreciably  in  heat  value. 

(ft)  Outdoor  exposure  results  in  a  loss  of  heat  value  varying  from  2 
to  10  per  cent. 

(c)  Dry  storage  has  no  advantage  over  storage  in  the  open  except 
with  high  sulphur  coals,  where  the  disintegrating  effect  of  sulphur  in  the 
process  of  oxidation  facilitates  the  escape  or  oxidation  of  the  hydrocar- 
bons. 

|*  (d)  In  most  cases  the  losses  in  storage  appear  to  be  practically  com- 
plete at  the  end  of  five  months.  From  the  seventh  to  the  ninth  month 
the  loss  is  inappreciable. 

This  paper  contains  also  a  historical  review  of  the  literature  on  weath- 
ering and  on  spontaneous  combustion,  with  a  summary  of  the  opinions 
of  various  authorities. 

Later  experiments  on  storing  carload  lots  of  Illinois  coals  (W.  F. 
Wheeler,  Trans.  A.  I.  M.  E.,  1908)  confirms  the  above  conclusions,  ex- 
cept that  4  per  cent  seems  to  be  amply  sufficient  to  coyer  the  losses  sus- 
tained by  Illinois  coals  under  regular  storage-conditions,  the  larger 
losses  indicated  in  the  former  series  being  probably  due  to  the  small  size 
of  the  samples  exposed. 

Investigations  by  the  U.  S.  Bureau  of  Mines  in  1910  (Technical 
Paper  No.  2)  showed  that  New  River  (Va.)  coal  lost  less  than  1%  in 
heating  value  in  one  year  by  weathering  in  the  open,  and  Pocahontas 
coal  less  than  0.4%. 

Pressed  Fuel.  -  (E.  F.  Loiseau,  Trans.  A.  I.  M.  E.,  viii.  314.) — 
Pressed  fuel  has  been  made  from  anthracite  dust  by  mixing  the  dust  with 
ten  per  cent  of  its  bulk  of  dry  pitch,  which  is  prepared  by  separating 
from  tar  at  a  temperature  of  572°  F.  the  volatile  matter  it  contains.  The 
mixture  is  kept  heated  by  steam  to  212°,  at  which  temperature  the  pitch 
acquires  its  cementing  properties,  and  is  passed  between  two  rollers,  on 
the  periphery  of  which  are  milled  out  a  series  of  semi-oval  cavities.  The 
lumps  of  the  mixture,  about  the  size  of  an  egg,  drop  out  under  the 
rollers  on  an  endless  belt,  which  carries  them  to  a  screen  in  eight  minutes, 
which  time  is  sufficient  to  cool  the  lumps,  and  they  are  then  ready  for 
delivery. 

The  enterprise  of  making  the  pressed  fuel  above  described  was  not 
commercially  successful,  on  account  of  the  low  price  of  other  coal.  In 
France,  however,  "briquettes"  are  regularly  made  of  coal-dust  (bitu- 
minous and  semi-bituminous). 

Experiments  with  briquets  for  use  in  locomotives  have  been  made 
by  the  Penna.  R.  R.  Co.,  with  favorable  results,  which  were  reported  at 
the  convention  on  the  Am.  Ry.  Mast.  Mechs.  Assn.  (Eng.  News,  July  2, 
1908).  A  rate  of  evaporation  as  high  as  19  Ib.  per  sq.  ft.  of  heating 
surface  per  hour  was  reached.  The  comparative  economy  of  raw  coal 
and  of  briquets  was  as  follows: 

Evap.persq.  ft.  heat.  surf. per  hr.,lbs.        8         10         12         14         16 
Evap.  from  and  at  /  Lloy  dell  coal.. .        9.5       8.8       8.0       7.3       6.6 
2 1 2°  per  Ib.  of  fuel    \Briquettedcoal.     10.7     10.2       9.7       9.2       8.7 

The  fuel  consumed  per  draw-bar  horse-power  with  the  locomotive 
running  at  37.8  miles  per  hour  and  a  cut-off  of  25%  was:  with  raw  coal, 
4.48  Ibs.;  with  round  briquets,  3.65  Ibs. 

Experiments  on  different  binders  for  briquets  are  discussed  by  J.  E. 
Mills  in  Bulletin  No.  343  of  the  U.  S.  Geological  Survey,  1908. 

Briquetting  tests  made  at  the  St,   Louis  exhibition,   1904,   with 


832 


FUEL. 


descriptions  of  the  machines  used  are  reported  in  Bulletin  No.  201  of 
the  U.  S.  Geological  Survey,  1905.  See  also  paper  on  Coal  Briquet  ting 
in  the  U.  S.,  by  E.  W.  Parker,  Trans.  A.  I.  M.  E.,  1907. 

Spontaneous  Combustion  of  Coal.  (Technical  Paper  16,  U.  S. 
Bureau  of  Mines,  1912.) — Spontaneous  combustion  is  brought  about 
by  slow  oxidation  in  an  air  supply  sufficient  to  support  the  oxidation, 
but  insufficient  to  carry  away  all  the  heat  formed.  Mixed  lump  and 
fine,  i.  e.,  run-of-mine,  with  a  large  percentage  of  dust,  and  piled  so  as 
to  admit  to  the  interior  a  limited  supply  of  air,  make  ideal  conditions 
for  spontaneous  heating.  High  volatile  matter  does  not  of  itself  in- 
crease the  liability  to  spontaneous  heating. 

Pocahontas  coal  gives  a  great  deal  of  trouble  with  spontaneous 
fires  in  the  large  storage  piles  at  Panama.  The  high- volatile  coals  of  the 
west  are  usually  very  liable  to  spontaneous  heating. 

The  influence  of  moisture  and  that  of  sulphur  upon  spontaneous 
heating  of  coal  are  questions  not  yet  settled.  Observation  by  the 
Bureau  of  Mines  in  many  actual  cases  has  not  developed  any  instances 
where  moisture  could  be  proven  to  promote  heating.  Sulphur  has  been 
shown  to  have,  in  most  cases,  only  a  minor  influence.  On  the  other 
hand,  a  Boston  company,  using  Nova  Scotia  coal  of  3  to  4  per  cent 
sulphur,  has  much  trouble  with  spontaneous  fires  in  storage. 

Freshly  mined  coal  and  even  fresh  surfaces  exposed  by  crushing 
lump  coal  exhibit  a  remarkable  avidity  for  oxygen,  but  after  a  time  be- 
come coated  with  oxidized  material,  "seasoned,"  as  it  were,  so  that  the 
action  of  the  air  becomes  much  less  vigorous.  It  is  found  that  if  coal 
which  has  been  stored  for  six  weeks  or  two  months  and  has  even  be- 
come already  somewhat  heated,  be  rehandled  and  thoroughly  cooled 
by  the  air,  spontaneous  heating  rarely  begins  again. 

While  the  following  recommendations  may  under  certain  conditions 
be  found  impracticable,  they  are  offered  as  being  advisable  precautions 
for  safety  in  storing  coal  whenever  their  use  does  not  involve  an  un- 
reasonable expense. 

1.  Do  not  pile  over  12  feet  deep  nor  so  that  any  point  in  the  interior 
will  be  over  10  feet  from  an  air-cooled  surface. 

2.  If  possible,  store  only  in  lump. 

3.  Keep  dust  out  as  much  as  possible;  therefore  reduce  handling 
to  a  minimum. 

4.  Pile  so  that  lump  and  fine  are  distributed  as  evenly  as  possible; 
not,  as  is  often  done,  allowing  lumps  to  roll  down  from  a  peak  and  form 
air  passages  at  the  bottom. 

5.  Rehandle  and  screen  after  two  months. 

6.  Keep  away  external  sources  of  heat  even  though  moderate  in 
degree. 

7.  Allow  six  weeks'  "seasoning"  after  mining  before  storing. 

8.  Avoid  alternate  wetting  and  drying. 

9.  Avoid  admission  of  air  to  interior  of  pile  through  interstices 
around  foreign  objects  such  as  timbers  or  irregular  brick  work;  also 
through  porous  bottoms  such  as  coarse  cinders. 

10.  Do  not  try  to  ventilate  by  pipes,  as  more  harm  is  often  done 
than  good. 

COKE. 

Coke  is  the  solid  material  left  after  evaporating  the  volatile  ingredi- 
ents of  coal,  either  by  means  of  partial  combustion  in  furnaces  called 
coke  ovens,  or  by  distillation  in  the  retorts  of  gas-works. 

Coke  made  in  ovens  is  preferred  to  gas  coke  as  fuel.  It  is  of  a  dark 
gray  color,  with  slightly  metallic  luster,  porous,  brittle,  and  hard. 

The  proportion  of  coke  yielded  by  a  given  weight  of  coal  is  very  differ- 
ent for  different  kinds  of  coal,  ranging  from  0.9  to  0.35. 

Being  of  a  porous  texture,  it  readily  attracts  and  retains  water  from 
the  atmosphere,  and  sometimes,  if  it  is  kept  without  proper  shelter, 
from  0.15  to  0,20  of  its  gross  weight  consists  of  moisture. 


COKE.  833 


Analyses  of  Coke. 

(From  report  of  John  R.  Proctor,  Kentucky  Geological  Survey.) 


Where  Made. 

Fixed 
Carb'n. 

Ash. 

Sul- 
phur. 

Connellsville,  Pa.      (Average  of  3  samples) 

88.96 
80.51 
87.29 
92.53 
92.38 
93.23 

9.74 
16.34 
10.54 
5.74 
7.21 
5.69 

0.810 
1.595 
1.195 
0.597 
0.562 
0.749 

Chattanooga,  Tenn.        "             4          '         

Birmingham,  Ala             "             4         ' 

Pocahontas,  Va.               "             3         ' 

New  River,  W.  Va.         "             8         '        

Big  Stone  Gap,  Ky.        "             7         '        

Experiments  In  Coking.     CONNELLSVILLE  REGION. 
(John  Fulton.'Amer.  Mfr.,  Feb.  10,  1893.) 


__ 

V 

X 

Per  cent  of  Yield. 

In 

S 

1 

•3 

.S  a 

aj  s. 

1 

1 

1   • 
U<d 

O 

•p  o; 

2% 

•g 

1 

?! 

^j£ 

§y 

O  § 

o 

So 

"d^ 

«g 

SS 

^ 

•^  s 

& 

So 

?3 

•^6 

^•-1 

1 

H 

O 

^ 

s 

a 

h 

2 

S 

s 

H 

1 

h.  m. 

Ib.  . 

Ib. 

Ib. 

Ib. 

Ib. 

1 

67    00 

12.420 

99 

385 

7,518 

7.903 

0.80 

3  10 

60.53 

63.63 

35.57 

2 

68    00 

11,090 

90 

359 

6.580 

6,939 

0.81 

3.24 

59  33 

62.57 

36.62 

3 

45    00 

9.120 

77 

272 

5.418 

5,690 

0.84 

2.98 

59.41 

62.39 

36.77 

4 

45    00 

9.020 

74 

349 

5.334 

5,683 

0.82 

3.87 

59.13 

63.00 

36.18 

These  results  show,  in  a  general  average,  that  Connellsville  coal  care- 
fully coked  in  a  modern  beehive  oven  will  yield  66.17%  of  marketable 
coke,  2.30%  of  small  coke  or  breeze,  and  0.82%  of  ash. 

The  total  average  loss  in  volatile  matter  expelled  from  the  coal  in 
coking  amounts  to  30.71  %. 

The  beehive  coke  9ven  is  12  feet  in  diameter  and  7  feet  high  at  crown 
of  dome.  It  is  used  in  making  48  and  72  hour  coke.  [The  Belgian  type 
of  beehive  oven  is  rectangular  in  shape.] 

In  making  these  tests  the  coal  was  weighed  as  it  was  charged  into  the 
oven;  the  resultant  marketable  coke,  small  coke  or  breeze  and  ashes 
weighed  dry  as  they  were  drawn  from  the  oven. 

Coal  Washing. — In  making  coke  from  coals  that  are  high  in  ash  and 
sulphur,  it  is  advisable  to  crush  and  wash  the  coal  before  coking  it.  A 
coal- washing  plant  at  Brookwood,  Ala.,  has  a  capacity  of  50  tons  per 
hour.  The  average  percentage  of  ash  in  the  coal  during  ten  days'  run 
varied  from  14 %  to  21  %,  in  the  washed  coal  from  4.8 %  to  8.1  %,  and  in 
the  coke  from  6.1%  to  10.5%.  During  three  months  the  average  re- 
duction of  ash  was  60.9%.  (Eng.  and  Mining  Jour.,  March  25,  1893.) 

An  experiment  on  washing  Missouri  No.  3  slack  coal  is  described  in 
Bulletin  No.  3  of  the  Engineering  Experiment  Station  of  Iowa  State  Col- 
lege, 1905.  The  raw  coal  analyzed:  moisture,  14.37;  ash,  28.39;  sul- 
phur, 4.30;  and  the  washed  coal,  moisture,  23.90;  ash,  7.59;  sulphur, 
2.89.  Nearly  25%  of  the  coal  was  lost  in  the  operation. 

Recovery  of  By-products  in  Coke  Manufacture. — In  Germany 
considerable  progress  has  been  made  in  the  recovery  of  by-products. 
The  Hoffman-Otto  oven  has  been  most  largely  used,  its  principal  feature 
being  that  it  is  connected  with  regenerators.  In  1884  40  ovens  on  this 
system  were  running,  and  in  1892  the  number  had  increased  to  1209. 

A  Hoffman-Otto  oven  in  Westphalia  takes  a  charge  of  6 1/4  tons  of  dry 
coal  and  converts  it  into  coke  in  48  hours.  The  product  of  an  oven 
annually  is  1025  tons  in  the  Ruhr  district,  1170  tons  in  Silesia,  and  960 
tons  in  the  Saar  district.  The  yield  from  dry  coal  is  75%  to  77%  of 
coke,  2.5%  to  3%  of  tar,  and  1.1%  to  1.2%  of  sulphate  of  ammonia  in 
the  Ruhr  district;  65%  to  70%  of  coke.  4%  to  4.5%  of  tar,  and  1%  to 
1 .25%  of  sulphate  of  ammonia  in  the  Upper  Silesia  region,  and  68%  to 
72%  of  coke,  4%  to  4,3%  of  tar  and  1.8%  to  1.9%  of  sulphate  of 


834  FUEL. 

ammonia  in  the  Saar  district.     A  group  of  60  Hoffman  ovens,  therefore, 
yields  annually  the  following: 


District. 

Coke, 
tons. 

Tar, 
tons. 

Sulphate 
Ammo- 
nia, tons. 

Ruhr                         .                             

51  300 

1  860 

780 

Upper  Silesia  

48.000 

3,000 

840 

Saar  

40.500 

2,400 

492 

An  oven  which  has  been  introduced  lately  into  Germany  in  connection 
with  the  recovery  of  by-products  is  the  Semet-Solyay,  which  works  hot- 
ter than  the  Hoffman-Otto,  and  for  this  reason  73  %  to  77  %  of  gas  coal 
can  be  mixed  with  23%  to  27%  of  coal  low  in  volatile  matter,  and  yet 
yield  a  good  coke.  Mixtures  of  this  kind  yield  a  larger  percentage  of 
coke,  but,  on  the  other  hand,  the  amount  of  gas  is  lessened,  and  there- 
fore the  yield  of  tar  and  ammonia  is  not  so  great. 

The  yield  of  coke  by  the  beehive  and  the  retort  ovens  respectively  is 
given  as  follows  in  a  pamphlet  of  the  Solvay  Process  Co. :  Connellsville 
coal :  beehive,  66  % ,  retort,  73  % ;  Pocahontas :  beehive,  62  % ,  retort,  83  % ; 
Alabama:  beehive,  60%,  retort,  74%.  (See  article  in  Mineral  Industry, 
vol.  viii.  1900.) 

References:  F.  W.  Luerman,  Verein  Deutscher  Eisenhuettenleute 
1891,  Iron  Age,  March  31,  1892;  Amer.  Mfr.,  April  28,  1893.  An  ex- 
cehent  series  of  articles  on  the  manufacture  of  coke,  by  John  Fulton,  of 
Johnstown,  Pa.,  is  published  in  the  Colliery  Engineer,  beginning  in 
January,  1893. 

Since  the  above  was  written,  great  progress  in  the  introduction  of  coke 
ovens  with  by-product  attachments  has  been  made  in  the  United  States, 
especially  by  the  Semet-Solvay  Co.,  Syracuse,  N.  Y.  See  paper  on  The 
Development  of  the  Modern  By-product  Coke-oven,  by  C.  G.  Atwater, 
Trans.  A.  I.  M.  E.,  1902. 

Generation  of  Steam  from  Waste  Heat  and  Gases  of  Coke-ovens. 
(Erskine  Ramsey,  Amer.  Mfr.,  Feb.  16,  1894.) — The  gases  from  a  num- 
ber of  adjoining  ovens  of  the  beehive  type  are  led  into  a  long  horizontal 
flue,  and  thence  to  a  combustion-chamber  under  a  battery  of  boilers. 
Two  plants  are  in  satisfactory  operation  at  Tracy  City,  Tenn.,  and  two 
at  Pratt  Mines,  Ala. 

A  Bushel  of  Coal. — The  weight  of  a  bushel  of  coal  in  Indiana  is  70 
Ibs.;  in  Penna.,  76  Ibs.;  in  Ala.,  Colo.,  Ga.,  111.,  Ohio,  Tenn.,  and  W. 
Va.,  it  is  80  Ibs. 

A  Bushel  of  Coke  is  almost  uniformly  40  Ibs.,  but  in  exceptional 
cases,  when  the  coal  is  very  light,  38,  36,  and  33  Ibs.  are  regarded  as  a 
bushel,  in  others  from  42  to  50  Ibs.  are  given  as  the  weight  of  a  bushel; 
in  this  case  the  coke  would  be  quite  heavy. 

Products  of  the  Distillation  of  Coal. — S.  P.  Sadler's  Handbook  of 
Industrial  Organic  Chemistry  gives  a  diagram  showing  over  50  chemical 
products  that  are  derived  from  distillation  of  coal.  The  first  derivatives 
are  coal-gas,  gas-liquor,  coal- tar,  and  coke.  From  the  gas-liquor  are 
derived  ammonia  and  sulphate,  chloride  and  carbonate  of  ammonia. 
The  coal-tar  is  split  up  into  oils  lighter  than  water  or  crude  naphtha, 
oils  heavier  than  water — otherwise  dead  oil  or  tar,  commonly  called 
creosote, — and  pitch.  From  the  two  former  are  derived  a  variety  of 
chemical  products. 

From  the  coal-tar  there  comes  an  almost  endless  chain  of  known  com- 
binations. The  greatest  industry  based  upon  their  use  is  the  manufac- 
ture of  dyes,  and  the  enormous  extent  to  which  this  has  grown  can  be 
judged  from  the  fact  that  there  are  over  600  different  coal-tar  colors  in 
use,  and  many  more  which  as  yet  are  too  expensive  for  this  purpose. 
Many  medicinal  preparations  come  from  the  series,  pitch  for  paving 
purposes,  and  chemicals  for  the  photographer,  the  rubber  manufacturers 
and  tanners,  as  well  as  for  preserving  timber  and  cloths. 

The  composition  of  the  hydrocarbons  in  a  soft  coal  is  im certain  and 
quite  complex;  but  the  ultimate  analysis  of  the  average  coal  shows  that 
it  approaches  quite  nearly  to  the  composition  of  CH4  (marsh-gas).  (W. 
H.  Blauvelt,  Trans.  A,  I,  M,  E,,  xx.  625.) 


WOOD   AS   FUEL. 


835 


WOOD  AS  FUEL. 

Wood,  when  newly  felled,  contains  a  proportion  of  moisture  which 
varies  very  much  in  different  kinds  and  in  different  specimens,  ranging 
between  30%  and  50%,  and  being  on  an  average  about  40%.  After  8 
or  12  months  ordinary  drying  in  the  air  the  proportion  of  moisture  is 
from  20  to  25%.  This  degree  of  dryness,  or  almost  perfect  dryness  if 
required,  can  be  produced  by  a  few  days'  drying  in  an  oven  supplied  with 
air  at  about  240°  F.  When  coal  or  coke  is  used  as  the  fuel  for  that  oven, 
1  Ib.  of  fuel  suffices  to  expel  about  3  Ib.  of  moisture  from  the  wood. 
This  is  the  result  of  experiments  on  a  large  scale  by  Mr.  J.  R.  Napier. 
If  air-dried  wood  were  used  as  fuel  for  the  oven,  from  2  to  2  H  Ib-  of 
wood  would  probably  be  required  to  produce  the  same  effect. 

The  specific  gravity  of  different  kinds  of  wood  ranges  from  0.3  to  1.2. 

Perfectly  dry  wood  contains  about  50%  of  carbon,  the  remainder  con- 
sisting almost  entirely  of  oxygen  and  hydrogen  in  the  proportions  which 
form  water.  The  coniferous  family  contains  a  small  quantity  of  turpen- 
tine, which  is  a  hydrocarbon.  The  proportion  of  ash  in  wood  is  from 
1  %  to  5  % .  The  total  heat  of  combustion  of  all  kinds  of  wood,  when  dry, 
is  almost  exactly  the  same,  and  is  that  due  to  the  50%  of  carbon. 

The  above  is  from  Rankine:  but  according  to  the  table  by  S.  P.  Sharp- 
less  in  Jour.  C.  I.  W.,  iv.  36,  the  ash  varies  from  0.03%  to  1.20%  in 
American  woods,  and  the  fuel  value,  instead  of  being  the  same  for  all 
woods,  ranges  from  3667  (for  white  oak)  to  5546  calories  (for  long-leaf 
pine)  =  6600  to  9883  British  thermal  units  for  dry  wood,  the  fuel  value 
of  0.50  Ib.  carbon  being  7300  B.T.U. 

Heating  Value  of  Wood. — The  following  table  is  given  in  several 
books  of  reference,  authority  and  quality  of  coal  referred  to  not  stated. 

The  weight  of  one  cord  of  different  woods  (thoroughly  air-dried)  in 
pounds  is  about  as  follows: 
Hickory  or  hard  maple .  .   4500  equal  to  1800  coal.     (Others  give  2000. 

White  oak 3850        "         1540    "         (  "  1715. 

Beech,  red  and  black  oak  3250        "        1300    "         (          "  1450. 

Poplar,  chestnut,  &  elm. .    2350        "  940    "         (  1050. 

The  average  pine 2000        "          800    "         (          "  925. 

Referring  to  the  figures  in  the  last  column,  it  is  said: 

From  the  above  it  is  safe  to  assume  that  2 1/4  Ib.  of  dry  wood  are  equal 
to  1  Ib.  average  quality  of  soft  coal  and  that  the  full  value  of  the  same 
weight  of  different  woods  is  very  nearly  the  same^— that  is,  a  pound  of 
hickory  is  worth  no  more  for  fuel  than  a  pound  of  pine,  assuming  both  to 
be  dry.  It  is  important  that  the  wood  be  dry,  as  each  10%  of  water  or 
moisture  in  wood  will  detract  about  12  %  from  its  value  as  fuel. 

Taking  an  average  wood  of  the  analysis  C  51  %,  H  6.5%,  O  42.0%,  ash 
0.5%,  perfectly  dry,  its  fuel  value  per  pound,  according  to  Dulong's 

formula, V  =  Fl4,600  C  +  62,000/H  -§)!>  is  8221  British  thermal 

units.  If  the  wood,  as  ordinarily  dried  in  air,  contains  25  %  of  moisture, 
then  the  heating  value  of  a  pound  of  such  wood  is  three  quarters  of 
8221  =  6165  heat-units,  less  the  heat  required  to  heat  and  evaporate  the 
1/4  Ib.  of  water  from  the  atmospheric  temperature,  and  to  heat  the  steam 
made  from  this  water  to  the  temperature  of  the  chimney  gases,  say 
150  heat-units  per  pound  to  heat  the  water  to  212°,  970  units  to  evap- 
orate it  at  that  temperature,  and  100  heat-units  to  raise  the  temperature 
of  the  steam  to  420°  F.,  or  1220  in  all  =  305  for  1/4  Ib.,  which,  subtracted 
from  the  6165,  leaves  5860  heat-units  as  the  net  fuel  value  of  the  wood 
per  pound,  or  about  0.4  that  of  a  pound  of  carbon. 

Composition  of  Wood. 
(Analysis  of  Woods,  by  M.  Eugene  Chevandier.) 


Woods. 

Carbon. 

Hydro- 
gen. 

Oxygen. 

Nitrogen. 

Ash. 

Beech  .  . 

49.36% 

6.01% 

42.69% 

0.91% 

1  06% 

Oak.  . 

49  64 

5.92 

41.16 

1  29 

1  97 

Birch  

50.20 

6.20 

41.62 

1   15 

0  81 

Poplar.  . 

49.37 

6  21 

41  60 

0  96 

1  86 

Willow  

49.96 

5.96 

39.56 

0.96 

3.37 

Average  

49.70% 

6.06% 

41.30% 

1.05% 

1,80% 

836 


The  following  table,  prepared  by  M.  Violette,  shows  the  proportion  of 
water  expelled  from  wood  at  gradually  increasing  temperatures: 

Temperature. 

Water  Expelled  from  100  Parts  of  Wood. 

Oak. 

Ash. 

Elm. 

Walnut. 

257°  Fahr 

15.26 
17.93 
32.13 
35.80 
44.31 

14.78 
16.19 
21.22 
27.51 
33.38 

15.32 
17.02 
36.94? 
33.38 
40.56 

15.55 
17.43 
21.00 
41.77? 
36.56 

302°  Fahr        

347°  Fahr.  . 

392°  Fahr     • 

437°  Fahr  

The  wood  operated  upon  had  been  kept  in  store  during  two  years. 
When  wood  which  has  been  strongly  dried  by  means  of  artificial  heat  is 
left  exposed  to  the  atmosphere,  it  reabsorbs  about  as  much  water  as  it 
contains  in  its  air-dried  state. 

A  cord  of  wood  =4X4X8=  128  cu.  ft.  About  56%  solid  wood  and 
44%  interstitial  spaces.  (Marcus  Bull,  Phila.,  1829.  J.  C.  I.  W.,  vol. 
i.  p.  293.) 

B.  E.  Fernow  gives  the  percentage  of  solid  wood  in  a  cord  as  deter- 
mined officially  in  Prussia  (J".  C.  I.  W.,  vol.  iii.  p.  20): 
Timber  cords,  74.07%    =  80  cu.  ft.  per  cord; 
Firewood  cords  (over  6"  diam.),  69.44%    =  75  cu.  ft.  per  cord; 
"Billet"  cords  (over  3"  diam.),  55.55%    =  60  cu.  ft.  per  cord; 
"Brush"  woods  less  than  3"  diam.,  18.52%;  Roots,  37.00%. 

CHARCOAL. 

Charcoal  is  made  by  evaporating  the  volatile  constituents  of  wood  and 
peat,  either  by  a  partial  combustion  of  a  conical  heap  of  the  material  to 
be  charred,  covered  with  a  layer  of  earth,  or  by  the  combustion  of  a 
separate  portion  of  fuel  in  a  furnace,  in  which  are  placed  retorts  con- 
taining the  material  to  be  charged. 

According  to  Peclet,  100  parts  by  weight  of  wood  when  charred  in  a 
heap  yield  from  17  to  22  parts  by  weight  of  charcoal,  and  when  charred 
in  a  retort  from  28  to  30  parts. 

This  has  reference  to  the  ordinary  condition  of  the  wood  used  in  char- 
coal-making, in  which  25  parts  in  100  consist  of  moisture.  Of  the  re- 
maining 75  parts  the  carbon  amounts  to  one  half,  or  37  ^  %  of  the  gross 
weight  of  the  wood.  Hence  it  appears  that  on  an  average  nearly  half  of 
the  carbon  in  the  wood  is  lost  during  the  partial  combustion  in  a  heap, 
and  about  one  quarter  during  the  distillation  in  a  retort. 

To  char  100  parts  by  weight  of  wood  in  a  retort,  12  ^  parts  of  wood 
must  be  burned  in  the  furnace.  Hence  in  this  process  the  whole  expen- 
diture of  wood  to  produce  from  28  to  30  parts  of  charcoal  is  112%  parts; 
so  that  if  the  weight  of  charcoal  obtained  is  compared  with  the  whole 
weight  of  wood  expended,  its  amount  is  from  25%  to  27%  and  the  pro- 
portion lost  is  on  an  average  11  Yz  +  37  %  =  0.3,  nearly. 

According  to  Peclet,  good  wood  charcoal  contains  about  0.07  of  its 
weight  of  ash.  The  proportion  of  ash  in  peat  charcoal  is  very  variable 
and  is  estimated  on  an  average  at  about  0.18.  (Rankine.) 

Much  information  concerning  charcoal  may  be  found  in  the  Journal  of 
the  Charcoal-iron  Workers'  Assn.,  vols.  i.  to  vi.  From  this  source  the 
following  notes  have  been  taken: 

Yield  of  Charcoal  from  a  Cord  of  Wood.— From  45  to  50  bushels 
to  the  cord  in  the  kiln,  and  from  30  to  35  in  the  meiler.  Prof.  Egleston 
in  Trans.  A.  I.  M.  E.,  viii,  395,  says  the  yield  from  kilns  in  the  Lake 
Champlain  region  is  often  from  50  to  60  bushels  for  hard  wood  and  50 
for  soft  wood;  the  average  is  about  50  bushels. 

The  apparent  yield  per  cord  depends  largely  upon  whether  the  cord  is 
a  full  cord  of  128  cu.  ft.  or  not. 

In  a  four  months'  test  of  a  kiln  at  Goodrich,  Term.,  Dr.  H.  M.  Pierce 
found  results  as  follows:  Dimensions  of  kiln — inside  diameter  of  base, 
28  ft.  8  in. ;  diam.  at  spring  of  arch,  26  ft.  8  in. ;  height  of  walls,  8  ft. ;  rise 
of  arch,  5  ft. ;  capacity,  30  cords.  Highest  yield  of  charcoal  per  cord  of 
wood  (measured)  59.27  bushels,  lowest  50.14  bushels,  average  53.65 
bushels.  No.  of  charges  12,  length  of  each  turn  or  period  from  one 
charging  to  another  11  days.  £7.  C.  I.  W.,  vol.  vi.  p.  26.) 


MISCELLANEOUS   SOLID   FUELS.  837 

Results  from  Different  Methods  of  Charcoal-making* 


Yield. 

11 

a! 

Coaling  Methods. 

Character  of  Wood  Used. 

Bg 

II 

to  O<  o 

•s|1 

jj*  0 
O  t, 

0 

0)  0 

V 

Hts 

^0,0 

Odelstjerna's  experiments 

Birch  dried  at  230  F  

^  9 

Mathieu's  retorts,  fuel  ex- 
cluded   

!Air  dry,  av.  good  yel- 
low    pine     weighing 
abt.281bs.percu.ft. 

77.0 
65.8 

28.3 
24.2 

63.4 
54.2 

15.7 
15.7 

Mathieu's  retorts,  fuel  in- 

Swedish  ovens,  av.  results 

f  Good  dry  fir  and  pine, 
\     mixed. 

81.0 

27.7 

66.7 

13.3 

Swedish  ovens,  av.  results 

(  Poor  wood,  mixed   fir 
\   and  pine. 

70.0 

25.8 

62.0 

13.3 

Swedish    meilers    excep- 

!Fir     and      white-pine 

72.2 

24.7 

59.5 

13.3 

tional             .        . 

wood  mixed.    Av.  25 

Swedish  meilers,  av.  results 

Ibs.  per  cu.  ft. 

52,5 

18.3 

43.9 

13.3 

American  kilns,  av.  results 

!Av.  good    yellow  pine 

54.7 

22.0 

45.0 

17.5 

American  meilers,  av.  re- 

weighing  abt.  25  Ibs. 

17.5 

eults... 

t>er  cu.  ft. 

42  9 

17  1 

35.0 

Consumption  of  Charcoal  in  Blast-furnaces  per  Ton  of  Pig  Iron: 

average  consumption  according  to  census  of  1880,  1.14  tons  charcoal  per 
ton  of  pig.  The  consumption  at  the  best  furnaces  is  much  below  this 
average.  As  low  as  0.853  ton  is  recorded  of  the  Morgan  furnace;  Bay 
furnace,  0.858;  Elk  Rapids,  0.884.  (1892.) 

Absorption  of  Water  and  of  Gases  by  Charcoal. — Svedlius,  in  his 
hand-book  for  charcoal-burners,  prepared  for  the  Swedish  Government, 
says:  Fresh  charcoal,  also  reheated  charcoal,  contains  scarcely  any  water, 
but  when  cool  it  absorbs  it  very  rapidly,  so  that,  after  twenty-four  hours, 
it  may  contain  4  %  to  8  %  of  water.  After  the  lapse  of  a  few  weeks  the 
moisture  of  charcoal  may  not  increase  perceptibly,  and  may  be  esti- 
mated at  10%  to  15%,  or  an  average  of  12%.  A  thoroughly  charred 
piece  of  charcoal  ought,  then,  to  contain  about  84  parts  carbon,  12  parts 
water,  3  parts  ash,  and  1  part  hydrogen. 

M.  Saussure,  operating  with  blocks  of  fine  boxwood  charcoal,  freshly 

burnt,  found  that  by  simply  placing  such  blocks  in  contact  with  certain 

gases  they  absorbed  them  in  the  following  proportion:  t 

Volumes.  Volumes. 

Ammonia 90 . 00      Carbonic  oxide 9 . 42 


Oxygen 9 . 25 

Nitrogen " 6 . 50 

Carburetted  hydrogen 5 . 00 

Hydrogen 1 . 75 


Hydrochloric-acid  gas 85 . 00 

Sulphurous  acid 65 . 00 

Sulphuretted  hydrogen  ....  55 . 00 
Nitrous  oxide  (laughing-gas)  40 . 00 
Carbonic  acid 35 . 00 

It  is  this  enormous  absorptive  power  that  renders  of  so  much  value  a 
comparatively  slight  sprinkling  of  charcoal  over  dead  animal  matter,  as  a 
preventive  of  the  escape  of  odors  arising  from  decomposition. 

In  a  box  or  case  containing  one  cubic  foot  of  charcoal  may  be  stored 
without  mechanical  compression  a  little  over  nine  cubic  feet  of  oxygen, 
representing  a  mechanical  pressure  of  one  hundred  and  twenty-six  pounds 
to  the  square  inch.  From  the  store  thus  preserved  the  oxgyen  can  be 
drawn  by  a  small  hand-pump, 

MISCELLANEOUS  SOLID  FUELS. 

Dust  Fuel — Dust  Explosions. — Dust  when  mixed  in  air  burns  with 
such  extreme  rapidity  as  in  some  cases  to  cause  explosions.  Explosions 
of  flour-mills  have  been  attributed  to  ignition  of  the  dust  in  confined 
passages.  Experiments  in  England  in  1876  on  the  effect  of  coal-dust  in 
carrying  flame  in  mines  showed  that  in  a  dusty  passage  the  flame  from  a 


838  FUEL. 

blown-out  shot  may  travel  50  yards.  Prof.  F.  A.  Abel  (Trans.  A.  I.  M.  E., 
xiii.  260)  says  that  coal-dust  in  mines  much  promotes  and  extends 
explosions,  and  that  it  may  readily  be  brought  into  operation  as  a 
fiercely  burning  agent  which  will  carry  flame -rapidly  as  far  as  its  mixture 
with  air  extends,  and  will  operate  as  an  explosive  agent  through  the  me- 
dium of  a  very  small  proportion  of  fire-damp  in  the  air  of  the  mine. 
The  explosive  violence  of  the  combustion  of  dust  is  largely  due  to  the 
instantaneous  heating  and  consequent  expansion  of  the  air.  (See  also 
paper  on  "Coal  Dust  as  an  Explosive  Agent."  by  Dr.  R.  W.  Raymond, 
Trans.  A.  I.  M.  E.,  1894.)  Experiments  made  in  Germany  in  1893 
show  that  pulverized  fuel  may  be  burned  without  smoke,  and  with  high 
economy.  The  fuel,  instead  of  being  introduced  into  the  fire-box  in  the 
ordinary  manner,  is  first  reduced  to  a  powder  by  pulverizers  of  any  con- 
struction. In  the  place  of  the  ordinary  boiler  fire-box  there  is  a  com- 
bustion chamber  in  the  form  of  a  closed  furnace  lined  with  fire-brick  and 
provided  with  an  air-injector.  The  nozzle  throws  a  constant  stream  of 
fuel  into  the  chamber,  scattering  it  throughout  the  whole  space  of  the 
fire-box.  When  this  powder  is  once  ignited,  and  it  is  very  readily  done 
by  first  raising  the  lining  to  a  high  temperature  by  an  open  fire,  the 
combustion  continues  in  an  intense  and  regular  manner  under  the  action 
of  the  current  of  air  which  carries  it  in.  (Mfrs.  Record,  April,  1893.) 

Records  of  tests  with  the  Wegener  powdered-coal  apparatus,  which  is 
now  (1900)  in  use  in  Germany,  are  given  in  Eng.  News,  Sept.  16,  1897. 
Illustrated  descriptions  of  different  forms  of  apparatus  are  given  in  the 
author's  "  Steam  Boiler  Economy."  Coal-dust  fuel  is  now  extensively 
used  in  the  United  States  in  rotary  kilns  for  burning  Portland  cement. 

Powdered  fuel  was  used  in  the  Crompton  rotary  puddling-furnace  at 
Woolwich  Arsenal,  England,  in  1873.  (Jour.  I.  &  S.  I.,  i.  3873,  p.  91.) 
Numerous  experiments  on  the  use  of  powdered  fuel  for  steam  boilers 
were  made  in  the  U.  S.  between  1895  and  1905,  but  they  were  not  com- 
mercially successful. 

Peat  or  Turf,  as  usually  dried  in  the  air,  contains  from  25  %  to  30%  of 
water,  which  must  be  allowed  for  in  estimating  its  heat  of  combustion. 
This  water  having  been  evaporated,  the  analysis  of  M.  Regnault  gives, 
in  100  parts  of  perfectly  dry  peat  of  the  best  quality:  C,  58%;  H,  6%; 
O,  31%;  Ash,  5%.  In  some  examples  of  peat  the  quantity  of  ash  is 
greater,  amounting  to  7%  and  sometimes  to  11%. 

The  specific  gravity  of  peat  in  its  ordinry  state  is  about  0.4  or  0.5. 
It  can  be  compressed  by  machinery  to  a  much  greater  density.  (Rankine.) 

Clark  (Steam-engine,  i.  61)  sives  as  the  average  composition  of  dried 
Irish  peat:  C,  59%;  H,  6%;  O,  30%;  N,  1.25%;  Ash,  4%. 

Applying  Dulong's  formula  to  this  analysis,  we  obtain  for  the  heating 
value  of  perfectly  dry  peat  10,260  heat-units  per  pound,  and  for  air- 
dried  peat  containing  25%  of  moisture,  after  making  allowance  for 
evaporating  the  water,  7,391  heat-units  per  pound. 

A  paper  on  Peat  in  the  U.  S.,  by  M.  R.  Campbell,  will  be  found  in 
Mineral  Resources  of  the  U.  S.  (U.  S.  Geol.  Survey)  for  1905,  p.  1319. 

Sawdust  as  Fuel. — The  heating  power  of  sawdust  is  naturally  the 
same  per  pound  as  that  of  the  wood  from  which  it  is  derived,  but  if 
allowed  to  get  wet  it  is  more  like  spent  tan  (which  see  below).  The 
conditions  necessary  for  burning  sawdust  are  that  plenty  of  room  should 
be  given  it  in  the  furnace,  and  sufficient  air  supplied  on  the  surface  of 
the  mass,  preferably  by  means  of  a  fan-blast.  The  same  applies  to  shav- 
ings, refuse  lumber,  etc.  Sawdust  is  frequently  burned  in  saw-mills,  etc., 
by  being  blown  into  the  furnace  by  a  fan-blast. 

Wet  Tan  Bark  as  Fuel. —  Tan,  or  oak  bark,  after  having  been  used 
in  the  processes  of  tanning,  is  burned  as  fuel.  The  spent  tan  consists  of 
the  fibrous  portion  of  the  bark.  The  principal  cause  of  poor  economy 
in  the  burning  of  tan  bark  besides  the  difficulty  of  securing  good  com- 
bustion in  the  furnace,  is  the  amount  of  heat  that  is  carried  away  in  the 
shape  of  superheated  steam  in  the  chimney  gases.  If  the  bark,  after 
partial  drying  by  compression,  were  further  dried  in  a  rotary  drier  by 
waste  heat  from  the  chimney  gases,  there  would  be  an  important  gain 
in  economy.  For  calculations  showing  the  advantages  of  drying,  and 
for  illustrations  of  tan-bark  furnaces,  see  "Steam  Boiler  Economy." 

D.  M.  Myers  (Trans.  A.  S.  M.  E.,  1909)  describes  some  experiments 
on  tan  as  a'boiler  fuel.  One  hundred  Ib.  of  air-dried  bark  fed  to  the 
mill  will  produce  213  Ib.  of  spent  tan  containing  65%  moisture.  Tak* 


MISCELLANEOUS   SOLID   FUELS.  839 

ing  9500  B.T.U.  as  the  heating  value  per  Ib.  of  dry  tan  and  500°  F.  as  the 
temperature  of  the  chimney  gases,  the  available  heat  in  1  Ib.  of  wet  tan 
is  2665  B.T.U.  Based  on  this  value  as  much  as  71%  efficiency  has 
been  obtained  in  a  boiler  test  with  a  special  furnace,  or  1.93  Ib.  of 
water  evaporated  from  and  at  212°  per  Ib.  of  wet  tan.  The  average 
heating  value  of  dry  hemlock  tan,  as  found  by  a  bomb  calorimeter  in  six 
tests  by  Dr.  Sherman,  is  9504  B.T.U.  The  composition  of  dry  tan  is 
Ash,  1.42;  C,  51.80;  H,6.04;  O,  40.74.  By  Dulong's  formula  the  heating 
value  would  be  8152  B.T.U. 

Straw  as  Fuel.  (Eng'g  Mechanics,  Feb.  1893,  p.  55.) — Experiments 
in  Russia  showed  that  winter-wheat  straw,  dried  at  230°  F.,  had  the 
following  composition,  C,  46.1;  H,  5.6;  N,  0.42:  O,  43.7;  Ash,  4.1.  Heat- 
ing value  in  British  thermal  units:  dry  straw,  6290;  with  6%  water. 
5770;  with  10%  water,  5448.  With  straws  of  other  grains  the  heating 
value  of  dry  straw  ranged  from  5590  for  buckwheat  to  6750  for  flax. 

Clark  (S.  E.,  vol.  1,  p.  62)  gives  the  mean  composition  of  wheat  and 
barley  straw  as  C,  36;  H,  5;  O,  38;  N,  0.50;  Ash,  4.75;  Water,  15.75,  the 
two  straws  varying  less  than  1  % .  The  heating  value  of  straw  of  this 
composition,  according  to  Dulong's  formula,  and  deducting  the  heat 
lost  in  evaporating  the  water,  is  5155  heat-units.  Clark  erroneously 
gives  it  as  8144  heat-units. 

Bagasse  as  Fuel  in  Sugar  Manufacture. — Bagasse  is  the  name  given 
to  refuse  sugar-cane,  after  the  juice  has  been  extracted.  Prof.  L.  A. 
Becuel,  in  a  paper  read  before  the  Louisiana  Sugar  Chemists'  Associa- 
tion, in  1892,  says:  "  With  tropical  cane  containing  12.5%  woody  fibre,  a 
juice  containing.  16. 13%  solids,  and  83.87%  water,  "bagasse  of,  say,  66% 
and  72%  mill  extraction  has  the  following  percentage  composition: 

66%  bagasse:  Woody  Fibre,  37;  Combustible  Salts,  10;  Water,  53. 

72%  bagasse:  Woody  Fibre,  45;  Combustible  Salts,    9;  Water,  46. 

"Assuming  that  the  woody  fibre  contains  51%  carbon,  the  sugar  and 
other  combustible  matters  an  average  of  42.1%,  and  that  12,906  units 
of  heat  are  generated  for  every  pound  of  carbon  consumed,  the  66% 
bagasse  is  capable  of  generating  297,834  heat-units  per  100  Ib.  as  against 
345,200,  or  a  difference  of  47,366  units  in  favor  of  the  72%  bagasse. 

"Assuming  the  temperature  of  the  waste  gases  to  be  450°  F.,  that  of 
the  surrounding  atmosphere  and  water  in  the  bagasse  at  86°  F.,  and  the 
quantity  of  air  necessary  for  the  combustion  of  one  pound  of  carbon  at 
24  Ib.,  the  lost  heat  will  be  as  follows:  In  the  waste  gases,  heating  air 
from  86°  to  450°F.,  and  in  vaporizing  the  moisture,  etc.,  the  66  %  bagasse 
will  require  112,546  heat-units,  and  116,150  for  the  72%  bagasse. 

"Subtracting  these  quantities  from  the  above,  we  find  that  the  66% 
bagasse  will  produce  185,288  available  heat-units  per  100  Ib.,  or  nearly 
24  %  less  than  the  72  %  bagasse,  which  gives  229,050  units.  Accordingly 
one  ton  of  cane  of  2000  Ib.  at  66%  mill  extraction  will  produce  680  Ib. 
bagasse,  equal  to  1,259,958  available  heat-units,  while  the  same  cane  at 
72%  extraction  will  produce  560  Ib.  bagasse,  equal  to  1,282,680  units. 

"A  similar  calculation  for  the  case  of  Louisiana  cane  containing  10% 
woody  fiore,  and  16%  total  solids  in  the  juice,  assuming  75%  mill  ex- 
traction, shows  that  bagasse  from  one  ton  of  cane  contains  1,573,956 
heat-units,  from  which  561,465  have  to  be  deducted,  which  makes  such 
bagasse  worth  on  an  average  nearly  92  Ib.  coal  per  ton  of  cane  ground. 

"It  appears  that  with  the  best  boiler  plants,  those  taking  up  all  the 
available  heat  generated,  by  using  this  heat  economically  the  bagasse 
can  be  made  to  supply  all  the  fuel  required  by  our  sugar-houses." 

The  figures  below  are  from  an  article  by  Samuel  Vickess  (The  Engineer, 
Chicago,  April  1,  1903). 

When  canes  with  12%  fibre  are  ground,  the  juice  extractions  and 
liquid  left  in  the  residual  bagasse  are  generally  as  follows: 


With 

Per  Cent  of  Normal 
Juice  Extracted  on 
Weight  of  Cane. 

Per  Cent  of  Liquid 
Left  in  Bagasse  on 
Weight"  of  Bagasse. 

Double  crushing  

70 
62 
72 
76 

82 

60 
68 
57 
50 

50 

Single  crushing 

Crusher  and  double  crushing  

Triple  Crushing    . 

Crusher    and    triple    crushing    with 
saturation  

840 


FUEL. 


The  value  of  bagasse  as  a  fuel  depends  upon  the  amount  of  woody 
fibre  it  contains,  and  the  amount  of  combustible  matter  (sucrose, 
glucose,  and  gums),  held  in  the  liquid  it  retains.  100  Ib.  cane  with 
triple  crushing  gives  76  Ib.  juice,  and  24  Ib.  bagasse,  which  consists  of  12 
Ib.  fibre  and  12  Ib.  juice.  The  12  Ib.  of  juice  contains  16%  or  1.92  Ib. 
sucrose,  0.5%  or  0.06  Ib.  glucose,  2.5%  other  organic  matter  and  1%  or 
0.12  Ib.  ash,  making  a  total  of  20%  or  2.4  Ib.  of  solid  matter,  and  80% 
or  9.6  Ib.  of  water.  Reducing  these  figures  to  quantities  corresponding 
to  1  Ib.  of  bagasse,  and  multiplying  by  the  heating  values  of  the  several 
substances  as  given  by  Stohlmann,  viz.:  fibre,  7461;  sucrose,  6957; 
glucose,  6646;  organic  matter,  7461,  we  find  the  heating  value  of  the  com- 
bustible in  1  Ib.  of  bagasse  to  be  4397  B.T.U.  This  is  the  gross  heating 
value  which  would  be  obtained  in  a  calorimeter  in  which  the  products 
of  combustion  were  cooled  to  the  temperature  of  the  atmosphere.  To 
find  approximately  the  heat  available  for  generating  steam  in  a  boiler 
we  may  assume  that  10  Ib.  of  air  is  used  in  burning  each  pound  of  ba- 
gasse, that  the  atmospheric  temperature  is  82°  and  the  flue  gas  tempera- 
ture 462°,  and  that  in  addition  to  the  0.4  Ib.  water  per  Ib.  bagasse  half 
of  the  remaining  0.6  Ib.  is  oxygen  and  hydrogen  in  proportions  which 
form  water,  making  0.7  Ib.  water  wrhich  escapes  in  the  flue  gas  as  super- 
heated steam.  The  heat  lost  in  the  flue  gases  per  pound  of  bagasse  is 
10  X  0.24  X  (462  -  82)  +  0.7  [(212  -  82)  +  970  +  0.5  (462  -  212)]  =  1770 
B.T.U. ,  which  subtracted  from  4397  leaves  2627  B.T.U.  as  the  net  or 
available  heating  value,  which  is  equivalent  to  an  evaporation  of  2.7  Ib. 
of  water  from  and  at  212°.  Mr.  Vickess  states  that  in  practice  1  Ib.  of 
such  green  bagasse  evaporates  2  to  21/4  Ib.  from  feed  water  at  100° 
into  steam  at  90  Ib.  pressure.  This  is  equivalent  to  from  2.31  to  2.59 
Ib.  from  and  at  212°. 

E.  W.  Kerr,  in  Bulletin  No.  117  of  the  Louisiana  Agricultural  Experi- 
ment Station,  Baton  Rouge,  La.,  gives  the  results  of  a  study  of  many 
different  forms  of  bagasse  furnaces.  An  equivalent  evaporation  of  2 1/4 
Ib.  of  steam  from  and  at  212°  was  obtained  from  1  Ib.  of  wet  bagasse  of 
a  net  calorific  value  of  3256  B.T.U.  This  net  value  is  that  calculated 
from  the  analysis  by  Dulong's  formula,  minus  the  heat  required  to 
evaporate  the  moisture  and  to  heat  the  vapor  to  the  temperature  of  the 
escaping  chimney  gases,  594°  F.  The  approximate  composition  of 
bagasse  of  75%  extraction  is  given  as  51%  free  moisture,  and  28%  of 
water  combined  with  21  %  of  carbon  in  the  fibre  and  sugar.  For  the 
best  results  the  bagasse  should  be  burned  at  a  high  rate  of  combustion, 
at  least  100  Ib.  per  sq.  ft  of  grate  per  hour.  Not  more  than  1.5  Ib.  of 
bagasse  per  sq.  ft.  of  heating  surface  per  hour  should  be  burned  under 
ordinary  conditions,  and  not  less  than  1.5  boiler  horse-power  should  be 
provided  per  ton  of  cane  per  24  hours. 

For  illustrations  of  bagasse  furnaces  see  "  Steam  Boiler  Economy." 

LIQUID  FUEL. 

Products  of  the  Distillation  of  Crude  Petroleum. 

Crude  American  petroleum  of  sp.  gr.  0.800  may  be  split  up  by  fractional 
distillation  as  follows  ("  Robinson's  Gas  and  Petroleum  Engines  "): 


Temp,  of 
Distillation 
Fahr. 

Distillate. 

Per- 
cent- 
ages. 

Specific 
Gravity. 

Flashing 
Point. 
Deg.  F. 

113° 

Rhigolene.     I 

traces. 

590  to  .625 

113  to  140° 
140  to  158° 

Chymogene.  J  
Gasoline  (petroleum  spirit)    . 

1.5 

.636  to  .657 

158  to  248° 
248° 
to 

Benzine,  naphtha  C.benzolene 
(  Benzine,  naphtha  B  
\  Benzine  naphtha  A  

10. 
2.5 
2. 

.680  to  .700 
.714  to  .718 
.725  to  .737 

14 
'"32  " 

347° 

(  Polishing  oils 

338°  and  ) 

Kerosene  (lamp-oil) 

50. 

802  to  .820 

100  to  122 

upwards.  J 
482°      ' 

Lubricating  oil 

15. 

.850  to  .915 

230 

2 

Residue  and  Loss  

16. 

LIQUID  FUEL. 


841 


Lima  Petroleum,  produced  at  Lima,  Ohio,  is  ol  a  dark  green  color, 
very  fluid,  and  marks  48°  Baume  at  15°  C.  (sp.  gr.,  0.792). 

The  distillation  in  fifty  parts,  each  part  representing  2%  by  volume, 
gave  the  following  results: 

Sp.     Per     Sp.      Per        Sp.    Per       Sp.     Per       Sp. 
cent. 
50      l 

52] 

to ! 

58  t 
60 
62 
64 


Per    Sp.    Per 

cent.  Gr.  cent.     Gr.    cent:    Gr. 

2    0.680    18    0.720  34    0.764 

.728  36       .768 

.730  38 

.735  40 

.740  42 

.742  44 

.746  46 


.683  20 

.685  22 

.690  24 

.694  26 

.698  28 

.700  30 

.706  32 


.760    48 


.772 
.778 
.782 
.788 
.792 
.800 

RETURNS. 


Gr. 

.802 

.806 

.800 
.804 
.808 
.812 

cent. 
68  0, 
70   , 
72 
73 
76   , 
78 
82 
86 

Gr. 

,820 
,825 
.830 
.830 
.810 
.820 
.818 
.816 

cent. 

88 
90 

92) 
to  [ 
100  J 

* 

Gr. 
0.815 
.815 

1 

1 
» 

16  per  cent  naphtha,  70°  Baume.         6  per  cent  parafflne  oil. 
68  per  cent  burning  oil.  10  per  cent  residuum. 

The  distillation  started  at  23°  C.,  this  being  due  to  the  large  amount  of 
naphtha  present,  and  when  60%  was  reached,  at  a  temperature  of  310° C. 
the  hydrocarbons  remaining  in  the  retort  were  dissociated,  when  gases 
escaped,  lighter  distillates  were  obtained,  and,  as  usual  in  such  cases,  the 
temperature  decreased  from  310°  C.  down  gradually  to  200°  C.,  until 
75%  of  oil  was  obtained,  and  from  this  point  the  temperature  remained 
constant  until  the  end  of  the  distillation.  Therefore  these  hydrocarbons 
in  statu  moriendi  absorbed  much  heat.  (Jour.  Am.  Chem.  Soc.) 

There  is  not  a  good  agreement  between  the  character  of  the  materials 
designated  gasoline,  kerosene,  etc.,  and  the  temperature  of  distillation 
and  densities  employed  in  different  places.  The  following  table  shows 
one  set  of  values  that  is  probably  as  good  as  any. 


Name. 

Boiling 
Point. 

Specific 
Gravity. 

Density  at 
59°  F. 

Petroleum,  ether 

°F. 
104-158 

0  650-0.660 

°Baume. 
85-80 

Gasoline                              

158-176 

.660-  .670 

80-78 

Naphtha  C  

176-212 

.670-    707 

78-68 

Naphtha  B 

212-248 

.707-  .722 

68-64 

Naphtha  A    

248-302 

.722-  .737 

64-60  , 

Kerosene  

302-572  . 

.753-  .864 

56-32 

Gasoline  is  different  from  a  simple  substance  with  a  fixed  boiling 
point,  and  therefore  theoretical  calculations  on  the  heat  of  combustion, 
air  necessary,  and  conditions  for  vaporizing  or  carbureting  air  are  of 
little  value.  (C.  E.  Lucke.) 

Value  of  Petroleum  as  Fuel. — Thos.  Urquhart,  of  Russia  (Proc. 
Inst.  M.  E.,  Jan.,  1889),  gives  the  following  table  of  the  theoretical 
evaporative  power  of  petroleum  in  comparison  with  that  of  coal,  as 
determined  by  Messrs.  Favre  and  Silbermann: 


Specific 
Gravity 

Cherh.  Comp. 

Heating 
power, 

Theoret. 
Evap., 
Lb.  of 

Fuel. 

•790   T7I 

British 

Water  per 

Thermal 

Ib.  Fuel, 

Water 
=  1.000 

C. 

H. 

0. 

Units. 

from  and 

at  212°  F. 

Penna.  heavy  crude  oil  .... 
Caucasian  light  crude  oil  .  . 

0.886 
0.884 

84.9 
86.3 

13.7 
13.6 

1.4 
0.1 

20.736 
22,027 

21.48 
22.79 

Caucasian  heavy  crude  oil  . 

0.938 

86.6 

12.3 

1.1 

20,138 

20.85 

Petroleum  refuse  

0.928 

87.1 

11.7 

1.2 

19,832 

20.53 

Good  English  coal  

1.380 

80.0 

5.0 

8.0 

14,112 

14.61 

In  experiments  on  Russian  railways  with  petroleum  as  fuel  Mr. 
Urquhart  obtained  an  actual  efficiency  equal  to  82  %  of  the  theoretical 


842 


FUEL. 


heating-value.  The  petroleum  is  fed  to  the  furnace  by  in  cans  of  a 
spray-injector  driven  by  steam.  An  induced  current  of  air  is  carried  in 
around  the  injector-nozzle,  and  additional  air  is  supplied  at  the  bottom 
of  the  furnace. 

Beaumont,  Texas,  oil  analyzed  as  follows  (Eng.  News,  Jan.  30,  1902) : 
C,  84.60;  H,  10.90;  S,  1.63;  O,  2.87.  Sp.  gr.;0.92;  flash  point,  142°  F.; 
burning  point,  181°  F. ;  heating  value  per  lb.,  by  oxygen  calorimeter, 
19,060  B.T.U.  A  test  of  a  horizontal  tubular  boiler  with  this  oil,  by 
J.  E.  Den  ton  gave  an  efficiency  of  78.5%.  As  high  as  82  %  has  been  re- 
ported for  California  oil. 

Bakersfield,  Cal.,  oil:  Sp.  gr.  16°  Baume;  Moisture,  1%;  Sulphur, 
0.5%.  B.T.U.  per  lb.,  18,500. 

Redondo,  Cal.,  oil.  six  lots:  Moisture,  1.82  to  2.70%;  Sulphur,  2.17  to 
2.60%;  B.T.U.  per  lb.,  17,717  to  17,966.  Kilowatt-hours  generated  per 
barrel  (334  lb.)  of  oil  in  a  5000  K.W.  plant,  using  water-tube  boilers, 
and  reciprocating  engines  and  generators  having  a  combined  efficiency  of 
90.2  to  94.75%  (boiler  economy  and  steam-rate  of  engine  not  stated). 
2000  K.W.  load,  237.3;  3000  K.W.,  256.7;  5000  K.W.,  253.4;  variable 
load,  24  hours,  243.8.  (C.  R.  Weymouth,  Trans.  A.  S.  M.  E.,  1908.) 

The  following  table  shows  the  relative  values  of  petroleum  and  coal. 
It  is  based  on  the  following  assumed  data:  B.T.U.  per  lb.  of  oil,  19,000; 
sp.  gr.,  0.90  =7.57  lb.  per  gal  ;  1  barrel  =  42  gal.  =315  lb. 


Coal,  B.T.U. 
per  lb. 

1  lb.  oil 
=  lb.  coal. 

1  barrel  oil 
=  lb.  coal. 

1  ton  coal 
=  barrels  oil. 

10,000 
11,000 
12,000 
13,000 
14,000 
15,000 

.9 

.727 
.583 
.462 
.357 
.267 

598 
544 
499 
460 
427 
399 

3.34 
3.68 
4.01 
4.34 
4.68 
5.01 

From  this  table  we  see  that  if  coal  of  a  heating  value  of  only  10,000 
B.T.U.  per  lb.  costs  $3.34  per  ton,  and  coal  of  14,000  B.T.U.  per  lb.  costs 
$4.68  per  ton,  then  the  price  of  oil  will  have  to  be  as  low  as  $1  a  barrel 
to  compete  with  coal;  or,  if  the  poorer  coal  is  $3.34  and  the  better  coal 
$4.68  per  ton,  then  oil  will  be  the  cheaper  fuel  if  it  is  below  $1  per  barrel. 

Heating  Values  of  California  Fuel  Oils. 

(R.  "W.  Fenn,  Eng.  News,  May  13,  1909.)  . 


Degree 

Baume. 

at 
P 

i! 

i 

|! 

offfl 

«c'> 
'5  g 

CO 

|! 

fr 

IS 

10 
12 
14 
16 

18 
20 
22 
24 
26 

1.000 
0.986 
0.972 
0.959 
0.947 
0.934 
0.922 
0.910 
0.899 

150 
346 
341 
336 
332 
327 
323 
319 
315 

18,380 
18,500 
18,620 
18,740 
18,860 
18,980 
19,100 
19,220 
19.340 

6442 
6394 
6345 
6302 
6257 
6212 
6173 
6133 
6093 

28 
30 
32 
34 
36 
38 
40 
42 
44 

0.887 
0.875 
0.865 
0.854 
0.844 
0.835 
0.825 
0.816 
0.806 

311 
307 
303 
299 
296 
293 
289 
286 
283 

19,460 
19,580 
19,700 
19,820 
19,940 
20,050 
20,150 
20,250 
20,350 

6051 
6008 
5973 
5935 
5901 
5865 
5827 
5789 
5751 

Fuel  Oil  Burners. — A  great  variety  of  burners  are  on  the  market, 
most  of  them  based  on  the  principle  of  using  a  small  jet  of  steam  at  the 
boiler  pressure  to  inject  the  oil  into  the  furnace,  in  the  shape  of  finely 
divided  spray,  and  at  the  same  time  to  draw  in  the  air  supply  and  mix  it 
intimately  with  the  oil.  So  far  as  economy  of  oil  is  concerned  these 
burners  are  all  of  about  equal  value,  but  their  successful  operation  de- 
pends on  the  construction  of  the  furnace.  This  should  have  a  large 
combustion  chamber,  entirely  surrounded  with  fire  brick,  and  the 
jet  should  be  so  directed  that  it  will  strike  a  fire-brick  surface  and  re- 
bound before  touching  the  heating  surface  of  the  boiler.  Burners 


ALCOHOL  AS  FUEL.  843 

using  air  at  high  pressure,  40  Ib.  per  sq.  in.,  without  steam,  have  been 
used  with  advantage.  Lower  pressures  have  been  found  not  sufficient 
to  atomize  the  oil.  Mechanical  atomizers  have  now  (1915)  largely 
replaced  steam  jet  oil  burners.  See  "Steam  Boiler  Economy." 

When  boilers  are  forced,  with  a  combustion  chamber  too  small  to 
allow  the  oil  spray  to  be  completely  burned  in  it  before  passing  to  the 
boiler  surface,  dense  clouds  of  smoke  result,  with  a  deposit  of  lampblack 
or  soot. 

Crude  Petroleum  vs.  Indiana  Block  Coal  for  Steam-raising  at 
the  South  Chicago  Steel  Works.— (E.  C.  Potter,  Trans.  A.  I.  M.  E., 
xvii.  807.) — With  coal,  14  tubular  boilers  16  ft.  X  5  ft.  required  25  men 
to  operate  them;  with  fuel  oil,  6  men  were  required,  a  saving  of  19  men 
at  $2  per  day,  or  $38  per  day. 

For  one  week's  work  2731  barrels  of  oil  were  used,  against  848  tons  of 
coal  required  for  the  same  work,  showing  3.22  barrels  of  oil  to  be  equiva- 
lent to  1  ton  of  coal  With  oil  at  60  cents  per  barrel  and  coal  at  $2.15 
per  ton,  the  relative  cost  of  oil  to  coal  is  as  $1.93  to  $2.15.  No  evapora- 
tion tests  were  made 

Petroleum  as  a  Metallurgical  Fuel.— C.  E.  Felton  (Trans.  A.  I. 
M.  E.,  xvii.  809)  reports  a  series  of  trials  with  oil  as  fuel  hi  steel-heating 
and  open-hearth  steel-furnaces,  and  in  raising  steam,  with  results  as 
follows:  1.  In  a  run  of  six  weeks  the  consumption  of  oil,  partly  refined 
(the  paraffine  and  some  of  the  naphtha  being  removed) ,  in  heating  14- 
inch  ingots  in  Siemens  furnaces  was  about  6 1/2  gallons  per  ton  of  blooms. 
2.  In  melting  in  a  30-ton  open-hearth  furnace  48  gallons  of  oil  were  used 
per  ton  of  ingots.  3.  In  a  six  weeks'  trial  with  Lima  oil  from  47  to  54 
gallons  of  oil  were  required  per  ton  of  ingots.  4.  In  a  six  months'  trial 
with  Siemens  heating-furnaces  the  consumption  of  Lima  oil  was  6  gal- 
lons per  ton  of  ingots.  Under  the  most  favorable  circumstances, 
charging  hot  ingots  and  running  full  capacity,  4 1/2  to  5  gallons  per  ton 
were  required.  5.  In  raising  steam  in  two  100-H.P.  tubular  boilers,  the 
feed- water  being  supplied  at  160°  F.,  the  average  evaporation  was  about 
12  pounds  of  water  per  pound  of  oil,  the  best  12  hours'  work  being  16 
pounds. 

Specifications  for  the  Purchase  of  Fuel  Oil.— The  U.  S.  government 
specifications  for  the  purchase  of  fuel  oil  (1914)  contain  the  following 
requirements : 

The  oil  should  not  have  been  distilled  at  a  temperature  high  enough 
to  burn  it,  nor  at  a  temperature  so  high  that  flecks  of  carbonaceous  mat- 
ter begin  to  separate. 

It  should  not  flash  below  140°  F.,  in  a  closed  Abel-Pensky  or  Pensky- 
Martins  tester. 

The  specific  gravity  should  range  from  0.85  to  0.96  at  59°  F. 

It  should  flow  readily,  at  ordinary  atmospheric  temperatures  and 
under  a  head  of  1  ft.  of  oil,  through  a  4-in.  pipe  10  ft.  in  length. 

It  should  not  congeal  nor  become  too  sluggish  to  flow  at  32°  F. 

It  should  have  a  calorific  value  of  not  less  than  18,000  B.T.U.  per  Ib. 
A  bonus  is  to  be  paid  or  a  penalty  deducted  as  the  fuel  oil  delivered 
is  above  or  below  the  standard. 

It  should  be  rejected  if  it  contains  more  than  2%  water,  more  than 
1  %  sulphur,  or  more  than  a  trace  of  sand,  clay  or  dirt. 

ALCOHOL  AS  FUEL. 

Denatured  alcohol  is  a  grain  or  ethyl  alcohol  mixed  with  a  denaturant 
in  order  to  make  it  unfit  for  beverage  or  medicinal  purposes.  Under  acts 
of  Congress  of  June  7,  1906,  and  March  2,  1907,  denatured  alcohol 
became  exempt  from  internal  revenue  taxation,  when  used  in  the 
industries. 

The  Government  formulae  for  completely  denatured  alcohol  are: 

1.  To  every  100  gal.  of  ethyl  or  grain  alcohol  (of  not  less  than  180% 
proof)  there  shall  be  added  10  gal.  of  approved  methyl  or  wood  alcohol 
and   %  gal.  of  approved  benzine.     (180%  proof  =  90%  alcohol,  10% 
water,  by  volume.) 

2.  To  every  100  gal.  of  ethyl  alcohol  (of  not  less  than  180%  proof) 
there  shall  be  added  2  gal.  of  approved  methyl  alcohol  and  Yi  gal.  of 
approved  pyridin  (a  petroleum  product)  bases. 


844 


FUEL. 


Methyl  alcohol,  benzine  and  pyridin  used  as  denaturants  must  con- 
form to  specifications  of  the  Internal  Revenue  Department. 

The  alcohol  which  it  is  proposed  to  manufacture  under  the  present 
law  is  ethyl  alcohol,  C^HsOH.  This  material  is  seldom,  if  ever,  obtained 
pure,  it  being  generally  diluted  with  water  and  containing  other  alco- 
hols when  used  for  engines. 

SPECIFIC  GKAVITY  OF  ETHYL  ALCOHOL  AT  60°  P.  COMPARED  WITH 
WATER  AT  60°.     (Smithsonian  Tables.) 


Sp.  Gr. 

Per  cent  Al- 
cohol. 

Sp.  Gr. 

Per  cent  Al- 
cohol. 

Sp.  Gr. 

Per  cent  Al- 
cohol. 

Weight. 

Vol. 

Weight. 

Vol. 

Weight. 

Vol. 

0.834 
.832 
.830 
.828 

85.8 
86.6 
87.4 
88.1 

90.0 
90.6 
91.2 
91.8 

0.826 
.824 
.822 
.820 

88.9 
89.6 
90.4 
91.1 

92.3 
92.9 
93.4 
94.0 

0.818 
.816 
.814 
.812 

91.9 
92.6 
93.3 
94.0 

94.5 
95.0 
95.5 
96.0 

The  heat  of  combustion  of  ethyl  alcohol,  94%  by  volume,  as  deter- 
mined by  the  calorimeter,  is  11,900  B.T.U.  per  Ib. — a  little  more  than 
half  that  of  gasoline  (Lucke).  Favre  and  Silbermann  obtained  12,913 
B.T.U  for  absolute  alcohol.  Dulong's  formula  for  C2H6OH  gives 
13,010  B.T.U. 

The  products  of  complete  combustion  of  alcohol  are  HzO  and  COz. 
Under  certain  conditions,  with  an  insufficient  supply  of  air,  acetic  acid  is 
formed,  which  causes  rusting  of  the  parts  of  an  alcohol  engine.  This 
may  be  prevented  by  addition  to  the  alcohol  of  benzol  or  acetylene. 

With  any  good  small  stationary  engine  as  small  a  consumption  as  0.70 
Ib.  of  gasoline,  or  1.16  Ib.  of  alcohol  per  brake  H.P.  hour  may  .reasonably 
be  expected  under  favorable  conditions  (Lucke) . 

References. — H.  Diederichs,  Intl.  Marine  Eng'g,  July,  1906;  Machy., 
Aug.,  1906.  C.  E.  Lucke  and  S.  M.  Woodward,  Farmer's  Bulletin,  No. 
277.  U.  S.  Dept.  of  Agriculture,  1907.  Eng.  Rec.,  Nov.  2,  1907.  T.  L. 
White,  Eng.  Mag.,  Sept.,  1908. 

VAPOR  PRESSURE  OF  SATURATION  FOR  VARIOUS  LIQUIDS,  IN 

MILLIMETERS  OF  MERCURY. 

(To  convert  into  pounds  per  sq.  in.,  multiply  by  0.01934;  to  convert 
into  inches  of  mercury,  multiply  by  0.03937.) 


Tem- 
pera- 
ture. 

Pure 
Ethyl 
Alco- 
hol. 

Pure 
Methyl 
Alco- 
hol. 

Water. 

Gaso- 
line. 

Tem- 
pera- 
ture. 

Pure 
Ethyl 
Alco- 
hol. 

Pure 
Methyl 
Alco- 
hol. 

Water. 

Gaso- 
line. 

0* 
5 
10 
15 

20 
25 
30 

32 
41 
50 
59 
68 
77 
86 

12 
17 
24 
32 
44 
59 
78 

30 
40 
54 
71 
94 
123 
159 

5 

9 
13 
17 

24 
32 

99 
115 
133 
154 
179 
210 
251 

35* 
40 
45 
50 
55 
60 
65 

95 
104 
113 
122 
131 
140 
149 

103 
134  . 
172 
220 
279 
350 
437 

204 
259 
327 
409 
508 
624 
761 

42 
55 
71 
92 
117 
149 
187 

301 
360 
422 
493 
561 
648 
739 

VAPOR  TENSION  OF  ALCOHOL  AND  WATER,  AND  DEGREE  OF  SATURATION 
OF  AlR  WITH  THESE  VAPORS. 


Temp., 
Degs.  F. 

Vapor  Tension,  Inches 
Mercury. 

1  Pound  of  Air  Contains  in  Saturated 
Condition,  in  Pounds. 

At  28.95  Inches. 

At  26.05  Inches. 

Alcohol 
Vapor. 

Water 
Vapor. 

Alcohol. 
Vapor. 

Water. 
Vapor. 

Alcohol 
Vapor. 

Water. 
Vapor. 

u      50 
59 
68 
77 
86 
104 
122 

0.950 
1.283 
1.723 
2.325 
3.090 
5.270 
8.660 

0.359 
0.500 
0.687 
0.925 
1.240 
2.162 
3.620 

0.055 
0.075 
0.104 
0.144 
0.200 
0.390 
0.827 

0.008 
0.011 
0.016 
0.022 
0.031 
0.063 
0.135 

0.061 
0.084 
0.117 
0.162 
0.227 
0.450 
1.002 

0.009 
0.013 
0.018 
0.025 
0.036 
0.072 
0.164 

. 


FUEL  GAS.  843 

FUEL  GAS. 

The  following  notes  are  extracted  from  a  paper  by  W.  J.  Taylor  on 
"The  Energy  of  Fuel"  (Trans.  A.  I.  M.  E.,  xviii.  205): 

Carbon  Gas. — In  the  old  Siemens  producer,  practically  all  the  heat 
of  primary  combustion — that  is,  the  burning  of  solid  carbon  to  carbon 
monoxide,  or  about  30%  of  the  total  carbon  energy — was  lost,  as  little 
or  no  steam  was  used  in  the  producer,  and  nearly  all  the  sensible  heat  of 
the  gas  was  dissipated  in  its  passage  from  the  producer  to  the  furnace, 
which  was  usually  placed  at  a  considerable  distance. 

Modern  practice  has  improved  on  this  plan,  by  introducing  steam 
with  the  air  blown  into  the  producer,  and  by  utilizing  the  sensible  heat  of 
the  gas  in  the  combustion-furnace.  It  ought  to  be  possible  to  oxidize 
one  out  of  every  four  Ibs.  of  carbon  with  oxygen  derived  from  water- 
vapor.  The  thermic  reactions  in  this  operation  are  as  follows: 

Heat-units. 
4  Ibs.  C  burned  to  CO  (3  Ibs.  gasified  with  air  and  1  Ib.  with 

water)  develop 17,600 

1  5  Ibs.  of  water  (which  furnish  1.33  Ibs.  of  oxygen  to  combine 

with  1  Ib.  of  carbon)  absorb  by  dissociation 10,333 

The  sas  consisting  of  9.333  Ibs.  CO,  0.167  Ib.  H,  and  13.39  Ibs.  N, 

heated  600°,  absorbs 3,748 

Leaving  for  radiation  and  loss .     3,519 

17,600 

The  steam  which  is  blown  into  a  producer  with  the  air  is  almost  all  conr 
densed  into  finely-divided  water  before  entering  the  fuel,  and  conse- 
quently is  considered  as  water  in  these  calculations. 

The  1.5  Ibs.  of  water  liberates  0:167  Ib.  of  hydrogen, which  is  delivered 
to  the  gas,  and  yields  in  combustion  the  same  heat  that  it  absorbs  in  the 
producer  by  dissociation.  According  to  this  calculation,  therefore,  60% 
of  the  heat  of  primary  combustion  is  theoretically  recovered  by  the  dis- 
sociation of  steam,  and,  even  if  all  the  sensible  heat  of  the  gas  be  counted, 
with  radiation  and  other  minor  items,  as  loss,  yet  the  gas  must  carry 
4  X  14,500  -  (3748  +  3519)  =  50,733  heat-units,  or  87%  of  the  calo- 
rific energy  of  the  carbon.  This  estimate  shows  a  loss  in  conversion  of 
13%  without  crediting  the  gas  with  its  sensible  heat,  or  charging  it  with 
the  heat  required  for  generating  the  necessary  steam,  or  taking  into 
account  the  loss  due  to  oxidizing  some  of  the  carbon  to  CO2.  In  good 
producer-practice  the  proportion  of  CO2  in  the  gas  represents  from  4% 
to  7%  of  the  C  burned  to  CO2,  but  the  extra  heat  of  this  combustion  should 
be  largely  recovered  in  the  dissociation  of  more  water-vapor,  and  there- 
fore does  not  represent  as  much  loss  as  it  would  indicate.  As  a  con- 
veyer of  energy,  this  gas  has  the  advantage  of  carrying  4.46  Ibs  less 
nitrogen  than  would  be  present  if  the  fourth  pound  of  coal  had  been 
gasified  with  air;  and  in  practical  working  the  use  of  steam  reduces  tha 
amount  of  clinkering  in  the  producer. 

Anthracite  Gas. — In  anthracite  coal  there  is  a  volatile  combustible 
varying  in  quantity  from  1.5%  to  over  7%.  The  amount  of  energy 
derived  from  the  coal  is  shown  in  the  following  theoretical  gasification 
made  with  coal  of  assumed  composition:  Carbon,  85%;  vol.  HC,  5%;  ash, 
10%-  80  Ibs  carbon  assumed  to  be  burned  to  CO;  5  Ibs.  carbon  burned 
to  COa;  three  fourths  of  the  necessary  oxygen  derived  from  air,  and  one 
fourth  from  water. 

r- Products. % 

Process.  Pounds.     Cubic  Feet.     Anal,  by  Vol. 

80  Ibs.  C  burned  to  CO 186.66  2529-24  33.4 

5  Ibs.  C  burned  to  CO2 18.33  157.64  2.0 

5  Ibs.  vol.  HC  (distilled) 5.00  116.60  1.6 

120  Ibs.  oxygen  are  required,  of 
which  30  Ibs.  from  H2O  liber- 
ate H 3.75  712.50  9.4 

90  Ibs.   from   air  are  associated 
with  N 301.05  4064.17  53.6 

614.79  7580.15  100.0 


846  FUEL. 

Energy  in  the  above  gas  obtained  from  100  Ibs.  anthracite: 

186. 66  Ibs.  CO 807,304  heat-units. 

5.00    "     CH4 117,500 

3.75    "     H 232,500          " 

1,157,304 

Total  energy  in  gas  per  Ib 2,248         " 

Total  energy  in  100  Ibs.  of  coal 1,349,500          " 

Efficiency  of  the  conversion 86%. 

The  sum  of  CO  and  H  exceeds  the  results  obtained  in  practice.  The 
sensible  heat  of  the  gas  will  probably  account  for  this  discrepancy  and 
therefore,  it  is  safe  to  assume  the  possibility  of  delivering  at  least  82% 
of  the  energy  of  the  anthracite. 

Bituminous  Gas.  —  A  theoretical  gasification  of  100  Ibs  of  coal,  con- 
taining 55%  of  carbon  and  32%  of  volatile  combustible  (which  is  above 
the  average  of  Pittsburgh  coal),  is  made  in  the  following  table.  It  is 
assumed  that  50  Ibs.  of  C  are  burned  to  CO  and  5  Ibs.  to  CO2;  one  fourth 
of  the  O  is  derived  from  steam  and  three  fourths  from  air;  the  heat  value 
of  the  volatile  combustible  is  taken  at  20,000  heat-units  to  the  pound. 
In  computing  volumetric  proportions  all  the  volatile  hydrocarbons, 
fixed  as  well  as  C9ndensing,  are  classed  as  marsh-gas,  since  it  is  only  by 
some  such  tentative  assumption  that  even  an  approximate  idea  of  the 
volumetric  composition  can  be  formed.  The  energy,  however,  is  calcu- 
lated from  weight: 

, : Prod  ucts . » 

Process.  Pounds.     Cubic  Feet.     Anal,  by  Vol. 

50  Ibs.  C  burned  to  CO 116.66         1580.7  27.8 

5  Ibs.  C  burned  to  CO2 18.33  157.6  2.7 

32  Ibs.  vol.  HC  (distilled) 32 . 00  746 . 2  13.2 

80  Ibs.  O  are  required,  of  which  20 
Ibs.,  derived  from  H2O,  liber- 
ate H 2.5  475.0  8.3 

60  Ibs.  O,  derived  from  air,  are  as- 
sociated with  N 200.70  2709.4  47.8 


370.19  5668.9                 99.8 

Energy  in  116.66  Ibs.  CO 504,554  heat-units. 

"     32.00  Ibs.  vol.  HC 640,000 

2.50  Ibs.  H 155,000 


1,299,554 

Energy  in  coal 1,437,500 

Per  cent  of  energy  delivered  in  gas 90.0 

Heat-units  m  1  Ib.  of  gas 3,484 

Water-gas.  —  Water-gas  is  made  in  an  intermittent  process,  by  blow- 
Ing  up  the  fuel-bed  of  the  producer  to  a  high  state  of  incandescence  (and 
in  some  cases  utilizing  the  resulting  gas,  which  is  a  lean  producer-gas), 
then  shutting  off  the  air  and  forcing  steam  through  the  fuel,  which  dis- 
sociates the  water  into  its  elements  of  oxygen  and  hydrogen,  the  former 
combining  with  the  carbon  of  the  coal,  and  the  latter  being  liberated. 

This  gas  can  never  play  a  very  important  part  in  the  industrial  field, 
owing  to  the  large  loss  of  energy  entailed  in  its  production,  yet  there  are 
places  and  special  purposes  where  it  is  desirable,  even  at  a  great  excess 
in  cost  per  unit  of  heat  over  producer-gas;  for  instance,  in  small  high- 
temperature  furnaces,  where  much  regeneration  is  impracticable,  or 
where  the  "blow-up"  gas  can  be  used  for  other  purposes  instead  of  being 
wasted. 

The  reactions  and  energy  required  in  the  production  of  1000  feet  of 
water-gas,  composed,  theoretically,  of  equal  volumes  of  CO  and  H,  are  as 
follows: 

500  cubic  feet  of  H  weigh 2 . 635  Ibs. 

500  cubic  feet  of  CO  weigh 36 . 89 

Total  weight  of  1000  cubic  feet 39 . 525  Ibs. 

Now,  as  CO  is  composed  of  12  parts  C  to  16  of  O',  the  weight  of  C  in 
36.89  Ibs.  is  15.81  Ibs.  and  of  O  21.08  Ibs.  When  this  oxygen  is  derived 


FUEL  GAS. 


847 


from  water  it  liberates,  as  above,  2.635  Ibs.  of  hydrogen.  The  heat  de- 
veloped and  absorbed  in  these  reactions  (roughly,  as  we  will  not  take 
into  account  the  energy  required  to  elevate  the  coal  from  the  tempera- 
ture of  the  atmosphere  to,  say,  1800°)  is  as  follows:  Heat-units 
2.635  Ibs.  H.  absorb  in  dissociation  from  water  2.635  X  62,000  =  163,370* 

15.81  Ibs.  C  burned  to  CO  develops  15.81   X  4400 =    69,564 

Excess  of  heat-absorption  over  heat-development =    93,806 

If  this  excess  could  be  made  up  from  C  burnt  to  CO2  without  loss  by 
radiation,  we  would  only  have  to  burn  an  additional  4.83  Ibs.  C  to  supply 
this  heat,  and  we  could  then  make  1000  feet  of  water-gas  from  20.64  Ibs. 
of  carbon  (equal  24  Ibs.  of  85%  coal).  This  would  be  the  perfection  of 

gas-making,  as  the  gas  would  contain  really  the  same  energy  as  the  coal; 
but  instead,  we  require  in  practice  more  than  double  this  amount  of  coal 
and  do  not  deliver  more  than  50%  of  the  energy  of  the  fuel  in  the  gas, 
because  the  supporting  heat  is  obtained  in  an  indirect  way  and  with 
imperfect  combustion.  Besides  this,  it  is  not  often  that  the  sum  of  CO 
and  H  exceed  90%,  the  balance  being  CO2  and  N.  But  water-gas  should 
be  made  with  much  less  loss  of  energy  by  burning  the  "blow-up"  (pro- 
ducer) gas  in  brick  regenerators,  the  stored-urj  heat  of  which  can  be 
returned  to  the  producer  by  the  air  used  in  blowing-up. 

The  following  table  shows  what  may  be  considered  average  volumetric 
analyses,  and  the  weight  and  energy  of  1000  cubic  feet,  of  the  four  types 
of  gases  used  for  heating  and  illuminating  purposes: 


Natural 
Gas. 

Coal- 
gas. 

Water- 
gas. 

Producer-gas. 

Anthra. 

Bitu. 

CO. 

0.50 
2.18 
92.6 
0.31 
0.26 
3.61 
0.34 

6.0 
46.0 
40.0 
4.0 
0.5 
1.5 
0.5 
1.5 
32.0 
735,000 

45.0 
45.0 
2.0 

27.0 
12.0 
1.2 

27.C 
12.0 
2.5 
0.4 
2.5 
56.2 
0.3 

H                   

CHt 

C2H4 

COa.  .  . 

4.0 
2.0 
0.5 
1.5 

45.6 
322,000 

2.5 
57.0 
0.3 

N                       

O  

Vapor                                      .   ... 

Pounds  in  1000  cubic  feet  

45.6 
1,100,000 

65.6 
137,455 

65.9 
156,917 

Heat-units  in  1000  cubic  feet  

Natural  Gas  in  Ohio  and  Indiana. 

(Enq.  and  M.  J.,  April  21,  1894.) 


Fos- 
toria, 
O. 

Find- 

Iaoy' 

St. 
Mary's, 
O. 

Muncie, 
Ind. 

Ander- 
son, 
Ind. 

Koko- 
mo, 
Ind. 

Mar- 
ion, 
Ind. 

Hydrogen  

1.89 

1.64 

1.94 

2.35 

1.86 

1.42 

1.20 

Marsh-gas  

92.84 

93.35 

93.85 

92.67 

93.07 

94.16  . 

93.57 

Olefiant  gas 

.20 

.35 

.20 

.25 

.47 

.30 

.15 

Carbon  monoxide  . 
Carbon  dioxide  
Oxygen  

.55 
.20 
.35 

.41 
.25 
.39 

.44 
.23 
.35 

.45 
.25 
.35 

.73 
.26 
.42 

.55 

.29 
.30 

.60 
.30 
.55 

Nitrogen  .... 

3.82 

3.41 

2.98 

3.53 

3.02 

2.80 

3.42 

Hydrogen  sulphide 

.15 

.20 

.21 

.15 

.15 

.18 

.20 

Natural  Gas  as  a  Fuel  for  Boilers.  — J.  M.  Whitham  (Trans.  A.  S. 
/.  E.,  1905)  reports  the  results  of  several  tests  of  water-tube  boilers  with 
natural  gas.    The  following  is  a  condensed  statement  of  the  results  : 

Kind  of  Boiler.  | Cook  Vertical. |  Heine.          |  Cahall  Vert. 


Rated  H.P.  of  boilers  
H.P.  developed   

1500 

1642 

1500 
1507 

200 
155 

200 
218 

200 

258 

300 
340 

300 
260 

Temperature   at  chimney 
Gas  pressure  at  burners,  oz. 
Cu.  ft.  of  gas  per  boiler.  . 
H.P.-hour    

521 
6.9 

44.9* 

494 
6.4 

41.0* 

386 
46.  Of 

450 
40.  7f 

465 
38.  3t 

406 
4.8 

42.3 

374 
7  to  30 

34 

Boiler  efficiency,  %  

72.7 

65.8 

74.9 

*Reduced  to  4  oz.  press,  and  62°  F.   fReduced  to  atmos.  press,  and  32°  F. 


848 


FUEL. 


Six  tests  by  Daniel  Ashworth  on  2-flue  horizontal  boilers  gave  cu.  ft.  of 
gas  per  boiler  H.P.  hour,  58.0;  59.7;  67.0;  63.0;  74.0;  47.0. 

On  the  first  Cook  boiler  test,  the  chimney  gas,  analyzed  by  the  Orsat 
apparatus,  showed  7.8  CO2;  8.05  O;  0.0  CO;  84.15  N.  This  shows  an 
excessive  air  supply. 

White  versus  Blue  Flame.  — Tests  were  made  with  the  air  supply  throt- 
tled at  the  burners,  so  as  to  produce  a  white  flame,  and  also  unthrottled, 
producing  a  blue  flame  with  the  following  results: 


Pressure  of  gas  at  burners,  oz  

4 

6 

8 

Kind  of  flame 

White 

Blue 

White 

Blue 

White 

Blue 

Boiler  H.P.made  per  250-H.P.  boiler 
Cu.  ft.  of  gas  (at  4  oz.  and  60°  F.)  per 
H.P.  hour  

247 
41 

213 

41 

297 
41.6 

271 

M  9 

255 
49 

227 
43  1 

Chimney  temperature  

436 

503 

478 

511 

502 

508 

Average  of  6  tests  —  White,  266  H.P.,  43.6  cu.  ft.;  Blue,  237  H.P., 
43.8  cu.  ft.,  showing  that  the  economy  is  the  same  with  each  flame,  but 
the  capacity  is  greatest  with  the  white  flame.  Mr.  Whitham's  principal 
conclusions  from  these  tests  are  as  follows: 

(1)  There  is  but  little  advantage  possessed  by  one  burner  over  another. 

(2)  As  good  economy  is  made  with  a  blue  as  with  a  white  or  straw  flame, 
and  no  better. 

(3)  Greater  capacity  may  be  made  with  a  straw-white  than  with  a  blue 
flame. 

(4)  An  efficiency  as  high  as  from  72  to  75  per  cent  in  the  use  of  gas  is 
seldom  obtained  under  the  most  expert  conditions. 

(5)  Fuel  costs  are  the  same  under  the  best  conditions  with  natural  gas 
at  10  cents  per  1000  cu.  ft.  and  semi-bituminous  coal  at  $2.87  per  ton  of 
2240  Ibs. 

(6)  Considering  the  saving  of  labor  with  natural  gas,  as  compared  with 
hand-firing  of  coal,  in  a  plant  of  1500  H.P.,  and  coal  at  $2  per  ton  of  2240 
Ibs.,  gas  should  sell  for  about  10  cents  per  1000  cu.  ft, 


ANALYSES  OF  NATURAL  GAS. 


Illuminants 

Carbonic  oxide 

Hydrogen 

Marsh  gas. 

Ethane 

Carbonic  acid 

Oxygen 

Nitrogen 

B.T.U.  per  cu.  ft.  at  60°  F.  and 
14.7  Ibs.  barometer 


0.45 

0.00 

0.20 

81.05 

17.60 

0.00 

0.15 

0.55 

1030 


0.15 

0.00 

0.30 

83.20 

15.55 

0.20 

0.10 

0.50 

1020 


0.50 

0.15 

0.25 

83.40 

15.40 

0.00 

0.00 

0.30 

1026 


1.6 
1.8 

0.3 

81.9 

13.2 

0.0 

0.4 

0.8 

1098 


The  first  three  analyses  are  of  the  gas  from  nine  wells  in  Lewis  Co., 
W.  Va.;  the  last  is  from  a  mixture  from  fields  in  three  states  supplying 
Pittsburg,  Pa.,  used  in  the  tests  of  the  Cook  boiler. 

Producer-gas  from  One  Ton  of  Coal. 

(W.  H.  Blauvelt,  Trans.  A.  I.  M.  E.,  xviii,  614.) 


Analysis  by  Vol  . 

Per 

Cent. 

Cubic  Feet. 

Lbs. 

Equal  to  — 

CO 

25  3 

33  213  84 

2451.20 

1050.51 

Ibs.  C  +  1400.  7  Ibs 

0 

H      

9.2 

12,077.76 

63.56 

63.56 

H. 

CH4  

3.1 

4,069.68 

174.66 

174.66 

CH4. 

C2H4 

0  8 

1,050  24 

77.78 

77.78 

C2H4. 

CO2      

3.4 

4,463.52 

519.02 

141.54 

C  +  377.  44  Ibs 

O 

N  (by  difference) 

58.2 

76,404.96 

5659.63 

7350.17 

Air. 

100.0 

131,280.00 

8945.85 

FUEL   GAS. 


849 


Calculated  upon  this  basis,  the  131,280  ft.  of  gas  from  the  ton  of  coal 
contained  20,311,162  B.T.U.,  or  155  B.T.U.  per  cubic  ft.,  or  2270  B.  T.U, 
per  Ib. 

The  composition  of  the  coal  from  which  this  gas  was  made  was  as 
follows:  Water,  1.26%;  volatile  matter,  36.22%;  fixed  carbon,  57.98%; 
sulphur,  0.70%;  ash,  3.78%.  One  ton  contains  1159.6  Ibs.  carbon  and 
724.4  Ibs.  volatile  combustible,  the  energy  of  which  is  31,302,200  B.T.U. 
Hence,  in  the  processes  of  gasification  and  purification  there  was  a  loss  of 
35.2%  of  the  energy  of  the  coal. 

The  composition  of  the  hydrocarbons  in  a  soft  coal  is  uncertain  and 
quite  complex;  but  the  ultimate  analysis  of  the  average  coal  shows  that 
it  approaches  quite  nearly  to  the  composition  of  CH4  (marsh-gas). 

Mr.  Blauvelt  emphasizes  the  following  points  as  highly  important  in 
soft-coal  producer-practice: 

Fii 


the  air  before  being  used.  To  prevent  these  sources  of  loss,  the  pr< 
should  be  placed  so  as  to  lose  as  little  as  possible  of  the  sensible  heat  of 
the  gas,  and  prevent  condensation  of  the  hydrocarbon  vapors.  A  high 
fuel-bed  should  be  carried,  keeping  the  producer  cool  on  top,  thereby 
preventing  the  breaking-down.of  the  hydrocarbons  and  the  deposit  of 
soot,  as  well  as  keeping  the  carbonic  acid  low. 

Second.  That  a  producer  should  be  blown  with  as  much  steam  mixed 
with  the  air  as  will  maintain  incandescence.  This  reduces  the  percentage 
of  nitrogen  and  increases  the  hydrogen,  thereby  greatlyt enriching  the  gas. 
The  temperature  of  the  producer  is  kept  down,  diminishing  the  loss  of  heat 
by  radiation  through  the  walls,  and  in  a  large  measure  preventing  clinkers. 

The  Combustion  of  Producer-gas.  (H.  H.  Campbell,  Trans.  A.  I. 
M.  E.,  xix,  128.)  — The  combustion  of  the  components  of  ordinary  pro- 
ducer-gas may  be  represented  by  the  following  formulEe: 

C2H4  4-  60  =  2C02  +2H20;          2H  -f  O  =  H2O; 
CH4  +  4  O  =     CO2  +  2  H2O;  CO  +  O  =  CO2. 

AVERAGE  COMPOSITION  BY  VOLUME  OF  PRODUCER-GAS:  A,  MADE  WITH 
OPEN  GRATES,  NO  STEAM  IN  BLAST;  B,  OPEN  GRATES,  STEAM-JET  IN 
BLAST.  10  SAMPLES  OF  EACH. 

002.  O.         C2H4         CO.  H.        CH4.  N. 

A  min 3.6  0.4         0.2         20.0         5.3         3.0         58.7 

A  max 5.6  0.4         0.4         24.8         8.5         5.2         64.4 

A  average 4.84  0.4         0.34       22.1         6.8         3.74       61.78 

B  min 4.6  0.4         0.2         20.8         6.9         2.2         57.2 

B  max 6.0  0.8         0.4         24. 0         9.8         3.4-      62. 0 

B  average 5.3  0.54       0.36       22.74       8.37       2.56       60.13 

The  coal  used  contained  carbon  82%,  hydrogen  4.7%. 
The  following  are  analyses  of  products  of  combustion: 

C02.  O.  CO.  CH4.          H.  N. 

Minimum 15.2  0.2         trace.       trace.       trace.  80.1 

Maximum 17.2  1.6  2.0  0.6  2.0  83.6 

Average 16.3  0.8  0.4  0.1  0.2  82.2 

Proportions  of  Gas  Producers  and  Scrubbers.  (F.  C.  Tryon,  Power, 
Dec.  1,  1908.)  — Small  inside  diameter  means  excessive  draft  through  the 
fire.  If  a  fire  is  forced,  as  will  be  necessary  with  too  small  an  inside  diam- 
eter, the  results  will  be  clinkers  and  blow-holes  or  chimneys  through  the 
fire  bed,  with  excess  CO2  and  weak  gas;  clinkers  fused  to  the  lining,  and 
burning  out  of  grates.  If  sufficient  steam  is  used  to  keep  down  the  ex- 
cessive heat,  the  result  is  likely  to  be  too  much  hydrogen  in  the  gas,  with 
the  attendant  engine  troubles. 

The  lining  should  never  be  less  than  9  in.  thick  even  in  the  smaller  sizes, 
and  a  100-H.P.,  or  larger,  producer  should  have  at  least  12  in.  of  generator 
lining.  The  lining  next  to  the  fire  bed  should  be  of  the  best  quality  of 
refractory  material.  A  good  lining  consists  of  a  course  of  soft  common 
bricks  put  in  edgewise  next  to  the  steel  shell  of  the  generator,  laid  in 
Portland  cement;  then  a  good  firebrick  6  in.  thick  laid  inside  to  fit  the 
circle,  the  bricks  being  dipped  as  laid  in  a  fine  grouting  of  ground  firebrick. 

If  we  take  H/4  Ibs.  of  coal  per  H.P.-hour  as  a  fair  average  and  10  Ibs,  of 


850 


FUEL. 


coal  per  hour  per  squaie  foot  of  internal  fuel-bed  cross-section,  with  9  in. 
of  refractory  lining  up  to  100  H.P.  and  at  least  12  in.  of  lining  on  larger 
sizes,  the  generator  will  give  good  gas  without  forcing  and  without  excess- 
ive heat  in  the  zone  of  complete  combustion.  A  200-H.P.  producer  on 
this  basis  consumes  250  Ibs.  of  coal  at  full  load,  and  at  10  Ibs.  per  sq.  ft. 
internal  area  25  sq.  ft.  will  be  necessary.  With  a  12-in.  lining  the  outside 
diameter  will  be  92  in. 

Practice  has  shown  that  the  depth  of  the  fuel  bed  should  never  be  less 
than  the  inside  diameter  up  to  6  ft.;  above  this  size  the  depth  can  be 
adjusted  as  experience  indicates  the  best  working  results.  Assuming  for 
a  200-H.P.  producer  18  in.  for  the  ashpit  below  the  grate,  12  in.  for  the 
thickness  of  the  grate  and  the  ashes  to  protect  it,  68  in.  depth  of  fuel  bed, 
24  in.  above  the  fuel  to  the  gas  outlet,  the  height  will  be  10  ft.  4  in.  to  the 
top  of  the  generator;  above  this  the  coal-feeding  hopper,  say  32  in.  high, 
is  mounted;  this  makes  the  height  over  all  13  ft. 

The  wet  scrubber  of  a  gas  producer  should  be  of  ample  size  to  cool  the 
gas  to  atmospheric  temperature  and  wash  out  most  of  the  impurities. 
A  good  rule  is  to  make  its  diameter  three-fourths  that  of  the  inside  diam- 
eter of  the  generator  and  the  height  one  and  one-half  times  the  height  of 
the  generator  shell.  For  a  100-H.P.  producer,  4  ft.  inside  diam.,  the  wet 
scrubber  should  be  3  ft.  inside  diam.,  and  if  the  generator  shell  is  8  ft. 
6  in.  high,  the  scrubber  should  be  12  ft.  9  in.  high.  When  filled  with  the 
proper  amount  of  baffling  and  scrubbing  material  (coke  is  commonly 
used),  the  scrubber  will  have  space  for  about  30  cu.  ft.  of  gas.  A  100-H.P. 
gas  engine  using  12,000  B.T.U.  per  H.P.-hour  will  use  160  cu.  ft.  of  125- 
B.T.U.  gas  per  minute.  The  wet  scrubber  will  therefore  be  emptied  51/3 
times  every  minute,  and  would  require  about  8  Va  gallons  of  water  per 
minute;  if  the  diameter  of  the  scrubber  were  reduced  one-third  the  vol- 
ume of  water  necessary  to  cool  and  scrub  the  gas  would  have  to  be  doubled. 
Gas  must  be  cooled  below  90°  F.  to  enable  it  to  give  up  the  impurities  it 
carries  in  suspension,  and  even  lower  than  this  to  condense  its  moisture. 

A  separate  dry  scrubber  with  two  compartments  should  always  be  pro- 
vided and  the  piping  between  the  two  scrubbers  so  arranged  that  the  gas 
can  be  turned  into  either  part  of  the  dry  scrubber  at  will.  The  dry 
scrubber  should  be  equal  in  area  to  the  inside  of  the  generator,  and  the 
depth  of  each  part  should  be  sufficient  to  accommodate  at  least  2  cu.  ft. 
of  scrubbing  material  and  give  1  cu.  ft.  of  space  next  to  the  outlet.  Oil- 
soaked  excelsior  is  a  good  scrubbing  material  and  should  be  packed  as 
closely  as  possible. 

Taking  as  the  standard  the  dimensions  above  stated  for  the  different 
parts  of  a  producer-gas  plant,  a  list  of  dimensions  for  different  horse-power 
capacities  would  be  about  as  in  the  following  table. 

DIMENSIONS  OF  GAS  PRODUCERS  AND  SCRUBBERS. 


H.P. 

Producers. 

Wet  Scrub- 
bers. 

Dry  Scrubbers. 

Inside 
Diam. 

Out- 
side 
Diam. 

Height. 

Diam. 

Height. 

Diam. 

Height. 

25 
35 
50 
60 
75 
100 
125 
150 
175 
200 

in, 
24 
28 
34 
37 
'    42 
48 
54 
58 
63 
68     • 

in. 
42 
46 
52 
55 
60 
72 
78 
82 
87 
92 

ft.  in. 
6      6 
6    10 
7      4 
7     7 
8     0 
8      6 
9      6 
9    10 
10      3 
10      8 

in. 
18 
21 
26 
28 
32 
36 
41 
44 
48 
51 

ft.  in. 
9    9 
10    3 
11     0 
11     5 
12    0 
12    9 
14    3 
14    9 
15    5 
16    0 

Single..  . 
.  .  do  .... 

in. 
24 
28 
34 
37 
42 
48 
52 
58 
63 
68 

ft.  in. 
3    0 
3    0 
6    0 
6    0 
6    0 
7    0 
7    0 
7    6 
7    6 
7    6 

Double  . 
...do.... 
...do.... 
...do.... 
...do.... 
...do.... 
...do.... 
...do.... 

The  inside   diameter  of  the   producers  corresponds  to  the  formula 
H.P.  =  6.25d2. 


GAS   PRODUCERS. 


851 


Gas  Producer  Practice.  —  The  following  notes  on  gas  producers  are 
condensed  from  the  catalogue  of  the  Morgan  Construction  Co. 

The  Morgan  Continuous  Gas  Producer  is  made  in  the  following  sizes: 

Diam.  inside  of  lining,  ft 6  8  10  12 

Area  of  gas-making  surface,  sq.  ft.  . . . 28  50  78.5  113 

24-hour  capacity  with  good  coal,  tons 4  7  10  15 

Diam.  of  outlet,  in 20  27  33  40 

The  best  coal  to  buy  for  a  producer  in  any  locality  is  that  which  by 
analysis  or  calorimeter  test  shows  the  most  heat  units  for  a  dollar.  It 
rarely  pays  to  buy  gas  coal  unless  it  can  be  had  at  a  moderate  cost  over  the 
ordinary  steam  bituminous  grade.  For  very  high  temperature  melting 
operations  a  fairly  high  percentage  of  volatile  matter  is  necessary  to  give  a 
luminous  flame  and  intensify  the  radiation  from  the  roof  of  the  furnace. 
Freely  burning  gas  coals  are  the  most  easily  gasified,  and  the  capacity  of 
the  producer  to  handle  these  coals  is  twice  as  great  as  when  a  slaty,  dirty 
coal,  high  in  ash  and  sulphur,  is  used.  It  is  usually  best  to  use  "run-of- 
mine"  coal,  crushed  at  the  mine  to  pass  a  4-in.  ring.  It  never  pays  to  use 
slack  coal,  for  it  cuts  down  the  capacity  by  choking  the  blast,  which  has 
to  be  run  at  high  pressure  to  get  through  the  fire,  overheating  the  gas  and 
lowering  the  efficiency  of  the  producer. 

There  is  always  a  certain  amount  of  CO2  formed,  even  in  the  best  practice; 
in  fact,  it  is  inevitable,  and  if  kept  within  proper  limits  does  not  constitute 
a  net  loss  of  efficiency,  especially  with  very  short  gas  flues,  because  the 
energy  of  the  fuel  so  burned  is  represented  in  the  sensible  heat  or  tem- 
perature of  the  gas,  and  results  in  delivering  a  hot  gas  to  the  furnace. 
The  best  result  is  at  about  4%  CO2,  a  gas  temperature  between  1100°  and 
1200°  F.,  and  flues  less  than  100  ft.  long. 

The  amount  of  steam  required  to  blow  a  gas  producer  is  from  33%  to 
40%  of  the  weight  of  the  fuel  gasified.  If  30  Ibs.  of  steam  is  called  a 
standard  horse-power,  we  have  therefore  to  provide  about  1  H.P.  of  steam 
for  every  80  Ibs.  of  coal  gasified  per  hour  or  for  every  ton  of  coal  gasified  in 
24  hours. 

In  the  original  Siemens  air-blown  producer  about  70%  of  the  whole  gas 
was  inert  and  30%  combustible.  Then  with  the  advent  of  steam-blown 
producers  the  dilution  was  reduced  to  about  60%,  with  40%  combustible. 
Now,  under  the  system  of  automatic  feed,  uniform  conditions,  perfect 
distribution  and  adjustment  of  the  steam  blast  here  presented,  we  are  able 
to  reduce  the  nitrogen  to  50%  and  sometimes  less. 

In  the  best  practice  the  volume  of  gas  from  the  producer  is  now  reduced 
to  about  60  cu.  ft.  per  pound  of  coal,  of  which  30  cu.  ft.  are  nitrogen. 
These  volumes  are  measured  at  60°  F. 

The  temperature  of  the  gas  leaving  the  producer  under  best  modern 
conditions  is  about  1200°  F.  It  can  be  run  cooler  than  this,  but  not  much, 
except  at  a  sacrifice  of  both  quantity  and  quality.  At  this  temperature, 
the  sensible  heat  carried  by  the  gas  is  1200  X  0.35  (average  specific  heat)  = 
420  B.T.U.  per  pound.  As  one  pound  of  good  gas  is  about  16  cu.  ft.  and 
carries  about  16  X  180  =  2880  heat  units  at  normal  temperature,  we  see 
that  the  sensible  heat  carried  away  represents  about  one-seventh,  or  over 
14%  of  the  combustive  energy,  which  is  much  too  large  a  percentage  to  lose 
whenever  it  can  be  utilized  by  using  the  gas  at  the  temperature  at  which 
it  is  made. 

Capacity  of  Producers.  —  The  capacity  of  a  gas  producer  is  a  varying 
quantity,  dependent  upon  the  construction  of  the  producer  and  upon  the 
quality  of  the  coal  supplied  to  it.  The  point  is,  not  to  push  the  producer  so 
hard  as  to  burn  up  the  gas  within  it;  also  to  avoid  blowing  dust  through 
into  the  flues.  These  two  limitations  in  a  well-constructed  automatically 
fed  gas  producer  occur  at  about  the  same  rate  of  gasification,  namely, 
at  about  10  Ibs.  per  sq.  ft.  of  surface  per  hour  with  bituminous  coal  carry- 
ing 10%  of  ash  and  1 1/3  %  of  sulphur.  With  gas  coal,  having  high  volatile 
percentage  and  low  ash,  this  rate  can  be  safely  increased  to  12  Ibs.  and  in 
some  cases  to  15  Ibs.  per  sq.  ft.  At  10  Ibs.  per  sq.  ft.,  the  capacity  of  a 
gas  producer  8  ft.  internal  diameter  is  500  Ibs.  per  hour,  which  with  gas 
coals  may  be  increased  to  a  maximum  of  about  700  Ibs.  It  frequently 
happens  that  the  cheapest  coal  available  is  of  such  quality  that  neither 
of  these  figures  can  be  reached,  and  the  gasification  per  sq.  ft.  has  to  be  cut 
down  to  6  or  7  Ibs.  per  hour  to  get  the  best  results. 


852 


FUEL 


Flues.  —  It  is  necessary  to  provide  large  flue  capacity  and  to  carry  the 
full  area  right  up  to  the  furnace  ports,  which  latter  may  be  slightly  reduced 
to  give  the  gas  a  forward  impetus.  Generally  speaking,  the  net  area  of  a 
flue  should  not  be  less  than  Vie  of  the  area  of  the  gas-making  surface  in  the 
producers  supplying  it.  Or  it  may  be  stated  thus:  —  The  carrying  capa- 
city of  a  hot  gas  flue  is  equivalent  to  200  Ibs.  of  coal  per  hour  per  sq.  ft.  of 
section. 

Loss  of  Energy  in  a  Gas  Producer.  —  The  total  loss  from  all  sources  in  the 
gasification  of  fuel  in  a  gas  producer  under  fairly  good  conditions,  when 
the  gas  is  used  cold  or  when  its  sensible  heat  is  not  utilized,  ranges  between 
20%  and  25%,  which  under  very  bad  conditions  may  be  increased  to  60%. 
The  loss  under  favorable  conditions,  using  the  gas  hot,  is  reduced  to  as 
low  as  10%,. which  also  includes  the  heat  of  the  steam  used  in  blowing. 

Test  of  a  Morgan  Producer.  —  The  following  is  the  record  of  a  test  made 
in  Chicago  by  Robert  W.  Hunt  &  Co.  The  coal  used  was  Illinois  "  New 
Kentucky"  run-of-mine  of  the  following  analysis:  — 

Fixed  carbon,  50.87;  volatile  matter,  37.32;  moisture,  5.08;  ash  (1.12 
sulphur)  ,6.73.  The  average  of  all  the  gas  analyses  by  volume  is  as  follows : 

CO,  24.5;  H,  17.8;  CH4  and  C2H4,  6.8;  total  combustibles,  49.1%;  CO2, 
3.7;  O,  0.4;  N,  46.8;  total  non-combustibles,  50.9%. 

Average  depth  of  fuel  bed,  3  ft.  4  in.  Average  pressure  of  steam  on 
blower,  4.7  Ibs.  per  sq.  in.  Analysis  of  ash:  combustible,  4.66%;  non- 
combustible,  95.34%.  Percentage  of  fuel  lost  in  the  ash,  4.66  X  6.73  •*• 
100  =  0.3%. 

High  Temperature  Required  for  Production  of  CO. —  In  an  ordinary 
coal  fire,  with  an  excess  of  air  CO2  is  produced,  with  a  high  temperature. 
When  the  thickness  of  the  coal  bed  is  increased  so  as  to  choke  the  air  sup- 
ply CO  is  produced,  with  a  decreased  temperature.  It  appears,  however, 
that  if  the  temperature  is  greatly  lowered,  CO2  instead  of  CO  will  be  pro- 
duced notwithstanding  the  diminished  air  supply.  Herr  Ernst  (Eng'g, 
April  4, 1893)  holds  that  the  oxidation  of  C  begins  at  752°  F.,  and  that  COz 
is  then  formed  as  the  main  product,  with  only  a  small  amount  of  CO, 
whether  the  air  be  admitted  in  large  or  in  small  quantities.  When  the 
rate  of  combustion  is  increased  and  the  temperature  rises  to  1292°  F.  the 
chief  product  is  CO2  even  when  the  exhaust  gases  contain  20%  by  volume 
of  COs,  which  is  practically  the  maximum  limit,  proving  that  all  the 
oxygen  has  been  consumed.  Above  1292°  F.  the  proportion  of  CO  rapidly 
increases  until  1823°  F.  is  reached,  when  CO  is  exclusively  produced. 

Experiments  reported  by  J.  K.  Clement  and  H.  A.  Grine  in  Bulletin  No. 
393  of  the  U.  S.  Geological  vSurvey,  1909,  show  that  with  the  rate  of  flow 
of  gas  and  the  depth  of  fuel  bed  which  obtain  in  a  gas  producer  a  temper- 
ature of  1100°  C.  (2012°  F.)  or  more  is  required  for  the  formation  of  90% 
CO  gas  from  CO2  and  charcoal,  and  1300°  (2372°  F.)  for  the  same  percen- 
tage from  CO2  and  coke,  and  from  CO2  and  anthracite  coal.  With  a  tem- 
perature 100°  C.  (180°  F.)  lower  than  these  the  resultant  gas  will  contain 
about  50%  CO.  It  follows  that  the  temperature  of  the  fuel  bed  of  the  gas 
producer  must  be  at  least  1300°  C.  in  order  to  yield  the  highest  possible 
percentage  of  CO. 

The  Mond  Gas  Producer  is  described  by  H.  A.  Humphrey  in  Proc.  Inst. 
C.  E.,  vol.  cxxix,  1897.  The  producer,  which  is  combined  with  a  by-prod- 
uct recovery  plant,  uses  cheap  bituminous  fuel  and  recovers  from  it  90 
Ibs.  of  sulphate  of  ammonia  per  ton,  and  yields  a  gas  suitable  for  gas 
engines  and  all  classes  of  furnace  work.  The  producer  is  worked  at  a  much 
lower  temperature  than  usual,  due  to  the  large  quantity  of  superheated 
steam  introduced  with  the  airr  amounting  to  more  than  twice  the  weight 
of  the  fuel.  The  gas  containing  the  ammonia  is  passed  through  an  absorb- 
ing apparatus,  and  treated  so  that  70%  of  the  original  nitrogen  of  the  fuel 
is  recovered.  The  result  of  a  test  showed  that  for  every  ton  of  fuel  about 
2.5  tons  of  steam  and  3  tons  of  air  are  blown  through  the  grate,  the  mixture 
being  at  a  temperature  of  about  480°  F.  The  greater  part  of  this  steam 
passes  through  the  producer  undecomposed,  its  heat  being  used  in  a 
regenerator  to  furnish  fresh  steam  for  the  producer.  More  than  0.5  ton 
of  steam  is  decomposed  in  passing  through  the  hot  fuel,  and  nearly  4.5  tons 
of  gas  are  produced  from  a  ton  of  coal,  equal  to  about  160,000  cu.  ft.  at 
ordinary  atmospheric  temperature.  The  gas  has  a  calorific  power  of  81  % 
of  that  of  the  original  fuel.  Mr.  Humphrey  gives  the  following  table 
Showing  the  relative  value  of  different  gases. 


FUEL  GAS. 


853 


«  i 

«  fl 

M 

/I 

, 

"."S— 

, 

!"*< 

fcjj^. 

I   . 

§ 

1 

Volume  per  cent. 

|p« 

£J 

200 

Ill 

II 

ti  . 

*| 

*M  o 

C  £ 

S**"1  " 
S  *  S 

03  ®  +i 

^8 

o.s 

^2  — 

J31 

m 

Is 

5 

s3 

Hydrogen  (H)  

24  8 

8  6 

18  73 

20.0 

56.9 

48  0 

22  0 

Marsh  gas  (CH4) 

2  3 

2  4 

0  31 

22  6 

39  5 

67  0 

CWH2^  gases  . 

nil 

nil 

0  31 

4  or?) 

3  0 

3.8 

6  0 

Carbonic  oxide  (CO)  

13  2 

24  4 

25  07 

21  0 

8.7 

7.5 

0.6 

Nitrogen  (N)    .  . 

46  8 

59  4 

48  98 

49  5 

5  8 

0  5 

3  0 

Carbonic  acid  (CO2)  

12  9 

5  2 

6  57 

5  0 

3.0 

nil 

0  6 

Total  volume 

100  0 

100  0 

100  0 

100  0 

100  0 

100  0 

100  0 

Total  combustible  gases  

40  3 

35  4 

44  42 

45  0 

91.2 

98  8 

95  6 

Theoretical. 

Air  required  for  combustion  .... 

112.4 

101.4 

113.2 

154.0 

410.0 

581.0 

806.0 

Calorific    value    per    cu.   ft.,    ) 
in  Ib.  °  C.  units  j 

85.9 

74.7 

88.9 

115.3 

284.0 

381.0 

495.8 

Do.,  B.T.U.  per  cu.  ft  

154.6 

134.5 

160.0 

207.5 

511.2 

658.8 

892.4 

Do.,  per  litre,  gram  °  C.  units  .  .  . 

1,374 

1,195 

1,432 

1,845 

4,544 

6,096 

7,932 

NOTE.  —  Where  the  volume  per  cent  does  not  add  up  to  100  the  slight 
difference  is  due  to  the  presence  of  oxygen. 

The  following  is  the  analysis  9f  gas' made  in  a  Mond  producer  at  the 
works  of  the  Solvay  Process  Co.  in  Detroit,  Mich.  (Mineral  Industry,  vol. 
viii,  1900):  CO2,  14.1;  O,  0.3;  N,  42.9;  H,  25.9;  CH4,  4.1;  CO,  12.7.  Com- 
bustible, 42.7%.  Calories  per  litre,  1540,  --=  173  B.T.U.  per  cu.  ft. 

Relative  Efficiencies  of  Different  Coals  in  Gas  Producer  and 
Engine  Tests.  —  The  following  is  a  condensed  statement  of  the  principal 
results  obtained  in  the  gas-producer  tests  of  the  U.  S.  Geological  Survey 
t  St.  Louis  in  1904.  (R.  H.  Fernald,  Trans.  A.  S.  M.  #.,  1905.) 


B.t.u. 

Pounds  per  elec- 
trical H.P.  hour 

B.t.u. 

Pounds  per  elec- 
trical H.P.  hour 

per 

at  switchboard. 

per 

at  switchboard. 

Sample. 

Ib. 

Sample. 

Ib. 

bus- 
tible. 

Coal 
as 
fired. 

Dry 

coal. 

Com- 
bus- 
tible. 

bus- 
tible. 

Coal 
as 
fired. 

Dry 
coal. 

Com- 
bus- 
tible. 

Ala.  No.  2... 

14820 

1.71 

.64 

.53 

Ky.No.  3.. 

14650 

2.05 

1.91 

.72 

Colo.  No.  3... 

13210 

2.14 

.71 

.58 

Mo.  No.  2.. 

14280 

1.94 

1.71 

.43 

111.  No.  3  

14560 

1.93 

.79 

.60 

Mont.  No.  1 

13580 

2.54 

2.25 

.98 

111.  No.  4  

14344 

2.01 

.76 

.57 

N.Dak.No.2 

12600 

3.80 

2.29 

2.05 

Ind.No.  1.... 

14720 

2.17 

.93 

.71 

Texas  No.  1 

12945 

3.34 

2.22 

.88 

Ind.No.2.... 

14500 

1.68 

.55 

39 

Texas  No.  2 

12450 

2.58 

1.71 

.52 

Okla.No.  1... 

14800 

1.92 

.83 

66 

W.Va.No.l 

15350 

1.60 

1.57 

.48 

Okla.No.4... 

13890 

1.57 

.43 

.17 

W.Va.No.4 

15600 

1.32 

1.29 

.17 

Iowa  No.  2.  .  . 

13950 

2.07 

.73 

.30 

W.Va.No.7 

15800 

1.53 

1.50 

.40 

Kan.  No.  5... 

15200 

1.69 

.62 

.43 

Wyo.No.2 

13820 

2.28 

2.07 

.60 

The  gas  was  made  in  a  Taylor  pressure  producer  rated  at  250  H.P.  Its 
inside  diam.  was  7  ft.,  area  of  fuel  bed  38.5  sq.  ft.,  height  of  casing  15  ft.; 
rotative  ash  table;  centrifugal  tar  extractor.  The  engine  was  a  3-cylinder 


851  FUEL. 

vertical  Westinghouse,  19  in.  diam.,  22  in.  stroke,  200  r.p.m.,  rated  at 
235  B.H.P.  Comparing  the  results  of  the  W.  Va.  No.  7  coal,  the  best 
on  the  list,  with  the  North  Dakota  coal,  the  one  which  gave  the  poorest 
results,  the  heat  values  per  Ib.  combustible  of  the  coals  are  as  1  to  0.808; 
reciprocal,  1  to  1.24;  the  Ibs.  combustible  per  E.  H.  P.  hour  as  1  to  1.75, 
and  Ibs.  coal  as  fired  per  E.  H.  P.  hour  as  1  to  2.88.  The  relative  thermal 
efficiencies  of  the  engine  with  the  two  coals  are  as  2.05  to  1.17,  or  as  1  to 
0.578.  The  analyses  by  volume  of  the  dry  gas  obtained  from  the  two 
coals  was: 

C02         O          CO          H         CH4         N          Total 

combustible. 

W.  Va 10.16     0.24     15.82     11.16     3.74     5888       30.72 

N.  Dak 8.69     0.23     20.90     14.33     4.85     51.00       40.08 

The  dry-gas  analysis  shows  the  North  Dakota  gas  to  be  by  far  the  best ; 
its  much  lower  result  in  the  engine  test  is  due  to  the  smaller  quantity  of 
gas  produced  per  Ib.  of  coal,  which  was  22.7  cu.  ft.  per  Ib.  of  coal  as  fired, 
as  compared  with  70.6  cu.  ft.  for  the  W.  Va.  coal,  measured  at  62°  F.  and 
14.7  Ib.  absolute  pressure. 

Use  of  Steam  in  Producers  and  in  Boiler-furnaces.  (R.  W.  Ray- 
mond, Trans.  A.  I.  M.  E.t  xx,  635.)  —  No  possible  use  of  steam  can  cause 
a  gain  of  heat.  If  steam  be  introduced  into  a  bed  of  incandescent  carbon 
't  is  decomposed  into  hydrogen  and  oxygen. 

The  heat  absorbed  by  the  reduction  of  one  pound  of  steam  to  hydrogen 
is  much  greater  in  amount  than  the  heat  generated  by  the  union  of  the 
oxygen  thus  set  free  with  carbon,  forming  either  carbonic  oxide  or  car- 
bonic acid.  Consequently,  the  effect  of  steam  alone  upon  a  bed  of  incan- 
descent fuel  is  to  chill  it.  In  every  water-gas  apparatus,  designed  to 
produce  by  means  of  the  decomposition  of  steam  a  fuel-gas  relatively 
Free  from  nitrogen,  the  loss  of  heat  in  the  producer  must  be  compensated 
by  some  reheating  device. 

This  loss  may  be  recovered  if  the  hydrogen  of  the  steam  is  subsequently 
burned,  to  form  steam  again.  Such  a  combustion  of  the  hydrogen  is 
contemplated,  in  the  case  of  fuel-gas,  as  secured  in  the  subsequent  use  of 
that  gas.  Assuming  the  oxidation  of  H  to  be  complete,  the  use  of  steam 
will  cause  neither  gain  nor  loss  of  heat,  but  a  simple  transference,  the 
heat  absorbed  by  steam  decomposition  being  restored  by  hydrogen  com- 
bustion. In  practice,  it  may  be  doubted  whether  this  restoration  is  ever 
complete.  But  it  is  certain  that  an  excess  of  steam  would  defeat  the 
reaction  altogether,  and  that  there  must  be  a  certain  proportion  of  steam, 
which  permits  the  realization  of  important  advantages,  without  too  great 
a  net  loss  in  heat. 

The  advantage  to  be  secured  (in  boiler  furnaces  using  small  sizes  of 
anthracite)  consists  principally  in  the  transfer  of  heat  from  the  lower 
side  of  the  fire,  where  it  is  not  wanted,  to  the  upper  side,  where  it  is 
wanted.  The  decomposition  of  the  steam  below  cools  the  fuel  arid  the 
grate-bars,  whereas  a  blast  of  air  alone  would  produce,  at  that  point, 
intense  combustion  (forming  at  first  CO2),  to  the  injury  of  the  grate,  the 
fusion  of  part  of  the  fuel,  etc. 

Gas  Analyses  by  Volume  and  by  Weight.  —  To  convert  an  analysis 
of  a  mixed  gas  by  volume  into  analysis  by  weight:  Multiply  the  percentage 
of  each  constituent  gas  by  its  relative  density,  viz:  CO2  by  11,  O  by  8, 
CO  and  N  each  by  7,  and  divide  each  product  by  the  sum  of  the  products. 
Conversely,  to  convert  analysis  by  weight  into  analysis  by  volume,  divide 
the  percentage  by  weight  of  each  gas  by  its  relative  density,  and  divide 
each  Quotient  by  the  sum  of  the  quotients. 

Gas-fuel  for  Small  Furnaces.  —  E.  P.  Reichhelm  (Am.  Mack.,  Jan. 
10,  1895)  discusses  the  use  of  gaseous  fuel  for  forge  fires,  for  drop-forging, 
in  annealing-ovens  and  furnaces  for  melting  brass  and  copper,  for  case- 
hardening,  muffle-furnaces,  and  kilns.  Under  ordinary  conditions,  in 
such  furnaces  he  estimates  that  the  loss  by  draught,  radiation,  and  the 
heating  of  space  not  occupied  by  work  is,  with  coal,  80%,  with  petro- 
leum 70%,  and  with  gas  above  the  grade  of  producer-gas  25%.  He 
gives  the  following  table  of  comparative  cost  of  fuels,  as  used  in  these 
furnaces: 


ACETYLENE   AND   CALCIUM   CAKfilDE. 


855 


Kind  of  Gas. 

"i2! 

E.S  3 
•SSS 
|1§ 

No.  of  Heat- 
units  in  Fur- 
naces f  after 
Deducting 
25  %  Loss. 

Average  Cost 
per  1000  Ft. 

Co?t  of  1,000,- 
000  Heat- 
units  Ob- 
tained in, 
Fiirnar.es. 

Natural 

1,000,000 
675,000 
646,000 
690,000 
313,000 
377,000 
185,000 
150,000 
306,365 

750,000 
506,250 
484,500 
517,500 
234,750 
282,750 
138,750 
112,500 
229,774 

Coal-gas  20  candle-power    

$1.25 
1.00 
.90 
.40 
.45 
.20 
.15 
.15 

$2.46 
2.06 
.73 
.70 
.59 
.44 
.33 
.65 
.73 
.73 

Gasolene  gas   20  candle-power  

\Vater-gas  from,  bituminous  coal  

Water-gas  and  producer-gas  mixed  — 
Producer-gas                          . 

Naphtha-gas,  fuel  21/2  gals,  per  1000  ft.  . 

Coal,  $4  per  ton,  per  1,000,000  heat-units 
Crude  petroleum,  3  cts.  per  gal.,  per  1,( 

utilized  

)00,000  heat-units  

Mr.  Reichhelm  gives  the  following  figures  from  practice  in  melting 
brass  with  coal  and  with  naphtha  converted  into  gas:  1800  Ibs.  of  metal 
require  1080  Ibs.  of  coal,  at  $4.65  pei  ton,  equal  to  $2.51,  or,  say,  15  cents 
per  100  Ibs.  Mr,.  T.'s  report:  2500  Ibs.  of  metal  require  47  gals,  of  naphtha, 
at  6  cents  per  gal.,  equal  to  $2.82,  or,  say,  111/4  cents  per  100  Ibs. 

Blast-Furnace  Gas.  —  The  waste-gases  from  iron  blast  furnaces 
were  formerly  utilized  only  for  heating  the  blast  in  the  hot-blast  ovens  and 
for  raising  steam  for  the  blowing-engine  pumps,  hoists  and  other  auxiliary 
apparatus.  Since  the  introduction  of  gas  engines  for  blowing  and  other 
purposes  it  has  been  found  that  there  is  a  great  amount  of  surplus  gas 
available  for  other  uses,  so  that  a  large  power  plant  for  furnishing  electric 
current  to  outside  consumers  may  easily  be  run  by  it.  H.  Freyn,  in  r<* 
paper  presented  before  the  Western  Society  of  Engineers  (Eng.  Rec., 
Jan.  13,  1906),  makes  an  elaborate  calculation  for  the  design  of  such  a 
plant  in  connection  with  two  blast  furnaces  of  a  capacity  of  400  tons  of 
pig  iron  each  per  day.  Some  of  his  figures  are  as  follows:  The  two  fur- 
naces would  supply  4,350,000  cu.  ft.  of  gas  per  hour,  of  90  B.T.U.  average 
heat  value  per  cu.  ft.  The  hot-blast  stoves  would  require  30%  of  this,  or 
1,305,000  cu.  ft.;  the  gas-blowing  engines  720,000  cu.  ft.;  pumps,  hoists 
and  lighting  machinery,  120,000  cu.  ft.;  gas-cleaning  machinery,  120,000 
cu.  ft.;  losses  in  piping,  48,000  cu.  ft.;  leaving  available  for  outside  uses,  in 
round  numbers,  2,000,000  cu.  ft.  per  hour.  At  the  rate  of  100  cu.  ft.  of  gas 
per  brake  H.P.  hour  this  would  supply  engines  of  20,000  H.P.,  but  assum- 
ing that  on  account  of  irregular  working  of  the  furnaces  only  half  this 
amount  would  be  available  for  part  of  the  time,  a  10,000-H.P.  plant  could 
be  run  with  the  surplus  gas  of  the  two  furnaces.  Taking  into  account  the 
cost  of  the  plant,  figured  at  $61.60  per  B.H.P.,  interest,  depreciation, 
labor,  etc-.,  the  annual  cost  of  producing  one  B.H.P.,  24  hours  a  day,  is 
$17.88,  no  value  being  placed  on  the  blast-furnace  gas,  and  1  K.W.  hour 
would  cost  0.295  cent,  which  is  far  below  the  lowest  figure  ever  reached 
with  a  steam-engine  power  plant. 

Blast-furnace  gas  is  composed  of  nitrogen,  carbon  dioxide  and  carbon 
monoxide,  the  latter  being  the  combustible  constituent.  An  analysis 
reported  in  Trans.  A.I.M.E.,  xyii,  50,  is,  by  volume,  CO2,  7.08;  CO,  27.80; 
O,  0.10;  N,  65.02.  The  relative  proportions  of  COa  and  CO  vary  con- 
siderably with  the  conditions  of  the  furnace. 

ACETYLENE  AND  CALCIUM  CARBIDE. 

Acetylene,  C2H2, contains  12  parts  C  and  1  part  H,  or  92.3%  C,7.7%  H. 
It  is  described  as  follows  in  a  paper  on  Calcium  Carbide  and  Acetylene 
by  J.  M.  Morehead  (Am.  Gas  Light  Jour.,  July  10,  1905.  Revised, 

Acetylene  is  a  colorless  and  tasteless  gas.  When  pure  it  has  a  sweef 
etheral  odor,  but  in  the  commercial  form  it  carries  small  percentages  of 
phosphoreted  and  sulphureted  hydrogen  which  give  it  a  pungent  odor. 


856  FtJEL. 

Pure  acetylene  is  -without  toxic  or  physiological  effect.  It  may  be  in- 
haled or  swallowed  with  impunity.  One  cu.  ft.  requires  11.91  cu.  ft.  of 
air  for  its  complete  combustion.  Its  specific  gravity  is  0.92,  air  being  1. 
It  is  the  nearest  approach  to  gaseous  carbon,  and  it  possesses  a  higher 
candle  power  and  flame  temperature  than  any  other  known  substance, 
240  candles  for  5  cu.  ft.,  4078°  F.  when  burned  in  air,  7878°  F.  in  oxygen. 
Its  ignition  temperature  with  air  is  804°  F.,  with  oxygen  782°  F.  It  is 
soluble  in  its  own  volume  of  water,  and  in  varying  proportions  in  ether, 
alcohol,  turpentine,  and  acetone.  The  solubility  increases  with  pressure. 
It  liquefies  under  a  pressure  of  700  Ibs.  per  sq.  in.  at  70°  F.  The  pres- 
sure necessary  for  liquefaction  varies  directly  with  the  temperature  up 
to  98°,  which  is  its  critical  temperature,  beyond  which  it  is  impossible 
to  liquefy  the  gas  at  any  pressure. 

When  calcium  carbide  is  brought  into  contact  with  water,  the  calcium 
robs  the  water  of  its  oxygen  and  forms  lime  and  thus  frees  the  hydrogen, 
which  combines  with  the  carbon  of  the  carbide  to  form  acetylene. 
Sixty-four  Ibs.  of  calcium  carbide  combine  with  thirty-six  Ibs.  of  water 
and  produce  twenty-six  Ibs.  of  acetylene  and  74  Ibs.  of  pure  slacked 
lime.  [The  chemical  reaction  is  CaC2  +  2H2O  =  C2H2  +  Ca(OH)2.] 

Chemically  pure  calcium  carbide  will  yield  at  70°  F.  and  30  in.  mer- 
cury 5.83  cu.  ft.  acetylene  per  pound  of  carbide.  Commercially  pure 
carbide  is  guaranteed  to  yield  5  cu.  ft.  of  acetylene  per  pound,  and 
usually  exceeds  the  guarantee  by  a  few  per  cent.  The  reaction  between 
calcium  carbide  and  water,  and  the  subsequent  slacking  of  the  calcium 
oxide  produced,  give  rise  to  considerable  heat.  This  heat  from  one  pound 
of  chemically  pure  calcium  carbide  amounts  to  sufficient  to  raise  the 
temperature  of  4.1  Ibs.  of  water  from  the  freezing  to  the  boiling  point. 

There  are  two  types  of  generators;  one  in  which  a  varying  quantity  of 
water  is  dropped  on  to  the  carbide,  the  other  in  which  the  carbide  is 
dropped  into  a  large  excess  of  water.  Owing  to  the  large  amount  of  heat 
generated  by  the  reaction,  and  the  susceptibility  of  the  acetylene  to 
heat,  the  first,  or  dry  type,  is*  confined  to  lamps  and  to  small  machines. 

Acetylene  produces  1475  B.T.U.  per  cubic  foot  (at  70°  F.  and  30  in.), 
as  compared  with  1000  for  natural  gas  and  600  for  coal  or  water  gas. 
At  the  present  state  of  development  of  the  acetylene  industry  and  the 
calcium  carbide  manufacture,  this  gas  will  not  compete  with  coal  gas  or 
water  gas,  or  with  electricity  as  supplied  in  our  cities. 

The  explosive  limits  of  acetylene  and  air  are  from  3  %  acetylene  and 
97%  air  to  24%  acetylene  and  76%  air,  the  point  of  maximum  explo- 
sibility  being  7.7%  acetylene  and  92.3%  air. 

The  combustion  of  acetylene  requires  theoretically  2  %  volumes  of 
oxygen  for  1  volume  of  acetylene.  In  autogenous  welding  and  other 
oxy-acetylene  processes,  however,  a  consid?rable  part  of  the  necessary 
oxygen  is  taken  from  the  air,  and  hence  only  from  1.25  to  1.75  cubic  feet 
of  oxygen  per  cubic  foot  of  acetylene  need  be  supplied. 

Of  the  1475  heat  units  contained  in  a  cubic  foot  of  acetylene,  227  are 
endothermic  energy,  which  it  is  believed  is  higher  than  that  for  any 
other  substance.  The  balance  of  the  energy  is  derived  from  the  com- 
bination of  the  carbon  and  hydrogen  of  the  acetylene  with  oxygen,  as 
is  the  case  with  other  combustible  gases. 

Due  to  the  extraordinary  endothermic  energy  of  acetylene  the  gas 
•will  explode  of  itself  if  it  is  ignited  while  at  a  pressure  slightly  in  excess 
of  15  Ibs.  to  the  square  inch.  The  compression,  storage,  use  and  trans- 
portation of  unabsorbed  acetylene  at  pressures  in  excess  of  this  figure 
are  forbidden  by  the  fire,  police,  insurance  and  transportation  authorities 
in  practically  all  cities.  Danger  of  explosion  from  compressed  acetylene 
is  removed  and  the  use  of  compressed  acetylene  is  rendered  safe  and 
feasible  for  motor  car,  yacht,  railroad  train  and  all  other  portable  uses 
by  absorbing  the  acetylene  in  acetone,  which  is  itself  absorbed  in  turn 
in  asbestos,  Keisselgour  or  other  non-inflammable  substances. 

Calcium  carbide  was  discovered  on  May  4,  1892,  at  the  plant  of  the 
Willson  Aluminum  Co.,  in  North  Carolina.  It  is  a  crystalline  body, 
hard,  brittle  and  varying  in  color  from  almost  black  to  brick  red.  Its 
specific  gravity  is  2.26.  A  cubic  foot  of  crushed  carbide  weighs  138  Ibs., 
and  in  weight,  color  and  most  of  its  physical  characteristics  is  about 
like  granite.  If  broken  hot,  the  fracture  shows  a  handsome,  bluish 
purple  iridescence  and  the  crystals  are  apt  to  be  quite  large. 


ACETYLENE  AND  CALCIUM  CARBIDE.      857 

Calcium  carbide,  CaC2,  contains  62.5%  Ca  and  37.5%  C.  It  is  in- 
soluble in  most  acids  and  in  all  alkalies;  it  is  non-inflammable,  infusible, 
non-explosive,  unaffected  by  jars,  concussions  or  time,  and,  except  for 
the  property  of  giving  off  acetylene  when  brought  in  contact  with  water, 
it  is  an  inert  and  stable  body.  It  is  made  by  the  reduction  in  an  electric 
arc  furnace  of  a  mixture  of  finely  pulverized  and  intimately  mixed  cal- 
cium oxide  or  quicklime  and  carbon  in  the  shape  of  coke  (CaO  +  3C  = 
CaC2  +  CO).  The  furnaces  employ  from  12,000  to  15,000  electric  H.P. 
each  and  produce  from  50  to  75  tons  per  day.  The  output  is  crushed  to 
different  sizes  and  it  is  sold  in  steel  drums  for  $70  per  ton  at  the  works. 

The  entire  use  for  calcium  carbide  is  for  the  production  of  acetylene. 
[Wohler,  in  1862,  obtained  calcium  carbide  by  heating  an  alloy  of  cal- 
cium and  zinc  together  with  carbon  to  a  very  high  temperature.] 

Acetylene  Generators  and  Burners. — Lewes  classifies  acetylene 
generators  under  four  types:  (1)  Those  in  which  water  drips  or  flows 
slowly  on  a  mass  of  carbide;  (2)  those  in  which  water  rises,  coming  in 
contact  with  a  mass  of  carbide;  (3)  those  in  which  water  rises,  coming  in 
contact  with  successive  layers  of  carbide;  (4)  those  in  which  the  carbide 
is  dropped  or  plunged  into  an  excess  of  water.  He  shows  that  the  first 
two  classes  are  dangerous;  that  some  generators  of  the  third-class, are 
good,  1)ut  that  those  of  the  fourth  are  the  best. 

Of  the  various  burners  used  for  acetylene,  those  of  the  Naphey  type 
are  among  the  most  satisfactory.  Two  tubes  leading  from  the  base  of 
the  burner  are  so  adjusted  as  to  cause  two  jets  of  flame  to  impinge  upon 
each  other  at  some  little  distance  from  the  nozzles,  and  mutually  to 
splay  each  other  out  into  a  flat  flame.  The  tips  of  the  nozzles,  usually 
of  steatite,  are  formed  on  the  principle  of  the  Bunsen  burner,  insuring  a 
thorough  mixture  of  the  acetylene  with  enough  air  to  give  the  best 
illumination.  (H.  C.  Biddle,  Cal  Jour,  of  Tech.,  1907.) 

Acetylene  gas  is  an  endothermic  'compound.  In  its  formation  heat  is 
absorbed,  and  there  resides  in  the  acetylene  molecule  the  power  of  spon- 
taneously decomposing  and  liberating  this  heat  if  it  is  subjected  to  a 
temperature  or  pressure  beyond  the  capacity  of  its  unstable  nature  to 
withstand.  (Thos.  L.  White,  Eng.  Mag.,  Sept.,  1908.)  Mr.  White 
recommends  the  use  of  acetylene  for  carbureting  the  alcohol  used  ir. 
alcohol  motors  for  automobiles. 

The  Acetylene  Blowpipe. — (Machy.,  July,  1907.) — The  acetylene 
is  produced  in  a  generator  and  stored  in  a  tank  at  a  pressure  of  2.2  to  3 
Ibs.  per  sq.  in.  The  oxygen  is  compressed  in  a  tank  at  about  150  Ibs. 
pressure.  The  acetylene  is  conveyed  to  the  burner  through  a  1-in.  pipe 
with  one  Y%-\n  branch  leading  to  each  blowpipe  connection.  The  oxygen 
is  conveyed  through  2/g-in.  pipe  with  ^-in.  branches.  The  blowpipe  is 
of  brass,  made  on  the  injector  principle.  As  acetylene  is  so  rich  in  car- 
bon— containing  92.3  % — it  is  possible,  when  mixed  with  air  in  a  Bunsen 
burner,  to.  obtain  3100°  F.,  and  when  combined  with  oxygen,  6300°  F., 
which  is  the  hottest  flame  known  as  a  product  of  combustion,  and  nearly 
equals  the  electric  arc.  This  is  about  1200°  higher  than  the  oyx- 
hydrogen  blowpipe  flame. 

In  lighting  the  blowpipe,  the  acetylene  is  first  turned  on  full;  then  the 
oxygen  is  added  until  the  flame  is  only  a  single  cone.  At  the  apex  of  this 
cone  is  a  temperature  of  6300°  F.  In  welding,  this  point  is  held  from  % 
to  ^t  in.  distant  from  the  metal  to  be  welded.  Too  much  acetylene  pro- 
duces two  cones  and  a  white  color ;  an  excess  of  oxygen  is  indicated  by  a 
violet  tint. 

Theoretically,  2  y<i  volumes  of  oxygen  are  required  for  complete  com- 
bustion of  1  volume  of  acetylene.  Practically,  however,  with  the  blow- 
pipe, the  best  welding  results  are  obtained  with  1.7  volumes  of  oxygen  to 
1  volume  of  acetylene.  The  acetylene  is,  therefore,  not  completely 
burned  with  the  blowpipe,  according  to  the  reaction: 

2C2H2  (4  vol.)  -f-  5O2.  (10  vol.)  =  4CO2  +  2H2O, 
but  it  is  incompletely  burned  according  to  the  reaction: 
C2H2  (2  vol.)  -f-  O2  (2  vol.)  =  2CO  +  H2. 

The  Theory  and  Practice  of  Oxy-Acetylene  Welding  is  described  in  an 
illustrated  article  by  J.  F.  Springer  in  Indust.  Eng'g.,  Oct.,  1909. 
The  Levoisite  process  of  making  oxygen  (99.9  %  pure) ,  used  in  acety- 


858 


ILLUMINATING  -  GAS. 


lene  welding,  is  described  by  Max  Mauran  in  Met.  and  Chem.  Eng'g., 
June,  1914. 

IGNITION  TEMPERATURE  OP  GASES. 

Mayer  and  Munch  (Bericht  der  deutscher  Gesellschaft,  xxvi,  2241)  give 
the  following: 

"      '  CH4,667°C.      1233°  F. 

C2He,  616  1141 

C3H8,  547  1017 

C2H2,  580  1076 

CaHe,  504  939 


Marsh-gas, 

Ethane, 

Propane, 

Acetylene, 

Propylene, 


French 
1022° 


Very  different  figures  are  given  by  other  authorities. 
Commission  obtained  for  hydrogen  1071°  F.;  CH4,  1436°;  , 

CO,  1202;  CO  in  presence  of  a  large  quantity  of  CO2,  1292°  F.  Vivian 
Lewes  gives  for  the  ignition  temperature  of  cannel  coal  668°  F.;  bi- 
tuminous, 766°,  semi-bituminous  870°  F.  W.  S.  Hutton  gives  for 
anthracite,  925°  F. 

ILLUMINATING-GAS. 

Coal-gas  is  made  by  distilling  bituminous  coal  in  retorts.  The*  retort 
is  usually  a  long  horizontal  semi-cylindrical  or  a  shaped  chamber,  holding 
from  160  to  300  Ibs.  of  coal.  The  retorts  are  set  in  "benches"  of  from 
3  to  9,  heated  by  one  fire,  which  is  generally  of  coke.  The  vapors  distilled 
from  the  coal  are  converted  into  a  fixed  gas  by  passing  through  the  retort, 
which  is  heated  almost  to  whiteness. 

The  gas  passes  out  of  the  retort  through  an  "ascension-pipe"  into  a 
long  horizontal  pipe  called  the  hydraulic  main,  where  it  deposits  a  por- 
tion of  the  tar  it  contains;  thence  it  goes  into  a  condenser,  a  series  of  iron 
tubes  surrounded  by  cold  water,  where  it  is  freed  from  condensable  vapors, 
as  ammonia-water,  then  into  a  washer,  where  it  is  exposed  to  jets  of 
water,  and  into  a  scrubber,  a  large  chamber  partially  filled  with  trays 
made  of  wood  or  iron,  containing  coke,  fragments  of  brick  or  paving- 
Atones,  which  are  wet  with  a  spray  of  water.  By  the  washer  and  scrubber 
the  gas  is  freed  from  the  last  portion  of  tar  and  ammonia  and  from  some 
of  the  sulphur  compounds.  The  gas  is  then  finally  purified  from  sulphur 
compounds  by  passing  it  through  lime  or  oxide  of  iron.  The  gas  is  drawn 
from  the  hydraulic  main  and  forced  through  the  washer,  scrubber,  etc., 
by  an  exhauster  or  gas  pump. 

The  kind  of  coal  used  is  generally  caking  bituminous,  but  as  usually 
this  coal  is  deficient  in  gases  of  high  illuminating  power,  there  is  added  to 
it  a  portion  of  cannel  coal  or  other  enricher. 

The  following  table,  abridged  from  one  in  Johnson's  Cyclopedia,  shows 
the  analysis,  candle-power,  etc.,  of  some  gas-coals  and  enrichers: 


Gas-ooals,  etc. 

Vol.  Matter. 

Fixed  Garb. 

^ 

II 
$S£ 

o^ 

Coke  per 
ton  of  2240 
Ibs. 

!~'i 
2  >>« 

5-°* 

Ibs. 

bush. 

Pittsburgh   Pa 

36.76 
36.00 
37.50 
40.00 
43.00 
46.00 
53.50 

51.93 
58.00 
56.90 
53.30 
40.00 
41.00 
44.50 

7.07 
6.00 
5.60 
6.70 
17.00 
13.00 
2.00 

Vo',642 
10,528 
10,765 
9800 
13,200 
15,000 

Westmoreland,  Pa  
Sterling,  O  

16.62 
18.81 
20.41 
34.98 
42.79 
28.70 

1544 
1480 
1540 
1320 
1380 
1056 

40 
36 
36 
32 
32 
44 

6420 
3993 
2494 
2806 
4510 

Despard,  W.  Va  

Petonia,  W.  Va  

Grahamite,  W.  Va  

The  products  of  the  distillation  of  100  Ibs.  of  average  gas-coal  are  about 
as  follows.  They  vary  according  to  the  quality  of  coal  and  the  tempera- 
ture of  distillation. 

Coke,  64  to  65  Ibs.;  tar,  6.5  to  7.5  Ibs.;  ammonia  liquor,  10  to  12  Ibs.; 
purified  gas,  15  to  12  Ibs.;  impurities  and  loss,  4.5%  to  3.5%. 
The  composition  of  the  gas  by  volume  ranges  about  as  follows ;  Hydro- 


ILLUMINATING^  GAS.  859 

gen,  38%  to  48%;  carbonic  oxide,  2%  to  14%;  marsh-gas  (Methane, 
CH4),  43%  to  31%;  heavy  hydrocarbons  (CwH2w,  ethylene,  propylene, 
benzole  vapor,  etc.),  7.5%  to  4.5%;  nitrogen,  1%  to  3%. 

In  the  burning  of  the  gas  the  nitrogen  is  inert:  the  hydrogen  and  car- 
bonic oxide  give  heat  but  no  light.  The  luminosity  of  the  flame  is  due  to 
the  decomposition  by  heat  of  the  heavy  hydrocarbons  into  lighter  hydro- 
carbons and  carbon,  the  latter  being  separated  in  a  state  of  extreme 
subdivision.  By  the  heat  of  the  flame  this  separated  carbon  is  heated  to 
intense  whiteness,  and  the  illuminating  effect  of  the  flame  is  due  to  the 
light  of  incandescence  of  the  particles  of  carbon. 

The  attainment  of  the  highest  degree  of  luminosity  of  the  flame  de- 
pends upon  the  proper  adjustment  of  the  proportion  of  the  heavy  hydro- 
carbons (with  due  regard  to  their  individual  character)  to  the  nature  or 
the  diluent  mixed  therewith. 

Investigations  of  Percy  F.  Frankland  show  that  mixtures  of  ethylene 
and  hydrogen  cease  to  have  any  luminous  effect  when  the  proportion  of 
ethylene  does  not  exceed  10%  of  the  whole.  Mixtures  of  ethylene  and 
carbonic  oxide  cease  to  have  any  luminous  effect  when  the  proportion  of 
the  former  does  not  exceed  20%,  while  all  mixtures  of  ethylene  and 
marsh-gas  have  more  or  less  luminous  effect.  The  luminosity  of  a  mix- 
ture of  10%  ethylene  and  90%  marsh-gas  being  equal  to  about  18  candles, 
and  that  of  one  of  20%  ethylene  and  80%  marsh-gas  about  25  candles. 
The  illuminating  effect  of  marsh-gas  alone,  when  burned  in  an  argand 
burner,  is  by  no  means  inconsiderable. 

For  further  description,  see  the  treatises  on  gas  by  King,  Richards, 
and  Hughes;  also  Appleton's  Cyc.  Mech.,  vol.  i.  p.  900. 

Water-gas.  —  Water-gas  is  obtained  by  passing  steam  through  a  bed 
of  coal,  coke,  or  charcoal  heated  to  redness  or  beyond.  The  steam  is 
decomposed,  its  hydrogen  being  liberated  and  its  oxygen  burning  the 
carbon  of  the  fuel,  producing  carbonic-oxide  gas.  The  chemical  reaction 
is,  C  +  H2O  =  CO  +  2  H,  or  2  C  +  2  H2O  =  C  +  CO2  +  4  H,  followed 
by  a  splitting  up  of  the  CO2,  making  2  CO  +  4  H.  By  weight  the  normal 
gas  CO  +  2  H  is  composed  of  C  +  O  +  H  =  28  parts  CO  and  2  parts  H, 

12  +  16  +   2 

or  93.33%  CO  and  6.67%  H;  by  volume  it  is  composed  of  equal  parts  of 
carbonic  oxide  and  hydrogen.  Water-gas  produced  as  above  described 
has  great  heating-power,  but  no  illuminating-power.  It  may,  however, 
be  used  for  lighting  by  causing  it  to  heat  to  whiteness  some  solid  sub- 
stance, as  is  done  in  the  Welsbach  incandescent  light. 

An  illuminating-gas  is  made  from  water-gas  by  adding  to  it  hydro- 
carbon  gases  or  vapors,  which  are  usually  obtained  from  petroleum  or 
some  of  its  products.  A  history  of  the  development  of  modern  illumi- 
nating water-gas  processes,  together  with  a  description  of  the  most  recent 
forms  of  apparatus,  is  given  by  Alex.  C.  Humphreys,  in  a  paper  on  "  Water- 
gas  in  the  United  States,"  read  before  the  Mechanical  Section  of  the 
British  Association  for  Advancement  of  Science,  in  1889.  After  describ- 
ing many  earlier  patents,  he  states  that  success  in  the  manufacture  of 
water-gas  may  be  said  to  date  from  1874,  when  the  process  of  T.  S.  C. 
Lowe  was  introduced.  All  the  later  most  successful  processes  are  the 
modifications  of  Lowe's,  the  essential  features  of  which  were  "an  apparatus 
consisting  of  a  generator  and  superheater  internally  fired;  the  super- 
heater being  heated  by  the  secondary  combustion  from  the  generator, 
the  heat  so  stored  up  in  the  loose  brick  of  the  superheater  being  used,  in 
the  second  part  of  the  process,  in  the  fixing  or  rendering  permanent  of  the 
hydrocarbon  gases;  the  second  part  of  the  process  consisting  in  the 
passing  of  steam  through  the  generator  fire,  and  the  admission  of  oil  or 
hydrocarbon  at  some  point  between  the  fire  of  the  generator  and  the 
loose  filling  of  the  superheater." 

The  water-gas  process  thus  has  two  periods:  first  the  "  blow,"  during 
which  air  is  blown  through  the  bed  coal  in  the  generator,  and  the  par- 
tially burned  gaseous  products  are  completely  burned  in  the  superheater, 
giving  up  a  great  portion  of  their  heat  to  the  fire-brick  work  contained 
in  it,  and  then  pass  out  to  a  chimney;  second,  the  "run"  during  which  the 
air  blast  is  stopped,  the  opening  to  the  chimney  closed,  and  steam  is 
blown  through  the  incandescent  bed  of  fuel.  The  resulting  water-gas 
passing  into  the  carburetting  chamber  in  the  base  of  the  superheater  is 
there  charged  with  hydrocarbon  vapors,  or  spray  (such  as  naphtha  and 
other  distillates  or  crude  oil) ,  and  passes  through  the  superheater,  where 


860 


ILJAJMINATING-  GAS. 


the  hydrocarbon  vapors  become  converted  into  fixed  illuminating  gases. 
From  the  superheater  the  combined  gases  are  passed,  as  in  the  coal-gas 
process,  through  washers,  scrubbers,  etc.,  to  the  gas-holder.  In  this 
case,  however,  there  is  no  ammonia  to  be  removed. 

The  specific  gravity  01  water-gas  increases  with  the  increase  of  the 
heavy  hydrocarbons  which  give  illuminating  power.  The  following 
figures,  taken  from  different  authorities,  are  given  by  F.  H.  Shelton  in  a 
paper  on  "  Water-gas,"  read  before  the  Ohio  Gas  Light  Association,  in 
1894: 

Candle-power....  19.5  20.22.5  24.  25.426.3  28.3  29.6  .30  to  31. 9 
Sp.  gr.  (Air  =  l)..  .571  .630  .589  .60  to  .67  .64  .602  .70  .65  .65  to  .71 

Analyses  of  Water-gas  and  Coal-gas  Compared. 

The  following  analyses  are  taken  frorn  a  report  of  Dr.  Gideon  E. 
Moore  on  the  Granger  Water-gas,  1885: 


Composition  by  Vol. 

Composition  by  Weight. 

Water-gas. 

Coal- 
gas. 
Heidel- 
berg. 

Water-gas. 

Coal- 
gas. 

Wor-   [  Lake, 
cester.  | 

Wor- 
cester. 

Lake. 

Nitrogen           .       ... 

2.64 
0.14 
0.06 
11.29 
0.00 
1.53 
28.26 
18.88 
37.20 

3.85 
0.30 
0.01 
12.80 
0.00 
2.63 
23.58 
20.95 
35.88 

2.15 
3.01 
0.65 
2.55 
1.21 
1.33 
8.88 
34.02 
46.20 

0.04402 
0.00365 
0.00114 
0.18759 

0.06175 
0.00753 
0.00018 
0.20454 

0.04559 
0.09992 
0.01569 
0.05389 
0.03834 
0.07825 
0.18758 
0.41087 
0.06987 

Carbonic  acid  

Oxygen 

Ethylene  

Propylene  

Benzole  vapor      .         . 

0.07077 
0.46934 
0.17928 
0.04421 

0.11700 
0.37664 
0.19133 
0.04103 

Carbonic  oxide  

Marsh-gas  ...... 

100.00 

100.00 

100.00 

1  .00000 

1  .00000 

1  .00000 

Density:  Theory  

0.5825 
0.5915 

0.6057 
0.6018 

0.4580 

Practice  .  .  . 

B.T.U.fromlcu.ft.: 
Water  liquid  

650.1 
597.0 

688.7 
646.6 

642.0 
577.0 

vapor  

Flame-temperature,  °F  .  .  . 

5311.2 

5281.1 

5202.9 

Average  candle-power  

22.06 

26.31 

The  heating- values  (B.T.U.)  of  the  gases  are  calculated  from  the 
analysis  by  weight,  by  using  the  multipliers  given  below  (computed 
from  results  of  J.  Thomsen),  and  multiplying  tha  result  by  the  weight 
Of  1  cu.  ft.  of  the  gas  at  62°  F.,  and  atmospheric  pressure. 

The  flame- temperatures  (theoretical)  are  calculated  on  the  assumption 
Of  complete  combustion  of  the  gases  in  air,  without  excess  of  air. 

The  candle-power  was  determined  by  photometric  tests,  using  a  pres- 
sure of  l/2-in.  water-column,  a  candle  consumption  of  120  grains  of  sper- 
maceti per  hour,  and  a  meter  rate  of  5  cu.  ft.  per  hour,  the  result  being 
corrected  for  a  temperature  at  62°  F.  and  a  barometric  pressure  of  30  in. 
It  appears  that  the  candle-power  may  be  regulated  at  the  pleasure  of  the 
person  in  charge  of  the  apparatus,  the  range  of  candle-power  being  from 
20  to  29  candles,  according  to  the  manipulation  employed. 

Calorific  Equivalents  of  Constituents  of  Illuminating-gas. 

Heat-units  from  1  Ib.  Heat-units  from  1  Ib. 

Water        Water  Water        Water 

Liquid.       Vapor.  Liquid.       Vapor. 

Ethylene 21,524.4     20,134.8  Carbonic  oxide  .   4,395.6       4,395.6 

Propylene.  ..  .21,222.0     19,834.2  Marsh-gas 24,021.0     21,592.8 

Benzole  vapor  .18,954.0    17,847.0  Hydrogen 61 .524.0    51  804,0 


ILLUMINATING-  GAS. 


861 


Efficiency  of  a  Water-gas  Plant. —  The  practical  efficiency  of  an 
illuminating  water-gas  setting  is  discussed  in  a  paper  by  A.  G.  Glasgow 
(Proe.  Am.  Gaslight  Assn.,  1890)  from  which  the  following  is  abridged: 

The  results  refer  to  1000  cu.  ft.  of  unpurifiedcarburetted  gas,  reduced  to 
60°  F.  The  total  anthracite  charged  per  1000  cu.  ft.  of  gas  was  33.4  Ibs., 
ash  and  unconsumed  coal  removed,  9.9  Ibs.,  leaving  total  combustible 
consumed,  23.5  Ibs.,  which  is  taken  to  have  a  fuel-value  of  14,500  B.T.U. 
per  pound,  or  a  total  of  340,750  heat-units. 


Com- 
posi- 
tion  by 
Vol. 

Weight 

KxTcu. 
Ft. 

Com- 
posi- 
tion by 
W'ht. 

Specific 
Heat. 

I.  Carburetted  Water-gas.  . 

CO2  +  H2S 
CMH2«.  ... 
CO  
CH4  
H... 

3.8 
14.6 
28.0 
17.0 
35.6 

.465842 
1.139968 
2.1868 
.75854 
.1991464 

0.09647 
.23607 
.45285 
.15710 
.04124 

0.02088 
.0872H 
.11226 
.09314 
.14041 

N  

1.0 

.078596 

.01627 

.00397 

100.0 

4.8288924 

1.00000 

.45786 

CO2  
CO... 

3.5 

43.4 

.429065 
3.389540 

.1019 
.8051 

.02205 
.19958 

II.  Uncarburetted  gas  

H  

51.8 

.289821 

.0688 

.23424 

N  

1.3 

.102175 

.0242 

.00591 

100.0 

4.210601 

1.0000 

.46178 

CO2... 

17.4 

2.133066 

.2464 

.05342 

III.  Blast  products  escap- 

o 

3.2 

.2856096 

.0329 

.00718 

ing  from  superheater  .  . 

N  

79.4 

6.2405224 

.7207 

.17585 

100.0 

8.6591980 

1.0000 

.23645 

CO2... 

9.7 

1.189123 

.1436 

.031075 

CO 

17.8 

1.390180 

.1680 

.041647 

IV.  Generator  blast-gases.  . 

N  

72.5 

5.698210 

.6884 

.167970 

100.0 

8.277513 

1.0000 

.240692 

The  heat-energy  absorbed  by  the  apparatus  is  23.5  X  14,500  =  340,750 
heat-units  =  A.     Its  disposition  is  as  follows* 
J3,  the  energy  of  the  CO  produced; 

C,  the  energy  absorbed  in  the  decomposition  of  the  steam; 

D,  the  difference  between  the  sensible  heat  of  the  escaping  iauminating- 
gases  and  that  of  the  entering  oil; 

E,  the  heat  carried  off  by  the  escaping  blast  products; 

F,  the  heat  lost  by  radiation  from  the  shells; 

Gt  the  heat  carried  away  from  the  shells  by  convection  (air-currents); 

//,  the  heat  rendered  latent  in  the  gasification  of  the  oil; 

7,  the  sensible  heat  in  the  asn  and  unconsumed  coal  recovered  from 
the  generator. 

The  heat  equation  lsA=B+C+D+E+F+G+H+I:    A 

280 
being  known.     A  comparison  of  the  CO  in  Tables  I  and  II  show  that  j^  t 

or  64.5%  of  the  volume  of  carburetted  gas,  is  pure  water-gas,  distributed 
thus:  CO2,  2.3%;  CO,  28.0%;  H,  33.4%;  N,  0.8%;  =  64.5%.  1  Ib.  of  CO 
at  60°  F.  =  13,531  cu.  ft.  CO  per  1000  cu.  ft.  of  gas  =  280  +  13.531 
=  20.694  Ibs.  Energy  of  the  CO  =  20.694  X  4395.6  =  91,043  heat- 
units  =  B.  1  Ib.  of  H  at  60°  F.  =  189.2  cu.  ft.  H  per  M  of  gas  =  334 
•*•  189.2  =  1.7653  Ibs.  Energy  of  the  H  per  Ib.  (according  to  Thomsen, 
considering  the  steam  generated  by  its  combustion  to  be  condensed  to 
water  at  75°  F.)  =  61,524  B.T.U.  In  Mr.  Glasgow's  experiments  the 
steam  entered  the  generator  at  331°  F.;  the  heat  required  to  raise  the 
product  of  combustion  of  1  Ib.  of  H,  viz.,  8.98  Ibs.  H2O,  from  water  at  75° 
to  steam  at  331°  must  therefore  be  deducted  from  Thomsen's  figure,  or 
61,524  -  (8.98  X  1140.2)  =  51,285  B.T.U.  per  Ib.  of  H.  Energy  of 
the  H,  then,  is  1.7653  X  51,285  =  90,533  heat-units  =  C.  The  best 


shell  of  the  apparatus  gave  figures  for  the  amount  of  heat  lost  by  radia- 
tion =  12,454  heat-units  =  F,  and  by 


S62  ILLUMINATING-GAS. 

lost  due  to  the  sensible  heat  in  the  illuminating-gases,  their  temperature 
being  1450°  F.,  and  that  of  the  entering  oil  235°  F.,  is  48.29  (weight) 
X.45786  (sp.  heat)  X  1215  (rise  of  temperature)  =  26,864  heat-units  =  D. 

(The  specific  heat  of  the  entering  oil  is  approximately  that  of  the 
issuing  gas.) 

The  heat  carried  off  in  1000  cu.  ft.  of  the  escaping  blast  products  is 
86.592  (weight)  X  .23645  (sp.  heat)  X  1474°  (rise  of  temp.)  =  30,180 
heat-units:  the  temperature  of  the  escaping  blast  gases  being  1550°  F., 
and  that  of  the  entering  air  76  «F.  But  the  amount  of  the  blast  gases, 
by  registration  of  an  anemometer,  checked  by  a  calculation  from  the 
analyses  of  the  blast  gases,  was  2457  cubic  feet  for  every  1000  cubic  feet 
of  carburetted  gas  made.  Hence  the  heat  carried  off  per  M.  of  carburetted 
gas  is  30,180  X  2.457  =  74,152  heat-units  =  E. 

Experiments  made  by  a  radiometer  covering  four  square  feet  of  the 

he  amount  of  heat  lost  by  radia- 
convection =  15,696  heat-units 
» 

The  heat  rendered  latent  by  the  gasification  of  the  oil  was  found  by 
taking  the  difference  between  all  the  heat  fed  into  the  carburetter  and 
superheater  and  the  total  heat  dissipated  therefrom  to  be  12,841  heat- 
units  =  H.  The  sensible  heat  in  the  ash  and  unconsumed  coal  is  9.9  Ibs. 
X  1500°  X  .25  (sp.  ht.)  =  3712  heat-units  =  /. 

The  sum  of  all  the  items  B+C+D+E+F+G+H+I  = 
327,295  heat-units,  which  subtracted  from  the  heat-energy  of  the  com- 
bustible consumed,  340,750  heat-units,  leaves  13,455  heat-units,  or  4  per 
cent  unaccounted  for. 

Of  the  total  heat-energy  of  the  coal  consumed,  or  340,750  heat-units, 
the  energy  wasted  is  the  sum  of  items  D,  E:  F,  G,  and  7,  amounting  to 
132,878  heat-units,  or  39  per  cent;  the  remainder,  or  207,872  heat-units, 
or  61  per  cent,  being  utilized.  The  efficiency  of  the  apparatus  as  a  heat 
machine  is  therefore  61  per  cent. 

Five  gallons,  or  35  Ibs.  of  crude  petroleum,  were  fed  into  the  carburetter 
per  1000  cu.  ft.  of  gas  made;  deducting  5  Ibs.  of  tar  recovered,  leaves 
30  Ibs.  X  20,000  =  600,000  heat-units  as  the  net  heating-  value  of  the 
petroleum  used.  Adding  this  to  the  heating-value  of  the  coal,  340,750 
B.T.U.,  gives  940,750  heat-units,  of  which  there  is  found  as  heat-energy 
in  the  carburetted  gas,  as  in  the  table  below,  764,050  heat-units,  or  81 
per  cent,  which  is  the  commercial  efficiency  of  the  apparatus,  i.e.,  the 
ratio  of  the  energy  contained  in  the  finished  product  to  the  total  energy 
of  the  coal  and  oil  consumed. 


The  heating-power  per  M.  cu.  ft.  of 
the  carburetted  gas  is 
CO2      38.0 
C3H6*146.0x.  117220x21222.0=363200 
CO      280.0  x.  078100  x   4395.6=    96120 
CH4    170.0  x.  044620x24021.0-  1822  10 
H       356.0  x.  005594x61524.0  =122520 
N          10.0 

1000.0                                      764050 

The  heating-power  per  M.  of  the 
un  carburetted  gas  is 
CO2   35.0 
CO  434.0  x.  0781  00  x  4395.6=148991 
H    518.0X.  005594X61524.0-  178277 
N       13.0 

1000.0                                      327268 

The  candle-power  of  the  gas  is  31,  or  6.2  candle-power  per  gallon  of  oil 
used.  The  calculated  specific  gravity  is  .6355,  air  being  1. 

For  description  of  the  operation  of  a  modern  carburetted  water-gas 
plant,  see  paper  by  J.  Stelfox,  Eng'g,  July  20,  1894,  p.  89. 

Space  Required  for  a  Water-gas  Plant.  —  Mr.  Shelton,  taking  15 
modern  plants  of  the  form  requiring  the  most  floor-space,  figures  the 
average  floor-space  required  per  1000  cubic  feet  of  daily  capacity  as 
follows: 

Water-gas  Plants  of  Capacity          Require  an  Area  of  Floor-space  for  each 
in  24  hours  of  1000  cu.  ft.  of  about 

100,000  cubic  feet 4  square  feet. 

200,000      "        "    3.5 

400,000      "         "    2.75     " 

600,000      "         "    2  to  2.5  sq.  ft. 

7  to  10  million  cubic  feet 1.25  to  1.5  sq.  ft. 

The  heating- value  of  the  illuminants  CnH2n  is  assumed  to  equal  that 


ILLUMINATING-GAS.  863 

These  figures  include  scrubbing  and  condensing  rooms,  but  not  boiler 
and  engine  rooms.  In  coal-gas  plants  of  the  most  modern  and  compact 
forms  one  with  16  benches  of  9  retorts  each,  with  a  capacity  of  1,500,000 
cubic  feet  per  24  hours,  will  require  4.8  sq.  ft.  of  space  per  1000  cu.  ft. 
of  gas,  and  one  of  6  benches  of  6  retorts  each,  with  300,000  cu.  ft.  capacity 
per  24  hours,  will  require  6  sq.  ft.  of  space  per  1000  cu.  ft.  The  storage- 
room  required  for  the  gas-making  materials  is:  for  coal-gas,  1  cubic  foot 
of  room  for  every  232  cubic  feet  of  gas  made;  for  water-gas  made  from 
coke,  1  cubic  foot  of  room  for  every  373  cu.  ft.  of  gas  made;  and  for 
water-gas  made  from  anthracite,  1  cu.  ft.  of  room  for  every  645  cu.  ft.  of 
gas  made. 

The  comparison  is  still  more  in  favor  of  water-gas  if  the  case  is  con- 
sidered of  a  water-gas  plant  added  as  an  auxiliary  to  an  existing  coal- 
gas  plant ;  for,  instead  of  requiring  further  space  for  storage  of  coke,  part 
of  that  already  required  for  storage  of  coke  produced  and  not  at  once 
sold  can  be  cut  off,  by  reason  of  the  water-gas  plant  creating  a  constant 
demand  for  more  or  less  of  the  coke  so  produced. 

Mr.  Shelton  gives  a  calculation  showing  that  a  water-gas  of  0.625sp.  gr. 
would  require  gas-mains  eight  per  cent  greater  in  diameter  than  the  same 
quantity  coal-gas  of  0.425  sp.  gr.  if  the  same  pressure  is  maintained  at  the 
holder.  The  same  quantity  may  be  carried  in  pipes  of  the  same  diam- 
eter if  the  pressure  is  increased  in  proportion  to  the  specific  gravity. 
With  the  same  pressure  the  increase  of  candle-power  about  balances  the 
decrease  of  flow.  With  five  feet  of  coal-gas,  giving,  say,  eighteen  candle- 
power,  1  cubic  foot  equals  3.6  candle-power;  with  water-gas  of  23  candle- 
power,  1  cubic  foot  equals  4.6  candle-power,  and  4  cubic  feet  gives  18.4 
candle-power,  or' more  than  is  given  by  5  cubic  feet  of  coal-gas.  Water- 
gas  may  be  made  from  oven-coke  or  gas-house  coke  as  well  as  from  an- 
thracite coal.  A  water-gas  plant  may  be  conveniently  run  in  connection 
with  a  coal-gas  plant,  the  surplus  retort  coke  of  the  latter  being  used  as 
the  fuel  of  the  former. 

In  coal-gas  making  it  is  impracticable  to  enrich  tne  gas  to  over  twenty 
candle-power  without  causing  too  great  a  tendency  10  smoke,  but  water- 
gas  of  as  high  as  thirty  candle-power  is  quite  common.  A  mixture  of 
coal-gas  and  water-gas  of  a  higher  C.P.  than  20  can  be  advantageously 
distributed. 

Fuel- value  of  Illuminating-gas.  —  E.  G.  Love  (School  of  Mines 
Qtly,  January,  1892)  describes  F.  W.  Hartley's  calorimeter  for  determin- 
ing the  calorific  power  of  gases,  and  gives  results  obtained  in  tests  of  the 
carbureted  water-gas  made  by  the  municipal  branch  of  the  Consoli- 
dated Co.  of  New  York.  The  tests  were  made  from  time  to  time  during 
the  past  two  years,  and  the  figures  give  the  heat-units  per  cubic  foot  at 
60°  F.  and  30 'inches  pressure:  715,  692,  725,  732,  691,  738,  735,  703,  734, 
730,  731,  727.  Average,  721  heat-units.  Similar  tests  of  mixtures  of 
coal-  and  water-gases  made  by  other  branches  of  the  same  company  give 
694,  715,  684,  692,  727,  665,  695,  and  686  heat-units  per  foot,  or  an 
average  of  694.7.  The  average  of  all  these  tests  was  710.5  heat-units, 
and  this  we  may  fairly  take  as  representing  the  calorific  power  of  the 
illuminating  gas  of  New  York.  One  thousand  feet  of  this  gas,  costing 
$1.25,  would  therefore  yield  710,500  heat-units,  which  would  be  equiva- 
lent to  568,400  heat-units  for  $1.00. 

The  common  coal-gas  of  London,  with  an  illuminating  power  of  16  to 
17  candles,  has  a  calorific  power  of  about  668  units  per  foot,  and  costs 
from  60  to  70  cents  per  thousand. 

The  product  obtained  by  decomposing  steam  by  incandescent  carbon, 
as  effected  in  the  Motay  process,  consists  of  about  40%  of  CO,  and  a 
little  over  50%  of  H. 

This  mixture  would  have  a  heating-power  of  about  300  units  per  cubic 
foot,  and  if  sold  at  50  cents  per  1000  cubic  feet  would  furnish  600,000  units 
for  $1.00,  as  compared  with  568,400  units  for  $1.00  from  illuminating  gas 
at  $1.25  per  1000  cubic  feet.  This  illuminating-gas  if  sold  at  $1.15  per 
thousand  would  therefore  be  a  more  economical  heating  agent  than  the 
fuel-gas  mentioned,  at  50  cents  per  thousand,  and  be  much  more  advan- 
tageous than  the  latter,  in  that  one  main,  service,  and  meter  could  be  used 
to  furnish  gas  for  both  lighting  and  heating. 

A  large  number  of  fuel-gases  tested  by  Mr.  Love  gave  from  184  to  470 
heat-units  per  foot,  with  an  average  of  309  units. 

Taking  the  cost  of  heat  from  illuminating-gas  at  tlie  lowest  figure  given 


864 


ILLUMINATING-GAS . 


by  Mr.  Love,  viz.,  $1.00  for  600,000  heat-units,  it  is  a  very  expensive  fuel, 
equal  to  coai  at  $40  per  ton  of  2000  Ibs.,  the  coal  having  a,  calorific  power 
of  only  12,000  heat-units  per  pound,  or  about  83%  of  that  of  pure  carbon. 
600,000:  (12,000  X  2000)  ::  $1  :  $40. 

FLOW  OF  GAS  IN  PIPES. 

The  rate  of  flow  of  gases  of  different  densities,  the  diameter  of  pipes 
required,  etc.,  are  given  in  King's  Treatise  on  Coal  Gas,  vol.  ii,  374,  aa 
follows: 

If  d  =  diameter  of  pipe  in  inches, 
Q  =  quantity  of  gas  in  cu.  ft.  per 

hour, 

I  =  length  of  pipe  in  yards,  /, 

h  =  pressure  in  inches  of  water, 
s  =  specific  gravity  of  gas,  air 
being  1, 

Moiesworth  gives  Q  =  1000  y  —• 

J.  P.  Gill,  Am.  Gas-light  Jour.,  1894,  gives  Q  =  1291 


(1350)2/i' 


(1350)2^ ' 
=  1350(^2 


=  1350  V~ 


291  \  - 

'    S 


-,-    -•  d") 

This  formula  is  said  to  be  based  on  experimental  data,  and  to  make 
allowance  for  obstructions  by  tar,  water,  and  other  bodies  tending  to  check 
the  flow  of  gas  through  the  pipe. 

King's  formula  translated  into  the  form  of  the  common  formula  for  the 
flow  of  compressed  air  9r  steam  in  pipes,  Q  =  c  */(PI  —  P2)  d*>/wL,  in 
which  Q  =  cu.  ft.  per  min.,  PI  —  p*  =  difference  in  pressure  in  Ibs.  per 
sq.  in;  w  =  density  in  Ibs.  per  cu.  ft.,  L  =  length  in  ft.,  d  =  diam.  in  ins., 
gives  56.6  for  the  value  of  the  coefficient  c,  which  is  nearly  the  same  as  that 
commonly  used  (60)  in  calculations  of  the  flow  of  air  in  pipes.  For  values 
of  c  based  on  Darcy's  experiments  on  flow  of  water  in  pipes  see  Flow  of 
Steam. 

An  experiment  made  by  Mr.  Clegg,  in  London,  with  a  4-in.  pipe,  6  miles 
long,  pressure  3  in.  of  water,  specific  gravity  of  gas  0.398,  gave  a  discharge 
into  the  atmosphere  of  852  cu.  ft.  per  hour.,  after  a  correction  of  33  cu.  ft. 
was  made  for  leakage. 

Substituting  this  value,  852  cu.  ft.,  for  Q  in  the  formula  Q  =  C  Vd5ft  -4-  si, 
we  find  C,  the  coefficient,  =  997,  which  corresponds  nearly  with  the  formula 
given  by  Moiesworth. 

Wm.  Cox  (Am.  Mach.,  Mar.  20,  1902)  gives  the  following  formula  for 
flow  of  gas  in  long  pipes. 


Q  _  3000 


Q=  discharge  in  cu.  ft.  per  hour  at  atmospheric  pressure;  d  =  diam. 
of  pipe  in  ins.;  pt  =  initial  and  p%  =  terminal  absolute  pressure,  Ibs.  per 
sq.  in.;  I  =  length  of  pipe  in  feet,  L  =  length  in  miles.  For  Pi2  —  p22 
may  be  substituted  (PI  +  p2)  (Pi .  —  £2).  The  specific  gravity  of  "the 
gas  is  assumed  to  be  0.65,  air  being  1.  For  fluids  of  any  other  sp.  gr., 
s,  multiply  the  coefficients  3000  or  41.3  by  V0.65/S.  For  air,  s  =  1,  the 
coefficients  become  2419  and  33.3.  J.  E.  Johnson  Jr.'s  formula  for  air, 
page  619,  translated  into  the  same  notation  as  Mr.  Cox's,  makes  the  coeffU 
cients  2449  and  33.5. 

Services  for  Lamps.    (Moiesworth.) 


Lamps. 

Ft.  from 
Main. 

Require 
Pipe-bore. 

Lamps. 

Ft  .  from 
Main. 

Require 
Pipe-bore. 

2 

40 

3  'gin. 

15 

130 

1  in. 

4  . 

40 

1/2  in. 

20... 

150 

11/4  in. 

6 

50 

5/8  in- 

25 

180 

1  1/9  in. 

to  

too 

3/4  in. 

30  

200 

1  3/4  in. 

(In  cold  climates  no  service  less  than  3/4  in.  shouH  te  used,) 


FLOW   OF   GAS   IN   PIPES. 


865 


Factors  for  Reducing  Volumes  of  Gas  to  Equivalent  Volumes  at 
60°  F.  and  30-inches  Barometer. 

(Multiply  the  observed  volume  by  the  factor  to  obtain  the 
equivalent  volume.) 


d^ 

Barometer. 

II 

HQ 

30.0 

29.8 

29.6 

29.4 

29.2 

29.0 

28.8 

28.6 

28.4 

28.2 

28.0 

-30 

2095 

1  2014 

1934 

1853 

1772 

1692 

1611 

1530 

1450 

1  1369 

1  1288 

-25 

.1956  1.1876 

.1796 

.1716 

.1637 

.1557 

.1476 

.1398 

.1318 

.1238 

.1159 

-20 

18201  1741 

1662 

1583 

1505 

1426 

1347 

1268 

1189 

1111 

1032 

-15 

.1687  1.1609 

.1531 

.1453 

.1375 

.1297 

.1219 

.1141 

.1064 

.0986 

.0908 

-10 

.15571.1480!  .1403 

.1326 

.1249 

.1172 

.1095 

.1018 

.0941 

.0863 

.0786 

-  5 

.14301.1354  .1277 

.1201 

.1125 

.1049 

.0973 

.0896 

.0820 

.0744 

.0668 

0 

.13061.1230!  .1155 

.1079 

.1004 

.0929 

.0853 

.0778 

.07031  .0627 

.0552 

5 

.1184;  1.1  109  .1035 

.0960 

.0885 

.0811 

.0736 

.0662 

.0587 

.0513 

.0438 

10 

.10651.0991  .0917 

.0843 

.0770 

.0696 

.0622 

.0548 

.0474 

.0401 

.0327 

15 

.09481.0875  .0802 

.0729 

.0656 

.0585 

.0510 

.0437 

.0364 

1.0291 

.0218 

20 

.0834 

1.0762  .0689 

.0617 

.0545 

.0473 

.0401 

.0328 

.0256 

1.0184 

.0112 

25 

.0722 

1.0651 

.0579 

.0508 

.0436 

.0365 

.0293 

.0222 

.0150 

1.0079 

.0007 

30 

.0613 

1.0542  .0471 

.0401 

.0330 

.0259 

.0188 

.0118 

.0047 

0.9976 

0.9905 

35 

.0506 

1.0435  .0365 

.0295 

.0225 

.0155 

.0085 

.0015 

0.9945 

.9875 

.9805 

40 

.0400 

1.0331!  .0261 

.0192 

.0123 

.0053 

0.9984 

0.9915 

.9845 

.9776 

.9707 

45 

.0297  1.0229J  .0160 

1.0091 

.0023 

0.9954 

.9885 

.9817 

.9748 

.9679 

.9611 

50 

.01961.0128  .0060 

0.9992 

0.9924 

.9856 

.9788 

.9720 

.9652 

.9584 

.9516 

55 

.0097  1.00300.9962 

.9895 

.9828 

.9761 

.9693 

.9626 

.9559 

.9491 

.9424 

60 

.00000.99331  .9867 

.9800 

.9733 

.9667 

.9600 

.9533 

.9467 

.9400 

.9333 

65 

0.9905 

.9838  .9772 

.9706 

.9640 

.9574 

.9508 

.9442 

.9376 

.9310 

.9244 

70 

.9811 

.9746  .9680 

.9615 

.9550 

.9484 

.9419 

.9353 

.9288 

.9223 

.9157 

75 

.9719 

.9655  .9590 

.9525 

.9460 

.9395 

.9331 

.9266 

.9201 

.9136 

.9071 

80 

.9629 

.9565  .9501 

.9437 

.9373 

.9308 

.9244 

.9180 

.9116 

.9052 

.8987 

85 

.9541 

.94773  .9414 

.9350 

.9286 

.9223 

.9159 

.9096 

.9032 

.8968 

.8905 

90 

.9454 

.9391 

.9328 

.9265 

.9202 

.9139 

.9076 

.9013 

.8950 

.8887 

.8824 

95 

.9369 

.9306 

.9244 

.9181 

.9119 

.9056 

.8994 

.8931 

.8869 

.8807 

.8744 

100 

.9285 

.9223 

.9161 

.9099 

.9037 

.8976 

.8914 

.8852 

.8790 

.8728 

.8666 

105 

.9203 

.9141 

.9080 

.9019 

.8957 

.8896 

.8835 

.8773 

.8712 

.8651 

.8589 

110 

.9122 

.9061 

.9000 

.8940 

.8879 

.8818 

.8757 

.8696 

.8636 

.8575 

.8514 

115 

.9043 

.8982 

.8922 

.8862 

.8801 

.8741 

.8681 

.8621 

.8560 

.8500 

.8440 

120 

.8965 

.8905 

.8845 

.8785 

.8726 

.8666  .8606 

.8546 

.8486 

.8427 

.8367 

Formula:    Equivalent  volume  =  observed  volume  X  .  .       '   >„•  X  ^r 

~~ 


Maximum  Supply  of  Gas  through  Pipes  in  cu.  ft.  per  Hour, 
Specific  Gravity  being  taken  at  0.45,  calculated  from  the 
Formula  Q  =  1000  \/d*ti TsL  ( Moles  worth .) 

LENGTH  OF  PIPE  =  10  YARDS. 


Diameter  of 


Pressure  by  the  Water-gage  in  Inches. 


Inches. 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

,:'= 

n/4 

1V2 

26 
73 
149 
260 
411 
843 

37 

103 
211 
368 
581 
1192 

46 
126 
258 
451 
711 
1460 

53 

145 
298 
521 
821 
1686 

59 
162 
333 
582 
918 
1886 

64 
187 
365 
638 
1006 
2066 

70 
192 
394 
689 
1082 
2231 

74 
205 
422 
737 
1162 
2385 

79 
218 
447 
781 
1232 
2530 

83 
230 
471 
823 
1299 
2667 

(Continued  on  p.  866) 


ILLUMINATING-  GAS. 


Maximum  Supply  of  Gas  through  Pipes  in  cu.  ft.  per  Hour, 
Specific  Gravity  being  taken  at  0.45,  calculated  from  the 
Formula  Q  =  1000  \/&h  4-  si.  (Molesworth.)— (Continued) 

LENGTH  OF  PIPE  =  100  YARDS. 


Diam. 
of  Pipe, 
Inches. 

Pressure  by  the  Water-gage  in  Inches. 

e.i 

0.2 

0.3 

0.4 

0.5 

0.75 

1.0 

1.25 

1.5 

2 

2.5 

3/4 

23 

32 

42 

46 

51 

63 

73 

81 

89 

103 

115 

1 

47 

67 

82 

94 

105 

129 

149 

167 

183 

211 

236 

M/4 

82 

116 

143 

165 

184 

225 

260 

291 

319 

368 

412 

1V> 

130 

184 

225 

260 

290 

356 

411 

459 

503 

581 

649 

2 

267 

377 

462 

533 

596 

730 

843 

943 

1033 

1193 

1333 

IVi 

466 

659 

807 

932 

1042 

1276 

1473 

1647 

1804 

2083 

2329 

3 

735 

1039 

1270 

1470 

1643 

2012 

2323 

2598 

2846 

3286 

3674 

3V2 

1080 

1528 

1871 

2161 

2416 

2958  !  3416 

3820 

4184 

4831 

5402 

4 

1508 

2133 

2613 

3017 

3373 

4131  I  4770 

5333 

5842 

6746 

7542 

LENGTH  OF  PIPE  =  1000  YARDS. 


Diam. 
of  Pipe, 
Inches. 

Pressure  by  the  Water-gage  in  Inches. 

0.5 

0.75 

1.0 

1.5 

2.0 

.  2.5 

3.0 

> 

f 

5 
6 

33 

92 
189 
329 
520 
1067 
1863 
2939 

41 
113 
231 
403 
636 
1306 
2282 
3600 

47 
130 
267 
466 
735 
1508 
2635 
4157 

58 
159 
327 
571 
900 
1847 
3227 
5091 

67 
184 
377 
659 
1039 
2133 
3727 
5879 

75 
205 
422 
737 
1162 
2385 
4167 
6573 

82 
226 
462 
807 
1273 
2613 
4564 
7200 

LENGTH  OF  PIPE  =  5000  YARDS. 


Diameter  of 
Pipe  in 
Inches. 

Pressure  by  the  Water-gage  in  Inches. 

1.0 

1.5 

2.0 

2.5 

3.0 

2 

119 

146 

169 

189 

207 

3 

329 

402 

465 

520 

569 

4 

675 

826 

955 

1067 

1168 

5 

1179 

1443 

1667 

1863 

2041 

6 

1859 

2277 

2629 

2939 

3220 

7 

2733 

3347 

3865 

4321 

4734 

8 

3816 

4674 

5397 

6034 

6610 

9 

5123 

6274 

7245 

8100 

8873 

10 

6667 

8165 

9428 

10541 

11547 

12 

10516 

12880 

14872 

16628 

18215 

Mr.  A.  C.  Humphreys  says  his  experience  goes  to  show  that  these 
tables  give  too  small  a  flow,  but  it  is  difficult  to  accurately  check  the 
tables,  on  account  of  the  extra  friction  introduced  by  rough  pipes, 
bends,  etc.  For  bends,  one  rule  is  to  allow  1/42  of  an  inch  pressure  for 
each  right-angle  bend. 

Where  there  is  apt  to  be  trouble  from  frost  it  is  well  to  use  no  service 
of  less  diameter  than  3/4  in.,  no  matter  how  short  it  may  be.  In  ex- 
tremely cold  climates  this  is  now  often  increased  to  1  in.,  even  for  a 
single  lamp.  The  best  practice  in  tUe  U.  S.  now  condemns  any  service 
less  than  3/4  in. 


STEAM.  867 

STEAM. 

The  Temperature  of  Steam  in  contact  with  water  depends  upon 
the  pressure  under  which  it  is  generated.  At  the  ordinary  atmospheric 
pressure  (14.7  Ib.  pej  sq.  in.)  its  temperature  is  212°  F.  As  the  pressure 
is  increased,  as  by  the  steam  being  generated  in  a  closed  vessel,  its  tem- 
perature, and  that  of  the  water  in  its  presence,  increases. 

Saturated  Steam  is  steam  of  the  temperature  due  to  its  pressure — 
not  superheated. 

Superheated  Steam  is  steam  heated  to  a  temperature  above  that  due 
to  its  pressure. 

Dry  Steam  is  steam  which  contains  no  moisture.  It  may  be  either 
saturated  or  superheated. 

Wet  Steam  is  steam  containing  intermingled  moisture,  mist,  or 
spray.  It  has  the  same  temperature  as  dry  saturated  steam  of  the  same 
pressure. 

Water  introduced  into  the  presence  of  superheated  steam  will  flash 
into  steam  until  the  temperature  of  the  steam  is  reduced  to  that  due  its 
pressure.  Water  in  the  presence  of  saturated  steam  has  the  same 
temperature  as  the  steam.  Should  cold  water  be  introduced,  lowering 
the  temperature  of  the  whole  mass,  some  of  the  steam  will  be  con- 
densed, reducing  the  pressure  and  temperature  of  the  remainder,  until 
equilibrium  is  established. 

Total  Heat  of  Saturated  Steam  (above  32°  F.). — According  to  Marks 
and  Davis,  the  formula  for  total  heat  of  steam,  based  on  researches 
by  Henning,  Knoblauch,  Linde  and  Klebe,  is  H  =  1150.3  +  0.3745  (t  - 
212°)  -  0.000550  (t  -  212)2,  in  which  H  is  the  total  heat  in  B.T.U.  above 
water  at  32°  F.  and  t  is  the  temperature  Fahrenheit. 

Latent  Heat  of  Steam. — The  latent  heat,  or  heat  of  vaporization,  is 
obtained  by  subtracting  from  the  total  heat  at  any  given  temperature 
the  heat  of  the  liquid,  or  total  heat  above  32°  in  water  of  the  same  tem- 
perature. 

The  total  heat  in  steam  (above  32°)  includes  three  elements: 

1st.  The  heat  required  to  raise  the  temperature  of  the  water  to  the 
temperature  of  the  steam. 

2d.  The  heat  required  to  evaporate  the  water  at  that  temperature, 
called  internal  latent  heat. 

3d.  The  latent  heat  of  volume,  or  the  external  work  done  by  the  steam 
in  making  room  for  itself  against  the  pressure  of  the  superincumbent  at- 
mosphere (or  surrounding  steam  if  inclosed  in  a  vessel) . 

The  sum  of  the  last  two  elements  is  called  the  latent  heat  of  steam. 

Heat  required  to  Generate  1  Ib.  of  Steam  from  water  at  32°  F. 

Heat-units. 

Sensible  heat,  to  raise  the  water  from  32°  to  212°  = 180.0 

Latent  heat,  1,  of  the  formation  of  steam  at  212°  = 897 . 6 

2,  of  expansion  against  the  atmospheric 
pressure,   2116.4  Ib.   per    sq.   ft.   X 
26.79  cu.  ft.  =  55,786  foot-pounds  -4- 

778= 72.8 

970.4 


Total  heat  above  32°  F 1150 . 4 

The  Heat-Unit,  or  British  Thermal  Unit.— The  old  definition  of 
the  heat-unit  (Rankine),  viz.,  the  quantity  of  heat  required  to  raise  the 
temperature  of  1  Ib.  of  water  1°  F.,  at  or  near  its  temperature  of  maxi- 
mum density  (39.1°  F.),  is  now  (1909)  no  longer  used.  Peabody  defines 
it  as  the  heat  required  to  raise  a  pound  of  water  from  62°  to  63°  F.,  and 
Marks  and  Davis  as  i/igo  of  the  heat  required  to  raise  1  Ib.  of  water  from 
32°  to  212°  F.  By  Peabody 's  definition  the  heat  required  to  raise  1  Ib.  of 
water  from  32°  to  212°  is  180.3  instead  of  180  units,  and  the  heat  of  va- 
porization at  212°  is  969.7  instead  of  970.4  units. 

Specific  Heat  of  Saturated  Steam.— When  a  unit  weight  of  saturated 
steam  is  increased  in  temperature  and  in  pressure,  the  volume  decreasing 
so  as  to  just  keep  it  saturated,  the  specific  heat  is  negative,  and  decreases 
as  temperature  increases.  (See  Wood,  Thermodynamics,  p.  147;  Pea- 
body,  Thermodynamics,  p.  93.) 


868 


'STEAM. 


Absolute  Zero. — The  value  of  the  absolute  zero  has  been  variously 
given  as  from  459.2  to  460.66  degrees  below  the  Fahrenheit  zero.  Marks 
and  Davis,  comparing  the  results  of  Berthelot  (1903) ,  Buckingham,  1907, 
and  Ross-Innes,  1908,  give  as  the  most  probable  value  — 459.64°  F. 
The  value— 460°  is  close  enough  for  all  engineering  .calculations. 

The  Mechanical  Equivalent  of  Heat. — The  value  generally  accepted, 
based  on  Rowland's  experiments,  is  778  ft.-lb.  Marks  and  Davis  give 
the  value  777.52  standard  ft.-lb.,  based  on  later  experiments,  and  on  the 
value  of  (7  =  980.665  cm.  per  sec.2,  =  32.174  ft.  per  sec.2,  fixed  by  inter- 
national agreement  (1901).  [With  this  value  of  g  and  the  mean  gram- 
calorie  being  taken  as  equivalent  to  4.1834  X  107  dyne-centimeters,  the 
equivalent  of  1  B.T.U.  is  777.54  ft.-lb.]  These  values  of  the  absolute 
zero  and  of  the  mechanical  equivalent  of  heat  have  been  used  by  Marks 
and  Davis  in  the  computation  of  their  steam  tables.  In  refined  in- 
vestigations involving  the  value  of  the  mechanical  equivalent  of  heat 
the  value  of  g  for  the  latitude  in  which  the  experiments  are  made  must 
be  considered. 

Marks  and  Davis  give  the  value  of  the  mean  gram-calorie  as  4.1834 
joules,  which  is  equivalent  to  777.54  ft.-lb.  =  1  B.T.U.  Goodenough, 
taking  1  mean  calorie  =  4.184  joules,  gives  1  mean  B.T.U.  =  777.64 
ft.-lb. 

Pressure  of  Saturated  Steam. — Holborn  and  Henning,  Zeit.  des 
Ver.  deutscher  Ingenieure,  Feb.  20,  1909,  report  results  of  measurements 
of  the  pressures  of  saturated  steam  at  temperatures  ranging  from  50°  to 
200°  C.  (112°  to  392°  F.).  Their  values  agree  closely  with  those  ob- 
tained in  1905  by  Knoblauch,  Linde  and  Klebe.  From  a  table  in  the 
article  giving  pressures  for  each  degree  from  0°  to  200°  C.,  the  following 
values  have  been  transformed  into  English  measurements  (Eng.  Digest, 
April,  1909). 


Deg.  F. 

Lb.  per  sq. 
in. 

Deg.  F. 

Lb.  per  sq. 

in. 

Deg.  F. 

Lb.  per  sq. 
in. 

32 
68 
100 

0.0885 
0.3386 
0.9462 

150 
200 
250 

3.715 
11.527 
29.819 

300 
350 
400 

66.972 
134.508 
248.856 

Volume  of  Saturated  Steam. — The  values  of  specific  volumes  of  satu- 
rated steam  are  computed  by  Clapeyron's  equation  (Marks  and  Davis's 
Tables),  which  gives  results  remarkably  close  to  those  found  in  the  ex- 
periments of  Knoblauch,  Linde  and  Klebe. 

Goodenough's  Steam  Tables.  (Properties  of  Steam  and  Ammonia, 
John  Wiley  &  Sons,  1915.) — These  tables  are  based  on  the  same  original 
data  as  those  of  Marks  and  Davis,  and  on  some  later  ones.  They  adopt 
the  same  definition  of  the  thermal  unit,  the  mean  B.T.U.  or  i/iso  of 
the  heat  required  to  raise  the  temperature  of  1  Ib.  of  water  from  32° 
to  212°  F.  The  differences  between  the  figures  given  in  the  two  sets 
of  tables  are  in  general  small ;  the  most  important  being  that  the  latent 
heat  of  steam  at  212°  F.  is  given  as  971.7  B.T.U.  instead  of  970.4,  the 
figure  given  by  Marks  and  Davis.  A  comparison  of  some  figures  from 
the  two  tables  is  given  on  p.  869,  Goodenough's  values  being  given  in 
the  upper  lines  (G),  and  Marks  and  Davis's  in  the  lower  lines  (M), 
only  the  digits  which  differ  from  those  in  the  upper  lines  being  given. 

Properties  of  Saturated  Steam  at  High  Temperatures. — (From  G.  A. 
Goodenough's  Properties  of  Steam  and  Ammonia,  1915.) 


Temp. 

o  F 

Pressure 
Lb.  per 
Sq.  in. 

Volume  of 
1  Lb., 
Cu.  ft. 

Weight  of 
1  Cu.  ft., 
Lb. 

Heat  of 
Liquid 
B.T.U. 

Heat  of 
Vapor, 
B.T.U. 

Latent 
Heat, 
B.T.U. 

600 
620 
640 
660 
680 
700 
706.3 

1540 
1784 
2057 
2361 
2699 
3075 
3200 

0.272 
0.226 
0.186 
0.151 
0.118 
0.080 
0.048 

3.68 
4.43 
5.38 
6.60 
8.5 
12.5 
20.90 

604.5 
633 
664 
700 
745 
820 
921 

1164.2 
1151 
1134 
1112 
1080 
1018 
921 

488.9 
452 
409 
358 
290 
171 
0 

STEAM 


869 


Properties  of  Saturated  Steam. 

Comparison  of  Goodenough  and  Marks  and  Davis  (see  p.  868.) 


Abso- 
lute 
Pres- 
sure. 

Tem- 
pera- 
ture 

o  p 

Total  Heat 
Above  32°. 

Latent 
Heat. 

Vol- 
ume, 
Cu.Ft. 
in 
1  Lb. 

Weight 
of 
1  Cu.Ft. 

Entropy. 

In 

Water. 

In 
Steam. 

Water. 

Vapor- 
ization. 

G. 

0.0887 

32 

0 

1073.0 

1073.0 

3296 

0.000304 

0 

2.1826 

M. 

'* 

" 

" 

.4 

.4 

4 

M 

" 

32 

G. 

0.949 

100 

68.00 

1104.6 

1036.6 

350.3 

0.002855 

0.1296 

1.8523 

M. 

11 

" 

7.97 

3.6 

5.6 

.8 

1 

5 

05 

G. 

14.7 

212 

180 

1151.7 

97f.7 

26.81 

0.03730 

0.3120 

1.4469 

M. 

" 

" 

0.4 

0.4 

.79 

2 

18 

47 

G. 

50 

281 

249.8 

1175.6 

925.9 

8.53 

0.1173 

0.4108 

1.2501 

M. 

" 

50.1 

3.6 

3.5 

5 

13 

468 

G. 

100 

327.8 

297.9 

1188.4 

890.5 

4.442 

0.2251 

0.4736 

1.1309 

M. 

" 

8.3 

6.3 

88.0 

29 

8 

43 

277 

G. 

150 

358.5 

329.8 

1194.7 

864.9 

3.020 

0.3311 

0.5131 

1.0573 

M. 

" 

" 

30.2 

3.4 

3.2 

12 

20 

42 

50 

G. 

200 

381.9 

354.5 

1198.5 

844.0 

2.292 

0.4364 

0.5426 

1.0030 

M. 

11 

" 

.9 

.1 

3,2 

0 

70 

37 

19 

G. 

250 

401.1 

374.9 

1200.6 

825.8 

1.846 

0.542 

0.5663 

0.9595 

M. 

" 

" 

5.2 

1.5 

6.3 

50 

1 

76 

600 

G. 

300 

417.5 

392.4 

1201.9 

809.4 

1.545 

0.647 

0.5863 

0.9229 

M. 

" 

M 

.7 

4.1 

11.3 

51 

5 

78 

51 

G. 

400 

444.8 

422.0 

1202.5 

780.6 

1.162 

0.860 

0.6190 

0.8631 

M. 

" 

" 

" 

8. 

6. 

70 

** 

210 

80 

G. 

500 

467.2 

446.6 

1201.7 

755.0 

0.928 

1.077 

0.6455 

0.8146 

M. 

" 

.3 

8. 

10. 

62. 

30 

80 

80 

220 

G. 

600 

486.5 

468.0 

1199.8 

731.8 

0.770 

1.30 

0.6679 

0.7735 

M. 

" 

.6 

9. 

210. 

41. 

60 

2 

700 

830 

Volume  of  Superheated  Steam.  —  Linde's  equation  (1905), 


pv  =  0.5962  T  -  p  (1  +  0.0014  p) 


in  which  p  is  in  Ib.  per  sq.  in.,  v  is  in  cu.  ft.  and  T  is  the  absolute 
temperature  on  the  Fahrenheit  scale,  has  been  used  in  the  computation 
of  Marks  and  Davis's  tables. 

Specific  Heat  of  Superheated  Steam.  —  Mean  specific  heats  from  the 
temperature  of  saturation  to  various  temperatures  at  several  pressures 
English  and  metric  units.  —  Knoblauch  and  Jakob  (from  Peabody's 
Tables). 


Kg.  per 
sq.  cm. 
Lb.  per 
sq.  in.  . 
Temp., 
sat.°C. 
Temp., 
sat.  °F. 

1 
14.2 
99 
210 

2 
28.4 
120 
248 

4 
56.9 
143 
289 

6 
85.3 
158 
316 

8 
113.3 
169 
336 

10 
142.2 
179 
350 

12 
170.6 
187 
368 

14 
199.1 
194 
381 

16 
227.5 
200 
392 

18 
256.0 
206 
403 

20 
284.4 
211 
412 

°F. 
212 
302 
392 
482 
572 
662 
752 

o  r~* 

100 
150 
200 
250 
300 
350 

0.463 
.462 
.462 
.463 
.464 
.468 

0.478 
.475 
.474 
.475 
.477 

0.515 
.502 
.495 
.492 
.492 

0.530 
.514 
.505 
.503 

0.560 
.532 
.517 
.512 

0.597 
.552 
.530 
.522 

0.635 
.570 
.541 
.529 

0.677 
.588 
.550 
536 

0.609 
.561 
543 

0.635 
.572 
550 

0.664 
.585 
557 

.473 

.481 

.494  .504 

.512 

.520 

.526 

.531 

.537 

.542 

.547 

870 


STEAM. 


Properties  of  Superheated  Steam.  —  See  the  table  on  page  875,  con- 
densed from  Marks  and  Davis's  tables. 

The  Specific  Density  of  Gaseous  Steam,  that  is,  steam  considerably 
superheated,  is  0.622,  that  of  air  being  1.  That  is  to  say,  the  weight  of  a 
cubic  foot  of  gaseous  steam  is  about  five-eighths  of  that  of  a  cubic  foot  of 
air,  of  the  same  pressure  and  temperature. 

The  density  or  weight  of  a  cubic  foot  of  gaseous  steam  is  expressible  by 
the  same  formula  as  that  of  air,  except  that  the  multiplier  or  coefficient 
is  less  in  proportion  to  the  less  specific  density.  Thus, 

1.684  p 
£+460' 


n= 


£+460 

in  which  D  is  the  weight  of  a  cubic  foot,  p  the  total  pressure  per  square 
inch  and  t  the  temperature  Fahrenheit.  (Clark's  "Steam-engine.) 

H.  M.  Prevost  Murphy  (Eng.  News,  June  18,  1908)  shows  that  the 
specific  density  is  not  a  constant,  but  varies  with  the  temperature,  and 

n  OQS*/ 
that  the  correct  value  is  0.6113  +  ^      / 

ooO  —  t 

The  Rationalization   of   Regnault's    Experiments   on   Steam.  — 

(J.  McFarlane  Gray,  Proc.  Inst.  M.  E.,  July,  1889.)  —  The  formulae  con- 
structed by  Regnault  are  strictly  empirical,  and  were  based  entirely  on 
his  experiments.  They  are  therefore  not  valid  beyond  the  range  of  tem- 
peratures and  pressures  observed. 

Mr.  Gray  has  made  a  most  elaborate  calculation,  based  not  on  experi- 
ments but  on  fundamental  principles  of  thermodynamics,  from  which  he 
deduces  formulae  for  the  pressure  and  total  heat  of  steam,  and  presents 
•  tables  calculated  therefrom  which  show  substantial  agreement  with 
Regnault's  figures.  He  gives  the  following  examples  of  steam-pressures 
calculated  for  temperatures  beyond  the  range  of  Regnault's  experiments. 


Temperature. 

Pounds  per 
Sq.  In. 

Temperature. 

Pounds  per 
Sq.  In. 

C. 

Fahr. 

C. 

Fahr. 

230 
240 
250 
260 
280 
300 
320 

446 
464 
482 
500 
536 
572 
608 

406.9 
488.9 
579.9 
691.6 
940.0 
1261.8 
1661.9 

340 
360 
380 
400 
415 
427 

644 
680 
716 
752 
779 
800.6 

2156.2 
2742.5 
3448.1 
4300.2 
5017.1 
5659.9 

These  pressures  are  higher  than  those  obtained  by  Regnault's 
formula,  which  gives  for  415°  C.  only  4067.1  Ibs.  per  square  inch. 

Available  Energy  in  Expanding  Steam.  —  Rankine  Cycle.  (J.  B. 
Stanwood,  Power,  June  9,  1908.)  —  A  simple  formula  for  finding,  with  the 
aid  of  the  steam  and  entropy  tables,  the  available  energy  per  pound  ol 
steam  in  B.T.U.  when  it  is  expanded  adiabatically  from  a  higher  to  a 
lower  pressure  is: 

U  =  H  -  Hi  +  T  (Ni  -  N). 

U  —  available  B.T.U.  in  1  Ib.  of  expanding  steam;  H  and  Hi  total  heat 
in  1  Ib.  steam  at  the  tw9  pressures;  T  =  absolute  temperature  at  the 
lower  pressure;  N  —  Ni,  difference  of  entropy  of  1  Ib.  of  steam  at  the  two 
pressures. 

EXAMPLE.  —  Required  the  available  B.T.U.  in  1  Ib.  steam  expanded 
from  100  Ibs.  to  14.7  Ibs.  absolute.  H  =  1186.3;  Hi  =  1150.4;  T  =  672; 
N  =  1.602;  Ni  =  1.756.  35.9  +  103.5  =  138.4. 

Efficiency  of  the  Cycle.  —  Let  the  steam  be  made  from  feed-water  at 
212°.  Heat  required  =  1186.3  —  180  —  1006.3;  efficiency  =  138.4  •*• 
1006.3  =  0.1375. 

Rankine  Cycle. — This  efficiency  is  that  of  the  Rankine  cycle,  which 
assumes  that  the  steam  is  expanded  adiabatically  to  the  exhaust  pres- 
sure and  temperature,  and  that  the  feed-water  from  which  the  steam  is 
made  is  introduced  into  the  system  at  the  temperature  of  the  exhaust. 
Carnot  Cycle. — The  Carnot  ideal  cycle,  which  assumes  that  all  the 
heat  entering  the  system  enters  at  the  highest  temperature,  and  in  which 
the  efficiency  is  (Ti  -  T2)  +  Ti,  gives  (327.8  -  212)  +  (327.8  +  460)  = 
0.1470  and  the  available  energy  in  B.T.U.  =  0.1470  X  1006.3  =  147.9  B.T.U. 


$71 
Properties  of  Saturated  Steam. 

(Condensed  from  Marks  and  Davis's  Steam  Tables  and  Diagrams,  1909, 
by  permission  of  the  publishers,  Longmans,  Green  &  Co.) 


2 

£  d" 

Total  Heat 

^ni 

U«g 

O 

4 

iP 

«.  . 

above  32°  F  . 

*r"i 

£° 

53 

I 

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1     3 

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S  w 

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£6si 

W 

K 

29.74 

0.0886 

32 

0.00 

1073.4 

1073.4 

3294 

0.000304 

0.0000 

2.1832 

29.67 

0.1217 

40 

8,05 

1076.9 

1068.9 

2438 

0.000410 

0.0162 

2.1394 

29.56 

0.1780 

50 

18.08 

1081.4 

1063.3 

1702 

0.000587 

0.0361 

2.0865 

29.40 

0.2562 

60 

28.08 

1085.9 

1057.8 

1208 

0.000828 

0.0555 

2.0358 

29.13 

0.3626 

70 

38.06 

1090.3 

1052.3 

871 

0.001148 

0.0745 

1.9868 

28.39 

0.505 

80 

48.03 

1094.8 

1046.7 

636.8 

0.001570 

0.0932 

1  .9398 

28.50 

0.696 

90 

58.00 

1099.2 

1041.2 

469.3 

0.002131 

0.1114 

1  .8944 

28.00 

0.946 

100 

67.97 

1103.6 

1035.6 

350.8 

0.002851 

0.1295 

1.8505 

27.88 

1 

101.83 

69.8 

1104.4 

1034.6 

333.0 

0.00300 

0.1327 

1.8427 

25.85 

2 

126.15 

94.0 

1115.0 

1021.0 

173.5 

0.00576 

0.1749 

1.7431 

23.81 

3 

141.52 

109.4 

1121.6 

1012.3 

118.5 

0.00845 

0.2008 

1.6840 

21.78 

4 

153.01 

120.9 

1126.5 

1005.7 

90.5 

0.01107 

0.2198 

.6416 

19.74 

3 

162.28 

130.1 

1130.5 

1000.3 

73.33 

0.01364 

0.2348 

1.6084 

17.70 

6 

170.06 

137.9 

1133.7 

995.8 

61.89 

0.01616 

0.2471 

.5814 

15.67 

7 

176.85 

44.7 

1136.5 

991.8 

53.56 

0.01867 

0.2579 

.5582 

13.63 

8 

182.86 

50.8 

1139.0 

988.2 

47.27 

0.02115 

0.2673 

.5380 

11.60 

9 

188.27 

56.2 

1141.1 

985.0 

42.36 

0.02361 

0.2756 

.5202 

9.56 

10 

193.22 

61.1 

1143.1 

982.0 

38.38 

0.02606 

0.2832 

.5042 

7.52 

11 

197.75 

65.  Z 

1144.9 

979.2 

35.10 

0.02849 

0.2902 

.4895 

5.49 

12 

201  .96 

69.9 

1146.5 

976.6 

32.36 

0.03090 

0.2967 

.4760 

3.45 

13 

205.87 

73.8 

1148.0 

974.2 

30.03 

0.03330 

0.3025 

.4639 

1.42 

14 

209.55 

77.5 

1149.4 

971.9 

28.02 

0.03569 

0.3081 

.4523 

Ibs. 

gage. 

14.70 

212 

80.0 

1150.4 

970.4 

26.79 

0.03732 

0.3118 

.4447 

0.3 

15 

213.0 

81.0 

1150.7 

969.7 

26.27 

0.03806 

0.3133 

.4416 

1.3 

16 

216.3 

84.4 

1152.0 

967.6 

24.79 

0.04042 

0.3183 

.4311 

2.3 

17 

219.4 

87.5 

1153.1 

965.6 

23.38 

0.04277 

0.3229 

.4215 

3.3 

18 

222.4 

90.5 

1154.2 

963.7 

22.16 

0.04512 

0.3273 

.4127 

4.3 

19 

225.2 

93.4 

1155.2 

961.8 

21.07 

0.04746 

0.3315 

.4045 

5.3 

20 

228.0 

96.1 

1156.2 

960.0 

20.08 

0.04980 

0.3355 

.3965 

6.3 

21 

230.6 

98.8 

1157.1 

958.3 

19.18 

0.05213 

0.3393 

.3887 

7.3 

22 

233.1 

201.3 

1158.0 

956.7 

18.37 

0.05445 

0.3430 

.3811 

8.3 

23 

235.5 

203.8 

1158.8 

955.1 

17.62 

0.05676 

0.3465 

.3739 

9.3 

24 

237.8 

206.1 

1159.6 

953.5 

16.93 

0.05907 

0.3499 

.3670 

10.3 

25 

240.1 

208.4 

1160.4 

952.0 

16.30 

0.0614 

0.3532 

.3604 

11.3 

26 

242.2 

210.6 

1161.2 

950r6 

15.72 

0.0636 

0.3564 

.3542 

12.3 

27 

244.4 

212.7 

1161.9 

949.2 

15.18 

0.0659 

0.3594 

.3483 

13.3 

28 

246.4 

214.8 

1162.6 

947.8 

14.67 

0.0682 

0.3623 

.3425 

14.3 

29 

248.4 

216.8 

1163.2 

946.4 

14.19 

0.0705 

0.3652 

.3367 

15.3 

30 

250.3 

18.8 

1163.9 

945.1 

13.74 

0.0728 

0.3680 

.3311 

16.3 

31 

252.2 

20.7 

1164.5 

943.8 

13.32 

0.0751 

0.3707 

.3257 

17.3 

32 

254.1 

22.6 

1165.1 

942.5 

12.93 

0.0773 

0.3733 

.3205 

18.3 

33 

255.8 

24.4 

1165.7 

941.3 

12.57 

0.0795 

0.3759 

.3155 

19.3 

34 

257.6 

26.2 

1166.3 

940.1 

12.22 

0.0818 

0.3784 

.3107 

20.3 

35 

259,3 

27.9 

1166.8 

938.9 

11.89 

0.0841 

0.3808 

.3060 

21.3 

36 

261,0 

29.6 

1167.3 

937.7 

11.58 

0.0863 

0.3832 

.3014 

22.3 

37 

262.6 

31.3 

1167.8 

936.6 

11.29 

0.0886 

0.3855 

.2969 

23.3 

38 

264.2 

32.9 

1168.4 

935.5 

11.01 

0.0908 

0.3877 

.2925 

24.3 

39 

265.8 

34.5 

1168.9 

934.4 

10.74 

0.0931 

0.3899 

.2882 

25.3 

40 

267.3 

36.1 

1169.4 

933.3 

10.49 

0.0953 

0.3920 

.2841 

41 

268.7 

37.6 

1169.8 

932.2 

10.25 

0.0976 

0.3941 

.2800 

27.3 

42 

270.2 

39.1 

1170.3 

931.2 

10.02 

0.0998 

0.3962 

1.2759 

28.3 

43 

271.7 

40.5 

1170.7 

930.2 

9.80 

0.1020 

0.3982 

1.2720 

29.3 

44 

273.1 

42.0 

1171.2 

929.2 

9.59 

0.1043 

0.4002 

1.2681 

30.3 

45 

274.5 

43.4 

1171.6 

928.2 

9.39 

0.1065 

0.4021 

1.2644 

872 


Properties  of  Saturated  Steam.    (Continued.) 


£  a* 

gd 

Total  Heat 

^J5> 

0) 

4,    * 

1? 

B 

II 

above  32°  F. 

|| 

£"8 

53 

£ 

£     -^ 

5     « 
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§       3 

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"^3  ii  £D 

"o-Scc 

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c£ 

O 

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H 

£     ^ 

£    W 

H 

> 

^ 

H 

W 

31.3 

46 

275.8    1244.8 

1172.0 

927.2 

9.20 

0.1087 

0.4040 

1.2607 

32.3 

47 

277.2 

246.1 

1172.4 

926.3 

9.02 

0.1109 

0.4059 

.2571 

33.3 

48 

278.5 

247.5 

1172.8 

925.3 

8.84 

0.1131 

0.4077 

.2536 

34.3 

49 

279.8 

248.8 

1173.2 

924.4 

8.67 

0.1153 

0.4095 

.2502 

35.3 

50 

281.0 

250.1 

1173.6 

923.5 

8.51 

0.1175 

0.4113 

.2468 

36.3 

51 

282.3 

251.4 

1174.0 

922.6 

8.35 

0.1197 

0.4130 

.2432 

37.3 

52 

283.5 

252.6 

1174.3 

921.7 

8.20 

0.1219 

0.4147 

.2405 

38.3 

53 

284.7 

253.9 

1174.7 

920.8 

8.05 

0.1241 

0.4164 

.2370 

39.3 

54 

285.9 

255.1 

1175.0 

919.9 

7.91 

0.1263 

0.4180 

.2339 

40.3 

55 

287.1 

256.3 

1175.4 

919.0 

7.78 

0.1285 

0.4196 

.2309 

41.3 

56 

288.2 

257.5 

1175.7 

918.2 

7.65 

0.1307 

0.4212 

.2278 

42.3 

57 

289.4 

258.7 

1176.0 

917.4 

7.52 

0.1329 

0.4227 

.2248 

43.3 

58 

290.5 

259.8 

1176.4 

916.5 

7.40 

0.1350 

0.4242 

.2218 

44.3 

59 

291.6 

261.0 

1176.7 

915.7 

7.28 

0.1372 

0.4257 

.2189 

45.3 

60 

292.7 

262.1 

1177.0 

914.9 

7.17 

0.1394 

0.4272 

.2160 

46.3 

61 

293.8 

263.2 

1177.3 

914.1 

7.06 

0.1416 

0.4287 

.2132 

47.3 

62 

294.9 

264.3 

1177.6 

913.3 

6.95 

0.1438 

0.4302 

.2104 

48.3 

63 

295.9 

265.4 

1177.9 

912.5 

6.85 

0.1460 

0.4316 

.2077 

49.3 

64 

297.0 

266.4 

1178.2 

911.8 

6.75 

0.1482 

0.4330 

.2050 

50.3 

65 

293.0 

267.5 

1178.5 

911.0 

6.65 

0.1503 

0.4344 

.2024 

51.3 

66 

29?.  0 

268.5 

1178.8 

910.2 

6  56 

0.1525 

0.4358 

1998 

52.3 

67 

300.0 

269.6 

1179.0 

909.5 

6.47 

0.1547 

0.4371 

.1972 

53.3 

68 

301.0 

270.6 

1179.3 

908.7 

6.38 

0.1569 

0.4385 

.1946 

54.3 

69  ' 

302.0 

271.6 

1179.6 

908.0 

6.29 

0.1590 

0.4398 

.1921 

55.3 

70 

302.9 

272.6 

1179.8 

907.2 

6.20 

0.1612 

0.4411 

.1896 

56.3 

71 

303.9 

273.6 

1180.1 

906.5 

6.12 

0.1634 

0.4424 

.1872 

57.3 

72 

304.8 

274.5 

1180.4 

905.8 

6.04 

0.1656 

0.4437 

.1848 

58.3 

73 

305.8 

275.5 

1180.6 

905.1 

5.96 

0.1678 

0.4449 

.1825 

59.3 

74 

306.7 

276.5 

1180.9 

904.4 

5.89 

0.1699 

0.4462 

.1801 

60.3 

75 

307.6 

277.4 

1181.1 

903.7 

5.81 

0.1721 

0.4474 

.1778 

61.3 

76 

308.5 

278.3 

1181.4 

903.0 

5.74 

0.1743 

0.4487 

.1755 

62.3 

77 

309.4 

279.3 

1181.6 

902.3 

5.67 

0.1764 

0.4499 

.1730 

63.3 

78 

310.3 

280.2 

1181.8 

901.7 

5.60 

0.1785 

0.4511 

.1712 

64.3 

79 

311.2 

281.1 

1182.1 

901.0 

5.54 

0.1808 

0.4523 

.1687 

65.3 

80 

312.0 

282.0 

1182.3 

900.3 

5.47 

0.1829 

0.4535 

.1665 

66.3 

81 

312.9 

282.9 

1182.5 

899.7 

5.41 

0.1851 

0.4546 

.1644 

67.3 

82 

313.8 

283.8 

1182.8 

899.0 

5.34 

0.1873 

0.4557 

.1623 

68.3 

83 

314.6 

284.6 

1183.0 

898.4 

5.28 

0.1894 

0.4568 

1602 

69.3 

84 

315.4 

285.5 

1183.2 

897.7 

5.22 

0.1913 

0.4579 

.'1581 

70.3 

85 

316.3 

286.3 

1183.4 

897.1 

5.16 

0.1937 

0.4590 

.1561 

71.3 

86 

317.1 

287.2 

1183.6 

896.4 

5.10 

0.1959 

0.4601 

.1540 

72.3 

87 

317.9 

288.0 

1183.8 

895.8 

5.05 

0.1980 

0.4612 

.1520 

73.3 

88 

318.7 

288.9 

1184.0 

895.2 

5.00 

0.2001 

0.4623 

.1500 

74.3 

89 

319.5 

289.7 

1184.2 

894.6 

4.94 

0.2023 

0.4633 

.1481 

75.3 

90 

320.3 

290.5 

1184.4 

893.9 

4.89 

0.2044 

0  4644 

.1461 

76.3 

91 

321.1 

291.3 

1184.6 

893.3 

4.84 

0.2065 

0.4554 

.1442 

77.3 

92 

321.8 

292.1 

1184.8 

892.7 

4.79 

0.2087 

0.4664 

.1423 

78.3 

93 

322.6 

292.9 

1185.0 

892.1 

4.74 

0.2109 

0.4674 

1404 

79.3 

94 

323.4 

293.7 

1185.2 

891.5 

4.69 

0.2130 

0.4684 

.1385 

80.3 

95 

324.1 

294.5 

1185.4 

890.9 

4.65 

0.2151 

0.4694 

1367 

81.3 

96 

324.9 

295.3 

1185.6 

890.3 

4.60 

0.2172 

0.4704 

.1348 

82.3 

97 

325.6 

296.1 

1185.8 

889.7 

4.56 

0.2193 

0.4714 

.1330 

83.3 

98 

326.4 

296.8 

1186.0 

889.2 

4.51 

0.2215 

0.4724 

.1312 

84.3 

99 

327.1 

297.6 

1186.2 

888.6 

4.47 

0.2237 

0.4733 

.1295 

85.3 

100' 

327.8 

298.3 

1186.3 

888.0 

4.429 

0.2258 

0.4743 

.1277 

87.3 

102 

329.3 

299.8 

1186.7 

886.9 

4.347 

0.2300 

0.4762 

.1242 

89.3 

104 

330.7 

301.3 

1187.0 

885.8 

4.268 

0.2343 

0.4780 

.1208 

Properties  of  Saturated  Steam.    (Continued.) 


873 


a?  . 

8"d 

Total  Heat 

1^4. 

. 

o 

i, 

£  d 

above32°F. 

^.8 

£"8 

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£ 

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91.3 

106 

332.0 

302.7 

1187.4 

884.7 

4.192 

0.2336 

0.4798 

.117 

93.3 

108 

333.4 

304.1 

1187.7 

883.6 

4.118 

0.2429 

0.4816 

.114 

95.3 

110 

334.8 

305.5 

1188.0 

882.5 

4.047 

0.2472 

0.4834 

.110 

97.3 

112 

336.  1 

306.9 

1188.4 

881.4 

3.978 

0.2514 

0.4852 

.107 

99.3 

114 

337.4 

308.3 

1188.7 

880.4 

3.912 

0.2556 

0.4869 

.104 

101.3 

116 

338.7 

309.6 

1189.0 

879.3 

3.848 

0.2599 

0.4886 

.101 

103.3 

118 

340.0 

311.0 

1189.3 

878.3 

3.786 

0.2641 

0.4903 

.098 

105.3 

120 

341.3 

312.3 

1189.6 

877.2 

3.726 

0.2683 

0.4919 

.095 

107.3 

122 

342.5 

313.6 

1189.8 

876.2 

3.668 

0.2726 

0.4935 

.092 

109.3 

124 

343.8 

314.9 

1190.1 

875.2 

3.611 

0.2769 

0.4951 

.089 

111.3 

126 

345.0 

316.2 

1190.4 

874.2 

3.556 

0.2812 

0.4967 

.086 

113.3 

128 

346.2 

317.4 

1190.  7 

873.3 

3.504 

0.2854 

0.4982 

.083 

115.3 

130 

347.4 

318.6 

1191.0 

872.3 

3.452 

0.2897 

0.4998 

.080 

117.3 

132 

348.5 

319.9 

1191.2 

871.3 

3  402 

0.2939 

0.5013 

.078 

119.3 

134 

349.7 

321.1 

1191.5 

870.4 

3.354 

0.2981 

0.5028 

.075 

121.3 

136 

350.8 

322.3 

1191.7 

869.4 

3.308 

0.3023 

0.5043 

.072 

123.3 

138 

352.0 

323.4 

1192.0 

868.5 

3.263 

0.3065 

0.5057 

.070 

125.3 

140 

353.  1 

324.6 

1192.2 

867.6 

3.219 

0.3107 

0.5072 

.067 

127.3 

142 

354.2 

325.8 

1192.5 

866.7 

3.175 

0.3150 

0.5086 

.064 

129.3 

144 

355.3 

326.9 

1192.7 

865.8 

3.133 

0.3192 

0.5100 

.062 

131.3 

146 

356.3 

328.0 

1192.9 

864.9 

3.092 

0.3234 

0.5114 

.059 

133.3 

148 

357.4 

329.1 

1193.2 

864.0 

3.052 

0.3276 

0.5128 

.057 

135.3 

150 

358.5 

330.2 

1193.4 

863.2 

3.012 

0.3320 

0.5142 

.055 

137.3 

152 

359.5 

331.4 

1193.6 

862.3 

2.974 

0.3362 

0.5155 

.052 

139.3 

154 

360.5 

332.4 

1193.8 

861.4 

2.938 

0.3404 

0.5169 

.050 

141.3 

156 

361.6 

333.5 

1194.1 

860.6 

2.902 

0.3446 

0.5182 

.047 

143.3 

158 

362.6 

334.6 

1194.3 

859.7 

2.868 

0.3488 

0.5195 

.045 

145.3 

160 

363.6 

335.6 

1194.5 

858.8 

2.834 

0.3529 

0.5208 

.043 

147.3 

162 

364.6 

336.7 

1194.7 

858.0 

2.801 

0  3570 

0.5220 

.040 

149.3 

164 

365.6 

337.7 

1194.9 

857.2 

2.769 

0.3612 

0.5233 

.038 

151.3 

166 

366.5 

338.7 

1195.1 

856.4 

2.737 

0.3654 

0.5245 

.036 

153.3 

168 

367.5 

339.7 

1195.3 

855.5 

2.706 

0.3696 

0.5257 

.034 

155.3 

170 

368.5 

340.7 

1195.4 

854.7 

2.675 

0.3738 

0.5269 

.032 

157.3 

172 

369.4 

341.7 

1195.6 

853.9 

2.645 

0.3780 

0.5281 

.030 

159.3 

174 

370.4 

342.7 

1195.8 

853.1 

2.616 

0.3822 

0.5293 

.027 

161.3 

176 

371.3 

343.7 

1196.0 

852.3 

2.588 

0.3864 

0.5305 

.025 

163.3 

178 

372.2 

344.7 

1196.2 

851.5 

2.560 

0.3906 

0.5317 

.023 

165.3 

180 

373.1 

345.6 

1196.4 

850.8 

2.533 

0.3948 

0.5328 

.021 

167.3 

182 

374.0 

346.6 

1196.6 

850.0 

2.507 

0.3989 

0.5339 

.019 

169.3 

184 

374.9 

347.6 

1196.8 

849.2 

2.481  . 

0.4031 

0.5351 

.017 

171.3 

186 

375.8 

348.5 

1196.9 

848.4 

2.455 

0.4073 

0.5362 

.015 

173.3 

183 

376.7 

349.4 

1197.1 

847.7 

2.430 

0.4115 

0.5373 

.013 

175.3 

190 

377.6 

350.4 

1197.3 

846.9 

2.406 

0.4157 

0.5384 

.Oil 

177.3 

192 

378.5 

351.3 

1197.4 

846.1 

2.381 

0.4199 

0.5395 

.009 

179.3 

194 

379.3 

352.2 

1197.6 

845.4 

2.358 

0.4241 

0.5405 

.007 

181.3 

196 

380.2 

353.1 

1197.8 

844.7 

2.335 

0.4283 

0.5416 

.005< 

183.3 

198 

381.0 

354.0 

1197.9 

843.9 

2.312 

0.4325 

0.5426 

.0031 

185.3 

200 

381.9 

354.9 

1198.1 

843.2 

2.290 

0.437 

0.5437 

.001 

190.3 

205 

384.0 

357.1 

1198.5 

841.4 

2.237 

0.447 

0.5463 

0.997 

195.3 

210 

386.0 

359.2 

1198.8 

839.6 

2.187 

0.457 

0.5488 

0.992 

200.3 

215 

388.0 

361.4 

1199.2 

837.9 

2.138 

0.468 

0.5513 

0.988 

205.3 

220 

389.9 

363.4 

1199.6 

836.2 

2.091 

0.478 

0.5538 

0.984 

210.3 

225 

391.9 

365.5 

1199.9 

834.4 

2.046 

0.489 

0.5562 

0.979 

215.3 

230 

393.8 

367.5 

1200.2 

832.8 

2.004 

0.499 

0.5586 

0.975 

220.3 

235 

395.6 

369.4 

1200.6 

831.1 

1.964 

0.509 

0.5610 

0.971 

225.3 

240 

397.4 

371.4 

1200.9 

829.5 

1.924 

0.520 

0.5633 

0.967 

230.3 

245 

399.3 

373.3 

1201.2 

827.9 

1.887 

0.530 

0.5655 

0.963 

874 


Properties  of  Saturated  Steam.    (Continued.) 


£  " 

tfd 

Total  Heat 

•^  ' 

0) 

D, 

S  • 

1^ 

oT-tJ 

above  32°  F. 

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£^ 

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5    S 

-5    8 

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g.-co 

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1 

c  o 
W 

235.3 

250 

401.1 

375.2 

1201.5 

826.3 

1.850 

0.541 

0.5676 

0.9600 

245.3 

260 

404.5 

378.9 

1202.1 

823.1 

1.782 

0.561 

0  5719 

0  9525 

255.3 

270 

407.9 

382.5 

1202.6 

820.1 

.718 

0.582 

0  5760 

0.9454 

265.3 

280 

411.2 

386.0 

1203.1 

817.  f 

.658 

0.603 

0.5800 

0.9385 

275.3 

290 

414.4 

389.4 

1203.6 

814.2 

.602 

0.624 

0.5840 

0  9316 

285.3 

300 

417.5 

392.7 

1204.1 

811.3 

.551 

0.645 

0  5878 

0.9231 

295.3 

310 

420.5 

395.9 

1204.5 

808.5 

.502 

0.666 

0.5915 

0.9187 

305.3 

320 

423.4 

399.1 

1204.9 

805.8 

.456 

0.687 

0.5951 

0.9125 

315.3 

330 

426.3 

402.2 

1205.3 

803.1 

.413 

0.708 

0.5986 

0  9065 

325.3 

340 

429.1 

405.3 

1205.7 

800.4 

.372 

0.729 

0.6020 

0  9006 

335.3 

350 

431.9 

408.2 

1206.1 

797.8 

.334 

0.750 

0.6053 

0.8949 

345.3 

360 

434.6 

411.2 

1206.4 

795.3 

.298 

0.770 

0.6085 

0.8894 

355.3 

370 

437.2 

414.0 

1206.8 

792.8 

.264 

0.791 

0.6116 

0.8840 

365.3 

380 

439.8 

416.8 

1207.1 

790.3 

.231 

0.812 

0.6147 

0.8788 

375.3 

390 

442.3 

419.5 

1207.4 

787.9 

.200 

0.833 

0.6178 

0.8737 

385.3 

400 

444.8 

422 

1208 

786 

.17 

0.86 

0.621 

0.868 

435.3 

450 

456.5 

435 

1209 

774 

.04 

0.96 

0.635 

0  844 

485.3 

500 

467.3 

448 

1210 

762 

0.93 

1.08 

0.648 

0.822 

535.3 

550 

477.3 

459 

1210 

751 

0.83 

1.20 

0.659 

0.801 

585.3 

600 

486.6 

469 

1210 

741 

0.76 

1.32 

0.670 

0.783 

Properties  of  Superheated  Steam,  Marks  &  Davis  and  Goodenough 
Compared. 

v  =  volume,  cu.  ft.  per  lb.;  h  =  total  heat  above  32°  F.;  n  =  entropy. 

The  figures  in  the  upper  lines  are  from  Marks  and  Davis 's  tables, 
those  in  the  lower  lines  (the  differing  digits  only  being  given)  are  inter- 
polated from  Goodenough 's  tables,  in  which  the  figures  are  for  steam 
of  given  temperatures,  not  even  degrees  of  superheat. 


Abso- 
lute 
Pres- 
sure. 

Temp. 

Sat. 
Steam. 

Superheat,  Degrees  Fahrenheit. 

50 

100 

150 

200 

250 

300 

400 

500 

20 

228.0 

V       21.69 

23.25 

24.80 

26.33 

27.85 

29.37 

32.39 

35.40 

8 

3 

.77 

.29 

1 

1 

1 

30 

h      1179.9 

1203.5 

1227.1 

1250.6 

1274.1 

1297.6 

1344.8 

1392.2 

7.3 

6.0 

9.8 

3.5 

7.0 

300.7 

8.5 

7.0 

n     K7652 

1.7961 

1.8251 

1.8524 

1.8781 

1.9026 

1.9479 

1.9893 

86 

8000 

92 

64 

823 

69 

530 

956 

100 

327.8 

V       4.79 

5.14 

5.47 

5.80 

6.12 

6.44 

7.07 

7.69 

" 

3 

6 

.79 

0 

1 

3 

4 

h      1213.8 

1239.7 

1264.7 

1289.4 

1313.6 

1337.8 

1385.9 

1434.1 

5.9 

42.5 

8.3 

93.6 

8.7 

43.7 

93.6 

43.9 

n     1.6358 

1.6658 

1.6933 

1.7188 

1.7428 

1.7656 

1.8079 

1.8468 

84 

91 

74 

235 

84 

720 

159 

566 

200 

381.9 

V         2.49 

2.68 

2.86 

3.04 

3.21 

3.38 

3.71 

.50 

9 

5 

2 

.18 

4 

.66 

h     1229.8 

1257.1 

1282.6 

1307.7 

1332.4 

1357.0 

1405.9 

I 

8.0 

5.7 

12.7 

9.0 

65.1 

16.8 

n     1.5823 

1.6120 

1.6385 

1.6632 

1.6862 

1.7082 

1.7493 

09 

5 

411 

76 

922 

156 

596 



300 

417.5 

v       1.69 

1.83 

1.96 

2.09 

2.21 

2.33 

2.55 

2 

4 

6 

.18 

.29 

0 

h      1240.3 

1268.2 

1294.0 

1319.3 

1344.3 

1369.2 

1418.6 

35.0 

5.9 

5.2 

23.3 

51.0 

78.1 

31.5 

n     1.5530 

1.5824 

1.6082 

1.6323 

1.6550 

1.6765 

1.7168 

458 

784 

76 

44 

94 

829         265 

STEAM. 


875 


Properties  of  Superheated  Steam. 

(Condensed  from  Marks  and  Davis's  Steam  Tables  and  Diagrams.) 
v  =  specific  volume  in  cu.   ft.  per  lb.,  h  =  total    heat,  from   water  at 
32°  F.  in  B.T.U.  per  lb.,  n  =  entropy,  from  water  at  32°. 


W  0> 

•°  a 

g^o? 
b 

if 

Degrees  of  Superheat. 

0 

20 

50 

100 

150 

200 

250 

300 

400 

500 

20 

228  0 

v20.08 

20.73 

21.69 

23.25 

24.80 

26.33 

27.85 

29.37 

32.39 

35.40 

h  1156.2 

1165.7 

1179.9 

1203.5 

1227.1 

1250.6 

1274.1 

1297.6 

1344.8 

1392.2 

n  1  .  7320 

1.7456 

1.7652 

1.7961 

1.8251 

1.8524 

1.8781 

1.9026 

1.9479 

1.9893 

40 

267.3 

v  10.49 

10.83 

11.33 

12.13 

12.93 

13.70 

14.48 

15.25 

16.78 

18.30 

h  1169  4 

1179.3 

1194.0 

1218.4 

1242.4 

1266.4 

1290.3 

1314.1 

1361.6 

1409.3 

n  1.6761 

1.6895 

1.7089 

1.7392 

1.7674 

1.7940 

1.8189 

1.8427 

1.8867 

1.9271 

60 

292.7 

v7.17 

7.40 

7.75 

8.30 

8.84 

9.36 

9.89 

10.41 

11.43 

12.45 

h  1177.0 

1187.3 

1202.6 

1227.6 

1252.1 

1276.4 

1300.4 

1324.3 

1372.2 

1420.0 

n  1.6432 

1.6568 

1.6761 

1  .  7062 

1.7342 

1.7603 

1.7849 

1  £081 

1.8511 

1.8908 

89 

312.0 

v5.47 

5.65 

5.92 

6.34 

6.75 

7.17 

7.56 

7>5 

8.72 

9  49 

h  1182.3 

1193.0 

1208.8 

1234.3 

1259.0 

1283.6 

1307.8 

1331.9 

1379.8 

1427.9 

11  1.6200 

1.6338 

1.6532 

1.6833 

1.7110 

1.7368 

1.7612 

1.7840 

1.8265 

1.8658 

100 

327.8 

v4.43 

4.58 

4.79 

5.14 

5.47 

5.80 

6.12 

6.44 

7.07 

7.69 

h  1186.3 

1197.5 

1213.8 

1239.7 

1264.7 

1289.4 

1313.6 

1337.8 

1385.9 

1434.1 

n  1.6020 

1.6160 

1.6358 

1.6658 

1.6933 

1.7188 

1.7428 

1.7656 

1.8079 

1.8468 

120 

341.3 

v3.73 

3.85 

4.04 

4.33 

4.62 

4.89 

5.17 

5.44 

5.96 

6.48 

h  1189.6 

1201.1 

1217.9 

1244.1 

1269.3 

1294.1 

1318.4 

1342.7 

1391.0 

1439.4 

n  1.5873 

1.6016 

1.62(6 

1.6517 

1.6789 

1.7041 

1.7280 

1.7505 

1.7924 

1.831 

(40 

353.1 

v3.22 

3.32 

3.49 

3.75 

4.00 

4.24 

4.48 

4.71 

5.16 

5.61 

h  1192.2 

1204.3 

1221.4 

1248.0 

1273.3 

1298.2 

1322.6 

1346.9 

1395.4 

1443.8 

n  1.5747 

1.5894 

1.6096 

1.6395 

1  .6666 

1.6916 

1.7152 

1.7376 

1  .  7792 

1.8177 

160 

363.6 

v2.83 

2.93 

3.07 

3.30 

3.53 

3.74 

3.95 

4.15 

4.56 

4.95 

h  1194.5 

1207.0 

1224.5 

1251.3 

1276.8 

1301.7 

1326.2 

1350.6 

1399.3 

1447.9 

n  1.5639 

1.5789 

1.5993 

1.6292 

K6561 

1.6810 

1.7043 

1.7266 

1.7680 

1.8063 

180 

373.1 

v2.53 

2.62 

2.75 

2.96 

3.16 

3.35 

3.54 

3.72 

4.09 

4.44 

h  1196.4 

1209.4 

1227.2 

1254.3 

1279.9 

1304.8 

1329.5 

1353.9 

1402.7 

1451.4 

n  1.5543 

1.5697 

1.5904 

1.6201 

1.6468 

1.6716 

1.6948 

1.7169 

1.7581 

1.7962 

200 

381.9 

v2.29 

2.37 

2.49 

2  68 

2.86 

3.04 

3.21 

3.38 

3.71 

4.03 

h  1198.1 

1211.  6 

1229.8 

1257.1 

1282.6 

1307.7 

1332.4 

1357.0 

1405.9 

1454.7 

n  1.5456 

1.5614 

1.5823 

1.6120 

1.6385 

1  .6632 

1.6862 

1.7082 

1.7493 

1.7872 

220 

389.9 

v2.09 

2.16 

2.28 

2.45 

2.62 

2.78 

2.94 

3.10 

3.40 

3.69 

h  1199.6 

1213.6 

1232.2 

1259.6 

1285.2 

1310.3 

1335.1 

1359.8 

1408.8 

1457.7 

n    .5379 

1.5541 

1.5753 

1.6049 

1.6312 

1  .6558 

1.6787 

1.7005 

1.7415 

1.7792 

240 

397.4 

v    .92 

1.99 

2.09 

2.26 

2.42 

2.57 

2.71 

2.85 

3.13 

3.40 

h    200.9 

1215.4 

1234.3 

1261.9 

1287.6 

1312.8 

1337.6 

1362.3 

1411  5 

1460.5 

n    .5309 

1.5476 

1.5690 

1.5985 

1.6246 

1.6492 

1  .6720 

1.6937 

1.7344 

1.7721 

260 

404.5 

v    .78 

1.84 

1.94 

2.10 

2.24 

2.39 

2.52 

2.65 

2.91 

3.16 

h    202.1 

1217.1 

1236.4 

1264  1 

1289.9 

1315.1 

1340.0 

1364.7 

1414.0 

1463.2 

n    .5244 

1.5416 

1.5631 

1.5926 

1.6186 

1.6430 

1.6658 

1.6874 

1.7280 

1.7655 

280 

411.2 

v    .66 

1.72 

1.81 

1.95 

2.09 

2.22 

2.35 

2.48 

2.72 

2.95 

h    203.1 

1218.7 

1238.4 

1266.2 

1291  .9 

1317.2 

1342.2 

1367.0 

1416.4 

1465.  7 

n    .5185 

1  .  5362 

1.5580 

1.5873 

1.6133 

1.6375 

1.6603 

1.6818 

1.7223 

1  7597 

300 

417.5 

v    .55 

J.60 

1.69 

1.83 

1.96 

2.09 

2.21 

2.33 

2.55 

2.77 

h    204.1 

1220.2 

1240.3 

1268.2 

1294.0 

1319.3 

1344.3 

1369.2 

1418.6 

1468.0 

n    .5129 

1.5310 

1.5530 

1.5824 

1  .6082 

1.6323 

1.6550 

1.6765 

1.7168 

1.7541 

350 

431.9 

v    .33 

1.38 

1.46 

1.58 

1.70 

1.81 

1.92 

2.02 

2.22 

2.41 

h    206.1 

1223.9 

1244.6 

1272.7 

1298.7 

1324.1 

1349.3 

1374.3 

1424.0 

1473.7 

n    .5002 

1.5199 

1.5423 

1.5715 

1.5971 

1.6210 

1  .6436 

1.6650 

1  .  7052 

1.7422 

400 

444.8 

v    .17 

1.21 

1.28 

1.40 

1.50 

1.60 

1.70 

1.79 

1.97 

2.14 

h    207.7 

1227.2 

1248.6 

1276.9 

1303.0 

1328.6 

1353.9 

1379.1 

1429.0 

1478.9 

n    .4894 

1.5107 

1.5336 

1.5625 

1.5880 

1.6117 

1.6342 

1.6554 

1.6955 

1.7323 

450 

456.5 

v    .04 

1.08 

1.14 

1.25 

1.35 

1.44 

1.53 

1.61 

1.77 

1.93 

h1209 

1231 

1252 

1281 

1307 

1333 

1358 

1383 

1434 

1484 

n  1.479 

1.502 

1.526 

1.554 

1.580 

1.603 

1.626 

1.647 

1.687 

1.723 

$00 

467.3 

vO.93 

0.97 

1.03 

1.13 

1.22 

1.31 

1.39 

1.47 

1.62 

1.76 

h  1210 

1233 

1256 

1285 

1311 

1337 

1362 

1388 

1438 

1489 

n  1.470 

1.496 

1.519 

1.548 

1.573 

1.597 

1.619 

1.640 

1.679 

1.713 

876 


STEAM. 


FLOW   OF    STEAM. 

Flow  of  Steam  through  a  Nozzle.  (From  Clark  on  the  Steam- 
engine.)  —  The  flow  of  steam  of  a  greater  pressure  into  an  atmosphere  of  a 
less  pressure  increases  as  the  difference  of  pressure  is  increased,  until  the 
external  pressure  becomes  only  58%  of  .the  absolute  pressure  in  the  boiler. 
The  flow  of  steam  is  neither  increased  nor  diminished  by  the  fall  of  the  ex- 
ternal pressure  below  58%,  or  about  4/7  of  the  inside  pressure,  even  to 
the  extent  of  a  perfect  "vacuum.  In  flowing  through  a  nozzle  of  the  best 
form,  the  steam  expands  to  the  external  pressure,  and  to  the  volume  aue  to 
this  pressure,  so  long  as  it  is  not  less  than  58%  of  the  internal  pressure. 
For  an  external  pressure  of  58%,  and  for  lower  percentages,  the  ratio  of 
expansion  is  1  to  1 .624. 

When  steam  of  varying  initial  pressures  is  discharged  into  the  atmos- 
phere—  the  atmospheric  pressure  being  not  more  than  58%  of  the  initial 
pressure— the  velocity  of  outflow  at  constant  density,  that  is,  supposing  the 
initial  density  to  be  maintained,  is  given  by  the  formula  V  =  3.5953  V&' 
V  =  velocity  in  feet  per  second,  as  for  steam  of  the  initial  density; 
h  =  the  height  in  feet  of  a  column  of  steam  of  the  given  initial  pressure, 
the  weight  of  which  is  equal  to  the  pressure  on  the  unit  of  base. 

The  lowest  initial  pressure  to  which  the  formula  applies,  when  the  steam 
is  discharged  into  the  atmosphere  at  14.7  Ibs.  per  sq.  in.,  is  (14.7  X  100/58) 
=  25.37  Ibs.  per  sq.  in. 

From  the  contents  of  the  table  below  it  appears  that  the  velocity  of  out- 
flow into  the  atmosphere,  of  steam  above  25  Ibs.  per  sq.  in.  absolute  pres- 
sure, increases  very  slowly  with  the  pressure,  because  the  density,  and  the 
weight  to  be  moved,  increase  with  the  pressure.  An  average  of  900  ft.  per 
sec.  may,  for  approximate  calculations,  be  taken  for  the  velocity  of  out- 
flow as  for  constant  density,  that  is,  taking  the  volume  of  the  steam  at  the 
initial  volume.  For  a  fuller  discussion  of  this  subject  see  "Steam  Tur- 
bines, page  1085- 

Outflow  of  Steam  into  the  Atmosphere.  —  External  pressure  per 
square  inch,  14.7  Ibs.  absolute.  Ratio  of  expansion  in  nozzle.  1.624. 


i 

£ 

<g  . 

feS* 

.  a  . 

'o 

fc 

«,£* 

bsolute  Initial 
Pressure  per 
square  inch. 

elocity  of  Out- 
flow as  at  Co 
stant  Density 

ctual  Velocity 
Outflow  Ex- 
panded. 

ischarge  per 
square  inch 
Orifice  per  mil 

orse-power  pe 
sq.  in.  of  Orifi 
if  H.P.  =  30  It 
per  hour. 

bsolute  Initial 
Pressure  per 
square  inch. 

elocity  of  Out- 
flow as  at  Co 
stant  Density 

ctual  Velocity 
Outflow  Ex- 
panded. 

ischarge  per 
square  inch  of 
Orifice  per  mi 
ute. 

orse-power  pe 
sq.  in.  of  Orifi 
if  H.P.  =  30  It 
per  hour. 

< 

> 

< 

Q 

H 

< 

> 

^ 

Q 

M 

Ibs. 

feet 
p.  sec. 

feet 
per  sec  . 

Ibs. 

H.P. 

Ibs. 

feet 
p.  sec. 

feet 
per  sec. 

Ibs. 

H.P. 

25.37 

863 

1401 

22.81 

45.6 

90 

895 

1454 

77.94 

155.9 

30 

867 

1408 

26.84 

53.7 

100 

898 

1459 

86.34 

172.7 

40 

874 

1419 

35.18 

70.4 

115 

902 

1466 

98.76 

197.5 

50 

880 

1429 

44.06 

88.1 

135 

906 

1472 

115.61 

231.2 

60 

885 

1437 

52.59 

105.2 

155 

910 

1478 

132.21 

264.4 

70 

889 

1444 

61.07 

122.1 

165 

912 

1481 

140.46 

280.9 

75 

891 

1447 

65.30 

130.6  ' 

215 

919 

1493 

181.58 

363.2 

Rateau's  Formula.  —  A.  Rateau,  in  1895-6,  made  experiments  with 
converging  nozzles  0.41,  0.59  and  0.95  in.  diam.,  on  steam  of  pressures  from 
1.4  to  170  Ibs.  per  sq.  in.  In  his  paper  read  at  the  Intl.  Eng'g.  Congress  at 
Glasgow  (Ena.  Rec.,  Oct.  16,  1901)  he  gives  the  following  formula,  appli- 
cable when  the  final  pressure,  absolute,  is  less  than  58%  of  the  initial. 
Pounds  per  hour  per  sq.  in.  area  of  orifice  =  3.6  P  (16.3  —  0.96  log  P). 
P  —  absolute  pressure,  Ibs.  per  sq.  in. 

Napier's  Approximate  Rule.  —  Flow  in  pounds  per  second  =  ab- 
solute pressure  X  area  in  square  inches  •*•  70.  This  rule  gives  results 


FLOW   OF  STEAM. 


877 


whfrh  closely  correspond  with  those  in  the  above  table,  and  with  results 
computed  by  Rateau's  formula,  as  shown  below. 

Abs.  press.,  Ibs. 

per  sq.  in  .......   25.37       40       60       75      100        135       165       215 

Discharge  per  m  in.  , 

by  table,  Ibs....   22.81  35.18  52.59  65.30  86.34  115.61  140.46  181.58 
By  Rateau's  for- 

mula %     22.76  35.43  52.49  65.25  86.28  115.47  140.28  181.39 

By  Napier's  rule.   21.74  34.29  51.43  64.29  85.71  115.71  141.43  184.29 

Flow  of  Steam  in  Pipes.  —  The  commonly  accepted  formula  for 


flow  of  air,  steam  or  gas  in  pipes  is  W  =  c 


w  (p*  ~ 


d" 


in  which 


W  =  the  weight  in  pounds  per  minute,  pi  and  p*  =  initial  and  final 
pressures  in  pounds  per  square  inch,  w  =  density  in  pounds  per  cubic 
foot,  d  =  internal  diameter  of  the  pipe  in  inches,  and  L  =  length  in 
feet,  and  c  an  experimental  coefficient,  which  varies  with  the  diameter 
of  the  pipe.  It  varies  also  with  the  velocity  and  with  the  smoothness 
of  the  pipe,  but  there  are  no  authentic  data  for  the  amount  of  the 
variations  due  to  these  causes.  For  the  derivation  of  the  formula,  see 
Ency.  Brit.,  llth  ed.,  vol.  xiv,  p.  67,  also  "Steam,"  1913  edition, 
published  by  the  Babcock  &  Wilcox  Co. 

The  value  of  the  coefficient  c,  as  deduced  by  G.  H.  Babcock  from 


: 


study  of  published  experiments,  is  87 


3.6/d 


It  is  probably  as 


Si, 

" 


learly  correct  as  can  be  derived  from  the  few  experimental  records  that 
are  available.  For  the  different  standard  sizes  of  lap  welded  pipe  the 
value  of  c  computed  from  Babcock's  formula  are  as  below: 


VALUES  OF  c  FOR  STANDARD  SIZES  OF  LAP-WELDED  PIPE. 


Size, 
In. 

"1/2 

,3/4 

H/4 
H/2 

21/2 

31/2 

Inter. 
Diam., 
In. 

c 

Size, 

In. 

Inter. 
Diam., 
In. 

e 

Size, 
In. 

Inter. 
Diam., 
In. 

c 

0.622 
0.824 
1  .049 
1.380 
1.610 
2.067 
2.469 
3.068 
3.548 

33.4 
37.5 
41.3 
45.8 
48.4 
52.5 
55.5 
59.0 
61  .3 

4 
4V, 

6 
7 
8 
9 
10 
11 

4.026 
4.506 
5.047 
6.065 
7.023 
7.981 
8.941 
10.02 
11  .00 

63.2 
64.8 
66.5 
68.7 
70.7 
72.2 
73.4 
74.5 
75.5 

12 
13 
14 
15 
17O.D. 
18O.D. 
20  O.D. 
22  O.D. 
24  O.D. 

12.00 
13.25 
14.25 
15.25 
16.214 
17.182 
19.182 
21.25 
23.25 

76.3 
77.  1 
77.7 
78.2 
78.7 
79.1 
79.8 
80.4 
81.0 

The  table,  page  878,  calculated  from  the  formula  with  the  above 
values  of  c  gives  the  flow  of  steam  in  pounds  per  minute  for  a  drop  of 
1  Ib.  pressure  per  1000  ft.  of  length.  For  any  other  ratio  of  drop  to 
length  multiply  the  figures  in  the  table  by  the  factors  given  below. 

FACTORS  FOR  CORRECTION  OF  TABLE  OF  FLOW  OF  STEAM. 
Drop  Ib.  per 

1000ft.    14         K  2  346          8  10         15        20      25 

Factor    0.5    0.707    1.414    1.732    2    2.45    2.83    3.16    3.87    4.47     5 

For  Flow  of  Steam  at  low  pressures,  see  Heating  and  Ventilation, 
page  699. 

Flow  of  Steam  in  Long  Pipes.  Ledoux's  Formula.  —  In  the  flow 
of  steam  or  other  gases  in  long  pipes,  the  volume  and  the  velocity  are 
increased  as  the  drop  in  pressure  increases.  Taking  this  into  account  a 
correct  formula  for  flow  would  be  an  exponential  one.  Ledoux  gives 


0  699 


.5/ 

\/ 

Y 


-  T:  -  r-s;  ,  his  notation  being  reduced  to  English  meas- 
pi1**4  —  pz 

Mines,  1S92;  Trans.  A.  S.  M.  E.,  xx.,  365;  Power,  June, 


ures.    (Annales  des  .     .    .          ., 

1907.)    See  Johnson's  formula  for  flow  of  air,  page  619. 


878 


m 

STEAM. 

iA  CN  <N  CO  •*  NO 

tN""! 

o  ----2as?«S3|=£S9||§i|=sii 

^•00 

CNiAO<N-^-ONiAOTj-TfTj-cnNOONONNO<NiA^ 

7  ii 

o  —  =ss?3ss|§Rasg|||||g|| 

O'S 

—  TGOONO  —  —  lAt^  —  fSiA\O  —  '^••Tj-miAiAfN 

II     II 

as 

>tN>     H  —  !£}-_  rs  J^  TJ- 

§jq 

^-CAt^sO'A'—  >ANOcoOcOOONCA<NvO  —  ^OO  — 

g* 

O              •—  <N  iA  00  <Arn  CO  rf  —  ON  00  ON  —  ONO  —  •"  NO  O  t^  ^lA  t^  ON 
—  —  —  CNCsJcn 

6% 

<SOOt^iAiA»A  —  CO  —  OOOiAO 

H  • 

—  —  —  fN<N 

°i 

|2^§5S?3?=5:3R5<.«**N-^*i».* 

Li 

*•$ 

o         -—  =2S«*K8ftSftg3!8s8!ii 

^'1 

S§SS3SsSasR8S!ss,o,*^«No.— 

II    • 
a£ 

^~^~f^2^=i 

t>, 

^S 
<Ng 

fx^iAO^OoO^t'OO 

5 

O                    —  (N  CO  NO  ON  CO  CO  TT  O  O  iA  Tf^-  00  ON  <N  ON  ^  "1-  ^1-  —  iA  — 

^ 

®8 

i5lsgSS5feSS!QS?S_^-^oo,a,o.^^ 

£l 

O                            —  CO  lA  00  CN  t^  CO  00  NO  ON  1^  Tj-  iA  fN  —  COCOOO  —  «ACNO 
—  —  fNcOiAr^OTTOOcoOvOcoOONOOfNON 
—  —  —  (NcOCO'^-«AiAt>.OCN 

ci 

5SiSSSSS95S5588!8$SSS«o.**_^ 

5  ii 

<N   § 

O                                      —  CN  CO  -3-  sO  ©  «A  <N  ON  ON  —  ^-  CO  O  ON  O  CO  f>  fN  NO 
—  —  <N<NCO>ANOoOO  —  •^•NO^OO'A 

c8  ^          • 

3SlpsliSllsi§i5§llasas22§a 

<j^   5 

Ml* 

QQQQQ 

;J<  5^  ^  ^  >                            ddddd 

FLOW   OF   STEAM. 


879 


Carrying  Capacity  of  Eitra  Heavy  Steam  Pipes. 

(Power  Specialty  Co.) 


_ 

«  rt  • 

200 

150 

100 

50 

_ 

•S  S  e 

200 

150 

100 

50 

J*oS 

5  |-S 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

J'o.S 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

ill 

l-g  " 

Pounds  of  steam  per 

1|| 

«  jj  * 

Pounds  of  steam  per 

£   2k, 

<5'w.S 

hour. 

£   a 

-<  2  .~ 

hour. 

1 

0.71 

1210 

872 

618 

362 

6 

25.93 

40800 

31600 

22600 

13210 

I  1/4 

1.27 

2000 

1555 

1105 

646 

7 

34.47 

54600 

42250 

30000 

17600 

1  V2 

1.75 

2750 

2140 

1525 

894 

8 

44.18 

69500 

54000 

38400 

22450 

2 

2.93 

4610 

3590 

2550 

1525 

9 

58.42 

92000 

71500 

50800 

29800 

21/2 

4.20 

6610 

5150 

3660 

2140 

10 

74.66 

117300 

91500 

65000 

38100 

6.56 

10300 

8050 

5720 

3450 

11 

90.76 

142800 

111500 

79200 

46300 

31/2 

8.85 

13900 

10820 

7720 

4520 

12 

108.43 

170500 

133000 

94750 

55400 

11.44 

18000 

14000 

10000 

5850 

14 

153.94 

242000 

188200 

133900 

78600 

41/2 

14.18 

22300 

17350 

12320 

7230 

16 

176.71 

277500 

216200 

153800 

90500 

18.19 

28610 

22250 

15800 

9300 

18 

226.98 

357000 

278000J197500 

115700 

The  quantities  in  the  above  table  are  based  on  the  following  velocities: 

Steam  superheated  degrees  F.         0         50       100       150       200         250 

Velocity,  ft.  per  min 8000     8500     8950     9450     9900     10450 

Resistance  to  Flow  by  Bends,  Valves,  etc.  (From  Briggs  on 
Warming  Buildings  by  Steam.)  —  The  resistance  at  the  entrance  to  a 
tube  when  no  special  bell-mouth  is  given  consists  of  two  parts.  The 
head  v*  •*•  20  is  expended  in  giving  the  velocity  of  flow;  and  the  head 
0.505  vz  -*-  2  g  in  .overcoming  the  resistance  of  the  mouth  of  the  tube 
Hence  the  whole  loss  of  head  at  the  entrance  is  1.505  v2  •*-  2g.  This  resist- 
ance is  equal  to  the  resistance  of  a  straight  tube  of  a  length  equal  to  about 
60  times  its  diameter.  The  loss  at  each  sharp  right-angled  elbow  is  the 
same  as  in  flowing  through  a  length  of  straight  tube  equal  to  about  40 
times  its  diameter.  For  a  globe  steam  stop-valve  the  resistance  is 
taken  to  be  I1 /a  times  that  of  the  right-angled  elbow. 

Sizes  of  Steam-pipes  for  Stationary  Engines.  —  An  old  common 
rule  is  that  steam-pipes  supplying  engines  should  be  of  such  size  that  the 
mean  velocity  of  steam  in  them  does  not  exceed  6000  feet  per  minute,  in 
order  that  the  loss  of  pressure  due  to  friction  may  not  be  excessive  The 
velocity  is  calculated  on  the  assumption  that  the  cylinder  is  filled  at  each 
stroke.  In  modern  practice  with  large  engines  and  high  pressures,  this 
rule  gives  unnecessarily  large  and  costly  pipes.  For  such  engines  the 
allowable  drop  in  steam  pressure  should  be  assumed  and  the  diameter 
calculated  by  means  of  the  formulae  given  above. 

An  article  in  Power,  May,  1893,  on  proper  area  of  supply-pipes  for 
engines  gives  a  table  showing  the  practice  of  leading  builders.  To  facili- 
tate comparison,  all  the  engines  have  been  rated  in  horse-power  at  40 
pounds  mean  effective  pressure.  The  table  contains  all  the  varieties  of 
simple  engines,  from  the  slide-valve  to  the  Corliss,  and  it  appears  that 
there  is  no  general  difference  in  the  sizes  of  pipe  used  in  the  different  types. 
The  averages  selected  from  this  table  are  as  follows: 

DIAMETERS  OF  CYLINDERS  CORRESPONDING  TO  VARIOUS  SIZES  OF 
STEAM-PIPES  BASED  ON  PISTON-SPEED  OF  ENGINE  OF  600  FT.  PER 
MINUTE,  AND  ALLOWABLE  MEAN  VELOCITY  OF  STEAM  IN  PIPE  OF 
4000,  6000,  AND  8000  FT.  PER  MINUTE.  (STEAM  ASSUMED  TO  BE 
ADMITTED  DURING  FULL  STROKE.) 

Diam.  of  pipe,  inches . .     2 

Vel.  4000 5.2 

Vel.  6000 6.3 

Vel.  8000 7.3 

Horse-power,  approx. . .     20 

Diam.  of  pipes,  inches .     7 

Vel.  4000 18.1  20.7 

Vel.  6000 22.1  25.3 

Vel.  8000 25.6  29.2 

Horse-power,  approx. . .  245    320 

Formula.     Area  of  pipe  =  A^ 

mean  velocity  of  steam  in  pipe 
For  piston-speed  of  600  ft.  per  min.  and  velocity  in  pipe  of  4000,  6000, 


2  V2 

3 

3V2 

4 

4V2 

5 

6 

6.5 

7.7 

9.0 

10.3 

11.6 

12.9 

15.5 

7.9 

9.5 

11.1 

12.6 

14.2 

15.8 

19.0 

9.1 

10.9 

12.8 

14.6 

16.4 

18.3 

21.9 

31 

45 

62 

80 

100 

125 

180 

8 

9 

10 

11 

12 

13 

14 

20.7 

23.2 

25.8 

28.4 

31.0 

33.6 

36.1 

25.3 

28.5 

31.6 

34.8 

37.9 

41.1 

44.3 

29.2 

32.9 

36.5 

40.2 

43.8 

47.5 

51.1 

320 

406 

500 

606 

718 

845 

981 

Area 

of  cy] 

Linder  X 

piston-speed  . 

880 


STEAM. 


and  8000  ft.  per  min.,  area  of  pipe  =  respectively  0.15,  0.10,  and  0.075< 
area  of  cylinder.  Diam.  of  pipe-respectively  0.3873, 0.3162, -and  0.2739X 
diam.  of  cylinder.  The  reciprocals  of  these  are  2. 582,3. 162and3. 651. 

The  first  line  in  the  above  table  may  be  used  for  proportioning  exhaust 
pipes,  in  which  a  velocity  not  exceeding  4000  ft.  pe*  minute  is  advisable. 
The  last  line,  apprpx.  H.P.  of  engine,  is  based  on  the  velocity  of  60CO  ft. 
per  min.  in  the  pipe,  using  the  corresponding  diameter  of  piston,  and 
taking  H.P.  =  1/2  (diam.  of  piston  in  inches)2. 

Sizes  of  Steam-pipes  for  Marine  Engines.  —  In  marine-engine 
practice  the  steam-pipes  are  generally  not  as  large  as  in  stationary  practice 
for  the  same  sizes  of  cylinder.  Seaton  gives  the  following  rules: 

Main  Steam-pines  should  be  of  such  size  that  the  mean  velocity  of  flow 
does  not  exceed  8000  ft.  per  min. 

In  large  engines,  1000  to  2000  H.P.,  cutting  off  at  less  than  half  stroke, 
the  steam-pipe  may  be  designed  for  a  mean  velocity  of  9000  ft.,  and 
10,000  ft.  for  still  larger  engines. 

In  small  engines  and  engines  cutting  off  later  than  half  stroke,  a  velocity 
of  less  than  8000  ft.  per  minute  is  desirable. 

Taking  8100  ft.  per  min.  as  the  mean  velocity,  S  speed  of  piston  in  feet 
per  min.,  and  D  the  diameter  of  the  cylinder, 


Diam.  of  main  steam-pipe*  v D2S  •*•  8100  =>!>  V&  +  90. 

Stop  and  Throttle  Valves  should  have  a  greater  area  of  passages  than  the 
area  of  the  main  steam-pipe,  on  account  of  the  friction  through  the  cir- 
cuitous passages.  The  shape  of  the  passages  should  be  designed  so  as  to 
avoid  abrupt  changes  of  direction  and  of  velocity  of  flow  as  far  as  possible. 

Area  of  Steam  Ports  and  Passages  — 

Area  of  piston  X  speed  of  piston  in  ft.  per  min.  __  (Diam.)2  X  speed 
6000  7639 

Opening  of  Port  to  Steam.  —  To  avoid  wire-drawing  during  admission 
the  area  of  opening  to  steam  should  be  such  that  the  mean  velocity  of 
flow  does  not  exceed  10,000  ft.  per  min.  To  avoid  excessive  clearance 
the  width  of  port  should  be  as  short  as  possible,  the  necessary  area  being 
obtained  by  length  (measured  at  right  angles  to  the  line  of  travel  of  the 
valve).  In  practice  this  length  is  usually  0.6  to  0.8  of  the  diameter  of 
the  cylinder,  but  in  long-stroke  engines  it  may  equal  or  even  exceed  the 
diameter. 

Exhaust  Passages  and  Pipes.  —  The  area  should  be  such  that  the  mean 
velocity  of  the  steam  should  not  exceed  6000  ft.  per  min.,  and  the  area 
should  be  greater  if  the  length  of  the  exhaust-pipe  is  comparatively  long. 
The  area  of  passages  from  cylinders  to  receivers  should  be  such  that  the 
velocity  will  not  exceed  5000  ft.  per  min. 

The  following  table  is  computed  on  the  basis  of  a  mean  velocity  of  flow 
of  8000  ft.  per  min.  for  the  main  steam-pipe,  10,000  for  opening  to  steam, 
and  6000  for  exhaust.     A  =  area  of  piston,  D  its  diameter. 
STEAM  AND  EXHAUST  OPENINGS. 


Piston- 
speed, 

Diam.  of 
Steam-pipe 

Area  of 
Steam-pipe 

Diam.  of 

Exhaust 

Area  of 
Exhaust 

Opening 
to  Steam 

ft.  per  min. 

^  D. 

+  A. 

•*•  £>. 

4-  A. 

•*-  A. 

300 

0.194 

0.0375 

0.223 

0.0500 

0.03 

400 

0.224 

0.0500 

0.258 

0.0667 

0.04 

500 

0.250 

0.0625 

0.288 

0.0833 

0.05 

600 

0.274 

0.0750 

0.316 

0.1000 

0.06 

700 

0.296 

0.0875 

0.341 

0.1167 

0.07 

800 

0.316 

0.1000 

0.365 

0.1333 

0.08 

900 

0.335 

0.1125 

0.387 

0.1500 

0.09 

1000 

0.353 

0.1250 

0.400 

0.1667 

0.10 

proportioning  Steam-Pipes  for  Minimum  Total  Loss  by  Radiation 
ana  Friction.  —  For  a  given  size  of  pipe  and  quantity  of  steam  to  be 
carried  the  loss  of  pressure  due  to  friction  is  calculated  by  formulae  given 
above,  or  taken  from  the  tables.  The  work  of  friction,  being  converted 
into  heat,  tends  to  dry  or  superheat  the  steam,  but  its  influence  is  usually 
so  small  that  it  may  be  neglected.  The  loss  of  heat  by  radiation  tends  to 
destroy  the  superheat  and  condense  some  of  the  steam  into  water.  For 


FLOW  OF  STEAM. 


881 


weU-covered  steam-pipes  this  loss  may  be  estimated  at  about  0.3 
B.T.U.  per  sq.  ft.  of  external  surface  of  the  pipe  per  hour  per  degree  of 
difference  of  temperature  between  that  of  the  steam  and  that  of  the 
surrounding  atmosphere  (see  Steam-pipe  Coverings,  p.  584). 

A  practical  problem  in  power-plant  design  is  to  find  the  diameter  of 
pipe  to  carry  a  given  quantity  of  steam  with  a  minimum  total  loss  of 
available  energy  due  to  both  radiation  and  friction,  considering  also  the 
money  loss  due  to  interest  and  depreciation  on  the  value  of  the  pipe 
and  covering  as  erected.  Each  case  requires  a  separate  arithmetical 
computation,  no  formula  yet  being  constructed  to  fit  the  general  case. 
An  approximate  method  of  solution,  neglecting  the  slight  gain  of  heat  by 
the  steam  from  the  work  of  friction,  and  assuming  that  the  water  con- 
densed by  radiation  of  heat  is  removed  by  a  separator  and  lost,  is  as  fol- 
lows: Calculate  the  amount  of  steam  required  by  the  engine,  in  pounds 
per  minute.  From  a  steam  pipe  formula  or  table  find  the  several  drops 
of  pressure,  in  Ibs.  per  sq.  in.,  in  pipes  of  different  assumed  diameters,  for 
the  given  quantity  of  steam  and  the  given  length  of  pipe.  Compute  from 
a  theoretical  indicator  diagram  of  steam  expanding  in  the  engine  the  loss 
of  available  work  done  by  1  Ib.  of  steam,  due  to  the  several  drops  already 
found,  and  the  corresponding  fraction  of  1  Ib.  of  steam  that  will  have  to 
be  supplied  to  make  up  for  this  loss  of  work.  State  this  loss  as  equiva- 
lent to  so  many  pounds  of  steam  per  1000  Ibs.  of  steam  carried.  Calcu- 
late the  loss  in  Ibs.  of  steam  condensed  by  radiation  in  the  pipes  of  the 
different  diameters,  per  1000  Ibs.  carried.  Add  the  two  losses  together 
for  each  assumed  size  of  pipe,  and  by  inspection  find  which  pipe  gives  the 
lowest  total  loss.  The  money  loss  due  to  cost  and  depreciation  may  also 
be  figured  approximately  in  the  same  unit  of  Ibs.  of  steam  lost  per  1000 
Ibs.  carried,  by  taking  the  cost  of  the  covered  pipe,  assuming  a  rate  of 
interest  and  depreciation,  finding  the  annual  loss  in  cents,  then  from  the 
calculated  value  of  steam,  which  depends  on  the  cost  of  fuel,  find  the 
equivalent  quantity  of  steam  which  represents  this  money  loss,  and 
the  equivalent  Ibs.  of  steam  per  1000  Ibs.  carried.  This  is  to  be  added  to 
the  sum  of  the  louses  due  to  friction  and  radiation,  and  it  will  be  found  to 
modify  somewhat  the  conclusion  as  to  the  diameter  of  pipe  and  the  drop 
which  corresponds  to  a  minimum  total  loss. 

Instead  of  determining  the  loss  of  available  work  per  pound  of  steam 
from  theoretical  indicator  diagrams,  it  may  be  computed  approximately 
on  the  assumption,  based  on  the  known  characteristics  of  the  engine, 
that  its  efficiency  is  a  certain  fraction  of  that  of  an  engine  working  between 
the  same  limits  of  temperature  on  the  ideal  Carnot  cycle,  as  shown  in 
the  table  below,  and  from  the  efficiency  thus  found,  compared  with  the 
efficiency  at  the  given  initial  pressure  less  the  drop,  the  loss  of  work  may 
be  calculated. 
AVAILABLE  MAXIMUM  THERMAL  EFFICIENCY  OF  STEAM  EXPANDED 

BETWEEN  THE  GIVEN  PRESSURES  AND  1  LB.  ABSOLUTE,  BASED  ON 

THE  CARNOT  CYCLE.     (E  =  Ti  -  Tz)  •*•  Ti. 


Initial  Pressure 
less  than  Maxi- 
mum, Lbs. 

Maximum  Initial  Absolute  Pressures. 

100 

125   |    150 

175    |    200 

225    |    250 

275    I    300 

Maximum  Thermal  Efficiency. 

o 

0.287 
.286 
.284 
.280 
.272 

0.302 
.301 
.299 
.296 
.290 

0.314 
.313 
.312 
.309 
.304 

0.324 
.323 
.322 
.320 
.316 

0.333 
.332 
.331 
.329 
.326 

0.341 
.340 
.339 
.337 
.335 

0.348 
.347 
.346 
.345 
.342 

0.354 
.354 
.353 
.352 
.349 

0.360 
.359 
.359 
.358 
.356 

2.  . 

5 

10.  . 

20  

This  table  shows  that  if  the  initial  steam  pressure  is  lowered  from 
100  Ibs.  to  80  Ibs.,  the  efficiency  of  the  Carnot  cycle  is  reduced  from 
0.287  to  0.272,  or  over  5%,  but  if  steam  of  300  Ibs.  is  lowered  to  280  Ibs. 
the  efficiency  is  reduced  only  from  0.360  to  0.356  or  1.1%.  With  high- 
pressure  steam,  therefore,  much  greater  loss  of  pressure  by  friction  of 
steam  pipes,  valves  and  ports  is  allowable  than  with  steam  of  low  pressure. 

Theoretically  the  loss  of  efficiency  due  to  drop  in  pressure  on  account 
of  friction  of  pipes  should  be  less  than  that  indicated  in  the  above  table, 
since  the  work  of  friction  tends  to  superheat  the  steam,  but  practically 
most,  if  not  all,  of  the  superheating  is  lost  by  radiation. 


882 


STEAM. 


By  a  method  of  calculation  somewhat  similar  to  that  above  outlined, 
the  following  figures  were  found,  in  a  certain  case,  of  the  cost  per  day 
of  the  transmission  of  50,000  Ibs.  of  steam  per  hour  a  distance  of  1000 
feet,  with  100  Ibs.  initial  pressure. 


Diameter  of  Pipe. 

6  in. 

7  in. 

8  in. 

10  in. 

12m. 

1.  Interest,  etc.,  12%  per  annum.  . 
2.  Condensation  

$0.39 
1.51 

$0.46 
1.76 

$0.53 
2.01 

$0.66 
2.51 

$0.84 
3.02 

3.  Friction 

0  86 

0  38 

0  19 

0  06 

0.02 

Total  per  day  

$2.76 

$2.60 

$2.73 

$3.23 

$3.88 

STEAM-PIPES. 

Bursting-tests  of  Copper  Steam-pipes.  (From  Ileport  of  Chief 
Engineer  Melville,  U.  S.  N.,  for  1892.)  —  Some  tests  were  made  at  the 
New  York  Navy  Yard  which  show  the  unreliability  of  brazed  seams  in 
copper  pipes.  Each  pipe  was  8  in.  diameter  inside  and  3  ft.  1 5/g  in.  long. 
Both  ends  were  closed  by  ribbed  heads  and  the  pipe  was  subjected  to  a 
hot-water  pressure,  the  temperature  being  maintained  constant  at  371°  F. 
Three  of  the  pipes  were  made  of  No.  4  sheet  copper  (Stubs  gauge)  and  the 
fourth  was  made  of  No.  3  sheet. 

The  following  were  the  results,  in  Ibs.  per  sq.  in.,  of  bursting-pressure: 

Pipe  number 1  2  3  4  4' 

Actual  bursting-strength. .    835         785          950       1225  •      1275 
Calculated  "  1336        1336        1569        1568        1568 

Difference 501         551         619         343         293 

The  tests  of  specimens  cut  from  the  ruptured  pipes  show  the  injurious 
action  of  heat  upon  copper  sheets;  and  that,  while  a  white  heat  does  not 
change  the  character  of  the  metal,  a  heat  of  only  slightly  gieater  degree 
causes  it  to  lose  the  fibrous  nature  that  it  has  acquired  in  rolling,  and  a 
serious  reduction  in  its  tensile  strength  and  ductility  results. 

A  Failure  of  a  Brazed  Copper  Steam-pipe  on  the  British  steamer 
Prodano  was  investigated  by  Prof.  J.  O.  Arnold.  He  found  that  the 
brazing  was  originally  sound,  but  that  it  had  deteriorated  by  oxidation 
of  the  zinc  in  the  brazing  alloy  by  electrolysis,  which  was  due  to  the 
presence  of  fatty  acids  produced  by  decomposition  of  the  oil  used  in  the 
engines.  A  full  account  of  the  investigation  is  given  in  The  Engineer, 
April  15,  1898. 

-Reinforcing  Steam-pipes.  (Eng.,  Aug.  11,  1893.)  — In  the  Italian 
Navy  copper  pipes  above  8  in.  diam.  are  reinforced  by  wrapping  them  with 
a  close  spiral  of  copper  or  Delta-metal  wire.  Two  or  three  independent 
spirals  are  used  for  safety  in  case  one  wire  breaks.  They  are  wound  at  a 
tension  of  about  11/2  tons  per  sq.  in. 

Materials  for  Pipes  and  Valves  for  Superheated  Steam.  (M.  W. 
Kellogg,  Trans.  A.  S.  M.  E.,  1907.)  — The  latest  practice  is  to  do  away 
with  fittings  entirely  on  high-pressure  steam  lines  and  put  what  are  known 
as  "nozzles"  on  the  piping  itself.  This  is  accomplished  by  welding 
wrought-steel  pipe  on  the  side  of  another  section,  so  as  to  accomplish 
the  same  result  as  a  fitting.  In  this  way  rolled  or  cast  steel  flanges  and  a 
Rockwood  or  welded  joint  can  be  used.  This  method  has  three  distinct 
advantages:  1.  The  quality  of  the  metal  used.  2.  The  lightening  of  the 
entire  work.  3.  The  doing  away  with  a  great  many  joints. 

As  a  general  average,  at  least  50%  of  the  joints  can  be  left  out;  some- 
times the  proportion  runs  up  as  high  as  70%. 

Above  575°  F.  the  limit  of  elasticity  in  cast  iron  is  reached  with  a 
pressure  varying  from  140  to  175  pounds.  Under  such  conditions  the 
material  is  strained  and  does  not  resume  its  former  shape,  eventually 
showing  surface  cracks  which  increase  until  the  pipe  breaks.  [This  state- 
ment concerning  cast  iron  does  not  seem  to  agree  with  the  one  on  page 
464,  to  the  effect  that  no  diminution  in  its  strength  takes  place  under 
900°  F.I 

Tests  by  Bach  on  cast  steel  show  that  at  572°  F.  the  reduction  in  break- 
ing strength  amounts  only  to  1.1%  and  at  752°  F.  to  about  8',  ( . 

The  effect  of  temperature  on  nickel  is  similar  to  that  on  cast  steel  and 
in  consequence  this  material  is  very  suitable  for  use  in  connection  with 


STEAM-PIPES.  883 

superheated  steam.  Bach  recommends  that  bronze  alloys  be 
done  away  with  for  use  on  steam  lines  above  a  temperature  of  about 
390°  F. 

The  old-fashioned  screwed  joint,  no  matter  how  well  made,  is  not 
suitable  for  superheated  steam  work. 

In  making  up  a  joint,  the  face  of  all  flanges  or  pipe  where  a  joint  is  made 
should  be  given  a  fine  tool  finish  and  a  plane  surface,  and  a  gasket  should 
be  used.  The  best  results  have  been  obtained  with  a  corrugated  soft 
Swedish  steel  gasket  with  "Smooth-on"  applied,  and  with  the  McKim 
gasket,  which  is  of  copper  or  bronze  surrounding  asbestos.  On  super- 
heated steam  lines  a  corrugated  copper  gasket  will  in  time  pit  out  iu 
some  part  of  the  flange  nearly  through  the  entire  gasket. 

Specifications  for  pipes  and  fittings  for  superheated  steam  service  were 
published  by  Crane  Co.,  Chicago,  in  the  Valve  World,  1907. 

Riveted  Steel  Steam-pipes  have  been  used  for  high  pressures.  See 
paper  on  A  Method  of  Manufacture  of  Large  Steam-pipes,  by  Chas.  H. 
Manning,  Trans.  A.  S.  M.  E.,  vol.  xv. 

Valves  in  Steam-pipes.  —  Should  a  globe-valve  on  a  steam-pipe  have 
the  steam-pressure  on  top  or  underneath  the  valve  is  a  disputed  question. 
With  the  steam-pressure  on  top,  the  stuffing-box  around  the  valve-stem 
cannot  be  repacked  without  shutting  off  steam  from  the  whole  line  of 
pipe;  on  the  other  hand,  if  the  steam-pressure  is  on  the  bottom  of  the 
valve  it  all  has  to  be  sustained  by  the  screw-thread  on  the  valve-stem, 
and  there  is  danger  of  stripping  the  thread. 

A  correspondent  of  the  American  Machinist,  1892,  says  that  it  is  a  very 
uncommon  thing  in  the  ordinary  globe- valve  to  have  the  thread  give  out, 
but  by  water-hammer  and  merciless  screwing  the  seat  will  be  crushed 
down  quite  frequently.  Therefore  with  plants  where  only  one  boiler  is 
used  he  advises  placing  the  valve  with  the  boiler-pressure  underneath  it. 
On  plants  where  several  boilers  are  connected  to  one  main  steam-pipe 
he  would  reverse  the  position  of  the  valve,  then  when  one  of  the  valves 
needs  repacking  the  valve  can  be  closed  and  the  pressure  in  the  boiler 
whose  pipe  it  controls  can  be  reduced  to  atmospheric  by  lifting  the  safety- 
valve.  The  repacking  can  then  be  done  without  interfering  with  the 
operation  of  the  other  boilers  of  the  plant. 

He  proposes  also  the  following  other  rules  for  locating  valves:  Place 
valves  with  the  stems  horizontal  to  avoid  the  formation  of  a  water-pocket. 
Never  put  the  junction-valve  close  to  the  boiler  if  the  main  pipe  is  above 
the  boiler,  but  put  it  on  the  highest  point  of  the  junction-pipe.  If  the  other 
plan  is  followed,  the  pipe  fills  with  water  whenever  this  boiler  is  stopped 
and  the  others  are  running,  and  breakage  of  the  pipe  may  cause  serious 
results.  Never  let  a  junction-pipe  run  into  the  bottom  of  the  main  pipe, 
but  into  the  side  or  top.  Always  use  an  angle- valve  where  convenient, 
as  there  is  more  room  in  them.  Never  use  a  gate  valve  under  high  pressure 
unless  a  by-pass  is  used  with  it.  Never  open  a  blow-off  valve  on  a  boiler 
a  little  and  then  shut  it;  it  is  sure  to  catch  the  sediment  and  ruin  the 
valve;  throw  it  well  open  before  closing.  Never  use  a  globe-valve  on  an 
indicator-pipe.  For  water,  always  use  gate  or  angle  valves  or  stop-cocks 
to  obtain  a  clear  passage.  Buy  if  possible  valves  with  renewable  disks. 
Lastly,  never  let  a  man  go  inside  a  boiler  to  work,  especially  if  he  is  to 
hammer  on  it,  unless  you  break  the  joint  between  the  boiler  and  the 
valve  and  put  a  plate  of  steel  between  the  flanges. 

The  "  Steam-Loop  "  is  a  system  of  piping  by  which  water  of  con- 
densation in  steam-pipes  is  automatically  returned  to  the  boiler.  In  its 
simplest  form  it  consists  of  three  pipes,  which  are  called  the  riser,  the 
horizontal,  and  the  drop-leg.  When  the  steam-loop  is  used  for  returning 
to  the  boiler  the  water  of  condensation  and  entrainment  from  the  steam- 
pipe  through  which  the  stearn  flows  to  the  cylinder  of  an  engine,  the  riser 
is  generally  attached  to  a  separator;  this  riser  empties  at  a  suitable 
height  into  the  horizontal,  and  from  thence  the  water  of  condensation  is 
led  into  the  drop-leg,  which  is  connected  to  the  boiler,  into  which  the 
water  of  condensation  is  fed  as  soon  as  the  hydrostatic  pressure  in  the 
drop-leg  in  connection  with  the  steam-pressure  in  the  pipes  is  sufficient  to 
overcome  the  boiler-pressure.  The  action  of  the  device  depends  on  the 
following  principles:  Difference  of  pressure  may  be  balanced  by  a  water- 
column;  vapors  or  liquids  tend  to  flow  to  the  point  of  lowest  pressure; 
rate  of  flow  depends  on  difference  of  pressure  and  mass;  decrease  of  static 
pressure  in  a  steam-pipe  or  chamber  is  proportional  to  rate  of  conden- 


884 


STEAM. 


sation;  In  a  steam-current  water  will  be  carried  or  swept  along  rapidly 
by  friction.  (Illustrated  in  Modern  Mechanism,  p.  807.  Patented  by 
J.  H.  Blessing,  Feb.  13,  1372,  Dec.  28,  1883.)  Mr.  Blessing  thus  describes 
the  operation  of  the  loop  in  Eng.  Review,  Sept.,  1907. 

The  heating  system  is  so  arranged  that  the  water  of  condensation  from 
the  radiators  gravitates  towards  some  low  point  and  thence  is»led  into  the 
top  of  a  receiver.  After  this  is  done  it  is  found  that  owing  to  friction 
caused  by  the  velocity  of  the  steam  passing  through  the  different  pipes 
and  condensation  due  to  radiation,  the  steam  pressure  in  the  small  drip 
receiver  is  much  less  than  that  in  the  boiler.  This  difference  will  deter- 
mine the  height,  or  the  length  of  the  loop,  that  must  be  employed  so  that 
the  water  will  gravitate  through  it  into  the  boiler;  that  is  to  say,  if  there  is 
10  Ibs.  difference  in  pressure,  the  descending  leg  of  the  loop  should  extend 
about  30  feet  above  the  water-level  in  the  boiler,  since  a  column  of  water 
2.3  ft.  is  equal  to  1  Ib.  pressure,  and  a  difference  in  pressure  of  10  Ibs. 
would  require  a  column  23  ft.  high.  If  we  make  the  loop  30  feet  high 
we  shall  have  an  additional  length  of  7  ft.  with  which  to  overcome  fric- 
tion. The  water,  after  it  reaches  the  top  of  the  loop,  composed  of  a 
larger  section  of  pipe,  will  flow  into  the  boiler  through  the  descending 
leg  with  a  velocity  due  to  the  extra  7  ft.  added  to  the  discharging  leg. 

Loss  from  an  Uncovered  Steam-pipe.  (Bjorling  on  Pumping- 
engines.)  —  The  amount  of  loss  by  condensation  in  a  steam-pipe  carried 
down  a  deep  mine-shaft  has  been  ascertained  by  actual  practice  at  the 
Clay  Cross  Colliery,  near  Chesterfield,  where  there  is  a  pipe  712  in.  internal 
diam.,  1100  ft.  long.  The  loss  of  steam  by  condensation  was  ascertained 
by  direct  measurement  of  the  water  deposited  in  a  receiver,  and  was  found 
to  be  equivalent  to  about  1  Ib.  of  coal  per'I.H.P.  per  hour  for  every  100  ft. 
of  steam-pipe;  but  there  is  no  doubt  that  if  the  pipes  had  been  in  the  up- 
cast shaft,  and  well  covered  with  a  good  non-conducting  material,  the  loss 
would  have  been  less.  (For  Steam-pipe  Coverings,  see  p.  584,  ante.) 

Condensation  in  an  Underground  Pipe  Line.  (W.  W.  Christie, 
Eng.  Rec.,  1904.)  —  A  length  of  300  ft.  of  4-in.  pipe,  enclosed  in  a  box 
of  li/4-in.  planks,  10  ins.  square  inside,  and  packed  with  mineral  wool, 
was  laid  in  a  trench,  the  upper  end  being  1  ft.  and  the  lower  end  5  ft.  below 
the  surface.  With  80  Ibs.  gauge  pressure  in  the  pipe  the  condensation 
was  equivalent  to  0.275  B.T.U.  per  minute  per  sq.  ft.  of  pipe  surface 
when  the  outside  temperature  was  31°  F.,  and  0.222  per  min.  when  the 
temperature  was  62°  F. 

Steam  Receivers  on  Pipe  Lines.  (W.  Andrews,  Steam  Eng'g,  Dec. 
10,  1902.)  —  In  the  four  large  power  houses  in  New  York  City,  with 
an  ultimate  capacity  of  60,000  to  100,000  H.P.  each,  the  largest  steam 
mains  are  not  over  20  ins.  in  diameter.  Some  of  the  best  plants  have 
pipes  which  run  from  the  header  to  the  engine  two  sizes  smaller  than  that 
called  for  by  the  engine  builders.  These  pipes  before  reaching  the  engine 
are  carried  into  a  steel  receiver,  wrhich  acts  also  as  a  separator.  This  ' 
receiver  has  a  cubical  capacity  of  three  times  that  of  the  high-pressure 
cylinder  and  is  placed  as  close  as  possible  to  the  cylinder.  The  pipe  from 
the  receiver  to  the  cylinder  is  of  the  full  size  called  for  by  the  engine 
builder.  The  objects  of  this  arrangement  are:  First,  to  have  a  full  supply 
of  steam  to  the  throttle;  second,  to  provide  a  cushion  near  the  engine  on 
which  the  cut-off  in  the  steam  chest  may  be  spent,  thereby  preventing 
vibrations  from  being  transmitted  through  the  piping  system;  and 
third,  to  produce  a  steady  and  rapid  flow  of  steam  in  one  direction  only, 
by  having  a  small  pipe  leading  into  the  receiver.  The  steam  flows 
rapidly  enough  to  make  good  the  loss  caused  during  the  first  quarter  of 
the  stroke.  Plants  fitted  up  in  this  way  are  successfully  running  where 
the  drop  in  steam  pressure  is  not  greater  than  4  Ibs.,  although  the  engines 
are  500  ft.  away  from  the  boilers. 

Equation  of  Pipes.  —  F9r  determining  the  number  of  small  sized 
pipes  that  are  equal  in  carrying  capacity  to  one  of  greater  size  the  table 
given  under  Flow  of  Air,  page  625,  is  commonly  used.  It  is  based  on  the 
equation  N  =  ^ds  +  di6,  in  which  N  is  the  number  of  smaller  pipes  of 
diameter  d\  equal  in  capacity  to  one  pipe  of  diameter  d.  A  more 
accurate  equation,  based  on  Unwin's  formula  for  flow  of  fluids,  is  N  = 

- — 1+  3'6  ;  (d  and  di  in  inches).    For  d=  2di,  the  first  formula  giv«« 
3.6 


THE   STEAM-BOILER. 


885 


JV  =  5.7,  and  the  second  N  =  6.15,  an  unimportant  difference,  but  for 
d  =  8di,  the  first  gives  N  =  181  and  the  second  N  =  274,  a  considerable 
difference.  (G.  F.  Gebhardt,  Power,  June,  1907). 

Identification  of  Power  House  Piping  by  Different  Colors.     (W. 

H.  Bryan,  Trans.  A.  S.  M.  E.,  1908.)  — In  large  power  plants  the  multi^ 
piicity  of  pipe  lines  carrying  different  fluids  causes  confusion  and  may 
lead  to  danger  by  an  operator  opening  a  wrong  valve.  It  has  therefore 
become  customary  to  paint  the  different  lines  of  different  colors.  The 
paper  gives  several  tables  showing  color  schemes  that  have  been  adopted 
in  different  plants.  The  following  scheme,  adopted  at  the  New  York 
Edison  Co.'s  Waterside  Station,  is  selected  as  an  example. 


Pipe  Lines. 

Colors  of  Pipe. 

Bands,  Cou- 
plings, Valves, 
etc. 

Steam,  high  pressure  to  engines,  boiler 
cross-overs  leaders  and  headers 

Black 
Buff 
Orange 
Orange 
Green 

Slate 
Dark  Brown 

Blue 
Maroon 

Green 
Slate 
Blue 
Vermilion 
Brown 
Brown 
Brown 
Black 

Brass 
Black 
Red 
Black 
Black 

Red 
Blue 

Red 
Same 

Red 
Black 
Black 
Same 
Black 
Green 
Red 
Same 

All  other  steam  lines  

Steam  exhaust 

Steam,  drips  including  traps  

Blow-offs,    drips    from   water    columns 

Drains  from  crank  pits 

Cold   water    to   primary   heaters  and 

Hot-water  mains,  primary  heaters   to 
pumps,  and  cooling-water  returns.  .  .  . 
Air  pump  discharge  to  hot  well     . 

Cooling  water  pumps  to  engines  

Fire  lines                   

Cylinder  oil  high  pressure  

Engine  oil                       .       

THE  STEAM-BOILER. 

The  Horse-power  of  a  Steam-boiler.  —  The  term  horse-power  has 
two  meanings  in  engineering:  First,  an  absolute  unit  or  measure  of  the  rate 
of  work,  that  is,  of  the  work  done  in  a  certain  definite  period  of  time,  by 
a  source  of  energy,  as  a  steam-boiler,  a  waterfall,  a  current  of  air  or  water, 
or  by  a  prime  mover,  as  a  steam-engine,  a  water-wheel,  or  a  wind-mill. 
The  value  of  this  unit,  whenever  it  can  be  expressed  in  foot-pounds  of 
energy,  as  in  the  case  of  steam-engines,  water-wheels,  and  waterfalls,  is 
33,000  foot-pounds  per  minute.  In  the  case  of  boilers,  where  the  work 
done,  the  conversion  of  water  into  steam,  cannot  be  expressed  in  foot- 
pounds of  available  energy,  the  usual  value  given  to  the  term  horse-power 
is  the  evaporation  of  30  Ibs.  of  water  of  a  temperature  of  100°  F.  into 
steam  at  70  Ibs.  pressure  above  the  atmosphere.  Both  of  these  units  are 
arbitrary;  the  first,  33,000  foot-pounds  per  minute,  first  adopted  by  James 
Watt,  being  considered  equivalent  to  the  power  exerted  by  a  good  London 
draught-horse,  and  the  30  Ibs.  of  water  evaporated  per  hour  being  con- 
sidered to  b^  the  pfparn  reauirement  per  indicated  horse-power  of  an 
average  engine  (in  1876). 

The  Committee  of  Judges  of  the  Centennial  Exhibition,  1876,  in  report- 
ing the  trials  of  competing  boilers  at  that  exhibition  adopted  the  unit, 
30  Ib.  of  water  evaporated  into  dry  steam  per  hour  from  feed-water  at 
100°  P.,  and  under  a  pressure  of  70  Ib.  per  square  inch  above  the  atmos- 
phere, these  conditions  being  considered  by  them  to  represent  fairly 
average  practice. 

The  A.  S.  M.  E.  Committee  on  Boiler  Tests,  1884,  accepted  the  same 
unit,  and  defined  it  as  equivalent  to  34.5  Ib.  evaporated  per  hour  from  a 


886  THE   STEAM-BOILER. 

feed-water  temperature  of  212°  into  steam  at  the  same  temperature. 
The  committee  of  1899  adopted  34.5  Ib.  per  hour,  from  and  at  212°,  as 
the  unit  of  commercial  horse-power,  and  it  was  reaffirmed  in  the  Boiler 
Code  of  the  Power  Test  Committee,  1915.  Using  the  figures  for 
total  heat  of  steam  given  in  Marks  and  Davis's  steam  tables  (1909), 
34  Yi  Ib.  from  and  at  212°,  is  equivalent  to  33,479  B.T.U.  per  hour,  or  to 
an  evaporation  of  30.018  Ib.  from  100°  feed- water  temperature  into 
steam  at  70  Ib.  pressure. 

The  second  definiti9n  of  the  term  horse-power  is  an  approximate  meas- 
ure of  the  size,  capacity,  value,  or  "rating"  of  a  boiler,  engine,  water- 
wheel,  or  other  source  or  conveyer  of  energy,  by  which  measure  it  may  be 
described,  bought  and  sold,  advertised,  etc.  No  definite  value  can  be 
given  to  this  measure,  which  varies  largely  with  local  custom  or  indivi- 
dual opinion  of  makers  and  users  of  machinery.  The  nearest 
approach  to  uniformity  which  can  be  arrived  at  in  the  term  "horse- 
power,' '  used  in  this  sense,  is  to  say  that  a  boiler,  engine,  water-wheel, 
or  other  machine,  "rated"  at  a  certain  horse-power,  should  be  capable 
of  steadily  developing  that  horse-power  for  a  long  period  of  time  under 
ordinary  conditions  of  use  and  practice,  leaving  to  local  custom,  to  the 
judgment  of  the  buyer  and  seller,  to  written  contracts  of  purchase  and 
sale,  or  to  legal  decisions  upon  such  contracts,  the  interpretation  of 
what  is  meant  by  the  term  "ordinary  conditions  of  use  and  practice." 
(Trans.  A.  5.  M.  £?.,  vol.  vii,  p.  226.) 

Contracts  for  power-plant  apparatus  should  specify  the  leading 
dimensions  of  the  apparatus  and  its  rated  capacity.  If  a  specific 
guarantee  of  capacity  is  made,  either  working  or  maximum  capacity, 
the  operating  conditions  under  which  the  guarantee  is  to  be  met  should 
be  clearly  set  forth;  such,  for  example,  as  steam  pressure,  speed,  vacuum, 
quality  of  fuel,  force  of  draft,  etc.  Likewise  if  a  contract  contains  a 
guarantee  of  economy  all  the  conditions  should  be  fully  specified. 

The  commercial  rating  of  capacity  determined  on  for  power-plant 
apparatus,  whether  for  the  purpose  of  contracts  for  sale  or  otherwise, 
should  be  such  that  a  sufficient  reserve  capacity  beyond  the  rating 
is  available  to  meet  the  contingencies  of  practical  operation ;  such  con- 
tingencies, for  example,  as  the  loss  of  steam  pressure  and  capacity  due 
to  cleaning  fires,  inferior  coal,  oversight  of  the  attendants,  sudden  de- 
mand for  an  unusual  output  of  steam  or  power,  etc. 

The  Committee  of  1899  says:  A  boiler  rated  at  any  stated  capacity 
should  develop  that  capacity  when  using  the  best  coal  ordinarily  sold  in 
the  market  where  the  boiler  is  located  ,when  fired  by  an  ordinary  fireman, 
without  forcing  the  fires,  while  exhibiting  good  economy;  and  further,  the 
boiler  should  develop  at  least  one-third  more  than  the  stated  capacity 
when  using  the  same  fuel  and  operated  by  the  same  fireman,  the  full 
draught  being  employed  and  the  fires  being  crowded;  the  available  draught 
at  the  damper,  unless  otherwise  understood,  being  not  less  than  1/2  inch 
water  column. 

Unit  of  Evaporation.  (Abbreviation,  U.  E.) — It  is  the  custom  to 
reduce  results  of  boiler-tests  to  the  common  standard  of  the  equivalent 
evaporation  from  and  at  the  boiling-point  at  atmospheric  pressure,  or 
"  from  and  at  212°  F."  This  unit  of  evaporation,  or  one  pound  of  water 
evaporated  from  and  at  212°,  is  equivalent  to  970.4  British  thermal 
units.  1  B.T.U.  =  the  mean  quantity  of  heat  'equired  to  raise  1  Ib.  of 
water  1°  F.  between  32°  and  212°. 

Measures  for  Comparing  the  Duty  of  Boi  ers. —  The  measure  of 
the  efficiency  of  a  boiler  is  the  number  of  pounds  >f  water  evaporated  per 
pound  of  combustible  (coal  less  moisture  and  ash),  the  evaporation 
being  reduced  to  the  standard  of  "from  and  ai  212°." 

The  measure  of  the  capacity  of  a  boiler  is  the  amount  of  "  boiler  horse- 
power" developed,  a  horse-power  being  defined  as  the  evaporation  of 
34.5  Ib.  per  hour  from  and  at  212°. 

The  measure  of  relative  rapidity  of  steaming  of  boilers  is  the  number 
of  pounds  of  water  evaporated  from  and  at  212°  per  hour  per  square 
foot  of  water-heating  surface. 

The  measure  of  relative  rapidity  of  combustion  of  fuel  in  boiler- 
furnaces  is  the  number  of  pounds  of  coal  burned  per  hour  per  square 
foot  of  grate-surface, 


STEAM-BOILER  PROPORTIONS.  887 

STEAM-BOILER  PROPORTIONS. 

Proportions  of  Grate  and  Heating  Surface  required  for  a  given 
Horse-power. — The  term  horse-power  here  means  capacity  to  evap- 
orate 34.5  Ib.  of  water  from  and  at  212°  F. 

Average  proportions  for  maximum  economy  for  land  boilers  fired  with 
good  anthracite  coal  (ordinary  hand  firing) : 

Heating  surface  per  horse-power 11 . 5  sq.  ft. 

Grate  surface  per  horse-power 1/3 

Ratio  of  heating  to  grate  surface 34 . 5 

Water  evap'd  from  and  at  212°  per  sq.  ft.  H.S.  per  hr . . .      3      Ib. 

Combustible  burned  per  H.P.  per  hour.  . 3 

Coal  with  1/6  refuse,  Ib.  per  H.P.  per  hour 3.6 

Combustible  burned  per  sq.  ft.  grate  per  hour 9 

Coal  with  1/6  refuse,  Ib.  per  sq.  ft.  grate  per  hour 10.8 

Water  evap'd  from  and  at  212°  per  Ib.  combustible. ...  11.5 
Water  evap'd  from  and  at  212°  per  Ib.  coal  (i/e  refuse) .  9.6 
Heating-surface.  —  For  maximum  economy  with  any  kind  of  fuel  a 
boiler  should  be  proportioned  so  that  at  least  one  square  foot  of  heating- 
surface  should  be  given  for  every  3  IDS.  of  water  to  be  evaporated  from 
and  at  212°  F.  per  hour.  Still  more  liberal  proportions  are  required  if  a 
portion  of  the  heating-surface  has  its  efficiency  reduced  by:  1.  Tendency 
of  the  heated  gases  to  short-circuit,  that  is,  to  select  passages  of  least 
resistance  and  now  through  them  with  high  velocity,  to  the  neglect  of 
other  passages.  2.  Deposition  of  soot  from  smoky  fuel.  3.  Incrusta- 
tion. If  the  heating-surfaces  are  clean,  and  the  heated  gases  pass  over 
it  uniformly,  little  if  any  increase  in  economy  can  be  obtained  by  increasing 
the  heating-surface  beyond  the  proportion  of  1  sq.  ft.  to  every  3  Ibs.  of 
water  to  be  evaporated,  and  with  all  conditions  favorable  but  little 
decrease  of  economy  will  take  place  if  the  proportion  is  1  sq.  ft.  to  every 
4  Ibs.  evaporated;  but  in  order  to  provide  for  driving  of  the  boiler  beyond 
its  rated  capacity,  and  for  possible  decrease  of  efficiency  due  to  the  causes 
above  named,  it  is  better  to  adopt  1  sq.  ft.  to  3  Ibs.  evaporation  per  hour 
as  the  minimum  standard  proportion. 

Where  economy  may  be  sacrified  to  capacity,  as  where  fuel  is  very 
cheap,  it  is  customary  to  proportion  the  heating-surface  much  less  liber- 
ally. The  following  table  shows  approximately  the  relative  results  that 
may  be  expected  with  different  rates  of  evaporation,  with  anthracite  coal. 

Lbs.  water  evapor'd  from  and  at  21 2°  per  sq.ft.  heating-surf  ace  per  hour: 
2  2.5       3  3.5       4  5  6  7  8  9         10 

Sq.  ft.  heating-surface  required  per  horse-power: 
17.3     13.8     11.5       9.8       8.6       6.8       5.8       4.9       4.3       3.8       3.5 

Ratio  of  heating  to  grate  surface  if  1/3  sq.  ft.  of  G.S.  is  required  per  H.P.: 
52       41.4     34.5     29.4     25.8     20.4     17.4     13.7     12.9     11.4     10.5 

Probable  relative  economy: 
100         100       100         95         90         85         80         75         70         65         60 

Probable  temperature  of  chimney  gases,  degrees  F.: 
450         450       450       518       585       652       720      787       855       922       990 

The  relative  economy  will  vary  not  only  with  the  amount  of  heating- 
surface  per  horse-power,  but  with  the  efficiency  of  that  heating-surface  as 
regards  its  capacity  for  transfer  of  heat  from  the  heated  gases  to  the  water, 
which  will  depend  on  its  freedom  from  soot  and  incrustation,  and  upon  the 
circulation  of  the  water  and  the  heated  gases. 

With  bituminous  coal  the  efficiency  will  largely  depend  upon  the 
thoroughness  with  which  the  combustion  is  effected  in  the  furnace. 

The  efficiency  with  any  kind  of  fuel  will  greatly  depend  upon  the  amount 
of  air  supplied  to  the  furnace  in  excess  of  that'  required  to  support  com- 
bustion. With  strong  draught  and  thin  fires  this  excess  may  be  great, 
causing  a  serious  loss  of  economy.  The  subject  is  further  discussed  below. 

Measurement  of  Heating-surface. — The  usual  rule  is  to  consider  as 
heating-surface  all  the  surfaces  that  are  surrounded  by  water  on  one  side 
and  by  flame  or  heated  gases  on  the  other,  using  the  external  instead  of 
the  internal  diameter  of  tubes,  for  greater  convenience  in  calculation, 
external  diameters  of  boiler-tubes  usually  being  made  in  even  inches  or 
half  inches.  This  method,  however,  is  inaccurate,  for  the  true  heating- 
surface  of  a  tube  is  the  side  exposed  to  the  hot  gases,  the  inner  surface  in  a 
fire-tube  boiler  and  the  outer  surface  in  a  water-tube  boiler.  The  re- 


888 


THE  STEAM-BOILER. 


Distance  to  the  passage  of  heat  from  the  hot  gases  on  one  side  of  a  tube  or 
plate  to  the  water  on  the  other  consists  almost  entirely  of  the  resistance  to 
the  passage  of  the  heat  from  the  gases  into  the  metal,  the  resistance  of  the 
metal  itself  and  that  of  the  wetted  surface  being  practically  nothing. 
See  paper  by  C.  W.  Baker,  Trans.  A.  S.  M.  E.,  vol.  xix. 

RULE  for  finding  the  heating-surface  of  vertical  tubular  boilers:  Multiply 
the  circumference  9f  the  fire-box  (in  inches)  by  its  height  above  the  grate; 
multiply  the  combined  circumference  of  all  the  tubes  by  their  length,  and 
to  these  two  products  add  the  area  of  the  lower  tube-sheet;  from  this  sum 
subtract  the  area  of  all  the  tubes,  and  divide  by  144:  the  quotient  is  the 
number  of  square  feet  of  heating-surface. 

RULE  for  finding  the  heating-surface  of  horizontal  tubular  boilers:  Take 
the  dimensions  in  inches.  Multiply  two-thirds  of  the  circumference  of  the 
shell  by  its  length;  multiply  the  sum  of  the  circumferences  of  all  the  tubes 
by  their  common  length;  to  the  sum  pi  these  products  add  two  thirds  of 
the  area  of  both  tube-sheets;  from  this  sum  subtract  twice  the  combined 
area  of  all  the  tubes;  divide  the  remainder  by  144.  to  obtain  the  result  in 
square  feet. 

RULE  for  finding  the  square  feet  of  heating-surface  in  tubes:  Multiply 
the  number  of  tubes  by  the  diameter  of  a  tube  in  inches,  by  its  length  in 
feet,  and  by  0.2618. 

Horse-power,  Builder's  Rating.  Heating-surface  per  Horse- 
power. —  It  is  a  general  practice  among  builders  to  furnish  about  10 
square  feet  of  heating-surface  per  horse-power,  but  as  the  practice  is  not 
uniform,  bids  and  contracts  should  always  specify  the  amount  of  heating- 
surface  to  be  furnished.  Not  less  than  one-third  square  foot  of  grate-sur- 
face should  be  furnished  per  horse-power  with  ordinary  chimney  draught, 
not  exceeding  0.3  in.  of  water  column  at  the  damper,  for  anthracite  coal, 
and  for  poor  varieties  of  soft  coal  high  in  ash,  with  ordinary  furnaces.  A 
smaller  ratio  of  grate  surface  may  be  allowed  for  high  grade  soft  coal  and 
for  forced  draught. 

Horse-power  of  Marine  and  Locomotive  Boilers.  —  The  term  horse- 
power is  not  generally  used  in  connection  with  boilers  in  marine  practice, 
or  with  locomotives.  The  boilers  are  designed  to  suit  the  engines,  and 
are  rated  by  extent  of  grate  and  heating-surface  only. 

Grate-surface.  —  The  amount  of  grate-surface  required  per  horse- 
power, and  the  proper  ratio  of  heating-surface  to  grate-surface  are  ex- 
tremely variable,  depending  chiefly  upon  the  character  of  the  coal  and 
upon  the  rate  of  draught.  With  good  coal,  low  in  ash,  approximately 
equal  results  may  be  obtained  with  large  grate-surface  and  light  draught 
and  with  small  grate-surface  and  strong  draught,  the  total  amount  of  coal 
burned  per  hour  being  the  same  in  both  cases.  With  good  bituminous 
coal,  like  Pittsburgh,  low  in  ash,  the  best  results  apparently  are  obtained 
with  strong,  draught  and  high  rates  of  combustion,  provided  the  grate- 
surfaces  are  cut  down  so  that  the  total  coal  burned  per  hour  is  not  too  great 
for  the  capacity  of  the  heating-surface  to  absorb  the  heat  produced. 

With  coals  high  in  ash,  especially  if  the  ash  is  easily  fusible,  tending  to 
choke  the  grates,  large  grate-surface  and  a  slow  rate  of  combustion  are 
required,  unless  means,  such  as  shaking  grates,  are  provided  to  get  rid  of 
the  ash  as  fast  as  it  is  made.     The  amount  of  grate-surface  required  per  " 
horse-power  under  various  conditions  may  be  estimated  as  follows: 


Si? 
^J. 
.  ScsT'eS 

03   O   .j   m   O 

^£  ta  ftO 

Lbs.  Coal 
per  H.P. 
per  hour. 

Pounds  of  Coal  burned  per  square 
foot  of  Grate  per  hour. 

8 

10 

12 

15 

20  |  25 

30  |  35  |  40 

Sq.  Ft.  Grate  per  H.P. 

.09 
.10 
.10 
.11 
.12 
.13 
.14 
.17 

.25 

Good  coal  and 
boiler, 

Fair  coal  or  boiler, 

Poor  coal  or  boiler, 

Lignite  and  poor 
boiler, 

)10 
[  9 
(   8.61 

•     R 

H 

(  6-9 

M 

{3.45 

3.45 
3.83 
4. 
4.31, 
4.93 
5. 
5.75 
6.9 

10. 

.43 
.48 
.50 
.54 
.62 
.63 
.72 
.86 

1.25 

.35 

.38 
.40 
.43 
.49 
.50 
.58 
.69 

1.00 

.28 
.32 
.33 
.36 
.41 
.42 
.48 
.58 

.83 

.23 
.25 
.26 
.29 
.33 
.34 
.38 
.46 

.67 

.17 
.19 
.20 
.22 
.24 
.25 
.29 
.35 

.50 

.14 
.15 
.16 

.17 
.20 
.20 
.23 
.28 

.40 

.11 
.13 
.13 
.14 
.17 
.17 
.19 
.23 

.33 

.10 
.11 
.12 
.13 
.14 
.15 
.17 
.22 

.29 

PERFORMANCE   OF   BOILERS.  889 

In  designing  a  boiler  for  a  given  set  of  conditions,  the  grate-surface 
should  be  made  as  liberal  as  possible,  say  sufficient  for  a  rate  of  combus- 
tion of  10  Ibs.  per  square  foot  of  grate  for  anthracite,  and  15  Ibs.  per  square 
foot  for  bituminous  coal,  and  in  practice  a  portion  of  the  grate-surface 
may  be  bricked  over  if  it  is  found  that  the  draught,  fuel,  or  other  condi- 
tions render  it  advisable. 

Proportions  of  Areas  of  Flues  and  other  Gas-passages.  —  Rules 
are  usually  given  making  the  area  of  gas-passages  bear  a  certain  ratio  to 
the  area  of  the  grate-surface;  thus  a  common  rule  for  horizontal  tubular 
boilers  is  to  make  the  area  over  the  bridge  wall  1/7  of  the  grate-surface, 
the  flue  area  1/8,  and  the  chimney  area  1/9. 

For  average  conditions  with  anthracite  coal  and  moderate  draught,  say 
a  rate  of  combustion  of  12  Ibs.  coal  per  square  foot  of  grate  per  hour,  and  a 
ratio  of  heating  to  grate  surface  of  30  to  1,  this  rule  is  as  good  as  any,  but 
it  is  evident  that  if  the  draught  were  increased  so  as  to  cause  a  rate  of  com- 
bustion of  24  Ibs.,  requiring  the  grate-surface  to  be  cut  down  to  a  ratio  of 
60  to  1,  the  areas  of  gas-passages  should  not  be  reduced  in  proportion. 
The  amount  of  coal  burned  per  hour  being  the  same  under  the  changed 
conditions,  and  there  being  no  reason  why  the  gases  should  travel  at  a 
higher  velocity,  the  actual  areas  of  the  passages  should  remain  as  before, 
but  the  ratio  of  the  area  to  the  grate-surface  would  in  that  case  be 
doubled. 

Mr.  Barrus  states  that  the  highest  efficiency  with  anthracite  coal  is 
obtained  when  the  tube  area  is  1/9  to  1/10  of  the  grate-surface,  and  with 
bituminous  coal  when  it  is  1/6  to  1/7,  for  the  conditions  of  medium  rates  of 
combustion,  such  as  10  to  12  Ibs.  per  square  foot  of  grate  per  hour,  and  12 
square  feet  of  heating-surface  allowed  to  the  horse-power. 

The  tube  area  should  be  made  large  enough  not  to  choke  the  draught 
and  so  lessen  the  capacity  of  the  boiler;  if  made  too  large  the  gases  are  apt 
to  select  the  passages  of  least  resistance  and  escape  from  them  at  a  high 
velocity  and  high  temperature. 

This  condition  is  very  commonly  found  in  horizontal  tubular  boilers 
where  the  gases  go  chiefly  through  the  upper  rows  of  tubes;  sometimes 
also  in  vertical  tubular  boilers,  where  the  gases  are  apt  to  pass  most  rapidly 
through  the  tubes  nearest  to  the  center.  It  may  to  some  extent  be 
remedied  by  placing  retarders  in  those  tubes  in  which  the  gases  travel  the 
quickest. 

Air-passages  through  Grate-bars.  —  The  usual  practice  is,  air- 
opening  =  30%  to  50%  of  area  of  the  grate;  the  larger  the  better,  to  avoid 
stoppage  of  the  air-supply  by  clinker;  but  with  coal  free  from  clinker  much 
smaller  air-space  may  be  used  without  detriment.  See  paper  by  F.  A. 
Scheffler,  Trans.  A.  S.  M .  E.,  vol.  xv,  p.  503. 

Distance  .from  Dead  Plate  to  Shell  in  Horizontal  Tubular  Boiler 
Settings. — Rules  of  the  Department  of  Smoke  Inspection,  Chicago, 
1912. 

Diameter  of  shell,  in 72         66         60         54         48         42         36 

Dead  plate  to  shell,  in. .  .      42         40         38         36         34         32         30 

The  department  has  required  that  all  boilers  be  set  higher  than  has 
formerly  been  the  practice  in  order  to  provide  greater  combustion 
space  and  to  allow  the  installation  of  proper  furnaces.    . 
PERFORMANCE  OF  BOILERS. 

The  performance  of  a  steam-boiler  comprises  both  its  capacity  for  gener- 
ating steam  and  its  economy  of  fuel.  Capacity  depends  upon  size,  both  of 
grate-surface  and  of  heating-surface,  upon  the  kind  of  coal  burned,  upon  the 
draught,  and  also  upon  the  economy.  Economy  of  fuel  depends  upon  the 
completeness  with  which  the  coal  is  burned  in  the  furnace,  on  the  proper 
regulation  of  the  air-supply  to  the  amount  of  coal  burned,  and  upon  the 
thoroughness  with  which  the  boiler  absorbs  the  heat  generated  in  the 
furnace.  The  absorption  of  heat  depends  on  the  extent  of  heating-sur- 
face in  relation  to  the  amount  of  coal  burned  or  of  water  evaporated,  upon 
the  arrangement  of  the  gas-passages,  and  upon  the  cleanness  of  the  sur- 
faces. The  capacity  of  a  boiler  may  increase  with  increase  of  economy 
when  this  is  due  to  more  thorough  combustion  of  the  coal  or  to  better  regu- 
lation of  the  air-supply,  9r  it  may  increase  at  the  expense  of  economy 
when  the  increased  capacity  is  due  to  overdriving,  causing  an  increased 
loss  of  heat  in  the  chimney  gases.  The  relation  of  capacity  to  economy 
is  therefore  a  complex  one,  depending  on  many  variable  conditions. 


890  THE   STEAM-BOILER. 

A  formula  expressing  the  relation  between  capacity,  rate  of  driving, 
or  evaporation  per  square  foot  of  heating-surface,  to  the  economy,  or 
evaporation  per  pound  of  combustible  is  given  on  page  893. 

Selecting  the  highest  results  obtained  at  different  rates  of  driving  with 
anthracite  coal  in  the  Centennial  tests  (in  1876)  and  the  highest  results 
with  anthracite  reported  by  Mr.  Barrus  in  his  book  on  Boiler  Tests,  the 
author  has  plotted  two  curves  showing  the  maximum  results  which  may 
be  expected  with  anthracite  coal,  the  first  under  exceptional  conditions 
such  as  obtained  in  the  Centennial  tests,  and  the  second  under  the  best 
conditions  of  ordinary  practice.  (Trans.  A.  S.  M.  E.,  xviii,  354). 
From  these  curves  the  following  figures  are  obtained. 

Lbs.  water  evaporated  from  and  at,  212°  per  sq.  ft.  heating-surface 
per  hour: 

1.6     1.7     2        2.6     3          3.5     4          4.5     5        6        7      8 
Lbs.  water  evaporated  from  and  at  212°  per  Ib.  combustible: 
Centennial...   11.8  11.9  12.0     12.1  12.05  12      11.85  11.7  11.5  10.85  9.8   8.5 

Barrus 11.4  11.5  11.55  11.6  11.6     11.5  11.2     10.9  10.6     9.9     9.2  8.5 

Avg.  Cent'l 12.0     11.6  11.2     10.8  10.4     10.0     9.6     8.8     8.0  7.2 

The  figures  in  the  last  line  are  taken  from  a  straight  line  drawn  as  nearly 
as  possible  through  the  average  of  the  plotting  of  all  the  Centennial  tests. 
The  poorest  results  are  far  below  these  figures.  It  is  evident  that  no  for- 
mula  can  be  constructed  that  will  express  the  relation  of  economy  to  rate  oi 
driving  as  well  as  do  the  three  lines  of  figures  given  above. 

'For  semi-bituminous  and  bituminous  coals  the  relation  of  economy  tc 
the  rate  of  driving  no  doubt  follows  the  same  general  law  that  it  does  with 
anthracite,  i.e.,  that  beyond  a  rate  of  evaporation  of  3  or  4  Ibs.  per  sq.  ft.  oi 
heating-surface  per  hour  there  is  a  decrease  of  economy,  but  the  figures 
obtained  in  different  tests  will  show  a  wider  range  between  maximum  and 
average  results  on  account  of  the  fact  that  it  is  more  difficult  with  bitumi- 
nous  than  with  anthracite  coal  to  secure  complete  combustion  in  the 
furnace. 

The  amount  of  the  decrease  in  economy  due  to  driving  at  rates  exceeding 
4  Ibs.  of  water  evaporated  per  square  foot  of  heating-surface  per  hour 
differs  greatly  with  different  boilers,  and  with  the  same  boiler  it  may  diffei 
with  different  settings  and  with  different  coal.  The  arrangement  and  size 
of  the  gas-passages  seem  to  have  an  important  effect  upon  the  relation  oi 
economy  to  rate  of  driving. 

A  comparison  of  results  obtained  from  different  types  of  boilers  leads  to 
the  general  conclusion  that  the  economy  with  which  different  types  oi 
boilers  operate  depends  much  more  upon  their  proportions  and  the  con- 
ditions under  which  they  work,  than  upon  their  type;  and,  moreover, 
that  when  the  proportions  are  correct,  and  when  the  conditions  are  favor- 
able, the  various  types  of  boilers  give  substantially  the  same  economic 
result. 

Conditions  of  Fuel  Economy  in  Steam-boilers.  —  1.  That  the  boiler 
has  sufficient  heating  surface  to  absorb  from  75  to  80%  of  all  the  heat 
generated  by  the  fuel.  2.  That  this  surface  is  so  placed,  and  the  gas  pas- 
sages so  controlled  by  baffles,  that  the  hot  gases  are  forced  to  pass  uni- 
formly over  the  surface,  not  being  short-circuited.  3.  That  the  furnace  is 
of  such  a  kind,  and  operated  in  such  a  manner,  that  the  fuel  is  completely 
burned  in  it,  and  that  no  unburned  gases  reach  the  heating  surface  of  the 
boiler.  4.  That  the  fuel  is  burned  with  the  minimum  supply  of  air  re- 
quired to  insure  complete  combustion,  thereby  avoiding  the  carrying  of  an 
excessive  quantity  of  heated  air  out  of  the  chimney. 

There  are  two  indices  of  high  economy.  1.  High  temperature,  ap- 
proaching 3000°  F.  in  the  furnace,  combined  with  low  temperature,  below 
600°  F.,  in  the  flue.  2.  Analysis  of  the  flue  gases  showing  between  4  ynd 
8%  of  free  oxygen.  Unfortunately  neither  of  these  indices  is  available 
to  the  ordinary  fireman;  he  cannot  distinguish  by  the  eye  any  temperature 
above  2000°,  and  he  cannot  know  whether  or  not  an  excessive  amount  oi 
oxygen  is  passing  through  the  fuel.  The  ordinary  haphazard  way  of  firing 
therefore  gives  an  average  of  about  10%  lower  economy  than  can  be 
obtained  when  the  firing  is  controlled,  as  it  is  in  many  large  plants,  by  re- 
cording furnace  pyrometers,  or  by  continuous  gas  analysis,  or  by  both- 
Low  CO2  in  the  flue  gases  may  indicate  either  excessive  air  supply  in  the 
furnace,  or  leaks  of  air  into  the  setting,  or  deficient  air  supply  with  the 
presence  qf  CO,  and,  therefore  imperfect  combustion.  The  latter,  if  exces- 


PERFORMANCE   OF   BOILERS.  891 

sive,  is  indicated  by  low  furnace  temperature.  The  analysis  for  CO2  should 
be  made  both  of  the  gas  sampled  just  beyond  the  furnace  and  of  the  gas 
sampled  at  the  flue.  Diminished  CO2  in  the  latter  indicates  air-leakage. 

Less  than  4%  of  free  oxygen  in  the  gases  is  usually  accompanied  with 
CO,  and  it  therefore  indicates  imperfect  combustion  from  deficient  air, 
supply.  More  than  8%  means  excessive  air  supply  and  corresponding 
waste  of  heat. 

Air  Leakage  or  infiltration  of  air  through  the  firebrick  setting  is  a 
common  cause  of  poor  economy.  It  may  be  detected  by  analysis  as  above 
Stated,  and  should  be  prevented  by  stopping  all  visible  cracks  in  the  brick- 
work, and  by  covering  it  with  a  coating  impervious  to  air. 

Autographic  CO2  Recorders  are  used  in  many  large  boiler  plants  for 
the  continuous  recording  of  the  percentage  of  carbon  dioxide  in  the  gases. 
When  the  percent  age  of  CO2is  between  12  and  16.it  indicates  good  fur- 
nace conditions,  when  below  12  the  reverse. 

Continuous  Records  are  an  important  element  in  securing  maximum 
economy  in  modern  boiler  plants.  They  include  records  of  coal  and 
water  consumption,  of  draft  at  the  furnace  and  the  chimney,  of  the 
analyses  of  the  gases,  of  the  flue  temperature,  and  of  the  steam  de- 
livered. For  description  of  steam  flow  meters  and  other  recording 
apparatus  see  Steam  Boiler  Economy.  2d  edition. 

Efficiency  of  a  Steam-boiler. — The  efficiency  of  a  boiler  is  the 
percentage  of  the  total  heat  generated  by  the  combustion  of  the  fuel 
which  is  utilized  in  heating  the  water  and  in  raising  steam.  With  anthra- 
cite coal  the  heating-value  of  the  combustible  portion  is  very  nearly 
14,800  B.T.U.  per  lb.,  equal  to  an  evaporation  from  and  at  212°  of  14,800 
•*•  970  =  15.26  Ibs.  of  water.  A  boiler  which  when  tested  with  anthra- 
cite coal  shows  an  evaporation  of  12  Ibs.  of  water  per  lb.  of  combustible, 
has  an  efficiency  of  12  -s-  15.26  =  78.6%,  a  figure  which  is  approximated, 
but  scarcely  ever  quite  reached,  in  the  best  practice.  With  bituminous 
coal  it  is  necessary  to  have  a  determination  of  its  heating-power  made 
by  a  coal  calorimeter  before  the  efficiency  of  the  boiler  using  it  can  be 
determined,  but  a  close  estimate  may  be  made  from  the  chemical  analysis 
of  the  coal.  (See  Coal.) 

The  difference  between  the  efficiency  obtained  by  test  and  100%  is 
the  sum  of  the  numerous  wastes  of  heat,  the  chief  of  which  is  the  necessary 
loss  due  to  the  temperature  of  the  chimney-gases.  If  we  tyave  an  analysis 
and  a  calorimetric  determination  of  the  heating-power  of  the  coal  (properly 
sampled),  and  an  average  analysis  of  the  chimney-gases,  the  amounts 
of  the  several  losses  may  be  determined  with  approximate  accuracy  by 
the  method  described  below. 

Data  given: 

1.    ANALYSIS  OF  THE  COAL.         2.    ANALYSIS  OF  THE  DRY  CHIMNEY- 
Cumberland  Semi-bituminous.  GASES,  BY  WEIGHT. 

Carbon .   80.55  C.  O.          N. 

Hydrogen 4.50       CO2  =   13.6  =  3.71       9.89     

Oxygen ...      2.70       CO    =     0.2  =  0.09       0.11      

Nitrogen 1.08       O      =    11.2= 11.20      

Moisture 2.92       N      =    75.0=.. 75.00 

Agh  c    05 

100.0       3.80     21.20     75.00 
100.00 

Heating-value  of  the  coal  by  Dulong's  formula,  14,243  heat-units. 
The  gases  being  collected  over  water,  the  moisture  in  them  is  not  deter- 
mined. 

3.  Ash  and  refuse  as  determined  by  boiler-test,  10.25,  or  2%  more  than 
that  found  by  analysis,  the  difference  representing  carbon  in  the  ashes 
Obtained  in  the  boiler-test. 

4.  Temperature  of  external  atmosphere,  60°  F. 

5.  Relative  humidity  of  air,  60%,  corresponding  (see  air  tables)  to 
0.007  lb.  of  vapor  in  each  lb.  of  air. 

6.  Temperature  of  chimney-gases,  560°  F. 
Calculated  results: 

The  carbon  in  the  chimney-gases  being  3.8%  of  their  weight,  the  total 
weight  of  dry  gases  per  lb.  of  carbon  burned  is  100  -*-  3.8  =  26.32  Ibs. 
Since  the  carbon  burned  is  80.55  -  2  =  78.55%  of  the  weight  of  the  coal, 
the  weight  of  the  dry  gases  per  lb.  of  coal  is  26.32  X  78.55  -f-  100  = 
20.67  Ibs. 


892  THE  STEAM-BOILER, 

Each  pound  of  coal  furnishes  to  the  dry  chimney-gases  0.7855  lb.  C, 
and  0.0108  N,  a  total  of  0.7963,  say  0.80  lb.  This  subtracted  from 
20.67  Ibs.  leaves  19.87  Ibs.  as  the  quantity  of  dry  air  (not  including 
moisture)  which  enters  the  furnace  per  pound  of  coal,  not  counting  the 
air  required  to  burn  the  available  hydrogen,  that  is,  the  hydrogen 
minus  one-eighth  of  the  oxygen  chemically  combined  in  the  coal.  Each 
lb.  of  coal  burned  contained  0.045  lb.  H,  which  requiras  0.045  X  8  = 
0.36  lb.  O  for  its  combustion.  Of  this,  0.027  lb.  is  furnished  by  the  coal 
itself,  leaving  0.333  lb.  to  come  from  the  air.  The  quantity  of  air 
needed  to  supply  this  oxygen  air  containing  23  %  by  weight  of  oxygen) 
is  0.333  -r-  0.23  =  1.45  lb.,  which  added  to  "the  19.87  Ibs.  already  found 
gives  21.32  Ibs.  as  the  quantity  of  dry  air  supplied  to  the  furnace  per 
lb.  of  coal  burned. 

The  air  carried  in  as  vapor  is  0.0071  lb.  for  each  lb.  of  dry  air,  or  21.3 
X  0.0071  =  0.15  lb.  for  each  lb.  of  coal.  Each  lb.  of  coaj  contained 
0.029  lb.  of  moisture,  which  was  evaporated  and  carried  into  the 
chimney-gases.  The  0.045  lb.  of  H  per  lb.  of  coal  when  burned  formed 
0.045  X  9  =  0.405  lb.  of  H2O. 

From  the  analysis  of  the  chimney-gas  it  appears  that  0.09  -^  3.80  = 
2.37%  of  the  carbon  in  the  coal,  or  0.0237  X  0.7855  =  0.0186  lb.  C 
per  lb.  of  coal,  was  burned  to  CO  instead  of  to  COz. 

We  now  have  the  data  for  calculating  the  various  losses  of  heat,  as 
follows,  for  each  pound  of  coal  burned: 


Heat-   Per  cent  of 
units.   Heat-value 

of  the  Coal. 

20.67  Ibs.  dry  gas  X  (560°  -  60°)  X  sp.  heat  0.24      = 

2480.4 

17.41 

0.15  lb.  vapor  in  air  X  (560°  -  60°)  X  sp.  ht.  0.46  --= 

34.5 

0.24 

0.029  lb.  moist,  in  coal  heated  from  60°  to  212°      = 

4.4 

0.03 

0.029  lb.  evap.  from  and  at  212°;  0.029  X  970      = 

28.1 

0.20 

0.029  lb.  steam  (heated  212°  to  560°)  X  348X  0.46  = 

4.6 

0.03 

0.405  lb.  H2O  from  H  in  coal  X  (152  +  970  + 

348    X  0.46) 

519.2 

3.65 

0.0186  lb.  C  burned  to  CO;  loss  by  incomplete 

combustion,  0.0186  X  (14,6QO   -  4450) 

188.8 

1.33 

0.02  lb.  carbon  lost  in  ashes:  0.02   X  14,600 

292.0 

2.05 

Radiation  and  unaccounted  for,  by  difference        = 

676.1 

4.75 

4228.1       29.69 

Utilized  in  making  steam,  equivalent  evapora- 
tion 10.37  Ibs.  from  and  at  212°  perlb.  of  coal      =  10,014.9       70.31 

14,243.0     100.00 

The  heat  lost  by  radiation  from  the  boiler  and  furnace  is  not  easily 
determined  directly,  especially  if  the  boiler  is  enclosed  in  brickwork,  or 
is  protected  by  non-conducting  covering.  It  is  customary  to  estimate 
the  heat  lost  by  radiation  by  difference,  that  is,  to  charge  radiation  with 
all  the  heat  lost  which  is  not  otherwise  accounted  for.  One  method  of 
determining  the  loss  by  radiation  is  to  block  off  a  portion  of  the  grate- 
surface  and  build  a  small  fire  on  the  remainder,  and  drive  this  fire  with 
just  enough  draught  to  keep  up  the  steam-pressure  and  supply  the  heat 
lost  by  radiation  without  allowing  any  steam  to  be  discharged,  weighing 
the  coal  consumed  for  this  purpose  during  a  test  of  several  hours'  dura- 
tion. 

Estimates  of  radiation  by  difference  are  apt  to  be  greatly  in  error,  as 
in  this  difference  are  accumulated  all  the  errors  of  the  analyses  of  the 
coal  and  of  the  gases.  An  average  value  of  the  heat  lost  by  radiation 
from  a  boiler  set  in  brickwork  is  about  3  % .  When  several  boilers  are  in 
a  battery  and  enclosed  in  a  boiler-house  the  loss  by  radiation  may  be  very 
much  less,  since  much  of  the  heat  radiated  from  the  boiler  is  returned  to 
it  in  the  air  supplied  to  the  furnace,  which  is  taken  from  the  boiler-room. 
An  important  source  of  error  in  making  a  "heat  balance"  such  as  the 
one  above  given,  especially  when  highly  bituminous  coal  is  used,  may  be 
due  to  the  non-combustion  of  part  of  the  hydrocarbon  gases  distilled  from 
the  coal  immediately  after  firing,  when  the  temperature  of  the  furnace  may 
be  reduced  below  the  point  of  ignition  of  the  gases.  Each  pound  of  hydro- 
gen which  escapes  burning  is  equivalent  to  a  loss  of  heat  in  the  furnace  of 


PERFORMANCE   OF  BOILERS.  893 

62,000  heat-units.  Another  source  of  error,  especiallywith  bituminous  slack 
coal  nigii  in  moisture,  is  due  to  the  formation  of  water-gas,  CO  +  H,  by  the 
decomposition  of  the  water,  and  the  consequent  absorption  of  heat,  this 
water-gas  escaping  unburned  on  account  of  the  choking  of  the  air  supply 
when  fine  fresh  coal  is  supplied  to  the  fire. 

In  analyzing  the  chimney-gases  by  the  usual  method  the  percentages  of 
the  constituent  gases  are  obtained  by  volume  instead  of  by  weight.  To 
reduce  percentages  by  volume  to  percentages  by  weight,  multiply  the  per- 
centage by  volume  of  each  gas  by  its  specific  gravity  as  compared  with  air, 
and  divide  each  product  by  the  sum  of  the  products. 

Instead  of  using  the  percentages  by  weight  of  the  gases,  the  percentage 
by  volume  may  be  used  directly  to  find  the  weight  of  gas  per  pound  of 
carbon  by  the  formula  given  below. 

If  O,  CO,  CO2,  and  N  represent  the  percentages  by  volume  of  oxygen, 
carbonic  oxide,  carbonic  acid,  and  nitrogen,  respectively,  in  the  gases  of 
combustion: 

Lb.  of  air  required  to  burn  )  =  3  .  032  N  ^ 
one  pound  of  carbon       J      CO2  +  CO 

N 
Ratio  Of  total  air  to  the  theoretical  requirement  =  j^_~3  782  (O  -  1/2  CO)* 

Lb.  of  air  per  pound  \  __  j  Lb.  of  air  per  pound  )  v  j  Per  cent  of  car-  [ 
of  coal  i        t      of  carbon  j  A  |      bon  in  coal      \ 

11CO2+80+7(CO+N) 
Lb.  dry  gas  produced  per  pound  of  carbon  =        —  37CO  4-  CO)  — 

Relation  of  Boiler  Efficiency  to  the  Rate  of  Driving,  Air  Supply, 
etc.  —  In  the  author's  Steam  Boiler  Economy  (p.  294)  a  formula  is  de- 
veloped showing  the  efficiency  that  may  be  expected,  when  the  com- 
bustion of  the  coal  is  complete,  under  different  conditions.  The 
formula  is 

Ba_        K-  tcf  970 


__  _ 

~E^~~  K  (1  +  RS/W)        K     (K  -  tcf)    S  ' 

K  =  heating  value  per  Ib.  of  combustible;  Ea=  actual  evaporation  from 
and  at  212°  per  Ib.  of  combustible;  Ep  =  possible  evaporation  =•  K  •*• 
970;  t  —  elevation  of  the  temperature  of  the  water  in  the  boiler  above 
the  atmospheric  temperature;  c  —  specific  heat  of  the  chimney  gases, 
taken  at  0.24;/  =  weight  of  flue  gases  per  Ib.  of  combustible;  S  —  square 
feet  of  heating  surface;  W  =  pounds  of  water  evaporated  per  hour; 
W/S  =  rate  of  driving;  R=  radiation  loss,  in  units  of  evaporation  per 
sq.  ft.  of  heating-surface  per  hour;  a  is  a  coefficient  found  by  experiment; 
it  may  be  called  a  coefficient  of  inefficiency  of  the  boiler,  and  it  depends 
on  and  increases  with  the  resistance  to  the  passage  of  heat  through  the 
metal,  soot  or  scale  on  the  metal,  imperfect  combustion,  short-circuiting, 
air  leakage,  or  any  other  defective  condition,  not  expressed  in  terms  in 
the  formula,  which  may  tend  to  lower  the  efficiency.  Its  value  is  between 
200  and  400  when  records  of  tests  show  high  efficiency,  and  above  400  for 
lower  efficiencies. 

The  coefficient  a  is  a  criterion  of  performance  of  a  boiler  when  all  the 
other  terms  of  the  formula  are  known  as  the  results  of  a  test.  By  trans- 
position its  value  is 

f  K-tcf  1     .  C*f*  W 

L970  (1  +  RS/W)        a\  '   (K-  tcf)  S 

On  the  diagram  below  (Fig.  159),  with  abscissas  representing  rates  of 
driving  and  ordinates  representing  efficiencies  are  plotted  curves  showing 
the  relation  of  the  efficiency  to  rate  of  driving  for  values  of  a=  100  to 
400  and  values  of  f  from  20  to  35.  together  with  a  broken  line  showing 
the  maximum  efficiencies  obtained  by  six  boilers  at  the  Centennial  Exhi- 
bition, and  other  lines  showing  the  poor  results  obtained  from  five  other 
boilers.  The  curves  are  also  based  on  the  following  values,  K  =  14.800; 
c  =  0.24;  £=  300  (except  one  curve,  t  =  250);  R  =  0.1. 

An  inspection  of  the  curves  shows  the  following.  1.  The  maximum 
Centennial  results  all  lie  below  the  curve  /  =  20,  a  =  200,  by  2  to  4%, 
but  they  follow  the  general  direction  of  the  curve.  This  curve  may 


894 


THE!   SiEAM-B  OILER. 


therefore  be  taken  as  representing  the  maximum  possible  boiler  per- 
formance  with  anthracite  coal,  as  the  results  obtained  in  1876  have  never 
been  exceeded  with  anthracite. 

2.  With/  =  20  and  a  =  200  the  efficiency  for  maximum  performance, 
according  to  the  curve,  is  a  little  less  than  82%  at  2  Ibs.  evaporation  pel 
sq.  ft.  of  heating-surface  per  hour,  but  it  decreases  very  slowly  at  hignei 
rates,  so  that  it  is  80%  at  31/2  Ibs.,  and  76%  at  5S/4  Ibs. 

With  a  =  200  and  /  greater  than  20,  the  efficiency  has  a  lower  maxi- 
mum, reaches  the  maximum  at  a  lower  rate  of  driving,  and  falls  off 
rapidly  as  the  rate  increases,  the  more  rapidly  the  higher  the  value  of  /. 
showing  excessive  air  supply  to  be  a  potent  cause  of  low  economy. 


12  3  4  5  6  *7 

Lbs.  of  Water  EvaporatecLfrom  and  at  212°  F.  per  s<j.  ft.  of;  Heating  Surface  per  Hour 
FIG.  359. 

3.  An  increase  in  the  value  of  a  from  200  to  400  with  /  =  20  is  much 
less  detrimental  to  efficiency  than  an  increase  in  /  from  20  to  30. 

In  the  diagram,  Fig.  T60,  are  plotted,  together  with  the  curve  for/  =  20, 
a=  200,  t  =  300,  and  K  =  15,750,  marked  R  =  0.1,  a  straight  line,  R  =  0, 
showing  the  theoretical  maximum  efficiency  when  there  is  no  loss  by 
radiation, Jand  the  plottings  of  the  results  of  two  series  of  tests,  one  of  a 
Thornycroft  boiler,  with  W/S  from  1.24  to  8.5,  and  the  other  of  a  Babcock 
&  Wilcox  marine  b9iler  with  W/S  from  5.18  to  13.67,  together  with  the 
maximum  Centennial  tests.  The  calculated  value  of  a  in  all  these  tests 
except  one  ranged  from  191  to  454,  the  highest  values  being  those  show- 
ing the  largest  departure  from  the  curve  R  =  0.1.  The  one  exception 
is  the  Thornycroft  test  showing  over  86%  efficiency;  this  gives  a  value 
of  a  =  57,  which  indicates  an  error  in  the  test,  as  such  a  low  value  is  far 
below  the  lowest  recorded  in  any  other  test. 

In  the  second  edition  of  Steam  Boiler  Economy  (page  316),  there  is 
developed  a  modification  of  the  efficiency  formula,  so  that  it  takes 


PERFORMANCE    OF   BOILERS. 


895 


account,  in  addition  to  the  other  variables,  of  hydrogen  and  moisture  in 
the  coal  and  of  incomplete  combustion.     It  is 

Ea  _       Ki  -  tcfi  970.4        fli  c2/i2        W_ 

Wp~  K+(1RS/W)         K~  K  (Ki  -  tcfi)  ~S" 
The  notation  is  the  same  as  in  the  original  formula  except  that  Ki  — 


K  -  101.5  C 


-  970-4   (°-09 


)  in  which  c»  H  and 


pj-         ™* 
C_/O  -p  \-s\Jz 

M  are  respectively  the  percentages  of  carbon,  hydrogen  and  moisture 
in  the  coal,  and  CO  and  CO2  percentages  by  volume  of  the  dry  flue 
gases,  and  f\  -  /+  0.28H  +  0.03  M. 

Computing  the  results  of  six  series  of  boiler  tests,  47  tests  in  all, 
which  have  given  high  efficiencies,  the  value  of  «i  is  found  to  average 
about  200.  Values  from  1  60  to  240  may  be  obtained  in  duplicate  tests 


1          2          3      '    4          5          6          7          8          9         10         11        12        13        14 
Lbs.  of  Water  Evaporated  from  and  at  212°  F«  per  s<j.  ft.  o£  Heating  Surface  per  Hour 

PIG.  160. 

in  which  all  the  conditions,  as  far  as  known,  are  identical,  the  dif- 
ference between  individual  and  average  values  being  probably  due  to 
errors.  Values  above  300,  if  not  due  to  errors,  represent  defective  per- 
formance which  may  be  due  to  short-circuiting  or  to  unclean  heating 
surfaces. 

Effect  of  Quality  of  Coal  upon  Efficiency.— Calculations  have  been 
made,  using  the  formula  given  above,  of  the  theoretical  efficiencies 
obtainable  from  five  different  kinds  of  coal  and  an  average  fuel  oil,  the 
analyses  of  which  are  given  below,  on  the  assumption  of  complete  com- 
bustion with  20%  excess  air  supply,  fli  =  200,  t  =  300,  c  =  0.24  aiid  rates 
of  driving  W/S  from  1  to  14  Ib.  The  results  are  shown  in  the  table. 
ANALYSES  OF  FUELS. 


Anthracite 
Dry  and  Free 
from  Ash. 

Semi-bitum. 

Pittsburgh 
Ash  and 
Sul.  Free. 

Illinois 

Lignite. 

California 
Fuel  Oil. 

C        94.3 
H        2.3 
O         2.4 
N         1.0 

B.T.U.  per 
Ib.     15,000 

Moist.      1.7 
N.S.Ash  4.6 
C        85.0 
H          4.5 
O          3.2 

14,950 

Moist.  2.0 
C     83.0 
H      5.5 
0       8.0 

N       1.0 

14,908 

Moist.  10.8 
C     61.0 
H       4.2 
0       9.6 
N       1.2 
Ash,  SI  3.  2 

10,640 

Moist.27.0 
C     47.4 
H      3.3 
0      12.0 
N       1.0 

8,250 

0.2 
84.9 
11.9 
1.9 
S  1.1 

19,600 

RELATION  OF  EFFICIENCY  TO  QUALITY  OF  COAL. 


Rate  of 
Driving,  W/S. 

1 

2 

3 

4 

6 

8 

10 

12 

14 

Anthracite 

81.85 
80.41 
79.78 
78.28 
75.83 
78.78 

84.56 
82.96 
82.30 
80.59 
77.76 
81.61 

Ef 
84.71 
83.00 
82.34 
80.44 
77.51 
82.01 

ficienc 
84.16 
82.38 
81.71 
79.64 
76.52 
81.74 

es 
82.39 
80.42 
79.76 
77.34 
73.98 
80.52 

80.25 
78.10 
77.45 
74.71 
70.90 
78.97 

77.95 
75.64 
75.01 
71.93 
67.79 
77.26 

75.59 
73.12 
72.48 
69.09 
64.62 
75.48 

73.19 
70.54 
69.92 
66.20 
61.40 
73.58 

Semi-bitum      

Pittsburgh  bitum  .  . 
Illinois  

Lignite 

Fuel  Oil  

896 


THE   STEAM-BOILER. 


Effect  of  Imperfect  Combustion  and  Excess  Air  Supply.— Taking 
a  Pittsburgh  bituminous  coal,  having  a  composition,  free  from  sul- 
phur and  ash,  of  83  C,  5.5  H,  8  O,  1.5  N,  and  2  Moisture,  and  a  heating 
value  of  14,908  B.T.U.  per  Ib.  fuel  =  15,222  B.T.U.  per  Ib.  combustible, 
and  assuming  it  to  be  burned  with  different  quantities  of  air,  as  in  the 
table  below,  we  may  compute  the  weight  of  air  supplied  per  pound  of 
fuel  and  per  pound  of  carbon,  and  the  analysis  by  volume  of  the  gases, 
giving  results  as  follows: 


Case. 

Per 
Cent 
of  C 
Burned 
to  CO. 

Per 
Cent 
Excess 
Air. 

Dry 
Gas 
per  Ib. 
Fuel 
=  /• 

Dry 
Gas 
per  Ib. 
Car- 
bon. 

Analysis  of  Dry  Gas  by  Volume. 

C02. 

CO. 

O. 

N. 

(1) 

0 
0 
0 
0 

5 

10 
20 

0 
20 
50 
100 
0 
20 
0 
0 

11.60 
13.83 
17.16 
22.72 
11.36 
13.23 
11.12 
10.65 

13.98 
16.66 
20.67 
27.37 
13.69 
15.93 
13.40 
12.83 

18.45 
15.30 
12.18 
9.10 
17.85 
15.18 
17.21 
15.88 

0 
0 
0 
0 
0.94 
0.80 
1.92 
3.97 

0 
3.56 
7.09 
10.57 
0 
3.12 
0 
0 

81.55 
81.14 
80.73 
80.33 
81.21 
80.90 
80.87 
80.15 

(2).  . 

(3) 

(4)      .  . 

A  

B 

C  
D  

H2O  in  gases  per  Ib.  fuel  =  0.09  H  +  0.01  M,  in  all  cases  =  0,515  Ib. 
Case  (1)  is  an  ideal  but  not  a  practicable  case,  since  it  is  not  possible 
in  practice  to  burn  all  the  C  to  CO2  without  excess  of  air.  Cases 
(2),  (3),  (4),  A  and  B  are  all  within  the  range  of  ordinary  practice 
(which  sometimes  shows  200%  or  more  excess  air)  and  cases  C  and  D 
represent  either  the  condition  of  too  heavy  firing  and  choked  air  supply, 
or  the  condition  existing  for  a  minute  or  two  after  firing  of  fine  moist 
slack  coal,  which  temporarily  chokes  the  air  supply  and  causes  the  for- 
mation of  a  great  volume  of  smoky  gas. 

Cases  2  and  A  represent  the  best  possible  practice,  reached  only 
when  all  conditions  are  most  favorable. 

Applying  the  formula  given  above,  we  take  K=  14,908;  i  =  300; 
c  =  0.24;  R  =  0.1;  a\  =  200;  /=  the  values  given  in  the  table;  K\  and 
J\  =  values  given  by  the  formulae  in  the  preceding  paragraph,  and 
W/S  different  values  from  0.5  to  14,  and  obtain  the  theoretical  efficiencies 
given  below: 

THEORETICAL  EFFICIENCIES  WITH   PITTSBURGH   COAL  UNDER   DIF- 
FERENT CONDITIONS. 


Case           

(1) 

(2) 

(3) 

(4) 

^ 

B 

c 

D 

Per  cent  C  to  CO. 

0 

0 

0 

0 

5 

5 

10 

20 

Per  cent  excess  air 

0 

20 

50 

100 

0 

20 

0 

0 

W/S  = 

Efficiencies,  Per  Cent. 

0.5 

74.76 

73.68 

72.05 

68.97 

72.53 

71.61 

69.77 

65.79 

1 

81.13 

79.78 

77.7.3 

73.72 

78,69 

77.54 

76.23 

71.34 

2 

84.06 

82.30 

79.60 

73.90 

81.53 

80.02 

78.98 

73.87 

3 

84,49 

82.34 

79.02 

71.72 

81.91 

80.09 

79.35 

74.16 

4 

84.24 

81.71 

77.79 

68.91 

81.64 

79.50 

79.09 

73.85 

6 

83.03 

79.76 

74.65 

62.60 

80.43 

77.65 

77.91 

72.64 

8 

81.47 

77.45 

71.17 

55.87 

78.87 

75.48 

76.39 

71.11 

10 

79.77 

75.01 

67.55 

49.20 

77.17 

73.15 

74.74 

69.45 

12 

77.99 

72.48 

63.86 

42.37 

75.41 

70.76 

73.02 

67.72 

14 

76.16 

69.92 

60.12 

35.48 

73.58 

68.32 

71.27 

65.97 

The  figures  in  the  table  show  the  great  falling  off  in  efficiency  at  high 
rates  of  driving  when  the  air  supply  is  excessive,  and  the  necessity  of 
gas  analysis  (or  of  a  CO2  or  an  oxygen  indicator)  if  high  efficiencies  are 
to  be  obtained  at  high  rates  of  driving. 

The  Straight-line  Formula  for  Efficiency . — An  examination  of  the 
curves  plotted  from  the  table  given  above  shows  that  when  the  rate  of 
driving  is  in  excess  of  3  Ib.  per  sq.  ft.  of  heating  surface  per  hour,  and 
the  effect  of  the  radiation  loss  is  therefore  of  small  importance,  the 
curves  become  approximately  straight  lines,  the  formula  of  which  is 


PERFORMANCE   OF   BOILERS. 


897 


E  =  E  max  -  C(W/S  -  3),  in  which  E  is  the  efficiency  at  any  rate  of 
driving  above  W/S  =  3,  E  max  is  the  efficiency  when  W/S  =  3,  and  C 
is  a  constant  which  depends  on  the  quality  of  the  coal  and  on  the 
furnace  conditions.  Taking  from  the  above  table  the  efficiencies  at 
W/S  =  3  and  W/S  =  14  and  calculating  the  value  of  C  in  the  above 
equation  of  a  straight  line  between  these  points,  we  obtain  the  following 
formulae  for  efficiency  for  the  several  cases  named: 


Cases. 

Per  Cent 
C  to  CO2 

Per  Cent 
Excess  Air. 

Formula. 

2 
3 

A 
B 
C 
D 

0 
0 
0 
0 
5 
5 
10 
20 

0 

20 
50 
100 
0 
20 
0 
0 

E 
E 
E 
E 
E 
E 
E 
E 

=  84.5  -  0.76(W/S 
=  82.3  -  \.\3(W/S 
=  79.0  -  \.72(W/S 
=  71.7  -  3.39(W/S 
=  81.9  -  0.76(W/S 
=  80.1  -  \.07(W/S 
=  79.4  -  0.74(W/S 
=  74.2  -  0.75(W/S 

1  1  1  I  1  1  1  1 

The  efficiencies  calculated  by  these  formulae  in  every  case  in  which 
W/S  is  between  3  and  14  are  slightly  lower  than  those  calculated  from 
the  complex  formula,  but  in  no  case  is  the  difference  as  great  as  1%. 
It  must  be  noted  that  all  the  efficiencies  are  theoretical  9nes,  based  on 
the  assumptions  that  there  are  no  leaks  of  air  into  the  boiler  setting,  no 
loss  due  to  unburned  hydrocarbons,  and  no  short  circuiting  or  deposit 
of  soot  on  the  tubes.  In  cases  1,  A,  C  and  D,  in  which  there  is  no  excess 
air  supply,  there  would  in  practice  be  probably  some  loss  from  unburned 
hydrocarbons. 

The  straight  line  formulae  obtained  from  the  figures  in  the  table 
showing  the  relation  of  quality  of  coal  to  efficiency,  assuming  complete 
combustion  and  20%  excess  air  supply,  are 

Anthracite E=  84.7-  1.05(1*75-3 

Semi-bituminous E  =  83 . 0  -  1 . 13  ( W/S  -  3 

Pittsburgh  bituminous E  =  82 . 3  —  1 . 13  ( W/S  -  3 

Illinois  bituminous J57  =  80 . 4  —  1 . 29(W/S  -  3 

Lignite E  =  77.5-  l.4Q(W/S-  3 

Fuel  oil E  =  82.0  -  0.77(W/S  -  3) 

Efficiencies  Obtained  in  Practice. — In  the  best  modern  practice, 
under  the  most  favorable  furnace  conditions,  the  highest  figures  in 
the  above  tables  have  almost  been  reached.  A  few  tests  with  fuel  oil 
have  shown  figures  slightly  higher  than  those  given  above.  The  best 
record  yet  obtained  with  coal  is  that  of  the  ten  best  out  of  the  sixteen 
tests  at  the  Delray  station  of  the  Detroit  Edison  Co.,  reported  by  D. 
S.  Jacobus  in  Trans.  A.  S.  M.  E.,  1911.  A  straight  line  drawn  through 
j  the  plotting  of  these  tests  corresponds  to  the  formula 

£=81-  1.33  (W/S-  3). 

No  account  is  taken  in  the  above  calculation  of  any  loss  due  to  un- 

!  consumed  hydrogen  or  hydrocarbons,  nor  of  absorption  of  heat  by 

I  decomposition  of  moisture  in  the  coal  by  the  reaction  C  +  H2O  =  2H 

•f  CO.     Serious  losses  may  be  due  to  these  causes  if  the  air  supply  is 

!  deficient  and   the  furnace  temperature  low  from,  the  firing  of  a  thick 

j  layer  of  fresh  and  moist  coal,  or  if  the  combustible  gases  are  chilled  by 

?  the  surface  of  the  boiler  to  a  temperature  below  that  of  ignition.     No 

,  account,  either,  has  been  taken  of  the  loss  due  to  moisture  in  the  air, 

which  loss  is  usually  not  over  0.5%,  but  may  reach  2%  with  excessive 

air  supply  of  high  temperature  and  humidity. 

The  highest  efficiencies  are  obtained  with  low  rates  of  driving,  say 
3  to  4  Ib.  evaporated  from  and  at  212°  per  sq.  ft.  of  heating  surface 
per  hour.  With  higher  rates  of  driving  high  efficiencies  can  be  obtained 
only  when  the  air  supply  is  carefully  regulated  according  to  the  in- 
dications of  gas  analyses,  when  the  coal  is  nearly  dry,  when  it  is  fed  at 
a  regular  rate  by  a  mechanical  stoker,  and  when  the  gases  from  the 
coal  are  completely  burned  in  a  large  fire-brick  combustion  chamber 
before  they  are  chilled  by  the  comparatively  cool  surfaces  of  the  boiler. 
Modern  practice  tends  to  extremely  large  combustion  chambers. 


K~  U 


898  THE   STEAM-BOILER* 

With  water-tube  boilers  of  the  Babcock  &  Wilcox  type  the  tubes  are 
often  placed  12  feet  or  more  above  the  grate  bars.  In  the  Stirling 
boilers  of  the  Detroit  Edison  Co.  the  combustion  chambers  are  over 
25  ft.  high. 

The  range  of  efficiency  between  the  highest  possible  and  that  which 
may  be  found  in  ordinary  practice  is  very  large.  While  80  per  cent 
efficiency  is  possible  with  anthracite  and  semi-bituminous  coals,  and 
with  bituminous  coals  containing  not  over  3%  moisture  and  not  over 
35%  volatile  matter  in  the  combustible,  it  is  difficult  to  get  over  65% 
with  Illinois  coals,  high  in  volatile  matter  and  in  moisture,  even  with 
mechanical  stokers  and  with  gas  analysis.  With  ordinary  hand- 
firing  the  average  efficiency  is  apt  to  be  at  least  15  %  lower  than  these 
figures.  For  numerous  records  of  boiler  tests  under  various  conditions, 
with  a  discussion  of  the  results,  see  "Steam  Boiler  Economy,"  2d 
edition. 

Maximum  Boiler  Efficiencies  at  Different  Rates  of  Driving. — The 
ten  best  tests  of  the  large  boilers  of  the  Detroit  Edison  Co.,  reported 
by  D.  S.  Jacobus  in  Jour.  A.  S.  M.  E.,  Nov.,  1911,  with  rates  of  driving 
from  3.24  to  7.29  Ib.  water  evaporated  from  and  at  212°  per  sq.  ft.  of 
heating  surface  per  hour  gave  efficiencies  which  are  represented  (within 
1%)  by  the  formula  E  =  81  -  1.33  (R  -  3),  in  which  E  is  the  efficiency 
per  cent  and  R  the  rate  of  driving.  Eight  tests  of  Babcock  &  Wilcox 
marine  boilers  built  for  the  U.  S.  war- vessels  Cincinnati  and  Wyoming 
(Indust.  Eng'g,  March,  1911),  at  rates  of  driving  from  8.42  to  14.76 
Ib.  correspond  within  3%  with  the  .formula  E  =  80  -  1.43  (R  -  3). 
The  Detroit  tests  were  made  with  bituminous  coal,  low  in  moisture, 
containing  about  30%  volatile  matter,  with  mechanical  stokers  and 
very  large  combustion  chambers.  The  marine  boiler  tests  were  made . 
with  semi-bituminous  coal  containing  about  20%  volatile  matter,  with 
hand-firing.  These  tests  establish  a  world's  record  for  boiler  efficiencies. 
The  formulse  give  the  following  efficiencies  for  the  several  rates  of 
driving  named,  the  first  being  used  for  rates  of  driving  of  3  to  7  Ib.  and 
tfee  second  for  rates  of  7  to  15  Ib. 

R   =       3        4  5  6  7  8          10         12         14         15 

E   =     81     79.7     78.3     77.0     75.7     72.9     70.0     67.1     64.3     62.8 

Some  High  Bates  of  Evaporation. — Eng'g,  May  9,  1884,  p.  415. 

Locomotive.  Torpedo-boat. 

Water  evap.  per  sq.  f t.  H .  S .  per  hour .  12 . 57  13 . 73  12 .54  20 . 74 
Water  evap.  per  Ib.  fuel  from  and  at 

212° 8.22         8.94         8.37         7.04- 

Thermal  units  transf'd  per  sq.  ft.  of 

H.S 12,142      13,263      12,113      20,034 

Efficiency  . , 0.586        0.637        0.542        0.468 

It  is  doubtful  if  these  figures  were  corrected  for  moisture  in  the  steam. 
BOILERS  USING  WASTE  GASES. 

Steam-boilers  Fired  with  Waste  Gases  from  Puddling  and  Heat- 
ing-Furnaces.— The  Iron  Age,  April  6,  1893,  contains  a  report  of  a 
number  of  tests  of  steam-boilers  utilizing  the  waste  heat  from  puddling 
and  heating-furnaces  in  rolling-mills.  The  following  principal  data  are 
selected:  in  Nos.  1,2,  and  4  the  boiler  is  a  Babcock  &  Wilcox  water- tube 
boiler,  and  in  No.  3  it  is  a  plain  cylinder  boiler,  42  in.  diam.  and  26  ft. 
long.  No.  4  boiler  was  connected  with  a  heating-furnace,  the  others 
with  puddling  furnaces. 

No.  1      No.  2      No.  3      No.  4 

Heating-surface,  sq.  ft 1026     1196         143       1380 

Grate-surface,  sq.  ft 19 . 9     13 . 6       13 . 6       16 . 7 

Ratio  H.S.  to  G.S 52      '87.2       10.5       82.8 

Water  evap.  per  hour,  Ibs 3358     2159       1812       3055 

Water  evap.  per  sq.  ft.  H.S.  per  hr.  Ibs. ..      3.3       1.8       12. 7         2.2 
Water  evap.  per  Ib.  coal  from  and  at  212°     5.9       6. 24       3. 76       6.31 
Water   evap.  per  Ib.   combustible  from 

and  at  212° 7.20       4.31       8.34 

In  No.  2,  1.38  Ib.  of  iron  were  puddled  per  Ib.  of  coal. 

In  No.  3,  1.14  Ib.  of  iron  were  puddled  per  Ib.  of  coal. 

No.  3  shows  that  an  insufficient  amount  of  heating-surface  was 
provided  for  the  amount  of  waste  heat  available. 


EULES  FOB  CONDUCTING  BOILER  TESTS. 


899 


Water-tube  Boilers  using  Blast-furnace  Gases. — D.  S.  Jacobus 
(Trans.  A.  /.  M.  E.,  xvii,  50)  reports  a  test  of  a  water-tube  boiler  using 
blast-furnace  gas  as  fuel.  The  heating-surface  was  2535  sq.  ft.  It 
developed  328  H.P.,  or  5.01  Ib.  of  water  from  and  at  212°  per  sq.  ft.  of 
heating-surface  per  hour.  Some  of  the  principal  data  obtained  were  as 
follows:  Calorific  value  of  1  Ib.  of  the  gas,  1413  B.T.U.,  including  the 
effect,  of  its  initial  temperature,  which  was  650°  F.  Amount  of  air  used 
to  burn  1  Ib.  of  the  gas  =  0.9  Ib.  Chimney  draught,  11/3  in.  of  water. 
Area  of  gas  inlet  300  sq.  in. ;  of  air  inlet,  100  sq.  in.  Temperature  of  the 
chimney  gases,  775°  F.  Efficiency  of  the  boiler  calculated  from  the 
temperatures  and  analyses  of  the  gases  at  exit  and  entrance,  61  %.  The 
average  analyses  were  as  follows,  hydrocarbons  being  included  in  the 
nitrogen : 


At  Entrance. 

At  Exit. 

At  Entrance. 

At  Exit. 

CO2. 

10  69 

26  37 

7  08 

18  64 

o  .  '  : 

0  11 

3  05 

0  10 

2  96 

CO  

26.71 

1.78 

27  80 

1  98 

Nitrogen  
C  in  CO2  

62.48 
2.92 

68.80 
7  19 

65.02 

76.42 

C  in  CO  

11.45 

0.76 

Total  C  

14.37 

7.95 

RULES  FOR  CONDUCTING  BOILER  TESTS. 

Object  of  an  Evaporation  Test. — The  principal  object  of  an 
evaporation  test  of  a  steam-boiler  is  to  find  out  how  many  pounds 
of  water  it  evaporates  under  a  certain  set  of  conditions  in  a  given 
time  and  how  many  pounds  of  coal  are  required  to  effect  this  evapo- 
ration. The  test  may  be  made  for  one  or  more  of  several  purposes,  ( 
viz: 

1.  To   determine  whether   or   not   the  stipulations   of   a  contract 
between  the  seller  and  the  buyer  of  a  boiler  (or  of  an  appendage  to 
tl>9  boiler,  such  as  a  furnace)  have  been  performed. 

2.  To  determine  the  relative  economy  of  different  kinds  of  fuel,  of 
different  kinds  of  furnaces,  or  of  different  methods  of  driving. 

3.  To  determine  whether  or  not  the  boilers,  as  ordinarily  run  under 
the  every-day  conditions  of  the  plant,  are   operated  as  economically 
as  they  should  be. 

4.  To  determine,  in  case  the  boilers  either  fail  to  furnish  easily  the 
quantity  of  steam  desired,  or  else  furnish  it  at  what  is  supposed  to  be 
an  excessive  cost  for  fuel,  whether  any  additional  boilers    are  needed 
or  whether  some  change  in  the  conditions  of  running  is  a  sufficient 
remedy  for  the  difficulty. 

For  the  first  of  the  above-named  purposes,  it  is  necessary  that  the 
test  should  be  made  with  every  precaution  to  insure  accuracy,  such 
as  those  described  in  the  Code  of  the  Committee  of  the  American 
•Society  of  Mechanical  Engineers,*  which  is  printed  in  abridged  form 
below. 

INSTRUCTIONS  REGARDING  TESTS  IN  GENERAL. 
(Code  of  1915). 

OBJECT. 

Ascertain  the  specific  object  of  the  test,  and  keep  this  in  view  not 
only  in  the  work  of  preparation,  but  also  during  the  progress  of  the 
test. 

If  questions  of  fulfillment  of  contract  are  involved,  there  should  be 

*  Trans.  A.S.M.E.,  1915.  Reprinted  in  pamphlet  form  by  the 
Society.  The  first  committee  of  the  society  on  boiler-tests  reported 
in  1885,  the  second  in  1899.  In  1909  a  committee  on  Tests  of  Power 
Plant  Apparatus  was  appointed;  its  preliminary  report  was  published 
In  1912.  and  its  final  reoort  in  1915. 


900  THE  STEAM-BOILER. 

a  clear  understanding  between  all  the  parties,  preferably  in  writing, 
as  to  the  operating  conditions  which  should  obtain  during  the  trial,' 
the  methods  of  testing  to  be  followed,  corrections  to  be  made  in  case 
the  conditions  actually  existing  during  the  test  differ  from  those 
specified,  and  all  other  matters  about  which  dispute  may  arise,  unless 
these  are  already  expressed  in  the  contract  itself, 

PREPARATIONS. 

Dimensions  —  Measure  the  dimensions  of  the  principal  parts  of 
the  apparatus  to  be  tested,  so  far  as  they  bear  on  the  objects  in  view, 
or  determine  them  from  working  drawings.  Notice  the  general 
features  of  the  apparatus,  both  exterior  and  interior,  and  make  sketches, 
if  needed,  to  show  unusual  points  of  design. 

The  areas  of  the  heating  surfaces  of  boilers  and  superheaters  to  be 
found  are  those  of  surfaces  in  contact  with  the  fire  or  hot  gases. 
The  submerged  surfaces  in  boilers  at  the  mean  water  level  should 
be  considered  as  water-heating  surfaces,  and  other  surfaces  which 
are  exposed  to  the  gases  as  superheating  surfaces. 

Examination  of  Plant.  —  Make  a  thorough  examination  of  the  phys- 
ical condition  of  all  parts  of  the  plant  or  apparatus  which  concern 
the  object  in  view,  and  record  the  conditions  found. 

In  boilers  examine  for  leakage  of  tubes  and  riveted  or  other  metal 
joints.  Note  the  condition  of  brick  furnaces,  grates  and  baffles. 
Examine  brick  walls  and  cleaning  doors  for  air  leaks,  either  by  shut- 
ting the  damper  and  observing  the  escaping  smoke  or  by  candle- 
flame  test.  Determine  the  condition  of  heating  surfaces  with  refer- 
ence to  exterior  deposits  of  soot  and  interior  deposits  of  mud  or  scale. 

If  the  object  .of  the  test  is  to  determine  the  highest  efficiency  or 
capacity  obtainable,  any  physical  defects,  or  defects  of  operation. 
tending  to  make  the  result  unfavorable  should  first  be  remedied;  all 
fouled  parts  being  cleaned,  and  the  whole  put  in  first-class  condition. 
If,  on  the  other  hand,  the  object  is  t9  ascertain  the  performance  under 
existing  conditions,  no  such  preparation  is  either  required  or  desired. 

Precautions  against  Leakage.  —  In  steam  tests  make  sure  that  there 
is  no  leakage  through  blow-offs,  drips,  etc.,  or  any  steam  or  water  con- 
nections, which  would  in  any  way  affect  the  results.  All  such  con- 
nections should  be  blanked  off,  or  satisfactory  assurance  should  be 
obtained  that  there  is  leakage  neither  out  nor  in. 

Apparatus  and  Instruments.  —  See  that  the  apparatus  and  instru- 
ments are  substantially  reliable,  and  arrange  them  in  such  a  way 
as  to  obtain  correct  data. 

Weighing  Scales.  —  For  determining  the  weight  of  coal,  oil,  water,  etc., 
ordinary  platform  scales  serve  every  purpose.  Too  much  depend- 
ence, however,  should  not  be  placed  upon  their  reliability  without 
first  calibrating  them  by  the  use  of  standard  weights,  and  carefully 
examining  the  knife-edges,  bearing  plates,  and  ring  suspensions, 
to  see  that  they  are  all  in  good  order. 

For  testing  locomotives  and  some  classes  of  marine  boilers,  wh< 
room  is  lacking,  sacks  or  bags  are  sometimes  required  to  facilitate 
the  handling  of  coal,  the  sacks  being  weighed  at  the  time  of  filling. 

/*  SAMPLING    AND    DRYING    COAL. 

Select  a  representative  shovelful  from  each  barrow-load  as  it  is 
drawn  from  the  coal-pile  or  other  source  of  supply,  and  store  the 
samples  in  a  cool  place  in  a  covered  metal  receptacle.  When  all 
the  coal  has  thus  been  sampled,  break  up  the  lumps,  thoroughly  mix 
the  whole  quantity,  and  finally  reduce  it  by  the  process  of  repeated 
shin 


-  -,  -  ,  ly 

filled  and  preserved  for  subsequent  determinations  of  moisture,  calorific 
value,  and  chemical  composition. 

When  the  sample  lot  of  coal  has  been  reduced  by  quartering  to 


RULES  FOR  CONDUCTING  BOILER  TESTS.          901 

8av  100  Ibs.,  a  portion  weighing  say  15  to  20  Iba.  should  be  with- 
drawn for  the  purpose  of  immediate  moisture  determination.  This 
is  placed  in  a  shallow  iron  pan  and  dried  on  the  hot  iron  boiler  flue 
for  at  least  12  hours,  being  weighed  before  and  after  drying  on  scales 
reading  to  quarter  ounces. 

The  moisture  thus   determined   is   approximately   reliable  for  an- 
thracite and  semi-bituminous  coals,  but  not  for  coals  containing  much 
inherent   moisture.     For  such  coals,    and  for   all   absolutely  reliable 
determinations  the  method  to  be  pursued  is  as  follows: 
Take  one  of  the  samples  contained  in  the  glass  jars,  and  subject  it 
to  a  thorough  air  drying,  by  spreading  it  in  a  thin  layer  and  exposing 
it  for  several  hours  to  the  atmosphere  of  a  warm  room,  weighing  it 
before  and  after,  thereby  determining  the  quantity  of  surface  moisture 
it  contains.     Then  crush  the  whole  of  it  by  running  it  through  an 
ordinary  coffee  mill  or  other  suitable  crusher  adjusted  so  as  to  pro- 
duce somewhat  coarse  grains  (less  than  Vie  in.),  thoroughly  mix  the 
crushed  sample,  select  from  it    a    portion  of  from  10  to  50  grams 
(say  MOZ.  to  2  oz.),  weigh  it  in  a  balance  which  will  easily  show  a 
*  variation  as  small  as  1  part  in  1000,  and  dry  it  for  one  hour  in  an 
air  or  sand  bath  at  a  temperature  between  240  and  280°  F.     Weigh 
it  and  record  the  loss,  then  heat  and  weigh  again  until  the  minimum 
weight  has  been  reached.     The  difference  between  the  original  and 
the  minimum  weight  is  the  moisture  in   the  air-dried  coal.     The 
sum  of  the  moisture  thus  found  and  that  of  the  surface  moisture 
is  the  total  moisture. 

If  a  larger  drying  oven  is  available  the  moisture  may  be  deter- 
mined by  heating  one  of  the  glass  jars  full  of  coal,  the  cover  being 
removed,  at  a  temperature  between  240°  and  280°  F.  until  it  reaches 
the  minimum  weight. 

SAMPLING    STEAM. 

Construct  a  sampling  pipe  or  nozzle  made  of  y2-m.  iron  pipe  and 
insert  it  in  the  steam  main  at  a  point  where,  the  entrained  moisture 
is  likely  to  be  most  thoroughly  mixed.  The  inner  end  of  the  pipe, 
which  should  extend  nearly  across  to  the  opposite  side  of  the  main, 
should  be  closed  and  the  interior  portion  perforated  with  not  less 
than  twenty  Vg-m.  holes  equally  distributed  from  end  to  end  and 
preferably  drilled  in  irregular  or  spiral  rows,  with  the  first  hole  not 
less  than  half  an  inch  from  the  wall  of  the  pipe. 
The  sampling  pipe  should  not  be  placed  near  a  point  where  water  may 

pocket  or  where  such   water  may  affect  the  amount  of  moisture 

contained  in  the  sample. 

RULES  FOR  CONDUCTING  EVAPORATIVE  TESTS  OF  BOILERS. 
OBJECT  AND  PREPARATIONS. 

Determine  the  object  of  the  test,  take  the  dimensions,  note  the 
physical  conditions,  examine  for  leakages,  install  the  testing  appli- 
ances, etc.,  as  pointed  out  in  the  general  instructions  and  make  prep- 
arations for  the  test  accordingly. 


Determine  the  character  of  fuel  to  be  used.  For  tests  of  maximum 
efficiency  or  capacity  of  the  boiler  to  compare  with  other  boilers, 
the  coal  should  be  of  some  kind  which  is  commercially  regarded  as 
a  standard  for  the  locality  where  the  test  is  made. 

A  coal  selected  for  maximum  efficiency  and  capacity  tests  should 
be  the  best  of  its  class,  and  especially  free  from  slagging  and  unusual 
clinker-forming  impurities. 

For  guarantee  and  other  tests  with  a  specified  coal  containing  not 
more  than  a  certain  amount  of  ash  and  moisture,  the  coal  selected 
should  not  be  higher  in  ash  and  in  moisture  than  the  stated  amounts 


902 


THE  STEAM-BO1LEK. 


because  any  increase  is  liable  to  reduce  the  efficiency  and  capacity 
more  than  the  equivalent  proportion  of  such  increase. 

OPERATING  CONDITIONS. 

Determine  what  the  operating  conditions  and  method  of  firing 
should  be  to  conform  to  the  object  in  view,  and  see  that  they  prevail 
throughout  the  trial,  as  nearly  as  possible. 

DURATION. 

The  duration  of  tests  to  determine  the  efficiency  of  a  hand-fired 
boiler  should  be  at  least  ten  consecutive  hours.  In  case  the  rate  of 
combustion  is  less  than  25  Ibs.  per  sq.  ft.  of  grate  per  hour  the  tests 
should  be  continued  for  such  a  time  as  may  be  required  to  burn  a  total 
of  250  Ibs.  of  coal  per  square  foot  of  grate.  Tests  of  longer^duration 
than  10  hours  are  advisable  in  order  to  obtain  greater  accuracy. 

In  the  case  of  a  boiler  using  a  mechanical  stoker,  the  duration, 
where  practicable,  should  be  at  least  24  hours.  If  the  stoker  is  of 
a  type  that  permits  the  quantity  and  condition  of  the  fuel  bed  at 
beginning  and  end  of  the  test  to  be  accurately  estimated,  the  dura- 
tion may  be  reduced  to  10  hours,  or  such  time  as  may  be  required 
to  bum  the  total  of  250  Ibs.  per  square  foot. 

STARTING    AND   STOPPING. 

The  conditions  regarding  the  temperature  of  the  furnace  and 
boiler,  the  quantity  and  quality  of  the  live  coal  and  ash  on  the  grates, 
the  water  level,  and  the  steam  pressure,  should  be  as  nearly  as  pos- 
sible the  same  at  the  end  as  at  the  beginning  of  the  test. 

To  secure  the  desired  equality  of  conditions  with  hand-fired  boilers, 
the  following  method  should  be  employed: 

The  furnace  being  well  heated  by  a  preliminary  run,  burn  the  fire  low* 
and  thoroughly  clean  it.  leaving  enough  live  coal  spread  evenly 
over  the  grate  (say  2  to  4  ins.),*  to  serve  as  a  foundation  for  the 
new  fire.  Note  quickly  the  thickness  of  the  coal  bed  as  nearly  as 
it  can  be  estimated  or  measured,  also  the  water  level, f  the  steam 
pressure,  and  the  time,  and  record  the  latter  as  the  starting  time. 
Fresh  coal  should  then  be  fired  from  that  weighed  for  the  test,  the  ash-pit 
thoroughly  cleaned  and  the  regular  work  of  the  test  proceeded  with. 

Before  the  end  of  the  test  the  tire  should  again  be  burned  low 
and  cleaned  in  such  a  manner  as  to  leave  the  same  amount  of  live 
coal  on  the  grate  as  at  the  start.  When  this  condition  is  reached, 
observe  quickly  the  water  level,  t  the  steam  pressure,  and  the 
time,  and  record  the  latter  as  the  stopping  time.  If  the  water 
level  is  lower  than  at  the  beginning,  a  correction  should  be  made 
by  computation,  rather  than  by  feeding  additional  water.  Finally 
remove  the  ashes  and  refuse  from  the  ashpit. 

In  a  plant  containing  several  boilers  where  it  is  not  practicable 
to  clean  them  simultaneously,  the  fires  should  be  cleaned  one  after 
the  other  as  rapidly  as  may  be,  and  each  one  after  cleaning  charged 
with  enough  coal  to  maintain  a  thin  fire  in  good  working  condition. 
After  the  last  fire  is  cleaned  and  in  working  condition,  burn  all 
the  fires  low  (say  4  to  6  ins.),  note  quickly  the  thickness  of  each, 
also  the  water  levels,  steam  pressure,  and  time,  which  last  is  taken 
as  the  starting  time.  Likewise  when  the  time  arrives  for  closing 
the  test,  the  fires  should  be  quickly  cleaned  one  by  one,  and  when 
this  work  is  completed  they  should  all  be  burned  low  the  same 
as  at  the  start  and  the  various  observations  made  as  noted. 

*  1  to  2  ins.  for  small  anthracite  coals. 

t  Do  not  blow  down  the  water-glass  column  for  at  least  one  hour 
before  these  readings  are  taken.  An  erroneous  indication  may  other- 
wise be  caused  by  a  change  of  temperature  and  density  of  the  water 
within  the  column  and  connecting  pipe. 


RULES   FOR   CONDUCTING    BOILER   TESTS.  903 

In  the  case  of  a  large  boiler  having  several  furnace  doors  requiring 
the  fire  to  be  cleaned  in  sections  one  after  the  other,  the  above 
directions  pertaining  to  starting  and  stopping  in  a  plant  of  several 
boilers  may  be  followed. 
To  obtain  the  desired  equality  of  conditions  of  the  fire  when  a 

mechanical  stoker  other  than  a  chain  grate  is  used,   the  procedure 

should  be  modified  where  practicable  as  follows: 

Regulate  the  coal  feed  so  as  to  burn  the  fire  to  the  low  condition 
required  for  cleaning.  Shut  off  the  coal-feeding  mechanism  and 
fill  the  hoppers  level  full.  Clean  the  ash  or  dump  plate,  note  quickly 
the  depth  and  condition  of  the  coal  on  the  grate,  the  water  level, 
the  steam  pressure,  and  the  time,  and  record  the  latter  as  the 
starting  time.  Then  start  the  coal-feeding  mechanism,  clean  the 
ashpit,  and  proceed  with  the  regular  work  of  the  test. 

When  the  time  arrives  for  the  close  of  the  test,  shut  off  the  coal- 
feeding  mechanism,  fill  the  hoppers  and  burn  the  fire  to  the  same 
low  point  as  at  the  beginning.  When  this  condition  is  reached, 
note  the  water  level,  the  steam  pressure,  and  the  time,  and  record 
the  latter  as  the  stopping  time.  Finally  clean  the  ash  plate  and 
haul  the  ashes. 

In  the  case  of  chain-grate  stokers,  the  desired  operating  conditions 
should  be  maintained  for  half  an  hour  before  starting  a  test  and 
for  a  like  period  before  its  close,  the  height  of  the  stoker  gate  or 
throat  plate  and  the  speed  of  the  grate  being  the  same  during  both 
these  periods. 

EECOEDS. 

Half-hourly  readings  of  the  instruments  are  usually  sufficient.     If 
there  are  sudden  and  wide  fluctuations,  the  readings  in  such  cases 
should  be  taken  every  fifteen  minutes,  and  in  some  instances  oftener. 
The  coal  should  be  weighed  and  delivered  to  the  firemen  in  portions 
sufficient  for  one  hour's   run,   thereby   ascertaining   the   degree   of 
uniformity  of  firing.     An  ample  supply  of  coal  should  be  maintained 
at  all  times,  but  the  quantity  on  the  floor  at  the  end  of  each  hour 
should  be  as  small  as  practicable,  so  that  the  same  may  be  readily 
estimated  and  deducted  from  the  total  weight. 

The  records  should  be  such  as  to  ascertain  also  the  consumption 
of  feed-water  each  hour,  and  thereby  determine  the  degree  of  uni- 
formity of  evaporation. 

QUALITY  OF  STEAM. 

If  the  boiler  does  not  produce  superheated  steam  the  percentage 
of  moisture  in  the  steam  should  be  determined  -by  the  use  of  a  throttling 
or  separating  calorimeter.  If  the  boiler  has  superheating  surface, 
the  temperature  of  the  steam  should  be  determined  by  the  use  of 
a  thermometer  inserted  in  a  thermometer  well. 

SAMPLING  AND  DRYING  COAL. 

During  the  progress  of  the  test  the  coal  should  be  regularly  sampled 
for  the  purpose  of  analysis  and  determination  of  moisture. 

ASHES  AND  REFUSE. 

The  ashes  and  refuse  withdrawn  from  the  furnace  and  ash-pit 
daring  the  progress  of  the  test  and  at  its  close  should  be  weighed  so 
far  as  possible  in  a  dry  state.  If  wet,  the  amount  of  moisture  should 
be  ascertained  and  allowed  for,  a  sample  being  taken  and  dried  for 
this  purpose.  This  sample  may  serve  also  for  analysis  and  the  deter- 
mination of  unburned  carbon. 

CALORIFIC  TESTS  AND  ANALYSES  OF  COAL. 

The  quality  of  the  fuel  should  be  determined  by  calorific  tests  and 
Analyses  of  the  coal  sample  above  ivferml  tO- 


904    •  THE   STEAM-BOILER. 

ANALYSES  OF  FLUE  GASES. 

For  approximate  determinations  of  the  composition  of  the  flue 
gases,  the  Orsat  apparatus,  or  some  modification  thereof,  should 
be  employed.  If  momentary  samples  are  obtained  the  analyses 
should  be  made  as  frequently  as  possible,  say  every  15  to  30  minutes, 
depending  on  the  skill  of  the  operator,  noting  at  the  time  the  sample 
is  drawn  the  furnace  and  firing  conditions.  If  the  sample  drawn 
is  a  continuous  one,  the  intervals  may  be  made  longer. 

SMOKE  OBSERVATIONS. 

In  tests  of  bituminous  coals  requiring  a  determination  of  the  amount 
of  smoke  produced,  observations  should  be  made  regularly  through- 
out the  trial  at  intervals  of  five  minutes  (or  if  necessary  every  minute)  , 
noting  at  the  same  time  the  furnace  and  firing  conditions.  For  tests 
of  furnaces,  methods  of  firing,  or  smoke  prevention  devices,  observations 
every  10  or  15  seconds,  continued  during  an  hour,  are  advisable. 

CALCULATION  OF  RESULTS. 

(a)  Corrections  for  Quality  of  Steam.  —  When  the  percentage  of  moisture 
is  less  than  2  per  cent  it  is  sufficient  merely  to  deduct  the  percentage 
from  the  weight  of  water  fed,  in  which  case  the  factor  of  correction 
for  quality  is 

_  %  moisture 
100 

When  the  percentage  is  greater  than  2  per  cent,  or  if  extreme  accu- 
racy is  required,  the  factor  of  correction  is 


- 

H-h 

in  which  P  is  the  proportion  of  moisture,  H  the  total  heat  of  1  Ib. 
of  saturated  steam,  hi  the  heat  in  water  at  the  temperature  of  satu- 
rated steam,  and  h  the  heat  in  water  at  the  feed  temperature. 

When  the  steam  is  superheated  the  factor  of  correction  for  quality 
of  steam  is 

Hs-h 

H-h 

in  which  Hs  is  the  total  heat  of  1  Ib.  of  superheated  steam  of  the 
observed  temperature  and  pressure. 

(6)  Correction  for  Live  Sleam,  if  any,  used  for  Aiding  Combustion.  —  The 
quantity  of  steam  or  power,  if  any,  used  for  producing  blast,  inject- 
ing fuel,  or  aiding  combustion  should  be  determined  and  recorded  in 
the  table  of  data  and  results. 

(c)  Equivalent   Evaporation.  —  The   equivalent   evaporation   from   and 
at  212°  is  obtained  by  multiplying  the  weight  of  water  evaporated, 
corrected  for  moisture  in  steam,  by  the  "factor  of  evaporation." 
The  latter  equals 

H-h 
970.4 

in  which  H  and  h  are  respectively  the  total  heat  of  saturated  steam 
and  of  the  feed-water  entering  the  boiler. 

The  "factor  of  evaporation"  and  the  "factor  of  correction  for 
quality  of  steam"   may   be  combined  into  one  expression  in  the 
case  of  superheated  steam  as  follows  : 
Hs-h 
"970.4* 

(d)  Efficiency.  —  The  "efficiency  of  boiler,  furnace  and  grate"  is  the 
relation  between  the  heat  absorbed  per  pound  of  coal  fired,  and 
the  calorific  value  of  1  Ib.  of  coal. 

The  "efficiency  based  on  combustible"  is  the  relation  between 


RULES   FOR  CONDUCTING  BOILER  TESTS.          905 

the  heat  absorbed  per  pound  of  combustible  burned,  and  the 
calorific  value  of  1  Ib.  of  combustible.  This  expression  of  efficiency 
furnishes  a  means  for  comparing  the  results  of  different  tests, 
when  the  losses  of  unburned  coal  due  to  grates,  cleanings,  etc.,  are 
eliminated. 

The  "combustible  burned"  is  determined  by  subtracting  from 
the  weight  of  coal  supplied  to  the  boiler,  the  moisture  in  the  coal, 
the  weight  of  ash  and  unburned  coal  withdrawn  from  the  furnace 
and  ash-pit,  and  the  weight  of  dust,  soot,  and  refuse,  if  any,  with- 
drawn from  the  tubes,  flues,  and  combustion  chambers,  including  ash 
carried  away  in  the  gases,,  if  any,  determined  from  the  analyses  of 
coal  and  ash.  The  "combustible"  used  for  determining  the  cal- 
orific value  is  the  weight  of  coal  less  the  moisture  and  ash  found  by 
analysis. 

The  "heat  absorbed"  per  pound  of  coal  or  combustible  is  cal- 
culated by  multiplying  the  equivalent  evaporation  from  and  at 
212°  per  pound  of  coal  or  combustible  by  970.4. 

CHART. 

In  trials  having  for  an  object  the  determination  and  exposition, 
of  the  complete  boiler  performance,  the  entire  log  of  readings  and 
data  should  be  plotted  on  a  chart  and  represented  graphically. 

Data  and  Results  of  Evaporative  Test.* 

1.  Test  of boiler  located  at 

2.  Number  and  kind  of  boilers 

3.  Kind  of  furnace 

4.  Grate  surface  (width length ) sq.  ft. 

5.  Water  heating  surface • sq.  ft. 

6.  Superheating  surface sq.  ft. 

7  Total  heating  surface sq.  ft. 

e.  Distance  from  center  of  grate  to  nearest  heating 

surface ft. 

DATE,  DURATION,  ETC. 

8.  Date 

9.  Duration hrs. 

10.  Kind  and  size  of  coal 

AVERAGE  PRESSURES,  TEMPERATURES,  ETC. 

11.  Steam  pressure  by  gage Ibs.  per  sq.  in. 

12.  Temperature  of  steam,  if  superheated degs. 

13.  Temperature  of  feed- water  entering  boiler degs. 

14.  Temperature  of  escaping  gases  leaving  boiler degs. 

15.  Force  of  draft  between  damper  and  boiler ins. 

c.  Draft  in  furnace ins. 

d.  Draft  or  blast  in  ash-pit ins. 

16.  State  of  weather 

a.  Temperature  of  external  air degs. 

&.  Temperature  of  air  entering  ash-pit degs. 

c.   Relative  humidity  of  air  entering  ash-pit degs 

17. 


QUALITY  OF  STEAM 


Percentage  of  moisture  in  steam  or  degrees  of  super- 
heating      %  or  degs. 

18.  Factor  of  correction  for  quality  of  steam %  or  degs. 

TOTAL  QUANTITIES. 

19.  Total  weight  of  COP!  as  fired Ibs. 

20.  Percentage  of  moisture  in  coal  as  fired- per  cent . 

21.  Total  weight  of  dry  coal  fired Ibs. 

*  This  table  contains  the  principal  items  of  the  table  in  the  Code 
of  1915  of  the  A.S.M.E.  Committee  on  Power  Tests. 


906 


THE  STEAM-BOILER. 


22.  Total  ash,  clinkers,  and  refuse  (dry)  .................   Ibs. 

23.  Total  combustible  burned  (.Item  21  —  Item  22)  .......   Ibs. 

24.  Percentage  pf  ash  and  refuse  in  dry  coal  .............   per  cent. 

25.  Total  weight  of  water  fed  to  boiler  ..................   Ibs. 

26.  Total  water  evaporated,  corrected  for  quality  of  steam 

(Item  25  X  Item  18)  ................................   Ibs. 

27.  Factor  of  evaporation  based  on  temperature  of  water 

entering  boiler  .................................. 

28.  Total  equivalent  evaporation  from  and  at  212°  (Item 

26  X  Item  27)  ..................................   Ibs. 

HOURLY  QUANTITIES  AND  RATES. 

29.  Dry  coal  per  hour  .................................   Ibs, 

30.  Dry  coal  per  square  foot  of  grate  surface  per  hour  .....   Ibs. 

31.  Water  evaporated  per  hour,  corrected  for  quality  of 

steam  ........................................  .  .   Ibs. 

32.  Equivalent  evaporation  per  hour  from  and  at  212°.  .  .  .   Ibs. 

33.  Equivalent  evaporation  per  hour  from  and  at  212°  per 

square  foot  of  water-heating  surface  ...............   Ibs. 

CAPACITY. 

34.  Evaporation  per  hr.  from  and  at  212°  (same  as  Item  32)  Ibs. 

a.  Boiler  horse-power  developed  (Item  34  +  34  >/2)  ...   Bl.  H.P. 

35.  Rated  capacity  per  hour,  from  and  at  212°  ...........    Ibs. 

a.  Rated  boiler  horse-p9wer  ......................   Bl.  H.P. 

36.  Percentage  of  rated  capacity  developed  ..............   per  cent. 

ECONOMY. 

37.  Water  fed  per  pound  of  coal  as  fired  (Item  25  -5-  Item  19)  Ibs. 

38.  Water  evaporated  per  pound  of  dry  coal  (Item  26  -5- 

Item  21)  ........  ...............................   Ibs. 

39.  Equivalent  evaporation  from  and  at  212°  per  pound  of 

coal  as  fired  (Item  28  -j-  Item  19)  .................   Ibs. 

40.  Equivalent  evaporation  from  and  at  212°   per  pound  of 

dry  coal  (Item  28  -f-  Item  21)  .....................   Ibs. 

41.  Equivalent  evaporation  from  and  at  212°  per  pound  of 

combustible  (Item  28  -*•  Item  23)  ..................   Ibs. 

EFFICIENCY. 

42.  Calorific  value  of  1  Ib.  of  dry  coal  by  calorimeter  ......   B.T.U. 

43.  Calorific  value  of  1  Ib.  of  combustible  by  calorimeter.  .    B.T.U. 

44.  Efficiency  of  boiler,  furnace  and  grate  ................   per  cent. 

„  Item  40X970.  4 
~~Item  42 

45.  Efficiency  based  on  combustible  ......................  per  cent. 

^  Item  41X970.  4 
Item  43 

COST   OF   EVAPORATION. 

46.  Cost  of  coal  per  ton  of  .  .  .  .Ibs.  delivered  in  boiler  room,  dollars. 

47.  Cost  of  coal  required  for  evaporating  1000  Ibs.  of  water 

under  observed  conditions  ........................   dollars. 

48.  Cost  of  coal  required  for  evaporating  1000  Ibs.  of  water 

from  and  at  212°  ......  .  .........................   dollars. 

SMOKE  DATA. 

49.  Percentage  of  smoke  as  observed  ....................   per  cent. 

FIRING  DATA. 

50.  Kind  of  firing,  whether  spreading,  alternate,  or  coking 

a.  Average   interval   between   times  of  leveling   or 

breaking  up  ................................   min. 


EXILES  FOR  CONDUCTING   BOILER  TESTS. 


ANALYSES  AND  HEAT  BALANCE. 


907 


51.  Analysis  of  dry  gases  by  volume. 

a.  Carbon  dioxide  (COa) per  cent. 

b.  Oxygen  (O) per  cent. 

c.  Carbon  monoxide  (CO) per  cent. 

d.  Hydrogen  and  hydrocarbons per  cent. 

e.  Nitrogen,  by  difference  (N). per  cent. 


As  Fired. 


Dry  Coal. 


Combustible. 


52.  Proximate  analysis  of  coal 


a.  Moisture 

b.  Volatile  Matter 

c.  Fixed  carbon 

d.  Ash 


100%  100%  100% 

e.   Sulphur,  separately  determined,  referred  to  dry  coal .  per  cent. 

53.  Ultimate  analysis  of  dry  coal. 

a.  Carbon  (C) per  cent. 

b.  Hydrogen  (H) per  cent. 

c.  Oxygen  (O) per  cent. 

d.  Nitrogen  (N) per  cent. 

e.  Sulphur  <S) per  cent. 

/.    Ash per  cent. 

54.  Analysis  of  ash  and  refuse,  etc 

55.  Heat  balance,  based  on  dry  coal  and  com- 

bustible. 

a.  Heat  absorbed  by  the  boiler  (Item  40 

or  41  X  970.4) : 

b.  Loss  due  to  evaporation  of  moisture 

in  coal 

C.  Loss  due  to  heat  carried  away  by 
steam  formed  by  the  burning  of 
hydrogen 

d.  Loss  due  to  heat  carried  away  in  the 

dry  flue  gases 

e.  Loss  due  to  carbon  monoxide ... 

/.    Loss  due  to  combustible  in  ash  and 

refuse 

g.  Loss  due  to  heating  moisture  in  air. 
h.  Loss  due  to  unconsumed  hydrogen 

and   hydrocarbons,    to   radiation, 

and  unaccounted  for 

i.   Total  calorific  value  of  1  Ib.  of  dr; 

coal  or  combustible.     (Items  4: 

and  43) 


Dry  Coal. 


B.T.U. 


Per  cent. 


100 


If  it  is  desired  that  the  heat  balance  be  based  on  coal  "as  fired,"  or 
on  combustible  burned,  the  items  in  the  first  column  are  multiplied  by 
( 100  -Item  20)  -^- 100  for  coal  as  fired  or  by  100 -T- (100  -  Item  55 /, 
per  cent)  for  combustible. 

PRINCIPAL  DATA  AND  RESULTS  OF  BOILER  TEST. 

1.  Grate  surface  (width length ) , sq.  ft. 

2.  Total  heating  surface sq.  ft. 

3.  Date 

4.  Duration hra. 

5.  Kind  and  size  of  coal 


908  THE   STEAM-BOILER. 

6.  Steam  pressure  by  gage. . ~. Ibs.  per  sq.  in. 

7.  Temperature  of  feed  water  entering  boiler degs. 

8.  Percentage  of  nioisture  in  steam  or  number  of  degrees 

of  superheating %  or  deg. 

9.  Percentage  of  moisture  in  coal per  cent. 

10.  Dry  coal  consumed  per  hour Ibs. 

11.  Dry  coal  consumed  per  square  foot  of  grate  surface  per 

hour Ibs. 

12.  Equivalent  evaporation  per  hour  from  and  at  212°  ....    Ibs. 

13.  Equivalent  evaporation  per  hour  from  and  at  212°  per 

square  foot  of  heating  surface Ibs. 

14.  Rated  capacity  per  hour,  from  and  at  212° Ibs. 

15.  Percentage  of  rated  capacity  developed per  cent 

16.  Equivalent  evaporation  from  and  at  212°  per  pound 

of  dry  coal Ibs. 

17.  Equivalent  evaporation  from  and  at  212°  per  pound 

of  combustible Ibs. 

18.  Calorific  value  of  1  Ib.  of  dry  coal  by  calorimeter B.T.U. 

19.  Calorific  value  of  1  Ib.  of  combustible  by  calorimeter. .   B.T.U. 

20.  Efficiency  of  boiler,  furnace  and  grate per  cent. 

21.  Efficiency  based  on  combustible per  cent. 

FACTORS  OF  EVAPORATION. 

The  figures  in  the  table  on  the  next  four  pages  are  calculated  from  the 
formula  F  «=(#  —  h)  •*•  970.4,  in  which  H  is  the  total  heat  above  32°  of 
1  Ib.  of  steam  of  the  observed  pressure,  h  the  total  heat  above  32°  of  the 
feed-water,  and  970.4  the  heat  of  vaporization,  or  latent  heat,  of  steam  at 
212°  F.  The  values  of  these  total  heats  and  of  the  latent  heat  are  those 
given  in  Marks  and  Davis's  steam  tables. 

The  factors  are  given  for  every  3°  of  feed -water  temperature  between 
32°  and  212°,  and  for  every  5  or  10  Ibs.  steam  pressure  within  the  ordinary 
working  limits  of  pressure.  Intermediate  values  correct  to  the  third 
decimal  place  may  easily  be  found  by  interpolation. 

The  factors  in  the  table  are  for  dry  saturated  steam  only. 

STRENGTH    OF    STEAM-BOILERS.     VARIOUS    RULES    FOR 
CONSTRUCTION. 

There  is  a  great  lack  of  uniformity  in  the  rules  prescribed  by  different 
writers  and  by  legislation  governing  the  construction  of  steam-boilers. 
In  the  United  States,  boilers  for  merchant  vessels  must  be  constructed 
according  to  the  rules  and  regulations  prescribed  by  the  Board  of  Super- 
vising Inspectors  of  Steam  Vessels;  in  the  U.  S.  Navy,  according  to  rules 
of  the  Navy  Department,  and  in  some  cases  according  to  special  acts  of 
Congress.  On  land,  in  some  States,  such  as  Massachusetts  and  Ohio, 
and  in  some  cities  in  other  States,  the  construction  of  boilers  is  governed 
by  local  laws;  but  in  many  places  there  are  no  laws  upon  the  subject, 
and  boilers  are  constructed  according  to  the  idea  of  individual  en- 
gineers and  boiler-makers.  In  recent  years,  however,  there  has  been  a 
great  improvement  in  this  matter.  The  wide  publication  of  the 
Massachusetts  boiler  rules,  the  activity  of  the  American  Boiler  Manu- 
facturers' Association,  of  the  American  Society  for  Testing  Materials, 
and  the  work  of  a  committee  of  the  American  Society  of  Mechanical 
Engineers,  which  completed  its  "Boiler  Code"  in  1915  (issued  in  pam- 

§hlet  form  by  the  Society),  have  all  tended  to  bring  about  a  great 
egree  of  uniformity  in  the  materials  and  the  methods  of  boiler  con- 
struction. The  matter  on  the  following  pages  consists  chiefly  of  ex- 
tracts from  the  Massachusetts  rules  and  the  A.  S.  M.  E.  Boiler  Code, 
and  is  condensed  from  a  fuller  treatment  of  the  subject  in  the  second 
edition  of  the  author's  "  Steam  Boiler  Economy." 

Materials  Used  in  Boilers. — For  the  shells,  tubes,  rivets  and  braces 
the  material  now  in  almost  universal  use  is  a  special  kind  of  soft  opeii- 
hearth  steel,  low  in  sulphur  and  phosphorus  and  of  a  tensile  strength 
not  exceeding  65,000  Ib.  per  sq.  in.  for  shell  plates  and  not  exceeding 
55,000  Ib.  per  sq.  in.  for  rivets. 

Cast  iron  is  used  for  fire-doors,,  grate-bars,  manhole  and  handhole 

(Continued  on  p.  913.) 


FACTOES   OF   EVAPORATION. 


909 


Lbs 
Gauge  press.  .0.3 
Abs.  press.  ...  15. 

10.3 
25. 

20.3 
35. 

30.3 
45. 

40.3 
55. 

50.3 
65. 

60.3 
75. 

70.3 
85. 

80.3 
95. 

85.3 
100 

Feed 
water. 

Factors  of  Evaporation. 

212°  F. 

1.0003 

1.0103 

1.0169 

1.0218 

1  .0258 

1  .0290 

1.0316 

1  .0340 

1  .0361 

1.0370 

209 

34 

34 

1.0200 

50 

89 

1.0321 

47 

71 

92 

1.0401 

206 

65 

65 

31 

81 

1  .032^ 

52 

79 

1.0402 

I  .0423 

32 

203 

% 

96 

62 

1.0312 

51 

83 

1.0410 

33 

54 

63 

200 

1.0127 

I  .0227 

93 

43 

82 

1.0414 

41 

64 

85 

94 

197 

58 

58 

1  .0324 

74 

1.0413 

45 

72 

95 

1.0516 

1  .0525 

194 

89 

89 

55 

1.0405 

44 

76 

1  0503 

1.0526 

47 

56 

191 

1  .0220 

1  .0320 

86 

36 

75 

1  .0507 

34 

57 

78 

87 

188 

51 

51 

.0417 

67 

1.0506 

38 

65 

88 

1.0609 

1.0618 

185 

82 

82 

48 

98 

37 

69 

96 

1.0619 

40 

49 

182 

1.0313 

1.0413 

79 

1  .0529 

68 

1  .0600 

1  .0627 

50 

71 

80 

179 

44 

44 

.0510 

60 

99 

31 

58 

81 

1  .0702 

1.0711 

176 

75 

75 

41 

91 

1.0630 

62 

89 

1.0712 

33 

42 

173 

1.0406 

1.0506 

72 

1  .0622 

61 

93 

1  .0720 

43 

64 

73 

170 

37 

37 

1.0603 

53 

.  92 

1.0724 

51 

74 

95 

1  .0804 

167 

68 

63 

34 

84 

1.0723 

55 

82 

.0805 

1.0826 

35 

164 

99 

99 

65 

1.0715 

54 

86 

1.0812 

36 

57 

66 

161 

1  .0530 

1.0630 

96 

45 

85 

1.0817 

43 

67 

88 

97 

158 

61 

61 

1  .0727 

76 

1.0816 

47 

74 

98 

1.0919 

1  .0928 

155 

92 

92 

58 

1.0807 

46 

78 

1.0905 

1  .0929 

50 

59 

152 

1  .0623 

1.0723 

89 

38 

77 

1.0909 

36 

60 

80 

90 

149 

54 

54 

.0820 

69 

1.0908 

40 

67 

91 

1.1011 

1.1021 

146 

85 

85 

51 

1.0900 

39 

71 

98 

1.1022 

42 

52 

143 

1.0715 

1.0815 

81 

31 

70 

1.1002 

1.1029 

52 

73 

82 

140 

46 

46 

.0912 

62 

1.1001 

33 

60 

83 

1.1104 

1.1113 

137 

77 

77 

43 

93 

32 

64 

91 

1.1114 

35 

44 

134 

1.0808 

1.0908 

74 

1.1023 

63 

95 

1.1121 

45 

66 

75 

131 

39 

39 

1.1005 

54 

93 

1.1125 

52 

76 

97 

1.1206 

128 

70 

70 

36 

85 

1.1124 

56 

83 

1.1207 

1.1227 

37 

125 

1.0901 

1.1001 

67 

1.1116 

55 

87 

1.1214 

38 

58 

68 

122 

31 

31 

97 

47 

86 

1.1218 

45 

69 

89 

98 

119 

62 

62 

1.1128 

78 

1.1217 

49 

76 

99 

1.1320 

1.1329 

116 

93 

93 

59 

.1209 

48 

80 

1  .  1306 

1.1330 

51 

60 

113 

1.1024 

1.1124 

90 

39 

79 

1.1310 

37 

61 

82 

91 

110 

55 

55 

.1221 

70 

.1309 

41 

68 

92 

1.1412 

1.1422 

107 

86 

86 

52 

1.1301 

40 

72 

99 

1.1423 

43 

53 

104 

1.1116 

1.1216 

82 

32 

71 

1.1403 

1.1430 

53 

74 

83 

101 

47 

47 

1.1313 

63 

1.1402 

34 

61 

84 

1.1505 

1.1514 

98 

78 

78 

44 

93 

33 

65 

91 

1.1515 

36 

45 

95 

1  .  1209 

1.1309 

75 

1.1424 

63 

95 

.1522 

46 

66 

76 

92 

40 

40 

1.1406 

55 

94 

1.1526 

53 

77 

97 

1.1607 

89 

71 

71 

37 

86 

.1525 

57 

84 

.1608 

.1628 

37 

86 

1.1301 

1.1401 

67 

.1518 

56 

88 

.1615 

38 

59 

68 

83 

32 

32 

98 

48 

87 

1.1619 

46 

69 

90 

99 

80 

63 

63 

.1529 

78 

1.1618 

50 

76 

1.1700 

1.1721 

1.1730 

77 

94 

94 

60 

1.1609 

48 

80 

1.1707 

31 

51 

61 

74 

1.1425 

1.1525 

91 

40 

79 

1.1711 

38 

62 

82 

92 

71 

55 

55 

1.1621 

71 

1.1710 

42 

69 

92 

1.1813 

.1822 

68 

86 

86 

52 

1.1702 

41 

73 

1.1800 

1.1823 

44 

53 

65 

1.1517 

1.1617 

83 

33 

72 

1.1804 

30 

54 

75 

84 

62 

48 

48 

1.1714 

63 

1.1803 

35 

61 

85 

.1906 

.1915 

59 

79 

79    45 

94 

33 

65 

92 

1.1916 

37 

46 

56 

1.1610 

1.17IO|    76 

1.1825 

64 

96 

.1923 

47 

67 

77 

53 

41 

41 

1.1807 

56 

95 

1.1927 

54 

78 

98 

1.2008 

50 

72 

72 

38 

87 

1.1926 

58 

85 

.2009 

1  .2029 

39 

47 

1.1703 

1.1803 

69 

1.1918 

57 

89 

.2016 

40 

60 

70 

44 

34 

34 

.1900 

49 

88 

1.2020 

47 

71 

91 

1.2101 

41 

65 

65 

31 

80 

.2019 

51 

78 

.2102 

1.2122 

32 

38 

96 

96 

62 

1.2011 

50 

82 

1.2109 

33 

53 

63 

35 

1.1827 

1.1927 

93 

42 

81 

1.2113 

40 

64 

84 

94 

32 

58 

58 

1.2024 

73 

1.2113 

44 

71 

95 

1.2216 

1.2225 

THE    STEAM-BOILER. 


Lbs. 
Gauge  press.  90.3 
Abs.  press.  .  105. 

95.3 
110. 

100.3 
115. 

105.3 
120. 

110.3 
125. 

115.3 
130. 

120.3 
135. 

125.3 
140. 

130.3 
145.  , 

135.3 
150. 

140  3 
155. 

Feed 
water. 

Factors  of  Evaporation. 

212°  F. 

1.0379 

1.0387 

1  .0396 

1.0404 

1.0411 

1.0418 

1  .0425 

1.0431 

1.0437 

1.0443 

1  .  0449 

209 

1.0410 

1.0419 

1  .0427 

35 

42 

49 

56 

62 

68 

74 

80 

206 

41 

50 

58 

66 

73 

81 

87 

93 

99 

1.0505 

1.0511 

203 

72 

81 

89 

97 

1.0504 

1.0512 

1.0518 

1.0524 

1.0530 

36 

43 

200 

1.0504 

1.0512 

1  .0520 

1  .0528 

35 

43 

49 

55 

61 

67 

74 

197 

35 

43 

51 

59 

66 

74 

80 

86 

92 

98 

1.0605 

194 

66 

74 

82 

90 

97 

1  .0605 

1.0611 

1.0617 

1  .0623 

1.0629 

36 

191 

97 

1  .0605 

1.0613 

1  .0621 

1.0629 

36 

42 

48 

54 

60 

67 

188 

1.0628 

36 

44 

52 

60 

67 

73 

79 

85 

91 

98 

185 

59 

67 

75 

83 

91 

98 

1  .0704 

1.0710 

1  0716 

1.0722 

1.0729 

182 

90 

98 

1  .0706 

1.0714 

1  .0721 

1  .0729 

35 

41 

47 

53 

60 

179 

1.0721 

1.0729 

37 

45 

52 

60 

66 

72 

78 

84 

91 

176 

52 

60 

68 

76 

83 

91 

97 

1.0803 

1.0809 

1.0815 

1.0822 

173 

82 

91 

99 

1.0807 

1.0814 

1.0822 

1.0828 

34 

40 

46 

53 

170 

1.0813 

1  .0822 

1  .0830 

38 

45 

53 

59 

65 

71 

77 

83 

167 

44 

53 

61 

69 

"  76 

84 

90 

96 

1  .0902 

1.0908 

1.0914 

164 

75 

84 

92 

1.0900 

1  .0907 

1.0914 

1  .0921 

1.0927 

33 

39 

45 

161 

1.0906 

1.0914 

1.0923 

31 

38 

45 

52 

58 

64 

70 

76 

158 

37 

45 

54 

62 

69 

76 

82 

89 

95 

1.1001 

1.1007 

155 

68 

76 

85 

93 

1.1000 

1.1007 

1.1013 

1.1020 

1.1026 

32 

38 

152 

99 

1.1007 

1.1015 

1.1024 

31 

38 

44 

51 

57 

63 

69 

149 

1  .  1030 

38 

46 

55 

62 

69 

75 

81 

88 

94 

1.1100 

146 

61 

69 

77 

86 

93 

1.1100 

1.1106 

1.1112 

1.1119 

1.1125 

31 

143 

92 

1.1100 

1.1108 

1.1116 

1.1124 

31 

37 

43 

49 

56 

62 

140 

1.1123 

31 

39 

47 

54 

62 

68 

74 

80 

86 

93 

137 

53 

62 

70 

78 

85 

93 

99 

1.1205 

1.1211 

1.1217 

1.1224 

134 

84 

93 

1.1201 

1.1209 

1.1216 

1.1223 

1.1230 

36 

42 

48 

54 

131 

1.1215 

1.1223 

32 

40 

47 

54 

60 

67 

73 

79 

85 

128 

46 

54 

62 

71 

78 

85 

91 

98 

1.1304 

1.1310 

1.1316 

125 

77 

85 

93 

1.1302 

1.1309 

1.1316 

1.1322 

1.1328 

35 

41 

47 

122 

1.1308 

1.1316 

1.1324 

32 

40 

47 

53 

59 

65 

71 

78 

119 

39 

47 

55 

63 

70 

78 

84 

90 

96 

1.1402 

1.1409 

116 

69 

78 

86 

94 

1.1401 

1.1408 

1.1415 

1.1421 

1.1427 

33 

39 

113 

1.1400 

1.1408 

1.1417 

1.1425 

32 

39 

45 

52 

58 

64 

70 

110 

31 

39 

47 

56 

63 

70 

76 

82 

89 

95 

1.1501 

T07 

62 

70 

78 

87 

94 

1.1501 

1.1507 

1.1513 

1.1519 

1.1526 

32 

104 

92 

1.1501 

1.1509 

1.1517 

1.1525 

32 

38 

44 

50 

56 

63 

101 

1.1523 

32 

40 

48 

55 

63 

69 

75 

81 

87 

93 

98 

54 

62 

71 

79 

86 

93 

1.1600 

1.1606 

1.1612 

1.1618 

1.1624 

95 

85 

93 

1.1602 

1.1610 

1.1617 

1  .  1624 

30 

37 

43 

49 

55 

92 

1.1616 

1.1624 

32 

41 

48 

55 

61 

67 

74 

80 

86 

89 

47 

55 

63 

71 

79 

86 

92 

98 

1.1704 

1.1711 

1.1717 

86 

78 

86 

94 

1.1702 

1.1710 

1.1717 

1.1723 

1.1729 

35 

41 

48 

83 

1.1708 

1.1717 

1.1725 

33 

40 

48 

54 

60 

66 

72 

78 

80 

39 

47 

56 

64 

71 

78 

85 

91 

97 

1.1803 

1.1809 

77 

70 

78 

86 

95 

1.1802 

1.1809 

1.1815 

1.1822 

1.1828 

34 

40 

74 

1.1801 

1.1809 

1.1817 

1.1826 

33 

40 

46 

52 

59 

65 

71 

71 

32 

40 

48 

56 

64 

71 

77 

83 

89 

96 

1.1902 

68 

62 

71 

79 

87 

94 

1  .  1902 

1.1908 

1.1914 

1.1920 

1.1926 

33 

65 

93 

1.1902 

1.1910 

1.1918 

1.1925 

33 

39 

45 

51 

57 

63 

62 

1.1924 

32 

41 

49 

56 

63 

70 

76 

82 

88 

94 

59 

55 

63 

72 

80 

87 

94 

1.2000 

1.2007 

1.2013 

1.2019 

1.2025 

56 

86 

94 

1.2002 

1.2011 

1.2018 

1.2025 

31 

38 

44 

50 

56 

53 

1.2017 

1.2025 

33 

42 

49 

56 

62 

68 

75 

81 

87 

50 

48 

56 

64 

73 

80 

87 

93 

99 

1.2106 

1.2112 

1  2118 

47 

79 

87 

95 

1.2104 

1.2111 

1.2118 

1.2124 

1.2130 

37 

43 

49 

44 

1.2110 

1.2118 

1.2126 

35 

42 

49 

55 

61 

68 

74 

80 

41 

41 

49 

57 

66 

73 

80 

86 

92 

99 

1.2205 

1.2211 

38 

72 

80 

88 

97 

1.2204 

1.2211 

1.2217 

1.2223 

1.2230 

36 

42 

35 

1.2203 

1.2211 

1.2219 

1.2228 

35 

42 

48 

55 

61 

67 

73 

32 

34 

42 

51 

59 

66 

73 

79 

86 

92 

98 

1.2304 

FACTORS   Of   EVAPORATION. 


911 


Lbs. 
augepress.145.3 
bs.  piess    .160. 

150.3 
165. 

155.3 
170. 

160.3 
175. 

165.3 
180. 

170.3 
185. 

175.3 
190. 

180.3 
195. 

185.3 
200. 

190.3 
205. 

195.3 
210 

Feed 
water. 

Factors  of  Evaporation. 

212°  F. 

1.0454 

1.0460 

1.0464 

1.0469 

1  .0474 

1  .0478 

1.0483 

1.0487 

1.0492 

1.0496 

1.0499 

209 

86 

91 

95 

1.0500 

1  .0505 

1  .0509 

1.0514 

1.0519 

1.0523 

1.0527 

1.0530 

206 

1.0517 

1  .0522 

1.0526 

31 

36 

40 

45 

50 

54 

58 

61 

203 

..  48 

53 

57 

62 

67 

71 

77 

81 

85 

89 

92 

200 

79 

84 

88 

93 

98 

1.0602 

1  .0608 

1.0612 

1.0616 

1.0620 

1.0623 

197 

1.0610 

1.0615 

1.0619 

1.0624 

1.0629 

33 

39 

.  43 

47 

51 

54 

194 

41 

46 

50 

55 

60 

64 

70 

74 

78 

82 

85 

191 

72 

77 

81 

86 

91 

95 

1.0701 

1.0705 

1  .  0709 

1.0713 

1.0716 

188 

1.0703 

I  .0708 

1.0712 

1.0717 

1.0722 

1  .0727 

32 

36 

40 

44 

47 

185 

34 

39 

43 

48 

53 

58 

63 

67 

71 

75 

78 

182 

65 

70 

74 

79 

84 

88 

94 

98 

1.0802 

1.0806 

1.0809 

179 

96 

1.0801 

1  .0805 

1.0810 

1.0815 

1.0819 

1.0825 

1  0829 

33 

37 

40 

176 

1  .0827 

32 

36 

41 

46 

50 

56 

60 

64 

68 

71 

173 

58 

63 

67 

72 

77 

81 

87 

91 

95 

9<i 

*.0902 

170 

89 

94 

98 

1  .0903 

1.0908 

1.0912 

1.0917 

1  0922 

1.0926 

1.0930 

33 

167 

1  .0920 

1.0925 

1  .0929 

34 

39 

43 

48 

53 

57 

61 

64 

164 

51 

56 

60 

65 

70 

74 

79 

84 

88 

92 

95 

161 

81 

87 

91 

96 

1.1001 

1.1005 

1.1010 

1  1014 

1.1019 

1  .  1023 

1  .  1026 

,158 

1.1012 

1.1018 

1  .  1022 

1  .  1027 

32 

36 

41 

45 

49 

54 

57 

155 

43 

48 

53 

58 

.  63 

67 

72 

76 

80 

85 

88 

152 

74 

79 

83 

89 

94 

98 

1.1103 

1.1107 

1.1111 

1.1115 

1.1119 

149 

1.1105 

1.1110 

1.1114 

1.1120 

1.1125 

1.1129 

34 

38 

42 

46 

49 

146 

36 

41 

45 

50 

56 

60 

65 

69 

73 

77 

80 

143 

67 

72 

76 

81 

86 

91 

96 

1.1200 

1.1204 

1  .  1208 

1.1211 

,140 

98 

1.1203 

1.1207 

1.1212 

1.1217 

1.1221 

1.1227 

31 

35 

39 

42 

137 

1.1229 

34 

38 

43 

48 

52 

58 

62 

66 

70 

73 

134 

59 

65 

69 

74 

79 

83 

88 

92 

97 

1.1301!  1.1304 

131 

90 

95 

1.1300 

1.1305 

1.1310 

1.1314 

1.1319 

1.1323 

1  .  1327 

32 

35 

128 

1.1321 

1.1326 

30 

36 

41 

45 

50 

54 

58 

62 

66 

125 

52 

57 

61 

66 

72 

76 

-  81 

85 

89 

93    % 

122 

83 

88 

92 

97 

1.1402 

1.1407 

1.1412 

1.1416 

1.1420 

1.1424 

1.1427 

119 

1.1414 

1.1419 

1.1423 

1.1428 

33 

37 

43 

47 

51 

55 

58 

116 

45 

50 

54 

59 

64 

68 

73 

78 

82 

86 

89 

113 

75 

81 

85 

90 

95 

99 

1.1504 

1.1508 

1.1512 

I.bl5 

1.1520 

no 

1.1506 

1.1511 

1.1515 

1.1521 

1.1526 

1  .  1  530 

35 

39 

43 

47 

50 

107 

37 

42 

46 

51 

57 

61 

66 

70 

74 

78 

81 

104 

68 

73 

77 

82 

87 

92 

97 

1.1601 

1.1605 

1.1609 

1.1612 

101 

99 

1.1604 

1.1608 

1.1613 

1.1618 

1.1622 

1.1627 

32 

36 

40 

43 

98 

1.1629 

35 

39 

44 

49 

53 

58 

62 

67 

71 

74 

95 

60 

65 

70 

75 

80 

84 

89 

93 

97 

1.1701 

1.1705 

92 

91 

96 

1.1700 

1.1705 

1.1711 

1.1715 

1.1720 

1.1724 

1  .  1  728 

32 

35 

89 

1.1722 

1.1727 

31 

36 

42 

46 

51 

.55 

59 

63 

66 

86 

53 

58 

62 

67 

72 

76 

82 

86 

90 

94 

97 

83 

84 

89 

93 

98 

1.1803 

1.1807 

1.1812 

1.1817 

1.1821 

1.1825 

1.1828 

80 

1.1814 

1.1820 

1.1824 

1.1829 

34 

38 

43 

47 

52 

56 

59 

77 

45 

50 

54 

60 

65 

69 

74 

78 

82 

86 

90 

74 

76 

81 

85 

90 

96 

1.1900 

1.1905 

1.1909 

1.1913 

1.1917 

1.1920 

71 

1.1907 

1.1912 

1.1916 

1.1921 

1.1926 

31 

36 

40 

44 

48 

51 

68 

38 

43 

47 

52 

57 

61 

67 

71 

75 

79 

82 

65 

69 

74 

78 

83 

88 

92 

97 

1.2002 

1.2006 

1.2010 

1.2013 

62 

99 

1  .2005 

1  .2009 

1.2014 

1.2019 

1.2023 

1.2028 

32 

36 

41 

44 

59 

1.2030 

35 

40 

45 

50 

54 

59 

63 

67 

72 

75 

56 

61 

66 

70 

76 

81 

85 

90 

94 

98 

1.2102 

1.2106 

53 

92 

97 

1.2101 

1.2107 

1.2112 

1.2116 

1.2121 

1.2125 

1.2129 

33 

36 

50 

1.2123 

1.2128 

32 

37 

43 

47 

52 

56 

60 

64 

67 

47 

54 

59 

63 

68 

74 

78 

83 

87 

91 

95 

98 

44 

85 

90 

94 

1.2200 

1.2205 

1.2209 

1.2214 

1.2218 

1.2222 

1.2226 

1.2229 

41 

1.2216 

1.2221 

1.2225 

31 

36 

40 

45 

49 

53 

57 

60 

38 

47 

52 

56 

62 

67 

71 

76 

80 

84 

88 

91 

35 

78 

83 

88 

93 

98 

1.2302 

1.2307 

1.2311 

1.2315 

1.2320 

1.2323 

32 

1.2309 

1.2315 

1.2319 

1.2324 

1.2329 

33 

38 

42 

46 

51 

54 

912 


THE   STEAM-BOILER. 


Lbs. 
Gauge  press.  200.3 
Abs.  press.  .  .215. 

205. 
220. 

J    210.. 
225. 

5    215J 
230. 

220.: 

235. 

J    225.3 
240. 

230.3 
245. 

235.3 
250. 

240.3 
255. 

245.) 
260. 

250.3 
265. 

Feed 
water. 

Factors  of  Evaporation. 

212°  F. 

1  .0503 

.0507 

.051C 

1.0513 

1.0517 

1.0520 

1.0523 

1.0527 

1.0529 

1.0533 

1.0535 

209 

34 

38 

41 

44 

52 

55 

58 

60 

64 

66 

206 

65 

69 

72 

75 

79 

83 

86 

89 

91 

95 

97 

203 

96 

1  .0600 

1.0603 

1.0606 

1.0611 

1.0614 

1.0617 

1  .0620 

1.0622 

1.0626 

1.0629 

200 

1.0627 

31 

34 

37 

42 

45 

48 

51 

53 

57 

60 

197 

58 

62 

65 

68 

73 

76 

79 

82 

84 

88 

91 

194 

89 

93 

96 

1  0700 

1  0704 

1  0707 

1  0710 

1.0713 

1  0715 

1  0719 

1  0722 

191 

1  .0720 

.0724 

1  .0727 

31 

35 

38 

41 

44 

46 

50 

53 

188 

51 

55 

58 

62 

66 

69 

72 

75 

78 

81 

84 

185 

82 

86 

89 

93 

97 

1.0800 

1  .0803 

.0806 

1  .0809 

1.0812 

1.0815 

182 

1.0813 

1.0817 

1.0820 

1  .0823 

1.0828 

31 

34 

37 

39 

43 

46 

179 

44 

48 

51 

54 

59 

62 

65 

68 

70 

74 

77 

176 

75 

79 

82 

86 

90 

93 

96 

99 

1  .0901 

1  .0905 

1.0908 

173* 

1  .0906 

1.0910 

1.0913 

1.0916 

1.0921 

1  .0924 

1.0927 

I  .0930 

32 

36 

39 

170 

37 

41 

44 

47 

51 

55 

58 

61 

63 

67 

69 

167 

68 

72 

75 

78 

82 

86 

89 

92 

94 

98 

1.1001 

164 

99 

1.1003 

1.1006 

1.1009 

1.1013 

1.1016 

.1019 

1.1023 

1.1025 

1.1029 

31 

161 

1  .  1030 

34 

37 

40 

44 

47 

50 

54 

56 

60 

62 

158 

61 

65 

68 

71 

75 

78 

81 

85 

87 

91 

93 

155 

92 

96 

99 

1.1102 

1.1106 

1.1109 

1.1112 

1.1115 

1.1118 

1.1122 

1.1124 

152 

1.1123 

1.1127 

1.1130 

33 

37 

40 

43 

46 

49 

53 

55 

149 

54 

58 

61 

64 

68 

71 

74 

77 

80 

83 

86 

146 

84 

89 

92 

95 

99 

1.1202 

1.1205 

.1208 

1.1211 

1.1214 

1.1217 

143 

1.1215 

1.1219 

1.1223 

1.1226 

1.1230 

33 

36 

39 

42 

45 

48  } 

140 

46 

50 

53 

56 

61 

64 

67 

70 

72 

76 

79 

137 

77 

81 

84 

87 

92 

95 

98 

1.1301 

1.1303 

1  .  1307 

1.1310 

134 

1.1308 

1.1312 

.1315 

1.1318 

1  .  1322 

1  .  1326 

1  .  1329 

32 

34 

38 

40 

131 

39 

43 

46 

49 

53 

56 

59 

62 

65 

69 

71 

128 

70 

74 

77 

80 

84 

87 

90 

93 

96 

1.1400 

1.1402  •' 

125 

1.1400 

1.1405 

1.1408 

1.1411 

1.1415 

1.1418 

1.1421 

1.1424 

1.1427 

30 

33 

122 

31 

35 

39 

42 

46 

49 

52 

55 

58 

61 

64  i 

119 

62 

66 

69 

72 

77 

80 

83 

86 

88 

92 

95 

116 

93 

97 

1.1500 

1.1503 

1.1507 

1.1511 

1.1514 

1.1517 

1.1519 

1.1523 

1.1525  : 

113 

1.1524 

1.1528 

31 

34 

38 

41 

44 

48 

50 

54 

56 

110 

55 

59 

62 

65 

69 

72 

75 

78 

81 

85 

87 

107 

85 

90 

93 

96 

1.1600 

1.1603 

1.1606 

1.1609 

1.1612 

1.1615 

1.1618 

104 

1.1616 

1  .  1620 

1.1624 

1.1627 

31 

34 

37 

40 

43 

46 

49 

101 

47 

51 

54 

57 

61 

65 

68 

71 

73 

77 

80 

98 

78 

82 

85 

88 

92 

95 

98 

1.1702 

1  .  1  704 

1.1708 

1.1710 

95 

1.1709 

1.1713 

1.1716 

.1719 

1.1723 

1.1726 

1.1729 

32 

35 

39 

41 

92 

39 

44 

47 

50 

54 

57 

60 

63 

66 

69 

72 

89 

70 

75 

78 

81 

85 

88 

91 

94 

97 

1.1800 

1.1803 

86 

1.1801 

1.1805 

1.1808 

1.1812 

1.1816 

1.1819 

.1822 

1.1825 

1.1827 

31 

34 

83 

32 

36 

39 

42 

46 

50 

53 

56 

58 

62 

64 

80 

63 

67 

70 

73 

77 

80 

83 

87 

89 

93 

95 

77 

94 

98 

1.1901 

1.1904 

.1908 

1.1911 

.1914 

1.1917 

1.1920 

1.1924 

1.1926 

74 

1.1924 

.1929 

32 

35 

39 

42 

45 

48 

51 

54 

57 

71 

55 

59 

63 

66 

70 

73 

76 

79 

82 

85 

88 

68 

86 

90 

93 

96 

.2001 

1.2004 

.2007 

.2010 

1.2012 

1.2016 

1.2019 

65 

1.2017 

.2021 

1.2024 

1.2027 

31 

35 

38 

41 

43 

47 

49 

62 

48 

52 

55 

58 

62 

65 

68 

72 

74 

78 

80 

59 

79 

83 

86 

89 

93 

96 

99 

.2102 

1.2105 

1.2109 

1.2111 

56 

1.2110 

.2114 

1.2117 

.2120 

.2124 

1.2127 

.2130 

33 

36 

40 

42 

53 

41 

45 

48 

51 

55 

58 

61 

64 

67 

70 

73 

50 

71 

76 

79 

82 

86 

89 

92 

95 

98 

1.2201 

1.2204 

47 

1.2202 

.2207 

1.2210 

.2213 

.2217 

.2220 

.2223 

.2226 

.2229 

32 

35 

44 

34 

38 

41 

44 

48 

51 

54 

57 

60 

63 

66 

41 

65 

69 

72 

75 

79 

82 

85 

88 

91 

94 

97 

38 

.2300 

1.2303 

.2306 

.2310 

1.2313 

.2316 

2319 

1.2322 

1.2325 

1.2328 

35 

1  2327 

31 

34 

37 

41 

44 

47 

50 

53 

57 

59 

32 

58 

62 

65 

68 

72 

/5 

78 

82 

84 

88 

90 

STRENGTH  OF  STEAM-BOILERS*  913 

plates,  headers  of  water-tube  boilers  (for  pressures  under  160  lb.),  mud 
drums  (not  exceeding  18  in.  diameter),  and  nozzles  for  pipe  attach- 
ments, but  there  is  a  tendency  to  substitute  rolled  or  forged  steel  for  all 
these  purposes  except  grate-bars. 

Quality  of  Steel.     (A.  S.  M.  E.  Boiler  Code,  1915.) 

FLANGE.  FIREBOX. 

Plates    3/4    in.    thick 

and  under  .  .  0  .  12—  0.  25% 
Plates    over    s/4    in. 
thick  ......  0.12—  0.30 

Manganese  .............  0.30  —  0.60%  0.30  —  0.50 

Pho«T^™>n«  j  Acid  ----  Not  °ver  0.05       Not  over  ...........   0.04 

Phosphorus  J  Basic        Not  over  0  04      Not  over  ...........  0  035 

Sulphur  ...........  >  .Not  over  0.05       Not  over  ...........   0.04 

Copper  ..............  Not  over  ...........   0.05 

Tensile  strength,  lb.  per  sq.  in.  .  .  .   55,000—65,000  55,000—63,000 

Yield  point,  min.,  lb.  per  sq.  in.  .  .   0.5  tens.  str.  0.5  tens.  str. 

.     1,500,000  1,500,000 

Elongation  in  8-m.,  mm.,  per  cent   ^^-^  -  Tens,  str.— 


For  material  over  3/4  in.  in  thickness  a  deduction  of  0.5  from  the 
percentage  of  elongation  shall  be  made  for  each  increase  of  1/8  in.  in 
thickness  above  3/4  in.,  to  a  minimum  of  20%. 

Cold  bending  and  quonch  bending  tests  are  also  required,  and  for  fire- 
box steel  a  homogeneity  test  (see  page  507). 

Rivet  steel:  Tensile  strength,  45,000-55,000,  Elongation  in  8  in. 
1,500,000  -T-  tensile  strength,  but  need  not  exceed  30%.  Stay  bolt  steel, 
T.  S.,  50,000-60,000. 

Queiich-bend  Tests.  —  The  test  specimen,  when  heated  to  a  light 
cherry  red  as  seen  in  the  dark  (not  less  than  1200°  F.),  and  quenched 
at  once  in  water  the  temperature  of  which  is  between  80°  and  90°,  shall 
bend  through  180°  without  cracking  on  the  outside  of  the  bent  portion, 
as  follows:  For  material  1  in.  or  under  in  thickness,  flat  on  itself;  for 
material  over  I  in.  in  thickness,  around  a  pin  of  a  diameter  equal  to 
the  thickness. 

Boiler  tubes  are  now  generally  made  of  soft  steel,  but  charcoal  iron 
tubes  are  still  preferred  by  some  users. 

Shells;  Water  and  Steam  Drums.  —  The  cylindrical  structure,  in- 
cluding the  ends,  of  a  fire-tube  boiler,  is  usually  called  the  shell.  The 
cylinder  superposed  on  the  tubes  of  a  water-tube  boiler  is  called  a" 
water  and  steam  drum.  Shells  of  marine  boilers  of  the  Scotch  type 
have  been  built  of  diameters  as  large  as  16  ft.  Water  and  steam  drums 
of  water-tube  boilers  are  rarely  made  of  greater  diameter  than  42  in. 

The  thickness  of  shell  for  a  given  pressure  is  found  from  the  common 
formula  for  safe  strength  of  thin  cylinders, 

P  =  2  1  Tf  *dF;  whence  t=PdF  +  2Tf. 

P  =  safe  working  pressure;  T  =  tensile  strength  of  plate,  both  in  lb. 
per  sq.  in.,  t  =  thickness  of  plate  in  inches:  /  =  ratio  of  the  strength  of  a 
riveted  joint  to  that  of  the  solid  plate;  F  =  factor  of  safety  allowed;  and 
d  =  diameter  of  shell  or  drum  in  inches. 

The  value  taken  for  T  is  commonly  that  stamped  on  the  plates  by  the 
manufacturer,  /  is  taken  from  tables  of  strength  of  riveted  joints  or  is 
computed,  and  F  must  be  taken  at  a  figure  not  less  than  is  prescribed 
by  local  or  State  laws,  or,  in  the  case  of  marine  boilers,  by  the  rules 
of  the  U.  S.  Board  of  Supervising  Inspectors,  and  may  be  more  than  this 
figure  if  a  greater  margin  of  safety  is  desired. 

Strength  of  Circumferential  Seam.  —  Safe  working  pressure  P  = 
4tT  f  +  dF;  t  =  PdF  +  4:Tf,  notation  as  above.  The  strength  of  a 
shell  against  rupture  on  a  circumferential  line  is  twice  that  against 
rupture  on  a  longitudinal  line,  therefore  single  riveting  is  sufficient 
on  the  circumferential  seams  while  double,  triple  or  quadruple  rivet- 
ing is  used  for  the  longitudinal  seams. 

Thickness  of  Plates;  Riveting.  (Mass.  Boiler  Rules,  1910).  —  The 
longitudinal  joints  of  a  boiler,  the  shell  or  drum  of  which  exceeds  36  in. 
diameter,  shall  be  of  butt  and  double  strap  construction;  if  it  does  not 


914 


THE  STEAM-BOILER. 


exceed  36  in.  lap-riveted  construction  may  be  used,  the  maximum 
pressure  on  such  shells  being  100  Ib.  per  sq.  in. 

Minimum  thickness  of  plates  in  flat-stayed  surfaces,  5/ie  in. 

The  ends  of  stay  bolts  shall  be  riveted  over  or  upset. 

Rivets  shall  be  of  sufficient  length  to  completely  fill  the  rivet  holes 
and  form  a  head  equal  in  strength  to  the  body  of  the  rivet. 

Rivets  shall  be  machine  driven  wherever  possible,  with  sufficient 
pressure  to  fill  the  rivet  holes,  and  shall  be  allowed  to  cool  and  shrink 
under  pressure. 

Rivet  holes  shall  be  drilled  full  size  with  plates,  butt  straps  and 
heads  bolted  in  position;  or  they  may  be  punched  not  to  exceed  1/4  in. 
less  than  full  size  for  plates  over  5/16  in.  thick,  and  1/8  in.  or  less  for 
plates  not  exceeding  5/i6  in.  thick,  and  then  drilled  or  reamed  to  full 
size  with  plates,  butt  straps  and  heads  bolted  up  in  position. 

The  longitudinal  joints,  of  horizontal  return-tubular  boilers  shall  be 
located  above  the  fire-line  of  the  setting. 

The  thickness  of  plates  in  a  shell  or  drum  shall  be  of  the  same  gage. 
Minimum  thickness  of  shell  plates  (Mass.  Rules  and  A.  S.  M.  E.  Code)  : 
Diam.  36  in.  or  under,  1/4  in.;  over  36  to  54  in.,  5/16  in.;  over  54  to  72 
in.,  3/8  m.;  over  72  in.,  1/2  in. 

Minimum  thickness  of  butt  straps: 


Straps,  in .  |       1/4 


Plates,  in. U/4  to  11/32  3/8  to  !3/32  7/16  to  l5/32  l/2  to  9/16  5/8  to  3/4  7/8  1  to  U/8  UA 


6/16 


Vl6       I       V2       |5/8 


3/4       I  VS 


Minimum  thickness  of  tube  sheets: 


Diam.  of  tube 
sheet,  in        .  . 

42  or  under 

Over  42  to  54 

Over  54  to  72 

Over  72 

Thickness,  in  

3/8 

7/16 

V2 

9/16 

Convex  or  Bumped  Heads. — Minimum  thickness  of  convex  heads, 
t  =  i/id  F  P  -T-  T-  d  =  diameter  in  inches;  F  =  5  =  factor  of  safety;  P  = 
working  pressure,  Ib.  per  sq.  in. ;  T  =  tensile  strength  stamped  on  the 
head. 

When  a  convex  head  has  a  manhole  opening  the  thickness  is  to  be 
increased  not  less  than  i/g  in. 

When  the  head  is  of  material  of  the  same  quality  and  thickness  as 
that  of  the  shell,  the  head  is  of  equal  strength  with  the  shell  when  the 
radius  of  curvature  of  the  head  equals  the  diameter  of  the  shell,  or  when 
the  rise  of  the  curve  =  0.134  diam.  of  shell. 

[The  A.  S.  M.  E.  Boiler  Code  specifies  a  higher  factor  of  safety,  5.5, 
and  adds  l/g  in.  to  the  thickness,  making  the  formula  t  =  2.75  PR/T 
+  l/g  in.,  R  being  the  radius  to  which  the  head  is  dished,  in  inches. 
When  R  is  less  than  0.8  d  the  thickness  shall  be  at  least  that  found  by 
the  formula  when  R  =  0.8  d.  Dished  heads  with  the  pressure  on  the 
convex  side  are  allowed  a  maximum  working  pressure  equal  to  60% 
of  that  for  heads  of  the  same  dimensions  with  the  pressure  on  the 
concave  side.  When  the  dished  head  has  a  manhole  opening  the  thick- 
ness as  found  by  these  rules  shall  be  increased  by  not  less  than  i/g  in. 
The  corner  radius  of  a  dished  head  shall  be  not  less  than  iy2  in.  nor 
more  than  4  in.,  and  not  less  than  0.03#.  A  manhole  opening  in  a 
dished  head  shall  be  flanged  to  a  depth  not  less  than  three  times  the 
thickness  of  the  head  measured  from  the  outside.] 

Efficiency  of  Riveted  Joints.     (Mass.  Boiler  Rules,  1910.)* 
X  =  efficiency  =  ratio  of  strength  of  unit  length  of  riveted  joint  to 

the  strength  of  the  same  length  of  a  solid  plate. 
T  =  tensile  strength  of  the  material,  in  pounds  per  square  inch. 
t  =  thickness  of  plate,  in  inches. 
b  =  thickness  of  butt  strap,  in  inches. 

JP  =  pitch  of  rivets,  in  inches,  on  the  row  having  the  greatest  pitch, 
d  =  diameter  of  rivet,  after  driving,  in  inches. 
a  =  cross-section  of  rivet  after  driving,  in  square  inches, 
s  =  strength  of  rivet  in  single  shear,  in  pounds  per  square  inch. 
S  =  strength  of  rivet  in  double  shear,  in  pounds  per  square  inch. 

*  The  same  rules  are  given  hTthe  A.  S.  M.  E.  Boiler  Code  of  1914, 
which  was  modeled  on  the  Massachusetts  Rules. 


STRENGTH   OF   STEAM-BOILERS.  915 

c  •-  crushing  strength  of  rivet,  in  pounds  per  square  inch. 
n  =  number  of  rivets  in  single  shear  in  a  length  of  joint  equal  to  P. 
2V  =  number  of  rivets  in  double  shear  in  the  same  length  of  joint. 
For  single-riveted  lap  joints: 

A  -  strength  of  solid  plate  =  PtT. 

B  =  strength  of  plate  between  rivet  holes  =  (P  —  d)tT. 

C  —  shearing  strength  of  one  rivet  =  nsa. 

D  =  crushing  strength  of  plate  in  front  of  one  rivet  =  dtc. 

~K        C*          T) 

X  =  -r  or  —  or  — ,  whichever  is  least. 
A      A        A 

For  double-riveted  lap  joints: 

A  and  B  as  above,  C  and  D  to  be  taken  for  two  rivets. 
X  =  B,  C,  or  D  (whichever  is  least)  divided  by  A. 
For  butt  and  double  strap  joint,  double-riveted: 
A  =  strength  of  solid  plate  =  PtT. 
B  =  strength  of  plate  between  rivet  holes  in  the  outer  row  = 

(P  -  d)tT. 
C  =  shearing  strength  of  two  rivets  in  double  shear,  plus  shearing 

strength  of  one  rivet  in  single  shear  =  NSa  -\-  nsa. 
D  =  strength  of  plate  between  rivet  holes  in  the  second  row,  plus 
the  shearing  strength  of  one  rivet  in  single  shear  in  the  outer 
row  =  (P  -  2d)tT  +  nsa. 

E  =  strength  of  plate  between  rivet  holes  in  the  second  row,  plus 
the  crushing  strength  of  butt  strap  in  front  of  one  rivet  in 
the  outer  row  =  (P  -  2d)tT  +  dbc. 

F  =  crushing  strength  of  plate  in  front  of  two  rivets,  plus  the 
crushing   strength  of  butt  strap   in  front  of  one  rivet  = 
Ndtc  +  7idbc. 
G  =  crushing  strength  of  plate  in  front  of  two  rivets,  plus  the 

shearing  strength  of  one  rivet  in  single  shear  =  Ndtc  •+•  nsa. 
X  =  B,  C,  D,  E,  F,  or  G  (whichever  is  least)  divided  by  A. 
For  butt  and  double  strap  joint,  triple-riveted: 

The  same  as  for  double-riveted,  except  that  four  rivets  instead  oi 

two  are  taken  for  N  in  computing  C,  F,  and  G. 
For  butt  and  double  strap  joint,  quadruple-riveted: 
A,  B,  and  D  the  same  as  for  double-riveted  joints. 
C  =  shearing  strength  of  eight  rivets  in  double  shear  and  three 

rivets  in  single  shear  =  NSa  +  nsa. 

E  =  strength  of  plate  between  rivet  holes  in  the  third  row  (the 
outer  row  being  the  first)  plus  the  shearing  strength  in  single 
shear  of  two  rivets  in  the  second  row  and  one  rivet  in  the 
outer  row  =  (P  —  4d)tT  -f-  nsa. 

F  =  strength  of  plate  between  rivet  holes  in  the  second  row,  plus 
the  crushing  strength  of  butt  strap  in  front  of  one  rivet  in 
the  outer  row  =  (P  -  2d)tT  +  dbc. 

G  =  strength  of  plate  between  rivet  holes  in  the  third  row,  plus 
the  crushing  strength  of  butt  strap  in  front  of  two  rivets 
in  the  second  row  and  one  rivet  in  the  outer  row  = 

(P  -4d)tT  +  ndbc. 

H  -  crushing  strength  of  plate  in  front  of  eight  rivets,  plus  the 
crushing  strength  of  butt  strap  in  front  of  three  rivets  = 
Ndtc  +  ndbc. 

I  =  crushing  strength  of  plate  in  front  of  eight  rivets,  plus  the 
shearing  strength  in  single  shear  of  two  rivets  in  the  second 
row  and  one  in  the  outer  row  =  Ndtc  +  nsa. 
X=  B,  C,  D,  E,  F,  G,  H,  or  /  (whichever  is  least)  divided  by  A. 
The  Massachusetts  Rules  allow  the  crushing  strength  of  mild  steel  to 
be  taken  at  95,000  Ib.  per  sq.  in.     The  maximum  shearing  strength  of 
rivets,  in  Ib.  per  sq.  in.  of  cross-section,  is  taken  as  follows: 
In  single  shear,  iron,  38,000;  steel,  42,000. 
In  double  shear,  iron,  70,OOO;  steel,  78,000. 
The  A.  S.  M.  Boiler  Code  also  allows  95,000  Ib.  per  sq.  in.  for 
ing  strength,  but  for  shearing  strength  gf  rivets  allows: 
In  single  shear,  iron  38,000;  steel  44,000. 
In  double  shear,  iron  76,000;  steel  88,000. 


916  THE  STEAM-BOILER. 

Allowable  Stresses  on  Braces  and  Staybolts.  (Massachusetts  Rules.) 
— The  maximum  allowable  stress  per  square  inch  net  cross-sectional 
area  of  stays  and  stay  bolts  shall  be  as  follows:  Weldless  mild  steel, 
head  to  head  or  through  stays,  8000  lb.,  9000  lb.;  diagonal  or  crow- 
foot stays,  7500  lb.,  8000  lb.;  mild  steel  or  wrought-iron  stay  bolts 
6500  lb.,  7000  lb.  The  first  figure  in  each  case  is  for  size  up  to  1 1/4 
in.  diameter  or  equivalent  area,  the  second  for  size  over  1  1/4  in.  or 
equivalent  area. 

The  A.  S.  M.  E.  Boiler  Code  allows  for  welded  stays  6000  lb.  per  sq. 
in.;  for  unwelded  stays  (a)  7500;  (&)  9500;  (c)  8500.  (a)  less  than  20 
diameters  long,  screwed  through  plates  with  ends  riveted  over;  (6) 
lengths  between  supports  not  exceeding  120  diameters;  (c)  exceeding  120 
diameters. 

Allowable  Pressure  on  Staybolted  Surfaces. — The  U.  S.  Supervising 
Inspectors'  rule  (for  steamboat  service)  is: 

P  =  W  +  S2 

P  =  allowable  pressure,  lb.  per  sq.  in.,  5  =  maximum  pitch  in  inches, 
t  =  thickness  in  sixteenths  of  an  inch,  k  =  112  for  plates  up  to  7/ie  in., 
and  120  for  plates  over  7/16  in. 

The  A.  S.  M.  E.  Boiler  Code  gives  the  same  formula  with  the  follow- 
ing values  of  the  constants:  For  stays  screwed  through  plates  with 
ends  riveted  over,  plates jnot  over  7/16  in.  thick,  C  —  112;  over  7/i6  in. 
thick,  C  =  120;  for  stays  screwed  through  plates  and  fitted  with  single 
nuts  outside  of  plate,  C  =  135;  for  stays  fitted  with  inside  nuts  and 
outside  washers,  the  diameters  of  washers  not  less  than  0.4  S  and 
thickness  not  less  than  t,  C  =  175. 

Staybolts. — Staybolts  in  water-legs  are  subject  not  only  to  longi- 
tudinal stress  due  to  the  boiler  pressure,  and  to  corrosion,  but  also  to 
bending  stress  caused  by  relative  motions  of  the  outer  and  inner  sheets 
of  the  furnace  or  waterleg  due  to  the  variations  in  temperature  to 
which  the  two  are  subjected.  A  staybolt  usually  fails  by  transverse 
fracture  close  to  the  outer  sheet,  which  is  supposed  to  be  due  to  the 
fact  that  the  fire-box  sheet  is  generally  thinner  than  the  outer  sheet,  and 
therefore  holds  the  end  of  the  stay  less  rigidly.  Staybolts  are  some- 
times drilled  with  a  small  hole  at  one  end  through  which  water  will  be 
blown  out  as  soon  as  a  fracture  extends  far  enough  across  the  section 
to  reach  the  hole,  thus  calling  attention  to  the  failure  of  the  stay.  A 
better  form  is  one  in  which  the  hole  extends  the  whole  length  of  the  stay. 
The  inner  portion  of  the  stay  is  turned  to  i/g  in.  smaller  diameter  than 
the  ends,  in  order  to  make  the  stay  more  flexible  and  diminish  the 
chances  of  fracture. 

Tube  Spacing  in  Horizontal  Tubular  Boilers. — In  modern  practice 
the  tubes  are  arranged  in  vertical  and  horizontal  rows  (not  staggered 
as  in  earlier  practice),  with  not  less  than  1  in.  space  between  adjacent 
tubes,  not  less  than  2  in.  between  the  two  central  vertical  rows,  and 
not  less  than  2  Y^  in.  between  the  shell  and  the  nearest  tube.  In  boilers 
60  in.  diameter  and  larger  a  manhole  is  put  in  the  front  head  beneath 
the  central  rows  of  tubes. 

Tubes  and  Tube  Holes.  (Mass.  Boiler  Rules) . — Tube  holes  shall  be 
drilled  full  size,  or  they  may  be  punched  not  to  exceed  ^  in.  less  than 
the  full  size,  and  then  drilled,  reamed  or  finished  full  size  with  a  rotating 
cutter.  The  edge  of  tube  holes  shall  be  chamfered  to  a  radius  of  about 
1/16  in.  A  fire-tube  boiler  shall  have  the  ends  of  the  tubes  substantially 
beaded.  The  ends  of  all  tubes,  suspension  tubes  and  nipples  shall  be 
flared  not  less  than  1/8  in.  over  the  diameter  of  the  tube  hole  on  all 
water-tube  boilers  and  superheaters,  and  shall  project  through  the  tube 
sheets  or  headers  not  less  than  1/4  in.  nor  more  than  1/2  in.  Separately 
fired  superheaters  shall  have  the  tube  ends  protected  by  refractory  ma- 
terial where  they  connect  with  drums  or  headers. 

Holding  Power  of  Expanded  Tubes.  (The  Locomotive,  Sept.,  1893.) 
— Tubes  3  in.  external  diameter,  0.109  in.  thick  were  expanded  in  a 
3/g-in.  plate  by  rolling  with  a  Dudgeon  expander,  without  the  pro- 
jecting part  being  flared  or  beaded.  Stress  was  applied  to  draw  the 
tubes  out  of  the  plates.  The  observed  stress  which  caused  yielding 
was,  in  three  specimens,  6500,  5000  and  7500  lb.  Two  other  specimens 
were  flared  so  that  the  diameter  of  the  extreme  end  of  the  tube  pro- 


STRENGTH   OF   STEAM-BOILERS. 


917 


jecting  3/i6  in.  beyond  the  plate  was  3.2  in.,  the  diameter  of  the  tube 
where  it  entered  the  plate  being  3.1  in.  The  observed  stress  which 
caused  the  yielding  of .  these  specimens  was  21,000  and  19.500  Ib. 
The  Locomotive  estimates  that  the  factor  of  safety  of  the  plain  rolled 
tubes  is  nearly  4  and  that  of  the  flared  tubes  about  15  against  the  stress 
to  which  they  are  subjected  in  a  boiler  at  100  Ib.  gage  pressure.  It  is 
considered  that  the  tubes  act  as  stays  for  that  portion  of  the  flat  head 
that  is  within  two  inches  of  the  upper  row  of  tubes,  and  that  the  seg- 
ment above  this  (except  that  portion  that  lies  with  3  in.  of  the  shell)  re- 
quires to  be  braced, 

Size  of  Boiler  Tubes.— The  following  table  gives  the  dimensions  of 
the  tubes  commonly  used  in  stoam-boilers,  together  with  their  calculated 
surface  per  foot  of  length,  and  the  length  per  square  foot  of  surface, 
internal  and  external: 

Dimensions  of  Standard  Boiler  Tubes 


.i  A 

1 

55 

J.  9    * 

t_,  •*•*  v 

£ 

£ 

External  D 
ameter,  Ii 

Standard 
Thickness 
In. 

11 

lij 

Length  per 
Sq.  ft.  of 
Inside 
Surface. 

Outside  Su] 
face  per  Fc 
of  Length 
Sq.  ft. 

¥.1 

Internal 
Area,  Sq. 

External 
Area,  Sq. 

2 

0.095 

1.810 

0.4738 

2.110 

0.5236 

.910 

0.0179 

0.0218 

21/4 

.095 

2.060 

.5393 

.854 

.5890 

.698 

.0231 

.0276 

.109 

2.282 

.5974 

.674 

.6545 

.528 

.0284 

.0341 

23/4 

.109 

2.532 

.6629 

.508 

.7199 

.389 

.0350 

.0412 

3 

.109 

2.782 

.7283 

.373 

.7854 

.273 

.0422 

.0491 

31/4 

.120 

3.010 

.7880 

.269 

.8508 

.175 

.0494 

.0576 

3V2 

.120 

3.260 

.8535 

.172 

.9163 

.091 

.0580 

.0668 

3V4 

.120 

3.510 

.9189 

.088 

.9817 

.018 

.0672 

.0767 

4 

.134 

3.732 

'   .9770 

.024 

1  .0472 

0.955 

.0760 

.0873 

Flues  Subjected  to  External  Pressure. — The  rules  of  the  U.  S.  Board 
of  Supervising  Inspectors,  Steamboat  Inspection  Service,  1909,  give  tile 
following  rules  for  flues  subjected  to  external  pressure  only: 

Plain  lap-welded  flues  7  to  13  in.  diameter. 

Furnaces. — The  tensile-  strength  of  steel  used  in  the  construction  of  ' 
corrugated  or  ribbed  furnaces  shall  not  exceed  67,000,  and  be  not  less 
than  54,000  Ib. ;  and  in  all  other  furnaces  the  minimum  tensile  strength 
shall  not  be  less  than  58,000,  and  the  maximum  not  more  than  67,000 
Ib.     The  minimum  elongation  in  8  inches  shall  be  20%. 

All  corrugated  furnaces  having  plain  parts  at  the  ends  not  ex- 
ceeding 9  inches  m  length  (except  flues  especially  provided  for),  when 
new,  and  made  to  practically  true  circles,  shall  be  allowed  a  steam 
pressure  in  accordance  with  the  formula  P  =  C  X  T  +  D. 

P  =  pressure  in  Ib.  per  sq.  in.,  T  =  thickness  in  inches,  C  =  a  con- 
stant, as  below. 

Leeds  suspension  bulb  furnace. . .  C  =  17,000,  T  not  less  than  5/i6  in. 

Morison  corrugated  type C  =  15,600,  T  not  less  than  5/16  in. 

Fox  corrugated  type C  =  14,000,  T  not  less  than  5/16  jn. 

Purves  type,  rib  projections C  =  14,000,  T  not  less  than  7/i6  in. 

Brown  corrugated  type C  =  14,000,  T  not  less  than  5/16  in. 

Type  having  sections  18  ins.  long  C  =  10,000,  T  not  less  than  7/ie  in. 

Limiting  dimensions  from  center  of  the  corrugations  or  projecting 
ribs,  and  of  their  depth,  are  given  for  each  furnace. 

Working  Pressure  on  Boilers  with  Triple  Riveted  Joints.— A  triple 
riveted  double  butt  and  strap  joint,  carefully  designed,  may  be  made 
to  have  an  efficiency  something  higher  than  85  per  cent.  Good  boiler 
plate  steel  may  be  considered  to  have  a  tensile  strength  of  55,000  Ib. 
per  sq.  in.  Taking  these  figures  and  a  iactor  of  safety  of  5,  we  have 
safe  working  pressure 

2T_tf  _  2  X  55, OOP  5<  1X0.85  _  187001 
dF    =  5d  d     ' 

from  which  the  following  table  is  calculated. 


918 


THE   STEAM-BOILER. 


Safe  Working  Pressure  for  Shells  with  Joints  of  85%  Efficiency. 


Thickness,  In.  .  . 

1/4 

5/16 

3/8 

7/16 

V2 

9/16 

5/8 

n/18 

3/4 

13/16 

V8 

15/16 

1 

Diameter,  In. 
24 

IP5 

747 

30  .. 

156 

195 

734 

36... 

no 

16? 

195 

777 

760 

42 

139 

167 

195 

773 

750 

48... 

1?? 

146 

170 

195 

719 

743 

54 

108 

no 

151 

173 

195 

716 

738 

60 

117 

136 

156 

175 

195 

714 

733 

66  .. 

106 

174 

147 

159 

177 

195 

71? 

730 

72 

114 

130 

146 

16? 

179 

195 

711 

??7 

78  

170 

135 

150 

165 

180 

195 

710 

775 

84... 

175 

139 

153 

167 

181 

195 

209 

223 

90 

117 

130 

143 

156 

169 

18? 

195 

708 

96  

121 

134 

146 

158 

170 

183 

195 

Shells  of  externally  fired  boilers  are  rarely  made  over  9/16  in.  thick. 

Pressures  Allowed  on  Boilers.  (Mass.  Boiler  Rules.)— The  pressure 
allowed  on  a  boiler  constructed  wholly  of  cast  iron  shall  not  exceed 
25  Ib.  per  sq.  in. 

The  pressure  allowed  on  a  boiler  the  tubes  of  which  are  secured  to 
cast-iron  headers  shall  not  exceed  160  Ib.  per  sq.  in. 

The  maximum  pressure  to  be  allowed  on  a  shell  or  drum  of  a  boiler 
shall  be  determined  from  the  minimum  thickness  of  the  shell  plates,  the 
lowest  tensile  strength  stamped  on  the  plates  by  the  manufacturer,  the 
efficiency  of  the  longitudinal  joint  or  of  the  ligament  between  the  tube 
holes,  whichever  is  least,  the  inside  diameter  of  the  outside  course,  and 
a  factor  of  safety  not  less  than  five. 

The  lowest  factor  of  safety  to  be  used  for  boilers  the  shells  or  drums 
of  which  are  exposed  to  the  products  of  combustion,  and  the  longi- 
tudinal joints  of  which  are  lap  riveted,  shall  be  as  follows:  5  for  boiler j 
not  over  10  years  old;  5.5  for  boilers  over  10  and  not  over  15  years  old; 
5.75  for  boilers  over  15  and  not  over  20  years  old;  6  for  boilers  over  20 
years  old.  The  lowest  factor  of  safety  to  be  used  for  boilers  the  longi- 
tudinal joints  of  which  are  of  butt  and  double  strap  construction  is  4.5 

A  hydrostatic  test  is  to  be  applied  if  in  the  judgment  of  the  in- 
spector or  of  the  insurance  company  it  is  advisable.  The  maximum 
pressure  in  a  hydrostatic  test  shall  not  exceed  1 1A  times  the  maximum 
allowable  working  pressure,  except  that  twice  the  maximum  allowable 
working  pressure  may  be  applied  on  boilers  permitted  to  carry  not 
over  25  Ib.  pressure,  or  on  pipe  boilers. 

Fusible  Plugs. — (A.  S.  M.  E.  Code.)  Fusible  plugs,  if  used,  shall  be 
filled  with  tin  with  a  melting  point  between  400  and  500°  P.  The  least 
diameter  of  fusible  metal  shall  be  not  lessithan  ^  in.,  except  for  maximum 
allowable  working  pressures  of  over  175  Ib.  per  sq.  in.  or  when  it  is 
necessary  to  place  a  fusible  plug  in  a  tube,  in  which  case  the  least 
diameter,  of  fusible  metal  shall  be  not  less  than  3/g  in. 

Steam-domes. — Steam-domes  or  drums  were  formerly  almost  uni- 
versally used  on  horizontal  boilers,  but  their  use  is  now  generally  discon- 
tinued, as  they  are  considered  a  useless  appendage  to  a  steam-boiler,  and 
unless  properly  designed  and  constructed  are  an  element  of  weakness. 


IMPROVED   METHODS   OF   FEEDING   COAL. 

Mechanical  Stokers.  (William  R.  Roney,  Trans.  A.  S.  M.  E.,  vol. 
xii.) — Mechanical  stokers  have  been  used  in  England  to  a  limited  extent 
since  1785.  In  that  year  one  was  patented  by  James  Watt.  (See  D.  K. 
Clark's  Treatise  on  the  Steam-engine.) 

After  1840  many  styles  of  mechanical  stokers  were  patented  in  England, 
but  nearly  all  were  variations  and  modifications  of  the  two  forms  of 
stokers  patented  by  John  Jukes  in  1841  and  by  E.  Henderson  in  1843. 
i     The  Jukes  stoker  consisted  of  longitudinal  fire-bars,  connected  by 


IMPROVED  METHODS  OF  FEEDING  COAL.    919 

links,  so  as  to  form  an  endless  chain.  The  small  coal  was  delivered  from 
a  hopper  on  the  front  of  the  boiler,  on  to  the  grate,  which,  slowly  movirfg 
from  front  to  rear,  gradually  advanced  the  fuel  into  the  furnace  and 
discharged  the  ash  and  clinker  at  the  back. 

The  Henderson  stoker  consists  primarily  of  two  horizontal  fans  revolv- 
ing on  vertical  spindles,  which  scatter  the  coal  over  the  fire. 

The  first  American  stoker  was  the  Murphy  stoker,  brought  out  in 
1878.  It  consists  of  two  coal  magazines  placed  in  the  side  walls  of  the 
boiler  furnace,  and  extending  back  from  the  boiler  front  6  or  7  feet.  In 
the  bottom  of  these  magazines  are  rectangular  iron  boxes,  which  are 
moved  from  side  to  side  by  means  of  a  rack  and  pinion,  and  serve  to 
push  the  coal  upon  the  grates,  which  incline  at  an  angle  of  about  35° 
from  the  inner  edge  of  the  coal  magazines,  forming  a  V-shaped  recep- 
tacle for  the  burning  coal.  The  grates  are  composed  of  narrow  parallel 
bars,  so  arranged  that  each  alternate  bar  lifts  about  an  inch  at  the  lower 
end,  while  at  the  bottom  of  the  V,  and  filling  the  space  between  the  ends 
of  the  grate-bars,  is  placed  a  cast-iron  toothed  bar,  arranged  to  be 
turned  by  a  crank.  The  purpose  of  this  bar  is  to  grind  the  clinker  com- 
ing in  contact  with  it.  Over  this  V-shaped  receptacle  is  sprung  a  fire- 
brick arch. 

In  the  Roney  mechanical  stoker  the  fuel  to  be  burned  is  dumped  into  a 
hopper  on  the  boiler  front.  Set  in  the  lower  part  of  the  hopper  is  a 
"pujher,"  which,  by  a  vibratory  motion,  gradually  forces  the  fuel  over 
the  'dead-plate"  and  on  the  grate.  The  grate-bars  in  their  normal  con- 
dition form  a  series  of  steps.  Each  bar  is  capable  of  a  rocking  motion 
through  an  adjustable  angle.  All  the  grate-bars  are  coupled  together  by 
a  "rocker-bar."  A  variable  back-and-forth  motion  being  given  to  the 
"rocker-bar,"  through  a  connecting-rod,  the  grate-bars  rock  in  unison, 
now  forming  a  series  of  steps,  and  now  approximating  to  an  inclined 
plane,  with  the  grates  partly  overlapping,  like  shingles  on  a  roof.  When 
the  grate-bars  rock  forward  the  fire  will  tend  to  work  down  in  a  body. 
But  before  the  coal  can  move  too  far  the  bars  rock  back  to  the  stepped 
position,  checking  the  downward  motion.  The  rocking  motion  is  slow, 
being  from  7  to  10  strokes  per  minute,  according  to  the  kind  of  coal. 
This  alternate  starting  and  checking  motion  is  continuous,  and  finally 
lands  the  cinder  and  ash  on  the  dumping-grate  below. 

The  Hawley  Down-draught  Furnace. —  A  foot  or  more  above  the 
ordinary  grate  there  is  carried  a  second  grate,  composed  of  a  series  of 
water-tubes,  opening  at  both  ends  into  steel  drums  or  headers,  through 
which  water  is  circulated.  The  coal  is  fed  on  this  upper  grate,  and  as  it 
is  partially  consumed  falls  through  it  upon  the  lower  grate,  where  the 
combustion  is  completed  in  the  ordinary  manner.  The  draught  through 
the  coal  on  the  upper  grate  is  downward  through  the  coal  and  the  grate. 
The  volatile  gases  are  therefore  carried  down  through  the  bed  of  coal, 
where  they  are  thoroughly  heated,  and  are  burned  in  the  space  beneath, 
where  they  meet  the  excess  of  hot  air  drawn  through  the  fire  on  the  lower 
grate.  In  tests  in  Chicago,  from  30  to  45  Ib.  of  coal  were  burned  per 
square  foot  of  grate  upon  this  system,  with  good  economical  results. 
(See  catalogue  of  the  Hawley  Down-draught  Furnace  Co.,  Chicago.) 

The  Chain  Grate  Stoker,  made  by  Jukes  in  1841,  is  now  (1909)  widely 
used  in  the  United  States.  It  is  made  by  the  Babcock  &  Wilcox  Co., 
Green  Engineering  Co.,  and  others. 

Under-feed  Stokers. — Results  similar  to  those  that  may  be  obtained 
with  downward  draught  are  obtained  by  feeding  the  coal  at  the  bottom 
of  the  bed,  pushing  upward  the  coal  already  on  the  bed  which  has  had 
its  volatile  matter  distihed  from  it.  The  volatile  matter  of  the  freshly 
fired  coal  then  has  to  pass  through  a  body  of  ignited  coke,  where  it 
meets  a  supply  of  hot  air.  (See  circular  of  The  Underfeed  Stoker  Co., 
Chicago.) 

The  Taylor  Gravity  Stoker  is  a  combination  of  an  underfeed  stoker 
containing  two  horizontal  rows  of  pushers  with  an  inclined  or  step  grate 
through  which  air  is  blown  by  a  fan. 

The  Riley  Stoker  is  an  underfeed  stoker  with  a  single  horizontal  row 
of  pushers  in  combination  with  moving  grate-bars,  and  moving  pushers 
at  the  rear  of  the  furnace  for  continuously  dumping  the  refuse. 


920 


THE  STEAM-BOILEK 


SMOKE  PREVENTION. 


The  following  article  was  contributed  by  the  author  to  a  "  Report  on 
Smoke  Abatement,"  presented  by  a  committee  to  the  Syracuse  Cham- 
ber of  Commerce,  published  by  the  Chamber  in  1907. 

Smoke  may  be  made  in  two  ways:  (1)  By  direct  distillation  of  tarry 
condensible  vapors  from  coal  without  burning;  (2)  By  the  partial  burn- 
ing or  splitting  up  of  hydrocarbon  gases,  the  hydrogen  burning  and  the 
carbon  Deing  left  unburned  as  smoke  or  soot.  These  causes  usually  act 
conjointly. 

The  direct  cause  of  smoke  is  that  the  gases  distilled  from  the  coal  are 
not  completely  burned  in  the  furnace  before  coming  in  contact  with  the 
surface  of  the  boiler,  which  chills  them  below  the  temperature  of  ignition. 

The  amount  and  quality  of  smoke  discharged  from  a  chimney  may 
vary  all  the  vyay  from  a  dense  cloud  of  jet-black  smoke,  which  may  be 
'  carried  by  a  light  wind  for  a  distance  of  a  mile  or  more  before  it  is  finally 
dispersed  into  the  atmosphere,  to  a  thin  cloud,  which  becomes  invisible 
a  few  feet  from  the  chimney.  Often  the  sanje  chimney  will  for  a  few 
minutes  immediately  after  firing  give  off  a  dense  black  cloud  and  then  a 
few  minutes  later  the  smoke  will  have  entirely  disappeared. 

The  quantity  and  density  of  smoke  depend  upon  many  variable  causes. 
Anthracite  coal  produces  no  smoke  under  any  conditions  of  furnace.  Semi- 
bituminous,  containing  12.5  to  25%  of  volatile  matter  in  the  combustible 
part  of  the  coal,  will  give  off  more  or  less  smoke,  depending  on  the  con- 
ditions under  which  it  is  burned,  and  bituminous  coal,  containing  from 
25  to  50%  of  volatile  matter,  will  give  off  great  quantities  of  smoke  with 
all  of  the  usual  old-style  furnaces,  even  with  skillful  firing,  and  this  smoke 
can  only  be  prevented  by  the  use  of  special  devices,  together  with  proper 
methods  of  firing  the  fuel  and  of  admission  of  air. 

Practically  the  whole  theory  of  smoke  production  and  prevention  may 
be  illustrated  by  the  flame  of  an  ordinary  gas  burner  or  gas  stove. 
When  the  gas  is  turned  down  very  low  every  particle  of  gas,  as  it  emerges 
from  the  burner,  is  brought  in  contact  with  a  sufficient  supply  of  hot  air  to 
effect  its  complete  and  instantaneous  combustion,  with  a  pale  blue  or 
almost  invisible  flame.  Turn  on  the  gas  a  little  more  and  a  white  flame 
appears.  The  gas  is  imperfectly  burned  in  the  center  of  the  flame.  Par- 
ticles of  carbon  ha^e  been  separated  which  are  heated  to  a  white  heat. 
If  a  cold  plate  is  brought  in  contact  with  the  white  flame,  these  carbon 
particles  are  deposited  as  soot.  Turn  on  the  gas  still  higher,  and  it  burns 
with  a  dull,  smoky  flame,  although  it  is  surrounded  with  an  unlimited 
quantity  of  air.  Now,  carry  this  smoky  flame  into  a  hot  fire-brick  or 
porcelain  chamber,  where  it  is  brought  in  contact  with  very  hot  air,  and 
it  will  be  made  smokeless  by  the  complete  burning  of  the  particles. 

We  thus  see:  (1)  That  smoke  may  be  prevented  from  forming  if  each 
particle  of  gas,  as  it  is  made  by  distillation  from  coal,  is  immediately 
mixed  thoroughly  with  hot  air,  and  (2)  That  even  if  smoke  is  formed 
by  the  absence  of  conditions  for  preventing  it,  it  may  afterwards  be 
burned  if  it  is  thoroughly  mixed  with  air  at  a  sufficiently  high  temperature. 
It  is  easy  to  burn  smoke  when  it  is  made  in  small  quantities,  but  when 
made  in  great  volumes  it  is  difficult  to  get  the  hot  air  mixed  with  it  unless 
special  apparatus  is  used.  In  boiler  firing  the  formation  of  smoke  must 
be  prevented,  as  the  conditions  do  not  usually  permit  of  its  being  burned. 
The  essential  conditions  for  preventing  smoke  in  boiler  fires  may  be 
enumerated  as  follows: 

1.  The  gases  must  be  distilled  from  the  coai  at  a  uniform  rate. 

2.  The  gases,  when  distilled,  must  be  brought  into  intimate  mixture 
with  sufficient  hot  air  to  burn  them  completely. 

3.  The  mixing  should  be  done  in  a  fire-brick  chamber. 

4.  The  gases  should  not  be  allowed  to  touch  the  comparatively  cold 
surfaces  of  the  boiler  until  they  are  completely  burned.     This  means  that 
the  gases  shall  have  sufficient  space  and  time  in  which  to  burn  before  they 
are  allowed  to  come  in  contact  with  the  boiler  surface. 

Every  one  of  these  four  conditions  is  violated  in  the  ordinary  method 
of  burning  coal  under  a  steam  boiler.  (1)  The  coal  is  fired  intermittently 
and  often  in  large  quantities  at  a  time,  and  the  distillation  proceeds  at  so 
rapid  a  rate  that  enough  air  cannot  be  introduced  into  the.  furnace  to  burn 
the  gas.  (2)  The  piling  of  fresh  coal  on  the  grate  in  itself  chokes  the  air 


SMOKE   PREVENTION.  921 


supply.  (3)  The  roof  of  the  furnace  is  the  cold  shell,  or  tubes,  of  the 
boiler,  instead  of  a  fire-brick  arch,  as  it  should  be,  and  the  furnace  is  not  of 
a  sufficient  size  to  allow  the  gases  time  and  space  in  which  to  be  thoroughly 
mixed  with  the  air  supply. 

In  order  to  obtain  the 'conditions  for  preventing:  smoke  it  is  necessary: 
(I)  That  the  coal  be  delivered  into  the  furnace  in  small  quantities  at  a 
time.  (2)  That  the  draught  be  sufficient  'o  carry  enough  air  into  the 
furnace  to  burn  the  gases  as  fast  as  they  are  distilled.  (3)  That  the  air 
itself  be  thoroughly  heated  either  by  passing  through  a  bed  of  white-hot 
coke  or  by  passing' through  channels  in  hot  brickwork,  or  by  contact  with 
hot  fire-brick  surfaces.  (4)  That  the  gas  and  the  air  be  brought  into 
the  most  complete  and  intimate  mixture,  so  that  each  paiticle  of  carbon 
it  the  gas  meets,  before  it  escapes  from  the  furnace,  its  necessary  supply 
ol  air.  (5)  That  the  flame  produced  by  the  burning  shall  be  completely 
extinguished  by  the  burning  of  every  particle  of  the  carbon  into  invisible 
carbon  dioxide. 

If  a  white  flame  touches  the  surface  of  a  boiler,'  it  is  apt  to  deposit 
soot  and  to  produce  smoke.  A  white  flame  itself  is  the  visible  evidence 
of  incomplete  combustion. 

The  first  remedy  for  smoke  is  to  9btain  anthracite  coal.  If  this  is  not 
commercially  practicable,  then  obtain,  if  possible,  coal  with  the  smallest 
amount  of  volatile  matter.  Coal  of  from  15  to  25%  of  volatile  matter 
makes  much  less  smoke  than  coals  containing  higher  percentages.  Pro- 
vide a  proper  furnace  for  burning  coal.  Any  furnace  is  a  proper  furnace 
which  secures  the  conditions  named  in  the  preceding  paragraphs.  Next, 
compel  the  firemen  to  follow  instructions  concerning  the  method  of 
firing. 

It  is  impossible  with  coal  containing  over  30%  of  volatile  matter  and 
with  a  water-tube  boiler,  with  tubes  set  close  to  the  grate  and  vertical 
gas  passages,  as  in  an  anthracite  setting,  to  prevent  smoke  even  by  the 
.  most  skillful  firing.  This  style  of  setting  for  a  water-tube  boiler  should 
be  absolutely  condemned.  A  Dutch  oven  setting,  or  a  longitudinal 
setting  with  fire-brick  baffle  walls,  is  highly  recommended'  as  a  smoke- 
preventing  furnace,  but  with  such  a  furnace  it  is  necessary  to  use  con- 
siderable skill  in  firing. 

Mechanical  mixing  of  the  gases  and  the  air  by  steam  jets  is  sometimes 
successful  in  preventing  smoke,  but  it  is  not  a  universal  preventive, 
especially  when  the  coal  is  very  high  in  volatile  matter,  when  the  firing 
is  done  unskillfully,  or  when  the  boiler  is  being  driven  beyond  its  normal 
capacity.  It  is  essential  to  have  sufficient  draught  to  burn  the  coal  prop- 
erly and  this  draught  may  be  obtained  either  from  a  chimney  or  a  fan. 
There  is  no  especial  merit  in  forced  draught. except  that  it  enables  a  larger 
quantity  of  coal  to  be  burned  and  the  boiler  to  be  driven  harder  in  case 
of  emergency,  and  usually  the  harder  the  boiler  is  driven,  the  more 
difficult  it  is  to  suppress  smoke. 

Down-draught  furnaces  and  mechanical  stokers  of  many  different  kinds 
are  successfully  used  for  smoke  prevention,  and  when  properly  designed 
and  installed  and  handled  skillfully,  and  usually  at  a  rate  not  beyond 
that  for  which  they  are  designed,  prevent  all  smoke.  If  these  appliances 
are  found  giving  smoke,  it  is  always  due  either  to  overdriving  or  to  un- 
skillful handling.  It  is  necessary,  however,  that  the  design  of  these 
stokers  be  suited  to  the  quality  of  the  coal  and  the  quantity  to  be  burned, 
and  great  care  should  be  taken  to  provide  a  sufficient  size  of  furnace  with 
a  fire-brick  roof  and  means  of  introducing  air  to  make  them  completely 
'successful. 

Burning  Illinois  Coal  without  Smoke.  (L.  P.  Breckenridge, 
'  Bulletin  No.  15  of  the  Univ.  of  111.  Eng'g  Experiment  Station,  1907.) 
—  Any  fuel  may  be  burned  economically  and  without  smoke  if  it  is 
mixed  with  the  proper  amount  of  air  at  a  proper  temperature.  The 
boiler  plant  of  the  University  of  Illinois  consists  of  nine  units  aggregating 
2000  H.P.  Over  200  separate  tests  have  been  made.  The  following  is  a 
condensed  statement  of  the  results  in  regard  to  smoke  prevention. 

Boilers  Nos.  1  and  2.  Babcock  &  Wilcox.  Chain-grate  stoker.  Usual 
vertical  baffling.  Can  be  run  without  smoke  at  from  50  to  120  %  of  rated 
capacity. 

No.  3.    Stirling  boiler.    Chain-grate  stoker.    Usual  baffling  and  com- 


922  THE   STEAM-BOILER. 

bustion  arches.     Can  be  run  without  smoke  at  capacities  of  50  to 

140%. 

No.  4.  National  water-tube.  Chain-grate  stoker.  Vertical  baffling 
No  smoke  at  capacities  of  50  to  120%.  With  the  Murphy  furnace  it  was 
smokeless  except  when  cleaning  fires. 

No.  5.  Babcock  &  Wilcox.  Roney  stoker.  Vertical  baffling  Nearly 
smokeless  (maximum  No.  2  on  a  chart  in  which  5  represents  black  smoke) 
up  to  100%  of  rating,  but  cannot  be  run  above  100%  without  objection- 
able smoke. 

No.  6.  Babcock  &  Wilcox.  Roney  stoker.  Horizontal  tile-roof  baf- 
fling. Can  be  run  without  smoke  at  capacities  of  50  to  100%  of  rating. 

N9S.  7  and  8.  Stirling,  equipped  with  Stirling  bar-grate  stoker.  Usual 
baffling  and  combustion  arches.  Can  be  run  without  smoke  at  50  to 
140%  of  rating. 

No.  9.  Heine  boiler.  Chain-grate  stoker.  Combustion  arch  and  tile- 
roof  furnace.  Can  be  run  without  smoke  at  capacities  of  50  to  140%. 
It  is  almost  impossible  to  make  smoke  with  this  setting  under  any  con- 
dition of  operation.  As  much  as  46  Ibs.  of  coal  per  sq.  ft.  of  grate  surface 
has  been  burned  without  smoke. 

Conditions  of  Smoke  Prevention.  —  Bulletin  No.  373  of  the  U.  S. 
Geological  Survey,  1909  (188  pages),  contains  a  report  of  an  extensive 
research  by  D.  T.  Randall  and  J.  T.  Weeks  on  The  Smokeless  Combustion 
of  Coal  in  Boiler  Plants.  A  brief  summary  of  the  conclusions  reached  is 
as  follows: 

Smoke  prevention  is  both  possible  and  economical.  There  are  many 
types  of  furnaces  and  stokers  that  are  operated  smokelessly. 

Stokers  or  furnaces  must  be  set  so  that  combustion  will  be  complete 
before  the  gases  strike  the  heating  surfaces  of  the  boiler.  When  partly 
burned  gases  at  a  temperature  of  say  2500°  F.  strike  the  tubes  of  a 
boiler  at  say  350°  F.,  combustion  may  be  entirely  arrested. 

The  most  economical  hand-fired  plants  are  those  that  approach  most 
nearly  to  the  continuous  feed  of  the  mechanical  stoker.     The  fireman  is  ' 
so  variable  a  factor  that  the  ultimate  solution  of  the  problem  depends  on 
the  mechanical  stoker  —  in  other  words,  the  personal  element  must  be 
eliminated. 

A  well  designed  and  operated  furnace  will  burn  many  coals  without 
smoke  up  to  a  certain  number  of  pounds  per  hour,  the  rate  varying  with 
different  coals.'  If  more  than  this  amount  is  burned,  the  efficiency  will 
decrease  and  smoke  will  be  made,  owing  to  the  lack  of  furnace  capacity 
to  supply  air  and  mix  gases. 

High  volatile  matter  in  the  coal  gives  low  efficiency,  and  vice  versa. 
When  the  furnace  was  forced  the  efficiency  decreased. 

With  a  hand-fired  furnace  the  best  results  were  obtained  when  firing 
was  done  most  frequently,  with  the  smallest  charge. 

Small  sizes  of  coal  burned  with  less  smoke  than  large  sizes,  but  developed 
lower  capacities. 

Peat,  lignite,  and  sub-bituminous  coal  burned  readily  in  the  tile-roofed 
furnace  and  developed  the  rated  capacity,  with  practically  no  smoke. 

Coals  which  smoked  badly  gave  efficiencies  three  to  five  per  cent  lower 
than  the  coals  burning  with  little  smoke. 

Briquets  were  found  to  be  an  excellent  form  for  using  slack  coal  in  a 
hand-fired  plant. 

In  the  average  hand-fired  furnace  washed  coal  burns  with  lower  effi- 
ciency and  makes  more  smoke  than  raw  coal.  Moreover,  washed  coal 
offers  a  means  of  running  at  high  capacity,  with  good  efficiency,  in  a 
well-designed  furnace. 

Forced  draught  did  not  burn  coal  any  more  efficiently  than  natural 
draught.  It  supplied  enough  air  for  high  rates  of  combustion,  but  as  the 
capacity  of  the  boiler  increased,  the  efficiency  decreased  and  the  per- 
centage of  black  smoke  increased. 

Fire-brick  furnaces  of  sufficient  length  and  a  continuous,  or  nearly 
continuous,  supply  of  coal  and  air  to  the  fire  make  it  possible  to  burn 
most  coals  efficiently  and  without  smoke. 

Coals  containing  a  large  percentage  of  tar  and  heavy  hydrocarbons 
are  difficult  to  burn  without  smoke  and  require  special  furnaces  ancj 
than  ordinary  care  in  firing. 


. 


FORCED   COMBUSTION  IN  STEAM-BOILERS.        923 
FORCED  COMBUSTION  IN  STEAM-BOILERS. 


For  the  purpose  of  increasing  the  amount  of  steam  that  can  be  gener- 
ated by  a  boiler  of  a  given  size,  forced  draught  is  of  great  importance. 
It  is  universally  used  in  the  locomotive,  the  draught  being  obtained  by  a 
steam-jet  in  the  smoke-stack.  It  is  now  largely  used  in  ocean  steamers, 
especially  in  ships  of  war,  and  to  a  small  extent  in  stationary  boilers. 
Economy  of  fuel  is  generally  not  attained  by  its  use,  its  advantages  be- 
ing confined  to  the  securing  of  increased  capacity  from  a  boiler  of  a 
given  bulk,  weight,  or  cost. 

There  are  three  different  modes  of  using  the  fan  for  promoting  com- 
bustion: 1,  blowing  direct  into  a  closed  ash-pit;  2,  exhausting  the  gases 
by  the  suction  of  the  fan ;  3,  forcing  air  into  an  air-tight  boiler-room 
or  stoke-hold.  Each  of  these  three  methods  has  its  advantages  and  dis- 
advantages. 

In  the  use  of  the  closed  ash-pit  the  blast-pressure  frequently  forces 
the  gases  of  combustion  from  the  joint  around  the  furnace  doors  in  so 
great  a  quantity  as  to  affect  both  the  efficiency  of  the  boiler  and  the 
health  of  the  firemen. 

The  chief  defect  of  the  second  plan  is  the  great  size  of  the  fan  required 
to  produce  the  necessary  exhaustion,  on  account  of  the  higher  exit  tem- 
perature enlarging  the  volume  of  the  waste  gases. 

The  third  method  that  of  forcing  cold  air  by  the  fan  into  an  air-tight 
boiler-room — the  closed  stoke-hold  system — though  it  overcame  the 
difficulties  in  working  ^belonging  to  the  two  forms  first  tried,  has  serious 
defects  of  its  own,  as  it  cannot  be  worked,  even  with  modern  high-class 
boiler-construction,  much,  if  at  all,  above  the  power  of  a  good  chimney 
draught,  in  most  boilers,  without  damaging  them.  (J.  Howden,  Proc. 
Eng'g  Congress  at  Chicago,  in  1893.) 

In  1880  Mr.  Howden  designed  an  arrangement  intended  to  overcome 
the  defects  of  both  the  closed  ash-pit  and  the  closed  stoke-hold  systems. 

An  air-tight  chamber  is  placed  on  the  front  end  of  the  boiler  and  sur- 
rounding the  furnaces.  This  reservoir,  which  projects  from  8  to  10 
inches  from  the  end  9f  the  boiler,  receives  the  air  under  pressure,  which 
is  passed  by  valves  into  the  ash-pits  and  over  the  fires  in  proportions 
suited  to  the  kind  of  fuel  and  the  rate  of  combustion.  The  air  used  above 
the  fires  is  admitted  to  a  space  between  the  outer  and  inner  furnace- 
doors,  the  inner  having  perforations  and  an  air-distributing  box  through 
which  the  air  passes  under  pressure.  By  means  of  the  balance  of  pres- 
sure above  and  below  the  fires  all  tendency  of  the  fire  to  blow  out  at 
the  door  is  removed. 

A  feature  of  the  system  is  the  combination  of  the  heating  of  the  air  of 
combustion  by  the  waste  gases  with  the  controlled  and  regulated  admis- 
sion of  air  to  the  furnaces.  This  arrangement  is  effected  most  conve- 
niently by  passing  the  hot  fire-gases  after  they  leave  the  boiler  through 
stacks  of  vertical  tubes  enclosed  in  the  uptake,  their  lower  ends  being 
immediately  above  the  smoke-box  doors.  Installations  on  Howden's 
system  have  been  arranged  for  a  rate  of  combustion  to  give  an  average 
of  from  18  to  22  I.H.P.  per  square  foot  of  fire-grate  with  fire-bars  from 
5  to  5  yz  ft.  in  length.  It  is  believed  that  with  suitable  arrangement  of 
proportions  even  30  I.H.P.  per  square  foot  can  be  obtained. 

For  an  account  of  uses  of  exhaust-fans  for  increasing  draught,  see 
paper  by  W.  R.  Roney,  Trans.  A.  S.  M.  E.,  vol.  xv. 

Calculations  for  Forced  Draft. — In  designing  a  forced  draft  installa- 
tion the  principal  data  needed  are:  1,  The  maximum  number  of  pounds 
of  coal  that  will  have  to  be  burned  per  hour  at  the  most  rapid  rate  of 
driving,  when  the  efficiency  of  the  boiler,  furnace  and  grate  is  lowest; 
2,  the  number  of  pounds  of  air  used  per  pound  of  coal.  If  C,  H  and  O 
are  respectively  the  carbon,  hydrogen  and  oxygen  in  1  Ib.  of  coal,  then 
the  number  of  pounds  of  air  required,  theoretically,  for  complete  com- 
bustion is  34.56(C/3  -f  H  +  O/8).  With  mechanical  stokers  and  CO2 
apparatus  for  control  of  the  air  supply  50%  excess  air  supply  is  ample, 
but  with  ordinary  hand-firing  the  actual  air  supply  may  be  100%  or 
more  in  excess,  In  the  author's  "  Steam  Boiler  Economy,"  2d  ed.  1915, 
p.  242,  there  is  given  a  calculation  of  the  number  of  cubic  feet  of  air 
per  minute  required  per  boiler  horsepower  developed,  giving  results  as 
follows: 


924 


THE  STEAM-BOtLEU. 


Cvstc  FEET  OF  Am  PEH  MINUTE  AT  706  F.  PEE  BOILER  HORSEPOWER. 

Semi-     East.      West. 
Fuel  Anth.       bit.        Bitu.      Bitu.    Lignite     Oil 

Air*    50%  excess .11,52     11.30     10.99     11.86     13.63     11.13 

Air  100%  excess 15.36     15.07     14.65     15.82     16.17     14.84 

Note  that  these  figures  are  based  not  upon  the  rated  horse-power  of 
the  boiler,  but  upon  that  actually  developed,  which  may  be  far  m  excess 
of  the  rated  power.  For  induced  draft  the  figures  given  should  be 
multiplied  by  (T+  460)  -i-  530,  in  which  T  is  the  temperature  of  the 
gases  to  be  handled  by  the  induced  draft  fan. 

FUEL  ECONOMIZERS. 

Economizers  for  boiler  plants  are  usually  made  of  vertical  cast-iron 
tubes  contained  in  a  long  rectangular  chamber  of  brickwork.  The  feed- 
water  enters  the  bank  of  tubes  at  one  end,  while  the  hot  gases  enter  the 
chamber  at  the  other  end  and  travel  in  the  opposite  direction  to  the 
water.  The  tubes  are  made  of  cast  iron  because  it  is  more  non-corrosive 
than  wrought  iron  or  steel  when  exposed  to  gases  of  combustion  at  low 
temperatures.  An  automatic  scraping  device  is  usually  provided  for 
the  purpose  of  removing  dust  from  the  outer  surface  of  the  tubes. 

The  amount  of  saying  of  fuel  that  may  be  made  by  an  economizer 
varies  greatly  according  to  the  conditions  of  operation.  With  a  given 
quantity  of  chimney  gases  to  be  passed  through  it,  its  economy  will  be 
greater '(1)  the  higher  the  temperature  of  these  gases;  (2)  the  lower  the 
temperature  of  the  water  fed  into  it ;  and  (3)  the  greater  the  amount  of  its 
heating  surface.  From  (1)  it  is  seen  that  an  economizer  will  save  more 
fuel  if  added  to  a  boiler  that  is  overdriven  than  if  added  to  one  driven  at 
a  nominal  rate.  From  (2)  it  appears  that  less  saving  can  be  expected 
from  an  economizer  in  a  power  plant  in  which  the  feed-water  is  heated  by 
exhaust  steam  from  auxiliary  engines  than  when  the  feed-water  entering 
it  is  taken  directly  from  the  condenser  hot-well.  The  amount  of  heat- 
ing surface  that  should  be  used  in  any  given  case  depends  not  only  on 
the  saving  of  fuel  that  may  be  made,  but  also  on  the  cost  of  coal,  and  on 
the  annual  C9sts  of  maintenance,  including  interest,  depreciation,  etc. 

The  following  table  shows  the  theoretical  results  possibly  attainable 
from  economizers  under  the  conditions  specified.  It  is  assumed  that  the 
coal  has  a  heating  value  of  15,000  B.T.U.  per  Ib.  of  combustible;  that  it 
is  completely  burned  in  the  furnace  at  a  temperature  of  2500°  F. ;  that 
the  boiler  gives  efficiencies  ranging  from  60  to  75  %  according  to  the  rate 
of  driving;  and  that  sufficient  economizer  surface  is  provided  to  reduce 
the  temperature  of  the  gases  in  all  cases  to  300°  F.  Assuming  the  specific 
heat  of  the  gases  to  be  constant,  and  neglecting  the  loss  of  heat  by  radi- 
ation, the  temperature  of  the  gases  leaving  the  boiler  and  entering  the 
economizer  is  directly  proportional  to  (100-  %  of  boiler  efficiency), 
and  the  combined  efficiency  of  boiler  and  economizer  is  (2500  —  300) 
-T-  2500  =  88%,  which  corresponds  to  an  evaporation  of  (15.000  -f-  970) 
X  0.88  =  13.608  Ib.  from  and  at  212°  per  Ib.  of  combustible;  or  as- 
suming the  feed-water  enters  the  economizer  at  100°  F.  and  the  boiler 
makes  steam  of  150  Ib.  absolute  pressure,  to  an  evaporation  of  11.729 
Ib.  under  these  conditions.  Dividing  this  figure  into  the  number  of 
heat  units  utilized  by  the  economizer  per  Ib.  of  combustible  gives  the 
heat-units  added  to  the  water,  from  which,  by  reference  to  a  steam 
table,  the  temperature  may  be  found.  With  these  data  we  obtain  the 
results  given  in  the  table  below. 


Boiler  Efficiency,  per  cent. 

60 

65 

70 

75 

B.T.U.  absorbed  by  boiler  per  Ib.  combustible  
g  'p  u  jjj  chimney  gases  leaving  boiler           

9000 
6000 
1000° 
300° 
4200 
28 
9.278 
4.330 
448° 
70 

9750 
5250 
875° 
300° 
3450 
23 
10.051 
3.557 
389° 
65.7 

10500 
4500 
750° 
300° 
2700 
18 
10.824 
2.884 
327° 
60 

11250 
3750 
625° 
300° 
1950 
13 
1  1  .598 
2.010 
265° 
52 

Estimated  temp,  of  gases  leaving  boiler  

Estimated  temp   of  gases  leaving  economizer          .  . 

J3  T  u  saved  by  economizer                 

Efficiency  gained  by  economizer  per  cent 

Equivalent  water  evap.  per  Ib.  comb,  in  boiler  
B.T.U.  saved  by  econ.  equivalent  to  evap.  of  Ib  
Temp  of  water  leaving  economizer                     .    ... 

Efficiency  of  the  economizer,  per  cent  

ECONOMIZEES. 


925 


Equation  of  the  Economizer.— Let  W '=*  Ib.  of  water  evaporated 
by  the  boiler,  under  actual  conditions  of  feed-water  temperature  and 
steam  pressure,  per  Ib.  of  combustible;  G  «=  Ib.  of  flue-gas  per  Ib. 
combustible;  Ti  and  T2  =  temperatures  of  gas  entering  and  leaving 
the  economizer;  ti  and  fa  =  temperatures  of  water  entering  and  leaving 
the  economizer;  then  assuming  no  loss  by  radiation  and  leakage,  and 
taking  the  specific  heat  of  the  gas  at  0.24  and  that  of  the  water  at  1, 

±           j.           U.<s4Cr    .—,  _,  .  ZTVT'  T1  \ 

fa—  ll  —  |Tf-  (jfl  —   22)  =  f  (2  1  —   12), 

in  which  F  has  the  values  in  the  following  table  for  given  values  of 
W  and  G. 


10 


I 


F  =0.24  G/W. 


G  =  18 

0.54 

0.48 

0.43 

0.39 

0.36 

21 

0.63 

0.56 

0.50 

0.46 

0.42 

24 

0.72 

0.64 

0.58 

0.52 

0.48 

27 

0.81 

0.72 

0.65 

0.59 

0.54 

30 

0.90 

0.80 

0.72 

0.65 

0.60 

Ti  is  usually  fixed  by  the  operating  conditions  of  the  boiler,  and  ti 
by  the  condenser  and  feed-water  heater  conditions. 

Taking  Ti  at  800°,  700°  and  600°,  corresponding  values  of  F  at  0.49, 
0.39  and  0.36,  and  ti  =  100°, 


100 


300,  then  fa  =  0.43(500)  -f-  100  =315° 
250,  0.39(450)  +  100  =266° 

220,  0.36(380)  +  100  =237° 


the 


••  0.43(800-  T2);let 
0.39(700-  T2); 
0.36(600-  T2); 

The  mean  temperature  difference  between  the  flue  gas  and 
water, 

t   =  TI  +  r2    fa+  h      Ti-fa  +  T2-u 

22  2 

For  the  three  cases  given  tm  =  343°,  292°,  242°. 

If  w  =  Ib.  of  water  heated  by  the  economizer  per  hour  from  t\  to  fa, 
S  =  sq.  ft.  of  economizer  surface,  and  C  =  heat-units  transmitted  per 
square  foot  of  surface  per  hour  per  degree  of  mean  temperature  dif- 
ference, then  w(fa  —  ti)  =  SCtm.  The  value  of  C  is  given  by  manu- 
facturers as  ranging  between  2  and  4  for  different  conditions  of  practice. 
It  probably  increases  in  some  proportion  to  the  increase  of  tm,  but  no 
records  of  experiments  have  been  published  from  which  the  law  of  this 
increase  may  be  determined. 

Amount  of  Heating  Surface. — The  Fuel  Economizer  Co.  says:  We 
have  found  in  practice  that  by  allowing  4  sq .  ft.  of  heating  surface  per 
boiler  H.P.  (34  Yi  Ib.  evap.  from  and  at  212°  =  1  H.P.)  we  are  able  to 
raise  the  feed-water  60°  F.  for  every  100°  reduction  in  the  temperature, 
the  gases  entering  the  economizer  at  450°  to  600°.  With  gases  at  600° 
to  700°  we  have  allowed  a  heating  surface  of  4 }/%  to  5  sq.  ft.  per  H.P., 
and  for  every  100°  reduction  in  temperature  .of  the  gases  we  have 
obtained  about  65°  rise  in  temperature  of  the  water;  the  feed-water 
entering  at  60  to  120°.  With  5000  sq .  ft.  of  boiler-heating  surface  (plain 
cylinder  boilers)  developing  1000  H.P.  we  should  recommend  5  sq.  ft.  of 
economizer  surface  per  boiler  H.  P.  developed,  or  an  economizer  of  about 
500  tubes,  and  it  should  heat  the  feed-water  about  300°. 

Heat  Transmission  in  Economizers.  (Carl  S.  Dow,  Indust.  Eng'g, 
April,  1909.) — The  rate  of  heat  transmission  (C)  per  sq.  ft.  per  hour  per 
degree  of  difference  between  the  average  temperatures  of  the  gases  and 
the  water  passing  through  the  economizer  varies  with  the  mean  tem- 
perature of  the  gas  about  as  follows:  Gas,  600°,  C=  3.25;  gas  500°, 
C  =  3;  gas  400°,  C  =  2.75;  gas  300°,  C  =  2.25. 

Calculation  of  the  Saving  made  by  an  Economizer. — The  usual 
method  of  calculating  the  saving  of  fuel  by  an  economizer  when  the 
boiler  and  the  economizer  are  tested  together  as  a  unit  is  by  the  formula 
(Hi  -  h)  -v-  (Hz  -  /i),  in  which  h  is  the  total  heat  above  32°  of  1  Ib.  of 


926 


THE  STEAM-BOILER. 


water  entering,  Hi  the  total  heat  of  1  Ib.  of  water  leaving  the  economizer, 
and  7/2  the  total  heat  above  32°  of  1  Ib.  of  steam  at  the  boiler  pressure. 
If  h  =  100,  Hi  =  210,  Hz  =  1200,  then  the  saving  according  to  the  for- 
mula is  (210  -  100)  ~  1100  =  10%.  This  is  correct  if  the  saving  is 
defined  as  the  ratio  of  the  heat  absorbed  by  the  economizer  to  the  total 
heat  absorbed  by  the  boiler  and  economizer  together,  but  it  is  not 
correct  if  the  saving  is  defined  as  the  saving  of  fuel  made  by  running  the 
combined  unit  as  compared  with  running  the  boiler  alone  making  the 
same  quantity  of  steam  from  feed-water  at  the  low  temperature,  so  as  to 
cause  the  boiler  to  furnish  Hz—  h  heat-units  per  Ib.  instead  of  Hz  —  Hi. 
In  this  case  the  boiler  is  called  on  to  do  more  work,  and  in  doing  it  it  may 
be  overdriven  and  work  with  lower  efficiency. 

In  a  test  made  by  F.  G.  Gasche,  in  Kansas  City  in  1897,  using  Mis- 
souri coal  analyzing  moisture  7.58;  volatile  matter,  36.69;  fixed  carbon, 
35.02;  ash,  15.69;  sulphur,  5.12,  he  obtained  an  evaporation  of  5.17  Ib. 
from  and  at  212°  per  Ib.  of  coal  with  the  boiler  alone,  and  when  the 
boiler  and  economizer  were  tested  together  the  equivalent  evaporation 
credited  to  the  boiler  was  5.55,  to  the  economizer  0.72,  and  to  the  com- 
bined unit  6.27,  the  saving  by  the  combined  unit  as  compared  with  the 
boiler  alone  being  (6.27  -  5.17)  -4-  6.27  =  17.5%,  while  the  saving  of 
heat  shown  by  the  economizer  in  the  combined  test  is  only  (6.27  — 
5.55)  -f-  6.27  =  11.5%,  or  as  calculated  by  Mr.  Gasche  from  the  formula 
(Hi  -  h)  -=-  (Hz  -  h),  (172.1  -  39.3)  ^  (1181.8  -i-  39.3)  =  11.6%. 

The  maximum  saving  of  fuel  which  may  be  made  by  the  use  of  an 
economizer  when  attached  to  boilers  that  are  working  with  reasonable 
economy  is  about  15  % .  Take  the  case  of  a  condensing  engine  iising 
steam  of  125  Ib.  gage  pressure,  and  with  a  hot-well  or  feed-water 
temperature  of  100°  P.  The  economizer  may  be  expected  under  the 
best  conditions  to  raise  this  temperature  about  170°  or  to  270°.  Then 
h=  68,  Hi  =  239,  H2=1190.  (Hi-  h).+l(Hz  -  ft)  =  171  -r- 1122  =  15.24%. 

If  the  boilers  are  not  working  with  fair  economy  on  account  of  being 
overdriven,  then  the  saving  made  by  the  addition  of  an  economizer  may 
be  much  greater. 

Test  of  a  Large  Economizer.  (R.  D.  Tomlinson,  Power,  Feb.,  1904.) 
— Two  tests  were  made  of  one  of  the  sixteen  Green  economizers  at  the 
74th  St.  Station  of  the  Rapid  Transit  Railway,  New  York  City.  Four 
520-H.P.  B.  &  W.  boilers  were  connected  to  the  economizer.  It  had  512 
tubes,  10  ft.  long,  49/16  in.  external  diam.;  total  heating  surface  6760  sq. 
ft.,  or  3.25  sq.  ft.  per  rated  H.P.  of  the  boilers.  Draught  area  through 
economizer,  3  sq.  in.  per  H.  P.  The  stack  for  each  16  boilers  and  four 
economizers  was  280  ft.  high,  17  ft.  internal  diam.  The  first  test  was 
made  with  the  boilers  driven  at  94%  of  rating,  the  second  at  113%. 
The  results  are  given  below,  the  figures  of  the  second  test  being  in 
parentheses. 

Water  entering  economizer  96°  (93.5°) ;  leaving  200°  (203.8°) ;  rise 
104  (110.3). 

Gases  entering  economizer  548°  (603°) ;  leaving  295  (325) ;  drop  253 
(278). 

Steam,  gage  pressure,  166  (165).  Total  B.  T.U.  per  Ib.  from  feed 
temp.  1132  (1134). 

Saving  of  heat  by  economizer,  per  cent,  9.17  (9.73). 

Reduction  of  draught  in  passing  through  economizer,  in.  of  water, 
0.16  (0.23). 

Results  from  Seven  Tests  of  Sturtevant  Economizers  (Catalogue  of 
B.  F.  Sturtevant  Co.) 


Plants 
Tested. 

Gases 
Entering. 
Deg.  F. 

Gases 
Leaving. 
Deg.  F. 

Water 
Entering. 
Deg.  F. 

Water 
Leaving. 
Deg.  F. 

Increase  in 
Tempera- 
ture. 

1 
2 
3 
4 
5 
6 
7 

650 
575 

470 
500 
460 
440 
525 

275 
290 
230 
240 
200 
220 
225 

180 
160 
130 
110 
90 
120 
180 

340 
320 
260 
230 
230 
236 
320 

160 
160 
130 
120 
140 
116 
140 

INCRUSTATION  AND   CORROSION.  927 

Explosions  of  Economizers. — Explosions  of  economizers  are  rare, 
but  their  possibility  should  be  recognized  and  guarded  against.  They 
may  occur  from  over-pressure,  due  to  closing  of  the  outlet  valve  or 
other  causes,  which  may  be  prevented  by  means  of  a  safety  valve. 
When  the  gas  inlet  damper  is  closed  there  is  a  possibility  that  it  may 
leak  combustible  gas  into  the  economizer  flue,  making  an  explosive 
mixture  which  might  be  ignited  by  a  lighted  torch.  The  headers  or 
tubes  may  be  weakened  by  internal  or  external  corrosion,  and  a  rup- 
ture might  occur  at  the  normal  working  pressure.  This  should  be 
guarded  against  by  annual  inspection  and  hydraulic  test  at  50  per 
cent  in  excess  of  the  working  pressure. 

THERMAL    STORAGE. 

In  Druitt  Halpin's  steam  storage  system  (Industries  and  Iron,  Mar.  22. 
1895)  he  employs  only  sufficient  boilers  to  supply  the  mean  demand,  and 
storage  tanks  sufficient  to  supply  the  maximum  demand.  These  latter 
not  being  subjected  to  the  fire  suffer  but  little  deterioration.  The  boilers 
working  continuously  at  their  most  economical  rate  have  their  excess  of 
energy  during  light  load  stored  up  in  the  water  of  the  tank,  from  wliich 
it  may  be  drawn  at  will  during  heavy  load.  He  proposes  that  the  boilers 
and  tanks  shall  work  under  a  pressure  of  265  Ibs.  per  square  inch  when 
fully  charged,  which  corresponds  to  a  temperature  of  406°  F.,  and  that 
the  engines  be  worked  at  130  Ibs.  per  square  inch,  which  corresponds  to 
347°  F.  The  total  available  heat  stored  when  the  reservoirs  are  charged 
is  that  due  to  a  range  of  59°.  The  falling  in  temperature  of  141/4  Ibs.  of 
water  from  407°- to  347°  will  yield  1  Ib.  of  steam.  To  allow  for  radia- 
tion of  loss  and  imperfect  working,  this  may  be  taken  at  16 Ibs.  of  water, 
per  pound  of  steam.  The  steam  consumption  per  effective  H.P.  maybe 
taken  at  18  Ibs.  per  hour  in  condensing  and  25  Ibs.  per  hour  in  non-con- 
densing engines.  The  storage-room  per  effective  H.P.  by  this  method 
would,  therefore,  be  (16  X  18) -^  62.5=  4.06  cu.  ft.  for  condensing  and 
(16  X  25)  -5-  62.5  =  6.4  cu.  ft.  for  non-condensing  engines. 

Gas  storage,  assuming  that  illuminating  gas  is  used,  would  require 
about  20  cu.  ft.  of  storage  room  per  effective  H.P.  hour  stored,  and  if 
ordinary  fuel  gas  were  stored  it  would  require  about  four  times  this 
capacity.  In  water  storage  317  cu.  ft.  would  be  required  at  an  elevation 
of  100  ft.  to  store  one  H.P.  hour,  so  that  of  the  three  methods  of  storing 
energy  the  thermal  method  is  by  far  the  most  economical  of  space. 

In  the  steam  storage  method  the  boiler  is  completely  filled  with  water 
and  the  storage  tank  nearly  so.  The  two  are  in  free  communication  by 
means  of  pipes,  and  a  constant  circulation  of  water  is  maintained  between 
the  two,  but  the  steam  for  the  engines  is  taken  only  from  the  top  of  the 
storage  tank  through  a  reducing  valve. 

In  the  feed  storage  system,  the  excess  of  energy  during  light  load  Is 
stored  in  the  tank  as  before,  but  the  boilers  are  not  completely  filled.  In 
this  system  the  strain  is  taken  exclusively  from  the  boilers,  the  super- 
heated water  of  the  storage  tanks  being  used  during  heavy  load  as  feed- 
water  to  the  boilers. 

A  third  method  is  a  combination  of  these  two.  In  the  "combined" 
feed  and  steam  storage  system  the  pressure  in  boiler  and  storage  tank  is 
equalized  by  connecting  the  steam  spaces  in  both  by  pipe,  and  the  steam 
for  the  engines  is,  therefore,  taken  from  both.  In  other  words  they  work 
in  parallel. 

INCRUSTATION  AND    CORROSION. 

Incrustation  or  Scale.  —  Incrustation  (as  distinguished  from  mere 
sediments  due  to  dirty  water,  which  are  easily  blown  out,  or  gathered 
up,  by  means  of  sediment-collectors)  is  due  to  the  presence  of  salts  in  the 
feed-water  (carbonates  and  sulphates  of  lime  and  magnesia  for  the  most 
part),  which  are  precipitated  when  the  water  is  heated,  and  form  hard 
deposits  upon  the  boiler-plates.  (See  Impurities  in  Water,  p.  720,  ante.) 

Where  the  quantity  of  these  salts  is  not  very  large  (12  grains  per 
gallon,  say)  scale  preventives  may  be  found  effective.  The  chemical 
preventives  either  form  with  the  salts  other  salts  soluble  in  hot  water; 
or  precipitate  them  in  the  form  of  soft  mud,  which  does  not  adhere  to 
the  plates,  and  can  be  washed  out  from  time  to  time.  The  selection  of 
the  chemical  must  depend  upon  the  composition  of  the  water,  an4  it 
should,  be  introduced  regularly  with  the  feed, 


928  THE   STEAM-BOILER. 

EXAMPLES. — Sulphate-of-lime  scale  prevented  by  carbonate  of  soda: 
The  sulphate  of  soda  produced  is  soluble  in  water;  and  the  carbonate  of 
lime  falls  down  in  grains,  does  not  adhere  to  the  plates,  and  may  there- 
fore be  blown  out  or  gathered  into  sediment-collectors.  The  chemical 
reaction  is: 

Sulphate  of  lime  +  Carbonate  of  soda  =  Sulphate  of  soda  -{-Carbonate  of  lime 
CaSO*  Na2CO3  Na2SO4  CaCO3 

Where  the  quantity  of  salts  is  large,  scale  preventives  are  not  of  much 
use.  Some  other  source  of  supply  must  be  sought,  or  the  bad  water 
purified  before  it  is  allowed  to  enter  the  boilers.  The  damage  done  to 
boilers  by  unsuitable  water  is  enormous. 

Pure  water  may  be  obtained  by  collecting  rain,  or  condensing  steam 
by  means  of  surface  condensers.  The  water  thus  obtained  should  be 
mixed  with  a  little  bad  water,  or  treated  with  a  little  alkali,  as  undiluted, 
pure  water  corrodes  iron;  or,  after  each  periodic  cleaning,  the  bad  water 
may  be  used  for  a  day  or  two  to  put  a  skin  upon  the  plates. 

Carbonate  of  lime  and  magnesia  may  be  precipitated  either  by  heat- 
ing the  water  or  by  mixing  milk  of  lime  (Porter-Clark  process)  with  it, 
the  water  being  then  filtered. 

Corrosion  may  be  produced  by  the  use  of  pure  water,  or  by  the  presence 
of  acids  in  the  water,  caused  perhaps  in  the  engine-cylinder  by  the  ac- 
tion of  high-pressure  steam  upon  the  grease,  resulting  in  the  production 
of  fatty  acids.  Acid  water  may  be  neutralized  by  the  addition  of  lime. 

Amount  of  Sediment  which  may  collect  in  a  100-H. P.  steam-boiler, 
evaporating  3000  Ibs.  of  water  per  hour,  the  water  containing  different 
amounts  of  impurity  in  solution  provided  that  no  water  is  blown  off: 
'Grains  of  solid  impurities  per  U.  S.  gallon; 

5       10         20         30         40         50        60  70      80         90       100 

Equivalent  parts  per  100,000: 

8.57  17.14  34.28  51.42  68.56  85.71  102.85  120  137.1  154.3  171.4 
Sediment  deposited  in  1  hour,  pounds: 

0.257  0.514  1.028    1.542    2.056    2.571     3.085        3.6      4.11      4.63      5.14 
In  one  day  of  10  hours,  pounds: 

2.57    5.14    10.28    15.42    20.56    25.71     30.85      36.0      41.1      46.3  .    51.4 
In  one  week  of  6  days,  pounds: 
15.43    30.85    61.7    92.55    123.4    154.3     185.1    216.0    246.8    277.6    308.5 

If  a  100-H.P.  boiler  has  1200  sq.  ft.  heating-surface,  one  week's  running 
without  blowing  off,  with  water  containing  100  grains  of  solid  matter  per 
gallon  in  solution,  would  make  a  scale  nearly  0.02  in.  thick,  if  evenly  depos- 
ited all  over  the  heating-surface,  assuming  the  scale  to  have  a  sp.  gr.  of 
2.5  =  156  Ibs.  Der  cu.  ft.;  0.02  X  1200  X  156  X  Vi2  =  312  Ibs. 

Effect  of  Scale  on  Boiler  Efficiency.  —  The  following  statement, 
or  a  similar  one,  has  been  published  and  republished  for  40  years  or  more 
by  makers  of  "boiler  compounds,"  feed-water  heaters  and  water:puri- 
fying  apparatus,  but  the  author  has  not  been  able  to  trace  it  to  its  original 
source:* 

"  It  has  been  estimated  that  scale  1/50  of  an  inch  thick  requires  the 
burning  of  5  per  cent  of  additional  fuel:  scale  1/25  of  an  inch  thick 
requires  10  per  cent  more  fuel;  Vie  of  an  inch  of  scale  requires 
cent  additional  fuel;  I/a  of  an  inch,  30  per  cent.,  and  1/4  of  an  inch,  bt>  per 
cent." 

The  absurdity  of  the  last  statement  may  be  shown  by  a  simple  caicti 
Mion.     Suppose  a  clean  boiler  is  giving  75%  efficiency  with  a  furnace 
temperature  of  2400°  F.  above  the  atmospheric  temperature,    Neglectn 
the  radiation  and  assuming  a  constant  specific  heat  for  the  gases,  the 
temperature  of  the  chimney  gases    will  be  600°.     A  certain  amount 
fuel  and  air  supply  will  furriish  100  Ibs.  of  gas.     In  the  boiler  with  1/4  iru 

*  A  committee  of  the  Am.  Ky.  Mast.  Mechs.  Assn.  in  1872  quoted 
from  a  paper  by  Dr.  Jos.  G.  Rodgers  before  the  Am.  Assn.  for  Adv.  of 
Science  (date  not  stated):  "It  has  been  demonstrated  [how  and  by 
whom  not  stated]  that  a  scale  Vie  in.  thick  requires  the  expenditure  of 
15%  more  fuel  As  the  scale  thickens  the  ratio  increases;  thus  when  it 
is  V4  in.  thick,  60%  more  is  required," 


INCRUSTATION  AND   CORROSION.  929 

scale  66%  more  fuel  will  make  66  Ibs.  more  gas.  As  the  extra  fuel  does 
no  work  in  evaporating  water,  its  heat  must  all  go  into  the  chimney 
gad.  We  have  then  in  the  chimney  gases 

100  Ibs.  at    600°  F.,  product    60,000 
66  Ibs.  at  2400°  F.,  product  158,400  ... 

— ^^— —     ^lo,4(JU 

which  divided  by  166  gives  1370°  above  atmosphere  as  the  temperature 
of  the  chimney  gas,  or  more  than  enough  to  make  the  flue  connection  and 
damper  red  hot.  (Makers  of  boiler  compounds,  etc.,  please  copy.) 

Another  writer  says:  "Scale  of  Vie  inch  thickness  will  reduce  boiler 
efficiency  Vs,  and  the  reduction  of  efficiency  increases  as  the  square  of 
the  thickness  of  the  scale." 

This  is  still  more  absurd,  for  according  to  it  if  Vie  in.  scale  reduces  the 
efficiency  i/g,  then  3/16  in.  will  reduce  it  9/s,  or  to  below  zero. 

From  a  series  of  tests  of  locomotive  tubes  covered  with  different  thick- 
nesses of  scale  up  to  Vs  in.  Prof.  E.  C.  Schmidt  (Bull.  No.  11  Univ.  of 
111.  Experiment  Station,  1907)  draws  the  following  conclusions: 

1.  Considering  scale  9f  ordinary  thickness,  say  varying  up  to  Vs  inch, 
the  loss  in  heat  transmission  due  to  scale  may  vary  in  individual  cases 
from  insignificant  amounts  to  as  much  as  10  or  12  per  cent. 

2.  The  loss  increases  somewhat  with  the  thickness  of  the  scale. 

3.  The  mechanical  structure  of  the  scale  is  of  as  much  or  more  impor- 
tance than  the  thickness  in  producing  this  loss. 

4.  Chemical  composition,  except  in  so  far  as  it  affects  the  structure 
of  the  scale,  has  no  direct  influence  on  its  heat-transmitting  qualities. 

In  1896  the  author  made  a  test  of  a  water-tube  boiler  at  Aurora.  111., 
which  had  a  coating  of  scale  about  1/4  in.  thick  throughout  its  whole 
heating  surface,  arid  obtained  practically  the  same  evaporation  as  in 
another  test,  a  few  days  later,  after  the  boiler  had  been  cleaned.  This 
is  only  one  case,  but  the  result  is  not  unreasonable  when  it  is  known 
that  the  scale  was  very  soft  and  porous,  and  was  easily  removed  from  the 
tubes  by  scraping. 

Prof.  R.  C.  Carpenter  (Am.  Electrician,  Aug.,  1900)  says:  So  far  as  I  am 
able  to  determine  by  tests,  a  lime  scale,  even  of  great  thickness,  has  no 
appreciable  effect  on  the  efficiency  of  a  bpiler,  as  in  a  test  which  was 
conducted  by  myself  the  results  were  practically  as  good  when  the  boiler 
was  thickly  covered  with  lime  scale  as  when  perfectly  clean.  .  .  .  Ob- 
servations and  experiments  have  shown  that  any  scale  porous  to  water 
has  little  or  no  detrimental  effect  on  economy  of  the  boiler.  There 
is,  I  think,  good  philosophy  for  this  statement;  the  heating  capacity  is 
affected  principally  by  the  rapidity  with  which  the  heated  gases  will 
surrender  heat,  as  the  water  and  the  metal  have  capacities  for  absorbing 
heat  more  than  a  hundred  times  faster  than  the  air  will  surrender  heat. 

A  thin  film  of  grease,  being  impermeable  to  water,  keeps  the  latter 
from  contact  with  the  metal  and  generally  produces  disastrous  results. 
It  is  much  more  harmful  than  a  very  thick  scale  of  carbonate  of  lime. 

Boiler-scale  Compounds. — The  Bavarian  Steam-boiler  Inspection 
Assn.  in  1885  reported  as  follows: 

Generally  the  unusual  substances  in  water  can  be  retained  in  soluble 
form  or  precipitated  as  mud  by  adding  caustic  soda  or  lime.  This  is 
especially  desirable  when  the  boilers  have  small  interior  spaces. 

It  is  necessary  to  have  a  chemical  analysis  of  the  water  in  order  to  fully 
determine  the  kind  and  quantity  of  the  preparation  to  be  used  for  the 
above  purpose. 

All  secret  compounds  for  removing  boiler-scale  should  be  avoided. 
(A  list  of  27  such  compounds  manufactured  and  sold  by  German  firms  is 
then  given  which  have  been  analyzed  by  the  association.) 

Such  secret  preparations  are  either  nonsensical  or  fraudulent,  or 
contain  either  one  of  the  two  substances  recommended  by  the  association 
for  removing  scale,  generally  soda,  which  is  colored  to  conceal  its  presence, 
and  sometimes  adulterated  with  useless  or  even  injurious  matter. 

These  additions  as  well  as  giving  the  compound  some  strange,  fanciful 
name,  are  meant  simply  to  deceive  the  boiler  owner  and  conceal  from  him 
the  fact  that  he  is  buying  colored  soda  or  similar  substances,  for  which 
he  is  paying  an  exorbitant  price. 

Kerosene  and  other  Petroleum  Oils:  Foaming,  —  Kerosene  ha? 
been  recom mended  as  a  scale  preventive.  See  paper  by  k.  F, 


930  THE   STEAM-BOILER. 

ffrans.  A.  S.  M.  E.,  ix.  247)^  The  Am.  Mach~'  May  22,  1890,~says: 
Kerosene  used  in  moderate  quantities  will  not  make  the  boiler  foam; 
it  is  recommended  and  used  for  loosening  the  scale  and  for  preventing  the 
formation  of  scale.  The  presence  of  oil  in  combination  with  other  im- 
purities increases  the  tendency  of  many  boilers  to  foam,  as  the  oil  with  the 
impurities  impedes  the  free  escape  of  steam  from  the  water  surface. 
The  use  of  common  oil  not  only  tends  to  cause  foaming,  but  is  dangerous 
otherwise.  The  grease  appears  to  combine  with  the  impurities  of  the 
water,  and  when  the  boiler  is  at  rest  this  compound  sinks  to  the  plates 
and  clings  to  them  in  a  loose,  spongy  mass,  preventing  the  water  from 
coming  in  contact  with  the  plates,  and  thereby  producing  overheating, 
which  may  lead  to  an  explosion.  Foaming  may  also  be  caused  by  forcing 
the  fire,  or  by  taking  the  steam  from  a  point  over  the  furnace  or  where 
the  ebullition  is  violent ;  the  greasy  and  dirty  state  of  new  boilers  is  another 
good  cause  for  foaming.  Kerosene  should  be  used  at  first  in  small  quan- 
tities, the  effect  carefully  noted,  and  the  quantity  increased  if  necessary 
for  obtaining  the  desired  results. 

R.  C.  Carpenter  (Trans.  A.  S.  M.  E.,  vol.  xi)  says:  The  boilers  of  the 
State  Argicultural  College  at  Lansing,  Mich.,  were  badly  incrusted  with 
a  hard  scale.  It  was  fully  3/8  in.  thick  in  many  places.  The  first  appli- 
cation of  the  oil  was  made  while  the  boilers  were  being  but  little  used, 
by  inserting  a  gallon  of  oil,  filling  with  water,  heating  to  the  boiling-point 
and  allowing  the  water  to  stand  in  the  boiler  two  or  three  weeks  before 
removal.  By  this  method  fully  one-half  the  scale  was  removed  during 
the  warm  season  and  before  the  boilers  were  needed  for  heavy  firing. 
The  oil  was  then  added  in  small  quantities  when  the  boiler  was  in  actual 
use.  For  boilers  4  ft.  in  diam.  and  12  ft.  long  the  best  results  were 
obtained  by  the  use  of  2  qts.  for  each  boiler  per  week,  and  for  each  boiler 
6  ft.  in  diam.  3  qts.  per  week.  The  water  used  in  the  boilers  has  the  fol- 
lowing analysis:  CaCO3,  206  parts  in  a  million;  MgCOs,  78  parts;  Fe2CO3, 
22  parts;  traces  of  sulphates  and  chlorides  of  potash  and  soda.  Total 
solids,  325  parts  in  1,000,000. 

Petroleum  Oils  heavier  than  kerosene  have  been  used  with  good  re- 
sults Crude  oil  should  never  be  used.  The  more  volatile  oils  it  contains 
make  explosive  gases,  and  its  tarry  constituents  are  apt  to  form  a  spongy 
Incrustation. 

Removal  of  Hard  Scale.  —  When  boilers  are  coated  with  a  hard  scale 
difficult  to  remove  the  addition  of  1/4  lb.  caustic  soda  per  horse-power, 
and  steaming  for  some  hours,  according  to  the  thickness  of  the  scale,  just 
before  cleaning,  will  greatly  facilitate  that  operation,  rendering  the  scale 
soft  and  loose.  This  should  be  done,  if  possible,  when  the  boilers  are  not 
otherwise  in  use.  (Steam.) 

Corrosion  in  Marine  Boilers.  (Proc.  Inst.  M.  E.,  Aug.,  1884.)  — 
The  investigations  of  the  Committee  on  Boilers  served  to  show  that  the 
internal  corrosion  of  boilers  is  greatly  due  to  the  combined  action  of  air 
and  sea-water  when  under  steam,  and  when  not  under  steam  to  the  com- 
bined action  of  air  and  moisture  upon  the  unprotected  surfaces  of  the 
metal.  There  are  other  deleterious  influences  at  work,  such  as  the  corro- 
sive action  of  fatty  acids,  the  galvanic  action  of  copper  and  brass,  and  the 
Inequalities  of  temperature;  these  latter,  however,  are  considered  to  be  of 
minor  importance. 

Of  the  several  methods  recommended  for  protecting  the  internal  sur- 
faces of  boilers,  the  three  found  most  effectual  are:  First,  the  formation 
of  a  .thin  layer  of  hard  scale,  deposited  by  working  the  boiler  with  sea- 
water-  second,  the  coating  of  the  surfaces  with  a  thin  wash  of  Portland 
cement  particularly  wherever  there  are  signs  of  decay;  third,  the  use  of 
tine  slabs  suspended  in  the  water  and  steam  spaces. 

As  to  general  treatment  for  the  preservation  of  boilers  when  laid  up 
In  the  reserve,  either  of  the  two  following  methods  is  adopted.  First, 
the  boilers  are  dried  as  much  as  possible  by  airing-stoves,  after  which 
2  to  3  cwt  of  quicklime  is  placed  on  trays  at  the  bottom  of  the  boiler  and 
Dn  the  tubes.  The  boiler  is  then  closed  and  made  as  air-tight  as  possible, 
inspection  is  made  every  six  months,  when  if  the  lime  be  found  slacked 
t  is  renewed.  Second,  the  boilers  are  filled  with  sea  or  fresh  water, 
saving  added  soda  to  it  in  the  proportion  of  1  lb.  to  every  100  or  120  Ibs. 
>f  water  The  sufficiency  of  the  saturation  can  be  tested  by  introducing: 

$  piece  of  clean  new  iron  and  leaving  it  in  tne  boiler  for  ten  or  twelve 


INCKUSTATION  AND   CORROSION.  931 

hours:  if  it  shows  signs  of  rusting,  mure  &oda  should  be  added.  It  is 
essential  that  the  boilers  be  entirely  filled,  to  the  complete  exclusion  of 
air. 

Mineral  oil  has  for  many  years  been  exclusively  used  for  internal 
lubrication  of  engines,  with  the  view  of  avoiding  the  effects  of  fatty  acid, 
as  this  oil  does  not  readily  decompose  and  possesses  no  acid  properties. 

Of  all  the  preservative  methods  adopted  in  the  British  service  the  use 
of  zinc  properly  distributed  and  fixed  has  been  found  the  most  effectual 
in  saving  the  iron  and  steel  surfaces  from  corrosion,  and  also  in  neutral- 
izing by  its  own  deterioration  the  hurtful  influences  met  with  in  water  as 
ordinarily  supplied  to  boilers.  The  zinc  slabs  now  used  in  the  navy 
boilers  are  12  in.  long,  6  in.  wide,  and  ^  in.  thick;  this  size  being  found 
convenient  for  general  application.  The  amount  of  zinc  used  in  new 
boilers  at  present  is  one  slab  of  the  above  size  for  every  20  I.H.P.,  or 
about  1  sq.  ft.  of  zinc  surface  to  2  sq.  ft.  of  grate  surface.  Rolled  zinc  is 
found  the  most  suitable  for  the  purpose.  Especial  care  must  be  taken 
to  insure  perfect  metallic  contact  between  the  slabs  and  the  stays  or 
plates  to  which  they  are  attached.  The  slabs  should  be  placed  in  such 
positions  that  all  the  surfaces  in  the  boiler  are  protected.  Each  slab 
should  be  periodically  examined  to  see  that  its  connection  remains  per- 
fect, and  to  renew  any  that  may  have  decayed;  this  examination  is 
usually  made  at  intervals  not  exceeding  three  months.  Under  ordinary 
circumstances  of  working  these  zinc  slabs  may  be  expected  to  last  in  fit 
condition  from  60  to  90  days,  immersed  in  hot  sea-water;  but  in  new 
boilers  they  at  first  decay  more  rapidly.  The  slabs  are  generally 
secured  by  means  of  iron  straps  2  in.  X  3/8  in.,  and  long  enough  to 
reach  the  nearest  stay,  to  which  the  strap  is  attached  by  screw-bolts. 

To  promote  the  proper  care  of  boilers  when  not  in  use  the  following 
order  has  been  issued  to  the  French  Navy  by  the  Government:  On  board 
all  ships  in  the  reserve,  as  well  as  those  which  are  laid  up,  the  boilers  will 
be  completely  filled  with  fresh  water.  In  the  case  of  large  boilers  with 
large  tubes  there  will  be  added  to  the  water  a  certain  amount  of  milk  of 
lime,  or  a  solution  of  soda.  In  the  case  of  tubulous  boilers  with  small 
tubes  milk  of  lime  or  soda  may  be  added,  but  the  solution  will  not  be 
so  strong  as  in  the  case  of  the  larger  tube,  so  as  to  avoid  any  danger  of 
contracting  the  effective  area  by  deposit  from  the  solution;  but  the 
strength  of  the  solution  will  be  just  sufficient  to  neutralize  any  acidity  of 
the  water.  (Iron  Age,  Nov.  2,  1893.) 

Use  of  Zinc.: — Zinc  is  often  used  in  boilers  to  prevent  the  corrosive 
action  of  water  on  the  metal.  The  action  appears  to  be  an  electrical 
one,  the  iron  being  one  pole  of  the  battery  and  the  zinc  being  the  other. 
The  hydrogen  goes  to  the  iron  shell  and  escapes  as  a  gas  into  the  steam. 
The  oxygen  goes  to  the  zinc. 

On  account  of  this  action  it  is  generally  believed  that  zinc  will  always 
prevent  corrosion,  and  that  it  cannot  be  harmful  to  the  boiler  or  tank. 
Some  experiences  go  to  disprove  this  belief,  and  in  numerous  cases  zinc 
has  not  only  been  of  no  use,  but  has  even  been  harmful.  In  one  case  a 
tubular  boiler  had  been  troubled  with  a  deposit  of  scale  consisting  chiefly 
of  organic  matter  and  lime,  and  zinc  was  tried  as  a  preventive.  The 
beneficial  action  of  the  zinc  was  so  obvious  that  its  continued  use  was 
advised,  with  frequent  opening  of  the  boiler  and  cleaning  out  of  detached 
scale  until  all  the  old  scale  should  be  removed  and  the  boiler  become 
clean.  Eight  or  ten  months  later  the  water-supply  was  changed,  it  be- 
ing now  obtained  from  another  stream  supposed  to  be  free  from  lime 
and  to  contain  only  organic  matter.  Two  or  three  months  after  its 
introduction  the  tubes  and  shell  were  found  to  be  coated  with  an  ob- 
stinate adhesive  scale,  composed  of  zinc  oxide  and  the  organic  matter 
or  sediment  of  the  water  used.  The  deposit  had  become  so  heavy  in 
places  as  to  cause  overheating  and  bulging  of  the  plates  over  the  fire. 
(The  Locomotive.) 

Effect  of  Deposit  on  the  Fire-surface  of  Flues.  (Rankine.) — An 
external  crust  of  a  carbonaceous  kind  is  often  deposited  from  the  flame 
and  smoke  of  the  furnaces  in  the  flues  and  tubes,  and  if  allowed  to  accu- 
mulate, seriously  impairs  the  economy  of  fuel.  It  is  removed  from  time 
to  time  by  means  of  scrapers  and  wire  brushes.  The  accumulation  of 
this  crust  is  the  probable  cause  of  the  fact  that  in  some  steamships  the 
consumption  of  coal  per  I.H.P.  per  hour  goes  on  gradually  increasing 


932  THE  STEAM-BOILER. 

until  it  reaches  one  and  a  half  times  its  original  amount,  and  sometimes 
more. 

Dangerous  Steam-boilers  discovered  by  Inspection.  —  Tlje  Hartford 
Steam-boiler  Inspection  and  Insurance  Co.  reported  in  The  Locomotive 
the  following  summary  of  defects  in  boilers  discovered  by  its  inspectors 
in  the  year  1912: 

Number  of  visits  of  inspection  made 183,519 

Total  number  of  boilers  examined 337,178 

Number  found  uninsurable 977 

Whole 
Nature  of  Defects  Number    Dangerous 

Cases  of  sediment  or  loose  scale 26,299  1,553 

Cases  of  adhering  scale 40,336  1,436 

Cases  of  grooving 2,700  252 

Cases  of  internal  corrosion „        15,403 

Cases  of  external  corrosion 10,411  895 

Cases  of  defective  bracing 1,391 

Cases  of  defective  staybolting 1,712  345 

Settings  defective 8,119  768 

Fractured  plates  and  heads 3,288  510 

Burned  plates 4,965  517 

Laminated  plates 445  55 

Cases  of  defective  riveting 1,816  405 

Cases  of  leakage  around  tubes 10,159  1,607 

Cases  of  defective  tubes  or  flues 11,488  4,780 

Cases  of  leakage  at  seams 5,304  401 

Water-gages  defective 3,663  816 

Blow-offs  defective 4,429  1,398 

Cases  of  low  water , 447  151 

Safety-valves  overloaded 1,349  380 

Safety-valves  defective 1,534  419 

Pressure-gages  defective 6,765  568 

Boilers  without  pressure-gages 633  102 

Miscellaneous  defects 2,268  420 


Total 164,924  18,932 

The  above-named  company  publishes  annually  a  summary  like  the 
above,  and  also  a  classified  list  of  boiler-explosions,  compiled  chiefly  from 
newspaper  reports,  showing  that  from  200  to  300  explosions  take  place  in 
the  United  States  every  year,  killing  from  200  to  300  persons,  and  in- 
juring from  300  to  450.  The  lists  are  not  pretended  to  be  complete,  and 
may  include  only  a  fraction  of  the  actual  number  of  explosions. 

Steam-boilers  as  Magazines  of  Explosive  Energy. — Prof.  R.  H. 
Thurston  (Trans.  A.  S.  M.  E.,  vol.  vi),  in  a  paper  with  the  above  title, 
presents  calculations  showing  the  stored  energy  in  the  hot  water  and 
steam  of  various  boilers.  Concerning  the  plain  tubular  boiler  of  average 
form  and  dimensions  he  says:  It  is  60  in.  in  diameter,  containing  66 
3-in.  tubes,  and  is  15  ft.  long.  It  has  850  sq .  ft.  of  heating  and  30  sq .  ft.  of 

erate  surface;  is  rated  at  60  H.P.,  but  is  oftener  driven  lip  to  75;  weighs 
500  lb.,  and  contains  nearly  its  own  weight  of  water,  but  only  21  lb. 
of  steam  when  under  a  pressure  of  75  lb.  per  sq.  in.,  which  is  below  its 
safe  allowance.  It  stores  52,000,000  foot-pounds  of  energy,  of  which 
but  4  %  is  in  the  steam,  and  this  is  enough  to  drive  the  boiler  just  about 
one  mile  into  the  air,  with  an  initial  velocity  of  nearly  600  ft.  per  second. 

SAFETY-VALVES. 

Calculation  of  Weight,  etc.,  for  Lever  Safety-valves. 

Let  W  =  weight  of  ball  at  end  of  lever;  w  =  weight  of  lever  itself;  V  = 
weight  of  valve  and  spindle,  all  in  pounds;  L  =  distance  between  ful- 
crum and  center  of  ball;  I  =  distance  between  fulcrum  and  center  of 
valve;  g  =  distance  between  fulcrum  and  center  of  gravity  of  lever,  all  in 
inches;  A  =  area  of  valve,  in  sq.  in.;  P  =  pressure  of  steam,  in  lb.  per 
set.  in.,  at  which  valve  will  open. 


SAFETY-VALVES.  933 

Then  PA  X  I  -  W  X  L  +  w  X  g  +  V  X  I; 

whence  P  =  (WL  +  wg  +  VI)  -h  Al;  W  =  (PAl  -  wg  -  VI)  -J-  L;  L  = 
(PAZ  -  w0  -  VO  -  W. 

EX\MPLE. — Diameter  of  valve,  4  in. ;  distance  from  fulcrum  to'center 
of  bail,  36  in. ;  to  center  of  valve,  4  in. ;  to  center  of  gravity  of  lever, 
15  y.  in.;  weight  of  valve  and  spindle,  3  lb.;  weight  of  lever,  7  lb.;  re- 
quired the  weight  of  ball  to  make  the  blowing-off  pressure  80  lib.  per  sq. 
in. ;  area  of  4-in.  valve  =  12.566  sq.  in.  Then 

=  PAl  -wg  -VI  =  80  X  12.566  X  4  -  7  X  151/2  -  3  X  4  =  1Qg  4  ^ 
L,  36 

By  the  rules  of  the  U.S.  Supervising  Inspectors  of  Steam  Vessels  the 
use  of  lever  safety-valves  is  prohibited  on  all  boilers  built  for  steam 
vessels  after  June' 30,  1906. 

A  method  for  calculating  the  size  of  safety-valve  is  given  in  The  Loco- 
motive July,  1892,  based  on  the  assumption  that  the  actual  opening 
should  be  sufficient  to  discharge  all  the  steam  generated  by  the  boiler. 
Napier's  rule  for  flow  of  steam  is  taken,  viz.,  flow  through  aperture  of  one 
sq.  in.  in  Ibs.  per  second  =  absolute  pressure  -s-  70,  or  in  Ibs.  per  hour  = 
51.43  X  absolute  pressure. 

If  the  angle  of  the  seat  is  45°,  the  area  of  opening  in  sq.  in.  =  circum- 
ference of  the  disk  X  the  lift  X  0.71,  0.71  being  the  cosine  of  45°;  or 
diameter  of  disk  X  lift  X  2.23. 

Spring-loaded  Safety-Valves. 

Spring-loaded  safety-valves  to  be  used  on  U.  S.  merchant  vessels  must 
conform  to  the  rules  prescribed  by  the  Board  of  Supervising  Inspectors, 
and  on  vessels  for  the  U.  S.  Navy  to  specifications  made  by  the  Bureau 
of  Steam  Engineering,  U.  S.  N.  Valves  to  be  used  on  stationary  boilers 
must  conform  in  many  cases  to  the  special  laws  made  by  various  states. 
Few  of  these  rules  are  on  a  logical  basis,  in  that  they  take  no  account  of 
the  lift  of  the  valve,  and  it  is  quite  clear  that  the  rate  of  steam  discharge 
through  a  safety-valve  depends  upon  the  area  of  opening,  which  varies 
with  the  circumference  of  the  valve  and  the  lift.  Experiments  made  by 
the  Consolidated  Safety  Valve  Co.  showed  that  valves  made  by  the  differ- 
ent manufacturers  and  employing  various  combinations  of  springs  with 
different  designs  of  valve  lips  and  huddling  chambers  give  widely  different 
lifts.  Lifts  at  popping  point  of  different  makes  of  safety-valves,  at  200 
Ibs.  pressure,  are  as  follows: 

4-in.  stationary  valves,  in.,  0.031,  0.056,  0.064,  0.082,  0.094,  0.094,  0.137. 

Av.  0.079  in. 
3V2-in.  locomotive  valves,  in.,  0.040,  0.051,  0.065,  0.072,  0.076-,  0.140  ins. 

Av.  0.074  in. 

United  States  Supervising  Inspectors'  Rule  (adopted  in  1904).  A  =» 
0.2074  W  /P.  A  =  area  of  safety  valve  in  sq.  in.  per  sq.  ft.  of  grate 
surface;  W  =  Ibs.  of  water  evaporated  per  sq.  ft.  of  grate  surface  per 
hour;  P  =  boiler  pressure,  absolute,  Ibs.  per  sq.  in.  This  rule  assumes 
a  lift  of  1/32  of  the  nominal  diameter,  and  75%  of  the  flow  calculated  by 
Napier's  rule.  This  75%  corresponds  nearly  to  the  cosine  of  45°,  or  0.707. 

Massachusetts  Rule  of  1909.  A  =  770  W/P,  in  which  W  =  Ibs.  evapo- 
rated per  sq.  ft.  of  grate  per  second;  A  and  P  as  above.  This  is  the 
same  as  the  U.  S.  rule  with  a  3.2%  larger  constant. 

Philadelphia  Rule.  —  A  =  22.5  G  -f-  (P  +  8.62).  A  =  total  area  of 
valve  or  valves,  sq.  in.;  G  =  grate  area,  sq.  ft.;  P  =  boiler  pressure 
(gauge).  This  rule  came  from  France  in  1868.  It  was  recommended 
to  the  city  of  Philadelphia  by  a  committee  of  the  Franklin  Institute, 
although  the  committee  "had  not  found  the  reasoning  upon  which  the 
rule  had  been  based." 

Philip  G.  Darling  (Trans.  A.  S.  M.  E.,  1909)  commenting  on  the  above 
rules  says:  The  principal  defect  of  these  rules  is  that  they  assume  that 
valves  of  the  same  nominal  size  have  the  same  capacity,  and  they  rate 
them  the  same  without  distinction,  in  spite  of  the  fact  that  in  actual  prac- 
tice some  have  but  one-third  of  the  capacity  of  others.  There  are  other 
.defects,  such  as  varying  the  assumed  lift  as  the  valve  diameter,  while  in 


934 


THE   STEAM-BOILER. 


reality  with  a  given  design  the  lifts  are  more  nearly  the  same  in  the  dif- 
ferent sizes,  not  varying  nearly  as  rapidly  as  the  diameters.  And 
further  than  this,  the  actual  lifts  assumed  for  the  larger  valves  are 
nearly  double  the  actual  average  obtained  in  practice.  The  direct  con- 
clusion is  that  existing  rules  and  statutes  are  not  safe  to  follow. 

Rules  of  the  A.  S.  M.  E.  Boiler  Code  Committee.— In  1914  the  Com- 
mittee had  several  conferences  with  the  principal  safety-valve  manu- 
facturers of  the  country  and  an  agreement  was  finally  reached  on  the 
rules  given  in  condensed  form  below.  The  discharging  capacity  of  a 
valve  is  based  on  Napier's  rule  with  a  coefficient  of  discharge  of  0.96. 
The  formula  being  W  =  3600  X  3.1416  XDLX  0.96  X  0.707  X  P/7Q 
or  W  =  109.66  D  L  P  pounds  per  hour  for  a  45°  bevel  seat  valve. 
For  flat  seat  valves  the  factor  0.707  is  omitted  and  the  formula  becomes 
W  =  155.11  DLP  pounds  per  hour.  The  following  table  is  calcu- 
lated from  the  first  formula. 

Discharge  Capacities  of  Direct  Spring-Loaded  Pop  Safety-Valves  with 
45°  Bevel  Seats.     Pounds  per  Hour. 


A 

Diam.  1  in. 

Diam.  1^  in. 

Diam.  2  in. 

Diam.  2y2  in. 

m« 
S.8. 

Lift,  in. 

rh-Q 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

cs 

0.02 

0.04 

0.05 

0.03 

0.05 

0.06 

0.04 

0.06 

0.07 

0.04 

0.06 

0.08 

15 

65 

131 

163 

~l46 

245 

293 

261 

391 

456 

326 

488 

651 

25 

87 

174 

218 

196 

326 

392 

349 

523 

610 

435 

653 

871 

50 

142 

284 

354 

320 

532 

639 

568 

851 

994 

710 

1064 

1419 

75 

197 

393 

492 

443 

738 

886 

787 

1181 

1377 

984 

1475 

1968 

100 

252 

503 

629 

566 

944 

1133 

1007 

1510 

1761 

1258 

1887 

2516 

125 

307 

613 

767 

689 

1149 

1379 

1224 

1836 

2145 

1532 

2299 

3064 

150 

362 

723 

904 

813 

1355 

1625 

1438 

2158 

2529 

1806 

2710 

3613 

175 

416 

833 

1040 

936 

1561 

1872 

1664 

2497 

2913 

2081 

3121 

4161 

200 

471 

941 

1178 

1060 

1766 

2119 

1884 

2826 

3296 

2354 

3532 

4709 

225 

526 

1052 

1315 

1183 

1972 

2366 

2104 

3154 

3680 

2629 

3944 

5258 

250 

581 

1161 

1451 

1307 

2177 

2613 

2322 

3484 

4064 

2903 

4355 

5807 

275 

635 

1271 

1589 

1430 

2383 

2860 

2542 

3813 

4448 

3177 

4766 

6355 

300 

698 

1397 

1746 

3155 

2589 

3107 

2762 

4143 

4832 

3452 

5177 

6903 

Capacities  of  Safety-Valves. — Continued. 


ri 

Diam.  3  in. 

Diam.  3  y2  in. 

Diam.  4  in. 

Diam.  4^  in. 

SP  § 

Lift,  in.   .,•-. 

*S 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

Min. 

Int. 

Max. 

0:2 

0.05 

0.08 

0.10 

0.06 

0.09 

0.11 

0.07 

0.10 

0.12 

0.08 

0.11 

0.13 

IT 

489 

782 

977 

684 

1026 

1254 

912 

1303 

1564 

1173 

1613 

1906 

25 

653 

1046 

1307 

914 

1372 

1676 

1219 

1742 

2090 

1568 

2156 

2547 

50 

1064 

1703 

2129 

1490 

2235 

2732 

1987 

2839 

3406 

2555 

3513 

4151 

75 

1475 

2361 

2951 

2066 

3099 

3788 

2754 

3935 

4722 

3542 

4870 

5756 

100 

1887 

3019 

3774 

2642 

3963 

4843 

3522 

5032 

6038 

4529 

6227 

7358 

125 

2299 

3677 

4596 

3218 

4826 

5899 

4290 

6128 

7354 

5516 

7583 

8963 

150 

2710 

4335 

5419 

3794 

5690 

6954 

5058 

7226 

8670 

6503 

8940 

10566 

175 

3121 

4993 

6242 

4369 

6553 

8010 

5824 

8320 

9984 

7490 

10298 

12173 

200 

3532 

5b5l 

7064 

4946 

7418 

9068 

6593 

9420 

11305 

8475 

11655 

13773 

225 

3944 

6310 

7890 

5521 

8280 

10120 

7361 

10514 

12616 

9465 

13013 

15383 

250 

4355 

6968 

8708 

6097 

9143 

11175 

8130 

11614 

13938 

10448 

14366 

16980 

275 

4766 

7620 

9533 

6672 

10005 

12333 

8895 

12707 

15248 

11438 

15728 

18585 

300 

5177 

8280 

10358 

7248 

10875 

13290 

9668 

13807 

16568 

12428 

17088 

20195 

Safety-Valve  Requirements. — Each  boiler  shall  have  two  or  more 
safety-valves,  except  a  boiler  for  which  one  safety-valve  3-in.  size  or 
smaller  is  required  by  these  Rules. 

The  safety-valve  capacity  for  each  boiler  shall  be  such  that  the 
safety-valve  or  valves  will  discharge  all  the  steam  that  can  be  generated 


SAFETY-VALVES.  935 

bv  the  boiler  without  allowing  the  pressure  to  rise  more  than  6%  above 
the  maximum  allowable  working  pressure,  or  more  than  6  %  above  the 
highest  pressure  to  which  any  valve  is  set. 

One  or  more  safety-valves  on  every  boiler  shall  be  set  at  or  below 
the  maximum  allowable  working  pressure.  The  remaining  valves  may 
be  set  within  a  range  of  3%  above  the  maximum  allowable  working 
pressure  but  the  range  of  setting  of  all  of  the  valves  on  a  boiler  shall 
not  exceed  10%  of  the  highest  pressure  to  which  any  valve  is  set. 

Safety-valves  shall  be  of  the  direct  spring-loaded  pop  type.  The 
vertical  lift  of  the  valve  disk  may  be  made  any  amount  desired  up  to  a 
maximum  of  0.15  in.  The  diameter  measured- at  the  inner  edge  of  the 
valve  seat  shall  be  not  less  than  1  in.  or  more  than  4  ^  in. 

Each  safety-valve  shall  have  plainly  stamped  or  cast  on  the  body: 
(a)  The  name  or  trade-mark  of  the  manufacturer,  (b)  The  nominal 
diameter  with  the  words  "  Bevel  Seat"  or  "  Flat  Seat."  (c)  The  steam 
pressure  at  which  it  is  set  to  blow,  (rf)  The  lift  of  the  valve  disk  from 
its  seat,  measured  immediately  after  the  sudden  lift  due  to  the  pop. 
(e)  The  weight  of  steam  discharged  in  pounds  per  hour  at  the  pressure 
for  which  it  is  set  to  blow. 

The  minimum  capacity  of  a  safety-valve  or  valves  to  be  placed  on  a 
boiler  shall  be  determined  on  the  basis  of  6  Ib.  of  steam  per  hour  per 
sq.  ft.  of  boiler  heating  surface  for  water  tube  boilers,  and  5  Ib.  for  all 
other  types  of  power  boilers,  and  upon  the  relieving  capacity  marked 
on  the  valves  by  the  manufacturer,  provided  such  marked  capacity 
does  not  exceed  that  given  in  the  table,  in  which  case  the  minimum 
safety-valve  capacity  shall  be  determined  on  the  basis  of  the  maximum 
relieving  capacity  given  in  the  table  for  the  particular  size  of  valve  and 
working  pressure  for  which  it  was  constructed.  The  heating  surface 
shall  be  computed  for  that  side  of  the  boiler  surface  exposed  to  the 
products  of  combustion,  exclusive  of  the  superheating  surface. 

Valves  1  M  in.  diam.  with  lifts  0.03,  0.04  and  0.05  in.  give  a  discharge 
for  0.04-in.  lift  the  same  as  that  of  a  1-in.  valve  with  0.05-in.  lift;  with 
0.03-in.  lift  25%  less  and  with  0.05-in.  lift  25%  greater. 

The  discharge  capacity  of  a  fl?t  seat  valve  is  1.41  times  that  of  a 
45°  bevel  seat  valve  of  the  same  diameter  and  lift. 

Safety-Valves  for  Locomotives. —A  Committee  of  theAmerican  Railway 
Master  Mechanics  Association  presented  a  report  on  safety-valves  in 
1912,  giving  the  following  formula  for  45°  bevel  seat  valves:  D  L  P  = 
0.036  H,  in  which  D  =  total  of  the  diameters  of  the  inner  edge  of 
the  seats  of  the  valves  required;  L  =  vertical  lift  in  inches;  P  = 
absolute  pressure,  Ib.  per  sq.  in. ;  H  =  total  heating  surface  of  boiler, 
sq.  ft.  (superheating  surface  not  included).  Every  locomotive  should 
be  equipped  with  not  less  than  two  and  not  more  than  three  safety- 
valves,  the  size  to  be  determined  by  the  formula.  The  valves  are  to 
be  set  as  follows:  The  first  at  boiler  pressure,  second  2  Ib.  in  excess, 
third  3  Ib.  in  excess  of  the  second.  Manufacturers  should  be  required 
to  stamp  on  the  valve  the  lift  in  inches  as  determined  by  actual  test. 

The  formula  corresponds  to  the  discharge  calculated  by  Napier's 
rule  with  a  coefficient  of  flow  of  0.973  and  an  evaporation  of  4  Ib.  per 
square  foot  of  heating  surface  per  hour.  It  is  evident  that  safety- 
valve?  proportioned  according  to  this  formula  will  have  a  relieving 
capacity  much  less  than  the  evaporative  capacity  of  locomotive 
boilers  with  large  fire-boxes  and  short  flues.  The  Consolidated  Safety 
Valve  Co.  suggests  the  formula  D  L  P  =  Ci  Hi  +  Cz  Hz  in  which  Hi  is 
fire-box  and  Hz  flue  heating-surface,  sq.  ft.,  and  Ci  and  Cz  are  constants 
to  be  determined  by  experiment.  Ci  being  considerably  larger  than  €2. 

Unequal  expansion  of  safety-valve  parts  under  steam  temperatures 
tends  to  cause  leakage,  and  as  this  temperature  effect  becomes  more 
serious  in  the  large  sizes  the  manufacturers  do  not  recommend  the  use 
of  valves  larger  than  4 1/2  ins.  If  greater  relieving  capacity  be  required 
it  is  the  best  practice  to  use  duplex  valves  or  additional  single  valves. 

For  an  extended  discussion  on  safety-valves,  see  Trans,  A.  5.  M.  E,, 


936 


THE   STEAM-BOILER. 


THE  INJECTOR. 

Equation  of  the  Injector. 

Let  S  be  the  number  of  pounds  of  steam  used; 

W  the  number  of  pounds  of  water  lifted  and  forced  Into  the  boiler; 
h  the  height  in  feet  of  a  column  of  water,  equivalent  to  the  absolute 

pressure  in  the  boiler; 

hQ  the  height  in  feet  the  water  is  lifted  to  the  injector;  t 
t\  the  temperature  of  the  water  before  it  enters  the  injector; 
tz  the  temperature  of  the  water  after  leaving  the  injector;    • 
H  the  total  heat  above  32°  F.  in  one  pound  of  steam  in  the  boiler, 

L  the  work  in  friction  and  the  equivalent  lost  work  due  to  radiation 

and  lost  heat; 

778  the  mechanical  equivalent  of  heat. 
Then 


-  =         ,- 

/  <o 

An  equivalent  formula,  neglecting  Who  +  L  as  small,  is 


or 


d  778J  H-(t*-32°)  . 

3.1851  p] 

[H -(£2-  32°)]  d  -0.1851  p' 
In  which  d  =  weight  of  1  cu.  ft.  of  water  at  temperature  tz ;  p  =  absolute 
pressure  of  steam,  Ibs.  per  sq.  in. 

The  rule  for  finding  the  proper  sectional  area  for  the  narrowest  part  of 
the  nozzles  is  given  as  follows  by  Rankine,  S.  E.,  p.  477: 


Area  in  square  inches  = 


cubic  feet  per  hour  gross  feed-water 
800  Vpressure  in  atmospheres 


An  important  condition  which  must  be  fulfilled  in  order  that  the  injec- 
tor will  work  is  that  the  supply  of  water  must  be  sufficient  to  condense 
the  steam.  As  the  temperature  of  the  supply  or  feed-water  is  higher, 
the  amount  of  water  required  for  condensing  purposes  will  be  greater. 

The  table  below  gives  the  calculated  value  of  the  maximum  ratio  of 
water  to  the  steam,  and  the  values  obtained  on  actual  trial,  also  the 
highest  admissible  temperature  of  the  feed-water  as  shown  by  theory 
and  the  highest  actually  found  by  trial  with  several  injectors. 


Gauge- 
pres- 
sure, 
pounds 
per 
sq.  in. 

Maximum  Ratio  Water 
to  Steam. 

Gauge- 
pres- 
sure, 
pounds 
per 
sq.  in. 

Maximum  Temperature 
of  Feed-Water. 

Calculated 
from 
Theory. 

Actual  Ex- 
periment. 

Theoreti- 
cal. 

Experimental 
Results. 

0) 

.  bo 
f*»£o' 

ill 

H.  * 

T3 

.8, 

°<%o' 

z£™ 

Oi  ocs 

H  2 

5 

H. 

P. 

M. 

S. 

H. 

P. 

M. 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 

36.5 
25.6 
20.9 
17.87 
16.2 
14.7 
13.7 
12.9 
12.1 
11.5 

30.9 
22.5 
19.0 
15.8 
13.3 
11.2 
12.3 
11.4 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
120 
150 

132° 
134 
134 
132 
131 
130 
130 
131 
132* 
132* 
134* 
121* 

19.9 
17.2 
15.0 
14.0 
11.2 
11.7 
11.2 

21.5 
19.0 
15.86 
13.3 
12.6 
12.9 

142° 
132 
126 
120 
114 
109 
105 
99 
95 
87 
77 

173° 
162 
156 
150 
143 
139 
134 
129 
125 
117 
107 

135° 

120° 

130° 

140 

113 

125 

14J* 
141* 

115 

iis 

123 
123 
122 

*  Temperature  of  delivery  above  212°.     Waste- valve  closed. 
H,  Hancock  inspirator;  P,  Park  injector;  M,  Metropolitan  injector; 
S,  Sellers  1876  injector. 


THE  INJECTOR.  937 

Efficiency  of  the  Injector.  —  Experiments  at  Cornell  University 
described  by  Prof.  R.  C.  Carpenter,  in  Cassier's  Magazine,  Feb.,  1892 
show  that  the  injector,  when  considered  merely  as  a  pump,  has  an  exceed- 
ingly low  efficiency,  the  duty  ranging  from  161,000  to  2,752,000  undei 
different  circumstances  of  steam  and  delivery  pressure.  Small  direct- 
acting  pumps,  such  as  are  used  for  feeding  boilers,  show  a  duty  of  from 
4  to  8  million  ft.-lbs.,  and  the  best  pumping-engines  from  100  to  140  mil- 
lion. When  used  for  feeding  water  into  a  boiler,  however,  the  injector 
has  a  thermal  efficiency  of  100%,  less  the  trifling  loss  due  to  radiation, 
since  all  the  heat  rejected  passes  into  the  water  which  is  carried  into  the 
boiler. 

The  loss  of  work  in  the  injector  due  to  friction  reappears  as  heat  which 
is  carried  into  the  boiler,  and  the  heat  which  is  converted  into  useful 
work  in  the  injector  appears  in  the  boiler  as  stored-up  energy. 

Although  the  injector  thus  has  a  perfect  efficiency  as  a  boiler-feeder,  it 
is  not  the  most  economical  means  for  feeding  a  boiler,  since  it  can  draw 
only  cold  or  moderately  warm  water,  while  a  pump  can  feed  water  which 
has  been  heated  by  exhaust  steam  which  would  otherwise  be  wasted. 

Performance  of  Injectors.  —  In  Am.  Mack.,  April  13,  1893,  are  a 
number  of  letters  from  different  manufacturers  of  injectors  in  reply  to  the 
question:  "What  is  the  best  performance  of  the  injector  in  raising  or 
lifting  water  to  any  height? "  Some  of  the  replies  are  tabulated  below. 

W.  Sellers  &  Co.  —  25.51  Ibs.  water  delivered  to  boiler  per  ib.  of  steam; 
temperature  of  water,  64°;  steam  pressure,  65  Ibs. 

Schaeffer  &  Budenberg  —  1  gal.  water  delivered  to  boiler  for  0.4  to 
0.8  Ib.  steam. 

injector  will  lift  by  suction  water  of 

140°  F.  136°  to  133°    122°  to  118°      113°  to  107° 

If  boiler  pres.  is  30  to  60  Ibs.    60  to  90  Ibs.    90  to  120  Ibs.    120tol501bs, 
If  the  water  is  not  over  80°  F.,  the  injector  will  force  against  a  pres- 
sure 75  Ibs.  higher  than  that  of  the  steam. 

Hancock  Inspirator  Co.: 

Lift  in  feet 22  22  22  11 

Boiler  pressure,  absolute,  Ibs 75.8         54.1         95.5         75.4 

Temperature  of  suction 34.9°       35.4°       47.3°       53. 2a 

Temperature  of  delivery 134°          117.4°      173.7°     131.1° 

Water  fed  per  Ib.  of  steam.  Ibs 11.02       13.67         8.18       13.3 

The  theory  of  the  injector  is  discussed  in  Wood's,  Peabody's,  and 
Rontgen's  treatises  on  Thermodynamics.  See  also  "Theory  and  Practice 
of  the  Injector,"  by  Strickland  L.  Kneass,  New  York,  1910. 

Boiler-feeding  Pumps.  —  Since  the  direct-acting  pump,  commonly 
used  for  feeding  boilers,  has  a  very  low  efficiency,  or  less  than  one-tenth 
that  of  a  good  engine,  it  is  generally  better  to  use  a  pump  driven  by  belt 
from  the  main  engine  or  driving  shaft.  The  mechanical  work  needed  to 
feed  a  boiler  may  be  estimated  as  follows:  If  the  combination  of  boilei 
and  engine  is  such  that  half  a  cubic  foot,  say  32  Ibs.  of  water,  is  needed 
per  horse-power,  and  the  boiler-pressure  is  100  Ibs.  per  sq.  in.,  then  the 
work  of  feeding  the  quantity  of  water  is  100  Ibs.  X  144  sq.  in.  X  1/2  ft.- 
Ib.  per  hour  =  120  ft.-lbs.  per  min.  =  120/33,000  =  .0036  H.P.,  or  less 
than  Vio  of  1%  of  the  power  exerted  by  the  engine.  If  a  direct-acting 
pump,  which  discharges  its  exhaust  steam  into  the  atmosphere,  is  used 
for  feeding,  and  it  has  only  Vio  the  efficiency  of  the  main  engine,  then  the 
steam  used  by  the  pump  will  be  equal  to  nearly  4%  of  that  generated  by 
the  boiler. 

The  low  efficiency  of  boiler-feeding  pumps,  and  of  other  small  auxiliary 
steam-driven  machinery,  is,  however,  of  no  importance  if  all  the  exhaust 
steam  from  these  pumps  is  utilized  in  heating  the  feed-water. 

The  following  table  by  Prof.  D.  S.  Jacobus  gives  the  relative  steam 
consumption  of  steam  and  power  pumps  and  injector,  with  and  with- 
out heater,  as  used  upon  a  boiler  with  80  Ibs.  gauge-pressure,  the  pump 
having  a  duty  of  10,000,000  ft.-lbs.  per  100  Ibs.  of  coal  when  no  heater 
Is  used;  the  injector  heating  the  water  from  60°  to  150°  F. 

Direct-acting  pump  feeding  water  at  60°,  without  a  heater ]  .000 

Injector  feeding  water  at  150°,  without  a  heater 0.985 

Injector  feeding  water  through  a  heater  in  which  it  is  heated  from 

150°  to  200° 0.938 


938 


THE  STEAM-BOILER. 


Direct-acting  pump  feeding  water  through  a  heater,  in  which  it  Is 

heated  from  60°  to  200° 0 . 879 

Geared  pump,  run  from  the  engine,  feeding  water  through  a  heater, 
in  which  it  is  heated  from  60°  to  200° 0 .868 

Gravity  Boiler-feeders.  —  If  a  closed  tank  be  placed  above  the  level 
of  the  water  in  a  boiler  and  the  tank  be  filled  or  partly  filled  with  water, 
then  on  shutting  off  the  supply  to  the  tank,  admitting  steam  from  the 
boiler  to  the  upper  part  of  the  tank,  so  as  to  equalize  the  steam-pressure 
in  the  boiler  and  in  the  tank,  and  opening  a  valve  in  a  pipe  leading  from 
the  tank  to  the  boiler,  the  water  will  run  into  the  boiler.  An  apparatus 
of  this  kind  may  be  made  to  work  with  practically  perfect  efficiency  as  a 
boiler-feeder,  as  an  injector  does,  when  the  feed-supply  is  at  ordinary 
atmospheric  temperature,  since  after  the  tank  is  emptied  of  water  and  the 
valves  in  the  pipes  connecting  it  with  the  boiler  are  closed  the  conden- 
sation of  the  steam  remaining  in  the  tank  will  create  a  vacuum  which  will 
lift  a  fresh  supply  of  water  into  the  tank.  The  only  loss  of  energy  in  the 
cycle  of  operations  is  the  radiation  from  the  tank  and  pipes,  which  may 
be  made  very  small  by  proper  covering. 

When  the  feed-water  supply  is  hot,  such  as  the  return  water  from  a 
heating  system,  the  gravity  apparatus  may  be  made  to  work  by  having 
two  receivers,  one  at  a  low  level,  which  receives  the  returns  or  other 
feed-supply,  and  the  other  at  a  point  above  the  boilers.  A  partial  vacuum 
being  created  in  the  upper  tank,  steam-pressure  is  applied  above  the 
water  in  the  lower  tank  by  which  it  is  elevated  into  the  upper.  The 
operation  of  such  a  machine  may  be  made  automatic  by  suitable  arrange- 
ment of  valves. 

FEED-WATER  HEATERS. 

Percentage  of  Saving  for  Each  Degree  of  Increase  in  Temperature 
of  Feed-water  Heated  by  Waste  Steam. 


Initial 
Temp, 
of 
Feed. 

Steam  Pressure  in  Boiler,  Ibs.  per  sq.  in.  above  Atmosphere. 

Initial 
Temp. 

0 

20 

40 

60 

80 

100 

120 

140 

160 

180 

200 

32° 

.0872 

.0861 

.0855 

.0851 

.0847 

.0844 

.0841 

.0839 

.0837 

.0835 

.0833 

32° 

40 

.0878 

.0867 

.0861 

.0856 

.0853 

.0850 

.0847 

.0845 

.0843 

.0841 

.0839 

40 

50 

.0886 

.0875 

.0868 

.0864 

.0860 

.0857 

.0854 

.0852 

.0850 

.0848 

.0846 

50 

60 

.0894 

.0883 

.0876 

.0872 

.0867 

.0864 

.0862 

.0859 

.0856 

.0855 

.0853 

60 

70 

0902 

.0890 

.0884 

.0879 

.0875 

.0872 

.0869 

.0867 

.0864 

.0862 

.0860 

70 

80 

.0910 

.0898 

.0891 

.0887 

.0883 

.0879 

.0877 

.0874 

.0872 

.0870 

.0868 

60 

90 

.0919 

0907 

.0900 

.0895 

.0888 

0887 

.0884 

.0883 

.0879 

.0877 

.0875 

90 

100 

.0927 

.0915 

.0908 

.0903 

.0899 

.0895 

.0892 

.0890 

.0887 

.0885 

.0883 

100 

110 

.0936 

.0923 

.0916 

.0911 

.0907 

.0903 

.0900 

.0898 

.0895 

.0893 

.0891 

110 

120 

.0945 

.0932 

.0925 

.0919 

.0915 

.0911 

.0908 

.0906 

.0903 

.0901 

.0899 

120 

130 

.0954 

0941 

.0934 

.0928 

.0924 

.0920 

.0917 

.0914 

.0912 

.0909 

.0907 

130 

140 

.0963 

.0950 

.0943 

.0937 

.0932 

.0929 

.0925 

.0923 

.0920 

.0918 

.0916 

140 

150 

.0973 

.0959 

.0951 

0946 

.0941 

.0937 

.0934 

.0931 

.0929 

.0926 

.0924 

150 

160 

.0982 

.0968 

.0961 

0955 

.0950 

.0946 

.0943 

.0940 

.0937 

.0935 

.0933 

160 

170 

0992 

.0978 

.0970 

.0964 

.0959 

.0955 

.0952 

.0949 

.0946 

.0944 

.0941 

170 

180 

.1002 

.0988 

.0981 

.0973 

.0969 

.0965 

.0961 

.0958 

.0955 

.0953 

.0951 

180 

190 

.1012 

.0998 

.0989 

.0983 

.0978 

.0974 

.0971 

.0968 

.0964 

.0962 

.0960 

190 

200 

.1022 

.1008 

.0999 

0993 

0988 

.0984 

.0980 

.0977 

.0974 

.0972 

.0969 

200 

210 

.1033 

.1018 

.1009 

.1003 

.0998 

.0994 

.0990 

.0987 

.0984 

.0981 

.0979 

210 

220 

.1029 

.1019 

.1013 

.1008 

.1004 

.1000 

.0997 

.0994 

.0991 

.0989 

220 

230 

.1039 

.1031 

.1024 

.1018 

.1012 

.1010 

.1007 

.1003 

.1001 

.0999 

230 

240 

.1050 

.1041 

.1034 

.1029 

.1024 

.1020 

.1017 

.1014 

.1011 

.1009 

240 

250 

.1062 

.1052 

.1045 

.1040 

.1035 

.1031 

.1027 

.1025 

.1022 

.1019 

250 

An  approximate  rule  for  the  conditions  of  ordinary  practice  is  that  a 
saving  of  1%  is  made  by  each  increase  of  11°  in  the  temperature  of  the 
feed-water.  This  corresponds  to  0.0909%  per  degree. 

The  calculation  of  saving  is  made  as  follows:  Boiler-pressure,  100  Ibs. 
gauge;  total  heat  in  steam  above  32°  =  1185  B.T.U.  Feed-water,  original 
temperature  60?,  final  temperature  209°  F.  Increase  in  heat-units,  150. 


FEED-WATER  HEATERS.  939 

Heat-units  above  32°  in  feed- water  of  original  temperature =28.  Heat- 
units  in  steam  above  that  in  cold  feed-water,  1185  —  28  =  1157.  Saving 
by  the  feed-water  heater  =  150/1157  =  12.96%.  The  same  result  is 
obtained  by  the  use  of  the  table.  Increase  in  temperature  150°  X 
tabular  figure  0.0864  =  12.96%.  Let  total  heat  of  1  Ib.  of  steam  at  the 
boiler-pressure  =  H '•  total  heat  of  1  Ib.  of  feed-water  before  entering  the 
heater  =  hi,  and  after  passing  through  the  heater  =  fo;  then  the  saving 

made  by  the  heater  is  ^  _  ^  • 

Strains  Caused  by  Cold  Feed-water.  —  A  calculation  is  made  In 
The  Locomotive  of  March,  1893,  of  the  possible  strains  caused  in  the  sec- 
tion of  the  shell  of  a  boiler  by  cooling  it  by  the  injection  of  cold  feed- 
water.  Assuming  the  plate  to  be  cooled  200°  F.,  and  the  coefficient  of 
expansion  of  steel  to  be  0.0000067  per  degree,  a  strip  10  in.  long  would 
contract  0.013  in.,  if  it  were  free  to  contract.  To  resist  this  contraction, 
assuming  that  the  strip  is  firmly  held  at  the  ends  and  that  the  modulus 
of  elasticity  is  29,000,000,  would  require  a  force  of  37,700  Ibs.  per  sq.  in. 
Of  course  this  amount  of  .strain  cannot  actually  take  place,  since  the  strip 
is  not  firmly  held  at  the  ends,  but  is  allowed  to  contract  to  some  extent 
by  the  elasticity  of  the  surrounding  metal.  But,  says  The  Locomotive, 
we  may  feel  pretty  confident  that  in  the  case  considered  a  longitudinal 
strain  of  somewhere  in  the  neighborhood  of  8,000  or  10,000  Ibs.  per  sq.  in. 
may  be  produced  by  the  feed- water  striking  directly  upon  the  plates; 
and  this,  in  addition  to  the  normal  strain  produced  by  the  steam-pressure, 
is  quite  enough  to'  tax  the  girth-seams  beyond  their  elastic  limit,  if  the 
feed-pipe  discharges  anywhere  near  them.  Hence  it  is  not  surprising  that 
the  girth-seams  develop  leaks  and  cracks  in  99  cases  out  of  every  100  in 
which  the  feed  discharges  directly  upon  the  fire-sheets. 

Capacity  of  Feed-water  Heaters.  (W.  R.  Billings,  Eng.  Rec., 
Feb.,  1898.)  —  Closed  feed-water  heaters  are  seldom  provided  with 
sufficient  surface  to  raise  the  feed  temperature  to  more  than  200°.  The 
rate  of  heat  transmission  may  be  measured  by  the  number  of  British 
thermal  units  which  pass  through  a  square  foot  of  tubular  surface  in  one 
hour  for  each  degree  of  difference  in  temperature  between  the  water  and 
the  steam.  One  set  of  experiments  gave  results  as  below: 


Difference  between 
final  temperatures 
of  water  and 
steam 


5°  F 67  B.T.U. 


6° 

8° 
11° 
15° 

18° 


79 

89 

.114 

,  129 

.139 


Transmitted  in  one 
hour  by  each  sq.  ft. 
of  surface  for  each 
degree  of  average 
difference  in  temper- 
atures. 


Even  with  the  rate  of  transmission  as  low  as  67  B.T.U.  the  water  was 
still  5°  from  the  temperature  of  the  steam.  At  what  rate  would  the  heat 
have  been  transmitted  if  the  water  could  have  been  brought  to  within 
2°  of  the  temperature  of  the  steam,  or  to  210°  when  the  steam  is  at  212°? 

For  commercial  purposes  feed-water  heaters  are  given  a  H.P.  rating 
which  allows  about  one-third  of  a  square  foot  of  surface  per  H.P.  —  a 
boiler  H.P.  being  30  Ibs.  of  water  per  hour.  If  the  figures  given  in  the 
table  above  are  accepted  as  substantially  correct,  a  heater  which  is  to 
raise  3000  Ibs.  of  water  per  hour  from  60°  to  207°,  using  exhaust  steam 
at  212°  as  a  heating  medium,  should  have  nearly  84  sq.  ft.  of  heating 
surface  or  nearly  a  square  foot  of  surface  per  H.P.  That  feed-water 
heaters  do  not  carry  this  amount  of  heating  surface  is  well  known. 

Calculation  of  Surface  of  Heaters  and  Condensers.  —  (H.  L.  Hep- 
burn, Power,  April,  1902.)  Let  W  =  Ibs.  of  water  per  hour;  A  =  area  of 
surface  in  sq.  ft.;  Ts  =  temperature. of  the  steam;  /  =  initial  tempera- 
ture of  the  water;  F  =  final  temperature  of  the  water;  S  =  Ibs.  of  steam 
per  hour;  H  =  B.T.U.  above  32°  F.  in  1  Ib.  of  steam;  N  =  B.T.U.  in 
L  Ib.  of  condensed  steam;  U  =  B.T.U.  transmitted  per  sq.  ft.  per  hr.  per 
deg.  of  mean  difference  of  temperature  between  the  steam  and  the  water. 

Then        A  U  =  W  loge  ^   ~  p ,  for  heaters. 


H  —  N  Ts  —  I 

A  U  M  S  -= j-  x  logg  -^ = ,  for  condensers. 

r   —  L  2s  ""•  f 


940 


THE  STEAM-BOILER, 


The  value  of  U  varies  widely  according  to  the  condition  of  the  surface 
whether  clean  or  coated  with  grease  or  scale,  and  also  with  the  velocity 
of  the  water  over  the  surfaces.  Values  of  300  to  350  have  been  obtained 
in  experiments  with  corrugated  copper  tubes,  but  ordinary  heaters  give 
much  lower  values.  From  the  experiments  of  Loring  and  Emery  on  the 
U.  S.  S.  Dallas,  Mr.  Hepburn  finds  U  =  192.  Using  this  value  he  finds 
the  number  of  square  feet  of  heating  surface  required  per  1000  Ibs.  of 
feed-water  per  hour  to  be  as  follows,  the  temperature  of  the  entering 
water  being  60°  F. 


Steam  Temperature,  212°. 

Steam  25  in.  Vacuum. 

F 

S 

F 

S 

F 

S 

F 

S 

194 
196 
198 
200 
202 

11.11 
11.73 
12.44 
13.20 
14.17 

204 
206 
208 
210 
212 

15.34 

16.85 
18.93 
22.52 
Infinite 

90 
95 
100 
105 
110 

2.38 
3.03 
3.76 
4.62 
5.65 

115 
120 
125 
130 
133 

6.78 
8.60 
11.15 
16.25 
Infinite 

F  =  final  temperature  of  feed-water,  S  =  sq.  ft.  of  surface.  From  this 
table  it  is  seen  that  if  30  Ibs,  of  water  per  hour  is  taken  to  equal  1  H.P. 
and  a  feed-water  heater  is  made  with  1/3  sq.  ft.  per  H.P.,  it  may  be  ex- 
pected to  heat  the  feed-water  from  60°  to  something  less  than  194°,  or  ii 
made  with  1/2  sq.  ft.  per  H.P.  it  may  heat  the  water  to  204°  F. 

For  a  further  discussion  of  this  subject,  see  Heat,  pages  587  to  591. 

Proportions  of  Open  Type  Feed-water  Heaters.  —  C.  L.  Hubbard 
(Practical  Engineer,  Jan.  1,  1909)  gives  the  following: 

Exhaust  heaters  should  be  proportioned  according  to  the  quality  of 
the  water  to  be  used,  the  size  being  increased  with  the  amount  of  mud 
or  scale-producing  properties  which  the  water  contains  regardless  of  the 
quantity  of  water  to  be  heated.  The  general  proportions  of  an  open 
heater  will  depend  somewhat  upon  the  arrangement  of  the  trays  or  pans, 
but  an  approximation  of  the  size  of  shell  for  a  cylindrical  heater  is  as 
follows:  A  =  H  -4-  aL;  L  =  H  •*•  a  A ;  in  which  A  =--  sectional  area  of  shell 
in  sq.  ft.;  L  =  length  of  shell  in  linear  ft.;  H  =  total  weight  of  water  to 
be  heated  per  hour  divided  by  the  weight  of  steam  used  per  horse-power 
per  hour  by  the  engine;  a  —  2.15  for  very  muddy  water,  6.0  for  slightly 
muddy  water,  and  8.0  for  clear  water. 

The  pan  or  tray  surface  varies  according  to  the  quality  of  the  water, 
both  as  regards  the  amount  of  mud  and  the  scale-making  ingredients. 
The  surface  in  square  feet  for  each  1000  Ibs.  of  water  heated  per  hour 
may  be  taken  as  follows,  for  the  vertical  and  horizontal  types  respectively: 

Very  bad  water 8.5  and  9 . 1 

Medium  muddy  water 6      and  6.5 

Clear  and  little  scale 2      and  2 . 2 

The  space  between  the  pans  is  made  not  less  than  0.1  the  width  for 
rectangular  and  0.25  the  diameter  for  round  pans.  Under  ordinary 
circumstances  it  is  not  cust9mary  to  use  more  than  six  pans  in  a  tier, 
in  order  to  obtain  a  low  velocity  over  each  pan.  The  size  of  the  storage 
or  settling  chamber  in  the  horizontal  type  varies  from  0.25  to  0.4  of  the 
volume  of  the  shell,  depending  on  the  quality  of  the  water;  0.33  is  about 
the  average.  In  the  case  of  vertical  heaters,  this  varies  from  0.4  to  0.6 
of  the  volume  of  the  shell.  Filters  occupy  from  10  to  15%  of  the  volume 
of  the  shell  in  the  horizontal  type  and  from  15  to  20%  in  the  vertical. 

Open  versus  Closed  Feed-water  Heaters.  (W.  E.  Harrington,  St. 
Rwy.  Jour.,  July  22,  1905.)  —  There  still  exists  some  difference  of  opinion 
as  to  the  relative  desirability  of  open  or  closed  type  of  feed-water  heater, 
but  the  degree  of  perfection  which  the  open  heater  has  attained  has  elimi- 
nated formerly  objectionable  features.  The  chief  objection  which  attended 
the  early  use  of  the  open  heater,  namely,  that  the  oil  from  the  exhaust 
steam  was  carried  into  the  boiler,  did  much  to  discourage  its  more  general 
adoption.  This  objection  does  not  hold  good  against  the  better  designs 
of  open  heaters  now  on  the  market.  There  are  thousands  of  installations 
in  which  the  open  heater  is  now  being  used  where  no  difficulty  is  experi- 
enced from  the  contamination  of  the  feed-water  by  oil.  The  perfection  of 
oil  separators  for  use  in  the  exhaust  steam  connection  to  the  heater  has 
rendered  this  possible. 


STEAM  SEPARATORS. 


941 


STEAM  SEPARATORS. 

If  moist  steam  flowing  at  a  high  velocity  in  a  pipe  has  its  direction 
suddenly  changed,  the  particles  of  water  are  by  their  momentum  pro- 
jected in  their  original  direction  against  the  bend  in  the  pipe  or  wall  of 
the  chamber  in  which  the  change  of  direction  takes  place.  By  making 
proper  provision  for  drawing  off  the  water  thus  separated  the  steam  may 
be  dried  to  a  greater  or  less  extent.  For  long  steam-pipes  a  large  drum 
should  be  provided  near  the  engine  for  trapping  the  water  condensed  in 
the  pipe.  A  drum  3  ft.  diameter,  15  ft.  high,  has  given  good  results  in 
separating  the  water  of  condensation  of  a  steam-pipe  10  in.  diameter 
and  800  ft.  long. 

Efficiency  of  Steam  Separators. — Prof.  R.  C.  Carpenter,  in  1891, 
made  a  series  of  tests  of  six  steam  separators,  furnishing  them  with 
steam  containing  different  percentages  of  moisture,  and  testing  the 
quality  of  steam  before  entering  and  after  passing  the  separator.  A 
condensed  table  of  the  principal  results  is  given  below. 


Make  of 
Separator. 

Test  with  Steam  of  about  10% 
of  Moisture. 

Tests  with  Varying  Moisture. 

Quality 
of  Steam 
before. 

Quality 
of  Steam 
after. 

Efficiency, 
per  cent. 

Quality  of 
Steam 
before. 

Quality  of 
Steam  after. 

Av'ge 
Effi- 
ciency. 

B 
A 
D 
C 
E 
F 

87.0% 
90.1 
89.6 
90.6 
88.4 
88.9 

98.8% 
•98.0 
95.8 
93.7 
90.2 
92.1 

90.8 
80.0 
59.6 
33.0 
15.5 
28.8 

66.1  to  97.5% 
51.9  "  98 
72.2  "  96.1 
67.1   "  96.8 
68.6  "  98.1 
70.4  "  97.7 

97.8  to  99% 
97.9       99.1 
95.5       98.2 
.93.7       98.4 
79.3       98.5 
84.1       97.9 

87.6 
76.4 
71.7 
63.4 
36.9 
28.4 

Conclusions  from  the  tests  were:  1.  That  no  relation  existed  between 
the  volume  of  the  several  separators  and  their  efficiency.  2.  No  marked 
decrease  in  pressure  was  shown  by  any  of  the  separators,  the  most  being 
1.7  Ibs.  in  E.  3.  Although  changed  direction,  reduced  velocity,  and  per- 
haps centrifugal  force  are  necessary  for  good  separation,  still  some  means 
must  be  provided  to  lead  the  water  out  of  the  current  of  the  steam.  The 
high  efficiency  obtained  from  B  and  A  was  largely  due  to  this  feature.  In 
B  the  interior  surfaces  are  corrugated  and  thus  catch  the  water  thrown 
out  of  the  steam  and  readily  lead  it  to  the  bottom.  In  A,  as  so  on  as  the 
water  falls  or  is  precipitated  from  the  steam,  it  comes  in  contact  with  the 
perforated  diaphragm  through  which  it  runs  into  the  space  below,  where 
it  is  not  subjected  to  the  action  of  the  steam.  Experiments  made  by 
Prof.  Carpenter  on  a  "Stratton"  separator  in  1894  showed  that>the 
moisture  in  the  steam  leaving  the  separator  was  less  than  1%  when  that 
in  the  steam  supplied  ranged  from  6%  to  21%. 

Experiments  by  Prof.  G.  F.  Gebhardt  (Power,  May  11,  1909)  on  six 
separators  of  different  makes  led  to  the  following  conclusions:  (1)  The 
efficiency  of  separation  decreases  as  the  velocity  of  the  steam  increases. 
(2)  The  efficiency  increases  as  the  percentage  of  moisture  in  the  enter- 
ing steam  increases.  (3)  The  drop  in  pressure  increases  rapidly  with  the 
increase  in  velocity.  The  six  separators  are  described  as  follows: 

U:  2-in.  vertical;  no  baffles;  current  reversed  once. 

V:  4-in.  horizontal  with  single  baffle  plate  of  the  fluted  type;  current 
reversed  once. 

W:  4-in.  vertical  with  two  baffle  plates  of  the  smooth  type;  current 
reversed  once. 

X:  3-in.  horizontal f  several  fluted  baffle  plates;  no  reversal  of  current. 

Y:  6-in.  vertical;  centrifugal  type;  current  reversed  once. 

Z:  3-in.  horizontal;  current  reversed  twice;  steam  impinges  on  hori- 
zontal fluted  baffle  during  reversal. 

The  efficiency  is  defined  as  the  ratio  of  the  water  removed  from  the 
steam  by  the  separator  to  the  water  injected  into  the  dry  steam  for  the 
purpose  of  the  test.  With  steam  at  100  Ibs.  pressure  containing  10% 
water,  the  efficiencies,  taken  from  plotted  curves,  were  as  follows: 

U    V   W   X   Y    Z 

At  2000  ft.  per  min 64   69   86   88   79   66 

At  3000  ft.  per  min 37   45   80   60   61   48 


942  THE  STEAM-BOILER. 

DETERMINATION   OF   THE    MOISTURE    IN    STEAM— STEAM 
CALORIMETERS. 

In  all  boiler-tests  it  is  important  to  ascertain  the  quality  of  the  steam, 
i.e.,  1st,  whether  the  steam  is  "saturated"  or  contains  the  quantity  of 
heat  due  to  the  pressure  according  to  standard  experiments;  2d,  whether 
the  quantity  of  heat  is  deficient,  so  that  the  steam  is  wet;  and  3d,  whether 
the  heat  is  in  excess  and  the  steam  superheated.  The  best  method  of 
ascertaining  the  quality  of  the  steam  is  undoubtedly  that  employed  by  a 
committee  which  tested  the  boilers  at  the  American  Institute  Exhibition 
of  1871-2,  of  which  Prof.  Thurston  was  chairman,  i.e.,  condensing  all  the 
water  evaporated  by  the  boiler  by  means  of  a  surface  condenser,  weighing 
the  condensing  water,  and  taking  its  temperature  as  it  enters  ana  as  it 
leaves  the  condenser;  but  this  plan  cannot  always  be  adopted. 

A  substitute  for  this  method  is  the  barrel  calorimeter,  which  with  careful 
operation  and  fairly  accurate  instruments  may  generally  be  relied  on  to 
give  results  within  two  per  cent  of  accuracy  (that  is,  a  sample  of  steam 
which  gives  the  apparent  result  of  2%  of  moisture  may  contain  anywhere 
between  0  and  4%).  This  calorimeter  is  described  as  follows:  A  sample 
of  the  steam  is  taken  by  inserting  a  perforated  l/2-inch  pipe  into  and 
through  the  main  pipe  near  the  boiler,  and  led  by  a  hose,  thoroughly 
felted,  to  a  barrel,  holding  preferably  400  Ibs.  of  water,  which  is  set  upon 
a  platform  scale  and  provided  with  a  cock  or  valve  for  allowing  the  water 
to  flow  to  waste,  and  with  a  small  propeller  for  stirring  the  water. 

To  operate  the  calorimeter  the  barrel  is  filled  with  water,  the  weight 
and  temperature  ascertained,  steam  blown  through  the  hose  outside  the 
barrel  until  the  pipe  is  thoroughly  warmed,  when  the  hose  is  suddenly 
thrust  into  the  water,  and  the  propeller  operated  until  the  temperature 
of  the  water  is  increased  to  the  desired  point,  say  about  110°  usually. 
The  hose  is  then  withdrawn  quickly,  the  temperature  noted,  and  the 
weight  again  taken. 

An  error  of  1/10  of  a  pound  in  weighing  the  condensed  steam,  or  an 
error  of  1/2  degree  in  the  temperature,  will  cause  an  error  of  over  1  %  in 
the  calculated  percentage  of  moisture.  See  Trans.  A .  S.  M.  E.,  vi,  293. 

The  calculation  of  the  percentage  of  moisture  is  made  as  below ; 


Q  =  quality  of  the  steam,  dry  saturated  steam  being  unity. 
H  =  total  heat  of  1  Ib.  of  steam  at  the  observed  pressure. 
T  =  total  heat  of  1  Ib.  of  water  at  the  temperature  of  steam  of  the 

observed  pressure. 

h   =  total  heat  of  1  Ib.  of  condensing  water,  original. 
hi  =  total  heat  of  1  Ib.  of  condensing  water,  final. 
W  =  weight  of  condensing  water,  corrected  for  water-equivalent  of 

the  apparatus. 

w  =  weight  of  the  steam  condensed. 
Percentage  of  moisture  =  1  —  Q. 

If  Q  is  greater  than  unity,  the  steam  is  superheated,  and  the  degrees  of 
superheating  =  2.0833  (H  -  T)  (Q  -  1). 

Difficulty  of  Obtaining  a  Correct  Sample.  —  Experiments  by  Prof. 
D.  S.  Jacobus  (Trans.  A.  S.  M.  E.,  xvi,  1017),  show  that  it  is  practically 
impossible  to  obtain  a  true  average  sample  of  the  steam  flowing  in  a  pipe. 
For  accurate  determinations  all  the  steam  made  by  the  boiler  should  be 
passed  through  a  separator,  the  water  separated  should  be  weighed  a-nd 
a  calorimeter  test  made  of  the  steam  just  after  it  has  passed  the  separator. 
Coil  Calorimeters.  —  Instead  of  the  open  barrel  in  which  the  steam 
is  condensed,  a  coil  acting  as  a  surface-condenser  may  be  used,  which  is 
placed  in  the  barrel,  the  water  in  coil  and  barrel  being  weighed  separately. 
For  a  description  of  an  apparatus  of  this  kind  designed  by  the  author, 
which  he  has  found  to  give  results  with  a  probable  error  not  exceeding 
1/2  per  cent  of  moisture,  see  Trans.  A.  S.  M.  E.,  vi,  294.  This  calorimeter 
may  be  used  continuously,  if  desired,  instead  of  intermittently.  In  this 
case  a  continuous  flow  of  condensing  water  into  and  out  of  the  barrel 
must  be  established,  and  the  temperature  of  inflow  and  outflow  and  of 
tne  condensed  steam  read  at  short  intervals  of  time 


DETEKMINATION  OF  THE  MOISTUBE  IN  STEAM.        943 


Throttling  Calorimeter.  —  For  percentages  of  moisture  not  exceed- 
ing 3  per  cent  the  throttling  calorimeter  is  most  useful  and  convenient 
and  remarkably  accurate.  In  this  instrument  the  steam  which  reaches 
it  in  a  i/2-inch  pipe  is  throttled  by  an  orifice  1/J6  inch  diameter;  opening 
into  a  chamber  which  has  an  outlet  to  the  atmosphere.  The  steam  in 
this  chamber  has  its  pressure  reduced  nearly  or  quite  to  the  pressure  of  the 
atmosphere,  but  the  total  heat  in  the  steam  before  throttling  causes  the 
steam  in  the  chamber  to  be  superheated  more  or  less  according  to  whether 
the  steam  before  throttling  was  dry  or  contained  moisture.  The  only 
observations  required  are  those  of  the  temperature  and  pressure  of  the 
steam  on  each  side  of  the  orifice. 

The  author's  formula  for  reducing  the  observations  of  the  throttling 
calorimeter  is  as  follows  (Experiments  on  Throttling  Calorimeters,  Am. 

Mach.,  Aug.  4,  1892):    w  =  100  XH^h~  ^  (T  ~  Q,   in  which  w  = 

percentage  of  moisture  in  the  steam;  H  =  total  heat,  and  L= latent 
heat  of  steam  in  the  main  pipe ;  h  =  total  heat  due  the  pressure  in 
the  discharge  side  of  the  calorimeter,  =  1150.4  at  atmospheric  pressure; 
K  =  specific  heat  of  superheated  steam ;  T  =  temperature  of  the 
throttled  and  superheated  steam  in  the  calorimeter;  t  =  temperature  due 
to  the  pressure  in  the  calorimeter,  =  212°  at  atmospheric  pressure. 

Taking  K  at  0.46  and  the  pressure  in  the  discharge  side  of  the  calo- 
rimeter as  atmospheric  pressure,  the  formula  becomes 


=  100  X 


H-  1150.4  -  0.46  (T  -  212°) 


From  this  formula  the  following  table  is  calculated: 
MOISTURE  IN  STEAM — DETERMINATIONS  BY  THROTTLING  CALORIMETER. 


Degree  of 
Super- 
heating 
T  -  212°. 

Gauge-pressures. 

5    |    10  |   20  |«  30  |   40  |   50 

60 

70 

75 

80   |   85   |   90 

Per  Cent  of  Moisture  in  Steam. 

0° 

10° 
20° 
30° 
40° 
50° 
60° 
70° 

Dif.  p.  deg..  . 

0.51 
0.01 

0.90 
0.39 

1.54 
1.02 
0.51 
0.00 

2.06 
1.54 
1.02 
0.50 

2.50 
1.97 
1.45 
0.92 
0.39 

2.90 
2.36 
1.83 
1.30 
0.77 
0.24 

3.24 
2.71 
2.17 
1.64 
1.10 
0.57 
0.03 

3.56 
3.02 
2.48 
1.94 
1.40 
0.87 
0.33 

3.71 
3.17 
2.63 
2.09 
1.55 
1.01 
0.47 

3.86 
3.32 
2.77 
2.23 
1.69 
1.15 
0.60 
0.06 

3.99 
3.45 
2.90 
2.35 
1.80 
1.26 
0.72 
0.17 

.0544 

4.13 
3.58 
3.03 
2.49 
1.94 
1.40 
0.85 
0.31 

.0503 

.0507 

.0515 

.0521 

.0526 

.0531 

.0535 

.0539 

.0541 

.0542 

.0546 

Degree  of 
Super- 
heating 
T  -  212°. 

Gauge-pressures. 

100  |  110  |  120 

130 

140 

150 

160 

170 

180  j  190  |  200  I  250 

Per  Cent  of  Moisture  in  Steam. 

0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 
80° 
90° 
100° 
110° 

4.39 
3.84 
3.29 
2.74 
2.19 
1.64 
1.09 
0.55 
0.00 

4.63 
4.08 
3.52 
2.97 
2.42 
1.87 
1.32 
0.77 
0.22 

4.85 
4.29 
3.74 
3.18 
2.63 
2.08 
1.52 
0.97 
0.42 

5.08 
4.52 
3.96 
3.41 
2.85 
2.29 
1.74 
1.18 
0.63 
0.07 

5.29 
4.73 
4.17 
3.61 
3.05 
2.49 
1.93 
1.38 
0.82 
0.26 

5.49 
4.93 
4.37 
3.80 
3.24 
2.68 
2.12 
1.56 
1.00 
0.44 

5.68 
5.12 
4.56 
3.99 
3.43 
2.87 
2.30 
1.74 
1.18 
0.61 
0.05 

5.87 
5.30 
4.74 
4.17 
3.61 
3.04 
2.48 
1.91 
1.34 
0.78 
0.21 

6.05 
5.48 
4.91 
4.34 
3.78 
3.21 
2.64 
2.07 
1.50 
0.94 
0.37 

6.22 
5.65 
5.08 
4.51 
3.94 
3.37 
2.80 
2.23 
1.66 
1.09 
0.52 

6.39 
5.82 
5.25 
4.67 
4.10 
3.53 
2.96 
2.38 
1.81 
1.24 
0.67 
0.10 

7.16 
6.58 
6.00 
5.41 
4.83 
4.25 
3.67 
3.09 
2.51 
1.93 
1.34 
0.76 
.0581 

Dif.  p.  deg.  .  . 

.0549 

.0551 

.0554 

.0556 

.0559 

.0561 

.0564 

.0566 

.0568 

.0570 

.0572 

Separating  Calorimeters. — For  percentages  of  moisture  beyond  the 
range  of  the  throttling  calorimeter  the  separating  calorimeter  is  used, 


944  CHIMNEYS. 

which  is  simply  a  steam  separator  on  a  small  scale.  An  improved  form 
of  this  calorimeter  is  described  by  Prof.  Carpenter  in  Power,  Feb.,  1893. 

For  fuller  information  on  various  kinds  of  calorimeters,  see  papers  by 
Prof.  Peabody,  Prof.  Carpenter,  and  Mr.  Barrus  in  Trans.  A.  S<  M.  E.t 
vols.  x,  xi,  xii,  1889  to  1891;  Appendix  to  Report  of  Com.  on  Boiler  Tests, 
A.  S.  M.  E.,  vol.  vi,  1884;  Circular  of  Schaeffer  &  Budenberg,  N.  Y., 
"Calorimeters,  Throttling  and  Separating." 

Identification  of  Dry  Steam  by  Appearance  of  a  Jet.  • —  Prof. 
Denton  (Trans.  A.  S.  M.  E.,  vol.  x)  found  that  jets  of  steam  show  un- 
mistakable change  of  appearance  to  the  eye  when  steam  varies  less  than 
1%  from  the  condition  of  saturation  in  the  direction  of  either  wetness 
or  of  superheating. 

If  a  jet  of  steam  flow  from  a  boiler  into  the  atmosphere  under  circum- 
stances such  that  very  little  loss  of  heat  occurs  through  radiation,  etc., 
and  the  jet  be  transparent  close  to  the  orifice,  or  be  even  a  grayish-white 
color,  the  steam  may  be  assumed  to  be  so  nearly  dry  that  no  portable 
condensing  calorimeter  will  be  capable  of  measuring  the  amount  of  water 
in  the  steam.  If  the  jet  be  strongly  white,  the  amount  of  water  may  be 
roughly  judged  up  to  about  2%,  but  beyond  this  only  a  calorimeter  can 
determine  -the  exact  amount  of  moisture. 

A  common  brase  pet-cock  may  be  used  as  an  orifice,  but  it  should,  if 
possible,  be  set  into  the  steam-drum  of  the  boiler  and  never  be  placed 
further  away  from  the  latter  than  4  feet,  and  then  only  when  the  inter- 
mediate reservoir  or  pipe  is  well  covered. 

Usual  Amount  of  Moisture  in  Steam  Escaping  from  a  Boiler.  — 
In  the  common  forms  of  horizontal  tubular  land  boilers  and  water-tube 
boilers  with  ample  horizontal  drums,  and  supplied  with  water  free  from 
substances  likely  to  cause  foaming,  the  moisture  in  the  steam  does  not 
generally  exceed  2%  unless  the  boiler  is  overdriven  or  the  water-level  is 
carried  too  high. 

CHIMNEYS. 

Chimney  Draught  Theory.  —  The  commonly  accepted  theory  of 
chimney  draught,  based  on  Peclet's  and  Rankine's  hypotheses  (Rankine, 
S  E.),  is  discussed  by  Prof.  De  Volson  Wood,  Trans.  A,  S.  M.  E.,  vol.  xi. 

Peclet  represented  the  law  of  draught  by  the  formula 


in  which  h  is  the  "head,"  defined  as  such  a  height  of  hot  gases  as,  if  added 
to  the  column  of  gases  in  the  chimney,  would  produce  the 
same  pressure  at  the  furnace  as  a  column  of  outside  air,  of 
the  same  area  of  base,  and  a  height  equal  to  that  of  the 
chimney; 

u  is  the  required  velocity  of  gases  in  the  chimney; 
G  a  constant  to  represent  the  resistance  to  the  passage  of  air 

through  the  coal; 

I  the  length  of  the  flues  and  chimney; 
m  the  mean  hydraulic  depth  or  the  area  of  a  cross-section  divided 

by  the  perimeter; 

/  a  constant  depending  upon  the  nature  of  the  surfaces  over 
which  the  gases  pass,  whether  smooth,  or  sooty  and  rough. 
Rankine's  formula  (Steam  Engine,  p.  288),.  derived  by  giving  certain 
values  to  the  constants  (so-called)  in  Peclet's  formula,  is 

^(  0.0807^  ,  x 

u=^  -  (H-H-Hs-i)* 

lo(o.084  ) 


in  which  H  •-  t^Wrfthe  —eyjn^eet^ 

T,=  absolute  temperature  of  the  gases  in  the  chimney; 
T2=  absolute  temperature  of  the  external  air. 


CHIMNEYS. 


945 


Prof.  Wood  derives  from  this  a  still  more  complex  formula  which  gives 
the  height  of  chimney  required  for  burning  a  given  quantity  of  coal  per 
second,  and  from  it  he  calculates  the  following  table,  showing  the  height 
of  chimney  required  to  burn  respectively  24,  20,  and  16  Ibs.  of  coal  per 
square  foot  of  grate  per  hour,  for  the  several  temperatures  of  the  chimney 
gases  given. 


Outside  Air. 

_L 

520° 
absolute  or 
I59°F. 

Chimney  Gas. 

Coal  per  sq.  ft.  of  grate  per  hour,  Ibs. 

Ti 
Absolute. 

Temp. 
Fahr. 

24 

20 

16 

Height  H,  feet. 

700 
800 
1000 
1100 
1200 
1400 
1600 
2000 

239 
339 
539 
639 
739 
939 
1139 
1539 

250.9 
172.4 
149.1 
148.8 
152.0     - 
159.9 
168.8 
206.5 

157.6 
115.8 
100.0 
98.9 
100.9 
105.7 
111.0 
132.2 

67.8 
55.7 
48.7 
48.2 
49.1 
51.2 
53.5 
63.0 

Rankine's  formula  gives  a  maximum  draught  when  ^  =  21/12*2,  or 
622°  F.,  when  the  outside  temperature  is  60°.  Prof.  Wood  says:  "This 
result  is  not  a  fixed  value,  but  departures  from  theory  in  practice  do  not 
affect  the  result  largely.  There  is,  then,  in  a  properly  constructed  chimney 
properly  working,  a  temperature  giving  a  maximum  draught,*  and  that 
temperature  is  not  far  from  the  value  given  by  Rankine,  although  in 
special  cases  it  may  be  50°  or  75°  more  or  less." 

All  attempts  to  base  a  practical  formula  for  chimneys  upon  the  theoret- 
ical formula  of  Peclet  and  Rankine  have  failed  on  account  of  the  impos- 
sibility of  assigning  correct  values  to  the  so-called  "constants"  G  and  /. 
(See  trans.  A.  S.  M.  E.,  xi,  984.) 

Force  or  Intensity  of  Draught.  —  The  force  of  the  draught  is  equal 
to  the  difference  between  the  weight  of  the  column  of  hot  gases  inside  of 
the  chimney  and  the  weight  of  a  column  of  the  external  air  of  the  same 
height.  It  is  measured  by  a  draught-gauge,  usually  a  U-tube  partly 
filled  with  water,  one  leg  connected  by  a  pipe  to  the  interior  of  the  flue, 
and  the  other  open  to  the  external  air. 

If  D  is  the  density  of  the  air  outside,  d  the  density  of  the  hot  gas  inside, 

in  Ibs.  per  cubic  foot,  h  the  height  of  the  chimney  in  feet,  and  0.192  the 

factor  for  converting  pressure  in  Ibs.  per  sq.  ft.  into  inches  of  water  column, 

then  the  formula  for  the  force  of  draught  expressed  in  inches  of  water  is, 

F  =  0.192/1  (D  -  d). 

The  density  varies  with  the  absolute  temperature  (see  Rankine). 

d=  ^0.084;  D  =  0.0807  —  , 

Tl  T2 

where  TO  is  the  absolute  temperature  at  32°  F.,  =  493,  TI  the  absolute 
temperature  of  the  chimney  gases  and  r2  that  of  the  external  air.  Sub- 
stituting these  values  the  formula  for  force  of  draught  becomes 

,.0.192  ft 


-  il^l)  -ft  (7-M  -  ™-5). 

T2  Tl      J  \    T2  Tl    / 


*  Much  confusion  to  students  of  the  theory  of  chimneys  has  resulted 
from  their  understanding  the  words  maximum  draught  to  mean  maxi- 
mum intensity  or  pressure  of  draught,  as  measured  by  a  draught-gauge. 
It  here  means  maximum  quantity  or  weight  of  gases  passed  up  the 
chimney.  The  maximum  intensity  is  found  only  with  maximum  tem- 
perature, but  after  the  temperature'  reaches  about  622°  F.  the  density  of 
the  gas  decreases  more  rapidly  than  its  velocity  increases,  so  that  the 
weight  is  a  maximum  about  622°  F,,  as  shown  by  Rankine.  —  W.  K. 


946 


CHIMNEYS. 


To  find  the  maximum  intensity  of  draught  for  any  given  chimney,  the 
heated  column  being  600°  F.,  arid  the  external  air  60°,  multiply  the  height 
above  grate  in  feet  by  0.0073,  and  the  product  is  the  draught  in  inches 
of  water. 

Height  of  Water  Column  Due  to  Unbalanced  Pressure  in  Chimney 
10O  Feet  High.'    (The  Locomotive,  1884.) 


'So! 

Temperature  of  the  External  Air  —  Barometer,  14.7  Ibs.  per  sq.  in. 

|l| 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

H     o 

200 

0.453 

0.419 

0.384 

0.353 

0.321 

0.292 

0.263 

0.234 

0.209 

0.182 

0.157 

220 

.488 

.453 

.419 

.388 

.355 

.326 

.298 

.269 

.244 

.217 

.192 

240 

.520 

.488 

.451 

.421 

.388 

.359 

.330 

.301 

.276 

.250 

.225 

260 

.555. 

.528 

.484 

.453 

.420 

.392 

.363 

.334 

.309 

.282 

.257 

280 

.584 

.549 

.515 

.482 

.451 

.422 

.394 

.365 

.340 

.313 

.288 

300 

.611 

.576 

.541 

.511 

.478 

.449 

.420 

.392 

.367 

.340 

.315 

320 

.637 

.603 

.568 

.538 

.505 

.476 

.447 

.419 

.394 

.367 

.342 

340 

.662 

.638 

.593 

.563 

.530 

.501 

.472 

.443 

.419 

.392 

.367 

360 

.687 

.653 

.618 

.588 

.555 

.526 

.497 

.468 

.444 

.417 

.392 

380 

.710 

.676 

.641 

.611 

.578 

.549 

.520 

.492 

.467 

.440 

.415 

400 

.732 

.697 

.662 

.632 

.598 

.570 

.541 

.513 

.488 

.461 

.436 

420 

.753 

.718 

.684 

.653 

.620' 

.591 

.563 

.534 

.509 

.482 

.457 

440 

.774 

.739 

.705 

.674 

.641 

.612 

.584 

.555 

.530 

.503 

.478 

460 

793 

.758 

.724 

694 

660 

.632 

603 

574 

549 

522 

497 

480 

.810 

.776 

.741 

.710 

.678 

.649 

.620 

.591 

.566 

.540 

.515 

500 

.829 

.791 

.760 

.730 

.697 

.669 

.639 

.610 

.586 

.559 

.534 

For  any  other  height  of  chimney  than  100  ft.  the  height  of  water  column 
is  found  by  simple  proportion,  the  height  of  water  column  being  directly 
proportioned  to  the  height  of  chimney. 

The  calculations  have  been  made  for  a  chimney  100  ft.  high,  with 
various  temperatures  outside  and  inside  of  the  flue,  and  on  the  supposition 
that  the  temperature  of  the  chimney  is  uniform  from  top  to  bottom. 
This  is  the  basis  on  which  all  calculations  respecting  the  draught-power 
of  chimneys  have  been  made  by  Rankine  and  other  writers,  but  it  is  very 
far  from  the  truth  in  most  cases.  The  difference  will  be  shown  by  com- 
paring the  reading  of  the  draught-gauge  with  the  table  given.  In  one 
case  a  chimney  122  ft.  high  showed  a  temperature  at  the  base  of  320°, 
and  at  the  top  of  230°. 

Box,  in  his  "Treatise  on  Heat,"  gives  the  following  table: 

DRAUGHT  POWERS  OF  CHIMNEYS,  ETC.,  WITH  THE  INTERNAL  AIR  AT  552° 
AND  THE  EXTERNAL  AIR  AT  62°,  AND  WITH  THE  DAMPER  NEARLY 
CLOSED. 


sf- 

-u.S  ^ 

Theoretical  Velocity 
in  feet  per  second. 

It 

di 

Theoretical  Velocity 
in  feet  per  second. 

til 

|s£ 

Cold  Air 

Hot  Air 

111 

3'~  03 

Cold  Air 

Hot  Air 

wg 

O  8*0 

Entering. 

at  Exit. 

*6 

PH 

Entering. 

at  Exit. 

10 

0.073 

17.8 

35.6 

80 

0.585 

50.6 

101.2 

20 

0.146 

25.3 

50.6 

90 

0.657 

53.7 

107.4 

30 

0.219 

31.0 

62.0 

100 

0.730 

56.5 

113.0 

40 

0.292 

35.7 

71.4 

120 

0.876 

62.0 

124.0 

50 

0.365 

40.0 

80.0 

150 

1.095 

69.3 

138.6 

60 

0.438 

43.8 

87.6 

175 

1.277 

74.3 

149.6 

70 

0.511 

47.3      . 

94.6 

200 

1.460 

80.0 

160.0 

CHIMNEYS. 


947 


Bate  of  Combustion  Due  to  Height  of  Chimney.  —  Trowbridge's 
"Heat  and  Heat  Engines"  gives  the  following  figures  for  the  heights  of 
chimney  for  producing  certain  rates  of  combustion  per  sq.  ft.  of  grate. 
They  may  be  approximately  true  for  anthracite  in  moderate  and  large 
sizes,  but  greater  heights  than  are  given  in  the  table  are  needed  to  secure 
the  given  rates  of  combustion  with  small  sizes  of  anthracite,  and  for 
bituminous  coal  smaller  heights  will  suffice  if  the  coal  is  reasonably  free 
from  ash  —  5%  or  less. 


Height, 
feet. 


I 


Lbs.  of 
Coal  per 
Sq.  Ft.  of 

Grate. 


7.5 
8.5 
9.5 
10.5 


Height, 
feet. 


45 
50 
55 
60 
65 


Lbs.  of 
Coal  per 
Sq.  Ft. of 

Grate. 


Height, 
feet. 


12.4 
13.1 
13.8 
14.5 
15.1 


70 
75 
80 
85 
90 


Lbs.  of 
Coal  per 
Sq.  Ft.  of 

Grate. 


15.8 
16.4 
16.9 
17.4 
18.0 


Height, 
feet. 


Lbs.  of 
Coal  per 
Sq.  Ft.  of 

Grate. 


95 
100 
105 
110 


18.5 
19.0 
19.5 
20.0 


W.  D.  Ennis  (Eng.  Mag.,  Nov.,  1907),  gives  the  following  as  the  force 
of  draught  required  for  burning  No.  1  buckwheat  coal: 

Draught,  in.  of  water 0.3     0.45     0.7     1.0 

Lbs.  coal  per  sq.  ft.  grate  per  hour 10       15         20       25 

Thurston's  rule  for  rate  of  combustion  effected  by  a  giyen  height  of 
chimney  (Trans.  A.  S.  M.  E.,  xi,  991)  is:  Subtract  1  from  twice  the  square 
root  of  the  height,  and  the  result  is  the  rate  of  combustion  in  pounds  per 
square  foot  of  grate  per  hour,  for  anthracite.  Or  rate  =  2  V/i  —  1,  in 
which  h  is  the  height  in  feet.  This  rule  gives  the  following: 

h  =    50         60         70       80         90    100    110     125     150     175     200 
- 1  =  13.14  14.49  15.73  16.8917.97  19  19.9721.3623.4925.4527.28 

The  results  agree  closely  with  Trowbridge's  table  given  above.  In 
practice  the  high  rates  of  combustion  for  high  chimneys  given  by  the 
formula  are  not  generally  obtained,  for  the  reason  that  with  high  chimneys 
there  are  usually  long  horizontal  flues,  serving  many  boilers,  and  the 
friction  and  the  interference  of  currents  from  the  several  boilers  are  apt  to 
cause  the  intensity  of  draught  in  the  branch  flues  leading  to  each  boiler 
to  be  much  less  than  that  at  the  base  of  the  chimney.  The  draught  of 
each  boiler  is  also  usually  restricted  by  a  damper  and  by  bends  in  the  gas- 
passages.  In  a  battery  of  several  boilers  connected  to  a  chimney  150  ft. 
high,  the  author  found  a  draught  of  3/4-inch  water-column  at  the  boiler 
nearest  the  chimney,  and  only  i/4-inch  at  the  boiler  farthest  away.  The 
first  boiler  was  wasting  fuel  from  too  high  temperature  of  the  chimney- 
gases,  900°,  having  too  large  a  grate-surface  for  the  draught,  and  the  last 
boiler  was  working  below  its  rated  capacity  and  with  poor  economy,  on 
account  of  insufficient  draught. 

The  effect  of  changing  the  length  of  the  flue  leading  into  a  chimney 
60  ft.  high  and  2  ft.  9  in.  square  is  given  in  the  following  table,  from  Box 
on  "Heat": 


Length  of  Flue  in 
feet. 

Horse-power. 

Length  of  Flue  in 
feet. 

Horse-power. 

50 
100 
200 
400 
600 

107.6 
100.0 
85.3 
70.8 
•      62.5 

800 
1,000 
1,500 
2,000 
3,000 

56.1 
51.4 
43.1. 
38.2 
31.7 

and 


The  temperature  of  the  gases  in  this  chimney  was  assume^  to  be  552°  F., 
id  that  or  the  atmosphere  62°. 


948  SIZE    OF   CHIMNEYS. 

High  Chimneys  not  Necessary.  —  Chimneys  above  150  ft.  in  height  I 
are  very  costly,  and  their  increased  cost  is  rarely  justified  by  increased  effi- 
ciency.   In  recent  practice  it  has  become  somewhat  common  to  build  two 
or  more  smaller  chimneys  instead  of  one  large  one.     A  notable  example  i 
is  the  Spreckels  Sugar  Refinery  in  Philadelphia,  where  three  separate 
chimneys  are  used  for  one  boiler-plant  of  7500  H.P.     The  three  chimneys 
are  said  to  have  cost  several  thousand  dollars  less  than  a  single  chimney 
of  their  combined  capacity  would  have  cost.     Very  tall  chimneys  have 
been  characterized  by  one  writer  as  "monuments  to  the  folly  of  their 
builders." 

Heights  of  Chimney  required  for  Different  Fuels.  —  The  minimum 
height  necessary  varies  with  the  fuel,  wood  requiring  the  least,  then  good 
bituminous  coal,  and  fine  sizes  of  anthracite  the  greatest.  It  also  varies 
with  the  character  of  the  boiler  —  the  smaller  and  more  circuitous  the 
gas-passages  the  higher  the  stack  required ;  also  with  the  number  of  boilers, 
a  single  boiler  requiring  less  height  than  several  that  discharge  into  a 
horizontal  flue.  No  general  rule  can  be  given. 

C.  L.  Hubbard  (Am.  Electrician,  Mar.,  1904)  says:  The  following  heights 
have  been  found  to  give  good  results  in  plants  of  moderate  size,  and  to 
produce  sufficient  draught  to  force  the  boilers  from  20  to  30  per  cent 
above  their  rating: 

With  free-burning  bituminous  coal,  75  feet;  with  anthracite  of  medium 
and  large  size,  100  feet:  with  slow-burning  bituminous  coal,  120  feet;  with 
anthracite  pea  coal,  130  feet;  with  anthracite  buckwheat  coal,  150  feet. 
For  plants  of  700  or  800  horse-power  and  over,  the  chimney  should  not 
be  less  than  150  feet  high  regardless  of  the  kind  of  coal  to  be  used. 

SIZE    OF   CHIMNEYS. 

The  formula  given  below,  and  the  table  calculated  therefrom  for  chim- 
neys up  to  96  in.  diameter  and  200  ft.  high,  were  first  published  by  the 
author  in  1884  (Trans.  A.  S.  M.  E.,  vi,  81).  They  have  met  with  much 
approval  since  that  date  by  engineers  who  have  used  them,  and  have  been 
frequently  published  in  boiler-makers'  catalogues  and  elsewhere.  The 
table  is  now  extended  to  cover  chimneys  up  to  12  ft.  diameter  and  300  ft. 
high.  The  sizes  corresponding  to  the  given  commercial  horse-powers 
are  believed  to  be  ample  for  all  cases  in  which  the  draught  areas  through 
the  boiler-flues  and  connections  are  sufficient,  say  not  less  than  20% 
greater  than  the  area  of  the  chimney,  and  in  which  the  draught  between 
the  boilers  and  chimney  is  not  checked  by  long  horizontal  passages  and 
right-angled  bends. 

Note  that  the  figures  in  the  table  correspond  to  a  coal  consumption  of  5  Ibs. 
of  coal  per  horse-power  per  hour.  This  liberal  allowance  is  made  to  cover 
the  contingencies  of  poor  coal  being  used,  and  of  the  boilers  being  driven 
beyond  their  rated  capacity.  In  large  plants,  with  economical  boilers 
and  engines,  good  fuel  and  other  favorable  conditions,  which  will  reduce 
the  maximum  rate  of  coal  consumption  at  any  one  time  to  less  than  5  it 
per  H.P.  per  hour,  the  figures  in  the  table  may  be  multiplied  by  the  ratio 
of  5  to  the  maximum  expected  coal  consumption  per  H.P.  per  hour. 
Thus,  with  conditions  which  make  the  maximum  coal  consumption  only 
2.5  Ibs.  per  hour,  the  chimney  300  ft.  high  X  12  ft.  diameter  should  be 
sufficient  for  6155  X  2  =  12,310  horse-power.  The  formula  is  based  on 
the  following  data: 

1.  The  draught  power  of  the  chimney  varies  as  the  square  root  of  the 
height. 

2.  The  retarding  of  the  ascending  gases  by  friction  may  be  considered 
as  equivalent  to  a  diminution  of  the  area  of  the  chimney,  or  to  a  lining  or 
the  chimney  by  a  layer  of  gas  which  has  no  velocity.     The  thickness  of 
this  lining  is  assumed  to  be  2  inches  for  all  chimneys,  or  the  diminution 
of  area  equal  to  the  perimeter  X  2  inches  (neglecting  the  overlapping  ol 
the  corners  of  the  lining).     Let  D  =  diameter  in  feet,  A  =  area,  and  E  = 
effective  area  in  square  feet: 

8  D  2    /"~~ 

For  square  chimneys,  E  =»  D8  — jy  "*  A  ~~  3      Am 

For  round  chimneys,   E  =  ^  (l)2  -  ^j\  =  A  -  0.591  ^A. 


i  CHIMNEYS.  949 

For  simplifying  calculations,  the  coefficient  of  VA  may  be  taken  as  0.6 
for  both  square  and  round  chimneys,  and  the  formula  becomes 

E  -  A  -  0.6  VI. 

3    The  power  varies  directly  as  this  effective  area  E. 

4.  A  chimney  should  be  proportioned  so  as  to  be  capable  of  giving 
sufficient  draught  to  cause  the  boiler  to  develop  much  more  than  its  rated 
power,  in  case  of  emergencies,  or  to  cause  the  combustion  of  5  Ibs.  of  fuel 
per  rated  horse-power  of  boiler  per  hour. 

5  The  power  of  the  chimney  varying  directly  as  the  effective  area,  /</, 
and'  as  the  square  root  of  the  height,  H,  the  formula  for  horse-power  of 
boiler  for  a  given  size  of  chimney  will  take  the  form  H.P.  =  CE  Vf/,  in 
which  C  is  a  constant,  the  average  value  of  which,  obtained  by  plotting 
the  results  obtained  from  numerous  examples  in  practice,  the  author 
finds  to  be  3.33. 

The  formula  for  horse-power  then  is 

H.P.  =  3.33  E  V#,  or  H.P.  =  3.33  (A  -  0.6  VI)  Vff. 

If  the  horse-power  of  boiler  is  given,  to  find  the  size  of  chimney,  the 
height  being  assumed, 

E  =  0.3  H.P.  ^  V//;  =  A  -  0.6  VI. 

For  round  chimneys,  diameter  of  chimney  =  diam.  of  E  -H  4". 
For  square  chimneys,  side  of  chimney  =  V#  +  4". 

•     If  effective  area  E  is  taken  in  square  feet,  the  diameter  m  inches  is  d  = 
13  54  V#  +  4",  and  the  side  of  a  square  chimney  in  inches  is  s  = 

»«V 

If 


'  /03HP\ 

f  horse-power  is  given  and  area  assumed,  the  height  //  =  ^  —  ^  -  J 


An  approximate  formula  for  chimneys  above  1000  H.P.  is  H.P.  = 
2.5  D2  V//.  This  gives  the  H.P.  somewhat  greater  than  the  figures  in 
the  table. 

In  proportioning  chimneys  the  height  should  first  be  assumed,  with  due 
consideration  of  the  heights  of  surrounding  buildings  or  hills  near  to  the 
proposed  chimney,  the  length  of  horizontal  flues,  the  character  of  coal  to 
be  used,  etc.  ;  then  the  diameter  required  for  the  assumed  height  and  horse- 
power is  calculated  by  the  formula  or  taken  from  the  table. 

For  Height  of  Chimneys  see  pages  947  and  948.  No  formula  for 
height  can  be  given  which  will  be  satisfactory  for  different  classes  of  coal, 
kinds  and  amounts  of  ash,  styles  of  grate-bars,  etc.  A  formula  in  "  Ingeni- 
eurs  Taschenbuch,"  translated  into  English  measures,  is  ft  =  0.216  R2  +  6d. 
h=  height  in  ft;  R  =  Ibs.  coal  burned  per  sq.  ft.  of  grate  per  hour;  d  = 
diam.  in  ft.  This  formula  gives  an  insufficient  height  for  small  sizes  of 
anthracite,  and  a  height  greater  than  is  necessary  for  free-burning  bitu- 
minous coal  low  in  ash. 

The  Protection  of  Tall  Chimney-shafts  from  Lightning.  —  C. 
Molyneux  and  J.  M.  Wood  (Industries,  March  28,  1890)  recommend  for 
tall  chimneys  the  use  of  a  coronal  or  heavy  band  at  the  top  of  the  chimney, 
with  copper  points  1  ft.  in  height  at  intervals  of  2  ft.  throughout  the  cir- 
cumference. The  points  should  be  gilded  to  prevent  oxidation.  The 
most  approved  form  of  conductor  is  a  copper  tape  about  8/4  in.  by  1/8  in. 
thick,  weighing  6  ozs.  per  ft.  If  iron  is  used  it  should  weigh  not  less  than 
21/4  Ibs.  per  ft.  There  must  be  no  insulation,  and  the  copper  tape  should 
be  fastened  to  the  chimney  with  holdfasts  of  the  same  material,  to  pre- 
vent voltaic  action.  An  allowance  for  expansion  and  contraction  should 
be  made,  say  1  in.  in  40  ft.  Slight  bends  in  the  tape,  not  too  abrupt, 
answer  the  purpose.  For  an  earth  terminal  a  plate  of  metal  at  least  3  ft. 
sq.  and  Vie  in.  thick  should  be  buried  as  deep  as  possible  in  a  damp  spot. 
The  plate  should  be  of  the  same  metal  as  the  conductor,  to  which  it 
should  be  soldered.  The  best  earth  terminal  is  water,  and  when  a  deep 
well  or  other  large  body  of  water  is  at  hand,  the  conductor  should  be 
carried  down  into  it.  Right-angled  bends  in  the  conductor  should  b« 
avoided.  No  bend  in  it  should  be  over  30°. 


950 


SIZE   OF   CHIMNEYS. 


IM3I  + 


•  •    -o      o^°S°i      —  <N°,C 

•  •     -oo       ommoo       —  TI^C 


—         OO 


u-\OO        OOmO—        Ot^ 

O^T»'         —  O  —  r^s         t^CM 

—    ^ 


\Oxo  —  r 
—  (Nm  c 
f^  ^-msi 


,  .^i  — —      rnr^r^c 
OorvjTj-       vo  oo  —  «  . 

~- .  —  _  <VJ  (Nl 


oo<2      p^^2r 


OvOOOT 

vi  r^  m  —         •    • 


f>t>«.OOaO 
O  •<»•  o  r^ 

o  '  —  '  (S  CM 


r^.        \O  ^  -—  OO 
m      i>»  -n-  m  o 

sd      !>.'  O  f^  so 


r^sO        O^  —  m  fA 
t^  r>.      —  o  N_  oo 

O  >o  (N  oo 
T^mm 


O  f*i  OO 

Sf^r^ 


O  OO  in  rA 

t>.r>iOv-- 


.2  w 
Q.2 


oo  —  -T  r^      OfAv 
«—  tM«s(s      tnc^ 


ofsoo-^-      oorsjoo      -«rorgT 
pt>.r>oQ 


CHIMNEYS. 


951 


Velocity  of  Gas  in  Chimneys.  —  The  velocity  of  the  heated  gas,  Teased 
on  the  chimney  porportions  given  in  the  table,  may  be  found  from  the 
following  data: 

A  =  Lb.  coal  per  hour  =  boiler  horsepower  X  5  ; 
B  =  Lb.  gas  per  lb.  coal  =  say  20  Ib.;' 

C  =  Cu.  ft.  of  gas  per  Ib.  Of  gas  =  12.4  X  (temp,  of  gas  +  460)  -f-  492; 

•-=  25  cu.  ft.  for  532°  F.  =  500  cu.  ft. 
per  lb.  coal; 

A  X  B  X  C1 
V  =  Velocity  of  gas.  feet  per  second  = 


chimney  area  (JqTftT 

Based  on  a  gas  temperature  of  532°  F.,  5  lb.  coal  per  hour  per  rated 
H.P.,  and  20  lb.  gas  per  lb.  of  coal  we  have 

Cu.  ft.  gas  per  second  per  lb.  of  coal  per  hour  =  0.1389; 

Cu.  ft.  gas  per  second  per  boiler  horse-power    =  0.6944; 
and  the  velocities  in  feet  per  second,  based  on  the  effective  areas  given 
in  the  table,  corresponding  to  different  heights  of  chimney  are: 


Height,  ft.  . 
Velocity,  ft. 
per  sec..  . 

50 

16  3 

60 
17  8 

70 
19  4 

80 
?0  7 

90 

77  0 

100 

73  7 

110 
74  3 

125 
75  Q 

150 

78  3 

175 
30  6 

200 
3?  7 

225 
34  7 

250 
36  6 

300 
40  1 

Chimney  Table  for  Oil  Fuel.  (C.  R.  Weymouth,  Journal  A.  S.  M.E.t 
October,  1912.) — Conditions:  Sea  level;  atmospheric  temperature, 
80°  F. ;  draught  at  chimney  side  of  damper,  0.30  in. ;  excess  air,  less  than 
50  % ,  assumed  50  %  for  calculations  of  efficiency  and  chimney  dimensions ; 
temperature  of  gases  leaving  chimney,  500°  F. ;  boiler  efficiency,  73  % ; 
actual  boiler  horse-power,  150  per  cent  of  rated;  lb.  gas  per  actual 
boiler  H.P.,54.6;  height  of  chimney  above  pointpf  draught  measurement. 
12  ft.  less  than  tabulated  height.  When  building  conditions  permit 
select  chimneys  of  least  height  in  table  for  minimum  cost  of  chimney. 
Chimney  capacities  stated  are  maximum  for  continuous  load  equally 
divided  on  all  boilers.  For  large  plants  or  swinging  load,  reduce  capacity 
10  to  20%.  Breeching  20%  in  excess  of  stack  area;  length  not  exceed- 
ing 10  chimney  diameters. 

Size  of  Chimneys  for  Oil  Fuel 


Height  in  Feet  above  Boiler  Room  Floor. 

Area, 
Sq.  ft. 

80    |    90    |    100  |    110 

120  |    130 

140 

150  |    160 

Actual  Horse-power  =  1  50  Per  cent  of  Rated. 

.„ 

1.77 

63 

75 

84         91 

96 

101 

104 

108 

110 

24 

3.14 

123 

148 

166|       180 

191 

201 

208 

215 

221 

30 

4.91 

206 

249 

280       304 

324 

340 

354 

366 

377 

36 

7.07 

312 

379 

427       466 

497 

523 

545 

564 

58! 

42 

9.62 

443 

539 

•     609|      665 

711 

749 

782 

810 

830 

48 

12.57 

599 

729 

827 

904 

967 

1,020 

1,070 

1,110 

1,145 

54 

15.90 

779 

951 

1,080 

1,180 

1,270 

1,340 

1,400 

1,460 

1,500 

60 

19.64 

985 

1,200 

1,370 

1,500 

1,610 

1,710 

1,790 

1,860 

1,920 

66 

23.76 

1,220 

1,490 

1,700 

1,860 

2,000 

2,120 

2,220 

2,310 

2,390 

72 

28.27 

1,470 

1,810 

2,060 

2,260 

2,430 

2,580 

2.710 

2,820 

2,910 

78 

33.18 

1,750 

2,150 

2,460 

2,710 

2,910 

3,000 

3.250 

3,380 

3,500 

84 

38.49 

2,060 

2,530 

2,900 

3,190 

3,440 

3,650 

3,840 

4,000 

4,150 

96 

50.27 

2,750 

3,390 

3,880 

4,290 

4,630 

4,920 

5,180 

5,400 

5,610 

108 

63.62 

3,550 

4,380 

5,020 

5,550 

6,000 

6,390 

6,730 

7,030 

7,300 

120 

78.54 

4.440 

5,490 

6,310 

6,990 

7.560 

8,060 

8,490 

8,890 

9,240 

132 

95.03 

5,450 

6,740|  7,760 

8,600 

9,310 

9,930 

10,500 

11,000:11.400 

144 

113.1 

6,550 

8,1  20i  9,350 

10.400 

11,200 

12,000 

12,700 

13.300!  13.800 

156 

132.7 

7,760 

9,630  11,100 

12,  300  113,400 

14,300 

15,100 

15.800  16,500 

168 

153.9 

9,060 

I1,300;i3,000 

14.400  15.700 

16,800 

17,700 

18,600  19.400 

180 

176.7 

10.500 

13,000  15.100 

16,700  18,200 

19,50020,600 

21,60022,600 

In  using  the  above  table  it  must  be  noted  that  the  conditions  upon 
which  it  is  based  are  aU  fairly  good.    With  unskilful  handling  of  oil 

952  CHIMNEYS. 

fuel  the  excess  air  is  apt  to  be  much  more  than  50%  and  the  efficiency 
much  less  than  73%.  In  that  case  the  actual  horse-power  developed 
by  a  given  size  of  chimney  may  be  much  less  than  the  figure  given  in 
the  table 

DRAUGHT  OF  CHIMNEYS  100  FT.  HIGH — OIL  FUEL. 

Temp. "of  gases  enter- 
ing chimney 300         400         500         600         700 

Net  chimney  draught,  inches  of  water 
f    60°  F.     0.367     0.460     0.534     0.593     0.642 

Temp,  of  outside  air.  \    80  0.325     0.417     0.490     0.550     0.599 

[100  0.284     0.377     0.451     0.510     0.559 

.  The  net  draught  is  the  theoretical  draught  due  to  the  difference  in 
weight  of  atmospheric  air  and  chimney  gases  at  the  stated  temperatures, 
multiplied  by  a  coefficient,  0.95,  for  temperature  drop  in  stack,  and  by 
6/6  as  a  correction  for  friction.  For  high  altitudes  the  draught  varies 
directly  as  the  normal  barometer.  For  other  heights  than  100  feet 
(measured  above  the  level  of  entrance  of  the  gases)  the  draught  varies 
as  the  square  root  of  the  height. 

Chimneys  with  Forced  Draught.— When  natural,  or  chimney,  draught 
only  is  used,  the  function  of  the  chimney  is  1,  to  produce  such  a  dif- 
ference of  pressure,  or  intensity  of  draught,  between  the  bottom  of  the 
chimney  and  the  ash-pit  as  will  cause  the  flow  of  the  required  quantity 
of  air  through  the  grate-bars  and  the  fuel  bed,  and  the  flow  of  the  gases 
of  combustion  through  the  gas  passages,  the  damper  and  the  breeching; 
ai^d  2,  to  convey  the  gases  above  the  tops  of  surrounding  buildings  and 
to  such  a  height  that  they  will  not  become  a  nuisance.  With  forced 
draught  the  blower  produces  the  difference  of  pressure,  and  the  only  use 
of  the  chimney  is  that  of  conveying  the  gases  to  a  place  where  they  will 
cause  no  inconvenience;  and  in  that  case  the  height  of  the  chimney  may 
")e  much  less  than  that  of  a  chimney  for  natural  draught. 

With  oil  or  natural  gas  for  fuel,  the  resistance  of  the  grates  and  of  the 
Aiiel  bed  is  eliminated,  and  the  height  of  the  chimney  may  be  much  less 
than  that  of  one  desired  for  coal  firing.  When  oil  or  gas  is  substituted 
for  coal,  and  the  chimney  is  a  high  one,  it  may  be  necessary  to  restrict 
its  draught  power  by  a  damper  or  other  means,  in  order  to  prevent  its 
creating  too  greata  negative  pressure  in  the  furnace  and  thereby  too  great 
an  admission  of  air,  which  will  cause  a  decrease  in  efficiency. 

The  Largest  Chimney  in  the  World,  in  1908,  is  that  of  the  Montana 
smelter,  at  Great  Falls,  Mont.  Height  506  ft.  Internal  diam.  at  top 
50  ft.  Built  of  Custodis  radial  brick.  Designed  to  remove  4,000,000  cu. 
ft.  of  gases  per  minute  at  an  average  temperature  of  600°  F.  Erected  on 
top  of  a  hill  500  ft.  above  the  city,  and  246  ft.  above  the  floor  of  the  fur- 
naces, which  are  about  2000  ft.  distant.  Designed  for  a  wind  pressure  of 
331/3  IDS.  per  sq.  ft.  of  projected  area;  bearing  pressure  limited  to  21  tons 
per  sq.  ft.  at  any  section.  Foundation:  111  ft.  max.  diam.,  221/2  ft.  deep; 
bearing  pressure  on  bottom  (shale  rock)  4.83  tons  per  sq.  ft.;  octagonal 
outside,  103  ft.  across  at  bottom,  81  ft.  at  top.  with  inner  circular  open- 
ing 47  ft.- diam.  at  bottom,  64  ft.  at  top;  made  of  1  cement,  3  sand,  5 
crushed  slag.  Four  flue  openings  in  the  base,  each  15  ft.  wide,  36  ft. 
high.  The  stack  proper  consists  of  an  octagonal  base,  46  ft.  in  height, 
which  has  a  taper  of  8%,  and  above  this  a  circular  barrel,  the  first  180  ft. 
above  the  base  having  a  taper  of  7%,  the  next  100  ft.  of  4%,  and  the 
remaining  180  ft.  to  the  cap  2%. 

The  chimney  wall  varies  from  66  in.  at  the  base  to  181/8  in.  at  the  top 
by  uniform  decrements  of  2  in.  per  section,  excepting  at  the  section  imme- 
diately above  the  top  of  the  base,  where  the  thickness  decreases  from  60  in. 
to  54  in.  The  outside  diameters  of  the  stack  are  781/2  ft.  at  the  base, 
53  ft.  9  in.  at  the  base  of  the  cap;  the  inside  diameters  range  from  661/2  ft. 
at  the  foundation  line  to  50  ft.  at  the  top.  The  chimney  is  lined  with  4- 
inch  acid-proof  brick,  laid  in  sections  carried  on  corbels  from  the  main 
shell.  A  description  of  the  methods  of  design  and  of  erection  of  the 
Great  Falls  chimney  is  given  in  Eng.  Rec.>  Nov.  28,  1908. 


CHIMNEYS. 


Some  Tall  Brick  Chimneys  (1895). 


953 


i 

Outside 
Diameter. 

Capacity  by  the 
Author's 
Formula. 

5 

Pounds 

•9 

g 

H.  P. 

Coal 

I- 

o 

G 
t—  i 

3 

tt 

D, 

per 
Hour. 

1.  Hallsbruekner    Hfltte, 

Saxony                   

460 

15  7' 

33' 

16' 

13  221 

66,105 

2    Townsend's  Glasgow 

454 

32 

3.  Tennant's,  Glasgow  
4.  Dobson    &   Barlow,  Bol- 

435 

13'  6" 

40 

9,795 

48,975 

ton    ling        

367  1/2 

13'  2" 

33'  10" 

8,245 

41,225 

5.  Fall  River  Iron  Co.,  Bos- 

350 

11 

30 

21 

5,558 

27,790 

6.  Clark  Thread  Co.,  New- 

ark N  J  

335 

11 

28'  6" 

14 

5,435 

27,175 

7.  Merrimac    Mills,  Lowell, 

Mass 

282'  9" 

12 

5,980 

29,900 

8.  Washington  Mills,   Law- 

250 

10 

3,839 

19,195 

9.  Amoskeag     Mills,     Man- 
chester N   H 

250 

10 

3,839 

19,195 

10.  Narragansett  E.  L.  Co., 

238 

14 

7,515 

37,575 

1  1  .  Lower  Pacific  Mills,  Law- 

rence Mass 

214 

8 

2,248 

11,240 

12.  Passaic     Print     Works, 

200 

9 

2,771 

13,855 

13.  Edison  Station  Brooklyn, 
Two  each                  .    .    . 

150 

50"  x  120" 

each 

1,541 

7,705 

NOTES  ON  THE  ABOVE  CHIMNEYS.  —  1.  This  chimney  is  situated  near 
Freiberg  at  an  elevation  of  219  ft.  above  that  of  the  foundry  works,  so 
that  its  total  height  above  the  sea  will  be  7113/4ft.  The  furnace-gases 
are  conveyed  across  river  to  the  chimney  on  a  bridge,  through  a  pipe 
3227  ft.  long.  It  is  built  of  brick,  and  cost  about  $40,000.  —  Mfr.  &  Bldr. 

2.  Owing  to  the  fact  that  it  was  struck  by  lightning,  and  somewhat 
damaged,  as  a  precautionary  measure  a  copper  extension  subsequently 
was  added  to  it,  making  its  entire  height  488  feet. 

1,  2,  3,  and  4  were  built  of  these  great  heights  to  remove  deleterious 
gases  from  the  neighborhood,  as  well  as  for  draught  for  boilers. 

5  The  structure  rests  on  a  solid  granite  foundation,  55  X  30  feet,  and 
16  feet  deep.  In  its  construction  there  were  used  1,700,000  bricks, 
2000  tons  of  stone,  2000  barrels  of  mortar,  1000  loads  of  sand,  1000  barrels 
of  Portland  cement,  and  the  estimated  cost  is  $40,000.  It  is  arranged  for 
two  flues,  9  feet  6  inches  by  6  feet,  connecting  with  40  boilers,  which  are 
to  be  run  in  connection  with  four  triple-expansion  engines  of  1350  horse- 
power each. 

6.  It  has  a  uniform  batter  of  2.85  ins.  to  every  10  ft.  Designed  for 
21  boilers  of  200  H.P.  each.  It  is  surmounted  by  a  cast-iron  coping 
which  weighs  six  tons,  and  is  composed  of  32  sections  bolted  together 
by  inside  flanges  so  as  to  present  a  smooth  exterior.  The  foundation 
is  40  ft.  square  and  5  ft.  deep.  Two  qualities  of  brickf  were  used;  the 
outer  portions  were  of  the  first  quality  North  River,  and  the  backing  up 
was  of  good  quality  New  Jersey  brick.  Every  twenty  feet  in  vertical 
measurement  an  iron  ring,  4  ins.  wide  and  3/4  to  1/2  in.  thick,  placed  edge- 
wise, was  built  into  the  walls  about  8  ins.  from  the  outer  circle  As  the 
chimney  starts  from  the  base  it  is  double.  The  outer  wall  is  5  ft.  2  ins. 
in  thickness,  and  inside  of  this  is  a  second  wall  20  ins.  thick  arid  spaced 


954  CHIMNEYS. 

off  about  20  ins.  from  main  wall.  From  the  interior  surface  of  the  main 
wall  eight  buttresses  are  carried,  nearly  touching  this  inner  or  main  flue 
wall  in  order  to  keep  it  in  line  should  it  tend  to  sag.  The  interior  wall, 
starting  with  the  thickness  described,  is  gradually  reduced  until  a  height 
of  about  90  ft.  is  reached,  when  it  is  diminished  to  8  inches.^.  At  165  ft. 
it  ceases,  and  the  rest  of  the  chimney  is  without  lining.  The  total  weight 
of  the  chimney  and  foundation  is  5000  tons.  It  was  completed  in  Sep- 
tember, 1888. 

7.  Connected  to  12  boilers,  with  1200  sq.  ft.  of  grate.     Draught  1 9/i6  ins. 

8.  Connected  to  8  boilers,  6  ft.  8  in.  diam.  X  18  ft.     Grate  448  sq.  ft. 

9.  Connected  to  64  Manning  vertical  boilers,  total  grate  surface  1810 
sq.  ft.     Designed  to  burn  18,000  Hxs.  anthracite  per  hour. 

10.  Designed  for  12,000  H.P.  of  engines;  (compound  condensing). 

11.  Grate-surface  434  square  feet;  H.P.  of  boilers  about  2500. 

13.  Eight  boilers  (water-tube)  each  450  H.P.;  12  engines,  each  300 
H.P.  For  the  first  60  feet  the  exterior  wall  is  28  ins.  thick,  then  24  ins.  for 
20  ft.,  20  ins.  for  30  ft.,  16  ins.  for  20  ft.,  and  12  ins.  for  20  ft.  The  inte- 
rior wall  is  9  ins.  thick  of  fire-brick  for  50  ft.,  and  then  8  ins.  thick  of  red 
brick  for  the  next  30  ft.  Illustrated  in  Iron  Age,  Jan.  2,  1890. 

A  number  of  the  above  chimneys  are  illustrated  in  Power,  Dec.,  1890. 

More  Recent  Brick  Chimneys  (1909).  —  Heller  &  Merz  Co.,  Newark, 
N.  J.  350  ft.  high,  inside  diam.,  8  ft.  Outside  diam.,  top  9  ft.  10 1/4  in., 
bottom  27  ft.  61/2  in.  Outside  taper  5.2  in  100.  Outer  shell  7Vs  in.  at 
the  top,  38  in.  at  the  bottom.  Custodis  radial  brick  laid  in  mortar  of 
1  cement,  2  lime,  5  sand.  The  changes  in  thickness  are  made  by  2-in. 
offsets  on  the  inside  every  20  ft.  Iron  band  3 1/2  X  5/i6  in.,  three  courses 
below  the  top.  Lined  with  4  in.  of  special  brick  to  resist  acids.  The 
lining  is  sectional,  being  carried  on  corbels  projecting  from  the  shell  every 
20  ft.  An  air  space  of  2  ins.  is  left  between  the  lining  and  the  shell. 
The  lining  bricks  are  laid  in  a  mortar  made  of  silicate  of  soda  and  white 
asbestos  wool,  tempered  to  the  consistency  of  fire-clay  mortar.  This 
mortar  is  acid-proof,  and  its  binding  power,  which  is  considerable  in 
comparison  to  that  of  fire-clay  mortar,  is  unaffected  by  temperatures  up 
to  2000°  F.  (Eng.  News,  Feb.  15,  1906.)  Supported  on  324  piles  driven 
60  ft.  to  solid  rock,  and  covering  an  area  45  ft.  square.  Total  cost  $32,000. 
The  standard  Custodis  radial  brick  is  4*/2  in.  thick  and  6 1/2  in.  wide; 
radial  lengths  are  4,  51/2,  7i/s,  85/s  and  105/sins.  The  smallest  size  has 
six  vertical  perforations,  1  in.  square,  and  the  largest  fifteen. 

Eastman  Kodak  Co.,  Rochester,  N.  Y.  Height  366  ft.;  internal  diam. 
at  top  9  ft.  10  ins.,  at  bottom  20  ft.  10 ins.;  outside  diam.,  top  11  ft.,  bottom 
27  ft.  10  ins.  Radial  brick,  with  4-in.  acid-resisting  brick  lining. 

Some  notable  tall  chimneys  built  by  the  Alphonse  Custodis  Chimney 
Construction  Co.  are:  Dolgeville,  N.  Y.,  6  X  175  ft.;  Camden,  N.  J.,  7  X  210 
ft.;  Newark,  N.  J.,  8  X  350  ft.;  Rochester,  N.  Y.,  9  X  366  ft.;  Constable 
Hook,  N.  J.,  10  X  365  ft.;  Providence.  R.  I..  16  X  308  ft.:  Garfield.  Utah. 
30  X  300  ft. ;  Great  Falls  Mont.,  50  X  506  ft. 

Interior  Stack  of  the  Equitable  Building,  New  York  City  (Eng. 
News,  Nov.  12,  1914). — The  stack  is  11  ft.  outside  diam.,  596  ft.  high, 
made  of  steel  plates  5/16  in.  thick.  It  is  supported  on  the.  steelwork  of 
the  building  at  every  other  story.  It  has  a  2-in.  lining  of  J.  &  M. 
Vitribestos,  alternate  layers  of  plain  and  corrugated  asbestos  board 
coated  with  a  supposedly  vitrified  compound.  The  rated  H.P.  of  this 
chimney,  taking  10  ft.  7  in.  as  the  inside  diameter,  is  6710,  equivalent 
to  the  burning  of  33,550  Ib.  of  coal  per  hour. 

Stability  of  Chimneys.  —  Chimneys  must  be  designed  to  resist  the 
maximum  force  of  the  wind  in  the  locality  in  which  they  are  built.  A 
general  rule  for  diameter  of  base  of  brick  chimneys,  approved  by  many 
years  of  practice  in  England  and  the  United  States,  is  to  make  the  diam- 
eter of  the  base  one-tenth  of  the  height.  If  the  chimney  is  square  of 
rectangular,  make  the  diameter  of  the  inscribed  circle  of  the  base  one- 
tenth  of  the  height.  The  "batter"  or  taper  of  a  chimney  should  be 
from  I/in  to  1/4  inch  to  the  foot  on  each  side.  The  brickwork  should  be 
one  brick  (8  or  9  inches)  thick  for  the  first  25  feet  from  the  top,  increasing 
1/2  brick  (4  or  41/2  inches)  for  each  25  feet  from  the  top  downwards, 
the  inside  diameter  exceeds  5  feet,  the  top  length  should  be  11/2  bricks; 
and  if  under  3  teet.  it  may  be  1/2  brick  for  ten  feet.. 

(From  The  Locomotive,  1884  ami  1886.)    For  chimneys  of  four  feet  in 


STABILITY   OF   CHIMNEYS.  955 

diameter  and  one  hundred  feet  high,  and  upwards,  the  best  form  is  cir- 
cular witn  a  straignt  oatter  on  me  outside. 

Chimneys  of  any  considerable  height  are  not  built  up  of  uniform 
thickness  from  top  to  bottom,  nor  with  a  uniformly  varying  thickness  of 
wall,  but  the  wall,  heaviest  of  course  at  the  base,  is  reduced  by  a  series 
of  steps. 

Where  practicable  the  load  on  a  chimney  foundation  should  not  exceed 
two  tons  per  square  foot  in  compact  sand,  gravel,  or  loam.  Where  a 
solid  rock-bottom  is  available  for  foundation,  the  load  may  be  greatly 
increased.  If  the  rock  is  sloping,  all  unsound  portions  should  be  removed, 
and  the  face  dressed  to  a  series  of  horiz9ntal  steps,  so  that  there  shall  IDO 
no  tendency  to  slide  after  the  structure  is  finished. 

All  boiler-chimneys  of  any  C9nsiderable  size  should  consist  of  an  outer 
stack  of  sufficient  strength  to  give  stability  to  the  structure,  and  an  inner 
stack  or  core  independent  of  the  outer  one.  This  core  is  by  many  engineers 
extended  up  to  a  height  of  but  50  or  60  feet  from  the  base  of  the  chimney, 
but  the  better  practice  is  to  run  it  up  the  whole  height  of  the  chimney:  it 
•may  be  stopped  off,  say,  a  couple  of  feet  below  the  top,  and  the  outer  shell 
contracted  to  the  area  of  the  core,  but  the  better  way  is  to  run  it  up  to 
about  8  or  12  inches  of  the  top  and  not  C9ntract  the  outer  shell.  But 
under  no  circumstances  should  the  core  at  its  upper  end  be  built  into  or 
connected  with  the  outer  stack.  This  has  been  done  in  several  instances 
by  bricklayers,  and  the  result  has  been  the  expansion  of  the  inner  core 
which  lifted  the  top  of  the  outer  stack  squarely  up  arid  cracked,  the  brick- 
work. 

For  a  height  of  100  feet  we  would  make  the  outer  shell  in  three  steps,  the 
first  20  feet  high,  16  inches  thick,  the  second  30  feet  high,  12  inches  thick, 
the  third  50  feet  high  and  8  inches  thick.  These  are  the  minimum 
thicknesses  admissible  for  chimneys  of  this  height,  and  the  batter  should 
be  not  less  than  1  in  36  to  give  stability.  The  core  should  also  be  built 
In  three  steps,  each  of  which  may  be  about  one-third  the  height  of  tha 
chimney,  the  lowest  12  inches,  the  middle  8  inches,  and  the  upper  step 
4  inches  thick.  This  will  insure  a  good  sound  core.  The  top  of  a  chimney 
may  be  protected  by  a  cast-iron  cap;  or  perhaps  a  cheaper  and  equally 
good  plan  is  to  lay  the  ornamental  part  in  some  good  cement,  and  plaster 
the  top  with  the  same  material. 

C.  L.  Hubbard  (Am.  Electrician,  Mar.,  1904)  says:  The  following 
approximate  method  may  be  used  for  determining  the  thickness  of  walls. 
If  the  inside  diameter  at  the  tpp  is  less  than  3  ft.  the  walls  may  be  4  ins. 
thick  for  the  first  10  ft.,  and  increased  4  ins.  for  each  25  ft.  downward. 
If  the  inside  diameter  is  more  than  3  ft.  and  less  than  5  ft.,  begin  with  a 
wall  8  ins.  thick,  increasing  4  ins.  for  each  25  ft.  downward.  If  the  diam- 
eter is  over  5  ft.,  begin  with  a  12-in.  wall,  increasing  below  the  first  10  ft. 
as  before.  The  lining  or  core  may  be  4  ins.  thick  for  the  first  20  ft.  from 
the  top,  8  ins.  for  the  next  30  ft.,  12  ins.  for  the  next  40  ft.,  16  ins.  for 
the  next  50  ft.,  and  20  ins.  for  the  next  50  ft.  .Using  this  method  for  an 
outer  wall  200  ft.  high  and  assuming  a  cubic  foot  of  brickwork  to  weigh 
130  Ibs.,  it  gives  a  maximum  pressure  of  8.2  tons  per  sq.  ft.  of  section  at 
the  base;  while  a  lining  190  ft.  high  would  have  a  maximum  pressure  of 
8.6  tons  per  sq.  ft.  The  safe  load  for  brickwork  may  be  taken  at  from 
8  to  10  tons  per  sq.  ft.,  although  the  strength  of  best  pressed  brick  will  run 
much  higher. 

James  B.  Francis,  in  a  report  to  the  Lawrence  Mfg.  Co.  in  1873  (Eng. 
News,  Aug.  28,  1880),  concerning  the  probable  effects  of  wind  on  that 
company's  chimney  as  then  constructed,  says: 

The  stability  of  the  chimney  to  resist  the  force  of  the  wind  depends 
mainly  on  the  weight  of  its  outer  shell,  and  the  width  of  its  base.  The 
cohesion  of  the  mortar  may  add  considerably  to  its  strength;  but  it  is  too 
uncertain  to  be  relied  upon.  The  inner  shell  will  add  a  little  to  the 
stability,  but  it  may  be  cracked  by  the  heat,  and  its  beneficial  effect,  if 
any,  is  too  uncertain  to  be  taken  into  account. 

The  effect  of  the  joint  action  of  the  vertical  pressure  due  to  the  weight 
of  the  chimney,  and  the  horizontal  pressure  due  to  the  force  of  the  wind  is 
to  shift  the  center  of  pressure  at  the  base  of  the  chimney,  from  the  axis 
toward  one  side,  the  extent  of  the  shifting  depending  on  the  relative 
magnitude  of  the  two  forces.  If  the  center  of  pressure  is  brought  too  near 
the  side  of  the  chimney,  it  will  crush  the  brickwork  ou  that  side,  and  the 


955  CHIMNEYS. 

chimney  will  fall.  A  line  drawn  through  the  center  of  pressure,  perpen- 
dicular to  the  direction  of  the  wind,  must  leave  an  area  of  brickwork 
between  it  and  the  side  of  the  chimney,  sufficient  to  support  half  the  weight 
of  the  chimney:  the  other  half  of  the  weight  being  supported  by  the  brick- 
work on  the  windward  side  of  the  line. 

Different  experimenters  on  the  strength  of  brickwork  give  very  different 
results.  Kirkaldy  found  the  weights  which  caused  several  kinds  of 
bricks,  laid  in  hydraulic  lime  mortar  and  in  Roman  and  Portland  cements, 
to  fail  slightly,  to  vary  from  19  to  60  tons  (of  2000  Ibs.)  per  sq.  ft.  If 
we  take  in  this  case  25  tons  per  sq.  ft.  as  the  weight  that  would  cause  it 
to  begin  to  fail,  we  shall  not  err  greatly. 

Rankine,  in  a  paper  printed  in  the  transactions  of  the  Institution  of 
Engineers,  in  Scotland,  for  1867-68,  says:  "It  had  previously  been  ascer- 
tained by  observation  of  the  success  and  failure  of  actual  chimneys,  and 
especially  of  those  which  respectively  stood  and  fell  during  the  violent 
storms  of  1856,  that,  in  order  that  a  round  chimney  may  be  sufficiently 
stable,  its  weight  should  be  such  that  a  pressure  of  wind,  of  about  55  Ibs.  per 
sq.  ft.  of  a  plane  surface,  directly  facing  the  wind,  or  27V2  Ibs.  per  sq.  ft.' 
of  the  plane  projection  of  a  cylindrical  surface,  .  .  .  shall  not  cause  the 
resultant  pressure  at  any  bed-joint  to  deviate  from  the  axis  of  the 
chimney  by  more  than  one-quarter  of  the  outside  diameter  at  that 
joint." 

Steel  Chimneys  are  largely  used,  especially  for  tall  chimneys  of  iron- 
works, from  150  to  300  feet  in  height.  The  advantages  claimed  are: 
greater  strength  and  safety;  smaller  space  required;  smaller  cost,  by 
30  to  50  per  cent,  as  compared  with  brick  chimneys;  avoidance  of  infiltra- 
tion of  air  and  consequent  checking  of  the  draught,  common  in  brick 
chimneys.  They  are  usually  made  cylindrical  in  shape,  with  a  wide  curved 
flare  for  10  to  25  feet  at  the  bottom.  A  heavy  cast-iron  base-plate  is 
provided,  to  which  the  chimney  is  riveted,  and  the  plate  is  secured  to  a 
massive  foundation  by  holding-down  bolts.  No  guys  are  used. 

Design  of  Self-supporting  Steel  Chimneys.  —  John  D.  Adams 
(Eng.  News,  July  20, 1905)  .gives  a  very  full  discussion  of  the  design  of  steel 
chimneys,  from  which  the  following  is  adapted.  The  bell-shaped  bottom 
of  the  chimney  is  assumed  to  occupy  one-seventh  of  the  total  height,  and 
the  point  of  maximum  strain  is  taken  to  be  at  the  top  of  this  bell  portion. 
Let  D  =  diam.  in  inches,  H  =  height  in  feet,  T  =  thickness  in  inches, 
S  =  safe  tensile  stress,  Ibs.  per  sq.  in.  The  general  formula  for  moment 
of  resistance  of  a  hollow  cylinder  is  M  =  1/32  it  (D*-  Z)i4)  S/D.  When 
the  thickness  is  a  small  fraction  of  the  diameter  this  becomes  approxi- 
mately M  =  0.7854  DZTS. 

With  steel  plate  of  60,000  Ibs.  tensile  strength,  riveting  of  0.6  efficiency, 
and  a  factor  of  safety  of  4,  we  have  S  =  9000  pounds  per  sq.  in.,  and  the 
safe  moment  of  resistance  =  7070  DZT. 

The  effect  of  the  wind  upon  a  cylinder  is  equal  to  the  wind  pressure 
multiplied  by  one-half  the  diametral  plane,  and  taking  the  maximum 
wind  pressure  at  50  Ibs.  per  sq.  ft.,  we  get 

Total  wind  pressure  =  50  X  1/12  D  X  1/2  X  */iR  =  25  DH/14. 

The  distance  of  the  center  of  pressure  above  the  top  of  the  bell  por- 
tion =  3/7  H,  multiplied  by  the  total  wind  pressure,  gives  us  the  bend- 
ing moment  due  to  the  wind, 

inch-pounds,  25  DH/14  X  8/7  H  X  12  =  9.184  DH*. 

Equating  the  bending  and  the  resisting  moment  we  have  T  =  0.0013 

With  this  formula  the  maximum  thickness  of  plates  was  calculated 
for  different  sizes  of  chimneys,  as  given  in  the  table  on  p.  957. 

In  t»lie  above  formula,  no  attention  has  been  paid  to  the  weight  of  the 
steel  in  the  stack  above  the  bell  portion,  which  weight  has  a  tendency 
to  decrease  the  tension  on  the  windward  side  and  increase  the  com- 
pression on  the  ieeward  side  of  the  stack.  A  column  of  steel  150  ft. 
high  would  exert  a  pressure  of  approximately  500  Ib.  per  sq.  in.,  which, 
with  steel  of  60,000  Ib.  tensile  strength,  is  less  than  1  %  of  the  ultimate 
strength,  and  may  safely  be  neglected. 

From  the  table'it  appears  that  a  chimney  12  X  120  ft.  requires,  as  far 
as  fracture  by  bending  of  a  tubular  section  is  concerned,  a  thickness  of 
but  little  over  i/g  in.  In  designing  a  stack  of  such  extreme  proportions 


SIZE  OF  CHIMNEYS. 


057 


as  12  X  120  ft.,  there  are  other  factors  besides  bending  to  take  Into  con- 
sideration that  ordinarily  could  be  neglected.  For  instance,  such  a  stack 
should  be  provided  with  stiffening  angles,  or  else  made  heavier,  to  guard 
against  lateral  flattening.  Ordinarily,  however,  the  strength  of  the 
chimney  determined  as  a  tubular  section  will  be  the  prime  factor  in  deter- 
mining the  maximum  thickness  of  plates. 

THICKNESS  OP  BASE-RING  PLATES  OF  SELF-SUPPORTING  STEEL  STACKS. 

For  normal  wind  pressure  of  50  Ibs.  per  sq.  ft.  on  half  the  diametral  plane 

Diameter  of  Stack  in  feet. 


S«l  >  5 

4 

5 

6 

7 

8 

8.5 

9 

9.5 

10 

11 

12 

70 

80 
90 
100 
110 
120 
130 
140 
150 
160 
170 
180 
190 
200 
210 
220 
230 
240 
250 

0.152 
0.198 
0.224 
0.310 
0.375 
0.446 
0.523 
0.607 
0.696 

.133 
.182 
.219 
.271 
328 
.390 
.458 
.531 
.609 
.693 

.106 
.139 
.175 
.217 
.262 
.312 
.366 
.425 
.487 
.555 
.626 
.702 

1  ... 

.116 

.146 
.181 
.218 
.260 
.305 
.354 
.406 
.462 
.522 
'.585 
.652 

-.099 
.125 
.155 
.187 
.223 
.262 
.303 
.348 
.396 
.447 
.501 
.559 
.620 
.682 

.111 
.135 
.164 
.195 
.228 
.265 
.305 
.346 
.391 
.439 
.489 
.542 
.596 
.655 
.717 

.127 
.154 
.183 
.215 
.250 
.286 
.326 
.368 
.413 
.460 
.510 
.562 
.617 
.674 
.734 

.120 
.146 
.173 
.203 
.236 
.271 
.308 
.348 
.390 
.434 
.481 
.531 
.582 
.637 
.693 
.752 

.138 
.164 
.193 
.223 
.257 
.292 
.330 
.370 
.411 
.456 
.503 
.552 
.603 
.657 
.713 

.131 
.156 
.183 
.212 
.244 
.277 
.313 
.351 
.391 
.433 
.478 
.524 
.573 
.624 
.677 

.119 
.142 
.166 
.193 
.222 
.252 
.285 
.319 
.356 
.394 
.434 
.476 
.521 
.567 
.615 

'J30' 
.153 
.180 
.203 
.231 
.261 
.293 
.326 
.361 
.398 
.437 
.477 
.520 
.564 

Foundation.  —  Neglecting  the  increase  of  wind  area  due  to  the  flare 
at  the  base  of  the  chimney,  which  has  but  a  very  small  turning  effect, 
if  all  dimensions  be  taken  in  feet,  we  have 

Total  wind  pressure  =  i/2  D  X  H  X  50  =  25  DH;  lever-arm  =*  l/2  H; 
hence,  turning  moment  =  12.5  DH2. 

Let  d  =  diameter  and  h  =  height  of  foundation.  For  average  con- 
ditions h  =s  0.4  d,  then  volume  of  foundation  =  0.7854  dzh,  and  for 
concrete  at  150  Ibs.  per  cu.  ft.,  weight  of  foundation  =  W  =  0.7854  d*h 
X  150  =  47.124  d>. 

The  stability  of  the  foundation  or  the  tendency  to  resist  overturning 
is  equal  to  the  weight  of  the  foundation  multiplied  by  its  radius  or  1/2  Wd 
= 23.562  d*.  Applying  a  factor  of  safety  of  21/2,  which  is  indicated  by 
current  practice,  gives  safe  stability  =  9.425  d4.  Equating  this  to  the 
overturning  moment  we  obtain  d=  1.07  <\JDH2,  in  which  all  dimensions 
are  in  feet. 

Anchor-bolts.  —  The  holding  power  of  the  bolts  depends  on  three 
factors:  the  number  of  bolts,  the  diameter  of  the  bolt  circle,  and  the 
diameter  of  the  bolts.  The  number  of  bolts  is  largely  conventional  and 
may  ^e  selected  so  as  not  to  necessitate  bolts  of  too  large  a  diameter.  The 
diameter  of  the  bolt  circle  is  also  more  or  less  arbitrary.  The  bolts  will 
be  stretched  and  therefore  strained,  in  proportion  to  their  distance  from 
the  ttxis  of  turning,  assuming,  as  we  must,  that  the  cast-iron  ring  at  the 
base  of  the  chimney  is  rigid.  The  leverage  at  which  any  bolt  acts  is  also 
directly  proportional  to  its  distance  from  the  axis  of  turning.  Therefore, 
since  the  effectiveness  of  any  one  bolt,  as  regards  overturning,  depends 
upon  the  strain  in  that  bolt,  multiplied  by  its  leverage,  it  is  evident  that 
the  effectiveness  of  any  bolt  varies  as  the  square  of  its  distance  from  the 
axis  of  turning.  If  we  lay  out,  say,  12  or  24  bolts  equidistant  on  a  circle 
and  :,dd  all  the  squares  of  these  distances,  we  will  find  that  we  may  con- 
sider the  total  as  though  the  bolts  were  all  placed  at  a  distance  of  3/8 
the  diameter  of  the  bolt  circle  from  the  axis  of  turning,  which  is  the  tan- 
gent to  the  bolt  circle. 

Let  &  SB  diameter  of  bolt  in  inches,  n  =  number  of  bolts,  diameter 


958 


CHIMNEYS. 


of  bolt  circle 


Take  safe  working  stress  at  8000  pounds  per  sq. 


inch.  Then  resistance  to  overturning^  =  0.7854  b2  X  8000  X  2/3d  x  3/8  X 
N  =  6283  b*Nd/4.  Equating  this  to  the  turning  moment,  12.5  DH*, 
gives  v  =  0.0257  H\/^7~d  for  12  bolts,  0.0222  H\/D/d  for  18  bolts, 
and  0.0182  H  VD/d  for  24  bolts. 

Reinforced  Concrete  Chimneys  began  extensively  to  come  into  use 
in  the  United  States  in  1901.  Some  hundreds  of  them  are  now  (1909) 
in  use.  The  following  description  of  the  method  of  construction  of  these 
chimneys  is  condensed  from  a  circular  of  the  Weber  Chimney  Co.,  Chicago. 

The  foundation  is  comparatively  light  and  made  of  concrete,  consisting 
of  1  cement,  3  sand,  and  5  gravel  or  macadam.  The  steel  reenforcement 
consists  of  two  networks  usually  made  of  T  steel  of  small  size.  The  bars 
for  the  lower  network  are  placed  diagonally  and  the  bars  for  the  second 
network  (about  4  to  6  ins.  above  .the  first  one)  run  parallel  to  the  sides. 
The  vertical  bars,  forming  the  reenforcement  of  the  chimney  itself,  also 
go  down  into  the  foundation  and  a  number  of  these  bars  are  bent  in  order 
to  secure  an  anchorage  for  the  chimney. 

f  The  chimney  shaft  consists  of  two  parts,  the  lower  double  shell  and  the 
single  shell  above,  which  are  united  at  the  offset.  The  inside  shell  is 
usually  4  ins.  thick,  while  the  thickness  of  the  outer  shell  depends  on  the 
height  and  varies  from  6  to  12  ins.  The  single  shell  is  from  4  to  10  ins. 
thick.  The  height  of  the  double  shell  depends  upon  the  purpose  of  the 
chimney,  nature  and  heat  of  the  gases,  etc. 

Between  the  two  shells  in  the  lower  part  there  is  a  circular  air  space  4 
ins.  in  width.  An  expansion  joint  is  provided  where  the  two  shells  unite. 

The  concrete  above  the  ground  level  consists  of  one  part  Portland 
cement  and  three  parts  of  sand.  No  gravel  or  macadam  is  used. 

The  bending  forces  caused  by  wind  pressure  are  taken  up  by  the  vertical 
steel  reenforcement.  The  resistance  of  the  concrete  itself  against  tension 
is  not  considered  in  calculation. 

The  vertical  T  bars  are  from  1  X  1  X  Vs  to  1 1/2  XI 1/2  X  1/2  in.,  the  weight 
and  number  depending  upon  the  dimensions  of  the  chimney.  The  bars 
are  from  16  to  30  ft.  long  and  overlap  .not  less  than  24  ins.  They  are 
placed  at  regular  intervals  of  18  ins.  and  encircled  by  steel  rings  bent  to 
the  desired  circle. 

The  following  is  a  list  of  some  of  the  tallest  concrete  chimneys  that 
have  been  built  of  their  respective  diameters:  Butte,  Mont.,  350  X 18 
ft.;  Seattle,  Wash.,  278  X  17  ft.;  Portland,  Ore.,  230  X  12  ft.;  Lawrence, 
Mass.,  250  X  11  ft.;  Cincinnati,  Ohio,  200  X  10  ft.;  Worcester,  Mass, 
220  X  9  ft.;  Atlanta,  Ga.,  225  X  8  ft.;  Chicago.  175  X  7  ft.;  Rockville, 
Conn.,  175  X  6  ft.;  Seymour,  Ind.,  150  X  5  ft.;  lola,  Kans.,  143  X  4  ft.; 
St.  Louis,  Mo.,  130  X  3  ft.  4  in.;  Dayton,  Ohio,  94  X  3  ft. 

Sizes  of  Foundations  for  Steel  Chimneys. 

(Selected  from  circular  of  Phila.  Engineering  Works.) 
HALF-LINED  CHIMNEYS. 

Diameter,  clear,  feet 3456 

Height,  feet 100      100       150        150 

Least  diam.  foundation..  15'9"  16' 4"    20'4"    21'10' 
Least  depth  foundation..     6'        6'  9' 

Height,  feet 125       200        200 

Least  diam.  foundation 18'5"     23'8"       25' 

Least  depth  foundation 7' 

Weight  of  Sheet-iron  Smoke-stacks  per  Foot 
(Porter  Mfg.  Co.) 


150 
22'7" 
9' 
250 
29'8" 
12' 

9 

150 
23'8" 
10' 
275 
33'6" 
12' 

11 

150^ 

10' 
300 
36' 
14' 

Diam. 
inches. 

Thick- 
ness. 
W.  G. 

Weight 
per  ft. 

Diam. 
inches. 

Thick- 
ness. 
W.  G. 

Weight 
per  ft. 

Diam. 
inches. 

Thick- 
ness. 
W.  G. 

Weight 
per  ft. 

10 
12 
14 
16 
20 
22 
24 

No.  16 

7.20 
8.66 
9.58 
11.68 
13.75 
15.00 
16.25 

26 
28 
30 
10 
12 
14 
16 

No;  16 
No    14 

17.50 
18.75 
20.00 
9.40 
11.11 
13.69 
15.00 

20 
22 
24 
26 
28 
30 

No;  14 

18.33 
20.00 
21.66 
23.33 
25.00 
26.66 

•  :  --^.^m 

THE    STEAM    ENGINE. 


959 


THE  STEAM-ENGINE. 

Expansion  of  Steam.  Isothermal  and  Adiabatic.  —  According  to 
Mariotte's  law,  the  volume  of  a  perfect  gas,  the  temperature  being  kept 
constant,  varies  inversely  as  its  pressure,  or  p  «  i/v;  pv  =  a  constant.  The 
curve  constructed  from  this  formula  is  called  the  isothermal  curve,  or 
curve  of  equal  temperatures,  and  is  a  common  or  rectangular  hyperbola. 
The  expansion  of  steam  in  an  engine  is  not  isothermal,  since  the  temper- 
ature decreases  with  increase  of  volume,  but  its  expansion  curve  approxi- 
mates the  curve  of  pv  =  a  constant.  The  relation  of  the  pressure  and 
volume  of  saturated  steam,  as  deduced  from  Regnault's  experiments,  and 
as  given  in  steam  tables,  is  approximately,  according  to  Rankine  (S.  E., 
p.  403),  for  pressures  not  exceeding  120  Ibs.,  p  cc  1/vii,  or  p  oc  -y~is  or  pv^  = 
pfli-0626—a  constant.  Zeuner  has  found  that  the  exponent  1.0646  gives  a 
closer  approximation. 

When  steam  expands  in  a  closed  cylinder,  as  in  an  engine,  according  to 
Rankine  (S.  E.,  p.  385),  the  approximate  law  of  the  expansion  is  p  oc  1/vV*. 
orp°c-y~9°'  or  pvl'm  =  a  constant.  The  curve  constructed  from  this 
formula  is  called  the  adiabatic  curve,  or  curve  of  no  transmission  of  heat. 

Peabody  (Therm.,  p.  112)  says:  "It  is  probable  that  this  equation  was 
obtained  by  comparing  the  expansion  lines  on  a  large  number  of  indicator- 
diagrams.  .  .  .  There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection,  .  .  .  and  the  action  of  a  lagged 
steam-engine  cylinder  is  far  from  being  adiabatic.  .  .  .  For  general  pur- 
poses the  hyperbola  is  the  best  curve  for  comparison  with  the  expansion 
curve  of  an  indicator-card.  ..."  Wolff  and  Denton,  Trans.  A.  S.  M.  E.t 
ii,  175,  say:  "  From  a  number  of  cards  examined  from  a  variety  of  steam- 
engines  in  current  use,  we  find  that  the  actual  expansion  line  varies  between 
the  10/9  adiabatic  curve  and  the  Mariotte  curve." 

Prof.  Thurston  (Trans.  A.S.  M.  E.,i\,  203)  says  he  doubts  if  the  exponent 
ever  becomes  the  same  in  any  two  engines,  or  even  in  the  same  engine 
at  different  times  of  the  day  and  under  varying  conditions  of  the  day. 

Expansion  of  Steam  according  to  Mariotte's  Law  and  to  the 
Adiabatic  Law.  (Trans.  A.  S.  M.  E.,  ii,  156.)  —  Mariotte's  law  pv  = 

vn        1 

PIVI;  values  calculated  from  formula  —  =  -5  (1  +  hyp  log  R),  in  which 

Pi          K 

R  =  v<i  -*-  vi,  Pi  —  absolute  initial  pressure,  Pm  =  absolute  mean  pressure, 
v\  =  initial  volume  of  steam  in  cylinder  at  pressure  pi,  vz  =  final  volume 
of  steam  at  final  pressure.  Adiabatic  law:  pv*£  —  pivi™:  values  calcu- 


lated  from  formula  - 


10  R  l- 


Ratio 
of  Ex- 
pansion 
R. 

Ratio  of  Mean 
to  Initial 
Pressure. 

Ratio 
of  Ex- 
pansion 
R. 

Ratio  of  Mean 
to  Initial 
Pressure. 

Ratio 
of  Ex- 
pansion 
R. 

Ratio  of  Mean 
to  Initial 
Pressure. 

Mar. 

Adiab. 

Mar. 

Adiab. 

Mar. 

Adiab. 

1.00 

1.000 

1.000 

3.7 

0.624 

0.600 

6. 

0.465 

0.438 

1.25 

.978 

.976 

3.8 

.614 

.590 

6.25 

.453 

.425 

1.50 

.937 

.931 

3.9 

.605 

.580 

6.5 

.442 

.413 

2'75 

.891 

.881 

4. 

.597 

.571 

6.75 

.431 

.403 

.847 

.834 

4.1 

.588 

.562 

7. 

.421 

.393 

2.2 

.813 

.798 

4.2 

.580 

.554 

7.25 

.411 

.383 

2.4 

.78! 

.765 

4.3 

.572 

.546 

7.5 

.402 

.374 

2.5 

.766 

.748 

4.4 

.564 

.538 

7.75 

.393 

.365 

2.6 

.752 

.733 

4.5 

.556 

.530 

8. 

.385 

.357 

2.8 

.725 

.704 

4.6 

.549 

.523 

8.25 

.377 

.349 

3. 

.700 

.678 

4.7 

.542 

.516 

8.5 

.369 

.342 

3.1 

.688 

.666 

4.8 

.535 

.509 

8.75 

.362 

.335 

3.2 

.676 

.654 

4.9 

.528 

.502 

9. 

.355 

.328 

3.3 

.665 

.642 

5  0 

.522 

.495 

9.25 

.349 

.321 

3.4 

.654 

.630 

5.25 

.506 

.479 

9.5 

.342 

.315 

35 

.644 

.620 

5.5 

.492 

.464 

9.75 

.336 

.309 

3.6 

.634 

.610 

5.75 

.478 

.450 

10. 

.330 

.303 

960 


THE   STEAM-ENGINE. 


Mean  Pressure  of  Expanded  Steam.  —  For  calculations  of  engine 
it  is  generally  assumed  that  steam  expands  according  to  Mariotte's  law, 
the  curve  of  the  expansion  line  being  a  hyperbola.  The  mean  pressure. 
measured  above  vacuum,  is  then  obtained  Irom  the  formula 

PM-H  1  +  hyP'°gfi.  or  Pm=Pt  (1  +  hyp  log  *). 

in  which  Pm  is  the  absolute  mean  pressure,  p\  the  absolute  initial  pressure 
taken  as  uniform  up  to  the  point  of  cut-off,  Pt  the  terminal  pressure,  and 
R  the  ratio  of  expansion.  If  I  =  length  of  stroke  to  the  cut-off,  L  =  total 
stroke.  £ 

l  +  hyplogft 
=       --  — 


Mean  and  Terminal  Absolute  Pressures.  —  Mariotte's  Law.  —  The 

values  in  the  following  table  are  based  on  Mariotte's  law,  except  those 
in  the  last  column,  which  give  the  mean  pressure  of  superheated  steam, 
which,  according  to  Rankine,  expands  in  a  cylinder  according  to  the 
law  p<xv~*%.  These  latter  values  are  calculated  from  the  formula 

—  —  =  -  -  .     R~iis  may  be  found  by  extracting  the  square  root 

of  —  four  times.   From  the  mean  absolute  pressures  given  deduct  the  mean 

ti 
back  pressure  (absolute)  to  obtain  the  mean  effective  pressure. 


Rate 
of 
Expan- 
sion. 

Cut- 
off. 

Ratio  of 
Mean  to 
Initial 
Pressure. 

Ratio  of 
Mean  to 
Terminal 
Pressure. 

Ratio  of 
Terminal 
to  Mean 
Pressure. 

Ratio  of 
Initial 
to   Mean 
Pressure. 

Ratio  of 
Mean  to 
Initial 
Dry  Steam. 

30 

28 

0.033 
0.036 

0.1467 
0.1547 

4.40 
4.33 

0.227 
0.231 

6.82 
6.46 

0.136 

26 

0.038 

0.1638 

4.26 

0.235 

6.11 

24 

0.042 

0.1741 

4.18 

0.239 

5.75 

22 

0.045 

0.1860 

4  09 

0.244 

5  38 

20 
18 

0.050 
0.055 

0.1998 
0  2161 

4.00 
3  89 

0.250 
0  256 

5.00 
4  63 

0.186 

16 

0.062 

0.2358 

3  77 

0.265 

4.24 

15 

0.066 

0.2472 

3.71 

0.269 

4.05 

14 

0.071 

0.2599 

3  64 

0  275 

3  85 

J3.33 
13 

0.075 
0.077 

0.2690 
0  2742 

3.59 
3  56 

0.279 
0  280 

3.72 
3  65 

0.254 

12 

0.083 

0.2904 

3  48 

0  287 

3  44 

11 

0.091 

0.3089 

3.40 

0.294 

3.24 

10 
9 
8 
7 

0.100 
0.111 
0.125 
0.143 

0.3303 
0.3552 
0.3849 
0.4210 

3.30 
3.20 
3.08 
2  95 

0.303 
0.312 
0.321 
0  339 

3.03 
2.81 
2.60 
2  37 

0.314 

'"o.m" 

6.66 
6.00 

0.150 
0.166 

0.4347 
0  4653 

2.90 
2  79 

0.345 
0  360 

2.30 
2  15 

0.417 

5.71 

0.175 

0.4807 

2  74 

0  364 

2  08 

5.00 
4.44 

0.200 
0.225 

0.5218 
0.5608 

2.61 
2  50 

0.383 
0  400 

.92 

78 

0.506 

4.00 
3.63 

0.250 
0.275 

0.5965 
0  6308 

2.39 
2  29 

0.419 
0  437 

.68 
58 

0.582 

3.33 
3.00 

0.300 
0.333 

0.6615 
0  6995 

2.20 
2  10 

0.454 
0  476 

.51 
43 

0.6  8 

2.86 
2.66 

0.350 
0  375 

0.7171 
0  7440 

2.05 
98 

0.488 
0  505 

.39 

34 

0.707 

2.50 
2.22 
2.00 
.82 
.66 
.60 
.54 
.48 

0.400 
0.450 
0.500 
0.550 
0.600 
0.625 
0.650 
0.675 

0.7664 
0.8095 
0.8465 
0.8786 
0.9066 
0.9187 
0.9292 
0.9405 

.91 
.80 
.69 
.60 
.51 
.47 
.43 
.39 

0.523 
0.556 
0.591 
0.626 
0.662 
0.680 
0.699 
0.718 

.31 
.24 
.18 
.14 
.10 
.09 
.07 
.06 

0.756 
0.800 
0.840 
0.874 
0.900 

"'6;926'" 

THE   STEAM-ENGINE. 


961 


Calculation   of  Moan  Effective  Pressure,   Clearance   and   Com- 
pression Considered,  —  In  the  above  tables  no  account  is  taken  of 

clearance,    which    in    actual 

___  I  ___  ^  steam-engines    modifies    the 

ratio  of  expansion  and  the 
mean  pressure  ;  nor  of  com- 
pression and  back-pressure, 
which  diminish  the  mean 
effective  pressure.  In  the 
following  calculation  these 
elements  are  considered. 

L  =  length  of  stroke,  I  = 
length  before  cut-off,  x  = 
length  of  compression  part  of 
stroke,  c  =  clearance,  pi  = 
initial  pressure,  p&  —  back 
pressure,  pc  =  pressure  of 
clearance  steam  at  end  of 
compression.  All  pressures 
are  absolute,  that  is,  measured 
from  a  perfect  vacuum. 

Area  of  ABCD  =  Pl  (l  +  c)  (l  4-  hyp  log  j^)  ; 
B  =•  pi,(L-x); 

C  -  Pec  (l  +  hyp  log  —^  =pb  (x+c)  (l  +  hyp  log  ^p); 
0  =  (Pi-Pe)  c  =  pi 
Area  of  A  =  ABCD-(B-f  C4-  D) 


-  \Pb  (L-x)+pb  (z  +  c)  (l  +  hyp  log  *-±^  +  plC-pb  (X  -4-c)] 
)  (l  +  hyp  log  ^±^ 

-  pb  [(L  -x)  +  (x  +  c)  hyp  log  £±£l  -pic. 


Mean  effective  pressure  - 


area  of  A 


EXAMPLE.  —  Let  L  =  l,  2  =  0.25,  rr  =  0.25,  c  =  0.1, 
Area  A  =  60  (0.25  +  0.1)  (l  +  hyp  log  ~^\ 


Ibs.,  p&  =  2  Ibs. 


-  2  [(1-0.25)  +0.35  hyp  log  ^yl  -60X0  1. 

=  21  (1  4-  1.145)  -2  [0.75  +  0.35  X  1.2531  -  6 

=  45.045  -  2.377  -  6  =  36.668  =  mean  effective  pressure. 

The  actual  indicator-diagram  generally  shows  a  mean  pressure  con- 
siderably less  than  that  due  to  the  initial  pressure  and  the  rate  of  expan- 
sion. The  causes  of  loss  of  pressure  are:  1.  Friction  in  the  stop-valves 
and  steam-pipes.  2.  Friction  or  wire-drawing  of  the  steam  during 
admission  and  cut-off,  due  chiefly  to  defective  valve-gear  and  contracted 
steam-passages.  3.  Liquefaction  during  expansion.  4.  Exhausting 
before  the  engine  has  completed  its  stroke.  5.  Compression  due  to  early 
closure  of  exhaust.  6.  Friction  in  the  exhaust-ports,  passages,  am} 
pipes, 


962  THE   STEAM-ENGINE. 

Re-evaporation  during  expansion  of  the  steam  condensed  during  admis- 
sion, and  valve-leakage  after  cut-off,  tend  to  elevate  the  expansion  line 
of  the  diagram  and  increase  the  mean  pressure. 

If  the  theoretical  mean  pressure  be  calculated  from  the  initial  pressure 
and  the  rate  of  expansion  on  the  supposition  that  the  expansion  curve 
follows  Mariotte's  law,  pv  =  a  constant,  and  the  necessary  corrections 
are  made  for  clearance  and  compression,  the  expected  mean  pressure  in 
practice  may  be  found  by  multiplying  the  calculated  results  by  the  factor 
(commonly  called  the  "diagram  factor")  in  the  following  table  according 
to  Seaton. 

Particulars  of  Engine.  Factor. 

Expansive  engine,  special  valye-gear,  or  with  a  sepa- 

rate cut-off  valve,  cylinder  jacketed  .............  0.94 

Expansive  engine  having  large  ports,  etc.,  and  good 

ordinary  valves,  cylinders  jacketed  ..............  0.9  to  0.92 

Expansive  engines  with  the  ordinary  valves  and  gear 

as  in  general  practice,  and  unjacketed  ...........  0  .  8  to  0  .  85 

Compound  engines,  with  expansion  valve  to  h.p. 
cylinder;  cylinders  jacketed,  and  with  large  ports, 
etc  .....  ......................................  0  .  9  to  0  .  91 

Compound  engines,  with  ordinary  slide-valves,  cylin- 

ders  jacketed,  and  good  ports,  etc  ...............  0  .  8  to  0  .  85 

Compound  engines  as  in  general  practice  in  the 
merchant  service,  with  early  cut-off  in  both  cylin- 
ders, without  jackets  and  expansion-  valves  .......  0  .  7  to  0  .  8 

Fast-running  engines  of  the  type  and  design  usually 

fitted  in  war-ships  ............................  0  .  6  to  0  .  8 

If  no  correction  be  made  for  clearance  and  compression,  and  the  engine 
Is  in  accordance  with  general  modern  practice,  the  theoretical  mean 
pressure  may  be  multiplied  by  0.96,  and  the  product  by  the  proper  factor 
in  the  table,  to  obtain  the  expected  mean  pressure. 

Given  the  Initial  Pressure  and  the  Average  Pressure,  to  Find  the 
Ratio  of  Expansion  and  the  Period  of  Admission. 

P  =  initial  absolute  pressure  in  Ibs.  per  sq.  in.; 

p  =  average  total  pressure  during  stroke  in  Ibs.  per  sq.  in.; 

L  =  length  of  stroke  in  inches; 

I  =  period  of  admission  measured  from  beginning  of  stroke; 

c  =  clearance  in  inches  ; 

R  =  actual  ratio  of  expansion  =   ,         .     .......     (1) 


R 
To  find  average  pressure  p,  taking  account  of  clearance, 

p  =  P(E  +  c)  +  P(l  +  c)hyplogg-Pc 

L 
whence  pL  +  Pc=P  (I  +  c)  (1  +  hyp  log  R)  ; 


(3) 


Given  p  and  P,  to  find  R  and  I  (by  trial  and  error).  —  There  being  two 
unknown  quantities  R  and  I,  assume  one  of  them,  viz.,  the  period  of 
admission  i,  substitute  it  in  equation  (3)  and  solve  for  R.  Substitute  this 

value  of  R  in  the  formula  (1),  or  I  =  —  =r-^  —  c,  obtained  from  formula 

K 

d),  and  find  I.  If  the  result  is  greater  than  the  assumed  value  of  I, 
then  the  assumed  value  of  the  period  of  admission  is  too  long;  if  less,  the 
assumed  value  is  too  short.  Assume  a  new  value  of  I,  substitute  it  ir 
formula  (3)  as  before,  and  continue  by  this  method  of  trial  and  error  till 
the  required  values  of  R  a.nd  I  are  obtained. 


THE  STEAM-ENGINE. 


963 


EXAMPLE. — P=70,  p  =  42.78,  L  = 
I  =  21  in. 

P  r  .  42.78 


60  In.,  c  =3  in.,  to  find  I.    Assume 


hyp  log  R  •• 
hyp  log  R 


-1  = 


70 


X  60 -f  3 


l+c  21  +  3 

=  0.653,  whence  R  =  1.92. 
L  +  c 


•  -1  =  1.653- 1«  0.653; 


which  Is  greater  than  the  assumed  value,  21  inches. 
Now  assume  I  =  15  inches: 
42.78  v 


hyp  log  R  = 


70 


-  X  60  -f  3 


15  +  3 


—  1  =  1.204,  whence  R  —  3.5; 


P  C-  —c=  r-^  -3  =  18  -3  =  15  inches,  the  value  assumed. 

K  o.O 


Therefore  R  =  3.5,  and  1  =  15  inches. 

Period  of  Admission  Required  for  a  Given  Actual  Ratio  of  Expansion: 

1 J-^-c,  in  inches (4) 

K 

100  +  p.  ct.  clearance 
percentage  of  stroke,  1= —         — 5 p.  ct.  clearance  .     (5) 

K 


In  percen 
Terminal 
Pressure 


_  .  .sure  at  any  other  Point  of  the  Expansion.  —  Let  L\  =  length  of 
stroke  up  to  the  given  point. 


Pressure  at  the  given  point  = 


Li  +  c 


(7) 


Mechanical  Energy  of  Steam  Expanded  Adiabatically  to  Various 
ressures.  —  The  figures  in  the  following  table  are  taken  from  a  chart 
nstructed  by  R.  M.  Neilson  in  Power,  Mar.  16,  1909.  The  pressures 
e  absolute,  IDS  per  sq.  in. 


•3*5) 

2  «  I  15 

££ 

20 

25 

40 

60 

80 

100 

120 

140 

170 

200 

250 

"a?    ^ 

E£ 

Mechanical  Energy,  Thousands  of  Foot-Pounds  per  Lb.  of  Steam. 

15 
12 

10 
8 
6 
4 
2 
1 

0 
12 
22 
34 
49 
68 
100 
131 

17 

29 
39 
50 
64 
85 
116 
147 

29.5 
41 
50.5 
62 
76 
95.5 
128 
157.5 

55.5 
66.5 
75.5 
86.5 
101 
120 
151 
181.5 

77.5 
88 
97 
109 
123 
142 
171 
200.5 

94.5 
104 
113 
124 
138 
157 
186.5 
215 

107 
116 
125 
136 
150 
168 
197.5 
225 

116.5 
126 
135.5 
147 
160 
177.5 
207 
234.5 

121 
135 
144 
155 

168.5 
186 
215 

243 

136.5 
145 
154 
165.5 
179.5 
196 
224 
250.5 

!46 
154.5 
163.5 
174.5 
188 
204.5 
232.5 
260.5 

160 
168.5 
176 
186 
199 
216 
244 
270.5 

Measures  for  Comparing  the  Duty  of  Engines.  — Capacity  is  meas- 
ured in  horse-powers,  expressed  by  the  initials,  H.P.:  1  H.P.  =  33,000 
ft.-lbs.  per  minute,  =550  ft.-lbs.  per  second,  =  1,980,000  ft.-lbs.  per  hour. 
1  ft.-lb.  =  a  pressure  of  1  Ib.  exerted  through  a  space  of  1  ft. 

Economy  is  measured,  1,  in  pounds  of  coal  per  horse-power  per  hour; 
2,  in  pounds  of  steam  per  horse-power  per  hour.  The  second  of  these 
measures  is  the  more  accurate  and  scientific,  since  the  enerine  uses  steam 
and  not  coal,  and  it  is  independent  of  the  economy  of  the  boiler.  A  still 
more  accurate  measure  is  the  heat  units  per  minute  (or  per  hour)  per 
horse-power. 


964 


THE  STEAM-ENGINE. 


In  gas-engine  tests  the  common  measure  is  the  number  of  cubic  feet 
of  gas  (measured  at  atmospheric  pressure)  per  horse-power,  but  as  all  gas 
is  not  of  the  same  quality,  it  is  necessary  for  comparison  of  tests  to  give 
the  analysis  of  the  gas.  When  the  gas  for  one  engine  is  made  in  one 
gas-producer,  then  the  number  of  pounds  of  coal  used  in  the  producer  per 
hour  per  horse-power  of  the  engine  is  a  measure  of  economy.  Since 
different  coals  vary  in  heating  value,  a  more  accurate  measure  is  the 
number  of  heat  units  required  per  horse-power  per  hour. 

Economy,  or  duty  of  an  engine,  is  also  measured  in  the  number  of  foot- 
pounds of  work  done  per  pound  of  fuel.  As  1  horse-power  is  equal  to 
1,980,000  ft.-lbs.  of  work  in  an  hour,  a  duty  of  1  Ib.  of  coal  per  H.P.  per 
hour  would  be  equal  to  1,980,000  ft.-lbs.  per  Ib.  of  fuel;  2  Ibs.  per  H.P. 
per  hour  equals  990,000  ft.-lbs.  per  Ib.  of  fuel,  etc. 

The  duty  of  pumping-engines  is  expressed  by  the  number  of  foot- 
pounds of  work  done  per  100  Ibs.  of  coal,  per  1000  Ibs.  of  steam,  or  per 
million  heat  units, 

When  the  duty  of  a  pumping-engine  is  given,  in  ft.-lbs.  per  100  Ibs.  of 
coal,  the  equivalent  number  of  pounds  of  fuel  consumed  per  horse-power 
per  hour  is  found  by  dividing  198  by  the  number  of  millions  of  foot-pounds 
of  duty.  Thus  a  pumping-engine  giving  a  duty  of  99  millions  is  equiva- 
lent to  198/99  =  2  Ibs.  of  fuel  per  horse-power  per  hour. 

Efficiency  Measured  in  Thermal  Units  per  Minute.  — The  efficiency 
of  an  engine  is  sometimes  expressed  in  terms  of  the  number  of  thermal 
units  used  by  the  engine  per  minute  for  each  indicated  horse-power,  instead 
of  by  the  number  of  pounds  of  steam  used  per  hour. 

The  heat  chargeable  to  an  engine  per  pound  of  steam  is  the  difference 
between  the  total  heat  in  a  pound  of  steam  at  the  boiler-pressure  and  that 
in  a  pound  of  the  feed-water  entering  the  boiler.  In  the  case  of  con- 
densing engines,  suppose  we  have  a  temperature  in  the  hot-well  of  100°  F., 
corresponding  to  a  vacuum  of  28  in.  of  mercury;  we  may  feed  the  water 
into  the  boiler  at  that  temperature.  In  the  case  of  a  non-condensing 
engine,  by  using  a  portion  of  the  exhaust  steam  in  a  good  feed-water 
heater,  at  a  pressure  a  trifle  above  the  atmosphere  (due  to  the  resistance 
of  the  exhaust  passages  through  the  heater),  we  may  obtain  feed-water 
at  212°.  One  pound  of  steam  used  by  the  engine  then  would  be  equivalent 
to  thermal  units  as  follows: 

Gauge  pressure 50           75          100         125         150  175  200 

Absolute  pressure.  ...65           90          115         140         165  190  215 
Total  heat  in  steam  above  32°: 

1178.5    1184.4  1188.8  1192.2  1195.0  1197.3  1199.2 

Subtracting  68  and  180  heat-units,  respectively,  the  heat  above  32°  in 
feed-water  of  100°  and  212°  F.f  we  have  — 

Heat  given  by  boiler  per  pound  of  steam: 

'Feed  at  100°..    ,.1110.5    1116.4    1120.8    1124.2    1127.0    1129.3    1131.2 
Feed  at  212° 998.5    1004.4    1008.8    1012.2    1015.0    1017.3    1019.2 

Thermal  units  per  minute  used  by  an  engine  for  each  pound  of  steam 
used  per  indicated  horse-power  per  hour: 

Feed  at  100°. .      . .  18.51      18.61      18.68      18.74      18.78      18.82      18.85 
Feed  at  212° 16.64      16.76      16.78      16.87      16.92      16.96      16.99 

EXAMPLES.  —  A  triple-expansion  engine,  condensing,  with  steam  at 
175  Ibs.  gauge,  and  vacuum  28 in.,  uses  13  Ibs.  of  water  per  I. H.P.  per  hour, 
and  a  high-speed  non-condensing  engine,  with  steam  at  100  Ibs.  gauge, 
uses  30  Ibs.  How  many  thermal  units  per  minute  does  each  consume?  • 

Ans.  —  13  X  18.82  =  244.7,  and  30  X  16.78  =  503.4  thermal  units 
per  minute. 

A  perfect  engine  converting  all  the  heat-energy  of  the  steam  into 
work  would  require  33,000  ft.-lbs.  «  777.54  =  42.44  thermal  units  per 
minute  per  indicated  horse-power.  This  figure,  42.44,  therefore,  divided 
by  the  number  of  thermal  units  per  minute  per  I. H.P.  consumed  by  an 
engine,  gives  its  efficiency  as  compared  with  an  ideally  perfect  engine. 
In  the  examples  above,  42.44  divided  by  244.7  and  by  503.4  gives 
J7.34%  and  8.43%  efficiency,  respectively. 


ACTUAL  EXPANSIONS. 


965 


ACTUAL,  EXPANSIONS 

With  Different  Clearances  and  Cut-offs0 

Computed  by  A.  F.  Nagle. 


Per  Cent  of  Clearance. 

Cut- 

off. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.01 

100.00 

50.5 

34.0 

25.75 

20.8 

17.5 

15.14 

13.38 

12.00 

10.9 

10 

.02 

50.00 

33.67 

25.50 

20.60 

17.33 

15.00 

13.25 

11.89 

10.80 

9.91 

9.17 

(H 

33  33 

25  25 

20  40 

17  16 

14  86 

13  12 

11  78 

10  70 

9  82 

9  08 

8  46 

.04 

25.00 

20.20 

17.00 

14.71 

13.00 

11.66 

10.60 

9.73 

9.00 

8.39 

7.86 

.05 

20.00 

16.83 

14.57 

12.87 

11.55 

10.50 

9.64 

8.92- 

8.31 

7.79' 

7.33 

.06 

16.67 

14.43 

12.75 

11.44 

10.40 

9.55 

8.83 

8.23 

7.71 

7.27 

6.88 

,07 

14.28 

12.62 

11.33 

10.30 

9.46 

8.75 

8.15 

7.64 

7.20 

6.81 

6.47 

.08 

12.50 

11.22 

10.2 

9.36 

8.67 

8.08 

7.57 

7.13 

6.75 

6.41 

6.11 

.09 

11.11 

10.10 

9.27 

8.58 

8.00 

7.50 

7.07 

6.69 

6.35 

6.06 

5.79 

.10 

10.00 

9.18 

8.50 

7.92 

7.43 

7.00 

6.62 

6.30 

6.00 

5.74 

5.50 

.11 

9.09 

8.42 

7.84 

7.36 

6.93 

6.56 

6.24 

5.94 

5.68 

5.45 

5.24 

.12 

8.33 

7.78 

7.29 

6.86 

6.50 

6.18 

5.89 

5.63 

5.40 

5.19 

5.00 

.14 

7.14 

6.73 

6.37 

6.06 

5.78 

5.53 

5.30 

5.10 

4.91 

4.74 

4.58 

.16 

6.25 

5.94 

5.67 

5.42 

5.20 

5.00 

4.82 

4.65 

4.50 

4.36 

4.23 

.20 

5.00 

4.81 

4.64 

4.48 

4.33 

4.20 

4.08 

3.96 

3.86 

3.76 

3.67 

.25 

4.00 

3.88 

3.77 

3.68 

3.58 

3.50 

3.42 

3.34 

3.27 

3.21 

3.14 

30 

3  33 

3.26 

3.19 

3.12 

3.06 

3.00 

2.94 

2.90 

2.84 

2.80 

?,  75 

40 

2  50 

2  46 

2  43 

2  40 

2  36 

2  33 

2  30 

2  28 

2  25 

2  22 

?  20 

.50 

2.00 

.98 

.96 

.94 

.92 

.90 

.89 

.88 

.86 

.85 

.83 

60 

.67 

.66 

.65 

.64 

.63 

.615 

.606 

.597 

.588 

.580 

571 

70 

43 

42 

42 

41 

.41 

.400 

.395 

.390 

.385 

.380 

375 

.80 

.25 

.25 

.244 

.241 

.238 

.235 

.233 

.230 

.227 

.224 

.222 

.90 

.111 

.11 

.109 

.108 

.106 

.105 

.104 

.103 

.102 

.101 

.100 

1.00 

.00 

.00 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

.000 

Relative  Efficiency  of  1  Ib.  of  Steam  with  and  without  Clearance; 

back  pressure  and  compression  not  considered. 

P  (I  +  c)  +  P  (I  +  c)  hyp  log  R  -  PC 

KL 
t  p  =  l;  L  =  100;  I  =  25;  c  =  7. 


Mean  total  pressure  —  p  =  '• 
et  P  =  1;  L  =  100;  I  =  25;  c 
32  +  32  hyp  log          - 


32  +  32X  1.207-7 
100 


=  0.636. 


100 

f  the  clearance  be  added  to  the  stroke,  so  that  clearance  becomes 
zero,  the  same  quantity  of  steam  being  used,  admission  /  being  then 
=  I  +  c  =  32,  and  stroke  L  +.c  =  107, 


PI-- 


32  +  32  hyp  log         -  0 
107 


32X^207 


The  work  of  one  stroke  =  pi(L  +  c)  =  0.660  X  107  =  70.6.  The 
amount  of  the  clearance  7  being  added  to  both  admission  and  the 
stroke,  the  same  quantity  of  steam  will  do  more  work  than  when  the 
clearance  is  7  in  the  ratio  706  :  636,  or  1 1  %  more, 

Back  Pressure  Considered. — If  backpressure  =0.10ofP,thisamount 
has  to  be  subtracted  from  p  and  p\  giving  p  =  0.536,  pi  =  0.560,  the 
work  of  a  given  quantity  of  steam  used  without  clearance  being  greater 
than  when  clearance  is  7%  in  the  ratio  (560  X  1.07)  :  536,  or  12%  more. 

Effect  of  Compression. — By  early  closure  of  the  exhaust,  so  that  a 
portion  of  the  exhaust-steam  is  compressed  into  the  clearance-space, 
much  of  the  loss  due  to  clearance  may  be  avoided.  If  expansion  is  con- 
tinued down  to  the  back  pressure,  if  the  back  pressureis  uniform  through- 
out the  exhaust-stroke,  and  if  compression  begins  at  such  point  that  the 


966 


THE   STEAM-ENGINE. 


exhaust-steam  remaining  in  the  cylinder  is  compressed  to  the  initial 
pressure  at  the  end  of  the  back  stroke,  then  the  work  of  compression  of  the 
exhaust-steam  equals  the  work  done  during  expansion  by  the  clearance- 
steam.  The  clearance-space  being  filled  by  the  exhaust-steam  thus  com- 
pressed, no  new  steam  is  required  to  fill  the  clearance-space  for  the  next 
forward  stroke,  and  the  work  and  efficiency  of  the  steam  used  in  the 
cylinder  are  just  the  same  as  if  there  were  no  clearance  and  no  compression. 
When,  however,  there  is  a  drop  in  pressure  from  the  final  pressure  of  the 
expansion,  or  the  terminal  pressure,  to  the  exhaust  or  back  pressure  (the 
usual  case),  the  work  of  compression  to  the  initial  pressure  is  greater  than 
the  work  done  by  the  expansion  of  the  clearance-steam,  so  that  a  loss  of 
efficiency  results.  In  this  case  a  greater  efficiency  can  be  attained  by 
inclosing  for  compression  a  less  quantity  of  steam  than  that  needed  to  fill 
the  clearance-space  with  steam  of  the  initial  pressure.  (See  Clark, 
S.  E.,  p.  399,  et  seq.;  also  F.  H.  Ball,  Trans.  A.  S.  M.  E.,  xiv,  1067.)  It  is 
shown  by  Clark  that  a  somewhat  greater  efficiency  is  thus  attained 
whether  or  not  the  pressure  of  the  steam  be  carried  down  by  expansion 
to  the  back  exhaust-pressure. 

Cylinder-condensation  may  have  considerable  effect  upon  the  best 
point  of  compression,  but  it  has  not  yet  (1893)  been  determined  by 
experiment.  (Trans.  A.  S.  M.  E.,  xiv,  1078.) 

Clearance  in  L.OW-  and  High-speed  Engines.  (Harris  Tabor,  Am. 
Mach.,  Sept.  17,  1891.)  — The  construction  of  the  high-speed  engine  is 
such,  with  its  relatively  short  stroke,  that  the  clearance  must  be  much 
larger  than  in  the  releasing-valve  type.  The  short-stroke  engine  is, 
of  necessity,  an  engine  with  large  clearance,  which  is  aggravated  when 
variable  compression  is  a  feature.  Conversely,  the  engine  with  releasing- 
valve  gear  is,  from  necessity,  an  engine  of  slow  rotative  speed,  where 
great  power  is  obtainable  from  long  stroke,  and  small  clearance  is  a 
feature  in  its  construction.  In  one  case  the  clearance  will  vary  from 
8%  to  12%  of  the  piston-displacement,  and  in  the  other  from  2%  to  3%. 
In  the  case  of  an  engine  with  a  clearance  equaling  10%  of  the  piston- 
displacement  the  waste  room  becomes  enormous  when  considered  in  con- 
nection with  an  early  cut-off.  The  system  of  compounding  reduces  the 
waste  due  to  clearance  in  proportion  as  the  steam  is  expanded  to  a  lower 
pressure.  The  farther  expansion  is  carried  through  a  train  of  cylinders 
the  greater  will  be  the  reduction  of  waste  due  to  clearance.  This  is  shown 
from  the  fact  that  the  high-speed,  engine,  expanding  steam  much  less  than 
the  Corliss,  will  show  a  greater  gain  when  changed  from  simple  to  com- 
pound than  its  rival  under  similar  conditions. 

Cylinder-condensation.  —  Rankine,  S.  E.,  p.  421,  says:  Conduction 
of  heat  to  and  from  the  metal  of  the  cylinder,  or  to  and  from  liquid  water 
contained  in  the  cylinder,  has  the  effect  of  lowering  the  pressure  at  the 
beginning  and  raising  it  at  the  end  of  the  stroke,  the  lowering  effect  being 
on  the  whole  greater  than  the  raising  effect.  In  some  experiments  the 
quantity  of  steam  wasted  through  alternate  liquefaction  and  evaporation 
in  the  cylinder  has  been  found  to  be  greater  than  the  quantity  which 
performed  the  work. 

Percentage  of  Loss  by  Cylinder-condensation,   taken  at  Cut-off. 

(From  circular  of  the  Ashcroft  Mfg.  Co.  on  the  Tabor  Indicator,  1889.) 


Percentage  of 
Stroke  com- 
pleted at 
Cut-ofif. 

Per  cent  of  Feed-water  ac- 
counted for  by  the  Indicator. 

Per  cent  of  Feed-water  due 
to  Cylinder-condensation. 

Simple 
Engines. 

Compound 
Engines, 
h.p.  cyl. 

Triple-ex- 
pansion 
Engines, 
h.p.  cyl. 

Simple 
Engines. 

Compound 
Engines, 
h.p.  cyl. 

Triple-ex- 
pansion 
Engines, 
h.p.  cyl. 

,       5 
10 
15 
20 

,    30 
1    40 
50 

58 
66 
71 

74 
78 

82 
86 

42 
34 
29 
26 
22 
18 
14 

74 
76 

78 
82 
85 
88 

26 
24 
22    ' 
18 
15 
12 

78 
80 
84 
87 
90 

22 
20 
16 
13 
iO 

CYLINDER   CONDENSATION. 


967 


Theoretical  Compared  with  Actual  Water-consumption,  Single- 
cylinder  Automatic  Cut-off  Engines.  (From  the  catalogue  of  the 
Buckeye  Engine  Co.)  —  The  following  table  has  been  prepared  on  the 
basis  of  the  pressures  that  result  in  practice  with  a  constant  boiler-pressure 
of  80  Ibs.  and  different  points  of  cut-off,  with  Buckeye  engines  and  others 
with  similar  clearance.  Fractions  are  omitted,  except  in  the  percentage 
column,  as  the  degree  of  accuracy  their  use  would  seem  to  imply  is  not 
attained  or  aimed  at. 


Cut-off 

Mean 
Effective 

Total 
Terminal 

Indicated 
Rate,  Ibs. 

Assumed. 

Product 

Part  of 

of  Cols. 

Stroke. 

Jr  ressure. 
Ibs.  per 
sq.  in. 

Ibs.  per 
sq.  in. 

I.H.P.  per 
hour. 

Act'lRate. 

%  Loss. 

1  and  6. 

0.10 

18 

11 

20 

32 

58 

5.8 

0.15 

27 

15 

19 

27 

41 

6.15 

0.20 

35 

20 

19 

25 

31.5 

6.3 

0.25 

42 

25 

20 

25 

25 

6.25 

0.30 

48 

30 

20 

24 

21.8 

6.54 

0.35 

53 

35 

21 

25 

19 

6.65 

0.40 

57 

38 

22 

26 

16.7 

6.68 

0.45 

61 

43 

23 

27 

15 

6.75 

0.50 

64 

48 

24 

27 

13.6 

6.8 

It  will  be  seen  that  while  the  best  indicated  economy  is  when  the  cut-off 
Is  about  at  0.15  or  0.20  of  the  stroke,  giving  about  30  Ibs.  M.E.P.,  and  a 
terminal  3  or  4  Ibs.  above  atmosphere,  when  we  come  to  add  the  per- 
centages due  to  a  constant  amount  of.  unindicated  loss,  as  per  sixth 
column,  the  most  economical  point  of  cut-off  is  found  to  be  about  0.30  of 
the  stroke,  giving  48  Ibs.  M.E.P.  and  30  Ibs.  terminal  pressure.  This 
showing  agrees  substantially  with  modern  experience  under  automatic 
cut-off  regulation. 

The  last  column  shows  that  the  actual  amount  of  cylinder  condensation 
is  nearly  a  constant  quantity,  increasing  only  from  5.8%  of  the  cylinder 
volume  at  0.10  cut-off  to  6.8%  at  0.50  cut-off.  • 

Experiments  on  Cylinder-condensation.  —  Experiments  by  Major 
Thos.  English  (Eng'g,  Oct.  7,  1887,  p.  386)  with  an  engine  10  X  14  in., 
jacketed  in  the  sides  but  not  on  the  ends,  indicate  that  the  net  initial 
condensation  (or  excess  of  condensation  over  re-evaporation)  by  the 
clearance  surface  varies  directly  as  the  initial  density  of  the  steam,  and 
inversely  as  the  square  root  of  the  number  of  revolutions  per  unit  of  time. 
The  mean  results  gave  for  the  net  initial  condensation  by  clearance-space 
per  sq.  ft.  of  surface  at  one  rev.  per  second  6.06  thermal  units  in  the  engine 
when  run  non-condensing  and  5.75  units  when  condensing. 

G.  R.  Bodmer  (Eng'g,  March  4,  1892,  p.  299)  says:  Within  the  ordinary 
limits  of  expansion  desirable  in  one  cylinder  the  expansion  ratio  has 
practically  no  influence  on  the  amount  of  condensation  per  stroke,  which 
for  simple  engines  can  be  expressed  by  the  following  formula  for  the 
weight  of  water  condensed  [per  minute,  probably;  the  original  does  not 

state]:    W  =  CJ  T      ~— .  where  T  denotes  the  mean  admission  temper- 

L$N* 

ature,  t  the  mean  exhaust  temperature,  S  clearance-surface  (square  feet)t 
N  the  number  of  revolutions  per  second,  L  latent  heat  of  steam  at  the 
mean  admission  temperature,  and  C  a  constant  for  any  given  type  of 
engine. 

Mr.  Bodmer  found  from  experimental  data  that  for  high-pressure  non- 
jacketed  engines  C  =  about  0.11,  for  condensing  non-jacketed  engines 
0.085  to  0.11,  for  condensing  jacketed  engines  0.085  to  0.053.  The 
figures  for  jacketed  engines  apply  to  those  jacketed  in  the. usual  way, 
and  not  at  the  ends. 

C  varies  for  different  engines  of  the  same  class,  but  is  practically  con- 
stant for  any  given  engine.  For  simple  high-pressure  non-jacketed 
engines  it  was  found  to  range  from  0.1  to  0.112. 

Applying  Mr,  Bodmer's  formula  to  the  case  of  a  Corliss  non-jacketed 


968 


THE   STEAM   ENGINE. 


non-condensing  engine,  4-ft.  stroke,  24  in.  diam.,  60  revs,  per  min.,  initial 
ressure  90  Ibs.  gauge,  exhaust  pressure  2  Ibs.,  we  have  T  -  t  =•  112°, 
=  1,    L  =  880,  S  =  7  sq.   ft.;   and,    taking  C  =  0.112   and    W=  Ibs. 
water    condensed    per    minute, 


pr 

M 


W  = 


0.09    Ib.    per 


minute,  or  5.4  Ibs.  per  hour.  If  the  steam  used  per  I.H.P.  per  hour 
nSc?r,King  to  the  diag™m  is  20  Ibs.,  the  actual  water  consumption  is 
25.4  Ibs.,  corresponding  to  a  cylinder  condensation  of  27%. 

INDICATOR-DIAGRAM  OF  A  SINGLE-CYLINDER  ENGINE. 

Definitions.  —  The  Atmospheric  Line,  AB,  is  a  line  drawn  by  the  pencil 
of  the  indicator  when  the  connections  with  the  engine  are  closed  and  both 

sides   of  the  piston 

-=-K  are     open     to     the 

atmosphere. 

The  Vacuum  Line, 
OX,  is  a  reference 
line  usually  drawn 
about  14.7  pounds 
by  scale  below  the 
atmospheric  line. 

The  Clearance 
Line,  OF,  is  a  refer- 
ence line  drawn  at  a 
distance  from  the 
end  of  the  diagram 
equal  to  the  same 
per  cent  of  its  length 
as  the  clearance  and 
B  waste  room  is  of  the 
piston-displacement  . 
-X  The  Line  of  Boiler- 

„  pressure,    JK,    is 

tic.  162.  drawn  parallel  to  the 

atmospheric  line,  and  at  a  distance  from  it  by  scale  equal  to  the  boiler- 
pressure  shown  by  the  gauge. 

The  Admission  Line,  CD,  shows  the  rise  of  pressure  due  to  the  admission 
of  steam  to  the  cylinder  by  opening  the  steam-valve. 

The  Steam  Line,  DE,  is  drawn  when  the  steam-valve  is  open  and  steam 
is  being  admitted  to  the  cylinder. 

The  Point  of  Cut-off,  E,  is  the  point  where  the  admission  of  steam  is 
stopped  by  the  closing  of  the  valve.  It  is  often  difficult.  to  determine 
the  exact  point  at  which  the  cut-off  takes  place.  It  is  usually  located 
where  the  outline  of  the  diagram  changes  its  curvature  from  convex  to 
concave. 

The  Expansion  Curve,  EF,  shows  the  fall  in  pressure  as  the  steam  in  the 
cylinder  expands  doing  work. 

The  Point  of  Release,  F,  shows  when  the  exhaust-valve  opens. 
The  Exhaust  Line,  FG,  represents  the  change  in  pressure  that  takes 
place  when  the  exhaust-valve  opens. 

The  Back-pressure  Line,  GH,  shows  the  pressure  against  which  the 
piston  acts  during  its  return  stroke. 

The  Point  of  Exhaust  Closure,  H,  is  the  point  where  the  exhaust-valve 
closes.  It  cannot  be  located  definitely,  as  the  change  in  pressure  is  at  first 
due  to  the  gradual  closing  of  the  valve. 

The  Compression  Curve,  HC,  shows  the  rise  in  pressure  due  to  the  com- 
pression of  the  steam  remaining  in  the  cylinder  after  the  exhaust-valve 
has  closed. 

The  Mean  Height  of  the  Diagram  equals  its  area  divided  by  its  length. 
The  Mean  Effective  Pressure  is  the  mean  net  pressure  urging  the  piston 
forward  =  the  mean  height  X  the  scale  of  the  indicator-spring. 

To  find  the  Mean  Effective  Pressure  from  the  Diagram.  —  Divide  the 
length,  LB,  into  a  number,  say  10,  equal  parts,  setting  off  half  a  part  at 
L,  half  a  part  at  B,  and  nine  other  parts  between;  erect  ordinates  perpen- 
dicular to  the  atmospheric  line  at  the  points  of  division  of  LB,  cutting 
the  diagram;  add  together  the  lengths  of  these  ordinates  intercepted 


INDlCAtOK-DIAGUAMS. 


969 


between  the  upper  and  lower  lines  of  the  diagram  and  divide  by  their 
number.  This  gives  the  mean  height,  which  multiplied  by  the  scale  of 
the  indicator-spring  gives  the  M.E.P.  Or  find  the  area  by  a  planimeter, 
or  other  means  (see  Mensuration,  p.  56),  and  divide  by  the  length  LB 
to  obtain  the  mean  height. 

The  Initial  Pressure  is  the  pressure  acting  on  the  piston  at  the  beginning 
of  the  stroke. 

The  Terminal  Pressure  is  the  pressure  above  the  line  of  perfect  vacuum 
that  would  exist  at  the  end  of  the  stroke  if  the  steam  had  not  been  released 
earlier.  It  is  found  by  continuing  the  expansion-curve  to  the  end  of  the 
diagram. 

A  single  indicator  card  shows  the  pressure  exerted  by  the  steam  at 
each  instant  on  one  side  of  the  piston;  a  card  taken  simultaneously  from 
the  opposite  end  of  the  engine  shows  the  pressure  exerted  on  the  other 
nrte.  By  superposing  these  cards  the  pressure  or  tension  on  the  piston 

I  may  be  determined.     The  pressure  or  pull  on  the  crank  pin  at  any 

itant  is  the  pressure  or  tension  in  the  rod  modified  by  the  angle  of  the 

innecting  rod  and  by  the  effect  of  the  inertia  of  the  reciprocating  parts. 

Dr  discussion  of  this  subject  see  Klein's  "High-speed  Steam  Engine," 

so  papers  by  S.  A.  Moss,  Trans.  A.  S.  M.  E.,  1904,  and  by  F.  W.  Holl- 

ann,  in  Power,-  April  6,  1909. 

Errors  of  Indicators.  —  The  most  common  error  is  that  of  the  spring, 
which  may  vary  from  its  normal  rating;  the  error  may  be  determined  by 
— oper  testing  apparatus  and  allowed  for.  But  after  making  this  correc- 

>n,  even  with  the  best  work,  the  results  are  liable  to  variable  errors 

lich  may  amount  to  2  or  3  per  cent.     See  Barrus,  Trans.  A.  S.  M.  E., 

310;  Denton,  Trans.  A.  S.  M.  E.,  xi,  329;  David  Smith,  U.  S.  N.,  Proc. 
*'g  Congress,  1893,  Marine  Division. 

.  ther  errors  of  indicator  diagrams  are  those  due  to  inaccuracy  of  the 
straight-line  motion  of  the  indicator,  to  the  incorrect  design  or  position 
of  the  "rig"  or  reducing  motion,  to  long  pipes  between  the  indicator  and 
the  engine,  to  throttling  of  these  pipes,  to  friction  or  lost  motion  in  the 
indicator  mechanism,  and  to  drum-motion  distortion.  For  discussion  of 
the  last  named  see  Power,  April,  1909.  For  methods  of  testing  indicators, 
see  paper  by  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  1898. 

Indicator  "Rigs,"  or  Reducing-motions;  Interpretation  of  Diagrams 
for  Errors  of  Steam-distribution,  etc.  For  these  see  circulars  of  manu- 
facturers of  Indicators;  also  works  on  the  Indicator. 

Pendulum  Indicator  Rig.  —  Power  (Feb.,  1893)  gives  a  graphical 
representation  of  the  errors  in  indicator-diagrams,  caused  by  the  use  of 
incorrect  forms  of  the  pendulum  rigging.  It 
is  shown  that  the  "brumbo"  pulley  on  the 
pendulum,  to  which  the  cord  is  attached, 
does  not  generally  give  as  good  a  reduction 
as  a  simple  pin  attachment.  When  the  end 
of  the  pendulum  is  slotted,  working  in  a  pin 
on  the  crosshead,  the  error  is  apt  to  be  con- 
siderable at  both  ends  of  the  card.  With  a 
vertical  slot  in  a  plate  fixed  to  the  cross- 
head,  and  a  pin  on  the  pendulum  working  in 
this  slot,  the  reduction  is  perfect,  when  the 
cord  is  attached  to  a  pin  on  the  pendulum, 
a  slight  error  being  introduced  if  the  brumbo 
pulley  is  used.  With  the  connection  be- 
tween the  pendulum  and  the  crosshead  made 
by  means  of  a  horizontal  link,  the  reduction 


whk 

1 

strai 


FIG.  163. 


is  nearly  perfect,  if  the  construction  is  such  that  the  connecting  link 
vibrates  equally  above  and  below  the  horizontal,  and  the  cord  is  attached 
by  a  pin.  If  the  link  is  horizontal  at  mid-stroke  a  serious  error  is  intro- 
duced, which  is  magnified  if  a  brumbo  pulley  also  is  used.  The  adjoin- 
ing figures  show  the  two  forms  recommended. 

The  Manograph,  for  indicating  engines  of  very  high  speed,  invented 
by  Prof.  Hospitalier,  is  described  by  Howard  Greene  in  Power,  June,  1907. 
It  is  made  by  Carpentier,  of  Paris.  A  small  mirror  is  tilted  upward  and 
downward  by  a  diaphragm  which  responds  to  the  pressure  variations  in 
the  cylinder,  and  the  same  mirror  is  rocked  from  side  to  side  by  a  reducing 
mechanism  which  is  geared  to  the  engine  and  reproduces  the  reciprocations 


D70  fHE   STEAM-ENGINE. 

of  the  engine  piston  on  a  smaller  scale.  A  beam  of  light  is  reflected  by 
the  mirror  to  the  ground-glass  screen,  and  this  beam,  by  the  oscillations 
of  the  mirror,  is  made  to  traverse  a  path  corresponding  to  that  of  the 
pencil  point  of  an  ordinary  indicator.  The  diagram,  therefore,  is  made 
continuously  but  varies  with  varying  conditions  in  the  cylinder. 

A  plate-holder  carrying  a  photographic  dry  plate  can  be  substituted  for 
the  ground  -glass  screen,  and  the  diagram  photographed,  the  exposure 
required  varying  from  half  a  second  to  three  seconds.  By  the  use  of 
special  diaphragms  and  springs  the  effects  of  low  pressures  and  vacuums 
can  be  magnified,  and  thus  the  instrument  can  be  made  to  show  with 
remarkable  clearness  the  action  of  the  valves  of  a  gas  engine  on  the  suction 
and  exhaust  strokes. 

The  Lea  Continuous  Recorder,  for  recording  the  steam  consumption 
of  an  engine,  is  described  by  W.  H.  Booth  in  Power,  Aug.  31,  1909.  It 
comprises  a  tank  into  which  flows  the  condensed  steam  from  a  condenser, 
a  triangular  notch  through  which  the  water  flows  from  the  tank,  and  a 
mechanical  device  through  which  the  variations  in  the  level  of  the  water 
In  the  tank  are  translated  into  the  motion  of  a  pencil,  which  motion  is 
made  proportionate  to  the  quantity  flowing,  and  is  recorded  on  paper 
moved  by  clockwork. 

INDICATED  HORSE-POWER  OF  ENGINES,  SINGLE-CYLINDER. 


Indicated  Horse-power,  I.H.P.  =     0, 

oo,000 

in  which  P  =  mean  effective  pressure  in  Ibs.  per  sq.  in.;  L  =  length  of 
stroke  in  feet;  a  =  area  of  piston  in  square  inches.  For  accuracy,  one 
half  of  the  sectional  area  of  the  piston-rod  must  be  subtracted  from  the 
area  of  the  piston  if  the  rod  passes  through  one  head,  or  the  whole  area  of 
the  rod  if  it  passes  through  both  heads;  n  =  No.  of  single  strokes  per  min. 
—  2  X  No.  of  revolutions  of  a  double-acting  engine. 

n~  r> 

I.H.P.  =^-7:7^  »  in  which  *S  =  piston  speed  in  feet  per  minute. 
00,000 


I.H.P.  =  =  =  0-0000238  PLd*n  =  0.0000238  P&S, 


In  which  d  =  diam.  of  cyl.  in  inches.  (The  figures  238  are  exact,  since 
7854  •*•  33  =  23.8  exactly.)  If  product  of  piston-speed  X  mean  effec- 
tive pressure  =  42,017,  then  the  horse-power  would  equal  the  square  of 
the  diameter  in  inches. 

Handy  Rule  for  Estimating  the  Horse-power  of  a  Single-cylinder 
Engine.  —  Square  the  diameter  and  divide  by  2.  This  is  correct  whenever 
the  product  of  the  mean  effective  pressure  and  the  piston-speed  =  1/2 
of  42,017,  or,  say,  21,000,  viz.,  when  M.E.P.  =  30  and  S  =  700;  when 
M.E.P.  =  35  and  S  =  600;  when  M.E.P.  =  38.2  and  S  =  550;  and  when 
M.E.P.  =  42  and  S  =  500.  These  conditions  correspond  to  those  of 
ordinary  practice  with  both  Corliss  engines  and  shaft-governor  high-speed 
engines. 

Given  Horse-power,  Mean  Effective  Pressure,  and  Piston-speed, 
to  find  Size  of  Cylinder.  — 


,  ..  ^.  ,  ./I.H. 

Area  =  --  -        -  •        Diameter  =  205  y     ps 


33,000  X  I.H.P          ^.  ,  ./I.H.P. 

--  -        -  •  =  • 


Brake  Horse-power  is  the  actual  horse-power  of  the  engine  as  measured 
at  the  fly-wheel  by  a  friction-brake  or  dynamometer.  It  is  the  indicated 
horse-power  minus  the  friction  of  the  engine. 

Electrical  Horse-power  is  the  power  in  an  electric  current,  usually 
measured  in  kilowatts,  translated  into  horse-power.  1  H.P.  =  33,000 
ft.  Ibs.  per  min.;  1  K.W.=  1.3405  H.P.;  1  H.P.  =  0.746  kilowatts,  or 
746  watts. 

EXAMPLE.  —  A  100-H.P.  engine,  with  a  friction  loss  of  10%  at  rated 
load,  drives  a  generator  whose  efficiency  is  90%,  furnishing  current  to  a 
motor  of  90%  effy.,  through  a  line  whose  loss  is  5%.      I.H.P.  = 
B.H.P.  =  90;  E.H.P.  at  generator  81,  at  end  of  line  76.95.     H.P,  delivered 
by  motor  69.26. 


INDICATED   HORSE-POWER  OP  ENGINES. 


971 


Table  for  Roughly  Approximating  the  Horse-power  of  a  Com- 
pound Engine  from  the  Diameter  of  its  Low-pressure  Cylinder.  — 

The  indicated  horse-power  of  an  engine  being    42017'  in  which  P=* 

mean  effective  pressure  per  sq.  in.,  s  =  piston-speed 'in  ft.  per  min.,  and 
d  =  diam.  of  cylinder  in  inches;  if  s  =  600  ft.  per  min.,  which  is  approxi- 
mately the  speed  of  modern  stationary  engines,  and  P  =  35  Ibs.,  which  is 
an  approximately  average  figure,  for  the  M.E.P.  of  single-cylinder  engines, 
and  of  compound  engines  referred  to  the  low-pressure  cylinder,  then 
I.H.P.  =  i/2^2;  hence  the  rough-and-ready  rule  for  horse-power  given 
above:  Square  the  diameter  in  inches  and  divide  by  2.  This  applies  to 
triple  and  quadruple  expansion  engines  as  well  as  to  single  cylinder  and 
compound.  For  most  economical  loading,  the  M.E.P.  referred  to  the 
low-pressure  cylinder  of  compound  engines  is  usually  not  greater  than 
that  of  simple  engines;  for  the  greater  economy  is  obtained  by  a  greater 
number  of  expansions  of  steam  of  higher  pressures,  and  the  greater  the 
number  of  expansions  for  a  given  initial  pressure  the  lower  the  mean 
effective  pressure.  The  following  table  gives  approximately  the  figures 
of  mean  total  and  effective  pressures  for  the  different  types  of  engines, 
together  with  the  factor  by  which  the  square  of  the  diameter  is  to  be 
multiplied  to  obtain  the  horse-power  at  most  economical  loading,  for  a 
piston-speed  of  600  ft.  per  minute. 


Type  of  Engine. 


- 

d  H  o 

SB'S 


Ill 

mi 


53  O> 


US 


o>  X 


Non-condensing. 


Single  Cylinder  .  . 
Compound 

100 
120 

5. 
7  5 

20 
16 

0.522 
402 

52.2 
48  2 

15.5 
15.5 

36.7 
32.7 

600 

0.524 
467 

Triple  

160 

10. 

16 

.330 

52.8 

15.5 

37.3 

n 

.533 

Quadruple  

200 

12.5 

16 

.282 

56.4 

15.5 

40.9 

" 

.584 

Condensing  Engines. 


Single  Cylinder.. 
Compound 

100 
120 

10. 
15 

10 

8 

0.330 

247 

33.0 
29  6 

2 

2 

31.0 
27  6 

600 

0.443 
390 

Triple   

160 

20. 

8 

.200 

32.0 

2 

30  0 

M 

.429 

Quadruple  

200 

25. 

8 

.169 

33.8 

2 

31.8 

" 

.454 

For  any  other  piston-speed  than  600  ft.  per  min.,  multiply  the  figurei 
in  the  last  column  by  the  ratio  of  the  piston-speed  to  600  ft. 

Horse-power  Constant  of  a  given  Engine  for  a  Fixed  Speed  — 
product  of  its  area  of  piston  in  square  inches,  length  of  stroke  in  feet 

and  number  of  single  strokes  per  minute  divided  by  33,000,  or      ' 

•  oo.UUU 

—  C.  The  product  of  the  mean  effective  pressure  as  found  by  the  dia- 
gram and  this  constant  is  the  indicated  horse-power. 

Horse-power  Constant  of  any  Engine  of  a  given  Diameter  of 
Cylinder,  whatever  the  length  of  stroke,  =  area  of  piston  -H  33,000  =  square 
of  the  diameter  of  piston  in  inches  X  0.0000238.  A  table  of  constants 
derived  from  this  formula  is  given  on  page  973. 

The  constant  multiplied  by  the  piston-speed  in  feet  per  minute  and 
by  the  M.E.P.  gives  the  I.H.P. 

Table  of  Engine  Constants  for  Use  in  Figuring  Horse-power.  — 
"Horse-power  constant"  for  cylinders  from  1  inch  to  60  inches  in  diam- 
eter, advancing  by  8ths.  for  one  foot  of  piston-speed  per  minute  and  one 
pound  of  M.E.P.  Find  the  diameter  of  the  cylinder  in  the  column  -at  the 
side.  If  the  diameter  contains  no  fraction  the  constant  will  be  found  in 
the  column  headed  Even  Inches.  If  the  diameter  is  not  in  even  inches, 
follow  the  line  horizontally  to  the  column  corresponding  to  the  required 
fraction.  The  constants  multiplied  by  the  piston-speed  and  by  the 
M.E.P.  give  the  horse-power. 


"972 


THE  STEAM-ENGINE. 


Engine  Constants,  Constant  X  Piston  Speed  X  M.E.P.  *=H.P. 


Diam.o 
Cylin- 
der. 

Even 
Inches. 

+  1/8 

+  1/4 

+  3/8 

+  1/2 

+  5/8 

+  3/4 

+  7/8 

1 

.0000238 

.0000301 

.0000372 

.0000450 

.0000535 

.0000628 

.0000729 

.0000837 

2 

.0000952 

.0001074 

.0001205 

.0001342 

.0001487 

.0001640 

.0001800 

.0001967 

3 

.0002142 

.0002324 

.0002514 

.0002711 

.0002915 

.0003127 

.0003347 

.0003574 

4 

.0003808 

.0004050 

.0004299 

.0004554 

.0004819 

.0005091 

.0005370 

.0005656 

5 

.0005950 

.0006251 

.0006560 

.0006876 

.0007199 

.0007530 

.0007869 

.0008215 

6 

.0008568 

.0008929 

.0009297 

.0009672 

.0010055 

.0010445 

.0010844 

.0011249 

7 

.0011662 

.0012082 

.0012510 

.0012944 

.0013387 

.0013837 

.0014295 

.0014759 

8 

.0015232 

.0015711 

.0016198 

.0016693 

.0017195 

.0017705 

.0018222 

.0018746 

9 

.0019278 

.0019817 

.0020363 

.0020916 

.0021479 

.0022048 

.0022625 

.0023209 

10 

.0023800 

.0024398 

.0025004 

.0025618 

.0026239 

.0026867 

.0027502 

.0028147 

11 

.0028798 

.0029456 

.0030121 

.0030794 

.0031475 

.0032163 

.0032859 

.0033561 

12 

.0034272 

.0034990 

.0035714 

.0036447 

.0037187 

.0037934 

.0038690 

.0039452 

13 

.0040222 

.0040999 

.0041783 

.0042576 

.0043375 

.0044182 

.0044997 

.0045819 

14 

.0046648 

0047484 

.0048328 

.0049181 

.0050039 

.0050906 

.0051780 

.0052661 

15 

.0053550 

0054446 

.0055349 

.0056261 

.0057179 

.0058105 

.0059039 

.0059979 

16 

.0060928 

0061884 

.0062847 

.0063817 

.0064795 

.0065780 

.0066774 

.0067774 

17 

0068782 

0069797 

.0070819 

.0071850 

.0072887 

.0073932 

.0074985 

.0076044 

18 

0077112 

0078187 

.0079268 

.0080360 

.0081452 

.0082560 

.0083672 

.0084791 

19 

0085918 

0087052 

0088193 

0089343 

.0090499 

.0091663 

.0092835 

.0094013 

20 

0095200 

0096393 

0097594 

0098803 

.0100019 

.0101243 

.0102474 

.0103712 

21 

0104958 

0106211 

0107472 

0108739 

.0110015 

.0111299 

.0112589 

.0113886 

22 

0115192 

0116505 

0117825 

0119152 

.0120487 

.0121830 

.0123179 

.0124537 

23 

0125902 

0127274 

0128654 

0130040 

.0131435 

.0132837 

.0134247 

.0135664 

24 

0137088 

0138519 

0139959 

0141405 

.0142859 

.0144321 

.0145789 

.0147266 

25 

0148750 

0150241 

0151739 

0153246 

.0154759 

.0156280 

.0157809 

.0159345 

26 

0160888 

0162439 

0163997 

0165563 

0167135 

.0168716 

.0170304 

.0171899 

27 

0173502 

0175112 

0176729 

0178355 

.0179988 

.0181627 

.0183275 

.0184929 

28 

0186592 

0188262 

0189939 

0191624 

0193316 

.0195015 

.0196722 

0198436 

29 

0200158 

0201887 

0203634 

0205368 

0207119 

.0208879 

.0210645 

0212418 

30 

0214200 

0215988 

0217785 

0219588 

0221399 

.0223218 

.0225044 

0226877 

31 

0228718 

0230566 

0232422 

0234285 

0236155 

.0238033 

.0239919 

0241812 

32 

0243712 

0245619 

0247535 

0249457 

0251387 

.0253325 

.0255269 

0257222 

33 

0259182 

0261149 

0263124 

0265106 

0267095 

.0269092 

.0271097 

0273109 

34 

0275128 

0277155 

0279189 

0281231 

0283279 

.0285336 

.0287399 

0289471 

35 

0291550 

0293636 

0295729 

0297831 

0299939 

.0302056 

.0304179 

0306309 

36 

0308448 

0310594 

0312747 

0314908 

0317075 

.0319251 

.0321434 

0323624 

37 

0325822 

0328027 

0330239 

0332460 

0334687 

.0336922 

.0339165 

0341415 

38 

0343672 

0345937 

0348209 

0350489 

0352775 

.0355070 

0357372 

.0359681 

39 

0361998 

0364322 

0366654 

0368993 

8371339 

.0373694 

0376055 

.0378424 

40 

0380800 

0383184 

0385575 

0387973 

0390379 

.0392793 

0395214 

.0397642 

41 

0400078 

0402521 

0404972 

0407430 

0409895 

.0412368 

0414849 

.0417337 

42 

0419832 

0422335 

0424845 

0427362 

0429887 

0432420 

0434959 

.0437507 

43 

0440062 

0442624 

0445194 

0447771 

0450355 

0452947 

0455547 

.0458154 

44 

0460768 

0463389 

0466019 

0468655 

0471299 

0473951 

0476609 

.0479276 

45 

0481950 

0484631 

0487320 

0490016 

0492719 

0495430 

0498149 

.0500875 

46 

0503608 

0506349 

0509097 

0511853 

0514615 

0517386 

0520164 

.0522949 

47 

0525742 

0528542 

0531349 

0534165 

0536988 

0539818 

0542655 

.0545499 

48 

0548352 

0551212 

0554079 

0556953 

0559835 

0562725 

0565622 

.0568526 

49 

0571438 

0574357 

0577284 

0580218 

0583159 

0586109 

0589065 

.0592029 

50 

0595000 

0597979 

0600965 

0603959 

0606959 

0609969 

0612984 

.0616007 

51 

0619038 

0622076 

0625122 

0628175 

0632235 

0634304 

0637379 

.0640462 

52 

0643552 

0646649 

0649753 

0652867 

0655987 

0659115 

0662250 

.0665392 

53 

0668542 

0671699 

0674864 

0678036 

0681215 

0684402 

0687597 

.0690799 

54 

0694008 

0697225 

0700449 

0703681 

0705293 

0710166 

0713419 

.0716681 

55  , 

0719950 

0724226 

0726510 

0729801 

0733099 

0736406 

0739719 

.0743039 

56 

0746368 

0749704 

0753047 

0756398 

0759755 

0763120 

0766494 

.0769874 

57 

0773262 

0776657 

0780060 

0783476 

0786887 

0790312 

0793745 

.0797185 

58 

0800632 

0804087 

0807549 

0811019 

0814495 

0817980 

0821472 

.0824971 

59 

0828478 

0831992 

0835514 

0839043 

0842579 

0846123 

.0849675 

.0853234 

60 

0856800 

0860374 

0863955 

0867543 

0871139 

0874743 

.0878354 

.0881973 

INDICATED  HORSE-POWER  OF  ENGINES. 


973 


Horse-power  per  Pound  Mean  Effective  Pressure. 

Formula,  Area  in  sq.  in.  X  piston-speed  -5-  33,000. 


Diam  of 
Cylinder, 
inches. 

Speed  of  Piston  in  feet  per  minute. 

100 

200 

300 

400 

500 

600 

700 

800 

900 

4 

.0381 

.0762 

.1142 

.1523 

.1904 

.2285 

.2666 

.3046 

.3427 

41/2 

.0482 

.0964 

.1446 

.1928 

.2410 

.2892 

.3374 

.3856 

.4338 

5 

.0595 

.1190 

.1785 

.2380 

.2975 

.3570 

.4165 

.4760 

.5355 

31/2 

.0720 

.1440 

.2160 

.2880 

.3600 

.4320 

.5040 

.5760 

.6480 

6 

.0857 

.1714 

.2570 

.3427 

.4284 

.5141 

.5998 

.6854 

.7711 

61/2 

.1006 

.2011 

.3017 

.4022 

.5028 

.6033 

.7039 

.8044 

.9050 

7 

.1166 

.2332 

.3499 

.4665 

.5831 

.6997 

.8163 

.9330 

.0496 

71/2 

.1339 

.2678 

.4016 

.5355 

.6694 

.8033 

.9371 

.0710 

.2049 

8 

.1523 

.3046 

.4570 

.6093 

.7616 

.9139 

.0662 

.2186 

.3709 

81/2 

.1720 

.3439 

.5159 

.6878 

.8598 

.0317 

.2037 

.3756 

.5476 

9 

.1928 

.3856 

.5783 

.7711 

.9639 

.1567 

.3495 

.5422 

.7350 

91/2 

.2148 

.4296 

.6444 

.8592 

1.0740 

.2888 

.5036 

.7184 

.9532 

10 

.2380 

.4760 

.7140 

.9520 

1.1900 

.4280 

.6660 

.9040 

2.1420 

11 

.2880 

.   .5760 

.8639 

1.1519 

1.4399 

.7279 

2.0159 

2.3038 

2.5818 

12 

.3427 

.6854 

.0282 

1.3709 

1.7136 

2.0563 

2.3990 

2.7418 

3.0845 

13 

.4022 

.8044 

.2067 

1  .6089 

2.0111 

2.4133 

2.8155 

3.2178 

3.6200 

14 

.4665 

.9330 

.3994 

1.8659 

2.3324 

2.7989 

3.2654 

3.7318 

4.1983 

15 

.5355 

.0710 

.6065 

2.1420 

2.6775 

3.2130 

3.7485 

4.2840 

4.8195 

16 

.6093 

.2186 

.8278 

2.4371 

3.0464 

3.6557 

4.2650 

4.8742 

5.4835 

17 

.6878 

.3756 

2.0635 

2.7513 

3.4391 

4.1269 

4.8147 

5.5026 

6.1904 

18. 

.7711 

.5422 

2.3134 

3.0845 

3.8556 

4.6267 

5.3978 

6.1690 

6.9401 

19 

.8592 

.7184 

2.5775 

3.4367 

4.2959 

5.1551 

6.0143 

6.8734 

7.7326 

20 

.9520 

.9040 

2.8560 

3.8080 

4.7600 

5.7120 

6.6640 

7.6160 

8.5680 

21 

.0496 

2.0992 

3.1488 

4.1983 

5'.  2479 

6.2975 

7.3471 

8.3966 

9.4462 

22 

.1519 

2.3038 

3.4558 

4.6077 

5.7596 

6.9115 

8.0634 

9.2154 

10.367 

23 

.2590 

2.5180 

3.7771 

5.0361 

6.2951 

7.5541 

8.8131 

10.072 

11.331 

24 

.3709 

2.7418 

4.1126 

5.4835 

6.8544 

8.2253 

9.5962 

10.967 

12.338 

25 

.4875 

2.9750 

4.4625 

5.9500 

7.4375 

8.9250 

10.413 

11.900 

13.388 

26 

.6089 

3.2178 

4.8266 

6.4355 

8.0444 

9.6534 

11.262 

12.871 

14.480 

27 

.7350 

3.4700 

5.2051 

6.9401 

8.6751 

10.410 

12.145 

13.880 

15.615 

28 

.8659 

3.7318 

5.5978 

7.4637 

9.3296 

1  1  .  196 

13.061 

14.927 

16.793 

29 

2.0016 

4.0032 

6.0047 

8.0063 

10.008 

12.009 

14.011 

16.013 

18.014 

30 

2.1420 

4.2840 

6.4260 

8.5680 

10.710 

12.852 

14.994 

17.136 

19.278 

31 

2.2872 

4.5744 

6.8615 

9.1487 

11.436 

13.723 

16.010 

18.297 

20.585 

32 

2.4371 

4.8742 

7.3114 

9.7485 

12.186 

14.623 

17.060 

14.497 

21.934 

»33 

2.5918 

5.1836 

7.7755 

10.367 

12.959 

15.551 

18.143 

20.735 

23.326 

34 

2.7513 

5.5026 

8.2538 

11.005 

13.756 

16.508 

19.259 

22.010 

24.762 

35 

2.9155 

5.8310 

8.7465 

11.662 

14.578 

17.493 

20.409 

23.324 

26.240 

36 

3.0845 

6.1690 

9.2534 

12.338 

15.422 

18.507 

21.591 

24.676 

27.760 

37 

3.2582 

6.5164 

9.7747 

13.033 

16.291 

19.549 

22.808 

26.066 

29.324 

38 

3.4367 

6.8734 

10.310 

13.747 

17.184 

20.620 

24.057 

27.494 

30.930 

39 

3.6200 

7.2400 

10.860 

14.480 

18.100 

2  .720 

25.340 

28.960 

32.580 

40 

3.8080 

7.6160 

11.424 

15.232 

19.040 

22.848 

26.656 

30.464 

34.272 

41 

4.0008 

8.0016 

12.002 

16.003 

20.004 

24.005 

28.005 

32.006 

36.007 

42 

4.1983 

8.3866 

12.585 

16.783 

20.982 

25.180 

29.378 

33.577 

37.775 

43 

4.4006 

8.8012 

13.202 

17.602 

22.003 

26.404 

30.804 

35.205 

39.606 

44 

4.6077 

9.2154 

13.823 

18.431 

23.038 

27.646 

32.254 

36.861 

4  .469 

45 

4.8195 

9.6390 

14.459 

19.278 

24.098 

28.917 

33.737 

38.556 

43.376 

46. 

5.0361 

10.072 

15.108 

20.144 

25.180 

30.216 

35.253 

40.289 

45.325 

47 

5.2574 

10.515 

15.772 

21  .030 

26.287 

31.545 

36.802 

42.059 

47.317 

48 

5.4835 

10.967 

16.451 

21.934 

27.418 

32.901 

38.385 

43.868 

49.352 

49 

5.7144 

11.429 

17.143 

22.858 

28.572 

34.286 

40.001 

45.715 

51.429 

50 

.9:00 

11.900 

17.850 

23.800 

29.750 

35.700 

41.650 

47.600 

3.550 

5! 

.1904 

12.381 

18.571 

24.762 

30.952 

37.142 

43.333 

49.523 

5.713 

52 

.4355 

12.871 

19.307 

25.742 

32.178 

38.613 

45.049 

1.484 

7.920 

53 

.6854 

13.371 

20.056 

26.742 

33.427 

40.113 

46.798 

3.483 

60.169 

54 

.9401 

13.880 

20.820 

27.760 

34.700 

41.640 

48.581 

5.521 

2.461 

55 

7.1995 

14.399 

2  .599 

28.798 

35.998 

43.197 

50.397 

7.596 

4.796 

56 

7.4637 

14.927 

22.391 

29.855 

37.318 

44.782 

52.246 

9.709 

7.173 

57 

7.7326 

15.465 

23.198 

30.930 

38.663 

46.396 

54.128 

1.861 

9.597 

58 

8.0063 

16.013 

24.019 

32.025 

40.032 

48.038 

56.044 

4.051 

2.054 

59 

8.2848 

16.570 

24.854 

33.139 

41.424 

49.709 

57.993 

6.278 

4.563 

60 

8.5680 

17.136 

25.704 

34.272 

42.840 

51.408 

59.976 

8.544 

7.112 

974 


THE   STEAM-ENGINE. 


Nominal  Horse-power. —  The  term  "nominal  horse-power  "originated 
in -the  time  of  Watt,  and  was  used  to  express  approximately  the  power 
of  an  engine  as  calculated  from  its  diameter,  estimating  the  mean  pressure 
in  the  cylinder  at  7  Ibs.  above  the  atmosphere.  It  has  long  been  obsolete. 

Horse-power  Constant  of  a  given  Engine  for  Varying  Speeds  = 
product  of  its  area  of  piston  and  length  of  stroke  divided  by  33,000. 
This  multiplied  by  the  mean  effective  pressure  and  by  the  number  of 
jingle  strokes  per  minute  is  the  indicated  horse-power. 

To  draw   the   Clearance-line  on   the  Indicator-diagram,  the  ac- 


tual clearance  not  being  known.  — The  clearance-line  may  be  obtained 
approximately  by  drawing  a  straight  line,  cbad,  across  the  compression 


FIG.  164. 

curve,  first  having  drawn  OX  parallel  to  the  atmospheric  line  and  14.7 
Ibs.  below.  Measure  from  a  the  distance  ad,  equal  to  cb,  and  draw  YO 
perpendicular  to  OX  through  d;  then  will  TB  divided  by  AT  be  the  per- 
centage of  clearance.  The  clearance  may  also  be  found  from  the  expan- 
sion-line by  constructing  a  rectangle  efhg,  and  drawing  a  diagonal  gj 
to  intersect  the  line  XO.  This  will  give  the  point  0,  and  by  erecting  a 
perpendicular  to  XO  we  obtain  a  clearance-line  OY. 

Both  these  methods  for  finding  the  clearance  require  that  the  expan- 
sion and  compression  curves  be  hyperbolas.  Prof.  Carpenter  (Power, 
Sept.,  1893)  says  that  with  good  diagrams  the  methods  are  usually  very 
accurate,  and  give  results  which  check  substantially. 

The  Buckeye  Engine  Co.,  however,  says  that,  as  the  results  obtained  are 
seldom  correct,  being  sometimes  too  little,  but  more  frequently  too  much, 
and  as  the  indications  from  the  two  curves  seldom  agree,  the  operation 
has  little  practical  value,  though  when  a  clearly  defined  and  apparently 
undistorted  compression  curve  exists  of  sufficient  extent  to  admit  of  the 
application  of  the  process,  it  may  be  relied  on  to  give  much  more  correct 
results  than  the  expansion  curve. 

To  draw  the  Hyperbolic  Curve  on  the  Indicator-diagram.  —  Select 

any  point  /  in  the  actual  curve,  and 
from  this  point  draw  a  line  perpen- 
dicular to  the  line  JB,  meeting  the 
latter  in  the  point  J.  The  line  JB 
may  be  the  line  of  boiler-pressure, 
but  this  is  not  material;  it  may  be 
drawn  at  any  convenient  height  near 
the  top  of  the  diagram  and  parallel 
to  the  atmospheric  line.  From  J 
draw  a  diagonal  to  K,  the  latter 
point  being  the  intersection  of  the 
_  vacuum  and  clearance  lines;  from  7 
FIG.  165.  draw  IL  parallel  with  the  atmos- 

pheric line.     From  L,  the  point  of 
Intersection  of  the  diagonal  JK  and  the  horizontal  line  /£,  draw  the  verti- 


WATER-CONSUMPTION   OF  ENGINES.  975 

<»al  line  LM.  The  point  M  is  the  theoretical  point  of  cut-off,  and  LM  the 
cut-off  line.  Fix  upon  any  number  of  points  1,  2,  3,  etc.,  on  the  line  JB, 
and  from  these  points  draw  diagonals  to  K.  From  the  intersection  of  these 
diagonals  with  LM  draw  horizontal  lines,  and  from  1,2,  3,  etc.,  vertical 
lines.  Where  these  lines  meet  will  be  points  in  the  hyperbolic  curve. 

Theoretical  Water-consumption  calculated  from  the  Indicator- 
card.  —  The  following  method  is  given  by  Prof.  Carpenter  (Power, 
Sept.,  1893):  p  —  mean  effective  pressure,  I  =  length  of  stroke  in  feet, 
a  =  area  of  piston  in  square  inches,  a  •*-  144  =  area  in  square  feet,  c  = 
percentage  of  clearance  to  the  stroke,  b  =  percentage  of  stroke  at  point 
where  water  rate  is  to  be  computed,  n  =  number  of  strokes  per  minute, 
60  n  =  number  per  hour,  w  —  weight  of  a  cubic  foot  of  steam  having  a 
pressure  as  shown  by  the  diagram  corresponding  to  that  at  the  point  where 
water  rate  is  required,  w'  =  that  corresponding  to  pressure  at  end  01 
compression. 

Number  of  cubic  feet  per  stroke =1  (-jr^)  TTT' 

ponding  weight  of  steam  per  stroke  in  Ibs.  =  1 1 10QC)  rrg  w. 
olume  of  clearance  =  • 


eight  of  steam  in  clearance  =- 


• 

14,4UO 

Total  weight  of  1  _  7  /&+  c\  wa  _    Icaw'  la     ,,.  ,    *  „„    „„  „ 

steam  per  stroke  J  ~~  6  V  100  /  144       14,400  ~  14,400  U   "*"   '  w~cw  J' 

Total  weight  of  steam  )        60  nla  ...        .  .. 

from  diagram  per  hour)  =  14^00  [(6  +  c)  w~cw]' 

The  indicated  horse-power  is  plan  •*-  33,000.     Hence  the  steam-con- 
sumption per  hour  per  indicated  horse-power  is 


33.000       - 

Changing  the  formula  to  a  rule,  we  have:  To  find  the  water  rate  from 
the  indicator  diagram  at  any  point  in  the  stroke. 

RULE.  —  To  the  percentage  of  the  entire  stroke  which  has  been  com- 
pleted by  the  piston  at  the  point  under  consideration  add  the  percentage 
of  clearance.  Multiply  this  result  by  the  weight  of  a  cubic  foot  of  steam, 
having  a  pressure  of  that  at  the  required  point.  Subtract  from  this  the 
product  of  percentage  of  clearance  multiplied  by  weight  of  a  cubic  foot 
of  steam  having  a  pressure  equal  to  that  at  the  end  of  the  compression. 
Multiply  this  result  by  137.50  divided  by  the  mean  effective  pressure.* 

NOTE.  —  This  method  applies  only  to  points  in  the  expansion  curve 
or  between  cut-off  and  release. 

The  beneficial  effect  of  compression  in  reducing  the  water-consumption 
of  an  engine  is  clearly  shown  by  the  formula.  If  the  compression  is 
carried  to  such  a  point  that  it  produces  a  pressure  equal  to  that  at  the 
point  under  consideration,  the  weight  of  steam  per  cubic  foot  is  equal, 
and  w  =  w'.  In  this  case  the  effect  of  clearance  entirely  disappears,  and 
the  formula  becomes  137.5  (bw)  -f-  p. 

In  case  of  no  compression,  w'  becomes  zero,  and  the  water-rate  = 
137.5  [(&  +  c)  w]  +  p. 

Prof.  R.  C.  Carpenter  (Sibley  Jour,  of  Eng'g,  Dec.,  1910)  states  that 
tests  of  engines  show  that  economy  is  really  decreased  by  high  com- 
pression. Armand  Duchesne  (Power,  Jan.  10,  1911)  gives  as  a  reason 
for  this  that  the  steam  undergoing  compression  is  superheated  and 
the  work  of  compressing  the  superheated  steam  is  greater  than  the  work 
which  it  gives  out  later  when  it  is  in  the  condition  of  saturated  steam. 

*  For  compound  or  triple-expansion  engines  read:  divided  by  the 
equivalent  mean  effective  pressure,  on  the  supposition  that  all  work  is 
done  in  one  cylinder. 


976 


THE    STEAM   ENGINE. 


Prof.  Denton  (Trans.  A.  S.  M.  E.,  xiv,  1363)  gives  the  following  tabl« 
of  theoretical  water-consumption  for  a  perfect  Mariotte  expansion  with 
steam  at  150  Ibs.  above  atmosphere,  and  2  Ibs.  absolute  back  pressure: 


Ratio  of  Expansion,  r. 

M.E.P.,  Ibs.  per  sq.  in. 

Lbs.  of  Water  per  hour 
per  horse-power,  W  . 

10 

52.4 

9.68 

15 

38.7 

8.74 

20 

30.9 

8.20 

25 

25.9 

7.84 

30 

22.2 

7.63 

35 

19.5 

7.45 

The  difference  between  the  theoretical  water-consumption  found  by  the 
formula  and  the  actual  consumption  as  found  by  test  represents  "water 
not  accounted  for  by  the  indicator,"  due  to  cylinder  condensation,  leak- 
age through  ports,  radiation,  etc. 

Leakage  of  Steam.  —  Leakage  of  steam,  except  in  rare  instances,  has 
so  little  effect  upon  the  lines  of  the  diagram  that  it  can  scarcely  be 
detected.  The  only  satisfactory  way  to  determine  the  tightness  of  an 
engine  is  to  take  it  when  not  in  motion,  apply  a  full  boiler-pressure  to 
the  valve,  placed  in  a  closed  position,  and  to  the  piston  as  well,  which 
is  blocked  for  the  purpose  at  some  point  away  from  the  end  of  the  stroke, 
and  see  by  the  eye  whether  leakage  occurs.  The  indicator-cocks  provide 
means  for  bringing  into  view  steam  which  leaks  through  the  steam- 
valves,  and  in  most  cases  that  which  leaks  by  the  piston,  and  an  opening 


made  in  the  exhaust-pipe  or  observations  at  the  atmospheric  escape- 
pipe,  are  generally  sufficie 
exhaust-valves. 


pipe,  are  generally  sufficient  to  determine  the  fact  with  regard  to  the 


The  steam  accounted  for  by  the  indicator  should  be  computed  for  both 
the  cut-off  and  the  release  points  of  the  diagram.  If  the  expansion-line 
departs  much  from  the  hyperbolic  curve  a  very  different  result  is  shown 
at  one  point  from  that  shown  at  the  other.  In  such  cases  the  extent  of 
the  loss  occasioned  by  cylinder  condensation  and  leakage  is  indicated  in  a 
much  more  truthful  manner  at  the  cut-off  than  at  the  release.  (Tabor 
Indicator  Circular.) 

COMPOUND   ENGINES. 

Compound,  Triple-  and  Quadruple-expansion  Engines.  —  A  com- 
pound engine  is  one  having  two  or  more  cylinders,  and  in  which  the  steam 
after  doing  work  in  the  first  or  high-pressure  cylinder  completes  its 
expansion  in  the  other  cylinder  or  cylinders. 

The  term  "compound"  is  commonly  restricted,  however,  to  engines  in 
which  the  expansiqn  takes  place  in  two  stages  only  —  high  and  low 
pressure,  the  terms  triple-expansion  and  quadruple-expansion  engines 
being  used  when  the  expansion  takes  place  respectively  in  three  and 
four  stages.  The  number  of  cylinders  may  be  greater  than  the  number 
of  stages  of  expansion,  for  constructive  reasons;  thus  in  the  compound  or 
two-stage  expansion  engine  the  low-pressure  stage  may  be  effected  in  two 
cylinders  so  as  to  obtain  the  advantages  of  nearly  equal  sizes  of  cylinders 
and  of  three  cranks  at  angles  of  120°.  In  triple-expansion  engines  there 
are  frequently  two  low-pressure  cylinders,  one  of  them  being  placed 
tandem  with  the  high-pressure,  and  the  other  with  the  intermediate 
cylinder,  as  in  mill  engines  with  two  cranks  at  90°.  In  the  triple-expan- 
sion engines  of  the  steamers  Camvania  and  Lucania,  with  three  cranks  at 
120°,  there  were  five  cylinders,  two  high,  one  intermediate,  and  two  low, 
the  high-pressure  cylinders  being  tandem  with  the  low. 

Advantages  of  Compounding. — -The  advantages  secured  by  divid- 
ing the  expansion  into  two  or  more  stages  arc  twofold:  1.  Reduction 
of  wastes  of  steam  by  cylinder-condensation,  clearance,  and  leakage; 
2.  Dividing  the  pressures  on  the  cranks,  shafts,  etc.,  in  large  engines  so 
as  to  avoirt  excessive  pressures  and  consequent  friction.  The  diminished 


COMPOUND   ENGINES. 


977 


loss  by  cylinder-condensation  is  effected  by  decreasing  the  range  of  tem- 
perature of  the  metal  surfaces  of  the  cylinders,  or  the  difference  of  tempera- 
•ture  of  the  steam  at  admission  and  exhaust.  When  high-pressure  steam 
is  admitted  into  a  single-cylinder  engine  a  large  portion  is  condensed  by 
the  comparatively  cold  metal  surfaces;  at  the  end  of  the  stroke  and  during 
the  exhaust  the  water  is  re-evaporated,  but  the  steam  so  formed  escapes 
into  the  atmosphere  or  into  the  condenser,  doing  no»work;  while  if  it  is 
taken  into  a  second  cylinder,  as  in  a  compound  engine,  it  does  work. 
The  steam  lost  in  the  first  cylinder  by  leakage  and  clearance  also  does 
work  in  the  second  cylinder.  Also,  if  there  is  a  second  cylinder,  the 
temperature  of  the  steam  exhausted  from  the  first  cylinder  is  higher  than 
if  there  is  only  one  cylinder,  and  the  metal  surfaces  therefore  are  not 
cooled  to  the  same  degree.  The  difference  in  temperatures  and  in  pres- 
sures corresponding  to  the  work  of  steam  of  150  Ibs.  gauge-pressure  ex- 
panded 20  times,  in  one,  two,  and  three  cylinders,  is  shown  in  the 
following  table,  by  W.  H.  Weightman,  Am.  Mack.,  July  28,  1892: 


Single 
Cyl- 
inder. 

Compound 
Cylinders. 

Triple-expansion 
Cylinders. 

teter  of  cylinders,  in.  . 
Area  ratios  

60 

33 
1 

61 
3.416 

28 
1 

46 
2.70 

61 

4.740 

Expansions                          •  . 

20 

5 

4 

2.714 

2.714 

2.714 

Initial  steam-pressures  — 
absolute  —  pounds  
Mean  pressures,  pounds.  .  . 

165 
32.96 

165 
86.11 

33 
19.68 

165 
121.44 

60.8 
44.75 

22.4 
16.49 

Mean  effective  pressures, 

pounds  .    . 

28.96 

53.11 

15.68 

60.64 

22.35 

12.49 

Steam  temperatures  into 

cylinders 

366° 

366° 

259.9° 

366° 

293.5° 

234.1° 

Steam  temperatures  out 
of  the  cylinders  

184.2° 

259.9° 

184.2° 

293.5° 

234.1° 

184.2° 

Difference  in  temperatures 

181.8 

106.1 

75.7 

72.5 

59.4 

49.9 

"Woolf "    and    Receiver    Types    of    Compound    Engines. —  The 

compound  steam-engine,  consisting  of  two  cylinders,  is  reducible  to  two 
forms,  1,  in  which  the  steam  from  the  h.p.  cylinder  is  exhausted  direct 
into  the  l.p.  cylinder,  as  in  the  Woolf  engine;  and  2,  in  which  the  steam 
from  the  h.p.  cylinder  is  exhausted  into  an  intermediate  reservoir,  whence 
the  steam  is  supplied  to,  and  expanded  in,  the  l.p.  cylinder,  as  in  the 
"  receiver-engine. " 

If  the  steam  be  cut  off  in  the  first  cylinder  before  the  end  of  the  stroke, 
the  total  ratio  of  expansion  is  the  product  of  the  two  ratios  of  expansion; 
that  is,  the  product  of  the  ratio  of  expansion  in  the  first  cylinder,  into  the 
ratio  of  the  volume  of  the  second  to  that  of  the  first  cylinder. 

Thus,  let  the  areas  of  the  first  and  second  cylinders  be  as  1  to  31/2,  the 
strokes  being  equal,  and  let  the  steam  be  cut  off  in  the  first  at  1/2  stroke; 
then 

•Expansion  in  the  1st  cylinder 1  to  2 

Expansion  in  the  2d  cylinder 1  to  31/2 

Total  or  combined  expansion,  the  product  of  the  two  ratios  1  to  7 

Woolf    Engine,     without     Clearance  —  Ideal    Diagrams.  —  The 

diagrams  of  pressure  of  an  ideal  Woolf  engine  are  shown  in  Fig.  166,  as' 
they  would  be  described  by  the  indicator,  according  to  the  arrows.  In 
these  diagrams  pq  is  the  atmospheric  line,  mn  the  vacuum  line,  cd  the 
admission  line,  dg  the  hyperbolic  curve  of  expansion  in  the  first  cylinder, 
and  gh  the  consecutive  expansion-line  of  back  pressure  for  the  return- 
Btroke  of  the  first  piston,  and  of  positive  pressure  for  the  steam-stroke 
of  the  second  piston.  At  the  point  h,  at  the  end  of  the  stroke  of  the 
second  piston,  the  steam  is  exhausted  into  the  condenser,  and  the  pressure 
falls  to  the  level  of  perfect  vacuum,  mn. 


978 


THE   STEAM-ENGINE. 


d  *_( 


P 


The  diagram  of  the  second  cylinder,  below  gh,  is  characterized  by  the 
absence  of  any  specific  period  of  admission;  the  whole  of  the  steam-line 

gh  being  expansional,  generated  by  the, 
expansion  of  the  initial  body  of  steam 
contained  in  the  first  cylinder  into  Urn 
seconci0  When  the  return-stroke  is 
completed,  the  whole  of  the  steam 
transferred  from  the  first  is  shut  into 
the  second  cylinder.  The  final  pres- 
sure and  volume  of  the  steam  in  the 
second  cylinder  are  the  same  as  if  the 
whole  of  the  initial  steam  had  been 
admitted  at  once  into  the  second  cylin- 
der, and  then  expanded  to  the  end  of 
the  stroke  in  the  manner  of  a  single- 
cylinder  engine.  The  net  work  of  the 
steam  is  also  the  same,  according  to 
both  distributions. 

Receiver-engine,  without  Clear- 
ance —  Ideal    Diagrams.  —  In    the 
AT  ideal  receiver-engine  the  pistons  of  the 

mAGRAMs  two  cylinders  are  connected  to  cranks 

-DIAGRAMS.  at  right  angleg  tQ  each  Qther  Qn  the 

same  shaft.  The  receiver  takes  the  steam  exhausted  from  the  first  cylin- 
der and  supplies  it  to  the  second,  in  which  the  steam  is  cut  off  and  then 
expanded  to  the  end  of  the  stroke.  On  the  assumption  that  the  initial 
pressure  in  the  second  cylinder  is  equal  to  the  final  pressure  in  the  first, 
and  of  course  equal  to  the  pressure  in  the  receiver,  the  volume  cut  off  in 
the  second  cylinder  must  be  equal  to  the  volume  of  the  first  cylinder,  for 
the  second  cylinder  must  admit  as  much  steam  at  each  stroke  as  is  dis- 
charged from  the  first  cylinder. 

In  Fig.  167,  cd  is  the  line  of  admission  and  kg  the  exhaust-line  for  the 
first  cylinder;  and  dg  is  the  expansion-curve  and  pq  the  atmospheric  line. 


iftfi 


^60  Ibs. 


FIG.  167. —  RECEIVER-ENGINE, 
IDEAL,  INDICATOR-DIAGRAM. 


FIG.  168.  —  RECEIVER  ENGINE,  IDEAL 
DIAGRAMS  REDUCED  AND  COMBINED. 
In  the  region  below  the  exhaust-line  of  the  first  cylinder,  between  it  and 
the  line  of  perfect  vacuum,  ol,  the  diagram  of  the  second  cylinder  is 
formed:  hi,  the  second  line  of  admission,  coincides  with  the  exhaust-line 
hg  of  the  first  cylinder,  showing  in  the  ideal  diagram  no  intermediate 
fall  of  pressure,  and  ik  is  the  expansion-curve.  The  arrows  indicate 
the  order  in  which  the  diagrams  are  formed. 

In  the  action  of  the  receiver-engine,  the  expansive  working  of  the 
steam,  though  clearly  divided  into  two  consecutive  stages,  is,  as  in  the 
Woolf  engine,  essentially  continuous  from  the  point  of  cut-off  in  the  first 
cylinder  to  the  end  of  the  stroke  of  the  second  cylinder,  where  it  is 
delivered  to  the  condenser;  and  the  first  and  second  diagrams  may  be 
placed  together  and  combined  to  form  a  continuous  diagram.  For  this 
purpose  take  the  second  diagram  as  the  basis  of  the  combined  diagram, 
namely,  hiklo,  Fig.  168.  The  period  of  admission,  hi,  is  one-third  of  the 
stroke,  and  as  the  ratios  of  the  cylinders  areas  1  to  3,  hi  is  also  the  propor- 


COMPOUND   ENGINES. 


979 


ism 
con 

P 

by 


il  length  of  the  first  diagram  as  applied  to  the  second.     Produce  oh  up- 
ards,  and  set  off  oc  equal  to  the  total  height  of  the  first  diagram  above  the 
vacuum-line;  and,  upon  the  shortened  base  hi,  and  the  height  he,  complete 
the  first  diagram  with  the  steam-line  cd  and  the  expansion  line  di. 

It  is  shown  by  Clark  (S.  E.,  p.  432  et  seq.)  in  a  series  of  arithmetical  calciu. 
lations,  that  the  receiver-engine  is  an  elastic  system  of  compound  engine,  in 
which  considerable  latitude  is  afforded  for  adapting  the  pressure  in  the  re- 
ceiver to  the  demands  of  the  second  cylinder,  without  considerably  dimin- 
ishing the  effective  work  of  the  engine.  In  the  Woolf  engine,  on  the* 
contrary,  it  is  of  much  importance  that  the  intermediate  volume  of  space 
"  ween  the  first  and  second  cylinders,  which  is  the  cause  of  an  interme- 

te  fall  of  pressure,  should  be  reduced  to  the  lowest  practicable  amount. 

Supposing  that  there  is  no  loss  of  steam  in  passing  through  the  engine, 
cooling  and  condensation,  it  is  obvious  that  whatever  steam  passes 
through  the  first  cylinder  must  also  find  its  way  through  the  second 
cylinder.  By  varying,  therefore,  in  the  receiver-engine,  the  period  of 
admission  in  the  second  cylinder,  and  thus  also  the  V9lume  of  steam  ad- 
mitted for  each  stroke,  the  steam  will  be  measured  into  it  at  a  higher 
pressure  and  of  a  less  bulk,  or  at  a  lower  pressure  and  of  a  greater  bulk; 
the  pressure  and  density  naturally  adjusting  themselves  to  the  volume 
that  the  steam  from  the  receiver  is  permitted  to  occupy  in  the  second 
cylinder.  With  a  sufficiently  restricted  admission,  the  pressure  in  the 
receiver  may  be  maintained  at  the  pressure  of  the  steam  as  exhausted 
from  the  first  cylinder.  On  the  contrary,  with  a  wider  admission,  the 
pressure  in  the  receiver  may  fall  or  "drop"  to  three-fourths  or  even  one- 
half  of  the  pressure  of  the  exhaust  steam  from  the  first  cylinder. 

(For  a  more  complete  discussion  of  the  action  of  steam  in  the  Woolf 
and  receiver  engines,  see  Clark  on  the  Steam-engine.) 

Combined  Diagrams  of  Compound  Engines.  —  The  only  way  of 
making  a  correct  combined  diagram  from  the  indicator-diagrams  of 
the  several  cylinders 
in  a  compound  engine 
is  to  set  off  all  the 
diagrams  on  the  same 
horizontal  scale  of  vol- 
umes, adding  the 
clearances  to  the  cyl- 
inder capacities  prop- 
er. When  this  is 
attended  to,  the  suc- 
cessive diagrams  fall 
exactly  into  their  right 
places  relatively  to  one 
another,  and  would 
compare  properly  with 
any  theroretical  ex- 
pansion-curve, (Prof. 
A.  B.  W.  Kennedy, 
Proc.  Inst.  M.  E.,  Oct., 
1886.) 

This  method  of  com- 
bining diagrams  is 
commonly  adopted, 
but  there  are  objec- 
tions to  its  accuracy, 
since  the  whole  quan- 
tity of  steam  con-  FIG.  169. 
sumed  in  the  first  cylinder  at  the  end  of  the  stroke  is  not  carried  forward 
to  the  second,  but  a  part  of  it  is  retained  in  the  first  cylinder  for  com- 
pression. For  a  method  of  combining  diagrams  in  which  compression 
is  taken  account  of,  see  discussions  by  Thomas  Mudd  and  others,  in  Proc. 
Inst.  M.  E.,  Feb.,  1887,  p.  48.  The  usual  method  of  combining  diagrams 
is  also  criticised  by  Frank  H.  Ball  as  inaccurate  and  misleading  (Am. 
Mach.,  April  12,  1894;  Trans.  A.  S.  M.  E.,  xiv,  1405,  and  xv,  403). 

Figure  169  shows  a  combined  diagram  of  a  quadruple-expansion  engine, 
drawn  according  to  the  usual  method,  that  is,  the  diagrams  are  first 
reduced  in  length  to  relative  scales  that  correspond  with  the  relative 


980 


THE   STEAM-ENGINE. 


piston-displacement  of  the  three  cylinders.  Then  the  diagrams  are 
placed  at  such  distances  from  the  clearance-line  of  the  proposed  combined 
diagram  as  to  represent  correctly  the  clearance  in  each  cylinder. 

Proportions  of  Cylinders  in  Compound  Engines.  —  Authorities 
differ  as  to  the  proportions  by  volume  of  the  high  and  lo_w  pressure 
cylinders  v  and  F._  Thus  Grashof  gives  V  •*-  v  =  0.85  Vr;  Hrabak, 
0.90  v^;  Werner,  VV;  and  Rankine,  ^/r2,  r  being  the  ratio  of  expansion. 
Busley  makes  the  ratio  dependent  on  the  boiler-pressure  thus: 

Lbs.  per  sq.  in 60         90  105  120 

V  -*-  v =3  4  4.5  5 

(See  Seaton's  Manual,  p.  95,  etc.,  for  analytical  method;  Sennett,  p.  496, 
etc.;  Clark's  Steam-engine,  p.  445,  etc.;  Clark's  Rules,  Tables,  Data,  p. 849, 
etc.) 

Mr.  J.  McFarlane  Gray  states  that  he  finds  the  mean  effective  pressure 
in  th6  compound  engine  reduced  to  the  low-pressure  cylinder  to  be  approx- 
imately the  square  root  of  6  times  the  boiler-pressure. 

Ratio  of  Cylinder  Capacity  in  Compound  Marine  Engines.  (Sea- 
ton.)  —  The  low-pressure  cylinder  is  the  measure  of  the  power  of  a  com- 
pound engine,  for  so  long  as  the  initial  steam-pressure  and  rate  of  expansion 
are  the  same,  it  signifies  very  little,  so  far  as  total  power  only  is  concerned, 
whether  the  ratio  between  the  low  and  high  pressure  cylinders  is  3  or 
4;  but  as  the  power  developed  should  be  nearly  equally  divided  between 
the  two  cylinders,  in  order  to  get  a  good  and  steady  working  engine, 
there  is  a  necessity  for  exercising  a  considerable  amount  of  discretion 
in  fixing  on  the  ratio. 

In  choosing  a  particular  ratio  the  objects  are  to  divide  the  power  evenly 
and  to  avoid  as  much  as  possible  "drop"  and  high  initial  strain.  [Some 
writers  advocate  drop  in  the  high-pressure  cylinder  making  it  smaller 
Mian  is  the  usual  practice  and  making  the  cylinder  ratio  as  high  as  6  or  7.] 

If  increased  economy  is  to  be  obtained  by  increased  boiler-pressures 
the  rate  of  expansion  should  vary  with  the  initial  pressure,  so  that  the 
pressure  at  which  the  steam  enters  the  condenser  should  remain  constant. 
In  this  case,  with  the  ratio  of  cylinders  constant,  the  cut-off  in  the  high- 
pressure  cylinder  will  vary  inversely  as  the  initial  pressure. 

Let  R  be  the  ratio  of  the  cylinders;  r  the  rate  of  expansion;  PI  the 
initial  pressure:  then  cut-off  in  high-pressure  cylinder  =*  R  -*•  r\  r  varies 
with  pi,  so  that  the  terminal  pressure  pn  is  constant,  and  consequently 
r  =  PI-*-  pn;  therefore,  cut-off  in  high-pressure  cylinder  =  R  X  pn  -*-  pi. 

Ratios  of  Cylinders  as  Found  in  Marine  Practice.  —  The  rate  of 
expansion  may  be  taken  at  one-tenth  of  the  boiler-pressure  (or  about  one- 
twelfth  the  absolute  pressure),  to  work  economically  at  full  speed.  There- 
fore, when  the  diameter  of  the  low-pressure  cylinder  does  not  exceed 
100  inches,  and  the  boiler-pressure  70  Ibs.,  the  ratio  of  the  low-pressure 
to  the  high-pressure  cylinder  should  be  3.5;  for  a  boiler-pressure  of  80  Ibs., 
3.75;  for  90  Ibs.,  4.0;  for  100  Ibs.,  4.5.  If  these  proportions  are  adhered 
to,  there  will  be  no  need  of  an  expansion-valve  to  either  cylinder.  If, 
however,  to  avoid  "drop,"  the  ratio  be  reduced,  an  expansion-valve 
should  be  fitted  to  the  high-pressure  cylinder. 

Where  economy  of  steam  is  not  of  first  importance,  but  rather  a  large 
power,  the  ratio  of  cylinder  capacities  may  with  advantage  be  decreased, 
so  that  with  a  boiler-pressure  of  100  Ibs.  it  may  be  3.75  to  4. 

In  tandem  engines  there  is  no  necessity  to'  divide  the  work  equally. 
The  ratio  is  generally  4,  but  when  the  steam-pressure  exceeds  90  Ibs. 
absolute  4.5  is  better,  and  for  100  Ibs.  5.0. 

When  the  power  requires  that  the  l.p.  cylinder  shall  be  more  than  100  in. 
diameter,  it  should  be  divided  in  two  cylinders.  -In  this  case  the  ratio  of  the 
combined  capacity  of  the  two  l.p.  cylinders  to  that  of  the  h.p.  may  be 
3.0  for  85  Ibs.  absolute,  3.4  for  95  Ibs.,  3.7  for  105  Ibs.,  and  4.0  for  115* Ibs. 

Receiver  Space  in  Compound  Engines  should  be  from  1  to  1.5  times 
the  capacity  of  the  high-pressure  cylinder,  when  the  cranks  are  at  an 
angle  of  from  90°  to  120°.  When  the  cranks  are  at  180°  or  nearly  this, 
the  space  may  be  very  much  reduced.  In  the  case  of  triple-compound 
engines,  with  cranks  at  120°,  and  the  intermediate  cylinder  leading  the 
high-pressur^  a  very  small  receiver  will  do.  The  pressure  in  the  receiver 
should  never  exceed  half  the  boiler-pressure.  (Seaton.) 


COMPOUND   ENGINES,  981 


Formula  for  Calculating  the  Expansion  and  the  Work  of  Steam 
in  Compound  Engines. 

(Condensed  from  Clark  on  the  "  Steam-engine. ") 

a  =  area  of  the  first  cylinder  in  square  inches; 
~'  =  area  of  the  second  cylinder  in  square  inches; 

=  ratio  of  the  capacity  of  the  second  cylinder  to  that  of  the  first ; 
=  length  of  stroke  in  feet,  supposed  to  be  the  same  for  bpth  cylinders; 
=  period  of  admission  to  the  first  cylinder  in  feet,  excluding  clearance; 
=  clearance  at  each  end  of  the  cylinders,  in  feet; 
=  length  of  the  stroke  plus  the  clearance,  in  feet; 
=  period  of  admission  plus  the  clearance,  in  feet; 
=  length  of  a  given  part  of  the  stroke  of  the  second  cylinder,  in  feet; 
=  total  initial  pressure  in  the  first  cylinder,  in  Ibs.  per  square  inch, 

supposed  to  be  uniform  during  admission; 
Pf  =  total  pressure  at  the  end  of  the  given  part  of  the  stroke  s; 
p  =  average  total  pressure  for  the  whole  stroke; 
R  =  nominal  ratio  of  expansion  in  the  first  cylinder,  or  L  -*-  l\ 
Rf  =  actual  ratio  of  expansion  in  the  first  cylinder,  or  L'  •*-  l'\ 
R"  —  actual  combined  ratio  of  expansion,  in  the  first  and  second  cylin- 
ders together; 
n  =  ratio  of  the  final  pressure  in  the  first  cylinder  to  any  intermediate 

fall  of  pressure  between  the  first  and  second  cylinders; 
N  —  ratio  of  the  volume  of  the  intermediate  space  in  the  Woolf  engine, 

,-; 


reckoned  up  to,  and  including  the  clearance  of,  the  second  pis- 
ton, to  the  capacity  of  the  first  cylinder  plus  its  clearance.  The 
value  of  N  is  correctly  expressed  by  the  actual  ratio  of  the 


volumes  as  stated,  on  the  assumption  that  the  intermediate  space 
is  a  vacuum  when  it  receives  the  exhaust-steam  from  the  first 
cylinder.  In  point  of  fact,  there  is  a  residuum  of  unexhausted 
steam  in  the  intermediate  space,  at  low  pressure,  and  the  value 
of  N  is  thereby  practically  reduced  below  the  ratio  here  stated, 


•  =  whole  net  work  in  one  stroke,  in  foot-pounds. 
atio  of  expansion  in  the  second  cylinder: 


In  the  Woolf  engine,  —        „  — 
(n-l)r 


In  the  receiver-engine,  - 

Total  actual  ratio  of  expansion  =  product  of  the  ratios  of  the  three 
consecutive  expansions,  in  the  first  cylinder,  in  the  intermediate  space, 
and  in  the  second  cylinder, 

In  the  Woolf  engine,  R'  (r  j-t  -f  #); 
In  the  receiver-engine,  r  -771  or  rRf. 
Combined  ratio  of  expansion  behind  the  pistons—  ^— -  rR'  =  R". 

Work  done  in  the  two  cylinders  for  one  stroke,  with  a  given  cut-off 
and  a  given  combined  actual  ratio  of  expansion: 

Woolf  engine,  w  =  aP  [l'(l  +  hyp  log  R")  -c]; 
Receiver  engine,  w  =  aP  llf  (1  +  hyp  log  R")  -c  (l-l-  ^r  )1» 
when  there  is  no  intermediate  fall  of  pressure. 


982  THE   STEAM-ENGINE. 

When  there  is  an  intermediate  fall,  when  the  pressure  falls  to  3/4f  2/« 
1/2  of  the  final  pressure  in  the  1st  cylinder,  the  reduction  of  work  is  0.2%, 
1.0%,  4.6%  of  that  when  there  is  no  fall. 

Total  work  in  the  two  cylinders  of  a  receiver-engine,  for  one  stroke 
for  any  intermediate  fall  of  pressure, 


EXAMPLE.  —  Let  a  =  I  sq.  in.,  P  =  63  Ibs.,  I'  =  2.42  ft  ,  n  =  4  R"  = 
5.969,  c  =  0.42  ft.,  r  =  3,  R'  =  2.653; 

w  =  l  X  63  [2.42  (5/4  hyp  log  5.969)  -.42  (l  +  -  -)1  =421.55  ft  .-Ibs. 

L  \  4  /s  ^.DOo  /  J 

Calculation  of  Diameters  of  Cylinders  of  a  compound  condensing 
engine  of  2000  H.P.  at  a  speed  of  700  feet  per  minute,  with  100  Ibs.  boiler- 
pressure. 

100  Ibs.  gauge-pressure  =  115  absolute,  less  drop  of  5  Ibs.  between 
boiler  and  cylinder  =  110  Ibs.  initial  absolute  pressure  Assuming 
terminal  pressure  in  l.p.  cylinder  =  6  Ibs.,  the  total  expansion  of  steam 
i  i  both  cylinders  =  110  -*-  6  =  18.33.  Hyp  log  18.33  =  2.909.  Back 
pressure  in  l.p.  cylinder,  3  Ibs.  absolute. 

The  following  formulae  are  used  in  the  calculation  of  each  cylinder: 

(1)  Area  of  cylinder         "/vX.3f'OQO      „. 

M.E.P.  X  piston-speed 

(2)  Mean  effective  pressure  =  mean  total  pressure  -  back  pressure. 

(3)  Mean  total  pressure  =  terminal  pressure  X  (1  +  hyp  log  R). 

(4)  Absolute  initial  pressure  =  absolute  terminal  pressure  X  ratio  of 
expansion. 

First  calculate  the  area  of  the  low-pressure  cylinder  as  if  all  the  work 
were  done  in  that  cylinder. 

From  (3),  mean  total  pressure  =  6  X  (1  +  hyp  log  18.33)  =  23.454 
Ibs. 

From  (2),  mean  effective  pressure  =  23.454  —  3  =  20.454  Ibs. 


From  (1).  area  of  cylinder  =  ™  ?'       =  4610  sq.ins.  =  76.6ins.  diam. 


If  half  the  work,  or  1000  H.P.',  is  done  in  the  l.p.  cylinder  the  M.E.P. 
will  be  half  that  found  above,  or  10.227  Ibs.,  and  the  mean  total  pressure 
10.227+  3  =  13.227  Ibs. 

From  (3),  1  +  hyp  log  R  =  13.227-  -s-  6  =  2.2045. 

Hyp  log  R  =  1.2045,  whence  R  in  l.p.  cyl.  =  3.335. 

From  (4),  3.335  X  6  =  20.01  Ibs.  initial  pressure  in  l.p.  cyl.  and  ter- 
minal piessure  in  h.p.  cyl.,  assuming  no  drop  between  cylinders. 

110  •*•  20.01  =  18.33  -4-  3.335  =  5.497,  Rin  h.p.  cyl. 

From  (3),  mean  total  pres.  in  h.p.  cyl.  =  20.01  X  (1  +  hyp  log  5.497) 

From  (2),  54.11  -  20.01  =  34.10,  M.E.P.  in  h.p.  cyl. 

i  nnn  v  33  nnn 
From  (1),  area  of  h.p.  cyl.  =    ""p*  34  1"      =1382  sq.  ins.  =  42  ins.  diam. 

Cylinder  ratio  =  4610  -f-  1382  =  3.336. 

The  area  of  the  h.p.  cylinder  may  be  found  more  directly  by  dividing 
the  area  of  the  l.p.  cyl.  by  the  ratio  of  expansion  in  that  cylinder.  4610 
•v-  3.335  =  1382  sq.ins. 

In  the  above  calculation  no  account  is  taken  of  clearance,  of  com- 
pression, of  drop  between  cylinders,  nor  of  area  of  piston-rods.  It  also 
assumes  that  the  diagram  in  each  cylinder  is  the  full  theoretical  diagram, 
with  a  horizontal  steam-line  and  a  hyperbolic  expansion  line,  with  no 
allowance  for  rounding  of  the  corners.  To  make  allowance  for  these, 
the  mean  effective  pressure  in  each  cylinder  must  be  multiplied  by  a 
diagram  factor,  or  the  ratio  of  the  area  of  an  actual  diagram  of  the  class 
of  engine  considered,  with  the  given  initial  and  terminal  pressures,  to  the 
area  of  the  theoretical  diagram.  Such  diagram  factors  will  range  from 
0.6  to  0.94,  as  in  the  table  on  p.  962. 

Best  Ratios  of  Cylinders.  —  The  question  what  is  the  best  ratio  of 
areas  of  the  two  cylinders  of  a  compound  engine  is  still  (1901)  a  disputed 
one,  but  there  appears  to  be  an  increasing  tendency  in  favor  of  large 


TRIPLE-EXPANSION  ENGINES.  983 

ratios,  even  as  great  as  7  or  8  to  1,  with  considerable  terminal  drop  in 
the  high-pressure  cylinder.  A  discussion  of  the  subject,  together  with  a 
description  of  a,  new  method  of  drawing  theoretical  diagrams  of  multiple- 
expansion  engines,  taking  into  consideration  drop,  clearance,  and  com- 
pression will  be  found  in  a  paper  by  Bert  C.  Ball,  in  Trans.  A.  S.  M.  E., 
Ed,  1092. 

TRIPLE-EXPANSION  ENGINES. 

Proportions  of  Cylinders.  —  H.  H.  Suplee,  Mechanics,  Nov.,  1887, 
gives  the  following  method  of  proportioning  cylinders  of  triple-expansion 
engines: 

As  in  the  case  of  compound  engines  the  diameter  of  the  low-pressure 
cylinder  is  first  determined,  being  made  large  enough  to  furnish  the  entire 
power  required  at  the  mean  pressure  due  to  the  initial  pressure  and 
expansion  ratio  given;  and  then  this  cylinder  is  given  only  pressure  enough 
to  perform  one-third  of  the  work,  and  the  other  cylinders  are  proportioned 
so  as  to  divide  the  other  two-thirds  between  them. 

Let  us  suppose  that  an  initial  pressure  of  150  Ibs.  is  used  and  that 
900  H.P.  is  to  be  developed  at  a  piston-speed  of  800  ft.  per  min.,  and  that 
an  expansion  ratio  of  16  is  to  be  reached  with  an  absolute  back-pressure 
of  2  Ibs. 

The  theoretical  M.E.P.  with  an  absolute  initial  pressure  of  150  +  14.7  =* 
164.7  Ibs.  initial  at  16  expansions  is 

P  (1  +  hyp  log  16)  _         ?      3.7726  =  3g  83> 

16  16 

less  2  Ibs.  back  pressure,  =  38.83  -  2  =  36.83. 

In  practice  only  about  0.7  of  this  pressure  is  actually  attained,  so  that 
36.83  x  0.7  =  25.781  Ibs.  is  the  M.E.P.  upon  which  the  engine  is  to  be 
proportioned. 

To  obtain  900  H.P.  we  must  have  33,000  X  900  =  29,700,000  Toot- 
pounds,  and  this  divided  by  the  mean  pressure  (25.78)  and  by  the  speed 
in  feet  (800)  will  give  1440  sq.  in.  as  the  area  of  the  l.p.  cylinder,  about 
equivalent  to  43  in.  diam. 

Now  as  one-third  of  the  work  is  to  be  done  in  the  l.p.  cylinder,  the 
M.E.P.  in  it  will  be  25.78  •*•  3  =  8.59  Ibs. 

The  cut-off  in  the  high-pressure  cylinder  is  generally  arranged  to  cut  off 
at  0.6  of  the  stroke,  and  so  the  ratio  of  the  h.p.  to  the  l.p.  cylinder  is  equal 
to  16  X  0.6  =  9.6,  and  the  h.p.  cylinder  will  be  1440  -*•  9.6  =  150  sg. 
in.  area,  or  about  14  in.  diameter,  and  the  M.E.P.  in  the  h.p.  cylinder  is 
equal  to  9.6  X  8.59  ==  82.46  Ibs. 

If  the  intermediate  cylinders  made  a  mean  size  between  the  other  two, 
.  its  size  would  be  determined  by  dividing  the  area  of  the  l.p.  cylinder  by 
the  square  root  of  the  ratio  between  the  low  and  the  high;  but  in  practice 
this  is  found  to  give  a  result  too  large  to  equalize  the  stresses,  so  that 
instead  the  area  of  the  int.  cylinder  is  found  by  dividing  the  area  of  the 
l.p.  piston  by  1.1  times  the  square  root  of  the  ratio  of  l.p.  to  h.p.  cylinder, 
which  in  this  case  is  1440  •*•  (1.1  V^6)  =  422.5  sq.in.,  or  a  little  more 
than  23  in.  diam. 

The  choice  of  expansion  ratio  is  governed  by  the  initial  pressure,  and  is 
generally  chosen  so  that  the  terminal  pressure  in  the  l.p.  cylinder  shall  be 
about  10  Ibs.  absolute. 

Formulae  for  Proportioning  Cylinder  Areas  of  Triple-Expansion 
Engines.  —  The  following  formulae  are  based  on  the  method  of  first 
finding  the  cylinder  areas  that  would  be  required  if  an  ideal  hyperbolic  dia- 
gram were  obtainable  from  each  cylinder,  with  no  clearance,  compression, 
wire-drawing,  drop  by  free  expansion  in  receivers,  or  loss  by  cylinder 
condensation,  assuming  equal  work  to  be  done  in  each  cylinder,  and 
then  dividing  the  areas  thus  found  by  a  suitable  diagram  factor,  such  as 
those  given  on  page  962,  expressing  the  ratio  which  the  area  of  an  actual 
diagram,  obtained  in  practice  from  an  engine  of  the  type  under  consider- 
ation, bears  to  the  ideal  or  theoretical  diagram.  It  will  vary  in  different 
classes  of  engine  and  in  different  cylinders  of  the  same  engine,  usual 
values  ranging  from  0.6  to  0.9.  When  any  one  of  the  three  stages  of 
expansion  takes  place  in  two  cylinders,  the  combined  area  of  these 
cylinders  equals  the  area  found  by  the  formulae. 


984 


THE  STEAM-ENGINE. 


NOTATION. 

Pi  =  initial  pressure  in  the  high-pressure  cylinder. 
Pt  =  terminal  pressure  in  the  low-pressure  cylinder. 
#5  =  back  pressure  in  the  low-pressure  cylinder. 

Pt  =  term,  press,  in  h.p.  cyl.  and  initial  press,  in  intermediate  cyl. 

p-3=  term,  press,  in  int.  cyl.  and  initial  press,  in  l.p.  cyl. 

Ri,  Ri,  Rz,  ratio  of  exp.  in  h.p.  int.  and  l.p.  cyls. 

R  =  total  ratio  of  exp.  =  Ri  x  Rz  X  Rz- 

P  =  M.E.P.  of  the  combined  ideal  diagram,  referred  to  the  l.p.  cyL 

Pi,  P2,  P3  =  M.E.P.  in  the  h.p.,  int.,  and  l.p.  cyls. 

//  P  =  horse-power  of  the  engine  =  PLASN  -4-  33,000. 

L  =  length  of  stroke  in  feet ;  N  =  number  of  single  strokes  per  niin. 

Ai,  A2,  Az,  areas  (sq.  ins.)  of  h.p.  int.  and  l.p.  cyls.  (ideal). 

W  =  work  done  in  one  cylinder  per  foot  of  stroke. 

r-z  =  ratio  of  A2  to  A\;  r3  =  ratio  of  Az  to  Ai. 

Fi,  F2,  F3,  diagram  factors  of  h.p.  int.  and  l.p.  cyl. 

Ci,  «2,  a3,  areas  (actual)  of  h.p.  int.  and  l.p.  cyl. 

Formulae. 

(1)  R   =  pl  -^  pt. 

(2)  P    =  pt  (1  +  hyp  log  R)  -  pbf 

"     Ps  =  V3  P. 

Hyp  log  #3  =  (Ps  -  Pt+  Pb)  -*•  Pf 

(5)  RiRz  =  R  -5-  Rz;  Ri  =  Rz  =  ^RiRz. 

(6)  ps  =  pt  X  Rs. 

S7)  P2  —  P3  X  #2. 
8)  pi  =  pz  X  Ri. 
9)  P2  =  pz  (hyp  log  fl2)  fe=  PzRs. 

10)  Pi  =  p2  (hyp  log  ^i)  =  P2^2. 

11)  W  =  11,000  HP  -5-  LN, 

12)  Ai  =  W  +  Pi;  At  =  W  +  Pz 

13)  r2    =  ^2  -*•  Ai  =  Pi  -4-  P2  =  I 

14)  01   = 


<3) 
(4) 


^3  =  W 
i  or  #2;  rs 


•*•  Ai  »  Pi  ~-  P8. 


From  these  formulae  the  figures  in  the  following  tables  have  been 
calculated: 
THEORETICAL  MEAN  EFFECTIVE  PRESSURES,  CYLINDER  RATIOS,  ETC., 

OF  TRIPLE-EXPANSION  ENGINES. 
Back  pressure,  3  Ibs.     Terminal  pressure,  8  Ibs.  (absolute). 


Pi. 

If. 

P. 

P3. 

Rz. 

Ri,  Rt, 

Or  T2. 

Ps. 

P2. 

P2. 

Pi. 

r, 

120 
140 
160 
180 
200 
220 
240 

15 
17.5 
20 
22.5 
25 
27.5 
30 

26.66 
27.90 
28.97 
29.91 
30.75 
31.51 
32.21 

8.89 
9.30 
9.66 
9.97 
10.25 
10.50 
10.74- 

.626 
.712 
.790 
.861 
.928 
.990 
2.049 

3.037 
3.197 
3.343 
3.477 
3.601 
3.718 
3.826 

13.01 
13.70 
14.32 
14.89 
15.42 
15.91 
16.39 

39.51 
43.79 
47.86 
51.77 
55.54 
59.16 
62.72 

14.45 
15.92 
17.29 
18.55 
19.76 
20.90 
22.00 

43.89 
50.89 
57.76 
64.52 
71.16 
77.69 
84.16 

4.939 
5.472 
5.980 
6.471 
6.942 
7.397 
7.839 

THEORETICAL  MEAN  EFFECTIVE  PRESSURES,  CYLINDER  RATIOS,  ETC., 

OF  TRIPLE-EXPANSION  ENGINES. 
Back  pressure,  3  Ibs.     Terminal  pressure,  10  Ibs.  (absolute). 


Pi. 

R. 

P. 

P3. 

R3. 

Ri,  Rt, 
or  rz. 

Pa. 

pz. 

P2. 

Pi. 

T3. 

120 
140 
160 
180 
200 
220 
240 

8 

16 
18 
20 
22 
24 

31.85 
33.39 
34.73 
35.90 
36.96 
37.91 
38.78 

10.62 
11.13 
11.58 
11.97 
12.32 
12.64 
12.93 

.436 
.511 
.580 
.643 
.702 
.757 
.809 

2.890 
3.044 
3.182 
3.310 
3.428 
3.538 
3.642 

14.36 
15.11 
15.80 
16.43 
17.02 
17.57 
18.09 

41.50 
45.99 
50.28 
54.38 
58.34 
62.15 
65.88 

15.24 
16.82 
18.29 
19.66 
20.97 
22.20 
23.38 

44.04 
51.20 
58.20 
65.09 
71.88 
78.54 
85.15 

4.148 
4.600 
5.027 
5.439 
5.834 
6.215 
6.587 

Given  the  required  H.P.  of  an  engine,  its  speed  and  length  of  stroke, 


TRIPLE-EXPANSION  ENGINES. 


985 


a,nd  the  assumed  diagram  factors  Fi.  F2,  Fs  for  the  three  cylinders,  tne 
areas  of  the  cylinders  may  be  found  by  using  formula  (11),  (12),  and 
(14),  and  the  values  of  Pi,  Pz,  and  Ps  in  the  above  table. 

A  Common  Rule  for  Proportioning  the  Cylinders  of  multiple- 
expansion  engines  is:  for  two-cylinder  compound  engines,  the  cylinder 
ratio  is  the  square  root  of  the  number  of  expansions,  and  for  triple- 
expansion  engines  the  ratios  of  the  high  to  the  intermediate  and  of  the 
intermediate  to  the  low  are  each  equal  to  the  cube  root  of  the  number  of 
expansions,  the  ratio  of  tht  high  to  the  low  being  the  product  of  the  two 
ratios,  that  is,  the  square  of  the  cube  root  of  the  number  of  expansi9ns. 
Applying  this  rule  to  the  pressures  above  given,  assuming  a  terminal 
pressure  (absolute)  of  10  Ibs.  and  8  Ibs.  respectively,  we  have,  for  triple- 
expansion  engines: 


Boiler- 
pressure 
(Absolute)  . 

Terminal  Pressure,  10  Ibs. 

Terminal  Pressure,  8  Ibs. 

No.  of  Ex- 
pansions. 

Cylinder  Ratios, 
areas. 

Nc.  of  Ex- 
pansions. 

Cylinder  Ratios, 
areas. 

130 
140 
150 
160 

13 
14- 
15 
16 

1  to  2.35  to  5.  53 
1  to  2.  41  to  5.81 
1  to  2.  47  to  6.  08 
1  to  2.  52  to  6.  35 

161/4 
171/2 

2083/4 

1  to  7.53  to  6.  42 
1  to  2.  60  to  6.  74 
1  to  2.  66  to  7.  06 
1  to  2.  71  to  7.37 

The  ratio  of  the  diameters  is  the  square  root  of  the  ratios  of  the  areas, 
and  the  ratio  of  the  diameters  of  the  first  and  third  cylinders  is  the  same 
as  the  ratio  of  the  areas  of  first  and  second. 

Seaton,  in  his  Marine  Engineering,  says:  When  the  pressure  of  steam 
employed  exceeds  115  Ibs.  absolute,  it  is  advisable  to  employ  three 
cylinders,  through  each  of  which  the  steam  expands  in  turn.  The  ratio 
of  the  low-pressure  to  high-pressure  cylinder  in  this  system  should  be  5, 
when  the  steam-pressure  is  125  Ibs..  absolute;  when  135  Ibs.,  5.4;  when 
145  Ibs.,  5.8;  when  155  Ibs.,  6.2;  when  165  Ibs.,  6.6.  The  ratio  of  low- 
pressure  to  intermediate  cylinder  should  be  about  one-half  that  between 
low-pressure  and  high-pressure,  as  given  above.  That  is,  if  the  ratio 
of  l.p.  to  h.p.  is  6,  that  of  l.p.  to  int.  should  be  about  3,  and  consequently 
that  of  int.  to  h.p.  about  2.  In  practice  the  ratio  of  int.  to  h.p.  is  nearly 
2.25,  so  that  the  diameter  of  the  int.  cylinder  is  1.5  that  of  the  h.p.  The 
introduction  of  the  triple-compound  engine  has  admitted  of  ships  being 
propelled  at  higher  rates  of  speed  than  formerly  obtained  without  exceed- 
ing the  consumption  of  fuel  of  similar  ships  fitted  with  ordinary  com- 
pound engines;  in  such  cases  the  higher  power  to  obtain  the  speed  has  been 
developed  by  decreasing  the  rate  of  expansion,  the  low-pressure  cylin- 
der being  only  6  times  the  capacity  of  the  high-pressure,  with  a  working 
pressure  of  170  Ibs.  absolute.  It  is  now  a  very  general  practice  to  make 
the  diameter  of  the  low-pressure  cylinder  equal  to  the  sum  of  the  diameters 
of  the  h.p.  and  int.  cylinders;  hence, 

Diameter  of  int.  cylinder  =1.5  diameter  of  h.p.  cylinder; 
Diameter  of  l.p.  cylinder  =  2.5  diameter  of  h.p.  cylinder. 

In  this  case  the  ratio  of  l.p.  to  h.p.  is  6.25;  the  ratio  of  int.  to  h.p.  is  2.26; 
and  ratio  of  l.p.  to  int.  is  2.78. 

Ratios  of  Cylinders  for  Different  Classes  of  Engines.  (Proc.  Inst. 
M.  E.,  Feb.,  1887,  p.  36.) —  As  to  the  best  ratios  for  the  cylinders  in  a 
triple  engine  there  seems  to  be  great  difference  of  opinion.  Considerable 
latitude,  however,  is  due  to  the  requirements  of  the  case,  inasmuch  as 
it  would  not  be  expected  that  the  same  ratio  would  be  suitable  for  an 
economical  land  engine,  where  the  space  occupied  and  the  weight  were  of 
minor  importance,  as  in  a  war-ship,  where  the  conditions  were  reversed. 
In  the  land  engine,  for  example,  a  theoretical  terminal  pressure  of  about 
7  Ibs.  above  absolute  vacuum  would  probably  be  aimed  at,  which  would 
give  a  ratio  of  capacity  of  high  pressure  to  low  pressure  of  1  to  8  Viz  or  1  to 
9;  whilst  in  a  war-ship  a  terminal  pressure  would  be  required  of  12  to  13 
Ibs.  which  would  need  a  ratio  of  capacity  of  1  to  5;  yet  in  both  these 
instances  the  cylinders  were  correctly  proportioned  and  suitable  to  the 
requirements  of  the  case.  It  is  obviously  unwise,  therefore,  to  introduce 
any  hard-and-fast  rule. 

Types  of  Three-stage   Expansion   Engines,  —  1.    Three  cranks  at 


THE  STEAM-ENGINE. 


120  (leg.  2.  Two  cranks  with  1st  and  2d, cylinders  tandem.  3.  Two 
cranks  with  1st  and  3d  cylinders  tandem.  The  most  common  type  is  the 
first,  with  cylinders  arranged  in  the  sequence  high,  intermediate,  low. 

Sequence  of  Cranks.  — Mr.  Wyllie  (Proc.  Inst.  M.  E.,  1887)  favors 
the  sequence  high,  low,  intermediate,  while  Mr.  Mudd  favors  high,  inter- 
mediate, low.  The  former  sequence,  high,  low,  intermediate,  gave  an 
approximately  horizontal  exhaust-line,  and  thus  minimizes  the  range  of 
temperature  and  the  initial  load;  the  latter  sequence  high,  intermediate, 
low,  increased  the  range  and  also  the  load.  • 

Mr.  Morrison,  in  discussing  the  question  of  sequence  of  cranks,  pre- 
sented a  diagram  showing  that  with  the  cranks  arranged  in  the  sequence 
high,  low,  intermediate,  the  mean  compression  into  the  receiver  was 
19V2  per  cent  of  the  stroke;  with  the  sequence  high,  intermediate,  low, 
it  was  57  per  cent. 

In  the  former  case  the  compression  was  just  what  was  required  to  keep 
the  receiver-pressure  practically  uniform ;  in  the  latter  case  the  compression 
caused  a  variation  in  the  receiver-pressure  to  the  extent  sometimes  of 
22V2  Ibs. 

Velocity  of  Steam  tjirough  Passages  in  Compound  Engines. 
(Proc.  Inst.  M.  E.,  Feb.,  1887.)  —  In  the  SS.  Para,  taking  the  area  of  the 
cylinder  multiplied  by  the  piston-speed  in  feet  per  second  and  dividing 
by  the  area  of  the  port  the  velocity  of  the  initial  steam  through  the  high- 
pressure  cylinder  port  would  be  about  100  feet  per  second;  the  exhaust 
would  be  about  90.  In  the  intermediate  cylinder  the  initial  steam  had 
a  velocity  of  about  180,  and  the  exhaust  of  120.  In  the  low-pressure 
cylinder,  the  initial  steam  entered  through  the  port  with  a  velocity  of  250, 
and  in  the  exhaust-port  the  velocity  was  about  140  feet  per  second. 

A  Double-tandem  Triple-expansion  Engine,  built  by  Watts, 
Campbell  &  Co.,  Newark,  N.  J.,  is  described  in  Am.  Mack.,  April  26,  1894. 
It  is  two  three-cylinder  tandem  engines  coupled  to  one  shaft,  cranks  at 
90°,  cylinders  21,  32  and  48  by  60  in.  stroke,  65  revolutions  per  minute, 
rated  H.P.  2000;  fly-wheel  28  ft.  diameter,  12  ft.  face,  weight  174,000 
bs.;  main  shaft  22  in.  diameter  at  the  swell;  main  journals  19  X  38  in.; 
^rank-pins  91/2  X  10  in.;  distance  between  center  lines  of  two  engines 
24  ft.  7 1/2  in.;  Corliss  valves,  with  separate  eccentrics  for  the  exhaust- 
calves  of  the  l.p.  cylinder. 


QUADRUPLE-EXPANSION  ENGINES. 

H.  H.  Suplee  (Trans.  A.  S.  M.  E.,  x,  583)  states  that  a  study  of  14 
different  quadruple-expansion  engines,  nearly  all  intended  to  be  operated 
at  a  pressure  of  180  Ibs.  per  sq.  in.,  gave  average  cylinder  ratios  of  1  to  2, 
to  3.78,  to  7.70,  or  nearly  in  the  proportions  1,  2,  4,  8. 

If  we  take  the  ratio  of  areas  of  any  two  adjoining  cylinders  as  the  fourth 
root  of  the  number  of  expansions,  the  ratio  of  the  1st  to  the  4th  will  be 
the  cube  of  the  fourth  root.  On  this  basis  the  ratios  of  areas  for  different 
pressures  and  rates  of  expansion  will  be  as  follows: 


Gauge- 
pressures. 

Absolute 
Pressures. 

Terminal 
Pressures. 

Ratio  of 
Expansion. 

Ratios  of  Areas 
of  Cylinders. 

!12 

14.6 

:  1  95  :  3  81  :  7  43 

160 

175 

10 
8 
SI2 

17.5 
21.9 
16.2 

:  2.  05:  4.  18:  8.55 
:  2.16:  4.68:  10.12 
:  2.01  :  4  02:  8.07 

180 

195 

'8 

19.5 
24.4 

:  2.10:  4.42:  9.28 
:  2  22  :  4  94  :  10  98 

200 
220 

215 
235 

P 

,1 

h 

17.9 
21.5 
26.9 
19.6 
23.5 
29.4 

:  2.  06:  4.  23:  8.70 
:  2.15:  4.64:  9.98 
:  2.28:  5.19:  11.81 
:  2.  10:  4.  43:  9.31 
:  2.20:  4.85:  10.67 
:  2.33:  5.42:  12.62 

Seaton  says:  When  the  pressure  of  steam  employed  exceeds  190  Ibs. 
absolute,  four  cylinders  should  be  employed,  with  tag  steam  expanding 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.     987 

through  each  successively;  and  the  ratio  of  l.p.  to  h.p.  should  be  at  least 
7.5,  and  if  economy  of  fuel  is  of  prime  .consideration  it  should  be  8;  then 
the  ratio  of  first  intermediate  to  h.p.  should  be  1.8,  that  of  second  inter- 
mediate to  first  int.  2,  and  that  of  l.p.  to  second  int.  2.2. 

.in  a  paper  read  before  the  North  East  Coast  Institution  of  Engineers 
and  Shipbuilders,  1890,  William  Russell  Cummins  advocates  the  use  of  a 
four-cylinder  engine  with  four  cranks  as  being  more  suitable  for  high 
speeds  than  the  three-cylinder  three-crank  engine.  The  cylinder  ratios, 
he  claims,  should  be  designed  so  as  to  obtain  equal  initial  loads  in  each 
cylinder.  The  ratios  determined  for  the  triple  engine  are  1,  2.04,  6.54, 
and  for  the  quadruple,  1,  2.08,  4.46,  10.47.  He  advocates  long  stroke,, 
high  piston-speed,  100  revolutions  per  minute,  and  250  Ibs.  boiler-pressure, 
unjacketed  cylinders,  and  separate  steam  and  exhaust  valves. 

ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES. 

Economy  of  Expansive  Working  under  Various  Conditions,  Single 
Cylinder. 

(Abridged  from  Clark  on  the  Steam  Engine.) 

1.  SINGLE  CYLINDERS  WITH  SUPERHEATED  STEAM,  NON-CONDENSING. — 
Inside  cylinder  locomotive,  cylinders  and  steam-pipes  enveloped  by  the 
hot  gases  in  the  smoke-box.     Net  boiler  pressure  100  Ibs.;  net  maximum 
pressure  in  cylinders  80  Ibs.  per  sq.  in. 

Cut-off,  per  cent 20       25       30       35       40       50       60       70         80 

Actual  ratio  of  expan- 
sion   3.91  3.31  2.87  2.53  2.26  1.86  1.59  1.39  1.23 

Water  per  I.H.P.  per 

hour,  Ibs 18.5  19.4  20  21.2  22.2  24.5  27  30  33 

2.  SINGLE   CYLINDERS    WITH   SUPERHEATED   STEAM,    CONDENSING.  — - 
The  best  results  obtained  by  Him,  with  a  cylinder  233/4  x  67  in.  and  steam 
superheated  150°  F.,  expansion  ratio  33/4  to  41/2,  total  maximum  pressure 
in  cylinder  63  to  69  Ibs.,  were  15.63  and  15.69  Ibs.  of  water  per  I.H.P.  per 
hour. 

3.  SINGLE  CYLINDERS,  NOT  STEAM-JACKETED,  CONDENSING.  —  The  best 
result  is  from  a  Corliss-Wheelock  engine  18  X  48  in.;  cut-off,   12.5%; 
actual  expansion  ratio,  6.95;   maximum  absolute  pressure  in  cylinder 
104  Ibs.;  steam  per  I.H.P.  hour,  19.58  Ibs.     Other  engines,  with  lowei 
steam  pressures,  gave  a  steam  consumption  as  high  as  26.7  Ibs. 

Feed-water  Consumption  of  Different  Types  of  Engines.  —  The 
following  tables  are  taken  from  the  circular  of  the  Tabor  Indicator  (Ash- 
croft  Mfg.  Co.,  1889).  In  the  first  of  the  two  columns  under  Feed-water 
required,  in  the  tables  for  .simple  engines,  the  figures  are  obtained  by 
computation  from  nearly  perfect  indicator  diagrams,  with  allowance 
lor  cylinder  condensation  according  to  the  table  on  page  936,  but  without 
.allowance  for  leakage,  with  back-pressure  in  the  non-condensing  table 
taken  at  16  Ibs.  above  zero,  and  in  the  condensing  table  at  3  Ibs.  above  zero. 
The  compression  curve  is  supposed  to  be  hyperbolic,  and  commences  at 
0.91  of  the  return-stroke,  with  a  clearance  of  3%  of  the  piston-displace- 
ment. 

Table  No.  2  gives  the  feed-water  consumption  for  jacketed  compound- 
condensing  engines  of  the  best  class.  The  water  condensed  in  the  jackets 
is  included  in  the  quantities  given.  The  ratio  of  areas  of  the  two  cylinders 
is  as  1  to  4  for  120  Ibs.  pressure:  the  clearance  of  each  cylinder  is  3% 
and  the  cut-off  in  the  two  cylinders  occurs  at  the  same  point  of  stroke. 
The  initial  pressure  in  the  l.p.  cylinder  is  1  Ib.  per  sq.  in.  below  the  back- 
pressure of  the  h.p.  cylinder.  The  average  back-pressure  of  the  whole 
stroke  in  the  l.p.  cylinder  is  4.5  Ibs.  for  10%  cut-off;  4.75  Ibs.  for  20% 
cut-off;  and  5  Ibs.  for  30%  cut-off.  The  steam  accounted  tor  by  the 
indicator  at  cut-off  in  the  h.p.  cylinder  (allowing  a  small  amount  for  leak- 
age) is  0.74  at  10%  cut-off,  0.78  at  20%,  and  0.82  at  30%  cut-off.  Tbe 
loss  by  condensation  between  the  cylinders  is  such  that  the  steam  ac- 
counted for  at  cut-off  in  the  l.p.  cylinder,  expressed  in  proportion  of  that 
shown  at  release  in  the  h.p.  cylinder,  is  0.85  at  10%  cut-off,  0.87  at  20% 
cut-off,  and  0.89  at  30%  cut-off. 


988 


THE  STEAM-ENGINE. 


TABLE   No.  1. 

FEED-WATER  CONSUMPTION,  SIMPLE  ENGINES. 
NON-CONDENSING  ENGINES.  CONDENSING  ENGINES. 


A 

Feed-water  Re- 

* 

Feed-  water  Re- 

o 

JS 

quired  per  I.H.P. 
per  Hour. 

1 

J 

quired  per  I.H.P. 
per  Hour. 

2? 

i 

3 

J4 

A"Sfi  . 

1 

1 

M 

41*« 

M 

£ 

o  v 

•S  3  yj 

£ 

o 

G  0 

^  g  3  M 

i 

PH 

o  >-3 

O  c3  JS  c3 

d 

M 

o  ^ 

°^  1-3 

td 
o 

£ 

o 

IJ 

§1  ^ 

! 

8 

0 

w§ 

605    ,S 

3 

on    . 

8 

K5-S 

^o^  2 

5 

CO      . 

'•£ 

*5"5 

'S—  °  -w 

•u 

£5 

& 

§  ||li 

vJ 

g 

&£ 

1 

|'?   CO 

111! 

§ 

3? 

a 

«  a~- 

sS£^ 

i 

!S  -" 

d 

«  a12. 

l* 

t-l 

1 

V 

Sa 

S 

g&flcj 

o^.S.S 

<o 

w  a 

o 

a 

£W)=3 

o^'""1 

80 

16.07 

27.61 

29.88 

80 

29.72 

17.30 

18.89 

90 

19.76 

25.43 

27.43 

90 

33.41 

17.15 

18.70 

100 

23.45 

23.90 

25.73 

100 

37.10 

17.02 

18.56 

/ 

80 

32.02 

24.04 

25.68 

/ 

80 

38.28 

17.60 

19.09 

20  5 

90 

37.47 

23.00 

24.57 

15 

90 

42.92 

17.45 

18.91 

( 

100 

42.92 

22.25 

23.77 

100 

47.56 

17.32 

18.74 

/ 

80 

43.97 

24.71 

26.29 

/ 

80 

45.63 

18.27 

19.69 

30  j 

90 

50.73 

23.91 

25.38 

20  j 

90 

51.08 

18.14 

19.51 

I 

100 

57.49 

23.27 

24.68 

100 

56.53 

18.02 

19.36 

80 

53.25 

25.76 

27.17 

t 

80 

57.57 

19.91 

21.25 

90 

61.01 

25.03 

26.35 

30  j 

90 

64.32 

19.78 

21.06 

too 

68.76 

24.47 

25.73 

100 

71.08 

19.67 

20.93 

80 

60.44 

26.99 

28.38 

80 

66.85 

21.36 

22.56 

90 

68.96 

26.32 

27.62 

90 

74.60 

21.24 

22.41 

100 

77.48 

25.78 

26.99 

100 

82.36 

21.13 

22.24 

TABLE  No.  2 
FEED-WATER   CONSUMPTION  FOR   COMPOUND   CONDENSING   ENGINES. 


Cut-off 
per  cent. 

Initial  Pressure  above 
Atmosphere. 

Mean  Effective  Press. 

Feed-water 
Required 
per  I.H.P.  per 
Hour,  Ib.     . 

h.p.Cyl.,lb.|l.p.Cyl.,lb. 

h.p.Cyl.,lb.|l.p.Cyl.,lb. 

•  ! 

80 
100 
120 

4.0 
7.3 
11.0 

11.67 
15.33 

18.54 

2.65 
3.87 
5.23 

16.92 
15.00 
13.86 

•  I 

80 
100 
120 

4.3 
8.1 
12.1 

26.73 
33.13 
39.29 

5.48 
7.56 
9.74 

14.60 
13.67 
13.09 

•  i 

80 
100 
120 

4.6 
8.5 
11.7 

37.61 
46.41 
56.00 

7.48 
10.10 
12.26 

14.99 
14.21 
13.87 

Sizes  and  Calculated  Performances  of  Vertical  High-speed 
EngineSo  — Thfc  following  tables  are  taken  from  an  old  circular,  describ- 
ing: the  engines  made  by  the  Lake  Erie  Engineering  Works,  Buffalo,  N.  Y. 
The  engines  are  fair  representatives  of  the  type  largely  used  for  driving 
dynamos  directly  without  belts.  The  tables  were  calculated  by  E  F 
Williams,  designer  of  the  engines.  They  are  here  somewhat  abridged  to 
save  space. 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.     089 


Simple  Engines  —  Non-condensing. 


li 

T:- 

rt     W 

Is 

Q'~ 

71/2 
81/2 
JOV2 

l>l/2 
16 
18 

22 
241/2 
27 

« 

.2 
cT 

rX 

2 

DQ 

Revs,  per 
Minute. 

H.P.w 

cutting 
at  1/5  str 

ten 
off 
oke. 

H.P.  when 
cutting  off 
at  1/4  stroke. 

H.P.  when 
cutting  off 
at  1/3  stroke 

Dimen- 
sions of 
Wheels, 
dia.    face 

Steam-pipe, 
ins. 

Exhaust- 
pip*.  1 

70 
Ibs. 

80 
Ibs. 

90 
Ibs. 

70 

Ibs. 

80 
Ibs. 

90 

Ibs. 

70 
Ibs. 

80 
Ibs. 

90 

Ibs. 

Ft. 

In. 

10 
12 
14 
16 
18 
20 
24 
28 
32 
34 

370 
318 
277 
246 
222 
181 
158 
138 
120 
112 

20 
27 
41 
53 
66 
95 
119 
179 
221 
269 

25 
32 
49 
64 
80 
115 
144 
216 
267 
325 

30 
39 
60 
77 
96 
138 
173 
26  1 
322 
392 

26 
34 
52 
67 
84 
120 
151 
227 
281 
342 

31 

41 
•62 
81 
100 
144 
181 
272 
336 
409 

36.5 

36 

47 
71 
93 
116 
166 
208 
313 
386 
470 

42 

32 
41 
63 
82 
102 
146 
183 
276 
340 
414 

37 

48 
74 
96 
120 
172 
215 
324 
400 
487 

43 
56 
85 

Hi 

198 
248 
373 
460 
560 

4 

41/9 

5'9" 
6'8" 

71/2 
8'4" 
10 

n'8" 

13'  4" 

14'  2* 

4 

61/2 

:i 

15 
19 
28 
34 
41 

18 

31/2 
4 

«% 

6 

7 
8 

3 
31/2 

4V2 

6 
7 
8 
9 
10 

M.E.P.,lb3.  ... 
Ratio  of  exp.... 

Term'!     press, 
(about),  Ibs.  . 
Cyl.  cond'n,  %- 
Steam  per  I.  H.  P. 
hour,  Ibs  

2.4 

29 

35 

30.5 

37 

43.5 

50 

Note.  —  The 
nominal-power 
rating  of  the  en- 
gines is  at  80  Ibs. 
gauge  pressure, 
steam  cut-off  at 
•    1/4  stroke. 

5 

4 

3 

17.9 
26 

32.9 

20 
26 

30 

22.3 
26 

27.4 

22.4 
24 

31.2 

25 
24 

29.0 

27.6 
24 

27.9 

29.8 
21 

32 

33.3 
21 

31.4 

36.8 
21 

30 

Compound  Engines  —  Non-condensing  —  High-pressure   Cylinder 
and  Receiver  Jacketed. 


Diam. 

Cylinder, 
inches. 

Stroke,  inches. 

Revolutions  per  1 
Minute.  | 

H.P.,  cutting  off 
at  1/4  Stroke 
in  h.p.  Cylinder. 

H.P.,  cutting  off 
at  1/3  Stroke 
in  h.p.  Cylinder. 

H.P.,  cutting  off 
at  1/2  Stroke 
in  h.p.  Cylinder. 

Cyls. 
31/s:  1. 

Cy!s. 
4i/2:  1. 

Cyls. 
3l/3:  1. 

Cyls. 
4i/2:  1. 

Cyls. 
31/3:  1. 

Cyk 

41/2:  *. 

cm 

W 

Pk 

w 

ti 
^ 

80 
Ibs. 

90 

Ibs. 

130 
Ibs. 

150 
Ibs. 

80 

Ibs. 

90 

Ibs. 

130 

Ibs. 

150 
Ibs. 

80 

Ibs. 

90 

Ibs. 

130 
Ibs. 

150 
Iba. 

53/4 
63/8 
73/4 

J02V2 

ir/2 

18 
20 

241/2 
281/2 

61/2 
71/2 

uv, 

!?$ 

l81/2 

2% 

I?1* 

12 
131/2 
16l/2 

gV2 

281/.> 

^ 

43 
52 
60 

10 
12 
14 
16 
18 
20 
24 
28 
32 
34 
42 
48 

370 

318 
277 
246 
222 
185 
158 
138 
120 
112 
93 
80 

7 
9 
14 
18 
26 
32 
43 
57 
74 
94 
138 
180 

15 
19 

28 
37 
53 
65 
88 
118 
152 
194 
285 
374 

19 
24 
36 
47 
68 
84 
112 
151 
194 
249 
365 
477 

32 
40 
60 

78 
112 
139 
186 
249 
321 
412 
603 
789 

23 
29 
43 
57 
81 
100 
135 
180 
232 
297 
436 
570 

31 
39 

58 
76 
109 
135 
181 
242 
312 
400 
587 
767 

35 
45 
67 
87 
125 
154 
206 
277 
357 
457 
670 
877 

46 
59 
87 
114 
164 
202 
271 
363 
468 
601 
880 
1151 

44 
56 
83 
109 
156 
192 
258 
346 
446 
572 
838 
1096 

55 
70 
104 
136 
195 
241 
323 
433 
558 
715 
1048 
1370 

64 
81 
121 
158 
226 
279 
374 
502 
647 
829 
1215 
1589 

79 
101 
159 
196 
231 
346 
464 
623 
803 
1030 
1508 
1973 

Mean  eff.  pressure,  Ibs.. 
Ratio  of  expansion  

Cyl.  condensation,  %  .  . 
Ter.  pres.  (abt.),  Ibs... 
Loss    from    expanding 
below  atmosphere,  % 
St.perl.H.P.hour.lbs. 

3.3 

6.8 

8.7 

14.4 

10.4 

14.0 

16 

21 

20 

25 

29 

36 

131/2 

181/4 

101/4 

133/4 

63/4 

91/4 

14 

7.3 

34 
55 

14 
7.7 

15 
42 

16 
7.9 

17. 
47 

16 
9 

3 

29 

12 
9.2 

5 
33.3 

12 
10.4 

0 
27.7 

13 
10.5 

0 

28.7 

13 
12 

0 

25.4 

10 
14 

0 
30 

10 
15.5 

0 
26.2 

11 
14.6 

0 
21 

It 

17.8 

0 

20 

990 


THE  STEAM-ENGINE. 


Compound  Engines  —  Condensing  —  Steam-jacketed. 


Diam. 
Cylinder, 
inches. 

Stroke,  inches. 

t-c 
0) 

ft 

GO 
|« 

"3  "5 

11 

rt 

370 
318 
277 
246 
222 
185 
158 
138 
120 
112 
93 
80 

H.P.  when 
cutting  off  at 
1/4  Stroke 
inh.p.  Cylinder. 

H.P.  when 
cutting  off  at 
1/3  Stroke 
inh.p.  Cylinder. 

H.P.  when 
cutting  off  at 
1/2  Stroke 
inh.p.  Cylinder. 

Ratio, 
3V3:  1. 

Ratio, 
4:  1. 

Ratio, 
31/s:  1. 

Ratio, 
4:  1. 

Ratio, 
31/3:  1. 

Ratio, 
4:  1. 

fc 
W 

^ 

w 

^ 

H-i 

80 
Ibs. 

110 

Ibs. 

115 

Ibs. 

125 

Ibs. 

80 

Ibs. 

110 

Ibs. 

115 

Ibs. 

125 

Ibs. 

80 

Ibs. 

110 
Ibs. 

115 
Ibs. 

125 
Ibs. 

106 
134 
200 
261 
374 
462 
619 
830 
1070 
1373 
2012 
2632 

6 

61/2 
8V4 

91/2 
11 

12V2 
14 
17 
19 
21 
26 
30 

61/2 
7l/2 

101/2 

131/2 
151/2 

181/2 
201/2 
221/2 
2f/2 

12 
131/2 
|6V2 

If/2 
281/2 

?8i/2 

43 
52 
60 

10 
12 
14 
16 
18 
20 
24 
28 
32 
34 
42 
48 

44 
56 
83 
109 
156 
192 
258 
346 
446 
572 
838 
1096 

59 
76 
112 
147 
210 
260 
348 
467 
602 
772 
1131 
1480 

53 
67 
100 
131 
187 
231 
310 
415 
535 
686 
1006 
1316 

62 
78 
116 
152 
218 
269 
361 
484 
624 
801 
1174 
1534 

55 
70 
104 
136 
195 
241 
323 
433 
558 
715 
1048 
1370 

70 
90 
133 
174 
250 
308 
413 
554 
.714 
915 
1341 
1757 

68 
87 
129 
169 
242 
298 
400 
536 
691 
887 
1299 
1699 

75 
95 
141 
185 
265 
327 
439 
588 
758 
972 
1425 
1863 

70 
90 
133 
174 
250 
308 
413 
554 
714 
915 
1341 
1757 

97 
123 
183 
239 
343 
423 
568 
761 
981 
1258 
1844 
2411 

95 
120 
179 
234 
335 
414 
555 
744 
959 
1230 
1801 
2356 

Mean  eff  .  press.,  Ibs  
Ratio  of  expansion  

Cyl.  condensation,  %.  .  . 
St.  per  I.H.P.  hour,  Ibs. 

20 

27 

24 

28 

25 

32 

31 

34 

32 

44 

43 

48 

131/2 

161/4 

10 

121/4 

63/4 

81/4 

18  I   18 
17.3)16.6 

20 
16.6 

20 
15.2 

15 
17.0 

15 
16.4 

18 
16.3 

18 
15.8 

12 
17.5 

12 
17.0 

14 
16.8 

14 
16.C 

Triple-expansion  Engines,  Non-condensing —  Receiver  only 
Jacketed. 


Diameter 
Cylinders, 
inches. 

I 
o 
r, 

1 

1 

Horse-power 
when  cutting 
off  at  42%  of 
Stroke  in  First 

Horse-power 
when  cutting 
off  at  50%  of 
Stroke  in  First 

Horse-power 
when  cutting 
off  at  67%  of 
Stroke  in  First 

oT 

Cylinder. 

Cylinder. 

Cylinder. 

n 

O    £ 

H.P. 

T.P. 

L.P. 

0)*jH 

180  Ibs. 

200  Ibs. 

180  Ibs. 

200  Ibs. 

180  Ibs. 

200  Ibs. 

'Jl 

PH 

43/4 

71/2 

12 

10 

370 

55 

64 

70 

84 

95 

108 

5V2 

81/2 

131/7 

12 

318 

70 

81 

90 

106 

120 

137 

61/2 

J61/? 

14 

277 

104 

121 

133 

158 

179 

204 

71/2 

12 

19 

16 

246 

136 

158 

174 

207 

234 

267 

9 

141/2 

221/3 

18 

222 

195 

226 

250 

296 

335 

382 

10 

16 

25 

ZO 

185 

241 

279 

308 

366 

414 

471 

111/2 

18 

281/2 

24 

158 

323 

374 

413 

490 

555 

632 

13 

22 

33l/? 

28 

138 

433 

502 

554 

657 

744 

848 

15 

241/2 

38 

32 

120 

558 

647 

714 

847 

959 

1093 

17 

27 

43 

34 

112 

715 

829 

915 

1089 

1230 

1401 

20 

33 

52 

42 

93 

1048 

1215 

1341 

1592 

1801 

2053 

231/2 

38 

60 

48 

80 

1370 

1589 

1754 

2082 

2356 

2685 

Mean  eff.  press.,  Ibs  

25 

29 

32 

38 

43 

49 

No.  of  expansions  

16 

13 

10 

Cyl.  condensation,  %  

14 

12 

10 

Steam  p.  I.H.P.p.hr.,  Ibs. 

20.76 

19J6 

19.25 

17.00 

17.89 

17.20 

Lbs.coalat81b.evap.,lbs. 

2.59 

2.39 

2.40 

2.12 

2.23 

2.15 

ECONOMIC   PERFORMANCE    OF   STEAM-ENGINES.       991 
Triple-expansion  Engines  —  Condensing  —  Steam- jacketed. 


IH 

Horse- 

Horse- 

Horse- 

Horse- 

Diameter 
Cylinders, 
inches. 

g 

1 

* 

lutions  p 
lute. 

power  when 
cutting  off 
at  1/4  Stroke 
in  First  Cyl. 

power  when 
cutting  off 
at  1/3  Stroke 
in  First  Cyl. 

power  when 
cutting  off 
at  1/2  Stroke 
in  First  Cyl. 

power  when 
cutting  off 
at  3/4  Stroke 
in  First  Cyl. 

AH 

fl| 

PH 

2 

o.a 
^ 

120 

140 

160 

120 

140 

160 

120 

140 

160 

120 

140 

160 

W 

^ 

CO 

« 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

43/4 

?!/•> 

12 

10 

370 

35 

42 

48 

44 

53 

59 

57 

72 

84 

81 

97 

110 

51/J 

«!/•> 

131/9 

12 

318 

45 

53 

62 

56 

67 

76 

73 

92 

107 

104 

123 

140 

6l/o 

101/9 

161/9 

14 

277 

67 

79 

92 

83 

100 

112 

108 

137 

159 

154 

183 

208 

71/2 

12 

19 

16 

246 

87 

103 

120 

109 

131 

147 

141 

180 

208 

201 

239 

272 

9 

141/9 

221/9 

18 

222 

125 

148 

172 

156 

187 

211 

203 

257 

299 

289 

343 

390 

10 

16 

25 

20 

185 

154 

183 

212 

192 

7.3  1 

7.60 

250 

317 

368 

356 

423 

481 

1U/9 

18 

281/9 

24 

158 

206 

245 

284 

258 

310 

348 

335 

426 

494 

477 

568 

645 

13 

22 

331/9 

28 

138 

277 

329 

381 

346 

415 

467 

450 

571 

663 

640 

761 

865 

15 

241/9 

38 

32 

120 

357 

424 

491 

446 

535 

602 

580 

736 

854 

825 

981 

1115 

n 

27 

43 

34 

112 

458 

543 

629 

572 

686 

777. 

744 

944 

1095 

1058 

1258 

1430 

20 

33 

52 

42 

93 

670 

796 

922 

838 

1006 

1131 

1089 

1383 

1605 

1551 

1844 

2096 

231/2 

38 

60 

.48 

80 

877 

1041 

1206 

1096 

1316 

1480 

1424 

1808 

2099 

2028 

2411 

2740 

Mean  eff.  press.,  Ibs  

16 

19 

22 

20 

24 

27 

26 

33 

38.3 

37 

44 

50 

No.  of  expansions  

26.8 

20.1 

13.4 

8  9 

Cyl.  condensation,  %  .  .  • 

19 

19 

19 

16 

16 

16 

12 

12 

12 

8 

8 

8 

St.  p.  I.H.P.  p.  hr.,  Ibs.. 

14  7 

n  9 

13  3 

14  3 

13  9 

13  2 

14  3 

13  6 

13  0 

15  7 

14  9 

14  7 

Coal  at  8  Ibs.  evap.,  Ibs- 

1.8 

1.73 

1.66 

1.78 

1.7 

41.65 

1.78 

1.70 

1.62 

1.96 

1.86 

1.72 

The  Willans  Law.     Total  Steam  Consumption  at  Different  Loads. 

—  Mr.  Willans  found  with  his  engine  that  when  the  total  steam  consump- 
tion at  different  loads  was  plotted  as  ordinates,  the  loads  being  abscissas, 
the  result  would  be  a  straight  inclined  line  cutting  the  axis  of  ordinates  at 
some  distance  above  the  origin  of  coordinates,  this  distance  representing 
the  steam  consumption  due  to  cylinder  condensation  at  zero  load.  This 
statement  applies  generally  to  throttling  engines,  and  is  known  as  the 
Willans  law.  It  applies  also  approximately  to  automatic  cut-off  engines 
of  the  Corliss,  and  probably  of  other  types,  up  to  the  most  economical 
load.  In  Mr.  Barrus's  book  there  is  a  record  of  six  tests  of  a  16  X  42-in. 
Corliss  twin-cylinder  non-condensing  engine,  which  gave  results  as  follows: 

I.H.P...                                            37        100      146       222     250*  287     342 

Feed-water  per  I.H.P.  hour.     73.63  38.28  31.47  25.83  25.0*  25.39  25.91 

Total  feed-water  per  hour...     2724    3825    4595    5734    6250  7287     8861 

*  Interpolated  from  the  plotted  curve. 

The  first  five  figures  in  the  last  line  plot  in  a  straight  line  whose  equa- 
tion is  y  =  2122  -I-  16.55  H.P.,  and  a  straight  line  through  the  plotted 
position  of  the  last  two  figures  has  the  equation  y  =  28.62  H.P.  —  927. 
These  two  lines  cross  at  253  H.P.,  which  is  the  most  economical  load,  the 
water  rate  being  24.96  Ibs.  and  the  total  feed  6314  Ibs. .  The  figure  2122 
represents  the  constant  loss  due  to  cylinder  condensation,  which  is  just 
over  one-third  of  the  total  feed-water  at  the  most  economical  load. 

In  Geo.  H.  Barrus's  book  on  "Engine  Tests  "  there  is  a  diagram  of 
condensation  and  leakage  in  tight  or  fairly  tight  simple  engines  using  sat- 
urated steam.  The  average  curve  drawn  through  the  several  observations 
shows  the  condensation  and  leakage  to  be  about  as  follows  for  different 
percentages  of  cut-off: 


Cut-off,  %  of  stroke  =  1 5      10      15     20 

Condens.  and  leakage,  %  =  p. . .     60      43      35     29 
c  =  IX  p  -4-  (100  -  p)  = 7.5     7.5        8    8.2 


25      30      35      42 
24      20       17      15 

7.9     7.5     7.2     7.4 


The  figures  in  the  last  line  represent  the  condensation  and  leakage  as 
a  percentage  of  the  volume  of  the  stroke  of  the  piston,  that  is,  in  the  same/ 


992  THE   STEAM-ENGINE. 

terms  as  the  first  line,  instead  of  as  a  percentage  of  the  total  steam  sup- 
plied, in  which  terms  the  figures  of  the  second  line  afe  expressed.  They 
indicate  that  the  amount  of  cylinder  condensation  is  nearly  a  constant 
quantity  for  a  given  engine  with  a  given  steam  pressure  and  speed,  what- 
ever may  be  the  point  of  cut-off. 

Economy  of  Engines  under  Varying  Loads.  (From  Prof.  W.  C. 
Unwin's  lecture  before  the  Society  of  Arts,  London,  1892.)  —  The  general 
result  of  numerous  trials  with  large  engines  was  that  with  a  constant  load  an 
indicated  horse-power  should  be  obtained  with  a  consumption  of  11/2  Ibs. 
of  coal  per  I.H.P.  for  a  condensing  engine,  and  13/4  Ibs.  for  a  non-conden- 
sing engine,  corresponding  to  about  13/4  Ibs.  to  2 1/8  Ibs.  per  effective  H. P. 

In  electric-lighting  stations  the  engines  work  under  a  very  fluctuating 
load,  and  the  results  are  far  more  unfavorable.  An  excellent  Willans 
non-condensing  engine,  which  on  full-load  trials  worked  with  under 
2  Ibs.  per  effective  H.P.  hour,  in  the  ordinary  daily  working  of  the  station 
used  71/2  Ibs.  in  1886,  which  was  reduced  to  4.3  Ibs.  in  1890  and  3.8  Ibs.  in 
1891 .  Probably  in  very  f ew  cases  were  the  engines  at  electric-light  stations 
working  under  a  consumption  of  41/2  Ibs.  per  effective  H.P.  hour.  In  the 
case  of  small  isolated  motors  working  with  a  fluctuating  load,  still  more 
extravagant  results  were  obtained. 

At  electric-lighting  stations  the  load  factor,  viz.,  the  ratio  of  the  average 
load  to  the  maximum,  is  extremly  small,  and  the  engines  worked  under 
very  unfavorable  conditions,  which  largely  accounted  for  the  excessive 
fuel  consumption  at  these  stations. 

In  steam-engines  the  fuel  consumption  has  generally  been  reckoned  on 
the  indicated  horse-power.  At  full-powet  trials  this  wras  satisfactory 
enough,  as  the  internal  friction  is  then  usually  a  small  fraction  of  the  total. 

Experiment  has,  however,  shown  that  the  internal  friction  is  nearly 
constant,  and  hence,  when  the  engine  is  lightly  loaded,  its  mechanical 
efficiency  is  greatly  reduced.  At  full  load  small  engines  have  a  mechan- 
ical efficiency  of  0.8  to  0.85,  and  large  engines  might  reach  at  least  0.9, 
but  if  the  internal  friction  remained  constant  this  efficiency  would  be 
much  reduced  at  low  powers.  Thus,  if  an  engine  working  at  100  I.H.P. 
had  an  efficiency  of  0.85,  then  when  the  I.H.P.  fell  to  50  the  effective  H.P. 
would  be  35  H.P.  and  the  efficiency  only  0.7.  Similarly,  at  25  H.P.  the 
effective  H.P.  would  be  10  and  the  efficiency  0.4. 

Experiments  on  a  Corliss  engine  at  Creusot  gave  the  following  results: 

Effective  power  at  full  load 1.0       0.75     0.50     0.25     0.125 

Condensing,  mechanical  efficiency 0 . 82     0.79     0.74     0 . 63     0 . 48 

Non-condensing,  mechanical  efficiency.  0 . 86     0.83     0 . 78     0 . 67     0 . 52 

Steam  Consumption  of  Engines  of  Various  Sizes.  —  W.  C.  Unwin 
(Cassier's  Magazine,  1894)  gives  a  table  showing  results  of  49  tests  of 
engines  of  different  types.  In  non-condensing  simple  engines,  the  steam 
consumption  ranged  from  65  Ibs.  per  hour  in  a  5-horse-power  engine  to  22 
Ibs.  in  a  134-H.P.  Harris-Corliss  engine.  In  non-condensing  compound 
engines,  the  only  type  tested  was  the  Willans,  which  ranged  from  27  Ibs. 
in  a  10-H.P.  slow-speed  engine,  122  ft.  per  minute,  with  steam-pressure 
of  84  Ibs.,  to  19.2  Ibs.  in  a  40-H.P.  engine,  401  ft.  per  minute,  with  steam- 
pressure  165  Ibs.  A  Willans  triple-expansion  non-condensing  engine, 
39  H.P.,  172  Ibs.  pressure,  and  400  ft.  piston  speed  per  minute,  gave  a 
consumption  of  18.5  Ibs.  In  condensing  engines,  nine  tests  of  simple 
engines  gave  results  ranging  only  from  18.4  to  22  Ibs.  In  compound- 
condensing  engines  over  100  H.P.,  in  13  tests  the  range  is  from  13.9  to 
20  Ibs.  In  three  triple-expansion  engines  the  figures  are  11.7,  12.2,  and 
12.45  Ibs.,  the  lowest  being  a  Sulzer  engine  of  360  H.P.  In  marine  com- 
pound engines,  the  Fusiyama  and  Colchester,  tested  by  Prof.  Kennedy, 
gave  steam  C9nsumption  of  21.2  and  21.7  Ibs.;  and  the  Meteor  and  Tartar 
triple-expansion  engines  gave  15.0  and  19.8  Ibs. 

Taking  the  most  favorable  results  which  can  be  regarded  as  not  excep- 
tional it  appears  that  in  test  trials,  with  constant  and  full  load,  the  ex- 
penditure of  steam  and  coal  is  about  as  follows: 

Ibs.  Per  I.H.P.  hour.  Per  Effective  H.P.  hr. 
Kind  of  Engine.     Co^       "    steam,'  'Coal,  Steam,' 

Non-condensing 1.80  16.5  2.00  18.0 

Condensing 1.50  13,5  1.75  15. 9 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.     993 


These  may  be  regarded  as  minimum  values,  rarely  surpassed  by  the 
most  efficient  machinery,  and  only  reached  with  very  good  machinery  in 
the  favorable  conditions  of  a  test  trial. 

Small  Engines  and  Engines  with  Fluctuating  Loads  are  usually 
very  wasteful  of  fuel.  The  following  figures,  illustrating  their  low  ^econ- 
omy, are  given  by  Prof.  Unwin,  Cassiw's  Magazine,  1894.  Small  engines 
in  workshops  in  Birmingham,  Eng. 


Probable  I.H.P.  at  full 
load 

Average  I.H.P.  during 
observation 

Coal  per  I.H.P.  per  hour 

during  observation,  Ibs.  36.0 


12         45 


60 


2.96      7.37      8.2 


45 
8.6 


75         60        60 
23.64    19.08    20.08 


21.25    22.61    18.13    11.68      9.53      8.50 


It  is  largely  to  replace  such  engines  as  the  above  that  power  will  be 
distributed  from  central  stations. 

Tests  at  Royal  Agricultural  Society's'show  at  Plymouth,  Eng.  Engi- 
neering, June  27,  1890. 


Rated 
H.P. 

Com-  • 
pound  or 
Simple. 

Diam.  of 
Cylinders. 

Stroke, 
ins. 

Max. 

Steam- 
pressure. 

Per  Brake  H.P. 
per  hour. 

££•3 

ce  »-  o 
£a 

h.p. 

l.p. 

Coal. 

Water. 

5 
3 
•  2 

simple 
compound 
simple 

7 
3 

41/2 

"6" 

10 
6 

7V2 

75 
110 

75 

12.12 
4.82 
11.77 

78.1   Ibs. 
42.03   " 
89  9     " 

6.  lib. 
8.72  " 
7.64" 

Steam-consumption,  of  Engines  at  Various  Speeds.  (Profs.  Den- 
ton  and  Jacobus,  Trans.  A.  S.  M.  E.,  x,  722.)  —  17  X  30  in.  engine, 
non-condensing,  fixed  cut-off,  Meyer  valve.  (From  plotted  diagrams.) 


Revs,  per  min . . 
1/8  cut-off,  Ibs. . . 
1/4  cut-off,  Ibs. . . 
1/2  cut-off,  Ibs. . . 


8  12  16  20 
39  35  32  30 
39  34  31  29.5 
39  36  34  33 


24 

29.3 

29 

32 


32 

29 

28.4 
30.8 


40 

28.7 

28 

29.8 


28.5 
27.5 
29.2 


56  72  88 

28.3  28  27.7 

27.1  26.3  25.6 

28.8  28.7    


Steam-consumption  of  same  engine ;  fixed  speed,  60  revs,  per  minute. 

Varying  cut-off  compared  with  throttling-engine  for  same  horse-power 
and  boiler-pressures: 
Cut-off,  fraction 

of  stroke 0.1      0.15   0.2  0.25    0.3      0.4      0.5      0.6     0.7     0.8 

Steam,  90  Ibs..  .    29     27.5      27  27     27.2    27.8    28.5 

Steam, 60  Ibs..  .    39     34.2    32.2  31.5    31.4    31.6    32.2    34.1    36.5      39 

Throttling-engine,  7/8  cut-off,  for  corresponding  horse-powers. 
Steam,  90  Ibs..  .   42       37     33.8   31.5    29.8     , 
Steam,  60  Ibs 50.1      49     46.8   44.6     41       ... 


Some  of  the  principal  conclusions  from  this  series  of  tests  are  as  follows: 

1.  There  is  a  distinct  gain  in  economy  of  steam  as  the  speed  increases 
for  1/2,  i/s,  and  1/4  cut-off  at  90  Ibs.  pressure.     The  loss  in  economy  for 
about  1/4  cut-off  is  at  the  rate  of  1/1?  Ib.  of  water  per  I.H.P.  per  hour  for  each 
decrease  of  a  revolution  per  minute  from  86  to  26  revolutions,  and  at  the 
rate  of  5/8  ib.  of  water  below  26  revolutions.     Also,  at  all  speeds  the  1/4 
cut-off  is  more  economical  than  either  the  1/2  or  1/8  cut-off. 

2.  At  90  Ibs.  boiler-pressure  and  above  1/3  cut-oftVto  produce  a  given 
H.P.  requires  about  20%  less  steam  than  to  cut  off  at  7/8  stroke  and  regu- 
late by  the  throttle. 

3.  For  the  same  conditions  with  60  Ibs.  boiler-pressure,  to  obtain,  by 
throttling,  the  same  mean  effective  pressure  at  7/g  cut-off  that  is  obtained 
by  cutting  off  about  1/3,  requires  about  30%  more  steam  than  for  the 
latter  condition. 

Capacity  and  Economy  of  Steam  Fire  Engines.  (Eng.  News, 
Mar.  28,  1895.) — Tests  of  fire  engines  by  Dexter  Brackett  for  the  Board 
of  Fire  Commissioners,  Boston,  Mass,  are  tabulated  on  p.  994. 


994 


THE  STEAM-ENGINE. 


Results  of  Tests  of  Steam  Fire  Engines. 


No.  of 
engine. 

Boiler  heating 
Surface. 

«s 

03      - 

sL 

J-sl 

c8  °"O 

y 

fiisi 

^  &£<s 

Av.  steam 
pressure. 

A  v.  water 
pressure. 

|j_ 

•*-"o"ai 

£18 

tJ  0>t4-4 

IP.O 

Av.  water 
pumped  per 
min,  1 

, 

101  0 

Ibs. 
191  0 

Ibs. 
2  26 

Ibs. 
90  2 

Ibs. 
143  2 

7  619  800 

galls. 
549 

1  

184  0 

92  3 

124  0 

9*632*700 

499 

2  . 

85  0 

191  0 

2  66 

78  4 

123  3 

5900  000 

535 

3... 

74  0 

141  6' 

3  57 

75  7 

113  8 

5'  882'  000 

482 

4 

86  5 

138  4 

2  88 

71  5 

136  4 

8*112  900 

459 

5  

86  0 

163  7 

102  7 

121  2 

8*736*300 

449 

5... 

103  3 

5  87 

72  1 

119  6 

14  026  000 

545 

6  

86  0 

181  6 

3  45 

92  7 

143  0 

9*678*400 

536 

7  .. 

112  0 

117  3 

4  94 

68  8 

119  2 

10*201*600 

596 

8... 

140  5 

172  1 

3  51 

101  3 

112  8 

7*758*300 

910 

9  

174  0 

142  5 

4  49 

76  5 

111  5 

7*187*400 

482 

10  .. 

225  0 

91   1 

4  22 

59  0 

102  1 

6*482*100 

419 

10... 

151  4 

4  10 

87  8 

126  8 

7*993*400 

564 

11.... 

229  0 

148  4 

3  76 

74  7 

128  1 

7  265  000 

572 

Nos.  1,  2,  3  and  4,  Amoskeag  engines;  Nos.  5,  6,  7  and  8,  Clapp  & 
Jones;  Nos.  9,  10,  11,  Silsby.  .  The  engines  all  show  an  exceedingly  high 
rate  of  combustion,  and  correspondingly  low  boiler  efficiency  and  pump 
duty. 

Economy  Tests  of  High-speed  Engines.  (F.  W.  Dean  and  A.  C. 
Wood,  Jour.  A.S.M.  E.,  June,  1908.)  —  S9me  of  these  engines  had  been  In 
service  for  a  long  time,  and  therefore  their  valves  may  not  have  been  in 
the  best  condition.  The  results  may  be  taken  as  fairly  representing  the 
economy  of  average  engines  of  the  type,  under  usual  working  conditions. 
The  engines  were  all  non-condensing.  The  16  X  15-in.  engine  was 
vertical,  the  others  horizontal.  They  were  all  direct-connected  to  gen- 
erators. 


No.  of  Test. 
Size  of  engine,  ins — 

Hours  in  service 

Revs,  per  min 

Valves ; . . . . 

Generator,  K.W 

Steam  per  I.H.P.-hr. 
Steam  per  K.W.-hr . . 


1 

15  X  H 

15,216 

240 

Iflat 

100 

37.2,t  36.2* 
60.2,     58.4 


2 

16X15 
20,000 
•  240 
Iflat 
2-50 

36.7,t    35.8 
61.0       59.7 


3 

14  X  12 

28,644 
300 

1  flat 

2-40 

31.7,f  32.0 
57.1,     57.4 


4 

16XM 

719 

270 

4  flat 

125 

37.5,*  36  7 
54.9,     54.7 


No.  of  Test. 
Size  of  engine,  ins.  . . 

Hours  in  service 

Revs,  per  min 

Valves 


Generator,  K.W 

Steam  per  I.H.P.-hr.. 
Steam  per  K.W.-hr. . . 


5 

18X18 

32,000 

220 

1  piston 

150 

39.3, f  34.7,*  29.51 
61.8,     51.8,     43.4 


15X  16 
5,600 
250 

1  piston 

100 

36.3,*    33.6 
55.2,      49.4 


7 

12  X  18 

10,800 

190 

f    2  flat  inlet 
\  2  Corliss  exh. 

44.0,  t  36.7,  34.1  § 
79.3,     60.5,  53.7 


*  3/4  load ;  f  V2  load ;  $  1 1/4  load ;  §1 1/2  load ;  the  others  full  load. 

Some  of  the  conclusions  of  the  authors  from  the  results  of  these  tests 
are  as  follows: 

The  performances  of  the  perfectly  balanced  flat  valve  engines  are  so 
relatively  poor  as  to  disqualify  them,  unless  this  type  of  valve  can  be  made 
with  some  mechanism  by  which  wear  will  not  increase  leakage.  The  four 
valve  engines,  which  were  built  to  be  more  economical  than  single-valve 


ECONOMIC   PERFORMANCE    OF   STEAM    ENGINES.      995 

engines,  have  utterly  failed  in  their  object.  The  duplication  of  valves 
used  in  both  four-valve  engines  simply  increased  the  opportunity  for  leak- 
age. The  most  economical  result  was  obtained  from  a  piston  valve  engine, 
No.  5,  heavily  loaded.  With  the  lighter  loads  that  are  comparable  the 
fiat  valve  engine,  No.  3,  surpassed  No.  5  in  economy.  The  Hat  valve 
engines  give  a  flatter  load  curve  than  the  piston  valve  engines.  Compar- 
ing the  results  of  the  flat  valve  engines,  the  most  economical  results  \\ere 
obtained  from  engine  No.  3,  which  had  a  valve  which  automatically  takes 
up  wear,  and  if  it  does  not  cut,  must  maintain  itself  tight  for  long  periods. 

From  the  results  we  are  justified  in  thinking  that  most  high-speed  en- 
gines rapidly  deteriorate  in  economy.  On  the  contrary,  slower  running 
Corliss  or  gridiron  valve  engines  improve  in  economy  for  some  time  and 
then  maintain  the  economy  for  many  years.  It  is  difficult  to  see  that 
the  speed  is  the  cause  of  this,  and  it  must  depend  on  the  nature  of  the 
valve. 

The  steam  consumption  of  small  single-valve  high-speed  engines  non- 
condensing,  is  not  often  less  than  30  Ibs.  per  I.H.P.  per  hour.  Two  Water- 
town  engines,  10  X  12  tested  by  J.  W.  Hill  for  the  Philadelphia  Dept.  of 
Public  Works  in  1904,  gave  respectively  30.67  and  29.70  Ibs.  at  full  load, 
61.8  and  63.9  I.H.P.,  and  28.87  and  29.54  Ibs.  at  approximately  half-load, 
37.63  and  36.36  I.H.P. 

High  Piston-speed  in  Engines.  (Proc.  Inst.  M.  E.,  July,  1883,  p. 
321.)  —  The  torpedo  boat  is  an  excellent  example  of  the  advance  towards 
high  speeds,  and  shows  what  can  be  accomplished  by  studying  lightness 
and  strength  in  combination.  In  running  at  22 1/2  knots  an  hour,  an  engine 
with  cylinders  of  16  in.  stroke  will  make  480  revolutions  per  minute,  which 
gives  1280  ft.  per  minute  for  piston-speed;  and  it  is  remarked  that  engines 
running  at  that  high  rate  work  much  more  smoothly  than  at  lower  speeds, 
and  that  the  difficulty  of  lubrication  diminishes  as  the  speed  increases. 

A  High-speed  Corliss  Engine.  —  A  Corliss  engine,  20  X  42  in.,  has 
been  running  a  wire-rod  mill  at  the  Trenton  Iron  Co.'s  works  since  1877,  at 
160  revolutions  or  1120  ft.  piston-speed  per  minute  (Trans.  A.  S.  M.  E.,  ii, 
72).  A  piston-speed  of  1200  ft.  per  min.  has  been  realized  in  locomotive 
practice. 

The  Limitation  of  Engine-speed.  (Chas.  T.  Porter,  in  a  paper  on  the 
Limitation  of  Engine-speed,  Trans.  A.  S.  M.  E.,  xiv,  806.)  —  The  practical 
limitation  to  high  rotative  speed  in  stationary  reciprocating  steam-engines 
is  not  found  in  the  danger  of  heating  or  of  excessive  wear,  nor,  as  is  gen^ 
erally  believed,  in  the  centrifugal  force  of  the  fly-wheel,  nor  in  the  tendency 
to  knock  in  the  centers,  nor  in  vibration.  He  gives  two  objections  to  very 
high  speeds:  First,  that  "engines  ought  not  to  be  run  as  fast  as  they  can 
be; "  second,  the  large  amount  of  waste  room  in  the  port,  which  is  required 
for  proper  steam  distribution.  In  the  important  respect  of  economy  of 
steam,  the  high-speed  engine  has  thus  far  proved  a  failure.  Large  gain 
was  looked  for  from  high  speed,  because  the  loss  by  condensation  on  a 
given  surface  would  be  divided  into  a  greater  weight  of  steam,  but  this 
expectation  has  not  been  realized.  For  this  unsatisfactory  result  we  have 
to  lay  the  blame  chiefly  on  the  excessive  amount  of  waste  room.  The 
ordinary  method  of  expressing  fhe  amount  of  waste  room  in  the  percentage 
added  by  it  to  the  total  piston  displacement,  is  a  misleading  one.  It 
should  be  expressed  as  the  percentage  which  it  adds  to  the  length  of 
steam  admission.  For  example,  if  the  steam  is  cut  off  at  1/5  of  the  stroke, 

7c  added  by  the  waste  room  to  the  total  piston  displacement  means 
40%  added  to  the  volume  of  steam  admitted.  Engines  of  four,  five  and 
six  feet  stroke  may  properly  be  run  at  from  700  to  800  ft.  of  piston  travel 
per  minute,  but  for  ordinary  sizes,  says  Mr.  Porter,  600  ft.  per  minute 
should  be  the  limit. 

British  High-speed  Engines.     (John  Davidson,  Power,  Feb.  9,  1909.) 

The  following  figures  show  the  general  practice  of  leading  builders: 

J.H.P.  50  100         200          500         750    1000    1500         2000 

Revs,  per  min.. 

600-700       550-600      500    350-375      325     250      200      160-180 
Piston  speed,  ft.  per  min. 

600  650         675          750         775     800      900          1000 

Rapid  strides  have  been  made  during  the  last  few  years,  despite  the 


996 


THE  STEAM-ENGINE. 


competition  of  the  steam  turbine.  The  single-acting  type  (Brotherhood, 
Willans  and  others)  has  been  superseded  by  double-acting  engines  with 
forced  lubrication.  There  is  less  wear  in  a  high-speed  than  in  a  low-speed 
engine.  A  500-H.P.  3-crank  engine  after  running  7  years,  12  hours  per 
day  and  300  days  per  year,  showed  the  greatest  wear  to  be  as  follows: 
crank  pins,  0.003  in.;  main  bearings,  0.003  in.;  eccentric  sheaves,  0.015  in.; 
crosshead  pins,  0.005  in.  All  pins,  where  possible,  are  of  steel,  case- 
hardened.  High-speed  engines  have  at  least  as  high  economy  and  effi- 
ciency as  any  other  type  of  engine  manufactured.  A  triple-expansion 
mill  engine,  with  steam  at  175  Ibs.,  vacuum  26  ins.,  superheat  100°  F.t 
gave  results  as  shown  below,  [figures  taken  from  curves  in  the  original]. 

Fraction  of  full 

load 0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0 

Lbs.  steam  per 

I.H.P.  hour..  12.7  11.85  11.4  11.1  10.9  10.S  10.75  10.75  10.8  11.0 
Lbs.  steam  per 

B.H.P.hour..  16.0  14.8     13.7  12.9     12.4  12.05  11.85  11.8     11,8  11.8 

Owing  to  the  fprced  lubrication  and  throttle-governing,  the  economical 
performance  at  light  loads  is  relatively  much  better  than  in  slow-speed 
engines.  The  piston  valves  render  the  use  of  superheat  practicable. 
At  200°  superheat  the  saving  in  steam  consumption  of  a  triple-expansion 
engine  is  26%.  [A  curve  of  the  relation  of  superheat  to  saving  shows 
that  the  percentage  of  saving  is  almost  uniformly  1.4%  for  each  additional 
10°  from  0°  to  160°  of  superheat.] 

The  method  of  governing  small  high-speed  engines  is  by  means  of  a 
plain  centrifugal  governor  fixed  to  the  crank  shaft  and  acting  directly 
on  a  throttle.  Several  makers  use  a  governor  which  at  light  loads  acts 
by  throttling,  and  at  heavy  loads  by  altering  the  expansion  in  the  high- 
pressure  cylinder.  The  crank-shaft  governor  used  in  America  has  been 
found  impracticable  for  high  speeds,  except  perhaps  for  small  engines. 

Advantage  of  High  Initial  and  Low  Back  Pressure. — The  theoretical 
advantage  due  to  the  use  of  high  steam  pressure  and  low  back  pressure 
or  high  vacuum  is  shown  in  the  following  table,  which  gives  the  effi- 
ciencies of  an  ideal  engine  operating  on  the  Rankine  cycle  with  different 
initial  and  back  pressures,  using  dry  saturated  steam.  The  method 
of  calculating  the  Rankine  cycle  efficiency,  and  a  table  showing  the 
efficiencies  with  superheated  steam  will  be  found  under  Steam  Turbines, 
page  1089. 

Rankine  Cycle  Efficiencies — Saturated  Steam. 


Initial 
Pressure, 
Absolute, 
Lb. 

Vacuum,  In.  of  Mercury. 

0 

26 

27 

28 

28.5    |        29 

Efficiencies,  Per  Cent. 

100... 

13.9 
16.7 
18.7 
19.4 
20.0 

23.6 
25.9 
27.4 
28.0 
28.6 

24.8 
27.0 
28.5 
29.1 
29.7 

26.3 
28.4 
29.9 
30.5 
31.0 

27-.  4 
29.4 
30.9 
31.4 
32.0 

28.9 
30.8 
32.2 
32.7 
33.2 

150 

200  ... 

225 

250  

In  practice  the  efficiencies  given  in  the  above  table  cannot  be  reached 
on  account  of  the  imperfection  of  the  engine  and  its  losses  due  to 
cylinder  condensation,  leakage,  radiation  and  friction.  The  relative 
advantages  of  high  pressure  and  low  back  pressure  are  probably  pro- 
portional to  the  figures  in  the  table,  provided  the  expansion  is  divided 
into  two  or  more  stages  at  pressures  above  100  Ib.  The  possibility  of 
obtaining  very  high  vacua  is  limited  by  the  temperature  of  the  con- 
densing water  available  and  by  the  imperfections  of  the  air  pump. 
The  use  of  high  initial  pressures  is  limited  by  the  safe  working  pressure 
of  the  boiler  and  engine. 


• 

EC 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.     997 

Comparison  of  the  Economy  of  Compound  and  Single-cylinder  Corliss 
Condensing  Engines,  each  expanding  about  Sixteen  Times.     (D.  S. 

Jacobus,  Trans.,  A.  S.  M.  E.,  xii,  943.) 

The  engines  used  in  obtaining  comparative  results  are  located  at 
Stations  I  and  II  of  the  Pawtucket  Water  Co. 

The  tests  show  that  the  compound  engine  is  about  30%  more  economical 
than  the  single-cylinder  engine.  The  dimensions  of  the  two  engines  are 
as  follows:  Single  20  X  48  ins.;  compound  15  and  301/8  X  30  ins.  The 
steam  used  per  I.H.P.  hour  was:  single  20.35  Ibs.,  compound  13.73  Ibs. 

Both  of  the  engines  are  steam-jacketed,  practically  on  the  barrels  only, 
with  steam  at  full  boiler-pressure,  viz.,  single  106.3  Ibs.,  compound  127.5  Ibs. 

The  steam-pressure  in  the  case  of  the  compound  engine  is  127  Ibs.,  or 
21  Ibs.  higher  than  for  the  single  engine.  If  the  steam-pressure  be  raised 
this  amount  in  the  case  of  the  single  engine,  and  the  indicator-cards  be 
increased  accordingly,  the  consumption  for  the  single-cylinder  engine 
would  be  19.97  Ibs.  per  hour  per  horse-power. 

Two-cylinder  vs.  Three-cylinder  Compound  Engine.  —  A  Wheelock 
triple-expansion  engine,  built  for  the  Merrick  Thread  Co.,  Holyoke,  Mass., 
is  constructed  so  that  the  intermediate  cylinder  may  be  cut  out  of  the 
circuit  and  the  high-pressure  and  low-pressure  cylinders  run  as  a  two- 
cylinder  compound,  using  the  same  conditions  of  initial  steam-pressure 
and  load.  The  diameters  of  the  cylinders  are  12,  16,  and  24 13/33  ins.,  the 
stroke  of  the  first  two  being  36  ins.  and  that  of  the  low-pressure  cylinder 
48  ins.  The  results  of  a  test  reported  by  S.  M.  Green  and  G.  I.  Rockwood, 
Trans.  A.  S.  M.  E.,  vol.  xiii,  647,  are  as  follows:  In  Ibs.  of  dry  steam  used 
per  I.H.P.  per  hour,  12  and  2413/32  in.  cylinders  only  used,  two  tests  13.06 
and  12,76  Ibs. .average  12.91.  All  three  cylinders  used,  two  tests  12.67 
and  12.90  Ibs.,  average  12.79.  The  difference  is  only  1%,  and  would 
indicate  that  more  than  two  cylinders  are  unnecessary  in  a  compound 
engine,  but  it  is  pointed  out  by  Prof.  Jacobus,  that  the  conditions  of  the 
test  were  especially  favorable  for  the  two-cylinder  engine,  and  not  rela- 
tively so  favorable  for  the  three  cylinders.  The  steam-pressure  was  142 
Ibs.  and  the  number  of  expansions  about  25.  (See  also  discussion  on 
the  Rockwood  type  of  engine,  Trans.  A.  S.  M.  E.,  vol.  xvi.) 

Economy  of  a  Compound  Engine.  (D.  S.  Jacobus,  Trang.A.S.M.E., 
1903.)  —  A  Rice  &  Sargent  engine,  20  and  40  X  42  ins.,  was  tested  with 
steam  about  149  Ibs.,  vacuum  27.3  to  28.8  ias.  or  0.82  to  1.16  Ibs.  abso- 
lute. r.D.m.  120  to  122.  with  results  as  follows: 

I.H.P 1004      853        820        627        491        340 

Water  per  I.H.P.  per  hr...    12.75     12.33     12.55     12.10     13.92     14.58 
B.T.U.  per  I.H.P.  per  min.  231.8     226.3     229.9     222.7     256.8     267.7 

The  Lentz  Compound  Engine  is  described  in  The  Engineer  (London), 
July  10,  1908.  It  is  the  latest  development  of  the  reciprocating  engine 
with  four  double-seated  poppet  valves  to  each  cylinder,  each  valve  op^ 
crated  by  a  separate  eccentric  mounted  on  a  lay-shaft  driven  by  bevel- 
gearing  from  the  main  shaft.  The  throw  of  the  high-pressure  steam 
eccentrics  is  varied  by  slide-blocks  which  are  caused  to  slide  along  the  lay- 
shaft  by  the  action  of  a  centrifugal  inertia  governor,  which  is  also  mounted 
on  the  lay-shaft.  No  elastic  packing  is  used  in  the  engine,  the  piste  n-rod 
stuffing  box  being  fitted  with  ground  cast-iron  rings,  and  the  valve  stems 
being  provided  with  grooves  and  ground  to  fit  long  bushings  to  0.001  in. 
Two  tests  of  a  Lentz  engine  built  in  England,  141/2  and  243/4  by  271/3  in., 
gave  results  as  follows: 

Saturated  steam,  170  Ibs.,  vacuum  26  in.,  I.H.P.  366,  steam  per  I.H.P. 
per  hour  12.3  Ibs.  Steam  170  Ibs.  superheated  150°  F.,  vac.  26  in.,  I.H.P. 
366,  steam  per  I.H.P.  per  hour,  10.4  Ibs.  Revs,  ner  min.  in  both  cases 
167.  Piston  speed  767  ft.  per  min.  Engines  are  built  for  speeds  up  to 
900  ft.  per  min.,  and  up  to  350  r.p.m.  The  Lentz  engine  is  built  in  the 
United  States  by  the  Erie  City  Iron  Works. 

The  Stumpf  Uniflow  Engine  is  a  single  cylinder  engine  with  a  very 
long  piston  and  with  exhaust  ports  in  the  middle  of  the  cylinder  which 
are  uncovered  as  the  piston  travels  beyond  them.  The  inlet  ports  are 
at  the  ends.  The  exhaust  steam  therefore  does  not  have  to  flow  back 
to  the  ends  of  the  cylinder  in  order  to  escape,  and  the  cooling  of  the 
ends  and  of  the  ports  is  thereby  avoided.  It  is  claimed  that  this  single 
cylinder  engine  gives  a  steam  economy  equal  to  that  of  a  compound 
engine.  Uniflow  engines  are  built  by  Ames  Iron  Works,  Oswego,  N.Y. 


998 


THE   STEAM-ENGINE. 


Steam  Consumption  of  Sulzcr  Compound  and  Triple-expansion 
Engines  with  Superheated  Steam. 

The  figures  in  the  table  below  were  furnished  to  the  author  in  1902 
by  Sulzer  Bros.,  Winterthur,  Switzerland.     Results  of  official  tests: 


Saturated  Steam. 

Superheated  Steam. 

£ 

. 

r 

• 

. 

« 

3 

«•-! 

r'  •—  ^ 

1  1 

fo 

*""  M 

OO 

Oo 

C    .f. 

l| 

dg" 

|l 

* 

1^     . 

0) 

a 

'Sb 

CC    W 

d| 

§  S 

gU 

ri 

gfi   t 

*SCL 

§  Q> 

\A 

0)  W^ 

c 

*sfi 

§  0) 

§« 

w 

<D  W^ 

Sr 

Hw 

>M 

W1"*^ 

H 

HoQ 

> 

00^^ 

130 

356 

26.4 

850 

13.30 

A     | 

132 
122 

428 
482 

26.4 
26.6 

842 
1719 

12.05 
12.42 

136 

357 

28 

481 

13.00 

) 

135 

547 

28 

515 

11.32 

134 

356 

28 

750 

13.10 

[     B     H 

132 

533 

27.8 

788 

11.52 

135 

356 

27.6 

1078 

14.10 

i             ( 

134 

546 

27.2 

1100 

11.88 

130 

358 

28.2 

1076 

14.10 

132 

496 

28.3 

1071 

11.73 

129 

358 

28 

1316 

14.50 

[  c  i 

136 

527 

* 

1021 

15.37 

190 

397 

27.2 

2880 

11.28 

D 

188 

606 

28 

2860 

8.97 

196 

381 

26.2 

3040 

11.57 

E 

189 

613 

27    ' 

2908 

9.41 

Superheated  Steam. 

)              ( 

127 

655 

27.2 

788 

9.91f 

135    1    557 

26.4 

519 

10.80f  \  F   G^ 

127 

664 

27.2 

797 

9.68f 

135    1    554 

26.4 

347 

10.35tl)             1 

128 

572 

27.1 

788 

10.70f 

A 
B 
C 
D 

E 
F 
G 


Normal,  H.P. 
1500  to  1800 

800  to  1000 

950  to  1150 
3000  triple  expan. 
3000  triple  expan. 

400  to  500 
1000  to  1200 


Cylinders,  In.  R.P.M. 

30.5  &  49.2  X  59.1  83 

24      &  40.4  X  51.2  83 

26      &  42.3  X  51.2  86 

32 1/4,  47 1/4,  &  58  X  59  85 

34,        49,       &  61  X  51  83.5 

17.7  &  30.5  X  35.4  110 

26.9  &  47.2  X  66.9  65 


*  Non-condensing,  t  With  intermediate  superheating.  Tempera- 
ture of  steam  at  entrance  to  low-pressure  cylinder,  307  to  349°  F. 

Test  of  a  Non-condensing  Engine  with  Superheated  Steam. — Prof. 
J.  A.  Moyer  reports  in  Power,  Dec.  2,  1913,  the  following  results  of  tests 
of  a  simple  Lentz  horizontal  engine,  cylinder,  191/32  in.  X  2015/16  in. 
stroke,  207  to  211  r.p.m.  Steam  pressure,  absolute,  170.1  to  171.9  Ib. 
Back  pressure,  0  to  0.34  in.  of  mercury. 

Indicated  horse-power ...  .    162 . 7       227 . 6       282 . 1       322 . 5 

Steam  per  I. H.P.  hour,  Ib 17.25       15.78       15.24       15.48 

Superheat,  deg.  F 98.3       139.4       141.5       159.7 

Saving  of  Steam  due  to  Superheating. — The  following  figures  are 
given  by  Power  Specialty  Co.,  makers  of  the  Foster  superheater. 

A  3300  horse-power  Lentz  cross-compound  engine  having  37  i/2-in. 
and  63-in.  cylinders,  55-in.  stroke,  at  Charlottenburg,  Germany,  with* 
192-lb.  gage  pressure,  26-in.  vacuum,  107  revs,  per  min.,  gave  the  follow- 
ing steam  consumption: 


Temp, 
of 

Steam. 

Super- 
heat. 

Load. 

•   V4 

V2 

3/4 

Vi 

V4 

570° 
660° 

185°F. 
275°  F. 

Steam  per  I.H.P.  hr.,  Ib  .  .  .  . 
Steam  per  I.H.P.  hr.,  Ib.  .  .  . 

11.1 

10.6 

10.1 
9.7 

9.5 
9.0 

9.2 
8.8 

9.7 
9.2 

The  saving  in  steam  effected  by  superheating  100  degrees,  as  com- 
pared with  saturated  steam,  is,  approximately,  for  steam  turbines, 
10  per  cent;  triple-expansion  engines,  12  per  cent;  compound  engines, 
14  per  cent;  simple  engines,  18  per  cent  and  over. 


ECi 


ECONOMIC  PEEFORMANCE  OF  STEAM-ENGINES.     999 

Tests  of  Buckeye  engines,  simple,  12  X  16  in.,  and  compound,  10  and 
'1/2  X  16  in.,  with  steam  at  100  to  110  Ib.  pressure,  gave  the  following: 


Engine. 

Per 
Cent  of 
Rated 
Load. 

Degrees  of  Superheat. 

0 

50 

100 

150 

200 

Lb.  Steam  per  I.H.P.  Hr. 

Simple,  non-condensing  
Simple,  non-condensing  

30 
50 
100 
100 
100 

35 
31.5 

28.5 

28 
25  ..5 
24.0 

24 
22 
20 
17.5 
14 

21.5 
19 
18 
15.5 
12.5 

19.5 
17.5 
17.5 
14.6 
11.5 

Simple  non-condensing 

Compound,  non-condensing  

Compound,  condensing  

18 

16.5 

Steam  Consumption  of  Different  Types  of  Engines. 

Tests  of  a  Ridgway  4- valve  non-condensing  engine,  19  X  18  in.,  at 
200  r.p.m.  and  100  Ib.  pressure,  are  reported  in  Power,  June,  1909,  as 


7.9 

9.75 

10.50 

11.80 


follows: 

Load 1/4  1/2  V4        Full  H/4 

Steam  per  I.H.P.  hour.  ...     30.7         24.4         23.2         23.8     |     25.4 

The  best  result  obtained  at  130  Ib.  pressure  was  21.6  Ib.;  at  115  Ib. 
pressure,  22.6  Ib. ;  and  at  85  Ib.  pressure,  24.3  Ib.  Maintained  economy 
In  this  type  of  engine  is  dependent  upon  reduction  of  unnecessary  over- 
travel,  properly  fitted  valves,  valves  which  do  not  span  a  wide  arc,  close 
approach  of  the  movement  of  the  valves  to  that  of  a  Corliss  engine,  and 
good  materials. 

The  probable  steam  consumption  of  condensing  engines  of  different 
types  with  different  pressures  of  steam  is  given  in  a  set  of  curves  by 
R.  H.  Thurston  and  L.  L.  Brinsmade,  Trans.  A.  S.  M.  E.,  1897,  from 
which  curves  the  following  approximate  figures  are  derived. 

Steam  pressure,  absolute,  Ibs.  per  sq.  in. 

250 
Ideal  Engine 

(Rankine  cycle) 
Quadruple  Exp. 

Wastes  20% 
Triple  Exp. 

Wastes  25% 
Compound. 

Wastes  33% 
Simple  Engine. 

Wastes  50%         14.00     15.00     15.80 

The  same  authors  give  the  records  of  tests  of  a  three-cylinder  engine 
at  Cornell  University,  cylinders  9,  16  and  24  ins.,  36-in.  stroke,  first  as  a 
triple-expansion  engine;  second,  with  the  intermediate  cylinder  omitted, 
making  a  compound  engine  with  a  cylinder  ratio  of  7  to  1 :  and  third, 
omitting  the  third  cylinder,  making  a  compound  engine  with  a  ratio  of 
a  little  over  3  to  1.  The  boiler  pressure  in  the  first  case  was  119  Ibs.. 
in  the  second  115,  and  in  the  third  117  Ibs.  Charts  are  given  showing 
the  steam  consumption  per  I.H.P.  and  per  B.H.P.  at  different  loads, 
from  which  the  following  figures  are  taken. 

Indicated  Horse-power 40       60       80      100      110      120      130 

Steam  consumption  per  I.H.P.  per  hour. 

Triple  Exp 19.1     16.7     15.3     14.2     13.7     13.8     14.4 

Comp.  7  to  1 . .  19.6     18.2     17.0     16.3     16.        15.8     15.8 

Comp.  3  to  1 19.7     18.4     18.1     18.5       

Steam  consumption  per  B.H.P.  hour. 

Triple  Exp 30.5     23.0     19.6     17.1      16.2     16.2     16.7 

Comp.  7  to  1 26.2     21.7     19.3     18.7     18.5     18.4     18.5 

Comp.  3  to  1 23.4     20.6     20.        20 

The  most  economical  performance  was  as  follows: 

Triple    Comp.  7  to  1    ComD.  3  to  1 

Indicated  Horse-power 112.7  130.0  67.7 

Steam  per  I.H.P.  hour 13.68  15.8  18.03 


400 

6.95 

8.75 

9.25 

10.50 

14.00 


300 

7.5 

9.15 

9.95 

11.25 

15.00 


200 
8.45 
10.50 
11.15 
12.70 
16.80 


150 
9.20 
11.60 
12.30 
13.90 
18.40 


100  75        50 

10.50  11.40  12.9 

13.0  14.0     15.8 

14.0  15.1     16.7 

15.6  16.9     18.S 

20.4  22.7     25.2 


1000  THE   STEAM-ENGINE. 

A  test  of  a  7500-#.P.  engine,  at  the  59th  St.  Station  of  the  Interborough 
Rapid  Transit  Co.,  New  York,  is  reported  in  Power,  Feb.,  1906.  It  is  a 
double  cross  compound  engine,  with  horizontal  h.p.  and  vertical  l.p. 
cylinders.  With  steam  at  175  Ibs.  gauge  and  vacuum  25.02  ins.,  75  r.p.m. 
it  developed  7365  I.H.P.,  5079  K.W.  at  switchboard.  Friction  and  elec- 
trical losses  417.3  K.W.  Dry  steam  per  K.W.  hour  17.34  Ibs.;  per  I.H.P. 
hour,  11. 96  Ibs. 

A  test  of  a  Fleming;  4-valve  engine,  15  and  40.5  in.  diam.,  27-in.  stroke, 
positive-driven  Corliss  valves,  fly-wheel  governor,  is  reported  by  B.  T. 
Allen  in  Trans.  A.  S.  M.  E.,  1903.  The  following:  results  were  obtained. 
The  speed  was  above  150  r.p.m.  and  the  vacuum  26  in. 

Fraction  of  full  load  about 1/6  5/8       Vio  Full  load     1.1 

Horse-power 87.1       321.5     348.3     501.6        553.5 

Steam  per  I:H.P.  hour 14.42       13.59     12.33     12.66       12.7 

Relative  Economy  of  Compound  Non-condensing  Engines 
under  Variable  Loads.  —  F.  M.  Rites,  in  a  paper  on  the  Steam  Dis- 
tribution in  a  Form  of  Single-acting  Engine  (Trans.  A.S.M.  E.,  xiii,  537), 
discusses  an  engine  designed  to  meet  the  following  problem:  Given  an 
extreme  range  of  conditions  as  to  load  or  steam-pressure,  either  or  both, 
to  fluctuate  together  or  apart,  violently  or  with  easy  gradations,  to 
construct  an  engine  whose  economical  performance  should  be  as  good  as 
though  the  engine  were  specially  designed  for  a  momentary  condition  — 
the  adjustment  to  be  complete  and  automatic.  In  the  ordinary  non-con- 
densing compound  engine  with  light  loads  -the  high-pressure  cylinder  is 
frequently  forced  to  supply  all  the  power  and  in  addition  drag  along  with 
it  the  low-pressure  piston,  whose  cylinder  indicates  negative  work.  Mr. 
Rites  shows  the  peculiar  value  of  a  receiver  of  predetermined  volume 
which  acts  as  a  clearance  chamber  for  compression  in  the  high-pressure 
cylinder.  The  Westinghouse  compound  single-acting  engine  is  designed 
upon  this  principle.  The  following  results  of  tests  of  one  of  these  engines 
rated  at  175  H.P.  for  most  economical  load  are  given: 

WATER  RATES  UNDER  VARYING  LOADS,  LBS.  PER  H.P.  PER  HOUR. 

Horse-power 210       170       140       115       100       80        50 

Non-condensing 22.6     21.9     22.2     22.2     22.4     24.6     28.8 

Condensing 18.4     18.1     18.2     18.2     18.3     18.3     20.4 

Efficiency    of    Non-condensing    Compound    Engines.     (W.    Lee 

Church,  Am.  Mach.,  Nov.  19,  1891.)  — The  compound  engine,  non-con- 
densing, at  its  best  performance  will  exhaust  from  the  low-pressure  cylin- 
der at  a  pressure  2  to  6  pounds  above  atmosphere.  Such  an  engine  will 
be  limited  in  its  economy  to  a  very  short  range  of  power,  for  the  reason 
that  its  valve-motion  will  not  permit  of  any  great  increase  beyond  its 
rated  power,  and  any  material  decrease  below  its  rated  power  at  once 
brings  the  expansion  curve  in  the  low-pressure  cylinder  below  atmos- 
phere. In  other  words,  decrease  of  load  tells  upon  the  compound  engine 
somewhat  sooner,  and  much  more  severely,  than  upon  the  non-compound 
engine.  The  loss  commences  the  moment  the  expansion  line  crosses  a 
line  parallel  to  the  atmospheric  line,  and  at  a  distance  above  it  repre- 
senting the  mean  effective  pressure  necessary  to  carry  the  frictional  load 
of  the  engine.  When  expansion  falls  to  this  point  the  low-pressure 
cylinder  becomes  an  air-pump  over  more  or  less  of  its  stroke,  the  power 
to  drive  which  must  come  from  the  high-pressure  cylinder  alone.  Under 
the  light  loads  common  in  many  industries  the  low-pressure  cylinder  is 
thus  a  positive  resistance  for  the  greater  portion  of  its  stroke.  A  careful 
study  of  this  problem  revealed  the  functions  of  a  fixed  intermediate 
clearance,  always  in  communication  with  the  high-pressure  cylinder, 
and  having  a  volume  bearing  trie  same  ratio  to  that  of  the  high-pressure 
cylinder  that  the  high-pressure  cylinder  bears  to  the  low-pressure.  Engines 
laid  down  on  these  lines  have  fully  confirmed  the  judgment  of  the  de- 
signers. The  effect  of  this  constant  clearance  is  to  supply  sufficient  steam 
to  the  low-pressure  cylinder  under  light  loads  to  hold  its  expansion  curve 
up  to  atmosphere,  and  at  the  same  time  leave  a  sufficient  clearance  volume 
in  the  high-pressure  cylinder  to  permit  of  governing  the  engine  on  its 
compression  under  light  loads. 

Tests  of  two  non-condensing  Corliss  engines  by  G.  H.  Barrus  are  re- 
ported in  Power,  April  27,  1909.  The  engines  were  built  by  Rice  & 
Sargent,  One  is  a  simple  engine  22  X  30,  and  the  other  a  tandern  j 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.      1001 


compound  22  and  36  X  36  ins.  Both  engines  are  jacketed  in  both 
heads,  and  the  compound  engine  has  a  reheating  receiver  with  0.6  sq.  ft. 
o{  brass  pipes  per  rated  H.P.  (600).  The  guarantees  were:  compound 
engine,  not  to  exceed  19  Ibs.  of  steam  per  I. H.P.  per  hour,  with  130  Ibs. 
steam  pressure  and  1  Ib.  back  pressure  in  the  exhaust  pipe,  and  the 
simple  engine  not  to  exceed  23  Ibs.  The  friction  load,  engine  run  with 
the  brushes  off  the  generator  and  the  field  not  excited,  was  not  to  exceed 
4V2  H.P.  in  either  engine.  The  results  were:  compound  engine,  99.2 
r.p.m.,  .608.3  H.P.;  18.33  Ibs.  steam  per  I. H.P.  per  hour;  friction  load 
3.8%  of  600  H.P.;  simple  engine,  98.5  r.p.m.;  306.2  LH.P.;  20.98  Ibs.  per 
I.H.P.  per  hour;  friction  3.6%  of  300  H.P. 

A  single-cylinder  engine  12  X  12  ins.,  made  by  the  Buffalo  Forge  Co., 
was  tested  by  Profs.  Reeve  and  Allen.  (EL  World,  May  23,  1903.) 
Some  of  the  results  were: 

I.H.P 16.39  37.20  56.00  69.00  74.10  81.4  89.3  125.9*  86.42f 

Water-rate...   52.3     35.3     33.3     31.9     30.6     34.6  33.1     27.6    27.5 

*  Steam  pressure  125  Ibs.  gauge,  all  the  other  tests  80  Ibs.  t  Con- 
densing, other  tests  all  non-condensing. 

Effect  of  Water  contained  in  Steam  on  the  Efficiency  of  the 
Steam-engine.  .(From  a  lecture  by  Walter  C.  Kerr,  before  the  Franklin 
Institute,  1891.)  —  Standard  writers  make  little  mention  of  the  effect 
of  entrained  moisture  on  the  expansive  properties  of  steam,  but  by 
common  consent  rather  than  any  demonstration  they  seem  to  agree  that 
moisture  produces  an  ill  effect  simply  proportional  to  the  percentage 
amount  of  its  presence.  That  is,  5%  moisture  will  increase  the  water  rate 
of  an  engine  5%. 

Experiments  reported  in  1893  by  R.  C.  Carpenter  and  L.  S.  Marks, 
Trans.  A.  S.  M.  E.,  xy,  in  which  water  in  varying  quantity  was  intro- 
duced into  the  steam-pipe,  causing  the  quality  of  the  steam  to  range  from 
99%  to  58%  dry,  showed  that  throughout  the  range  of  qualities  used  the 
consumption  of  dry  steam  per  indicated  horse-power  per  hour  remains 
practically  constant,  and  indicated  that  the  water  was  an  inert  quantity, 
doing  neither  good  nor  harm. 

Influence  of  Vacuum  and  Superheat  on  Steam  Consumption.  (Eng. 
Digest,  Mar.,  1909.) — Herr  Roginsky  ("Die  Turbine")  discusses  the 
economies  effected  by  the  use  of  superheat  and  high  vacuums. 

In  a  certain  triple-expansion  engine,  working  under  good  average 
conditions,  there  was  found  a  saving  of  approximately  6%  for  each  10% 
increase  in  vacuum  beyond  50%. 

The  Batulli-Tumlirz  formula  for  superheated  steam  is:  p  (v  +  a)  =  RT. 
in  which  p  =  steam  pressure  in  kgs.  per  sq.  meter,  v  =  cubic  meters  in 
1  kg.  of  superheated  steam  at  pressure  pt  a  =  0.0084,  R  =  46.7,  and 
T  =  absolute  temperature  in  deg.  C. 

Using  this  expression,  it  is  found  that,  neglecting  the  fuel  used  for 
superheating,  for  each  10°  C.  of  superheat  at  pressures  ranging  from 
100  to  185  Ibs.  per  sq.  in.  there  is  an  average  increase  of  volume  of  2.8%. 
The  work  done  by  the  expansion  of  superheated  steam,  as  shown  by 
diagrams,  is  about  1.6%  less  for  10°  of  superheating,  so  that  the  net 
saving  for  each  10°  of  superheat  is  2.8  —  1.6  =  1.2%,  approx.  (0.66% 
for  each  10°  F.). 

Rateau's  formula  for  the  steam  consumption  (K)  per  H.P.-hr.  of  an 
ideal  steam  turbine,  in  which  the  steam  expands  from  pressure  p\  to  pa,  in 

K  =  0.85  (6.95  -  0.92  log  p2) /(log  P!  -  log  p2\ 

K  being  in  kilograms  and  p\  and  pz  in  kgs.  per  sq.  meter.  From  this 
formula  the  following  table  is  calculated,  the  values  being  transformed 
into  British  units. 


Lbs.  per 
sq.  in. 

Lbs.  Steam 
at  50% 
Vacuum. 

Reduction  of  Steam  Consumption  (%)  by 
using  a  Vacuum  of 

60% 

70% 

80% 

90% 

?5% 

184.9 
156.5 
128 
99.6 

11.11 
11.75 
12.57 
13.84 

5. 

5.8 
6.6 
7.6 

11.1 
11.8 
12.9 

14.4 

18.  1\ 
19.3 
20.5 
22. 

27.8 
28.8 
20.8 
33.3 

34.6 
36.4 
38.5 
40.6 

1002 


THE  STEAM-ENGINE. 


From  the  entropy  diagram  it  is  seen  that  in  expanding  from  pressures 
in  excess  of  100  Ibs.  per  sq.in.  down  to  1.42  Ibs.  absolute,  approximately 
1  %  more  work  is  performed  for  every  10°  F.  of  superheat.  The  effect  of 
increasing  the  degree  of  vacuum  is  summed  up  in  the  following  table: 


Increasing 
the 
Vacuum  from 

Decreases  Steam  Consumption. 

in  Reciprocating 
Engines. 

in  Steam 
Turbines. 

50%  to  60% 
50%  to  70% 
50%  to  80% 
50%  to  90% 
50%  to  95% 

5.8% 
11.6% 
17.3% 
23.1% 
26.0% 

6.2% 
12.6% 
20.0% 
30.1% 

37.4% 

In  the  last  case  (from  50%  to  95%)  the  decrease  in  steam  consumption 
Is  44%  greater  for  a  steam  turbine  than  for  a  reciprocating  engine. 

The  following  results  of  tests  of  a  compound  engine  using  superheated 
steam  are  reported  in  Power,  Aug.,  1905.  The  cylinders  were  21  and 
36  X  36  ins.  The  steam  pressure  was  about  117  Ibs.  gauge.  R.p.m.  100, 
vacuum  26.5  ins. 

Test  No 1 

Indicated  H.P 481 

Superheat    of    steam 

entering  h.p.  cyl. . .  253°  F 
B.T.U.  supplied   per 

I.H.P.  per  min 198.2 

B.T.U.    theoretically 

required.   Rankine 

cycle 142.4 

Efficiency  ratio 0.72 

Thermal  efficiency  %    21.39 
Lbs.  steam  per  I.H.P. 

hour 9.098       9.267       8.886       8.585       8.682       8.742 

The  Practical  Application  of  Superheated  Steam  is  discussed  in  a 
paper  by  G.  A.  Hutchinson  in  Trans.  A.  S.  M.  E.t  1901.  Many  different 
forms  of  superheater  are  illustrated. 

Some  results  of  tests  on  a  3000-H.P.,  four-cylinder,  vertical,  triple-ex- 
pansion Sulzer  engine,  using  steam  from  Schmidt  independently  fired 
superheaters,  are  as  follows.  (Eng.  Rec.t  Oct.  13,  1900.) 


2 

461 

3 
347 

4 
145 

5 
333 

6 

258 

242* 

221° 

202° 

232° 

210° 

201.7 

197.6 

192.1 

194.0 

194.0 

142.5 
0.71 
21.02 

130.2 
0.66 
21.46 

128.0 
0.67 
22.07 

126.0 
0.65 
21.86 

128.5 
0.66 
21.86 

Tests  Using  Steam. 

Highly  Superheated. 

Mod- 
erately 
Super- 
heated 

Saturated. 

Initial  pressure  in  h.p.  cyl. 
(absolute)  Ibs    . 

187.3 

582 
2,900 
9.64 

477 

195.5 

585 
2,779 
.9.67 
482 

188.4 

614 
2,868 
9.56 
479 

190.3 

531 

2,850 
10.29 
447 

194.6 

381 
2,951 
11.77 
438 

195.9 

381 
2,999 
11.75 
435 

Temp,  of  steam  in  valve 
chest  deg.  F           ... 

Total  I.H.P  

Lbs.  steam  per  I.H.P.  hour 
Watt  hours  per  Ib.  of  coal. 

The  saving  due  to  the  use  of  highly  superheated  steam  is  (482-438)  •*• 
482  =  9.1%. 

Tests  of  a  4000-H.P.  double-compound  engine  (Van  den  Kerchove,  of 
Brussels)  with  superheated  steam  are  reported  in  Power,  Dec.  29,  1908. 
The  cylinders  are  34 1/4  and  60  ins.,  stroke  5  ft.  Ratio  of  areas  2.97.  The 
following  are  the  principal  results,  the  first  figures  given  being  for  the  full- 
load  test,  and  the  second  (in  parentheses)  for  the  half-load  test.  Steam 
pressure  at  drier,  136.5  Ibs.  (137.9).  R.p.m.  84.3  (84.06).  Temp,  of 
steam  entering  engine  519°  F.  (498),  leaving  l.p.  cyl.  121.5°  (121.5). 
Vacuum  in  condenser,  ins.,  27.5  (27).  I.H.P.  3776  (2019).  Steam  per 
I.H.P.  hour,  Ibs.,  9.62  (9.60). 

The  saving  due  to  the  use  of  superheated  steam  is  reported  in  numerous 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.        1003 

tests  as  being  all  the  way  from  less  than  10%  to  more  than  40%.  The 
greater  saving  is  usually  found  with  engines  that  are  the  most  inefficient 
with  saturated  steam,  such  as  single-cylinder  engines  with  light  loads,  in 
which  the  cylinder  condensation  is  excessive. 

R.  P.  Bolton  (Eng.  Mag.,  May,  1907)  states  that  tests  of  superheated 
steam  in  locomotives,  by  the  Prussian  Railway  authorities  in  1904,  with 
50°,  104°  and  158°  F.  superheat,  showed  a  saving  of  water  respectively 
of  2.5,  10  and  16%,  and  a  saving  of  coal  of  2,  7  and  12%.  Mr.  Bolton's 
paper  concludes  with  a  long  list  of  references  on  the  subject  of  super- 
heated steam.  A  paper  by  J.  R.  Bibbins  in  Elec.  Jour.,  March,  1906,  gives 
a  series  of  charts  showing  the  saving  made  by  different  degrees  of  super- 
heating in  different  types  of  engines,  including  steam  turbines. 

For  description  of  the  Foster  superheater,  see  catalogue  of  the  Power 
Specialty  Co.,  New  York. 

The  Wolf  (French)  semi-portable  compound  engine  of  40  H.P.  with 
superheater  and  reheater,  the  engine  being  mounted  on  the  boiler,  is 
reported  by  R.  E.  Mathot,  Power,  July,  1906,  to  have  given  a  steam 
consumption  as  low  as  9.9  IDS.  per  I. H.P.  hour,  and  10.98  Ibs.  per  B.H.P. 
hour.  The  steam  pressure  in  the  boiler  was  172.6  Ibs.,  and  was  super- 
heated initially  to  657°  F.,  and  reheated  to  361°  before  entering  the  l.p. 
cylinder.  This  is  a  remarkable  record  for  a  small  engine. 

A  testfof  a  Rice  &  Sargent  cross-compound  horizontal  engine  16  and 
28X42  ins.,  with  superheated  steam,  is  reported  by  D.  S.  Jacobus  in 
Trans.  A.  S.  M.  E. ,  1904.  The  steam  pressure  at  the  throttle  was  140 Ibs. 
gauge,  the  superheating  was  350  to  400°,  and  the  vacuum  25  to  26  ins., 
r.p.m.  102.  In  three  tests  with  superheated  and  one  with  saturated, 
steam  the  results  were: 

I.H.P.  developed ! . . .  .474.5       420.4       276.8       406.7 

Water  consumption  per  I. H.P.  hour 9.76         9.56     "9.70       13.84 

Coal  consumption  per  I.H.P.  hour 1.265       1.257       1.288       1.497 

B.T.U.  per  min.  per  I.H.P 205.0       203.7       208.8       248.2 

Temp,  of  steam  entering  h.p.  cyl 634          659          672        

Temp,  of  steam  leaving  h.p.  cyl 346          331          288      262 

Temp,  of  steam  entering  l.p.  cyl 408          396         354      269 

Temp,  of  steam  leaving  l.p.  cyl 135          141          117        

Performance  of  a  Quadruple  Engine. — O.  P.  Hood  (Trans.  A.  S, 
M.  E.,  1906)  describes  a  test  of  a  high-duty  air  compressor,  with  four 
steam  cylinders,  14.5,  22,  38  and  54  in.  diam.,  48-in.  stroke.  The  clearr 
ances  were  respectively  6,  5.7,  4.4  and  3.5%.  R.p.m.  57.  Steam  pressure, 
gauge,  near  throttle,  242.8  Ibs.,  in  1st.  receiver  120.7  Ibs.,  in  2d,  30.8  Ibs., 
in  3d,  vac.,  —  1.24  ins.  Moisture  in  steam  near  throttle,  5.74%.  Steam 
in  No.  1  receiver,  dry;  in  No.  2,  17°  superheat;  in  No.  3,  9°  superheat. 
The  engine  has  poppet  valves  on  the  h.p.  cylinder  and  Corliss  valves  on 
the  other  cylinders.  The  feed-water  heaters  are  four  in  number,  in  series, 
on  the  Nordberg  system;  No.  1  receives  its  steam  from  the  exhaust  of 
No.  4  cylinder;  No.  2  from  the  jacket  of  No.  4  cyl.;  No.  3  from  the  jackets 
of  No.  3  cylinder  and  No.  3  reheater;  No.  4  from  the  jacket  of  No.  2 
cylinder.  The  reheaters  are  supplied  with  steam  from  the  boilers.  The 
temperatures  of  steam  and  water  were  as  follows:  Temperatures  of  steam: 
Fed  to  No.  1  engine,  403°;  leaving  receivers,  No.  1,  351°;  No.  2,  291°; 
No.  3,  216°.  Exhaust  entering  preheater,  114°.  Temperature  corre- 
sponding to  condenser  pressure,  109.6°.  Temperatures  of  water:  Fed  to 
preheater,  93°;  fed  to  heaters,  No.  1,  114°;  No.  2,  173°;  No..3.  202°;  No.  4, 
269°;  leaving  heater  No.  4  as  boiler  feed,  334°. 

The  principal  results  of  the  test  are  as  follows: 

Cylinder 1  2  3  4 

I.H.P.  developed  in  steam  cylinders 181.47  256.96  275.71  275.56 

I.H.P.  used  in  the  cylinders 220.04  222.12  226.20  214.84 

Total  indicated  horse-power,  steam  cylinders 989.7 

Total  horse-power  used  in  air  cylinders 883.2 

Total  indicated  horse-power  of  auxiliaries 11.0 

Horse-power   representing   friction   of   the 

machine  95.5 

Per  cent  of  friction 9.65% 

Mechanical  efficiency  engine  and  compressor 90.35% 

Heat  consumed  by  engine  per  hour  per  I.H.P.,  10,157  B.T.U. ;  per 
B.H.P.,  11,382  B.T.U.  Equivalent  standard  coal  consumption  per 


1004  THE   STEAM-ENGINE. 

hour  assuming  10,000  B.T.U.  imparted  to  the  boiler  per  pound  coal,  per 
I.H.P.,  1,016  IDS.;  per  B.H.P.,  1,138  Ibs.  Dry  steam  per  hour  per 
I.H.P.,  11.23  Ibs.;  per  B.H.P.,  12.58  Ibs.  Heat  units  consumed  per 
minute,  per  I.H.P.,  169.29  B.T.U. ;  per  B.H.P.,  189.70  B.T.U. 

Efficiency  of  Carnot  cycle  between  the  temperature  of  incoming 

steam  and  that  corresponding  to  pressure  in  the  condenser... 34.0  % 

Actual  heat  efficiency  attained  by  this  engine 25.05% 

Relative  efficiency  compared  with  Carnot  cycle 73.69% 

Relative  efficiency  compared  with  Rankine'cycle 88.2  % 

Duty,  ft.-lbs.  per  million  B.T.U.  supplied 194,930,000 

This  engine  establishes  a  new  low  record  for  the  heat  consumed  per  hour 
per  I.H.P.,  being  9%  lower  than  that  used  by  the  Wild  wood  pumping 
engine  reported  in  1900.  (See  Pumping  Engines.) 

The  Use  of  Reheaters  in  the  receivers  of  multiple-expansion  engines  is 
discussed  by  R.  H.  Thurston  in  Trans.  A.S.M.E.,  xxi,  893.  He  shows  that 
such  receivers  improve  the  economy  of  an  engine  very  little  unless  they 
are  also  superheaters;  in  which  case  marked  economy  may  be  effected 
by  the  reduction  of  cylinder  condensation.  The  larger  the  amount  of 
cylinder  condensation  and  the  greater  the  losses,  exterior  and  interior, 
the  greater  the  effect  of  any  given  amount  of  superheating.  The  same 
statement  will  hold  of  the  use  of  reheaters:  the  more  wasteful  the  engine 
without  them  and  the  more  effectively  they  superheat,  the  larger  the 
gain  by  their  use.  A  reheater  should  be  given  such  area  of  heating  surface 
as  will  insure  at  least  moderate  superheating. 

Influence  of  the  Steam-jacket.  —  Tests  of  numerous  engines  with 
and  without  steam-jackets  show  an  exceeding  diversity  of  results,  ranging 
all  the  way  from  30%  saying  down  to  zero,  or  even  in  some  cases  showing 
an  actual  loss.  The  opinions  of  engineers  at  this  date  (1894)  is  also  as 
diverse  as  the  results,  but  there  is  a  tendency  towards  a  general  belief 
that  the  jacket  is  not  as  valuable  an  appendage  to  an  engine  as  was  for- 
merly supposed.  An  extensive  rtsum&  of  facts  and  opinions  on  the  steam- 
jacket  is  given  by  Prof.  Thurston  in  Trans.  A.  S.  M.  E.,  xiv,  462.  See 
also  Trans.  A.  S.  M.  E.t  xiv,  873  and  1340;  xiii,  176;  xii,  426  and  1340; 
and  Jour.  F.  I.,  April,  1891,  p.  276.  The  following  are  a  few  statements 
selected  from  these  papers. 

/The  results  of  tests  reported  by  the  research  committee  on  steam-jackets 
appointed  by  the  British  Institution  of  Mechanical  Engineers  in  1886, 
indicate  an  increased  efficiency  due  to  the  use  of  the  steam-jacket  of  from 
1%  to  over  30%,  according  to  varying  circumstances. 

Professor  Unwin  considers  that  "in  all  cases  and  "on  all  cylinders  the 
jacket  is  useful;  provided,  of  course,  ordinary,  not  superheated,  steam  is 
used;  but  the  advantages  may  diminish  to  an  amount  not  worth  the  in- 
terest on  extra  cost." 

Professor  Cotterill  says:  Experience  shows  that  a  steam-jacket  is  advan- 
tageous, but  the  amount  to  be  gained  will  vary  according  to  circumstances. 
In  many  cases  it  may  be  that  the  advantage  is  small.  Great  caution  is 
necessary  in  drawing  conclusions  from  any  special  set  of  experiments  on 
the  influence  of  jacketing. 

In  the  Pawtucket  pumping-engine,  15  and  30 1/8  X  30  in.,  50  revs,  per 
min., steam-pressure  125  Ibs. gauge,  cut-off  i/4in  h.p.  and  1/3  in  l.p.  cylinder, 
the  barrels  only  jacketed,  the  saving  by  the  jackets  was  from  1%  to  4%. 

The  superintendent  of  the  Holly  Mfg.  Co.  (compound  pumping-engines) 
says:  "In  regard  to  the  benefits  derived  from  steam-jackets  on  our  steam- 
cylinders,  I  am  somewhat  of  a  skeptic.  From  data  taken  on  our  own 
engines  and  tests  made  I  am  yet  to  be  convinced  that  there  is  any  practical 
value  in  the  steam-jacket." 

Professor  Schrooter  from  his  work  on  the  triple-expansion  engines  at 
Augsburg,  and  frlm  the  results  of  his  tests  of  the  jacket  efficiency  on  a 
small  engine  of  the  Sulzer  type  in  his  own  laboratory,  concludes:  (1)  The 
value  of  the  jacket  may  vary  within  very  wide  limits,  or  even  become 
negative.  (2)  The  shorter  the  cut-off  the  greater  the  gain  by  the  use  of  a 
jacket.  (3)  The  use  of  higher  pressure  in  the  jacket  than  in  the  cylinder 
produces  an  advantage.  The  greater  this  difference  the  better.  (4)  The 
high-pressure  cylinder  may  be  left  unjacketed  without  great  loss,  but  the 
other  should  always  be  jacketed. 

The  test  of  the  Laketon  triple-expansion  pumping-engine  showed  a  gain 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.    1005 


of  8.3  %  by  the  use  of  the  jackets,  but  Prof.  Denton  points  out  (Trans. 
A.  S.  M.  E.,  xiv,  1412)  that  all  but  1.9%  of  the  gain  was  ascribable  to  the 
greater  range  of  expansion  used  with  the  jackets. 

Test  of  a  Compound  Condensing  Engine  with  and  without  Jackets 
at  different  Loads.  (R.  C.  Carpenter,  Trans.  A.  S.  M.  E.,  xiv,  428.)  — 
Cylinders  9  and  16  in.  X  14  in.  stroke;  112  Ibs.  boiler- pressure;  rated 
capacity  100  H.P.;  265  revs,  per  min.  Vacuum,  23  in.  From  the  results 
of  several  tests  curves  are  plotted,  from  which  the  following  principal 
figures  are  taken. 


Indicated  HP.. 

30 

40 

50 

60 

70 

80 

90 

100 

1  10 

120 

125 

Steam  per  I.H.P.  per  hr. 
With  jackets,  Ibs  
Without  jackets,  Ibs..  . 

22.6 

21.4 

20.3 

19  6 
22 

19 
?0  5 

18.7 
19  6 

18.6 
19  ? 

18.9 
19  1 

19.5 
19  3 

20.4 
20  1 

21.0 

Saving  by  jacket.  %  ... 

10  9 

7  3 

4  6 

3  1 

1  0 

-1  0 

-1  5 

This  table  gives  a  clue  to  the  great  variation  in  the  apparent  saving 
due  to  the  steam-jacket  as  reported  by  different  experimenters.  With 
this  particular  engine  it  appears  that  when  running  at  its  most  econom- 
ical rate  of  100  H.P.,  without  jackets,  very  little  saving  is  made  by  use 
of  the  jackets.  When  running  light  the  jacket  makes  a  considerable 
saving,  but  when  overloaded  it  is  a  detriment. 

At  the  load  which  corresponds  to  the  most  economical  rate,  with  no 
steam  in  jackets,  or  100  H.P.,  the  use  of  the  jacket  makes  a  saving  of 
only  1%;  but  at  a  load  of  60  H.P.  the  saving  by  use  of  the  jacket  is 
about  11%,  and  the  shape  of  the  curve  indicates  that  the  relative  ad- 
vantage of  the  jacket  would  be  still  greater  at  lighter  loads  than  60  H.P. 

The  Best  Economy  of  the  Piston  Steam-Engine  at  the  Advent  of 
the  Steam  Turbine  is  the  subject  of  a  paper  by  J.  E.  Denton  at  the 
International  Congress  of  Arts  and  Sciences,  St.  Louis,  1904.  (Power 
Oct.  26,  1905.)  Prof.  Denton  says: 

During  the  last  two  years  the  following  records  have  been  established: 

(1)  With  an  850:H.P.  Rice  &  Sargent  compound  Corliss  engine,  running 
at  120  r.p.m.,  having  a  4  to  1  cylinder  ratio,  clearances  of  4%  and  7% 
live  jackets  on  cylinder  heads  and  live  steam  in  reheater,  Prof.  Jacobus 
found  for  600  H.P.  of  load,  with  150  Ibs.  saturated  steam,  28.6  ins.  vacuum, 
and  33  expansions,  12.1  Ibs.  of  water  per  I.H.P.,  with  a  cylinder-conden- 
sation loss  of  22%,  and  a  jacket  consumption  of  10.7%  of  the  total  steam 
consumption. 

(2)  With  a  250-H.P.  Belgian  poppet-valve  compound  engine,  126  r.p.m. 
with  2.97  to  1  cylinder  ratio,  clearances  of  4%,  steam-chest  jackets  on 
barrels  and  head,  and  no  reheater,  Prof.  Schroter,  of  Munich,  found  with 
117  H.P.  of  load,  130  Ibs.  saturated  steam,  27.6  ins.  of  vacuum,  and  32  ex- 
pansions, 11.98  Ibs.  of  water  per  H.P.  per  hour,  with  a  cylinder-condensa- 
tion loss  of  23.5%,  and  a  jacket  consumption  of  7%  of  the  total  steam 
consumption  in  the  high  cylinder  jacket  and  7%  in  the  low  jacket. 

(3)  With  the  Westinghouse  twin  compound  combined  poppet-valve 
and  Corliss-valve  engine,  at  the  New  York  Edison  plant,  running  76  r  p  m 
with  5.8  to  1  cylinder  ratio,  clearances  of  10.5%  and  4%,  without  jackets 
or  reheater,  Messrs.  Andrew,  Whitham  and  Wells  found  for  the  full  load 

if  5400  H.P     185  Ibs.  steam  pressure,  27.3  ins.  vacuum,  and  29  expan- 
sions^l  1.93  Ibs.  of  water  per  I.H.P.  per  hour,  with  an  initial  condensation 

These  facts  show  that  the  minimum  water  consumption  of  the  compound 
engine  of  the  present  date,  using  saturated  steam,  is  not  dependent  upon 
any  particular  cylinder  ratio  and  clearance  nor  upon  any  system  of  jacket- 
ing, but  that  tne  essential  condition  is  the  use  of  a  ratio  of  expansion 
ai  about  30,  above  which  the  cylinder-condensation  loss  is  liable  to  prevail 
over  the  influence  of  the  law  of  expansion.     The  conclusion  appears 
warranted,  therefore,  that  if  this  ratio  of  expansion  is  secured  with  any 
the  current  cylinder  and  clearance  ratios,  and  with  any  existing  system 
of  jackets  and  reheaters,  or  without  them,  a  water  consumption  of  12  4  Ibs 
horse-power  is  possible,  and  that  a  variation  of  04  Ib.  below  or  above 
igure  may  occur  by  the  accidental  favorable,  or  unfavorable,  jacket 
ad  cylinder-wall  expenses  which  are  beyond  the  control  of  the  designer 
Compound  Piston  Engine  Economy  vs.  that  of  Steam  Turbine. — In  order 
to  compare  the  economy  of  the  piston  engine  with  that  of  the  steam  tur- 


1006  THE   STEAM-ENGINE. 

bine,  we  must  use  the  water  consumption  per  brake  horse-power,  since  no 
indicator  card  is  possible  from  the  turbine;  and  furthermore,  we  must  use 
the  average  water  consumption  for  the  range  of  loads  to  which  engines  are 
subject  in  practice. 

In  all  of  the  public  turbine  tests  to  date,  with  one  exception  the  output 
was  measured  through  the  electric  power  of  a  dynamo  whose  efficiency  is 
not  given  for  the  range  of  loading  employed,  so  that  the  average  brake 
horse-power  is  not  known.  This  exception  is  the  Dean  and  Main  test  of 
a  600-H.P.  Westinghouse-Parsons  turbine  using  saturated  steam  at  150  Ibs. 
pressure,  and  a  28-in.  vacuum.  We  may  compare  the  results  of  this  test 
with  that  of  the  850-H.P.  Rice  &  Sargent  and  of  the  250-H.P.  Belgian 
engine,  by  assuming  that  the  power  absorbed  by  friction  in  these  en- 
gines is  3  %  of  the  indicated  load  plus  the  power  shown  by  friction  cards 
taken  with  the  engine  unloaded.  The  latter  showed  5%  of  the  rated 
power  in  the  R.&  S.  engine  and  8  %  in  the  Belgian  engine.  The  results  are : 
Per  cent  of  full  load 41  75  100  125  Avg.  85% 

Lbs.  Water  per  Brake  H.P.  Hour. 

600-H.P.  Turbine 13.62       13.91       14.48       16.05       14.51 

800-H. P.  Comp.  Engine 13.78       13.44       13.66       17.36       14.56 

250  H.P.  Belgian  Engine 15.10       14.15       13.99       15.31       14.64 

These  figures  show  practical  equality  in  economy  of  the  types  of  engines. 
The  full  report  of  the  Van  den  Kerchove  Belgian  engine  is  given  in  Power, 
June,  1903. 

For  large-sized  units  Prof.  Denton  compares  the  Elberfeld  test  of  a 
Parsons  turbine  at  the  full  load  of  1500  electric  H.P.,  allowing  5%  for 
attached  air  pump,  95%  for  generator  efficiency,  with  the  5400-H.P. 
Westinghouse  compound  engine  at  the  New  York  Edison  station,  whose 
friction  at  full  load  was  found  to  be  4%.  The  turbine  with  150  Ibs.  steam 
and  28  ins.  vacuum  required  13.08  Ibs.  of  saturated  steam  per  B.H.P. 
hour,  a  gain  of  4%  over  the  600-H.P.  turbine.  The  engine  with  18.5  Ibs. 
boiler  pressure  gave  12.5  Ibs.  per  B.H.P.  hour.  Crediting  the  turbine 
with  the  possible  influence  of  the  difference  in  size  and  steam  pressure, 
there  is  again  practical  equality  in  economy  between  it  and  the  piston 
engine. 

Triple-expansion  Pumping  Engines.  —  The  triple-expansion  engine  has 
failed  to  supplant  the  compound  for  electric  light  and  mill  service,  be- 
cause the  gain  in  fuel  economy  due  to  its  use  was  not  sufficient  to  over- 
come its  higher  first  cost,  depreciation,  etc.  It  is,  however,  almost  uni- 
versally used  in"  marine  practice,  and  also  in  large-sized  pumping  engines. 
Prof.  Denton  says:  Pumping  engines  in  the  United  States  have  been  de- 
veloped in  xthe  triple-expansion  fly- wheel  type  to  a  degree  of  economy 
superior  to  that  afforded  by  any  compound  mill  or  electric  engine,  and, 
for  saturated  steam,  superior  to  that  of  the  pumping  engines  of  any  other 
country.  This  is  because  their  slow  speed  permits  of  greater  benefit 
from  jackets  and  reheaters  and  of  less  losses  from  wire-drawing  and  back 
pressure.  These  causes,  together  with  the  greater  subdivision  of  the  range 
of  expansion,  have  resulted  in  records  made  between  1894  and  1900  of 
11.22,  11.26  and  11.05  Ibs.  of  saturated  steam  per  I.H.P.,  with  175  Ibs. 
steam  pressure  and  from  25  to  33  expansions,  in  the  cases  of  the  Leavitt, 
Snow  and  Allis  pumping  engines,  respectively,  the  corresponding  heat 
consumption  being  by  different  dispositions  of  the  jacket  drainage,  204, 
208  and- 212  thermal  units  per  I.H.P.  minute;  while  later  the  Allis  pump, 
with  185  Ibs.  steam  pressure,  has  lowered  the  record  to  10.33  Ibs.  of  satu- 
rated steam  per  I.H.P.,  with  196  B.T.U.  per  H.P.  minute. 

Gain  from  Superheating.  —  In  the  Belgian  compound  engine  above  de- 
scribed, with  steam  at  130  Ibs.,  vacuum  27. 6  ins.,  the  average  consumption 
of  saturated  steam,  between  45  and  ]25%  of  load,  was  12.45  Ibs.  per 
I.H.P.  hour,  or  225  B.T.U.  per  I.H.P.  minute.  With  steam  superheated 
224°  F.  the  average  consumption  for  the  same  loads  was  10.09  Ibs.  per 
I.H.P.  hour,  computed  to  be  equivalent  to  209  B.T.U.  per  H.P.  minute, 
a  gain  due  to  superheating  of  7%.  With  steam  supei heated  307°  and 
the  load  about  80%  of  rating  the  water  consumption  \\as  8.99  Ibs.  per 
I.H.P.  hour,  equivalent  to  192  B.T.U.  per  H.P.  minute.  The  same  load 
with  saturated  steam  requires  221  B.T.U.,  showing  a  gain  due  to  super- 
heating of  13%. 
.The  best  performance  reported  for  superheated  steam  used  in  the  tur- 


ECONOMIC  PERFORMANCE  OF  STEAM-ENGINES.    1007 


bine  is  that  of  Brown  &  Boveri  Parsons,  Frankfort,  4000-H.P.  machine, 
which,  with  183  Ibs.  gauge  pressure  and  190°  F.  superheat,  afforded  10.28 
Ibs.  per  B.H.P.  hour,  assuming  a  generator  efficiency  of  0.95.  Reckoning 
from  the  feed  temperature  of  its  vacuum  of  27.5  ins.,  the  heat  consumption 
is  214  B.T.U.  per  H.P.  minute. 

The  heat  consumption  of  the  250-H.P.  Belgian  compound  engine  per 
B.H.P.  hour  at  the  highest  superheating  of  307°  F.  is  220  B.T.U.  The 
turbine,  therefore,  probably  holds  the  record  for  brake  horse-power  econ- 
omy over  the  piston  engine  for  superheated  steam  by  a  margin  of  about 
3%,  although  had  the  compound  engine  been  of  the  same  horse-ppwer  as 
the  turbine,  so  that  its  friction  load  would  be  only  8%  of  its  power  instead 
of  the  13%  here  allowed,  it  would  have  excelled  the  turbine  in  brake 
horse-power  economy  by  a  margin  of  about  2.5%. 

The  Sulphur-dioxide  'Addendum.  —  If  the  expansion  in  piston  engines 
could  continue  until  the  pressure  of  1  pound  was  attained  before  exhaust 
occurred,  considerable  more  work  could  be  obtained  from  the  steam. 
This  cannot  be  done,  for  two  reasons:  first,  because  the  low  cylinder  would 
have  to  be  about  five  times  greater  in  volume,  which  is  commercially 
impracticable;  and,  second,  because  the  velocity  of  exit  through  the 
largest  exhaust  ports  possible  is  so  great  that  the  frictional  resistance  of 
the  steam  makes  the  back  pressure  from  1  to  3  pounds  higher  than  the 
condenser  pressure  in  the  best  engines  of  ordinary  piston  speed. 

All  the  work  due  to  this  extra  expansion  can  be  obtained  by  exhausting 
the  steam  at  6  Ibs.  pressure  against  a  nest  of  tubes  containing  sulphur 
dioxide  which  is  thereby  boiled  to  a  vapor  at  about  170  Ibs.  pressure. 

Professor  Josse,  of  Berlin,  has  perfected  this  sulphur-dioxide  system 
of  improvement,  and  reliable  tests  have  shown  that  if  cooling  water  of 
65°  is  available,  and  to  the  extent  of  about  twice  the  quantity  usually  em- 
ployed for  condensing  steam  under  28  ins.  of  vacuum,  a  sulphur-dioxide 
cylinder  of  about  half  the  size  of  the  high-pressure  cylinder  of  a  com- 
pound engine  will  do  sufficient  work  to  improve  the  best  economy  of 
such  engines  at  least  15%.  The  steam  turbine  expands  its  steam  to  the 
pressure  of  its  exhaust  chamber,  and  as  unlimited  escape  ports  can  bo 
provided  from  this  chamber  to  a  condenser,  it  follows  that  the  turbine 
can  practically  expand  its  steam  to  the  pressure  of  the  condenser.  There- 
fore a  steam  turbine  attached  to  a  piston  engine  to  operate  with  the  latter's 
exhaust  should  effect  the  same  saving  as  the  sulphur-dioxide  cylinder. 

Standard  Dimensions  of  Direct-connected  Generator  Sets.  From 
a  report  by  a  committee  of  the  A.  S.  M.  E.,  1901. 

Capacity  of  unit,  K.W 25       35       50       75     100     150     200 

Revolutions  per  minute 310     300     290     275     260     225     200 

Armature  bore,  center  crank  engines. ..  4  4  41/2  51/2  678 
Armature  bore,  side-crank  engines 41/2  51/2  61/2  71/2  81/210  11 

The  diameter  of  the  engine  shaft  at  the  armature  fit  is  0.001  in. 
greater  than  the  bore,  for  bores  up  to  and  including  6  ins.,  and  0.012 
in.  greater  for  bores  6 1/2  ins.  and  larger. 

Dimensions  of  Some  Parts  of  Large  Engines  in  Electric  Plants. — 
The  Electrical  World,  Sept.  27,  1902,  gives  a  table  of  dimensions  of 
the  engines  in  the  five  large  power  stations  in  New  York  City  at  that 
date.  The  following  figures  are  selected  from  the  table. 


Name  of  station  

Metro- 
politan. 

Manhat- 
tan. 

Kings- 
bridge. 

Rapid 
Transit. 

Edison. 

Type  of  engine  .  ... 

Vert. 
Cross- 

Double, 
2  hor. 

Vert. 
Cross- 

Double 
2  hor. 

3  Cyl.  Vert. 

Comp. 

2  vert. 
Cyls. 

Comp. 

2  vert. 
Cyls. 

Rated  H.P..  . 
Cylinders,  (60"  stroke) 
Piston  rods,  diam.,  in. 
Crank  pins  

4500 
46,  86  in. 
9,  10 
14  X  14 

8000 
44,  88  in. 
8 
18  X  18 

4500 
46,  86  in. 
9,  10 
14  X  14 

8900 
42,  86  in. 
8,  10 
20  X  18 

5200 
43l/2,2-75J/"in. 
9 
22  &  16  X  14 

Wrist  pins  

14  X  14 

12  X  12 

14  X  14 

12  X  12 

14  X  H 

Shaft  length  
max.  diam  
bearings  

27  ft.  4  in. 
37  in. 
34  X  60 

25  ft.  3  in. 
37  in. 
34  X60 

27ft. 
39  in. 
34  X60 

25  ft.  3  in. 
37  in. 
34  X60 

35  ft. 
293/8    in. 
26  X  60 

1008 


THE   STEAM-ENGINE. 


The  shafts  are  hollow,  with  a  16-in.  hole,  except  the  Edison  which  has 
10  in.  The  speed  of  all  the  engines  is  75  r.p.m.,  or  750  ft.  per  min.  The 
crank-pins  of  the  Manhattan  and  Rapid  Transit  engines  each  are  at- 
tached to  two  connecting-rods,  side  by  side,"hor.  and  vert.,  each  rod  hav- 
ing a  bearing  9  in.  long  on  the  pin.  The  crank-pins  of  the  Edison  en- 
gine are  16  in.  diam.  for  the  side-cranks,  and  22  in.  for  the  center-crank. 

The  four  8000-horse-power  engines  in  the  Manhattan  station,  new  in 
1902,  were  replaced  in  1914-15,  although  still  as  good  as  new,  by  four 
30,000  K.W.  steam  turbines  occupying  the  same  space.  The  turbines 
will  have  a  water  rate  30  per  cent  lower  than  the  engines.  (Power, 
April  27,  1915.) 

Some  Large  Rolling-Mill  Engines. 


Cylinders. 

§ 
(^ 

tf 

Type. 

8.3 

pu^ 

Fly-wheel. 

Location. 

Builders. 

Diam. 
Ft. 

Wt. 
Lbs. 

44  &  82  X60 

65 

Cross-C  . 

140 

24 

150,000 

Republic  I.  &  S. 

Filer   & 

Co.,         Youngs- 

Stowell. 

town,  Ohio. 

46  &  80X60 

80 

Tandem. 

150 

24 

110.000 

Carnegie   S.    Co., 

Wiscon- 

Donora, Pa. 

sin  Eng. 

Co. 

52  &  90X60. 

Tandem 

25 

250,000 

Carnegie    S.    Co., 

Wm.  Tod 

Youngstown, 

Co. 

Ohio. 

2  each  
42  &  70  X54 

Double. 
Tandem. 

150 

none 

Carnegie    S.    Co., 
S.    Sharon,    Pa. 

Allis 
Chal- 

mers Co. 

Carnegie  S. 

Co.,  Du- 

Mackin- 

quesne, Pa. 

tosh, 

2  each  .  . 

60 

Double. 

150 

none 

Jones  & 

Hemp- 

44  &  70X60 

Tandem. 

Laughlin 

hill  & 

Steel  Co., 

Co. 

Aliquippa,Pa. 

Some  details:  Main  bearings,  No.  1,  25  X  431/2  in.;  No.  2,  30  X  52  in.; 
No.  3,  30  X  60  in.  Shaft  diam.  at  wheel  pit,  No.  1,  26  in.;  No.  3,  36  in. 
Crank  pins,  No.  1,  h.p.  14  X  14;  l.p.,  14  X  23  in.;  No.  2,  18  X  18  in. 
Crosshead  pins,  No.  1,  12  X  14;  No.  2,  16  X  20  in.  No.  4  is  a  reversing 
engine,  with  the  Marshall  gear.  No.  5  is  a  reversing  engine  with  piston 
valves  below  the  cylinders. 

Counterbalancing  Engines.  —  Prof.  Unwin  gives  the  formula  for 

counterbalancing  vertical  engines:  Wi  =  Wzr/p, (1) 

in  which  W\  denotes  the  weight  of  the  balance  weight  and  p  the  radius  to 
its  center  of  gravity,  W 2  the  weight  of  the  crank-pin  and  half  the  weight  of 
the  connecting-rod,  and  r  the  length  of  the  crank.  For  horizontal  engines: 

Wi  =  2/3  (Wz  +  TF3)  r/p  to  3/4  (Wz  +  TF3)  r/p (2) 

In  which  TF3  denotes  the  weight  of  the  piston,  piston-rod,  cross-head,  and 
the  other  half  of  the  weight  of  the  connecting-rod. 

The  American  Machinist,  commenting  on  these  formulae,  says:  For 
horizontal  engines  formula  (2)  is  often  used;  formula  (1)  will  give  a  coun- 
terbalance too  light  for  vertical  engines.  We  should  use  formula  (2)  for 
computing  the  counterbalance  for  both  horizontal  and  vertical  engines, 
excepting  locomotives,  in  which  the  counterbalance  should  be  heavier. 

For  an  account  of  experiments  on  counterbalancing  large  engines,  with 
a  method  of  recording  vibrations,  see  paper  by  D.  S.  Jacobus,  Trans. 
A.  S.  M.  #.,  1905. 

Preventing  Vibrations  of  Engines.  —  Many  suggestions  have  been 
made  for  remedying  the  vibration  and  noise  attendant  on  the  working 
of  the  big  engines  which  are  employed  to  run  dynamos.  A  plan  which  has 
given  great  satisfaction  is  to  build  hair-felt  into  the  foundations  of  the 
engine.  An  electric  company  has  had  a  90-horse-power  engine  removed 
from  its  foundations,  which  were  then  taken  up  to  the  depth  of  4  feet.  A 


COMMERCIAL  ECONOMY — COSTS   OF   POWER.      1009 

layer  of  felt  5  inches  thick  was  then  placed  on  the  foundations  and  run 
tip  2  feet  on  all  sides,  and  on  the  top  of  this  the  brickwork  was  built  up.  — 
Safety  Valve. 

Steam-engine  Foundations  Embedded  in  Air. — In  the  sugar- 
refinery  of  Claus  Spreckels,  at  Philadelphia,  Pa.,  the  engines  are  distrib- 
uted practically  all  over  the  buildings,  a  large  proportion  of  them  being 
on  upper  floors.  Some  are  bolted  to  iron  beams  or  girders,  and  are  con- 
sequently innocent  of  all  foundation.  Some  of  these  engines  ran  noise- 
lessly and  satisfactorily,  while  others  produced  more  or  less  vibration  and 
rattle.  To  correct  the  latter  the  engineers  suspended  foundations  from 
the  bottoms  of  the  engines,  so  that,  in  looking  at  them  from  the  lower 
floors,  they  were  literally  hanging  in  the  air.  —  Iron  Age,  Mar.  13,  1890. 

COMMERCIAL,  ECONOMY.  —  COSTS  OF  POWER. 

The  Cost  of  Steam  Power  is  an  exceedingly  variable  quantity.  The 
principal  items  to  be  considered  in  estimating  total  annual  cost  are:  load 
factor ;  hours  run  per  year ;  percentage  of  full  load  at  different  hours  of 
the  day ;  cost  and  quality  of  fuel ;  boiler  efficiency  and  steam  consumption 
of  engines  at  different  loads ;  cost  of  water  and  other  supplies ;  cost  of 
labor,  first  cost  of  plant,  depreciation,  repairs,  interest,  insurance  and  taxes. 

In  figuring  depreciation  not  only  should  the  probable  life  of  the  several 
parts  of  the  plant,  such  as  buildings,  boilers,  engines,  condensers,  etc.,  be 
considered,  but  also  the  possibility  of  part  of  the  plant,  or  the  whole  of  it, 
depreciating  rapidly  in  value  on  account  of  obsolescence  of  the  machinery 
or  of  changes  in  the  conditions  of  the  business. 

When  all  of  the  heat  in  the  exhaust  steam  from  engines  and  pumps,  in- 
cluding water  of  condensation,  is  used  for  heating  purposes  the  fuel  cost  of 
steam-engine  power  may  be  practically  nothing,  since  the  exhaust  contains 
all  of  the  heat  in  the  steam  delivered  to  the  engine  except  from  5  to  10 
per  cent  which  is  converted  into  work,  and  a  trifling  amount  lost  by 
radiation. 

Most  Economical  Point  of  Cut-off  in  Steam-engines.  (See  paper 
by  Wolff  and  Denton,  Trans.  A.  S.  M.  E.,  vol.  ii,  p.  147-281;  also,  Ratio 
of  Expansion  at  Maximum  Efficiency,  R.  H.  Thurston,  vol.  ii,  p.  128.) 
— The  problem  of  the  best  ratio  of  expansion  is  not  one  of  economy  of  con- 
sumption of  fuel  and  economy  of  cost  of  boiler  alone.  The  question  of  in- 
terest on  cost  of  engine,  depreciation  of  value  of  engine,  repairs  of  engine, 
etc.,  enters  as  well;  for  as  we  increase  the  rate  of  expansion,  and  thus, 
within  certain  limits  fixed  by  the  back-pressure  and  condensation  of 
steam,  decrease  the  amount  of  fuel  required  and  cost  of  boiler  per  unit  of 
work,  we  have  to  increase  the  dimensions  of  the  cylinder  and  the  size 
of  the  engine,  to  attain  the  required  power. 

Type  of  Engine  to  be  used  where  Exhaust-steam  is  needed  for 
Heating.  —  In  many  factories  more  or  less  of  the  steam  exhausted  from 
the  engines  is  utilized  for  boiling,  drying,  heating,  etc.  Where  all  the 
exhaust-steam  is  so  used  the  question  of  economical  use  of  steam  in  the 
engine  itself  is  eliminated,  and  the  high-pressure  simple  engine  is  entirely 
suitable.  Where  only  part  of  the  exhaust-steam  is  used,  and  the  quantity 
so  used  varies  at  different  times,  the  question  of  adopting  a  simple,  a 
condensing,  or  a  compound  engine  becomes  more  complex.  This  problem 
is  treated  by  C.  T.  Main  in  Trans.  A.  S.  M.  E.,  vol.  x,  p.  48.  He  shows 
that  the  ratios  of  the  volumes  of  the  cylinders  in  compound  engines  should 
vary  according  t9  the  amount  of  exhaust-steam  that  can  be  used  for 
heating.  A  case  is  given  in  which  three  different  pressures  of  steam  are 
required  or  could  be  used,  as  in  a  worsted  dye-house:  the  high  or  boiler 
pressure  for  the  engine,  an  intermediate  pressure  for  crabbing,  and  low- 
pressure  for  boiling,  drying,  etc.  If  it  did  not  make  too  much  compli- 
cation of  parts  in  the  engine,  the  boiler-pressure  might  be  used  in  the  high- 
pressure  cylinder,  exhausting  into  a  receiver  from  which  steam  could  be 
taken  for  running  small  engines  and  crabbing,  the  steam  remaining  in  the 
receiver  passing  into  the  intermediate  cylinder  and  expanded  there  to 
from  5  to  10  Ibs.  above  the  atmosphere  and  exhausted  into  a  second 
receiver.  From  this  receiver  is  drawn  the  low-pressure  steam  needed  for 
drying,  boiling,  warming  mills,  etc.,  the  steam  remaining  in  the  receiver 
passing  into  the  condensing  cylinder. 

Cost  of  Steam-power.  (Chas.  T.  Main,  Trans.  A.  S.  M.  E.,  x,  48.) — 
Estimated  costs  in  New  England  in  1888,  per  horse-power,  using  com- 


1010 


THE   STEAM-ENGINE. 


pound  condensing,  and  non-condensing  engines,  and  based  on  engines 
of  1000  H.P.  are  as  follows: 

Compound     Condens-     Non-con- 
Engine.      ing  Engine,    densing 


1.  Cost  engine  and  piping,  complete $25.00  . 

2.  Engine-house 8.00 

3.  Engine  foundations 7.00 

4.  Total  engine  plant 40.00 

5.  Depreciation,  4%  on  total  cost, l  60 

6.  Repairs,  2%  on  total  cost 0.80 

7.  Interest,  5%  on  total  cost 2.00 

8.  Taxation,  1.5%  on  3/4  cost 0  45 

9.  Insurance  on  engine  and  house 0  165 


Total  of  lines  5,  6,  7,  3,  9 5.015 


10. 


11.  Cost  boilers,  feed-pumps,  etc 9.33 

12.  Boiler-house 2.92 

13.  Chimney  and  flues 6. XI 

Total  boiler-plant 18.36 


14. 

15.  Depreciation,  5%  on  total  cost 0.918 

16.  Repairs,  2%  on  total  cost 0.367 

17.  Interest,  5%  on  total  cost 0.918 

18.  Taxation,  1.5%  on  3/4  cost 0.207 

19.  Insurance,  0.5%  on  total  cost 0.092 

20.  Total  of  lines  15  to  19 2.502 

21.  Coal  used  per  I.H.P.  per  hour,  Ibs.  . .  1.75 

22.  Cost  of  coal  per  I.H.P.  per  day  of  10 1/4  cts. 

hours  at  $5.00  per  ton  t>f  2240  Ibs. . . .  4.00 

23.  Attendance  of  engine  per  day 0.60 

24.  Attendance  of  boilers  per  day 0.53 

25.  Oil,  waste,  and  supplies,  per  day . .  „ .  0.25 


Total  daily  expense 5.38 


26. 

27.  Yearly  running  expense,  308  days,  per 

I.H.P. : . '.  P. .  $16.570 

28.  Total    yearly   expense,   lines   10.  20, 

and  27 24.087 

29.  Total   yearly  expense  per  I.H.P.  for 

power  if  50%  of  exhaust-steam  is 

used  for  heating 12.597 

30.  Total  if  all  exhaust-steam  is  used  for 

heating 8.624 


33.00 

1.32 

0.66 

1.65 

0.371 

0.138 

4.139 


24.80_ 

1.240 
0.496 
1.240 
0.279 
0.124 

3.379 


2.50 

cts. 
5.72 
0.40 
0.75 
0.22 

7.09 


$21.837 
29.355 

14.907 
7.916 


Engine. 

$17.50 
7.50 
4.50 

29.50 


1.18 

0.59 

1.475 

0.332 

0.125 

3.702 


5.00 
8.00 


29.00 


1.450 
0.580 
1.450 
0.326 
0.145 

3.951 
3.00 

cts. 
6.86 
0.35 
0.90 
0.20 

8.31 


When  exhaust-steam  or  a  part  of  the  receiver-steam  is  used  for  heating, 
or  if  part  of  the  steam  in  a  condensing  engine  is  diverted  from  the  con- 
denser, and  used  for  other  purposes  than  power,  the  value  of  such  steam 
should  be  deducted  from  the  cost  of  the  total  amount  of  steam  generated 
in  order  to  arrive  at  the  cost  properly  chargeable  to  power.  The  figures 
in  lines  29  and  30  are  based  on  an  assumption  made  by  Mr.  Main  of  losses 
of  heat  amounting  to  25%  between  the  boiler  and  the  exhaust-pipe,  an 
allowance  which  is  probably  too  large. 

See  also  two  papers  by  Chas.  E.  Emery  on  "Cost  of  Steam  Power," 
Trans.  A.  S.  M.  E.,  vol.  xii,  Nov.,  1883,  and  Trans.  A.  1.  E.  E.,  vol.  x, 

ac'ost  of  Coal  for  Steam-power. — The  following  table  shows  the 
amount  and  the  cost  of  coal  per  day  and  per  year  for  various  horse-powers 
from  1  to  1000,  based  on  the  assumption  of  4  Ibs.  of  coal  being  used  per 


COMMERCIAL  ECONOMY — COSTS   OF   POWER.      1011 

hour  per  horse-power.  It  is  useful,  among  other  things,  in  estimating  the 
saving  that  may  be  made  in  fuel  by  substituting  more  economical  boilers 
and  engines  for  those  already  in  use.  Thus  with  coal  at  $3.00  per  ton  of 
2000  ibs.,  a  saving  of  $9000  per  year  in  fuel  may  be  made  by  replacing  a 
steam  plant  of  1000  H.P.,  requiring  4  Ibs.  of  coal  per  hour  per  horse-power, 
with  one  requiring  only  2  Ibs. 


Coal  Consumption,  at  4  Ibs. 

per  H.P.  hour;  10  hours  a 
day;  300  days  per  Year. 

$2  per 
Short 

$3  per 

Short 

$4  per 
Short 

® 

Ton. 

Ton. 

Ton. 

1 

Lbs. 

Long  Tons. 

Short 
Tons. 

e 

Cost  in 

Cost  in 

Cost  In 

1 

Per 

Per 

Per 

VOQ  T» 

Per 

Per 

Y- 

Dollars. 

Dollars. 

Dollars. 

Day. 

Day. 

lear. 

Day. 

r. 

Day. 

Yr. 

Day. 

Yr. 

Day. 

Yr. 

1 

40 

0.0179 

53.57 

0.02 

6 

0.04 

12 

0.06 

18 

0.08 

24 

10 

400 

0.1786 

53.57 

0.20 

60 

0.40 

120 

0.60 

180 

0.80 

240 

25 

1,000 

0.4464 

133.92 

0.50 

150 

1.00 

300 

1.50 

450 

2.00 

600 

50 

2,000 

0.8928 

267.85 

1.00 

300 

2.00 

600 

3.00 

900 

4.00 

1,200 

75 

3,000 

1  .3393 

401.78 

1.50 

450 

3.00 

900 

4.50 

1,350 

6.00 

1,800 

100 

4,000 

1.7857 

535.71 

2.00 

600 

4.00 

1,200 

6.00 

1.800 

8.00 

2,400 

150 

6,000 

2.6785 

803.56 

3.00 

900 

6.00 

1,800 

9.00 

2,700 

12.00 

3,600 

200 

8,000 

3.5714 

1,071.42 

4.00 

1,200 

8.00 

2,400 

12.00 

3,600 

16.00 

4,800 

250 

10,000 

4.4642 

1,339.27 

5.00 

1,500 

10.  CO 

3,000 

15.00 

4.500 

20.00 

6,000 

300 

12,000 

5.3571 

1,607.13 

6.00 

1,800 

12.00 

3,600 

18.00 

5,400 

24.00 

7,200 

350 

14,000 

6.2500 

1,874.98 

7.00 

2,100 

14.00 

4,200 

21.00 

6,200 

28.00 

8,400 

400 

16,000 

7.1428 

2,142.84 

8.00 

2,400 

16.00 

4,800 

24.00 

7,200 

32.00 

9600 

450 

18,000 

8.0356 

2,410.69 

9.00 

2,700 

18.00 

5,400 

27.00 

8,100 

36.00 

10^800 

500 

20.000 

8.9285 

2,678.55 

10.00 

3,000 

20.00 

6,000 

30.00 

9,000 

40.00 

12,000 

600 

24,000 

10.7142 

3,214.26 

12.00 

3,600 

24.00 

7,200 

36.00 

10,800 

48.00 

14,400 

700 

28,000 

12.4999 

3,749.97 

14.00 

4,200 

28,00 

8,400 

42.00 

11,600 

56.00 

16,800 

800 

32,000 

14.2856 

4,285.68 

16.00 

4,800 

32.00 

9,600 

48.00 

12,400 

64.00 

19,200 

900 

36,000 

16.0713 

4,821.39 

18.00 

5,400 

36.00 

10,800 

54.00 

14,200 

72.00 

21,600 

1000 

40,000 

17.8570 

5,357.10 

20.00 

6,000 

40.00 

12,000 

60.00 

18,000 

80.00 

24,000 

It  is  usual  to  consider  that  a  factory  working  10  hours  a  day  requires 
101/2  hours  coal  consumption  on  account  of  the  coal  used  in  banking  or 
in  starting  the  fires,  and  that  there  are  306  wprking  days  in  the  year.  For 
these  conditions  multiply  the  costs  given  in  the  table  by  1.071.  For 
24  hours  a  day  365  days  in  the  year,  multiply  them  by  2.68.  For  other 
rates  of  coal  consumption  than  4  Ibs.  per  H.P.  hour,  the  figures  are  to  be 
modified  proportionately. 

Relative  Cost  of  Different  Sizes  of  Steam-engines. 

(From  catalogue  of  the  Buckeye  Engine  Co.,  Part  III.) 


Horse-power..  .  . 
Cost  per  H.  P.,  $ 

50 
20 

75 
171/2 

100 
16 

125 
15 

150 

141/2 

200 
131/2 

250 
13 

300 

123/4 

350 

12.5 

400 
12.6 

500 
12.8 

600 
131/4 

700 
14 

800 
15 

Power  Plant  Economies.  (H.  G.  Stott,  Trans.  A.  I.  E.  E.,  190G.)— 
The  table  on  the  following  page  gives  an  analysis  of  the  heat  losses  found 
in  a  year's  operation  of  one  of  the  most  efficient  plants  in  existence. 

The  following  notes  concerning  power-plant  economy  are  condensed 
from  Mr.  Stott's  paper. 

Item  1.  B.T.U.per  Ib.  of  coal.  The  coal  is  bought  and  paid  for  on 
the  basis  of  the  B.T.U,  found  by  a  bomb  calorimeter, 


1012  THE   STEAM-ENGINE. 

AVERAGE  LOSSES  IN  THE  CONVERSION  OF  1  LB.  OF  COAL  INTO  ELECTRICITY,, 

B.T.U.     %         B.T.U.     % 


1. 

B.T.U.  per  Ib.  of  coal  supplied    14,150     100.0 

2. 

Loss  in  ashes  

340 

2.4 

3. 

Loss  to  stack  

3,212 

22.7 

4. 
5. 

Loss  in  boiler  radiation  and  air  leakage 
Returned  by  feed-water  heater  441         3.1 

1,131 

8.0 

6. 

Returned  by  economizer  960         6.8 

7. 

Loss  in  pipe  radiation  

28 

0.2 

8. 

Delivered  to  circulator  

223 

1.6 

9. 

Delivered  to  feed  purnp  

203 

1.4 

10. 

Loss  in  leakage  and  high-pressure  drips 

152 

1.1 

11. 

Delivered  to  small  auxiliaries  

51 

0.4 

12. 

Heating  _.  

31 

0.2 

13. 

Loss  in  engine  friction   

111 

0.8 

14. 

Electrical  losses  

36 

0.3 

15. 

Engine  radiation  losses  

28 

0.?. 

16. 

Rejected  to  condenser  

8,524 

60.1 

17. 

To  house  auxiliaries  

29 

0.2 

15,551     109.9     14,099     99.6 
14,099       99.6 

Delivered  to  bus  bar        1,452      10.3 

Item  3.  The  chimney  loss  is  very  large,  due  to  admitting  too  much  air 
to  the  combustion  chamber.  This  loss  can  be  reduced  about  half  by  the 
use  of  a  CO2  recorder  and  proper  management  of  the  fire. 

Item  4.  This  loss  is  largely  due  to  infiltration  of  air  into  the  brick 
setting.  It  can  be  saved  by  having  an  air-tight  sheet-iron  casing  enclosing 
a  magnesia  lining  outside  of  the  brickwork. 

Item  5.  All  auxiliaries  should  be  driven  by  steam,  so  that  their  exhaust 
may  be  utilized  in  the  feed-water  heater. 

Item  6.  In  all  cases  where  the  load  factor  exceeds  25%  the  investment 
in  economizers  will  be  justified. 

Item  7.  The  pipes  are  covered  with  two  layers  of  covering,  each  about 
1.5  in.  thick. 

Item  10.  The  high-pressure  drips  can  be  returned  to  the  boiler,  so 
practically  all  the  loss  under  this  heading  is  recoverable. 

Item  13.  Recent  tests  of  a  7500-H.P.  reciprocating  engine  show  a 
mechanical  efficiency  of  93.65%,  or  an  engine  friction  of  6.35%.  The 
engine  is  lubricated  by  the  flushing  system. 

Item  16.  The  maximum  theoretical  efficiency  of  an  engine  working 
between  175  Ibs.  gauge  and  28  ins.  vacuum  is 

(Ti  -  T2)  -f-  Ti  =  (837  -  560)  -^  837  =  33%. 

The  actual  best  efficiency  of  this  engine  is  17  Ibs.  per  K.W.-hour  =  16.7% 
thermal  efficiency:  dividing  by  0.98,  the  generator  efficiency,  gives  the  net 
thermodynamic  efficiency  of  the  engine,  =  17%.  The  difference  between 
the  theoretical  and  the  actual  efficiency  is  33  -  17  =  16%,  of  which  6.35% 
is  due  to  engine  friction,  and  the  balance.  9.65%,  is  due  to  cylinder  con- 
densation,  incomplete  expansion,  and  radiation.  [Some  of  this  difference 
is  due  to  the  fact  that  the  engine  does  not  work  on  the  Carnot  cycle,  in 
which  the  heat  is  all  received  at  the  highest  temperature,  and  part  of  this 
loss  might  be  saved  by  the  Nordberg  feed-water  heating  system.  There 
may  also  be  a  slight  loss  from  leakage.  W.K.J  Superheated  steam,  to 
such  an  extent  as  to  insure  dry  steam  at  the  point  01  cut-off  in  the  low- 
pressure  cylinder,  might  save  5  or  6%. 

The  present  type  01  power  plant  using  reciprocating  engines  can  be  im- 
proved in  efficiency  as  follows:  Reduction  of  stack  losses,  12%;  boiler 
radiation  and  leakage,  5%;  by  superheating,  6%;  resulting  in  a  net  in- 
crease of  thermal  efficiency  of  the  entire  plant  of  4.14%  and  bringing  the 
total  from  10.3  to  14.44%. 

The  Steam  Turbine.  —  The  best  results  from  the  steam  turbine  up  to 
date  show  that  its  economy  on  dry  saturated  steam  is  practically  equal 
to  that  of  the  reciprocating  engine,  and  that  200J  superheat  reduces  its 
steam  consumption  13.5%.  The  shape  of  the  economy  curve  is  much 


c< 


iOMMERCIAL   ECONOMY — COSTS   OF   POWER.      1013 
Maintenance  and  Operation  Costs  of  Different  Types  of  Plant. 


Recip- 
rocating 
Engines. 

Steam 
Turbines 

Recip- 
rocating 
Engines 
and 
Steam 
Turbines. 

Gas- 
Engine 
Plant. 

Gas 

Engines 
and 
Steam 
Turbines. 

MAINTENANCE. 
1.  Engine  room  mechan- 
ical   

2.57 

0.51 

1.54 

2.57 

1.54 

2.  Boiler  room  or  pro- 
ducer room 

4  61 

4  30 

3.52 

1.15 

1.95 

3.  Coal-    and    ash-han- 
dling apparatus  .  .  . 
4.  Electrical  apparatus 
OPERATION. 
5.  Coal;    and    ash-han- 
dling labor  

0.58 
1.12 

2  26 

0.54 
1.12 

2.11 

0.44 
1.12 

1.74 

0.29 
1.12 

1.13 

0.29 
1.12 

1.13 

6.  Removal  of  ashes  
7.  Dock  rental  

1.06 
0.74 

0.94 
0.74 

0.80 
0.74 

0.53 
0.74 

0.53 
0.74 

8.  Boiler-room  labor.  .  .  . 
9.  Boiler-  room  oil.waste, 

7.15 
0.17 

6.68 
0.17 

5.46 
0.17 

1.79 

0.17 

3.03 
0.17 

10   Coal           

61  30 

57  30 

46.87 

26.31 

25.77 

1  1  .  Water  

7.14 

0.71 

5.46 

3.57 

2.14 

12.  Engine-room     me- 
chanical labor  
13.  Lubrication  
14.  Waste,  etc  

6.71 
1.77 
0  30 

1.35 
0.35 
0.30 

4.03 
1.01 
0.30 

6.71 
1.77 
0.30 

4.03 
1.06 
0.30 

15.  Electrical  labor 

2  52 

2  52 

2  52 

2.52 

2.52 

Relative  cost  of  mainte- 
nance and  operation  .  . 

100.00 

79.64 

75.72 

50.67 

46.32 

Relative   investment   in 
per  cent  

100.00 

82.50 

77.00 

100.00 

91.20 

flatter  [from  3300  to  8000  K. W.  the  range  of  steam  consumption  is  between 
14.6  and  15.0  Ibs.  per  K.W.-hour],  so  that  the  all-day  efficiency  would  be 
considerably  better  than  that  of  the  reciprocating  engine,  and  the  cost 
would  be  about  33%  less  for  the  combined  steam  motor  and  electric 
generator. 

High-pressure  Reciprocating  Engine  with  Low-pressure  Turbine. —  The 
reciprocating  engine  is  more  efficient  than  the  turbine  in  the  higher  pres- 
sures, while  the  turbine  can  expand  to  lower  pressures  and  utilize  the  gain 
of  full  expansion.  The  combination  of  the  two  would  therefore  be  more 
efficient  than  a  turbine  alone. 

The  Gas  Engine.  — The  best  result  up  to  date  obtained  from  gas  pro- 
ducers and  gas  engines  is  about  as  follows:  Loss  in  producer  and  auxiliaries, 
20%;  in  jacket  water,  19%;  in  exhaust  gases,  30%;  in  engine  friction, 
6.5%;  in  electric  generator,  0.5%.  Total  losses,  76%.  Converted  into 
electric  energy,  24%.  Only  one  important  objection  can  be  raised  to  this 
motor,  that  its  range  of  economical  load  is  practically  limited  to  between 
50%  and  full  load.  This  lack  of  overload  capacity  is  probably  a  fatal 
defect  for  the  ordinary  railway  power  plant  acting  under  a  violently 
fluctuating  load,  unless  protected  by  a  large  storage-battery. 

At  light  loads  the  economy  of  gas  and  liquid  fuel  engines  fell  off  even 
more  rapidly  than  in  steam-engines.  The  engine  friction  was  large  and 
nearly  constant,  and  in  some  cases  the  combustion  was  also  less  perfect 
at  light  loads.  At  the  Dresden  Central  Station  the  gas-engines  were  kept 
working  at  nearly  their  full  power  by  the  use  of  storage-batteries.  The 
results  of  some  experiments  are  given  below: 


1014  THE   STEAM-ENGINE. 


Brake-load,  per    Gas-engine,  cu.  ft. 
cent  of  full          of  Gas  per  Brake 

Petroleum  Eng., 
Lbs.  of  Oil  per 

Petroleum  Eng., 
Lbs.  of  Oil  per 

Power. 

H.P.  per  hour. 

B.H.P.  per  hr. 

B.H.P.  per  hr. 

100 

22.2 

0.96 

0.88 

75 

23.8 

1.11 

0.99 

59 

28.0 

1.44 

1.20 

20 

40.8 

2.38 

1.82 

121/2 

66.3 

4.25 

3.07 

Combination  of  Gas  Engines  and  Turbines.  —  A  steam  turbine  unit  can 
be  designed  to  take  care  of  100%  overload  -for  a  few  seconds.  If  a  plant 
were  designed  with  50%  of  its  normal  capacity  in  gas  engines  and  50% 
in  steam  turbines,  any  fluctuations  in  load  likely  to  arise  in  practice  could 
be. taken  care  of.  By  utilizing  the  waste  heat  of  the  gas  engine  in  econ- 
omizers and  superheaters  there  can  be  saved  approximately  37%  of  this 
waste  heat,  to  make  steam  for  the  turbines.  The  average  total  thermal 
efficiency  of  such  a  combination  plant  would  be  24.5%.  This  combina- 
tion offers  the  possibility  of  producing  the  kilowatt-hour  for  less  than  one- 
half  its  present  cost. 

The  table  on  p.  1013  shows  the  distribution  of  estimated  relative  main- 
tenance and  operation  costs  of  five  different  types  of  plant,  the  total  cost 
of  current  with  the  reciprocating  engine  plant  being  taken  at  100. 

Storing  Heat  in  Hot  Water.  — (See  also  p.  927.)  There  is  no  satisfac- 
tory method  for  equalizing  the  load  on  the  engines  and  boilers  in  electric- 
light  stations.  Storage-batteries  have  been  used,  but  they  are  expensive 
in  first  cost,  repairs,  and  attention.  Mr.  Halpin,  of  London,  proposes  to 
store  heat  during  the  day  in  specially  constructed  reservoirs.  As  the 
water  in  the  boilers  is  raised  to  250  Ibs.  pressure,  it  is  conducted  to  cylin- 
drical reservoirs  resembling  English  horizontal  boilers,  and  stored  there 
for  use  when  wanted.  In  this  way  a  comparatively  small  boiler-plant 
can  be  used  for  heating  the  water  to  250  Ibs.  pressure  all  through  the 
twenty-four  hours  of  the  day,  and  the  stored  water  may  be  drawn  on  at 
any  time,  according  to  the  magnitude  of  the  demand.  The  steam-engines 
are  to  be  worked  by  the  steam  generated  by  the  release  of  pressure  from 
this  water,  and  the  valves  are  to  be  arranged  in  such  a  way  that  the  steam 
shall  work  at  130  Ibs.  pressure.  A  reservoir  8  ft.  in  diameter  and  30  ft. 
long,  containing  84,000  Ibs.  of  heated  water  at  250  Ibs.  pressure,  would 
supply  5250  Ibs.  of  steam  at  130  Ibs.  pressure.  As  the  steam  consump- 
tion of  a  condensing  electric-light  engine  is  about  18  Ibs.  per  horse-power 
hour,  such  a  reservoir  would  supply  286  effective  horse-power  hours.  In 
1878,  in  France,  this  method  of  storing  steam  was  used  on  a  tramway. 
M.  Francq,  the  engineer,  designed  a  smokeless  locomotive  to  work  by 
steam-power  supplied  by  a  reservoir  containing  400  gallons  of  water  at 
220  Ibs.  pressure.  The  reservoir  was  charged  with  steam  from  a  stationary 
boiler  at  one  end  of  the  tramway. 

An  installation  of  the  Rateau  low-pressure  turbine  and  regenerator 
system  at  the  rolling  mill  of  the  International  Harvester  Co.,  in  Chicago, 
is  described  in  Power,  June,  1907.  The  regenerator  is  a  cylindrical  shell 
11 1/2  ft.  diam.,  30  ft.  long,  containing  six  large  elliptical  tubes  perforated 
with  many  3/4_in.  holes  through  which  exhaust  steam  from  a  reversing 
blooming-mill  engine  enters  the  water  contained  in  the  shell.  A  large 
steam  pipe  leads  from  the  shell  to  the  turbine.  A  series  of  tests  of  the 
combination  was  made,  giving  results  as  follows:  The  42  X  60  in.  blooming 
mill  engine  developed  820  I. H.P.  on  the  average,  with  a  water  rate  of  64 
Ibs.  per  I. H.P.  hour.  It  delivered  its  exhaust,  averaging  a  little  above  at- 
mospheric pressure,  to  the  regenerator,  at  an  irregular  rate  corresponding 
to  the  varying  work  of  the  rolling-mill  engine.  The  regenerator  furnished 
steam  to  the  turbine,  which  in  four  different  tests  developed  444,  544, 
727  and  869  brake  H.P.  at  the  turbine  shaft,  with  a  steam  consumption 
of  47.7,  37.1,  30.7  and  33.7  Ibs.  of  steam  per  B.H.P.  hour  at  the  turbine. 
Had  the  turbine  been  of  sufficient  capacity  to  use  all  the  exhaust  of  the 
mill  engine,  1510  H.P.  might  have  been  delivered  at  the  switchboard, 
which  added  to  the  820  of  the  mill  engine  would  make  2330  H.P.  for 
52,400  Ibs.  of  steam,  or  a  steam'  rate  of  22,5  Ibs.  per  H,P.  liour  for  tne 
.combination, 


EULES  FOR  CONDUCTING  ENGINE  TESTS.       1015 

UTILIZING  THE  SUN'S  HEAT  AS  A  SOURCE  OF  POWER. 

John  Ericsson,  1868-1875,  experimented  on  "solar  engines,"  in  which 
reflecting  surfaces  concentrated  the  sun's  rays  at  a  central  point  causing 
them  to  boil  water.  A  large  motor  of  this  type  was  built  at  Pasadena, 
Cal.,  in  1898.  The  rays  were  concentrated  upon  a  water  heater  through 
which  ether  or  sulphur  dioxide  was  pumped  in  pipes,  and  utilized  in  a 
vapor  engine.  The  apparatus  was  commercially  unsuccessful  on  account 
of  variable  weather  conditions.  Eng.  News,  May  13,  1909,  describes  the 
solar  heat  systems  of  F.  Shuman  and  of  H.  E.  Willsie  and  John  Boyle,  Jr. 

In  the  Shuman  invention  a  tract  of  land  is  rolled  level,  forming  a  shallow 
trough.  This  is  lined  with  asphaltum  pitch  and  covered  with  about 
3  ins.  of  water.  Over  the  water  about  Vie  in.  of  paraffine  is  flowed,  leaving 
between  this  and  a  glass  cover  about  6  ins.  of  dead  air  space.  It  is  esti- 
mated that  a  power  plant  of  this  type  to  cover  a  heat-absorption  area  of 
160,000  sq.  ft.,  or  nearly  four  acres,  would  .develop  about  1000  H.P. 
Provision  is  made  for  storing  hot  water  in  excess  of  the  requirements  of 
a  low-pressure  turbine  during  the  day,  to  be  utilized  for  running  the 
turbine  during  the  period  when  there  is  no  absorption  of  heat.  The 
heated  water  is  run  from  the  heat  absorber  to  the  storage  tank,  thence 
to  the  turbine,  through  a  condenser  and  back  to  the  heat  absorber.  The 
water  enters  the  thermally  insulated  storage  tank,  or  the  turbine,  at  about 
202°  F.  With  a  vacuum  of  28  ins.  in  the  condenser,  the  boiling-point  of 
the  water  is  reduced  to  102°,  and  as  it  enters  the  turbine  nearly  10% 
explodes  into  steam.  Mr.  Shuman  estimates  that  a  1000-H.P.  plant  built 
upon  his  plan  would  cost  about  $40,000. 

The  Willsie  and  Boyle  plant  also  utilizes  the  indirect  system  of  absorb- 
ing solar  heat  and  storing  the  hot  water  in  tanks.  This  hot  water  cir- 
culates in  a  boiler  containing  some  volatile  liquid,  and  the  vapor  generated 
is  used  to  operate  the  engine,  is  condensed,  and  returned  to  the  boiler 
to  be  used  again.  Mr.  Willsie  compares  the  cost  per  H.P.-hour  in  a 
400-H.P.  steam-electric  and  solar-electric  power  plant,  and  finds  that  the 
steam  plant  would  have  to  obtain  its  coal  for  $0.66  a  ton  to  compete  with 
the  sun  power  plant  in  districts  favorable  to  the  latter. 

RULES    FOR    CONDUCTING   TESTS   FOR   RECIPROCATING 
STEAM-ENGINES. 

(Abstract  of  the  1915  Code  of  the  Power  Test  Committee  of    the 
Am.  Soc.  M.  E.) 

The  code  for  steam  engine  tests  applies  to  tests  for  determining 
the  performance  of  the  engine  alone  (including  reheaters  and  jackets, 
if  any)  apart  from  that  of  steam-driven  auxiliaries  which  are  neces- 
sary to  its  operation.  For  tests  of  engine  and  auxiliaries  combined, 
and  tests  of  multiple  expansion  engines  from  which  steam  is  with- 
drawn Jf  or  heating  feed  water  or  otherwise,  refer  to  the  Code  for  Com- 
plete Steam  Power  Plants. 

OBJECT   AND    PREPARATIONS. 

^  Determine  the  object  of  the  test,  take  the  dimensions,  and  note 
the  physical  conditions,  not  only  of  the  engine,  but  of  all  parts  of 
the  plant  that  are  concerned  in  the  determinations,  examine  for 
leakages,  install  the  testing  appliances,  etc.,  and  prepare  for  the 
test  accordingly . 

The  determination  of  the  heat  and  steam  consumption  of  an  engine 
by  feed-water  test  requires  the  measurement  of  the  various  supplies 
of  water  fed  to  the  boiler;  that  of  the  water  wasted  by  separators 
and  drips  on  the  main  steam  line,  that  of  steam  used  for  other  purposes 
than  the  main  engine  cylinders,  and  that  of  water  and  steam  which 
escape  by  leakage  of  the  boiler  and  piping;  all  of  these  last  being  de- 
ducted from  the  total  feed  water  measured. 

Where  a  surface  condenser  is  provided  and  the  steam  consumption 
is  determined  from  the  water  discharged  by  the  air  pump,  no  such 
measurement  of  drips  and  leakage  is  required,  but  assurance  must 
be  had  that  all  the  steam  passing  into  the  cylinders  finds  -its  way 


1016  THE  STEAM-ENGINE. 

into  the  condenser.  If  the  condenser  leaks,  the  defects  causing 
such  leakage  should  be  remedied,  or  suitable  correction  should  be 
made. 

When  no  other  method  is  available  the  steam  consumption  may 
be  determined  by  the  use  of  a  steam  meter,  bearing  in  mind  the  caution 
that  it  should  be  calibrated  under  the  exact  conditions  of  use. 

The  steam  consumed  by  steam-driven  auxiliaries  which  are  re- 
quired for  the  operation  of  the  engine  should  be  included  in  the  total 
steam  from  which  the  heat  consumption  is  calculated  and  the  quan- 
tity of  steam  thus  used  should  be  determined  and  reported. 

OPERATING  CONDITIONS. 

Determine  what  the  operating  conditions  should  be  to  conform 
to  the  object  in  view,  and  see  that  they  prevail  throughout  the  trial. 

DURATION. 

A  test  for  steam  or  heat  consumption,  with  substantially  constant 
load,  should  be  continued  for  such  time  as  may  be  necessary  to  obtain 
a  number  of  successive  hourly  records,  during  which  the  results  are 
reasonably  uniform.  For  a  test  involvirg  the  measurement  of  feed- 
water  for  this  purpose,  five  hours'  duration  is  sufficient.  Where  a 
surface  condenser  is  used,  and  the  measurement  is  that  of  the  water 
discharged  by  the  air  pump,  the  duration  may  be  somewhat  shorter. 
In  this  case,  successive  half-hourly  records  may  be  compared  and  the 
time  correspondingly  reduced. 

When  the  load  varies  widely  at  different  times  of  the  day,  the 
duration  should  be  such  as  to  cover  the  entire  period  of  variation. 

STARTING  AND  STOPPING. 

The  engine  and  appurtenances  having  been  set  to  work  and  thor- 
oughly heated  under  the  prescribed  conditions  of  test  (except  in  cases 
where  the  object  is  to  obtain  the  performance  under  working  condi- 
tions) note  the  water  levels  in  the  boilers  and  feed  reservoir,  take  the 
time  and  consider  this  the  starting  time.  Then  begin  the  measure- 
ments and  observations  and  carry  them  forward  until  the  end  of  the 
period  determined  on.  When  this  time  arrives,  the  water  levels  and 
steam  pressure  should  be  brought  as  near  as  practicable  to  the  same 
points  as  at  the  start.  This  being  done,  again  note  the  time  and 
consider  it  the  stopping  time  of  the  test.  If  there  are  differences  in 
the  water  levels,  proper  corrections  are  to  be  applied. 

Where  a  surface  condenser  is  used,  the  collection  of  water  dis- 
charged by  the  air  pump  begins  at  the  starting  time,  and  the  water 
is  thereafter^measured  or  weighed  until  the  end  of  the  test. 

RECORDS. 

Half-hourly  readings  of  the  instruments  are  sufficient,  excepting 
where  there  are  wide  fluctuations.  A  set  of  indicator  diagrams  should 
be  obtained  at  intervals  of  15  or  20  minutes,  and  often er  if  the  nature 
of  the  test  makes  it  necessary.  Mark  on  each  card  the  cylinder  and 
the  end  on  which  it  was  taken,  also  the  time  of  day.  Record  on  one 
card  of  each  set  the  readings  of  the  steam  pressure  and  vacuum  gages. 
These  records  should  be  subsequently  entered  on  the  general  log, 
together  with  the  areas,  pressures,  lengths,  etc.,  measured  from  the 
diagrams,  when  these  are  worked  up. 

CALCULATION  OF  RESULTS. 

Dry  Steam. — The  quantity  of  dry  steam  consumed  is  determined 
by  deducting  the  moisture,  if  any,  found  by  the  calorimeter  test 
from  the  total  amount  of  feed-water  (the  latter  being  corrected 
for  leakages  and  other  losses)  or  from  the  amount  of  air-pump  dis- 
charge, as  the  case  may  be.  If  the  steam  is  superheated,  no  cor- 
rection is  to  be  made  for  the  superheat. 

Heat  Consumption. — The  number  of  heat-units  consumed  by  the 
engine  is  found  by  multiplying  the  weight  of  feed-water  consumed, 


RULES  FOR  CONDUCTING  STEAM-ENGINE  TESTS.    1017 

corrected  for  moisture  in  the  steam,  if  any,  and  for  plant  leakages 
and  other  exterior  losses,  by  the  total  heat  of  I  Ib.  of  steam  (sat- 
urated or  superheated)  less  the  heat  in  1  Ib.  of  water  at  the  tem- 
perature corresponding  to  the  pressure  in  the  exhaust  pipe  near 
the  engine. 

Indicated  Horse-power.  —  In  a  single  double-acting  cylinder  the  indi- 
cated horse-power  is  found  by  using  the  formula 

PLAN 
33,000* 

in  which  P  represents  the  average  mean  effective  pressure  in  pounds 
per  square  inch  measured  from  the  indicator  diagrams,  L  the  length 
of  stroke  in  feet,  A  the  area  of  the  piston  less  9ne-half  the  area 
of  the  piston  rod,  or  the  mean  area  of  the  rod  if  it  passes  through 
both  cylinder  heads,  in  square  inches,  and  N  the  number  of  single 
strokes  per  minute. 

Brake  Horse-power. — The  brake  horse-power  is  found  by  multiplying 
the  net  pressure  or  weight  in  pounds  on  the  brake  arm  (the  gross 
weight  minus  the  weight  when  the  brake  is  entirely  free  from  the 
pulley)  in  pounds,  the  circumference  of  the  circle  whose  radius 
is  the  horizontal  distance  between  the  center  of  the  shaft  and  the 
bearing  point  at  the  end  of  the  brake  arm  in  feet,  and  the  number 
of  revolutions  of  the  brake  shaft  per  minute;  and  dividing  the 
product  by  33,000. 

Electrical  Horse-power. — The  electrical  horse-power  of  a  direct-con- 
nected generator  is  found  by  dividing  the  output  at  the  terminals 
expressed  in  kilowatts,  by  the  decimal  0.7457.  With  alternating 
current  generators  the  net  output  is  to  be  used,  this  being  the  total 
output  less  that  consumed  for  excitation  and  for  separately-driven 
ventilating  fans. 

Efficiency. — The  thermal  efficiency,  that  is,  the  percentage  of  the 
total  heat  consumption  which  is  converted  into  work,  is  found 
by  dividing  the  quantity  2546.5,  which  is  the  B.T.U.  equivalent 
of  one  H. P. -hour,  by  the  number  of  heat-units  actually  consumed 
per  H! P. -hour. 

The  Rankine  cycle  efficiency  is  found  by  dividing  the  heat  con- 
sumption of  an  ideal  engine  conforming  to  the  Rankine  cycle  by 
the  actual  heat  consumption. 

Steam  Accounted  for  by  Indicator  Diagrams  at  Points  Near  Cut-off 
and  Release. — The  steam  accounted  for,  expressed  in  pounds  per 
I.H.P.  per  hour,  may  be  found  by  using  the  formula 

IJOOrKC  +  E)  Wc  -  (H  +  E}  Wh], 

•   in  which 

M.E.P.  =  mean  effective  pressure; 

C  =  proportion  of  direct  stroke  completed  at  points  on  ex- 
pansion line  near  cut-off  or  release; 
E  =  proportion  of  clearance; 
H  =  proportion    of    return   stroke   uncompleted    at    point    on 

compression  line  just  after  exhaust  closure; 
Wc  =  weight  of  1  cu.  ft.  steam  at  pressure  shown  at  cut-off  or 

release  point; 

Wn  =  weight  of  1  cu.  ft.  steam  at  pressure  shown  at  compres- 
sion point. 

In  multiple  expansion  engines  the  mean  effective  pressure  to  be 
used  in  the  above  formula  is  the  aggregate  M.E.P.  referred  to  the 
cylinder  under  consideration.  In  a  compound  engine  the  aggregate 
M.E.P.  for  the  h.p.  cylinder  is  the  sum  of  the  actual  M.E.P.  of 
the  h.p.  cylinder  and  that  of  l.p.  cylinder  multiplied  by  the  cyl- 
inder ratio.  Likewise  the  aggregate  M.E.P.  for  the  l.p.  cylinder 
is  the  sum  of  the  actual  M.E.P.  of  the  l.p.  cylinder  and  the  M.E.P. 
of  the  h.p.  cylinder  divided  by  the  cylinder  ratio. 

The  relation  between  the  weight  of  steam  shown  by  the  indicator 
at  any  point  in  the  expansion  line  and  the  weight  of  the  mixture 
of  steam  and  water  in  the  cylinder,  may  be  represented  graphically 
by  plotting  on  the  diagram  a  saturated  steam  curve  showing  the 


1018  THE  STEAM-ENGINE. 

total  consumption  per  stroke  (including  steam  retained  at  com- 
pression) and  comparing  the  abscissae  of  this  curve  with  the  absciss* 
of  the  expansion  line,  both  measured  from  the  line  of  no  clearance. 
Cut-off  and  Ratio  of  Expansion. — To  find  the  percentage  of  cut-off, 
or  what  may  best  be  termed  the  "commercial  cut-off,"  the  fol- 
lowing rule  should  be  observed: 

Through  the  point  of  maximum  pressure  during  admission 
draw  a  line  parallel  to  the  atmospheric  .line.  Through  a 
point  on  the  expansion  line  where  the  cut-off  is  complete, 
draw  a  hyperbolic  curve.  The  intersection  of  these  two  lines 
is  the  point  of  commercial  cut-off,  and  the  proportion  of  cut-off 
is  found  by  dividing  the  length  measured  on  the  diagram 
up  to  this  point  by  the  total  length. 

To  find  the  ratio  of  expansion  divide  the  volume  corresponding 
to  the  piston  displacement,  including  clearance,  by  the  volume  of 
the  steam  at  the  commercial  cut-off,  including  clearance. 

In  a  multiple  expansion  engine,  the  ratio  of  expansion  is  found 
by  dividing  the  volume  of  the  l.p.  cylinder,  including  clearance, 
by  the  volume  of  the  h.p.  cvlinder  at  the  commercial  cut-off,  in- 
cluding clearance. 

DATA    AND    RESULTS. 

The  data  and  results  should  be  reported  in  accordance  with  the 
form  given  herewith,  adding  lines  for  data  not  provided  for,  or  omitting 
those  not  required,  as  may  conform  to  the  object  in  view.  If  the 
principal  data  and  results  pertaining  to  steam  consumption  only  are 
desired,  the  subjoined  abbreviated  table  may  be  used. 

DATA  AND   RESULTS  OF  STEAM-ENGINE  TEST 
Code  of  1915. 

1.  Test  of engine  located  at 

To  determine 

Test  conducted  by , 


DIMENSIONS,    ETC. 

2.  Type  of  engine  (simple  or  multiple  expansion). 

3.  Class  of  service  (mill,  marine,  electric,  etc.) .  .  . 


4.  Auxiliaries  (steam  or  electric  driven) . 

5.  Rated  power  of  engine 

1st  2d  3d 

6.  Diameter  of  cylinders in!      

7.  Stroke  of  pistons ft 

(a)  Diameter  of  piston-rod,  each  end, 

in : 

8.  Clearance  (average)  in  per  cent  of  piston 

displacement 1  to  —      

9.  H.  P;  constant  1  Ib.  1  rev H.P .      

(a)   Cylinder  ratio  (based  on  net  pis- 
ton displacement 1  to  —      

10.  Capacity  of  generator  or  other  apparatus 

consuming  power  of  engine H.P 

DATE    AND    DURATION. 

11.  Date ' 

12.  Duration hr. 

AVERAGE  PRESSURES  AND  TEMPERATURES. 

13.  Pressure  in  steam  pipe  near  throttle,  by  gage Ibs.  per  sq,  in. 

14.  Barometric  pressure ins. 

15.  Pressure  in  1st  receiver,  by  gage Ibs.  per  sq.  in. 

16.  Pressure  in  2d  receiver,  by  gage Ibs.  per  sq.  in. 

17.  Vacuum  in  condenser ins. 

18.  Pressure  in  jackets  and  reheaters .  .  . Ibs.  per  sq.  in. 

19.  Temperature  of  steam  near  throttle,  if  superheated degs. 

20.  Temperature  corresponding  to  pressure  in  exhaust  pipe 

near  engine 


I     RULES   FOR  CONDUCTING   STEAM-ENGINE   TESTS.      1019 

QUALITY    OF    STEAM. 

;  21.  Percentage  of  moisture  in  steam  near  throttle,  or  degrees 

of  superheating %  or  deg. 

TOTAL    QUANTITIES. 

Water  fed  to  boilers,  from  main  supply Ibs. 

Water  fed  to  boilers  from  additional  supplies Ibs. 

Total  water  fed  to  boilers Ibs. 

Total  condensed  steam  from  surface  condenser  (corrected 
for  condenser  leakage) Ibs. 

26.  Total  dry  steam  consumed  (Item  24  to  25  less  moisture 

in  steam) - Ibs. 

HOURLY    QUANTITIES. 

27.  Water  fed  to  boilers  from  main  supply  per  hour Ibs. 

2S.   Water  fed  to  boilers  from  additional  supplies  per  hour.  .  Ibs. 

29.  Total  water  fed  to  boilers  or  drawn  from  surface  con- 

denser per  hour Ibs. 

30.  Total  -dry  steam  consumed  for  all  purposes  per  hour 

(Item  26  ~  Item  12) Ibs. 

31.  Steam  consumed  per  hour  for  all  purposes  foreign  to  the 

main  engine  (including  drips  and  leakage  of  plant) . . .   Ibs. 

32.  Dry  stearn  consumed  by  engine  per  hour   (Item  30  — 

Item  31) Ibs. 

33.  Heat  units  consumed  by  engine  per  hour   (Item  32  X 

total  heat  of  steam  per  Ib.  above  exhaust  temperature 

of  Item  20) B.T.U. 

INDICATOR    DIAGRAMS. 

lstCyl.2dCyl.  3d  Cyl. 

34.  Commercial  cut-off  in  per  cent  of  stroke, 

per  cent    

35.  Initial  pressure  above  atmosphere 

Ibs.  per  sq.  in 

36.  Back  pressure  at  lowest  point   above  or 

below  atmosphere Ibs.  per  sq.  in 

37.  Mean  effective  pressure Ibs.  per  sq.  in 

38.  Aggregate    M.E.P.   referred   to    each   cyl- 

inder  Ibs.  per  sq.  in . .  ,  f 

39.  Steam    accounted    for    per    I.H.P.-hr.    at 

point    on   expansion   line   shortly    after 

cut-off Ibs 

40.  Stearn    accounted    for    per    I.H.P.-hr.    at 

point    on    expansion    line    just    before 
release Ibs.    . 


SPEED. 

41.  Revolutions  per  minute R.P.M. 

42.  Piston  speed  per  minute ft. 

(a)  Variation  of  speed  between  no  load  and  full  load .    per  cent. 

(b)  Momentary    fluctuation    of    speed    on    suddenly 

changing  from  full  load  to  half  load per  cent. 


43.  Indicated  H.P.  developed,  whole  engine. I.H.P. 

(a)  I.H.P.  developed  by  1st  cylinder I.H.P. 

(b)  I.H.P.  developed  by  2d  cylinder I.H.P. 

(c)  I.H.P.  developed  by  3d  cylinder I.H.P. 

44.  Brake  H.P B.H.P. 

45.  Friction  of  engine  (Item  43  —  Item  44) H.P. 

(a)  Friction  expressed  in  percentage  of  I.H.P.  (Item 

45  -4-  Item  43  X  100) per  cent. 

(&)  Indicated  H.P.  with  no  load,  at  normal  speed. .  . .  I.H.P. 


1020  THE  STEAM-ENGINE. 

ECONOMY    RESULTS. 

46.  Dry  steam  consumed  by  engine  per  I.H.P.  per  hr Ibs. 

47.  Dry  steam  consumed  by  engine  per  brake  H.P.-hr Ibs. 

48.  Percentage  of  steam  consumed  by  engine  accounted  for 

by  indicator  at  point  near  cut-off per  cent. 

49.  Percentage  of  steam  consumed  near  release per  cent. 

50.  Heat-units  consumed   by  engine  per   I. H.P.-hr.    (Item 

33  -r-  Item  43) B.T.U. 

51.  Heat-units  consumed  by  engine  per  brake  H.P.-hr.  (Item 

33  -=-  Item  44) B.T.U. 

52.  Heat-units    consumed    per    H.P.-hr.    by    ideal    engine, 

based  on  Rankine  cycle B.T.U. 

EFFICIENCY    RESULTS. 

53.  Thermal  efficiency  of  engine  referred  to  I.H.P.  (2546.5  -4- 

Item  50) per  cent. 

54.  Thermal  efficiency   of   engine   referred   to   Brake   H.P. 

(2546.5  -i-  Item  51) per  cent. 

65.  Efficiency  of  engine  based  on  Rankine  cycle  referred  to 

I.H.P.  (Item  52  4-  Item  50) per  cent. 

56.  Efficiency  of  engine  referred  to  Brake  H.P.  (Item  52  -r-  * 

Item  51) per  cent. 

WORK    DONE    PER    HEAT-UNIT. 

57.  Foot-pounds    of    net    work   per    B.T.U.    consumed    by 

engine  (1,980,000  -r-  Item  51) ft.-lbs. 

SAMPLE    DIAGRAMS. 

58.  Sample  diagrams  from  each  cylinder 

NOTE: — For  an  engine  driving  an  electric  generator  the  form  should 
be  enlarged  to  include  the  electrical  data,  embracing  the  average 
voltage,  number  of  amperes  each  phase,  number  of  watts,  number 
of  watt-hours,  average  power  factor,  etc.;  and  the  economy  results 
based  on  the  electric  output  embracing  the  heat-units  and  steam 
consumed  per  electric  H.P.  per  hour  and  per  kw.-hr.,  together  with 
the  efficiency  of  the  generator. 

Likewise,  in  a  marine  engine  having  a  shaft  dynamometer,  the 
form  should  include  the  data  obtained  from  this  instrument,  in  which 
case  the  Brake  H.P.  becomes  the  Shaft  H.P. 

PRINCIPAL  DATA  AND  RESULTS  OF  RECIPROCATING  ENGINE  TEST. 

1.  Dimensions  of  cylinders 

2.  Date 

3.  Duration hrs. 

4.  Pressure  in  steani  pipe  near  throttle  by  gage Ibs.  per  sq.  in. 

5.  Pressure  in  receivers Ibs.  per  sq.  in. 

6.  Vacuum  in  condenser ins. 

7.  Percentage  of  moisture  in  steam  near  throttle  or 

number  of  degrees  of  superheating  / %  or  deg. 

8.  Net  steam  consumed  per  hour Ibs. 

9.  Mean  effective  pressure  in  each  cylinder.  . Ibs.  per  sq.  in. 

10.  Revolutions  per  minute R.P.M. 

11.  Indicated  horse-power  developed H.P. 

12.  Steam  consumed  per  I.H.P.  per  hr Ibs. 

13.  Steam  accounted  for  at- cut-off  each  cylinder Ibs. 

14.  Heat  consumed  per  I.H.P.  per  hr B.T.U. 


DIMENSIONS  OP  PARTS  OF  ENGINES. 


1021 


DIMENSIONS  OF  PARTS  OF  ENGINES. 

The  treatment  of  this  subject  by  the  leading  authorities  on  the  steam- 
engine  is  very  unsatisfactory,  being  a  confused  mass  of  rules  and  for- 
mulae based  partly  upon  theory  and  partly  upon  practice.  The  practice 
of  builders  shows  an  exceeding  diversity  of  opinion  as  to  correct  dimen- 
sions. The  treatment  given  below  is  chiefly  the  result  of  a  study  of  the 
works  of  Rankine,  Seaton,  Unwin,  Thurston,  Marks,  and  Whitham,  and 
is  largely  a  condensation  of  a  series  of  articles  by  the  author  published 
in  the  American  Machinist,  in  1894,  with  many  alterations  and  much 
additional  matter. 

(Two  notable  papers  on  the  subject,  however,  have  appeared:  1,  Cur- 
rent Practice  in  Engine  Proportions,  by  Prof.  John  H.  Barr,  1897;  and 
2,  Current  Practice  in  Steam-engine  Design,  by  Ole  N.  Trooien,  1909. 
Both  of  these  are  abstracted  on  pages  1039  and  1040.) 

Cylinder.  (Whitham)  —  Length  of  bore  =  stroke  4-  breadth  of  pis- 
ton-ring —  i/8-to  1/2  in.;  length  between  heads  =  stroke  +  thickness  of 
piston  -f  sum  of  clearances  at  both  ends ;  thickness  of  piston  =  breadth 
of  ring  -f-  thickness  of  flange  on  one  side  to  carry  the  ring  +  thickness 
of  follower-plate. 

Thickness  of  flange  or  follower.  . .     3 /g  to  1/2  in.     3/4  in.  1  in. 

For  cylinder  of  diameter 8  to  10  in.     36  in.     60  to  100  in. 

Clearance  of  Piston.  (Seaton.) — The  clearance  allowed  varies  with 
the  size  of  the  engine  from  i/g  to  3/g  m-  f°r  roughness  of  castings  and 
1/16  to  i/s  in.  for  each  working  joint.  Naval  and  other  very  fast-running 
engines  have  a  larger  allowance.  In  a  vertical  direct-acting  engine  the 
parts  which  wear  so  as  to  bring  the  piston  nearer  the  bottom  are  three, 
viz.,  the  shaft  journals,  the  crank-pin  brasses,  and  piston-rod  gudgeon- 
brasses. 

Thickness  of  Cylinder. — In  the  earlier  editions  of  this  book  eleven 
formulae,  from  seven  different  authorities,  were  given  for  thickness  of 
cylinders  and  they  were  applied  to  six  engines,  the  dimensions  of  which 
are  given  in  the  following  table. 

DIMENSIONS,  ETC.,  OF  ENGINES. 


Indicated  horse-pow'er 

I.H  P 

50 

450 

1250 

Diam.  of  cyl.,  in  

D 

10 

30 

50 

Stroke,  feet. 

L 

1        2 

2V2       5 

4        8 

Revs,  per  min  

T 

250    .    125 

130        65 

90        45 

Piston  speed,  ft.  per  min  

s 

500 

650 

700 

Area  of  piston,  sq.  in.    .    .    . 

OL 

78  54 

706  86 

1963  5 

Mean  effective  pressure 

M  E  P. 

42 

32  3 

30 

Max.  total  unbalanced  pressure. 
Max.  total  pressure  per  sq.  in.  .  . 

P 
P 

7854 
100 

70,686 
100 

196.350 
100 

The  thickness  of  the  cylinders  of  these  engines,  according  to  the 
eleven  formulae,  ranges  for  engines  1  and  2  from  0.33  to  1.13  in.,  for 
3  and  4  from  0.99  to  2.00  in.,  and  for  5  and  6  from  1.56  to  3.00  in. 
The  averages  of  the  eleven  are,  for  1  and  2,  0.76  in.;  for  3  and  4,  1.48 
in.;  for  5  and  6,  2.26  in. 

The  average  corresponds  nearly  to  the  formula  t  =  0.00037  Dp  -}-  0.4 
in.  A  convenient  approximation  is  t  =  0.0004  Dp  -f  0.3  in.,  which  gives 
for 

Diameters 10         20         30         40         50         60  in. 

Thicknesses 0 . 70     1 . 10     1 . 50     1 . 90     2 . 30     2 . 70  in. 

The  last  formula  corresponds  to  a  tensile  strength  of  cast  iron  of 
12,500  lb.,  with  a  factor  of  safety  of  10  and  an  allowance  of  0.3  in.  for 
reboring. 

Thickness  of  Cylinder  and  Its  Connections  for  Marine  Engines. 

(Seaton.) — D  =  the  diam.  of  the  cylinder  in  inches;  p  =  load  on  the 
safety-valves  in  lb.  per  sq.  in. ;  /,  a  constant  multiplier,  =  thickness  of 
barrel  +  0.25  in. 


1022  THE  STEAM-ENGINE. 

Thickness  of  metal  of  cylinder  barrel  or  liner,  not  to  be  less  thai* 
PXD  +  3000  when  of  cast  iron.* 

Thickness  of  cylinder-barrel  =  p  X  D  -~  5000  +  O.G  in. 
Thickness  of  liner  =  1.1  X  / 

Thickness  of  liner  when  of  steel  =  p  X  D  -5-  0000  +  0.5  in. 
Thickness  of  metal  of  steam-ports     =  0.6    X  /. 
Thickness  of  metal  valve-box  sides    =  0.65  X  /. 
Thickness  of  metal  of  valve-box  covers  =  0.7    X  /. 

cylinder  bottom  =1.1    X  /,  if  single  thickness. 

=  0.65  X/.  if  double 
covers     =1.0    X/,  if  single 
=  0.6    X/,  if  double 
cylinder  flange  =1.4    x/. 

cover-flange  =1.3  X/. 
valve-box  flange  =  1.0  X/. 
door-flange  =0.9  X  /. 

face  over  ports     =1.2    X/. 

"          =  1.0    X/,  when  there  is  a  false- 

face. 
false-face  =0.8    X  /,  when  cast  iron. 

=  0.6    X  /,  when  steel  or  bronze. 

Cylinder-heads.  —  Applying  six  different  formulae  to  the  engines  of  10, 
30,  and  50  inches  diameter,  with  maximum  unbalanced  steam-pressure 
of  100  Ib.  per  sq.  in.,  we  have 

For  cylinder  10  in.  diam.,  0.35  to  1,15  in.;  for  30  in.  diam.,  0.90  to 
1.75  in.  ;  for  50-in.  diam.,  1.50  to  2.75  in.  The  averages  are  respectively 
0.65,  1.38,  and  2.10  in. 

The  average  is  expressed  by  the  formula  t  =  0.00036  Dp  -{-  0.31  inch. 

Web-stiffened  Cylinder-covers.  —  Seaton  objects  to  webs  for 
stiffening  cast-iron  cylinder-covers  as  a  source  of  danger.  The  strain  on 
one  web  is  one  of  tension,  and  if  there  should  be  a  nick  ©r  defect  in  the 
outer  edge  of  the  web  the  sudden  application  of  strain  is  apt  to  start 
a  crack.  He  recommends  that  high-pressure  cylinders  over  24  in.  and 
low-pressure  cylinders  over  40  in.  diam.  should  have  their  covers  cast 
hollow,  with  two  thicknesses  of  metal.  The  depth  of  the  cover  at  the 
middle  should  be  about  1/4  the  diam.  of  the  piston  for  pressures  of  80  Ib. 
and  upwards,  and  that  of  the  low-pressure  cylinder-cover  of  a  com- 
pound engine  equal  to  that  of  the  high-pressure  cylinder.  Another 
rule  is  to  make  the  depth  at  the  middle^not  less  than  1.3  times  the 
diameter  of  the  piston-rod.  In  the  British  Navy  the  cylinder-covers 
are  made  of  steel  castings,  3/4  to  1  1/4  in.  thick,  generally  cast  without 
webs,  stiffness  being  obtained  by  their  form,  which  is  often  a  series  of 
corrugations. 

Cylinder-head  Bolts.  —  Diameter  of  bolt-circle  for  cylinder-head  = 
diameter  of  cylinder  +  2  X  thickness  of  cylinder  +  2  X  diameter  of  bolts. 
The  bolts  should  not  be  more  than  6  in.  apart  (Whitham). 

Marks  gives  for  number  of  bolts  b  =  0.7854  Dip  -=-  5000  c,  in  which 
c  =  area  of  a  single  bolt,  p  =  boiler-pressure  in  Ib.  per  sq.  in.;  5000  Ib. 
is  taken  as  the  safe  strain  per  sq.  in.  on  the  nominal  area  of  the  bolt. 

Thurston  says:  Cylinder  flanges  are  made  a  little  thicker  than  the 
cylinder,  and  usually  of  equal  thickness  with  the  flanges  of  the  heads. 
Cylinder-bolts  should  be  so  closely  spaced  as  not  to  allow  springing  of  the 
flanges  and  leakage,  say,  4  to  5  times  the  thickness  of  the  flanges.  Their 
diameter  should  be  proportioned  for  a  maximum  stress  of  not  over  4000 
to  5000  Ib.  per  square  inch. 

If  D  =  diameter  of  cylinder,  p  =  maximum  steam-pressure,  b  = 
number  of  bolts,  s  =  size  or  diameter  of  each  bolt,  and.  5000  Ib.  be 
allowed  per  sq.  in.  of  actual  area  at  the  root  of  the  thread,  0.7854  D?p  = 
3927  &s2;  whence  652  =  0.0002  D*p. 

b  =  0.0002  5^;  s  =  0.01414  DA  [?.     For  the  three  engines  we  have: 


*  When  made  of  exceedingly  good  material,  at  least  twice  melted, 
the  thickness  may  be  0.8  of  that  given  by  the  above  rules. 


DIMENSIONS  OF  PARTS   OF  ENGINES. 


1023 


Diameter  of  cylinder,  inches 10  30        50 

Diameter  of  bolt-circle,  approx 13  35         57,5 

Circumference  of  circle,  approx 40.8  110       180 

Minimum  no.  of  bolts,  circ. -T- 6 7  18        30 

Diam  of  bolts,  s  =  0.01414  D+f£ 3/4  in.       1 . 00     1 . 29 


The  diameter  of  bolt  for  the  10-inch  cylinder  is  0.54  in.  by  the  formula, 
but  3/4  inch  is  as  small  as  should  be  taken,  on  account  of  possible  over- 
strain by  the  wrench  in  screwing  up  the  nut. 

The  Piston.  Details  of  Construction  of  Ordinary  Pistons.  (Seaton.) 
— Let  D  be  the  diameter  of  the  piston  in  inches,  p  the  effective  pressure 
per  square  inch  on  it,  x  a  constant  multiplier,  found  as  follows: 

x  =  (D  +  50)  X  VP~+  1. 
The  thickness  of  front  of  piston  near  the  b9ss    =  0.2    X  x. 

rim 
back 

boss  around  the  rod 
flange  inside  packing-ring 

at  edge 
packing-ring 
junk- ring  at  edge 

inside  packing-ring 
at  bolt-holes 

metal  around  piston  edge 
breadth  of  packing-ring 
depth  of  piston  at  center 
lap  of  junk-ring  on  the  piston 
space  between  piston  body  and  packing-ring  =  0.3 
diameter  of  junk-ring  bolts  =0.1 


=  0.17  X  x. 
=  0.18  X  x. 
=  0.3  X  x. 
=  0.23  X  x. 
=  0.25  X  x. 
=  0.15  X  x. 

•-  0.23  X  x. 
=  0.21  X  x. 

••  0.35  X  X. 

»  0.25  X*. 
=  0.63  X  x. 
=  1.4  X  x. 
=  0.45  X  x. 
X  x. 
X  x  +0.25  in. 


pitch  of  junk-ring  bolts  =  10  diameters. 

number  of  webs  in  the  piston  =  (D  -f  20)  -5-  12. 

thickness  of  webs  in  the  piston  =  0.18  X  x. 

Marks  gives  the  approximate  rule:   Thickness  of  pist9n-head 
m  which  I  =  length  of  stroke,  and  D  =  diameter  of  cylinder  in  inches. 
Whitham  says:  In  a  horizontal  engine  the  rings  support  the  piston,  or  at 
least  a  part  of  it,  under  ordinary  conditions.     The  pressure  due  to  the 
weight  of  the  piston  upon  an  area  equal  to  0.7  the  diameter  of  the 
cylinder  X  breadth  of  ring-face,  should  never  exceed  200  Ib.  per  sq.  in. 
He  also  gives  a  formula  much  used  in  this  country:    Breadth  of  ring- 
face  =  0.15  X  diameter  of  cylinder. 
For  our  engines  we  have  diameter  =  .......       10          30          50 

Thickness  of  piston-head. 
Marks,  'i/lD;  long  stroke  ............     3.31       5.48         7.00 

Marks,  'f/lD';  short  stroke  ............     3  .  94       6.51 

Seaton,  depth  at  center  =\Ax  ........      4.20       9.80 

Seaton,  breadth  of  ring  =  0.63  x  .......      1  .  89       4  .  41 

Whitham,  breadth  of  ring  =  0.  15  D  ____      1  .  50       4  .  50 


8  .32 
15.40 

6  .  93 

7  .  50 


Diameter  of  Piston  Packing-rings.  —  These  are  generally  turned, 
before  they  are  cut,  about  1/4  inch  diameter  larger  than  the  cylinder, 
for  cylinders  up  to  20  inches  diameter,  and  then  enough  is  cut  out  of  the 
rings  to  spring  them  to  the  diameter  of  the  cylinder.  For  larger  -cylin- 
ders the  rings  are  turned  proportionately  larger.  Seaton  recommends 
an  excess  of  1  %.  of  the  diameter  of  the  cylinder. 

A  theoretical  paper  on  Piston  Packing  Rings  of  Modern  Steam  En- 
gines by  O.  C.  Reymann  will  be  found  in  Jour.  Frank.  Inst.,  Aug.,  1897. 

Cross-section  of  the  Rings.  —  The  thickness  is  commonly  made 
1/30  of  the  diam.  of  cyl.  +  i/g  inch,  and  the  width  =  thickness  +  i/ginch. 
For  an  eccentric  ring  the  mean  thickness  may  be  the  same  as  for  a  ring 
of  uniform  thickness,  and  the  minimum  thickness  =  2/3  the  maximum. 

A  circular  issued  by  J.  H.  Dunbar,  manufacturer  of  packing-rings, 
Youngstown,  Ohio,  says:  Unless  otherwise  ordered,  the  thickness  of 
rings  will  be  made  equal  to  0.03  X  their,  diameter.  This  thickness  has 
been  found  to  be  satisfactory  in  practice.  It  admits  of  the  ring  being 


1024  THE  STEAM-ENGINE. 

made  about  3/i6  in.  to  the  foot  larger  than  the  cylinder,  and  has,  when 
new,  a  tension  of  about  two  pounds  per  inch  of  circumference,  which  is 
ample  to  prevent  leakage  if  the  surface  of  the  ring  and  cylinder  are 
smooth. 

As  regards  the  width  of  rings,  authorities  "scatter"  from  very  narrow 
to  very  wide,  the  latter  being  fully  ten  times  the  former.  For  instance, 
Unwin  gives  W  =  0.014  d  +  0.08.  Whitham's  formula  is  W  =  0.15  d. 
In  both  formulae  W  is  the  width  of  the  ring  in  inches,  and  d  the  diameter 
of  the  cylinder  in  inches.  Un win's  formula  makes  the  width  of  a  20-in, 
ring  W  =  20  X  0.014  -f  0.08  =  0.36  in.,  while  Whitham's  is  20  X  0.15  = 
3  in.  for  the  same  diameter  of  ring.  There  is  much  less  difference  in  the 
practice  of  engine-builders  in  this  respect,  but  there  is  still  room  for  a 
standard  width  of  ring.  It  is  believed  that  for  cylinders  over  16  in. 
diameter  8/4  in.  is  a  popular  and  practical  width,  and  1/2  in.  for  cylinders 
of  that  size  and  under. 

Fit  of  Piston-rod  into  Piston.  (Seaton.) — The  most  convenient 
and  reliable  practice  is  to  turn  the  piston-rod  end  with  a  shoulder  of  i/ie 
inch  for  small  engines,  and  i/s  inch  for  large  ones,  make  the  taper  3  in.  to 
the  foot  until  the  section  of  the  rod  is  three-fourths  of  that  of  the  body, 
then  turn  the  remaining  part  parallel ;  the  rod  should  then  fit  into  the 
piston  so  as  to  leave  i/g  in.  between  it  and  the  shoulder  for  large  pistons 
and  1/16  in.  for  small.  The  shoulder  prevents  the  rod  from  splitting  the 
piston,  and  allows  of  the  rod  being  turned  true  after  long  wear  without 
encroaching  on  the  taper. 

The  piston  is  secured  to  the  rod  by  a  nut,  and  the  size  of  the  rod  should 
be  such  that  the  strain  on  the  section  at  the  bottom  of  the  thread  does 
not  exceed  5500  Ib.  per  sq.  in.  for  iron,  7000  Ib.  for  steel.  The  depth 
of  this  nut  need  not  exceed  the  diameter  which  would  be  found  by  allow- 
ing these  strains.  The  nut  should  be  locked  to  prevent  its  working 
loose. 

Diameter  of  Piston-rods. — Taking  d  =  diam.  of  piston-rod,  D  = 
diam.  of  piston,  I  =  length  of  stroke,  p  =  maximum  unbalanced  pres- 
sure, Ib.  per_sq.  in.,  Unwin  gives,  for  iron  rods,  d  =  0.0167  D\/p;  steel, 
0.0144  D^/p.  Marks  gives:  (1)  d  =  0.0179  Z>Vp"for  iron;  (2)  0.0105 
ZVp  for  steel;  and  (3)  d  =  0.0390  ^DU^p  for  iron;  (4)  0.0352  «ffDH*p 
for  steel.  Deduce  the  diameter  of  the  rod  by  (1)  or  (2)  and  if  this 
diameter  is  less  than  1/12?  then  use  (3)  or  (4).  Applying  these  four 
formulae  to  the  six  engines  and  taking  the  average  results,  we  have  the 
following : 

Diameter  of  Piston-rods. 


Diameter  of  Cylinder,  inches  

1 

0 

3 

0 

5 

0 

Stroke,  inches 

12 

24 

30 

60 

48 

96 

Diam.  of  rod,  average  for  iron  
"             "     average  for  steel  

1.49 
1.33 

1.82 
1.59 

4.30 
3.83 

5.26 
4.52 

7.11 
6.33 

8.74 
7.46 

An  empirical  formula  which  gives  results  approximating  the  above 
averages  is  d"  =  c\/Dlp,  the  values  of  c  being  for  short  stroke  engines, 
iron,  0.0145;  steel,  0.0129;  and  for  long  stroke  engines,  iron,  0.0126, 
steel,  0.0108. 

The  calculated  results  for  this  formula,  for  the  six  engines,  are,  re- 
spectively: 

Iron 1.59     1.95     4.35     5.36     7.11     8.73 

Steel 1.31     1.67     3.87     4.58     6.32     7.48 

In  considering  an  expansive  engine,  p,  the  effective  pressure,  should  be 
taken  as  the  absolute  working  pressure,  or  15  Ib.  above  that  to  which 
the  boiler  safety-valve  is  loaded ;  for  a  compound  engine  the  value  of  p 
for  the  high-pressure  piston  should  be  taken  as  the  absolute  pressure, 
less  15  Ib.,  or  the  same  as  the  load  on  the  safety-valve;  for  the  medium- 
pressure  the  load  may  be  taken  as  that  due  to  half  the  absolute  boiler- 
pressure;  and  for  the  low-pressure  cylinder  the  pressure  to  which  the 
escape- valve  is  loaded  +  15  Ib.,  or  the  maximum  absolute  pressure 
which  can  be  got  in  the  receiver,  or  about  25  Ib.  It  is  an  advantage  to 
make  all  the  rods  of  a  compound  engine  alike,  and  this  is  now  the  rule. 

Piston-rod  Guides.— The  thrust  on  the  guide,  when  the  connecting- 


DIMENSIONS   OF   PARTS   OF   ENGINES.  1025 

rod  is  at  its  maximum  angle  with  the  line  of  the  piston-rod,  is  found  from 
the  formula:  Thrust  =  total  load  on  piston  X  tangent  of  maximum  angle 
of  connecting-rod  =  p  tan  0.  '  This  angle,  9,  is  the  angle  whose  sine  = 
half  stroke  of  piston  -~  length  of  connecting-rod. 

Ratio  of  length  of  connecting-rod  to  stroke  .  .  2  21/2  3 

Maximum  angle  of  connecting-rod  with  line 

of  piston-rod  ..........................  14°  29'  11°  33'  9°  36' 

Tangent  of  the  angle  .......................      0.258  0.204  0.169 

Secant  of  the  angle  ..................  ......      1.0327     1.0206     1  .014 

Thurston  says:  The  rubbing  surfaces  of  guides  are  so  proportioned 
that  if  V  be  their  relative  velocity  in  feet  per  minute,  and  p  be  the  in- 
tensity of  pressure  on  the  guide  hi  Ib.  per  sq.  in.,  pV  <  60,000  and 
pV>  40,000. 

The  lower  is  the  safer  limit;  but  for  marine  and  stationary  engines  it 
is  allowable  to  take  p  =  60,000  -s-  V.  According  to  Rankine,  for  loco- 

motives, p  =    •-TTo/     where  p  is  the  pressure  in  Ib.  per  sq.  in.  and  V 


the  velocity  of  rubbing  in  feet  per  minute.  This  includes  the  sum  of 
all  pressures  forcing  the  two  rubbing  surfaces  together. 

Some  British  builders  of  portable  engines  restrict  the  pressure  between 
the  guides  and  cross-heads  to  less  than  40,  sometimes  35  Ib.  per  sq.  in. 

For  a  mean  velocity  of  600  feet  per  minute,  Prof.  Thurston's  formulae 
give,  p  <  100,  p  >  66.7;  Rankine's  gives  p  =  72.2  Ib.  per  sq.  in. 

Whitham  gives, 

A  =  area  of  slides  in  square  inches  =  -  -—==.  =  —  —        P- 

pQ  \/n2  -  1      pQ  Vn2  -  I 

in  which  P  =  total  unbalanced  pressure,  pi  =  pressure  per  square  inch 
on  piston,  d  =  diameter  of  cylinder,  p0  =  pressure  allowable  per  square 
inch  on  slides,  and  n  =  length  of  connecting-rod  -j-  length  of  crank. 
This  is  equivalent  to  the  formula,  A  =  P  tan  6  ~  po.  For  n  =  5,  p\  = 
100  and  pa  =  80,  A  =  0.2004  d2.  For  the  three  engines  10,  30,  and  50  in. 
diam.,  this  would  give  for  area  of  slides,  A  =  20,  180,  and  500  sq.  in., 
respectively.  Whitham  says:  The  normal  pressure  on  the  slide  may  be 
as  high  as  500  Ib.  per  sq.  in.,  but  this  is  when  there  is  good  lubrication 
and  freedom  from  dust.  Stationary  and  marine  engines  are  usually 
designed  to  carry  100  Ib.  per  sq.  in.,  and  the  area  in  this  case  is  reduced 
from  50%  to  60%  by  grooves.  In  locomotive  engines  the  pressure 
ranges  from  40  to  50  Ib.  per  sq.  in.  of  slide,  on  account  of  the  inaccessi- 
bility of  the  slide,  dirt,  cinder,  etc. 

The  Connecting-rod.  Ratio  of  length  of  connecting-rod  to  length  of 
stroke.  —  Experience  has  led  generally  to  the  ratio  of  2  or  2  1/2  to  1,  the 
latter  giving  a  long  and  easy-working  rod,  the  former  a  rather  short,  but 
yet  a  manageable  one  (Thurston)  .  Whitham  gives  the  ratio  of  from  2 
to  4  1/2  and  Marks  from  2  tcL.4. 

Dimensions  of  the  Connecting-rod.  —  The  calculation  of  the  diameter 
of  a  connecting-rod  on  a  theoretical  basis,  considering  it  as  a  strut  sub- 
ject to  both  compressive  and  bending  stresses,  and  also  to  stress  due  to 
its  inertia,  in  high-speed  engines,  is  quite  complicated.  See  Whitham, 
Steam-engine  Design,  p.  217;  Thurston,  Manual  of  S.  E.,  p.  100. 

Applying  seven  formulae  given  by  different  authorities  to  the  six 
engines  the  average  diameters  (at  the  middle  of  the  rod)  are  given 
below  : 

Diameter  of  Connecting-rods. 


Diameter  of  Cylinder,  inches 

1 

0 

3 

0 

5 

0 

Stroke,  inches 

12 

24 

30 

60 

48 

96 

Length  of  connecting-rod  1  

30 

60 

75 

150 

120 

240 

Diameter  of  rod,  inches  

2.24 

2.26 

6.38 

6.27 

10.52 

10.26 

The  average  figures  show  but  little  difference  in  diameter  between 
long-  and  short-stroke  engines;  this  is  what  might  be  expected,  for  while 
the  connecting-rod,  considered  simply  as  a  column,  would  require  an 
Increase  of  diameter  for  an  increase  of  length,  the  load  remaining  the 


1026  THE   STEAM-ENGINE. 

same,  yet  in  an  engine  generally  the  shorter  the  connecting-rod  the 
greater  the  number  of  revolutions,  and  consequently  the  greater  the 
strains  due  to  inertia.  The  influences  tending  to  increase  the  diameter 
therefore  tend  to  balance  each  other,  and  to  render  the  diameter  to 
some  extent  independent  of  the  length.  The_average  figures  correspond 
nearly  to  the  simple  formula  d  =  0.021  D\/p.  The  diameters  of  rod  for 
the  three  diameters  of  engine  by  this  formula  are,  respectively,  2.10, 
6.30,  and  10.50  in.  Since  the  total  pressure  on_the  piston  P  =  0.7854 
D*p,  the  formula  is  equivalent  to  d  =  0.0237  \/~P. 

Seaton  and  Sennett  give  the  diameter  at  the  necks  of  a  connecting- 
rod  =  0.9  the  dianv  at  the  middle.  Whitham  gives  it  as  1.0  to  1.1  the 
diam.  of  the  piston-rod. 

Connecting-rod  Ends. — For  a  connecting-rod  end  of  the  marine 
type,  where  the  end  is  secured  with  two  bolts,  each  bolt  should  be  pro- 
portioned for  a  safe  tensile  strength  equal  to  two-thirds  of  the  maximum 
pull  or  thrust  in  the  connecting-rod. 

The  cap  is  to  be  proportioned  as  a  beam  loaded  with  the  maximum 
pull  of  the  connecting-rod,  and  supported  at  both  ends.  The  calcula- 
tion should  be  made  for  rigidity  as  well  as  strength,  allowing  a  maximum 
deflection  of  Vioo  inch.  For  a  strap^and-key  connecting-rod  end  the 
strap  is  designed  for  tensile  strength,  considering  that  two-thirds  of  the 
|)ull  on  the  connecting-rod  may  come  on  one  arm.  At  the  point  where 
the  metal  is  slotted  for  the  key  and  gib,  the  straps  must  be  thickened  to 
make  the  cross-section  equal  to  that  of  the  remainder  of  the  strap.  Be- 
tween the  end  of  the  strap  and  the  slot  the  strap  is  liable  to  fail  in  double 
shear,  and  sufficient  metal  must  be  provided  at  the  end  to  prevent  such 
failure. 

The  breadth  of  the  key  is  generally  one-fourth  of  the  width  of  the 
strap,  and  the  length,  parallel  to  the  strap,  should  be  such  that  the  cross- 
section  will  have  a  shearing  strength  equal  to  the  tensile  strength  of  the 
section  of  the  strap.  The  taper  of  the  key  is  generally  about  5/8  inch 
to  the  foot. 

Tapered  Connecting-rods. — In  modern  high-speed  engines  it  is  cus- 
tomary to  make  the  connecting-rods  of  rectangular  instead  of  circular 
section,  the  sides  being  parallel,  and  the  depth  increasing  regularly  from 
the  cross-head  end  to  the  crank-pin  end.  According  to  Grashof,  the 
bending  action  on  the  rod  due  to  its  inertia  is  greatest  at  6/1()  the  length 
from  the  cross-head  end,  and,  according  to  this  theory,  that  is  the  point 
at  which  the  section  should  be  greatest,  although  in  practice  the  section 
is  made  greatest  at  the  crank-pin  end. 

Professor  Thurston  furnished  the  author  with  the  following  rule  for 
tapered  connecting-rods  of  rectangular  section:  Take  the  section  as  com- 
puted by  the  formula  d"  =  0.1  A/ 'DL\/~p~+  3/4  for  a  circular  section, 
and  for  a  rod  4/3  the  actual  length,  placing  the  computed  section  at 
2/3  the  length  from  the  small  end,  and  carrying  the  taper  straight 
through  this  fixed  section  to  the  large  end.  This  brings  the  computed 
section  at  the  surge  point  and  makes  it  heavier  than  the  rod  for  which 
a  tapered  form  is  not  required. 

Taking  the  above  formula,  multiplying  L  by  4/3.  and  changing  it  to  I 

in  inches,  it  becomes  d  =  1/30  V-DJ  \/P~+  3/4  in.  Taking  a  rectangular 
section  of  the  same  area  as  the  round  section  whose  diameter  is  rf, 
and  making  the  depth  of  the  section  h  =  twice  the  thickness  t,  we  have 

0.7854  d*  =  hi  =  2  &,  whence  t  =  0.627;  d  =  0.0209  V  Dl\/l)  +  0.47in., 
which  is  the  formula  for  the  thickness  or  distance  between  the  parallel 
sides  of  the  rod.  Making  the  depth  at  the  cross-head  end  =  1.5  t,  and 
at  2/3  the  length  =  2  t,  the  equivalent  depth  at  the  crank  end  is  2.25  t. 
Applying  the  formula  to  the  short-stroke  engines  of  our  examples,  we  have 


Diameter  of  cylinder,  inches                  

10 

30 

50 

Stroke,  inches                        .            

12 

30 

48 

Length  of  connecting-rod                                

30 

75 

120 

Thickness  t  -  0  0209  "V  '  Dl  VP+  0  47  =    

1.61 

3.60 

5.59 

2.42 

5.41 

8.39 

Depth  at  crank  end,  21/42  

3.62 

8.11 

12.58 

DIMENSIONS  OF  PARTS  OF  ENGINES. 


1027 


The  thicknesses  t,  found  by  the  formula  t  =  0.0209  V  Dl\/P  +  0.47, 
agree  closely  with  the  more  simple  formula  t  =  0.01  D\/~p  +  0.60  in.,  the 
thicknesses  calculated  by  this  formula  being  respectively  1.6,  3.6,  and 
5.6  in. 

The  Crank-Pin. — A  crank-pin  should  be  designed  (1)  to  avoid  heat- 
ing, (2)  for  strength,  (3)  for  rigidity.  The  heating  of  a  crank-pin 
depends  on  the  pressure  on  its  rubbing  surface,  and  on  the  coefficient 
of  friction,  which  latter  varies  greatly,  according  to  tile  effectiveness  of 
the  lubrication.  It  also  depends  upon  the  facility  with  which  the  heat 
produced  may  be  carried  away :  thus  it  appears  that  locomotive  crank- 
pins  may  be  prevented  to  some  degree  from  overheating  by  the  cooling 
action  of  the  air  through  which  they  pass  at  a  high  speed. 

Marks  states  as  a  general  law,  within  reasonable  limits  as  to  pressure 
and  speed  of  rubbing,  the  longer  a  bearing  is  made,  for  a  given  pressure 
and  number  of  revolutions,  the  cooler  it  will  work;  and  its  diameter  has 
no  effect  upon  its  heating. 

Whitham  recommends  for  pressure  per  square  inch  of  projected  area, 
for  naval  engines  500  pounds,  for  merchant  marine  engines  400  pounds, 
for  paddle-wheel  engines  800  to  900  pounds. 

Thurston  says  the  pressure  on  a  steel  crank-pin  should,  in  the  steam- 
engine,  never  exceed  1000  or  1200  pounds  per  square  inch.     He  gives 
the  formula  for  length  of  a  steel  pin,  in  inches. 
I  =  PR  +  600,000, 

in  which  P  and  R  are  the  mean  total  load  on  the  pin  in  pounds,  and  the 
number  of  revolutions  per  minute.  For  locomotives,  the  divisor  may  be 
taken  as  500,000.  Pins  so  proportioned,  if  well  made  and  well  lubri- 
cated, may  always  be  depended  upon  to  run  cool;  if  not  well  formed, 
perfectly  cylindrical,  well  finished,  and  kept  well  oiled,  no  crank-pin 
can  be  relied  upon.  It  is  assumed  above  that  good  bronze  or  white- 
metal  bearings  are  used. 

By  calculating  lengths  of  iron  crank-pins  for  the  engines  10,  30,  and 
50  inches  diametor,  long  and  short  stroke,  by  the  formulae  given  by  dif- 
ferent writers,  it  is  found  that  there  is  a  great  difference  in  the  results, 
so  that  one  formula  in  certain  cases  gives  a  length  three  times  as  great 
as  another. 

The  average  of  the  calculated  lengths  of  iron  crank-pins  for  the 
several  cases  by  five  formulae  are  given  in  the  table  below,  together 
with  the  calculated  lengths  by  two  formulee  for  steel. 

Length  of  Crank-pins. 


Diameter  of  cylinder    ...»              D 

10 

250 
50 
7,854 
42 
3,299 
2.72 

W2 

'§ 

7,854 
42 
3,299 
1.36 

30 

% 

450 
70,686 
32.3 
22,832 
9.86 

30 

65 

450 
70,686 
32.3 
22,832 
4.93 

50 
4 
90 
1,250 
196,350 
30 
58,905 
17.12 

50 
8 
45 

1.250 
196,350 
30 
58,905 
8.56 

Stroke                                                L  (ft  ) 

Revolutions  per  minute     ...              R 

Horse-power  .s  I.H.P. 

Maximum  pressure        Ibs. 

Mean  pressure                                           P. 

Length  of  crank-pin,  average  for  iron.  . 

Unwin,  best  steel,  I  =0.1  I.H.P.  -=-r  
Thurston,  steel,  I  =  P  R  +  600,000  

0.83 
1.37 

0.42 
0.69 

3.0 
4.95 

1.5 

2.47 

5.21 

8.84 

2.61 

4.42 

The  calculated  lengths  for  the  long-stroke  engines  are  too  low  to  pre- 
vent excessive  pressures.  See  "Pressures  on  the  Crank-pins,"  below. 

The  Strength  of  the  Crank-pin  is  determined  substantially  as  is  that 
of  the  crank.  In  overhung  cranks  the  load  is  usually  assumed  as 
carried  at  the  middle  of  the  pin,  and,  equating  its  moment  with  that  of 
the  resistance  of  the  pin, 


l/2  PI 


and   d= 


5.1  PI 


in  which  d  •• 


_     ••  diameter  of  pin  in  inches,  P  —  maximum  load  on  the 

piston,  t  =  the  maximum  allowable  stress  on  a  square  inch  of  the  metal. 
For  iron  it  may  be  taken  at  9000  Ibs,  For  steel  the  diameters  found  by 
this  formula  may  be  reduced  10%.  (Thurston.) 


1028 


THE   STEAM-ENGINE. 


Unwin  gives  the  same  formula  in  another  form,  viz.: 


the  last  form  to  be  used  when  the  ratio  of  length  to  diameter  is  assumed, 
For  wrought  iron,  t  =  6000  to  9000  Ibs.  per  sq.  in., 

-\/5.1/£="o.0947  to  0.0827;     ^/57l7i  =  0.0291  to  0.0238. 
For  steel,  t  =  9000  to  13,000  Ibs.  per  sq.  in., 

<y5JL/i  =  0,0827  to  0.0723:     V5.1#  =  0.0238  to  0.0194, 
Marks,  calculating  the  diameter  for  rigidity,  gives 
d  =  0.066 


=  0.945 


•+•  LN; 


p  =  maximum  steam-pressure  in  pounds  per  square  inch,  D  =  diameter 
of  cylinder  in  inches,  L  =  length  of  stroke  in  feet,  N  =  number  of  single 
strokes  per  minute.  He  says  there  is  no  need  of  an  investigation  of  the 
strength  of  a  crank-pin,  as  the  condition  of  rigidity  gives  a  great  excess 
of  strength. 

Marks's  formula  is  based  upon  the  assumption  that  the  whole  load 
may  be  concentrated  at  the  outer  end,  and  cause  a  deflection  of  0.01  in. 
at  that  point.  It  is  serviceable,  he  says,  for  steel  and  for  wrought  iron 
alike. 

Using  t.he  average  lengths  of  the  crank-pins  already  found,  we  have 
the  following  for  our  six  engines  : 


Diameter  of  Crank-pins. 


10 

10 

30 

30 

50 

50 

Stroke  ft..  .                               

J 

2 

21/0 

5 

4 

8 

2.72 

1.36 

986 

4.93 

17.12 

fi  (>6 

2  29 

1  82 

7  34 

5  82 

12  40 

9  84 

Marks,  d  =  0.066  ^p^F2  

1.39 

0.85 

6.44 

3.78 

12.41 

7.39 

Pressures  on  the  Crank-pins.  — -  If  we  take  the  mean  pressure  upon 
the  crank-pin  =  mean  pressure  on  piston,  neglecting  the  effect  of  the 
varying  angle  of  the  connecting-rod,  we  have  the  following,  using  the 
average  lengths  already  found,  and  the  diameters  according  to  Unwin 
and  Marks: 


Engine  No                  

1 

2 

3 

4 

5 

6 

Diameter  of  cylinder  inches            .... 

10 

10 

30 

30 

50" 

50 

Stroke,  feet  

1 

2 

2V2 

5 

4 

8 

3,299 

3,299 

22,832 

22,832 

58,905 

58,905 

Projected  area  of  pin,  Unwin  

6  23 

2  36 

72.4 

28.7 

2!2  3 

84  2 

Projected  area  of  pin  Marks 

3  78 

1   16 

63  5 

18  6 

212  5 

63  3 

Pressure  per  square  inch,  Unwin  
Pressure  per  square  inch,  Marks  

530 
873 

1,398 
2,845 

315 
360 

7% 
1,228 

277 
277 

700 
930 

The  results  show  that  the  application  of  the  formulae  for  length  and 
diameter  of  crank-pins  give  quite  low  pressures  per  square  inch  of  pro- 
jected area  for  the  short-stroke  high-speed  engines  of  the  larger  sizes,  but 
too  high  pressures  for  all  the  other  engines.  It  is  therefore  evident  that 
after  calculating  the  dimensions  of  a  crank-pin  according  to  the  formulae 
given,  the  results  should  be  modified,  if  necessary,  to  bring  the  pressure 
per  square  inch  down  to  a  reasonable  figure. 

In  order  to  bring  the  pressures  down  to  500  pounds  per  square  inch, 
we  divide  the  mean  pressures  by  500  to  obtain  the  projected  area,  or 


DIMENSIONS   OF  PARTS  OF  ENGINES.  1029 

product  of  length  by  diameter.  Making  I  =  1.5  d  for  engines  Nos.  1, 
2,  4,  and  6,  the  revised  table  for  the  six  engines  is  as  follows: 

Engine  No 1  2  3  4  5  6 

Length  of  crank-pin,  inches. .  3.15  3.15  9.86  8.37  17.12  13.30 
Diameter  of  crank-pin 2 . 10  2.10  7 . 34  5 . 58  12  ..40  8 . 87 

Crosshead-pin  or  Wrist-pin. — Seaton  says  the  area,  calculated  by 
multiplying  the  diameter  of  the  journal  by  its  length,  should  be  such 
that  the  pressure  does  not  exceed  1200  Ib.  per  sq.  in.,  taking  the  maxi- 
mum load  on  the  piston  as  the  total  pressure  on  the  pin. 

For  small  engines  with  the  gudgeon  shrunk  into  the  jaws  of  the  con- 
necting-rod, and  working  in  brasses  fitted  into  a  recess  in  the  piston-rod 
end  and  secured  by  a  wrought-iron  cap  and  two  bolts,  Seaton  gives: 

Diameter  of  gudgeon  =  1 . 25  X  diam.  cf  piston-rod, 

Length  of  gudgeon  =  1 . 4  X  diam.  of  piston-rod. 

If  the  pressure  on  the  section,  as  calculated  by  multiplying  length  by 
diameter,  exceeds  1200  Ibs.  per  sq.  in.,  this  length  should  be  increased. 

J.  B.  Stanwood,  in  his  "Ready  Reference"  book,  gives  for  length  of 
crosshead-pin  0.25  to  0.3  diam.  of  piston,  and  diam.  =0.18  to  0.2 
diam.  of  piston.  Since  he  gives  for  diam.  of  piston-rod  0.14  to  0.17 
diam.  of  piston,  his  dimensions  for  diameter  and  length  of  crosshead-pin 
are  about  1.25  and  1.8  diam.  of  piston-rod  respectively.  Taking  the 
maximum  allowable  pressure  at  1200  Ibs.  per  sq.  in.  and  making  the 
length  of  the  crosshead-pin  =  4/3  of  its  diameter,  we  have  d=  v 'p  ~-  40, 1  = 
Vp-*.  30,  in  which  P=  maximum  total  load  on  piston  in  Ibs.,  d  =  diam. 
and  1=  length  of  pin  in  inches.  For  the  engines  of  our  example  we  haves 

Diameter  of  piston,  inches 10  30  50 

Maximum  load  on  piston,  Ibs 7854  70,686          196,350 

Diameter  of  crosshead-pin,  inches. ....       2. 22  6 . 65  11 . 08 

Length  of  crosshead-pin,  inches -     2.96  8.86  14.77 

Stanwood's  rule  gives  diameter,  ins. ...  1.8  to  2  5 . 4  t  :>  6  9.0  to  10 
Stanwood's  rule  gives  length,  inches. . .  2.5  to  3  7.5  to  9  12.5  to  15 
Stanwood's  largest  dimensions  give 

pressure  per  sq.  in.,  Ibs 1309  1329  1309 

These  pressures  are  greater  than  the  maximum  allowed  by  Seaton. 

The  Crank-arm.  —  The  crank-arm  is  to  be  treated  as  a  lever,  so  that 
If  ais  the  thickness  in  adirection  parallel  to  the  shaft-axis  and  b  its  breadth 
at  a  section  x  inches  from  the  crank-pin  center,  then,  bending  moment 
M  at  that  section  =  Px,  P  being  the  thrust  of  the  connecting-rod,  and 
/  the  safe  strain  per  square  inchr 


1030 


THE  STEAM-ENGINE. 


The  crank-eye  or  boss  into  which  the  pin  is  fitted  should  bear  the  same 
relation  to  the  pin  that  the  bo»s  does  to  the  shaft. 

The  diameter  of  the  shaft-end  onto  which  th^  crank  is  fitted  should 
be  1.1  X  diameter  of  shaft. 

Tnurston  says:  Tne  empirical  proportions  adopted  by  builders  will 
commonly  be  found  to  tali  well  within  tne  calculated  safe  margin. 
Tne.se  proportions  are,  from  the  practice  of  successful  designers,  about 
as  follows: 

The  hub  is  1.75  to  1.8  times  the  least  diameter  of  that  part  of  the 
shaft  carrying  full  load;  the  eye  is  2.0  to  2.25  tne  diameter  of  the  inserted 
portion  of  tne  pin  and  their  depths  are,  for  the  hub,  1.0  to  1.2  the 
diameter  of  snaft,  anc*  for  tne  eye,  1.25  to  1.5  the  diameter  of  pin.  The 
web  is  made  vj.7  to  0.75  the  widtn  of  the  adjacent  hub  or  eye,  and  is 
given  a  depth  of  0.5  to  0.6  that  of  the  adjacent  hub  or  eye. 

Tne  cranK-shaft  is  usually  enlarged  at  the  seat  of  the  crank  to  about 
1.1  its  diameter  at  the  journal.  The  size  should  be  nicely  adjusted  to 
allow  for  the  shrinkage  or  forcing  on  of  the  crank.  A  difference  of 
diameter  of  0.2  %  will  usually  suffice. 

Tne  formulae  given  by  different  writers  for  crank-arms  practically 
agree,  since  they  all  consider  the  crank  as  a  beam  loaded  at  one  end  and 
fixed  at  the  other.  The  relation  of  breadth  to  thickness  may  vary 
according  to  the  taste  of  the  designer.  Calculated  dimensions  for  our 
six  engines  are  as  follows: 

Dimensions  of  Crank-arms. 


Diam  of  cylinder  ins. 

10 

10 

30 

30 

50 

50 

Stroke  S  ins      

12 

24 

30 

60 

48 

96 

Max.    pressure    on     pin    P 
(approx  )    Ibs 

7854 

7854 

70,686 

70,686 

196,350 

196,350 

Diam  crank-pin  d     

2.10 

2.10 

7.34 

5.58 

12.40 

8.87 

Dv^ff   J-T\/             '    D 

(a'=  4.69,  5.  09  and  5.  22).... 
Length  of  boss,  0.8  D  
Thickness  of  boss,  0.4  D  
Diam.  of  boss,  1.8  D  
Length  crank-pin  eye,  0.8  d 
Thickness  of  crank-pin  eye, 
0  4d         

2.74 

2.19 
1.10 
4.93 
1.76 

0.88 

3.46 

2.77 
1.39 
6,23 
1.76 

0.88 

7.70 

6  16 
3.08 
13.86 
5.87 

2.94 

9.70 

7.76 
3.88 
17.46 
4.46 

2.23 

12.55 

10.04 
5.02 
22.59 
9.92 

4.46 

15.82 

12.65 
6.32 
28.47 
7.10 

3.55 

Max.   mom.  T  at  distance 
V2*SrV2£>  from  center  of 

37  149 

80  661 

• 
788  149 

1  848  439 

3  479,322 

7,871,671 

Thickness  of  crank-arm  a  = 
0  75  D                      

2.05 

2  60 

5.78 

7.28 

9.41 

11.87 

Greatest  breadth, 

b  =  V6  T  •*•  9000  a 
Min.  mom.  TO  at  distance 
d  from  center  of  pin=  Pd. 
Least  breadth, 

3.48 
16,493 

4.55 
16,493 

9.54 

528,835 

13.0 
394,428 

15.7 
2,434,740 

21.0 
1,741,625 

&1=  V6  T0  +  9000  a 

2.32 

2.06 

7.81 

6.01 

13.13 

9.89 

The    Shaft.  —  Twisting   Resistance.  —  From   the   general   formula 
for  torsion,  we  have:   T  =  -^  d*S  =  0.19635  d?S,  whence  d  =  ^I^-LT^ 

in  which  T  =  torsional  moment  in  inch-pounds,  d  =  diameter  in  inches, 
and  ,S  =  the  shearing  resistance  of  the  material,  Ib.  per  sq.  in. 

If  a  constant  force  P  were  applied  to  the  crank-pin  tangentially  to  its 

path,  the  work  done  in  foot-pounds  per  minute  would  be 

P  X  L  X  2rr  X  R  +  12  =  33,000  X  I.H.P., 

in  which  L  =  length  of  crank  in  inches,  and  R  =  revs,  per  min.,  and  the 

mean  twisting  moment  T  =  l.H.P.  -*-  H  X  63,025.     Therefore 


T  -T-  S  =    ^321,427  l.H.P.  -*•  ^^'. 


DIMENSIONS   OF   PARTS   OP   ENGINES. 


1031 


This  may  take  the  form 

d  =   ^I.H.P.X  FIR,  or  d  =  a  S/I.H.P.  +  Rt 

in  which  F  and  a  are  factors  that  depend  on  the  strength  of  the  material 
and  on  the  factor  of  safety.     Taking  S  at  45,000  pounds  per  square  inch 
for  wrought  iron,  and  at  60,000  for  steel,  we  have,  for  simple  twisting  by 
a  uniform  tangential  force, 
Factor  of  safety    =568          10  56810 

Iron F  =   35.7    42.8    57.1    71.4    a  =  3.3    3.5      3.85    4.15 

Steel F=   26.8    32.1    42.8    53.5    a  =  3.0    3.18    3.5      3.77 

Unwin,  taking  for  safe  working  strength  of  wrought  iron  9000  Ibs., 
steel  13,500  Ibs.,  and  cast  iron  4500  Ibs.,  gives  a  =  3.294  for  wrought 
iron,  2.877  for  steel,  and  4.15  for  cast  iron.  Thurston,  for  crank-axles 
of  wrought  iron,  gives  a  =  4.15  or  more. 

Seaton  says:  For  wrought  iron,  /,  the  safe  strain  per  square  inch,  should 
not  exceed  9000  Ibs.,  and  when  the  shafts  are  more  than  10  inches  diameter, 
8000  Ibs.  Steel,  when  made  from  the  ingot  and  of  good  materials,  will 
admit  of  a  stress  of  12,000  Ibs.  for  small  shafts,  and  10,000  Ibs.  for  those 
above  10  inches  diameter. 

The  difference  in  the  allowance  between  large  and  small  shafts  is  to  com- 
pensate for  the  defective  material  observable  in  the  heart  of  large  shaft- 
ing, owing  to  the  hammering  failing  to  affect  it. 

The  formula  d  =  a  -\/I.H.P.  -4-  R  assumes  the  tangential  force  to  be 
uniform  and  that  it  is  the  only  acting  force.  For  engines,  in  which  the 
tangential  force  varies  with  the  angle  between  the  crank  and  the  connect- 
ing-rod, and  with  the  variation  in  steam-pressure  in  the  cylinder,  and  also 
is  influenced  by  the  inertia  of  the  reciprocating  parts,  and  in  which  also 
the  shaft  may  be  subjected  to  bending  as  well  as  torsion,  the  factor 
a  must  be  increased,  to  provide  for  the  maximum  tangential  force  and 
for  bending. 

Seaton  gives  the  following  table  showing  the  relation  between  the 
maximum  and  mean  twisting  moments  of  engines  working  under  various 
conditions,  the  momentum  of  the  moving  parts  being  neglected,  which  is 
allowable: 


Max. 

Description  of  Engine. 

Steam  Cut-off 
at 

Twist 
Divided 
by 

Cube 
Root 

of  the  • 

Mean 
Twist. 

Ratio. 

* 

Moment. 

Single-crank  expansive  .          

0.2 

2.625 

.38 

0.4 

2  125 

29 

•i                   i< 

0.6 

.835 

.22 

«*                   « 

0  8 

698 

20 

Two-cylinder  expansive,  cranks  at  90°  . 

0.2 

.616 

.17 

•               .     «i 

0.3 

.415 

.12 

•                    •• 

0.4 

.298 

.09 

*                    " 

0.5 

.256 

.08 

i                    « 

0.6 

.270 

.08 

'                    " 

0.7 

.329 

.10 

»                    «« 

0.8 

.357 

.11 

Three-cylinder  compound,  cranks  120°. 
Three-cylindercompound.l.p.  cranks  op 
oosite  one  another,  and  h.p.  midway 

i 

h.p.  0.5,  l.p.0.66 

.40 
.26 

.12 

.08 

For  the  engines  we  are  considering  it  will  be  a  very  liberal  allowance  for 
ratio  of  maximum  to  mean  twisting  moment  if  we  take  it  as  equal  to  the 
ratio  of  the  maximum  to  the  mean  pressure  on  the  piston.  The  factor  a, 
then,  in  the  formula  for  diameter  of  the  shaft  will  be  multiplied  by  the  cube 


root  of  this  ratio,  or 


— 


^~  =  1  .49 


for  the  10.  30,  and  50-in.  engines,  respectively.     Taking  a  =  3.5,  which 
corresponds  to  a  shearing  strength  of  60,000  a.nd  a  factor  of  safety  of  8  for 


1032 


THE   STEAM-ENGINE. 


steel,  or  to  45,000  and  a  factor  of  6  for  iron,  we  have  for  the  new  coeffi- 
cient ai  in  the  formula  d\  —  a\  •y'l.H.P.  -*-  R,  the  values  4.69,  5.08,  and 
5.22  from  which  we  obtain  the  diameters  of  shafts  of  the  six  engines  as 
follows: 

Engine  No 1         2  3  4  5  6 

Diam.  of  cyl 10       10         30         30         50         50 

Horse-power,  I.H.P 50       50       450       450     1250  "  1250 

Revs,  per  min.,  R 250     125        130         65         90         45 

Diam.  of  shaft  d  = 2.743.46     7.67    9.7012.5515.82 

These  diameters  are  calculated  for  twisting  only.  When  the  shaft  is 
also  subjected  to  bending  strain  the  calculation  must  be  modified  as 
below: 

Resistance  to  Bending.  —  The  strength  of  a  circular-section  shaft 
to  resist  bending  is  one-half  of  that  to  resist  twisting.  If  B  is  the  bending 
moment  in  inch-lbs.,  and  d  the  diameter  of  the  shaft  in  inches, 

B  =    §2  X  ^'  and  d  = 

/  is  the  safe  strain  per  square  inch  of  the  material  of  which  the  shaft  is 
composed,  and  its  value  may  be  taken  as  given  above  for  twisting  (Seaton). 

Equivalent  Twisting  Moment.  —  When  a  shaft  is  subject  to  both 
twisting  and  bending  simultaneously,  the  combined  strain  on  any  section 
of  it  may  be  measured  by  calculating  what  is  called  the  equivalent  twisting 
moment;  that  is,  the  two  strains  are.  so  combined  as  to  be  treated  as  a 
twisting  strain  only  of  the  same  magnitude  and  the  size  of  shaft  calculated 
accordingly.  Rankine  gave  the  following  solution  of  the  combined  action 
of  the  two  strains. 

If  T  =  the  twisting  moment,  and  B  =  the  bending  moment  on  a  section 
of  a  shaft,  then  the  equivalent  twisting  moment  T\  =  B+  v/^2  +  T2. 

The  two  principal  strains  vary  throughout  the  revolution,  and  the 
maximum  equivalent  twisting  moment  can  only  be  obtained  accurately 
by  a  series  of  calculations  of  bending  and  twisting  moments  taken  at 
fixed  intervals,  and  from  them  constructing  a  curve  of  strains. 

Considering  the  engines  of  our  examples  to  have  overhung  cranks,  the 
maximum  bending  moment  resulting  from  the  thrust  of  the  connecting- 
rod  on  the  crank-pin  will  take  place  when  the  engine  is  passing  its  centers 
•  (neglecting  the  effect  of  the  inertia  of  the  reciprocating  parts),  and  it  will 
be  the  product  of  the  total  pressure  on  the  piston  by  the  distance  between 
two  parallel  lines  passing  through  the  centers  of  the  crank-pin  and  of  the 
shaft  bearing,  at  right  angles  to  their  axes;  which  distance  is  equal  to 
1/2  length  of  crank-pin  bearing  +  length  of  hub  4-  1/2  length  of  shaft- 
bearing  +  any  clearance  that  may  be  allowed  between  the  crank  and  the 
two  bearings.  For  our  six  engines  we  may  take  this  distance  as  equal 
to  1/2  length  of  crank-pin  +  thickness  of  crank-arm  +  1.5  X  the  diam- 
eter of  the  shaft  as  already  found  by  the  calculation  for  twisting.  The 
calculation  of  diameter  is  then  as  below: 


Engine  No. 

1 

2 

3 

4 

5 

6 

Diam.  of  cyl.,  in.... 
Horse-power  . 

10 
50 

10 
50 

30 
450 

30 
450 

50 
1250 

50 

1250 

Revs,  per  rain  
Max.  press,  on  pis,P 
Leverage,*  L  in  
Bd.mo.P£=£in.-lb 
Twist,  mom.  T  .... 
Equiv.  twist  morn. 

250 
7,854 
6.32 
49,637 
47,124 

125 

7,854 
7.94 
62,361 
94,248 

130 
70,686 
22.20 
1,569,222 
1,060,290 

65 
70,686 
26.00 
1,837,836 
2,120,580 

90 
196,350 
36.80 
7,225,680 
4,712,400 

45 

196,350 
42.25 
8,295,788 
9,424,800 

Ti=  B+  Vj32+r2 
(approx.)  

118,000 

175,000 

3,463,000 

4,647,000 

15,840,000 

20,850,000 

*  Leverage  =  distance  between  centers  of  crank-pin  and  shaft  bearing 
-  1/2  Z  +  2.25d. 

Having  already  found  the  diameters,  on  the  assumption  that  the  shafts 
were  subjected  to  a  twisting  moment  T  only,  we  may  find  the  . 


DIMENSIONS   OF  PAHTS   OF  ENGINES.  1033 


for  resisting  combined  bending  and  twisting  by  multiplying  the  diameters 
already  found  by  the  cube  roots  of  the  ratio  T\  -*•  T,  or 

1.40     1.27     1.46     1.34      1.64      1.36 
Giving  correqted  diameters  di  =  3.84     4.3911.3512.99    20.58    21.52 

By  plotting  these  results,  using  the  diameters  of  the  cylinders  for  abscis- 
sas and  diameters  of  the  shafts  for  ordinates,  we  find  that  for  the  long- 
stroke  engines  the  results  lie  almost  in  a  straight  line  expressed  by  the 
formula,  diameter  of  shaft  =  0.43  X  diameter  of  cylinder;  for  the  short- 
stroke  engines  the  line  is  slightly  curved,  but  does  not  diverge  far  from  a 
straight  line  whose  equation  is,  diameter  of  shaft  =  0.4  diameter  of 
cylinder.  Using  these  two  formulas,  the  diameters  of  the  shafts  will  be 
4.0,  4.3,  12.0,  12.9,  20.0,  21.5. 

J.  B,  Stanwood,  in  Engineering,  June  12,  1891,  gives  dimensions  of 
shafts  of  Corliss  engines  in  American  practice  for  cylinders  10  to  30  in. 
diameter.  The  diameters  range  from  415/16  to  1415/ie,  following  precisely 
the  equation,  diameter  of  shaft  =  1/2  diameter  of  cylinder  —  Vie  inch. 

Fly-wheel  Shafts.  —  Thus  far  we  have  considered  the  shaft  as  resist- 
ing the  force  of  torsion  and  the  bending  moment  produced  by  the  pressure 
on  the  crank-pin.  In  the  case  of  fly-wheel  engines  the  shaft  on  the 
opposite  side  of  the  bearing  from  the  crank-pin  has  to  be  designed  with 
reference  to  the  bending  moment  caused  by  the  weight  of  the  fly-wheel, 
the  weight  of  the  shaft  itself,  and  the  strain  of  the  belt.  For  engines 
in  which  there  is  an  outboard  bearing,  the  weight  of  fly-wheel  and  shaft 
being  supported  by  two  bearings,  the  point  of  the  shaft  at  which  the 
bending  moment  is  a  maximum  may  be  taken  as  the  point  midway 
between  the  two  bearings  or  at  the  middle  of  the  fly-wheel  hub,  and  the 
amount  of  the  moment  is  the  product  of  the  weight  supported  by  one  of 
the  bearings  into  the  distance  from  the  center  of  that  bearing  to  the 
middle  point  of  the  shaft.  The  shaft  is  thus  to  be  treated  as  a  beam 
supported  at  the  ends  and  loaded  in  the  middle.  In  the  case  of  an  over- 
hung fly-wheel,  the  shaft  having  only  one  bearing,  the  point  of  maximum 
moment  should  be  taken  as  the  middle  of  the  bearing,  and  its  amount  is 
very  nearly  the  product  of  half  the  weight  of  the  fly-wheel  and  the  shaft 
into  the  distance  of  the  middle  of  its  hub  from  the  middle  of  the  bear- 
ing. The  bending  moment  should  be  calculated  and  combined  with  the 
twisting  moment  as  above  shown,  to  obtain  the  equivalent  twisting 
moment,  and  the  diameter  necessary  at  the  point  of  maximum  moment 
calculated  therefrom. 

In  the  case  of  our  six  engines  we  assume  that  the  weights  of  the  fly- 
wheels, together  with  the  shaft,  are  double  the  weight  of  fly-wheel  rim 

d?s 
obtained  from  the  formula  T7=  785,400  ff2^2  (given  under  Fly-wheels); 

that  the  shaft  is  supported  by  an  outboard  bearing,  the  distance  between 
the  two  bearings  being  2 1/2,  5,  and  10  feet  for  the  10-in.,  30-in.,  and  50-in. 
engines,  respectively.  The  diameters  of  the  fly-wheels  are  taken  such 
that  their  rim  velocity  will  be  a  little  less  than  6000  feet  per  minute. 

Engine  No 1  2  3  4  5  6 

Diam.  of  cyl.,  inches 10          10          30        30  50  50 

Diam.  of  fly-wheel,  ft. ...         7.5          15     14.5         29  21  42 

Revs,  per  min 250        125       130         65  90  45 

Half  wt.   fly-wheel   and 

shaft,  Ibs 268        536    5,968   11,936     26,384       52,769 

Lever  arm  for  maximum 

moment,  in 15         15       30  30  60  60 

Maximum   bending   mo- 
ment, in.-lbs 4020  8040  179,040  358,080  1,583,070  3,166,140 

As  these  are  very  much  less  than  the  bending  moments  calculated  from 
the  pressures-  on  the  crank-pin,  the  diameters  already  found  are  sufficient 
for  the  diameter  of  the  shaft  at  the  fly-wheel  hub. 

In  the  case  of  engines  with  heavy  band  fly-wheels  and  with  long  fly- 
wheel shafts  it  is  of  the  utmost  importance  to  calculate  the  diameter  of 
the  shaft  with  reference  to  the  bending  moment  due  to  the  weight  of  the 
fly-wheel  and  the  shaft. 

B.  H.  Coffey  (Power,  October,  1892)  gives  the  formula  for  combined 
bending  jmd  twisting  resistance,  Ti  =  0.196  d*S,  in  which  T\  =  B  + 
2;  r  being  the  maximum,  not  the  mean  twisting  moment;  and 


1034 


THE  STEAM-ENGINE. 


finds  empirical  working  values  for  0.196  S  as  below.  He  says:  Four 
points  should  be  considered  in  determining  this  value:  First,  the  nature 
of  the  material;  second,  the  manner  of  applying  the  loads,  with  shock 
or  otherwise;  third,  the  ratio  of  the  bending  moment  to  the  torsional 
moment  —  the  bending  moment  in  a  revolving  shaft  produces  reversed 
strains  in  the  material,  which  tend  to  rupture  it;  fourth,  the  size  of  the 
section.  Inch  for  inch,  large  sections  are  weaker  than  small  ones.  He 
puts  the  dividing  line  between  large  and  small  sections  at  10  in.  diameter, 
and  gives  the  following  safe  values  of  S  X  0.196  for  steel,  wrought  iron, 
and  cast  iron,  for  these  conditions. 

VALUE  OF  S  X  0.196. 


Ratio. 

Heavy  Shafts 
with  Shock. 

Light  Shafts 
with  Shock. 
Heavy  Shafts 
No  Shock. 

Light  Shafts 
No  Shock. 

B  to  T. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

3  to  10  or  less  

1045 
941 
855 

784 

880 
785 
715 
655 

440 
393 
358 
328 

1566 
1410 
1281 
1176 

1320 
1179 
1074 
984 

660 
589 
537 
492 

2090 
1882 
1710 
1568 

1760 
1570 
1430 
1310 

880 
785 
715 
655 

3  to  5  or  less  

1  to  1  or  less 

B  greater  than  T.  .  . 

Mr.  Coffey  gives  as  an  example  of  improper  dimensions  the  fly-wheel 
shaft  of  a  1500  H.P.  engine  at  Willimantic,  Conn.,  which  broke  while  the 
engine  was  running  at  425  H.P.  The  shaft  was  17  ft.  5  in.  long  between 
centers  of  bearings,  18  in.  diam.  for  8  ft.  in  the  middle,  and  15  in.  diam. 
for  the  remainder,  including  the  bearings.  It  broke  at  the  base  of  the 
fillet  connecting  the  two  large  diameters,  or  561/2  in.  from  the  center  of 
the  bearing.  He  calculates  the  mean  torsional  moment  to  be  446,654 
inch-pounds,  and  the  maximum  at  twice  the  mean;  and  the  total  weight 
on  one  bearing  at  87,530  Ibs.,  which,  multiplied  by  561/2  in.,  gives 
4,945,445  in.-lbs.  bending  moment  at  the  fillet.  Applying  the  formula 
Ti  =  B+^/B*  +  Tz,  gives  for  equivalent  twisting  moment  9,971,045  in.- 
lbs.  Substituting  this  value  in  the  f9rmula  T\  =  0.196/ScZ3  gives  for  S 
the  shearing  strain  15,070  Ibs.  persq.  in.,  or  if  the  metal  had  a  shearing 
strength  of  45,000  lb.,  a  factor  of  safety  of  only  3.  Mr.  Coffey  considers 
that  6000  lb.  is  all  that  should  be  allowed  for  S  under  these  circum- 
stances. This  would  give  d  =  20.35  in.  If  we  take  from  Mr.  Coffey's 
table  a  value  of  0.196  5  =  1100,  we  obtain  cP  =  9000  nearly,  or  d  =  20.8 
in.  instead  of  15  in.,  the  actual  diameter. 

Length  of  Shaft-bearings. — There  is  as  great-  a  difference  of  opinion 
among  writers,  and  as  great  a  variation  in  practice  concerning  length  of 
journal-bearings,  as  there  is  concerning  crank-pins.  The  length  of  a 
journal  being  determined  from  considerations  of  its  heating,  the  observa- 
tions concerning  heating  of  crank-pins  apply  also  to  shaft-bearings,  and 
the  formulee  for  length  of  crank-pins  to  avoid  heating  may  also  be  used, 
using  for  the  total  load  upon  the  bearing  the  resultant  of  all  the  pres- 
sures brought  upon  it,  by  the  pressure  on  the  crank,  by  the  weight  of  the 
fly-wheel,  and  by  the  pull  of  the  belt.  After  determining  this  pressure, 
however,  we  must  resort  to  empirical  values  for  the  so-called  constants 
of  the  formulae,  really  variables,  which  depend  on  the  power  of  the 
bearing  to  carry  away  heat,  and  upon  the  quantity  of  heat  generated, 
which  latter  depends  on  the  pressure,  on  the  number  of  square  feet  of 
rubbing  surface  passed  over  in  a  minute,  and  upon  the  coefficient  of 
friction.  This  coefficient  is  an  exceedingly  variable  quantity,  ranging 
from  0.01  or  less  with  perfectly  polished  journals,  having  end-play,  and 
lubricated  by  a  pad  or  oil-bath,  to  0.10  or  more  with  ordinary  oil-cup 
lubrication. 

Thurston  says  that  the  maximum  allowable  mean- intensity  of  pressure 
may  be,  for  all  cases,  computed  by  his  formula  for  journals,  I  -  PV  + 
60,000  d,  or  by  Rankine's,  I  =  P(V ±  20)  4-  44,800  d,  in  which  P  is  the 
mean  total  pressure  in  pounds,  V  the  velocity  of  rubbing  surface  in  feet 
per  minute,  and  d  the  diameter  of  the  shaft  in  inches.  It  must  be  borne 
in  mind,  he  says,  that  the  friction  work  on  the  main  bearing  next  the  crank 
is  the  sum  of  that  due  the  action  of  the  piston  on  the  pin  and  that  due 


DIMENSIONS  OF  PARTS  OF  ENGINES. 


1035 


that  portion  of  the  weight  of  wheel  and  shaft  and  of  pull  of  the  belt  which 
is  carried  there.  The  outboard  bearing  carries  practically  only  the 
latter  two  parts  of  the  total.  The  crank-shaft  journals  will  be  made 
longer  on  one  side,  and  perhaps  shorter  on  the  other,  than  that  of  the 
crank-phi,  in  proportion  to  the  work  falling  upon  each,  i.e.,  to  their 
respective  products  of  mean  total  pressure,  speed  of  rubbing  surfaces,  and 
coefficients  of  friction. 

Unwin  says:  Journals  running  at  150  revolutions  per  minute  are  often 
only  one  diameter  long.  Fan  shafts  running  150  revolutions  per  minute 
have  journals  six  or  eight  diameters  long.  The  ordinary  empirical  mode 
of  proportioning  the  length  of  journals  is  to  make  the  length  proportional 
to  the  diameter,  and  to  make  the  ratio  of  length  to  diameter  increase 
with  the  speed.  For  wrQught-iron  journals: 

Revs.permin.  =  50  100  150  200  250  500  1000  Z/d«  0.004  fl  +  1. 
Length  +  diam.  =  1.2  1.4  1.6  1.8  2.0  3.0  5.0. 

Cast-iron  journals  may  have  l  +  d  =  9/10,  and  steel  journals  Z-s-cf  =  li/4, 
of  the  above  values. 

Unwin  gives  the  following,  calculated  from  the  formula  I  =  0 . 4  H.P.  -r-  rr 
in  which  r  is  the  crank  radius  in  inches,  and  H.P.  the  horse-power  trans- 
mitted to  the  crank-pin. 

THEORETICAL  JOURNAL  LENGTH  IN  INCHES. 


Load  on 
Journal  in 
Pounds. 

Revolutions  of  Journal  per  minute. 

50 

100 

200 

300 

500 

1000 

1,000 
2,000 
4,000 
5,000 
10,000 
15,000 
20,000 
30,000 
40,000 
50.000 

0.2 
0.4 
0.8 
1.0 
2. 
3. 
4. 
6. 
8. 
10. 

0.4 
0.8 
1.6 

4! 
6. 
8. 
12. 
16. 
20. 

0.8 
1.6 
3.2 
4. 
8. 
12. 
16. 
24. 
32. 
40. 

1.2 

2.4 
4.8 
6. 
12. 
18. 
24. 
36. 

2. 
4. 
8. 
10. 
20. 
30. 
40. 

4. 
8. 
16. 
20. 
40. 

Applying  six  different  formulae  to  our  six  engines,  we  have: 


Engine  No  .   

1 

2 

3 

4 

5 

6 

Diam.  cyl  

10 

10 

30 

30 

50 

50 

Horse-power  

50 

50 

450 

450 

1  250 

1  250 

Revs  per  min 

250 

125 

130 

65 

90 

45 

Mean  pressure  on  crank-pin  =  S  
Half  wt.  of  fly-wheel  and  shaft  =  Q.  .  .  . 
Resultant  pressure  on  bearing 

3,299 
268 

3,299 
536 

23,185 
5,968 

23,185 
11,936 

58,905 
26,470 

58,905 
52,940 

V^+5-Bj. 

Diam.  of  shaft  journal  

3,310 
3  84 

3,335 
4  39 

23,924 
11  35 

26,194 
12  99 

64,580 
20  58 

79,200 
21  52 

Length  of  shaft  journal: 
Marks,       2  =  0.0000325  /#i#(/=0.10) 
Whitham,Z  =  0.00005  15  fR1R(f  =0.10) 
Thurston,  Z  =  PFn-  (60,000  d)  
Rankine,    l=P(V+20)  +  (44,800  d)..  . 
Unwin,       Z=(0.  004/2+  1)  d.  ... 

5.38 
4.27 
3.61 
5.22 
7  68 

2.71 
2.15 
1.82 
2.78 
6  59 

20.87 
16.53 
14.00 
21.70 
17  25 

11.07 
8.77 
7.43 
10.85 
16  36 

37.78 
29.95 
25.36 
35.16 
27  99 

23.17 
18.35 
15.55 
22.47 
25  39 

Unwin,       Z  =  0.4H.P.-*-r  

3  33 

1  60 

12  00 

6  00 

20  83 

10  42 

Average  

4.92 

2.99 

17.05 

10.00 

29.54 

19.22 

If  we  divide  the  mean  resultant  pressure  on  the  bearing  by  the  pro- 
jected area,  that  is,  by  the  product  of  the  diameter  and  length  of  the 
journal,  using  the  greatest  and  smallest  lengths  out  Of  the  seven  lengths 


1036 


THE  STEAM-ENGINE. 


for  each  journal  given  above,  we  obtain  the  pressure  per  square  inch 
upon  the  bearing,  as  follows: 


Engine  No 

1 

2 

3 

4 

5 

6 

Press,  per  sq.  in.,  shortest  journal  
Longest  journal  

259 
112 

455 
115 

176 
97 

336 
123 

151 
83 

353 
145 

Average  journal 

175 

254 

124 

202 

106 

191 

Journal  of  length  =  diam  

173 

155 

175 

Many  of  the  formulas  give  for  the  long-stroke  engines  a  length  of  journal 
less  than  the  diameter,  but  such  short  journals  are  rarely  used  in  practice. 
The  last  line  in  the  above  table  has  been  calculated  on  the  supposition 
that  the  journals  of  the  long-stroke  engines  are  made  of  a  length  equal 
to  the  diameter. 

In  the  dimensions  of  Corliss  engines  given  by  J.  B.  Stanwood  (Eng., 
June  12,  1891),  the  lengths  of  the  journals  for  engines  of  diam.  of  cyl. 
10  to  20  in.  are  the  same  as  the  diam.  of  the  cylinder,  and  a  little  more 
than  twice  the  diam.  of  the  journal.  For  engines  above  20  in.  diam.  of 
cyl.  the  ratio  of  length  to  diam.  is  decreased  so  that  an  engine  of  30  in. 
diam.  has  a  journal  26  in.  long,  its  diameter  being  1415/16  in.  These 
lengths  of  journal  are  greater  than  those  given  by  any  of  the  formulae 
above  quoted. 

There  thus  appears  to  be  a  hopeless  confusion  in  the  various  formulae 
for  length  of  shaft  journals,  but  this  is  no  more  than  is  to  be  expected 
from  the  variation  in  the  coefficient  of  friction,  and  in  the  heat-conducting 
power  of  journals  in  actual  use,  the  coefficient  varying  from  0.10  (or 
even  0.16  as  given  by  Marks)  down  to  0.01,  according  to  the  condition 
of  the  bearing  surfaces  and  the  efficiency  of  lubrication.  Thurston's 


formula,  I  = 


»  reduces  to  the  form  I  =  0.000004363  PR,  in  which 


P  =  mean  total  load  on  journal,  and  R  =  revolutions  per  minute.  This 
is  of  the  same  form  as  Marks's  and  Whitham's  formulae,  in  which,  if  /,  the 
coefficient  of  friction,  be  taken  at  0.10,  the  coefficients  of  PR  are,  respec- 
tively, 0.0000065  and  0.00000515.  Taking  the  mean  of  these  three 
formulae,  we  have  I  =  0.0000053  PR,  if  /  =  0.10  or  I  =  0.000053  fPR 
for  any  other  value  of  /.  The  author  believes  this  to  be  as  safe  a  formula 
as  any  for  length  of  journals,  with  the  limitation  that  if  it  brings  a  result 
of  length  of  journal  less  than  the  diameter,  then  the  length  should  be 
made  equal  to  the  diameter.  Whenever,  with/  =  0.10  it  gives  a  length 
which  is  inconvenient  or  impossible  of  construction  on  account  of  limited 
space,  then  provision  should  be  made  to  reduce  the  value  of  the  coefficient 
of  friction  below  0.10  by  means  of  forced  lubrication,  end  play,  etc.,  and 
to  carry  away  the  heat,  as  by  water-cooled  journal-boxes.  The  value  of 
P  should  be  taken  as  the  resultant  of  the  mean  pressure  on  the  crank, 
and  the  load  brought  on  the  bearing  by  the  weight  of  the  shaft,  fly-wheel, 

etc.,  as  calculated  by  the  formula  already  given,  viz.,  Ri  =  ^Q2  +  £2  for 
horizontal  engines,  and  Ri  =  Q  4-  S  for  vertical  engines. 

For  our  six  engines  the  formula  I  =  0.0000053  PR    gives,  with  the 
limitation  for  the  long-stroke  engines  that  the  length  shall  not  be  less 
than  the  diameter,  the  following: 
Engine  No  .............       1          2 

Length  of  journal  .......   4.39     4.39 

Pressure  per  square  inch 

on  journal  ............     196       173 

Crank-shafts  with    Center-crank 

center-crank  engines,  one  of  the  crank-arms,  and  its  adjoining  journal, 
called  the  after  journal,  usually  transmit  the  power  of  the  engine  to  the 
work  to  be  done,  and  the  journal  resists  both  twisting  and  bending  mo- 
ments, while  the  other  journal  is  subjected  to  bending  moment  only. 
For  the  after  crank-  journal  the  diameter  should  be  calculated  the  same 
as  for  an  overhung  crank,  using  the  formula  for  combined  bending  and 
twisting  moment,  T\  =  B  +  \/  B*  +  T2,  in  which  Ti  is  the  equivalent 
twisting  moment,  B  the  bending  moment,  and  T  the  twisting  moment. 
This  value  of  T\  is  -to  be  used  in  the  formula,  diameter  =  tyliTTTIS.  The 


3 

16.48 


4 
12.99 


5 

30.80 


6 

21.52 


128         155  102  171 

and    Double-crank    Arms.— In 


DIMENSIONS  OF  PARTS  OF  ENGINES. 


1037 


bending  moment  is  taken  as  the  maximum  load  on  piston  multiplied  Dy 
one-f9urth  of  the  length  of  the  crank-shaft  between  middle  points  of  the 
two  journal  bearings,  if  the  center  is  midway  between  the  bearings,  or 
by  one-half  the  distance  measured  parallel  to  the  shaft  from  the  middle 
of  the  crank-pin  to  the  middle  of  the  after  bearing.  This  supposes  the 
crank-shaft  to  be  a  beam  loaded  at  its  middle  and  supported  at  the  ends, 
but  Whitham  would  make  the  bending  moment  only  one-half  of  this, 
considering  the  shaft  to  be  a  beam  secured  or  fixed  at  the  ends,  with  a 
point  of  contraflexure  one-fourth  of  the  length  from  the  end.  The  first 
supposition  is  the  safer,  but  since  the  bending  moment  will  in  any  case 
be  much  less  than  the  twisting  moment,  the  resulting  diameter  will  be 
but  little  greater  than  if  Whitham's  supposition  is  used.  For  the  for- 
ward journal,  which  is  subjected  to  bending  moment  only,  diameter  of 

shaft  =  ^/10.2  BIS,  in  which  B  is  the  maximum  bending  moment  and 
S  the  safe  shearing  strength  of  the  metal  per  square  inch. 

For  our  six  engines,  assuming  them  to  be  center-crank  engines,  and 
considering  the  crank-shaft  to  be  a  beam  supported  at  the  ends  and 
loaded  in  the  middle,  and  assuming  lengths  between  centers  of  shaft 
bearings  as  given  below,  we  have: 


Length    of^  shaft, 

assumed,  in.,  L.  . 

20 

24 

48 

60 

76 

96 

Max.      press,      on 

crank-pin,  P  
Max.  bending  mo- 

7,854 

7,854 

70,686 

70,686 

196,350 

196,350 

ment,  B  =1/4  PL, 
Twisting  mom.,   T 

39,270 
47,124 

49,637 
94,248 

848,232 
1,060,290 

1,060,290 
2,120,580 

3,729,750 
4,712,400 

4,712,400 
9,424,800 

Equiv.  twist,  mom. 

B  +  ^B2  +  T2  ... 
Diam.  of  after  jour. 

101,000 

156,000 

2,208,000 

3,430,000 

9,740,000 

15,240,000 

-       4/5.1  Ti 

3QO 

4  AH 

ni  ^ 

i  -j   nn 

d       V    8000   •" 

.  vo 

.OU 

.  \j 

\j  .UU 

18.25 

21  .20 

Diam.  of  forw.  jour., 

d    iV10-2jB 

3Afl 

3QQ 

1  A     00 

dl       V   8000  ••••• 

.DO 

.  yy 

lu.zo 

1  1  .  16 

16.82 

18.  18 

The  lengths  of  the  journals  would  be  calculated  in  the  same  manner  as 
in  the  case  ot  overhung  cranks,  by  the  formula  I  =  0.000053  fPR,  in 
which  P  is  the  resultant  of  the  mean  pressure  due  to  pressure  of  steam  op 
the  piston,  and  the  load  of  the  fly-wheel,  shaft,  etc.,  on  each  of  the  two 
bearings.  Unless  the  pressures  are  equally  divided  between  the  twc 
bearings,  the  calculated  lengths  of  the  two  will  be  different;  but  it  is 
usually  customary  to  make  them  both  of  the  same  length,  and  in  no  casb 
to  make  the  length  less  than  the  diameter.  The  diameters  also  are  usually 
made  alike  for  the  two  journals,  using  the  largest  diameter  found  by 
calculation. 

The  crank-pin  for  a  center  crank  should  be  of  the  same  length  as  for 
an  overhung  crank,  since  the  length  is  determined  from  considerations 
of  heating,  and  not  of  strength.  The  diameter  also  will  usually  be  the 
same,  since  it  is  made  great  enough  to  make  the  pressure  per  square  inch 
on  the  projected  area  (product  of  length  by  diameter)  small  enough  to 
allow  of  free  lubrication,  and  the  diameter  so  calculated  will  be  greater 
than  is  required  for  strength. 

Crank-shaft  with  Two  Cranks  coupled  at  90°.  —  If  the  whole 
power  of  the  engine  is  transmitted  through  the  after  journal  of  the  after 
crank-shaft,  the  greatest  twisting  moment  is  equal  to  1.414  times  the 
maximum  twisting  moment  due  to  the  pressure  on  one  of  the  crank-pins. 
If  T  =  the  maximum  twisting  moment  produced  by  the  steam-pressure 
on  one  of  the  pistons,  then  27i,  the  maximum  twisting  moment  on  the 
after  part  of  the  crank-shaft,  and  on  the  line-shaft  produced,  when  each 
crank  makes  an  angle  of  45°  with  the  center  line  of  the  engine,  is  1.414  T. 
Substituting  this  value  in  the  formula  for  diameter  to  resist  simple 
torsion,  viz..  d  =  ^5.1  T  -r  S,  we  have  d  =  ^5.1  X  1.414  T  -r  St  or 


1038  THE  STEAM-ENGINE. 

d  =  1.932  ty  T/S,  in  which  T  is  the  maximum  twisting  moment  pro- 
duced by  one  of  the  pistons,  d  =  diameter  in  inches,  and  S  =  safe 
working  shearing  strength  of  the  material.  For  the  forward  journal  of 
the  after  crank,  and  the  after  journal  of  the  forward  crank,  the  torsional 
moment  is  that  due  to  the  pressure  of  steam  on  the  forward  piston  only, 
and  for  the  forward  journal  of  the  forward  crank,  if  none  of  the  power 
of  the  engine  is  transmitted  through  it,  the  torsional  moment  is  zero,  and 
its  diameter  is  to  be  calculated  for  bending  moment  only. 

For  Combined  Torsion  and  Flexure.  —  Let  B^  =  bending  moment 
on  either  journal  of  the  forward  crank  due  to  maximum  pressure  on 
forward  piston,  B2  =  bending  moment  on  either  journal  of  the  after  crank 
due  to  maximum  pressure  on  after  piston,  T\  =  maximum  twisting 
moment  on  after  journal  of  forward  crank,  and  Tz  =  maximum  twisting 
moment  on  after  journal  of  after  crank,  due  to  pressure  on  the  after 
piston. 

Then  equivalent  twisting  moment  on  after  journal  of  forward  crank  — 
Bi  +  Vtfi*  -}-  T7!2. 

On  forward  journal  of  after  crank  =»          _  _ 

On  after  journal  of  after  crank  =  J52-f  ^B<?+  (T\+  772)2. 

These  values  of  equivalent  twisting  moment  are  to  be  used  in  the 

formula  for  diameter  of  journals  d  =  \J5.l  T/S.    For   the    forward 

Journal  of  the  forward  crank-shaft  d  =  ^10.2  Bi/S. 

It  is  customary  to  make  the  two  journals  of  the  forward  crank  of  one 
diameter,  viz.,  that  calculated  for  the  after  journal. 

For  a  Three-cylinder  Engine  with  cranks  at  120°,  the  greatest 
twisting  moment  on  the  after  part  of  the  shaft,  if  the  maximum  pressures 
on  the  three  pistons  are  equal,  is  equal  to  twice  the  maximum  pressure  on 
any  one  piston,  and  it  takes  place  when  two  of  the  cranks  make  angles 
of  30°  with  the  center  line,  the  third  crank  being  at  right  angles  to  it. 
(For  demonstration,  see  Whitham's  "Steam-engine  Design,"  p.  252.) 
For  combined  torsion  and  flexure  the  same  method  as  above  given  for 
two  -crank  engines  is  adopted  for  the  first  two  cranks;  and  for  the 
third,  or  after  crank,  if  all  the  power  of  the  three  cylinders  is  transmitted 
through  it,  we  have  the  equivalent  twisting  moment  on  the  forward 

Journal  =  Ba  -f  ^B£  +  (Ti  +  r2)2,  and   on  the  after    journal  =  B3  + 


(Ti  +  T2  +  773)2,  B3  and  Ts  being  respectively  the  bending  and 
twisting  moments  due  to  the  pressure  on  the  third  piston. 

Crank-shafts  for  Triple-expansion  Marine  Engines,  according  to 
an  article  in  The  Engineer,  April  25,  1890,  should  be  made  larger  than  the 
formulae  would  call  for,  in  order  to  provide  for  the  stresses  due  to  the 
racing  of  the  propeller  in  a  sea-way,  which  can  scarcely  be  calculated. 
A  kind  of  unwritten  law  has  sprung  up  for  fixing  the  size  of  a  crank- 
shaft, according  to  which  the  diameter  of  the  shaft  is  made  about  0.45  D, 
where  D  is  the  diameter  of  the  high-pressure  cylinder.  This  is  for  solid 
shafts.  When  the  speeds  are  high,  as  in  war-ships,  and  the  stroke  short, 
the  formula  becomes  0.4  D,  even  for  hollow  shafts. 

The  Valve-stem  or  Valve-rod.  —  The  valve-rod  should  be  designed 
to-  move  the  valve  under  the  most  unfavorable  conditions,  which  are  when 
the  stem  acts  bv  thrusting,  as  a  long  column,  when  the  valve  is  unbalanced 
(a  balanced  valve  may  become  unbalanced  bv  the  joint  leaking)  and  when 
it  is  imperfectly  lubricated.  The  load  on  the  valve  is  the  product  of  the 
area  into  the  greatest  unbalanced  pressure  upon  it  per  square  inch,  and 
the  coefficient  of  friction  may  be  as  high  as  20%.  The  product  of  this 
coemcient  and  the  load  is  the  force  necessary  to  move  the  valve,  which 
equals  the  maximum  thrust  on  the  valve-rod.  From  this  force  the 
diameter  of  the  valve-rod  may  be  calculated  by  the  usual  formula  for 
columns.  An  empirical  formula  given  by  Seaton  is:  Diam.  of  rod  = 
d  =  \/lbp/F,  in  which  7  =  length,  and  b  =  breadth  of  valve,  in  inches; 
p  =  maximum  absolute  pressure  on  the  valve  in  Ib.  per  sq.  in.,  and 
F  a  coemcient  whose  values  are,  for  iron:  long  rod  10,000,  short  12,000; 
for  steel:  long  rod  12,000,  short  14,500. 

Whitham  gives  the  short  empirical  rule:  Diam.  of  valve-rod  =  1/30 
diam.  of  cyl.  =  1/3  diam.  of  piston-rod. 


DIMENSIONS   OF  PARTS  OF  ENGINES.  1039 

The  Eccentric.—  Diarn.  of  eccentric-sheave  =  2.4  X  throw  of  eccen- 
tric +  1.2  X  diam.  of  shaft.     D  =  diam.  of  valve  rod  (Seaton). 

Breadth  of  the  sheave  at  the  shaft  ......  =  1.15  X  D  +  0.65  in. 

Breadth  of  the  sheave  at  the  strap  ......  =  D  +  0.6  in. 

Thickness  of  metal  around  the  shaft.  .  .  .  =  0.7    X  D  +  0.5  in. 

Thickness  of  metal  at  circumference.  .  .  .  =  0.6    X  D  -j-  0.4  in. 

Breadth  of  key  .......................  =0.7    X  D  +  0.5  in. 

Thickness  of  key  .....................  =  0.25  X  D  +  0.5  in. 

Diam.  of  bolts  connecting  parts  of  strap.  =  0.6    X  D  -f  0.1  in. 

THICKNESS  OF  ECCENTRIC-STRAP. 

When  of  bronze  or  malleable  cast  iron  : 

Thickness  of  eccentric-strap  at  the  middle.  .  .  =  0.4    X  D  +  0.6  in. 
Thickness  of  eccentric-strap  at  the  sides  .....  =0.3    X  £)  +  0.5  in. 

When  of  wrought  iron  or  cast  steel  : 

Thickness  of  eccentric-strap  at  the  middle.  .  .  =  0.4    X  D  +  0.5  in. 
Thickness  of  eccentric-strap  at  the  sides  .....  =  0.27  X  D  +  0.4  in. 

The  Eccentric-rod.  —  The  diameter  of  the  eccentric-rod  in  the  body 
and  at  the  eccentric  end  may  be  calculated  in  the  same  way  as  that  of 
the  connecting-rod,  the  length  being  taken  from  center  of  strap  to 
center  of  pin.  Diameter  at  the  link  end  =  0.8  D  +  0.2  in. 

This  is  for  wrought  iron  ;  no  reduction  in  size  should  be  made  for  steel. 

Eccentric-rods  are  often  made  of  rectangular  section. 

Reversing-gear  should  be  so  designed  as  to  have  more  than  sufficient 
strength  to  withstand  the  strain  of  both  the  valves  and  their  gear  at  the 
same  time  under  the  most  unfavorable  circumstances;  it  will  then  have 
the  stiffness  requisite  for  good  working. 

Assuming  the  work  done  in  reversing  the  link-motion,  W,  to  be  only 
that  due  to  overcoming  the  friction  of  the  valves  themselves  through  their 
whole  travel,  then,  if  T  be  the  travel  of  valves  in  inches,  for  a  compound 
engine 

fl  x  b  x  P\  _L.  T  (IL  X  61  X  PI\ 


_  ?.  fl 
~12\ 


li,  bit  and  PI  being  length,  breadth,  and  maximum  steam-pressure 
valve  of  the  second  cylinder;  and  for  an  expansive  engine 


To  provide  for  the  friction  of  link-motion,  eccentrics,  and  other  gear, 
and  for  abnormal  conditions  of  the  same,  take  the  work  at  one  and  a  half 
times  the  above  amount. 

To  find  the  strain  at  any  part  of  the  gear  having  motion.  when  reversing, 
divide  the  work  so  found  by  the  space  moved  through  by  that  part  in 
feet;  the  quotient  is  the  strain  in  pounds;  the  size  may  be  found  from  the 
ordinary  rules  of  construction  for  any  of  the  parts  of  the  gear.  (Seaton.) 

Current  Practice  in  Engine  Proportions,  1897.  (Compare  pages  1021 
to  1039.)  —  A  paper  with  this  title  by  Prof.  John  H.  Barr,  in  Trans. 
A.  S.  M.  E.,  xviii,  737,  gives  the  results  of  an  examination  of  the  propor- 
tions of  parts  of  a  great  number  of  single-cylinder  engines  made  by 
different  builders.  The  engines  classed  as  low  speed  (L.  S.)  are  Corliss 


la  speed  or  200  to  300  revs,  per  i 
are  expressed  in  formulas  of  rational  form  with  empirical  coefficients, 
and  are  here  abridged  as  follows  (dimensions  in  inches): 

Thickness  of  Shell,  L.  S.  only.  —  t  =  CD  +  B;  D  =  diam.  of  piston  in 
in. ;  B  =  0 . 3  in. ;  C  varies  from  0  04  to  0 . 06,  mean  =-  0 . 05. 

Flanges  and  Cylinder-heads. —  l  to  1 . 5  X  thickness  of  shell,  mean  1 . 2. 

Cylinder-head  Studs.  —  No  studs  less  than  3/4  in.  nor  greater  than  13/gin. 
diam.  Least  number,  8,  for  10  in.  diam.  Average  number  =  0.7D. 
Average  diam.  =  D  /40  -f  i/2  in 

Ports  and  Pipes.  —a=  area" of  port  (or  pipe)  in  sq.  in.:  A  =  area  of 
piston,  sq.  m.;  V  =  mean  piston-speed,  ft.  per  min.:  a  '=  AV  1C,  in  which 
C=mean  velocity  of  steam  through  the  port  or  pipe  in  ft.  per  min. 


1040  THE  STEAM-ENGINE. 

Ports,  H.  S.  (same  ports  for  steam  as  for  exhaust).  —  C  =  4500  to 
6500,  mean  5500.  For  ordinary  piston-speed  of  600  ft.  per  min.  a  = 
KA;  K  =  0.09  to  0.13,  mean  0.11. 

melnT  09  S'  ~~  °  =  500°  t0  9000'  mean  6800;  K  "  °'°8  tO  °'10' 

Exhaust-ports,  L.  S.  —  £  =  4000  to  7000,  mean  5500;  #  =  0.10  to  0.125, 
mean  u  .  1  1  . 


'x   s-  T  ?  =  580°  to  70°°'  mean  65°°-  Tf  d  =  diam-  of 

D  =  diam.  of  piston,  d  =  0  .  29  D  to  0  .  32  D,  mean  0  .  30  D. 

'S'  —  G  =  5000  to  8000,  mean  6000;  d  =  0".  27  to  0.35  D; 


=  °'33  t0 
28°°  tO  47°°'  mean  38°°;  d  =  °'35  to 


0        7meo'      '        ~ 

y^V9'  ~~F  =  face*  D  =  Diameter.     F  =  CD.     H.  S.:  C  - 
0.  meanO.46.     L.  S.:<7  -  0.25  toO.  45,  mean  0.32. 
-rods.  ~d  =  diam.  of  rod;  D  =  diam.  of  piston;  L  =  stroke,  in.: 
=          DL      H  g  .  £,_  0  12  to  Q  175    mean  L  • 

0.13,  mean  0.11. 

Connecting-rods.  —  H.  S.  (generally  6  cranks  loner,  rectangular  section): 
Breadth;    h  =  height    of   section;    Li  =  length    of   connecting-rod; 


D  =  diam.  of  piston;  &  =  C^DLi;  C  =  0.045  to  0.07,  mean  0.057; 
n,  =>  Kb;  K  =  2.2  to  4,  mean  2.7.  L.  S.  (generally  5  cranks  long,  cir- 
cular sections  only):  C  =  0.082  to  0.105.  mean  0.092. 

Cross-head  Slides.  —  Maximum  pressure  in  Ibs.  per  sq.  in.  of  shoe,  due 
to  the  vertical  component  of  the  force  on  the  connecting-rod.  H.  S.: 
10.5  to  38,  mean  27.  L.  S.:  29  to  58,  mean  40. 

Cross-head  Pins.  —  I  =  length;  d  =  diam.;  projected  area  =  a  =  dl  — 
CA;  A  =  area  of  piston;  I  =  Kd.  H.  S.:  C  =  0.06  to  0.11,  mean  0.08; 
K  =  1  to  2,  mean  1.25.  L.  S.:  C  =  0.054  to  0.10,  mean  0.07;  K  =  1  to 
1  .*5,  mean  1  .  3. 

Crank-pin.  —  H.  P.  =  horse-power    of   engine;    L=  length    of   stroke; 

1  =  length  of  pin;  I  =  C  X  H.P.  /L+  B;  d  =  diam.  of  pin;  A  =  area  of 
piston;  dl  =  KA.     H.  S.:  C  =  0.13  to  0.46,  mean  0.30;  B  =  2.5  in.; 
K  =  0.17  to  0.44,  mean  0.24.     L.  S.:  C  =  0.4  to  0.8,  mean  0.6;  B  = 

2  in.;  K  =  0.065  to  0.115,  mean  0.09.     _ 

Crank-shaft  Main  Journal.  —  d=  C  ^/H.P.-J-  N;  d=  diam.;  Z  =  length; 
N  =  revs,  per  min.;  projected  area  =  MA;  A  =  area  of  piston.  H.  S.: 
(7  =  6.5  to  8.5,  mean  7.3;  l  =  Kd;  K  =  2  to  3,  mean  2.2;  M  =  0.37  to 
0.70,  mean  0.46.  L.  S.:  C  =  6'to  8,  mean  6.8;  K=  1.7  to  2.1,  mean 
1.9;  M  =  0.46  to  0.64,  mean  0.56. 

Piston-speed.  —  H.  S.:  530  to  660,  mean  600;  L.  S.:  500  to  850,  mean 
600. 

Weight  of  Reciprocating  Parts  (piston,  piston-rod,  cross-head,  and  one- 
half  of  connecting-rod).  —  W  =  CD2  •*-  LNZ\  D  =  diam.  of  piston; 
L  =  length  of  stroke,  in.;  AT  =  revs,  per  min.  H.  S.  only:  C  =  1,200,000 
to  2,300,000,  mean  1,860,000. 

Belt-surface  per  I  HfP.  —  S  =  C  X  H.P.  +  B;  S  =  product  of  width  of 
belt  in  feet  by  velocity  of  belt  in  ft.  per  min.  H.  S.:  C  =  21  to  40,  mean 
28;  5  =  1800.  L.  S.;  S  =  CX  H.P.,  C  =  30  to  42,  mean  =  35. 

Fly-wheel  (H.  S.  only).  —  Weight  of  rim  in  Ibs.:  W  =  C  X  H.P.-*- 
DrW3;  Di  =  diam.  of  wheel  in  in.;  C  =  65  X  1010  to  2  X  1012  mean  = 
12  X  10",  or  1,200,000,000,000. 

Weight  of  Engine  per  I.H.P.  in  Ibs.,  including  flv-wheel.  —  W  = 
C  X  H.P.  H.  S.:  C=  100  to  135,  mean  115.  L.  S.:  "C  =  135  to  240, 
mean  175. 

Current  Practice  in  Steam-engine  Design,  1909.  (Ole  N.  Trooien, 
Bull.  Univ'y  of  Wis.,  No.  252;  Am.  Mach.,  April  22,  1909.)  —  Practice  in 
prop9rtioning  standard  steam-engine  parts  has  settled  down  to  certain 
definite  values,  which  have  by  long  usage  been  found  to  give  satisfactory 
results.  These  values  can  readily  be  expressed  in  formulas  showing  the 
relation  between  the  more  important  factors  entering  the  problem  of 
design. 

These  formulae  may  be  considered  as  partly  rational  and  partly  em- 


DIMENSIONS  OF  PAKTS  OP  ENGINES.  1041 

pirical;  rational  in  the  sense  that  the  variables  enter  in  the  same  manner 
as  in  a  strict  analysis,  and  empirical  in  the  sense  that  the  constants, 
instead  of  being  obtained  from  assumed  working  strength,  bearing 
pressures  etc.,  are  derived  from  actual  practice  and  include  elements 
whose  values  are  not  accurately  known  but  which  have  been  found  safe 
and  economical. 

The  following  symbols  of  notation  are  used  in  the  formulas  given: 
D  =  diameter  of  piston.  A  =  area  of  piston.  L  =  length  of  stroke. 
7>  =  unit  steam  pressure,  taken  as  125  Ibs.  per  sq.  in.  above  exhaust  as 
a  standard  pressure.  H.P.  =  rated  horse-power.  N  =  revs,  per  min. 
Cand  K,  constants,  and  tf  =  diam.  and  Z  =  length  of  unit  under  consider- 
ation. All  dimensions  in  inches. 

The  commercial  point  of  cut-off  is  taken  at  1/4  of  the  stroke.  H.  S., 
high-speed  engines.  L.  S.,  low-speed,  or  long-stroke  engines. 

Piftton  Rod  —  d  =  C  ^DL.  H.  S.:  (7  =  0.15  (min.,  0.125;  max., 
0.187):  L.  S.:  C  =  0.114  (min.,  0.1;  max.,  0.156). 

Winder.  —Thickness  of  wall  in  ins.  «  CD  4-0.28.  C  =0.054 
(min.,  0.035;  max..  0.072).  Clearance  volume  5  to  11%  for  H.S.  engines, 
and  from  2  to  5%  for  Corliss  eneines. 

Stud  BoUs.  —  Number  =0.72  D  for  H.  S.  (0.65  D  for  Corliss.)  Diam. 
in  ins.  =  0.04D  -1-0.375. 

Ratio  (C)  of  Stroke  to  Cylinder  Diameter  (L  /DV  —  For  N  >  200, 
C  =  1.07  (min..  0.82;  max.,  1.55):  for  N  =  110  to  200,  C  =  136  (min., 
1  .  03:  max.,  1  .  88)  ;  for  AT  <  110  (Corliss  engines),  C  =  (L  -  8)  /D  =  1  .  63 
(min.,  1.15;  max.,  2.4). 

Piston.  —  Width  of  face  in  ins.  =  CD  +  1.  Mean  value  of  C  =  0.32 
for  H.  S,  (0,26  for  Corliss).  Thickness  of  shell  =  thickness  of  cylinder 
wall  X  0.6  (0.7  for  Corliss). 

Piston  Speeds.  —  H.  S.,  605  ft.  per  min.  (min.  320;  max.,  920)-  Corliss, 
592  ft.  per  min.  (min.,  400;  max.,  800). 

Cross-head.  —  Area  of  shoes  in  sq.  ins.  =0.53  A  (min.,  0.37;  max., 
0.72). 

Cross-head  Pin.  —  Diameter  =  0  .  25  D  (min.,  0.17;  max.,  0.28). 
Length  for  H.S.  =  diam.  X  1.25  (min.,  I;  max.,  1.5);  for  Corliss  = 
diam.  X  1.43  (min.,  1;  max.,  1.9).  _ 

Connecting-rods.  —  Breadth  for  H.  S.  =0.073  ^LCD  (min.,  0.55;  max., 
0.094).  Height  =  breadth  X  2.28  (min.,  1.85;  max.,  3).  For  L.  S.,  diam. 
of  circular  rod  =0.092  ^LCD  (min.,  0.081;  max.,  0.104).  Lc  =  length 

center  to  center  of  bearings. 

Crank-pin.  —  Diam.    for    H.S.  center-crank  engines  *=  0  .  4  D    (min., 
0.28;    max.,    0.526).     Diam.    for   side-crank    Corliss  =  0.27    D    (min.," 
0.21;    max.,    0.32).     Length    for    H.  S.  =  diam.  X0.87    (min.,    0.66; 
max.,  1.25).     Length  for  Corliss  =  diam.  X  1.14  (min.,  1;  max.,  1.3). 

Main  Journals  of  Crank-shaft.  —  For  H.  S.  center-crank  engines,  diam. 
=  6.6    ^H.P./iV  (min.,  5.4;  max.,  8.2).      For  Corliss,  diameter  =  7^2 
(min.,  6.4;  max.,  8). 


... 

Fly-wheels.  —  Total  weight  in  pounds  for  H.S.  up  to  175  H.P. 
=  1  300,000,000,000  H.P.  /DrW3,  where  Di  =  diam.  of  wheel  in  ins. 
(min.,  660,000,000,000;  max.,  2,800,000,000,000).  For  larger  H.S. 
engines,  weight  =  (C  X  H.P.  /Z>i2A73)  4-  1000,  where  C  =  720,000,000,000 
(min.,  330,000,000,000;  max.,  1,140,000,000,000).  For  Corliss  engines, 
weight  =  (C  X  H.P.  /DW3)  -K,  where  C  =  890,000,000,000  (min.,  625,- 
000,000,000;  max.,  1,330,000,000,000),  and  #  =  4000  (min.,  2,800;  max., 
6000).  Diam.  in  ins.=  4.4X  length  of  stroke. 

Belt  Surface  per  I.  H.P.  —  Square  feet  of  belt  surface  per  minute  (S) 
for  H.  S.  =  H.P.  X  26.5  (min.,  10;  max.,  55).  For  Corliss  engines, 
S  =  1000  +  (21  X  H.P.)  (min.,  18.2;  max.,  35). 

•  Velocity  of  Wheel  Rim.  —  For  H.  S.  70  ft.  per  sec.  (min.,  48;   max., 
70);  for  Corliss,  68  ft.  per  sec.  (min.,  40;  max.,  68). 

Weight  of  Reciprocating  Parts  (Piston  +  piston  rod  +  crosshead  +  1/2 
connecting-rod).  —  Weight  in  Ibs.  W  =  (D2/ZJV2)  X  2,000,000  (min., 
1,370,000;  max.,  3,400,000).  Balance  weight  opposite  crank-pin  = 

'Weight  of  engine  per  I.H.P.—  Lbs.  per  I.  H.P.  for  belt-connected  H.  S. 


1042  THE  STEAM-ENGINE. 

engines  =  H.P.  X  82  (min.,  52;  max.,  120).  Do.,  for  Corliss  =»  H.P. 
X  1^2  (min.,  102;  max.,  164). 

Shafts  and  Bearings  of  Engines.  (James  Christie,  Proc. 
Engrs.  Club  of  Phila.,  1898.)  —  The  dimensions  are  determined  by  two 
independent  considerations:  1.  Sufficient  size  to  prevent  excessive 
deflection  or  torsional  yield.  2.  To  provide  sufficient  wearing  surface; 
to  prevent  excessive  wear  of  journals.  Usually,  when  the  first  condi- 
tion is  preserved,  the  other  is  provided  for.  When  the  bearings  are 
flexible,  —  and  excessive  deflection  within  the  limit  of  ordinary  safety 
affects  nothing  external  to  the  bearings,  —  considerable  deflection  can  be 
tolerated.  When  bearings  are  rigid,  or  deflection  may  derange  external 
mechanism,  —  for  example,  an  overhung  crank,  —  then  the  deflection 
must  be  more  restricted.  The  effect  of  deflection  is  to  concentrate 
pressure  on  the  ends  of  journals,  rendering  the  apparent  bearing  surface 
Inefficient. 

In  direct-driven  electric  generators  a  deflection  of  0.01  in.  per  foot  of 
length  has  caused  much  trouble  from  hot  bearings.  I  have  proportioned 
such  shafts  so  that  the  deflection  will  not  exceed  one-half  this  extent. 

In  some  shafts,  especially  those  having  an  oscillating  movement, 
torsional  elasticity  is  a  prime  consideration,  and  the  limits  can  be  known 
only  by  experience.  Reuleaux  says:  "Limit  the  torsional  yield  to  0.1 
degree  per  foot  of  length."  This  in  some  cases  can  be  readily  tolerated; 
in  others,  it  has  proved  excessive.  I  have  adopted  the  following  as  a 
general  guide:  Permissible  twist  per  foot  of  length  =  0.10  degree  for 
easy  service,  without  severe  fluctuation  of  load ;  0.075  degree  for  fluctu- 
ating loads  suddenly  applied ;  0.050  degree  f9r  loads  suddenly  reversed. 

Sufficiency  of  wearing  surface  and  the  limitation  of  pressure  per  unit 
of  surface  are  determined  by  several  conditions:  1.  Speed  of  movement. 
2.  Character  of  material.  3.  Permissible  wear  of  journals  or  bearings. 
4.  Constancy  of  pressure  in  one  direction.  5.  Alternation  of  the  direction 
of  pressure. 

Taking  the  product  of  pressure  per  sq.  in.  of  surface  in  Ibs.,  and  speed 
of  movement  in  ft.  per  min.,  we  obtain  a  quantity,  which  we  can  term 
the  permissible  foot-pounds  per  minute  for  each  sq.  in.  of  wearing  surface. 
This  product  varies  in  good  practice  under  various  conditions  from 
50,000  to  500,000  ft.-lbs.  per  min.  For  instance,  good  practice,  in  later 
years,  has  largely  increased  the  area  of  crosshead  slide  surfaces.  For 
crossheads  having  maximum  speed  of  1000  feet  per  minute,  the  pressure 
per  inch  of  wearing  surface  should  not  exceed  50  pounds,  giving  50,000 
ft.-lbs.  per  min.;  whereas  crank-pins  of  the  requisite  grade  of  steel,  with 
good  lining  metal  in  the  boxes  and  efficient  lubrication,  will  endure 
200,000  ft.-lbs.  per  min.  satisfactorily,  and  more  than  double  this  when 
speeds  are  very  high  and  the  pressure  intermittent.  On  main  shafts, 
with  pressures  constant  in  one  direction,  it  is  advisable  not  to  exceed 
50,000  ft.-lbs.  per  min.  for  heavily  loaded  shafts  at  low  velocity.  This 
may  be  increased  to  100,000  for  lighter  loads  and  higher  velocities.  It 
can  be  inferred,  therefore,  that  the  product  of  speed  and  pressure  cannot 
be  used,  in  any  comprehensive  way,  as  a  rational  basis  for  proportioning 
wearing  surfaces.  The  pressure  per  unit  of  surface  must  be  reduced  as  the 
speed  is  increased,  but  not  in  a  constant  ratio.  A  g9od  example  of 
journals  severely  tested  are  the  recent  110,000-pound  freight  cars,  which 
bear  a  pressure  of  400  Ibs.  per  sq.  in.  of  journal  bearing,  and  at  a  speed 
of  ten  miles  per  hour  make  about  60,000  foot-pounds  per  minute.  . 

Calculating  the  Dimensions  of  Bearings.  (F.  E.  Cardullo,  Mach'y, 
Feb".,  1907.)  —  The  durability  of  the  lubricating  film  is  affected  in  great 
measure  by  the  character  of  the  load  that  the  bearing  carries.  When  the 
load  is  unvarying  in  amount  and  direction,  as  in  the  case  of  a  shaft  carry- 
ing a  heavy  bandwheel,  the  film  is  easily  ruptured.  In  those  cases  where 
the  pressure  is  variable  in  amount  and  direction,  as  in  railway  journals 
and  crank-pins,  the  film  is  much  more  durable.  When  the  journal  only 
rotates  through  a  small  arc,  as  with  the  wrist-pin  of  a  steam-engine,  the 
circumstances  are  most  favorable.  It  has  been  found  that  when  all  other 
circumstances  are  exactly  similar,  a  car  journal  will  stand  about  twice 
the  unit  pressure  that  a  fly-wheel  journal  will.  A  crank-pin,  since  the 
load  completely  reverses  every  revolution,  will  stand  three  times,  and  a 
wrist-Din  will  stand  four  times  the  unit  pressure  that  the  fly-wheel  journal 


DIMENSIONS   OF  PARTS   OF  ENGINES.  1043 

The  amount  of  pressure  that  commercial  oils  will  endure  at  low  speeds 
without  breaking  down  varies  from  500  to  1000  Ibs.  per  sq.  in.,  where  the 
load  is  steady.  It  is  not  safe,  however,  to  load  a  bearing  to  this  extent, 
since  it  is  only  under  favorable  circumstances  that  the  film  will  stand  this 
pressure  without  rupturing.  On  this  account,  journal  bearings  should 
not  be  required  to  stand  more  than  two-thirds  of  this  pressure  at  slow 
speeds,  and  the  pressure  should  be  reduced  when  the  speed  increases. 
The  approximate  unit  pressure  which  a  bearing  will  endure  without 
seizing  is  p  =  PK  -*-  (DN  +  A')  (1).  p  =  allowable  pressure  in  Ibs.  per 
sq.  in.  of  projected  area,  D  =  diam.  of  the  bearing  in  ins.,  N  =  r.p.m. 
and  P  and  K  depend  upon  the  kind  of  oil,  manner  of  lubrication,  etc. 

P  is  the  maximum  safe  unit  pressure  for  the  given  circumstances,  at  a 
very  slow  speed.  In  ordinary  cases,  its  value  is  200  for  collar  thrust 
bearings,  400  for  shaft  bearings,  800  for  car  journals,  1200  for  crank-pins, 
and  1600  for  wrist-pins.  In  exceptional  circumstances,  these  values 
may  be  increased  by  as  much  as  50%,  but  only  when  the  workmanship 
is  of  the  best,  the  care  the  most  skillful,  the  bearing  readily  accessible, 
and  the  oil  of  the  best  quality,  and  unusually  viscous.  In  the  great  units 
of  the  Subway  power  plant  in  New  York,  the  value  of  P  for  the  crank- 

The  factor  K  depends  upon  the  method  of  oiling,  the  rapidity  of  cool- 
ing,  and  the  care  which  the  journal  is  likely  to  get.  It  will  have  about 
the  following  values:  Ordinary  work,  drop-feed  lubrication,  700;  first- 
class  care,  drop-feed  lubrication,  1000;  force-feed  lubrication  or  ring- 
oiling  1200  to  1500;  extreme  limit  for  perfect  lubrication  and  air-cooled 
bearings,  2000.  The  value  2000  is  seldom  used,  except  in  locomotive 
work  where  the  rapid  circulation  of  the  air  cools  the  journals.  Higher 
values  than  this  may  only  be  used  in  the  case  of  water-cooled  bearings. 

In  case  the  bearing  is  some  form  of  a  sliding  shoe,  the  quantity  240  V 
should  be  substituted  for  the  quantity  DN,  V  being  the  velocity  of  rubbing 
in  feet  per  second.  There  are  a  few  cases  where  a  unit  pressure  sufficient 
to  break  down  the  oil  film  is  allowable,  such  as  the  pins  of  punching  and 
shearing  machines,  pivots  of  swing  bridges,  etc, 

In  general,  the  diameter  of  a  shaft  or  pin  is  fixed  from  considerations  of 

strength  or  stiffness.     Having  obtained  the  proper  diameter,  we  must 

next  make  the  bearing  long  enough  so  that  the  unit  pressure  shall  not 

exceed  the  required  value.    This  length  may  be  found  by  the  equation: 

L  =  (W  +  PK)  X  (N  +K/D)  ......     (2) 

where  L  is  the  length  of  the  bearing  in  ins.,  W  the  load  upon  it  in  lbs.( 
and  P,  K,  N,  and  D  are  as  before. 

A  bearing  may  give  poor  satisfaction  because  it  is  too  long,  as  well  as 
because  it  is  too  short.  Almost  every  bearing  is  in  the  condition  of  a 
loaded  beam,  and  therefore  it  has  some  deflection. 

Shafts  and  crank-pins  must  not  be  made  so  long  that  they  will  allow 
the  load  to  concentrate  at  any  point.  A  good  rule  for  the  length  is  to 


make  the  ratio  of  length  to  diameter  about  equal  to  VsV.  This 
quantity  may  be  diminished  by  from  10  to  20%  in  the  case  of  crank-pins 
and  increased  in  the  same  proportion  in  the  case  of  shaft  bearings,  but 
it  is  not  wise  to  depart  too  far  from  it.  In  the  case  of  an  engine  making 
100  r.p.m.,  the  bearings  would  be  by  this  rule  from  11/4  to  11/2  diams.  in 
length.  In  the  case  of  a  motor  running  at  1000  r.p.m.,  the  bearings 
would  be  about  4  diams.  long. 

The  diameter  of  a  shaft  or  pin  must  be  such  that  it  will  be  strong  and 
stiff  enough  to  do  its  work  properly.  In  order  to  design  it  for  strength 
and  stiffness,  it  is  first  necessary  to  know  its  length.  This  may  be  assumed 
tentatively  from  the  equation 


K.     ......     .     (3) 

The  diameter  may  then  be  found  by  any  of  the  standard  equations  for 
the  strength  of  shafts  or  pins  given  in  the  different  works  on  machine 
design.  [See  The  Strength  of  the  Crank-pin,  page  1027.]  The  length  is 
then  recomputed  from  formula  No.  2,  taking  this  new  value  if  it  does 
not  differ  materially  from  the  one  first  assumeoU  If  it  does,  and  espe- 
cially if  it  is  greater  than  the  assumed  length,  take  the  mean  .value  of  the 
assumed  and  computed  lengths,  and  try  again. 
.  EXAMPLE.  —  We  will  take  the  case  of  the  crank-pin  of  an  engine  with  a 


1044  THE   STEAM-ENGINE. 

20-in.  cylinder,  running  at  80  r.p.m.,  and  having  a  maximum  unbalanced 
steam  pressure  of  100  Ibs.  per  sq.  in.  The  total  steam  load  on  the  piston 
is  31,400  pounds.  P  is  taken  at  1200,  and  K  as  1000.  We  will  therefore 
obtain  for  our  trial  length: 

L  =  (20X  31  ,400  X  ^80)  -s-  (  1200X1000)  =  4.  7,  or  say  43/4  ins. 
In  order  that  the  deflection  of  the  pin  shall  not  be  sufficient  to  destroy 
the  lubricating  film  we  have 


which  limits  the  deflection  to  0.003  in.     This  gives  D=  3.85  or  say  37/s 
ins.     With  this  diameter,  formula  No.  2  gives  L  =  8.9,  say  9  ins. 

The  mean  of  this  value  and  the  one  obtained  before  is  about  7  ins. 
Substituting  this  in  the  equation  for  the  diameter,  we  get  5  1/4  ins.  sub- 
stituting this  new  diameter  in  equation  No.  2  we  have  L  =  7.05,  say 

Probably  most  good  designers  would  prefer  to  take  about  half  an  inch 
off  the  length  of  this  pin,  and  add  it  to  the  diameter,  making  it  53/4  X61/2 
inches,  and  this  will  bring  the  ratio  of  the  length  to  the  diameter  nearer 

~ 


Engine-frames  or  Bed-plates. — No  definite  rules  for  the  design 
of  engine-frames  have  been  given  by  authors  of  works  on  the  steam- 
engine.  The  proportions  are  left  to  the  designer  who  uses  "rule  of 
thumb  "  or  copies  from  existing  engines.  F.  A.  Halsey  (Am.  Mach., 
Feb.  14,  1895)  has  made  a  comparison  of  proportions  of  the  frames  of 
horizontal  Corliss  engines  of  several  builders.  The  method  of  comparison 
is  to  compute  from  the  measurements  the  number  of  square  inches  in  the 
smallest  cross-section  of  the  frame,  that  is,  immediately  behind  the 
pillow  btock,  also  to  compute  the  total  maximum  pressure  upon  the  piston, 
and  to  divide  the  latter  quantity  by  the  former.  The  result  gives  the 
number  of  pounds  pressure  upon  the  piston  allowed  for  each  square  inch 
of  metal  in  the  frame.  He  finds  that  the  number  of  Ibs.  per  sq.  in.  of 
smallest  section  of  frame  ranges  from  217  for  a  10  X  30  in.  engine  up  to 
575  for  a  28  X  48  in.  A  30  X  60  in.  engine  shows  350  Ibs.,  and  a  32-in. 
engine  which  has  been  running  for  many  years  shows  667  Ibs.  Generally 
the  strains  increase  with  the  size  of  the  engine,  and  more  cross-section  of 
metal  is  allowed  with  relatively  long  strokes  than  with  short  ones. 

From  the  above  Mr.  Halsey  formulates  the  general  rule  that  in  engines 
of  moderate  speed,  and  having  strokes  up  to  1 1/2  times  the  diameter  of  the 
cylinder,  the  load  per  square  inch  of  smallest  section  should  be  for  a  10-in. 
engine  300  ibs.,  which  figure  should  be  increased  for  larger  bores  up  to  500 
Ibs.  for  a  30-in.  cylinder  of  the  same  relative  stroke.  For  high  speeds  or 
for  longer  strokes  the  load  per  square  inch  should  be  reduced. 

FLY-WHEELS. 

The  function  of  a  fly-wheel  is  to  store  up  and  to  restore  the  periodical 
fluctuations  of  energy  given  to  or  taken  from  an  engine  or  machine,  and 
thus  to  keep  approximately  constant  the  velocity  of  rotation.  Eankine 

calls  the  quantity  -^-=r  the  coefficient  of  fluctuation  of  speed  or  of  un- 

Z  Ji/Q 

steadiness,  in  which  E0  is  the  mean  actual  energy,  and  A/7  the  excess 
of  energy  received  or  of  work  performed,  above  the  mean,  during  a 
given  interval.  The  ratio  of  the  periodical  excess  or  deficiency  of  energy 
A£"  to  the  whole  energy  exerted  in  one  period  or  revolution  General 
Morin  found  to  be  from  i/e  to  1/4  for  single-cylinder  engines  using  expan- 
sion; the  shorter  the  cut-off  ^he  higher  the  value.  For  a  pair  of  engines 
with  cranks  coupled  at  90°  the  value  of  the  ratio  is  about  1/4,  and  for 
three  engines  with  cranks  at  120°,  1/12  of  its  value  for  single-cylinder 
engines.  For  tools  working  at  intervals,  such  as  punching,  slotting  and 
plate-cutting  machines,  coining-presses,  etc.,  &E  is  nearly  equal  to  the 
whole  work  performed  at  each  operation. 

A  fly-wheel  reduces  the  coefficient  to  a  certain  fixed  amount,  being 

2     lilQ 

about  1/32  for  ordinary  machinery,  and  1/50  or  Veo  for  machinery  for  fine 
purposes. 


FLY-WHEELS.  1045 

If  m  be  the  reciprocal  of  the  intended  value  of  the  coefficient  of  fluc- 
tuation of  speed,  A#  the  fluctuation  of  energy,  /  the  moment  of  inertia 

of  the  fly-wheel  alone,  and  a0  its  mean  angular  velocity,  /  =        2  •  •     As 

the   rim  of  a  fly-wheel  is  usually  heavy  in  comparison  with  the  arms, 
/  may  be  taken  to  equal  VFr2,  in  which  W  =  weight  of  rim  in  pounds,  and 


r  the  radius  of  the  wheel;  then  W  =  ^~  =  -^~  ,  if  v  be  the  velocity 

of  the  rim  in  feet  per  second.     The  usual  mean  radius  of  the  fly-wheel 
in  steam-engines  is  from  three  to  five  times  the  length  of  the  crank.     The 
ordinary  values  of  the  product  mg,  the  unit  of  time  being  the  second,  lie 
between  1000  and  2000  feet.     (Abridged  from  Rankine,  S.  E.,  p.  62.) 
Thurston  gives  for  engines  with  automatic  valve-gear  W  =  250,000 

,  in  which  A  =  area  of  piston  in  square  inches,  S  =  stroke  in  feet, 

p  =  mean  steam-pressure  in  Ibs.  per  sq.  in.,  R  =  revolutions  per  minute, 
D  =  outside  diameter  of  wheel  in  feet.  Thurston  also  gives  for  ordinary 
forms  of  non-condensing  engine  with  a  ratio  of  expansion  between  3  and 


5t  w  =  jL™,  in  which  a  ranges  from  10,000,000  to  15,000,000,  averaging 


12,000,000.  For  gas-engines,  in  which  the  charge  is  fired  with  every 
revolution,  the  American  Machinist  gives  this  latter  formula,  with  a 
doubled,  or  24,000,000.  Presumably,  if  the  charge  is  fired  every  other 
revolution,  a  should  be  again  doubled. 

Rankine   ("Useful  Rules  and  Tables,"  p.  247)   gives   ^=475,000 
ASx) 

VD*R*  '  ia  whicil  V  is  the  variation  of  speed,  per  cent  of  the  mean  speed. 
Thurston's  first  rule  above  given  corresponds  with  this  if  we  take  V  =  1.9. 

Hartnell  (Proc.  InsL  M.  E.,  1882,  427)  says:  The  value  of  V,  or  the 
variation  permissible  in  portable  engines,  should  not  exceed  3%  with  an 
ordinary  load,  and  4%  when  heavily  loaded.  In  fixed  engines,  for  ordi- 
nary purposes,  V  =  2  1/2  to  3%.  For  good  governing  or  special  purposes, 
such  as  cotton-spinning,  the  variation  should  not  exceed  11/2  to  2%. 

F.  M.  Rites   (Trans.  A.  S.  M.  E.,  xiv,  100)  develops  a  new  formula  for 

C  X  I  H  P 
weight  of  rim,  viz.,  W  =  —   32  '     ,  and  weight  of  rim  per  horse-power 


,  in  which  C  varies  from  10,000,000,000  to  20,000,000,000;  also 


using  the  latter  value  of  C,  he  obtains  for  the  energy  of  the  fly-wheel 
M&  =  W  (3.14)2Z>2/?2  =  CX  H.P.  (3.14)2  D2/?2  =  850,000  H.P.  F1 

2          64.4        3600  =     WD*  X  64  .  4  X  3600  R 

wheel  energy  per  H.P.  =  850,000  -s-  R. 

The  limit  of  variation  of  speed  with  such  a  weight  of  wheel  from  excess 
of  power  per  fraction  of  revolution  is  less  than  0.0023. 

The  value  of  the  constant  C  given  by  Mr.  Rites  was  derived  from 
practice  of  the  Westinghouse  single-acting  engines  used  for  electric- 
lighting.  For  double-acting  engines  in  ordinary  service  a  value  of  C  — 
5,000,000,000  would  probably  be  ample. 

From  these  formulas  it  appears  that  the  weight  of  the  fly-wheel  for  a 
given  horse-power  should  vary  inversely  with  the  cube  of  the  revolutions 
and  the  square  of  the  diameter. 

J.  B.  Stanwood  (Eng'g,  June  12,  1891)  says:  Whenever  480  feet  is  the 
lowest  piston-speed  probable  for  an  engine  of  a  certain  size,  the  fly-wheel 
weight  for  that  speed  approximates  closely  to  the  formula 

W  =  700,000  (Ps  -f-  D2#2. 

W  =  weight  in  pounds,  d  =  diameter  of  cylinder  in  inches,  s  =  stroke 
in  inches,  D  =  diameter  of  wheel  in  feet,  R  =  revolutions  per  minute, 
corresponding  to  480  feet  piston-speed. 

In  a  Ready  Reference  Book  published  by  Mr.  Stanwood,  Cincinnati; 
1892,  he  gives  the  same  formula,  with  coefficients  as  follows:  For  slide- 
valve  engines,  ordinary  duty,  350,000:  same,  electric  lighting,  700,000; 
for  automatic  high-speed  engines,  1,000,000;  for  Corliss  engines,  ordinary 
duty  700,000,  electric  lighting  1,000,000. 


1046 


THE  STEAM-ENGINE. 


Thurston's  formula  above  given,  W  =  aAS  -j-  R*D*  with  a  =12,000,000 
if  reduced  to  terms  of  d  and  s  in  ins.,  becomes  W  =  785,400  d"s  -H  R^D*. 
If  we  reduce  it  to  terms  of  horse-power,  we  have  I.H.P.  =  2  ASPR  + 
33,000,  in  which  P  =  mean  effective  pressure.  Taking  this  at  40  Ibs., 
we  obtain  W  =  5,000,000,000  I.H.P.  -=-  RW*.  If  mean  effective  pres- 
sure =  30  Ibs.,  then  W  =  6,666,000,000  I.H.P.  -=-  jR3£)2. 

Emil  Theiss  (Am.  Mach.,  Sept.  7  and  14,  1893)  gives  the  following 
values  of  d,  the  coefficient  of  steadiness,  which  is  the  reciprocal  of  what 
Rankine  calls  the  coefficient  of  fluctuation: 
For  engines  operating — 

Hammering  and  crushing  machinery d  =    5 

Pumping  and  shearing  machinery d  =  20  to  30 

Weaving  and  paper-making  machinery d  =  40 

Milling  machinery d  =  50 

Spinning  machinery d  =  50  to  100 

Ordinary     driving-engines     (mounted     on     bed- 
plate) ,  belt  transmission d  =  35 

Gear-wheel  transmission d  =  50 

Mr.  Theiss's  formula  for  weight  of  fly-wheel  in  pounds  is  W  =  i  X 
d  X  I  H  P 
V2  v   — *'  wnere  ^  *s  tne  coefficient  of  steadiness,  V  the  mean  velocity 

of  the  fly-wheel  rim  in  feet  per  second,  n  the  number  of  revolutions  per 
minute,  i  =  a  coefficient  obtained  by  graphical  solution,  the  values  of 
which  for  different  conditions  are  given  in  the  following  table.  In 
the  lines  under  "cut-off,"  p  means  "compression  to  initial  pressure," 
and  O  "no  compression." 

VALUES  OF  i.     SINGLE-CYLINDER  NON-CONDENSING  ENGINES. 


Piston- 
speed,  ft. 
per  min. 

Cut-off,  1/6. 

Cut-off,  1/4. 

Cut-off,  1/3. 

Cut-off,  1/2. 

Comp. 
P 

0 

Comp. 
P 
242,010 
208,200 
168,590 
162,070 

O 

Comp. 
P 
220,760 
188.510 
165.210 

0 

Comp. 
P 

0 

200 
400 
600 
800 

272,690 
240,810 
194,670 
158,200 

218,580 
187,430 
145,400 
108.690 

209,170 
179,460 
1  36.460 
135,260 

201,920 
170.040 
146,610 

193,340 
174.630 

182.840 
167,860 

SINGLE-CYLINDER  CONDENSING  ENGINES. 


Piston- 
speed,  ft. 
per  min. 

Cut-off,  1/8. 

Cut-off,  1/6- 

Cut-off,  1/4. 

Cut-off,  .1/3. 

Cut-off,  1/9. 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

O 

Comp. 
P 

0 

Comp. 
P 

0 

200 

400 
600 

265.560 
194,550 
148,780 

176,560 
117,870 
140,090 

234,160 
174,380 

173,660 
118,350 

204,210 
164,720 

167,140 
133,080 

189,600 
174.630 

161,830 
151,680 

172,690 

156,990 

TWO-CYLINDER  ENGINES,  CRANKS  AT  90°. 


Piston- 

Cut-off,  l/e. 

Cut-off,  1/4. 

Cut-off,  1/3. 

Cut-off,  1/2. 

speed,  ft. 

Comp. 

Q 

Comp. 

o 

Comp. 

Q 

Comp. 

Q 

P 

P 

P 

P 

200 
400 
600 

71,980 
70,160 
70.040 

} 
{  Mean 
[60,140 

59,420 
57,000 
57,480 

Mean 
54,340 

49.272 
49.150 

40  9?ft 

Mean 
50,000 

37,920 
35,000 

1  Mean 
\  36,950 

800 

70.040 

J 

60.140 

J 

THREE-CYLINDER  ENGINES,  CRANKS  AT  120°. 


Piston- 
speed,  ft. 
per  min. 

Cut-off,  1/6. 

Cut-off,  1/4. 

Cut-off,  1/3. 

Cut-off,  1/2. 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

O 

200 
800 

33.810 
30.190 

32.240 
31,570 

33,810 
35,140 

35,500 
33,810 

34,540 
36,470 

33.450 
32,850 

35,260 
33,810 

32.370 
32.370 

As  a  mean  value  of  i  for  these  engines  we  may  use  33,810. 


FLY-WHEELS.  1047 

Weight  of  Fly-wheels  for  Alternating-current  Units.  —  (J.  Begtrup, 
Am.  Mach.,  July  10,  1902.)— 


In  which  T7=  weight  of  rim  of  fly-wheel  in  pounds,  D  =  mean  diameter 
of  rim  in  feet,  W\  =  weight  of  armature  in  pounds,  D\=  mean  diameter 
of  armature  in  feet,  //  =  rated  horse-power  of  engine,  U  =  a  factor  of 
steadiness,  N  =  number  of  revolutions  per  minute,  V  =  maximum 
instantaneous  displacement  in  degrees,  not  to  exceed  5  degrees  divided 
by  the  number  of  poles  on  the  generator,  according  to  the  rule  of  the 
General  Electric  Company. 

For  simple  horizontal  engines,  length  of  connecting-rod  =  5  cranks, 
U  =  90;  (ditto,  no  account  being  taken  of  angularity  of  connecting-rod, 
U  =  64)  ;  cross-compound  horizontal  engines,  connecting-rod  =  5  cranks, 
U  =  51;  ditto,  vertical  engines,  heavy  reciprocating  parts,  unbalanced, 
U  =  78;  vertical  compound  engines,  cranks  180  degrees  apart,  recipro- 
cating parts  balanced,  U  =  60. 

The  small  periodical  variation  in  velocity  (not  angular  displacement) 
can  be  determined  from  the  following  formula: 

„          387,700,000  HZ 


in  which  H  =  rated  horse-power,  Z  =  a  factor  of  steadiness,  N  =  revs. 
per  min.,  D  =  mean  diameter  of  fly-wheel  rim  in  feet,  W=  weight  of  fly- 
wheel rim  in  pounds,  Di  =  mean  diameter  of  armature  or  field  in  feet, 
Wi  =  weight  of  armature,  F  =  variation  in  per  cent  of  mean  speed. 

For  simple  engines  and  tandem  compounds,  Z  =  16;  for  horizontal 
cross-compounds,  Z  =  8.5;  for  vertical  cross-compounds,  heavy  recip- 
rocating parts,  Z  =  12.5;  for  vertical  compounds,  cranks  opposite, 
weights  balanced,  Z  —  14.  F  represents  here  the  entire  variation, 
between  extremes  —  not  variation  from  mean  speed.  It  generally  varies 
from  0.25%  of  mean  speed  to  0.75%  —  evidently  a  negligible  quantity. 

A  mathematical  treatment  of  this  subject  will  be  found  in  a  paper 
by  J.  L.  Astrom,  in  Trans.  A.  8.  M.  E.,  1901. 

Centrifugal  Force  in  Fly-wheels.  —  Let  W  =  weight  of  rim  in 
pounds;  R  =  mean  radius  of  rim  in  feet;  r  =  revolutions  per  minute, 
g  =  32.16;  v  =  velocity  of  rim  in  feet  per  second  =  2nRr  •*-  60. 

Centrifugal  force  of  whole  rim  =  F  =  ^  =  *™^?r*  =  0.000341  WRr*. 

ffK  oOUU  Q 

The  resultant,  acting  at  right  angles  to  a  diameter,  of  half  of  this  force 
tends  to  disrupt  one  half  of  the  wheel  from  the  other  half,  and  is  resisted 
by  the  section  of  the  rim  at  each  end  of  the  diameter.  The  resultant  of 
half  the  radial  forces  taken  at  right  angles  to  the  diameter  is  1  -5-  i/V  = 
2/7T  of  the  sum  of  these  forces  ;  hence  the  total  force  F  is  to  be  divided  by 
2X2X1.  5708  =  6.  2832  to  obtain  the  tensile  strain  on  the  cross-section 
of  the  rim,  or,  total  strain  on  the  cross-section  =  S  =  0.00005427  WRr*. 
The  weight  IFi  of  a  rim  of  cast  iron  1  inch  square  in  section  is  2  nR  X 
3.125  =  19.635/2  pounds,  whence  strain  per  square  inch  of  sectional 
area  of  rim  =  Si  =  0.0010656  /?2r2  =  0.0002664  D2r2  =  0.0000270  Fa, 
In  which  D  =  diameter  of  wheel  in  feet,  and  V  is  velocity  of  rim  in  feet 
per  minute.  Si  =  0.  0972  v2,  if  v  is  taken  in  feet  per  second. 

For  wrought  iron: 

.Sj  =  0.0011366  #2r2  =  0.0002842  D2r2  =  0.0000288  V2. 

For  steel: 

Si  =  0.0011593  #2r2  =  0.0002901  £>2r2  =  0.0000294  V2. 

For  wood: 

Si  =  0.0000888  #V2  =  0.0000222  £>V2  =  0.00000225  V2. 
The  specific  gravity  of  the  wood  being  taken  at  0.6  =  37.5  Ibs.  per  cu. 
ft.,  or  1/12  the  weight  of  cast  iron. 

EXAMPLE.  —  Required  the  strain  per  square  inch  in  the  rim  of  a  cast- 
iron  wheel  30  ft.  diameter,  60  revolutions  per  minute. 

Answer.  —  152  X  602  X  0.0010656  =  863.  1  Ibs. 

Required  the  strain  per  square  inch  in  a  cast-iron  wheel-rim  running 
a  mile  a  minute.  Answer.—  0.000027  X  52802  =  752.7  Ibs. 


1048  THE  STEAM-ENGINE. 

In  cast-iron  fly-wheel  rims,  on  account  of  their  thickness,  there  is 
difficulty  in  securing  soundness,  and  a  tensile  strength  of  10,000  Ibs. 
per  sq.  in.  is  as  much  as  can  be  assumed  with  safety.  Using  a  factor  of 
safety  of  10  gives  a  maximum  allowable  strain  in  the  rim  of  1000  Ibs. 
per  sq.  in.,  which  corresponds  to  a  rim  velocity  of  6085  ft.  per  minute. 

For  any  given  material,  as  cast  iron,  the  strength  to  resist  centrifugal 
force  depends  only  on  the  velocity  of  the  rim,  and  not  upon  its  bulk  or 
weight. 

Chas.  E.  Emery  (Cass.  Mag.,  1892)  says:  It  does  not  appear  that  fly- 
wheels of  customary  construction  should  be  unsafe  at  the  comparatively 
low  speeds  now  in  common  use  if  proper  materials  are  used  in  con- 
struction. The  cause  of  rupture  of  fly-wheels  that  have  failed  is  usually 
either  the  "running  away  of  the  engine,  such  as  may  be  caused  by 
the  breaking  or  slackness  of  a  governor-belt,  or  incorrect  design  or  de- 
.  fective  materials  of  the  fly-wheel. 

Chas.  T.  Porter  (Trans.  A.S.M.E.,  xiv,  808)  states  that  no  case  of  the 
bursting  of  a  fly-wheel  with  a  solid  rim  in  a  high-speed  engine  is  known. 
He  attributes  the  bursting  of  wheels  built  in  segments  to  insufficient 
strength  of  the  flanges  and  bolts  by  which  the  segments  are  held  together. 
[The  author,  however,  since  the  above  was  written,  saw  a  solid  rim  fly- 
wheel of  a  high-speed  engine  which  had  burst,  the  cause  being  a  large 
shrinkage  hole  at  the  junction  between  one  of  the  arms  and  the  rim.  The 
wheel  was  about  6  ft.  diam.  Fortunately  no  one  was  injured  by  the 
accident.]  (See  also  Thurston,  "Manual  of  the  Steam-engine,"  Part  II, 
page  413.) 

Diameters  of  Fly-wheels  for  Various  Speeds.  —  If  6000  feet  per 
minute  be  the  maximum  velocity  of  rim  allowable,  then  6000  =  nRD, 
in  which  R  =  revolutions  per  minute,  and  D=  diameter  of  wheel  in  feet, 
whence  D  =  6000  •*•  irR  =  1910  -s-  R. 

W.  H.  Boehm,  Supt.  of  the  Fly-wheel  Dept.  of  the  Fidelity  and  Casu- 
alty Co.  (Eng.  News,  Oct.  2,  1902),  says:  For  a  given  material  there  is  a 
definite  speed  at  which  disruption  will  occur,  regardless  of  the  amount 
of  material  used.  This  mathematical  truth  is  expressed  by  the  formula: 

V  =  1.6  VSIW\ 

In  which  V  is  the  velocity  of  the  rim  of  the  wheel  in  feet  per  second  at 
which  disruption  will  occur,  W  the  weight  of  a  cubic  inch  of  the  material 
used,  and  S  the  tensile  strength  of  1  square  inch  of  the  material. 

For  cast-iron  wheels  made  in  one  piece,  assuming  20,000  Ibs.  per  sq. 
in.  as  the  strength  of  small  test  bars,-  and  10,000  Ibs.  per  sq.  in.  in  large 
castings,  and  applying  a  factor  of  safety  of  10,  V  =  1.6  ^1000/0.26  = 
100  ft.  per  second  for  the  safe  speed.  For  cast  steel  of  60,000  Ibs.  per 
sq.  in.,  V  =  1.6  Veooo  •*-  0.28  =  233  ft.  per  second.  This  is  for  wheels 
made  in  one  piece.  If  the  wheel  is  made  in  halves,  or  sections,  the 
efficiency  of  the  rim  joint  must  be  taken  into  consideration.  For  belt 
wheels  with  flanged  and  bolted  rim  joints  located  between  the  arms,  the 
joints  average  only  one-fifth  the  strength  of  the  rim,  and  no  such  joint 
can  be  designed  having  a  strength  greater  than  one-fourth  the  strength 
of  the  rim.  If  the  rim  is  thick  enough  to  allow  the  joint  to  be  reinforced 
by  steel  links  shrunk  on,  as  in  heavy  balance  wheels,  one-third  the 
strength  of  the  rim  may  be  secured  in  the  joint;  but  this  construction  can 
not  be  applied  to  belt  wheels  having  thin  rims. 

For  hard  maple,  having  a  tensile  strength  of  10,500  Ibs.  per  sq.  in., 
and  weighing  0.0283  Ib.  per  cu.  in.,  we  have,  using  a  factor  of  safety  of 
20,  and  remembering  that  the  strength  is  reduced  one-half  because  the 
wheel  is  built  up  of  segments,  F  =  1.6  ^262.5  -*-  0.0283  =  154  ft.  per 
second.  The  stress  in  a  wheel  varies  as  the  square  of  the  speed,  and  the 
factor  of  safety  on  speed  is  the  square  root  of  the  factor  of  safety  on 
strength. 

Mr.  Boehm  gives  the  following  table  of  safe  revolutions  per  minute 
of  cast-iron  wheels  of  different  diameters.  The  flange  joint  is  taken  at 
0 . 25  of  the  strength  of  a  wheel  with  no  joint,  the  pad  joint,  that  is  a  wheel 
made  in  six  segments,  with  bolted  flanges  or  pads  on  the  arms,  =  0.50. 
and  the  link  joint  =-  0.60  of  the  strength  of  a  solid  rim. 


FLY-WHEELS. 


1049 


SAFE  REVOLUTIONS  PER  MINUTE  OF  CAST-IRON  FLY-WHEELS. 


No 

Flange 

Pad 

Link 

No 

Flange 

Pad 

Link 

joint. 

joint. 

joint. 

joint. 

joint. 

joint. 

joint. 

joint. 

Diam. 

3iam. 

in 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

in 

R.P.M. 

R.P.M 

R.P.M. 

R.P.M. 

Ft. 

Ft. 

1 

1910 

955 

1350 

1480 

16 

120 

60 

84 

92 

2 

955 

478 

675 

740 

17 

112 

56 

79 

87 

3 

637 

318 

450 

493 

18 

106 

53 

75 

82 

A 

478 

239 

338 

370 

19 

100 

50 

71 

78 

5 

382 

191 

270 

296 

20 

95 

48 

68 

74 

6 

318 

159 

225 

247 

21 

91 

46 

65 

70 

7 

273 

136 

193 

212 

22 

87 

44 

62 

67 

8 

239 

119 

169 

185 

23 

84 

42 

59 

64 

9 

212 

106 

150 

164 

24 

80 

40 

56 

62 

10 

191 

96 

135 

148 

25 

76 

38 

54 

59 

11 

174 

87 

123 

135 

26 

74 

37 

52 

57 

12 

159 

80 

113 

124 

27 

71 

35 

50 

55 

13 

147 

73 

104 

114 

28 

68 

34 

48 

53 

14 

136 

68 

96 

106 

29 

66 

33 

47 

51 

_L 

128 

64 

90 

99 

30 

64 

32 

45 

49 

The  table  is  figured  for  a  margin  of  safety  on  speed  of  approximately 
3,  which  is  equivalent  to  a  margin  on  stress  developed,  or  factor  of  safety 
in  the  usual  sense,  of  9.  (Am.  Mack.,  Nov.  17,  1904.) 

Strains  in  the  Rims  of  Fly-band  Wheels  Produced  by  Centrif- 
ugal Force.  (James  B.  Stanwood,  Trans.  A.  S.  M.  E.,  xiv,  251.)  — 
Mr.  Stanwood  mentions  one  case  of  a  fly-band  wheel  where  the  periphery 
velocity  on  a  17  ft.  9  in.  wheel  is  over  7500  ft.  per  minute. 

In  band-saw  mills  the  blade  of  the  saw  is  operated  successfully  over 
wheels  8  and  9  ft.  in  diameter,  at  a  periphery  velocity  of  9000  to  10,000  ft. 
per  minute.  These  wheels  are  of  cast  iron  throughout,  of  heavy  thick- 
ness, with  a  large  number  of  arms. 

In  shingle-machines  and  chipping-machines  where  cast-iron  disks 
from  2  to  5  ft.  in  diameter  are  employed,  with  knives  inserted  radially, 
the  speed  is  frequently  10,000  to  11,000  ft.  per  minute  at  the  periphery. 

If  the  rim  of  a  fly-wheel  alone  be  considered,  the  tensile  strain  in  pounds 
per  square  inch  of  the  rim  section  is  T  =  F2/10  nearly,  in  which  V  = 
velocity  in  feet  per  second;  but  this  strain  is  modified  by  the  resistance 
of  the  arms,  which  prevent  the  uniform  circumferential  expansion  of  the 
rim,  and  induce  a  bending  as  well  as  a  tensile  strain.  Mr.  Stanwood 
discusses  the  strains  in  band-wheels  due  to  transverse  bending  of  a  section 
of  the  rim  between  a  pair  of  arms. 

When  the  arms  are  lew  in  number,  and  of  large  cross-section,  the  rim 
will  be  strained  transversely  to  a  greater  degree  than  with  a  greater  num- 
ber of  lighter  arms.  To  illustrate  the  necessary  rim  thicknesses  for  vari- 
ous rim  velocities,  pulley  diameters,  number  of  arms,  etc.,  the-  following 
table  is  given,  based  upon  the  formula 


t-  0.475  <!+*. 


(£  -jL) 


in  which  t=  thickness  of  rim  in  inches,  d=  diameter  of  pulley  in  inches, 
N  =  number  of  arms,  V  =  velocity  of  rim  in  feet  per  second,  and  F=  the 
greatest  strain  in  pounds  per  square  inch  to  which  any  fiber  is  subjected. 
The  value  of  F  is  taken  at  0000  ibs.  per  sq.  in. 


1050 


THE   STEAM-ENGINE. 


THICKNESS  OF  RIMS  IN  SOLID  WHEELS. 


Diameter  of 
Pulley  in 
inches. 

Velocity  of 
Rim  in  feet  per 
second. 

Velocity  of 
Rim  in  feet  per 
minute. 

No.  of  Arms. 

Thickness  in 
inches. 

24 

50 

3,000 

6 

2/10 

24 

88 

5,280 

6 

15/32 

48 

88 

5,280 

6 

15/18 

108 

184 

11,040 

16 

2V2 

108 

184 

11,040 

36 

1/3 

If  the  limit  of  rim  velocity  for  all  wheels  be  assumed  to  be  88  ft.  per 
second,  equal  to  1  mile  per  minute,  F  =  6000  IDS.,  the  formula  becomes 

t  =  0.475d  -i-  0.672V2  =  0.7  d  -J-  N*. 

When  wheels  are  made  in  halves  or  in  sections,  the  bending  strain  may 
be  such  as  to  make  t  greater  than  that  given  above.  Thus,  when  the 
joint  comes  half  way  between  the  arms,  the  bending  action  is  similar  to 
a  beam  supported  simply  at  the  ends,  uniformly  loaded,  and  t  is  50% 

greater.    Then  the  formula  becomes  t  =  0.712  d  +  N*\-^-2  —  -TQ),  or  for  a 

fixed  maximum  rim  velocity  of  88  ft.  per  second  and  F  —  6000  Ibs.,  (•= 
1.05d  -s-  N2.  In  segmental  wheels  it  is  preferable  t9  have  the  "joints 
opposite  the  arms.  Wheels  in  halves,  if  very  thin  rims  are  to  be  em- 
ployed,  should  have  double  arms  along  the  line  of  separation. 

Attention  should  be  given  to  the  proportions  of  large  receiving  and 
tightening  pulleys.  The  thickness  of  rim  for  a  48-in.  wheel  (shown  in 
table)  with  a  rim  velocity  of  88  ft.  per  second,  is  15/ie  in.  Many  wrecks 
have  been  caused  by  the  failure  of  receiving  or  tightening  pulleys  whose 
rims  have  been  too  thin.  Fly-wheels  calculated  for  a  given  coefficient 
of  steadiness  are  frequently  lighter  than  the  minimum  safe  weight.  This 
is  true  especially  of  large  wheels.  A  rough  guide  to  the  minimum  weight 
of  wheels  can  be  deduced  from  our  formulae.  The  arms,  hub,  lugs,  etc., 
usually  form  from  one-quarter  to  one-third  the  entire  weight  of  the  wheel. 


sectional  wheels  (joint  between  arms)  t  =  1.05  d  -*•  Nz.  Weight  of  rim 
for  solid  wheels,  w  =  0 . 57  d2b  -s-  Nz,  in  pounds.  Weight  of  rim  in  sec- 
tions wheels  with  joints  between  arms,  w  =  0.86  d?b  •*•  A'2,  in  pounds. 
Total  weight  of  wheel:  for  solid  wheel,  W  =  0.76  d?b  -s-  A72  to  0.86  dzb  -*- 
N2,  in  pounds.  For  segmental  wheels  with  joint  between  arms,  W  = 
1 .05  d?b  -f-  N2  to  1 .3  d?b  •*•  N*,  in  pounds. 

(This  subject  is  further  discussed  by  Mr.  Stanwood,  in  vol.  xv,  and  by 
Prof.  Gaetano  Lanza,  in  vol.  xvi,  Trans.  A.  S.  M.  E.) 

Arms  of  Fly-wheels  and  Pulleys.  —  Professor  Torrey  (Am.  Mack* 
July  30,  1891)  gives  the  following  formula  for  arms  of  elliptical  cross- 
section  of  cast-iron  wheels: 

W  =  load  in  pounds  acting  on  one  arm:  S  =  strain  on  belt  in  pounds 
per  inch  of  width,  taken  at  56  for  single  and  112  for  double  belts;  v  = 
width  of  belt  in  inches;  n  =  number  of  arms;  L  =  length  of  arm  in  feet; 
b  =  breadth  of  arm  at  hub;  d  =  depth  of  arm  at  hub,  both  in  inches; 
W  =  Sv  +  n;  b  =  WL  ^  30  d2.  The  breadth  of  the  arm  is  its  least 
dimension  =  minor  axis  of  the  ellipse,  and  the  depth  the  major  axis. 
This  formula  is  based  on  a  factor  of  safety  of  10. 

In  using  the  formula,  first  assume  some  depth  for  the  arm,  and  calcu- 
late the  required  breadth  to  go  with  it.  If  it  gives  too  round  an  arm, 
assume  the  depth  a  little  greater,  and  repeat  the  calculation.  A  second 
trial  will  almost  always  give  a  good  section. 

The  size  of  the  arms  at  the  hub  having  been  calculated,  they  may  be 
somewhat  reduced  at  the  rim  end.  The  actual  amount  cannot  be  cal- 
culated, as  there  are  too  many  unknown  quantities.  However,  the  depth 


FLY-WHEELS.  1051 

and  breadth  can  be  reduced  about  one-third  at  the  rim  without  danger, 
and  this  will  give  a  well-shaped  arm. 

Pulleys  are  often  cast  in  halves,  and  bolted  together.  When  this  is 
done  the  greatest  care  should  be  taken  to  provide  sufficient  .metal  in  the 
bolts.  This  is  apt  to  be  the  very  weakest  point  in  such  pulleys.  The 
combined  area  of  the  bolts  at  each  joint  snould  be  about  28/100  the 
cross-section  of  the  pulley  at  that  point.  (Torrey.) 

Unwin gives  d  =  0 . 6337  ^/ BD/n  for  single  belts; 

d  =  0 . 798  ^jBD/n  for  double  belts ; 


D  being  the  diameter  of  the  pulley,  and  B  the  breadth  of  the  rirn,  both  in 
inches.  These  formulae  are  based  on  an  elliptical  section  of  arm  in  which 
b  =  0.4dqrd  =  2.56ona  width  of  belt  =  4/s  the  width  of  the  pulley 
rim,  a  maximum  driving  force  transmitted  by  the  belt  of  56  Ibs.  per  inch 
of  width  for  a  single  belt  and  112  Ibs.  for  a  double  belt,  and  a  safe  working 
stress  of  cast  iron  of  2250  Ibs.  per  square  inch. 

If  in  Torrey's  formula  we  make  6  =  0.4  c/,  it  reduces  to 

/    WL  .  .,         */WL 
o  —  < 


.        V 
=  V  1 


EXAMPLE.  —  Given  a  pulley  10  feet  diameter;  8  arms,  each  4  feet  long:; 
face,  36  inches  wide;  belt,  30  inches:  required  the  breadth  and  depth  of  the 
arm  at  the  hub.  According  to  Unwin, 

d  =  0.6337  $ 'BD/n  =0.633^/36X  120/8  =  5.16  for  single  belt,  6  =  2.06; 
d  =  0.798  -yBD/n  =  0.798  ^36  X  120/8  =  6.50  for  double  belt,  6  =  2.60. 

According  to  Torrey,  if  we  take  the  formula  6  =  WL  -f-  30  d2  and 
assume  d  =  5  and  6.5  inches,  respectively,  for  single  and  double  belts, 
we  obtain  6  =•=  1.08  and  1.33,  respectively,  or  practically  only  one-half 
of  the  breadth  according  to  Unwin,  and,  since  transverse  strength  is  pro- 
portional to  breadth,  an  arm  only  one-half  as  strong. 

Torrey's  formula  is  said  to  be  based  on  a  factor  of  safety  of  10,  but  this 
factor  can  be  only  apparent  and  not  real,  since  the  assumption  that  the 
strain  on  each  arm  is  equal  to  the  strain  on  the  belt  divided  by  the  num- 
ber of  arms,  is,  to  say  the  least,  inaccurate.  It  would  be  more  nearly 
correct  to  say  that  the  strain  of  the  belt  is  divided  among  half  the  number 
of  arms.  Unwin  makes  the  same  assumption  in  developing  his  formula, 
but  says  it  is  only  in  a  rough  sense  true,  and  that  a  large  factor  of  safety 
must  be  allowed.  He  therefore  takes  the  low  figure  of  2250  Ibs.  per  square 
inch  for  the  safe  working  strength  of  cast  iron.  Unwin  says  that  his 
equations  agree  well  with  practice. 

A  Wooden-rim  Fly-wheel,  built  in  1891  for  a  pair  of  Corliss  engines 
at  the  Amoskeag  Mfg.  Co.'s  mill,  Manchester,  N.H.,  is  described  by 
C.  H.  Manning  in  Trans.  A.  S.  M.  E.,  xiii,  618.  It  is  30  ft.  diam.  and 
108  in.  face.  The  rim  is  12  inches  thick,  and  is  built  up  of  44  courses  of 
ash  plank,  2,  3,  and  4  inches  thick,  reduced  about  1/2  inch  in  dressing, 
set  edgewise,  so  as  to  break  joints,  and  glued  and  bolted  together.  There 
are  two  hubs  and  two  sets  of  arms,  12  in  each,  all  of  cast  iron.  The  weights 
are  as  follows: 

Weight  (calculated)  of  ash  rim 31,855     Ibs. 

Weight  of  24  arms  (foundry  45,020) 40  349 

Weight  of  2  hubs  (found ry* 35,030) 31, 394  ±    " 

Counter-weights  in  6  arms 664       " 

Total,  excluding  bolts  and  screws 104, 262 ±   " 

The  wheel  was  tested  at  76  revs,  per  min.,  being  a  surface  speed  of 
nearly  7200  feet  per  minute. 

Wooden  Fly-wheel  of  the  Willimantic  TJnen  Co.  (Illustrated  in 
Power,  March,  1893.)  —  Rim  28  ft.  diam.,  110  in.  face.  The  rim  is 
carried  upon  three  sets  of  arms,  one  under  the  center  of  each  belt,  with 
12  arms  in  each  set. 

The  material  of  the  rim  is  ordinary  whitewood,  7/8  in.  in  thickness,  cut 
into  segments  not  exceeding  4  feet  in  length,  and  either  5  or  8  inches  in 


1052 


THE   STEAM-ENGINE. 


width.  These  were  assembled  by  building  a  complete  circle  13  inches  in 
width,  first  with  the  8-inch  inside  and  the  5-inch  outside,  and  then  beside 
it  another  circle  with  the  widths  reversed,  so  as  to  break  joints.  Each 
piece  as  it  was  added  was  brushed  over  with  glue  and  nailed  with  three- 
inch  wire  nails  to  the  pieces  already  in  position.  The  nails  pass  through 
three  and  into  the  fourth  thickness.  .At  the  end  of  each  arm  four  14- 
inch  b9lts  secure  the  rim,  the  ends  being  covered  by  wooden  plugs  glued 
and  driven  into  the  face  of  the  wheel. 

Wire-wound  Fly-wheels  for  Extreme  Speeds.  (Eng'g  News, 
August  2,  1890.) — The  power  required  to  produce  the  Mannesmann 
tubes  is  very  large,  varying  from  2000  to  10,000  H.P.,  according  to  the 
dimensions  of  the  tube.  Since  this  power  is  needed  for  only  a  short  time 
(it  takes  only  30  to  45  seconds  to  convert  a  bar  10  to  12  ft.  long  and  4  in. 
in  diameter  into  a  tube),  and  then  some  time  elapses  before  the  next  bar 
is  ready,  an  engine  of  1200  H.P.  provided  with  a  large  fly-wheel  for  stor- 
ing the  energy  will  supply  power  enough  for  one  set  of  rolls.  These 
fly-wheels  are  so  large  and  run  at  such  great  speeds  that  the  ordinary 
method  of  constructing  them  cannot  be  followed.  A  wheel  at  the  Mannes- 
mann Works,  made  in  Komotau,  Hungary,  in  the  usual  manner,  broke  at 
a  tangential  velocity  of  125  ft.  per  second.  The  fly-wheels  designed  to 
hold  at  more  than  double  this  speed  consist  of  a  cast-iron  hub  to  which 
two  steel  disks,  20  ft.  in  diameter,  are  bolted;  around  the  circumference 
of  the  wheel  thus  formed  70  tons  of  No.  5  wire  are  wound  under  a  tension 
of  50  Ibs.  In  the  Mannesmann  Works  at  Landore,  Wales,  such  a  wheel 
makes  240  revolutions  a  minute,  corresponding  to  a  tangential  velocity 
of  15,080  ft.  or  2.85  miles  per  minute. 

THE  SLIDE-VALVE. 

Definitions.  —  Travel  =  total  distance  moved  by  the  valve. 

Throw  of  the  Eccentric  =  eccentricity  of  the  eccentric  =  distance  from 
the  center  of  the  shaft  to  the  center  of  the  eccentric  disk  =  1/2  the  travel 
of  the  valve. 

Lap  of  the  valve,  also  called  outside  lap  or  steam-lap  =  distance  the 
outer  or  steam  edge  of  the  valve  extends  beyond  or  laps  over  the  steam 
edge  of  the  port  when  the  valve  is  in  its  central  position. 

Inside  lap,  or  exhaust-lap  =  distance  the  inner  or  exhaust  edge  of  the 
valve  extends  beyond  or  laps  over  the  exhaust  edge  of  the  port  when  the 
valve  is  in  its  central  position.  The  inside  lap  is  sometimes  made  zero, 
or  even  negative,  in  which  latter  case  the  distance  between  the  edge  of 
the  valve  and  the  edge  of  the  port  is  sometimes  called  exhaust  clearance, 
or  inside  clearance. 

Lead  of  the  valve  =  the  distance  the  steam-port  is  opened  when  the 
engine  is  on  its  center  and  the  piston  is  at  the  beginning  of  the  stroke. 

Lead-angle  =  the  angle  between  the  position  of  the  crank  when  the 
valve  begins  to  be  opened  and  its  position  when  the  piston  is  at  the 
beginning  of  the  stroke. 

The  valve  is  said  .to  have  lead  when  the  steam-port  opens  before  the 
piston  begins  its  stroke.  If  the  piston  begins  its  stroke  before  the  admis- 
sion of  steam  begins,  the  valve  is  said  to  have  negative  lead,  and  its  amount 
is  the  lap  of  the  edge  of  the  valve  over  the  edge  of  the  port  at  the  instant 
when  the  piston  stroke  begins. 

Lap-angle  =  the  angle  through  which  the  eccentric  must  be  rotated  to 
cause  the  steam  edge  to  travel  from  its  central  position  the  distance  of 
the  lap. 

Angular  advance  of  the  eccentric  =  lap-angle  +  lead-angle. 

Linear  advance  =  lap  +  lead. 

Effect  of  Lap,  Lead,  etc.,  upon  the  Steam  Distribution.  —  Given 
valve-travel  2  3/4  in.,  lap  3/4  in.,  lead  Vie  in.,  exhaust-lap  Vs  in.,  required 
crank  position  for  admission,  cut-off,  release  and  compression,  and 
greatest  port-opening.  (Halsey  on  Slide-valve  Gears.)  Draw  a  circle 
of  diameter  fh  =  travel  of  valve.  From  O  the  center  set  off  Oa  =  lap 
and  ab  =  lead,  erect  perpendiculars  Oe,  ac,  bd;  then  ec  is  the  lap-angle 
and  cd  the  lead-angle,  measured  as  arcs.  Set  off  fg  =  cd,  the  lead- 
angle;  then  Og  is  the  position  of  the  crank  for  steam  admission.  Set  off 
2ec  +  cd  from  h  to  i\  then  Oi  is  the  crank-angle  for  cut-off,  and  fk  •*•  fh 
is  the  fraction  of  stroke  completed  at  cut-off.  Set  off  01  =  exhaust* 


THE  SLIDE-VALVE. 


1053 


lap  and  draw  lm;  em  is  the  exhaust-lap  angle.  Set  off  hn  =  ec  +  cd  —  em, 
and  On  is  the  position  of  crank  at  release.  Set  off  fp.=  ec  +  cd  +  em, 
and  Op  is  the  position  of  crank  for  compression,  fo  -*-  fh  is  the  fraction 
of  stroke  completed  at  release,  and  hq  •*-  hf  is  the  fraction  of  the  return 
stroke  completed  when  compression  begins;  Oh,  the  throw  of  the  eccentric, 
minus  Oa  the  lap,  equals  ah  the  maximum  port-opening. 


iCut-off 


FIG.  170. 


If  a  valve  has  neither  lap  nor  lead,  the  line  joining  the  center  of  the 
eccentric  disk  and  the  center  of  the  shaft  being  at  right  angles  to  the  line 
of  the  crank,  the  engine  would  follow  full  stroke,  admission  of  steam 
beginning  at  the  beginning  of  the  stroke  and  ending  at  the  end  of  the 
stroke. 

Adding  lap  to  the  valve  enables  us  to  cut  off  steam  before  the  end  of 
the  stroke.  The  eccentric  being  advanced  on  the  shaft  an  amount  equal 
to  the  lap-angle  enables  steam  to  be  admitted  at  the  beginning  of  the 
stroke,  as  before  lap  was  added,  and  advancing  it  a  further  amount  equal 
to  the  lead-angle  causes  steam  to  be  admitted  before  the  beginning  of  the 
stroke. 

Having  given  lap  to  the  valve,  and  having  advanced  the  eccentric 
on  the  shaft  from  its  central  position  at  right  angles  to  the  crank, 
through  the  angular  advance  =  lap-angle  4-  lead-angle,  the  four  events, 
admission,  cut-off,  release  or  exhaust-opening,  and  compression  or  exhaust- 
closure,  take  place  as  follows:  Admission,  when  the  crank  lacks  the  lead- 
angle  of  having  reached  the  center;  cut-off,  when  the  crank  lacks  two 
lap-angles  and  one  lead-angle  of  having  reached  the  center.  During 
the  admission  of  steam  the  crank  turns  through  a  semicircle  less  twice 
the  lap-angle.  The  greatest  port-opening  is  equal  to  half  the  travel  of  the 
valve  less  the  lap.  Therefore  for  a  given  port-opening  the  travel  of  the 
valve  must  be  increased  if  the  lap  is  increased.  When  exhaust-lap  is 
added  to  the  valve  it  delays  the  opening  of  the  exhaust  and  hastens  its 
closing  by  an  angle  of  rotation  equal  to  the  exhaust-lap  angle,  which  is 
the  angle  through  which  the  eccentric  rotates  from  its  middle  position 


1054 


THE   STEAM-ENGINE. 


while  the  exhaust  edge  of  the  valve  uncovers  its  lap.  Release  then 
takes  place  when  the  crank  lacks  one  lap-angle  and  one  lead-angle  minus 
one  exhaust-lap  angle  of  having  reached  the  center,  and  compression  when 
the  crank  lacks  lap-angle  +  lead-angle  4-  exhaust-lap  angle  of  having 
reached  the  center. 

The  above  discussion  of  the  relative  position  of  the  crank,  piston,  and 
valve  for  the  different  points  of  the  stroke  is  accurate  only  with  a  con- 
necting-rod of  infinite  length. 

For  actual  connecting-rods  the  angular  position  of  the  rod  causes  a 
distortion  of  the  position  of  the  valve,  causing  the  events  to  take  place  too 
late  in  the  forward  stroke  and  too  early  in  the  return.  The  correction  of 
this  distortion  may  be  accomplished  to  some  extent  by  setting  the  valve 
so  as  to  give  equal  lead  on  both  forward  and  return  stroke,  and  by  alter- 
ing the  exhaust-lap  on  one  end  so  as  to  equalize  the  release  and  com- 
pression. F.  A.  Halsey,  in  his  Slide-valve  Gears,  describes  a  method  of 
equalizing  the  cut-off  without  at  the  same  time  affecting  the  equality  of 
the  lead.  In  designing  slide-valves  the  effect  of  angularity  of  the  con- 
necting-rod should  be  studied  on  the  drawing-board,  and  preferably  by 
the  use  of  a  model. 

Sweet's  Valve-diagram.  —  To  find  outside  and  inside  lap  of  valve 
for  different  cut-offs  and  compressions  (see  Fig.  171):  Draw  a  circle 
whose  diameter  equals  travel  of  valve.  Draw  diameter  BA  and  con- 
tinue to  A,1,  so  that  the  length  AA1  bears  the  same  ratio  to  XA  as  the 


FIG.  171.  —  Sweet's  Valve  Diagram. 

length  of  connecting-rod  does  to  length  of  engine-crank.  Draw  small 
circle  K  with  a  radius  equal  to  lead.  Lay  off  AC  so  that  ratio  of  AC  to 
AB  =  cut-off  in  parts  of  the  stroke.  Erect  perpendicular  CD.  Draw 
DL  tangent  to  K\  draw  XS  perpendicular  to  DL;  XS  is  then  outside  lap 
of  valve. 

To  find  release  and  compression:  If  there  is  no  inside  lap,  draw  FE 
through  X  parallel  to  DL.  F  and  E  will  be  position  of  crank  for  release 
and  compression.  If  there  is  an  inside  lap,  draw  a  circle  about  X,  in 
which  radius  XY  equals  inside  lap.  Draw  HG  tangent  to  this  circle  and 
parallel  to  DL;  then  H  and  G  are  crank  positions  for  release  and  for  com- 
pression. Draw  HN  and  MG,  then  AN  is  piston  position  at  release  and 
A'M  piston  position  at  compression,  AB  being  considered  stroke  of 
engine. 

To  make  compression  alike  on  each  stroke  it  is  necessary  to  increase 
the  inside  lap  on  crank  end  of  valve,  and  to  decrease  by  the  same  amount 
the  inside  lap  on  back  end  of  valve.  To  determine  this  amount,  through 
M  with  a  radius  MM1  =  AA1,  draw  arc  MP,  from  P  draw  PT  perpen- 
dicular to  AB,  then  TM  is  the  amount  to  be  added  to  inside  lap  on  crank 
end,  and  to  be  deducted  from  inside  lap  on  back  end  of  valve,  inside  lap 
being  XY. 

For  the  Bilgram  Valve-Diagram,  see  Halsey  on  Slide-valve  Gears. 

The  Zeuner  Valve-diagram  is  given  in  most  of  the  works  on  the 
steam-engine,  and  in  treatises  on  valve-gears,  as  Zeuner's,  Peabody's,  and 
Spangler's.  The  following  paragraphs  show  how  the  Zeuner  valve-diagram 
may  be  employed  as  a  convenient  means  (1)  f9r  finding  the  lap,  lead, 
etc.,  of  a  slide-valve  when  the  points  of  admission,  cut-off,  and  release 


THE    SLIDE-VALVE. 


1055 


are  given;  and  (2)  for  obtaining  the  points  of  admission,  cut-off,  release, 
and  compression,  etc.,  when  the  travel,  the  laps,  and  the  lead  of  the  valve 
are  given.  In  working  out  these  two  problems,  the  connecting-rod  is 
supposed  to  be  of  infinite  length. 

Determination  of  the  Lap,  Lead,  etc.,  of  a  Slide-valve  for  Given  Steam 
Distribution.  —  Given  the  points  of  admission,  cut-off ,  and  release,  to  find 
the  point  of  compression,  the  lap,  the  lead,  the  exhaust  lap,  the  angular 
advance,  and  the  port-openings  at  different  fractions  of  the  stroke. 

Draw  a  straight  line  A  A',  Fig.  172,  to  represent  on  any  scale  the  travel 
of  the  valve,  and  on  it  draw  a  circle,  with  the  center  0,  to  represent  the 
path  of  the  center  of  the  eccentric.  The  line  and  the  circle  will  also  repre- 
sent on  a  different  scale  the  length  of  stroke  of  the  piston  and  the  path 
of  the  crank-pin.  On  the  circle,  which  is  called  the  crank  circle,  mark  B, 


Valve  , 


(Cut-off 


Center  of\Y 
Eccentric 


B\Admiss£on 


FIG.  172. — Zeuner's  Valve  Diagram. 

the  position  of  the  crank-pin  when  admission  of  steam  begins,  the  direc* 
tion  of  motion  of  the  crank  being  shown  by  the  arrow;  C,  the  position  of 
the  crank-pin  at  cut-off;  and  L,  its  position  at  release.  From  these  points 
draw  perpendiculars  BM,  CN,  and  LVt  to  the  line  A  A';  M,  N,  and  V 
will  then  represent  the  positions  of  the  piston  at  admission,  cut-off,  and 
release  respectively,  the  admission  taking  place,  as  shown,  before  the 
piston  reaches  the  end  of  the  stroke  in  the  direction  OA,  and  release 
taking  place  before  the  end  of  the  stroke  in  the  direction  OA'. 

Bisect  the  arc  BC  at  D,  and  draw  the  diameter  DOD' .  On  DO  draw 
the  circle  DHOGE,  called  the  valve  circle.  Draw  OB,  cutting  the  valve 
circle  at  G;  and  OC,  cutting  it  at  H.  Then  OG  =  OH  is  the  lap  of  the 
valve,  measured  on  the  scale  in  which  OA  is  the  half-travel  of  the  valve. 
With  OG  as  radius  draw  the  arc  GF1I,  called  the  steam-lctp  circle,  or,  for 
short,  the  lap  circle. 


1056  THE   STEAM-ENGINE. 

Mark  the  point  E,  at  which  the  valve  circle  cuts  the  line  OA.  The 
distance  FE  represents  the  lead  of  the  valve,  and  BG  =  AF  is  the  max- 
imum port-opening.  A  perpendicular  drawn  from  OA  at  E  will  cut  the 
valve  circle  and  tne  crank  circle  at  D,  since  the  triangle  DEO  is  a  right- 
angled  triangle  drawn  in  the  semicircle  DEGO. 

Erect  the  perpendicular FJ,  then  angle  DOJ  =  AOB  is  the  lead-angle 
and  JOK  is  the  lap-angle,  OK  being  a  perpendicular  to  AA1  drawn  from 
O.  DOK  is  the  sum  of  the  lap  and  lead  angles,  that  is,  the  angular 
advance,  by  which  the  eccentric  must  be  set  beyond  90°  ahead  of  the 
crank.  Set  off  KY  =  KD ;  then  Y  is  the  position  of  the  center  of  the 
eccentric  when  the  crank  is  in  the  position  OA. 

To  find  the  point  of  compression,  set  off  D'P  =  D'L;  then  P  is  the 
point  of  compression. 

Draw  OP  and  OL.  On  OB'  draw  the  valve  circle  ORD'S,  cutting 
OL  at  R  and  OP  at  S.  With  OR  as  a  radius  draw  the  arc  of  the  exhaust- 
lap  circle,  RTS;  OR  =  OS  is  the  exhaust  lap. 

The  port-opening  at  any  part  of  the  stroke,  or  corresponding  position 
of  the  crank,  is  represented  by  the  radial  distances,  as  EF,  DW,  and  J'X, 
intercepted  between  the  lap  and  the  valve  circles  on  radii  drawn  from  O. 
Thus,  on  the  radius  OB,  the  port-opening  is  zero  when  steam  admission  is 
about  to  begin;  on  the  radius  OA,  when  the  crank  is  on  the  dead  center 
the  opening  is  EF,  or  equal  to  the  lead  of  the  valve;  on  the  radius  DO, 
midway  between  the  point  of  admission  and  the  point  of  cut-off,  the 
opening  is  a  maximum  DW  —  AF  =  BG\  on  the  radius  OC  it  is  zero 
again  when  steam  has  just  been  cut  off. 

In  like  manner  the  exhaust  opening  is  represented  by  the  radial  dis- 
tances intercepted  between  the  exhaust-lap  circle,  RR'TS,  and  the  valve 
circle,  ORD'S.  On  the  radius  OL  it  is  zero  when  release  begins;  on  OD' 
it  is  TDr,  a  maximum;  and  on  OP  it  is  zero  again  when  compression  begins. 

Determination  of  the  Steam  Distribution,  etc.,  for  a  Given  Valve.  • —  Given 
the  valve  travel,  the  lap,  the  lead,  and  the  exhaust  lap,  to  find  the  maxi- 
mum port-opening,  the  angular  advance,  and  the  points  of  admission, 
cut-off,  release,  and  compression. 

This  problem  is  the  reverse  of  the  preceding.  Draw  AOA'  to  represent 
the  valve  travel  on  a  certain  scale,  O  being  the  middle  point,  and  on  this 
line  on  the  same  scale  set  off  OF  =  the  lap,  FE  —  the  lead,  and  OR'  = 
the  exhaust  lap.  AF  then  will  be  the  maximum  port-opening.  Draw  the 
perpendiculars  OK  and  ED.  DOK  is  the  angular  advance. 

Draw  the  diameter  DODf,  and  on  DO  and  D'O  draw  the  two  valve 
circles.  From  0,  the  center,  with  a  radius  OF,  the  lap,  draw  the  arc  of 
the  steam-lap  circle  cutting  the  valve  circle  in  G  and  H.  Through  G 
draw  OB,  and  through  H  draw  OC',  B  then  is  the  point  of  admission, 
and  C  the  point  of  cut-off.  With  OR,  the  exhaust  lap,  as  a  radius,  draw 
the  arc  of  the  exhaust-lap  circle,  RTS,  cutting  the  valve  circle  in  R  and 
S.  Through  R  draw  OL,  and  through  S  draw  OP.  Then  L  is  the  point 
of  release  and  P  the  point  of  compression.  Draw  the  perpendiculars 
BM,  CN,  LV,  and  PP',  to  find  M,  N,  V,  and  P',  the  respective  positions 
on  the  stroke  of  the  piston  when  admission,  cut-off,  release,  and  com- 
pression take  place. 

Practical  Application  of  Zeuner's  Diagram.  —  In  problems  solved  by 
paeans  of  the  Zeuner  diagram,  the  results  obtained  on  the  drawings  are 
relative  dimensions  or  the  ratios  of  the  several  dimensions  to  a  given 
dimension  the  scale  of  which  is  known,  such  as  the  valve  travel,  the 
maximum  port-opening,  or  the  length  of  stroke.  In  problems  similar  to 
the  first  problem  given  above,  the  known  dimensions  are  usually  the 
length  of  stroke,  the  maximum  port-opening,  AF,  which  is  calculated 
from  data  of  the  dimensions  of  cylinder,  the  piston  speed,  and  the  allow- 
able velocity  of  steam  through  the  port.  The  length  of  the  stroke  being 
represented  on  a  certain  scale  by  AA',  the  points  of  admission,  cut-off, 
release,  and  compression,  in  fractions  of  the  stroke,  are  measured  respec- 
tively by  A'M ,  AN,  AV,  and  A'P  on  the  same  scale.  The  actual  dimen- 
sion of  the  maximum  port-opening  is  represented  on  a  different  scale  by 
AF,  therefore  the  actual  dimensions  of  the  lap,  lead,  and  exhaust  lap  are 
measured  respectively  by  OF,  FE,  and  OR'  on  the  same  scale  as  AF; 
or,  in  other  words,  the  lap,  lead,  and  exhaust  lap  are  respectively  the 
f)  fl*  FF  OTff 

ratios -j-p'  -7~p»  and-7-rp  each  multiplied  by  the  maximum  port-opening. 


THE    SLIDE-VALVE. 


1057 


In  problems  similar  to  the  second  problem,  the  actual  dimensions  of 
the  lap,  the  lead,  the  exhaust  lap,  and  the  valve  travel  are  all  known, 
and  are  laid  down  on  the  same  scale  on  the  line  AA',  representing  the 
valve  travel;  and  the  maximum  port-opening  is  found  by  the  solution  of 
the  problem  to  be  AF,  measured  on  the  same  scale;  or  the  maximum 
port-opening  =  1/2  valve  travel  minus  the  lap.  Also  in  this  problem 
A  A'  represents  the  known  length  of  stroke  on  a  certain  scale,  and  the 
points  of  admission,  cut-off,  release,  and  compression,  in  fractions  of  the 
stroke,  are  represented  by  the  ratios  which  A'M,  AN,  AV,  and  A'P, 
respectively,  bear  to  AA'. 

Port-opening.  —  The  area  of  port-opening  is  usually  made  such  that 
the  velocity  of  the  steam  in  passing  through  it  should  not  exceed  6000  ft. 
per  min.     The  ratio  of  port  area  to  piston  area  will  vary  with  the  piston- 
speed  as  follows: 
Forspeed^iston.J    10Q  200  30Q  400  500  600  700  800  900  1000  12QO 

Port  area  =  piston  }0017   Q33   Q5   Q67   Og3    x    10?    133    15    167      2 

tiled  A  } 

For  a  velocity  of  6000  ft.  per  min., 

Port  area  =  sq.  of  diam.  of  cyl.X  piston  speed  -s-  7639. 

The  length  of  the  port-opening  may  be  equal  to  or  something  less  thaiv 
the  diameter  of  the  cylinder,  and  the  width  =  area  of  port-opening  -fr- 
its length. 

The  bridge  between  steam  and  exhaust  ports  should  be  wide  enough 
to  prevent  a  leak  of  steam  into  the  exhaust  due  to  overtravel  of  the 
valve. 

The  width  of  exhaust  port  =  width  of  steam  port  +  1/2  travel  of  valve 
+  inside  lap  —  width  of  bridge. 

Lead.  (From  Peabody's  Valve-gears.)  —  The  lead,  or  the  amount 
that  the  valve  is  open  when  the  engine  is  on  a  dead  point,  varies,  with  the 
type  and  size  of  the  engine,  from  a  very  small  amount,  or  even  nothing 
up  to  3/8  of  an  inch  or  more.  Stationary-engines  running  at  slow  speed 
may  have  from  1/64  to  Vie  inch  lead.  The  effect  of  compression  is  to  fill 
the  waste  space  at  the  end  of  the  cylinder  with  steam;  consequently, 
engines  having  much  compression  need  less  lead.  Locomotive-engines 
having  the  valves  controlled  by  the  ordinary  form  of  Stephenson  link- 
motion  may  have  a  small  lead  when  running  slowly  and  with  a  long 
cut-off,  but  when  at  speed  with  a  short  cut-off  the  lead  is  at  least  1/4  inch; 
and  locomotives  that  have  valve-gear  which  gives  constant  lead  com- 
monly have  1/4  inch  lead.  The  lead -angle  is  the  angle  the  crank  makes 
with  the  line  of  dead  points  at  admission.  It  may  vary  from  0°  to  8°. 

Inside  Lead. — Weisbach  (vol.  ii,  p.  296)  says:  Experiment  shows 
that  the  earlier  opening  of  the  exhaust  ports  is  especially  of  advantage, 
and  in  the  best  engines  the  lead  of  the  valve  upon  the  side  of  the  exhaust, 
or  the  inside  lead,  is  1/25  to  1/15;  i.e.,  the  slide-valve  at  the  lowest  or  highest 
position  of  the  piston  has  made  an  opening  whose  height  is  1/25  to  1/15  of 
the  whole  throw  of  the  slide-valve.  The  outside  lead  of  the  slide-valve 
or  the  lead  on  the  steam  side,  on  the  other  hand,  is  much  smaller,  and  is 
often  only  1/100  of  the  whole  throw  of  the  valve. 

Effect  of  Changing  Outside  Lap,  Inside  Lap,  Travel  and 
Angular  Advance.     (Thurston.) 


Admission. 

Expansion. 

Exhaust. 

Compression. 

Incr. 
O.L. 

is  later, 
ceases  sooner 

occurs  earlier, 
continues  longer 

is  unchanged 

begins  at 
same  point 

Incr. 
I.L. 

unchanged 

begins  as  before, 
continues  longer 

occurs  later, 
ceases  earlier 

begins  sooner, 
continues  longel 

Incr. 

begins  sooner, 

begins  later, 

begins  later, 

begins  later, 

T. 

continues  longer 

ceases  sooner 

ceases  later 

ends  sooner 

Incr. 
A.A 

begins  earlier, 
period  unaltered 

begins  sooner, 
per.  the  same 

begins  earlier, 
per.  unchanged 

begins  earlier, 
per.  the  same 

1058 


THE    STEAM-ENGINE. 


Zeuner  gives  the  following  relations  (Weisbach-Dubois,  vol.  ii,  p.  307), 
It  S  =  travel  of  valve,  p  =  maximum  port  opening; 
L  =  steam-lap,  I  =  exhaust-lap; 

L 


li 


•  ratio  of  steam-lap  to  half  travel  =     ^  „,  L  =  —  X  S\ 


r  =  ratio  of  exhaust-lap  to  half  travel  = 


I 


0.5S 


If  a  =  angle  BOG  between  positions  of  crank  at   admission  and  at 
cut-off,  and  ft  =  angle  LOP  between  positions  of  crank  at  release  and  at 

,.  sin  (180°  -a)           ,    sin  (180°  -/3) 
Bompression,  then  R  =  1/2 3 — r, '>  r  =  l/2  3 — ;       —  • 

Sin  1/2   a  Sill  1/2 ft 

Crank-angles  for  Connecting-rods  of  Different  Lengths. 

FORWARD  AND  RETURN  STROKES. 


Ratio  of  Length  of  Connecting-rod  to  Length  of  Stroke. 


II  1 

2 

21/2 

3 

31/2 

4 

5 

Infi- 
nite 

ta  **  B 

For. 

cc  o 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

or 

o 

Ret. 

.01 

10.3 

13.2 

10.5 

12.8 

10.6 

12.6 

10.7 

12.4 

10.8 

12.3 

10.9 

12.1 

11.5 

.02 

14.6 

18.7 

14.9 

18.1 

15.1 

17.8 

15.2 

17.5 

15.3 

17.4 

15.5 

17.1 

16.3 

.03 

17.9 

22.9 

18.2 

22.2 

18.5 

21.8 

18.7 

21.5 

18.8 

21.3 

19.0 

21.0 

19.9 

.04 

20.7 

26.5 

21.1 

25.7 

21.4 

25.2 

21.6 

24.9 

21.8 

24.6 

22.0 

24.3 

23.1 

.05 

23.2 

29.6 

23.6 

28.7 

24.0 

28.2 

24.2 

27.8 

24  4 

27.5 

24.7 

27.2 

25.8 

.10 

33.1 

41.9 

33.8 

40.8 

34.3 

40.1 

34.6 

39.6 

34.9 

39.2 

35.2 

38.7 

36.9 

.15 

41 

51.5 

41.9 

50.2 

42.4 

49.3 

42.9 

48.7 

43.2 

48.3 

43.6 

47.7 

45.6 

.20 

48 

59.6 

48.9 

58.2 

49.6 

57.3 

50.1 

56.6 

50.4 

56.2 

50.9 

55.5 

53.1 

.25 

54.3 

66.9 

55.4 

65,4 

56.1 

64.4 

56.6 

63.7 

57.0 

63.3 

57.6 

62.6 

60.0 

.30 

60.3 

73.5 

61.5 

72.0 

62.2 

71.0 

62  8 

70.3 

63.3 

69.8 

63.9 

69.1 

66.4 

.35 

66.1 

79.8 

67.3 

78.3 

68.1 

77.3 

68.8 

76.6 

69.2 

76.1 

69.9 

75.3 

72.5 

.40 

71.7 

85.8 

73.0 

84.3 

73.9 

83.3 

74.5 

82.6 

75.0 

82.0 

75.7 

81.3 

78.5 

.45 

77  2 

91  5 

78.6 

90.1 

79  6 

89  1 

80  2 

88  4 

80  7 

87  9 

81  4 

87.1 

84  3 

.50 

82.8 

97.2 

84.3 

95.7 

85.2 

94.8 

85.9 

94.1 

86.4 

93.6 

87.1 

92.9 

90.0 

.55 

88.5 

102.8 

89.9 

101.4 

90.9 

100.4 

91.6 

99.8 

92.1 

99.3 

92  9 

98  6 

95.7 

.60 

94.2 

108.3 

95.7 

107.0 

96.7 

106.1 

97.4 

105.5 

98.0 

105.0 

98.7 

104.3 

101.5 

.65 

100.2 

113.9 

101.7 

112.7 

102.7 

111.9 

103.4 

III.  2 

103.9 

110.8 

104.7 

110.1 

107.5 

.70 

106.5 

119.7 

108.0 

118.5 

109.0 

117.8 

109.7 

117.2 

110.2 

116.7 

110.9 

116.1 

113.6 

.75 

113.1 

125.7 

114.6 

124.6 

115.6 

123.9 

116.3 

123.4 

116.7 

123.0 

117.4 

122.4 

120.0 

.80 

120.4 

132 

121.8 

131.1 

122.7 

130.4 

J23.4 

129.9 

123.8 

129.6 

124.5 

129.1 

126.9 

.85 

128.5 

139 

129.8 

138.1 

130.7 

137.6 

131.3 

137.1 

131.7 

136.8 

132.3 

136.4 

134.4 

.90 

138.  1 

146.9 

139.2 

146.2 

139.9 

145.7 

140.4 

145.4 

140.8 

145.1 

141.3 

144.8  143.1 

.95 

150.4 

156.8 

151.3 

156.4 

151.8 

156.0 

152.2 

155.8 

152.5 

155.6 

152.8 

155.3 

154.2 

.96 

153.5 

159.3 

154.3 

158.9 

154.8 

158.6 

155.1 

158.4 

155.4 

158.2 

155.7 

158.0 

156.9 

.97 

157.1 

162.1 

157.8 

161.8 

158.2 

161.5 

158.5 

161.3 

158.7 

161.2 

159.0 

161.0 

160.1 

.98 

161.3 

165.4 

161.9 

165.1 

162.2 

164.9 

162.5 

164.8 

162.6 

164.7 

162.9 

164.5  163.7 

.99 

166.8 

169  7 

167  2 

169  5 

167  4 

169  4 

167  6 

169  3 

167  7 

169  2 

167  9 

169  1  168.5 

1.00 

180 

180 

180 

180 

180 

180 

180      180 

180 

180 

180 

180 

180 

Ratio  of  Lap  and  of  Port-opening  to  Valve-travel.  — The  table 
on  page  1059,  giving  the  ratio  of  lap  to  travel  of  valve  and  ratio  of  travel 
to  port-opening,  is  abridged  from  one  given  by  Buei  in  Weisbach-Dubois, 


THE   SLIDE- V At VE. 


1059 


vol.  ii.  It  is  calculated  from  the  above  formulae.  Intermediate  values 
may  be  found  by  the  formulae,  or  with  sufficient  accuracy  by  interpolation 
from  the  figures  in  the  table.  By  the  table  on  page  1068  the  crank-angle 
may  be  found,  that  is,  the  angle  between  its  position  when  the  engine  is 
on  the  center  and  its  position  at  cut-off,  release,  or  compression,  when 
these  are  known  in  fractions  of  the  stroke.  To  illustrate  the  use  of  the 
tables  the  following  example  is  given  by  Buel:  width  of  port  =  2.2  in.; 
width  of  port-opening  =  width  of  port  +0.3  in.;  overtravel  =  2.5  in.; 
length  of  connecting-rod  =  2 1/2  times  stroke;  cut-off  =  0.75  of  stroke; 
release  =  0.95  of  stroke;  lead-angle,  10°.  From  the  first  table  we  find 
crank-angle  =  114.6;  add  lead-angle,  making  124.6°.  From  the  second 
table,  for  angle  between  admission  and  cut-off,  125°,  we  have  ratio  of 
travel  to  port-opening  =  3.72,  or  for  124.6°  =  3.74,  which,  multiplied 
by  port-opening  2.5,  gives  9.45  in.  travel.  The  ratio  of  lap  to  travel, 
by  the  table,  is  0.2324,  or  9.45  X  0.2324  =  2.2  in.  lap.  For  exhaust- 
lap,  we  have  for  release  at  0.95,  crank-angle  =  151.3;  add  lead-angle 
10°  =  161 .3°.  From  the  second  table,  by  interpolation,  ratio  of  lap  to 
travel  =  0.0811,  and  0.0811  X  9.45  =  0.77  in.,  the  exhaust-lap. 

Lap-angle  =  1/2(180°  —  lead-angle  —  crank-angle  at  cut-off); 

=  1/2(180°  -  10  -  114.6)  =  27.7°. 

Angular  advance    —lap-angle  +  lead-angle  =  27.7  +  10  =  37.7°. 
Exhaust  lap-angle  =  crank-angle  at  release  +  lap-angle  +  lead -angle  — 180° 

=  151. 3+27. 7+10-180°  =  9°. 
Crank-angle  at  com- ) 

pression  measured  >  =  1 80°  —  lap-angle  —  lead-angle  —  exhaust  lap-angle 
on  return  stroke     ) 

=  180-27.7-10-9=133.3°;   corresponding,  by 
table,  to  a  piston  position  of  0  .81  of  the  return  stroke;  or 
Crank-angle  at  compression  =  180°—  (angle  at  release—  angle  at  cut-off) 

+  lead-angle 
=  180  -  (151  .3-114. 6) +10=  133.3°. 

The  positions  determined  above  for  cut-off  and  release  are  for  the 
forward  stroke  of  the  piston.  On  the  return  stroke  the  cut-off  will  take 
place  at  the  same  angle,  114.6°,  corresponding  by  table  to  66.6%  of  the 
return  stroke,  instead  of  75%.  By  a  slight  adjustment  of  the  angular 
advance  and  the  length  of  the  eccentric-rod  the  cut-off  can  be  equalized. 
The  width  of  the  bridge  should  be  at  least  2.5  +  0  .23  -  2.2  =  0  .55  in. 

Lap  and  Travel  of  Valve. 


S'Sfcg 

*o 

£i 

«^^"± 

*o 

>i 

S*Ste"£ 

ti 

>i 

IIP 

I'3°12 
flf38 

o  Travel 

el  of  Vab 
Port-ope 

fill 

o'oO-c 
ftp^ncj  fl 

o  Travel 

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C5 
5| 

ajpL, 

iixl 

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0-50^3 

d^§ 

o  Travel 

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cs  a 
>  o 
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-«£ 

«  *  c  S 

a 

>«*-, 

£  ° 

S  *  c  « 

0, 

ft 

«  *  c  S 

a 

|*o  . 

®  §'i"S.2 

c5 

3 

^TJ 

«  §  !•§  o 

A 

I'c'i  J  g 

a 

H^ 

"3b«*-i  ""^  ^  *•« 

II 

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Slsl 

II 

1|  b- 

|ojff! 

ii 

o^  ^ 

r 

I°'S 

y 

|3.a 

|;0t8? 

r 

I5'£ 

30° 

0.4830 

58.70 

85° 

0.3686 

7.61 

135° 

0.1913 

3.24 

35 

.4769 

43.22 

90 

.3536 

6.83 

140 

.1710 

3.04 

40 

.4699 

33.17 

95 

.3378 

6.17 

145 

.1504 

2.86 

45 

.4619 

26.27 

100 

.3214 

5.60 

150 

.1294 

2.70 

50 

.4532 

21.34 

105 

.3044 

5.11 

155 

.1082 

2.55 

55 

.4435 

17.70 

110 

.2868 

4.69 

160 

.0868 

2.42 

60 

.4330 

14.93 

115 

.2687 

4.32 

165 

.0653 

2.30 

65 

.4217 

12.77 

120 

.2500 

4.00 

170 

.0436 

2.19 

70 

.4096 

11.06 

125 

.2309 

3.72 

175 

.0218 

2.09 

75 

.3967 

9.68 

130 

.2113 

3.46 

180 

.0000 

2.00 

80 

3830 

8  55 

1 

1060 


THE   STEAM-ENGINE. 


Relative  Motions  of  Crosshead  and  Crank.  — L  =  length  of  coru 
necting-rod,  R  —  length  of  crank,  0  =  angle  of  crank  with  center  line  of 
engine,  D  =  displacement  of  crosshead  from  the  beginning  of  its  stroke, 
V  =  velocity  of  crank-pin,  Ft  =  velocity  of  piston. 


sin0±  (L- 


COS<? 


For  /2-1 


From  these  formulae  Mr.  A.  F.  Nagle  computes  the  following: 
PISTON  DISPLACEMENT  AND  PISTON  VELOCITY  FOR  EACH  10°  OF  MOTION 

OF    CRANK.      Length    of    crank  =  1.      Length    of    connecting-rod  =  5. 

Piston  velocity  Fi  for  vel.  of  crank-pin  =  1. 


Angle 
of 
Cr'nk 

10° 
20° 
30° 
40° 
50° 

Displacement. 

Velocity. 

Angle 
of 
Cr'nk 

Displacement. 

Velocity. 

For- 
ward. 

Back. 

For- 
ward. 

Back. 

For- 
ward. 

Back. 

For- 
ward. 

Back. 

0.018 
0.072 
0.159 
0.276 
0.416 

0.012 
0.048 
0.109 
0.192 
0.298 

0.207 
0.406 
0.587 
0.742 
0.865 

60° 
70° 
80° 
84° 
90° 

0.576 
0.747 
0.924 
1.000 
1.101 

0.424 
0.569 
0.728 

0  954 
1.005 
1.019 
1.011 
1.000 

0.778 
0.875 
0.950 

'i.'ooo 

0.899 

PERIODS  OF  ADMISSION,  OR  CUT-OFF,  FOR  VARIOUS  LAPS 
AND  TRAVELS  OF  SLIDE-VALVES. 

The  two  following  tables  are  from  Clark  on  the  Steam-engine.  In  the 
first  table  are  given  the  periods  of  admission  corresponding  to  travels  of 
valve  of  from  12  in.  to  2  in.,  and  laps  of  from  2  in.  to  3/8  in.,  with  1/4  in. 
and  Vs  in.  of  lead.  With  greater  leads  than  those  tabulated,  the  steam 
would  be  cut  off  earlier  than  as  shown  in  the  table. 

The  influence  of  a  lead  of  S/IQ  in.  for  travels  of  from  l-r>/8  in.  to  6  in., 
and  laps  of  from  1/2  in.  to  11/2  in-»  as  calculated  for  in  the  second  table, 
is  exhibited  by  comparison  of  the  periods  of  admission  in  the  table,  for 
the  same  lap  and  travel.  The  greater  lead  shortens  the  period  of  admis- 
sion, and  increases  the  range  for  expansive  working. 

Periods  of  Admission,  or  Points  of 'Cut-off,  for  Given  Travels  and 
Laps  of  Slide-valves. 


1M 

-6 

Periods  of  Admission,  or  Points  of  Cut-off,  for  the 
following  Laps  of  Valves  in  inches. 

H°£ 

!• 

A 

2 

l3/4 

H/2 

U/4 

1 

7/8 

3/4 

5/8 

VL> 

3/8 

in. 
12 

1/4 

88 

3 

8 

95 

96 

°V 

98 

98 

99 

99 

10 

V4 

82 

87 

89 

92 

95 

96 

97 

98 

98 

99 

8 

V4 

72 

78 

84 

88 

92 

94 

95 

96 

98 

98 

6 

1/4 

50 

62 

71 

79 

86 

89 

91 

94 

96 

97 

51/2 

1/8 

43 

56- 

68 

77 

85 

88 

91 

94 

96 

97 

1/8 

32 

47 

61 

72 

82 

86 

89 

92 

95 

97 

41/2 

1/8 

14 

35 

51 

66 

78 

83 

87 

90 

94 

96 

4 

1/8 

17 

39 

57 

72 

78 

83 

88 

92 

95 

31/2 

1/8 

20 

44 

63 

71 

79 

84 

90 

94 

1/8 

23 

50 

61 

71 

79 

86 

91 

21/2 

1/8 

27 

43 

57 

70 

80 

88 

2 

Vg 

33 

52 

70 

81 

THE  SLIDE-VALVE. 


1061 


Periods  of  Admission,  or  Points  of  Cut-off,  for  given  Travels  and 
Laps  of  Slide-valves. 

Constant  lead,  5/16- 


Travel. 

I 

,ap. 

* 

Inches. 

V2 

V8 

3/4  ' 

•      7/8 

1 

U/8 

H/4 

13/8 

1  1/2 

]5/8 

19 

13/4 

39 

17/8 

47 

17 

2 

55 

34 

21/8 

61 

42 

14 

21/4 

65 

50 

30 

23/8 

68 

55 

38 

13 

21/2 

71 

59 

45 

27 

25/8 

74 

63 

49 

36 

12 

23/4 

76 

67 

56 

43 

26 

27/8 

78 

70 

59 

47 

32 

11 

3 

80 

73 

62 

50 

38 

23 

31/8 

81 

74 

65 

55 

44 

30 

10 

31/4 

83 

•     76 

68 

59 

48 

34 

22 

33/8 
31/2 

84 
85 

78 
80 

71 
73 

62 
64 

51 
53 

40 
45 

29 
34 

9 
20 

\i 

»<* 

41/4 

41/2 
43/4 

5V3 

86 
87 
87 
88 
89 
90 
92 
93 
94 
95 

81 
82 
83 
84 
86 
87 
89 
90 
92 
93 

75 
76 
78 
79 
81 
83 
85 
87 
89 
91 

66 
68 
70 
72 
76 
79 
81 
83 
86 
88 

57 
60 
63 
66 
70 
73 
76 
78 
82 
85 

49 
52 
55 
58 
63   . 
67 
70 
73 
78 
82 

38 
42 
46 
49 
56 
61 
65 
67 
73 
78 

26 
32 
36 
40 
47 
54 
58 
62 
68 
74 

9 
19 
25 
29 
37 
45 
51 
56 
63 
69 

Platon- valve.  —  The  piston-valve  is  a  modified  form  of  the  slide- 
valve.  The  lap,  lead,  etc.,  are  calculated  in  the  same  manner  as  for  the 
common  slide-valve.  The  diameter  of  valve  and  amount  of  port-opening 
are  calculated  on  the  basis  that  the  most  contracted  portion  of  the  steam- 
passage  between  the  valve  and  the  cylinder  should  have  an  area  such  that 
the  velocity  of  steam  through  it  will  not  exceed  6000  ft.  per  minute.  The 
area  of  the  opening  around  the  circumference  of  the  valve  should  be  ab9ut 
double  the  area  of  the  steam-passage,  since  that  portion  of  the  opening 
that  is  opposite  from  the  steam-passage  is  of  little  effect. 

Setting  the  Valves  of  an  Engine.  —  The  principles  discussed  above 
are  applicable  not  only  to  the  designing  of  valves,  but  also  to  adjustment 
of  valves  that  have  been  improperly  set;  but  the  final  adjustment  of  the 
eccentric  and  of  the  length  of  the  rod  depends  upon  the  amount  of  lost 
motion,  temperature,  etc.;  and  can  be  effected  only  after  trial.  After 
the  valve  has  been  set  as  accurately  as  possible  when  cold,  the  lead  and 
lap  for  the  forward  and  return  strokes  being  equalized,  indicator  diagrams 
should  be  taken  and  the  length  of  the  eccentric-rod  adjusted,  if  necessary, 
to  correct  slight  irregularities. 

To  Put  an  Engine  on  its  Center.  —  Place  the  engine  in  a  position 
where  the  piston  will  have  nearly  completed  its  outward  stroke,  and 
opposite  some  point  on  the  crosshead,  such  as  a  corner,  make  a  mark 
upon  the  guide.  Against  the  rim  of  the  pulley  or  crank-disk  place  a 
pointer  and  mark  a  line  with  it  on  the  pulley.  Then  turn  the  engine  over 
the  center  until  the  crosshead  is  again  in  the  same  position  on  its  inward 
stroke.  This  will  bring  the  crank  as  much  below  the  center  as  it  was 
above  it  before.  With  the  pointer  in  the  same  position  as  before  make 
a  second  mark  on  the  pulley  rim.  Divide  the  distance  between  the  marks 
in  two  and  mark  the  middle  point.  Turn  the  engine  until  the  pointer 
is  opposite  this  middle  point,  and  it  will  then  be  on  its  center.  To  avoid 


1062  THE  STEAM-ENGINE. 

the  error  that  may  arise  from  the  looseness  of  crank-pin  and  wrist-pin 
bearings,  the  engine  should  be  turned  a  little  above  the  center  and 
then  be  brought  up  to  it,  so  that  the  crank-pin  will  press  against  the 
same  brass  that  it  does  when  the  first  two  marks  are  made. 

Link  Motion. — Link-motions,  of  which  the  Stephenson  link  is  the 
most  commonly  used,  are  designed  for  two  purposes:  first,  for  reversing 
the  motion  of  the  engine,  and  second,  for  varying  the  point  of  cut-off 
by  varying  the  travel  of  the  valve.  The  Stephenson  link-motion  is  a 
combination  of  two  eccentrics,  called  forward  and  back  eccentrics,  with 
a  link  connecting  the  extremities  of  the  eccentric-rods ;  so  that  by  vary- 
ing the  position  of  the  link  the  valve-rod  may  be  put  in  direct  connec- 
tion with  either  eccentric,  or  may  be  given  a  movement  controlled  in 
part  by  one  and  in  part  by  the  other  eccentric.  When  the  link  is  moved 
by  the  reversing  lever  into  a  position  such  that  the  block  to  which  the 
valve-rod  is  attached  is  at  either  end  of  the  link,  the  valve  receives  its 
maximum  travel,  and  when  the  link  is  in  mid-gear  the  travel  is  the 
least  and  cut-off  takes  place  early  in  the  stroke. 

In  the  ordinary  shifting-link  with  open  rods,  that  is,  not  crossed,  the 
lead  of  the  valve  increases  as  the  link  is  moved  from  full  to  mid-gear, 
that  is,  as  the  period  of  steam  admission  is  shortened.  The  variation  ot 
lead  is  equalized  for  the  front  and  back  strokes  by  curving  the  link  to 
the  radius  of  the  eccentric-rods  concavely  to  the  axles.  With  crossed 
eccentric-rods  the  lead  decreases  as  the  link  is  moved  from  full  .to  mid- 
gear.  In  a  valve-motion  with  stationary  link  the  lead  is  constant. 
(For  illustration  see  Clark's  "Steam-engine,"  vol.  ii,  p.  22.) 

The  linear  advance  of  each  eccentric  is  equal  to  that  of  the  valve  in 
full  gear,  that  is,  to  lap  +  lead  of  the  valve,  when  the  eccentric-rods 
are  attached  to  the  link  in  such  position  as  to  cause  the  half-travel  of 
the  valve  to  equal  the  eccentricity  of  the  eccentric. 

The  angle  between  the  two  eccentric  radii,  that  is,  between  lines 
drawn  from  the  center  of  the  eccentric  disks  to  the  center  of  the  shaft, 
j  equals  180°  less  twice  the  angular  advance. 

i  Buel,  in  Appletpn's  "Cyclopedia  of  Mechanics,"  vol.  ii,  p.  3 16,  discusses 
the  Stephenson  link  as  follows:  "The  Stephenson  link  does  not  give  a 
perfectly  correct  distribution  of  steam;  the  lead  varies  for  different 
points  of  cut-off.  The  period  of  admission  and  the  beginning  of  ex- 
haust are  not  alike  for  both  ends  of  the  cylinder,  and  the  forward 
motion  varies  from  the  backward. 

"The  correctness  of  the  distribution  of  steam  by  Stephenson's  link- 
motion  depends  upon  conditions  which,  as  much  as  the  circumstances 
will  permit,  ought  to  be  fulfilled,  namely:  1.  The  link  should  be  curved 
in  the  arc  of  a  circle  whose  radius  is  equal  to  the  length  of  the  eccentric- 
rod.  2.  The  eccentric-rods  ought  to  be  long,  the  longer  they  are  in  pro- 
portion to  the  eccentricity  the  more  symmetrical  will  the  travel  of  the 
valve  be  on  both  sides  of  the  center  of  motion.  3.  The  link  ought  to  be 
short.  Each  of  its  points  dascribes  a  curve  in  a  vertical  plane,  whose 
ordinates  grow  larger  the  farther  the  considered  point  is  from  the  center 
of  the  link;  and  as  the  horizontal  motion  only  is  transmitted  to  the 
valve,  vertical  oscillation  will  cause  irregularities.  4.  The  link-hanger 
ought  to  be  long.  The  longer  it  is  the  nearer  will  be  the  arc  in  which 
the  link  swings  to  a  straight  line,  and  thus  the  less  its  vertical  oscillation. 
If  the  link  is  suspended  at  its  center,  the  curves  tkat  are  described  by 
points  equidistant  on  both  sides  from  the  center  are  not  alike,  and 
hence  results  the  variation  between  the  forward  and  backward  gears. 
If  the  link  is  suspended  at  its  lower  end,  its  lower  half  will  have  less 
vertical  oscillation  and  the  upper  half  more.  5.  The  center  from  which 
the  link-hanger  swings  changes  its  position  as  the  link  is  lowered  or 
raised,  and  also  causes  irregularities.  To  reduce  them  to  the  smallest 
amount  the  arm  of  the  lifting-shaft  should  be  made  as  long  as  the 
eccentric-rod,  and  the  center  of  the  lifting-shaft  should  be  placed  at 
the  height  corresponding  to  the  central  position  of  the  center  on  which 
the  link-hanger  swings." 

All  these  conditions  can  never  be  fulfilled  in  practice,  and  the  variations 
in  the  lead  and  the  period  of  admission  can  be  somewhat  regulated  in  an 
artificial  way,  but  for  one  gear  only.  This  is  accomplished  by  giving 
different  lead  to  the  two  eccentrics,  which  difference  will  be  smaller  the 
longer  the  eccentric-rods  are  and  the  shorter  the  link,  and  by  suspending 


THE   STEPHENSON   LINK-MOTION. 


1063 


the  link  not  exactly  on  its  center  line  but  at  a  certain  distance  from  it, 
giving  what  is  called  "the  offset." 

For  application  of  the  Zeuner  diagram  to  link-motion,  see  Holmes  on 
the  Steam-engine,  p.  290.  See  also  Clark's  Railway  Machinery  (1855), 
Clark's  Steam-engine,  Zeuner's  and  Auchincloss's  Treatises  on  Slide- 
valve  Gears,  and  Halsey's  Locomotive  Link  Motion.  (See  page  1119.) 

The  following  rules  are  given  by  the  American  Machinist  for  laying  out 
a  link  for  an  upright  slide-valve  engine.  By  the  term  radius  of  link  is 
meant  the  radius  of  the  link-arc,  ab,  Fig.  173,  drawn  through  the  center 
of  the  slot ;  this  radius  is  generally  made  equal  to  the  distance  from  the 


Fig.  173. 

center  of  shaft  to  center  of  the  link-block  pin  P  when  the  latter  stands 
midway  of  its  travel.  The  distance  between  the  centers  of  the  eccentric- 
rod  pins  e\  62  should  not  be  less  than  2 1/2  times,  and,  when  space  will 
permit,  three  times  the  throw  of  the  eccentric.  By  the  throw  we  mean 
twice  the  eccentricity  of  the  eccentric.  The  sl9t  link  is  generally  sus- 
pended from  the  end  next  to  the  forward  eccentric  at  a  point  in  the  link- 
arc  prolonged.  This  will  give  comparatively  a  small  amount  of  slip  to  the 
link-block  when  the  link  is  in  forward  gear;  but  this  slip  will  be  increased 
when  the  link  is  in  backward  gear.  This  increase  of  slip  is,  however, 
considered  of  little  importance,  because  marine  engines,  as  a  rule,  work 
but  very  little  in  the  backward  gear.  When  it  is  necessary  that  the 
motion  shall  be  as  efficient  in  backward  gear  as  in  forward  gear,  then  the 
link  should  be  suspended  from  a  point  midway  between  the  two  eccentric- 
rod  pins;  in  marine  engine  practice  this  point  is  generally  located  on  the 
link-arc;  for  equal  cut-offs  it  is  better  to  move  the  point  of  suspension 
a  small  amount  towards  the  eccentrics. 

For  obtaining  the  dimensions  of  the  link  in  inches:  Let  L  denote  the 
length  of  the  valve,  5  the  breadth,  p  the  absolute  steam-pressure  per  sq.  in., 
and  R  a  factor  of  computation  used  as  below;  then  R  =  0.01  *^L  XB  X  p 

••    RX  1.6 
RX  0.8 
••    72X2.5 
(RX  0.7)  +  l/4ih. 
(RX  0.6)  + 1/4  in. 
(RX  0.8) +  1/4  in. 
=    R  +  1/4  in. 
Diameter  of  block-pin  when  secured  at  both  ends .  =  (R  X  0 . 8)  + 1/4  io. 


Breadth  of  the  link. 

Thickness  T  of  the  bar 

Length  of  sliding-block 

Diameter  of  eccentric-rod  pins 

Diameter  of  suspension-rod  pin 

Diameter  of  suspension-rod  pin  when  overhung. .  . 
Diameter  of  block-pin  when  overhung. 


1064  THE  STEAM-ENGINE. 

The  length  of  the  link,  that  is,  the  distance  frcm  a  to  6,  measured  on  a 
straight  line  joining  the  ends  of  the  link-arc  in  the  slot,  should  be  such 
as  to  allow  the  center  of  the  link-block  pin  P  to  be  placed  in  a  line  with 
the  eccentric-rod  pins,  leaving  sufficient  room  for  the  slip  of  the  block. 
Another  type  of  link  frequently  used  in  marine  engines  is  the  double-bar 
link,  and  this  type  is  again  divided  into  two  classes:  one  class  embraces 
those  links  which  have  the  eccentric-rod  ends  as  well  as  the  valve-spindle 
end  between  the  bars,  as  shown  at  B  (with  these  links  the  travel  of  the 
valve  is  less  than  the  throw  of  the  eccentric);  the  other  class  embraces 
those  links,  shown  at  C,  for  which  the  eccentric-rods  are  made  with  fork- 
ends,  so  as  to  connect  to  studs  on  the  outside  of  the  bars,  allowing  the 
block  to  slide  to  the  end  of  the  link,  so  that  the  centers  of  the  eccentric- 
rod  ends  and  the  block-pin  are  in  line  when  in  full  gear,  making  the  travel 
of  the  valve  equal  to  the  throw  of  the  eccentric.  The  dimensions  of  these 
links  when  the  distance  between  the  eccentric-rod  pins  is  2 1/2  to  23/4  times 
the  throw  of  eccentrics  can  be  found  as  follows: 

Depth  of  bars.. =  (R  X  1.25)4-  Vain. 

Thickness  of  bars =  (R  X  0.5  )  -f  1/4 in. 

Diameter  of  center  of  sliding-block =    R  X  1.3 

When  the  distance  between  the  eccentric-rod  pins  is  equal  to  3  or  4 
times  the  throw  of  the  eccentrics,  then 

Depth  of  bars =  (R  X  1 . 25)  +  3/4  in. 

Thickness  of  bars =  (R  X  0 . 5  )  -f  1/4  in. 

All  the  other  dimensions  may  be  found  by  the  first  table.  These  are 
empirical  rules,  and  the  results  may  have  to  be  slightly  changed  to  suit 
given  conditions.  In  marine  engines  the  eccentric-rod  ends  for  all 
classes  of  links  have  adjustable  brasses.  In  locomotives  the  slot-link  is 
usually  employed,  and  in  these  the  pin-holes  have  case-hardened  bushes 
driven  into  the  pin-holes,  and  have  no  adjustable  brasses  in  the  ends  of 
the  eccentric-rods.  The  link  in  B  is  generally  suspended  by  one  of  the 
eccentric-rod  pins;  and  the  link  in  C  is  suspended  by  one  of  the  pins  in 
the  end  of  the  link,  or  by  one  of  the  eccentric-rod  pins.  (See  note  on 
Locomotive  Link  Motion,  p.  1119.) 

The  Walschaerts  Valve-gear.  Fig.  174. — This  gear,  which  was 
invented,  in  Belgium,  has  for  many  years  been  used  on  locomotives  in 
Europe,  and  it  has  now  (1909)  come  largely  into  use  in  the  United  States. 
The  return  crank  Q,  which  takes  the  place  of  an  eccentric,  through  the 
rod  B  oscillates  the  link  on  the  fixed  pin  F.  The  block  D  is  raised  and 
lowered  in  the  link  by  the  reversing  rod  I,  operating  through  the  bell- 


FIG.  174. — The  Walschaerts  Valve-gear. , 


crank  levers  H ,  H,  and  the  supporting  rod  G.  When  the  block  is  in  its 
lowest  position  the  radius  rod  U  has  a  motion  corresponding  in  direction 
to  that  of  the  rod  B ;  when  the  block  is  at  its  upper  position  U  moves  in 
an  opposite  direction  to  B.  The  valve-rod  E  is  moved  by  the  combined 
action  of  U  and  a  lever  T  whose  lower  end  is  connected  through  the 
rod  S  to  the  cross-head  R.  Constant  lead  is  secured  by  this  gear.  (The 
main  crank  and  the  return  crank  should  be  shown  in  the  cut  as  inclin- 
ing to  the  right  to  correspond  with  the  position  of  the  cross-hea.<J.) 


GOVERNORS.  1065 

Other  Forms  of  Valve-gear,  as  the  Joy,  Marshall,  Hackworth, 
Brerame,  Walschaerts,  Corliss,  etc.,  are  described  in  Clark's  Steam- 
engine,  vol.  ii.  Power,  May  11,  1909,  illustrates  the  Stephenson,  Gooch, 
Allen,  Polenceau,  Marshall,  Joy,  Waldegg,  Walschaerts,  Fink,  and 
Baker-Pilliod  gears.  The  design  of  the  Reynolds-Corliss  valve-gear  is 
discussed  by  A.  H.  Eldridge  in  Power,  Sept.,  1893.  See  also  Henthorn 
on  the  Corliss  Engine.  Rules  for  laying  down  the  center  lines  of  the 
Joy  valve-gear  are  given  in  American  Machinist,  Nov.  13,  1890.  For 
Joy's  "Fluid-pressure  Reversing-  valve,"  see  Eng'g,  May  25,  1894. 

GOVERNORS. 

Pendulum  or  Fly-ball  Governor.  —  The  inclination  of  the  arms  of  a 
revolving  pendulum  to  a  vertical  axis  is  such  that  the  height  of  the  point 
of  suspension  h  above  the  horizontal  plane  in  which  the  center  of  gravity 
of  the  balls  revolves  (assuming  the  weight  of  the  rods  to  be  small  compared 
with  the  weight  of  the  balls)  bears  to  the  radius  r  of  the  circle  described 
by  the  centers  of  the  balls  the  ratio 

h  _          weight  _    w    _  gr 

r  ~  centrifugal  force  ~~  wv'2  ~  v2  ' 
gr 

which  ratio  is  independent  of  the  weight  of  the  balls,  v  being  the  velocity 
of  the  centers  of  the  balls  in  feet  per  second. 

If  T  =  number  of  revolutions  of  the  balls  in  1  second,  v  =  2-nrT  =  ar, 
in  which  a  =  'the  angular  velocity,  or  2  vT,  and 

0r2  g  0.8146.  9.775.     . 

h  =  V  =  4^'   or   h  -  —  ^-  feet  =  -^r  inches, 

g  =  32.16.     If  N  =  revs,  per  minute,  h  =  35,190  •*-  N*. 

For  revolutions  per  minute.  ...        40          45          50  60          75 

The  height  in  inches  will  be  ...     21.99    17.38    14.08    9.775    6.256 

Number  of  turns  per  minute  required  to  cause  the  arms  to  take  a  given 
angle  with  the  vertical  axis:  Let  I  =  length  of  the  arm  in  inches  from 
the  center  of  suspension  to  the  center  of  gyration,  and  a  the  required 
angle;  then 


The  simple  governor  is  not  isochronous;  that  is,  it  does  not  revolve 
at  a  uniform  speed  in  ail  positions,  the  speed  changing  as  the  angle  of  the 
arms  changes.  To  remedy  this  defect  loaded  governors,  such  as  Porter's, 
are  used.  From  the  balls  of  a  common  governor  whose  collective  weight 
is  A  let  there  be  hung  by  a  pair  of  links  of  lengths  equal  to  the  pendulum 
arms  a  load  B  capable  of  sliding  on  the  spindle,  having  its  center  of  gravity 
in  the  axis  of  rotation.  Then  the  centrifugal  force  is  that  due  to  A  alone, 
and  the  effect  of  gravity  is  that  due  to  A  +  2  B;  consequently  the  alti- 
tude for  a  given  speed  is  increased  in  the  ratio  (A  +  2  B)  :  A,  as  com- 
pared with  that  of  a  simple  revolving  pendulum,  and  a  given  absolute 
variation  in  altitude  produces  a  smaller  proportionate  variation  in  speed 
than  in  the  common  governor.  (Rankine,  S.  E.,  p.  551.) 

For  the  weighted  governor  let  1=  the  length  of  the  arm  from  the  point 
of  suspension  to  the  center  of  gravity  of  the  ball,  and  let  the  length  of  the 
suspending-link  h  =  the  length  of  the  portion  of  the  arm  from  the  point 
of  suspension  of  the  arm  to  the  point  of  attachment  of  the  link;  G  =  the 
weight  of  one  ball,  Q  =  half  the  weight  of  the  sliding  weight,  h  =  the 
height  of  the  governor  from  the  point  of  suspension  to  the  plane  of  revolu- 
tion of  the  balls,  a  =  the  angular  velocity  =  2  irT,  T  being  the  number  of 

revolutions  per  second  ;  then  a  =  y/T^1  +  ¥l);  fcsJ^  (*  +  T  §) 
in  feet,  or  h  =  ^^(l  +  ^r  §)  in  inches,  N  being  the  number  of  revo- 
lutions per  minute. 


1066  THE   STEAM-ENGINE. 

J.  H.  Barr  gives  h  =  (^^)*  B  +^  W  ,in  which  B  is  the  combined 

weight  of  the  two  balls  and  W  the  central  weight. 

For  various  forms  of  governor  see  App.  Cyl.  Mech.,  vol.  ii,  61,  and 
Clark's  Steam-engine,  vol.  ii,  p.  65. 

To  Change  the  Speed  of  an  Engine  Having  a  Fly-ball  Governor.  — 

A  slight  difference  in  the  speed  of  a  governor  changes  the  position  of  its 
weights  from  that  required  for  full  load  to  that  required  for  no  load. 
It  is  evident  therefore  that,  whatever  the  speed  of  the  engine,  the  normal 
speed  of  the  governor  must  be  that  for  which  the  governor  was  designed; 
i.e.,  the  speed  of  the  governor  must  be  kept  the  same.  To  change  the 
speed'  of  the  engine  the  problem  is  to  so  adjust  the  pulleys  which  drive 
the  governor  that  the  engine  at  its  new  speed  shall  drive  it  just  as  fast  as 
it  was  driven  at  its  original  speed.  In  order  to  increase  the  engine-speed 
we  must  decrease  the  pulley  upon  the  shaft  of  the  engine,  i.e.,  the  driver, 
or  increase  that  on  the  governor,  i.e.,  the  driven,  in  the  proportion  that 
the  speed  of  the  engine  is  to  be  increased. 

Fly-wheel  or  Shaft-governors.  —  At  the  Centennial  Exhibition  in 
1876  there  were  shown  a  few  steam-engines  in  which  the  governors  were 
contained  in  the  fly-wheel  or  band-wheel,  the  fly-balls  or  weights  revolving 
around  the  shaft  in  a  vertical  plane  with  the  wheel  and  shifting  the  eccen- 
tric so  as  automatically  to  vary  the  travel  of  the  valve  and  the  point  of 
cut-off.  This  form  of  governor  has  since  come  into  extensive  use,  espe- 
cially for  high-speed  engines.  In  its  usual  form  two  weights  are  carried  on 
arms  the  ends  of  which  are  pivoted  to  two  points  on  the  pulley  near  its 
circumference,  180°  apart.  Links  connect  these  arms  to  the  eccentric. 
The  eccentric  is  not  rigidly  keyed  to  the  shaft  but  is  free  to  move  trans- 
versely across  it  for  a  certain  distance,  having  an  oblong  hole  which  allows 
of  this  movement.  Centrifugal  force  causes  the  weights  to  fly  towards 
the  circumference  of  the  wheel  and  to  pull  the  eccentric  into  a  position  of 
minimum  eccentricity.  This  force  is  resisted  by  a  spring  attached  to 
each  arm  which  tends  to  pull  the  weights  towards  the  shaft  and  shift  the 
eccentric  to  the  position  of  maximum  eccentricity.  The  travel  of  the  valve 
is  thus  varied,  so  that  it  tends  to  cut  off  earlier  in  the  stroke  as  the  engine 
increases  its  speed.  Many  modifications  of  this  general  form  are  in  use. 
In  the  Buckeye  and  the  Mclntosh  &  Seymour  engines  the  governor  shifts 
the  eccentric  around  on  the  shaft  so  as  to  vary  the  angular  advance. 
In  the  Sweet  "Straight-line"  engine  and  in  some  others  a  single  weight 
and  a  single  spring  are  used.  For  discussions  of  this  form  of  governor 
see  Hartnell,  Proc.  Inst.  M.  E.,  1882,  p.  408;  Trans.  A.  S.  M.  E.,  ix,  300; 
xi,  1081;  xiv,  92:  xy,  929;  Modern  Mechanism,  p.  399:  Whitham's  Con- 
structive Steam  Engineering;  J.  Begtrup,  Am.  Mach.,  Oct.  19  and  Dec.  14, 
1893,  Jan.  18  and  March  1,  1894. 

Mare  recent  references  are:  J.  Richardson,  Proc.  Inst.  M.  E.,  1895 
(includes  electrical  regulation  of  steam-engines);  A.  K.  Mansfield,  Trans. 
A.  S.  M.  E.,  1894;  F.  H.  Ball,  Trans.  A.  S.  M.  E.,  1896;  R.  C.  Carpenter, 
Power,  May  and  June,  1898;  Thos.  Hall,  EL  World,  June  4,  1898;  F.  M. 
Rites,  Power,  July,  1902;  E.  R.  Briggs,  Am.  Mach.,  Dec.  17,  1903 

The  Rites  Inertia  Governor,  which  is  the  most  common  form  of  the 
shaft  governor  at  this  date  (1909).  has  a  long  bar,  usually  made  heavy  at 
the  ends,  like  a  dumb-bell,  instead  of  the  usual  weights.  This  is  carried 
on  an  arm  of  the  fly-wheel  by  a  pin  located  at  some  distance  from  the 
center  line  of  the  bar,  and  also  at  some  distance  from  its  middle  point. 
To  pins  located  at  two  other  points  are  attached  the  valve-rod  and  the 
spring.  The  bar  acts  both  by  inertia  and  by  centrifugal  force.  When 
the  wheel  increases  its  speed  the  inertia  of  the  bar  tends  to  make  it  fall 
behind,  and  thus  to  change  the  relative  position  of  the  fly-wheel  arm  and 
the  bar,  and  to  change  the  travel  of  the  valve.  A  small  book  on  "  Shaft 
Governors  "  (Hill  Pub.  Co.,  1908)  describes  and  illustrates  this  and  many 
other  forms  of  shaft  governors,  and  gives  practical  directions  for  adjusting 
them. 

Calculation  of  Springs  for  Shaft-governors.  (Wilson  Hartnell, 
Proc.  Tnst.  M.  E.,  Aug.,  1882.)  —  The  springs  for  shaft-governors  may  be 
conveniently  calculated  as  follows,  dimensions  being  in  inches: 

Let   W  =  weight  of  the  balls  or  weights,  in  pounds: 

n  and  ra  =  the  maximum  and  minimum  radial  distances  of  the 
center  of  the  balls  or  of  the  centers  of  gravity  of  the  weights; 


GOVERNORS.  1067 

la  and  h  =  the  leverages,  i.e.,  the  perpendicular  distances  from  the 
center  of  the  weight-pin  to  a  line  in  the  direction  of  the  centrif- 
ugal force  drawn  through  the  center  of  gravity  of  the  weights 
or  balls  at  radii  n  and  rz; 

mi  and  m^  =  the  corresponding  leverages  of  the  springs; 

Ci  and  CT2  =  the  centrifugal  forces,  for  100  revolutions  per  minute, 
at  radii  n  and  rz; 

Pi  and  P2  =  the  corresponding  pressures  on  the  spring; 

(It  is  convenient  to  calculate  these  and  note  them  down  for  refer- 
ence.) 

Cs  and  C4  =  maximum  and  minimum  centrifugal  forces; 

S  =  mean  speed  (revolutions  per  minute); 

Si  and  Sz  =  the  maximum  and  minimum  number  of  revolutions 
per  minute; 

Ps  and  PI  =  the  pressures  on  the  spring  at  the  limiting  number 
of  revolutions  (Si  and  £2); 

P4  —  Ps  =  D  =  the  difference  of  the  maximum  and  minimum 
pressures  on  the  springs; 

V  =  the  percentage  of  variation  from  the  mean  speed,  or  the 
sensitiveness; 

t   =  the  travel  of  the  spring; 

u  =  the  initial  extension  of  the  spring; 

v  =  the  stiffness  in  pounds  per  inch ; 

w  —  the  maximum  extension  =  u  +  t. . 

The  mean  speed  and  sensitiveness  desired  are  supposed  to  be  given, 

fsv  sv 

S1  =  S—T7^'  St^S+TF^' 

It  is  usual  to  give  the  spring-maker  the  values  of  P4  and  of  v  or  w. 
To  ensure  proper  space  being  provided,  the  dimensions  of  the  spring  should 
be  calculated  by  the  formulas  for  strength  and  extension  of  springs,  and 
the  least  length  of  the  spring  as  compressed  be  determined. 

The  governor-power =—^2 — *X  T-X- 
With  a  straight  centripetal  line,  the  governor-power 

~V^X  ("IT"1)' 

For  a  preliminary  determination  of  the  governor-power  it  may  be  taken 
as  equal  to  this  in  all  cases,  although  it  is  evident  that  with  a  curved  cen- 
tripetal line  it  will  be  slightly  less.  The  difference  D  must  be  constant  for 
the  same  spring,  however  great  or  little  its  initial  compression.  Let  the 
spring  be  screwed  up  until  its  minimum  pressure  is  P5.  Then  to  find  the 
speed  Po  =  P$  +  D, 


0.28XnX  W-,  Ca  =  0  .28  X  rz  X  W; 


„  »  „_*„,_* 

t  v  v 


The  speed  at  which  the  governor  would  be  isochronous  would  be 


Suppose  the  pressure  on  the  spring  with  a  speed  of  100  revolutions,  at 
the  maximum  and  minimum  radii,  was  200  Ibs.  and  100  Ibs.,  respectively, 


10G8 


THE  STEAM-ENGINE. 


then  the  pressure  of  the  spring  to  suit  a  variation  from  95  to  105  revolu- 
tions will  be  100  X  (^)2  =  90  .2  and  200  X  (^)2  =  220  .5    That  is,  the 

increase  of  resistance  from  the  minimum  to  the  maximum  radius  must  be 
220 -90  =  130  Ibs. 

The  extreme  speeds  due  to  such  a  spring,  screwed  up  to  different 
pressures,  are  shown  in  the  following  table: 


Revolutions  per  minute  balls  shut  

80 

00 

9S 

100 

no 

120 

Pressure  on  springs  balls  shut  

64 

81 

90 

100 

121 

M4 

Increase  of  pressure  when  balls  open  fully  

no 

no 

no 

no 

no 

130 

Pressure  on  springs,  balls  open  fully  

1Q4 

?n 

??0 

?so 

?*>! 

?74 

Revolutions  per  minute,  balls  open  fully  

Q8 

10? 

105 

107 

11? 

117 

Variation  per  cent  of  mean  speed 

to 

6 

5 

^ 

1 

_  i 

The  speed  at  which  the  governor  would  become  isochronous  is  114. 

Any  spring  will  give  the  right  variation  at  some  speed;  hence  in  experi- 
menting with  a  governor  the  correct  spring  may  be  found  from  any  wrong 
one  by  a  very  simple  calculation.  Thus,  if  a  governor  with  a  spiing 
whose  stiffness  is  50  Ibs.  per  inch  acts  best  when  the  engine  runs  at  95,  90 

/90  \2 
being  its  proper  speed,  then  50  X  (  ^  j  =45  Ibs.  is  the  stiffness  of  spring 

required. 

To  determine  the  speed  at  which  the  governor  acts  best,  the  spring 
may  be  screwed  up  until  the  governor  begins  to  "hunt"  and  then  be 
slackened  until  it  is  as  sensitive  as  is  compatible  with  steadiness. 

CONDENSERS,  AIR-PUMPS,  CIRCULATING-PUMPS,  ETC. 

The  Jet  Condenser.  —  In  practice  the  temperature  in  the  hot-well 
varies  from  110°  to  120°,  and  occasionally  as  much  as  130°  is  maintained. 
To  find  the  quantity  of  injection-water  per  pound  of  steam  to  be  condensed: 
Let  T\  =  temperature  of  steam  at  the  exhaust  pressure;  T0  =  temper- 
ature of  the  cooling-water;  T%  =  temperature  of  the  water  after  condensa- 
tion, or  of  the  hot-well;  Q  =  pounds  of  the  cooling-water  per  Ib.  of  steam 
condensed;  then 


prr  TT 

Another  formula  is:  Q=— 5-,  in  which  W  is  the  weight  of  steam  con- 

K 

densed,  H  the  units  of  heat  given  up  by  1  Ib.  of  steam  in  condensing,  and 
R  the  rise  in  temperature  of  the  cooling-water.  This  is  applicable  both 
to  jet  and  to  surface  condensers. 

Quantity  of  Cooling-water.  —  The  quantity  depends  chiefly  upon 
Its  initial  temperature,  which  in  Atlantic  practice  may  vary  from  40°  in 
the  winter  of  temperate  zone  to  80°  in  subtropical  seas.  To  raise  the 
temperature  to  100°  in  the  condenser  will  require  three  times  as  many 
thermal  units  in  the  former  case  as  in  the  latter,  and  therefore  only  one- 
third  as  much  cooling-water  will  be  required  in  the  former  case  as  in  the 
latter.  It  is  usual  to  provide  pumping  power  sufficient  to  supply  40  times 
the  weight  of  steam  for  general  traders,  and  as  much  as  50  times  for  ships 
stationed  in  subtropical  seas,  when  the  engines  are  compound.  If  the 
circulating  pump  is  double-acting,  its  capacity  may  be  1/53  in  the  former 
and  1/42  in  the  latter  case  of  the  capacity  of  the  low-pressure  cylinder. 
(Seaton.) 

The  following  table,  condensed  from  one  given  by  W.  V.  Terry  in  Power, 
Nov.  30,  1909,  shows  the  amount  of  circulating  water  required  under 
different  conditions  of  vacuum,  temperature  of  water  entering  the  con- 
denser, and  drop.  The  "drop"  is  the  difference  between  the  temperature 
of  steam  due  to  a  given  vacuum  and  the  temperature  of  the  water  leaving 
the  condenser. 


CONDENSERS,   AIR-PUMPS,   ETC, 


1069 


POUNDS  OF  CIRCULATING  WATER  PER  POUND  OP  STEAM  CONDENSED. 


Vac- 
uum. 
Ins. 

Drop. 

Dff 

Injection  Water  Temperature,  Deg.  F. 

45 

50 

55 

60 

65 

70 

75 

80 

85 

90 

29.0 

6 

37.5 

45.7 

58.3 

80.8 

12 

47.8 

61.8 

87.5 

18 

65.7 

95.5 

28.5 

6 

25.6 

29.2 

33.9 

40.3 

50.0 

65.7 

95.5 

12 

30.0 

35.0 

42.0 

52.5 

70.0 

18 

36.2 

43.8 

55.3 

75.0 

28.0 

6 

21.5 

23.9 

26.9 

30.9 

36.3 

43.8 

55.3 

75.0 

12 

24.4 

27.7 

31.8 

37.5 

45.7 

58.3 

80.8 

18 

28.4 

32.8 

38.9 

47.8 

61.8 

87.5 

27.0 

6 

16.4 

17.8 

19.5 

21.5 

23.9 

27.0 

30.9 

36.2 

43.8 

55.3 

12 

18.1 

19.8 

21.9 

24.4 

27.7 

31.8 

37.5 

45.7 

58.3 

80.8 

18 

20.3 

22.4 

25.0 

28.4 

32.8 

38.9 

47.8 

61.8 

87.5 

26.0 

6 

14.0 

15.0 

16.2 

17.5 

19.1 

21.0 

23.4 

26.3 

30.0 

35.0 

12 

15,2 

16.4 

17.8 

19.5 

21.5 

23.9 

26.9 

30.9 

36.3 

43.8 

18 

16.8 

18.1 

19.8 

21.9 

24.4 

27.7 

31.8 

37.5 

45.7 

58.3 

Ejector  Condensers.  —  For  ejector  or  injector  condensers  (Bulkley's, 
Schutte's,  etc.)  the  calculations  for  quantity  of  condensing-water  is  the 
same  as  for  jet  condensers. 

The  Barometric  Condenser  consists  of  a  vertical  cylindrical  chamber 
mounted  on  top  of  a  discharge  pipe  whose  length  is  34  ft.  above  the  level 
of  the  hot  well.  The  exhaust  steam  and  the  condensing  water  meet  in  the 
upper  chamber,  the  water  being  delivered  in  such  a  manner  as  to  expose 
a  large  surface  to  the  steam.  The  external  atmosphere  maintains  a  col- 
umn of  water  in  the  tube,  as  a  column  of  mercury  is  maintained  in  a 
barometer,  and  no  air  pump  is  needed.  The  Bulkley  condenser  is  the 
original  form  of  the  type.  In  some  modern  forms  a  small  air  pump  draws 
from  the  chamber  the  residue  of  air  which  is  not  drawn  out  by  the  de- 
scending column  of  water,  discharging  it  into  the  column  below  the 
chamber. 

The  Surface  Condenser  —  Cooling  Surface.  —  In  practice,  with  the 
compound  engine,  brass  condenser-tubes,  18  B.W.G.  thick,  13   Ibs.  of 
steam  per  sq.  ft.  per  hour,  with  the  cooling-water  at  an  initial  temperature 
of  60°,  is  considered  very  fair  work  when  the  temperature  of  the  feed- 
water  is  to  be  maintained  at  120°.     It  has  been  found  that  the  surface  in 
the  condenser  may  be  half  the  heating  surface  of  the  boiler,  and  under 
some  circumstances  considerably  less  than  this.     In  general  practice  the 
following  holds  good  when  the  temperature  of  sea-water  is  about  60°: 
Terminal  pres.,  Ibs.,  abs.  .         30      20         15       121/2       10          8          6 
Sq.  ft.  per  I.H.P 3     2.50     2.25     2.00     1.80     1.60     1.50 

For  ships  whose  station  is  in  the  tropics  the  allowance  should  be  in- 
creased by  20%,  and  for  ships  which  occasionally  visit  the  tropics  10% 
increase  will  give  satisfactory  results.  If  a  ship  is  constantly  employed 
in  cold  climates  10%  less  suffices.  (Seaton,  Marine  Engineering.) 

Whitham  (Steam-engine  Design,  p.  283,  also  Trans.  A.S.M.  E.,  ix,  43] ) 

gives  the  following:  S=  ,,„  _.  ,  in  which  S  =  condensing-surface  in 

sq.  ft.;  Ti  =  temperature  Fahr.  of  steam  of  the  pressure  indicated  by  the 
vacuum-gauge;  t  =  mean  temperature  of  the  circulating  water,  or  the 
arithmetical  mean  of  the  initial  and  final  temperatures:  L  =  latent  heat 
of  saturated  steam  at  temperature  T\\  k  =  perfect  conductivity  of  1  sq. 
ft.  of  the  metal  used  for  the  condensing-surface  for  a  range  of  1°  F.  (or 
550  B.T.U.  per  hour  for  brass,  according  to  Isher wood's  experiments); 
c  =  fraction  denoting  the  efficiency  of  the  condensing-surface;  W  = 


1070  THE   STEAM-ENGINE. 

v 

pounds  of  steam  condensed  per  hour.     From  experiments  by  Loring  and 
Emery,  on  U.S.S.  Dallas,  c  is  found  to  be  0.323,  and  ck  =  180;  making 

the  equation  B  =  180^_t)- 

Whitham  recommends  this  formula  for  designing  engines  having  inde- 
pendent circulating-pumps..  When  the  pump  is  worked  by  the  main 
engine  the  value  of  S  should  be  increased  about  10%. 

Taking  Ti  at  135°  F.,  and  L  =  1020,  corresponding  to  25  in.  vacuum, 

and  t  for  summer  temperatures  at  75°,  we  have:  5=^ 77-77   L — =^n=~TS7r 

LoU  (loO —  to'         loU 

Much  higher  results  than  those  quoted  by  Whitham  are  obtained  from 
modern  forms  of  condensers.  The  literature  on  the  subject  of  condensers 
from  1900  to  1909  has  been  quite  voluminous,  and  much  difference  of 
opinion  as  to  rules  of  proportioning  condensers  is  shown. 

Coefficient  of  Heat  Transference  in  Condensers.  (Prof.  E.  Josse 
of  Berlin.  Condensed  from  an  abstract  in  Power,  Feb.  2,  1909.  See  also 
Transmission  of  Heat  from  Steam  to  Water,  pages  587  to  5890 

The  coefficient  U,  the  number  of  heat  units  transferred  per  hour  through 
1  sq.  ft.  of  metallic  condenser  wall  when  the  temperature  of  the  steam  is 
1°  F.  higher  than  that  of  the  water,  can  be  deduced  from  the  formula 
l/U  =  l/Ai  +  d,L  +  1/Az, 

in  which  \/A\  is  the  resistance  to  transmission  from  steam  to  metal,  1/Ag 
the  resistance  to  transmission  from  metal  to  water,,  and  d/L  the  resistance 
to  transmission  of  heat  through  the  metal,  d  being  the  usual  thickness  of 
condenser  tubes  (1  m.m.  or  0  .0393  in.).  For  this  thickness  the  value  of 
L  is  fairly  well  known  and  may  be  given  as  18,430  for  brass,  6,500  for 
„  copper,  11,270  for  iron,  5740  for  zinc,  11,050  for  tin  and  2660  for  alumi- 
num. The  middle  term  d/L  would  have  the  value  of  1/18,430  and  be  of 
comparatively  little  importance. 

The  term  l/Az  is  the  most  important  and  has  been  investigated  with 
the  aid  of  two  concentric  tubes,  water  being  sent  both  through  the  inner 
tube  and  the  annular  jacket.     The  values  of  various  experimenters  differ 
greatly.     Ser  gives  the  approximate  formula__ 
A  -  2  =  510  vY, 

where  V  is  the  velocity  of  water  through  the  tubes  in  ft.  per  sec.  This 
velocity  is  far  more  important  than  the  material  of  the  condenser  tubes 
and  their  thickness,  and  also  of  greater  consequence  than  the  velocity 
of  the  steam,  about  which,  or,  rather,  the  term  1/Ai,  there  is  even  less 
agreement.  Prof.  Josse  adopts  the  figure  3900.  The  velocity  of  the 
steam  has  its  influence,  but  the  whole  term  does  not  count  for  much. 
For  water  flowing  at  the  rate  of  1 .64  ft.  per  sec.  Josse's  formula  would  be: 
l/U  =  1/3900  -f  1/18,430  +  1/653  =  1/445, 

and  U  =  445. 

If  A  i  be  increased  to  twice  its  value  U  would  rise  only  to  475,  and  if  the 
tube  thickness  be  doubled  U  would  hardly  be  affected.  An  increase, 
however,  in  the  rate  of  flow  of  water  from  1.64  to  5  feet  per  second  would 
raise  U  to  625.  As  an  increase  of  the  steam  flow  is  undesirable  'the  best 
plan  is  to  accelerate  the  flow  of  the  circulating  water,  and  by  introducing 
the  baffle  strips  or  retarders  into  his  condenser  tubes,  in  order  to  break  the 
water  currents  up  into  vortices,  Josse  raised  the  value  of  U  at  a  velocity  of 
3.28  feet  per  second  from  614  to  922. 

Opinions  differ  concerning  the  increase'  of  U  with  greater  differences  of 
temperature.  According  to  some  the  heat  transferred  should  increase 
proportionately  to  the  difference;  according  to  Weiss  and  others,  pro- 
portionally to  the  square  of  the  temperature  differences.  Josse's  investi- 
gations were  conducted  by  placing  thermo  couples  in  different  portions 
of  the  condenser  tubes.  If  the  heat  transferred  increases  as  a  linear 
function  of  the  difference,  then  the  rise  of  the  temperature  in  the  cool- 
ing water  should  follow  an  exponential  law,  and  it  was  found  to  be  so. 

Curves  showing  the  relation  of  the  extent  of  surface  to  the  temperatures 
Of  steam  and  water  show  an  agreement  with  the  formula 


Surface 


6  j-^ 


CONDENSERS,  AIR-PUMPS,  ETC. 


1071 


where  tsis  the  saturation  temperature  and  £cthe  temperature  of  the  cooling- 
water  at  entrance,  t  being  the  discharge  temperature;. 

Air  Leakage.  —  Air  passes  into  the  condenser  with  the  exhaust  steam, 
the  temperature  of  the  air  being  that  of  the  steam;  the  pressure  of  the 
mixture  will  be  the  sum  of  the  partial  stearn  pressure  and  of  the  partial 
air  pressure.  The  air  must  be  withdrawn  by  the  air-pump.  If  the  with- 
drawal takes  place  at  the  temperature  corresponding  to  the  condenser 
pressure  the  partial  steam  pressure  would  be  equal  to  the  condenser 
pressure, 'and  the  pump  would  have  to  deal  with  an  enormous  air  volume. 
The  air  temperature  should,  therefore,  be  lowered,  at  the  spot  where  the 
air  is  withdrawn,  below  the  saturation  temperature  of  the  condenser 
pressure. 

In  steam  turbines  it  is  more  easy  to  keep  air  out  than  in  reciprocating 
engines.  Experiments  with  a  300-kw.  Parsons  turbine  show  that  not  more 
than  1/2  Ib.  of  air  was  delivered  per  hour  when  6600  Ibs.of  steam  was  used 
per  hour. 

Condenser  Pumps.  —  The  air  and  condensed  water  may  either  be 
removed  separately,  by  a  so-called  dry-air  pump,  or  both  together,  by 
a  wet-air  pump.  As  dry-air  pumps  have  to  deal  with  high  compression 
ratios,  with  high  vacua  and  single-stage  pumps,  the  clearances  must  be 
small.  When  the  clearance  amounts  to  5%  the  vacuum  cannot  be  main- 
tained at  more  than  95%,  and  the  clearance  must  be  reduced,  or  other 
expedients  adopted.  Three  are  mentioned:  (1)  the  air-pump  may  be 
built  in  two  stages;  (2)  the  pump  may  be  fitted  with  an  equalizing  pipe 
so  that  the  two  sides  of  the  piston  are  connected  near  the  end  of  each 
stroke;  the  volumetric  efficiency  is  raised  by  this  expedient,  but  consider- 
ably more  power  is  absorbed  to  accomplish  the  result;  (3)  with  the  wet- 
air  pump  the  clearance  space  is  made  to  receive  the  condensed  water, 
which  will  fill  at  least  part  of  it. 

Contraflow  and  Ordinary  Flow.  —  Prof.  Josse  questions  the  distinction 
between  contraflow  and  ordinary  flow.  For  the  greater  portion  of  the 
condenser  there  is  a  rise  of  temperature  only  on  the  water  side;  the  tem- 
perature of  the  steam  side  remains  that  of  the  saturated  steam,  and  the 
term  "contraflow"  should,  strictly  speaking,  only  be  applied  if  there  is  a 
temperature  fall  in  the  one  direction  and  a  corresponding  temperature  rise 
in  the  opposite  direction.  As  far  as  the  condensation  is  concerned,  it  is 
immaterial  in  which  direction  the  water  flows.  The  contraflow  principle 
is,  however,  correct  and  necessary  for  the  smaller  portion  of  the  condenser 
in  which  the  condensed  liquid  is  cooled  together  with  the  air;  for  the 
air  must  be  withdrawn  from  the  coldest  spot.  It  seems  inadvisable  to 
attempt  to  direct  the  flow  of  the  steam  on  the  contraflow  principle,  as  that 
would  obstruct  the  steam  flow  and  create  a  pressure  difference  between 
different  portions  of  the  condenser  which  would  be  injurious  to  the  main- 
tenance of  high  vacua. 

The  Power  Used  for  Condensing  Apparatus  varies  from  about 
1 1/2  to  5%  of  the  indicated  power  of  the  main  engine,  depending  on  the 
efficiency  of  the  apparatus,  on  the  degree  of  vacuum  obtained,  the  tem- 
perature of  the  cooling-water,  the  load  on  the  engine,  etc.  J.  R.  Bibbins 
(Power,  Feb.,  1905)  gives  the  records  of  test  of  a  300-kw.  plant  from  which 
the  following  figures  are  taken.  Cooling-water  per  Ib.  of  steam  32  to  37 
Ibs.  Vacuum  27.3  to  27.8  ins.  Temp,  cooling-water  73.  Hot-well  102 
to  105. 


Indicated  H.P  

151 

220 

238 

260 

291 

294 

457 

589 

%  of  total  power  used  .  .  . 

4.69 

3.51 

3.22 

3.22 

3.08 

2.97 

2.80 

2.47 

%  for  air  cylinder  

1.63 

1.36 

1.27 

1.21 

1.19 

1.09 

0.95 

0.83 

%  for  water  pump  

3.07 

2.14 

1.95 

2.00 

1.90 

1.89 

1.85 

1.52 

Vacuum,  ins.  of  Mercury,  and  Absolute  Pressures. — The  vacuum 
as  shown  by  a  mercury  column  is  not  a  direct  measure  of  pressure,  but 
only  of  the  difference  between  the  atmospheric  pressure  and  the  absolute 
pressure  in  the  vacuum  chamber.  Since  the  atmospheric  pressure  varies 
with  the  altitude  and  also  with  atmospheric  conditions,  it  is  necessary 
when  accuracy  is  desired  to  give  the  reading  of  the  barometer  as  well  as 
that  of  the  vacuum  gauge,  or  preferably  to  give  the  absolute  pressure  in 
Ibs.  per  SQ.  in.  above  a  perfect  vacuum. 


1072 


THE  STEAM-ENGINE. 


Temperatures,  Pressures  and  Volumes  of  Saturated  Air.— (D.  B, 

Morison,  on  the  influence  of  Air  on  Vacuum  in  Surface  Condensers, 
Eng'g,  April  17,  1908.) 

VOLUME  OF  1  LB.  OF  Am  WITH  ACCOMPANYING  VAPOR. 


& 
& 

!.* 

2^ 

£rt 

Vacuum,  ins.  of  Mercury,  and  Ibs.  absolute. 

24  in., 
2.947. 

26  in., 
1.962. 

27  in., 
1.474. 

28  in., 
0.9823. 

28.5  in., 
0.7368. 

28.8  in., 
0.5894. 

29  in., 
0.4912. 

50 
60 
70 
80 
90 
100 
110 
120 

0.17 
0.25 
0.36 
0.50 
0.69 
0.94 
1.26- 
1.68 

P 

2.78 
2.70 
2.59 
2.45 
2.26 
2.01 
1.69 
1.27 

V 

68 
71 
75 
81 
90 
103 
125 
170 

P 

.79 
.71 
.60 
.46 
.27 
.02 
0.70 
0.28 

V 

105 
113 
124 
137 
163 
203 
304 
770 

P 
1.30 
1.22 
1.11 
0.97 
0.78 
0.53 
0.21 

V 
147 
158 
178 
204 
260 
390 
(a) 

P 

0.81 
0.73 
0.62 
0.48 
0.29 
0.042 

V 
233 
263 
315 
420 
700 
(&) 

P 
0.57 
0.49 
0.38 
0.24 
0.05 

V 
336 
393 
520 
832 
(c) 

P 

0.42 
0.34 
0.23 
0.09 

V 
450 
566 
852 

(d) 

P 

0.32 
0.24 
0.13 

V 
592 
800 
1536 

P  =  partial  pressure  of  air,  Ibs.  per  sq.  in.  V  =  volume  of  1  Ib.  of 
air  with  accompanying  vapor,  cu.  ft.  (a)  over  1000;  (6)  nearly  5000; 
(c)  about  4000;  (d)  over  2000. 

TEMPERATURES  AND  PRESSURES  OF  SATURATED  AIR. 


Vacuum,  Ins. 


Proportions  of  Air  and  Steam  by  Weight. 


with  Barom. 
at  30  in. 

Saturated 
Steam. 

Air,  0.25. 
Steam,  1. 

Air,  0.5. 
Steam,  1. 

Air,  0.75. 
Steam,  1. 

Air,  1. 
Steam,  1. 

29 
28 
27 
26 
25 
24 

79.  5°  F. 
101.5 
115 
126 
134 
141 

75 
96.5 
110 
120.2 
128.4 
•135.2 

71 
92.4 
105.6 
115.5 
123.5 
130.3 

67.5 
88.8 
1C1.7 
111.5 
119  2 
125.8 

64.5 
85.3 
98.6 
108.3 
116.2 
122.3 

From  this  table  it  is  seen  that  a  temperature  of  126°  F.  corresponds  to 
a  24-in.  vacuum  if  the  steam  in  the  condenser  has  75%  of  its  weight  of 
air  mingled  with  it,  and  to  a  26-in.  vacuum  if  it  is  free  from  air. 

One  cubic  foot  of  air  measured  at  60°  F.  and  atmospheric  pressure 
becomes  10  cii.  ft.  at  27  in.  and  30  cu.  ft.  at  29  in.  vacuum  at  the  same 
temperature;  10.9  cu.  ft.  at  105°  and  27  in.;  30.5  cu.  ft.  at  70°  F.  and 
29  in.  The  same  cu.  ft.  of  air  saturated  with  water  vapor  at  70°  F.  and 
29  in.  becomes  124.3  cu.  ft.,  or  44.9  cu.  ft.  at  105°  and  27  in.  vacuum. 
The  temperatures  105°  and  70°  are  about  10%  below  the  temperatures 
of  saturated  steam  at  27  in.  and  29  in.  respectively. 

Condenser  Tubes  are  generally  made  of  solid-drawn  brass  tubes,  and 
tested  both  by  hydraulic  pressure  and  steam.  They  are  usually  made  of 
a  composition  of  68%  of  best  selected  copper  and  32%  of  best  Silesian 
spelter.  The  Admiralty,  however,  always  specify  the  tubes  to  be  made 
of  70%  of  best  selected  copper  and  to  have  1%  of  tin  in  the  composition, 
and  test  the  tubes  to  a  pressure  of  300  Ibs.  per  sq.  in.  (Seaton.) 

The  diameter  of  the  condenser  tubes  varies  from  1/2  in.  in  small  con- 
densers, when  they  are  very  short,  to  1  in.  in  very  large  condensers  and 
long  tubes.  In  the  mercantile  marine  the  tubes  are,  as  a  rule,  3/4  in. 
diam.  externally,  and  18  B.W.G.  thick  (0.049  inch);  and  16  B.W.G. 
(0  .065),  under  some  exceptional  circumstances.  In  the  British  Navy  the 
tubes  are  also,  as  a  rule,  3/4  in.  diam.,  and  18  to  19  B.W.G.,  tinned  on 
both  sides:  when  the  condenser  is  brass  the  tubes  are  not  required  to  be 
tinned.  Some  of  the  smaller  engines  have  tubes  5/g  in.  diam.,  and  19 
B.  W.  G.  The  smaller  the  tubes,  the  larger  is  the  surface  which  can  be 
put  in  a  certain  space.  (Seaton.) 

In  the  merchant  service  the  almost  universal  practice  is  to  circulate 
the  water  through  the  tubes. 

Whitham  says  the  velocity  of  flow  through  the  tubes  should  not  be 
less  than  400  nor  more  than  700  ft.  per  min. 


CONDENSERS,  AIR-PUMPS,   ETC. 


1073 


Tube-plates  are  usually  made  of  brass.  Rolled-brass  tube-plates 
snould  be  from  1.1  to  1.5  times  the  diameter  of  tubes  in  thickness, 
depending  on  the  method  of  packing.  When  the  packings  go  completely 
through  the  plates,  the  latter  thickness,  but  when  only  partly  through, 
the  former,  is  sufficient.  Hence,  for  3/4_in.  tubes  the  plates  are  usually 
7/8  to  1  in.  thick  with  glands  and  tape-packings,  and  1  to  11/4  ins.  thick 
with  wooden  ferrules.  The  tube-plates  should  be  secured  to  their  seat- 
ings  by  brass  studs  and  nuts,  or  brass  screw-bolts:  in  fact  there  must  be 
no  wrought  iron  of  any  kind  inside  a  condenser.  When  the  tube-plates 
are  of  large  area  it  is  advisable  to  stay  them  by  brass  rods,  to  prevent 
them  from  collapsing. 

Spacing  of  Tubes,  etc.  —  The  holes  for  ferrules,  glands,  or  india- 
rubber  are  usually  1/4  inch  larger  in  diameter  than  the  tubes;  but  when 
absolutely  necessary  the  wood  ferrules  may  be  only  3/32  inch  thick. 

The  pitch  of  tubes  when  packed  with  wood  ferrules  is  usually  1/4  inch 
more  than  the  diameter  of  the  ferrule-hole.  For  example,  the  tubes  are 
generally  arranged  zigzag,  and  the  number  which  may  be  fitted  into  a 
square  foot  of  plate  is  as  follows: 


Pitch  of 
Tubes, 
In. 

No.  in  a 
Sq.  Ft. 

Pitch  of 
Tubes, 
In. 

No.  in  a 
Sq.  Ft. 

Pitch  of 
Tubes, 
In. 

No.  in  a 

Sq.  Ft. 

1  Vl6 

H/8 

172 
150 
137 

1  5/32 
13/16 
1  V32 

128 
121 
116 

1  1/4 
19/32 
1  5/16 

110 
106 
99 

Air-Pump. — The  air-pump  in  all  condensers  abstracts  the  water  con- 
densed and  the  air  originally  contained  in  the  water  when  it  entered  the 
boiler.  In  the  case  of  jet-condensers  it  also  pumps  out  the  water  of  con- 
densation and  the  air  which  it  contained.  The  size  of  the  pump  is  calcu- 
'  la  ted  from  these  conditions,  making  allowance  for  efficiency  of  the  pump. 

In  surface  condensation  allowance  must  be  made  for  the  water  oc- 
casionally admitted  to  the  boilers  to  make  up  for  waste,  and  the  air 
cpntained  in  it,  also  for  slight  leaks  in  the  joints  and  glands,  so  that  the 
air-pump  is  made  about  half  as  large  as  for  jet-condensation. 

Seaton  says:  The  efficiency  of  a  single-acting  air-pump  is  generally 
taken  at  0.5  and  that  of  a  double-acting  pump  at  0.35.  When  the 
temperature  of  the  sea  is  60°,  and  that  of  the  (jet)  condenser  is  120°, 
Q  being  the  volume  of  the  cooling-water  and  q  the  volume  of  the  con- 
densed water  in  cubic  feet,  and  n  the  number  of  strokes  per  minute, 

The  volume  of  the  single-acting  pump  ='2.74  (Q  +  q)  4-  n. 

The  volume  of  the  double-acting  pump  =  4  (Q  +  q)  +  n. 

W.  H.  Booth,  in  his  "Treatise  on  Condensing  Plant,"  says  the 
volume  to  be  generated  by  an  air-pump  bucket  should  not  be  less  than 
0.75  cu.  ft.  per  pound. of  steam  dealt  with  by  the  condensing  plant. 
Mr.  R.  W.  Allen  has  made  tests  with  as  little  air-pump  capacity  as  0.5 
cu.  ft.  and  lie  gives  0.6  cu.  ft.  as  a  minimum.  An  Edwards  pump  with 
three  14-in.  barrels,  12-in.  stroke,  single-acting,  150  r.p.m.,  is  rated  at 
45,000  Ibs.  of  steam  per  hour  from  a  surface  condenser,  which  is  equiva- 
lent to  0.66  cu.  ft.  per  pound  of  feed-water. 

In  the  Edwards  pump,  the  base  of  the  pump  and  the  bottom  of  the 
piston  are  conical  in  shape.  The  water  from  the  condenser  flows  by 
gravity  into  the  space  below  the  piston,  which  descending  projects  it' 
through  ports  into  the  space  in  the  barrel  above  the  piston,  whence  on 
the  ascending  stroke  of  the  piston  it  is  discharged  through  the  outlet 
valves.  There  are  no  bucket  or  foot- valves,  and  the  pump  may  be  run 
at  much  higher  speeds  than  older  forms  of  pump.  (See  Catalogue  of 
the  Wheeler  Condenser  and  Engineering  Co.) 

The  Area  through  Valve-seats  and  past  the  valves  should  not  be 
less  than  will  admit  the  full  quantity  of  water  for  condensation  at  a 
velocity  not  exceeding  400  ft.  per  minute.  In  practice  the  area  is  gen- 
erally in  excess  of  this.  (Seaton.) 

Area  through  foot-valves      =  D2  X  <S  -f-  1000  square  inches. 
Area  through  head-valves     =  Z>2  X  S_+    800  square  inches. 
Diameter  of  discharge-pipe  =»  D  X  \/S  •*•  35  inches. 
D  =  diam.  of  air-pump  in  inches,  S  =  its  speed  in  ft.  per  min. 

James  Tribe  (Am.  Mach.,  Oct.  8, 1891)  gives  the  following  rule  for  air- 


1074 


THE  STEAM-ENGINE. 


pumps  used  with  jet-condensers:  Volume  of  single-acting  air-pumpdrivea 
by  main  engine  =  volume  of  low-pressure  cylinder  in  cubic  feet,  multiplied 
by  3.5  and  divided  by  the  number  of  cubic  feet  contained  in  one  pound 
of  exhaust  steam  of  the  given  density.  For  a  double-acting  air-pump  the 
same  rule  will  apply,  but  the  volume  of  steam  for  each  stroke  of  the 
pump  will  be  but  one-half.  Should  the  pump  be  driven  independently 
of  the  engine,  then  the  relative  speed  must  be  considered.  Volume  of  jet- 
condenser  =  volume  of  air-pump  X  4.  Area  of  injection  valve  =  vol.  of 
air-pump  in  cubic  inches  •*-  520. 

The  Work  done  by  an  Air-pump,  per  stroke,  is  a  maximum  the- 
oretically, when  the  vacuum  is  between  21  and  22  ins.  of  mercury.  As- 
suming adiabatic  compression,  the  mean  effective  pressure  per  stroke 

is  P  =  3 .46  PI  If  —  j      -  1 1 1  where  p = absolute  pressure  of  the  vacuum 

and  pz  the  terminal,  or  atmospheric,  pressure,  =  14 .7  Ibs.  per  sq.  in.    The 
horse-power  required  to  compress  and  deliver  1  cu.  ft.  of  air  per  minute, 
measured  at  the  lower  pressure,  is,  neglecting  friction,  P  X  144  -5-  33,000. 
The  following  table  is  calculated  from  these  formulae  (R.  R.  Pratt,  Power, 
Sept.,,7,  1909). 


Vac.  in 
Ins.  of 
Mer- 

Abs. 
Press., 
Ins.  of 
Mer- 

P2 
Pi 

Theo- 
retic. 
M.E.P. 

Theo- 
retic. 
H.P. 

Vac.  in 
Ins.  of 
Mer- 

Abs. 
Press., 
Ins.  of 
Mer- 

P2 

Pi 

Theo- 
retic. 
M.E.P. 

Theo- 
retic. 
H.P. 

cury. 

cury. 

cury. 

cury. 

29 

1 

30.00 

2.86 

0.0124 

18 

12 

2.50 

6.21 

0.0271 

26 

2 

15.00 

4.05 

0.0177 

16 

14 

2.14 

5.89 

0.0256 

27 

3 

10.00 

4.83 

0.0211 

14 

16 

.87 

5.42 

0.02.36 

26 

4 

7.50 

5.40 

0.0235 

12 

18 

.67 

4.88 

0.0212 

25 

5 

6.00 

5.78 

0.0252 

10 

20 

.50 

4.23 

0.0184 

24 

6 

5.00 

6.05 

0.0264 

8 

22 

.36 

3.52 

0  4153 

23 

7 

4.28 

6.23 

0.0271 

6 

24 

.25 

2.73 

0.0119 

22 

8 

3.75 

6.33 

0.0276 

4 

26 

.15 

1.88 

0.0082 

21 

9 

3.33 

637 

0.0278 

2 

28 

.07 

0.96 

0.0042 

20 

10 

3.00 

6.36 

0.0277 

1 

29 

.03 

0.49 

0  002! 

The  work  done  by  the  air-pump  is  to  compress  the  saturated  mixture 
if  air  and  water  vapor  at  the  condenser  pressure  to  atmospheric  pressure 
and  to  discharge  it  into  the  atmosphere  together  with  the  water  of 
condensation  (and  with  the  cooling  water  in  the  case  of  jet  condensers 
operated  vith  an  air-pump).  The  amount  of  air  to  be  discharged 
varies  with  the  amount  of  air  in  the  feed-water  and  with  the  leakage  of 
air  through  the  stuffing-boxes.  Geo.  A.  Orrok  (Jour.  A.  S.  M.  E.,  1912, 
p.  1625)  found  the  volume  of  air  in  city  water  at  52  deg.  F.  to  be  over  4 
per  cent;  and  in  feed-water  at  187  degrees  less  than  1  per  cent.  With 
turbines  of  from  5,000  to  20,000  kw.  capacity  the  air  discharged  by 
the  air-pump  at  atmospheric  pressure  and  temperature  varied  from 
1  cu.  ft.  per  min.  with  the  units  in  the  best  condition  to  15  or  20  when 
ordinary  leakage  was  present,  or  to  30  to  50  when  the  units  were  in  bad 
condition.  Stodola  states  that  we  may  ordinarily  expect  the  air  to 
•  amount  to  1.5  to  2.5  cu.  ft.  per  min.  for  each  1000  kw.  capacity. 
T.  C.  McBride  (Power,  July  14,  1908)  gives  results  of  tests  in  which 
the  amount  of  air  varied  from  18  to  74  volumes  per  10,000  volumes  of 
exhaust  steam.  C.  L.  W.  Trinks  (Proc.  Engrs.  Soc.  of  W.  Penna.,  June, 
1914)  gives  the  weight  of  air  normally  expected  by  builders  of  air- 
pumps  as  0.25  to  0.50  per  cent  of  the  weight  of  steam. 

W.  H.  Herschel  (Power,  June  1,  1915),  after  quoting  the  above  figures, 
gives  the  results  of  calculations  based  upon  assumed  air  leakages  of 
20,  40,  and  60  volumes  of  air  per  10,000  volumes  of  steam,  corresponding 
respectively  to  0.31,  0.62,  and  0.93  per  cent  of  the  weight  of  steam,  or 
approximately  to  15,  30,  and  45  cu.  ft.  per  min.  for  every  1000  kw. 
capacity,  the  smallest  amount  being  that  which  may  be  obtained  with 
stuffing-boxes  in  the  best  condition,  while  the  largest  value  may  be 
reached,  or  even  exceeded,  with  stuffing-boxes  in  poor  condition. 
Following  are  his  figures  for  the  extreme  conditions: 


CONDENSERS,  AIR-PUMPS,  ETC. 


1075 


TOTAL  WORK  OF  AN  AIR-PUMP,  INCLUDING  DISCHARGE  OF  COOLING  WATER. 


•SM^ 
Hi 

Vacuum,  In.,  Leakage  0.31  %. 

i 

Vacuum,  In.,  Leakage  0.93%. 

29 

28.5 

28 

27 

26 

29 

28.5 

28 

27    |    26 

Temperature  of  Condenser  °F. 

Temperature  of  Condenser  °F. 

32° 
50° 
60° 
70° 
80° 

Ft.-lb 
32° 
50° 
60° 
70° 
80° 

Lb. 
32° 
50° 
60° 
70° 
80° 

63 
68 
71 
76 

Work 
2150 
3300 
4820 
8220 

71 
77 
79 
83 
86 

perLb 
1560 
2120 
2740 
4010 
7750 

g  Wat 
25.6 
36.7 
52.3 
75.8 
164.0 

78 
83 
86 
89 
94 

.  Stearr 
1280 
1650 
2000 
2670 
3930 

er  per 
21.7 
30.2 
37.9 
52.2 
70.0 

87 
92 
96 
100 
104 

iCond 
1000 
1210 
1410 
1700 
2110 

Lb.  S 
18.2 
24.7 
27.5 
32.8 
41  .0 

96 
100 
104 
109 
111 

ensed 
840 
990 
1120 
1280 
1530 

;eam. 
15.6 
19.9 
22.6 
25.2 
31  .8 

32° 
50° 
60° 
70° 
80° 

Ft.-lb. 
32° 
50° 
60° 
70° 
80° 

Lb. 
32° 
50° 
60° 
70° 
80° 

55 
64 

68 

72 

Work 
3840 
5760 
8440 
13250 

62 
71 
75 
80 
82 

perLb 
2880 
3730 
4720 
6610 
11330 

ig  Wat« 
32.8 
47.3 
66.0 
98.8 
493.0 

68 
78 
82 
86 
92 

Stearr 
2380 
2920 
3450 
4410 
6960 

3r  per 
28.0 
35.5 
45.1 
61.8 
82.0 

77 
85 
88 
95 
99 

iCond 
1840 
2150 
2440 
2850 
3520 

Lb.  St 
24.5 
28.6 
35.7 
39.6 
52.0 

77 
9t 
96 
103 
106 

ensed. 
1530 
1760 
1960 
2210 
2560 

earn. 
21.5 
24.5 
27.8 
30.1 
38.1 

Coolin 
32.1 
55.0 
89.8 
164.0 

Coolir 
42.7 
70.8 
123.8 
494.0 

Most  Economical  Vacuum  for  Turbines. — Mr.  Herschel,  taking  the 
air-pump  work  given  in  the  above  table  for  the  several  conditions 
named,  an  efficiency  of  50  per  cent  for  the  air-pump,  and  assuming  a 
turbine  working  with  dry  steam  150-lb.  gage,  without  superheat,  cal- 
culates the  net  work  of  the  turbine  in  foot-pounds  per  Ib.  of  steam 
with  the  most  economical  vacuum  for  different  temperatures  of  cooling 
water.  He  compares  the  results  with  those  calculated  for  the  same 
air-pump  conditions,  but  for  a  turbine  using  steam  of  140  Ib.  super- 
heated 218°  F.  The  results  are  tabulated  below,  the  vacuum  giving 
the  best  economy  being  given  in  parentheses.  The  lines  marked  S  are 
for  the  superheated  steam  turbine.  It  appears  that  29  in.  vacuum  is 
the  most  economical  only  for  low  temperatures  of  cooling  water,  and 
that  the  vacuum  giving  the  best  economy  decreases  with  increase  of 
leakage  and  with  increasing  temperature  of  the  cooling  water. 


Temperature  of  cooling  water,  °F.    32      I         50        |        60         |        70 
Net  Work  of  Turbine,  Ft.-lb.  per  Lb.  of  Steam. 


80 


Leakage  of  (o.31% 

air    % 
weight  of    ] 

steam.        0.93% 


I       56000(29)  I  53700(29) 
I  S.  76200(29)  I  73900(29) 


I  52120(28.5)  I  50360(28)     I  48980(27) 
I  71620(28.5)  I  69080(28.5)  |  65240(28) 


52620(29)  150140(28.5)  I  48800(28) 
8.72820(29)  |  69640(28.5)  167660(28.5) 


I  47500(27) 
I  64280(28) 


I  46160(27) 
I  62060(27) 


Circulating-pump.  —  Let  Q  be  the  quantity  of  cooling-water  in 
cubic  feet,  n  the  number  of  strokes  per  minute,  and  S  the  length  of  stroke 
in  feet. 

Capacity  of  circulating-pump  =  Q  •*•  n  cubic  feet. 

Diameter  of  circulating-pump  =  13.55  ^Q-^-nS  inches. 

The  clear  area  through  the  valve-seats  and  past  the  valves  should  be 
such  that  the  mean  velocity  of  flow  does  not  exceed  450  feet  per  minute. 
The  flow  through  the  pipes  should  not  exceed  500  ft.  per  min,  in  small 
pipes  and  600  in  large  pipes.  (Seaton.) 

For  Centrifugal  Circulating-pumps,  the  velocity  of  flow  in  the  inlet  and 
outlet  pipes  should  not  exceed  400  ft.  per  min.  The  diameter  of  the  fan- 
wheel  is  from  21/2  to  3  times  the  diam,  of  the  pipe,  and  the  speed,  at  H$ 
periphery  450  to  500  ft.  per  min. 


1076  THE  STEAM-ENGINE. 

The  Leblanc  Condenser  (made  by  the  Westinghouse  Machine  Co.) 

accomplishes  the  separate  removal  of  water  and  air  by  means  of  a  pair  ol 
relatively  small  turbine-type  rotors  on  a  common  shaft  in  a  single  casing, 
which  is  integral  with  or  attached  directly  to  the  lower  portion  of  the 
condensing  chamber.  The  condensing  chamber  itself  is  but  little  more 
than  an  enlargement  of  the  exhaust  pipe.  The  injection  water  is  pro- 
jected downwards  through  a  spray  nozzle,  and  the  combined  injection 
water  and  condensed  steam  flow  downward  to  a  centrifugal  discharge 
pump  under  a  head  of  2  or  3  ft.,  which  insures  the  filling  of  the  pump. 
The  space  above  the  water  level  in  the  condensing  chamber  is  occupied 
by  water  vapor  plus  the  air  which  entered  with  the  injection  water  and 
with  the  exhaust  steam,  and  this  space  communicates  with  the  air-pump 
through  a  relatively  small  pipe. 

The  air-pump  differs  from  pumps  of  the  ejector  type  in  that  the  vanes 
in  traversing  the  discharge  nozzle  at  high  speed  constitute  a  series  of 
pistons,  each  one  of  which  forces  ahead  of  it  a  small  pocket  of  air,  the 
high  velocity  of  which  effectually  prevents  its  return  to  the  condenser. 
A  small  quantity  of  water  is  supplied  to  the  suction  side  of  the  air-purnp 
to  assist  in  the  performance  of  its  functions.  The  power  required  for  the 
pumps  is  said  to  approximate  2  to  3  per  cent  of  the  power  generated  by 
the  main  engine. 

Feed-pumps  for  Marine  Engines.  —  With  surface-condensing 
engines  the  amount  of  water  to  be  fed  by  the  pump  is  the  amount  con- 
densed from  the  main  engine  plus  what  may  be  needed  to  supply  auxiliary 
engines  and  to  supply  leakage  and  waste.  Since  an  accident  may  happen 
to  the  surface-condenser,  requiring  the  use  of  jet-condensation,  the  pumps 
of  engines  fitted  with  surface-condensers  must  be  sufficiently  large  to  do 
duty  under  such  circumstances.  With  jet-condensers  and  boilers  using 
salt  water  the  dense  salt  water  in  the  boiler  must  be  blown  off  at  intervals 
to  keep  the  density  so  low  that  deposits  of  salt  will  not  be  formed.  Sea- 
water  contains  about  1/32  of  its  weight  of  solid  matter  in  solution.  The 
boiler  of  a  surface-condensing  engine  may  be  worked  with  safety  when 
the  quantity  of  salt  is  four  times  that  in  sea-water.  If  Q  —  net  quantity 
of  feed-water  required  in  a  given  time  to  make  up  for  what  is  used  as 
steam,  n  —  number  of  times  the  saltness  of  ^he  water  in  the  boiler  is  to 
that  of  sea-water,  then  the  gross  feed-water = nQ  -s-  (n  —  1).  In  order  to  be 
capable  of  filling  the  boiler  rapidly  each  feed-pump  is  made  of  a  capacity 
equal  to  twice  the  gross  feed-water.  Two  feed-pumps  should  be  supplied 
so  that  one  may  be  kept  in  reserve  to  be  used  while  the  other  is  out  of 
repair.  If  Q  be  the  quantity  of  net  feed-water  in  cubic  feet,  I  the  length 
of  stroke  of  feed-pump  in  feet ,  and  n  the  number  of  strokes  per  minute, 

Diameter  of  each  feed-pump  plunger  in  inches  =  ^550  Q  +  nl. 
If  W  be  the  net  feed-water  in  pounds, 

Diameter  of  each  feed-pump  plunger  in  inches  =  ^8.9  W+nl. 

An  Evaporative  Surface  Condenser  built  at  the  Virginia  Agricul- 
tural College  is  described  by  James  H.  Fitts  (Trans.  A.S.  M.  E.,  xiv,  690). 
It  consists  of  two  rectangular  end  chambers  connected  by  a,  series  of 
horizontal  rows  of  tubes,  each  row  of  tubes  immersed  in  a  pan  of  water. 
Through  the  spaces  between  the  surface  of  the  water  in  each  pan  and  the 
bottom  of  the  pan  above  air  is  drawn  by  means  of  an  exhaust-fan.  At 
the  top  of  one  of  the  end  chambers  is  an  inlet  for  steam,  and  a  horizontal 
diaphragm  about  midway  causes  the  steam  to  traverse  the  upper  half 
of  the  tubes  and  back  through  the  lower.  An  outlet  at  the  bottom  leads 
to  the  air-pump.  The  passage  of  air  over  the  water  surfaces  removes 
the  vapor  as  it  rises  and  thus  hastens  evaporation.  The  heat  necessary 
to  produce  evaporation  is  obtained  from  the  steam  in  the  tubes,  causing 
the  steam  to  condense.  It  was  designed  to  condense  800  Ibs.  steam  per 
hour  and  give  a  vacuum  of  22  in.,  with  a  terminal  pressure  in  the  cylinder 
of  20  Ibs.  absolute.  Results  of  tests  show  that  the  cooling-water  required 
is  practically  equal  in  amount  to  the  steam  used  by  the  engine.  And 
since  the  consumption  of  steam  is  reduced  by  the  application  of  a  con- 
denser, its  use  will  actually  reduce  the  total  quantity  of  water  required. 

The  Continuous  Use  of  Condensing-water  is  described  in  a  series 
of  articles  in  Power,  Aug.-Dec.,  1892.  It  finds  its  application  in  situations 
where  water  for  condensing  purposes  is  expensive  or  difficult  to  obtain. 


CONDENSERS,   AIR-PTTMPS,   ETC. 


1077 


The  different  methods  described  include  cooling  pans  on  the  roof; 

fountains  and  other  spray  pipes  in  ponds,  fine  spray  discharged  at  an 
elevation  above  a  pond;  trickling  the  water  discharged  from  the  hot-well 
over  parallel  narrow  metal  tanks  contained  in  a  large  wooden  structure, 
while  a  fan  blower  drives  a  current  of  air  against  the  films  of  water  falling 
from  the  tanks,  etc.  These  methods  are  suitable  for  small  powers,  but 
for  large  powers  they  are  cumbersome  and  require  too  much  space,  and 
are  practically  supplanted  by  cooling  towers. 

The  Increase  of  Power  that  may  be  obtained  by  adding  a  condenser 
giving  a  vacuum  of  26  inches  of  mercury  to  a  non-condensing  engine  may 


..-.-....,..•     M          *•  *        f         j-         ffiP"' 

/   /     /  /  /  /  /Ab'sqiut'e  Mean  Pressure'in  Pounds   /         "7        ///  / 
30J  4/5,0    60  /TO    8fo /90 /1 00/1 1 01 20  1  30 1 40  1 50^160  1 7,0 1  SOxtgO-^OO 


120  60     40    30    24   20    17     15    13    12     11    10 

Per  Cent  ot  Power  Gained  by  Vacuum 


Fig.  175. 

toe  approximated  by  considering  it  to  be  equivalent  to  a  net  gain  of  12  Ibs. 
mean  effective  pr  essure  per  sq.  in.  of  piston  area.  If  A  =  area  of  piston 
in  sq  ins  ,  S  =  piston  speed  in  ft.  per  min.,  then  12  AS  •«•  33,000  ** 
AS  -t  2750  =  H.P.  made  available  by  the  vacuum.  If  the  vacuum  « 
13  2  Ibs  per  sq.  in.  =  27  .9  in.  of  mercury,  then  H.P.  =  AS  j  2500.  t 
The  saving  of  steam  for  a  given  horse-power  will  be  represented  approxi- 
mately by  the  shortening  of  the  cut-off  when  the  engine  is  run  with  the 
condenser.  Clearance  should  be  included  in  the  calculation.  To  the 
mean  effective  pressure  non-condensing,  with  a  given  actual  cut-off 
clearance  considered,  add  3  Ibs.  to  obtain  the  approximate  mean  total 
pressure,  condensing.  From  tables  of  expansion  of  steam  find  what 
actual  cut-off  will  give  this  mean  total  pressure  The  difference  between 
this  and  the  original  actual  cut-off,  divided  by  the  latter  and  by  100,  will 

' 


catalogue  of  H.  R.  Worthington)  shows 

the  percentage  of  power  that  may  be  gained  by  attaching  a  condenser 
to  a  non-condensing  engine  assuming  that  the  vacuum  is  12  Ibs.  per  sq. 


1078  THE  STEAM-ENGINE. 

in.    The  diagram  also  shows  the  mean  pressure  in  the  cylinder  for  a  given 
initial  pressure  and  cut-off,  clearance  and  compression  not  considered. 

The  pressures  given  in  the  diagram  are  absolute  pressures  above  a 
vacuum. 

To  find  the  mean  effective  pressure  produced  in  an  engine  cylinder  with 
90  Ibs.  gauge  (=  105  Ibs.  absolute)  pressure,  cut-off  at  1/4  stroke:  find 
105  in  the  left-hand  or  initial-pressure  column,  follow  the  horizontal  line 
to  the  right  until  it  intersects  the  oblique  line  that  corresponds  to  the  1/4 
cut-off,  and  read  the  mean  total  pressure  from  the  row  of  figures  directly 
above  the  point  of  intersection,  which  in  this  case  is  63  Ibs.  From  this 
subtract  the  mean  absolute  back  pressure  (say  3  Ibs.  for  a  condensing 
engine  and  15  Ibs.  for  a  non-condensing'  engine  exhausting  into  the 
atmosphere)  to  obtain  the  mean  effective  pressure,  which  in  this  case,  for 
a  non-condensing  engine,  gives  48  Ibs.  To  find  the  gain  of  power  by  the 
use  of  a  condenser  with  this  engine,  read  on  the  lower  scale  the  figures 
that  correspond  in  position  to  48  Ibs.  in  the  upper  row,  in  this  case  25%. 
As  the  diagram  droes  not  take  into  consideration  clearance  or  compression, 
the  results  are  only  approximate. 

Advantage  of  High  Vacuum  in  Reciprocating  Engines.  (R.  D. 
Tomli#son,  Power,  Feb.  23,  1909.)  —  Among  the  transatlantic  liners, 
the  best  ships  with  reciprocating  engines  are  carrying  from  26  to -28  and 
more  inches  of  vacuum.  Where  the  results  are  looked  into,  the  engineers 
are  required  to  keep  the  vacuum  system  tight  and  carry  all  the  vacuum 
they  can  get,  and  while  it  is  true  that  greater  benefits  can  be  derived 
from  high  vacua  in  a  steam  turbine  than  in  a  reciprocating  engine,  it  is 
also  true  that,  where  primary  heaters  are  not  used,  the  higher  the  vacuum 
carried  the  greater  is  the  justifiable  economy  which  can  be  obtained  from 
the  plant. 

The  Interborough  Rapid  Transit  Company,  New  York  City,  changed 
the  motor-driven  air-pump  and  jet-condenser  for  a  barometric  type  of 
condenser  and  increased  the  vacuum  on  each  of  the  8000-H.P.  Allis- 
Chalmers  horizontal  vertical  engines  at  the  74th  Street  station  from 
26  to  28  ins.,  thereby  increasing  the  power  on  each  of  the  eight  units 
approximately  275  H.P.,  and  the  economy  of  the  station  was  increased 
nearly  in  the  same  ratio.  This  change  was  made  about  seven  years  ago 
and  the  plant  is  still  operating  with  28  ins.  of  vacuum,  measured  with 
mercury  columns  connected  to  the  exhaust  pipe  at  a  point  just  below  the 
exhaust  nozzle  of  the  low-pressure  cylinders. 

A  careful  test  made  on  the  59th  Street  station  showed  a  decrease 
steam  consumption  of  8%  when  the  vacuum  was  raised  from  25  to  28  ins. 
These  engines  drive  5000-kw.  generators. 

The  Choice  of  a  Condenser.  —  Condensers  may  be  divided  into  two 
general  classes: 

First.  —  Jet  condensers,  including  barometric  condensers,  siphon 
condensers,  ejector  condensers,  etc.,  in  which  the  cooling-water  mingl~~ 
with  the  steam  to  be  condensed. 

Second.  —  Surface  condensers,  in  which  the  cooling-water  is  separated 
from  the  steam,  the  cooling- water  circulating  on  one  side  of  this  surface 
and  the  steam  coming  into  contact  with  the  other. 

In  the  jet-condenser  the  steam,  as  soon  as  condensed,  becomes  mixed 
with  the  cooling-water,  and  if  the  latter  should  be  unsuitable  for  boiler- 
feed  because  of  scale-forming  impurities,  acids,  salt,  etc.,  the  pure  distilled 
water  represented  by  the  condensed  steam  is  wasted,  and,  if  it  were 
necessary  to  purchase  other  water  for  boiler-feeding,  this  might  represent 
a  considerable  waste  of  money.  On  the  other  hand,  if  the  cooling- water 
is  suitable  for  boiler-feeding,  or  if  a  fresh  supply  of  good  water  is  easily 
obtainable,  the  jet-condenser,  because  of  its  simplicity  and  low  cost,  is 
unexcelled. 

Surface  condensers  are  recommended  where  the  cooling-water  is  un- 
fitted for  boiler-feed  and  where  no  suitable  and  cheap  supply  of  pure 
boiler-feed  is  available. 

Where  a  natural  supply  of  cooling-water,  as  from  a  well,  spring,  lake  or 
river,  is  not  available,  a  water-cooling  tower  can  be  installed  and  the  same 
cooling-water  used  over  and  over.  (Wheeler  Condenser  and  Eng.  Co.) 

Owing  to  their  great  cost  as  compared  with  jet-condensers,  surface 
condensers  should  not  be  used  except  where  absolutely  necessary,  i.e., 
where  lack  of  feed- water  for  the  boiler  warrants  the  extra  cost.  Of  course 
there  are  cases,  such  as  at  sea,  where  surface  condensers  are  indispensable. 


1/11 
he 

in 

vo 

on 

Les 

*d 


COOLING  TOWEBS.  1079 


On  land,  suitable  feed-water  can  always  be  obtained  at  some  expense, 
and  that  cost  capitalized  makes  it  a  simple  arithmetical  problem  to 
determine  the  extra  investment  permissible  in  order  to  be  able  to  return 
condensed  steam  as  feed-water  to  the  boiler.  Unfortunately  there  is 
another  point  which  greatly  complicates  the  matter,  and  one  which  makes 
it  impossible  to  give  exact  figures,  viz.,  the  corrosion  and  deterioration  of 
the  condenser  tubes  themselves,  the  exact  cause  of  which  is  not  often 
understood.  With  clean,  fresh  water,  free  from  acid,  the  tubes  of  a  con- 
denser last  indefinitely,  but  where  the  cooling-water  contains  sulphur, 
as  in  drainage  from  coal  mines,  or  sea-water  contaminated  by  sewage, 
such  as  harbor  water,  the  deterioration  is  exceedingly  rapid. 

A  better  vacuum  may  possibly  be  obtained  from  a  surface  condenser 
where  there  is  plenty  of  cooling-water  easily  handled.  The  better  vacuum 
is  due  to  the  fact  that  the  air-pump  will  have  much  less  air  to  handle  inas- 
much as  the  air  carried  in  suspension  by  the  cooling-water  does  not  have 
to  be  extracted  as  in  the  case  of  jet-condensers.  Water  in  open  rivers, 
the  ocean,  etc.,  is  said  to  carry  in  suspension  5%  by  volume  of  air.  It 
may  be  said  that  except  for  leakages,  which  should  not  exist,  the  air- 
pump  will  have  no  work  to  do  at  all  inasmuch  as  the  water  will  have  no 
opportunity  to  become  aerated.  On  the  other  hand,  if  the  cooling-water 
is  limited,  these  advantages  are  offset  by  the  fact  that  a  surface  condenser 
cannot  heat  the  cooling-water  so  near  to  the  temperature  of  the  exhaust 
steam  as  can  a  jet-condenser.  (F.  Hodgkinson,  El.  Jour.,  Aug.,  1909.) 

A  barometric  condenser  used  in  connection  with  a  15,000-k.w.  steam- 
engine-turbine  unit  at  the  59th  St.  station  of  the  Rapid  Transit  Co.,  New 
York,  contains  approximately  25,000  sq.  ft.  of  cooling  surface  arranged  in 
the  double  two-pass  system  of  water  circulation,  with  a  30-in.  centrifugal 
circulating  pump  having  a  maximum  capacity  of  30,000  gal.  per  hour. 
The  dry  vacuum  pump  is  of  the  single-stage  type,  12-  and  29-in.  X  24-in., 
with  Corliss  valves  on  the  air  cylinder.  The  condensing  plant  is  capable 
of  maintaining  a  vacuum  within  1.1  in.  of  the  barometer  when  condensing 
150,000  Ib.  of  steam  per  hour  when  supplied  with  circulating  water  at  70°  F. 
—  (H.  G.  Stott,  Jour.  A.S.M.E.,  Mar.,  1910.) 

Cooling  Towers  are  usually  made  in  the  shape  of  large  cylinders  of 
sheet  steel,  filled  with  narrow  boards  or  lath  arranged  in  geometrical 
forms,  or  hollow  tile,  or  wire  network,  so  arranged  that  while  the  water, 
which  is  sprayed  over  them  at  the  top,  trickles  down  through  the  spaces  it 
is  met  by  an  ascending  air  column.  The  air  is  furnished  either  by  disk 
fans  at  the  bottom  or  is  drawn  in  by  natural  draught.  In  the  latter  case 
the  tower  is  made  very  high,  say  60'to  100  ft.,  so  as  to  act  like  a  chimney. 
When  used  in  connection  with  steam  condensers,  the  water  produced  by 
the  condensation  of  the  exhaust  steam  is  sufficient  to  compensate  for  the 
evaporation  in  the  tower,  and  none  need  be  supplied  to  the  system.  There 
is,  on  the  contrary,  a  slight  overflow,  which  carries  with  it  the  oil  from 
the  engine  cylinders,  and  tends  to  clean  the  system  of  oil  that  would 
otherwise  accumulate  in  the  hot-well. 

The  cooling  of  water  in  a  pond,  spray,  or  tower  goes  on  in  three  ways  — 
first,  by  radiation,  which  is" practically  negligible;  second,  by  conduction 
or  absorption  of  heat  by  the  air,  which  may  vary  from  one-fifth  to  one- 
third  of  the  entire  effect;  and,  lastly,  by  evaporation.  The  latter  is  the 
chief  effect.  Under  certain  conditions  the  water  in  a  cooling  tower  can 
actually  be  cooled  below  the  temperature  of  the  atmosphere,  as  water  is 
cooled  by  exposing  it  in  porous  vessels  to  the  winds  of  hot  and  dry  climates. 

The  evaporation  of  1  Ib.  of  water  absorbs  about  1000  heat  units.  The 
rapidity  of  evaporation  is  determined,  first,  by  the  temperature  of  the 
water,  and,  second,  by  the  .vapor  tension  in  the  air  in  immediate  contact 
with  the  water.  In  ordinary  air  the  vapor  present  is  generally  in  a  con- 
dition corresponding  to  superheated  steam,  that  is,  the  air  is  not  saturated. 
If  saturated  air  be  brought  into  contact  with  colder  water,  the  cooling 
of  the  vapor  will  cause  some  of  it  to  be  precipitated  out  of  the  air;  on  the 
other  hand,  if  saturated  air  be  brought  into  contact  with  warmer  water, 
,  some  of  the  latter  will  pass  into  the  form  of  vapor.  This  is  what  occurs  in 
the  cooling  tower,  so  that  the  latter  is  in  a  large  measure  independent 
of  climatic  conditions;  for  even  if  the  air  be  saturated,  the  rise  in  tem- 
perature of  the  atmospheric  air  from  contact  with  the  hot  water  in  the 
cooling  tower  will  greatly  increase  the  water-carrying  capacity  of  the  air, 
enabling  a  large  amount  of  beat  to  be  absorbed  through  the  evaporation 


1080 


THE  STEAM-ENGINE. 


of  the  water.  The  two  things  to  be  sought  after  in  coofing-towei  design 
are,  therefore,  first,  to  present  a  large  surface  of  water  to  the  air,  and, 
second,  to  provide  for  bringing  constantly  into  contact  with  this  surface 
the  largest  possible  volume  of  new  air  at  the  least  possible  expenditure  of 
energy.  (Wheeler  Condenser  and  Engineering  Co.) 

The  great  advantage  of  the  cooling  tower  lies  in  the  fact  that  large 
surfaces  of  water  can  be  presented  to  the  air  while  the  latter  is  kept  in 
rapid  motion. 

Calculation  of  the  Air  Supply  for  a  Cooling  Tower.  —  Let  T\  and  T% 
be  the  temperatures  of  the  water  entering  and  leaving;  t\  temperature 
of  the  air  supply;  z  its  relative  humidity;  t2,  temperature  of  the  air 
leaving;  mi  mz,  pounds  of  moisture  in  one  pound  of  saturated  air  at 
temperatures  ti,  t-2',  e\.,  e-2,  total  heat,  B.T.U.,  above  32°  F.  per  pound 
of  water  vapor  at  temperatures  ti,  t%\  A  —  Ib.  of  air  supplied  per  Ib.  of 
entering  water.  All  temperatures  are  in  degrees  F. 

Then,  for  each  1  Ib.  of  water  entering  the  tower  the  heat  (B.T.U.) 
carried  in  is:  by  the  water,  Ti—  32;  by  the  air,  0.2375  A  (ti—  32)  +A  m\  e\z. 
The  heat  carried  out  is:  by  the  water,  [l-(ra2-rai2)]  X  (T2-32);  by 
the  air,  0.2375  A  (tz-32)  +  A  (mz  e-2).  Neglecting  loss  by  radiation,  the 
heat  carried  into  the  tower  equals  the  heat  leaving  it.  Equating  these 
Quantities  and  solving  for  A  we  have: 

Ti  -  Tz  +  (mi  -  miZ)  (r2-32) 


0.2375  (fa  -  ti)   + 
From  this  equation  the  table  on  p.  1081  has  been  calculated. 

Water  Evaporated  in  a  Cooling  Tower.  —  The  following  table 
gives  the  values  of  (mz—miz)  per  pound  of  air  in  the  cooling-tower  formula. 
Multiplying  these  values  by  the  number  of  pounds  of  air  per  pound  of 
water  for  the  given  conditions,  wri.U  give  the  amount  of  water  evapo- 
rated, or  make-up  water  required  with  surface  condensers,  per  pound 
of  the  inflowing  water. 

Pounds  Water  Evaporated  per  Pound  of  Air. 


li  =  50° 

70° 

80° 

Ti=  100° 

2=0.5 

0.7 

0.9 

0.5 

0.7 

0.9 

0.5 

0.7 

0.9 

(  92 

*2=  {  88 
(  84 

.02912 
.02503 
.02141 

.02761 
.02352 
.01990 

.02610 
.02201 
.01839 

.02510 
.02101 
.01739 

.02198 
.01789 
.01427 

.01887 
.01478 
.01116 

.02188 
.01779 
.01417 

.01748 
.01339 
.00977 

.01308 
.00899 
.00537 

TI=  110° 

li  =  50° 

70° 

90° 

(  102 
tf-X  98 

/  94 

.04179 
.03626 
.03135 

.04028 
.03475 
.02984 

.03877 
.03324 
.02833 

.03777 
.03224 
.02733 

.03465 
.02912 
.02421 

.03154 
.02601 
.02110 

.03017 
.02464 
.01972 

.02402 
.01848 
.01357 

.01785 
.01232 
.00741 

Ti=  120° 

ti  =  50° 

70° 

90° 

(112 
«2=  J108 
(104 

.05905 
.05151 
.04482 

.05754 
.05000 
.04331 

.05603 
.04845 
.04180 

.05503 
.04749 
.04080 

.05191 
.04437 
.03768 

.04880 
.04126 
.03457 

.04743 
.03989 
.03320 

.04127 
.03373 
.02704 

.03511 
.02757 
.02088 

Tests  of  a  Cooling  Tower  and  Condenser  are  reported  by  J.  H.  Vail 
in  Trans.  A  .  S.  M .  E .,  1898.  The  tower  was  of  the  Barnard  type,  with  two 
chambers,  each  12  ft.  3  in.  X  18  ft.  X  29  ft.  6  in.  high,  containing  gal- 
vanized-wire  mats.  Four  fans  supplied  a  strong  draught  to  the  two  cham- 
bers. The  rated  capacity  of  each  section  was  to  cool  the  circulating 
water  needed  to  condense  12,500  Ibs.  of  steam,  from  132°  to  80°  F.,  when 
the  atmosphere  does  not  exceed  75°  F.  nor  the  humidity  85%.  The  fol- 
lowing is  a  record  of  some  observations. 


Date,  1898. 

Jan. 
31. 

Feb. 

June 
20. 

July. 

Aug. 
26. 

Nov. 
4. 

Aug.  2. 

Max. 

Min. 

Temperature  atmosphere  . 
Temp,  condenser  discharge 
Temp,  water  from  tower.. 
Heat  extracted  by  tower.  . 
Speed  of  fans,  r.p.m  
Vacuum,  inches  

30° 
110° 
65° 

45° 
36 

251/2 

36° 
110° 
84° 
26° 
0 
26 

78° 
120° 
84° 
36° 
145 
25 

96° 
130° 
93° 
37° 
'162 
241/2 

85° 
'118° 
88° 
30° 
150 
251/2 

59° 
129° 
92° 
37° 
148 
25 

103° 
128° 
98° 
32° 
160 
26 

83° 
106° 
9,0 

21° 
140 
26 

The  quantity  of  steam  condensed  or  of  water  circulated  is  uot  stated, 

COOLING  TOWERS. 


1081 


Pounds  of  Air  per  Pound  of  Circulating  Water. 

Outflowing  air  saturated. 


Ti=100° 

«i  = 

50° 

70° 

80° 

T2   *, 

2=0.5 

0.7 

0.9 

0.5 

0.7 

0.9 

0.5 

0.7 

0.9 

(92 

0  739 

0.767 

0.798 

0.962 

1.044 

.175 

1.144 

1.382 

1.755 

70-^88 
(84 

0.846 
0.975 

0.884 
1  .026 

0.926 
1.083 

1  .124 
1  .366 

1  .278 
1.604 

.482 
.944 

1.428 
1.850 

1.831 
2.598 

2.562 
4.394 

(92 

80  •<  88 

0.508 
0  580 

0.527 
0  605 

0.547 
0.632 

0.644 
0.767 

0.713 
0.869 

0.800 
.004 

0.783 
0.971 

0.939 
1.239 

1.187 
1.725 

(84 

0.665 

0.699 

0.737 

0.927 

1.086 

.312 

1.253 

1.751 

2.947 

(  92 

0.280 

0.287 

0.297 

0.348 

0.382 

0.424 

0.422 

0.496 

0.619 

90^88 

0.313 
0.356 

0.326 
0.372 

0.338 
0.390 

0.409 
0.491 

0.460 
0.569 

0.527 
0.680 

0.514 
0.655 

0.647 
JO.  904 

0.888 
1.500 

T^llO0 

/!  = 

50° 

70° 

90° 

(  102 

0  710 

0  729 

0.750 

0.838 

0.898 

0.966 

.135 

1.388 

1.790 

7CK    98 

0.804 

0.829 

0.856 

0.975 

1.056 

1.155 

.406 

1.821 

2.596 

j    94 

0.915 

0.948 

0.983 

1  .144 

1.260 

1  .403 

.796 

2.543 

4.395 

(  102 

0  546 

0.561 

0.576 

0.644 

0.688 

0.739 

0.868 

1  .055 

1  .358 

80  <    98 

0.617 

0.636 

0.655 

0.746 

0.807 

0.880 

.071 

1.382 

1.962 

(    94 

0.700 

0.724 

0.751 

0.873 

0.960 

1.067 

.364 

1  .898 

3.312 

(  102 

0.383 

0.392 

0.402 

0.449 

0.478 

0.512 

0.600 

0.726 

0.926 

90  K    98 

0.430 

0.442 

0.455 

0.517 

0.558 

0.606 

0.736 

0.942 

1.328 

(    94 

0.484 

0.501 

0.518 

0.602 

0.659 

0.730 

0.931 

1.311 

2.229 

T!=120° 

h  = 

50° 

70° 

90° 

(  112 

0.651 

0.663 

0.677 

0.732 

0.767 

0.806 

0.394 

1  .007 

1.155 

70^  108 

0.733 

0  .  749 

0.766 

0.839 

0.886 

0.939 

1  .061 

1.227 

1  .458 

(  104 

0.828 

0.849 

0.871 

0.967 

1.031 

1  .104 

.278 

1.530 

1.918 

(  112 

0.533 

0.544 

0.554 

0.599 

0.627 

0.656 

0.729 

0.820 

0.938 

80^  108 

0.599 

0.612 

0.625 

0.687 

0.722 

0.764 

0.863 

0.996 

1  .180 

f  104 

0.675 

0.692 

0.710 

0.787 

0.838 

0.896 

1  .037 

1.246 

1.548 

(  112 

0.416 

0.423 

0.432 

0.468 

0.487 

0.510 

0.565 

0.633 

0.721 

90-  108 

0.465 

0.475 

0.485 

0.531 

0.558 

0  .  590 

0.666 

0.765 

0.902 

1  104 

0.522 

0.535 

0.548 

0.607 

0.645 

0.688 

0.796 

0.947 

1.178 

Temp.  deg.F.  .       50 

B.  T.  U 1081.4 

Temp.  deg.  F. . .      94 

..  1101.0 


VALUES  OF  e\  OR  ez. 

70  80  84 

1090.3  1094.8  1096.6 

98  102  104 

1102.7  1104.5  1105.4 


88  92 

1098.3  1100.1 

108  112 

1107.1  1108.9 


Temp.  d< 
B.  T.  U 

Weight  of  Water  Vapor  Mixed  with  1  Lb.  of  Air  at  Atmospheric 
Pressure. 

Full  Saturation.     Values  interpolated  from  table  on  page  613. 


Deg. 
F. 

Mois- 
ture, 
Ib. 

Deg. 

Mois- 
ture, 
Ib. 

Deg. 

Mois- 
ture. 
Ib. 

Deg. 

Mois- 
ture, 
Ib. 

Deg. 

Mois- 
ture, 
Ib. 

32 

0.00374 

54 

0.00874 

76 

0.01917 

98 

0.04002 

120 

0.08099 

34 

.00406 

56 

.00940 

78 

.02054 

100 

.04270 

122 

.08629 

36 

.00439 

58 

.01012 

80 

.02200 

102 

.04555 

124 

.09193 

38 

.00475 

60 

.01089 

82 

.02353 

104 

.04858 

126 

.09794 

40 

.00514 

62 

.01171 

84 

.02517 

106 

.05182 

128 

.10437 

42 

.00555 

64 

.01259 

86 

.02692 

108 

.05527 

130 

.11123 

44 

.00600 

66 

..01353 

88 

.02879 

110 

.05893 

132 

.11855 

46 

.00648 

68 

.01453 

90 

.03077 

112 

.06281 

134 

.12637 

48 

.00699 

70 

.01557 

92 

.03288 

114 

.06695 

136 

.13473 

50 

.00753 

72 

.01669 

94 

.03511 

116 

.07134 

138 

.14367 

52 

.00812 

74 

.01789 

96 

.03750 

118 

.07601 

140 

.15324 

- 


1082  THE   STEAM-ENGINE. 

Iwt  in  the  two  tests  on  Aug.  2  the  H.P.  developed  was  900  I.H^P.  in  the 
first  and  400  in  the  second,  the  engine  being  a  tandem  compound,  Corliss 
type,  20  and  36  X  42  in.,  120  r.p.m. 

J.  R.  Bibbins  (Trans.  A.S.M.E.,  1909)  gives  a  large  amount  of  informa- 
tion on  the  construction  and  performance  of  different  styles  of  cooling 
towers.  He  suggests  a  type  of  combined  fan  and  natural  draft  tower 
suited  to  most  efficient  running  on  peak  as  well  as  light  loads. 

Evaporators  and  Distillers  are  used  with  marine  engines  for  the  pur- 
pose of  providing  fresh  water  for  the  boilers  or  for  drinking  purposes. 

Weir's  Evaporator  consists  of  a  small  horizontal  boiler,  contrived  so  as 
to  be  easily  taken  to  pieces  and  cleaned.  The  water  in  it  is  evaporated  by 
the  steam  from  the  main  boilers  passing  through  a  set  of  tubes  placed  in 
its  bottom.  The  steam  generated  in  this  boiler  is  admitted  to  the  low- 

Sressure  valve-chest,  so  that  there  is  no  loss  of  energy,  and  the  water  con- 
ensed  in  it  is  returned  to  the  main  boilers. 

In  Weir's  Feed-heater  the  feed-water  before  entering  the  boiler  is  heated 
up  very  nearly  to  boiling-point  by  means  of  the  waste  water  and  steam 
from  the  low-pressure  valve-chest  of  a  compound  engine. 

ROTARY  STEAM-ENGINES  —  STEAM  TURBINES. 

Rotary  Steam-engines,  other  than  steam  turbines,  have  been  invented 
by  the  thousands,  but  not  one  has  attained  a  commercial  success,  as  regards 
economy  of  steam.  For  all  ordinary  uses  the  possible  advantages,  such 
as  saving  of  space,  to  be  gained  by  a  rotary  engine  are  overbalanced  by 
its  waste  of  steam.  Rotary  engines  are  in  use,  however,  for  special  pur- 
poses, such  as  steam  fire-engines  and  steam  feeds  for  sawmills,  in  which 
steam  economy  is  not  a  matter  of  importance. 

impulse  and  Reaction  Turbines. —  A  steam  turbine  of  the  simplest 
form  is  a  wheel  similar  to  a  water  wheel,  which  is  moved  by  a  jet  of  steam 
impinging  at  high  velocity  on  its  blades.  Such  a  wheel  was  designed 
by  Branca,  an  Italian,  in  1629.  The  De  Laval  steam  turbine,  which  is 
similar  in  many  respects  to  a  Pelton  water  wheel,  is  of  this  class.  It  is 
known  as  an  impulse  turbine.  In  a  book  written  by  Hero,  of  Alexan- 
dria, about  150  B.C.,  there  is  shown  a  revolving  hollow  metal  ball,  into 
which  steam  enters  through  a  trunnion  from  a  boiler  beneath,  and 
escapes  tangentially  from  the  outer  rim  through  two  arms  which  are 
bent  backwards,  so  that  the  steam  by  its  reaction  causes  the  ball  to 
rotate  in  an  opposite  direction  to  that  of  the  escaping  jets.  This  wheel 
is  the  prototype  of  a  reaction  turbine.  In  most  modern  steam  turbines 
both  the  impulse  and  reaction  principles  are  used,  jets  of  steam  striking 
blades  or  buckets  inserted  in  the  rim  of  a  wheel,  so  as  to  give  it  a  forward 
impulse,  and  escaping  from  it  in  a  reverse  direction  so  as  to  react  upon 
it.  The  name  impulse  wheel,  however,  is  now  generally  given  to  wheels 
like  the  De  Laval,  in  which  the  pressure  on  the  two  sides  of  a  wheel  con- 
taining the  blades  is  the  same,  and  the  name  reaction  wheel  to  one  in 
which  the  steam  decreases  in  pressure  in  passing  through  the  blades. 
The  Parsons  turbine  is  of  this  class. 

The  De  Laval  Turbine.  —  The  distinguishing  features  of  this  turbine 
are  the  diverging  nozzles,  in  which  the  steam  expands  down  to  the  at- 
mospheric pressure  in  non-condensing,  and  to  the  vacuum  pressure  in 
condensing  wheels;  a  single  forged  steel  disk  carrying  the  blades  on  its 
periphery;  a  slender,  flexible  shaft  on  which  the  wheel  is  mounted  and 
which  rotates  about  its  center  of  gravity;  and  a  set  of  reducing  gears, 
usually  10  to  1  reduction,  to  change  the  very  high  speed  of  the  turbine 
to  a  moderate  speed  for  driving  machinery.  Following  are  the  sizes 
and  speeds  of  some  De  Laval  turbines: 

Horse-power 5  30  100  300 

Revolutions  per  minute 30,000      20,000      13,000      10,000 

Diam.  to  center  of  blades,  ins.       3.94         8.86       19.68       29.92 

The  number  and  size  of  nozzles  vary  with  the  size  of  the  turbine. 
The  nozzles  are  provided  with  valves,  so  that  for  light  loads  some  of 
them  may  be  closed,  and  a  relatively  high  efficiency  is  obtained  at  light 
loads.  The  taper  of  the  nozzles  differs  for  condensing  and  non-condens- 
ing turbines.  Some  turbines  are  provided  with  two  sets  of  nozzles,  one 
for  condensing  and  the  other  for  non-condensing  operation. 

The  disk  of  the  De  Laval  turbine  is  not  mounted  midway  between 
the  shaft  bearings,  but  considerably  nearer  to  the  spherical  bearing 


ROTARY  STEAM-ENGiNES — STEAM   TURBINES.      1Q83 

at  the  governor  end.  At  low  speeds  the  shaft  bends,  but  as  the  speed 
increases  the  gyroscopic  action  of  the  disk  causes  it  to  rotate  in  a  plane 
at  right  angles  to  an  axis  through  the  center  of  gravity  of  the  shaft 
and  disk.  The  speed  just  below  that  at  which  this  takes  place,  and  at 
which  the  vibration  of  the  shaft  is  greatest,  is  called  the  critical  speed. 
It  is  about  1/5  to  1/8  of  the  normal  speed  of  the  turbine. 

The  diameter  of  the  shaft  of  a  De  Laval  100-H.P.  turbine  is  1  in., 
and  that  of  a  300-H.P.  about  15/i6  in.  The  teeth  of  the  pinions  of 
the  reducing  gear  are  cut  in  an  enlarged  section  of  the  shaft.  The  pitch 
of  the  gears  is  very  small,  0.15  in.  in  the  smallest  and  0.26  in.  in  the 
largest  sizes.  The  shaft  is  said  to  be  made  of  0.60  to  0.80  C  steel  and 
the  gears  of  0.20  C  steel. 

The  Zolley  or  Rateau  Turbine.  —  The  Zolley  or  Rateau  turbines 
are  developments  of  the  De  Laval  and  consist  of  a  number  of  De  Laval 
elements  in  series,  each  succeeding  element  utilizing  the  exhaust  steam 
from  the  preceding.  The  steam  is  partly  expanded  in  the  first  row  of 
nozzles,  strikes  the  first  row  of  buckets  and  leaves  them  with  practically 
zero  velocity.  It  is  then  further  expanded  through  the  second  row  of 
nozzles,  strikes  a  second  row  of  moving  buckets  and  again  leaves  them 
with  zero  velocity.  This  process  is  repeated  until  the  steam  is  com- 
pletely expanded. 

The  Parsons  Turbine.  —  In  the  Parsons,  or  reaction  type  of  turbine, 
there  are  a  large  number  of  rows  of  blades,  mounted  on  a  rotor  or  revolv- 
ing drum.  Between  each  pair  of  rows  there  is  a  row  of  stationary  blades 
attached  to  the  casing,  which  take  the  place  of  nozzles.  A  set  of  sta- 
tionary blades  and  the  following  set  of  moving  blades  constitute  what  is 
known  as  a  stage.  The  steam  expands  and  loses  pressure  in  both  sets. 
The  speed  of  rotation,  the  peripheral  speed  of  the  blades  and  the  velocity 
of  the  steam  through  the  blades  are  very  much  lower  than  in  the  De  Laval 
turbine.  The  rotor,  or  drum,  on  which  the  moving  blades  are  carried, 
Is  usually  made  in  three  sections  of  different  diameters,  the  smallest  at 
the  high-pressure  end  where  steam  is  admitted,  and  the  largest  at  the 
exhaust  end.  In  each  section  the  radial  length  of  the  blades  and  also 
their  width  increase  from  one  end  to  the  other,  to  correspond  with  the 
increased  volume  of  steam.  The  Parsons  turbine  is  built  in  the  United 
States  by  the  Westinghouse  Machine  Co.  and  by  the  Allis-Chalmers  Co. 

The  Westinghouse  Double- flow  Turbine. — For  sizes  above  5000  K.W. 
a  turbine  is  built  in  which  the  impulse  and  reaction  types  are  combined. 
It  has  a  set  of  non-expanding  nozzles,  an  impulse  wheel  with  two  velocity 
stages  (that  is  two  wheels  with  a  set  of  stationary  non-expanding  blades 
between),  one  intermediate  section  and  two  low-pressure  sections  with 
Parsons  blading.  After  steam  has  passed  through  the  impulse  wheel 
and  the  intermediate  section  it  is  divided  into  two  parts,  one  going  to 
the  right  and  the  other  to  the  left  hand  low-pressure  section.  There  is 
an  exhaust  pipe  at  each  end.  In  this  turbine,  the  end  thrust,  which  has 
to  be  balanced  in  reaction  turbines  of  the  usual  type,  is  almost  entirely 
avoided.  Other  advantages  are  the  reduction  in  size  and  weight,  due  to 
higher  permissible  speed;  blades  and  casing  are  not  exposed  to  high 
temperatures;  reduction  of  size  of  exhaust  pipes  and  of  length  of  shaft; 
avoidance  of  large  balance  pistons. 

The  Curtis  Turbine,  made  by  the  General  Electric  Company,  is  an 
impulse  wheel  of  several  stages.  Steam  is  expanded  in  nozzles  and 
enters  a  set  of  three  or  more  blades,  at  least  one  of  which  is  stationary. 
The  blades  are  all  non-expanding,  and  the  pressure  is  practically  the  same 
on  both  sides  of  any  row  of  blades*.  In  smaller  sizes  of  turbines,  only 
one  set  of  stationary  and  movable  blades  is  used,  but  in  large  sizes  there 
are  from  two  to  five  sets,  each  forming  a  pressure  stage,  separated  by 
diaphragms  containing  additional  sets  of  nozzles.  The  smaller  sizes  have 
horizontal  shafts,  but  the  larger  ones  have  vertical  shafts  supported  on  a 
step  bearing  supplied  with  oil  or  water  under  a  pressure  sufficient  to 
support  the  whole  weight  of  the  shaft  and  its  attached  rotating  disks. 
Curtis  turbines  are  made  in  sizes  from  15  K.W.  at  3600  to  4000  revs,  per 
minute  up  to  9000  K.W.  at  750  revs,  per  minute. 

The  Spiro  Turbine  consists  of  two  "  herring-bone"  helical  gear  wheels 
meshed  together  and  revolving  in  a  closely  fitting  casing.  The  steam 
enters  through  two  non-expanding  nozzles  at  mid-length  of  the  gears, 
expands  into  the  spaces  between  adjacent  gear  teeth  and  escapes  at 


1084  THE  STEAM-ENGINE. 

the  outer  ends  of  the  teeth  when  they  pass  the  line  of  contact  between 
the  two  rotors.  The  turbine  is  made  in  small  sizes,  under  100  H.P., 
and  is  used  non-condensing.  Its  merits  are  compactness  and  simplicity, 
but  it  is  not  economical  of  steam. 

Mechanical  Theory  of  the  Steam  Turbine. — In  the  impulse  turbine 
of  the  De  Laval  type,  with  a  single  disk  containing  blades  at  its  rim, 
steam  at  high  pressure  enters  the  smaller  end  or  throat  of  a  tapering 
nozzle,  and,  as  it  passes  through  the  nozzle,  is  expanded  adiabatically 
down  to  the  pressure  in  the  casing  of  the  turbine,  that  is  to  the  pressure 
of  the  atmosphere,  in  a  non-condensing  turbine,  or  to  the  pressure  of 
the  vacuum,  if  the  turbine  is  connected  to  a  condenser.  The  steam 
thus  expanded  has  its  volume  and  its  velocity  enormously  increased, 
its  pressure  energy  being  converted  into  energy  of  velocity.  It  then 
strikes  tangentially  the  concave  surfaces  of  the  curved  blades,  and  thus 
drives  the  wheel  forward.  In  passing  through  the  blades  it  has  its  direc- 
tion reversed,  and  the  reaction  of  the  escaping  jet  also  helps  'to  drive  the 
wheel  forward.  If  it  were  possible  for  the  direction  of  the  jet  to  be  com- 
pletely reversed,  or  through  an  arc  of  180°,  and  the  velocity  of  the  blade 
in  the  direction  of  the  entering  jet  was  one-half  the  velocity  of  the  jet, 
then  all  the  kinetic  energy  due  to  the  velocity  of  the  jet  would  be  con- 
verted into  work  on  the  blade,  and  the  velocity  of  the  jet  with  reference 
to  the  earth  would  be  zero.  This  complete  reversal,  however,  is  impos- 
sible, since  room  has  to  be  allowed  between  the  blades  for  the  passage  of 
the  steam,  and  the  blades,  therefore,  are  curved  through  an  arc  consid- 
erably less  than  180°,  and  the  jet  on  leaving  the  wheel  still  has  some 
kinetic  energy,  which  is  lost.  The  velocity  of  the  entering  steam  jet 
also  is  so  great  that  it  is  not  practicable  to  give  the  wheel  rim  a  velocity 
equal  to  one-half  that  of  the  jet,  since  that  would  be  beyond  a  safe  speed. 
The  speed  of  the  wheel  being  less  than  half  that  of  the  entering  jet,  also 
causes  the  jet  to  leave  the  wheel  with  some  of  its  energy  unutilized. 
The  mechanical  efficiency  of  the  wheel,  neglecting  radiation,  friction,  and 
other  internal  losses,  is  expressed  by  the  fraction  (E^  —  #2)  •*•  EI,  in 
which  EI  is  the  kinetic  energy  of  the  steam  jet  impinging  on  the  wheel 
and  Ez  that  of  the  steam  as  it  leaves  the  blades. 

In  multiple-stage  impulse  turbines,  the  high  velocity  of  the  wheel  is 
reduced  by  causing  the  steam  to  pass  through  two  or  more  rows  of 
blades,  which  rows  are  separated  by  a  row  of  stationary  curved  blades 
which  direct  the  steam  from  the  outlet  of  one  row  to  the  inlet  of  the 
next.  The  passages  through  all  the  blades,  both  movable  and  secondary, 
are  parallel,  or  non-expanding,  so  that  the  steam  does  not  change  its 
pressure  in  passing  through  them.  The  wheel  with  two  rows  of  movable 
blades  running  at  half  the  velocity  of  a  single-stage  turbine,  or  one  with 
three  rows  at  one-third  the  velocity,  causes  the  same  total  reduction  in 
velocity  as  the  single-stage  wheel;  and  a  greater  reduction  in  the  velocity 
of  the  wheel  can  be  obtained  by  increasing  the  number  of  rows.  It  is, 
therefore,  possible  by  having  a  sufficient  number  of  rows  of  blades,  or 
velocity  stages,  to  run  a  wheel  at  comparatively  slow  speed  and  yet 
have  the  steam  escape  from  the  last  set  of  blades  at  a  lower  absolute 
velocity  than  is  possible  with  a  single-stage  turbine.  In  the  reaction 
turbine .  the  reduction  of  the  pressure  and  its  conversion  into  kinetic 
energy,  or  energy  of  velocity,  takes  place  in  the  blades,  which  are  made 
of  such  shape  as  to  allow  the  steam  to  expand  while  passing  through  them. 
The  stationary  blades  also  allow  of  expansion  in  volume,  thus  taking 
the  place  of  nozzles. 

In  all  turbines,  whether  of  the  impulse,  reaction,  or  combination 
type,  the  object  is  to  take  in  steam  at  high  pressure  and  to  discharge  it 
into  the  atmosphere,  or  into  the  condenser,  at  the  lowest  pressure  and 
largest  volume  possible,  and  with  the  lowest  possible  absolute  velocity, 
or  velocity  with  reference  to  the  earth,  consistent  with  getting  the  steam 
away  from  the  wheel,  and  to  do  this  with  the  least  loss  of  energy  in  the 
wheel  due  to  friction  of  the  steam  through  the  passages,  to  shock  due 
to  incorrect  shape,  or  position  of  the  blades,  to  windage  of  frictional 
resistance  of  the  steam  in  contact  with  the  rotating  wheel,  or  other 
causes.  The  minimizing  of  these  several  losses  is  a  problem  of  extreme 
difficulty  which  is  being  solved  by  costly  experiments. 

Heat  Theory  of  the  Steam  Turbine.— The  steam  turbine  may  also  be 
considered  as  a  heat  engine,  the  object  of  which  is  to  take  a  pound  of 


NOTARY  STEAM-ENGINES — STEAM  TURBINES.    1085 

steam  containing  a  certain  quantity  of  heat,  Hi,  transform  as  great  a 
part  of  this  heat  as  possible  into  work,  and  discharge  the  remaining  part, 
HZ,  into  the  condenser.  The  thermal  efficiency  of  the  operation  is 
(Hi  -  HZ)  -J-  HI,  and  the  theoretical  limit  of  this  efficiency  is  (Ti  —  TZ) 
•i-  T2,  in  which  Ti  is  the  initial  and  T2  the  final  absolute  temperature. 

Referring  to  temperature  entropy  dia- 
gram, Fig.  176,  the  total  heat  above  32°  F.  ff 
of  1  Ib.  of  steam  at  the  temperature  Ti  is  J[ 
represented  by  the  area  OACDG  and  its                                   ^       /I 
entropy  is  0!.     Expanding  adiabatically  to              r>            Ti      d  D/   ] 
TZ  part  of  its  heat  energy  is  converted  into               / 
work,    represented    by    the    area    BCDF,               I 

while    OABFG   represents    the   heat    dis-  / Ta/1  F 

charged   into   the   condenser.     The   total          B/ — H — 

heat  of  1  Ib.  of  dry  saturated  steam  at  TZ  / 
is  greater  than  this  by  the  area  EFGH,  the 
fraction  FE  -5-  BE  representing  moisture  in 
the  1  Ib.  of  wet  steam  discharged.  If 
HI  =  heat  units  in  1  Ib.  of  dry  steam  at  the 
state-point  D,  and  HZ  =  heat  units  in  1  Ib. 
of  dry  steam  at  the  state-point  E,  at  the 
temperature  Tz,  then  the  energy  converted 
into  work  =BCDF=Hi  -Hz+  (02  -  0i)  T2. 
This  quantity  is  called  the  available  en- 
ergy Ea,  of  1  Ib.  of  steam  between  the 


j 


JG 


temperatures  TI  and  T2.  ^ „, ^  ,  - 

If  the  steam  is  initially  wet,  as  repre-       L _!.$ ]J 

sented  by  the  state-point  d  and  entropy       L ZlzU-*— 

0*,  then  the  work  done  in  adiabatic  expan-       ^~ 

sion  is  BCdfB,    which  is  equal  to  Ea  =  FIG.  176. 

HI  -H2  +  (02  -  0i)  T2  -  (0i  -  0*)  (.Ti  -Tz). 

The   quantity    0!  -  0*  =  (L/T{)    (l-x),  in   which   L  =  latent  heat 

of  evaporation  at  the  temperature  Ti,  and  x  =  the  moisture  in  1  Ib.  of 

steam.     The  values  of  Hi,  HZ,  4>i,  02,  etc.,  for  different  temperatures, 

may  be  taken  from  steam  tables  or  diagrams. 

If  the  steam  is  initially  superheated  to  the  temperature  Ts,  as  repre- 
sented by  the  state-point  j,  the  entropy  being  <£3,  then  the  total  heat  at 
j  is  Hi  +  C  (Ts  -  Ti),  in  which  C  is  the  mean  specific  heat  of  super- 
heated steam  between  T\  and  Ts.  The  increase  of  entropy  above  0i 
is  03  -0!  =  C  loge  (Ts/Ti).  The  energy  converted  into  work  is  Ea  = 

Hi  -  H2  +   (02  -  0l)    TZ  +  [V2  (Ts  +  TI)  -   TZ}   (03  -  0l)« 

Velocity  of  Steam  in  Nozzles. — Having  obtained  the  total  available 
energy  in  steam  expanding  adiabatically  between  two  temperatures,  as 
shown  above,  the  maximum  possible  flow  into  a  vacuum  is  obtained 


from  the  common  formula,  Energy,  in  foot-pounds,  =  1/2  W/g  X  V2,  in 
which  Wis  the  weight  (in  this  case  1  Ib.),  V  is  the  velocity  in  feet  per 
second,  and  g  =  32.2.  As  the  energy  Ea  is  in  heat  units,  it  is  multi- 


which  Wis  the  weight  (in  this  case  1  Ib.),  V  is  the  velocity  in  feet  per 
second,  and  g  =  32.2.      As  the  energy  Ea  is  in  heat  units 
plied  by  778  to  convert  it  into  foot-pounds,  and  we  have 

V  =  V778X2gEa  =  223.8  \/~Wa. 


This  is  the  theoretically  maximum  possible  velocity.  It  cannot  be 
obtained  in  a  short  nozzle  or  orifice,  but  is  approximated  in  the  long 
expanding  nozzles  used  in  turbines.  In  the  throat  or  narrow  section  of 
an  orifice,  the  velocity  and  the  weight  of  steam  flowing  per  second  may 
be  found  by  Napier's  or  Bateau's  formula,  see  page  876,  or  from  Gras- 
hof's  formula  as  given  by  Moyer,  F  =  AoPiW?  -H  60,  or  A0  =  60  F  -f- 
PO-97,  in  which  A0  is  the  area  of  the  smallest  section  of  the  nozzle, 
sq.  in.,  F  is  the  flow  of  steam  (initially  dry  saturated)  in  Ibs.  per  sec., 
and  P  is  the  absolute  pressure,  Ibs.  per  sq.  in.  This  formula  is  appli- 
cable in  all  cases  where  the  final  pressure  P2  does  not  exceed  58  %  of  the 
initial  pressure.  For  wet  steam  the  formula  becomes  F  =  AoP\wi  -v- 
60  \/~x,  Ao  =  60  F  \/~x  -T-  PiO.97,  in  which  x  is  the  dryness  quality  of  the 
inflowing  steam,  1  —  x  being  the  moisture. 

For    superheated    steam    F  =  ^oPiO-97  (i  -f  0.00065  D)  -r-  60;    A0  => 
60  F  -i-  P^-97  (1  -f  0.00065  D),  D  being  the  superheat  in  degrees  F. 


1086 


THE   STEAM-ENGINE. 


When  the  final  pressure  p2  is  greater  than  0.58  P?.,  a  coefficient  is  to 

be  applied  to  F  in  the  above  formulae,  the  value  of  which  is  most  con- 

veniently taken  from  a  curve  given  by  Rateau.     The  values  of  this  co- 

efficient, c,  for  different  ratios  of  Pi/Pz,  are  approximately  as  follows: 

P2-e-Pi=    0.580.60    0.62    0.64    0.66    0.68     0.70     0.720.740.760.78 

C=    1.       0.995  0.985  0.975  0.965  0.955  0.945  0.93  0.91  0.88  0.85 

Pa  -7-  Pi  =    0.800.82     0.84     0.86    0.88    0.90     0.92     0.940.960.981.00 

c=    0.82  0.79     0.76    0.72    0.675  0.625  0.57     0.51  0.42  0.30  0.00 

The  quality  of  steam  after  adiabatic  expansion,  xz,  is  found  from  the 
formula  xz  =  (x1Li/7Ti  +  0X  —  #2)  7VZ/2,  (8) 

in  which  Q\  and  61  are  the  entropies  of  the  liquid,  LI  and  Lt  the  latent 
heats  of  evaporation,  and  Xi  and  xz  the  dryness  quality,  at  the  initial 
and  final  conditions  respectively.  Curves  of  steam  quality  are  plotted  in 
an  entropy-total  heat  chart  given  in  Moyer's  "Steam  Turbines"  and 
also  in  Marks  and  Da  vis's  "Steam  Tables  and  Diagrams." 

The  area  of  the  smallest  section  or  throat  of  the  nozzle  being  found, 
the  area  of  any  section  beyond  the  throat  is  inversely  proportional  to  the 
velocity  and  directly  proportional  to  the  specific  volume  and  to  the 
dryness,  or  Ai/A0=  V0/Vi  X  Vi/v0X  XI/XQ,  in  which  A  is  in  the  area  in 
sq.  ins.,  V  the  velocity  in  ft.  per  sec.,  v  the  volume  of  1  Ib.  of  steam  in 
cu.  ft.,  and  x  the  dryness  fraction,  the  subscript  0  referring  to  the 
smallest  section  and  the  subscript  1  to  any  other  section.  The  ratio 
Ai/Ao  for  the  largest  cross  section  of  a  properly  designed  nozzle  depends 
upon  the  ratio  of  the  initial  to  the  final  pressure.  Moyer  gives  it  as 
Ai/A0  =  0.172  Pi/Pa  +  0.70,  and  for  Pi/P2  greater  than  25,  Ai/Ao  =  0.175 


In  practice  expanding  nozzles  are  usually  made  so  that  an  axial  sec- 
tion shows  the  inner  walls  in  straight  lines.  The  transverse  section  is 
usually  either  a  circle  or  a  square  with  rounded  corners.  The  diver- 
gence of  the  walls  is  about  6  degrees  from  the  axis  for  the  non-condens- 
ing and  as  much  as  12  degrees  for  condensing  turbines  for  low  vacuums. 
'Mover  gives  an  empirical  formula  for  the  length  between  the  throat  and 

'the  mouth,  L  =  Vl5  ,40  inches.  The  De  Laval  turbine  uses  a  much 
longer  nozzle  for  mechanical  reasons.  The  entrance  to  the  nozzle  above 
the  throat  should  be  well  rounded.  The  efficiency  of  a  well-made  nozzle 
with  smooth  surfaces  as  measured  by  the  velocity  is  about  96  to  97%, 
corresponding  to  an  energy  efficiency  of  92  to  94%. 

Speed  of  the  Blades.  —  If  VI  =  peripheral  velocity  of  the  blade, 
Vi  =  absolute  velocity  of  the  steam  entering  the  blades  and  a  the  nozzle 
angle,  or  angle  of  the  nozzle  to  the  plane  of  the  wheel,  then  (in  impulse 
turbines  with  equal  entrance  and  exit  angles  of  the  blade  with  the  plane 
of  the  wheel)  for  maximum  theoretical  efficiency  of  the  blade,  Vb  =  1/2  Vi 
cos  a.  The  nozzle  angle  is  usually  about  20°,  cos  a  =  0.940,  and  the 
efficiency  of  a  single  row  of  blades  is  (0.94  -  Vb/  Vi)  4  Vb/  Vi. 

For  Vi  =  3000  ft.  per  sec.,  the  efficiency  for  different  blade  speeds  is 
about  as  follows: 

200   400   600   800    1000    1200    1400    1600    1800   2000 
23      44      60      72        81        87        89        87        80        71 
The    highest    efficiency   is    obtained    when 
h.    •  Vb  =  about  1/2  V2.     It  is  difficult,  for  mechan- 

ical reasons,  to  use  speeds  much  greater  than 
500  ft.   per   sec.,    therefore   the   highest   effi- 
ciencies   are    often    sacrificed    in    commercial 
I  machines.     The  blade  speeds  used  in  practice 
vary  from  500  to   1200  ft.  per  sec.     For  an 
impulse  wheel  with  more  than  one  row  of  mov- 
ing blades  in  a  single  pressure  stage,  efficiency 
4NVb 


Referring  to  Fig.  177,  if  Vi  is  the  absolute 
direction  and  velocity  of  the  entering  jet,  Vb 
the  direction  and  velocity  of  the  blade,  the 
resultant,  Vr,  is  the  velocity  and  direction  of  the  jet  relatively  to  th 
blade,  and  the  edge  of  the  blade  is  made  tangent  to  this  direction.    Also 


™       .  77 


ROTARY   STEAM-ENGINES — STEAM   TURBINES.       1087 

Vx,  the  resultant  of  V^  and  Vr~at  the  other  edge  of  the  blade,  is  the 
absolute  velocity  and  direction  of  the  steam  escaping  from  the  wheel. 
If  Q  is  the  angle  between  Vr  and  Vfr,  the  maximum  energy  is  abstracted 
from  the  steam  when  the  angle  between  Vx  and  VJF,  =  90  -  1/2  8,  and 
the  efficiency  is  cos  Q  +  cos2 1/2  @. 

For  details  of  design  of  blades,  and  of  turbines  in  general,  see  Moyer, 
Foster,  Thomas,  Stodola  and  other  works  on  Steam  Turbines,  also 
Peabody's  "Thermodynamics."  Calculations  of  stages,  nozzles,  etc., 
are  much  facilitated  by  the  use  of  Peabody's  "  Steam  Tables"  and  Marks 
and  Davis's  "Steam  Tables  and  Diagrams." 

Comparison  of  Commercial  Impulse  and  Reaction  Turbines.  (Moyer.) 
IMPULSE.  REACTION. 

1.  Few  stages.  1.   Many  stages. 

2.  Expansion  in  nozzles.  2.    No  nozzles. 

3.  Large  drop  in  pressure  in  a        3.   Small  drop  in  pressure  in  a 

stage.  stage. 

4.  Initial  steam  velocities  1000  to        4.   All  steam  velocities  low,  300  to 

4000  ft.  per  sec.  600  ft.  per  sec. 

5.  Blade  velocities  400  to  1200  ft.         5.   Blade  velocities  150  to  400  ft. 

per  sec.  per  sec. 

6.  Best  efficiency  when  the  blade         6.    Best  efficiency  when  the  blade 

velocity  is  nearly  half  the  ini-  velocity  is  nearly  equal  to 

tial  velocity. of  steam.  the  highest  velocity  of  the 

steam. 

Xoss  due  to  Windage  (or  friction  of  a  turbine  wheel  rotating  in  steam). 
—  Moyer  gives  for  the  friction  of  a  plain  disk  without  blades,  Fw,  and  of 
one  row  of  blades  without  the  disk,  F^,  in  horse-power: 

Fw=  0.08  <J2  (M/lOO)*8  w  -J-  (1  +  0.00065  D)*, 
F&-X>.3dl«^tt/100)«to-*.  (1  +  0.00065  D)*, 

in  which  d  =  diam.  of  disk  to  inner  edge  of  blade,  in  feet ;  u  =  peripheral 
velocity  of  disk,  in  ft.  per  sec.:  w  =  density  of  dry  saturated  steam  at 
the  pressure  surrounding  the  disk,  in  Ibs.  per  cu.  ft.,  and  D  =  super- 
heat in  degrees  F.  The  sum  of  Fw  and  Fb  is  the  friction  of  the  disk  and 
blades.  For  moist  sieam  the  term  1  +  0.00065  D  if  to  be  omitted,  and 
the  expression  multiplied  by  a  coefficient  c,  whose  value  is  approxi- 
mately as  follows: 

^fure^nSeam     2         4         6         8         10        12        16        20        24 

Coefficient  c. ..  1.01  1.05  1.10  1.16  1.25  1.37  1.65  2.00  2.44 
At  high  rotative  speeds  the  rotation  loss  of  a  non-condensing  turbine 
with  wheels  revolving  in  steam  at  atmospheric  pressure  is  quite  large, 
and  in  small  turbines  it  may  be  as  much  as  20%  of  the  total  output. 
The  loss  decreases  rapidly  with  increasing  vacuum.  In  a  turbine  with 
more  than  one  stage  part  of  the  friction  loss  of  rotation  is  converted  into 
heat  which  in  the  next  stage  is  converted  into  kinetic  energy,  thus  partly 
compensating  for  the  loss. 

Efficiency  of  the  Machine.  —  The  maximum  possible  thermodynamic 
efficiency  of  a  steam  turbine,  as  of  any  other  steam  engine,  is  expressed 
by  the  ratio  which  the  available  energy  between  two  temperatures  bears 
to  the  total  heat,  measured  above  absolute  zero,  of  the  steam  at  the 
higher  temperature.  In  the  temperature-entropy  diagram  Fig.  176  it  is 
represented  by  the  ratio  of  the  area  BCDF  to  OACDG.  Of  this  avail- 
able energy,  from  50  to  75  and  possibly  80  per  cent  is  obtainable  at  the 
shaft  of  turbines  of  different  sizes  and  designs.  As  with  steam  engines, 
the  highest  mechanical  and  thermal  efficiencies  are  reached  only  with 
large  sizes  and  the  most  expensive  designs.  The  several  losses  which 
tend  to  reduce  the  efficiency  of  turbines  below  the  theoretical  maximum 
are-  1,  residual  velocity,  or  the  kinetic  energy  due  to  the  velocity  of  the 
steam  escaping  from  the  turbine;  2,  friction  and  imperfect  expansion 
in  the  nozzles;  3,  windage,  or  friction  due  to  rotation  of  the  wheel  in 
steam;  4,  friction  of  the  steam  traveling  through  the  blades;  5,  shocks, 
impacts,  eddies,  etc.,  due  to  imperfect  shape  or  roughness  of  blades;  6, 
leakage  around  the  ends  of  the  blades  or  through  clearance  spaces;  7,  shaft 
friction:  8,  radiation.  The  sum  of  all  these  losses  amounts  to  about 
25%  of  the  available  energy  in  the  largest  and  best  design  and 
or  more  in  small  sizes  or  poor  Designs, 


1088 


THE  STEAM-ENGINE. 


Steam  Consumption  of  Turbines.  — The  steam  consumption  of  any 
steam  turbine  is  so  greatly  influenced  by  the  conditions  of  pressure, 
moisture  or  superheat,  and  vacuum,  that  it  is  necessary  to  know  the  effect 
of  these  conditions  on  any  turbines  whose  performances  are  to  be  com- 
pared with  each  other  or  with  a  given  standard.  Manufacturers  usually 
furnish  with  their  guarantees  of  performance  under  standard  conditions 
of  pressure,  superheat  and  vacuum,  a  statement  or  set  of  curves  showing 
the  amount  that  the  steam  consumption  per  K.W.-hour  will  be  increased 
or  diminished  by  stated  variations  from  these  standard  conditions. 
When  a  test  of  steam  consumption  is  made  under  any  conditions  varying 
from  the  standard,  the  results  should  be  corrected  in  order  to  compare 
them  with  other  tests.  Moyer  gives  the  following  example  of  applying 
corrections  to  a  pair  of  tests  made  in  1907,  to  reduce  them  both  to  a  steam 
pressure  of  179  Ibs.  gauge,  28.5  iris,  vacuum,  and  100°  F.  superheat. 


7500-K.W. 
Westing- 
house- 
Parsons. 

Correc- 
tions, 
per  cent. 

9000-K.W. 
Curtis. 

Correc- 
tions, 
per  cent. 

Averacre  steam  pressure 

177.5 

-0  15 

179 

0 

Average  vacuum,  ins.,  referred 

27.3 

-3.36 

29  55 

+  12  39 

Avera.se  superheat  deg  F.       . 

95  7 

-0  29 

116 

+   1  28 

Average  load  on  generator  K  TV. 

9830  5 

8070 

Steam  cons    Ibs.  per  K  W.-hr.  . 

15.15 

13  0 

Net  correction,  per  cent/  

-3.80 

+  13.67 

Corr.  st.  cons.,  Ibs.  per  K.W.-hr. 

14.57 

14.77 

For  the  7500-K.W.  turbine,  the  following  corrections  given  by  the  manu- 
facturer were  used:  pressure,  0.1%  for  each  pound;  vacuum,  2.8%  for 
each  inch;  superheat,  7%  for  each  100°  F.  For  the  9000-K.W.  turbine, 
the  following  corrections  were  used:  superheat,  8%  for  100°  F.;  vacuum, 
8%  for  each  inch. 

The  results  as  corrected  show  that  the  two  turbines  would  give  practi- 
cally the  same  economy  if  tested  under  uniform  conditions.  The  results 
are  equivalent  respectively  to  9.58  and  9.72  Ibs.  per  I. H. P. -hour,  as- 
suming 97%  generator  efficiency  and  91%  mechanical  efficiency  of  a 
steam-engine. 

The  proper  correction  for  moisture  in  a  steam  turbine  test  is  stated  to 
be  a  little  more  than  twice  the  percentage  of  moisture.  There  is  a  large 
increase  in  the  disk  and  blade  rotation  losses  when  wet  steam  is  used. 

Effect  of  Vacuum  on  Steam  Turbines. — M.  R.  Bump  (Power,  June 
15,  1909)  gives  the  following  as  the  steam  consumption  per  K.W.  hour 
of  a  1000  K.W.  turbine  at  full  rated  load,  175  Ib.  gage  pressure,  100° 
superheat: 

Vacuum,  in..     29        28         27         26         25         24        23       22       21 
Steam  per 
K.W.  hr.  Ib. .  15.35    16.55    17.50    18.55    19.35    20.00   20.6    21.1    21.6 

The  gain  in  economy  per  inch  of  vacuum  at  different  vacuums  is 
given  as  follows  in  Mech.  Engr.,  Feb.  24,  1906. 


Inches  of  Vacuum. 

28 

27 

26 

25 

Curtis,  per  cent  gain  per  inch  of  vacuum.  . 
Parsons,  per  cent  gain  per  inch  of  vacuum 

5.1 
5.0 

4.8 
4.0 

4.6 
3.5 

4.2 
3.0 

Westi  .ghouse-  Parsons,  per  cent  gain  per 

inch  of  vacuum                    .       

3  14 

3.05 

2  95 

2  87 

Theoretical  per  cent  gain  per  inch  of  vac.. 

5.2 

4.4 

3.7 

3.0 

Tests  of  Turbines. — The  following  results  of  tests  of  turbines  are 
selected  from  a  series  of  tables  in  Moyer 's  "Steam  Turbines." 


ROTARY  STEAM-ENGINES — STEAM   TURBINES.       1089 


3^ 
&* 

Bfe 

<§« 

o>  en 

Ig 

^ 

*J* 

|1s? 

£•*-* 

Vacuum, 
ins. 

^ 

&&  2 
A™A 

•g£ 

jH 

& 

£W- 
<§« 

S| 

3& 

|l1 

£•*-* 

a 

SI 

£ 

Si 

S®* 

2000  ( 
C.  \ 

555 
1067 
2024 

155 
170 
166 

204 
120 
207 

28.5 
28.4 
28.5 

18.09 
16.31 
15.02 

300  ( 
W.-P.j 

233 

461 
688 

145 
145 
140 

4.1 

4.8 
7.0 

28.0 
28.0 
27.2 

15.99 
13.99 
15.73 

5374 

182 

133 

29.4 

13.15 

383 

153 

2 

28.2 

14.15 

8070 

179 

116 

7.9.4 

13.00 

756 

149 

1 

27.8 

13.28 

10186 

176 

147 

29.5 

12.90 

500 

1122 

149 

5 

26.5 

14.32 

13900 

198 

140 

29.3 

13.60 

W.-P. 

386 

148 

3 

0.8 

24.94 

1500  ( 

530 
1071 

145 
131 

110 
124 

28.9 
28.3 

21.58 
18.24 

767 
1144 

147 
126 

3 

11 

0.8 
0.8 

22.10 
24.36 

P.  ) 

1585 

128 

125 

27.5 

17.60 

1  nnn  ( 

752 

151 

0 

27.5 

14.77 

300  ( 
P.  I 

303 
297 

158 
161 

0 
0 

26.6 
0 

23.15 

34.20 

IUUU  ) 

W.-P.| 

1503 
2253 

147 
145 

0 
0 

27.0 
25.2 

13.61 
15.29 

1000  J 

194 

425 

171 
144 

47 
21 

27.7 
27.6 

31.97 

24.91 

3000  ( 
W.-P.I 

2295 
4410 

152 
144 

102 

87 

26.2 
26.2 

12.36 
11.85 

R.  1 

871 

166 

11 

23.6 

24.61 

3OA 

196 

198 

16 

27.4 

15.62 

1024 

164 

•  10 

25.0 

21.98 

J\J(J 

298 

197 

64 

27.4 

14.35 

352 

199 

84 

27.2 

13.94 

C.,  Curtis;  P.,  Parsons;  W.-P.,  Westinghouse-Parsons;  R.,  Rateau; 
DM  De  Laval.  Note  that  the  figures  of  steam  consumption  in  the  first 
half  of  the  table  are  in  Ibs.  per  K.W.-hour;  in  second  half,  in  Ibs.  per  Brake 
H.P.-hour. 

A  test  of  a  Westinghouse  double-flow  turbine  at  the  Williamsburff 
power  station,  Brooklyn  N.  Y.,  gave  the  following  results  (Eng.  News, 
Dec.  30, 1909):  Speed,  750  r.p.m.;  Steam  pressure  at  throttle,  203.4  Ibs.; 
Superheat,  80.1°  F.;  Vacuum,  28.6  ins.;  Load,  13,384  K.W.;  Steam  per 
K.W.-hour,  14.4.  Ibs.;  Efficiency  of  generator,  98%;  Windage,  2.0%; 
Equivalent  B.  H.  P.,  18,620;  Steam  per  B.  H.  P.-hour,  10.3  Ib. 

Efficiency  of  the  Rankine  Cycle,  and  the  Rankine  Cycle  Ratio.— 

An  ideal  engine  operating  on  the  Rankine  cycle  expands  the  steam 
adiabatically  to  the  condenser  pressure  and  the  exhaust  steam  heats 
the  feed  water  to  the  condenser  temperature.  It  has  no  clearance  nor 
loss  by  leakage  or  radiation.  The  efficiency  of  the  Rankine  cycle  is 
the  quotient  of  the  number  of  heat-units  converted  into  work  by  the 
ideal  engine  per  Ib.  of  steam  divided  by  the  difference  between  the 
total  heat  per  Ib.  of  the  entering  steam  and  the  total  heat  of  1  Ib.  of 
feed- water  at  the  condenser  temperature. 

The  Rankine  Cycle  Ratio  is  the  ratio  between  the  thermal  efficiency 
of  an  actual  engine  or  turbine  and  the  efficiency  of  an  ideal  engine 
operating  on  the  Rankine  cycle  between  the  same  temperature  and 
pressure  limits  as  those  of  the  actual  engine. 

The  available  energy  of  1  Ib.  of  steam  supplied  =  heat  utilized  per 
Ib.  in  an  ideal  engine  operating  on  the  Rankine  cycle  =  U  =  H_  —Hz  + 
Tz(Nz  -  Ns)  in  which 

H  •  =  heat-units  per  Ib.  of  the  entering  steam,  whether  saturated  or 
superheated. 

H2  =  heat  units  per  Ib.  of  the  exhaust  steam. 
Tz  —  absolute  temperature  of  the  exhaust. 

N    and  Nz  =  respectively  the  entropy  of  the  entering  and  of  the 
exhaust  steam. 

If  the  exhaust  steam  is  superheated  (as  it  roay  be  in  the  case  of  the 
high-pressure  cylinder  of  a  triple  expansion  engine  using  highly  super- 
heated steam)  U  =  Hs  -  H2  -  Tz(Nb  -~  sit).  (These  formulae  may  be 
derived  from  a  study  of  the  «aitropy  temperature  diagram,  page  1085.) 

EXAMPLE.— A  steam  curbine  operating  with  225  Ib.  absolute  pre,°~ 
sure,  150°  superheat,  and  28,5  in.  vacuum  uses  10  Ib.  of  steam  per 


1090 


THE  STEAM-ENGINE. 


brake  horse-power  hour.     Required  the  available  energy  per  Ib.  steam, 
the  Bankine  cycle  efficiency  and  the  Rankine  cycle  ratio. 

Hs  =  1285.9;  H*  =  1099.2;  Tz  =  549.6;  h  =  heat  units  per  Ib.  of 
feed-water  at  the  temperature  T2  =  58.  W  =  Ib.  steam  per  H.P.-hour  = 
10.  A  =  heat  equivalent  of  one  H.P.-hour  =  1,980,000  -r-  777.54  = 
2546.5  B.T.U.;  JVS  =  1.6296;  N2  =  2.0058  W(HS  -  h)  =  total  heat 
per  H.P.-hour  =  10  X  (1285.9  -  58)  =  12,279  B.T.U.  Thermal 


ficiency  E  =  2546.5  +  W(H  -  h)  =  20.74%.  Available  energy  per 
Ib.,  U  =  1285.9  -  1099.2  +  549.6  (2.0058  -  1.6296)  =  393.5  B.T.U. 
Rankine  cycle  efficiency  ER  =  U  -r-  (Hs  -  h)  =  393.5  -=- 1227.9  =  32.04%. 
Rankine  cycle-ratio  R  =  E  +  ER  =  20.74  +  32  =  64.7%. 

Factors  for  Reduction  to  Equivalent  Rankine  Efficiency. — When 
engines  are  tested  with  different  pressures,  superheat  and  vacuum, 
it  is  often  desirable  to  reduce  the  results  to  a  common  standard  of 
assumed  conditions.  The  conditions  stated  in  the  above  example 
correspond  with  good  modern  practice  and  they  probably  furnish  as 
good  a  standard  for  comparison  as  any  other.  The  Rankine  cycle 
efficiency  ER,  for  this  set  of  conditions  is  32.04% ;  the  thermal  efficiency, 
for  W  =  10  Ib.  is  20.74  % ;  and  the  ratio  E  -f-  ER  is  64.7  %.  For  another 
set  of  conditions,  pressure  150  Ib.,  vacuum  27  in.,  and  dry  saturated 
steam  ER  is  27.0.  The  quotient  32.04  -r  27.0  =  1.187,  may  be  used 
as  a  factor  to  reduce  the  Rankine  efficiency,  the  Rankine  cycle  ratio, 
and  the  steam  consumpti9n  per  H.P.-hour  to  the  equivalent  for  stand- 
ard conditions;  thus,  equivalent  E  =  27  X  1.187  =  32.04,  equivalent  R 
(assuming  W=  11.87  and  E  =  17.48%)  =  17.48  X  1.187  =  20.74,  and 
equivalent  W  =  11.87  -r-  1.187  =  10  Ib.,  provided  the  percentage  losses 
due  to  friction,  radiation  and  leakage  are  the  same  for  the  two  condi- 
tions. The  factor  is  used  as  a  multiplier  to  obtain  the  equivalent 
thermal  efficiency  and  Rankine  cycle  ratio,  and  as  a  divisor  to  obtain 
the  equivalent  steam  consumption.  The  factor  may  be  found  also 

32.04  (Hs-  h), 
from  the  equation  F  = pj -in  which  Hs,  h,  and  U  are  the 

values  for  the  given  set  of  conditions.  The  factors  computed  by  this 
formula  and  the  efficiency  of  the  Rankine  cycle  for  different  conditions 
are  given  in  the  table  at  the  top  of  p.  1091. 

Effect  of  Increase  in  Pressure,  Vacuum  and  Superheat  on  Efficiency. — 

Selecting  from  the  table  on  p.  1091  the  figures  for  Rankine  cycle  efficiency 
given  in  the  table  below  and  comparing  them  by  taking  differences 
between  consecutive  figures  in  both  the  horizontal  and  the  vertical  rows, 
we  find  that  the  increase  of  efficiency  due  to  increasing  either  the  pres- 
sure, the  superheat  or  the  vacuum  cannot  be  expressed  as  a  constant 
percentage,  but  that  it  varies  with  variations  in  each  condition. 
EFFECT  OF  VARYING  CONDITIONS  ON  RANKINE  CYCLE  EFFICIENCY. 


Pressure, 
Absolute  . 

150 

Vacuum, 
In. 

Superheat. 

0° 

Diff. 

150° 

Diff. 

300° 

Diff. 

,27,, 
28,, 
(  29.... 

27.0 
28.4 
30.8 

0.5 
1.4 
0.6 
2.4 
0.6 

27.5 
29.0 
31.4 

1.1 
1.5 
1.0 
2.4 
1.0 

28.6 
30.0 
32.4 

1.4 
2.4 

200 

,27,, 
28,, 
(29.... 

28.5 
29.9 
32.2 

0.6  (1.5) 
1.4 
0.6  (1.5) 

0.6  (1.4) 

29.1 
30.5 
32.8 

1.4 

2.3 
1.0(1.4) 

30.1 
31.5 
33.8 

1.4 

2.3 

(1.4) 

250 

,27, 

28,, 

(29.... 

29.7 
31.0 
33.2 

0.6  (1.2) 
1.3 
0.6(1.1) 
2.2 
0.6  (1.0) 

30.3 
31.6 
33.9 

0.9  (1.2) 
0.9(1.1) 

31.2 
32.6 
34.2 

1.4 
2.8 

The  figures  in  parentheses  show  the  increase  in  efficiency  due  taf 


ROTARY  STEAM-ENGINES — STEAM  TURBINES.       1091 


Efficiency  of  Bankine  Cycle,  ER  (per  cent)  and  Factor  JPfor  Reduction 
to  Standard  Conditions, 

(225  Lb.  Absolute   Pressure,  150°  Superheat,   28.5  In.  Vacuum  and 
Rankine  Cycle  efficiency  of  32  per  cent  being  taken  as  standard.) 


Absolut. 
Pres- 
sure, 
Lb.  per 
Sq.  In. 

Vacuum 
In. 
Mercury  . 

Superheat,  Degrees  Fahrenheit.    . 

0 

50 

100 

150 

200 

250 

300 

150 

27  ir 

oo       j  EiR 

28    ]p 
28.5  {  f* 
29    |F" 

27.0 
1.187 
28.4 
1.127 
29.4 
1.088 
30.8 
1.040 

27.1 
1.182 
28.5 
1.122 
29.6 
1.083 
31.0 
1.035 

27.3 
1.174 
28.7 
1.115 
29.8 
1.076 
31.1 
1.028 

27.5 
1.163 
29.0 
1.105 
30.0 
1.067 
31.4 
1.020 

27.8 
1.150 
29.3 
1.094 
30.3 
1.057 
31.7 
1.011 

28.2 
1.136 
29.6 
1.081 
30.6 
1.046 
32.0 
1.001 

28.6 
1.122 
30.0 
1.068 
31.0 
1.033 
32.4 
0.989 

200 

27    {£« 
28    ]£«' 
28.5  {f- 
29    {f. 

28.5 
1.124 
29.9 
1.072 
30.9 
1.038 
32.2 
0.995 

28.6 
1.119 
30.0 
1.067 
31.0 
1.033 
32.3 
0.990 

28.8 
1.111 
30.2 
1.060 
31.2 
1.026 
32.6 
0.984 

29.1 
1.100 
30.5 
1.051 
31.5 
1.018 
32.8 
0.977 

29.4 
1.090 
30.8 
1.041 
31.8 
1.009 
33.1 
0.968 

29.7 
1.078 
31.1 
1.030 
32.1 
0.998 
33.4 
0.959 

30.1 
1.064 
31.5 
1.018 
32.4 
0.988 
33.8 
0.949 

225 

- 

250 

27    {f" 
28    {?« 
28.5  |f* 
29    jf* 

29.1 
1.101 
30.5 
1.052 
31.4 
1.019 
32.7 
0.978 

29.2 
1.096 
30.6 
1.047 
31.6 
1.014 
32.9 
0.973 

29.5 
1.087 
30.8 
1.040 
31.8 
1.008 
33.1 
0.967 

29.7 
1.078 
31.1 
1.031 
32.0 
1.000 
33.4- 
0.960 

30.0 
1.068 
31.3 
1.022 
32.3 
0.991 
33.6 
0.952 

30.3 
1.056 
31.7 
1.011 
32.6 
0.981 
34.0 
0.943 

30.7 
1.044 
32.0 
1.000 
33.0 
0.971 
34.3 
0.934 

27    jf« 

78      JE* 
28     JF 

90  r  j  ER 

28.5  JF 
29     j£* 

29.7 
1.079 
31.0 
1.033 
32.0 
1.002 
33.2 
0.963 

29.8 
1.075 
31.1 
1.029 
32.1 
0.998 
33.4 
0.959 

30.0 
1.068 
31.3 
1.022 
32.3 
0.992 
33.6 
0.953 

30.3 
1.059 
31.6 
1.014 
32.6 
0.984 
33.9 
0.946 

30.5 
1.049 
31.9 
1.005 
32.8 
0.975 
34.1 
0.938 

30.9 
1.038 
32.2 
0.995 
33.2 
0.966 
34.5 
0.930 

31.2 
1.026 
32.6 
0.984 
33.5 
0.956 
34.8 
0.920 

increase  of  50  Ib.  in  pressure,  the  superheat  and  the  vacuum  being 
constant. 


Constant. 

Increase  of 

Increases 

Efficiency. 

Pressure  and  vacuum 

j  Superheat  frc 

>m      0 
150 

to  150° 
"  300 

0.5  t 
0.9 

o  0.6  a 
1.1 

v.  0.6 
1.0 

Pressure  and 

j  Vacuum 

27 

"     28 

1.3 

1.5 

1.4 

Superheat 

1 

28 

"      29 

2.2 

2.4 

2.3 

Superheat  and 

j  Pressure 

150 

"   200 

1.4 

1.6 

1.5 

vacuum 

1 

200 

"   250 

1.0 

1.2 

1.1 

W.  H.  Wallis  (Eng'g,  April  21,  1911)  finds  as  the  results  of  tests  of 
a  compound  reaction  turbine  that  the  percentage  reduction  of  steam 
consumption  by  increasing  the  vacuum  from  25  in.  to  the  figures  given 
was  as  follows:  Vacuum,  27  in.;  reduction,  71/2%;  28  in.,  12%;  28.6  in., 

Steam  Consumption  and  Heat  Consumption  of  the  Ideal  Engine.— 

If  the  Rankine  cycle  efficiency  is  given  for  a  stated  set  of  conditions, 


1092  THE  STEAM-ENGINE. 

the  corresponding  theoretical  steam  consumption  per  H.  P. -hour  may  be 


For  the  extreme  cases  in  the  table  on  p.  1090,  we  have: 


Pres- 
sure, 
Lb. 

Vac., 
In. 

Super- 
heat. 

** 

h. 

Es. 

U. 

W. 

Hs-h 

W  (Hf-h). 

150 
250 

27 
29 

0 
300° 

1193.4 
1363.5 

82.0 
44.6 

27.0 

34.8 

299.7 
459.1 

8.49 
5.60 

1114.4 
1318.9 

9461 
7376 

The  figures  in  the  last  column,  W(HS  -  h),  show  the  B.T.U.  con- 
sumed (or  supplied  by  the  boiler)  per  H. P. -hour.  The  number  of 
pounds  of  steam  supplied  under  the  second  set  of  conditions  is  33.3  %  less 
than  that  supplied  under  the  first  set,  but  the  saving  of  heat  is  only 
(9461  -  7376)- -v-  9461  =  22%. 

Westinghouse  Turbines  at  the  Manhattan  74th  Street  Station, 
New  York. — Each  of  the  30,000  Kw.  cross-compound  units  consists 
of  two  turbines,  a  high  and  a  low  pressure,  side  by  side.  Each  half 
drives  a  generator,  the  high  pressure  running  1500  r.p.m.  and  the  low 
pressure  750,  the  generators  being  tied  together  electrically.  The  tur- 
bines are  reaction  throughout,  having  no  impulse  wheel.  The  h.p. 
is  a  single  flow  machine  and  the  l.p.  a  double  flow.  The  turbines  are 
to  have  a  vacuum  of  97%  =  29.1  in.  mercury,  or  0.442  Ib.  per  sq.  in. 
absolute.  The  boilers  will  run  at  215  Ib.  pressure,  and  at  peak  of  the 
load,  twice  each  day  of  24  hours,  will  run  at  300%  of  rating.  Under- 
feed stokers.  Superheat  at  throttle,  120°.  (Power,  April  27,  1915). 

A  Steam  Turbine  Guarantee. — A  22,500-Kw.  steam  turbine  built 
in  1913  by  C.  A.  Parsons  Co.,  Newcastle,  England,  for  the  Common- 
wealth Edison  Co.,  Chicago,  was  guaranteed  as  follows:  At  750  r.p.m. 
200  Ib.  pressure  by  gage,  29  in.  vacuum  in  the  condenser 

Load,  Kw..  10,000      15,000      20,000      25,000 

Steam  per  Kw  .-hour,  Ib 12.50        11.65        11.25        11.65 

Efficiency  of  a  5000-Kw.  Steam  Turbine  Generator.  (F.  W.  Ballard, 
Trans.  A.  S.  M.  E.,  1914.) — A  plotted  diagram  of  a  series  of  tests  shows 
that  the  total  steam  consumption  at  different  loads  follows  the  Willans 
straight-line  law  up  to  the  point  of  maximum  efficiency.  The  turbine 
was  of  the  Allis-Chalmers-Parsons  type,  rated  at  5000  Kw.,  1800  r.p.m., 
11,000  volts,  A.C.  With  steam  at  225  Ib.  gage,  superheat  125°  F., 
vacuum  281/2  in.,  90%  power  factor,  the  steam  consumption  at 
different  loads  was  as  follows  (figures  approximate,  from  the  chart) : 

Load,  Kw 2,000  4,000  5,000  6,000  6,500  7,000  7,900 

Steam  per  Kw.- 

hour,  Ib 15.5  13.75  13.50  13.20  13.00  13.10  13.30 

Total  steam  per 

hour,  Ib 31,000  55,000  67,500  79,000  85,000  91,500  105,000 

Up  to  a  load  of  6500  Kw.  the  total  consumption  is  9000  +  12  X 
Kw.  load,  nearly.  The  efficiency  ratio  on  the  Rankine  cycle  was  0.68 
at  6500  Kw. 

Comparison  of  Large  Turbines  and  Reciprocating  Engines. — Moyer 
gives  a  set  of  curves  of  the  steam  consumption  of  a  standard  5000-Kw. 
turbine  generator  and  a  4-cylinder  compound  reciprocating  steam- 
engine  generator,  assuming  both  units,  operating  under  the  same  con- 
ditions. The  following  figures  are  taken  from  the  curves: 

Load  in  Kilowatts 3000     4000     5000     6000     7000     7500 

Lb.  Steam  per  Kilowatt-hour. 
Turbine 16.0     15.5     15.315.25     15.4     15.5 

Reciprocating  engine: 

With  equal  work  in  cylinders.     18.0     17.4     17.8  19.0       20.8     22.0 
Unequal  work  in  cylinders. .      18 . 4     17 . 0     17 . 2  17 . 5       18.4     19.0 


EOTAHY   STEAM-ENGINES  —  STEAM  TTJEBINES.      1093 


Steam  Consumption  of  Small  Steam  Turbines.  —  Small  turbines, 
from  5  to  200  H.P.,  are  extensively  used  for  purposes  where  high  speed  of 
rotation  is  not  an  objection,  such  as  for  driving  electric  generators,  cen- 
trifugal fans,  etc.,  and  where  economy  of  fuel  is  not  as  important  as 
saving  of  space,  convenience  of  operation,  etc.  The  steam  consump- 
tion of  these  turbines  varies  as  greatly  as  does  that  of  small  high-speed 
steam-engines,  according  to  the  design,  speed,  etc.  A  paper  by  Geo.  A. 
Orrok  in  Trans.  A.  S.  M.  E.,  1909,  discusses  the  details  of  several  makes 
of  machines.  From  a  curve  presented  by  R.  H.  Rice  in  discussion  of 
this  paper  the  following  figures  are  taken  showing  the  steam  consumption 
in  Ibs.  per  B.H.P.-hour  of  different  makes  of  impulse  turbines. 


Type. 

Sturte- 
vant. 

Terry. 

Bliss. 

Bliss. 

Kerr. 

Curtis. 

Curtis. 

Rated  H.P  

20 

50 

100 

200 

150 

50 

200 

StolPufl°load.'; 

11  1/4  load.  .  . 

72 
65 
61 
58 

59 

49 

46 
44 

58 
48 
43 
40 

55 

47 
42 
39 

52 
44 
41 
39 

44 
36 
33 
31 

32 
30 

29 
28 

Dry  steam,  150  Ibs.  pressure;  atmospheric  exhaust. 

Mr.  Orrok  shows  that  the  steam  consumption  of  these  turbines  largely 
depends  on  their  peripheral  speed.     From  a  set  of  curves  plotted  with 
speed  as  the  base  it  appears  that  the  steam  consumption  per  B.H.P.-hour 
ranges  about  as  follows: 
Peripheral    speed,  ft. 

per  min 5,000        10,000        15,000        20,000       25,000 

Steam  per  B.H.P.-hour    45  to  70     38  to  60     31  to  52     29  to  45     29  to  40 

Low-Pressure  Steam  Turbines. — Turbines  designed  to  utilize  the  ex- 
haust steam  from  reciprocating  engines  are  used  to  some  extent.  For 
steam  at  or  below  atmospheric  pressure  the  turbine  has  a  great  advan- 
tage over  reciprocating  engines  in  its  ability  to  expand  the  steam  down 
to  the  vacuum  pressure,  while  a  reciprocating  condensing  engine  generally 
does  not  expand  below  8  or  10  Ibs.  absolute  pressure.  In  order  to  ex- 
pand to  lower  pressures  the  low-pressure  cylinder  would  have  to  be 
inordinately  large,  and  therefore  costly,  and  the  increased  loss  from 
cylinder  condensation  and  radiation  would  more  than  counterbalance 
the  gain  due  to  greater  expansion. 

Mr.  Parsons  (Proc.  Inst.  Nav.  Arch.,  1908)  gives  the  following  figures 
showing  that  the  theoretical  economy  of  the  combination  of  a  recipro- 
cating engine  and  an  exhaust  steam  turbine  is  about  the  same  whether 
the  turbine  receives  its  steam  at  atmospheric  pressure  or  at  7  Ibs.  abso- 
lute, the  initial  steam  pressure  in  the  engine  being  200  Ibs.  absolute  and 
the  vacuum  28  ins. 

Back  pressure  of  engines,  Ibs.  abs 16  131/2      8 

Initial  pressure,  turbine,  Ibs.  abs 15  121/2     7 

'in  engine 178         189      218 

in  turbine 142  .      131      100 

total 320         320      318 

The  following  figures,  by  the  General  Electric  Co.,  show  the  percentage 
over  the  output  of  a  condensing  reciprocating  engine  that  may  be  made 
by  installing  a  low-pressure  turbine  between  the  engine  and  the  con- 
denser, the  vacuum  being  281/2  ins. 
Inches  vacuum  at  admission 

valve 0  4  8          12         16         20       24 

PC*  cent  of  work  gained  ...      26.1     26.5     26.8     26.3     25.3     23.6     20 

It  appears  that  a  well-designed  reciprocating  compound  engine  work- 
ing down  to  about  atmospheric  pressure  is  a  more  efficient  machine  than 
a  turbine  with  the  same  terminal  pressure,  and  that  between  the  atmos- 
phere and  the  condenser  pressure  the  turbine  is  far  more  economical; 
therefore  a  combination  of  an  engine  and  a  turbine  can  be  designed 
which  will  give  higher  economy  than  either  an  engine  or  a  turbine  work- 
ing through  the  whole  range  of  pressure. 


B.T.U. 

utilized  per  Ib.  of  steam 


1094  THE   STEAM-ENGINE. 

When  engines  are  run  intermittently,  such  as  rolling-mill  and  hoisting 
engines,  their  exhaust  steam  may  be  made  to  run  low-pressure  turbines 
by  passing  it  first  into  a  heat  accumulator,  or  thermal  storage  system, 
where  it  gives  up  its  heat  to  water,  the  latter  furnishing  steam  continu- 
ously to  the  turbines.  (See  Thermal  Storage,  pages  927  and  1014.) 

The  following  results  of  tests  of  a  Westinghouse  low-pressure  turbine 
are  reported  by  Francis  Hodgkinson. 


Steam  press.. 

Ib.  abs 

17.4 

12.4 

11.8 

7.7 

5 

.2 

11.6 

8.7 

6.1 

4.5 

Vacuum, 

ins. 

26.0 

26.0 

27.0 

27.0 

27. 

.0 

27.8 

28.0 

27.9 

28.0 

Brake  H 

.P.. 

920 

472 

592 

321 

102 

586 

458 

234 

114 

Steam      per 
B.H.P.-hr., 

Ibs 

27.9 

37.1 

29.9 

37.3 

64, 

4 

28.0 

30.4 

38.6 

54.8 

Tests  of  a  1000-K.W.  low-pressure  double-flow  Westinghouse  turbine 
are  reported  to  have  given  results  as 'follows.  (Approximate  figures, 
from  a  curve.) 

Load,  Brake  H.P 200     400     600     800     1000     1200     1500     2000 

Pressure  at  inlet,  Ibs. 

abs....- 4.1     5.1     6.1     7.2      8.3        9.4     11.0     13.5 

Steam  per   )  2?1/2  in  yac>    ?5   4?  5       3g       33       3Q       2g         26 . 5     24 . 5 

hour  Ibs  )  28  in' vac'      62      42        33       29       27        25.5     24.5     22.5 

The  total  steam  consumption  per  hour  followed  the  Wilians  law, 
being  directly  proportional  to  the  power  after  adding  a  constant  for 
0  load,  viz.:  for  27i/2-in.  vacuum  the  total  steam  consumption  per  hour 
was  12,000  Ibs.  +  18  X  H.P.,  and  for  28-in.  vacuum,  9000  Ibs.  +  18  X 
H.P.  (approx.). 

The  guaranteed  steam  consumption  of  a  7000-K.W.  Rateau-Smoot 
low-pressure  turbine  generator  is  given  in  a  curve  by  R.  C.  Smoot  (Power, 
June  22,  1909),  from  which  the  following  figures  are  taken.  The  admis- 
sion pressure  is  taken  at  16  Ibs.  absolute  and  the  vacuum  281/2  ins. 

K.W.  output 1500     2000     3000     4000     5000     6000     7000 

Steam  per  K.W.-hr.,  Ib..  ..       40         37     32.5     29.5     27.6     26.2     25.7 
Over-all  efficiency,  % 43         47         54         60         65         68         70 

The  performance  of  a  combined  plant  of  several  reciprocating  2000- 
K.W.  engines  and  a  7000-K.W.  low-pressure  turbine  is  estimated  as  fol- 
lows, the  engines  expanding  the  steam  from  215  to"16  Ibs.  absolute,  and 
the  turbines  from  16  Ibs.  to  0.75  Ib.,  the  vacuum  being  28.5  ins.  with 
the  barometer  at  30  ins. 

Engine.     Turbine. 

Theoretical  steam  per  K.W.-hour,  Ibs 18  17.8 

Steam  per  K.W.-hr.  at  switchboard,  Ibs 27.7        26.6 

Combined  efficiency  of  engine  and  dynamo,  per  cent ...  65  67 

Steam   per  K.W.-hour  for  combined   plant  =  1  -i-  (1/27.7  4-  1/26.6)  = 

13.6  Ibs. 

The  combined  efficiency  is  66%,  representing  the  ratio  of  the  energy 
at  the  switchboard  to  the  available  energy  of  the  steam  delivered  to  the 
engine  and  expanded  down  to  the  condenser  pressure,  after  allowing  for 
all  losses  in  engine,  turbine,  and  dynamo. 

Very  little  difference  is  made  in  the  plant  efficiency  if  the  intermediate 
pressure  is  taken  anywhere  from  3  or  4  Ibs.  below  atmosphere  to  15  or 
20  Ibs.  above. 

M.  B.  Carroll  (Gen.  Elec.  Rev.,  1909)  gives  an  estimate  of  the  steam 
consumption  of  a  combined  unit  of  a  1000-K.W.  engine  and  a  low-pres- 
sure turbine.  The  engine,  non-condensing,  will  develop  1000  H.P., 
with  32,000  Ibs.  of  steam  per  hour.  Allowing  8%  for  moisture  in  the 
exhaust,  29,440  Ibs.  of  dry  steam  will  be  available  for  the  turbine,  which 
at  33  Ibs.  per  K.W.-hour  will  develop  893  K.W.,  making  a  total  output  of 
1893  K.W.  for  32,000  Ibs.  steam,  or  16.9  Ibs.  per  K.W.-hour.  The  engine 
alone  as  a  condensing  engine  will  develop  1320  K.W.  at  24.2  Ibs.  per  K.W.- 
hour.  The  combined  unit  therefore  develops  573  K.W.,  or  43.5%  more 
than  the  condensing  engine  using  the  same  amount  of  steam.  The 
maximum  capacity  of  the  engine,  non-condensing,  is  1265  K.W.,  an<i 
condensing,  1470  K...W,,  and  of  the  combined  unit  2500  K.W. 


INTERNAL-COMBUSTION   ENGINES.  1095 

Tests  of  a  15,000  K.W.  Steam-Engine-Turbine  Unit  are  reported 
by  H.  G.  Stott  and  R.  J.  S.  Pigott  in  Jour.  A.S.M.E.,  Mar.,  1910.  The 
steam-engine  is  one  of  the  7500  K.W.  Manhattan  type  engines  at  the  59th 
St.  station  of  the  Rapid  Transit  Co.,  New  York,  with  two  42-in.  horizontal 
h.p.  and  two  86-in.  vertical  l.p.  cylinders,  and  the  turbine,  also  7500  K.W., 
is  of  the  vertical  three-stage  impulse  type.  The  principal  results  are  sum-, 
marized  as  follows:  An  increase  of  100%  in  the  maximum  capacity  and 
146%  in  the  economical  capacity  of  the  plant;  a  saving  of  about  85%  of 
the  condensed  steam  for  return  to  the  boilers  [it  was  previously  wasted]; 
an  average  improvement  in  economy  of  13%  over  the  best  high-pressure 
turbine  results,  and  of  2.5%  (between  7500  and  15,000  K.W.)  over  the  re- 
sults obtained  by  the  engine  alone;  an  average  thermal  efficiency  between 
6500  and  15,500  K.W.  of  20.6%.  [This  efficiency  is  not  quite  equal  to 
that  reached  by  triple-expansion  pumping  engines.  See  page  806.] 

Reduction  Gear  for  Steam  Turbines. — Double  spiral  reduction  gears, 
usually  of  a  ratio  of  1  to  10,  are  used  with  the  DeLaval  turbine  to  obtain 
a  velocity  of  rotation  suitable  for  dynamos,  centrifugal  pumps,  etc.  G.  W. 
Melville  and  J.  H.  McAIpine  have  designed  a  similar  gear,  with  the  pinion 
carried  in  a  floating  frame  supported  at  a  single  point  between  the  bear- 
ings to  equalize  the  strain  on  the  gear  teeth,  for  reducing  the  speed  of 
large  horizontal  turbines  to  suitable  speeds  for  marine  propellers.  A 
6000  H.P.  gear  with  reduction  from  1500  to  300  r.p.m.  has  given  an  effi- 
ciency of  98.5%  (Eng'g,  Sept.  17;  Eng.  News,  Oct.  21  and  Dec.  30,  1909). 

The  Fottinger  Transformer  or  Hydraulic  Pinion  is  an  apparatus  for 
reducing  the  speed  of  a  propeller  shaft  below  the  speed  of  the  steam- 
turbine  shaft.  It  consists  of  a  turbine  wheel  9r  water  motor,  mounted 
on  the  end  of  the  propeller  shaft,  and  a  centrifugal  pump  mounted  on 
the  shaft  of  the  steam  turbine.  The  water  is  delivered  by  the  pump 
to  the  motor  and  from  the  motor  it  passes  to  a  tank  and  thence  to  the 
inlet  of  the  pump.  The  ratio  of  reduction  is  determined  by  the  design 
of  the  turbine  and  pump.  The  ratios  hitherto  applied  range  from  1.2:1 
to  6:1.  Reversing  is  accomplished  by  means  of  a  second  turbine  on 
the  propeller  shaft,  a  valve  directing  the  water  to  either  the  ahead  or 
astern  turbine  as  required.  Hydraulic  pinions  transmitting  10,000 
shaft  horse-power  have  shown  an  over-all  efficiency  of  about  92  per  cent. 
An  illustrated  description  will  be  found  in  Engineering  of  Sept.  25,  1914. 

HOT-AIR  ENGINES. 

Hot-air  (or  Caloric)  Engines. — Hot-air  engines  are  used  to  some 
extent,  but  their  bulk  is  enormous  compared  with  their  effective  power. 
For  an  account  of  the  largest  hot-air  engine  ever  built  (a  total  failure)  see 
Church's  Life  of  Ericsson.  For  theoretical  investigation,  see  Rankin'3 
Steam-engine  and  Roentgen's  Thermodynamics.  For  description  of  con- 
structions, see  Appleton's  Cyc.  of  Mechanics  and  Modern  Mechanism,  and 
Babcock  on  Substitutes  for  Steam,  Trans.  A.  S.  M.  E.,  vii,  p.  693. 

Test  of  a  Hot-air  Engine  (Robinson). — A  vertical  double-cylinder 
(Caloric  Engine  Co.'s)  12  nominal  H.P.  engine  gave  20.19  I. H.P.  in  the 
working  cylinder  and  11.38  I. H.P.  in  the  pump,  leaving  8.81  net  I.H.P.; 
while  the  effective  brake  H.P.  was  5.9,  giving  a  mechanical  efficiency  of 
67%.  Consumption _of.  coke,  3.7  Ibs.  per  brake.  H.P.  per  hour.  Mean 
pressure  on  pistons  15.37  Ibs.  per  square  inch,  and  in  pumps  15.9  Ibs.,  the 
area  of  working  cylinders  being  twice  that  of  the  pumps.  The  air  was 
supplied  about  1160°  F.  and  rejected  at  end  of  stroke  about  890°  F. 

INTERNAL-COMBUSTION  ENGINES. 

References.— For  theory  of  the  internal-combustion  engine,  see 
paper  by  Dugald  Clerk,  Proc.  Inst.  C.  E.,  1882,  vol.  Ixix;  and  Van 
Nostrand's  Science  Series,  No.  62.  See  also  Wood's  Thermodynamics; 
Standard  works  on  gas-engines  are  "  A  Text-book  on  Gas,  Air,  and  Oil 
Engines,"  by  Bryan  Donkin;  "The  Gas  and  Oil  Engine,"  by  Dugald 
Clerk;  "Internal  Combustion  Engines,"  by  Carpenter  and  Diederichs; 
"  Gas  Engine  Design,"  by  C.  E.  Lucke;  "Gas  and  Petroleum  Engines," 
by  W.  Robinson;  "The  Modern  Gas  Engine  and  the  Gas  Producer,"  by 
A.  M.  Levin,  and  "The  Gas  Engine,"  by  C.  P.  Poole. r*  For  prac- 
tical operation  cf  gas  and  oil  engines,  see  "The  Gas  Engine,  by 
F.  {I,  Jones,  and  "Tlie  Gas  Engine  Handbook,"  by  £,  w, 


1096  INTERNAL-COMBUSTION    ENGINES. 

For  descriptions  of  large  gas-engines  using  blast  furnace  gas  see  papers 
in  Proc.  Iron  and  Steel  Inst.,  1906,  and  Trans.  A.  I.  M.  E.,  1906.  Many 
papers  on  gas-engines  are  in  Trans.  A.8.M.E.,  1905  to  1909. 

An  Internal-combustion  Engine  is  an  engine  in  which  combustible 
gas,  vapor,  or  oil  is  burned  in  a  cylinder,  generating  a  high  temperature 
and  high  pressure  in  the  gases  of  combustion,  which  expand  behind  a 
piston,  driving  it  forward.  ^Rotary  gas-engines  or  gas  turbines,  are  still, 
1915,  in  the  experimental  stage.) 

Four-cycle  and  Two-cycle  Gas-Engines. — In  the  ordinary  type  of 
single-cylinder  gas-engine  (for  example  the  Otto)  known  as  a  four-cycle 
engine,  one  ignition  of  gas  takes  place  in  one  end  of  the  cylinder  every 
two  revolutions  of  the  fly-wheel,  or  every  two  double  strokes.  The  fol- 
lowing sequence  of  operations  takes  place  during  four  consecutive  strokes: 
(a)  inspiration  of  a  mixture  of  gas  and  air  during  an  entire  stroke;  (6) 
compression  during  the  second  (return)  stroke;  (c)  ignition  at  or  near  the 
dead-point,  and  expansion  during  the  third  stroke;  (d)  expulsion  of  the 
burned  gas  during  the  fourth  (return)  stroke.  Beau  de  Rochas  in  1862 
laid  down  the  law  that  there  are  four  conditions  necessary  to  realize  the 
best  results  from  the  elastic  force  of  gas:  (1)  The  cylinders  should  have 
the  greatest  capacity  with  the  smallest  circumferential  surface;  (2)  the 
speed  should  be  as  high  as  possible;  (3)  the  cut-off  should  be  as  early  as 
possible;  (4)  the  initial  pressure  should  be  as  high  as  possible. 

(Strictly  speaking  four-cycle  should  be  called  four-stroke-cycle,  but  the 
term  four-cycle  is  generally  used  in  the  trade.) 

The  two  great  sources  of  waste  in  gas-engines  are:  1.  The  high  tempera- 
ture of  the  rejected  products  of  combustion;  2.  Loss  of  heat  through  the 
cylinder  walls  to  the  water-jacket.  As  the  temperature  of  the  water- 
jacket  is  increased  the  efficiency  of  the  engine  becomes  higher. 

Fig.  178  is  an  indicator  diagram  of  a  four-cycle  gas-engine.     AB,  the 
lower  line,  shows  the  admission  of  the  mixture,  at  a  pressure  slightly 
below  the  atmosphere  on  account  of  the  re- 
sistance of  the  inlet  valve,  EC  is  the  com- 
pression into   the  clearance  space,  ignition 
taking   place   at  C    and    combustion  with 
increase  of  pressure  continuing  from  C  to  D. 
The  gradual  termination  of  the  combustion 
is  shown  by  the  rounded  corner  at  D.    DE 
is  the  expansion  line,  EF  the  line  of  pressure 
drop  as  the  exhaust  valve  opens,  and  FA  the 
w  p  line  of  expulsion  of  the  burned  gases,  the 
— *  ^     pressure   being  slightly  above   the  atmos- 
A  T?T^  i  no  B  phere  on  account  of   the  resistance  of   the 

*IG'178>  exhaust  valve. 

In  a  two-cycle  single-acting  engine  an  explosion  takes  place  with  every 
revolution,  or  with  each  forward  stroke  of  the  piston.  Referring  to  the 
diagram  Fig.  178  and  beginning  at  E,  when  the  exhaust  port  begins  to 
open  to  allow  the  burned  gases  to  escape,  the  pressure  drops  rapidly  to  F. 
Before  the  end  of  the  stroke  is  reached  an  inlet  port  opens,  admitting 
a  mixture  of  gas  and  air  from  a  reservoir  in  which  it  has  been  compressed. 
This  mixture  being  under  pressure  assists  in  driving  the  burned  gases 
out  through  the  exhaust  port.  The  inlet  port  and  the  exhaust  port  close 
early  in  the  return  stroke,  and  during  the  remainder  of  the  stroke  BC 
the  mixture,  which  may  include  some  of  the  burned  gas,  is  compressed  and 
the  ignition  takes  place  at  C,  as  in  the  four-cycle  engine. 

In  one  form  of  the  two-cycle  engine  only  compressed  air  is  admitted 
while  the  exhaust  port  is  open,  the  fuel  gas  being  admitted  under  pressure 
after  the  exhaust  port  is  closed.  By  this  means  a  greater  proportion  ol 
the  burned  gases  are  swept  out  of  the  cylinder.  This  operation  is  known 
as  "  scavenging." 

Theoretical  Pressures  and  Temperatures  in  Gas-Engines. — Referring 
to  Fig.  178,  let  Ps  be  the  absolute  pressure  at  B,  the  end  of  the  suction 
stroke,  Pc  the  pressure  at  C,  the  end  of  the  compression  stroke;  P^the 
maximum  pressure  at  D,  when  the  gases  of  combustion  are  at  their 
highest  temperature;  Pe  the  pressure  at  E,  when  the  exhaust  valve  begii 
to  open  For  the  hypothetical  case  of  a  cylinder  with  walls  incapable  of 
absorbing  or  conducting  heat,  and  of  perfect  and  instantaneous  combustion 


INTEKNAL  COMBUSTION   ENGINES.  lOlJ? 

or  explosion  of  the  fuel,  ail  ideal  diagram  might  be  constructed  which 
would  have  the  following  characteristics.  In  a  four-cycle  engine  receiv- 
ing a  charge  of  air  and  gas  at  atmospheric  pressure  and  temperature, 
the  pressure  at  B,  or  Ps,  would  be  14.7  Ibs.  per  sq.  in.  absolute,  and  the 
temperature  say  62°  F.f  or  522°  absolute.  The  pressure  at  C,  or  Pc,  would 
depend  on  the  ratio  Vt  -i-  Vz,  V\  being  the  original  volume  of  the  mixture 
in  the  cylinder  before  compression,  or  the  piston  displacement  plus  the 
volume  of  the  clearance  space,  and  Vz  the  volume  after  compression,  or 
the  clearance  volume,  and  its  value  would  be  Pc  =  Ps  (Vi/Vz)n.  The 
absolute  temperature  at  the  end  of  compression  would  be  Tc  =  522  X 
( IV  F2)n~\  or  it  may  be  found  from  the  formula  PSF5-H  Ts  =  PCVC  +  Tc, 
the  subscripts  s  and  c  referring  respectively  to  conditions  at  the  beginning 
and  end  of  compression.  The  compression  would  be  adiabatic,  and  the 
value  of  the  exponent  n  would  be  about  the  value  for  air,  or  1.406.  The 
work  done  in  compressing  the  mixture  would  be  calculated  by  the  formula 
for  compressed  air  (see  page  634).  The  theoretical  rise  of  tempera- 
ture at  the  end  of  the  explosion,  Tx,  above  the  temperature  at  the  end  of 
the  compression  Tc  may  be  found  from  the  formula  (Tx  -  Tc)  Cv  =  H, 
in  which  //  is  the  amount  of  heat  in  British  thermal  units  generated  by 
the  combustion  of  the  fuel  in  1  Ib.  of  the  mixture,  and  Cv  the  mean  specific 
heat,  at  constant  volume,  of  the  gases  of  combustion  between  the  tem- 
peratures Tx  and  Tc.  Having  obtained  the  temperature,  the  correspond- 

n 

Ing  pressure  Px  may  be  found  from  the  formulaP^  =  PCX  (Tx/Tc}n~'i. 
In  like  manner  the  pressure  and  temperature  at  the  end  of  expansion, 
Pe  and  Te,  and  the  work  done  during  expansion,  may  be  calculated  by 
the  formula  for  adiabatic  expansion  of  air. 

The  ideal  diagram  of  the  adiabatic  compression  of  air,  instantaneous 
heating,  and  adiabatic  expansion,  differs  greatly  from  the  actual  diagram 
of  a  gas-engine,  and  the  pressures,  temperatures,  and  amount  of  work 
done  are  different  from  those  obtained  by  the  method  described  above. 
In  the  first  place  the  mixture  at  the  beginning  of  the  compression  stroke 
is  usually  below  atmospheric  pressure,  on  account  of  the  resistance  of 
the  inlet  valve,  in  a  four-cycle  engine,  but  may  be  above  atmospheric 
pressure  in  a  two-cycle  engine,  in  which  the  mixture  is  delivered  from  a 
receiver  under  pressure.  Then  the  temperature  is  much  higher  than 
that  of  the  atmosphere,  since  it  is  heated  by  the  walls  of  the  cylinder 
as  it  enters.  The  compression  is  not  adiabatic,  since  heat  is  received 
from  the  walls  during  the  first  part  of  the  stroke.  If  the  clearance  space 
is  small  and  the  pressure  and  temperature  at  the  end  of  compression  there- 
fore high,  the  gas  may  give  up  some  heat  to  the  walls  during  the  latter 
part  of  the  stroke.  The  explosion  is  not  instantaneous,  and  during  its 
continuance  heat  is  absorbed  by  the  cylinder  walls,  and  therefore  neither 
the  temperature  nor  the  pressure  found  by  calculation  will  be  actually 
reached.  Poole  states  that  the  rise  in  temperature  produced  by  com- 
bustion is  from  0.4  to  0.7  of  what  it  would  be  with  instantaneous  com- 
bustion and  no  heat  loss  to  the  cylinder  walls.  Finally  the  expansion 
is  not  adiabatic,  as  the  gases  of  combustion,  at  least  during  the  first  part 
of  the  expanding  stroke,  are  giving  up  heat  to  the  cylinder. 

Calculation  of  the  Power  of  Gas-Engines.—  If  the  mean  effective  pres- 
sure in  a  gas-engine  cylinder  be  obtained  from  an  indicator  diagram,  its 
power  is  found  by  the  usual  formula  for  steam-engines,  H.P.  =  PLAN  + 
33,000,  in  which  P  is  the  mean  effective  pressure  in  Ibs.  per  sq.  in.,  L  the 
length  of  stroke  in  feet,  A  the  area  of  the  piston  in  square  inches,  and  N 
the  number  of  explosion  strokes  per  minute. 

For  purposes  of  design,  however,  the  mean  effective  pressure  either 
has  to  be  assumed  from  a  knowledge  of  that  found  in  other  engines  of 
the  same  type  and  working  under  the  same  conditions  as  those  of  the 
design,  or  it  may  be  calculated  from  the  ideal  air  diagram  and  modified 
by  the  use  of  -a  coefficient  or  diagram  factor  depending  on  the  kind  of 
fuel  used  and  the  compression  pressure.  Lucke  gives  the  following 


1098 


INTEKNALr-COMBUSTtON   ENGINES. 


factors  for  four-cycle  engines  by  which  the  mean  effective  pressure 
of  a  theoretical  air  diagram  is  to  be  multiplied  to  obtain  the  actual  M.E.P. 
for  the  several  conditions  named. 


Kind  of  Fuel  and  Method  of  Use. 

Compres- 
sion. 
Gauge 
Pressure. 

Factor. 
Per  Cent- 

Kerosene  when  previously  vaporized 

Lb. 
45-75 

30-40 

Kerosene  injected  on  a  hot  bulb  may  be  as  low  as 

20 

Gasoline  used  in  carburetor  requiring  a  vacuum 

25-40 

Gasoline  with  but  little  initial  vacuum.  

80-130 

50-30 

Producer  gas     

100-160 

56-40 

Coal  gas                                                                      . 

Av.  80 

Av.  45 

Blast-furnace  gas             •        

130-180 

48-30 

Natural  gas.  

90-140 

52-40 

Factors  for  two-cycle  engines  are  about  O.S  those  for  four-cycle  engines. 

Pressures  and  Temperatures  at  end  of  Compression  and  at  Re- 
lease.—  The  following  tables,  greatly  condensed  from  very  full  tables 
given  by  C.  P.  Poole,  show  approximately  the  pressures  and  tempera- 
tures that  may  be  realized  in  practice  under  different  conditions.  Poole 
says  that  the  value  of  n,  the  exponent  in  the  formula  for  compression, 
ranges  from  1.2  to  1.38,  these  being  extreme  cases;  the  values  most 
commonly  obtained  are  from  1.28  to  1.35.  The  tables  for  compression 
pressures  and  temperatures  are  based  on  n  =  1.3  and  1.4,  on  compres- 
sion ratios  or  Vi/Va  from  3  to  8,  on  absolute  pressures  in  the  cylinder 
before  compression  from  13  to  16  Ibs.,  and  on  absolute  temperatures 
before  compression  of  620°  to  780°  (160°  to  320°  F.).  The  release  pres- 
sures and  temperatures  are  based  on  values  of  n  of  1.29  and  1.32,  abso- 
lute pressures  at  the  end  of  the  explosion  from  240  to  360  Ibs.  per  sq.  in., 
and  absolute  temperatures  at  the  end  of  the  explosion  of  1800°  to  3000°  F. 

COMPRESSION  PRESSURES. 


sd*f 

n=  1.3. 

I  C   n° 

n=  1.34. 

a  o.2 

o    oi 

0 

Ps=13 

13.5 

14 

15 

16 

J"tf 

Ps=13 

13.5 

,4 

15 

16 

3.00 

54.2 

56.3 

58.4 

62.6 

66.7 

3.00 

56.7 

58.9 

61.0 

65.4 

69.7 

4.00 

78.8 

81.9 

84  9 

90.9 

97.0 

4.00 

83.3 

86.5 

89  7 

96.1 

102.5 

5.00 

105.4 

109.4 

113,5 

121.6 

129.7 

5.00 

112.3 

116.7 

121.0 

129.6 

138.3 

6.00 

133.5 

138.7 

143.8 

154.1 

164.3 

6.00 

143.4 

148.9 

154.5 

165.5 

176.5 

7.00 

163.2 

169.4 

175  7 

188.3 

200.8 

7.00 

176.3 

183.1 

189.9 

203.5 

217.0 

8.00 

194.0 

201.5 

209.0 

223.9 

238.7 

8.00 

210.9 

219.0 

227.1 

243.4 

259.6 

COMPRESSION  TEMPERATURES. 


Compres- 
sion 
Ratio  rc. 

n  =  1.3, 

Compres- 
sion 
Ratio  rc. 

n=1.34. 

T 

1  s 

620° 

660° 

700° 

740° 

780° 

Ts= 
620° 

901 
993 
1072 
1140 
1201 
1257 

660° 

959 
1057 
1141 
1214 
1279 
1338 

700° 

740° 

780° 

1133 
1250 
1348 
1434 
1512 
1582 

3.00 
4.00 
5.00 
6.00 
7.00 
8.00 

862 
940 
1005 
1061 
1112 
1157 

918 
1000 
1070 
1130 
1183 
1232 

973 
1061 
1134 
1198 
1255 
1306 

1029 
1122 
1199 
1267 
1327 
1381 

1084 
1182 
1264 
1335 
1398 
1456 

3.00 
4.00 
5.00 
6.00 
7.00 
8.00 

1017 
1122 
1210 
1287 
1357 
1420 

1075 
1186 
1279 
1361 
1434 
1501 

INTERNAL-COMBUSTION   ENGINES. 


1009 


ABSOLUTE  PRESSURES  PER  SQUARE  INCH  AT  RELEASE. 
Corresponding  to  Explosion  Pressures  commonly  obtained. 
NOTE: — The  expansipn  ratios  in  the  left-hand  column  are  based  on 
the  volume  behind  the  piston  when  the  exhaust  valve  begins  to  open. 


"w  *••* 

ne=1.29. 

a 
_o  ^ 

n.-IJ2. 

K  "^ 

Value  of  Pa- 

a-| 

Value  of  Px 

p4« 

240      270       300       330       360 

&# 

240       270        300       330       360 

3.00 

58.2 

65.4 

72.7 

80.0 

87.2 

3  00 

56.3 

63  3 

70.4 

77.4 

84.4 

4.00 

40.1 

45.2 

50.2 

55.2 

60.2 

4.00 

38.5 

43.3 

48.1 

52.9 

57.8 

5.00 

30.1 

33.9 

37.6 

41.4 

45.1 

5  00 

28.7 

32.3 

35.8 

39.4 

43.0 

6.00 

23.8 

26.8 

29.7 

32.7 

35.7 

6.00 

22.5 

25.4 

28.2 

31.0 

33.8 

7.00 

19.5 

21.9 

24.4 

26.8 

29.2 

7  00 

18.4 

20.7 

23.0 

25.3 

27.6 

8.00 

16.4 

18.5 

20.5 

22.6 

24.6 

8.00 

15.4 

17.3 

19.3 

21.2 

23.1 

ABSOLUTE  TEMPERATURES  AT  RELEASE. 
Corresponding  to  Explosion  Temperatures  commonly  obtained. 


Expansion 
Ratio  re. 

ne=1.29. 

Expansion 
Ratio  re. 

ne=1.32. 

Value  of  Tx 
1800  2100   2400  2700  3000 

Value  of  Tx 
1800   2100  2400  2700  3000 

3  00 
4.00 
5.00 
6.00 
7.00 
8.00 

1309 
1204 
1129 
1070 
1024 
985 

1527 
1405 
1317 
1249 
1194 
1149 

1745 
1606 
1505 
1427 
1365 
1313 

1963 
1806 
1693 
1606 
1536 
1477 

2182 
2007 
1881 
1784 
1706 
1641 

3.00 
4.00 
5.00 
6.00 
7.00 
8.00 

1266 
1155 
1075 
1015 
966 
925 

1478 
1348 
1255 
1184 
1127 
1079 

1689 
1540 
1434 
1353 
1288 
1234 

1900 
1733 
1613 
1522 
1449 
1388 

2111 
1925 
1792 
1691 
1610 
1542 

Pressures  and  Temperatures  after  Combustion.  —  According  to 
Poole,  the  maximum  temperature  after  combustion  may  be  as  high  as 
3000°  absolute,  F.,  and  the  maximum  pressure  as  high  as  400  Ibs.  per 
sq.  in.  absolute;  these  are  high  figures,  however,  the  more  usual  figures 
being  about  2300°  and  250  Ibs.  Poole  gives  the  following  figures  for 
the  average  rise  in  pressure,  above  the  pressure  at  the  end  of  compres- 
sion, produced  by  combustion  of  different  fuels,  with  different  ratios  of 
compression. 

AVERAGE  PRESSURE  RISE  IN  LBS.  PER  SQ.  IN.  PRODUCED  BY 
COMBUSTION. 


4 
A 

d 

1 

Ilium.  Gas 
650B.T.U.* 

Gasoline. 

o 

0> 

M 

4 

3 

d 
1 

Natural  Gas 
1000  B.T.U.* 

to 

eg 
K 

d 

1 

Producer  Gas 
150B.T.U.* 

.2 

I 

d 
1 

Blast-Furnace 
Gas 
100  B.T.U.* 

4.0 
4.2 
4.4 
4.6 
4.8 
5.0 

146 
156 
166 
175 
185 
195 

195 
208 
221 
234 
247 
260 

168 
179 
190 
202 
213 
224 

5.0 
5.2 
5.4 
5.6 
5.8 
6.0 

192 
202 
211 
221 
230 
240 

6.0 
6.2 
6.4 
6.6 
6.8 
7.0 

225 
234 
243 
252 
261 
270 

7.0 
7.2 
7.4 
7.6 
7.8 
8.0 

211 

218 
225 
232 
239 
246 

*  Per  cubic  foot  measured  at  32°  F. 
The  following  figures  are  given    by  Poole  as  a  rough  approximate 
ide  to  the  mean  effective  pressures  iu  Ibs.  per  sq.  in.  obtained  with 


1100 


INTERNAL-COMBUSTION  ENGINES. 


different  fuels  and  different  compression  pressures  in  a  four-cycle  engine. 
In  a  two-cycle  engine  the  mean  effective  pressure  of  the  pump  diagram 
should  be  subtracted.  The  delivery  pressure  is  usually  from  4  to  8  Ibs. 
per  sq.  in.  above  the  atmosphere,  and  the  corresponding  mean  effective 
pressure  of  the  pump  about  3.8  to  7. 

PROBABLE  MEAN  EFFECTIVE  PRESSURE. 


SUCTION  ANTHRACITE  PRODUCER  GAS. 

MOND  PRODUCER  GAS. 

Engine 

Compression  Pressure, 
abs.  Ibs.  per  sq.  in. 

Engine 
H.P. 

Compression  Pressure. 

too 

115 

130 

145 

160 

100 

115 

130 

145 

160 

10 
25 
50 
100 
250 
500 

55 
60 
65 
70 
75 
80 

60 
65 
70 
75 
80 
85 

65 

70 
75 

80 
85 
90 

75 
80 
85 
90 
90 

80 
85 
90 
90 

10 
25 
50 
100 
250 
500 

60 
65 
65 
70 
75 

65 
65 
70 
70 
75 
80 

65 
65 
70 

75 
80 
85 

65 

70 
75 
80 
85 
90 

75 
80 
85 
90 
90 

NATURAL  AND  ILLUMINATING  GASES. 


Engine 

Compression  Pressure. 

Engine 
H.P. 

Compression  Pressures. 

65 

75 

85 

100 

115 

75 

85 

100 

115 

130 

10 
25 
50 

60 
65 
70 

65 
70 
75 

70 
75 
80 

75 
80 
90 

85* 
90 

100 
250 
500 

80 
85 

85 
90 
95 

90 
95 
100 

95 
100 
105 

100 
105 
110 

KEROSENE  SPRAY. 

GASOLINE  VAPOR. 

Engine 
H.P. 

^ 

Compression  Pressures. 

Engine 
H.P. 

Compression  Pressures. 

65 

75 

85 

100 

115 

65 

70 
75 
80 
85 

75 

85 

80 
85 
90 
95 

100 

85 
90 
90 
95 



5 

10 
25 
50 

50 
55 
60 
65 

55 
60 
65 
70 

60 
65 
70 
75 

65 
70 
75 
80 

70 
75 
80 
85 

5 

10 
25 
50 

75 
80 
85 
90 

Sizes  of  Large  Gas  Engines.  —  From  a  table  of  sizes  of  the  Nu'rnberg 
gas  engine,  as  built  by  the  Allis-Chalmers  Co.,  the  following  figures  are 
taken.  These  figures  relate  to  two-cylinder  tandem  double-acting  engines. 


Diam.  cyl.,  ins  
Stroke  cyl.,  ins  
Revs,  per  min  

18 
24 
150 

20 
24 
150 

21 
30 
125 

22 
30 
125 

24 

30 
125 

24 
36 
115 

26 
36 
115 

28 
36 
115 

30 
42 
100 

32 
42 
100 

Piston  speed,  ft.  per 
min  

600 

600 

625 

625 

625 

690 

690 

690 

700 

700 

Rated  B.H.P  

260 

320 

370 

405 

490 

545 

630 

740 

855 

985 

Factor  C  

Diam.,  ins  
Stroke,  ins  

0.8 

34 

42 

0.8 

36 
48 

0.84 

38 
48 

0.84 

40 

48 

0.85 

42 
54 

0.95 

44 

54 

0.93 

46 
54 

0.94 

48 
60 

0.95 

50 
60 

0.96 

52 
62 

Revs,  per  min    . 

100 

92 

92 

92 

86 

86 

86 

78 

78 

78 

Piston  speed... 

700 

736 

736 

736 

774 

774 

774 

780 

780 

780 

Rated  B.H  P. 

1105 

1300 

1460 

1630 

1875 

2080 

2280 

2475 

2720 

2950 

Factor  C... 

0.96 

1 

1.01 

1.02 

1.0ft 

1.07 

1  08 

1.07 

1.09 

1  Oft 

The  figures  "factor  C"  are  the  values  of  C  in  the  equation  B.H.P.  = 
C  X  -D2,  in  which  D  =  diam.  of  cylinder  in  ins.  For  twin-cylinder  double- 
acting  engines,  multiply  the  B.H.P.  and  the  value  of  C  by  0.95;  for  twin- 


INTEKNAL-COMBTISTION  ENGINES. 


,1101 


tandem  double-acting  engines,  multiply  by  2;  for  two-cylinder  single- 
acting,  or  for  single-cylinder  double-acting  engines,  divide  by  2;  for 
single-acting  single-cylinders,  divide  by  4.  The  figures  for  B.H.P.  corre- 
spond to  mean  effective  pressures  of  about  66,  68,  and  70  Ibs.  per  sq.  in. 
for  20,  40,  and  50  in.  cylinders  respectively  if  we  assume  0.85  as  the  me- 
chanical efficiency,  or  the  ratio  B.H.P.  •*•  I.H.P. 

.Engine  Constants  for  Gas  Engines.  —  The  following  constants  for 
figuring  the  brake  H.P.  of  gas  engines  are  given  in  Power,  Dec.  7,  1909. 
They  refer  to  four-stroke  cycle  single-cylinder  engines,  single  acting;  for 
double-acting  engines  multiply  by  2.  Producer  gas,  0.000056.  Illumi- 
nating gas,  0.000065.  Natural  gas,  0.00007.  Constant  X  diam.2  X  stroke 
in  ins.  X  revs,  per  min.=  probable  B.H.P.  A  deduction  should  be  made 
for  the  space  occupied  by  the  piston  rods,  about  5%  for  small  engines  up 
to  10%  for  very  large  engines. 

Rated  Capacity  of  Automobile  Engines.—  The  standard  formula  for 
the  American  Licensed  Automobile  Manufacturers  Association  (called 
the  A.  L.  A.  M.  formula)  for  approximate  rating  of  gasoline  engines 
used  in  automobiles  is  Brake  H.P.  =  Diam.2  X  No.  of  cylinders  -*•  2.5. 
It  is  based  on  an  assumed  piston  speed  of  1000  ft.  per  min.  The  following 
ratings  are  derived  from  the  formula: 

Bore,  ins  .........       2  1/2       3  3  1/2 

Bore,  mm  .........     64  76         89 

H.  P.,  1  cylinder...  .      2V2      3.6       4.9 

9.8 

19.6 

29.4 


.    .,  .. 

H.P.,  2  cylinders... 
H.P.,  4  "  ... 
H.P.,  6  "  ... 


5 

10 
15 


. 
7.2 

14.4 
21.6 


4 
102 

6.4 
12.8 


25.6 
38. 


4V2 
114 
8.1 
16.2 

?2~:46 


5 

127 
10 
20 


5V2 
140 
12.1 

24.2 


4     48 


6 

154 

14.4 

28.8 

57.6 

86.4 


A  committee  of  the  Institution  of  Automobile  Engineers  recommends 
the  following  formula:  B.H.P.  =  0.45  (d  +  s)  (d  -  1.18)N,  in  which 
d  =  diam.,  in.,  s  =  stroke,  in.,  N  =  number  of  cylinders.  The  formula 
was  derived  from  the  results  of  tests  of  engines  in  first-class  condition 
on  the  test  bench.  For  ordinary  engines  on  the  road  the  result  should 
be  multiplied  by  0.6.  (Eng'g,  Feb.  10,  1911.) 

The  American  Power  Boat  Association's  formula  for  rating  2-cycle 
engines  is  H.P.  =  area  of  piston  X  number  of  cylinders  X  length  of 
stroke  X  1.5. 

Approximate  Estimate  of  the  Horse-power  of  a  Gas  Engine..— 
From  the  formula  I.H.P.  =  PLAN  -*•  33,000,  in  which  P=  mean  effective 
pressure  in  Ibs.  per  sq.  in.,  L  =  length  of  stroke  in  ft.,  A  =  area  of  piston 
in  sq.  ins.,  N  =  No.  of  explosion  strokes  per  min.,  we  have  I.H.P.  =  Pd25-*- 
42,017,  in  which  c/  =  diam.  of  piston,  and  S  =  piston  speed  in  ft.  per  min., 
for  an  engine  in  which  there  are  two  explosion  strokes  in  each  revolution, 
as  in  a  4-cycle  double-acting,  2-cylinder  engine,  or  a  2-cycle,  2-cylinder, 
single-acting  engine.  If  the  mechanical  efficiency  is  taken  at  0.84.  then 
the  brake  horse  power  B.H.p.  =  Pd*S  •*•  50,000.  Under  average  con- 
ditions the  product  of  P  and  S  is  in  the  neighborhood  of  50,000,  and  in 
that  case  B.H.P.  =  d2.  -Generally,  B.H.P.  =  CX  d2,  in  which  C  is  a 
coefficient  having  values  as  below: 


M.E.P. 
Lbs.  per 
Sq.  In. 

Piston  Speed,  Ft.  per  Minute. 

500              600             700             800             900             1000 

Value  of  C  for  Two  Explosions  per  Revolution. 

150 
60 
70 
80 
90 
100 
110 

0.50 
0.60 
0.70 
0.80 
0.90 
1.00 
1.10 

0.60 
0.72 
0.84 
0.96 
1.08 
1.20 
1.32 

0.70 
0.84 
0.98 
1.12 
1.26 
1.40 
1.54 

0.80 
0.96 
.12 
.28 
.44 
.60 
.76 

0.90 
.08 
.26 
.44 
.62 
.80 
.98 

1.00 
1.20 
1.40 
1.60 
1.80 
2.00 
2.20 

These  values  of  C  apply  to  4-cylinders,  4-cycle,  single-acting,  to  2- 
cyl.,  2-cycle,  single-acting,  and  to  1-cyl.,  2-cycle  double-acting.  For 
single  cylinders,  4-cycle,  single-acting,  divide  by  4;  for  single  cylinders, 
4-cycle,  double-acting,  or  2-cycle,  single-acting,  divide  by  2. 

Oil  and  Gasoline  Engines. — The  lighter  distillates  of  petroleum,  such 
as  gasoline,  are  easily  vaporized  at  moderate  temperatures,  and  a  gaso- 
line engine  differs  from  a  gas-engine  only  in  having  an  atomizer  attached, 


1102  INTERNAL-COMBUSTION  ENGINES. 

for  spraying  a  fine  jet  of  the  liquid  into  the  air-admission  pipe.  With 
kerosene  and  other  heavier  distillates,  or  crude  oils,  it  is  necessary  to 
provide  some  method  of  atomizing  and  vaporizing  the  oil  at  a  high 
temperature,  such  as  injecting  it  into  a  hot  vaporizing  chamber  at  the 
end  of  the  cylinder,  or  into  a  chamber  heated  by  the  exhaust  gases. 
1  The  Diesel  Oil  Engine. — The  distinguishing  features  of  the  Diesel 
engine  are:  It  compresses  air  only,  to  a  predetermined  temperature  above 
the  firing  point  of  the  fuel.  This  fuel  is  blown  as  a  cloud  of  vapor  (by 
air  from  a  separate  small  compressor)  into  the  cylinder  when  compres- 
sion has  been  completed,  ignites  spontaneously  without  explosion, 
solely  by  reason  of  the  heat  of  the  air  generated  by  the  compression, 
and  burns  steadily  with  no  essential  rise  in  pressure.  The  temperature 
of  gases,  developed  and  rejected,  is  much  lower  than  with  engines  of  the 
explosive  type.  The  engine  uses  crude  oil  and  residual  petroleum  prod- 
ucts. Guarantees  of  fuel  consumption  are  made  as  low  as  8  gallons  of 
oil  (not  heavier  than  19°  Baume)  for  each  100  brake  H.P.  hour  at  any 
load  between  half  and  full  rated  load. 

American  Diesel  engines  are  built  for  stationary  purposes,  in  sizes  of 
120,  170,  and  225  H.P.  in  three  cylinders,  and  in  "double  units"  (six 
cylinders)  of  240,  340  and  450  H.P.  See  catalogue  of  the  American 
Diesel  Engine  Co.,  St.  Louis,  1909. 

Much  larger  sizes  have  been  built  in  Europe,  where  they  are  also 
built  for  marine  purposes,  including  submarines  in  the  French  and  other 
navies.  For  the  theory  of  the  Diesel  engine  see  a  lecture  by  Rudolph 
Diesel,  in  Zeit.  des  Ver  Deutscher  Ing.,  1897,  trans,  in  Progressive  Age, 
Dec.  1  and  15,  1897,  and  paper  by  E.  D.  Meier  in  Jour.  Frank.  Inst.t 
Oct.  1898. 

The  De  La  Vergne  Oil  Engine  is  described  in  Eng.  News,  Jan.  13, 1910. 
It  is  a  four-cycle  engine.  After  the  charge  of  air  is  compressed  to  about 
200  Ibs.  per  sq.  in.,  the  charge  of  oil  is  injected,  by  a  jet  of  air  at  about 
600  Ibs.  per  sq.  in.,  into  a  vaporizing  bulb  at  the  end  of  the  cylinder.  Ig- 
nition of  the  oil  is  caused  by  the  high  temperature  in  this  bulb.  Average 
results  of  tests  of  an  engine  developing  128  H.P.  showed  an  oil  consump- 
tion per  B.H.P.  hour  of  0.408  Ib.  with  Solar  fuel  oil,  and  0.484  Ib.  with 
California  crude  oil. 

Alcohol  Engines.  —Bulletin  No.  392  of  the  U.S.  Geol.  Survey  (1909,) 
on  Comparisons  of  Gasolene  and  Alcohol  Tests  in  Internal  Combustion 
Engines,  by  R.  M.  Strong,  contains  the  following  conclusions: 

The  "low"  heat  value  of  completely  denatured  alcohol  will  average 
10,500  B.T.U.  per  Ib.,  or  71,900  B.T.U.  per  gallon.  The  low  heat  value 
of  0.71  to  0.73  sp.  gr.  gasolene  will  average  19,200  B.T.U.  per  Ib.,  or 
115,800  B.T.U.  per  gallon. 

A  gasolene  engine  having  a  compression  pressure  of  70  Ibs.  but  other- 
wise as  well  suited  to  the  economical  use  of  denatured  alcohol  as  gasolene, 
will,  when  using  alcohol,  deliver  about  10%  greater  maximum  power 
than  when  using  gasolene. 

When  the  fuels  for  which  they  are  designed  are  used  to  an  equal  advan- 
tage, the  maximum  B.H.P.  of  an  alcohol  engine  having  a  compression 
pressure  of  180  Ibs.  is  about  30%  greater  than  that  of  a  gasolene  engine 
of  the  same  size  and  speed  having  a  compression  pressure  of  70  Ibs. 

Alcohol  diluted  with  water  in  any  proportion,  from  denatured  alcohol, 
which  contains  about  10%  water,  to  mixtures  containing  about  as  much 
water  as  denatured  alcohol,  can  be  used  in  gasolene  and  alcohol  engines  if 
the  engines  are  properly  equipped  and  adjusted. 

When  used  in  an  engine  having  constant  compression,  the  amount  of 
pure  alcohol  required  for  any  given  load  increases  and  the  maximum 
available  horse- power  of  the  engine  decreases  with  diminution  in  the 
percentage  of  pure  alcohol  in  the  diluted  alcohol  supplied.  The  rate  of 
increase  and  decrease,  respectively,  however,  is  such  that  the  use  of 
80%  alcohol  instead  of  90%  has  but  little  effect  upon  the  performance; 
so  that  if  80%  alcohol  can  be  had  for  15%  less  cost  than  90%  alcohol  and 
could  be  sold  without  tax  when  denatured,  it  would  be  more  economical 
to  use  the  80%  alcohol. 

Ignition.  — The  "hot-tube"  method  of  igniting  the  compressed  mixture 
of  gas  and  air  in  the  cylinder  is  practically  obsolete,  and  electric  systems 
are  used  instead,  Of  these  the  "  make-and-break  "  and  the  "  jump- 
Spark  "  systems  are  in  common  use,  In  the  former  two  insulated  contact 


INTEKNAIi-COMBUSTiON  ENGINES.  1103 

pieces  are  located  in  the  end  of  the  cylinder,  and  through  them  an  electric 
current  passes  while  they  are  in  contact.  A  spark-coil  is  included  in  the 
circuit,  and  when  the  circuit  is  suddenly  broken  at  the  proper  time  for 
ignition,  by  mechanism  operated  from  the  valve-gear  shaft,  a  spark  is 
made  at  the  contacts,  which  ignites,  the  gas.  In  the  "jump-spark" 
system  two  insulated  terminals  separated  about  0.03  in.  apart  are  located 
in  the  cylinder,  and  the  secondary  or  high-tension  current  of  an  induction 
coil  causes  a  spark  to  jump  across  the  space  between  them  when  the 
circuit  of  the  primary  current  is  closed  by  mechanism  operated  by  the 
engine.  In  some  oil  engines  the  mixture  of  air  and  oil  vapor  is  ignited 
automatically  by  the  temperature  generated  by  compression  of  the  vapor, 
in  a  chamber  at  the  end  of  the  cylinder,  called  the  vaporizer,  which  is 
not  water-jacketed  and  therefore  is  kept  hot  by  the  repeated  ignitions. 
Before  starting  the  engine  the  vaporizer  is  heated  by  a  Bunsen  burner 
or  other  means. 

Timing.  —  By  adjusting  the  cam  or  other  mechanism  operated  by  the 
valve-gear  shaft  for  causing  ignition,  the  time  at  which  the  ignition  takes 
place,  with  reference  to  the  end  of  the  compression  stroke,  can  be  regulated. 
The  mixture  is  usually  ignited  before  the  end  of  the  stroke,  the  advance 
depending  upon  the  inflammability  of  the  mixture  and  on  the  speed  of 
the  engine.  A  slow-burning  mixture  requires  to  be  ignited  earlier  than 
a  rapid-burning  one  and  a  high-speed  earlier  than  a  slow-speed  engine, 

Governing.  — -  Two  methods  of  governing  the  speed  of  an  engine  are 
in  common  use,  the  "  hit-and-miss  "  and  the  throttling  methods.  In  the 
former  the  engine  receives  its  usual  charge  of  air  and  gas  only  when  the 
engine  is  running  at  or  below  its  normal  speed;  at  higher  speeds  the  ad- 
mission of  the  charge  is  suspended  until  the  engine  regains  its  normal 
speed.  One  method  of  accomplishing  this  is  to  interpose  between  the 
valve-rod  and  its  cam  or  other  operating  mechanism,  a  push-rod,  or 
other  piece,  the  position  of  which  with  reference  to  the  end  of  the  valve- 
rod  is  controlled  by  a  centrifugal  governor  so  that  it  hits  the  valve-rod  if 
the  speed  is  at  or  below  normal  and  misses  it  if  the  speed  is  above  normal. 
The  hit-and-miss  method  is  economical  of  fuel,  but  it  involves  irregularity 
of  speed,  making  a  large  and  heavy  fly-wheel  necessary  if  reasonable 
uniformity  of  speed  is  desired.  The  throttling  method  of  regulating  is 
similar  to  that  used  in  throttling  steam  engines;  the  quantity  of  mixture 
admitted  at  each  charge  being  varied  by  varying  the  position  of  a  butter- 
fly valve  in  the  inlet  pipe.  Cut-off  methods  of  governing  are  also  used, 
such  as  varying  the  time  of  closing  the  admission  valve  during  the  suction 
stroke,  or  varying  the  time  of  admission  of  the  gas  alone,  or  "  quality 
regulation." 

Gas  and  Oil  Engine  Troubles.  —  The  gas  engine  is  subject  to  a 
greater  number  of  troubles  than  the  steam  engine  on  account  of  its  greater 
mechanical  complexity  and  of  the  variable  quality  of  its  operating  fluid. 
Among  the  causes  of  troubles  are:  the  variable  composition  of  the  fuel; 
too  much  or  too  little  air  supply;  compression  ratio  not  right  for  the 
kind  of  fuel;  ignition  timer  set  too  late  or  too  early;  pre-ignition;  back- 
firing; electrical  and  mechanical  troubles  with  the  igniting  system; 
carbon  deposits  in  the  cylinder  and  on  the  igniting  contacts.  For  a  very 
full  discussion  of  these  and  many  other  troubles  and  the  remedies  for 
them,  see  Jones  on  the  Gas-Engine. 

Conditions  of  Maximum  Efficiency. — The  conditions  which  appear 
to  give  the  highest  thermal  efficiency  in  gas  and  oil  engines  are:  1,  high 
temperature  of  cooling  water  in  the  jackets;  2,  high  pressure  at  the  end 
of  compression;  3,  lean  mixture;  4,  proper  timing  of  the  ignition;  5, 
maximum  load.  The  higher  economy  of  a  lean  mixture  may  be  due  to 
the  fact  that  high  compressions  may  be  used  with  such  a  mixture,  while 
with  rich  mixtures  high  compression  pressures  cannot  be  used  without 
danger  of  pre-ignition.  The  effect  of  different  timing  on  economy  is 
shown  in  a  test  by  J.  R.  Bibbins,  reported  by  Carpenter  and^)iederichs,  of 
an  engine  using  natural  gas  of  a  lower  heating  value*  of  934  B.T.U.  per 
cu.  ft.,  delivering  71  H.P.  at  297  revs,  per  min.  The  maximum  thermal 
efficiency,  23.3%,  was  obtained  when  the  timing  device  was  set  for  igni-- 

*  By  "lower  heating  value"  is  meant  the  value  computed  after  sub- 
tracting the  latent  heat  of  evaporation  of  9  Ibs.  of  water  per  pound  of 
hydrogen  contained  in  the  gas.  bee  page  561. 


1104 


INTERNAL-COMBUSTION   ENGINES. 


tlon  30°  in  advance  of  the  dead  center,  while  the  efficiency  with  ignition 
at  the  center  was  19%,  and  with  ignition  55°  in  advance  17.3%. 

Other  things  being  equal,  the  hotter  the  walls  of  the  cylinder  the  less 
heat  is  transferred  into  them  from  the  hot  gases,  and  therefore  the  highei 
the  efficiency.  Cool  walls,  however,  allow  of  higher  compression  without 
pre-ignition,  and  high  compression  is  a  cause  of  high  efficiency.  Cool 
walls  also  tend  to  give  the  engine  greater  capacity,  since  with  hot  walls 
the  fuel  mixture  expands  more  on  entering  the  cylinder,  reducing  the 
weight  of  charge  admitted  in  the  suction  stroke. 

Heat  Losses  in  the  Gas  Engine* — The  difference  between  the  thermal 
efficiency,  which  is  the  proportion  of  heat  converted  into  work  in  the 
engine,  and  100%, is  the  loss  of  heat,  which  includes  the  heat  carried  away 
in  the  jacket  water,  that  carried  away  in  the  waste  gases,  and  that  lost 
by  radiation.  The  relative  amounts  of  these  three  losses  vary  greatly, 
depending  on  the  size  of  the  engine  and  on  the  amount  of  water  used  for 
cooling.  Thurston,  in  Heat  as  a  Form  of  Energy,  reports  a  test  in  which 
the  heat  distribution  was  as  follows:  Useful  work,  17.3%;  jacket  water, 
52%;  exhaust  gas,  16%;  radiation,  15%.  Carpenter  and  Diederichs 
quote  the  following,  showing  that  the  distribution  of  the  heat  losses 
varies  with  the  rate  of  compression  and  with  the  speed. 


Ratio 
of 
Com- 
pres- 
sion. 

R.p.m. 

M.E.P. 

Ibs. 
per  sq. 
in. 

Ratio 
Air  to 
Gas. 

Heat- 
ing 
Value 
of 
Charge, 
B.T.U. 

Work 
done 
by  1 
B.T.U., 
Ft.-lbs. 

Ex- 
haust 
Temp. 
Deg.  F. 

Heat  Distribution, 
Per  Cent. 

Work. 

Jacket 
Water. 

Ex- 
haust. 

2.67 

187 

54.3 

7.11 

18.5 

.140 

1022 

18.0 

51.2 

30.8 

2.67 

247 

51.5 

7.35 

17.4 

141 

1137 

18.1 

45.6 

36.3 

4.32 

187 

69.3 

7.43 

17.0 

190 

867 

24.4 

53.8 

21.8 

4.32 

247 

65.2 

7.40 

16.8 

184 

992 

23.7 

49.5 

26.8 

In  the  long  table  of  results  of  tests  reported  by  Carpenter  and  Diede- 
richs, figures  of  the  distribution  of  heat  show  that  of  the  total  heat  re- 
ceived by  the  engines  the  heat  lost  in  the  jacket  water  ranged  from  25.0 
to  50.4%,  and  that  lost  in  the  exhaust  gases  from  55  to  23.4%. 

In  small  air-cooled  gasoline  engines,  such  as  those  used  in  some  auto- 
mobile engines,  in  which  the  cylinders  are  surrounded  by  thin  metal 
ribs  to  increase  the  radiating  surface,  and  air  is  propelled  against  them 
by  a  fan,  the  air  takes  the  place  of  the  jacket  water,  and  the  total  loss 
of  heat  is  that  carried  away  by  the  air  and  by  the  exhaust  gases. 

Economical  Performance  of  Gas  Engines.  —  The  best  performance 
of  a  gas  engine  using  producer  gas  (1909)  is  about  30%  better  than  the 
best  recorded  performance  of  a  triple-expansion  steam  engine,  or  about 
0.71  Ib.  coal  per  I.H.P.  hour,  as  compared  with  1.06  Ibs.  for  the  steam 
engine.  It  is  probable  that  the  performance  of  the  combination  of  a 
high-pressure  reciprocating  engine,  using  superheated  steam  generated  in 
a  well-proportioned  boiler  supplied  with  mechanical  stokers  and  an  econo- 
mizer, and  a  low-pressure  steam  turbine  will  ere  long  reduce  the  steam 
engine  record  to  0.9  Ib.  per  I.H.P.  hour.  As  compared  with  an  ordinary 
steam  engine,  however,  the  gas  engine  with  a  good  producer  is  far  more 
economical  than  the  steam  engine.  Where  gas  can  be  obtained  cheaply, 
such  as  the  waste-gas  from  blast  furnaces,  or  natural  gas,  the  gas-engine 
can  furnish  power  much  more  cheaply  than  it  can  be  obtained  from  the 
same  gas  burned  under  a  boiler  to  furnish  steam  to  a  steam  engine. 

In  tests  made  for  the  U.  S.  Geological  Survey  at  the  St.  Louis  Exhibi- 
tion, 1904,  of  a  235-H.P.  gas  engine  with  different  coals,  made  into  gas 
In  the  same  producer,  the  best  result  obtained  was  1.12  Ibs.  of  West 
•  Virginia  coal  per  B.H.P.  hour,  and  the  poorest  result  3.23  Ibs.  per  B.H.P. 
•hour,  with  North  Dakota  lignite. 

A  170-H.P.  Crossley  (Otto)  engine  tested  in  England  in  1892,  using 
producer  gas,  gave  a  consumption  of  0.85  Ib.  coal  per  I.H.P.  hour,  or  a 
thermal  efficiency  of  engine  and  producer  combined  of  21.3%. 

Experiments  on  a  Taylor  gas  producer  using  anthracite  coal  and  a 


TESTS  OF   GAS  AND   OIL  ENGINES.  1105 

100-H.P.  Otto  gas  engine  showed  a  consumption  of  0.97  Ib.  carbon  per 
I.H.P.  hour.  (Iron  Age,  1893.) 

In  a  table  in  Carpenter  and  Diederichs  on  Internal  Combustion  Engines 
the  lowest  recorded  coal  consumption  per  B.H.P.  hour  is  0.71  Ib.,  with 
a  Tangye  engine  and  a  suction  gas  producer,  using  Welsh  anthracite  coal. 
Other  tests  show  figures  ranging  from  0.74  Ib.  to  1.95,  the  last  with  a 
Westingnouse  500-H.P.  engine  and  a  Taylor  producer  using  Colorado 
bituminous  coal. 

In  the  same  book  are  given  the  following  figures  of  the  thermal  efficiency 
on  brake  H.P.  with  different  gas  and  liquid  fuels.  Illuminating  gas, 
6  tests,  16.1  to  31.0%;  natural  gas,  4  tests,  16.1  to  29.0%;  coke-oven  gas, 
1  test,  27.5%;  Morid  gas,  1  test,  23.7%;  blast-furnace  gas,  Stests,  20.4  to 
28.2%;  gasoline,  8  tests,  10.2  to  28%;  kerosene,  Diesel  engine,  3  tests, 
25. 8  to  31.9%;  kerosene,  other  engines,  8  tests,  9.2  to  19.7%;  crude  oil, 
Diesel  engine,  1  test,  28.1%;  alcohol,  4  tests,  21.8  to  32.7%. 

Tests  of  Diesel  engines  operating  centrifugal  pumps  in  India  are 
reported  in  Eng.  News,  Nov.  25,  1909.  Using  Borneo  petroleum  residue 
of  0.934  sp.  gr.,  and  a  fuel  value  of  18,600  B.T.U.  per  Ib.,  an  average  of 
151  B.H.P.  during  a  season,  for  a  total  of  6003  engine  hours,  was  obtained 
with  a  consumption  of  0.462  Ib.  of  fuel  per  B.H.P.  hour,  or  one  B.H.P. 
for  about  8600  B.T.U.  per  hour,  equal  to  a  thermal  efficiency  of  29.5%. 
The  pump  efficiency  at  maximum  lift  of  14  to  16  ft.  was  70%,  and  the 
fuel  consumption  per  water  H.P.  hour  at  the  same  lift  was  0.7  Ib. 

Utilization  of  Waste  Heat  from  Gas  Engines. — The  exhaust  gases 
from  a  gas  engine  may  be  used  to  heat  air  by  passing  them  across  a  nest 
of  tubes  through  which  air  is  flowing.  A  design  of  this  kind,  for  heating 
the  Ives  library  building,  New  Haven,  Conn.,  by  Harrison  Engineering 
Co.,  New  York,  is  illustrated  in  Heat,  and  Vent.  Mag.,  Jan.,  1910. 

The  waste  heat  might  also  be  used  in  a  boiler  to  generate  steam  at  or 
below  atmospheric  pressure,  for  use  in  a  low  pressure  steam  turbine.  On 
account  of  the  comparatively  low  temperature  of  the  exhaust  gases, 
however,  the  boiler  would  require  a  much  greater  extent  of  heating  sur- 
face for  a  given  capacity  than  a  boiler  with  an  ordinary  coal-fired  furnace. 

RULES   FOR   CONDUCTING  TESTS   OF   GAS  AND  OIL 
ENGINES. 

(Abstract  from  the  A.  S.  M.  E.  Code  of  1915.) 

Object  and  Preparations. 

Determine  the  object,  take  the  dimensions,  note  the  physical  condi- 
tion of  the  engine  and  its  appurtenances,  install  the  testing  appliances, 
etc.,  as  explained  in  the  general  instructions,  and  make  preparations 
for  the  test  accordingly. 

Operating  Conditions. 

Determine  what  the  operating  conditions  should  be  to  conform 
to  the  object  in  view,  and  see  that  they  prevail  throughout  the  trial. 

Duration. 

The  test  of  a  gas  or  oil  engine  with  substantially  constant  load 
should  be  continued  for  such  time  as  may  be  necessary  to  obtain  a 
number  of  successive  records  covering  periods  of  half  an  hour  or  less 
during  which  the  results  are  found  to  be  uniform.  In  such  cases  a 
duration  of  three  to  five  hours  is  sufficient  for  all  practical  purposes. 

Starting  •  and  Stopping. 

The  engine  having  been  set  to  work  under  the  prescribed  condi- 
tions, the  test  is  begun  at  a  certain  predetermined  time  by  commencing 
to  weigh  the  oil,  or  measure  the  gas,  as  the  case  may  be,  and  taking 
other  data  concerned;  after  which  the  regular  measurements  and 
observations  are  carried  forward  until  the  end. 

Calorific  Tests  and  Analyses. 

The  quality  of  the  oil  or  gas  should  be  determined  by  calorific  tests 
and  analyses  made  on  representative  samples. 


1106  INTERNAL-COMBUSTION   ENGINES. 

Calculation  of  Results. 

The  ascertained  volume  of  gas  is  reduced  to  the  equivalent  volume  at 
a  temperature  of  60  deg.  and  at  atmospheric  pressure  of  30  in. 

The  number  of  heat  units  consumed  by  the  engine  is  found  by  mul- 
tiplying the  heat  units  per  Ib.  of  oil  or  per  cu.  ft.  of  gas  (higher  value), 
as  determined  by  calorimeter  test,  by  the  total  weight  of  oil  in  Ib.  or 
volume  of  dry  gas  in  cu.  ft.  consumed. 

The  indicated  horse-power,  brake  horse-power,  and  efficiency  are 
computed  by  the  same  methods  as  those  explained  in  the  Steam  Engine 
Code. 

Heat  Balance. 

The  various  quantities  showing  the  distribution  of  heat  in  the  heat 
balance  are  computed  in  the  following  manner: 

The  heat  converted  into  work  per  I.H.P.-hour  (2546.5  B.T.U.)  is 
found  by  dividing  the  work  representing  1  H.P.,  or  1,980,000  ft.-lb., 
per  hour  by  the  number  of  ft.-lb.  representing  1  B.T.U.,  or  777.5. 

The  heat  rejected  in  the  cooling  water  is  obtained  by  multiplying 
the  weight  of  water  supplied  by  the  number  of  degrees  rise  of  tem- 
perature, and  dividing  the  product  by  the  indicated  horse-power. 

The  heat  rejected  in  the -dry  exhaust  gases  per  I.H.P.-hr.  is  found 
by  multiplying  the  weight  of  these  gases  per  I.H.P.-hr.  by  the  sensible 
heat  of  the  gas  reckoned  from  the  temperature  of  the  air  hi  the  room 
and  by  its  specific  heat.  The  weight  of  the  dry  exhaust  gases  per 
I.H.P.-hr.  is  the  product  of  the  weight  of  fuel  per  I.H.P.-hr.  by  the 
weight  of  the  dry  gatees  per  Ib.  of  fuel.  The  latter  is  the  product  of 
the  proportion  of  carbon  in  1  Ib.  of  fuel  by  the  weight  of  the  dry  gases 
per  Ib.  of  carbon,  which  may  be  found  by  the  formula 

_n_CO2  +  8  O  +  7  (CO  +JN)__ 

3  (CO2  +  CO)  ~ 

in.  which  CO2,  O,  CO,  and  N  are  percentages  of  the  dry  exhaust  gases 
by  volume. 

When  the  weight  of  air  supplied  per  Ib.  of  fuel  is  determined  the 
weight  of  dry  gas  per  pound  of  fuel  may  be  found  by  the  formula 

1  +  Ib.  air  per  Ib.  fuel  -  9  H 
in  which  H  te  the  proportion  of  hydrogen  in  1  Ib.  of  fuel. 

The  heat  lost  in  the  moisture  formed  by  the  burning  of  hydrogen 
in  the  fuel  gas  is  found  by  multiplying  the  total  heat  of  1  Ib.  of  super- 
heated steam  at  the  temperature  of  the  exhaust  gases,  reckoning  from 
the  temperature  of  the  air  in  the  room,  by  the  proportion  of  the 
hydrogen  in  the  fuel  as  determined  from  the  analysis,  and  multiplying 
the  result  by  9. 

The  heat  lost  in  superheating  the  moisture  contained  in  the  gas 
and  air  is  determined  by  multiplying  the  difference  between  the 
temperature  of  the  exhaust  gases  and  that  of  the  gas  and  air  by  the 
average  specific  heat  of  superheated  steam  for  the  range  of  temperature 
and  pressure. 

The  heat  lost  through  incomplete  combustion  is  obtained  by  analyz- 
ing the  exhaust  gases  and  computing  the  heat  of  the  unburned  products 
wlu'ch  would  have  been  produced  by  their  combustion. 

The  above  rules  do  not  apply  to  engines  with  hit-and-miss  governors. 

Data  and  Results. 

The  data  and  results  should  be  reported  in  accordance  with  the 
form  given  herewith,  adding  lines  for  data  not  provided  for,  or  omitting 
those  not  required,  as  may  conform  to  the  object  in  view.  If  a  shorter 
form  is  desired,  items  designated  by  letters  of  the  alphabet  may  be 
omitted.  Unless  otherwise  indicated,  the  items  should  be  the  aver- 
ages of  the  data. 

DATA  AND    RESULTS    OF   GAS   OR   OIL   ENGINE    TEST. 

Code  of  1915. 

1.  Test  of engine,  located  at 

To  determine 

Test  conducted  by 


TESTS  OF  GAS  AND  OIL  ENGINES.  1107 

Dimensions,  Etc. 

2.  Type  of  engine,  whether  oil  or  gas 

3.  Class  of  engine,    (mill,   marine,   motor  for  vehicle,   pumping,  or 

other) 

(a)  Number  of  strokes  of  piston  for  one  cycle,  and  class  of  cycle. 
(6)   Method  of  ignition 

(c)  Single  or  double  acting 

(d)  Arrangement  of  cylinders 

(e)  Vertical  or  horizontal 

5.  Diameter  of  working  cylinders in. 

6.  Stroke  of  pistons ft. 

4.  Rated  power H.P 

Date,  Duration,  Etc. 

7.  Date,  r- 

8.  Duration hr. 

9.  Kind  of  oil  or  gas 

Average  Pressure  and  Temperature. 

10.  Pressure  of  gas  near  meter in. 

11.  Temperature  of  gas  near  meter deg. 

(a)  Temperature  of  cooling  water,  inlet 

(&)   Temperature  of  cooling  water,  outlet 

(c)  Temperature  of  air  by  dry-bulb  thermometer .... 

(d)  Temperature  of  air  by  wet-bulb  thermometer .... 

(e)  Temperature  of  exhaust  gases  at  cylinder 

Total  Quantities. 

12.  Gas  or  oil  consumed cu.  ft.  or Ib. 

13.  Moisture  in  gas,  in  per  cent  by  weight,  referred  to  dry  gas  per  cent 

14.  Equivalent  dry  gas  at  60  deg.  and  30  in cu.  ft. 

(a)  Air  supplied  in  cu.  ft 

15.  Cooling  water  supplied  to  jackets Ib. 

(a)  Water  or  steam  fed  to  cylinder ' 

16.  Calorific  value  of  oil  per  Ib.,  or  of  dry  gas  per  cu.  ft.  at 

60  deg.  and  30  in.  by  calorimeter  test  (higher  value) .  .B.T.U. 

Hourly  Quantities. 

17.  Gas  or  oil  consumed  per  hour cu.ft.orlb. 

18.  Equivalent  dry  gas  per  hour  at  60  deg.  and  30  in cu.  ft. 

19.  Cooling  water  supplied  per  hour Ib. 

20.  Heat  units  consumed  per  hour  (Item  16  X  Item  18) B.T.U. 

Analyses. 

21-24.  Analysis  of  oil:  C;  H;  O;  S;  moisture 

25-30.  Analysis  of  Fuel  Gas  by  Volume:  CO2;  CO;  O;  H; 

CH4;  Cn  Hm  ;  N  by  difference 

31-34.  Analysis  of  Exhaust  Gases  by  Volume:  CO2;  CO; 

O;  N 

Indicator  Diagrams. 

35.  Pressure  in  Ib.  per  sq.  in.  above  atmosphere Ib. 

(a)  Maximum  pressure 

(&)   Pressure  at  beginning  of  stroke . . 

(c)  Pressure  at  end  of  expansion .... 

(d)  Exhaust  pressure  at  lowest  point 

36.  Mean  effective  pressure  in  Ib.  per  sq.  in 

Speed. 

37.  Revolutions  per  minute rev, 

38.  Average   number   of   explosions   or   firing   strokes   per 

minute . 


(a)  Variation  of  speed  between  no  load  and  full  load . .  rev, 

(b)  Momentary   fluctuation   of  speed   on   suddenly 

changing  from  full  load  to  half  load * 


1108  LOCOMOTIVES. 

Power. 

39.  Indicated  horse-power I.H.P. 

40.  Brake  horse-power br.  H.P. 

41    Friction  horse-power  by  difference  (Item  39  -  Item  40)*  fr.-H.P. 

(a)  Friction  horse-power  by  friction  diagrams 

42.  Percentage    of    indicated   horse-power   lost   in    friction 

Item  41 per  cent 

Economy  Results. 

43.  Heat  units  consumed  by  engine  per  J.H.P.-hourf B.T.U. 

44.  Heat  units  consumed  by  engine  per  B.H.P.-hour 

45.  Pounds  of  oil  or  cubic  feet  of  dry  gas  at  60  deg.  and  .'50 

in.  consumed  per  I.H.P.  hour Ib.  cu.  ft. 

46.  Pounds  of  oil  or  cubic  feet  of  dry  gas  per  B.H.P.-hour.  . 

Efficiency. 

47.  Thermal  efficiency  referred  to  indicated  horse-power  . . .   per  cent 

48.  Thermal  efficiency  referred  to  brake  horse-power 

Work  Done  per  Heat  Unit. 

49.  Ft.-lb.  of  net  work  per  B.T.U.  consumed  (1,980,000  ~ 

Item  40) ft.-lb. 

HEAT   BALANCE. 

50.  Heat  balance,  based  on  B.T.U.  per  I.H.P.  per  hour 

B.T.U.  Per  cent 

(a)  Heat  converted  into  work 2546 .5     

(&)   Heat  rejected  in  cooling  water * 

(c)  Heat  rejected  in  the  dry  exhaust  gases 

(d)  Heat  lost  due  to  moisture  formed  by 

burning  of  hydrogen 

(e)  Heat  lost  in  superheating  moisture  in 

gas  and  air 

(/)    Heat  lost  by  incomplete  combustion 

(0)  Heat  unaccounted  for,  including  radia- 
tion   

(h)  Total  heat  consumed  per  I.H.P.-hr., 

same  as  Item  43 

Sample  Diagrams. 

51.  Sample  indicator  diagrams  from  each  cylinder  and  if 

possible  a  stop-motion  light-spring  diagram  showing 
inlet  and  exhaust  pressures 

LOCOMOTIVES. 

Resistance  of  Trains. — Resistance  due  to  Speed. — Various  formulae 
and  tables  for  the  resistance  of  trains  at  different  speeds  on  a  straight 
level  track  have  been  given  by  different  writers.  Among  these  are 
the  following: 

By  D.  L.  Barnes,  Eng.  Mag.,  June,  1894: 

Speed,  miles  per  hour 50       60         70       80     90     100 

Resistance,  pounds  per  gross  ton . .   12     12 . 4     13 . 5     15     17       20 

By  Engineering  News,  March  8,  1894: 

Resistance  in  Ibs.  per  ton  of  2000  Ibs.  =  1/4  v  +  2. 

Speed 5       10     15  20   25     30     35     40    50     60    70    80   90    100 

Resistance. 3  1/4   4.5   53/4  7   81/4  9.5   103/4  12    14.5  17  19.5  22  24.5    27 

*  In  two  cycle  engines  this  includes  the  power  required  for  compres- 
sion. 

t  If  these  results,  in  the  case  of  a  gas  engine,  are  based  on  the  low 
value  of  the  heat  of  combustion  that  fact  should  be  so  stated. 


LOCOMOTIVES.  1109 

This  formula  seems  to  be  more  generally  accepted  than  the  others. 
It  gives  results  too  small,  however,  below  10  miles  an  hour.  At  starting, 
the  resistance  is  about  17  Ibs.  per  ton,  dropping  to  4  or  5  Ibs.  at  5  miles 
an  hour. 

By  Baldwin  Locomotive  Works: 

Resistance  in  Ibs.  per  ton  of  2000  Ibs.  =  3  +  v  •*-  6. 

Speed..      .5    10   15  20   2530  35  40     45     50     55  60    70     80  90   100 
Resistance. 3.8  4.7  5.5  6.3  7.2  8   8.8  9.7  10.5  11.3  12.2  13  14.7  16.3  18  19.7 

The  resistance  due  to  speed  varies  with  the  condition  of  the  track,  the 
number  of  cars  in  a  train,  and  other  conditions. 

For  tables  showing  that  the  resistance  varies  with  the  area  exposed  to 
the  resistance  and  friction  of  the  air  per  ton  of  loads,  see  Dashiell,  Trans. 
A.  S.  M.  E.,  vol.  xiii.  p.  371. 

P.  H.  Dudley  (Bulletin  International  Ry.  Congress,  1900,  p.  1734) 
shows  that  the  condition  of  the  track  is  an  important  factor  of  train 
resistance  which  has  not  hitherto  been  taken  account  of.  The  resist- 
ance of  heavy  trains  on  the  N.  Y.  Central  R.  R.  at  20  miles  an  hour  is 
only  about  31/2  Ibs.  per  ton  on  smooth  80-lb.  5i/8-m.  rails.  The  resist- 
ance of  an  80-car  freight  train,  60,000  Ibs.  per  car,  as  given  by  indicator 
cards,  at  speeds  between  15  and  25  miles  per  hour,  is  represented  by  the 
formula  R  =  1  +  1/8  V,  in  which  R  =  resistance  in  Ibs.  per  ton  and 
V  =  miles  per  hour.  These  values  are  much  below  the  average  and 
should  not  be  used  in  estimating  the  hauling  power  needed. 

New  Formulas  for  Re-nstance.  —  The  Amer.  Locomotive  Co.  (Bulletin 
No.  1001,  Feb.,  1910)  states  that  the  figures  obtained  from  the  old  formulae 
for  train  resistance  are  much  too  high  foj*  modern  loaded  freight  cars 
of  40  to  50  tons  capacity,  and  in  some  instances  too  low  for  very  light 
or  empty  cars.  The  best  data  available  show  that  the  resistance  varies 
from  about  2.5  to  3  Ibs.  per  ton-  (of  2000  Ibs.)  for  72-ton  cars  (including 
weight  of  empty  car)  to  6  to  8  Ibs.  for  20-ton  cars.  From  speeds  between 
5  to  10  and  30  to  35  miles  an  hour,  the  resistance  of  freight  cars  is  prac- 
tically constant.  The  resistance  of  the  engine  and  tender  is  figured 
separately,  and  is  composed  of  the  following  factors:  (a)  Engine  friction  = 
22.2  Ibs.  per  ton,  or  1.11%  of  the  weight  on  drivers.  (6)  Head  air  resist- 
ance =  cross-sectional  area  (taken  at  120  sq.  ft.)  X  0.002  V2,  V  being 
the  speed  in  miles  per  hour,  (c)  Resistance  due  to  weight  on  engine 
trucks  and  trailing  wheels,  and  t9  the  tender,  the  same  per  ton  as  that 
due  to  the  cars,  (d)  Grade  resistance  =  20  Ibs.  per  ton  for  each  per 
cent  of  grade,  (e)  Curve  resistance,  which  varies  with  the  wheel-base 
of  the  locomotive,  and  is  taken  as  0.4  +  cD  Ibs.  per  ton,  in  which  D  is 
the  degree  of  the  curve  and  c  a  constant  whose  value  is, 
For  wheel-base,  ft.  5  6  7  8  9  12  13  15  16-  20 
Value  of  c 0.380  .415  .460  .485  .520  .625  .660  .730  .765  .905 

The  sum  of  these  resistances  is  to  be  deducted  from  the  tractive  force  of 
the  locomotive  to  obtain  the  available  tractive  force  for  overcoming  tht 
resistance  of  the  cars.  (See  Tractive  Force,  below.)  The  maximum 
tractive  force  is  taken  for  low  speeds  at  85%  of  that  due  to  the  boiler 
pressure;  for  piston  speeds  over  250  ft.  per  min.  this  is  to  be  multiplied 
by  a  speed  factor  to  obtain  the  actual  force.  Speed  factors  and  percent- 
ages of  maximum  horse-power  corresponding  to  different  piston  speeds 
are  given  below.  S  =  piston  speed,  ft.  per  min.,  F  =  speed  factor, 
p  =  %•  of  maximum  H.P. 

S 250     300     350     400     450     500     550     600     650     700     750 

F 1.00    .954    .908   .863    .817    .772   .727    .680    .636    .592    .550 

P 60.469.177.283.789.093.596.898.799.7    100     100 

S...      .  800  850  900  950  1000  1100  1200  1300  1400  1500  1600 

F 0.517  .487  .460  .435  .412  .372  .337  .307  .283  .261  .241 

P 100     100     100     100     100      9997.896.895.7   94.793.5 

The  resistance  of  freight  cars,  according  to  experiments  on  the  Penna. 
R.R.,  varies  with  the  weight  in  tons  per  car  as  follows: 

Tons  per  car 10       20       25       30       40       50       60       70       72 

Resistance,  Ibs.  per  ton 

13.10  7.84  6.62  5.78  4.66  3.94  3.44  3.06  3.00 


1110  LOCOMOTIVES. 

From  plotted  curves  of  resistances  of  trains  of  empty  and  loaded  cars 
the  following  figures  are  derived.  R  =•  resistance  in  IDS.  per  ton. 

Wt.  loaded,  tons..,  75  70  65  60  55  50 

Wt.  empty,  tons 21  20.3  19.5  18.6  17.6  165 

Per  cent  of  loaded  wt 28  29  30  31  32  33 

R  loaded 2.90  3.07  3.24  3.43  3.65  3.90 

R  empty 5.63  5.82  6.00  6.26  6.50  6.85 

Wt.  loaded,  tons 45  40         35  30         25  20         15 

Wt.  empty,  tons 15.3  14.0  12.6  11.1  9.5  7.8  6.0 

Percent  of  loaded  wt....  34         35         36  37         38  39         40 

R  loaded 4.18  4.40  4.74  5.07  5.44  5.91  6.40 

R  empty 7.26  7.65  8.05  8.45  9.05  9.60  10.3 

'the  resistance  of  passenger  cars  is  derived  from  the  formula  R  =  5.4  + 
0.002(7  -  15)2+  100  ^  (V  +  2)».  V  in  miles  per  hour,  R  =  resistance 
in  Ibs.  per  ton  (2000  Ibs.)  H.P.  =•  horse-power  per  ton. 

V  = 5          10         15         20         25         30         35 

R= 5.89     5.51     5.42     5.46     5.60     5.85     6.20 

H.P.  = 0.079.147     .217      .291      .374      .469      .578 

F=..,  40         45         50         60         70         80        90 

R  = 6.65     7.20     7.85     9.4511.4513.8516.65 

H.P.= 709      .864     1.047  1.515  2.135    2.95     4.00 

Resistance  of  Electric  Railway  Cars  and  Trains.  —  W.  J.  Davis,  Jr. 
(Street  Ry.  Jour.,  Dec.  3,  1904),  gives  as  a  result  of  numerous  experiments 
the  following  formulae: 

(A)  For  light  open  platform  street  cars,  8  tons  to  20  tons;  maximum 
speed,  30  miles  per  hour;  cross-section,  85  sq.  ft. 

O  ^  V2 

R  =  6  +  0.11V  +  ^|^-  [l-f-0.1  (n-  1)J. 

(B)  For  standard  interurban  electric  cars,  25  tons  to  40  tons;  maximum 
speed,  60  m.p.h.;  cross  section,  100  sq.  ft. 

R  =  5-fO.lSF-f  O.SFV^fl-f  0.1  (n  -  1)}. 

(C)  For  heavy  interurban  electric  cars,  or  steam  passenger  coaches, 
40  tons  to  50  tons;  maximum  speed,  75  m.p.h.;  crosss-ection,  110  sq.  ft. 

R  =  4  +  0.13  V  +  0.33  FV?7  [1  -f  0.1  (n  -  1)]. 

(D)  For  heavy  freight  trains,  cars  weighing  45  tons  loaded;  maximum 
speed,  35  m.p.h.;  average  cross-section,  110  sq.  ft. 

R  =  3.5  +0. 13  V-f-  0.385  V^/T(l+  0.1  (n  -  1)]. 

R  =  resistance  in  Ibs.  per  ton  of  2000  Ibs.,  V=  speed  in  miles  per  hour 
T  =  weight  of  train  in  tons,  n  =  number  of  cars  in  train,  including  lead- 
ing motor  car.  The  cross-section  includes  the  space  bounded  by  the  wheels 
between  the  top  of  rails  and  the  body. 

Resistance  due  to  Grade.  —  The  resistance  due  to  a  grade  of  1  ft.  per 
mile  is,  per  ton  of  2000  Ibs.,  2000  X  1/5280  =  0.3788  Ib.  per  ton,  or  if 
Rg  =  resistance  in  Ibs.  per  ton  due  to  grade  and  G  =  ft.  per  mile  Rg  = 
0.3788  G. 

If  the  grade  is  expressed  as  a  percentage  of  the  length,  the  resistance  is 
20  Ibs.  per  ton  for  each  per  cent  of  grade. 

Resistance  due  to  Curves.  —  Mr.  G.  R.  Henderson  in  his  book  entitled 
"Locomotive  Operation"  gives  the  resistance  due  to  curvature  at  0.7 
Ib.  per  ton  of  2000  Ibs.  per  degree  of  the  curve.  (For  definition  of 
degrees  of  a  railroad  curve  see  p.  54.)  For  locomotives,  this  factor  is 
sometimes  doubled,  making  the  resistance  in  Ibs.  per  ton  =  0.7  c  for  cars 
and  1.4  c  for  locomotives,  c  being  the  number  of  degrees. 

The  Baldwin  Locomotive  Works  take  the  approximate  resistance  due 
to  each  degree  of  curvature  as  that  due  to  a  straight  grade  of  1 1/2  ft.  per 
mile.  This  corresponds  to  Rc  »  0.5682  c. 

The  Amer.  Locomotive  Co.  takes  0.8  Ib.  per  ton  per  degree  of  curva- 
ture for  the  resistance  of  cars  on  curves. 


LOCOMOTIVES.  HH 

For  mine  cars,  with  short  wheel-bases  and  wheels  loose  on  the  axles, 
experiments  quoted  by  the  Baldwin  Locomotive  Works,  1904,  lead  to  the 
formula,  Resistance  due  to  curvature,  in  pounds,  =  0.20  X  wheel-base  X 
weight  of  loaded  cars  in  pounds,  •*•  radius  of  curve  in  feet. 

Resistance  due  to  Acceleration.  —  This  may  be  calculated  by  the  ordi- 
nary formula  (see  page  529),  or  reduced  to  common  railroad  units,  and 
including  the  rotative  energy  of  wheels  and  axles,  which  increases  the 
effect  of  the  weight  of  the  cars  by  an  equivalent  of  about  5%,  we  have 

p  =  70  ^  =95.6  ?  =  70  V**  ~  Fl*  ,  where   P=  the   accelerating   force  in 

o  t  o 

pounds  per  ton,.  V  =  the  velocity  in  miles  per  hour,  S  =  the  distance 
In  feet,  and  t  =  the  time  in  seconds  in  which  the  acceleration  takes 
place.  Fi  and  Vi  =  the  smaller  and  greater  velocities,  respectively, 
in  miles  per  hour,  for  a  change  of  speed. 

Total  Resistance.  —  The  total  resistance  in  Ibs.  per  ton  of  2000  Ibs.  due 
to  speed,  to  grade,  to  curves,  and  to  acceleration  is  the  sum  of  the  resist- 
ances calculated  above. 

The  Baldwin  Locomotive  Works  in  their  "Locomotive  Data'  take  the 
total  resistance  on  a  straight  level  track  at  slow  speeds  at  from  6  to  10  Ibs. 
per  ton,  and  in  a  communication  printed  in  the  fourth  edition  (1898)  of 
this  Pocket-book,  p.  1076,  say:  "We  know  that  in  some  cases,  for  in- 
stance in  mine  construction,  the  frictional  resistance  has  been  shown  to 
be  as  much  as  60  Ibs.  per  ton  at  slow  speed.  The  resistance  should  be 
approximated  to  suit  the  conditions  of  each  individual  case,  and  the 
increased  resistance  due  to  speed  added  thereto." 

Resistance  due  to  friction.  —  In  the  above  formulae  no  account  has  been 
taken  of  the  resistance  due  to  the  friction  of  rhe  working  parts.  This  is 
rather  an  obscure  subject.  Mr.  Henderson  estimates  the  percentage  of 
the  indicated  power  consumed  by  friction  to  be  0.15  V  +  c,  where 
V  =  speed  in  miles  per  hour  and  c  =-  a  constant,  whose  value  may 
vary  from  2  to  8,  the  latter  figure  being  the  safest  to  use  for  heavy  work 
at  slow  speeds.  Ordinarily  8%  of  the  indicated  power  is  consumed  by 
internal  resistance  under  these  conditions.  Professor  Goss  gives  the 
following  formula,  obtained  from  tests  at  the  Purdue  locomotive  testing 
laboratory: 

Let  d  =  diameter  of  cylinder:  S  =  stroke  of  piston;  D  =  diameter  of 
drivers,  all  in  inches.  Then  the  internal  friction  =  3.8d2£/Z),  in  pounds 
at  the  circumference  of  the  drivers. 

Concerning  the  effect  of  increasing  speed  on  tractive  force,  Mr.  Render- 
son  says  (1906): 

From  a  number  of  tests  and  information  from  various  roads  and  au- 
thorities it  seems  as  if,  for  ordinary  simple  engines,  the  coefficient  0.8 


in  the  equation  Actual  tractive  force  =    >s  could  be  modified  in  ac- 

cordance with  the  speed  in  order  to  obtain  the  actual  tractive  force  at 
various  speeds  about  as  follows: 

Revs,  per  min.  =      20  40  60        80      100  120  140  160 

Coefficient  =  0  .  80  0.80  0.80    0.70    0.61  0.53  0.46  0.40 

Revs,  per  min.  =     180  200  220      240-     260  280  300  320     340 

Coefficient  =  0.35  0.31  0.28    0.26    0.24  0.23  0.21  0.20    0.19 

Efficiency  of  the  Mechanism  of  a  locomotive.  —  Frank  C.Wagner 
(Proc.  A.  A.  A.  S.j  1900,  p.  140)  gives  an  account  of  some  dynamometer 
tests4  which  indicate  that  in  ordinary  freight  service  the  power  used  to 
drive  the  locomotive  and  tender  and  to  overcome  the  friction  of  the 
mechanism  is  from  10%  to  35%  of  the  total  power  developed  in  the  steam- 
cylinder.  In  one  test  the  weight  of  the  locomotive  and  tender  was  16% 
of  the  total  weight  of  the  train,  while  the  power  consumed  in  the  loco- 
motive and  tender  was  from  30%  to  33%  of  the  indicated  horse-power. 

Adhesion.  —  The  limit  of  the  hauling  capacity  of  a  locomotive  is  the 
adhesion  due  to  the  weight  on  the  driving  wheels.  Holmes  gives  the 
adhesion,  in  English  practice,  as  equal  to  0.15  of  the  load  on  the  driving 
wheels  in  ordinary  dry  weather,  but  only  0.07  in  damp  weather  or  when 
the  rails  are  greasy.  In  American  practice  it  is  generally  taken  as  from 
Vi  to  1/5  of  the  load  on  the  drivers. 


1112 


LOCOMOTIVES. 


Tractive  Force  of  a  Locomotive.  —  Single  Expansion. 
Let  F  =  indicated  tractive  force  in  Ibs. 

p  =»  average  effective  pressure  in  cylinder  in  Ibs.  per  sq.  in. 
S  =»  stroke  of  piston  in  inches. 
d  =  diameter  of  cylinders  in  inches. 
D  =  diameter  of  driving-wheels  in  inches.     Then 
„_  4  7cdzpS _  (J2pS 

4  nD  D 

The  average  effective  pressure  can  be  obtained  from  an  indicator* 
diagram,  or  by  calculation,  when  the  initial  pressure  and  ratio  of  expan- 
sion are  known,  together  with  the  other  properties  of  the  valve-motion. 
The  subjoined  table  from  Auchincloss  gives  the  proportion  of  mean 
effective  pressure  to  boiler-pressure  above  atmosphere  for  various  pro- 
portions of  cut-off. 


Stroke, 
Cut-off  at  — 

M.E.P. 

(Boiler- 
pres.  =1). 

Stroke, 
Cut-off  at— 

M.E.P. 

(Boiler- 
pres.  =  1). 

Stroke, 
Cut-off  at  — 

M.E.P. 

(Boiler- 
pres.  =  1). 

0.1 

0.15 

0.333  =  1/3 

0.5=   1/2 

0.625  =  5/8 

0.79 

.125  =  l/8 

.2 

.375  =  3/8 

.55 

'  .666  =  2/3 

.82 

.15 

.24 

.4 

.57 

.7 

.85 

.175 

.28 

.45 

.62 

.75    =  3/4 

.89 

.2 

.32 

.5      =  l/2 

.67 

.8 

.93 

.25  =  1/4 

.4 

.55 

.72 

.875  =  7/8 

.98 

.3 

.46 

These  values  were  deduced  from  experiments  with  an  English  locomo- 
tive by  Mr.  Gooch.  As  diagrams  vary  so  much  from  different"  causes, 
this  table  will  only  fairly  represent  practical  cases.  It  is  evident  that 
the  cut-off  must  be  such  that  the  boiler  will  be  capable  of  supplying 
sufficient  steam  at  the  given  speed. 

We  can,  however,  allow  for  wire  drawing  to  the  steam  chest  and  drop  in 
pressure  due  to  expansion,  and  internal  friction  by  writing  the  formula: 

0  8  Pd2S 
Actual  Tractive  Force  =  —  '-  —  ^  -  ,  d,  S,  and  D  being  as  before  and  P 

representing  boiler  pressure  in  Ibs.  per  sq.  in. 

Compound  Locomotives.  —  The  Baldwin  Locomotive  Works  give  the  fol- 
lowing formulae  for  compound  engines  of  the  Vauclain  four-cylinder  type: 
„,      C*S  X  2/3  P  ,   c*S  X  1/4  P 
~~D~~  ~D~ 

T—  tractive  force  in  Ibs.  C=  diam.  of  high-pressure  cylinder  in  ins. 
c=  diam.  of  low-pressure  cylinder  in  ins.  P=  boiler-pressure  in  Ibs. 
S=  stroke  of  piston  in  ins.  Z>=  diam.  of  driving-wheels  in  ins. 

For  a  two-cylinder  or  cross-compound  engine  it  is  only  necessary  to  con- 
sider the  high-pressure  cylinder,  allowing  a  sufficient  decrease  in  boiler 
pressure  to  compensate  for  the  necessary  back-pressure.  The  formula  is 


D 

The  above  formulae  are  for  speeds  of  from  5  to  10  miles  an  hour,  or 
less;  above  that  the  capacity  9f  the  boiler  limits  the  cut-off  which  can  be 
used,  and  the  available  tractive  force  is  rapidly  reduced  as  the  speed 
increases.  _  For  a  full  discussion  of  this,  see  page  375  of  Henderson's 
"  Locomotive  Operation." 

The  Size  of  Locomotive  Cylinders  is  usually  taken  to  be  such  that 
the  engine  will  just  overcome  the  adhesion  of  its  wheels  to  the  rails  under 
favorable  circumstances. 

The  adhesion  is  taken  by  a  committee  of  the  Am.  Ry.  Master  Mechan- 
ics' Assn.  as  0.25  of  the  weight  on  the  drivers  fop  passenger  engines,  0.24 
for  freight,  and  0.22  for  switching  engines;  and  the  mean  effective  pres- 
sure in  the  cylinder,  when  exerting  the  maximum  tractive  force,  is  taken 
at  0.85  of  the  boiler-pressure. 


LOCOMOTIVES. 


1113 


Let  W  =  weight  on  drivers  in  Ibs.;  P  =  tractive  force  In  Ibs.,  =  say 
0.25  W;  pi  =  boiler-pressure  in  Ibs.  per  sq.  in.;  p  =  mean  effective 
pressure,  =  0.85  p\\  d  =  diam.  of  cylinder,  8  =  length  of  stroke,  and 
D  =  diam.  of  driving-wheels,  all  in  inches.  Then 

4ff  X  0.8 


Whence 

Von  Borries's  rule  for  the  diameter  of  the  low-pressure  cylinder  of  a 
compound  locomotive  is  d-  =  2  ZD  -f-  ph,  in  which  d=  diameter  of  l.p. 
cylinder  in  inches;  D  =  diameter  of  driving-wheel  in  inches;  p  =  mean 
effective  pressure  per  sq.  in.,  after  deducting  .internal  machine  friction; 
h  =  stroke  of  piston  in  inches;  Z  =  tractive  force  required,  usually  0.14 
to  0.16  of  the  adhesion. 

The  value  of  p  depends  on  the  relative  volume  of  the  two  cylinders, 
and  from  indicator  experiments  may  be  taken  as  follows: 

ri*cc  r»t  TTnm-nA      Ratio  of  Cylinder    pin  percent  of     p  for  Boiler-pres' 

Volumes.          Boiler-pressure,     sure  of  176  Ibs. 
Large-tender  eng's.    1  :  2  or  1  :  2.05  42  74 

Tank-engines 1  :  2  or  1  :  2.2  40  71 

Horse-power  of  a  Locomotive.  —  For  each  cylinder  the  horse-powei 
is  H.P.  =  pLaN  •*-  33,000,  in  which  p  =  mean  effective  pressure,  L  = 
stroke  in  feet,  a  =  area  of  cylinder  =  1/4  ?rd2,  N  =  number  of  single 
strokes  per  minute,  LN  =  piston  speed,  ft.  per  min.  Let  M  =  speed  of 
train  in  miles  per  hour,  S  =  length  of  stroke  in  inches,  and  D  =  diam- 
eter of  driving-wheel  in  inches.  Then  LN  =  MX8&X2S  +  xD. 
Whence  for  the  two  cylinders  the  horse-power  is 


xD  X  33,000 


375  D 


REVOLUTIONS  PER  MINUTE  FOR  VARIOUS  DIAMETERS  OF  WHEELS 
AND  SPEEDS. 


Miles  per  Hour. 


Diameter 
of  Wheel. 

10 

20 

30 

40 

50 

60 

70 

80 

50  in. 

67 

134 

201 

268 

336 

403 

470 

538 

56  in. 

60 

120 

180 

240 

300 

360 

420 

480 

60m. 

56 

112 

168 

224 

280 

336 

392 

448 

62  in. 

54 

108 

162 

217 

271 

325 

379 

433 

66  in. 

51 

102 

153 

204 

255 

306 

357 

408 

68  in. 

49 

99 

148 

198 

247 

296 

346 

395 

72  in. 

47 

93 

140 

187 

233 

279 

326 

373 

78  in. 

43 

86 

129 

172 

215 

258 

301 

344 

80  in. 

42 

84 

126 

168 

210 

252 

294 

336 

84  in. 

40 

80 

120 

160 

200 

240 

280 

320 

90  in. 

37 

75 

112 

150 

186 

224 

261 

299 

The  Size  of  Locomotive  Boilers.  (Forney's  Catechism  of  the  Loco- 
motive.) —  They  should  be  proportioned  to  the  amount  of  adhesive 
weight  and  to  the  speed  at  which  the  locomotive  is  intended  to  work. 
Thus  a  locomotive  with  a  great  deal  of  weight  on  the  driving-wheels 
could  pull  a  heavier  load,  would  have  a  greater  cylinder  capacity  than 
one  with  little  adhesive  weight,  would  consume  more  steam,  and  there- 
fore should  have  a  larger  boiler. 

The  weight  and  dimensions  of  locomotive  boilers  are  in  nearly  all 
cases  determined  by  the  limits  of  weight  and  space  to  which  they  are 
necessarily  confined.  It  may  be  stated  generally  that  within  these  limits 
Q  locomotive  boiler  cannot  be  made  too  large.  In  other  words,  boilers  for 


1114 


LOCOMOTIVES. 


locomotives  should  ahyays  be  made  as  large  as  is  possible  under  the 
conditions  that  determine  the  weight  and  dimensions  of  the  locomotives. 
(See  also  Holmes  on  the  Steam-engine,  pp.  371  to  377  and  383  to  389 
and  the  Report  of  the  Am.  Ry.  M.  M.  Ass'n.  for  1897,  pp.  218  to  232.)  ' 
Holmes  gives  the  following  from  English  practice: 

Evaporation,  9  to  12  Ibs.  of  water  from  and  at  212°. 

Ordinary  rate  of  combustion,  65  Ibs.  per  sq.  ft.  of  grate  per  hour. 

Ratio  of  grate  to  heating  surface,  1  :  60  to  90. 

Heating  surface  per  Ib.  of  coal  burnt  per  hour.  0.9  to  1.5  sq.  ft 
Mr.  Henderson   states  the  approximate  heating  surface  needed   per 
indicated  horse-power  as  follows: 

Compound  Locomotives 2  square  feet. 

Simple  Locomotives  (cut-off  1/2  stroke  or  less) 2 1/3  square  feet. 

Simple  Locomotives  (cut-off  1/2  to  3/4  stroke) 2 2/3  square  feet. 

Simple  Locomotives  (full  stroke) 3  square  feet. 

For  the  ratio  of  heating  surface  to  grate  area  the  Master  Mechanics 
Ass'n  Committee  of  1902  advised  as  below: 


Fuel. 

Passenger. 

Freight. 

Simple. 

Com- 
pound. 

Simple. 

Com- 
pound . 

65  to  90 
50  to  65 
40  to  50 

35  to  40 
28  to  35 

75  to  95 
60  to  75 
35  to  60 

30  to  35 

24  to  30 

70  to  85 
45  to  70 
35  to  45 

30  to  35 
25  to  30 

65  to  85 
50  to  65 
45  to  50 

40  to  45 
30  to  40 

Slow  burning  bituminous  

Bituminous  slack  and  free  burning.  . 

Low  grade  bituminous,  lignite  and 
slow  burning  anthracite  

A.  E.  Mitchell,  (Eng'g  News,  Jan.  24,  1891)  says:  Square  feet  of  boiler- 
heating  surface  for  bituminous  coal  should  not  be  less  than  4  times  the 
square  of  the  diameter  in  inches  of  a  cylinder  1  inch  larger  than  the 
cylinder  to  be  used.  One  tenth  of  this  should  be  in  the  fire-box.  On 
anthracite  locomotives  more  heating-surface  is  required  in  the  fire-box,  on 
account  of  the  larger  grate-area  required,  but  the  heating-surface  of  the 
flues  should  not  be  materially  decreased. 

Wootten's  Locomotive.  (Clark's  Steam-engine;  see  also  Jour. 
Frank.  Inst.  1891,  and  Modern  Mechanism,  p.  485.) — J.  E.  Wootten 
designed  and  constructed  a  locomotive  boiler  for  the  combustion  of  an- 
thracite and  lignite,  though  specially  for  the  utilization  as  fuel  of  the 
waste  produced  in  the  mining  and  preparation  of  anthracite.  The  special 
feature  of  the  engine  is  the  fire-box,  which  is  made  of  great  length  and 
breadth,  extending  clear  over  the  wheels,  giving  a  grate-area  of  from 
64  to  85  sq.  ft.  The  draught  diffused  over  these  large  areas  is  so  gentle 
as  not  to  lift  the  fine  particles  of  the  fuel.  A  number  of  express-engines 
having  this  type  of  boiler  are  engaged  on  the  fast  trains  between  Phila- 
delphia and  Jersey  City.  The  fire-box  shell  is  8  ft.  8  in.  wide  and  10  ft. 
5  in.  long;  the  fire-box  is  8  X  91/2  ft.,  making  76  sq.  ft.  of  grate-area. 
The  grate"  is  composed  of  bars  and  water-tubes  alternately.  The  regular 
types  of  cast-iron  shaking  grates  are  also  used.  The  height  of  the  fire- 
box is  only  2  ft.  5  in.  above  the  grate.  The  grate  is  terminated  by  a 
bridge  of  fire-brick,  beyond  which  a  combustion-chamber,  27  in.  long, 
leads  to  the  flue-tubes,  about  184  in  number,  13/4  in.  diam.  The  cylin- 
ders are  21  in.  diam.,  with  a  stroke  of  22  inches.  The  driving-wheels, 
four-coupled,  are  5  ft.  8  in.  diam.  The  engine  weighs  44  tons,  of  which 
29  tons  are  on  driving  wheels.  The  heating-surface  of  the  fire-box  is 
135  sq.  ft.,  that  of  the  flue-tubes  is  982  sq.  ft.:  together,  1117  sq.  ft.,  or 
14.7  times  the  grate-area.  Hauling  15  passenger-cars,  weighing  with 
passengers  360  tons,  at  an  average  speed  of  42  miles  per  hour,  over  ruling 
gradients  of  1  in  89,  the  engine  consumes  62  Ibs,  of  fuel  per  mile,  of 
34  Vl  Iks,  per  sq,  ft,  of  grate  per  hour, 


LOCOMOTIVES. 


1115 


Grate-surface,  Smoke-stacks,  and  Exhaust-nozzles  for  Ix>como- 
motives.  —  A.  E.  Mitchell,  Supt.  of  Motive  Power  of  the  Erie  R.  R.,  says 
(1895)  that  some  roads  use  the  same  size  of  stack,  131/2  in.  diam.  at 
throat,  for  all  engines  up  to  20  in.  diam.  of  cylinder. 

The  area  of  the  orifices  in  the  exhaust-nozzles  depends  on  the  quantity 
and  quality  of  the  coal  burnt,  size  of  cylinder,  construction  of  stack, 
and  the  condition  of  the  outer  atmosphere.  It  is  therefore  impossible 
to  give  rules  for  computing  the  exact  diameter  of  the  orifices.  All  that 
can  be  done  is  to  give  a  rule  by  which  an  approximate  diameter  can  be 
found.  The  exact  diameter  can  only  be  found  by  trial.  Our  experi- 
ence leads  us  to  believe  that  the  area  of  each  orifice  in  a  double  exhaust- 
nozzle  should  be  equal  to  1/400  part  of  the  grate-surface,  and  for  single 
nozzles  1/200  of  the  grate-surface.  These  ratios  have  been  used  in  finding 
the  diameters  of  the  nozzles  given  in  the  following  table.  The  same 
sizes  are  often  used  for  either  hard  or  soft  coal-burners.  [These  sizes  are 
small  at  the  present  day  (1909)  as  locomotives  have  enormously  in- 
creased in  size.] 


Double 

Single 

Size  of 
Cylinders, 
in  inches. 

Grate-area 
for  Anthra- 
cite Coal,  in 
sq.  in, 

Grate-area 
for  Bitumin- 
ous Coal,  in 
sq.  in. 

Diameter 
of  Stacks, 
in  inches. 

Nozzles. 

Nozzles. 

Diam.  of 
Orifices,  in 

Diam.  of 
Orifices,  in 

inches. 

inches. 

12x20 

1591 

1217 

91/2 

2 

213/16 

13x20 

1873 

1432 

101/2 

21/8 

3 

14x20 

2179 

1666 

111/4 

25/ie 

3V4 

15x22 

2742 

2097 

121/2 

29/i6 

311/16 

16x24 

3415 

2611 

14 

27/8 

41/16 

17x24 

3856 

2948 

15 

3Vl6 

45/16 

18x24 

4321 

3304 

153/4 

31/4 

-     45/g 

19x24 

4810 

3678 

161/2 

37/16 

413/ie 

20x24 

5337 

4081 

171/2 

35/8 

51/16 

Exhaust-nozzles  in  Locomotive  Boilers.  —  A  committee  of  the 
Am.  Ry.  Master  Mechanics'  Ass'n.  in  1890  reported  that  they  had,  after 
two  years  of  experiment  and  research,  come  to  the  conclusion  that, 
owing  to  the  great  diversity  in  the  relative  proportions  of  cylinders  and 
boilers,  together  with  the  difference  in  the  quality  of  fuel,  any  rule  which 
does  not  recognize  each  and  all  of  these  factors  would  be  worthless. 

The  committee  was  unable  to  devise  any  plan  to  determine  the  size 
of  the  exhaust-nozzle  in  proportion  to  any  other  part  of  the  engine  or 
boiler.  The  conditions  desirable  are:  That  it  must  create  draught 
enough  on  the  fire  to  make  steam,  and  at  the  same  time  impose  the  least 
possible  amount  of  work  on  the  pistons  in  the  shape  of  back  pressure. 
It  should  be  large  enough  to  produce  a  nearly  uniform  blast  without 
lifting  or  tearing  the  fire,  and  be  economical  in  its  use  of  fuel.  The 
Annual  Report  of  the  Association  for  1896  contains  interesting  data  on 
this  subject. 

Much  important  information  regarding  stacks  and  exhaust  nozzles  is 
embodied  in  the  tests  at  Purdue  University,  reported  to  the  Master 
Mechanics'  Ass'n.  in  1896  and  in  the  tests  reported  in  the  American 
Engineer  in  1902  and  1903. 

Fire-brick  Arches  in  Locomotive  Fire-boxes.  —  A  committee  of 
the  Am.  Ry.  Master  Mechanics'  Ass'n.  in  1890  reported  strongly  in  favor 
of  the  use  of  brick  arches  in  locomotive  fire-boxes.  They  say:  It  is  the 
unanimous  opinion  of  all  who  use  bituminous  coal  and  brick  arch,  that 
it  is  most  efficient  in  consuming  the  various  gases  composing  black 
smoke  and  by  impeding  and  delaying  their  passage  through  the  tubes, 
and  mingling  and  subjecting  them  to  the  heat  of  the  furnace,  greatly 
lessens  the  volume  ejected,  and  intensifies  combustion,  and  does  not  in 
the  least  check  but  rather  augments  draught,  with  the  consequent  saving 
of  fuel  and  increased  steaming  capacity  that  might  be  expected  from 
such  results,  This  in  particular  when  used  in  connctioa  with  extension 
front, 


1116  WCOMOTIVES. 

Arches  now  (1009)  ate  not  quite  so  much  in  favor,  largely  on  account 
of  the  difficulty  and  delay  caused  to  workmen  when  flues  must  be  calked, 
as  occurs  frequently  in  bad  water  districts,  and  some  of  their  former 
advocates  are  now  omitting  them  altogether. 

Economy  of  High  Pressures.  —  Tests  of  a  Schenectady  locomotive 
with  cylinders  16  X  24  ins.,  at  the  Purdue  University  locomotive  testing 
plant,  gave  results  as  follows:  (Eng.  Digest,  Mar.,  1909;  Bull.  No.  26,  Univ. 
of  111.  Expt.  Station). 

Boiler  pressure,  Ibs.  per  sq.  in.  120  140  160  180  200  220  240 
Steam  per  1  H.P.  hour,  Ibs.  29.1  27.7  26.6  26.  25.5  25.1  24.7 
Coal  per  1  H.P.  hour,  Ibs.  4  3.77  3.59  3.50  3.43  3.37  3.31 

In  the  same  series  of  tests  the  economy  of  the  boiler  at  different  rates  of 
driving  and  different  pressures  was  determined,  the  results  leading  to  the 
formula  E  =  11.305  —  0.221  H,  in  which  E  =  Ibs.  evaporated  from  and 
at  212"  per  Ib.  of  Youghiogheny  coal,  and  H  the  equivalent  evaporation 
per  sq.  ft.  of  heating  surface  per  hour,  with  an  average  error  for  any 
pressure  which  does  not  exceed  2.1%. 

Leading  American  Types  of  Locomotive  for  Freight  and 
Passenger  Service0 

1.  The  eight-wheel  or  '*  American"  passenger  type,  having  four  coupled 
driving-wheels  and  a  four-wheeled  truck  in  front. 

2.  The  "ten-wheel"  type,  for  mixed  traffic,  having  six  coupled  drivers 
and  a  leading  four-wheel  truck. 

3.  The  "Mogul"  freight  type,  having  six  coupled  driving-wheels  and 
a  pony  or  two-wheel  truck  in  front. 

4.  The  "Consolidation"  type,  for  heavy  freight  service,  having  eight 
coupled  driving-wheels  and  a  pony  truck  in  front. 

Besides  these  there  is  a  great  variety  of  types  for  special  conditions  of 
service,  as  four-wheel  and  six-wheel  switching-engines,  without  trucks; 
the  Forney  type  used  on  elevated  railroads,  with  four  coupled  wheels 
under  the  engine  and  a  four-wheeled  rear  truck  carrying  the  water-tank 
and  fuel;  locomotives  for  local  and  suburban  service  with  four  coupled 
driving-wheels,  with  a  two-wheel  truck  front  and  rear,  or  a  two-wheel 
truck  front  and  a  four-wheel  truck  rear,  etc.  "Decapod"  engines  for 
heavy  freight  service  have  ten  coupled  driving-wheels  and  a  two-wheel 
truck  in  front, 

O     OA  n       O     O    O    OB 

O     O     OB  O     O     O       h    F 

O  O  O  Oc       O   O   O   o 

o  o  n  on  o  on  o   OH 

Classification  of  Locomotives  (Penna.  R.  R.  Co.,  1900).  —  Class  A, 
two  pairs  of  drivers  and  no  truck.  Class  B,  three  pairs  of  drivers  and  no 
truck.  Class  C,  four  pairs  of  drivers  and  no  truck.  Class  D,  two  pairs  of 
drivers  and  four-wheel  truck.  Class  E,  two  pairs  of  drivers,  four-wheel 
truck,  and  trailing  wheels.  Class  F,  three  pairs  of  driving-wheels  and 
two-wheel  truck.  Class  G,  three  pairs  of  drivers  and  four-wheel  truck. 
Class  H,  four  pairs  of  drivers  and  two-wheel  truck.  Class  A  is  com- 
monly called  a  "four-wheeler";  B,  a  "six-wheeler";  D,  an  "eight- 
wheeler,"  or  "American"  type;  E,  "Atlantic"  type;  F,  "Mogul"; 
Gs  "ten- wheeler";  H,  "Consolidation." 

Modern  Classification.  —  The  classes  shown  above,  lettered  A,  B,  C, 
etc.,  are  commonly  represented  respectively  by  the  symbols  0-4-0; 
0-6-0;  0-8-0,  4-4-0;  4-4-2,  2-6-0;  4-6-0;  2-8-0;  the  first  figure  being 
the  number  of  wheels  in  the  truck,  the  second  the  driving-wheels,  and  the 
tbird  the  trailers.  Other  types  are  the  "Pacific,"  4-6-2;  the  "Prairie,"  2-6-2; 


LOCOMOTIVES. 


1117 


and  the  "Santa  Fe,"  2-10-2.    Engines  on  the  Mallet  system,  with  two 
locomotive  engines  under  one  boiler,  are  classified  0-8-8-0,  2-6-6-2,  etc. 

Formulae  for  Curves.     (Baldwin  Locomotive  Works.) 
Approximate  Formula  for  Radius.  Approximate  Formula  for  Swing, 

R  -  0.7646  W  +  2  P.  '     (T  -  TF)  T  -H  2  S  -  R. 


R  =-  radius  of  min.  curve  in  feet. 
P  —  play    of    driving-wheels   in 

decimals  of  1  ft. 
W  =  rigid  wheel-base  in  feet. 


W  =  rigid  wheel-base. 
T  =  total  wheel-base. 
R  =  radius  of  curve. 
S  =  swing  on  each  side  of  centre. 


Steam-distribution  for  High-speed  Locomotives. 

(C.  H.  Quereau,  Eng'g  News,  March  8,  1894. 

Balanced  Valves.  —  Mr.  Philip  Wallis,  in  1886,  when  Engineer  of  Tests 
for  the  C.,  B.  &  Q.  R.  R.,  reported  that  while  6  H.P.  was  required  to 
work  unbalanced  valves  at  40  miles  per  hour,  for  the  balanced  valves 
2.2  H.P.  only  was  necessary. 

[Later  tests  were  reported  by  the  Master  Mechanics'  Committee  in  1896. 
Unbalanced  valves  required  from  3/4  to  2 1/2  per  cent  of  the  I. H.P.  for 
their  motion,  balanced  valves  from  1/3  to  1/2  as  much,  and  piston  valves 
about  1/5  or  I/G.  Generally  in  balanced  valves,  the  area  of  balance  = 
area  of  exhaust  port  +  area  of  two  bridges  4-  area  of  one  steam  port.J 

Effect  of  Speed  on  Average  Cylinder-pressure.  —  Assume  that  a  locomo- 
tive has  a  train  in  motion,  the  reverse  lever  is  placed  in  the  running 
notch,  and  the  track  is  level;  by  what  is  the  maximum  speed  limited? 
The  resistance  of  the  train  and  the  load  increase,  and  the  power  of  the 
locomotive  decreases  with  increasing  speed  till  the  resistance  and  power 
are  equal,  when  the  speed  becomes  uniform.  The  power  of  the  engine 
depends  on  the  average  pressure  in  the  cylinders.  Even  though  the 
cut-off  and  boiler-pressure  remain  the  same,  this  pressure  decreases  as 
the  speed  increases;  because  of  the  higher  piston-speed  and  more  rapid 
valve-travel  the  steam  has  a  shorter  time  in  which  to  enter  the  cylinders 
at  the  higher  speed.  The  following  table,  from  indicator-cards  taken 
from  a  locomotive  at  varying  speeds,  shows  the  decrease  of  average 
pressure  with  increasing  speed: 


Miles  per  hour 46  51  51 

Speed,  revolutions 224  248  248 

Average  pressure  per  sq.  in.: 

Actual 51.5  44.0  47.3 


. 
Calculated .......  T    46l5 


53 

258 


43.0 

44.7 


54 
263 


41.3 

43.8 


57 

277 


42.5 
41.6 


60 

292 


66 
321 


37.3  36.3 
39.5  35.9 


The  "average  pressure  calculated"  was  figured  on  the  assumption  that 
the  mean  effective  pressure  W9uld  decrease  in  the  same  ratio  that  the 
speed  increased.  The  main  difference  lies  in  the  higher  steam-line  at 
the  lower  speeds,  and  consequent  higher  expansion-line,  showing  that 
more  steam  entered  the  cylinder.  The  back  pressure  and  compression- 
lines  agree  quite  closely  for  all  the  cards,  though  they  are  slightly  better 
for  the  slower  speeds.  That  the  difference  is  not  greater  may  safely  be 
attributed  to  the  large  exhaust-ports,  passages,  and  exhaust  tip,  which 
is  5  in.  diameter.  These  are  matters  of  great  importance  for  high  speeds. 

Boiler-pressure.  —  Assuming  that  the  train  resistance  increases  as  the 
speed  after  about  20  miles  an  hour  is  reached,  that  an  average  of  50  Ibs. 
per  sq.  in.  is  the  greatest  that  can  be  realized  in  the  cylinders  of  a  given 
engine  at  40  miles  an  hpur.  and  that  this  pressure  furnishes  just  sufficient 
power  to  keep  the  train  at  this  speed,  it  follows  that,  to  increase  the 
speed  to  50  miles,  the  mean  effective  pressure  must  be  increased  in  the 
same  proportion.  To  increase  the  capacitv  for  speed  of  any  locomotive 
its  power  must  be  increased,  and  at  least  by  as  much  as  the  speed  is  to 
ue  increased.  One  way  to  accomplish  this  is  to  increase  the  boiler- 


1118  LOCOMOTIVES. 

pressure.  That  this  is  generally  realized,  is  shown  by  the  increase  In 
boiler-pressure  in  the  last  ten  years.  For  twenty-three  single-expansion 
locomotives  described  in  the  railway  journals  this  year  the  steam-pres- 
sures are  as  follows:  3,  160  Ibs.;  4,  165  Ibs.;  2,  170  Ibs.;  13  180  Ibs.- 
1,  190  Ibs. 

Valve-travel.  —  An  increased  average  cylinder-pressure  may  also  be 
obtained  by  increasing  the  valve-travel  without  raising  the  boiler- 
pressure,  and  better  results  will  be  obtained  by  increasing  both.  The 
longer  travel  gives  a  higher  steam-pressure  in  the  cylinders,  a  later 
exhaust-opening,  later  exhaust-closure,  and  a  larger  exhaust-opening  — 
all  necessary  for  high  speeds  and  economy.  I  believe  that  a  20-in. 
port  and  6i/2-in.  (or  even  7-in.)  travel  could  be  successfully  used  for 
high-speed  engines,  and  that  frequently  by  so  doing  the  cylinders  could 
be  economically 'reduced  and  the  counter-balance  lightened.  Or,  better 
still,  the  diameter  of  the  drivers  increased,  securing  lighter  counterbal" 
ance  and  better  steam-distribution. 

Size  of  Drivers.  —  Economy  will  increase  with  increasing  diameter  of 
drivers,  provided  the  work  at  average  speed  does  not  necessitate  a  cut-off 
longer  than  one  fourth  the  stroke.  The  piston-speed  of  a  locomotive 
with  62-in.  drivers  at  55  miles  per  hour  is  the  same  as  that  of  one  with 
68-in.  drivers  at  61  miles  per  hour. 

Steam-ports.  — The  length  of  steam-ports  ranges  from  15  in.  to  23  in., 
and  has  considerable  influence  on  the  power,  speed,  and  economy  of  the 
locomotive.  In  cards  from  similar  engines  the  steam-line  of  the  card 
from  the  engine  with  23-in.  ports  is  considerably  nearer  boiler-pressure 
than  that  of  the  card  from  the  engine  with  171/4-in.  ports.  That  the 
higher  steam-line  is  due  to  the  greater  length  of  steam-port  there  is  little 
room  for  doubt.  The  23-in.  port  produced  531  H.P.  in  an  18i/2-in. 
cylinder  at  a  cost  of  23.5  Ibs.  of  water  per  I. H.P.  per  hour.  The  171/4 
in.  port,  424  H.P.,  at  the  rate  of  22.9  Ibs.  of  water,  in  a  19-in.  cylinder. 

Allen  Valves.  —  There  is  considerable  difference  of  opinion  as  to  the 
advantage  of  the  Allen  ported-valve.  (See  Eng.  News,  July  6,  1893.) 

A  Report  on  the  advantage  of  Allen  valves  was  made  by  the  Master 
Mechanics'  Committee  of  1896. 

Speed  of  Railway  Trains.  —  In  1834  the  average  speed  of  trains  on 
the  Liverpool  and  Manchester  Railway  was  20  miles  an  hour;  in  1838  it 
was  25  miles  an  hour.  But  by  1840  there  were  engines  on  the  Great 
Western  Railway  capable  of  running  50  miles  an  hour  with  a  train  and 
80  miles  an  hour  without.  (Trans.  A.  S.  M.  E.,  vol.  xiii,  363.) 

The  limitation  to  the  increase  of  speed  of  heavy  locomotives  seems  at 
present  to  be  the  difficulty  of  counterbalancing  the  reciprocating  parts. 
The  unbalanced  vertical  component  of  the  reciprocating  parts  causes 
the  pressure  of  the  driver  on  the  rail  to  vary  with  every  revolution. 
Whenever  the  speed  is  high,  it  is  of  considerable  magnitude,  and  its 
change  in  direction  is  so  rapid  that  the  resulting  effect  upon  the  rail  is 
not  inappropriately  called  a  "hammer  blow."  Heavy  rails  have  been 
kinked,  and  bridges  have  been  shaken  to  their  fall  under  the  action  of 
heavily  balanced  drivers  revolving  at  high  speeds.  The  means  by 
which  the  evil  is  to  be  overcome  has  not  yet  been  made  clear.  See 
paper  by  W.  F.  M.  Goss,  Trans.  A.  S.  M.  E.,  vol.  xvi. 

Much  can  be  accomplished,  however,  by  carefully  designing  and 
proportioning  the  counter-balance  in  the  wheels  and  by  using  light,  but 
strong,  reciprocating  parts.  Pages  41-74  of  "Locomotive  Operation," 
gives  complete  rules  and  results. 

Balanced  compound  locomotives,  with  4  cylinders,  the  adjacent  pis- 
tons and  crossheads  being  connected  180°  apart  have  also  done  much 
to  reduce  the  disturbance  of  the  moving  parts. 

Engine  No.  999  of  the  New  York  Central  Railroad  ran  a  mile  in  32 
seconds  equal  to  112  miles  per  hour,  May  11,  1893. 

Speed     in)  _  circum.  of  driving-wheels  in  in.  X  no.  of  rev,  per  min.  X  60 
hour       )  63,360 

=  diam.,  of  driving-wheels  in  in.  X  no.  of  rev.  per  min.  X.003 

(approximate,  giving  result  8/10  of  1  per  cent  too  great). 
Performance  of  a  High-speed  Locomotive.  —  The  Baldwin  com- 
pound locomotive  No.  1027,  on  the  Phila.  &  Atlantic  City  Ry.,  in  1897 
made  a  record  as  follows: 


LOCOMOTIVES. 


1119 


For  the  52  days  the  train  ran,  from  July  2d  to  August  31st,  the  average 
time  consumed  on  the  run  of  551/2  miles  from  Camden  to  Atlantic  City 
was  48  minutes,  equivalent  to  a  uniform  rate  of  speed  from  start  to  stop 
Of  69  miles  per  hour.  On  July  14th  the  run  from  Carnden  to  Atlantic 
City  was  made  in  461/2  min.,  an  average  of  71.6  miles  per  hour  for  the  total 
distance.  On  22  days  the  train  consisted  of  5  cars  and  on  30  days  it  was 
made  up  of  6,  the  weight  of  cars  being  as  follows:  combination  car,  57,200 
Ibs.;  coaches,  each,  59,200  Ibs.;  Pullman  car,  85,500  Ibs. 

The  general  dimensions  of  the  locomotive  are  as  follows:  cylinders, 
13  and  22  X  26  in.;  height  of  drivers,  841/4  in.;  total  wheel-base,  26  ft. 
7  in.;  driving-wheel  base,  7  ft.  3  in.;  length  of  tubes,  13  ft.;  diameter  of 
boiler,  583/4  in.;  diameter  of  tubes,  13/4in.;  number  of  tubes,  278;  length 
of  fire-box,  1137/gin.;  width  of  fire-box,  96  in.;  heating-surface  of  fire- 
box, 136.4  sq.  ft.;  heating-surface  of  tubes,  1614.9  sq.  ft.;  total  heating- 
surface,  1835.1  sq.  ft.;  tank  capacity,  4000  gallons;  boiler-pressure, 
200  Ibs.  per  sq.  in.;  total  weight  of  engine  and  tender,  227,000  Ibs.; 
weight  on  drivers  (about),  78,600  Ibs. 

Fuel  Efficiency  of  American  Locomotives.  —  Prof.  W.  M.  Goss,  as 
a  result  of  a  series  of  tests  run  on  the  Purdue  locomotive,  finds  the  dis- 
position of  the  heat  developed  by  burning  coal  in  a  locomotive  fire-box 
to  be  on  the  average  ab9ut  as  shown  in  the  following  table: 

Absorbed  by  steam  in  the  boiler,  52  %;  by  the  superheater,  5  %; 
total,  57  %.  Losses:  In  vaporizing  moisture  in  the  coal,  5  %;  discharge 
of  CO.,  1  %;  high  temperature  of  the  products  of  combustion,  14  %; 
unconsumed  fuel  in  the  form  of  front-end  cinders,  3  % ;  cinders  or  sparks 
passed  out  of  the  stack,  9  %;  unconsumed  fuel  in  the  ash,  4  %;  radia- 
tion, leakage  of  steam  and  water,  etc.,  7  %.  Total  losses,  43  %. 

It  is  probable  that  these  losses  are  considerably  less  than  the  losses 
which  are  experienced  in  the  average  locomotive  in  regular  railway 
service.  -*-  (Bulletin  No.  402,  U.S.  Geol.  Survey,  1909.) 

Locomotive  Link  Motion.  —  Mr.  F.  A.  Halsey,  in  his  work  on  "  Loco- 
motive Link  Motion,"  1898,  shows  that  the  Iocati9n  of  the  eccentric-rod 
pins  back  of  the  link-arc  and  the  angular  vibrations  of  the  eccentric- 
rods  introduce  two  errors  in  the  motion  which  are  corrected  by  the 
angular  vibration  of  the  connecting-rod  and  by  locating  the  saddle-stud 
back  of  the  link-arc.  He  holds  that  it  is  probable  that  the  opinions  of 
the  critics  of  the  locomotive  link  motion  are  mistaken  ones,  and  that  it 
comes  little  short  of  all  that  can  be  desired  for  a  locomotive  valve  motion. 
The  increase  of  lead  from  full  to  mid  gear  and  the  heavy  compression  at 
mid  gear  are  both  advantages  and  not  defects.  The  cylinder  problem  of 
a  locomotive  is  entirely  different  from  that  of  a  stationary  engine.  With 
the  latter  the  problem  is  to  determine  the  size  of  the  cylinder  and  the  dis- 
tribution of  steam  to  drive  economically  a  given  load  at  a  given  speed. 
With  locomotives  the  cylinder  is  made  of  a  size  which  will  start  the 
heaviest  train  which  the  adhesion  of  the  locomotive  will  permit,  and  the 
problem  then  is  to  utilize  that  cylinder  to  the  best  advantage  at  a  greatly 
increased  speed,  but  under  a  greatly  reduced  mean  effective  pressure. 

Negative  lead  at  full  gear  has  been  used  in  the  recent  practice  of  some 
railroads.  The  advantages  claimed  are  an  increase  in  the  power  of  the 
engine  at  full  gear,  since  positive  lead  offers  resistance  to  the  motion  of 
the  piston;  easier  riding;  reduced  frequency  of  hot  bearings;  and  a 
slight  gain  in  fuel  economy.  Mr.  Halsey  gives  the  practice  as  to  lead  on 
several  roads  as  follows,  showing  great  diversity: 


Full  Gear 
Forward,  in. 

Full  Gear 
Back,  in. 

Reversing 
Gear,  in. 

New  York,  New  Haven  & 
Hartford         

1/16  POS. 

1/4  neg. 

1/4  pos. 

Majne  Central 

o 

1/4  neg. 

Illinois  Central       .   .       .   . 

1/32  POS. 

abt  3/16 

Lake  Shore  

1/16  neg. 

9/64  neg. 

*Yl6  pos. 

Chicago  Great  Western  
Chicago  &  Northwestern 

0 
3/16  neg. 

0 

3/16  to  9/16 
1/4  pos 

1120 


LOCOMOTIVES. 


DIMENSIONS  OF  SOME  LARGE  AMERICAN 
LOCOMOTIVES,  1893  AND  1904. 

Of  the  four  locomotives  described  in  the  table  on  the  next  page  the 
first  two  were  exhibited  at  the  Chicago  Exposition  in  1893.  The  dimen- 
sions are  from  Engineering  News,  June,  1893.  The  first,  or  Decapod 
engine,  has  ten-coupled  driving-wheels.  It  is  one  of  the  heaviest  and 
most  powerful  engines  built  up  to  that  date  for  freight  service.  The 
second  is  a  simple  engine,  of  the  standard  American  8-wheel  type,  4 
driving-wheels,  and  a  4- wheel  truck  in  front.  This  engine  held  the 
world's  record  for  speed  in  1893  for  short  distances,  having  run  a  mile 
in  32  seconds. 

The  other  two  engines  formed  part  of  the  exhibit  of  the  Baldwin 
Locomotive  Works  at  the  St.  Louis  Exposition  in  1904.  The  Santa  Fe 
type  engine  has  five  pairs  of  driving-wheels,  and  a  two-wheeled  truck  at 
the  front  and  at  the  rear.  It  is  equipped  with  Vauclain  tandem  com- 
pound cylinders. 

Dimensions  of  Some  American  Locomotives. 

(Baldwin  Loco.  Wks.  1904-8.) 


i 

Boilers. 

Tubes. 

Heating 
Surface. 

Driving 
Wheels 

Weight,  Ibs. 

11 

gS 

B«a 

«J 

N,. 

|« 

1) 

X 

*£ 

Diam., 

on 

Total 

1 

QQ 

<A  g 

a 

<§* 

S's 

1 

1* 

1* 

ins. 

Drivers 

Engine 

ft.  in. 

1 

150 

42 

9 

97 

2 

11     7 

41 

586 

37 

44,420 

52,720 

2 

160 

50 

14.6 

160 

2 

10    6 

75 

873 

48 

72,150 

84,650 

3 

200 

60 

25  9 

287 

2 

11     7 

133 

1733 

69 

83,680 

124,420 

4 

200 

62 

30 

272 

2 

16     1 

136 

2279 

68 

112,000 

159,000 

5 

200 

76 

37.2 

298 

2V4 

13  10 

200 

2414 

51 

164,000 

179,500 

6 

200 

68 

35 

306 

21/4 

14    6 

195 

2593 

56 

166,000 

186,000 

7 

7.00 

66 

49.5 

273 

21/4 

18  10 

190 

3015 

79 

101,420 

193,760 

8 

200 

70 

53  5 

318 

21/4 

19 

195 

3543 

79 

144,600 

209,210 

9 

210 

70 

55 

303 

21/4 

21 

190 

3772 

74 

151,290 

230,940 

10 

225 

78 

58.5 

463 

21/4 

19 

210 

5155 

57 

237,800 

267,800 

11 

200 

84 

68.4 

401 

2V4 

21 

232 

4941- 

57 

394,150 

425,900 

Type  and  cylinder  size:  1,  Mogul,  13  X  18;  2,  Mogul,  16  X  20;  3,  Am- 
erican, 18  X  24;  4,  10-wheel  balanced  compound,  16  X  26  and  26  X  28; 
5,  Consolidation,  22  X  28;  6,  Consolidation,  23  and  35  X  32;  7,  Atlantic, 
15  and  25  X  26;  8,  Prairie,  17  and  28  X  28;  9,  Pacific,  22  X  28;  10,  Deca- 
pod, 19  and  32  X  32;  11,  Mallet,  two  each  26  and  40  X  30. 

The  Mallet  Compound  Locomotive. — The  Mallet  articulated  loco- 
motive consists  principally  of  two  sets  of  engines  flexibly  connected  un- 
der one  boiler;  the  rear,  which  is  a  high-pressure  engine  of  two  cylinders, 
fixed  rigid  with  the  boiler  and  receiving  the  steam  direct  from  the  dome. 
The  front  or  low-pressure  engine,  also  provided  with  two  cylinders,  is 
capable  of  lateral  movement  to  adjust  itself  to  the  curvature  of  the  road 
on  the  same  general  principle  as  a  radial  truck.  The  high-pressure 
engine  exhausts  into  a  receiver  flexibly  connecting  the  cylinders  of  the 
two  sets  of  engines,  from  which  the  low-pressure  engine  receives  its 
steam  supply  and  is  exhausted  from  the  latter  through  a  flexible  pipe 
to  the  stack.  Each  cylinder  has  its  independent  valve  and  gear  con- 
nected to  and  operated  with  a  common  reversing  rigging.  By  this 
means  the  tractive  power  can  be  doubled  over  that  of  the  ordinary 
engine  for  a  given  weight  of  rail  with  a  substantial  saving  in  fuel. 
(See  paper  by  C.  J.  Mellin,  Trans.  A.  S.  M.  E.,  1909.) 

This  type  of  locomotive  is  adapted  to  a  wider  range  of  service  than  per- 
haps any  other  design.  It  was  originally  intended  for  narrow-gage  roads 
of  light  construction,  necessitating  sharp  curves  and  steep  grades,  in  com- 
bination with  light  rails.  The  characteristics  of  this  design  are  flexibility 
and  uniform  distribution  of  weight  combined  with  the  use  of  two  separate 
engines  which  would  not  slip  at  the  same  time,  and  the  total  weight  carried 
on  the  drivers,  giving  great  tractive  power.  The  first  engine  of  this  rhi ,^s 


LARGE   AMERICAN    LOCOMOTIVES 


1121 


Baldwin. 
N.Y.,  L.E. 
&W.R.R. 
Decapod 
Freight. 

N.Y.  C.  & 
H.R.R. 
Empire 
State 
Express. 
No.  999. 

Baldwin. 
Santa  Fe 
Type 
2-10-2 
Freight. 

Baldwin. 
Pacific 
Type  4-6-2 
Passenger. 

Running-gear: 

Driving-wheels,  diam.  . 
Truck                       '     .  . 
Journals,  driving-axles 
truck- 
tender- 
Wlieel-base: 
Driving  
Total  engine 

50  in. 
30  " 
9     XlOin. 
5      X10" 
41/2X  9  " 

18ft.  10  in. 
27  "     3  " 

86  in. 
40  " 
9    X  121/2  in. 
61/4X10      " 
4l/8X  8      " 

8ft.    6  in. 
23"    11     " 

57  in. 
29  1/4  &  40" 

11      X12" 
61/2XIO" 
71/2X12"* 

19  ft,  9  in. 
35  "  11  " 

77  in. 
33  1/2  &  45" 
10X12  in. 
6X10  " 
8X12  "  * 

13  ft.  4  in. 
33  "   4  " 

tender.  

16  "     8  " 

15  "2  1/9    ' 

eng.  and  tender.  . 
Wt.  in  working-order: 

On  drivers 

53  "     4  " 
1700001bs 

47  "  81/8  " 
84  000  Ibs 

66ft.  Oin. 
234  580  Ibs 

62'  83/4" 
141  290 

On  truck-wheels  
Engine,  total  

29,500    " 
192,500   " 

40^000    "  ' 
124000    " 

52,660   " 
287,240    " 

81  [230 
222,520 

Tender 

117,500   " 

so'ooo  " 

Eng.  and  tend.,  loa'ded 
Cylinders: 
h.p.  (2)  

310,000   " 
16X28  in. 

204,000   " 
19X24  in 

450,000    " 
19X32  in. 

357,000 
22X28  in. 

l.p.  (2)  ' 

27X28  " 

32X32  " 

22X28  " 

Piston-rod,  diam 

4  in. 

33/8  in 

Connecting-rod,  1'gth.  . 

9/  87/16" 

8ft.  1  1/2  in 

Steam-ports  

28  1/2X2  in. 

H/2X18  in. 

293/4X15/8" 

307/8X11/2" 

Exhaust-ports  

281/2X8  " 

23/4X18  " 

and  13/4" 
293/4X63/4" 

307/8X3" 

Valves,  out.  lap,  h.p. 
out.  lap,  l.p.  .  .  . 

7/8  in. 

5/8  " 

1  in. 

7/8  in. 
3/4  " 

1  in. 

"        in.  lap  h.p  . 

1/10  in 

neg  1/4  in 

rie**  Vie" 

in  .  lap,  l.p.  .  . 

neg  3/8  " 

max.  travel   .  .  . 
lead,  h.p. 

6  in. 
1/16  in. 

5l/2  in. 

6  in. 
0    " 

6  in. 
3/32  in 

lead,  l.p   

5/16  " 

l/8    " 

Boiler.  —  Type 

Straight 

\Vagon  top 

\Vagon  to 

Straight 

Diam.  barrel  inside  
Thickness  of  plates  .  .  . 
Height    from     rail    to 
center  line  
Length  of  smoke-box 

6ft.  21/2  in. 
3/4  in. 

8ft.O      in. 

5  "    77/8  " 

4ft.  9  in. 
9/16  in. 

7ft.  11  1/2  in. 

4  "     8 

783/4  in. 
7/8  &1  Vl6" 

70  in. 
H/1G  in. 

Working  pressure  

180  Ibs. 

190  Ibs 

225  Ibs. 

Firebox.—  type  

Wootten 

Buchanan 

Length  inside  

lO'  119/ie" 

9ft   63/8  in 

108  in 

108  in. 

8ft.  2  V»  in 

3  "    47/8   " 

78    " 

66 

Depth  at  front  

4  "     6       " 

6  "    li/4  " 

80  1/4  in 

68 

Thickness  side  plates.  . 
back  plate  .  . 
crown-sheet, 
tube  sheet..  . 
Grate-area 

5/l6in. 
5/16  " 
3/8  " 
V2  " 
89  6  sq  ft 

5/16  in. 
5/16  " 
3/8" 
V2  " 
30  7  sq  ft 

781/4  ' 
3/8    ' 
3/8    ' 
3/8    ' 
9/16    ' 

64 

3/8 
3/8 
3/8 

1/2 

Stay-bolts,  1  1/8  in    . 

pitch  41/4  in 

4  in 

58  5  sq  ft 

49  5  sq  ft. 

Tubes  —  iron 

268 

391 

245 

Pitch  

23/4  in 

Diam.,  outside  
Length  

11  ft.  11  in. 

2  in. 
12ft  0  in 

21/4  in. 
20ft 

2  1/4  in. 
20ft 

Heating-surface  : 

Tubes,  exterior  
Fire-box  

2,208.8  ft. 
234  3  " 

1,697  sq.ft. 
233       " 

4,586  sq.ft. 
210     " 

2,874  sq.ft. 
179     " 

Miscellaneous: 

Exhaust-nozzle,  diam 

5  in 

3  1/2  in 

Stack,  smal'st  diam.  .  . 

1  ft.  6  in. 

1  ft.  3  1/4  in. 

height      from 
rail  to  top  

15  ft.  6l/2  in. 

14ft.  10  in. 

'  Back  truck  journals. 


1122 


LOCOMOTIVES^ 


was  built  about  1887,  and  in  1909  there  were  approximately  500  running  in 
Europe.  They  are  now  extensively  in  use  in  the  United  States  for  the 
heaviest  service.  The  largest  locomotive  yet  built  is  described  in  Eng. 
News,  April  29,  1909.  It  was  built  by  the  Baldwin  Locomotive  Works 
for  use  on  the  heavy  grades  of  the  Southern  Pacific  R.R.  The  principal 
dimensions  areas  follows:  Cylinders,  26  and  40  X  30  ins.;  valves,  balanced 
piston;  boiler  (steel):  diameter,  84  ins.;  thickness,  13/16  and  27/32  ins.;  work- 
ing pressure,  200  Ibs.  per  sq.  in.;  fuel,  oil;  fire-tubes,  401,  2i/4ins.  dia.  X 
21  ft.;  firebox:  length,  126  ins.,  width,  781/4  ins.,  depth,  front,  751/2  ins., 
depth,  back,  701/2  ins.;  water  spaces,  5  ins.;  grate  area,  68.4  sq.  ft.; 
feed-water  heater:  length,  63  ins.,  tubes,  401,  21/4  ins.  dia.;  heating  sur- 
face: firebox,  232  sq.  ft.,  fire-tubes,  4941  sq.  ft.,  feed-water  heater  tubes, 
1220  sq.  ft.;  smokebox  superheater,  655  sq.  ft.;  wheels:  driving  (16), 
57  ins.  O.  dia.,  main  journals,  11X12  ins.,  other  journals,  10  X  12  ins.; 
truck  (4),  301/2  ins.  dia.,  journals,  6  X  10  ins.;  tender  (8),  331/2  ins.  dia., 
journals,  6X  11  ins.;  wheelbase:  driving,  39  ft.  4  ins.,  rigid,  15  ft.,  total 
engine,  56  ft.  7  ins.,  total  engine  and  tender,  83  ft.  6  ins.;  length  over  all, 
93ft.  61/2 ins.;  weight:  on  drivers,  394,150  Ibs.,  on  front  truck,  14,500  Ibs., 
on  back  truck,  17,250  Ibs.,  total  engine  425,900  Ibs.,  total  engine  and 
tender  596,000  Ibs.;  tender:  water  tank  capy.,  9000  gals.,  oil  tank  capy., 
2850  gals. 

Indicated  Water  Consumption  of  Single  and  Compound  Loco- 
motive Engines  at  Varying  Speeds. 

C.  H.  Quereau,  Eng'g  News,  March  8,  1894. 


Two-cylinder  Compound. 

Single-expansion  . 

Revolutions. 

Speed, 
miles  per 
hour. 

Water  per 
I.H.P.  per 
hour. 

Revolu- 
tions. 

Miles  per 
Hour. 

Water. 

100  to  150 
150  to  200 
200  to  250 
250  to  275 

21  to  31 
31  to  41 
41  to  51 
51  to  56 

18.33  Ibs. 
18.  9  Ibs. 
19.7    Ibs. 
21.4    Ibs. 

151 
219 
253 
307 
321 

31 
45 
52 
63 
66 

21.70 
20.91 
20.52 
20.23 
20.01 

It  appears  that  the  compound  engine  is  the  more  economical  at  low 
speeds, -the  economy  decreasing  as  the  speed  increases,  and  that  the 
simple  engine  increases  in  economy  with  increase  of  speed  within  ordinary 
limits,  becoming  more  economical  than  the  compound  at  speeds  of  more 
than  50  miles  per  hour. 

The  C.,  B.  &  Q.  two-cylinder  compound,  which  was  about  30%  less 
economical  than  simple  engines  of  the  same  class  when  tested  in  passenger 
service,  has  since  been  shown  to  be  15%  more  economical  in  freight 
service  than  the  best  single-expansion  engine,  and  29%  more  economical 
than  the  average  record  of  40  simple  engines  of  the  same  class  on  the 
same  division. 

The  water  rate  is  also  affected  by  the  cut-off;  the  following  table  gives 
what  we  should  consider  very  good  results  in  practice,  though  better 
(i.e.  lower  results)  have  occasionally  been  obtained.  (G.  R.  Henderson, 
1906.) 

Cut-off  per  cent  of  stroke 10 

Lbs.  water  per  I.H.P.  hour  —  simple.  .     26 
Lbs.  water  per  I.H.P.  hour — compound     . . 

Cut-off  per  cent  of  stroke 60 

Lbs.  water  per  I.H.P.  hour  —  simple. .  .     24 
Lbs.  water  perl  H.P.  hour  —  compound    181/2 

Indicator-tests    of     a    Locomotive    at   High    Speed.      (Locomotive 
Eng'g,  June,  1893.)  -  Cards  were  taken  by  Mr.   Angus  SiiiHair  on  the  , 
noUve  drawing  tlie  Empire  State  Express, 


20 

30 

40 

50 

23 

22 

22 

23 

18 

18 

18 

70 

80 

90 

100 

26 

29 

33 

38 

19l/2 

201/2 

221/2 

25 

LOCOMOTIVES.  1123 

RESULTS  OF  INDICATOR-DIAGRAMS. 
Miles  Miles 


Card  No.  Revs,  per  hour.  I.H.P. 

1  160  37.1  648 

2  260  60.8  728 

3  190  44  551 

4  250  58  891 

5  260  60  960 

6  298  69  983 


Card  No.  Revs,  per  hour.  I.H.P. 

7  304  70.5  977 

8  296  68.6  972 

9  300  69.6  1,045 

10  304  70.5  1,059 

11  340  78.9  1,120 

12  310  71.9  1,026 


The  locomotive  was  of  the  eight-wheel  type,  built  by  the  Schenectady 
Locomotive  Works,  with  19  X  24  in.  cylinders,  78-in.  drivers,  and  a 
large  boiler  and  fire-box.  Details  of  important  dimensions  are  as  fol- 
lows: Heating-surface  of  fire-box,  150.8  sq.  ft.;  of  tubes,  1670.7  sq.  ft.; 
of  boiler,  1821.5  sq.  ft.  Grate  area,  27.3  sq.  ft.  Fire-box:  length, 
8  ft.;  width,  3  ft.  47/8  in.  Tubes,  268;  outside  diameter,  2  in.  Ports: 
steam,  18  X  1 1/4  in.;  exhaust,  18X23/4  in.  Valve-travel,  51/2  in. 
Outside  lap,  1  in. ;  inside  lap,  1/54  in.  Journals:  driving-axle,  8  1/2  X  10 1/2 
in. ;  truck-axle,  6  X  10  in. 

The  train  consisted  of  four  coaches,  weighing,  with  estimated  load, 
340,000  Ibs.  The  locomotive  and  tender  weighed  in  working  order  200,- 
000  Ibs.,  making  the  total  weight  of  the  train  about  270  tons.  During 
the  time  that  the  engine  was  first  lifting  the  train  into  speed  diagram 
No.  1  was  taken.  It  shows  a  mean  cylinder-pressure  of  59  Ibs.  Accord- 
ing to  this,  the  power  exerted  on  the  rails  to  move  the  train  is  6553  Ibs., 
or  24  Ibs.  per  ton.  The  speed  is  37  miles  an  hour.  When  a  speed  of 
nearly  60  miles  an  hour  is  reached  the  average  cylinder-pressure  is 
40.7  Ibs.,  representing  a  total  traction  force  of  4520  Ibs.,  without  mak- 
ing deductions  for  internal  friction.  If  we  deduct  10%  for  friction,  it 
leaves  15  Ibs.  per  ton  to  keep  the  train  going  at  the  speed  named.  Cards 
6,  7,  and  8  represent  the  work  of  keeping  the  train  running  70  miles  an 
hour.  They  were  taken  three  miles  apart,  when  the  speed  was  almost 
uniform.  The  average  cylinder-pressure  for  the  three  cards  is  47.6  Ibs. 
Deducting  10%  again  for  friction,  this  leaves  17.6  Ibs.  per  ton  as  the 
power  exerted  in  keeping  the  train  up  to  a  velocity  of  70  miles. 
Throughout  the  trip  7  Ibs.  of  water  were  evaporated  per  Ib.  of  coal. 
The  work  of  pulling  the  train  from  New  York  to  Albany  was  done  on  a 
coal  consumption  of  about  3  Vs  Ibs.  per  H.  P.  per  hour.  The  highest 
power  recorded  was  at  the  rate  of  1120  H.P. 

Locomotive-testing  Apparatus  at  the  Laboratory  of  Purdue  Uni- 
versity. (W.  F.  M.  Goss,  Trans.  A.  S.  M.  E.,  vol.  xiv,  826.) — The 
locomotive  is  mounted  with  its  drivers  upon  supporting  wheels  which 
are  carried  by  shafts  turning  in  fixed  bearings,  thus  allowing  the  engine 
to  be  run  without  changing  its  position  as  a  whole.  Load  is  supplied  by 
four  friction-brakes  fitted  to  the  supporting  shafts  and  offering  resistance 
to  the  turning  of  the  supporting  wheels.  Traction  is  measured  by  a 
dynamometer  attached  to  the  draw-bar.  •  The  boiler  is  fired  in  the 
usual  way,  and  an  exhaust-blower  above  the  engine,  but  not  in  pipe 
connection  with  it,  carries  off  all  that  may  be  given  out  at  the  stack. 

A  Standard  Method  of  Conductincj  Locomotive-tests  is  given  in  a  report  by 
a  Committee  of  the  A.S.M.E.  in  vol.  xiv  of  the  Transactions,  page  1312 

Locomotive  Tests  of  the  Penna.  R.  B.  Co. — Eight  locomotives  were 
tested  in  the  dynamometer  testing  plant  built  by  the  P.  R.  R.  Co.  at 
the  St.  Louis  Exhibition  in  1903.  Among  the  principal  results  obtained 
and  conclusions  derived  are  the  following: 

BOILER  PERFORMANCE. 
Coal  per  sq.  ft.  grate  per  hour,  Ibs. 

20        40  60  80  100  120 

Equiv.  evap.  per  sq.  ft.  H.  S.  per  hour 

3-5     5-7.5     7-10     8.2-12     10.4-14     11.4-15.3 
Coal  per  sq.  ft.  H.  S.  per  hour 

0.6  0.8  1.0  1.2  1.4          .  1.6  1.8 

Equiv.  evap.  per  Ib.  dry  coal 

10-11.5     9-10.5     8.2-9.7     7.7-9.1     7.1-8.5     6.6-8.1     6.2-7.7 
Equiv.  evap.  per  sq.  ft.  H.  S.  per  hour 

4  6  8  10  32  14 

Equiv.  evap.  per  Ib.  dry  coal 

9.7-12.1     8.8-11.3     7.8-10.5     6.8-9.6     5.8-8.8     5.5-8 


1124 


LOCOMOTIVES,, 


The  coal  used  In  these  tests  was  a  semi-bituminous,  containing  16.25% 
volatile  combustible,  7.00%  ash  and  0.90%  moisture. 

The  maximum  boiler  capacity  ranged  from  81/2  to  more  than  16  Ibs. 
or  water  evaporated  per  hour  per  sq.  ft.  of  heating  surface.  Little  or  no 
advantage  was  found  in  the  use  of  Serve  or  ribbed  tubes. 

The  boiler  efficiency  decreases  as  the  rate  of  power  developed  increases. 

Furnace  losses  due  to  excess  air  are  no  greater  with  large  grates  properly 
fired  than  with  smaller  ones.  The  boilers  with  small  grates  were  inferior 
in  capacity  to  those  with  la'ge  grates. 

No  special  advantage  is  derived  from  large  fire-box  heating  surface;  the 
tube  heating  surface  is  effective  in  absorbing  heat  not  taken  up  by  the 
fire-box. 

ENGINE  PERFORMANCE. 

Maximum  I.H.P.,  four  freight  locomotives,        1041,  1050,  1098,  1258 

Maximum  I.H.P.,  four  passenger  locomotives,     816,    945,  1*622,  1641 


Kind  of  Locomotive. 

Simple 
Freight. 

Com- 
pound 
Freight. 

Com- 
pound 
Passen- 
ger. 

Minimum  water  per  I.H.P.  hour  

23.67 
23.83 
28.95 

20.26 
22.03 
25.31 

18.86 
21.39 
24.41 

Water  per  I.H.P.  hr.  at  maximum.  load  

Water  per  I.H.P.  hr.  at  max.  consumption.  .. 

The  steam  consumption  of  simple  locomotives  operating  at  all  speeds 
and  cut-offs  commonly  employed  on  the  road  falls  between  the  limits 
of  23.4  and  28.3  Ibs.  per  I.H.P.  hour;  compound  locomotives  between 
18.6  and  27  Ibs.;  and  with  superheating  the  minimum  steam  consumption 
was  reduced  to  16.6  Ibs.  of  superheated  steam. 

Comparing  a  simple  and  a  compound  locomotive,  the  simple  enerine 
used  40%  more  steam  than  the  compound  at  40  revs,  per  min.,  27%  more 
at  80  revs.,  and  only  7%  more  at  160  revs,  per  min. 

The  frictional  resistance  of  the  engines  showed  an  extreme  variation 
ranging  from  6  to  38%  of  the  indicated  horse-power.  The  frictional 
losses  increased  rapidly  at  speeds  in  excess  of  160  revs,  per  min.  It 
appears  that  the  matter  of  machine  friction  is  closely  related  to  that  of 
lubrication.  With  oil  lubrication  a  stress  at  the  draw-bar  of  approxi- 
mately 500  Ibs.  is  required  to  overcome  the  friction  of  each  coupled  axle, 
while  with  grease  the  required  force  is  from  800  to  1100  Ibs. 

The  lowest  figures  for  dry  coal  consumed  per  dynamometer  H.P.  hour 
were  approximately  as  follows: 
Revs,  per  min 40        80 

Compound  freight  engine,       { oVp^       500°    foQ5 
Compound  passenger  engine,  {  DH^P.         .*.' '.'     600 

A  complete  report  of  the  St.  Louis  locomotive  tests  is  contained  in  a 
k>ok  of  734  pages  and  over  800  illustrations,  published  by  the  Penna.  R.R. 
Co.,  Philadelphia,  1906.  See  also  pamphlet  on  Locomotive  Tests,  pub- 
lished by  Amer.  Locomotive  Co.,  New  York,  1906,  and  Trans.  A.S.  M.  E.t 
vii,  610. 

Weights  and  Prices  of  Locomotives,  1885  and  1905. 
(Baldwin  Loco.  Wks.) 


160 

3.25 

800 

2.3 

900 


240 


3.0 
1000 


Type. 

W'gt 

Price 

Price 
per 
Ib. 

• 

Type. 

W'ght 

Price 

Price 
per 
Ib. 

American.  .  .  . 
Mogul 

80,857 
72,800 
85,000 
92,400 

$6,695 
6,662 
7.583 
7,888 

$  0828 
.0912 
.0892 
.0854 

American  
Atlantic  

102,000 
187,200 
227,000 
156,000 
192,460 

$9,410 
15,750 
15,830 
13,690 
14,500 

$.092 
.083 
.070 
.088 
.075 

Ten  wheel.  .  . 
Consolidation 

Pacific  

Ten  wheel  
Consolidation  . 

LOCOMOTIVES. 


1125 


The  price  per  pound  is  figured  from  the  weight  of  the  engine  in  working 
order,  without  the  tender. 

Depreciation  of  Locomotives. — (Baldwin  Loco.  Wks.) — It  is  suggested 
that  for  the  first  five  years  the  full  second-hand  value  of  the  locomotive 
(75%  of  first  cost)  be  taken;  for  the  second  five  years  85%  of  this  value; 
for  the  third  five  years,  70% ;  after  15  years,  50%  of  the  second-hand  value; 
and  after  20  years,  and  as  long  as  the  engine  remains  in  use,  25%  of  the 
first  cost. 

The  Average  Train  Loads  of  14  railroads  increased  from  229  tons  of 
2000  Ibs.  in  1895  to  385  tons  in  1904.  On  the  Chicago,  Milwaukee  &  St. 
Paul  Ry.  the  average  load  increased  from  152  tens  in  1895  to  281  tons  in 
1903,  and  on  the  Lake  Shore  &  Michigan  Southern  Ry.  from  318  tons  in 
1895  to  615  tons  in  1903.  In  the  same  time  the  average  cost  of  transpor- 
tation per  ton  mile  on  the  C.,  M.  &  St.  P.  Ry.  decreased  from  0.67  to  0.58 
cent;  and  on  the  L.  S.  &  M.  S.  Ry.  increased  from  0.39  to  0.41  cent,  the 
decrease  in  cost  due  to  heavier  train  loads  being  offset  by  higher  cost  for 
labor  and  material. 


Tractive  Force  of  Locomotives,  1893  and  1905. 

(Baldwin  Loco.  Wks.) 


Passenger,  1893. 

Weight 
on 
Driver. 

Trac- 
tive 
Force. 

Passenger,  1905. 

Weight 
on 
Driver. 

Trac- 
tive 
Force. 

American,  single-ex. 
American,  comp  

75,210 
83,860 

17,270 
12,900 

Atlantic,  comp.  ..  . 
Atlantic,  single-ex. 

101,420 
103,600 

22,180 
23,800 

American,  single-ex.. 
American,  comp  .... 
Ten-  wheel  type,  com. 

64,560 
78,480 
93,850 

15,550 
14,050 
16,480 

15,250 

Pacific,  single-ex.  . 
Pacific,  single-ex.  . 
Atlantic,  single-ex. 

141,290 
114,890 
80,930 

29,910 
25,610 
21,740 

24,648 

Freight,  1893. 

Freight,  1905. 

Consolidation,  comp. 
Ten-wheel,  s'gle-ex.. 
Mogul,  single-ex  
Decapod,  compound 

120,600 
101,000 
91,340 
172,000 

21,190 
23,310 
21,030 
35,580 

Sante  Fe  type,  comp. 
3onsol.,  2-cyl.  comp.. 
3onsol.,  single-ex..  .. 
3onsol.,  single-ex.... 
Consol.,  single-ex.  .  .  . 

234,580 
166,000 
151,490 
171,560 
165,770 

62,740 
40,200 
40,150 
44,080 
45,170 

25,277 

46,468 

Waste  of  Fuel  in  Locomotives.  —  In  American  practice  economy 
of  fuel  is  necessarily  sacrificed  to  obtain  greater  economy  due  to  heavy 
train-loads.  D.  L.  Barnes,  in  Eng.  Mag.,  June,  1894,  gives  a  diagram 
showing  the  reduction  of  efficiency  of  boilers  due  to  high  rates  of  com- 
bustion, from  which  the  following  figures  are  taken: 


Lbs.  of  coal  per  sq.  ft.  of  grate  per  hour. . .   12 
Per  cent  efficiency  of  boiler 80 


80 
67 


120 
59 


160 
51 


200 
43 


A  rate  of  12  Ibs.  is  given  as  representing  stationary-boiler  practice,  40 
Ibs.  English  locomotive  practice,  120  Ibs.  average  American,  and  200 
Ibs.  maximum  American,  locomotive  practice. 

Pages  473  and  475  of  Henderson's  "Locomotive  Operation"  giv* 
diagrams  of  evaporation  per  Ib.  of  various  kinds  of  coal  for  different 
rates  of  combustion  per  sq.  ft.  grate  area  and  heating  surface. 

Advantages  of  Compounding.  —  Report  of  a  Committee  of  the 
American  Railway  Master  Mechanics'  Association  cm  Compound  Loco, 
motives  (Am,  Mack.,  July  3,  1890)  gives  the  following  summary  of  the 
advantages  gained  by  compounding:  (a)  It  has  achieved  a  saving  in  the 
fuel  burnt  averaging  18%  at  reasonable  boiler-pressures,  with  encourag- 
in?  possibilities  of  further  improvement  in  pressure  and  in  fuel  and  water 
economy.  (6)  It  has  lessened  the  amount  of  water  (dead  weight)  to  bt 


1126  LOCOMOTIVES* 

hauled,  so  that  (c)  the  tender  and  its  load  are  materially  reduced  In 
weight,  (d)  It  has  increased  the  possibilities  of  speed  far  beyond  60 
miles  per  hour,  without  unduly  straining  the  motion,  frames,  axles,  01 
axle-boxes  of  the  engine,  (e)  It  has  increased  the  haulage-power  at 
full  speed,  or,  in  other  words,  has  increased  the  continuous  H.P.  devel- 
oped, per  given  weight  of  engine  and  boiler.  (/)  In  some  classes  has 
increased  the  starting-power,  (g)  It  has  materially  lessened  the  slide- 
valve  friction  per  H.P.  developed,  (h)  It  has  equalized  or  distributed 
the  turning  force  on  the  crank-pin,  over  a  longer  portion  of  its  path, 
which,  of  C9urse,  tends  to  lengthen  the  repair  life  of  the  engine,  (i)  In 
the  two-cylinder  type  it  has  decreased  the  oil  consumption,  and  has  even 
done  so  in  the  Woolf  four-cylinder  engine,  (j)  Its  smoother  and  steadier 
draught  on  the  fire  is  favorable  to  the  combustion  of  all  kinds  of  soft 
coal;  and  the  sparks  thrown  being  smaller  and  less  in  number,  it  lessens 
the  risk  to  property  from  destruction  by  fire,  (k)  These  advantages 
arid  economies  are  gained  without  having  to  improve  the  man  handling 
the  engine,  less  being  left  to  his  discretion  (or  careless  indifference)  than 
in  the  simple  engine.  (I)  Valve- motion,  of  avery  ^comotive  type,  can 
be  used  in  its  best  working  and  most  effective  position,  (m)  A  wider 
elasticity  in  locomotive  design  is  permitted;  as,  if  desired,  side-rods  can 
be  dispensed  with,  or  articulated  engines  of  100  tons  weight,  with  inde- 
pendent trucks,  used  for  sharp  curves  on  mountain  service,  as  suggested 
by  Mallet  and  Brunner. 

Of  27  compound  locomotives  in  use  on  the  Phila.  and  Reading  Rail- 
road (in  1892),  12  are  in  use  on  heavy  mountain  grades,  and  are  designed 
to  be  the  equivalent  of  22  X  24  in.  simple  consolidations;  10  are  in  some- 
what lighter  service  and  correspond  to  20  X  24  in.  consolidations;  o  are 
in  fast  passenger  service.  The  monthly  coal  record  shows: 

Gain  in  Fuel 
Class  of  Engine.  No0  Economy. 

Mountain  locomotives. . . . . .   12  25%  to  30% 

Heavy  freight  service 10  12%  to  17% 

Fast  passenger 5  9%  to  11  % 

(Report  of  Com.  A.  R.  M.  M.  Assn.  1892.)  For  a  description  of  the 
various  types  of  compound  locomotive,  with  discussion  of  their  relative 
merits,  see  paper  by  A.  Von  Borries,  of  Germany,  the  Development  of 
the  Compound  Locomotive,  Trans.  A.  S.  M.  E.,  1893,  vol.  xiv,  p.  1172. 

As  a  rule  compounds  cost  considerably  more  for  repairs,  and  require 
^  better  class  of  engineers  and  machinists  to  obtain  satisfactory  results. 
(Henderson.) 

Balanced  Compound  Locomotives,  —  There  are  two  high-pressure 
cylinders  placed  between  the  frames  and  two  low-pressure  cylinders 
outside.  The  inside  crank  shaft  has  cranks  90°  apart,  and  each  outside 
crank  pin  is  180°  from  the  inside  crank  pin  on  the  same  side,  so  that  the, 
engine  on  each  side  is  perfectly  balanced.  The  balanced  piston  valve  is 
so  made  that  high-pressure  steam  may  be  admitted  to  the  low-pressure 
cylinder  for  starting.  See  circular  of  the  Baldwin  Loco.  Wks.,  No.  62, 1907. 

Superheating  in  Locomotives.  (R.  R.  Age  Gazelle,  Nov.  20, 1908.)  — 
Superheating  steam  in  locomotives  has  been  found  to  effect  a  saving  of 
10  to  15%  in  the  fuel  consumption  of  a  locomotive,  and  8  to  12%  of  the 
water  used,  or  with  the  same  fuel  to  increase  the  horse-power  and  the 
tractive  force.  The  Baldwin  Locomotive  Works  builds  a  superheater  in 
the  smoke-box,  where  it  utilizes  part  of  the  heat  of  the  waste  gases  in 
drying  the  steam  and  superheating  it  50  to  100°  F.  The  heating  surface 
of  the  superheater  is  from  12  to  22%  of  the  heating  surface  in  the  tubes  and 
fire-box  of  the  boiler.  It  is  recommended  to  use  a  boiler  pressure  of  about 
160  Ibs.  when  a  superheater  is  used,  and  to  have  cylinders  of  larger  dimen- 
sions than  when  ordinary  steam  of  200  Ibs.  pressure  is  used.  For  an  illus- 
trated and  historical  description  of  the  use  of  superheating  in  locomotives, 
see  paper  by  H.  H.  Vaughan,  read  before  the  Am.  Ry.  Mast.  Mechs.'  Assn., 
Eng.  News,  June  22,  1905. 

Counterbalancing  Locomotives.  —  Rules  for  counterbalancing, 
adopted  by  different  locomotive-builders,  are  quoted  in  a  paper  by  Prof. 
Lanza  (Trans.  A.  *S.  M.  E.,  x,  302.)  See  also  articles  on  Counterbalan- 
cing Locomotives,  in  R.  R.  &  Eng.  Jour.,  March  and  April,  1890;  Trans. 
A.  £.  M .  E.,  vol.  xvi,  305;  and  Trans.  Amc  Ry.  Master  Mechanics'  Assru 


LOCOMOTIVES.  1127 

1897.  W.  E.  Dalby's  book  on  the  "Balancing  of  Engines"  (Longmans, 
Green  &  Co.,  1902)  contains  a  very  full  discussion  of  this  subject.  See 
also  Henderson's  "Locomotive  Operation"  (The  Railway  Age,  1904). 

Narrow-gauge  Railways  in  Manufacturing  Works.  —  A  tramway 
of  18  inches  gauge,  several  miles  in  length,  is  in  the  works  of  the  Lan- 
cashire and  Yorkshire  Railway.  Curves  of  13  feet  radius  are  used. 
The  locomotives  used  have  the  following  dimensions  (Proc.  Inst.  M.  E.. 
July,  1888):  The  cylinders  are  5  in.  in  diameter  with  6  in.  stroke,  and 
2  ft.  31/4  in.  centre  to  centre.  Wheels  161/4 in.  diameter,  the  wheel-base 
2  ft.  9  in.;  the  frame  7  ft.  4*/4  in.  long,  and  the  extreme  width  of  the 
engine  3  feet.  Boiler,  of  steel,  2  ft.  3  in.  outside  diam.  and  2  ft.  long 
between  tube-plates,  containing  55  tubes  of  13/8  in.  outside  diam.;  fire- 
box, of  iron  and  cylindrical,  2  ft.  3  in.  long  and  17  in.  inside  diam.  Heat- 
ing-surface 10.42  sq.  ft.  in  the  fire-box  and  36.12  in  the  tubes,  total  46.54 
sq.  ft.;  grate-area,  1.78  sq.  ft.;  capacity  of  tank,  261/2  gallons;  working- 
pressure,  170  Ibs,  per  sq.  in.  tractive  power,  say,  1412  Ibs.,  or  9.22  Ibs.  per 
fb.  of  effective  pressure  per  sq.  in.,  on  the  piston.  Weight,  empty,  2.80 
tons;  full  and  in  working  order,  3.19  tons. 

For  description  of  a  system  of  narrow-gauge  railways  for  manufac- 
tories, see  circular  of  the  C.  W.  Hunt  Co.,  New  York, 

Light  Locomotives.  —  For  dimensions  of  light  locomotives  used  for 
mining,  etc.,  arid  for  much  valuable  information  concerning  them,  see 
catalogue  of  H.  K.  Porter  Co.,  Pittsburgh. 

Petroleum-burning  Locomotives.  (From  Clark's  Steam-engine.)  — 
The  combustion  of  petroleum  refuse  in  locomotives  has  been  success- 
fully practised  by  Mr.  Thos.  Urquhart,  on  the  Grazi  and  Tsaritsin  Rail- 
way, Southeast  Russia.  Since  November,  1884,  the  whole  stock  of  143 
locomotives  under  his  superintendence  has  been  fired  with  petroleum 
refuse.  The  oil  is  injected  from  a  nozzle  through  a  tubular  opening  in 
the  back  of  the  fire-box,  by  means  of  a  jet  of  steam,  with  an  induced 
current  of  air. 

A  brickwork  cavity  or  "regenerative  or  accumulative  combustion, 
chamber"  is  formed  in  the  fire-box,  into  which  the  combined  current 
breaks  as  spray  against  the  rugged  brickwork  slope.  In  this  arrange- 
ment the  brickwork  is  maintained  at  a  white  heat,  and  combustion  is 
complete  and  smokeless.  The  form,  mass,  and  dimensions  of  the  brick- 
work are  the  most  important  elements  in  such  a  combination. 

Compressed  air  was  tried  instead  of  steam  for  injection,  but  no  appre- 
ciable reduction  in  consumption  of  fuel  was  noticed. 

The  heating-power  of  petroleum  refuse  is  given  as  19,832  heat-units, 
equivalent  to  the  evaporation  of  20.53  Ibs.  of  water  from  and  at  212°  F., 
or  to  17.1  Ibs.  at  81/2  atmospheres,  or  125  Ibs.  per  sq.  in.,  effective  pres- 
sure. The  highest  evaporative  duty  was  14  Ibs.  of  water  under  81/2 
atmospheres  per  Ib.  of  the  fuel,  or  nearly  82%  efficiency. 

There  is  no  probability  of  any  extensive  use  of  petroleum  as  fuel  for 
locomotives  in  the  United  States,  on  account  of  the  unlimited  supply  of 
coal  and  the  comparatively  limited  supply  of  petroleum.  Texas  and 
California  oils  are  now  (1902)  used  in  locomotives  of  the  Southern  Pacific 
Railway  and  the  Santa  Fe  System. 

Self-propelled  Railway  Cars.  —  The  use  of  single  railway  cars  con- 
taining a  steam  or  gasolene  motor  has  become  quite  common  in  Europe. 
For  a  description  of  different  systems  see  a  paper  on  European  Railway 
Motor  Cars  by  B.  D.  Gray  in  Trans  A.  S.  M.  E.,  1907. 

Tireless  Locomotive. — The  principle  of  the  Francq  locomotive  is 
that  it  depends  for  the  supply  of  steam  on  its  spontaneous  generation 
from  a  body  of  heated  water  in  a  reservoir.  As  steam  is  generated  and 
drawn  off  the  pressure  falls;  but  by  providing  a  sufficiently  large  volume 
of  water  heated  to  a  high  temperature,  at  a  pressure  correspondingly 
high,  a  margin  of  surplus  pressure  may  be  secured,  and  means  may  tmif 
be  provided  for  supplying  the  required  quantity  of  steam  for  the  trip. 

The  fireless  locomotive  designed  for  the  service  of  the  Metropolitan 
Railway  of  Paris  has  a  cylindrical  reservoir  having  segmental  ends, 
about  S^ft.  7  in.  in  diameter,  261/4  ft.  in  length,  with  a  capacity  of  about 
620  cubic  feet.  Four-fifths  of  the  capacity  is  occupied  by  water,  which 
3  heated  by  the  aid  of  a  powerful  jet  of  steam  supplied  from  stationary 
boilers.  The  water  is  heated  until  equilibrium  is  established  between 
the  boilers  and  the  reservoir.  The  temperature  is  raised  to  about  390°  F.t 
corresponding  to  225  Ibs.  per  sq.  in.  The  steam  from  the  reservoir  it 


1128 


LOCOMOTIVES 


passed  through  a  reducing-valve,  by  which  the  steam  is  reduced  to  the 
required  pressure.  It  is  then  passed  through  a  tubular  superheater 
situated  within  the  receiver  at  the  upper  part,  and  thence  through  the 
Ordinary  regulator  to  the  cylinders.  The  exhaust-steam  is  expanded  to 
a  low  pressure,  in  order  to  obviate  noise  of  escape.  In  certain  cases  the 
exhaust-steam  is  condensed  in  closed  vessels,  which  are  only  in  part 
filled  with  water. 

In  working  off  the  steam  from  a  pressure  of  225  Ibs.  to  67  Ibs.,  53G 
cubic  feet  of  water  at  390°  F.  is  sufficient  for  the  traction  of  the  trains, 
for  working  the  circulating-pump  for  the  condensers,  for  the  brakes, 
and  for  electric-lighting  of  the  train.  At  the  stations  the  locomotive 
takes  from  2200  to  3300  Ibs.  of  steam  —  nearly  the  same  as  the  weight 
of  steam  consumed  during  the  run  between  two  consecutive  charging 
stations.  There  is  210  cubic  feet  of  condensing  water.  Taking  the 
initial  temperature  at  60°  F.,  the  temperature  rises  to  about  180°  F. 
after  the  longest  runs  underground. 

The  locomotive  has  ten  wheels,  on  a  base  24  ft  long,  of  which  six  are 
coupled.  41/2  ft.  in  diameter.  The  extreme  wheels  are  on  radial  axles. 
The  cylinders  are  231/2  in.  in  diameter,  with  a  stroke  of  231/2  in. 

The  engine  weighs,  in  working  order,  53  tons,  of  which  36  tons  are  on 
the  coupled  wheels.  The  speed  varies  from  15  miles  to  25  miles  per  hour. 
The  trams  weigh  about  140  tons. 

Compressed-air  Locomotives.  —  A  compressed-air  locomotive  con- 
sists essentially  of  a  storage  tank  mounted  upon  driving  wheels,  with  two 
engines  similar  to  those  of  a  steam  locomotive.  One  or  more  reservoirs  or 
storage  tanks  are  located  on  the  line,  from  which  the  locomotive  tank  is 
charged.  These  reservoirs  are  usually  riveted  steel  cylinders,  designed 
for  about  1000  Ibs.  working  pressure;  but  sometimes  seamless  steel  cylinders 
of  small  diameter,  designed  for  a  working  pressure  of  2000  Ibs.  or  upwards, 
are  used.  The  customary  maximum  pressure  in  the  locomotive  tank  is 
800  Ibs.  gauge,  and  the  working  pressure  in  the  cylinders  is  from  130  to 
140  Ibs.  The  following  table  is  condensed  from  one  in  a  circular  of  the 
Baldwin  Locomotive  Works,  No.  46,  1904. 

See  account  of  the  Mekarski  compressed-air  locomotives,  page  652  ante. 

DIMENSIONS  AND  TRACTIVE  POWER  OF  FOUR  COUPLED  COMPRESSED-AIR 
LOCOMOTIVES  HAVING  Two  STORAGE  TANKS. 


Class  

4-4-C 

4-6-C 

4-8-C 

4-10-C 

4-1  2-C 

4-16-C 

4-18-C 

Cylinders,  inches  .... 
Diam.  of  drivers  
Wheel  base 

5X10 
22" 
4f  0" 

6X10 
24" 
4'  3" 

7X12 
24" 
4'  6" 

8X14 
26" 
5'  Vf 

9X14 
28" 

y   y, 

11X14 

28" 

y  6" 

12X16 
30" 
6'  0" 

Approx.  weight,  Ibs.. 
Inside  dia.  of  tanks.  . 
Aggregate  tank  vol., 
cu.  ft  

10,000 
26" 

75 

14,000 
28* 

100 

18,000 
30" 

130 

23,000 
32" 

170 

27,000 
34" 

200 

37,000 
38" 

280 

44,00$ 
40* 

320 

App.  height  

4  y 

4  10" 

y  o" 

y  4» 

5'  8" 

6'  0* 

d  4* 

App.     width     ever 
tanks               .   . 

4'  10* 

y  2" 

y  6" 

y  10* 

&  yi 

7'  0* 

7  4* 

App.  width  over  cyl- 

Gauge 
+24" 

Gauge 
+26" 

Gauge 
+27" 

Gauge 
+28" 

Gauge 
+30" 

Gauge 
+32" 

Gauge 
+  33" 

App.     length     over 

12'  0" 

If  0" 

15'  0" 

17'  0" 

18'  0" 

2(X  0" 

207  6' 

£  t,Full  stroke  
'£  g  3/4  Stroke  cut-off 
§  o  V2  Stroke  cut-off 
£PL,  l/4  Stroke  cut-off 

1350 
1290 
940 
510 

1785 
1700 
1240 
670 

2915 
2780 
2025 
1100 

4100 
3900 
2840 
1540 

4820 
4580 
3345 
1815 

7200 
6860 
4995 
2710 

9140 
8705 
6340 
3440 

Draw-bar  pull  on  any  grade=  tractive  power  -  (.0075  +  %  of  grade) 
X  weight  of  engine. 

Working  pressure  in  cylinders  140  Ibs.;  tank  storage  pressure,  800  Ibs. 

Other  sizes  of  engines  are  51/2X  10  in.,  6X12  in.,  and  8  X12in.,  24-in, 
item,  of  drivers;  9X14  in.,  26-in.  drivers,  and  10  X  14  in..  28-in.  drivers.  . 


COMPRESSED-AIK   LOCOMOTIVES. 


1129 


CUBIC  FEET  OF  Am,  AT  ^DIFFERENT  STORAGE  PRESSURES,  REQUIRED  TO 
HAUL  ONE  TON  ONE  MILE  AT  HALF  STROKE  CUT-OFF,  WITH  20,  30 
AND  40  LBS.  FRICTIONAL  RESISTANCE  PER  TON.  (Baldwin  Loco.  Wks.) 


Storage   pressure 
Cylinder  working 
pressure  

600 
130 

700 
135 

800 
140 

600 
130 

700 
135 

800 
140 

600 
130 

700 
135 

800 
140 

Grade. 

R 

V 

V 

V 

R 

V 

V 

V 

R 

V 

V 

V 

1.74 
2.23 
2.73 
1  70 

Level     

20.0 
31.2 

42.4 
64.8 
87.2 
109  6 

1.16 

1.81 
2.47 
1  7ft 

0.99 
1.56 
2.12 
1  74 

0.87 
1.36 
1.85 
7  8S 

30.0 
41.2 
52.4 
74  8 

1.74 
2.40 
3.05 

4  15 

1.50 
2.05 
2.61 
^  73 

1.31 
1.79 

2.28 
3  76 

40.0 
51.2 
62.4 
84  8 

2.33 
2.98 
3.64 
4  94 

1.99 
2.56 
3.11 

4  ?4 

1/2% 

1% 

2%  

3% 

5.08 
6  39 

4.35 
5  48 

3.81 
4  79 

97.2 
119  6 

5.67 
6  97 

4.86 
5  97 

4.25 
5  7^ 

107.2 
129  6 

6.25 
7  56 

5.35 
6  47 

4.69 
5.67 
6.64 

4%.. 

5% 

132.0 

7.69 

6.60 

5.77 

142.0 

8.27 

7.09 

6.20 

152.0 

8.86 

7.60 

R= resistance  per  ton  of  2240  Ibs.  in  pounds.    V  =  cubic  feet  of  air. 

Air  Locomotives  with  Compound  Cylinders  and  Atmospheric  Interheater^ 
are  built  by  H.  K.  Porter  Co.  The  air  enters  the  high-pressure  cylinder 
at  250  Ibs.  gauge  pressure  and  is  expanded  down  to  50  Ibs.,  overcoming 
resistance,  while  the  temperature  drops  about  140°  F.  This  loss  of  heat 
is  practically  all  restored  in  the  atmospheric  interheater,  which  is  a 
cylindrical  reservoir  filled  with  brass  tubes  located  in  the  passage-way 
from  the  high-  to  the  low-pressure  cylinder.  The  air  enters  the  low- 
pressure  cylinder  at  50  Ibs.  gauge  and  a  temperature  within  10  or  20°  of 
that  of  the  surrounding  atmosphere.  The  exhaust  is  used  to  induce  a 
draught  of  atmospheric  air  through  the  tubes  of  the  interheater.  This 
combination  permits  of  expanding  the  air  from  250  Ibs.  down  to  atmos- 
phere without  unmanageable  refrigeration. 

The  following  calculation  shows  the  relative  economy  of  a  single- cylinder 
locomotive  using  air  at  150  Ibs.  and  of  a  compound  using  air  at  250  Ibs. 
in  the  high-pressure  and  50  Ibs.  in  the  low-pressure  cylinder,  non-expan- 
sive working  being  assumed  in  both  cases. 

11.2  cu.  ft.  of  free  air  at  150  Ibs.  gauge  and  atmospheric  temperature 
would  fill  a  cylinder  of  1  cu.  ft.  capacity,  and  in  moving  a  piston  of  1  sq. 
ft.  area  one  foot  would  develop  144  X  150  =  21,600  ft.  Ibs.  of  energy. 

11.2  cu.  ft.  of  free  air  at  250  Ibs.  gauge  if  used  in  a  cylinder  0.623  sq.  ft. 
area  and  1  ft.  stroke  would  develpp  0.623  X  144  X  250=  22,425  ft.  Ibs. 

If  expanded  in  two  cylinders  with  a  ratio  of  4  to  1  the  energy  developed 
would  be  0.623  X  144  X  200  plus  4  X  0.623  X  144  X  50  =  35,880  ft.  Ibs.,  if 
the  heat  is  restored  between  the  two  cylinders.  Gain  by  compounding 
with  interheating,  over  simple  cylinders  with  150  Ibs.  initial  pressure, 
35,880  ^  21,600  =  1.66. 

.  These  results  are  about  the  best  that  can  be  obtained  with  either 
simple  or  compound  locomotives,  as  any  improvement  due  to  expansive 
working  just  about  balances  the  losses  due  to  clearance  and  initial  refrig- 
eration. The  work  done  per  cubic  foot  of  free  air  in  the  two  systems  is: 
with  simple  cylinders,  21,600  •*•  11.2  =  1840  ft.  Ibs.;  with  compound 
cylinders  and  atmospheric  interheater,  35,880  -*•  11.2  =  3205  ft.'  Ibs. 

The  above  calculations  have  been  practically  confirmed  by  actual 
tests  which  show  1900  ft.  Ibs.  of  work  per  cubic  foot  of  free  air  with  the 
simple  locomotive  and  3000  ft.  Ibs.  with  the  compound,  the  gain  due  to 
expansive  working  and  the  losses  due  to  internal  friction  being  some- 
what greater  in  the  compound  than  in  the  simple  machine. 

In  the  operation  of  compressed-air  locomotives  the  air  compressor  is 
generally  delivering  compressed  air  at  a  pressure  fluctuating  between 
30  and  1000  Ibs.  per  sq.  in.  into  the  storage  reservoir,  and  it  requires  an 
average  of  about  12,000  ft.  Ibs.  per  cubic  foot  of  free  air  to  compress  and 
deliver  it  at  these  pressures.  The  efficiency  of  the  two  systems  then  is: 
1900  -4-  12000  =  16%  for  the  simple  locomotive,  and  3000  -*-  12000  =» 
25%  for  the  compound  with  atmospheric  mterheater. 


SHAFTING. 


SHAFTING. 

(See  also  TORSIONAL  STRENGTH;  also  SHAFTS  OF  STEAM  ENGINES.) 
For  shafts  subjected  to  torsion  only,  let  d  =  diam.  of  the  shaft  in  ins., 
P  =  a  force  in  Ibs.  applied  on  a  lever  arm  at  a  distance  =  a  ins.  from 
the  axis,  S  =  shearing  resistance  at  the  outer  fiber,  in  Ibs.  per  sq.  in.,  then 


If  R  =  revolutions  per  minute,  then  the  horse-power  transmitted  = 

Pa27cR  nd*S  X2xR  RSd*    . 

33,000X12       16X33,000X12       321,000' 


3/321,OOOH.'pT_   A3/CXH.P. 

"  V  "      RS  =  V        W~ 


In  practice,  empirical  values  are  given  to  S  and  to  the  coefficients 
K  =  S/5.1and  C  =  321,000/5,  according  to  the  factor  of  safety  assumed, 
depending  on  the  material,  on  whether  the  shaft  is  subjected  to  steady, 
fluctuating,  bending,  or  reversed  strains,  on  the  distance  between  bear- 
ings, etc.  Kimball  and  Barr  (Machine  Design)  state  that  the  following 
factors  of  safety  are  indicated  by  successful  practice:  For  head  shafts, 
15;  for  line  shafts  carrying  pulleys,  10;  for  small  short  shafts,  counter- 
shafts, etc.,  7.  For  steel  shafting  the  allowable  stress,  S,  for  the  above 
factors  would  be  about  4000,  6000  and  8500  Ibs.  respectively,  whence 


8  i  > 

t/80  ^'P' ; 


for  head  shafts  d=  i/       p     •" ;  for  line  shafts  d=  i/       p     •  ;  for  short 
shafts  d  = 


•/QO    TT    T> 

7dS  U..V. 

V—R— 


Jones  &  Laughlin  Steel  Co.  gives  the  following  for  steel  shafts: 

Turned.  Cold-rolled. 

For  simply  transmitting  power ) 

and  short  countershafts,  bear-J  H.P.  =  dzR  •*•    50     H.P  =  d3R  -*•      40 

ings  not  more  than  8  ft.  apart ) 
As  second  movers,  or  line  shafts,  I  TT  -p       ^ar>   .     on     u  r>        MT>   ,     7n 

bearings  8  ft.  apart }  H'P'  =  d  R  * 

As  prime  movers  or  head  shafts! 

carrying  mairi  driving  pulley  I  TT  r>   _  ,731?   .   10*     w  T>   _  ^ao   •   inn 

or   gear,    well    supported    by\a"^'~aK  ' 

bearings J 

Jones  &  Laughlins  give  the  following  notes:  Receiving  and  transmit- 
ting pulleys  should  always  be  placed  as  close  to  bearings  as  possible; 
and  it  is  good  practice  to  frame  short  "headers"  between  the  main  tie- 
beams  of  a  mill  so  as  to  support  the  main  receivers,  carried  by  the  head 
shafts,  with  a  bearing  close  to  each  side  as  is  contemplated  in  the  for- 
mulae. But  if  it  is  preferred,  or  necessary,  for  the  shaft  to  span  the  full 
width  of  the  "bay"  without  intermediate  bearings,  or  for  the  pulley  to 
be  placed  away  from  the  bearings  towards  or  at  the  middle  of  the  bay, 
the  size  of  the  shaft  must  be  largely  increased  to  secure  the  stiffness 
necessary  to  support  the  load  without  undue  deflection. 

Diameter  of_sh_aft  D  to  carry  load  at  center  of  bays  from  2  to  12  ft. 

span,  D  =  t/- d4,  in  which  d  is  the  diameter  derived  from  the  formula 

for  head  shafts,  c  =  length  of  bay  in  inches,  and  Ci=  distance  in  inches 
between  centers  of  bearings  in  accordance  with  the  formula  for  horse- 


SHAFTING. 


1131 


power  of  head  shafts.     (Jones  &  Laughlin  Steel  Co.) 
different  diameters  d  are  as  follows: 


Values  of  c\  for 


d                 Cj 

d            c, 

d        GI 

d          d 

d      c\ 

d       Cj 

1  to  13/8           15 

213/10               25 

3  15/ie  &  4     37 

51/4  &  SS/g   55 

63/8   71 

73/8     88 

Ul/16  &  l3/4    16 

27/8  to  3           26 

43/16        •      40 

51/2                57 

61/2   73 

71/2     95 

H3/16  &  17/8     17 

3  l/s  to  3  1/4      28 

41/4                41 

55/8                59 

65/8   75 

75/s     93 

1  15/16  to  2  l/s    18 

33/8                    30 

47/ie  &  41/2  44 

53/4                61 

63/4    77 

73/4    96 

23/16  &  2  1/4     19 
25/16  to  27/ifl  20 
21/2  to  25/8      24 

37/ie  &  31/2      31 
39/16&35/8     33 
3  11/ie  &  3  3/4    34 

43/4                 47 
413/16             49 
5                    51 

57/8                63 
6                     65 
61/8                67 

67/8    79 
7         81 
71/8   84 

77/8     99 
8         101 
81/2   112 

'2H/16  &  23/4    22 

37/8                   36 

5V8                52 

61/4                69 

71/4   86 

9        123 

Should  the  load  be  applied  near  one  end  of  the  span  or  bay  instead  of 
at  the  center,  multiply  the  fourth  power  of  the  diameter  of  the  shaft 
required  to  carry  the  load  at  the  center  of  the  span  or  bay  by  the  prod- 
uct of  the  two  parts  of  the  shaft  when  the  load  is  near  one  end,  and 
divide  this  product  by  the  product  of  the  two  parts  of  the  shaft  when 
the  load  is  carried  at  the  center.  The  fourth  root  of  this  quotient  will 
be  the  diameter  required. 

The  shaft  in  a  line  which  carries  a  receiving-pulley,  or  which  'carries  a 
transmitting-pulley  to  drive  another  line,  should  always  be  considered  a 
head-shaft,  and  should  be  of  the  size  given  by  the  rules  for  shafts  carrying 
main  pulleys  or  gears. 

The  greatest  admissible  distance  between  bearings  of  shafts  subject  to 
no  transverse  strain  except  from  their  own  weight  is  for  cold-rolled.  shafts, 

L  =  <y  330,608  X  D2,  and  for  turned  shafts,  Lt=  -^319,586  X  D2.  D  = 
diam.  and  L  =  length  of  shaft,  in  inches.  These  formulae  are  based  on 
an  allowable  deflection  at  the  center  of  Vso  in.  per  foot  of  length,  weight 
of  steel  490  Ibs.  per  cu.  ft.,  and  modulus  of  elasticity  =  29,000,000  for 
turned  and  30,000,000  for  cold-rolled  shafting.  [In  deriving  these  formulae 
the  weight  of  the  shaft  has  been  taken  as  a  concentrated  instead  of  a  dis- 
tributed load,  giving  additional  safety.] 

Kimball  and  Barr  say  that  the  lateral  deflection  of  a  shaft  should  not 
exceed  0.01  in.  per  foot  of  length,  to  insure  proper  contact  at  the  bear- 
ings. For  ordinary  small  shafting  they  give_the  following  as  the  allow- 


able distance  between  the  hangers:  L  =  7  ^d?,  for  shaft  without  pulleys; 
L  =  5  -\J  d?,  for  shaft  carrying  pulleys.     (L  in  ft.,  d  in  ins.) 

Deflection  of  Shafting.  (Pencoyd  Iron  Works.)  —  For  continuous 
iine-shafting  it  is  considered  good  practice  to  limit  the  deflection  to  a 
maximum  of  1/100  of  an  inch  per  foot  of  length.  The  weight  of  bare  shaft- 
ing in  pounds  =  2.6  d2L  =  W,  or  when  as  fully  loaded  with  pulleys  as  is 
customary  in  practice,  and  allowing  40  Ibs.  per  inch  of  width  for  the 
vertical  pull  of  the  belts,  experience  shows  the  load  in  pounds  to  be  about 
13  d2L  =  W.  Taking  the  modulus  of  transverse  elasticity  at  26,000,000 
Ibs.,  we  derive  from  authoritative  formulae  the  following: 


L  =  -^  873  d*,  d  -- 
L  =  -x/175d2,  d  •• 


'  LV873,  for  bare  shafting; 

/LV175,  for  shafting  carrying  pulleys,  etc. , 


L  being  the  maximum  distance  in  feet  between  bearings  for  continuous 
shafting  subjected  to  bending  stress  alone,  d  =  diam.  in  inches. 

The  torsional  stress  is  inversely  proportional  to  the  velocity  of  rota- 
tion, while  the  bending  stress  will  not  be  reduced  in  the  same  ratio.  It 
is  therefore  impossible  to  write  a  formula  covering  the  whole  problem 
and  sufficiently  simple  for  practical  application,  but  the  following  rules 
are  correct  within  the  range  of  velocities  usual  in  practice. 

For  continuous  shafting  so  proportioned  as  to  deflect  not  more  than 


1132 


SHAFTING, 


1/100  of  an  Inch  per  foot  of  length,  allowance  being  made  for  the  weaken- 
ing effect  of  key-seats, 

d  =  ^50  H.P.  -*-  R,  L  =  ^720  d*t  for  bare  shafts; 

d  =»  ^70  H.P.  -*-  R,  L  =  ^140  d2,  for  shafts  carrying  pulleys,  etc. 

d  =  diam.  in  inches,  L  =  length  in  feet,  R  =  revs,  per  min. 

The  following  are  given  by  J.  B.  Francis  as  the  greatest  admissible  dis- 
tances between  the  bearings  of  continuous  steel  shafts  subject  to  no  trans- 
verse strain  except  from  their  own  weight,  as  would  be  the  case  were  the 
power  given  off  from  the  shaft  equal  on  all  sides,  and  at  an  equal  distance 
from  the  hanger-bearings. 

Diam.  of  shaft,  in.  ...23  45  67  8  9 

Dist.  bet.  bearings,  ft.     15.9     18.2     20.0     21.6     22.9     24.1     25.2     26.2 

These  conditions,  however,  do  not  usually  obtain  in  the  transmission  of 
power  by  belts  and  pulleys,  and  the  varying  circumstances  of  each  case 
render  it  impracticable  to  give  any  rule  which  would  be  of  value  for 
universal  application. 

For  example,  the  theoretical  requirements  would  demand  that  the 
bearings  be  nearer  together  on  those  sections  of  shafting  where  most 
power  is  delivered  from  the  shaft,  while  considerations  as  to  the  location 
and  desired  contiguity  of  the  driven  machines  may  render  it  impracti- 
cable to  separate  the  driving-pulleys  by  the  intervention  of  a  hanger  at 
the  theoretically  required  location.  (Joshua  Rose.) 

Horse-Power  Transmitted  by  Cold-rolled  Steel  Shafting  at  Different 
Speeds  as  Prime  Movers  or  Head  Shafts  Carrying  Main  Driving 
Pulley  or  Gear,  well  Supported  by  Bearings. 

Formula  H.P.  =  <f3JR  -^  100. 


Revolutions  per  minute. 

Revolutions  per  minute. 

Diam. 

100 

200 

300 

400 

500 

Diam. 

100 

200 

300 

400 

500 

n/2 

3.4 

6.7 

10.1 

13.5 

16.9 

27/8 

24 

48 

72 

95 

119 

19/16 

3.8 

7.6 

11.4 

15.2 

19.0 

215/16 

25 

51 

76 

101 

127 

>5/8 

4.3 

8.6 

12.8 

17.1 

21 

3 

27 

54 

81 

108 

135 

1  n/16 

4.8 

9.6 

14.4 

19.2 

24 

3V8 

31 

61 

91 

122 

152 

13/4 

5.4 

10.7 

16.1 

21 

27 

33/ie 

32 

65 

97 

129 

162 

1  !3/i6 

5.9 

11.9 

17.8 

24 

30 

31/4 

34 

69 

103 

137 

172 

17/8 

6.6 

13.1 

19.7 

26 

33 

33/8 

38 

77 

115 

154 

192 

115/16 

7.3 

14.5 

22 

29 

36 

37/i6 

41 

81 

122 

162 

203 

2 

8.0 

16.0 

24 

32 

40 

3V2 

43 

86 

128 

171 

214 

2Vl6 

8.8 

17.6 

26 

35 

44 

39/16 

45 

90 

136 

180 

226 

2V8 

9.6 

19.2 

29 

38 

48 

35/s 

48 

95 

143 

190 

238 

23/16 

10.5 

21 

31 

42 

52 

3U/16 

50 

100 

150 

200 

251 

21/4 

11.4 

23 

34 

45 

57 

33/4 

55 

105 

158 

211 

264 

25/16 

12.4 

25 

37 

49 

62 

37/8 

58 

116 

174 

233 

291 

23/8 

13.4 

27 

40 

54 

67 

315/16 

61 

122 

183 

244 

305 

27/16 

14.5 

29 

43 

58 

72 

4 

64 

128 

192 

256 

320 

21/2 

15.6 

31 

47 

62 

78 

43/16 

74 

147 

221 

294 

367 

29/16 

16.8 

34 

50 

67 

84 

41/4 

77 

154 

230 

307 

383 

25/8 

18.1 

36 

54 

72 

90 

47/16 

88 

175 

263 

350 

438 

211/16 

19.4 

39 

58 

77 

97 

4V2 

91 

182 

273 

365 

456 

23/4 

21 

41 

62 

83 

104 

43/4 

107 

214 

322 

429 

537 

213/16 

22 

44 

67         89 

111 

5 

125 

250 

375 

500 

625 

For  H.P.  transmitted  by  turned  steel  shafts,  as  prime  movers,  etc., 

Cold-rolled     Turned 
1.43  1.11 


. 

multiply  the  figures  by  0.8. 
For  sha 


.. 

hafts,  as  second  movers  or  line  shafts,  ) 
bearings  8  ft.  apart,  multiply  by  J 

For  simply  transmitting  power,  short  counter- 
shafts, etc.,  bearings  not  over  8  ft.  apart,  multi- 
ply by 


2.50 


SHAFTING. 


1133 


The  horse-power  is  directly  proportional  to  the  number  of  revolutions 
per  minute. 

SPEED  OF  SHAFTING.  —  Machine  shops 120  to  240 

Wood-working 250  to  300 

Cotton  and  woollen  mills . .     300  to  400 

Flange  Couplings. — The  bolts  should  be  designed  so  that  theii 
combined  resistance  to  a  torsional  moment  around  the  axis  of  the  shaft 
is  at  least  as  great  as  the  torsional  strength  of  the  shaft  itself;  and  the 
bolts  should  be  accurately  fitted  so  as  to  distribute  the  load  evenly 
among  them.  Let  D  =  diam.  of  the  shaft,  d  =  diam.  of  the  bolts, 
r  =  radius  of  bolt  circle,  in  inches,  n  =  number  of  bolts,  S  =  allowable  shear- 
ing  stress  per  sq.  in.,  then  ;rd3*$f-r-16  =  i/4  ndzrS,  whence  d=  0.5  V'DVCw)- 
Kimball  and  Barr  give  n  =  3  +D/2,  but  this  number  may  be  modified  for 
convenience  in  spacing,  etc. 

Effect  of  Cold  Boiling.  —  Experiments  by  Prof.  R.  H.  Thurston  in 
1902  on  hot-rolled  and  cold-rolled  steel  bars  (Catalogue  of  Jones  & 
Laughlin  Steel  Co.)  showed  that  the  cold-rolled  steel  in  tension  had  its 
elastic  limit  increased  15  to  97%;  tensile  strength  increased  20  to  45%; 
ductility  decreased  40  to  69%.  In  transverse  tests  the  resistance  in- 
creased 11  to  30%  at  the  elastic  limit  and  13  to  69%  at  the  yield  point. 
In  torsion  the  resistance  at  the  yield  point  increased  31  to  64%,  and  at 
the  point  of  fracture  it  decreased  4  to  10%.  The  angle  of  torsion  at 
the  elastic  limit  increased  59  to  103%,  while  the  ultimate  angle  de- 
creased 19  to  28%.  Bars  turned  from  13/4  in.  diam.  to  various  sizes 
down  to  0.35  in.  showed  that  the  change  in  quality  produced  by  cold 
rolling  extended  to  the  center  of  the  bar.  The  maximum  strength  of 
the  cold-rolled  bar  of  full  size  was  82,200  Ibs.  per  sq.  in.,  and  that  of  the 
smallest  bar  73,600  Ibs.  In  the  hot-rolled  steel  bars  the  maximum 
strength  of  the  full-sized  bar  was  62,900  Ibs.  and  that  of  the  smallest  bar 
58,600  Ibs.  per  sq.  in. 

Hollow  Shafts.  —  Let  d  be  the  diameter  of  a  solid  shaft,  and  dtd2  the 
external  and  internal  diameters  of  a  hollow  shaft  of  the  same  material. 

Then  the  shafts  will  be  of  equal  torsional  strength  when  d3  =  -J— ^ — -  • 

a\ 

A  10-inch  holtow  shaft  with  internal  diameter  of  4  inches  will  weigh  16% 
less  than  a  solid  10-inch  shaft,  but  its  strength  will  be  only  2.56%  less. 
If  the  hole  were  increased  to  5  inches  diameter  the  weight  would  be 
25%  less  than  that  of  the  solid  shaft,  and  the  strength  6.25%  less. 

Table  for  Laying  Out  Shafting.  —  The  table  on  the  next  page 
(from  the  Stevens  Indicator,  April,  1892)  is  used  by  Wm.  Sellers  &  Co.  to 
facilitate  the  laying  out  of  shafting. 

The  wood-cuts  at  the  head  of  this  table  show  the  position  of  the  hangers 
and  position  of  couplings,  either  for  the  case  of  extension  in  both  direc- 
tions from  a  Central  head-shaft  or  extension  in  one  direction  from  that 
head -shaft. 

Sizes  of  Collars  for  Shafting,  Wm.  Sellers  &  Co.,  Am.  Mack.  Jan.  28, 
1897.  —  D,  diam.  of  collar;  T,  thickness;  d,  diam.  of  set  screw;  I,  length. 
All  in  inches. 

LOOSE  COLLARS. 


Shaft 

D 

T 

d 

I 

Shaft 

D 

T 

d 

I 

Shaft 

D 

t 

d 

H/4 

11/2 
15/8 
l3/4 

13/4 
17/8 

21/4 
25/8 
23/4 

3/4 
13/16 
15/16 

U/16 

H/8 

7/16 
7/16 

7/16 
7/16 

V2 
5/8 

5/16 
3/8 
7/16 
7/16 
9/16 
9/16 

21/4 
2V2 
23/4 

31/4 

3V2 

33/8 
33/4 
4 
41/2 
47/8 
53/ie 

13/16 
H/4 
15/16 
17/16 
15/8 
13/4 

5/8 
5/8 

5/8 
5/8 
3/4 

3/4 

5/8 
11/16 
H/16 
13/16 
13/16 
15/16 

4 

41/2 

51/2 
6 

513/16 
67/16 
615/ie 
71/2 

17/8 
17/8 

n/8 

2 

3/4 

3/4 
3/4 
3/4 
3/4 

FAST  COLLARS. 


Shaft 

D 

T 

Shaft 

D 

T 

Shaft 

D 

T 

Shaft 

D 

T 

13/16 
U/4 
13/8 
11/2, 

U/2 
13/4 

2V4 

2 

2V4 
25/8 

1/2 
1/2 
1/2 
9/16 

2V2 
23/4 

3V4 

31/4 
35/8 

4V4 

9/16 
5/8 
H/16 
U/16 

31/2 
4 

41/2 

45/8 
53/8 
6 
7 

7/8 
15/16 

H/8 

51/2 
6 
61/2 

^/8 
81/4 

93/4 

1134 


SHAFTING. 


m 

Jl! 

•eaqonr 

ffj&fl  ?5l  §l^5f  §|l 

•saqoui 
'q^Sua^j 

•sui  'xog  jo  *sui 
-j'eag  jo  t^Siiarj 

00 

11 

'c  2  S  *-"«                    =1 

~  &"C'  ^  §                            ^ 

£" 

cK 

!i!li'    - 

- 

Distance  from  Center  of  Bearing  to  End  of  Shaft  for  Coupling.  See  B,  Figs.  1,  2,  an 

!«H5 

.S  y  —  *  .           «*N  *^  p^ 

« 

USE  OF  TABLE.  —  Look  for  size  of  first  shaft  i 
under  the  head  of  Size  of  first  shaft,  and  in  the  top  1 
Size  of  second  shaft,  find  the  size  of  the  shaft  to  be 
intersection  gives  the  length  R  •  this  added  to  the  le 
Irom  center  to  center  of  bearing,  and  in  cases  simil 
length  C,  gives  the  length  of  the  first  shaft,  thus  •  as  in 
length  ;  Fig.  2,  C  +  A  +  S  —  length. 

{3W^^rt                    M                 «S 

*§•  •S     2"    S 

NO 

s"||i|  s|RSf 

Ir> 

s?5|s|_ 

£ 
1          % 

affslls 

!           *N 
!              ^T 

asassssl 

» 

* 

slaaafaftf 

1              ^M 

—  —  —  ^(Nf^csr^r^ 

C<1                       M                W 

.& 

c*                   ^  N 

w" 

5     »»     £ 

__  —  tsr^j 

^ 

;?  2        ;?  p*~§d 

N 

43  £  **  w     c 

r>l 

c^>      **•      N                    rt  n>  £  £  ^  J; 

£¥  £  g  bo  $  § 

«" 

If-fjj             fjsfjj 

S 

»~                 "Illil 

Nominal 
Size  of 
2d  Shaft. 

IN?  . 
'§  £$  s   : 

^^mi.L^H. 

Ij 

"OTS  «-      » 

"W^-O   S     f     ' 

N         N        00  •*»<  •*»«  •*<  00-C         00  »H  •*  00  M  N  1« 

H*    is*    i«"^f«5"^rt^J9    ^•«*^"e<r^r^H~«rr 

it  ^  T  IA  lf\  sC  «  fN  l>00  O  —  (Nl  r^  T  m  vO  tx 

PULLEYS.  1135 

PULLEYS. 


ft  =  breadth  of  arm  at  hub • 


Proportions  of  Pulleys.  (See  also  Fly-wheels,  page  1049.)  —  Let 
n  =  number  of  arms,  D  =  diameter  of  pulley,  S  =  thickness  of  belt, 
t  =  thickness  of  rim  at  edge,  T  =  thickness  in  middle,  B  =  width  of  rim, 
0  =  width  of  belt,  h  =  breadth  of  arm  at  hub,  hi  =  breadth  of  arm  at 
rim,  e  —  thickness  of  arm  at  hub,  e\  =  thickness  of  arm  at  rim,  c  = 
amount  of  crowning;  dimensions  in  inches. 

Unwin.  Reuleaux. 

B  =  width  of  rim. 9/8  (p  +  o  .4)  %  P  to  5/4  # 

t  =  thickness  at  edge  of  rim 0.75+0 .005  D     {  (^  to  V?ft 

T  =  thickness  at  middle  of  rim ...          2t+  c 

For  single  /BD 

belts  =  0.6337V  IT  R         n 

— —  1/  '  a.  _  -i_  „ 
For  double  .  3/BD  /4in<  "*"  4  *  20~n 
belts  =  0.798  y  T 

hi  =  breadth  of  arm  at  rim 2/3 h  O.Sh 

e  —  thickness  of  arm  at  hub 0 A  h  0 .5  h 

ei  =  thickness  of  arm  at  rim 0 .4  hi  0 .5  hi 

n  =  number  of  arms,  for  a  single  set  3  +  ^^7)  */2  ( 5  +  ^-g ) 

{B  for  sin.-arrr> 
pulleys. 
2  B  for  double, 
arm  pulleys. 

M  =  thickness  of  metal  in  hub htoS/ih 

c  =  crowning  of  pulley 1/24  B  

The  number  of  arms  is  really  arbitrary,  and  may  be  altered  if  necessary, 
(Unwin.) 

Pulleys  with  two  or  three  sets  of  arms  may  be  considered  as  two  or  three 
separate  pulleys  combined  in  one,  except  that  the  proportions  of  the  arms 
should  be  0 .8  or  0  .7  that  of  single-arm  pulleys.  (Reuleaux.) 

EXAMPLE.  —  Dimensions  of  a  pulley  60  in.  diam.,  16  in.  face,  for  double 
belt  1/2  in.  thick. 

Solution  by  n      h        hi       e         e\        t       T       L      M      c 

Unwin 9    3.792.531.521.010.651.9710.73.80.67 

Reuleaux 4    5.0     4.0     2.5     2.0        1.25        16      5 

The  following  proportions  are  given  in  an  article  in  the  Amer.  Machinist 
authority  not  stated: 

h  =  0  .0625  D  +  0  .5  in.,  hi  =  0  .04  D  +  0  .3125  in.,  e  =  0  .025  D  +  0  .2 
In.,  ei  =  0  .016  D  +  0  .125  in. 

These  give  for  the  above  example:  h  =  4.25  in.,  hi  =  2.71  in.,  e  = 
1.7  in.,  ei  =  1 .09  in.  The  section  of  the  arms  in  all  cases  is  taken  as 
elliptical. 

The  following  solution  for  breadth  of  arm  is  proposed  by  the  author: 
Assume  a  belt  pull  of  45  Ibs.  per  inch  of  width  of  a  single  belt,  that  the 
whole  strain  is  taken  in  equal  proportions  on  one-half  of  the  arms,  and  that 
the  arm  is  a  beam  loaded  at  one  end  and  fixed  at  the  other.  We  have 
the  formula  for  a  beam  of  elliptical  section  fP  =  0  .0982  Rbdz  +1,  in  which 
P  =  the  load,  R  =  the  modulus  of  rupture  of  the  cast  iron,  b  =  breadth, 
d  =  depth,  and  I  =  length  of  the  beam,  and/  =  factor  of  safety.  Assume 
a  modulus  of  rupture  of  36,000  Ibs.,  a  factor  of  safety  of  10,  and  an  addi- 
tional allowance  for  safety  in  taking  I  =  1/2  the  diameter  of  the  pulley 
instead  of  1/2  D  less  the  radius  of  the  hub. 

Take  d  =  h,  the  breadth  of  the  arm  at  the  hub,  and  6  =  e  «  0.4  h 

the  thickness.    We  then  have  fP  -  10  X -^^  =  900  -  =  3535xo-4/i3- 


n  1/2  D 


'    QOO  7?  D  *V  7?  7) 

whence  h  =  i/     ™°     =  0.633\/  — ,  which  is  practically  the  same  as 

v   oooo  n,  V'     ?i 

the  value  reached  by  Unwin  from  a  different  set  of  assumptions. 


1136 


PtILLEYS. 


Relation  of  Belt  Width  to  Pulley  Pace.  (Am.  Mach.,  Feb.  11, 
1915.) — Carl  G.  Barth  recommends  that  the  relation  between  the  face 
of  the  pulley  and  the  belt  be  expressed  by  the  formula  F  »  1 3/j8  B  +  3/g 
in.,  in  which  F  and  B  are  the  widths  respectively  of  the  pulley  face 
and  belt,  both  in  inches.  If  the  limits  of  design  make  it  impractical 
to  use  the  dimension  given  by  the  equation,  the  following  equation 
may  be  substituted:  F  =  1  3/32  B  +  3/16  in. 

Convexity  of  Pulleys. — Authorities  differ.  Morin  gives  a  rise  equal 
to  1/10  of  the  face;  Molesworth,  1/24;  others  from  i/g  to  Vge-  Scott  A. 
Smith  says  the  crown  should  not  be  over  1/8  inch  for  a  24-inch  face. 
Pulleys  for  shifting  belts  should  be  "  straight,"  that  is,  without  crowning. 
Mr.  Barth  uses  the  formula  H  =  0.03125  F  2/3,  in  which  H  is  the  height 
of  crown  and  F  the  width  of  face  in  inches. 

CONE  OB  STEP  PULLEYS. 

To  find  the  diameters  for  the  several  steps  of  a  pair  of  cone-pulleys: 

1.  Crossed  Belts.  —  Let  D  and  d  be  the  diameters  of  two  pulleys 
connected  by  a  crossed  belt,  L  =  the  distance  between  their  centers, 
and  £  =  the  angle  either  half  of  the  belt  makes  with  a  line  joining  the 

centers  of  the  pulleys:  then  total  length  of  belt  =(D+c?)  ~  +  (D  +  d)  ^~ 

•f  2  L  cos  p.     fl  **  angle  whose  sine  is  •  .    L  Cos  p=  i/L2  —  (    ?    j  ' 

The  length  of  the  belt  is  constant  when  D  +  d  is  constant;  that  is,  in  a 
pair  of  step-pulleys  the  belt  tension  will  be  uniform  when  the  sum  of  the 
diameters  of  each  opposite  pair  of  steps  is  constant.  Crossed  belts  are 
seldom  used  for  cone-pulleys,  on  account  of  the  friction  between  the 
rubbing  parts  of  the  belt. 

To  design  a  pair  of  tapering  speed-cones,  so  that  the  belt  may  fit 
equally  tight  in  all  positions:  When  the  belt  is  crossed,  use  a  pair  of  equal 
and  similar  cones  tapering  opposite  ways. 

2.  Open  Belts.  —  When  the  belt  is  uncrossed,  use  a  pair  of   equal 
and  similar  conoids,  tapering  opposite  ways,  and  bulging  in  the  middle, 
according  to  the  following  formula:  Let  L  denote  the  distance  between 
the  axes  of  the  conoids;  R  the  radius  of  the  larger  end  of  each;  r  the  radius 
of  the  smaller  end;  then  the  radius  in  the  middle,  r0,  is  found  as  follows: 


R  +  r      (R  -  r)2 
2  6.28L 


(Rankine.) 


If  DO  =  the  diameter  of  equal  steps  of  a  pair  of  cone-pulleys,  D  and 
d  =  the  diameters  of  unequal  opposite  steps,  and  L  =  distance  between 

the  axes,  DO 


D+d       (D  -  d)2 
2  12. 566 L' 


If  a  series  of  differences  of  radii  of  the  steps,  R  —  r,  be  assumed,  then 
for  each  pair  of  steps  — - — •  =  r\>  —      '  ~  Tr    ,  and  the  radii  of  each  may 

A  O  .ZO  Li 

be  computed  from  their  half  sum  and  half  difference,  as  follows: 

R  +  r      R  -  r 


R 


R+r      R  —  r 
2  2      ; 


2  2 

A.  J.  Frith  (Trans.  A.  S.  M.  E.,  x,  298)  shows  the  following  application 
of  Rankine's  method:  If  we  had  a  set  of  cones  to  design,  the  extreme 
diameters  of  which,  including  thickness  of  belt,  were  40  ins.  and  10  ins., 
and  the  ratio  desired  4,  3,  2,  and  1,  we  would  make  a  table  as  follows, 
L  being  100  ins.: 


Trial 
Sum  of 
D+  d 

Ratio. 

Trial  Diams. 

Values  of 
(D-d)s 

Amount 
to  be 
Added. 

Corrected  Values. 

D      |       d 

12.56  L 

D 

d 

50 
50 
50 
50 

4 
3 

2 

40 
37.5 
33.333 
25 

10 
12.5 
16.666 
25 

0.7165 

.4975 
.2212 
.0000 

0.0000 
.2190 
.4953 
.7165 

40 
37.7190 
33.8286 
25.7165 

10 
12.7190 
17.1619 
25.7165 

The  above  formulae,  are  approximate,  and  they  do  not  give  satisfactory 


CONE  AND  S?£t>  PULLEYS.  1137 

results  when  the  difference  of  diameters  of  opposite  steps  is  large  and 
when  the  axes  of  the  pulleys  are  near  together,  giving  a  large  belt-angle. 
Two  more  accurate  solutions  of  the  problem,  one  by  a  graphical  method, 
and  another  by  a  trigonometrical  method  derived  from  it,  are  given  by 
C.  A.  Smith  (Trans.  A.  S.  M.  E.  x,  269).  These  were  copied  in  earlier 
editions  of  this  Pocket-book,  but  are  now  replaced  by  formulae  derived 
from  a  graphical  solution  by  Burmester  ("  Lehrbuch  der  Kinematic"; 
Mach'y  Reference  Series,  No.  14,  1908),  which  give  results  far  more 
accurate  than  are  required  in  practice. 

In  all  cases  0.8  of  the  thickness  of  the  belt  should  be  subtracted  from 
che  calculated  diameter  to  obtain  the  actual  diameter  of  the  pulley. 
This  should  be  done  because  the  belt  drawn  tight  around  the  pulleys  is 
not  the  same  length  as  a  tape-line  measure  around  them.  —  (C.  A.  Smith.) 

Using  Burmester's  diagram  the  author  has  devised  an  algebraic  solu- 
tion of  the  problem  (Indust.  Eng.,  June,  1910)  which  leads  to  the  follow- 
ing equations: 

Let  L  =  distance  between  the  centers. 

TO  =  radius  of  the  steps  of  equal  diameter  on  the  two  cones. 
r,f  r2  =  radii  of  any  pair  of  steps. 
a  =  0.79057  L  -  TO. 


If  r,  is  given,  r2  =  Vi.25  L2  -  (0.79057  L  -  r0+  rj)2  -  0.79057  L  +  r0. 
If  the  ratio  TZ  -*•  rt  is  given,  let  r^r\  =  c:  r2  =  cr\. 


We  then  have  a  +  crt  =  VRZ—  (a  +  ri)2f  which  reduces  to 

(1  +  c2)  rj2  +  2  a  (1  +  c)  rt  =  1.25  L2  -  2  a2,  a  quadratic  equation,  In 
which  a  =  0.79057  L  —  r0.     Substituting  the  value  of  a  we  have 

(l  +  ct)rkH-(1.58ll«£  -2  r0)  (l+c)rt  =  3.16228Z,r0  -  2r02, 
in  which  L,  r0  and  c  are  given  and  rt  is  to  be  found. 

Let  L  =  100,  c  =  4,  r0  =  12.858  as  in  Mr.  Frith's  example,  page  1136. 

Then  17ri2  +  10art,  =  12,500  -8764.62,  from  which  rt  =5.001,  r2=20.004. 

If  c  =  3,  r,  =  6.304,  r2  =  18.912.     If  c  =  2,  rj  =  8.496,  r2  =  16.992. 

Checking  the  results  by  the  approximate   formula  for  length  of  belt. 
page  1148,  viz,  Length  =  2  L  +  *  (rt  +  r2)  +  (r2  -  n)2  -*•  L,  we  have 
for  c  =  1,  200  +  80.79  +  0       =  280.79 

2,  2004-80.07  +  0.72  =  280.79 

3,  200+  79.22+  1.59  =  280.81 

4,  200+  78.56  +  2.25  =  280.81 
The  maximum  difference  being  only  1  part  in  14,000. 

J.  J.  Clark  (Indust.  Eng.,  Aug.,  1910)  gives  the  following  solution: 
Using  the  same  notation  as  above, 


ir(c+l)ri«2icro  ..................  (1). 

^|f)=2,ro  ............  .......  (2) 

s-(ra-r,)«  -*•!,*  ..........................  (3) 

The  quadratic  equation  (1)  gives  the  value  of  ri  with  an  approximation 
to  accuracy  sufficient  for  all  practical  purposes.  If  greater  accuracy  is  for 
any  reason  desired  it  may  be  obtained  by  (2)  and  (3),  using  in  (3)  the  values 
of  r,  and  r2,  =  crlt  already  found  from  (1).  Taking  n  =  3.1415927,  the  re- 
sult will  be  correct  to  the  seventh  figure. 

Speeds  of  Shaft  with  Cone  Pulleys.  —  If  S  —  speed  (revs,  per  min.) 
of  the  driving  shaft, 

si,  s2,  s3,  sn  =  speeds  of  the  driven  shaft, 
Z>i,  Z>2,  Z>3,  Dn=  diameters  of  the  pulleys  on  the  driving  cone, 

di,  dz,  ds,  dn=diams.  of  corresponding  pulleys  on  the  driven  cone, 
SDi^s^;  SDz  =szdzt  etc. 
Si/S  =  Dl/dl  =  ri;  sn/S  =  Dn/dn,  =  rn. 
The  speed  of  the  driving  shaft  being  constant,  the  several  speeds  of 


1138  BELTING* 

the  driven  shaft  are  proportional  to  the  ratio  of  the  diameter  of  the 
driving  pulley  to  that  of  the  driven,  or  to  D/d. 

Speeds  in  Geometrical  Progression.  —  If  it  is  desired  that  the  speed 
ratios  shall  increase  by  a  constant  percentage,  or  in  geometrical  progres- 
sion, thenr2/rl  —  rz/r2  =  rn/rn_l  =  c,  a  constant. 


EXAMPLE.     If  the  speed  ratio  of  the  driven  shaft  at  its  lowest  speed, 
to  the  driving  shaft  be  0.76923,  and  at  its  highest  speed  2.197,  the  speeds 
being  in  geometrical  progression,  what  is  the  constant  multiplier  if  w=5? 
Log  2.197       =  0.341830 
Log  0.76923  =  1.886056 

0.455774 

Divide  by  n-  !,=»  4,    0.113943  =  log  of  1.30. 

If   Dz/dz  =  1,    then   Dt/di  =  1  -s-  1.3  =  0.769;    Z>3d3  =  1.30;   ZVct«* 
l.u<);  X/5/(*5  ==s  2.197* 

BELTING. 

Theory  of  Belts  and  Bands.  —  A  pulley  is  driven  by  a  belt  by  means 
of  the  friction  between  the  surfaces  in  contact.  Let  T\  be  the  tension  on 
the  driving  side  of  the  belt,  Tz  the  tension  on  the  loose  side;  then  £,=  T\ 
—  ITa,  is  the  total  friction  between  the  band  and  the  pulley,  which  is 
equal  to  the  tractive  or  driving  force.  Let  /  =  the  coefficient  of  friction, 
6  the  ratio  of  the  length  of  the  arc  of  contact  to  the  length  of  the  radius, 
a  =  the  angle  of  the  arc  of  contact  in  degrees,  e  =  the  base  of  the  Nape- 
rian  logarithms  =  2.71828,  m=  the  modulus  of  the  common  logarithms  = 
0.434295.  The  following  formulae  are  derived  by  calculus  (Rankine's 
Mach'y  and  Mill  work,  p.  351;  Carpenter's  Exper.  Eng'g,  p.  173): 

AjL—  pf&~     To  —  •      Ti  —  .  To  —  Ti  —  —  *   —  Ti  n   —  p'~f&\ 

T*          '   l2~  efe'    1/1     l2~~         efd  - 
T!  _  T2  =  Ti  (1  -  e~fe)  =  Ti  (1  -  10  ~fem)  =>  Ti  (1  -  lO"0'00758/^)  I 

_1  =  1()0.00758>;      Ti  a  Tz 


If  the  arc  of  contact  between  the  band  and  the  pulley  expressed  in 
turns  and  fractions  of  a  turn  =  n,  6  =  2*n;  efe=  lo2-7288-/";  that  is,  ef6  is 
the  natural  number  corresponding  to  the  common  logarithm  2.7288/n. 

The  value  of  the  coefficient  of  friction  /depends  on  the  state  and  mate- 
rial of  the  rubbing  surfaces.  For  leather  oelts  on  iron  pulleys,  Morin 
found  /  =  0  .56  when  dry,  0  .36  when  wet,  0  .23  when  greasy,  and  0  .15 
when  oily.  In  calculating  the  proper  mean  tension  for  a  belt,  the  smallest 
value,  /  =  0  .15,  is  to  be  taken  if  there  is  a  probability  of  the  belt  becom- 
ing wet  with  oil.  The  experiments  of  Henry  R.  Towne  and  Robert 
Briggs,  however  (Jour.  Frank.  Inst.,  1868),  show  that  such  a  state  of 
lubrication  is  not  of  ordinary  occurrence;  and  that  in  designing  machinery 
we  may  in  most  cases  safely  take  /  =  0  .42.  Reuleaux  takes  /  =  0  .25. 
Later  writers  have  shown  that  the  coefficient  is  not  a  constant  quantity, 
but  is  extremely  variable,  depending  on  the  velocity  of  slip,  the  condition 
of  the  surfaces,  and  even  on  the  weather. 

The  following  table  shows  the  values  of  the  coefficient  2.7288  /,  by 
which  n  is  multiplied  in  the  last  equation,  corresponding  to  different 
values  of  /;  also  the  corresponding  values  of  various  ratios  among  the 
forces,  when  the  arc  of  contact  is  half  a  circumference: 


/=0.15  0.25  0.42  0.56 

88/=0.4 


2.7288/=0.41  0.68  1.15  1.53 
Let  0  =  TT  and  n  =  1/2,  then 

Ti  -*•  T2  =  1 .603  2.188  3.758  5.821 

Ti  -*•     S  =  2.66  1.84  1.36  1.21 

-*•  2S=  2.16  1.34  0.86  0.71 


BELTING.  1139 

Tn  ordinary  practice  it  is  usual  to  assume  Tz  =  S;  Ti  =  2  5;  T\  +  Tz  -5- 
25  =  1.5.  This  corresponds  to  /  =  0.22  nearly. 

For  a  wire  rope  on  cast  iron  /  may  be  taken  as  0  .15  nearly;  and  if  the 
groove  of  the  pulley  is  bottomed  with  gutta-percha,  0  .25.  (Rankine.) 

Centrifugal  Tension  of  Belts.  —  When  a  belt  or  band  runs  at  a  high 
velocity,  centrifugal  force  produces  a  tension  in  addition  to  that  existing 
when  the  belt  is  at  rest  or  moving  at  a  low  velocity.  This  centrifugal 
tension  diminishes  the  effective  driving  force. 

Rankine  says:  If  an  endless  band,  of  any  figure  whatsoever,  runs  at  a 
given  speed,  the  centrifugal  force  produces  a  uniform  tension  at  each 
cross-section  of  the  band,  equal  to  the  weight  of  a  piece  of  the  band  whose 
length  is  twice  the  height  from  which  a  heavy  body  must  fall  in  oraer 
to  acquire  the  velocity  of  the  band.  (See  Cooper  on  Belting,  p.  101.) 
If  Tc=  centrifugal  tension; 

V—  velocity  in  feet  per  second; 

g=  acceleration  due  to  gravity  =  32.2;  • 

W=  weight  of  a  piece  of  the  belt  1  ft.  long  and  1  sq.  In.   sectional 

area,  —  - 
Leather  weighing  56  Ibs.  per  cubic  foot  gives  W  =  56  +  144  =  0  .388. 

Tc  =-  WV*  *  g  =-  0.388  V2  +  32.2  =  0  .01272. 

Belting  Practice.  Handy  Formulae  for  Belting.  —  Since  in  the 
practical  application  of  the  above  formulae  the  value  of  the  coefficient  of 
friction  must  be  assumed,  its  actual  value  varying  within  wide  limits 
(15%  to  135%),  and  since  the  values  of  T\  and  Tz  also  are  fixed  arbi- 
trarily, it  is  customary  in  practice  to  substitute  for  these  theoretical 
formulae  more  simple  empirical  formula  and  rules,  some  of  which  are 
given  below. 

Let  d=diam.  of  pulley  in  inches;  *d=  circumference; 

V  —  velocity  of  belt  in  ft.  per  second;  v  =  vel.  in  ft.  per  minute; 
a  =  angle  of  the  arc  of  contact: 

L  =  length  of  arc  of  contact  in  feet  ==  irda  •*•  (12  X  360); 
F=tractive  force  per  square  inch  of  sectional  area  of  belt; 
w  =  width  in  inches;  t  =  thickness; 
S  =  tractive  force  per  inch  of  width  =  F  X  t; 
r.p.m.  =  revs.  per  minute;  r.p.s.  =  revs,  per  second  =  r.p.m.  -s-  60. 


v=  j2  X  r.p.m.;  =  0  .2618  d  X  r.p.m. 

„  „       Svw        SVw     Swd  X  r.p.m. 
Horse-power,  H.P.  =5^  =  -^  -       126050  -- 

If  F=  working  tension  per  square  inch  =275  Ibs.,  and  t=  7/32  inch, 
-  60  Ibs.  nearly,  then 


H.P.=  -^  =0.109  Vw  =  0  .000476  wd  X  r.p.m.  =  wa  *T*'m'  -       (1) 


If  F  =  180  Ibs.  per  square  inch,  and  t  =  Va  inch,  S  =  30  Ibs.,  then 
H.P.  =  ~  =0.055  Vw  =0.000238  wd  X  r.p.m.  =  ^^g'™'  •        (2) 

If  the  working  strain  is  60  Ibs.  per  inch  of  width,  a  belt  1  inch  wide 
traveling  550  ft.  per  minute  will  transmit  1  horse-power.  If  the  working 
strain  is  30  Ibs.  per  inch  of  width,  a  belt  1  inch  wide  traveling  1100  ft. 
per  minute  will  transmit  1  horse-power.  Numerous  rules  are  given  by 
different  writers  on  belting  which  vary  between  these  extremes.  A  rule 
commonly  used  is:  1  inch  wide  traveling  1000  ft.  per  min.  =  1H.P. 


H'P-=l?^=0-067w  =  0-000262^Xr-P-m-=!£E^F1*-       (3) 


This  corresponds  to  a  working  strain  of  33  Ibs.  per  inch  of  width. 

Many  writers  give  as  safe  practice  for  single  belts  in  good  condition  a 
working  tension  of  45  Ibs.  per  inch  of  width.     This  gives 

H.P.  =  ^|  =  0.08187^=0.  000357  ^  X  r.p.m.  =  ^^  .      (4) 


1140 


BELTING. 


For  double  belts  of  average  thickness,  some  writers  say  that  the  trans- 
mitting efficiency  is  to  that  of  single  belts  as  10  to  7,  which  would  give 

H.P.   =          =  0.1169  Vw  =  0.00051  wd  X  r.p.m.  =  Wd  *'m'         (5) 


(1)  For  S  =  60  Ibs.  per  inch  wide; 

(2)  "    8  =  30     " 

(3)  "    S  =  33     " 

(4)  ••    s  =  45     " 

(5)  "    S  =  64.3" 


Other  authorities,  however,  make  the  transmitting  power  of  double  belts 
twice  that  of  single  belts,  on  the  assumption  that  the  thickness  of  a  double 
belt  is  twice  that  of  a  single  belt. 

Rules  for  horse-power  of  belts  are  sometimes  based  on  the  number  of 
square  feet  of  surface  of  the  belt  which  pass  over  the  pulley  in  a  minute. 
Sq.  ft.  per  min.  =  wv  •*•  12.  The  above  formulae  translated  into  this 
form  give: 

H.P.  =  46  sq.  ft.  per  minute. 

H.P.  =  92       " 

H.P.  =  83       " 

H.P.  =  61 

H.P.  =-  43  '    (double  belt). 

The  above  formulae  are  all  based  on  the  supposition  that  the  arc  of  con- 
tact  is  180°.  For  other  arcs,  the  transmitting  power  is  approximately 
proportional  to  the  ratio  of  the  degrees  of  arc  to  180°. 

Some  rules  base  the  horse-power  on  the  length  of  the  arc  of  contact  in 


feet.     Since  L  - 


and  H.P. 


12  X  360 
we  obtain  by  substitution  H.P. 


33000  "  33000  X  12  X  r-P'm'  X  180* 


Sw 


X  L  X  r.p.m.,  and  the  five  for- 


H.P.  = 


(4); 


muise  then  take  the  following  form  for  the  several  values  of  S: 

_wL  X  r.p.m.         wL  X  r.p.m.         wL  X  r.p.m  wL  X  r.p.m. 

275         '".'  "        550         UJI  500  367 

TT  T»  /j     T-I    i-  i^v      wL  X  r.p.m.  ,_,. 

H.P.  (double  belt)  = ^^ —  (5). 

^o/ 

None  of  the  handy  formulae  take  into  consideration  the  centrifugal 
tension  of  belts  at  high  velocities.  When  the  velocity  is  over  3000  ft. 
per  minute  the  effect  of  this  tension  becomes  appreciable,  and  it  should 
be  taken  account  of,  as  in  Mr.  Nagle's  formula,  which  is  given  below. 

Horse-power  of  a  Leather  Belt  One  Inch  wide.     (Nagle.) 

Formula:  H.P.  =  CVtw  (S  -  0.012  V«)  -5-  550. 

For/  =  0.40,  a  =  180°,  C  =  0.715,  w  =  1. 


*i 

Laced  Belts,  S  =  275. 

u 

-S 

Riveted  Belts,  S  =  400. 

ft 

Thickness  in  inches  =  t. 

£fc 

»  P, 

Thickness  in  inches  =  t. 

L 

1/7 

1/6 

3/16 

7/32 

1/4 

5/16 

1/3 

o   . 
"a  if 
> 

7/32 

1/4 

5/16 

1/3 

3/8 

7/16 

1/2 

10 

0.51 

0.59 

0.63 

0.73 

0.84 

1.05 

1.18 

15 

1.69 

1.94 

2.42 

2.58 

2.91 

3.39 

3.87 

15 

0.75 

0.88 

1.00 

1.16 

1.32 

1.66 

1.77 

20 

2.24 

2.57 

3.21 

3.42 

3.85 

4.49 

5.13 

20 

.00 

1.17 

1.32 

1.54 

1.75 

2.19 

2.34 

25 

2.79 

3.19 

3.98 

4.25 

4.78 

5.57 

6.37 

25 

.23 

1.43 

1.61 

1.88 

2.16 

2.69 

2.86 

30 

3.31 

3.79 

4.74 

5.05 

5.67 

6.62 

7.58 

30 

.47 

1.72 

1.93 

2.25 

2.58 

3.22 

3.44 

35 

3.82 

4.37 

5.46 

5.83 

6.56 

7.65 

8.75 

35 

.69 

1.97 

2.22 

2.59 

2.96 

3.70 

3.94 

40 

4.33 

4.95 

6.19 

6.60 

7.42 

8.66 

9.90 

40 

.90 

2.22 

2.49 

2.90 

3.32 

4.15 

4.44 

45 

4.85 

5.49 

6.86 

7.32 

8.43 

9.70 

10.98 

45 

2.09 

2.45 

2.75 

3.21 

3.67 

4.58 

4.89 

50 

5.26 

6.01 

7.51 

8.02 

9.02 

10.52 

12.03 

50 

2.27 

2.65 

2.98 

3.48 

3.98 

4.97 

5.30 

55 

5.68 

6.50 

8.12 

8.66 

9.74 

11.36 

13.00 

55 

2.44 

2.84 

3.19 

3.72 

4.26 

5.32 

5.69 

60 

6.09 

6.96 

8.70 

9.28 

10.43 

12.17 

13.91 

60 

2.58 

3.01 

3.38 

3.95 

4.51 

5.64 

6.02 

65 

6.45 

7.37 

9.22 

9.83 

11.06 

12.90 

14.75 

65 

2.71 

3.16 

3.55 

4.14 

4.74 

5.92 

6.32 

70 

6.78 

7.75 

9.69 

10.33 

11.62 

13.56 

15.50 

70 

2.81 

3.27 

3.68 

4.29 

4.91 

6.14 

6.54 

75 

7.09 

8.11 

10.13 

10.84 

12.16 

14.18 

16.21 

75 

2.89 

3.37 

3.79 

4.42 

5.05 

6.31 

6.73 

80 

7.36 

8.41 

10.51 

11.21 

12.61 

14.71 

16.81 

80 

2.94 

3.43 

3.86 

4.50 

5.15 

6.44 

6.86 

85 

7.58 

8.66 

10.82 

11.55 

13.00 

15.16 

17.32 

85 

2.97 

3.47 

3.90 

4.55 

5.20 

6.50 

6.93 

90 

7.74 

8.85 

11.06 

11.80 

13.27 

15.48 

17.69 

90 

2.97 

3.47 

3.90 

4.55 

5.20 

6.50 

6.93 

100 

7.96 

9.10 

11.37 

12.13 

13.65 

15.92 

18.20 

The  H.P.  becomes  a  maximum 

The  H.P.  becomes  a  maximum  at 

at  87,  41  ft.  per  sec.  =  5245ft.  p.  min. 

105.4  ft.  per  sec.  =  6324  ft.  per  min. 

BELTING. 


1141 


In  the  above  table  the  angle  of  subtension,  a,  is  taken  at  180°. 


Should  it  be  ....... 

Multiply  above 
values  by  .....  . 


100C 
.70 


110* 
.75 


120< 


130' 
.83 


140< 
.87 


150' 
-.91 


160( 
.94 


170' 
,.97 


180< 


200° 
1.05 


A.  F.  Nagle's  Formula  (Trans.  A.  S:  M.  E.,  vol.  ii,  1881,  p.  91. 
Tables  published  in  1882). 


550         /' 

C  =  1  -  io-°-00758-fc:  t  =  thickness  in  inches; 

a  =  degrees  of  belt  contact;         v  =  velocity  in  feet  per  second; 
/  =  coefficient  of  friction;  S=  stress  upon  belt  per  square  Inch. 

w  =  width  in  inches: 

Taking  S  at  275  Ibs.  per  sq.  in.  for  laced  belts  and  400  Ibs.  per  sq.  in, 
for  lapped  and  riveted  belts,  the  formula  becomes 

H.P.=  CVtw(0.50  -  0.0000218  F2)  for  laced  belts: 
H.P.  =  C  Vtw  (0  .727  -  0  .0000218  V2)  for  riveted  belts. 
VALUES  OF  C=  1  -  10-0-00758  fa.    (NAGLE.) 


Degrees  of  contact  =  a. 


j  =  coeuicient 
of  friction. 

90° 

100° 

110° 

120° 

130° 

140° 

150° 

160° 

170° 

180° 

200° 

0.15 

0.210 

0.230 

0.250 

0.270 

0.288 

0.307 

0.325 

0.342 

0.359 

0.376 

0.408 

.20 

.270 

.295 

.319 

.342 

.364 

.386 

.408 

.428 

.448 

.467 

.503 

.25 

.325 

.354 

.381 

.407 

.432 

.457 

.480 

.503 

.524 

.544 

.582 

.30 

.376 

.408 

.438 

.467 

.494 

.520 

.544 

.567 

.590 

.610 

.649 

.35 

.423 

.457 

.489 

.520 

.548 

.575 

.600 

.624 

.646 

.667 

.705 

.40 

.467 

.502 

.536 

.567 

.597 

.624 

.649 

.673 

.695 

.715 

.753 

.45 

.507 

.544 

.579 

.610 

.640 

.667 

.692 

.715 

.737 

.757 

.792 

.50 

.543 

.582 

.617 

.649 

.679 

.705 

.730 

.753 

.772 

.792 

.826 

.55 

.578 

.617 

.652 

.684 

.713 

.739 

.763 

.785 

.805 

.822 

.853 

.60 

.610 

.649 

.684 

.715 

.744 

.769 

.792 

.813 

.832 

.848 

.877 

1.00 

.792 

.825 

.853 

.877 

.897 

.913 

.927 

.937 

.947 

.956 

.969 

The  following  table  gives  a  comparison  of  the  formulae  already  given 
for  the  case  of  a  belt  one  inch  wide,  with  arc  of  contact  180°. 

Horse-power  of  a  Belt  One  Inch  wide,  Arc  of  Contact  180°. 

COMPARISON  OF  DIFFERENT  FORMULAE. 


.2« 
v 

*? 

.3  a' 

$z 

»i 

Form.  I 
H.P.  = 

Form  .2 
H.P.  = 

Form.  3 
H.P.  = 

Form.  4 
H.P.  = 

Form.  5 
double 
belt 

Nagle's  Form. 
7/32-in-  single 

•sff 

's  ft 

£  d 

wv 

.wv 

wv 

wv 

H.P.= 

belt. 

•>*** 

"53^ 
!><" 

-*2 

550 

1100 

1000 

733 

wv 
513 

Laced. 

Riv't'd 

10 

600 

50 

1.09 

0.55 

0.60 

0.82 

1.17 

0.73 

1.14 

70 

1200 

100 

2.18 

1.09 

1.20 

1.64 

2.34 

1.54 

2.24 

30 

1800 

150 

3.27 

1.64 

1.80 

2.46 

3.51 

2.25 

3.31 

40 

2400 

200 

4.36 

2.18 

2.40 

3.27 

4.68 

2.90 

4.33 

50 

3000 

250 

5.45 

2.73 

3.00 

4.09 

5.85 

3.48 

5.26 

60 

3600 

300 

6.55 

3.27 

3.60 

4.91 

7.02 

3.95 

6.09 

70 

4200 

350 

7.63 

3.82 

4.20 

5.73 

8.19 

4.29 

6.78 

80 

4800 

400 

8.73 

4.36 

4.80 

6.55 

9.36 

4.50 

7.36 

90 

5400 

450 

9.82 

4.91 

5.40 

7.37 

10.53 

4.55 

7.74 

100 

6000 

500 

10.91 

5.45 

6.00 

8.18 

11.70 

4.41 

7.96 

110 

6600 

550 

4.05 

7.97 

120 

7200 

600 

3.49 

7.75 

Width  of  Belt    for  a    Given    Horse-power.  —  The   width  of  belt 
required  for  any  given  horse-power  may  be  obtained  by  transposing  the 


1142 


BELTING. 


formulae  for  horse-power  so  as  to  give  the  value  of  w.    Thus: 

From  formula  (1),  w-«°-.H*=-  ^7  H  P'-  2101  H  P'  -  275  H'P- 


From  formula  (2),  w  = 
From  formula  (3) ,  w  = 
From  formula  (4),  w- 
From  formula  (5),*iy  = 


v  V  d  X  r.p.m.     L  Xr.p.m." 

1100  H.P.^  18. 33  H.P.  =  4202  H.P.  ^530  H.P.  . 
v  V  dX  r.p.m.     LXr.p.m." 

1000  H.P.  =  16  .67  H.P.  =  3820  H.P.  ^    500  H.P. , 
v  V  d  X  r.p.m.""  L  x  r.p.m. 

733  H.P.  =  12  .22  H.P.  =  2800  H.P.  _   360  H.P. 

v  V  dx  r.p.m.     L  xr.p.m/ 

513  H.P.      8. 56  H.P.      1960  H.P.  _  257  H.P 

L  Xr.p.m.* 


v  V  d  Xr.p.m.      _,,...,  ___ 

Many  authorities  use  formula  (1)  for  double  belts  and  formula  (2)  or 
(3)  for  single  belts. 


To  obtain  the  width  by  Nagle's  formula,  u>  = 


F2). 


divide  the  given  horse-power  by  the  figure  in  the  table  corresponding  to 
the  given  thickness  of  belt  and  velocity  in  feet  per  second. 

The  formula  to  be  used  in  any  particular  case  is  largely  a  matter  of  judg- 
ment. A  single  belt  proportioned  according  to  formula  (1),  if  tightly 
stretched,  and  if  the  surface  is  in  good  condition,  will  transmit  the  horse- 
power calculated  by  the  formula,  but  one  so  proportioned  is  objectionable, 
first,  because  it  requires  so  great  an  initial  tension  that  it  is  apt  to  stretch, 
slip,  and  require  frequent  restretching  and  relacing;  and  second,  because 
this  tension  will  cause  an  undue  pressure  on  the  pulley-shaft,  and  therefore 
an  undue  loss  of  power  by  friction.  To  avoid  these  difficulties,  formula 
(2),  (3),  or  (4),  or  Mr.  Nagle's  table,  should  be  used;  the  latter  especially 
in  cases  in  which  the  velocity  exceeds  4000  ft.  per  min. 

The  following  are  from  the  notes  of  the  late  Samuel  Webber.  (Am. 
Mach.  May  11,  1909.) 

Good  oak-tanned  leather  from  the  back  of  the  hide  weighs  almost 
exactly  one  avoirdupois  ounce  for  each  one-hundredth  of  an  inch  in  thick- 
ness, in  a  piece  of  leather  one  foot  square,  so  that 


Lbs. 

P1tsq' 

Approx. 
Thick- 
ness. 

Actual 
Thick- 
ness. 

Vel.  per 
Inch  for 
1  H.P. 

Safe  Strain 
per  Inch 
Width. 

Single  belt.....  

16  oz. 

1/0  in. 

0  16  in 

625ft 

52  8  Ib-? 

Light  double  

24  " 

1/4  " 

0  24  " 

417  " 

78.1    " 

Medium  

28  " 

5/16  " 

0.28  " 

357  " 

92.5   " 

Standard  

33  " 

Vq  " 

0  33  " 

303  " 

109       " 

3-oly  

45  " 

•&  - 

0.45  " 

222  " 

148       " 

The  rule  for  velocity  per  inch  width  for  1  H.P.  is: 

Multiply  the  denominator  of  the  fraction  expressing  the  thickness  of 
the  belt  in  inches  by  100,  and  divide  it  by  the  numerator; 

Good,  well-calendered  rubber  belting  made  with  30-ounce  duck  and 
new  (i.  e..  not  reclaimed  vulcanized)  rubber  will  be  as  follows: 


Nomenclature. 

Approximate 
Thickness. 

Safe  Working 
Strain  for  1  Inch 
Width. 

Velocity  per  Inch  for 
for  1  H.P. 

}* 

6 

l? 

0.18h 
0.24  ' 
0.30  ' 
0.35  ' 
0.40  • 
0.45  4 

i. 

45  pounds 
65      " 
85      " 
105       •• 
125       •• 
145       " 

735  ft.  p 
508" 
388" 
314" 
264" 
218" 

er  mm. 

M 
M 

The  thickness  of  rubber  belt  does  not  necessarily  govern  the  strength, 
but  the  weight  of  duck  does,  and  with  30-ounce  duck,  the  safe  working 
strains  are  as  above. 

Belt  Factors.     W.  W.  Bird  (Jour.  Worcester  Polyt.  Inst.,  Jan.  1910.) 

—  The  factors  given  in  the  table  below,  for  use  in  the  formula  H.P.  =* 

vw  •+•  F,tp.  which  F  is  an  empirical  factor,  are  based  on  the  following 

assumptions:  A  belt   of  single  thickness  will  stand  a  stress  on | the  tight 

*For  double  Jbelts, 


BELTING. 


1143 


side,  Ti,  of  60  Ibs.  per  inch  of  width,  a  double  belt  105  Ibs.,  and  a 
triple  belt  150  Ibs.,  and  have  a  fairly  long  life,  requiring  only  occasional 
taking  up;  the  ratio  of  tensions  Ti/Tz  should  not  exceed  2  on  small, 
2.  5  on  'medium  and  3  on  large  pulleys ;  the  creep  (travel  of  the  belt 
relative  to  the  surface  of  t£e  pulley  due  to  the  elasticity  of  the  belt 
and  not  to  slip)  should  not  exceed  1% — this  requires  that  the  differ- 
ence m  tensions  T\  -  Tz  should  not  be  greater  than  40  ibs.  per  Inch  of 
width  for  single,  70  for  double  and  100  for  triple  belts. 


Pulley  diam, 

Under 
8  in. 

8  to 
36  in. 

Over 
3ft. 

Under 
14  in. 

14  to 
60  in. 

Over 

5ft. 

Under 
21  in. 

21  to 
84  in. 

Over 
7ft. 

Belt  thick- 
ness. 

Single. 

S'gle. 

S'gle. 

Dbl. 

Dbl. 

Dbl. 

Triple. 

Triple. 

Triple. 

Factor  
Ti-T*  
Creep,  %.... 
?\-  T2  
71,  

1100 
30 
0.74 
2 
60 

920 
36 
0.89 
2.5 
60 

830 
40 
0.99 
3 
60 

630 
52.5 
0.74 
2 
105 

520 
63 
0.89 
2.5 
105 

470 
70 
0.99 
3 
105 

440 
75 
0.74 
2 
150 

370 
90 
0.89 
2.5 
150 

330 
100 
0.99 
3 
150 

These  factors  are  for  an  arc  of  contact  of  180°.  For  other  arcs  they 
are  to  be  multiplied  by  the  figures  given  below. 

Arc 220°    210°   200°    190°    170°    160°    150°    140°    130°    120° 

Multiply  by...   0.89  0.92  0.95  0.97  1.04  1.07  1.11   1.16  1.21   1  27 

Taylor's  Rules  for  Belting.  —  F.  W.  Taylor  (Trans.  A.  S,  M.  E., 
xv,  204)  describes  a  nine  years'  experiment  on  belting  in  a  machine  shop, 
giving  results  of  tests  of  42  belts  running  night  and  day.  Some  of  these 
belts  were  run  on  cone  pulleys  and  others  on  shifting,  or  fast-and-loose, 
pulleys.  The  average  net  working  load  on  the  shifting  belts  was  only 
0.4  of  that  of  the  cone  belts. 

The  shifting  belts  varied  in  dimensions  from  39  ft.  7  in.  long,  3.5  in. 
wide,  0  .25  in.  thick,  to  51  ft.  5  in.  long,  6  .5  in.  wide,  0  .37  in.  thick.  The 
cone  belts  varied  in  dimensions  from  24  ft.  7  in.  long,  2  in.  wide,  0  .25  in. 
thick,  to  31  ft.  10  in.  long,  4  in.  wide,  0  .37  in.  thick. 

Belt-clamps  were  used  having  spring-balances  between  the  two  pairs 
of  clamps,  so  that  the  exact  tension  to  which  the  belt  was  subjected  was 
accurately  weighed  when  the  belt  was  first  put  on,  and  each  time  it  war 
tightened.  The  tension  under  which  each  belt  was  spliced  was  care 
fully  figured  so  as  to  place  it  under  an  initial  strain — while  the  belt 
was  at  rest  immediately  after  tightening — of  71  Ibs.  per  inch  of  width 
of  double  belts.  This  is  equivalent,  in  the  case  of 

Oak  tanned  and  fulled  belts,  to  192  Ibs.  per  sq.  in.  section; 
Oak  tanned,  not  fulled  belts,  to  229    " 
Semi-raw-hide  belts,  to  253    ' 

Raw-hide  belts  to  284    ' 

From  the  nine  years  experiment  Mr.  Taylor  draws  a  number  of  con. 
elusions,  some  of  which  are  given  in  an  abridged  form  below. 

In  using  belting  so  as  to  obtain  the  greatest  economy  and  the  most 
satisfactory  results,  the  following  rules  should  be  observed: 


Oak  Tanned 
and  Fulled 
Leather  Belts. 

Other  Types 
of  Leather 
Belts  and 
6-  to  7-ply 
Rubber  Belts. 

A  double  belt,  having  an  arc  of  contact  of 
180°,  will  give  an  effective  pull  on  the  face 
of  a  pulley  per  inch  of  widtn  of  belt  of  
Or,  a  different  form  of  same  rule: 
The  number  of  sq.  ft.  of  double  belt  passing 
around  a  pulley  per  minute  required  to 
transmit  one  horse-power  is        

35  Ibs. 
80  sq.  ft. 

30  ibs. 
90  sq.  ft. 

Or:  The  number  of  lineal  feet  of  double 
belting  1  in.  wide  passing  around  a  pulley 
per  minute  required  to  transmit  one  horse- 
power is                                                    

950  ft. 

1100ft. 

Or:  A  double  belt  6  in.  wide,  running  4000  to 
5000  ft.  per  min.,  will  transmit  

30  H.P. 

25  H.P. 

1144  BELTING. 

The  terms  "initial  tension,"  "effective  pull,'*  etc.,  are  thus  explained 
by  Mr.  Taylor:  When  pulleys  upon  which  belts  are  tightened  are  at  rest 
both  strands  of  the  belt  (the  upper  ana  lower)  are  unaer  the  same  stress 
per  in.  of  width.  By  "tension,"  "initial  tension,"  or  "tension  while  at 
rest,"  we  mean  the  stress  per  in.  of  width,  or  sq.  in.  of  section,  to  which 
one  of  the  strands  of  the  belt  is  tightened,  when  at  rest.  After  the  belts 
are  in  motion  and  transmitting  power,  the  stress  on  the  slack  side,  or 
strand,  of  the  belt  becomes  less,  while  that  on  the  tight  side  —  or  the  siae 
which  does  the  pulling  —  becomes  greater  than  when  the  belt  was  at  rest. 
By  the  term  "total  load"  we  mean  the  total  stress  per  in.  of  width,  or 
sq.  in.  of  section,  on  the  tight  side  of  belt  while  in  motion. 

The  difference  between  the  stress  on  the  tight  side  of  the  belt  and  its 
slack  side,  while  in  motion,  represents  the  effective  force  or  pull  which  is 
transmitted  from  one  pulley  to  another.  By  the  terms  "working  load," 
"net  working  load,"  or  "effective  pull,"  we  mean  the  difference  in  the 
tension  of  the  tight  and  slack  sides  of  the  belt  per  in.  of  width,  or  sq.  in. 
section,  while  in  motion,  or  the  net  effective  force  that  is  transmitted  from 
one  pulley  to  another  per  in.  of  width  or  sq.  in.  of  section. 

The  discovery  of  Messrs.  Lewis  and  Bancroft  (Trans.  A.  S.  M.  E., 
vii,  549)  that  the  "sum  of  the  tension  on  both  sides  of  the  belt  does  not 
remain  constant,"  upsets  all  previous  theoretical  belting  formulae. 

The  belt  speed  for  maximum  economy  should  be  from  4000  to  4500  ft. 
per  minute. 

The  best  distance  from  center  to  center  of  shafts  is  from  20  to  25  ft. 

Idler  pulleys  work  most  satisfactorily  when  located  on  the  slack  side 
of  the  belt  about  one-quarter  way  from  the  driving-pulley. 

Belts  are  more  durable  and  work  more  satisfactorily  made  narrow  and 
thick,  rather  than  wide  and  thin. 

It  is  safe  and  advisable  to  use:  a  double  belt  on  a  pulley  12  in.  diameter 
or  larger;  a  triple  belt  on  a  pulley  20  in.  diameter  or  larger;  a  quadruple 
belt  on  a  pulley  30  in.  diameter  or  larger. 

As  belts  increase  in  width  they  should  also  be  made  thicker. 

The  ends  of  the  belt  should  be  fastened  together  by  splicing  and  cement- 
ing, instead  of  lacing,  wiring,  or  using  hooks  or  clamps  of  any  kind. 

A  V-splice  should  be  used  on  triple  and  quadruple  belts  and  when 
idlers  are  used.  Stepped  splice,  coated  with  rubber  and  vulcanized  in 
place,  is  best  for  rubber  belts. 

For  double  belting  the  rule  works  well  of  making  the  splice  for  all  belts 
up  to  10  in.  wide,  10  in.  long;  from  10  in.  to  18  in.  wide  the  splice  should 
be  the  same  width  as  the  belt,  18  in.  being  the  greatest  length  of  splice 
required  for  double  belting. 

Belts  should  be  cleaned  and  greased  every  five  to  six  months. 

Double  leather  belts  will  last  well  when  repeatedly  tightened  under 
a  strain  (when  at  rest)  of  71  Ibs.  per  in.  of  width,  or  240  Ibs.  per  sq.  in. 
section,  but  they  will  not  maintain  this  tension  for  any  length  of  time. 

Belt-clamps  having  spring-balances  between  the  pairs  of  clamps  should 
be  used  for  weighing  the  tension  of  the  belt  each  time  it  is  tightened. 

The  stretch,  durability,  cost  of  maintenance,  etc.,  of  belts  proportioned 

(A)  according  to  the  ordinary  rules  of  a  total  load  of  111  Ibs.  per  inch  of 
width,  corresponding  to  an  effective  pull  of  65  Ibs.  per  inch  of  width,  and 

(B)  according  to  a  more  economical  rule  of  a  total  load  of  54  Ibs.,  corre- 
sponding to  an  effective  pull  of  26  Ibs.  per  inch  of  width,  are  found  to  be 
as  follows: 

When  it  is  impracticable  to  accurately  weigh  the  tension  of  a  belt  in 
tightening  it,  it  is  safe  to  shorten  a  double  belt  one-half  inch  for  every 
10  ft.  of  length  for  (A)  and  one  inch  for  every  10  ft.  for  (B),  if  it  requires 
tightening. 

Double  leather  belts,  when  treated  with  great  care  and  run  night  and 
day  at  moderate  speed,  should  last  for  7  years  (A);  18  years  (B). 

The  cost  of  all  labor  and  materials  used  in  the  maintenance  and  repairs 
of  double  belts,  added  to  the  cost  of  renewals  as  they  give  out,  through  a 
term  of  years,  will  amount  on  an  average  per  year  to  37%  of  the  original 
cost  of  the  belts  (A);  14%  or  less  (B). 

In  figuring  the  total  expense  of  belting,  and  the  manufacturing  cost 
chargeable  to  this  account,  by  far  the  largest  item  is  the  time  lost  on  the 
machines  while  belts  are  being  relaced  and  repaired. 

The  total  stretch  of  leather  belting  exceeds  6%  of  the  original  length. 


BELTING.  1145 


The  stretch  during  the  first  six  months  of  the  life  of  belts  is  36%  ol 
their  entire  stretch  (A);  15%  (B). 

A  doubie  belt  will  stretch  0.47%  of  its  length  before  requiring  to  be 
tightened  (A);  0.81%  (B). 

The  most  important  consideration  in  making  up  tables  and  rules  for  the 
use  and  care  of  belting  is  how  to  secure  the  minimum  of  interruptions  to 
manufacture  from  this  source. 

The  average  double  belt  (A),  when  Tunning  night  and  day  in  a  machine- 
shop,  will  cause  at  least  26  interruptions  to  manufacture  during  its  life, 
or  5  interruptions  per  year,  but  with  (B)  interruptions  to  manufacture 
will  not  average  oftener  for  each  belt  than  one  in  sixteen  months. 

The  oak-tanned  and  fulled  belts  showed  themselves  to  be  superior  in 
all  respects  except  the  coefficient  of  friction  to  either  the  oak-tanned 
not  fulled,  the  semi-raw-hide,  or  raw-hide  with  tanned  face. 

Belts  of  any  width  can  be  successfully  shifted  backward  and  forward 
on  tight  and  loose  pulleys.  Belts  running  between  5000  and  6000  ft. 
per  min.  and  driving  300  H.P.  are  now  being  daily  shifted  on  tight  and 
loose  pulleys,  to  throw  lines  of  shafting  in  and  out  of  use. 

The  best  form  of  belt-shifter  for  wide  belts  is  a  pair  of  rollers  twice  the 
width  of  belt,  either  of  which  can  be  pressed  onto  the  flat  surface  of  the 
belt  on  its  slack  side  close  to  the  driven  pulley,  the  axis  of  the  roller 
making  an  angle 'of  75°  with  the  center  line  of  the  belt. 

Remarks  on  Mr.  Taylor's  Rules.  (W.  Kent,  Trans.  A.  S,  M.  E.,  xy, 
242.) — The  most  notable  feature  in  Mr.  Taylor's  paper  is  the  great  dif- 
ference between  his  rules  for  proper  proportioning  of  belts  and  those 
given  by  earlier  writers.  A  very  commonly  used  rule  is,  one  horse-power 
may  be  transmitted  by  a  single  belt  1  in.  wide  running  x  ft.  per  min.,  sub- 
stituting for  x  various  values,  according  to  the  ideas  of  different  engineers, 
ranging  usually  from  550  to  1100. 

The  practical  mechanic  of  the  old  school  is  apt  to  swear  by  the  figure 
600  as  being  thoroughly  reliable,  while  the  modern  engineer  is  more  apt 
to  use  the  figure  1000.  Mr.  Taylor,  however,  instead  of  using  a  figure 
from  550  to  1100  for  a  single  belt,  uses  950  to  1100  for  double  belts.  If 
we  assume  that  a  double  belt  is  twice  as  strong,  or  will  carry  twice  as  much 
power,  as  a  single  belt,  then  he  uses  a  figure  at  least  twice  as  large  as  that 
used  in  modern  practice,  and  would  make  the  cost  of  belting  for  a  given 
shop  twice  as  large  as  if  the  belting  were  proportioned  according  to  the 
most  liberal  of  the  customary  rules. 

This  great  difference  is  to  some  extent  explained  by  the  fact  that  the 

Eroblem  which  Mr.  Taylor  undertakes  to  solve  is  quite  a  different  one 
rom  that  which  is  solved  by  the  ordinary  rules  with  their  variations.  The 
problem  of  the  latter  generally  is,  "How  wide  a  belt  must  be  used,  or  how 
narrow  a  belt  may  be  used,  to  transmit  a  given  horse-power?"  Mr. 
Taylor's  problem  is:  "  How  wide  a  belt  must  be  used  so  that  a  given  horse- 
power may  be  transmitted  with  the  minimum  cost  for  belt  repairs,  the 
longest  life  to  the  belt,  and  the  smallest  loss  and  inconvenience  from  stop- 
ping the  machine  while  the  belt  is  being  tightened  or  repaired?" 

The  difference  between  the  old  practical  mechanic's  rule  of  a  l-in.« 
.wide  single  belt,  600  ft.  per  min.,  transmits  one  horse-power,  and  the  rule 
commonly  used  by  engineers,  in  which  1000  is  substituted  for  600,  is  due 
to  the  belief  of  the  engineers,  not  that  a  horse-power  could  not  be  trans- 
mitted by  the  belt  proportioned  by  the  older  rule,  but  that  such  a  pro- 
portion involved  undue  strain  from  overtightening  to  prevent  slippinge 
which  strain  entailed  too  much  journal  friction,  necessitated  frequent 
tightening,  and  decreased  the  length  of  the  life  of  the  belt. 

Mr.  Taylor's  rule  substituting  1100  ft.  per  min.  and  doubling  the  belt. 
Is  a  further  step,  and  a  long  one,  in  the  same  direction.  Whether  it  will 
be  taken  in  any  case  by  engineers  will  depend  upon  whether  they  appre- 
ciate the  extent  of  the  losses  dne  to  slippage  of  belts  slackened  by  use 
under  overstrain,  and  the  loss  of  time  in  tightening  and  repairing  belts, 
to  such  a  degree  as  to  induce  them  to  allow  the  first  cost  of  the  belts  to 
be  doubled  in  order  to  avoid  these  losses. 

It  should  be  noted  that  Mr.  Taylor's  experiments  were  made  on  rather 
narrow  belts,  used  for  transmitting  power  from  shafting  to  machinery, 
and  his  conclusions  may  not  be  applicable  to  heavy  a»u4  wide  belts, 
%3  engine  fly-wheel  belts. 


1146  BELTING. 

Earth's  Studies  on  Belting.  (Trans.  A.  S.  M.  E.,  1909.)  —  Mr. 
Carl  G.  Barth  has  made  an  extensive  study  of  the  work  of  earlier  writers 
on  the  subject  of  belting,  and  has  derived  several  new  formulae  and  dia- 
grams showing  the  relation  of  the  several  variables  that  enter  into  the 
belt  problem.  He  has  also  devised  a  slide  rule  by  which  calculations  of 
belts  may  easily  be  made.  He  finds  that  the  coefficient  of  friction  de- 
pends on  the  velocity  of  the  belt,  and  may  be  expressed  by  the  formula 

/  =  0.54  -  50Q+  y,  in  which  V  is  the  velocity  in  feet  per  minute. 


Taking  Mr.  Taylor's  data  as  a  starting  point,  Mr  Earth  has  adopted 
the  rule,  as  a  basis  for  use  of  belts  on  belt-driven  machines,  that  for  the 
driving  belt  of  a  machine  the  minimum  initial  tension  must  be  such 
that  when  the  belt  is  doing  the  maximum  amount  of  work  intended,  the 
sum  of  the  tension  in  the  tight  side  of  the  belt  and  one-half  the  tension  in 
the  slack  side  will  equal  240  Ibs.  per  square  inch  of  cross-section  for  all 
belt  speeds;  and  that  for  a  belt  driving  a  countershaft,  or  any  other  belt 
inconvenient  to  get  at  for  retightening  or  more  readily  made  of  liberal 
dimensions,  this  sum  will  equal  160  Ibs.  Further,  the  maximum  initial 
tension,  that  is,  the  initial  tensi9n  under  which  a  belt  is  to  be  put  up  in 
the  first  place,  and  to  which  it  is  to  be  retightened  as  often  as  it  drops 
to  the  minimum,  must  be  such  that  the  sum  defined  above  is  320  Ibs. 
for  a  machine  belt,  and  240  Ibs.  for  a  counter-shaft  belt  or  a  belt  simi- 
larly circumstanced. 

From  a  set  of  curves  plotted  by  Mr.  Barth  from  his  formula  the  follow- 
ing tables  are  derived.  The  figures  are  based  upon  the  conditions  named 
in  the  above  rule,  and  on  an  arc  of  contact  =  180°. 

Belts  on  Machines.    Tension  in  tight  side  -f-  1/2  tension  in  slack  side 


JJOll/O     VJ1J.      J-TiOr^lilUCO. 

=  240  Ibs. 

J.  CHOHJ. 

LJ      111 

ngi 

1U     • 

IU.C 

T   VZ    I 

custiuu 

in 

BUbUJ 

v  t 

>1UC! 

Velocity,  ft.  per  min.  .  . 

500 

1000 

2000 

3000 

4000 

5000 

6000 

Initial  tension,  £0  

124 

120 

121 

128 

136 

144 

152 

Centrifugal  tension  tc  . 

0  + 

3 

13 

31 

56 

86 

124 

Difference,  t0  —  tc 

123 

117 

108 

97 

80 

58 

28 

Tension  on  tight  side,  h 

210 

212 

211 

207 

198 

187 

173 

Tension  on  slack  side,  tz 

60 

54 

57 

68 

84 

107 

134 

^Effective  pull,  ti  -  h.  . 

150 

158 

154 

139 

114 

80 

39 

Sum  of  tensions  ti  4-  tz 

270 

268 

269 

274 

282 

294 

307 

H.P.  per  sq.  in.  of  sec- 

tion   

2.27 

4.79 

9 

.33 

1 

2.64 

13.82 

12 

.12 

7 

.09 

H.P.  per  in.  width,  5/16 

in.  thick  

0.71 

1.50 

2 

.82 

3.95 

4.32 

3 

.71 

2 

.22 

Belts  driving  countershafts, 

1  1  +  1/2  tz  = 

=  160  Ibs. 

Velocity  of  belt,  ft.  per  min  

500 

1000 

2000 

3000 

4000 

5000 

Initial  tension,  £0  

82 

81 

83 

89 

96 

102 

Tension  on  tight  side,  t\ 

...... 

140 

141 

140 

134 

125 

114 

Tension  on  slack  side,  tz 

40 

38 

41 

53 

69 

92 

Effective  pull,  fc  -  tz 

100 

103 

99 

81 

56 

22 

Sum  of  tensions  

180 

179 

181 

187 

194 

206 

H.P.  per  sq.  in.  of  section  

1 

.51 

3 

.12 

6.04 

7.36 

6 

.79 

3 

.33. 

H.P.  per  in.  width,  s/16  in.  thick     0 

.47 

0 

.97 

1.87 

2.30 

2 

.12 

1 

.04 

MISCELLANEOUS  NOTES  ON  BELTING. 

Formulas  are  useful  for  proportioning  belts  and  pulleys,  but  they  fur- 
nish no  means  of  estimating  how  much  power  a  particular  belt  may  be 
transmitting  at  any  given  time,  any  more  than  the  size  of  the  engine  is  a 
measure  of  the  load  it  is  actually  drawing,  or  the  known  strength  of  a 
horse  is  a  measure  of  the  load  on  the  wagon.  The  only  reliable  means  of 
determining  the  power  actually  transmitted  is  some  form  of  dynamometer. 
(See  Trans.  A.  S.  M.  E.,  vol.  xii,  p.  707.) 

If  we  increase  the  thickness,  the  power  transmitted  ought  to  increase 
in  proportion;  and  for  double  belts  we  should  have  half  the  width  required 
for  a  single  belt  under  the  same  conditions.  With  large  pulleys  and 
moderate  velocities  of  belt  it  is  probable  that  this  holds  good.  With 
l  pulleys,  however,  when  a  double  belt. is  used,  there  is  not  such  per- 


MISCELLANEOUS  NOTES  ON  BELTING.     1147 

feet  contact  between  the  pulley-face  and  tlie  belt,  due  to  the  rigidity  of 
the  latter,  and  more  work  is  necessary  to  bend  the  belt-fibers  than  when  a 
thinner  and  more  pliable  belt  is  used.  The  centrifugal  force  tending  to 
throw  the  belt  from  the  pulley  also  increases  with  the  thickness,  and  for 
these  reasons  the  width  of  a  double  belt  required  to  transmit  a  given, 
horse-power  when  used  with  small  pulleys  is  generally  assumed  not  less 
than  seven-tenths  the  width  of  a  single  belt  to  transmit  the  same  power, 
(Flather  on  "Dynamometers  and  Measurement  of  Power.") 

F.  W.  Taylor,  however,  finds  that  great  pliability  is  objectionable,  and 
favors  thick  belts  even  for  small  pulleys.  The  power  consumed  in  bending 
the  belt  around  the  pulley  he  considers  inappreciable.  According  to 
Rankine's  formula  for  centrifugal  tension,  this  tension  is  proportional  to 
the  sectional  area  of  the  belt,  and  hence  it  does  not  increase  with  increase 
of  thickness  when  the  width  is  decreased  in  the  same  proportion,  the 
sectional  area  remaining  constant. 

Scott  A.  Smith  (Trans.  A.S.M.  E.,  x,  765)  says:  The  best  belts  are  made 
from  all  oak-tanned  leather,  and  curried  with  the  use  of  cod  oil  and 
tallow,  all  to  be  of  superior  quality.  Such  belts  have  continued  in  use 
thirty  to  forty  years  when  used  as  simple  driving-belts,  driving  a  proper 
amount  of  power,  and  having  had  suitable  care.  The  flesh  side  should 
not  be  run  to  the  pulley-face,  for  the  reason  that  the  wear  from  contact 
with  the  pulley  should  come  on  the  grain  side,  as  that  surface  of  the  belt 
is  much  weaker  in  its  tensile  strength  than  the  flesh  side;  also  as  the  grain 
is  hard  it  is  more  enduring  for  the  wear  of  attrition;  further,  if  the  grain  is 
actually  worn  off,  then  the  belt  may  not  suffer  in  its  integrity  from  a 
ready  tendency  ef  the  hard  grain  side  to  crack. 

The  most  intimate  contact  of  a  belt  with  a  pulley  comes,  first,  in  the 
smoothness  of  a  pulley-face,  including  freedom  from  ridges  and  hollows 
left  by  turning-tools;  second,  in  the  smoothness  of  the  surface  and  even- 
ness jn  the  texture  or  body  of  a  belt ;  third,  in  having  the  crown  of  the  driv- 
ing and  receiving  pulleys  exactly  alike,  —  as  nearly  so  as  is  practicable 
in  a  commercial  sense;  fourth,  in  having  the  crown  of  pulleys  not  over 
1/8  in.  for  a  24-in.  face,  that  is  to  say,  that  the  pulley  is  not  to  be  over 
1/4  in.  larger  in  diameter  in  its  center;  fifth,  in  having  the  crown  other 
than  two  planes  meeting  at  the  center;  sixth,  the  use  of  any  material 
on  or  in  a  belt,  in  addition  to  those  necessarily  used  in  the  currying 
process,  to  keep  them  pliable  or  increase  their  tractive  quality,  should 
wholly  depend  upon  the  exigencies  arising  in  the  use  of  belts;  non-use  is 
safer  than  over-use;  seventh,  with  reference  to  the  lacing  of  belts,  it 
seems  to  be  a  good  practice  to  cut  the  ends  to  a  convex  shape  by  using  a 
former,  so  that  there  may  be  a  nearly  uniform  stress  on  the  lacing  through 
the  center  as  compared  with  the  edges.  For  a  belt  10  ins.  wide,  the  center 
of  each  end  should  recede  1/10  in, 

Lacing  of  Belts.  —  In  punching  a  belt  for  lacing,  use  an  oval  punch, 
the  longer  diameter  of  the  punch  being  parallel  with  the  sides  of  the  belt. 
Punch  two  rows  of  holes  in  each  end,  placed  zigzag.  In  a  3-in.  belt  there 
should  be  four  holes  in  each  end  —  two  in  each  row.  In  a  6-in.  belt, 
seven  holes  —  four  in  the  row  nearest  the  end.  A  10-in.  belt  should  have 
nine  holes.  The  edge  of  the  holes  should  not  come  nearer  than  3/4  in. 
from  the  sides,  nor  7/g  in.  from  the  ends  of  the  belt.  The  second  row 
should  be  at  least  13/4  ins.  from  the  end.  On  wide  belts  these  distances 
should  be  even  a  little  greater. 

Begin  to  lace  in  the  center  of  the  belt  and  take  care  to  keep  the  ends 
exactly  in  line,  and  to  lace  both  sides  with  equal  tightness.  The  lacing 
should  not  be  crossed  on  the  side  of  the  belt  that  runs  next  the  pulley. 
In  taking  up  belts,  observe  the  same  rules  as  in  putting  on  new  ones. 

Setting  a  Belt  on  Quarter-twist.  —  A  belt  must  run  squarely  on  to 
the  pulley.  To  connect  with  a  belt  two  horizontal  shafts  at  right  angles 
with  each  other,  say  an  engine-shaft  near  the  floor  with  a  line  attached  to 
the  ceiling,  will  require  a  quarter-turn.  First,  ascertain  the  central  point 
on  the  face  of  each  pullev  at  the  extremity  of  the  horizontal  diameter 
where  the  belt  will  leave  the  pulley,  and  then  set  that  point  on  the  driven 
pulley  plumb  over  the  corresponding  point  on  the  driver.  This  will  cause 
the  belt  to  run  squarely  on  to  each  pulley,  and  it  will  leave  at  an  angle 
greater  or  less,  according  to  the  size  of  the' pulleys  and  their  distance  from 
each  other. 

In  quarter-twist  belts,  in  order  that  the  belt  may  remain  on  the  pulleys* 


1148 


BELTING. 


the  central  plane  on  each  pulley  must  pass  through  the  point  of  delivery 
of  the  other  pulley.    This  arrangement  does  not  admit  of  reversed 
motion. 
To  find  the  Length  of  Belt  required  for  two  given  Pulleys.  — 

When  the  length  cannot  be  measured  directly  by  a  tape-line,  the  follow- 
ing approximate  rule  may  be  used:  Add  the  diameter  of  the  two  pulleys 
together,  divide  the  sum  by  2,  and  multiply  the  quotient  by  31/4,  and 
add  the  product  to  twice  the  distance  between  the  centers  of  the  shafts. 
(See  accurate  formula  below.) 

To  find  the  Angle  of  the  Arc  of  Contact  of  a  Belt.  —  Divide  the 
difference  between  the  radii  of  the  two  pulleys  in  inches  by  the  distance 
between  their  centers,  also  in  inches,  and  in  a  table  of  natural  sines  find 
the  angle  most  nearly  corresponding  with  the  quotient.     Multiply  this 
angle  by  2,  and  add  the  product  to  180°  for  the  angle  of  contact  with  the 
larger  pulley,  or  subtract  it  from  180°  for  the  smaller  pulley. 
Or,  let  R  =  radius  of  larger  pulley,  r  =  radius  of  smaller; 
L  =  distance  between  centers  of  the  pulleys; 
a  =  angle  whose  sine  is  (R  —  r)  •*•  L. 

Arc  of  contact  with  smaller  pulley  =  180°  —  2  a; 
Arc  of  contact  with  larger  pulley    =  180°  +  2  a. 

To  find  the  Length  of  Belt  in  Contact  with  the  Pulley.  —  For  the 

larger  pulley,  multiply  the  angle  a,  found  as  above,  by  0  .0349,  to  the 

Sroduct  add  3.1416,  and  multiply  the  sum  by  the  radius  of  the  pulley. 
r  length  of  belt  in  contact  with  the  pulley 

=  radius  X  (*  +  0  .0349  a)  =  radius  X  w(l  +  3/90). 
For  the  smaller  pulley,  length  =  radius  X  OT—  0  .0349  a) 
=  radius  X  *r(l  -  a)  -s-90. 

The  above  rules  refer  to  Open  Belts.     The  accurate  formula  for  length 
of  an  open  belt  is, 

Length  =  irR(l  +  a/90)  +  wr(l  -a/90)  -f  2  L  cos  a. 

=  R  (IT  +  0.0349  a)  +  r  (TT-O  .0349  a)  +  2  L  cos  a, 

in  which  R  =  radius  of  larger  pulley,  r  =  radius  of  smaller  pulley, 

L  ~  distance  between  centers  of  pulleys,  and  a  =  angle  whose 
sine  is 


(R  «-  r)  -J-  L;  cos  a  = 
An  approximate  formula  Is 
Length  =  2  L  -f-  *  (R  +  r)  '4-  (R  -  r)V£ 

For    L  =  4,  R  =  2,  r  =  1,  this   formula  gives  length  =  17.6748,   the 
accurate  formula  giving  17.6761 
For  Crossed  Belts  the  formula  is 

Length  of  belt  =  irR(l  +j8/90)  -f-  irr  (1  4-  £/90)  4-  2  L  cos  /5 
=  (R  +  r)  X  (^  +  0.0349  £)  +  2  L  cos  j8, 

In  which  /3  =  angle  whose  sine  is  (R  +  r)  -s-  L  ;  cos  £  =  V'z,2  —  (R  +  r)2  +  L. 

To  find  the  Length  of  Belt  when  Closely  Rolled.  —  The  sum  of  the 

diameter  of  the  roll,  and  of  the  eye  in  inches,  X  the  npmber  of  turns  made 
by  the  belt  and  by  0.1309,  =  length  of  the  belt  in  feet. 

To  find  the  Approximate  Weight  of  Belts.  —  Multiply  the  length 
of  belt,  in  feet,  by  the  width  in  inches,  and  divide  the  product  by  13  for 
single  and  8  for  double  belt. 

Good  oak-tanned  leather  from  the  back  of  the  hide  weighs  almost 
exactly  1  oz.  per  sq.  ft.  per  0.01  in.  thickness.  The  thickness  of  single 
belts  is  0.16  in.  ;  of  light  double  belts,  0.24  in.  ;  of  medium  weight  double 
belt,  0.28  in.;  of  standard  double  belt,  0.33  in.;  of  3-ply  belts,  0.45  in. 
(W.  O.  Webber,  in  Trans.  Natl.  Assoc.  Cotton  Mfrs.,  1908,  p.  345.) 

Relations  of  the  Size  and  Speeds  of  Driving  and  Driven  Pulleys. 
—  The  driving  pulley  is  called  the  driver,  D,  and  the  driven  piillcy  the 
driven,  'd.  If  the  number  of  teeth  in  gears  is  used  instead  of  diameter, 
in  these  calculations,  number  of  teeth  must  be  substituted  wherever 
diameter  occurs.  R  =  revs,  per  min.  of  driver,  r  =  revs,  per  min.  of 
driven. 

D 


MISCELLANEOUS  NOTES  ON  BELTING. 


1149 


Diam.  of  driver  »  diam.  of  driven  X  revs,  of  driven  -r  revs,  of  driver. 

d  =  DR  -r  r; 
Diam.  of  driven  =  diam.  of  driver  x  revs,  of  driver  +  revs,  of  driven. 

R  =  dr  -s-  D\ 
Revs,  of  driver  =  revs,  of  driven  x  diam.  of  driven  •*•  diam.  of  driver. 

r  =  DR  +  d\ 
Revs,  of  driven  =  revs,  of  driver  X  diam.  of  driver  -s-  diam.  of  driven. 

Evils  of  Tight  Belts.  (Jones  and  Laughlins.)  —  Clamps  with  power- 
ful screws  are  often  used  to  put  on  belts  with  extreme  tightness,  and  with 
most  injurious  strain  upon  the  leather.  They  should  be  very  judiciously 
used  for  horizontal  belts,  which  should  be  allowed  sufficient  slackness 
to  move  with  a  loose  undulating  vibration  on  the  returning  side,  as  a  test 
that  they  have  no  more  strain  imposed  than  is  necessary  simply  to  trans- 
mit the  power. 

On  this  subject  a  New  England  cotton-mill  engineer  of  large  experience 
says:  I  believe  that  three-quarters  of  the  trouble  experienced  in  broken 
pulleys,  hot  boxes,  etc.,  can  be  traced  to  the  fault  of  tight  belts.  The 
enormous  and  useless  pressure  thus  put  upon  pulleys  must  in  time  break 
them,  if  they  are  made  in  any  reasonable  proportions,  besides  wearing 
out  the  whole  outfit,  and  causing  heating  and  consequent  destruction  of 
the  bearings.  Below  are  figures  showing  the  power  taken,  in  average 
modern  mills  with  first-class  shafting,  to  drive  the  shafting  alone: 


Mill 
No. 

Whole 
Load, 
H.P. 

Shafting  Alone. 

Mill 
No. 

Whole 
Load, 
H.P. 

Shafting  Alone. 

Horse- 
power. 

Per  cent 
of  whole. 

Horse- 
power. 

Per  cent 
of  whole. 

4 

199 

472 
486 
677 

51 
111.5 
134 
190 

25.6 
23.6 
27.5 
28.1 

5 
6 
7 
8 

759 
235 
670 
677 

172.6 
84.8 
262.9 
182 

22.7 
36.1 
39.2 
26.8 

These  may  be  taken  as  a  fair  showing  of  the  power  that  is  required  in 
many  of  our  best  mills  to  drive  shafting.  It  is  unreasonable  to  think  that 
all  that  power  is  consumed  by  a  legitimate  amount  of  friction  of  bearings 
and  belts.  I  know  of  no  cause  for  such  a  loss  of  power  but  tight  belts. 
These,  when  there  are  hundreds  or  thousands  in  a  mill,  easily  multiply 
the  friction  on  the  bearings,  and  would  account  for  the  figures. 

Sag  of  Belts.  Distance  between  Pulleys. —  In  the  location  of  shafts 
that  are  to  be  connected  with  each  other  by  belts,  care  should  be  taken 
to  secure  a  proper  distance  one  from  the  other.  This  distance  should  be 
such  as  to  allow  of  a  gentle  sag  to  the  belt  when  in  motion. 

A  general  rule  may  be  stated  thus:  Where  narrow  belts  are  to  be  run 
over  small  pulleys  15  feet  is  a  good  average,  the  belt  having  a  sag  of 
1 1/2  to  2  inches. 

For  larger  belts,  working  on  larger  pulleys,  a  distance  of  20  to  25  feet 
does  well,  with  a  sag  of  21/2  to  4  inches. 

For  main  belts  working  on  very  large  pulleys,  the  distance  should  be  25 
to  30  feet,  the  belts  working  well  with  a  sag  of  4  to  5  inches. 

If  too  great  a  distance  is  attempted,  the  belt  will  have  an  unsteady 
flapping  motion,  which  will  destroy  both  the  belt  and  machinery. 

Arrangement  of  Belts  and  Pulleys.  —  If  possible  to  avoid  it,  con- 
nected shafts  should  never  be  placed  one  directly  over  the  other,  as  in 
such  case  the  belt  must  be  kept  very  tight  to  do  the  work.  For  this 
purp9se  belts  should  be  carefully  selected  of  well-stretched  leather. 

It  is  desirable  that  the  angle  of  the  belt  with  the  floor  should  not  exceed 
45°.  It  is  also  desirable  to  locate  the  shafting  and  machinery  so  that 
belts  should  run  off  from  each  shaft  in  opposite  directions,  as  this  arrange- 
ment will  relieve  the  bearings  from  the  friction  that  would  result  when 
the  belts  all  pull  one  way  on  the  shaft. 

In  arranging  the  belts  leading  from  the  main  line  of  shafting  to  the 
counters,  those  pulling  in  an  opposite  direction  should  be  placed  as  near 
each  other  as  practicable,  while  those  pulling  in  the  same  direction 
should  be  separated.  This  can  often  be  accomplished  by  changing  the 
relative  positions  of  the  pulleys  on  the  counters.  By  this  procedure 
much  of  the  friction  on  the  journals  may  be  avoided. 

If  possible,  machinery  should  be  so  placed  that  the  direction  of  the  belt 


1150  BELTING. 

motjon  shall  be  from  the  top  of  the  driving  to  the  top  of  the  driven  pulley, 
when  the  sag  will  increase  the  arc  of  contact. 

The  pulley  should  be  a  little  wider  than  the  belt  required  for  the  work. 

The  motion  of  driving  should  run  with  the  laps  of  the  belts. 

Tightening  or  guide  pulleys  should  be  applied  to  the  slack  side  of  belts 
and  near  the  smaller  pulley. 

Jones  and  Laughlins,  in  their  Useful  Information,  say:  The  diameter  of 
the  pulleys  should  be  as  large  as  can  be  admitted,  provided  they  will  not 
produce  a  speed  of  more  than  4750  feet  of  belt  motion  per  minute. 

They  also  say:  It  is  better  to  gear  a  mill  with  small  pulleys  and  run 
them  at  a  high  velocity,  than  with  large  pulleys  and  to  run  them  slower. 
A  mill  thus  geared  costs  less  and  has  a  much  neater  appearance  than  with 
large  heavy  pulleys. 

M.  Arthur  Achard  (Proc.  Inst.  M.  E.,  Jan.,  1881,  p.  62)  says:  When  the 
belt  is  wide  a  partial  vacuum  is  formed  between  the  belt  and  the  pulley 
at  a  high  velocity.  The  pressure  is  then  greater  than  that  computed  from 
the  tensions  in  the  belt,  and  the  resistance  to  slipping  is  greater.  This 
has  the  advantage  of  permitting  a  greater  power  to  be  transmitted  by  a 
given  belt,  and  of  diminishing  the  strain  on  the  shafting. 

On  the  other  hand,  some  writers  claim  that  the  belt  entraps  air  between 
itself  and  the  pulley,  which  tends  to  diminish  the  friction,  and  reduce 
the  tractive  force.  On  this  theory  some  manufacturers  perforate  the 
belt  with  numerous  holes  to  let  the  air  escape. 

Care  of  Belts.  —  Leather  belts  should  be  well  protected  against  water, 
loose  steam,  and  all  other  moisture,  with  which  they  should  not  come  in 
contact.  But  where  such  conditions  prevail  fairly  good  results  are 
obtained  by  using  a  special  dressing  prepared  for  the  purpose  of  water- 
proofing leather,  though  a  positive  water-proofing  material  has  not  yet 
been  discovered. 

Belts  made  of  coarse,  loose-fibered  leather  will  do  better  service  in  dry 
and  warm  places,  but  if  damp  or  moist  conditions  exist  then  the  very 
finest  and  firmest  leather  should  be  used.  (Fayerweather  &  Ladew.) 

Do  not  allow  oil  to  drip  upon  the  belts.    It  destroys  the  life  of  the  leather. 

Leather  belting  cannot  safely  stand  above  130°  of  heat. 

"Duxbak"  waterproof  belt  is  advertised  to  withstand  any  amount 
of  moisture,  and  temperatures  up  to  200  degrees. 

Strength  of  Belting. — The  ultimate  tensile  strength  of  belting  does 
not  generally  enter  as  a  factor  in  calculations  of  power  transmission.  j 

The  strength  of  the  solid  leather  in  belts  is  from  2000  to  5000  Ibs.  per 
square  inch;  at  the  lacings,  even  if  well  put  together,  only  about  1000  to 
1500.  If  riveted,  the  joint  should  have  half  the  strength  of  the  solid 
belt.  The  working  strain  on  the  driving  side  is  generally  taken  at  not 
over  one-third  of  the  strength  of  the  lacing,  or  from  one-eighth  to  one- 
sixteenth  of  the  strength  of  the  solid  belt.  Dr.  Hartig  found  that  the 
tension  in  practice  varied  from  30  to  532  Ibs.  per  sq.  in. ,  averaging  273  Ibs. 

Effect  of  Humidity  Upon  a  Leather  Belt.  (W.  W.  Bird  and  F.  W. 
Roys,  Trans.  A.  S.  M.  E.,  1915.) — Tests  with  a  4-in.  oak-tanned  single 
belt,  with  constant  horse-power  transmitted,  and  with  the  center  dis- 
tance and  humidity  varying,  showed  increase  of  the  sum  of  the  tensions 
as  the  humidity  decreased,  figures  taken  from  curves  of  the  results 
being  as  follows: 

Center  distance:  9  ft.  6  in.,  9  ft.  61/2  in.,  9  ft.  7  in.,  9  ft.  71/2  in. 
Relative  Humidity.  Sum  of  the  Tensions,  pounds. 

90 95  210  325  445 

55 125  260  400  550 

20 150  310  465  620 

Increase  of  temperature  as  well  as  increase  of  humidity  tends  to 
lengthen  the  belt  and  decrease  the  tension.  The  most  important  con- 
clusions are: 

1.  If  a  belt  be  set  up  at  a  medium  relative  humidity,  the  tensions  will 
not  be  excessive  at  lower  relative  humidities,  nor  will  there  be  any 
great  danger  of  slipping  at  high  relative  humidities  unless  there  are 
excessive  temperature  changes. 

2.  If  a  belt  be  set  up  at  any  relative  humidity  with  a  spring  or 
gravity  tightener,  a  load  50  per  cent  greater  than  the  standard  can 
be  transmitted  at  either  high  or  low  humidity  without  danger  of  stretch- 
ing the  belt,  slipping,  or  excessive  pressure  on  the  bearings. 


MISCELLANEOUS  NOTES  ON  BELTING.  1151 

Adhesion  Independent  of  Diameter.  (Schultz  Belting  Co".)  — 
1.  The  adhesion  of  the  belt  to  the  pulley  is  the  same  —  the  arc  or  number 
of  degrees  of  contact,  aggregate  tension  or  weight  being  the  same  — 
without  reference  to  width  of  belt  or  diameter  of  pulley. 

2.  A  belt  will  slip  just  as  readily  on  a  pulley  four  feet  in  diameter  as  It 
will  on  a  pulley  two  feet  in  diameter,  provided  the  conditions  of  the  faceg 
of  the  pulleys,  the  arc  of  contact,  the  tension,  and  the  number  of  feet 
the  belt  travels  per  minute  are  the  same  in  both  cases. 

3.  To  obtain  a  greater  amount  of  power  from  belts  the  pulleys  may  be 
covered  with  leather;  this  will  allow  the  belts  to  run  very  slack  and  give 
25%  more  durability. 

Endless  Belts.  —  If  the  belts  are  to  be  endless,  they  should  be  put  on 
and  drawn  together  by  "belt  clamps"  made  for  the  purpose.  If  the  belt 
is  made  endless  at  the  belt  factory,  it  should  never  be  run  on  to  the  pulleys, 
(est  the  irregular  strain  spring  the  belt.  Lift  out  one  shaft,  place  the 
belt  on  the  pulleys,  and  force  the  shaft  back  into  place. 

Belt  Data.  —  A  fly-wheel  at  the  Amoskeag  Mfg.  Co.,  Manchester,  N.H., 
30  feet  diameter,  110  inches  face,  running  61  revs,  per  min.,  carried  two 
heavy  double-leather  belts  40  inches  wide  each,  and  one  24  inches  wide. 
The  engine  indicated  1950  H.P.,  of  wliich  probably  1850  H.P.  was  trans- 
mitted by  the  belts.  The  belts  were  heavily  loaded,  but  not  overtaxed, 
the  speed  being  323  ft.  per  min.  for  1  H.P.  per  inch  of  width. 

Samuel  Webber  (Am.  Mach.,  Feb.  22,  1894)  reports  a  case  of  a  belt  30 
ins.  wide,  3/8  in.  thick,  running  for  six  years  at  a  velocity  of  3900  ft.  per 
min.,  on  to  a  pulley  5  ft.  diameter,  and  transmitting  556  H.P.  This  gives 
a  velocity  of  210  ft.  per  min.  for  1  H.P.  per  in.  of  width.  By  Mr.  Nagle's 
table  of  riveted  belts  this  belt  would  be  designed  for  332  H.P.  By  Mr. 
Taylor's  rule  it  would  be  used  to  transmit  only  123  H.P. 

The  above  may  be  taken  as  examples  of  what  a  belt  may  be  made  to 
do,  but  they  should  not  be  used  as  precedents  in  designing.  It  is  not 
stated  how  much  power  was  lost  by  the  journal  friction  due  to  over- 
tightening  of  these  belts. 

The  United  States  Navy  Department  Specifications  for  Leather 
Belting. — Belting  to  be  cut  from  No.  1  native  packer  steer  hides  or 
their  equal.  ~A11  hides  to  be  tanned  with  white  or  chestnut  oak  by 
slow  process  (six  to  eight  months)  and  chemical  processes  imist  not  be 
used.  The  leather  is  to  be  thoroughly  cured  by  hand  and  must  not 
be  stuffed  or  loaded  for  artificial  weight.  Leather  must  not  crack 
open  on  grain  side  when  doubled  strongly  by  hand  with  grain  side 
out.  Belting  is  to  be  cut  from  central  part  of  the  hide  no  further 
than  15  in.  from  backbone  or  more  than  48  in.  from  tail  toward  shoulder. 

Belts  8  in.  and  over  must  be  cut  to  include  backbone.  All  leather 
is  to  be  stretched  6  in.  in  lengthwise  direction  of  the  butt  and  is 
not  to  exceed  54  in.  after  stretching.  Centers  and  sides  are  to  be 
stretched  6  in.  separately.  That  is,  all  side  leathers  from  which  widths 
under  8  in.  are  to  be  cut,  must  be  stretched  after  the  belting  is  removed 
from  the  backbone  center  section.  Center  sections  are  to  be  stretched 
in  exactly  the  same  size  for  which  they  are  to  be  used. 

For  single  belts  up  to  6  in.,  laps  must  not  exceejd.  6  in.  nor  be  less 
than  3  1/2  in.  long.  For  single  belts  over  6  in.  laps  must  not  be  more 
than  1  in.  wider  than  belt. 

For  double  belts,  laps  must  not  exceed  5  1/2  in.  nor  to  be  less  than 
31/2  in.  No  filling  straps  will  be  permitted.  All  laps  must  be  held 
securely  at  every  part  with  the  best  quality  of  belt  cement,  and  when 
pulled  apart  shall  show  no  resinous,  vitreous,  oily  or  watered  condition. 
Belting  is  to  be  stretched  again  after  manufacture. 

Belting  is  to  weigh  for  all  sizes  of  single  belts  16  oz.  per  sq.  ft.  and 
for  double  belts  per  sq.  ft.  as  follows:  1  to  2  in.,  26  oz.;  21/2  to  4  in., 
28  oz.;  41/2  to  5  in.,  30  oz.;  6  in.  and  over,  32  oz. 

Only  hand  cut,  green  slaughter  hides  of  the  best  quality  are  to  be 
used  for  lacing.  Raw  hide  laces  to  be  cut  1/4.  5/i6,  3/8,  7/i6,  V2,  5/8, 
and  3/4-in.  sizes.  They  must  be  cut  lengthwise  from  the  hide  and 
have  an  ultimate  tensile  strength  of  not  less  than 

Width,  in 1/4        5/16         3/8       7/i6         l/2         5/8         8/4 

Tensile  strength,  Ib 95       125       155       165       180       205     J230 

Belt  Dressings. — We  advise  that  no  belt  dressing  should  be  used, 
except  when  the  belt  becomes  d.ry  and  husky,  and  iu  sucb  instances  wa 


1152  BELTING. 

recommend  the  use  of  a  dressing.  Where  this  is  not  used  beef  tallow  at 
blood-warm  temperature  should  be  applied  and  then  dried  in,  either  by 
artificial  heat  or  the  sun.  The  addition  of  beeswax  to  the  tallow  will  be 
of  some  service  if  the  belts  are  used  in  wet  or  damp  places.  Resin 
should  never  be  used  on  leather  belting.  (Fayerweather  &  Ladew.) 

Belts  should  not  be  soaked  in  water  before  oiling,  and  penetrating  oils 
should  only  be  used  when  a  belt  gets  very  dry  and  husky  from  neglect. 
It  may  then  be  moistened  a  little,  and  neatsfoot  oil  applied.  Frequent 
applications  of  such  oils  to  a  new  belt  render  the  leather  soft  and  flabby, 
thus  causing  it  to  stretch,  and  making  it  liable  to  run  out  of  line.  A 
composition  of  tallow  and  oil,  with  a  little  resin  or  beeswax,  is  better  to 
use.  Prepared  castor-oil  dressing  is  good,  and  may  be  applied  with  a 
brush  or  rag  while  the  belt  is  running.  (Alexander  Bros.) 

Some  forms  of  belt  Dressing,  the  compositions  of  which  have  not  been 
published,  appear  to  have  the  property  of  increasing  the  coefficient  of 
friction  between  the  belt  and  the  pulley,  enabling  a  given  power  to  be 
transmitted  with  a  lower  belt  tension  than  with  undressed  belts.  C.  W. 
Evans  (Power,  Dec.,  1905),  gives  a  diagram,  plotted  from  tests,  which 
shows  that  three  of  these  compositions  gave  increased  transmission  for 
a  given  tension,  ranging  from  about  10%  for  90  Ibs.  tension  per  inch  of 
width  to  100%  increase  with  20  Ibs.  tension. 

Cement  for  Doth,  or  Leather.  (Moles worth.)  — 16  parts  gutta- 
percha,  4  india-rubber,  2  pitch,  1  shellac,  2  linseed-oil,  cut  small,  melted 
together  and  well  mixed. 

Rubber  Belting.  —  The  advantages  claimed  for  rubber  belting  are 
perfect  uniformity  in  width  and  thickness;  it  will  endure  a  great  degree  of 
heat  and  cold  without  injury;  it  is  also  specially  adapted  for  use  in  damp 
or  wet  places,  or  where  exposed  to  the  action  of  steam;  it  is  very  durable, 
and  has  great  tensile  strength,  and  when  adjusted  for  service  it  has  the 
most  perfect  hold  on  the  nullevs.  hence  is  less  liable  to  slip  than  leather. 

Never  use  animal  oil  or  grease  on  rubber  belts,  as  it  will  soon  destroy! 
them. 

Rubber  belts  will  be  improved,  and  their  durability  increased,  by 
putting  on  with  a  painter's  brush,  and  letting  it  dry,  a  composition  made 
of  equal  parts  of  red  lead,  black  lead,  French  yellow,  and  litharge,  mixed 
with  boiled  linseed-oil  and  japan  enough  to  make  it  dry  quickly.  The 
effect  of  this  will  be  to  produce  a  finely  polished  surface.  If,  from  dust 
or  other  cause,  the  belt  should  slip,  it  should  be  lightly  moistened  on  the 
pulley  side  with  boiled  linseed-oil.  (From  manufacturers'  circulars . ) 

The  best  conditions  are  large  pulleys  and  high  speeds,  low  tension  and 
reduced  width  of  belt.  4000  ft.  per  min.  is  not  an  excessive  speed  on 
proper  sized  pulleys. 

H.P.  of  a  4-plv  rubber  belt  =  flength  of  arc  of  contact  on  smaller  pulley 
in  ft.  X  width  of  belt  in  ins.  X  revs,  per  min.)  -r-  325.  For  a  5-ply  belt 
multiply  by  ll/s,  for  a  6-ply  by  12/3,  for  a  7-ply  by  2,  for  an  8-ply  by  21/3. 
When  the  proper  weight  of  duck  is  used  a  3-  or  4-piy  rubber  belt  is  equal 
to  a  single  leather  belt  and  a  5-  or  6-oly  rubber  to  a  double  leather  belt. 
When  the  arc  of  contact  is  180°,  H.P.  of  a  4-ply  belt  =  width  in  ins.  X 
velocity  in  ft.  per  min.  -r-  650.  (Boston  Belting  Co.) 

Steel  Belts. — The  Eloesser-Kraftband-Gesellschaft,  of  Berlin,  has 
introduced  a  steel  belt  for  heavy  power  transmission  at  high  speeds 
(Am.  Mach.,  Dec.  24,  1908).  It  is  a  thin  flat  band  of  tempered  steel. 
The  ends  are  soldered  and  then  clamped  by  a  special  device  consisting  of 
%wo  steel  plates,  tapered  to  thin  edges,  which  are  curved  to  the  radius 
of  the  smallest  pulley  to  be  used,  and  joined  together  by  small  screws 
which  pass  through  holes  in  the  ends  of  the  belt.  It  is  stated  that  the 
slip  of  these  belts  is  less  than  0.1%;  they  are  about  one-fifth  the  width 
of  a  leather  belt  for  the  same  power,  and  they  are  run  at  a  speed  of  10,000 
ft.  per  minute  or  upwards.  The  following  figures  give  a  comparison  of 
a  rope  drive  with  six  ropes  1.9  ins.  diam.,  a  leather  belt  9.6  ins.  wide  and 
a  steel  belt  4  ins.  wide,  for  transmitting  100  H.P.  on  pulleys  3  ft.  diam. 
30  ft.  apart  at  200  r.p.m. 

Rope     Leather      Steel 
Drive.      Belt.         Belt. 

Weight  of  pulley,  Ibs 2200         1120        460 

Weight  of  rope  or  belt,  Ibs 530  240          30 

Total  cost  of  drive $335         $425      $250 

?ower  lost,  percent  of  100  H.P,,.. ,..„,,,.,         13  6  0,5 


EOLLER  CHAIN  AND   SPROCKET  DRIVES.        1153 

ROLLER  CHAIN  AND  SPROCKET  DRIVES. 

The  following  is  abstracted  from  an  article  by  A.  E.  Michel,  in 
Mach'y,  Feb.,  1905.  (Revised,  March,  1915.) 

Steel  chain  of  accurate  pitch,  high  tensile  strength,  and  good  wearing 
qualities,  possesses,  when  used  within  proper  limitations,  advantages 
enjoyed  by  no  other  form  of  transmission.  It  is  compact,  affords  a  posi- 
tive speed  ratio,  and  at  slow  speeds  is  capable  of  transmitting  heavy 
strains.  On  short  transmissions  it  is  more  efficient  than  belting  and  will 
operate  more  satisfactorily  in  damp  or  oily  places.  There  is  no  loss  of 
power  from  stretch,  and  as  it  allows  of  a  low  tension,  journal  friction  is 
minimized. 

Roller  chain  has  been  known  to  stand  up  at  a  speed  of  4,000  ft.  per 
min.,  and  transmit  25  H.P.  at  1,250  ft.  per  min.;  but  speeds  of  1,000  ft. 
per  min.  and  under  give  better  satisfaction.  Block  chain  is  adapted  to 
slower  speeds,  say  700  ft.  per  min.  and  under,  and  is  extensively  used  on 
bicycles,  small  motor  cars  and  machine  tools.  Where  speed  and  pull  are 
not  fixed  quantities,  it  is  advisable  to  keep  the  speed  high,  and  chain 
pull  low,  yet  it  should  be  borne  in  mind  that  high  speeds  are  more  de- 
structive to  chains  of  large  than  to  those  of  small  pitch. 

The  following  table  of  tensile  strengths,  based  on  tests  of  "  Diamond" 
chains  taken  from  stock,  may  be  considered  a  fair  standard: 

ROLLER  CHAIN. 

Pitch,  in  .....     1/2        5/8        3/4          l          11/4          11/2        13/4         2      ' 
Tens,  strength, 

Jbs  ........   2,500  3,900  5,600  10,000  15,600  18,500  30,500  40,000 

Block  chain..  .   1  inch,     1,200  to  2,500;     11/2  inch,     5,000. 

The  safe  working  load  of  a  chain  is  dependent  on  the  amount  of  rivet 
bearing  surface,  and  varies  from  i/e  to  1/30  of  the  tensile  strength,  ac- 
cording to  the  spead,  size  of  sprockets,  and  other  conditions  peculiar  to 
each  case.  The  tendency  now  is  to  use  the  widest  possible  chain  in 
order  to  secure  maximum  rivet  bearing  surface,  thus  insuring  minimum 
wear  from  friction.  Manufacturers  are  making  heavier  chains  than 
heretofore  for  the  same  duty.  As  short  pitch  is  always  desirable, 
special  double  and  even  triple  width  chains  are  now  made  to  conform 
to  the  requirements  when  a  heavy  single  width  chain  of  greater  pitch 
is  not  practical.  A  double  chain  has  a  little  more  than  twice  the  rivet 
bearing  surface  and  half  again  as  much  tensile  strength  as  the  corre- 
sponding single  one. 

The  length  of  chain  for  a  given  drive  may  be  found  by  the  following 
formula: 

All  dimensions  in  inches.  D  =  Distance  between  centers  of  shafts. 
L  =  Distance  between  limiting  points  of  contact.  R  =  Pitch  radius  of 
large  sprocket,  r  =  Pitch  radius  of  small  sprocket.  N  =  Number  of 
teeth  of  large  sprocket,  n  =  Number  of  teeth  of  small  sprocket.  P  = 
Pitch  of  chain  and  sprockets.  (180°  +  2  a)  ==  angle  of  contact  on  large 
sprocket.  (180°  -  2  a)  =  angle  of  contact  on  small  sprocket.  a  = 
angle  whose  sine  is  (R  —  r)/D.  A  =  D  cos  ct. 

Length  of  chain  required: 


For  block  chain,  the  total  length  specified  in  ordering  should  be  in 
multiples  of  the  pitch.  For  roller  chain,  the  length  should  be  in  multi- 
ples of  twice  the  pitch,  as  a  union  of  the  ends  can  be  effected  only  with 
an  outside  and  an  inside  link. 

Wherever  possible,  the  distance  between  centers  of  shafts  should  per- 
mit of  adjustment  in  order  to  regulate  the  sag  of  the  chain.  A  chain  should 
be  adjusted,  in  proportion  to  its  length,  to  show  slack  when  running,  care 
being  taken  to  have  it  neither  too  tight  nor  too  loose,  as  either  condition 
is  destructive.  If  a  fixed  center  distance  must  be  used,  and  results  in 
too  much  sag,  the  .looseness  should  be  taken  up  by  an  idler,  and  when 
there  is  any  considerable  tension  on  the  slack  side,  this  idler  must  be 
a  sprocket.  Where  an  idler  is  not  practical,  another  combination  of 
sprockets  giving  approximately  the  same  speed  ratio  may  be  tried,  and 
in  this  manner  a  combination  giving  the  proper  sag  may  always  be 
obtained.  The  Diamond  Chain  and  Mfg.  Co.  says  that  the  center 


1154  BELTING. 

line  distance  between  sprockets  should  not  be  less  than  H/2  times  the 
diameter  of  the  larger  sprocket  nor  more  than  10  or  12  ft. 

In  automobile  drives,  too  much  sag  or  too  great  a  distance  between 
shafts  causes  the  chain  to  whip  up  and  down — a  condition  detrimental 
to  smooth  running  and  very  destructive  to  the  chain.  In  this  class 
of  work  a  center  distance  of  over  4  ft.  has  been  used,  but  greater  effi- 
ciency and  longer  life  are  secured  from  the  chain  on  shorter  lengths, 
say  3  ft.  and  under. 

Sprocket  Wheels.  Properly  proportioned  and  machined  sprockets  are 
essential  to  successful  chain  gearing.  The  important  dimensions  of  a 
sprocket  are  the  pitch  diameter  and  the  bottom  and  outside  diameters. 
For  block  chain  these  are  obtained  as  follows: 

N  =  No.  of  teeth,  b  =  Diameter  of  round  part  of  chain  block.  B  = 
Center  to  center  of  holes  in  chain  block.  A  =  Center  to  center  of  holes 
in  side  links,  a  =  180°/JV.  Tan  Q  =  sin  a  4-  (B/A  +  cos  a). 

M  Pitch  diameter  =  A  /sin  Q. 

Bottom  diam.  =  pitch  diam.  -  6.     Outside  diam.  =  pitch  diam.  -f  b. 

For  roller  chain:  N  =  Number  of  teeth.  P  =  Pitch  of  chain.  D  = 
Diameter  of  roller,  a  =  180° /N.  Pitch  diameter  =  P/sin  a. 

Bottom  diam.    =  pitch  diam.   —  D. 

For  sprockets  of  17  teeth  and  over,  outside  diam.  =  pitch  diam.  +  D. 

The  outside  diameters  of  small  sprockets  are  cut  down  so  that  the 
teeth  will  clear  the  roller  perfectly  at  high  speeds. 

Outside  diam.  =  pitch  diam.  -f  D  —  E. 


Pitch. 

Values  of  E. 

8  to  12 
Teeth. 

13  to  16 
Teeth. 

1/2  in.  to  3/4  in        .  . 

0.062  in. 
0.125  in. 

0.031  in. 
0.062  in. 

1  in.  to  2  in  

Sprocket  diameters  should  be  very  accurate,  particularly  the  base 
diameter,  which  should  not  vary  more  than  0.002  in.  from  the  calculated 
values.  Sprockets  should  be  gauged  to  discover  thick  teeth  and  inaccur- 
ate diameters.  A  poor  chain  may  operate  on  a  good  sprocket,  but  a  bad 
sprocket  will  ruin  a  good  chain.  Sprockets  of  12  to  60  teeth  give  best 
results.  Fewer  may  oe  used,  but  cause  undue  elongation  In  the  chain, 
wear  the  sprockets  and  consume  too  much  power.  Eight-tooth  sprockets 
ruin  almost  every  roller  chain  applied  to  them,  and  ten  and  eleven  teeth 
are  fitted  only  for  medium  and  slow  speeds  with  other  conditions  unusu- 
ally favorable. 

Sprocket  teeth  seldom  break  from  insufficient  strength,  but  the  tooth 
must  be  properly  shaped.  A  chain  will  not  run  well  unless  the  sprockets 
have  sidewise  clearance  and  teeth  narrowed  at  the  ends  by  curves  begin- 
ning at  the  pitch  line. 

Calling  W  the  width  cf  the  chain  between  the  links, 

A  =  1/2  W  =  width  of  tooth  at  top.    B  =  uniform  width  below  pitch  line. 
B  =  W  —  1/64  in.  when  W  =  1/4  in.  or  less. 

=  jp  —  1/32  in.  when  W  =  5/ie  to  5/g  in.  inclusive. 

«  W—  Vie  in.  when  W  =  3/4  in.  or  over. 

If  the  sprocket  is  flanged  the  chain  must  seat  itself  properly  without  the 
side  bars  coming  into  contact  with  the  flange. 

The  principal  cause  of  trouble  within  the  chain  is  elongation.  It  Is 
the  result  of  stretch  of  material  or  natural  wear  of  rivets  and  their  bearings. 
To  guard  against  the  former,  chain  makers  use  special  materials  of  high 
tensile  strength,  but  a  chain  subjected  to  jars  and  jolts  bey9nd  the  limit  ; 
of  elasticity  of  the  material  may  be  put  in  worse  condition  in  an  instant 
than  in  months  of  natural  wear.  If  for  any  reason  a  link  elongates 
unduly  it  should  be  replaced  at  once,  as  one  elongated  link  will  eventually 
ruin  the  entire  chain.  Such  elongation  frequently  results  from  all  the 
load  being  thrown  on  at  once. 

To  minimize  natural  wear,  chains  should  be  well  greased  inside  and  , 
out  protected  from  mud  and  heavy  grit,  cleaned  often  and  replaced  to  , 


ROLLER  CHAIN  AND  SPROCKET  DRIVES.         1153 

run  in  the  same  direction  and  same  side  up.  A  new  chain  should  never 
be  applied  to  a  much-worn  sprocket. 

Importance  of  pitch  line  clearances:  In  a  sprocket  with  no  clearances 
a  new  chain  fits  perfectly,  but  after  natural  wear  the  pitch  of  chain  and 
sprocket  become  unlike.  The  chain  is  then  elongated  and  climbs  the 
teeth,  which  act  as  wedges,  producing  enormous  strain,  and  it  quickly 
wrecks  itself.  With  the  same  chain  on  a  driven  sprocket,  cut  with 
clearances,  all  rollers  seat  against  their  teeth.  After  long  and  useful  life, 
the  working  roller  shifts  to  the  top,  and  the  other  rollers  still  seat  with 
the  same  ease  as  when  new.  Theoretically,  all  the  rollers  share  the  load. 
This  never  occurs  in  practice,  for  infinitesimal  wear  within  the  chain 
causes  one,  and  only  one,  roller  to  bear  perfectly  seated  against  the 
working  face  of  the  sprocket  tooth  at  any  one  time.  Clearance  alone  on 
the  driver  will  not  provide  for  elongation.  To  operate  properly  the 
pitch  of  the  driver  must  be  lengthened,  which  is  done  by  increasing  the 
pitch  diameter  by  an  amount  dependent  upon  the  clearance  allowed. 
For  theoretical  reasoning  on  this  subject  see  "  Roller  Chain  Gear,"  a 
treatise  on  English  practice,  by  Hans  Renold. 

When  the  load  reverses,  each  sprocket  becomes  alternately  driver  and 
driven.  This  happens  in  a  motor  car  during  positive  and  negative  accel- 
eration, or  in  ascending  or  descending  a  hill.  In  this  event,  the  above 
construction  is  not  applicable,  for  a  driven  sprocket  of  longer  pitch  than 
the  chain  will  stretch  it.  No  perfect  method  of  equalizing  the  pitch  of  a 
roller  chain  and  its  sprockets  under  reversible  load  and  at  all  periods  of 
chain  elongation  has  been  found.  This  fault  is  eliminated  in  the  "  silent  " 
type  of  chain;  hence  it  runs  smooth  at  a  very  much  greater  speed  than 
roller  chain  will  stand. 

In  practice  there  are  comparatively  few  roller  chain  drives  with  chain 
pull  always  in  the  same  direction,  so  manufacturers  generally  cut  the 
driver  sprockets  for  these  with  normal  pitch  diameter,  same  as  the 
driven.  Recent  experiments  have  proven  that  the  difficulties  are  greatly 
lessened  by  cutting  both  driver  and  driven  with  liberal  pitch  line  clear- 
rfhce.  Accordingly,  chain  makers  now  advise  the  following  pitch  line 
clearance  for  standard  rollers: 

Pitch,  in.,  1/2  3/4        1  11/4          1V2        i3/4     2 

Clearance,  In.,       1/32         Vie         3/32         3/i6  7/32        Vs       5/32 

Cutters  may  be  obtained  from  Brown  &  Sharpe  Mfg.  Co.  with  thia 
clearance. 

Belting  versus  Chain  Drives. — Chains  are  suitable  for  positive 
transmissions  of  very  heavy  powers  at  slow  speed.  They  are  properly 
used  for  conveying  ashes,  sand,  chemicals  and  liquids  which  would  cor- 
rode or  destroy  belting.  Chains  of  this  kind  are  generaUy  made  of 
malleable  iron.  For  conveyers  for  clean  substances, 'flour,  wheat  ana 
other  grains,  belts  are  preferable,  and  in  the  best  installations  leather  is 
preferred  to  cotton  or  rubber,  being  more  durable.  Transmission 
chains  have  to  be  carefully  made.  If  the  chain  is  to  run  smoothly, 
noiselessly,  and  without  considerable  friction,  both  the  links  and  the 
sprockets  must  be  mathematically  correct.  This  perfection  of  design 
is  found  only  in  the  highest  and  best  makes  of  steel  chain. 

Deterioration  of  chains  starts  in  with  the  beginning  of  service.  Even 
in  such  light  and  flexible  duty  as  bicycle  transmission,  a  chain  is  sub- 
jected to  sudden  severe  strains,  which  either  stretch  the  chain. or  distort 
the  bearing  surfaces.  Either  mishap  is  fatal  to  smooth,  frictionless 
running.  If  the  transmissi9n  is  positive,  as  from  motor  or  shaft  to  a 
machine  tool,  sudden  variations  in  strain  become  sledge-hammer  blows, 
and  the  chain  must  either  break  or  the  parts  yield.  To  avoid  the  evils 
arising  from  the  stretching  of  the  chain,  self-ad  justing  forms  of  teeth 
have  been  invented,  and  the  Renold  and  the  Morse  silent-chain  gears 
are  examples. 

Chain  drives  are  recommended  for  use  under  the  following  conditions: 
(1)  Where  room  is  lacking  for  the  proper  size  pulleys  for  belts.  (2) 
Where  the  centers  between  shafts  are  too  short  for  belts.  (3)  Where  a 
positive  speed  ratio  is  desired.  (4)  Where  there  is  moisture,  heat  or 
dust  that  would  prevent  a  belt  working  properly.  (5)  Where  a  maxi- 
mum power  per  inch  of  width  is  desired. 

The  Renold  and  the  Morse  chain  gears  use  springs  in  the  sprocket 


1156 


BELTING. 


wheel  to  absorb  the  shock  when  a  reversal  of  strain  takes  place,  which 
is  infrequent  in  ordinary  power  transmission,  but  is  found  in  reciprocat- 
ing air-compressors  and  pumps,  in  gas-engine  drives  where  an  insufficient 
balance  wheel  is  supplied,  and  where  a  heavy  shock  load  occurs  and  it  is 
desirable  to  cushion  the  effect  by  mounting  the  wheel  on  springs. 

Nickel  steel  is  generally  used  for  the  chains.  The  joint  pins  are 
made  from  31/2%  nickel  chrome  steel,  heat-treated.  The  ends  of  the 
joint  pins  are  softened  by  an  electric  arc  to  facilitate  riveting  to  the 
chain  links. 

Data  Used  in  the  Preliminary  Design  of  Morse  Silent  Chain  Drives 


Pitch,  in  

1/2 

5/8 

3/4 

9/10 

12/10 

1  1/2 

2 

3 

Minimum  no.  of  teeth: 
Small  sprocket  driver.. 
Small  sprocket  driven  . 

13 
17 

13 
17 

13 
21 

15 
25 

15 
29 

17 
29 

17 
31 

17 
35 

19-31 

Desirable    no.    of    teeth 
in  small  sprockets  

15-17 

17-21 

17-21 

17-23 

17-23 

17-27 

17-31 

Maximum  no.  of  teeth  in 
large  sprockets.      (See 
Note  3.)  

99 

109 

115 

125 

129 

129 

129 

131 

Desirable  no.  of  teeth  in 
large  sprockets  

55-75 

55-75 

55-85 

55-95 

55-105 

55-115 

55-115 

55-115 

Pitch  diam.  of  wheel  = 
no.  of  teeth  X  

0.159 

0.199 

0.239 

0.2865 

0.382 

0.477 

0.636 

0.955 

Addendum    for    outside 
diam.  of  sprockets  20  to 
130T.  (See  Note  1.),  in. 

0.10 

0.12 

0.15 

0.18 

0.24 

0.30 

0.40 

0.60 

Maximum  r.p.m  

2400 

1800 

1200 

1100 

850 

600 

400 

250 

Tension  per  in.  width  of 
chain,  lb.: 
Small  sprocket  driver.. 
Small  sprocket  driven  . 

80 
65 

100 
80 

120 
95 

150 
120 

200 
160 

270 
210 

450 
350 

750 
600 

Radial  clearance  beyond 
tooth      required      for 
chain,  in  

0.50 

0.62 

0.75 

0.90 

1.2 

1.5 

2.0 

3.0 

Approx.  weight  of  chain 
per  in.  wide,  1  ft.  long, 

1.00 

1.20 

1.50 

1.80 

2.50 

3.00 

4.00 

6.00 

C  for  solid  pinions  

0.0045 

0.0063 

0.009 

0.013 

0.023 

0.035 

0.058 

0.145 

C  for  armed  sprockets   .  . 

0.16 

0.25 

0.35 

0.45 

0.7 

1.0 

2.0 

4.0 

APPROXIMATE  WEIGHTS  FOR  SOLID  AND  ARMED  SPROCKETS. 
T  =  Number  of  teeth.  F  =  Face  in  inches. 

C  =  Constant  in  lb.  per  in.  in  face  per  tooth  as  per  table. 
Weight  of  armed  sprocket  =  T  X  F  X  C. 
Add  25  %  for  split  and  50  %  for  spring  and  split  sprockets. 
r   Weight  of  solid  pinion  =  T2  x  (F  +  1)  X  C. 

NOTES. 
1. — Number  of  teeth  =  T. 

Exact  outside  diameter  =  D. 
For  T  less  than  20  teeth,  D  =  pitch  diameter. 
For  T  more  than  20  teeth,  D  =  pitch  diameter  -f  addendum. 
2. — Use  sprockets  having  an  odd  number  of  teeth  whenever  possible. 
3. — When  specially  authorized,  a  larger  number  of  teeth  than  shown 

may  be  cut  in  large  sprocket. 
4. — Thickness  of  sprocket  rim,  including  teeth,   should  be  at  least 

1.2  times  the  chain  pitch. 

5. — The  number  of  grooves  in  the  sprocket,  their  width  and  distance 
apart,  varies  according  to  pitch  and  width  of  chain.  Leave  the 
designing  and  turning  of  grooves  to  the  manufacturer. 
6. — The  width  of  the  sprocket  should  be  i/g  to  1/4  in.  greater  on  small 
drives,  and  1/4  to  1/2  in.  greater  on  large  drives  than  the  nomina1 
width  of  the  chain. 


GEARING.  1157 

7. — An  even  number  of  links  in  the  chain  and  an  odd  number  of  teeth 

in  the  wheels  are  desirable. 

8. — Horizontal   drives  preferred;   tight  chain   on   top   necessary  for 
short  drives  without  center  adjustment,  and  desirable  for  long 
drives  with  or  without  center  adjustment. 
9. — Adjustable   wheel   centers   desirable   for   horizontal   drives   and 

necessary  for  vertical  drives. 
10. — Avoid  vertical  drives. 
11. — Allow  a  side  clearance  for  chain  (parallel  to  axis  of  sprockets  and 

measured  from  nominal  width  of  chain)  equal  to  the  pitch. 
12. — Maximum  linear  velocity  for  commercial  service,   1200  to  1600 
ft.  per  min. 

Comparison  of  Rope  and  Chain  Drives. — Horse-power,  1200;  240 
to  80  r.p.m. 

Rope.  Chain. 

Distance  between  centers 42  ft.  8  ft.  4  in. 

Diameter  driving  sheave  or  sprocket 6  ft.  4  1/2  in.       30.21  in. 

Diameter  driven  sheave  or  sprocket 20  ft.  89.42  in. 

The  rope  drive  has  30  ropes,  each  1 3/4  in.  diameter.     The  chain  drive 
has  a  Morse  silent  chain,  length,  33.5  ft.;  width,  27  in.;  pitch,  3  in. 

Data  of  Some  Chain  Drives  that  Have  Given  Good  Service 


Speed, 

Sprockets, 

Center 

Rev. 

H.P. 

Pitch, 

Width, 

Ft.  per 

No  of 

Distance, 

per 

Trans- 

In. 

In. 

Min. 

Teeth. 

In. 

Min. 

mitted. 

V8 

21/2 

1550 

17  &  75 

25.5 

1750  &  397 

7.5 

H/2 

12 

1150 

95  &  95 

85 

97  &  97 

200 

H/2 

18 

715 

59  &  95 

169 

97  &  60 

200 

2 

5 

1400 

29  &  57 

68 

418  &  290 

85 

3* 

12 

1450 

61  &  77 

135 

95  &  75 

500 

3 

24 

1450 

61  &  83 

103 

95  &  70 

1000 

3 

27 

1870 

30  &  89 

100 

240  &  80 

1200 

2 

24 

780 

26  &  120 

144 

300  &  65 

350 

A  chain  transmission  gear  of  5000  H.P.  has  been  built,  with  the 
total  width  of  chain  168  in.  The  efficiency  of  the  best  chain  drives 
when  in  good  condition  is  claimed  to  be  from  98  to  99%. 

GEARING. 

TOOTHED-WHEEL,  GEARING. 

Pitch,  Pitch-circle,  etc.  —  If  two  cylinders  with  parallel  axes  are 
pressed  together  and  one  of  them  is  rotated  on  its  axis,  it  will  drive  the 
other  by  means  of  the  friction  between  the  surfaces.  The  cylinders  may 
be  considered  as  a  pair  of  spur-wheels  with  an  infinite  number  of  very  small 
teeth.  If  actual  teeth  are  formed  upon  the  cylinders,  making  alternate 
elevations  and  depressions  in  the  cylindrical  surfaces,  the  distance  between 
the  axes  remaining  the  same,  we  have  a  pair  of  gear-wheels  which  will 
drive  one  another  by  pressure  upon  the  faces  of  the  teeth,  if  the  teeth  are 
properly  shaped.  In  making  the  teeth  the  cylindrical  surface  may 
entirely  disappear,  but  the  position  it  occupied  may  still  be  considered  as 
a  cylindrical  surface,  which  is  called  the  "pitch-surface,"  and  its  trace 
on  the  end  of  the  wheel,  or  on  a  plane  cutting  the  wheel  at  right  angles  to 
its  axis,  is  called  the  "pitch-circle"  or  "pitch-line."  The  diameter  of 
this  circle  is  called  the  pitch-diameter,  and  the  distance  from  the  face 
of  one  tooth  to  the  corresponding  face  of  the  next  tooth  on  the  same 
wheel,  measured  on  an  arc  of  the  pitch-circle,  is  called  the  "pitch  of  the 
tooth,"  or  the  circular  pitch. 

If  two  wheels  having  teeth  of  the  same  pitch  are  geared  together  so 
that  their  pitch-circles  touch,  it  is  a  property  of  the  pitch-circles  that 
their  diameters  are  proportional  to  the  number  of  teeth  in  the  wheels, 
and  vice  versa;  thus,  if  one  wheel  is  twice  the  diameter  (measured  on  the 
pitch-circle)  of  the  other,  it  has  twice  as  many  teeth.  If  the  teeth  are 
properly  shaped  the  linear  velocities  of  the  two  wheels  are  equal,  and  the 
angular  velocities,  or  speeds  of  rotation,  are  inversely  proportional  to  the 


1158 


GEARING. 


Thus  the  wheel  that  has  twice  as 
*,/ 
" 


number  of  teeth  and  to  the  diameter, 
many  teeth  as  the  other  will  revolve 
just  half  as  many  times  in  a  minute. 

The  "pitch,"  or  distance  meas- 
ured on  an  arc  of  the  pitch-circle 
from  the  face  of  one  tooth  to  the 
face  of  the  next,  consists  of  two 
parts  —  the  "thickness"  of  the 
tooth  and  the  "space"  between  it 
and  the  next  tooth.  The  space  is 
larger  than  the  thickness  by  a  small 
amount  called  the  "backlash," 
which  is  allowed  for  imperfections 
of  workmanship.  In  finely  cut 
gears  the  backlash  may  be  almost 
nothing. 

The  length  of  a  tooth  in  the 
direction  of  the  radius  of  the  wheel 
is  called  the  "depth,"  and  this  is  divided  into  two  parts:  First,  the 
"addendum,"  the  height  of  the  tooth  above  the  pitch  line;  second,  the 
"dedendum, "  the  depth  below  the  pitch-line,  which  is  an  amount  equal  to 
the  addendum  of  the  mating  gear.  The  depth  of  the  space  is  usually 
given  a  little  "clearance"  to  allow  for  inaccuracies  of  workmanship, 
especially  in  cast  gears. 

Referring  to  Fig.  178 ,  pi,  pi  are  the  pitch-lines,  al  the  addendum-line, 
rl  the  root-line  or  dedendum-line,  cl  the  clearance-line,  and  b  the  back- 
lash.    The  addendum  and  dedendum  are  usually  made  equal  to  each 
Other.    (Some  writers  make  the  dedendum  include  the  clearance.) 
No  of  teeth  3.1416 

Diametral  pitch  = 


Circular  pitch  = 


diam.  of  pitch-circle  in  inches 
diam.X  3.1416  3.1416 


circular  pitch' 


No.  of  teeth  .      diametral  pitch 


Some  writers  use  the  term  diametral  pitch  to  mean 
circular  pitch 


diam. 


No.  of  teeth 
but  the  first  definition  is  the  more  common  and  the  more 


3.1416 

convenient.     A  wheel  of  12  in.  diam.  at  the  pitch-circle,  with  48  teeth,  is 

48/12  =4  diametral  pitch,  or  simply  4  pitch.     The  circular  pitch  of  the 

same  wheel  is  12   X  3.1416   -r-  48   =  0.7854,  or  3.1416   -;-_4   =  0.7854  in. 

Relation  of  Diametral  to  Circular  Pitch.' 


Diame- 
tral 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

Circular 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

1 

3.  142  in. 

11 

0.286  in. 

3 

.047 

15/16 

3.351 

1  1/2 

2.094 

12 

.262 

21/2 

.257 

7/8 

3.590 

2 

1.571 

14 

.224 

2 

.571 

13/16 

3.867 

21/4 

1.396 

16 

.196 

7/8 

.676 

3/4 

4.189 

21/2 

1.257 

18 

.175 

3/4 

.795 

H/16 

4.570 

23/4 

1.142 

20 

.157 

5/8 

.933 

5/8 

5.027 

3 

1.047 

22 

.143 

1/2 

2.094 

9/16 

5.585 

3l/2 

0.898 

24 

.131 

7/16 

2.185 

1/2 

6.283 

4 

.785 

26 

.121 

3/8 

2.285 

7/16 

7.181 

5 

.628 

28 

.112 

5/16 

2.394 

3/8 

8.378 

6 

.524 

30 

.105 

1/4 

2.513 

5/16 

10.053 

7 

.449 

32 

.098 

3/16 

2.646 

1/4 

12.566 

8 

.393 

36 

.087 

1/8 

2.793 

3/16 

16.755 

9 

.349 

40 

.079 

1/16 

2.957 

1/8 

25.133 

10 

.314 

48 

.065 

3.142 

1/16 

50.266 

Since  circ.  pitch  = 


diam.  X  3.1416 
No.  of  teeth 


diam. 


circ.  pitch  X  No.  of  teeth 
3.1416 


which  always  brings  out  the  diameter  as  a  number  with  an  inconvenient 
fraction  if  the  pitch  is  in  even  inches  or  simple  fractions  of  an  inch.    By 


TOOTHED-WHEEL   GEARING. 


1159 


the  diametral-pitch  system  this  inconvenience  is  avoided.  The  diameter 
may  be  in  even  inches  or  convenient  fractions,  and  the  number  of  teeth 
is  usually  an  even  multiple  of  the  number  of  inches  in  the  diameter. 

Diameter   of  Pitch-line   of  Wheels   from   10   to   100   Teeth   of  1  In. 
Circular  Pitch. 


0*5 

*£ 

5 

4 

;> 

I.a 
5 

0*1 

*£ 

is 

Q 

4 

1  d 

s. 

6*1 

*& 

is 

Q 

•ol 

*£ 

|.a 

10 

3.183 

26 

8.276 

41 

13.051 

56 

17.825 

71 

22.600 

86 

27.375 

11 

3.501 

27 

8.594 

42 

13.369 

57 

18.144 

72 

22.918 

87 

27.693 

12 

3.820 

28 

8.913 

43 

13.687 

58 

18.462 

73 

23.236 

88 

28.011 

13 

4.138 

29 

9.231 

44 

14.006 

59 

18.781 

74 

23.555 

89 

28.329 

14 

4.456 

30 

9.549 

45 

14.324 

60 

19.099 

75 

23.873 

90 

28.648 

15 

4.775 

31 

9.868 

46 

14.642 

61 

19.417 

76 

24.192 

91 

28.966 

16 

5.093 

32 

10.186 

47 

14.961 

62 

19.735 

77 

24.510 

92 

29.285 

17 

5.411 

33 

10.504 

48 

15.279 

63 

20.054 

78 

24.828 

93 

29.603 

18 

5.730 

34 

10.823 

49 

15.597 

64 

20.372 

79 

25.146 

94 

29.921 

19 

6.048 

35 

11.141 

50 

15.915 

65 

20.690 

80 

25.465 

95 

30.239 

20 

6.366 

36 

11.459 

51 

16.234 

66 

21.008 

81 

25.783 

96 

30.558 

21 

6.685 

37 

11.777 

52 

16.552 

67 

21  .327 

82 

26.101 

97 

30.876 

22 

7.003 

38 

12.096 

53 

16.870 

68 

21  .645 

83 

26.419 

98 

31  194 

23 

7.321 

39 

12.414 

54 

17.189 

69 

21.963 

84 

26.738 

99 

31.512 

24 

7.639 

40 

12.732 

55 

17.507 

70 

22.282 

85 

27.056 

100 

31.831 

25 

7.958 

For  diameter  of  wheels  of  any  other  pitch  than  1  in.,  multiply  the  figures 
in  the  table  by  the  pitch.  Given  the  diameter  and  the  pitch,  to  find  the 
number  of  teeth.  Divide  the  diameter  by  the  pitch,  look  in  the  table 
under  diameter  for  the  figure  nearest  to  the  quotient,  and  the  number 
of  teeth  will  be  found  opposite. 

_  Proportions  of  Teeth.     Circular  Pitch  =  1. 

~ 


2.     |    3. 


4. 


5.     |    6. 


Depth  of  tooth  above  pitch-line  

0.35 

0  30 

0  37 

0.33 

0  30 

0  30 

Depth  of  tooth  below  pitch-line  
Working  depth  of  tooth  
Total  depth  of  tooth  

.40 
.70 
.75 

.40 
.60 
.70 

.43 
.73 
80 

"]66 
.75 

.40 
'76 

.35 

65 

Clearance  at  root  
Thickness  of  tooth 

.05 

45 

.10 
45 

.07 
47 

45 

475 

485 

Width  of  space.  .  . 

54 

55 

53 

55 

525 

515 

Backlash     

09 

'10 

06 

10 

05 

03 

Thickness  of  rim  

47 

45 

70 

65 

Depth  oi  tooth  above  pitch- 
line.  . 

0  25  to  0  33 

0  30 

0  318 

1  '  P 

Depth  of  tooth  below  pitch- 
line.  . 

35  to     42 

35+  08" 

369 

1   157  •  p 

Working  depth  of  tooth.  .  . 

637 

2  +  P 

Total  depth  of  tooth  
Clearance  at  root  

.6  to  .75 

.65  +.08" 

.687 
.04  to    05 

2.157+P 

0    157-rP 

Thickness  of  tooth 

48  to   485 

48—  03" 

48  to    5  { 

1.51   +  Pto 

Width  of  space  

.52  to   515 

52+  03" 

52  to    5  { 

1.57  -v-P 
1.57  -5-Pto 

Backlash  

.04  to  .03 

.04+  .06" 

.0   to  .04 

1.63  -T-  P 
.Oto  .06-7-  P 

*  In  terms  of  diametral  pitch. 

AUTHORITIES.  —  1.  Sir  Wm.  Fairbairn.  2,  3.  Clark,  R.  T.  D.;  "used 
by  engineers  in  good  practice. "  4.  Molesworth.  5,6.  Coleman  Sellers: 
5  for  cast,  6  for  cut  wheels.  7,  8.  Unwin.  9,  10.  Leading  American 
manufacturers  of  cut  gears. 

The  Chordal  Pitch  (erroneously  called  "true  pitch"  by  some  authors) 
is  the  length  of  a  straight  line  or  chord  drawn  from  center  to  center  of  two 
adiacent  teeth.  The  term  is  now  but  little  used,  except  in  connection 
frtth  chain  and  sprocket  gearing, 


1160 


GEARING. 


Chordal  pitch  =  diam.  of  pitch-circle  X  sine  of 


Chordal 


180° 

No.  of  teeth 

pitch  of  a  wheel  of  10  in.  pitch  diameter  and  10  teeth,  10  X  sin  18°  — 
3.0902  in.  Circular  pitch  of  same  wheel  =  3.1416.  Chorda!  pitch  is 
used  with  chain  or  sprocket  wheels,  to  conform  to  the  pitch  of  the  chain. 

Gears  with  Short  Teeth.  —  There  is  a  tendency  in  recent  years  to 
depart  widely  from  the  proportions  of  teeth  given  in  the  above  and  to 
use  much  shorter  teeth,  especially  for  heavy  machinery.  C.  W.  Hunt 
gives  addendum  and  dedendum  each  =  0.25,  and  the  clearance  0.05  of 
the  circular  pitch,  making  the  total  depth  of  tooth  0.55  of  the  circular 
pitch.  The  face  of  the  tooth  is  involute  in  form,  and  the  angle  of  action 
is  141/2°,  C.  H.  Logue  uses  a  20°  involute  with  the  following  proportions: 
Addendum  0.25P'  =  0.7854  -^P;  dedendum  0.30  P'  =  0.9424  -*•  P; 
clearance,  0.05P'  =  0.157P:  whole  depth  0.55P'  =  1.7278  •*-  P.  P'  = 
circular  pitch,  P  =  diametral  pitch.  See  papers  by  R.  E.  Flanders  and 
Norman  Litchfield  in  Trans.  A.  S.  M.  E.,  1908. 

John  Walker  (Am.  Mach.,  Mar.  11,  1897)  says:  For  special  purposes  of 
slow-running  gearing  with  great  tooth  stress  I  should  prefer  a  length  of 
tooth  of  0.4  of  the  pitch,  but  for  general  work  a  length  of  0.6  of  the  ititch. 
In  1895  Mr.  Walker  made  two  pairs  of  cut  steel  gears  for  the  Chicago 
cable  railway  with  6-in.  circular  pitch,  length  =  0.4  pitch.  The  pinions 
had  42  teeth  and  the  gears  62,  each  20-in.  face.  The  two  pairs  were 
set  side  by  side  on  their  shafts,  so  as  to  stagger  the  teeth,  making  the 
total  face  40  ins.  The  gears  transmitted  1500  H.P.  at  60  r.p.m.  replac- 
ing cast-iron  gears  of  7V2  in.  pitch  which  had  broken  in  service. 
Formulae  for  Determining  the  Dimensions  of  Small  Gears. 
(Brown  &  Sharpe  Mfg.  Co.) 

P  =  diametral  pitch  or  the  number  of  teeth  to  one  inch  of  diameter  of 
pitch-circle; 


Larger 

Wheel. 

* 

These 

df  ~  diameter  of  pitch-circle  

together. 

Smaller 

Wheel. 

V  =  velocity  

a  =  distance  between  the  centers  of  the  two  wheels; 

b  =  number  of  teeth  in  both  wheels; 

t  =  thickness  of  tooth  or  Cutter  on  pitch-circle; 

s  =  addendum; 
D"  =  working  depth  of  tooth; 

/  =  amount  added  to  depth  of  tooth  for  rounding  the  corners  and  for 

clearance; 
D"  +  f  =  whole  depth  of  tooth; 

TT  =  3.1416. 

P'  =  circular  pitch,  or  the  distance  from  the  center  of  one  tooth  to  tha 
center  of  the  next  measured  on  the  pitch-circle. 

Formulae  for  a  single  wheel: 


N+2 

D 
N_ 
D''1 


£>'  = 


DX^V 

N  +2' 

N 


2 

T\rr _  o  « i 

D  -p-2S, 
JV  =  PD-2; 


5 


=1=^=0.3183P'; 


D' 

N 


D 


D  = 


fry? 

1.57 


«  +  /=j>(l+f0) -0.3685  P. 


=1/2  P'. 


Formulae  for  a  pair  of  wheels: 


nv 
V  : 


PD'V 

v     ' 
PD'V 


2a(AT+2) 

6 
2  a  (n+2) 


TOOTHED-WHEEL  GEARING. 


1161 


TV_ 

~ 


2 
2aV 

=  v  +  V' 


Width  of  Teeth.  —  The  width  of  the  faces  of  teeth  is  generally  made 
from  2  to  3  times  the  circular  pitch,  that  is  from  6.28  to  9.42  divided  by 
the  diametral  pitch.  There  is  no  standard  rule  for  width. 

The  following  sizes  are  given  in  a  stock  list  of  cut  gears  in  "  Grant's 
Gears:" 

Diametral  pitch. .         346  8  12  16 

Face,  inches 3  and  4  21/2  13/4and  2  1 1/4  and  1 1/2  3/4and  1  l/2and  5/8 

The  Walker  Company  gives: 
Circular  pitch,  in. .    1/2      5/g 


3/4    7/8     1 


2     21/2     3    4     5     6 


11/2 

Face,  in.* ' li/4     li/2     13/4     2     21/2    41/2     6     7V2    9121620 

The  following  proportions  of  gear-wheels  are  recommended  by  Prof. 
Coleman  Sellers^     (Stevens  Indicator,  April,  1892.) 

Proportions  of  Gear-wheels. 


Inside  of  Pitch-line. 

Width  of  Space. 

Diametral 
Pitch. 

Circular 
Pitch. 
P 

Outside  of 
Pitch-line. 
P  X0.3. 

For  Cast 
or  Cut 
Bevels  or 
for  Cast 
Spurs. 

For  Cut 
Spurs. 
PX0.35. 

For  Cast 
Spurs  or 
Bevels. 
PX0.525. 

For  Cut 
Bevels  or 
Spurs. 
PX0.51. 

PX0.4. 

12 

0.2618 

0.075 
.079 

0.100 
.105 

0.088 
.092 

0.131 
.137 

0.128 
.134 

10 

0.31416 

.094 

.126 

.11 

.165 

.16 

3/8 

.113 

.150 

.131 

.197 

.191 

8 

0.3927 

.118 

.157 

.137 

.206 

.2 

7 

0.4477 

.134 

.179 

.157 

.235 

.228 

6 

V2 
0.5236 

.15 
.157 

.20 
.209 

.175 
.183 

.263 

.275 

.255 
.267 

9/16 

.169 

.225 

.197 

.295 

.287 

5 

0.628832 

.188 
.188 

.25 
.251 

.219 

.22 

.328 
.33 

.319 
.32 

4 

3/4 
0.7854 

.225 
.236 

.3 

.314 

.263 
.275 

.394 
.412 

.383 
.401 

7/8 

.263 

.35 

.307 

.459 

.446 

1 

.3 

.4 

.35 

.525 

.51 

3 

1.0472 

.314 

.419 

.364 

.55 

.534 

•        H/8 

.338 

.45 

.394 

.591 

.574 

2  3/4 

1.1424 

.343 

.457 

.40 

.6 

.583 

21/2 

1.25664 

.375 
.377 

.5 

.503 

.438 
.44 

.656 
.66 

.638 
.641 

13/8 

.413 

.55 

.481 

.722 

.701 

U/2 

.45 

.6 

.525 

.788 

.765 

2 

1.5708 

.471 

.628 

.55 

.825 

.801 

13/4 

.525 

.7 

.613 

.919 

.893 

2 

.6 

.8 

.7 

.05 

.02 

U/2 

2.0944 

\628 

.838 

.733 

.1 

.068 

21/4 

.675 

.9 

.788 

.181 

.148 

2V2 

.75 

.0 

.875 

.313 

.275 

23/4 

.825 

.1 

.963 

.444 

.403 

3 

.9 

.2 

1.05 

.575 

.53 

3.1416 

.942 

.257 

1.1 

.649 

.602 

31/4 

.975 

.3 

1.138 

.706 

.657 

31/2 

1.05 

.4 

1  225 

838 

.785 

Thickness  of  rim  below  root  =  depth  of  toottu 


1162  GEARING. 

Rules  for  Calculating  the  Speed  of  Gears  and  Pulleys,  —  The 

relations  of  the  size  and  speed  of  driving  and  driven  gear-wheels  are  the 
same  as  those  of  belt  pulleys.  In  calculating  for  gears,  multiply  or 
divide  by  the  diameter  of  the  pitch-circle  or  by  the  number  of  teeth,  as 
may  be  requiied.  In  calculating  for  pulleys,  multiply  or  divide  by  their 
diameter  in  inches. 

If  D  =  diam.  of  driving  wheel,  d  =  diam.  of  driven,  R  =  revolution* 
per  minute  of  driver,  r  =  revs,  per  min.  of  driven,  RD  =  rd; 
R  =  rd  ~  D;  r  =  RD  +  d;  D  =  dr  -r  R;  d  =  DR  -r  r. 

If  N  =  No.  of  teeth  of  driver  and  n  =  No.  of  teeth  of  driven,  NR  =  nr; 
N  =  nr  -?•  R;    n  =  NR  -^  r;     R  =  rn  •*•  N-    r=  RN  ~  n. 

To  find  the  number  of  revolutions  of  the  last  wheel  at  the  end  of  a 
train  of  spur-wheels,  all  of  which  are  in  a  line  and  mesh  into  one  another, 
when  the  revolutions  of  the  first  wheel  and  the  number  of  teeth  or  the 
diameter  or  the  first  and  last  are  given:  Multiply  the  revolutions  of  the 
first  wheel  by  its  number  of  teeth  or  its  diameter,  and  divide  the  product 
by  the  number  of  teeth  or  the  diameter  of  the  last  wheel. 

To  find  the  number  of  teeth  in  each  wheel  for  a  train  of  spur-wheels, 
each  to  have  a  given  velocity:    Multiply  the  number  of  revolutions  of 
,  the  driving-wheel  by  its  number  of  teeth,  and  divide  the  product  by  the 
number  of  revolutions  each  wheel  is  to  make. 

To  find  the  number  of  revolutions  of  the  last  wheel  in  a  train  of  wheels 
and  pinions,  when  the  revolutions  of  the  first  or  driver,  and  the  diameter, 
the  teeth,  or  the  circumference  of  all  the  drivers  and  pinions  are  given; 
Multiply  the  diameter,  the  circumference,  or  the  number  of  teeth  of  all 
the  driving-wheels  together,  and  this  continued  product  by  the  number 
of  revolutions  of  the  first  wheel,  and  divide  this  product  by  the  contin- 
ued product  of  the  diameter,  the  circumference,  or  the  number  of  teeth 
of  all  the  driven  wheels,  and  the  quotient  will  be  the  number  of  revolutions  • 
of  the  last  wheel. 

EXAMPLE.  —  1.  A  train  of  wheels  consists  of  four  wheels  each  12  in. 
diameter  of  pitch-circle,  and  three  pinions  4,  4,  and  3  in.  diameter.  The 
large  wheels  are  the  drivers,  and  the  first  makes  36  revs,  per  mill.  Re- 
quired the  speed  of  the  last  wheel. 


2.  What  is  the  speed  of  the  first  large  wheel  if  the  pinions  are  the 
drivers,  the  3-in.  pinion  being  the  first  driver  and  making  36  revs,  per  min.  ? 


Milling  Cutters  for  Interchangeable  Gears.  —  The  Pratt  &  Whit- 
ney Co.  makes  a  series  of  cutters  for  cutting  epicycloidal  teeth.  The 
number  of  cutters  to  cut  from  a  pinion  of  12  teeth  to  a  rack  is  24  for 
each  pitch  coarser  than  10.  The  Brown  &  Sharpe  Mfg.  Co.  makes  a 
similar  series,  and  also  a  series  for  involute  teeth,  in  which  eight  cutters 
are  made  for  each  pitch,  as  follows: 

No.  1  2345678 

Will  cut  from      .    135  55         35         26         21         17    •    14         12 

to  Rack        134         54         34         25         20         16         13 

FORMS  OF  THE  TEETH. 

In  order  that  the  teeth  of  wheels  and  pinions  may  run  together  smoothly 
and  with  a  constant  relative  velocity,  it  is  necessary  that  their  working 
faces  shall  be  formed  of  certain  curves  called  odontoids.  The  essential 
property  of  these  curves  is  that  when  two  teeth  are  in  contact  the  com- 
mon normal  to  the  tooth  curves  at  their  point  of  contact  must  pass  through 
the  pitch-point,  or  point  of  contact  of  the  two  pitch-circles.  Two  such 
curves  are  in  common  use  —  the  cycloid  and  the  involute. 

The  Cycloidal  Tooth.  —  In  Fig.  179  let  PL  and  pi  be  the  pitch- 
circles  of  two  gear-wheels:  GC  and  gc  are  two  equal  generating-cm 
whose  radii  should  be  taken  as  not  greater  than  one-half  of  the  raaius 
of  the  smaller  pitch-circle.  If  the  circle  gc  be  rolled  to  the  left  on  tne 
larger  pitch-circle  PL,  the  point  0  will  describe  an  epicycloid,  Qefgri.  ir 
the  other  srenerating-circle  GC  be  rolled  to  the  right  on  PL.  the  point  C 
will  describe  a  bypocycloid  0  a&ccZ.  These  two  curves,  which  are  tangent 


FORMS   OF  THE   TEETH. 


1163 


at  0,  form  the  two  parts  of  a  tooth  curve  for  a  gear  whose  pitch-circle  is 
PL  The  upper  part  Oh  is  called  the  face  and  the  lower  part  Gd  is  called 
the'flank.  If  the  same  circles  be  rolled  on  the  other  pitch-circle  pi,  they 
will  describe  the  curve  for  a  tooth  of  the  gear  pi,  which  will  work  properly 

The  cvcloidal  curves  may  be  drawn  without  actually  rolling  the  gen- 
erating-circle as  follows:  On  the  line  PL,  from  0,  step  off  and  mark  equal 
distances,  as  1,  2,  3,  4,  etc.  From  1,  2,  3,  etc.,  draw  radial  lines  toward 
the  center  of  PL,  and  from  6,  7,  8,  etc.,  draw  radial  lines  from  .the  same 
center  but  beyond  PL.  With  the  radius  of  the  generating-circle,  and 
w1?h  centers  successively  placed  on  these  radial  lines  draw  arcs  of  circles 
tangent  to  PL  at  1,  2,  3,  6,  7.  8,  etc.  _  With  the  dividers  set jto one ,of  the 


and  lay  them  on  on  me  several  arcs  oe,  //,  oy,  vit,,  <*i 
through  the  points  efgh  and  abed  draw  the  tooth  curves. 


FIG.  179. 


The  curves  for  the  mating  tooth  on  the  other  wheel  may  be  found  in 
like  manner  by  drawing  arcs  of  the  generating-circle  tangent  at  equidistant 
points  on  the  pitch-circle  pi. 

The  tooth  curve  of  the  face  Oh  is  limited  by  the  addendum-line  r  or  rt, 
and  that  of  the  flank  OH  by  the  root  curve  R  or  Rlt  R  and  r  represent 
the  root  and  addendum  curves  for  a  large  number  of  small  teeth,  and  Rir 
the  like  curves  for  a  small  number  of  large  teeth.  The  form  or  appearance 
of  the  tooth  therefore  varies  according  to  the  number  of  teeth,  while  the 
•  pitch-circle  and  the  generating-circle  may  remain  the  same. 

In  the  cycloidal  system,  in  order  that  a  set  of  wheels  of  different  diam- 
eters but  equal  pitches  shall  all  correctly  work  together,  it  is  necessary 
that  the  generating-circle  used  for  the  teeth  of  all  the  wheels  shall  be 
the  same,  and  it  should  have  a  diameter  not  greater  than  half  the  diam- 
eter of  the  pitch-line  of  the  smallest  wheel  of  the  set.  The  customary 
standard  size  of  the  generating-circle  of  the  cycloidal  system  is  one  having 
a  diameter  equal  to  the  radius  of  the  pitch-circle  of  a  wheel  having  12 
teeth.,  (gome  gear-makers  adopt  15  teeth.)  This  circle  gives  a  radial 
flank  to  the  teeth  of  a  wheel  having  12  teeth.  A  pinion  of  10  or  even  a 
smaller  number  of  teeth  can  be  made,  but  in  that  case  the  flanks  will  be 


1164 


GEARING. 


undercut,  and  the  tooth  will  not  be  as  strong  as  a  tooth  with  radial 
flanks.  If  in  any  case  the  describing  circle  be  half  the  size  of  the  pitch- 
circle,  the  flanks  will  be  radial;  if  it  be  less,  they  will  spread  out  toward 
the  root  of  the  tooth,  giving  a  stronger  form;  but  if  greater,  the  flanks 
will  curve  in  toward  each  other,  whereby  the  teeth  become  weaker  and 
difficult  to  make. 

In  some  cases  cycloidal  teeth  for  a  pair  of  gears  are  made  with  the 
generating-circle  of  each  gear  having  a  radius  equal  to  half  the  radius 
of  its  pitch-circle.  In  this  case  each  of  the  gears  will  have  radial  flanks. 
This  method  makes  a  smooth  working  gear,  but  a  disadvantage  is  that 
the  wheels  are  not  interchangeable  with  other  wheels  of  the  same  pitch 
but  different  numbers  of  teeth. 

The  rack  in  the  cycloidal  system  is  equivalent  to  a  wheel  with  an 
infinite  number  of  teeth.  The  pitch  is  equal  to  the  circular  pitch  of 
the  mating  gear.  Both  faces  and  flanks  are  cycloids  formed  by  rolling 
the  generating-circle  of  the  mating  gear-wheel  on  each  side  of  the 
straight  pitch-line  of  the  rack. 

Another  method  of  drawing  the  cycloidal  curves  is  shown  in  Fig.  180. 
It  is  known  as  the  method  of  tangent  arcs.  The  generating-circles,  as 
before,  are  drawn  with  equal  radii,  the  length  of  the  radius  being  less 
than  half  the  radius  of  pi,  the  smaller  pitch-circle.  Equal  divisions  1,  2, 


FIG.  180. 


3,  4,  etc.,  are  marked  off  on  the  pitch-circles  and  divisions  of  the  same 
length  stepped  off  on  one  of  the  generating-circles,  as  0,  a,  b,  c.  From  the 
points  1,  2,  3,  4,  5  on  the  linepO,  with  radii  successively  equal  to  the  chord 
distances  0 a,  06,  Oc,  Od,Qe,  draw  the  five  small  arcs  F.  A  line  drawn 
through  the  outer  edges  of  these  small  arcs,  tangent  to  them  all,  will  be 
the  hypocycloidal  curve  for  the  flank  of  a  tooth  below  the  pitch-line  pi. 
From  the  points  1,  2,  3,  etc.,  on  the  line  01,  with  radii  as  before,  draw  the 
small  arcs  G.  A  line  tangent  to  these  arcs  will  be  the  epicycloid  for  the 
face  of  the  same  tooth  for  which  the  flank  curve  has  already  been  drawn. 
In  the  same  way,  from  centers  on  the  line  PO,  and  OL,  with  the  same 
radii,  the  tangent  arcs  H  and  K  may  be  drawn,,  which  will  Rive  the  tooth 
for  the  gear  whose  pitch-circle  is  PL. 


FORMS  OF  THE  TEETH. 


1165 


If  the  generating-circle  had  a  radius  just  one-half  of  the  radius  of  pi, 
the  hypocycloid  F  would  be  a  straight  line,  and  the  flank  of  the  tootb 
would  have  been  radial. 

The  Involute  Tooth.  —  In  drawing  the  involute-tooth  curve,  Fig.  181, 
the  angle  of  obliquity,  or  the  angle  which  a  common  tangent  to  the  teeth, 
when  they  are  in  contact  at  the  pitch-point,  makes  with  a  line  joining 
the  centers  of  the  wheels,  is  first  arbitrarily  determined.  It  is  customary 
to  take  it  at  15°.  The  pitch-lines  pi  and  PL  being  drawn  in  contact  at  O, 
the  line  of  obliquity  AB  is  drawn  through  O  normal  to  a  common  tangent 
to  the  tooth  curves,  or  at  the  given  angle  of  obliquity  to  a  common  tan- 
gent to  the  pitch-circles.  In  the  cut  the  angle  is  20°.  Erom  the  centers 
ol  the  pitch-circles  draw  circles  c  and  d  tangent  to  the  line  AB.  These 
circles  are  called  base-lines  or  base-circles,  from  which  the  involutes  F 
and  K  are  drawn.  By  laying  off  convenient  distances,  0,  1,  2,  3,  which 
should  each  be  less  than  Vio  of  the  diameter  of  the  base-circle,  small  arcs 
can  be  drawn  with  successively  increasing  radii,  which  will  form  the 
involute.  The  involute  extends  from  the  points  F  and  K  down  to  their 


FIG.  181. 

respective  base-circles,  where  a  tangent  to  the  involute  becomes  a  radius 
of  the  circle,  and  the  remainders  of  the  tooth  curves,  as  G  and  H,  are 
radial  straight  lines. 

To  draw  the  teeth  of  a  rack  which  is  to  gear  with  an  involute  wheel  (Fig. 
182).  —  Let  AB  be  the  pitch-line  of  the  rack  and  AI=  IT  =  the  pitch. 
Through  the  pitch-point  /  draw  EF  at  the  given  angle  of  obliquity. 


FIG.  182. 


Draw  AE  and  1'F  perpendicular  to  EF.  Through  E  and  F  draw  lines 
EGG'  and  FH  parallel  to  the  pitch-line.  EGG'  will  be  the  addendum- 
line  and  HF  the  flank-line.  From  /  draw  IK  perpendicular  to  AB  equal 
to  the  greatest  addendum  in  the  set  of  wheels  of  the  given  pitch  and 
obliquity  plus  an  allowance  for  clearance  equal  to  1/8  of  the  addendum. 
Through  K,  parallel  to  AB,  draw  the  clearance-line.  The  fronts  of  the 
teeth  are  planes  perpendicular  to  EF,  and  the  backs  are  planes  inclined 
at  the  same  angle  to  AB  in  the  contrary  direction.  The  outer  half  of  the 
working  face  AE  may  be  slightly  curved.  Mr.  Grant  makes  it  a  circular 
arc  drawn  from  a  center  on  the  pitch-line' with  a  radius  =  2.1  Jnches 
divided  by  the  diametral  pitch,  or  0.67  in.  X  circular  pitch. 

In  the  involute  system  the  customary  standard  form  of  tooth  is  one 
having  an  angle  of  obliquity  of  15°  (Brown  and  Sharpe  use  14 1/2°).  an 


1166  GEARING. 

addendum  of  about  one-third  the  circular  pitch,  and  a  clearance  of  about 

one-eighth  of  the  addendum.  In  this  system  the  smallest  gear  ol  a  set 
has  12  teeth,  this  being  the  smallest  number  of  teeth  that  will  gear  together 
when  made  with  this  angle  of  obliquity.  In  gears  with  less  than  30  teeth 
the  points  of  the  teeth  must  be  slightly  rounded  over  to  avoid  interference 
(see  Grant's  Teeth  of  Gears).  All  involute  teeth  of  the  same  pitch  and 
with  the  same  angle  of  obliquity  work  smoothly  together.  The  rack  to 
gear  with  an  involute-toothed  wheel  has  straight  faces  on  its  teeth,  which 
make  an  angle  with  the  middle  line  of  the  tooth  equal  to  the  angle  of 
obliquity,  or  in  the  standard  form  the  faces  are  inclined  at  an  angle  ot 
30°  with  each  other. 

To  Draw  an  Angle  of  15°  without  using  a  Protractor.  —  From  C,  on  the 
line  A (7,  with  radius  AC,  draw  an  arc  AB,  and  from  A,  with  the  same 

radius,  cut  the  arc  at  B.  Bisect 
the  arc  BA  by  drawing  small  arcs 
at  D  from  A  and  B  as  centers, 
with  the  same  radius,  which  must 
be  greater  than  one-half  of  AB. 
Join  DC,  cutting  BA  at  E.  The 
angle  EGA  is  30°.  Bisect  the  arc 
AE  in  like  manner,  and  the  angle 
FCA  will  be  15°. 

A  property  of  involute-toothed 
wheels  is  that  the  distance  between 
the  axes  of  a  pair  of  gears  may  be 
altered  to  a  considerable  extent 
without  interfering  with  their  ac- 
tion.  The  backlash  is  therefore 
variable  at  will,  and  may  be  ad- 
FIG.  183.  justed  by  moving  the  wheels  farther 

from  or  nearer  to  each  other,  and 

may  thus  be  adjusted  so  as  to  be  no  greater  than  is  necessary  to  prevent 
jamming  of  the  teeth. 

The  relative  merits  of  cycloidal  and  involute-shaped  teeth  are  a 
subject  of  dispute,  but  there  is  an  increasing  tendency  to  adopt  the 
involute  tooth  for  all  purposes. 

Clark  (R.  T.  D.,  p.  734)  says:  Involute  teeth  have  the  disadvantage  of 
being  too  much  inclined  to  the  radial  line,  by  which  an  undue  pressure  is 
exerted  on  the  bearings. 

Unwin  (Elements  of  Machine  Design,  8th  ed.,  p.  265)  says:  The  obliquity 
of  action  is  ordinarily  alleged  as  a  serious  objection  to  involute  wheels. 
Its  importance  has  perhaps  been  overrated. 

George  B.  Grant  (Am.  Mach.,  Dec.  26,  1885)  says: 

1.  The  work  done  by  the  friction  of  an  involute  tooth  is  always  less 
than  the  same  work  for  any  possible  epicycloidal  tooth. 

2.  With  respect  to  work  done  by  friction,  a  change  of  the  base  from  a 
gear  of  12  teeth  to  one  of  15  teeth  makes  an  improvement  for  the  epicycloid 
of  less  than  one-half  of  one  per  cent. 

3.  For  the  12-tooth  system  the  involute  has  an  advantage  of  11/5  per 
cent,  and  for  the  15-tooth  system  an  advantage  of  3/4  per  cent. 

4.  That  a  maximum  improvement  of  about  one  per  cent  can  be  accom- 
plished by  the  adoption  of  any  possible  non-interchangeable  radial  flank 
tooth  in  preference  to  the  12-tooth  interchangeable  system. 

5.  That  for  gears  of  very  few  teeth  the  involute  has  a  decided  advan- 
tage. 

6.  That  the  common  opinion  among  millwrights  and  the  mechanical 
public  in  general  in  favor  of  the  epicycloid  is  a  prejudice  that  is  founded 
on  long-continued   custom,  and  not  on  an  intimate  knowledge  of  the 
properties  of  that  curve. 

Wilfred  Lewis  (Proc.  Engrs.  Club  of  Phila.,  vol.  x,  1893)  says  a  strong 
reaction  in  favor  of  the  involute  system  is  in  progress,  and  he  believes 
that  an  involute  tooth  of  22 1/2°  obliquity  will  finally  supplant  all  other 
forms. 

Approximation  by  Circular  Arcs.  —  Having  found  the  form  of  the 
actual" tooth-curve  on  the  drawing-board,  circular  arcs  may  be  found  by 
trial  which  will  give  approximations  to  the  true  curves,  and  these  may  be 
used  in  completing  the  drawing  and  the  pattern  of  the  gear-wheels.  The 


FORMS   Of  THE  TEETH. 


1167 


root  of  the  curve  is  connected  to  the  clearance  by  a  fillet,  which  should 
be  as  large  as  possible  to  give  increased  strength  to  the  tooth,  provided 
it  is  not  large  enough  to  cause  interference. 

Molesworth  gives  a  method  of  construction  by.circular  arcs  as  follows : 
From  the  radial  line  at  the  edge  of  the  tooth  on  the  pitch-line,  lay  off  the 
line  HK  at  an  angle  of  75°  with  the  radial  line;  on  this  line  will  be  the 
centers  of  the  root  AB  and  the  point  EF.  The  lines  struck  from  these 
centers  are  shown  hi  thick  lines.  Circles  drawn  through  centers  thus 
found  will  give  the  lines  in  which  the  remaining  centers  will  be.  The 
radius  DA  for  striking  the  root  AB  is  the  pitch  +  the  thickness  of  the 
tooth.  The  radius  CE  for  striking  the  point  of  the  tooth  EF  =  the  pitch. 


FIG.  184. 

George  B.  Grant  says:  It  is  sometimes  attempted  to  construct  the  curve 
by  some  handy  method  or  empirical  rule,  but  such  methods  are  generally 
worthless. 

Stub  Gear  Teeth. — The  stub  gear  tooth  developed  by  the  Fellows 
Gear  Shaper  Co.  has  been  largely  adopted  for  automobile  drives.  The 
stub  gear  tooth  has  a  shorter  addendum  and  dedendum  than  the 
ordinary  involute  tooth.  The  pressure  angle  is  20°  and  the  teeth  are 
based  on  two  diametral  pitches,  one  of  which  is  used  to  obtain  the 
dimensions  of  the  addendum  and  dedendum,  while  the  other  is  used 
for  the  dimensions  of  the  tooth  thickness,  the  number  of  teeth  and 
pitch  diameter.  Stub  tooth  gears  are  designated  by  a  fraction  as 
Vs  pitch,  10/12  pitch,  etc.  The  numerator  designates  the  pitch  deter- 
mining the  thickness  of  the  tooth  and  number  of  teeth.  The  denomi- 
nator designates  the  pitch  determining  depth  of  the  tooth.  The 
clearance  is  (0.25 -T- diametral  pitch).  The  advantages  of  this  form 
of  tooth  compared  to  the  ordinary  involute  gear  tooth  are:  greater 
strength;  same  arc  of  rolling  contact  as  in  141/2°  involute  tooth;  avoid- 
ance of  extreme  sliding  contact;  more  even  wearing  contact.  Dimen- 
sions of  the  Fellows  system  of  stub  gear  teeth  are  given  in  the  table 
below: 

Fellows  Stub  Gear  Tooth  System  (Dimensions  in  Inches). 


Diametral 
Pitch. 

Thick- 
ness of 
Tooth. 

Adden- 
dum. 

Working 
Depth. 

Depth  of 
Space 
Below 
Pitch 
Line. 

Clear- 
an  e. 

Whole 
Depth  of 
Tooth. 

4/5 
5/7 

6/8 
7/9 
8/10 
9/11 
10/12 
12/u 

0.3927 
.3142 
.2618 
.2244 
.1963 
.1745 
.1571 
.1309 

0.2000 
.1429 
.1250 

JOOO 
.0909 
.0833 
.0714 

0.4000 
.2858 
.2500 
.2222 
.2000 
.1818 
.1667 
.1429 

0.2500 
.1786 
.1562 
.1389 
.1250 
.1136 
.1041 
.0993 

0.0500 
.0357 
.0312 
.0278 
.0250 
.0227 
.0208 
.0179 

0.4500 
.3214 
.2812 
.2500 
.2250 
.2045 
.1875 
.1607 

Another  system  of  stub  gear  teeth  is  also  in  use,  in  which  the  tooth 
dimensions  are  based  upon  circular  pitcL.  The  addendum  is  0.250  X 
circular  pitch,  and  the  dedendum  is  0.300  X  circular  pitch.  The  former 
system  is  the  ons  in  more  general  use. 


1168 


GEARING. 


Stepped  Gears.  —  Two  gears  of  the  same  pitch  and  diameter  mounted 
side  by  side  on  the  same  shaft  will  act  as  a  single  gear.  If  one  gear  is 
keyed  on  the  shaft  so  that  the  teeth  of  the  two  wheels  are  not  in  line, 
but  the  teeth  of  one  wheel  slightly  in  advance  of  the  other,  the  two  gears 
form  a  stepped  gear.  If  mated  with  a  similar  stepped  gear  on  a  parallel 
shaft  the  number  of  teeth  in  contact  will  be  twice  as 
great  as  in  an  ordinary  gear,  which  will  increase  the 
strength  of  the  gear  and  its  smoothness  of  action. 

Twisted  Teeth.  —  If  a  great  number  of  very  thin 
gears  were  placed  together,  one  slightly  in  advance  of 
the  other,  they  would  still  act  as  a  stepped  gear.  Con- 
tinuing the  subdivision  until  the  thickness  of  each 
separate  gear  is  infinitesimal,  the  faces  of  the  teeth 
instead  of  being  in  steps  take  the  form  of  a  spiral  or 
twisted  surface,  and  we  have  a  twisted  gear.  The  twist 
may  take  any  shape,  and  if  it  is  in  one  direction  for  half 
the  width  of  the  gear  and  in  the  opposite  direction  for 
the  other  half,  we  have  what  is  known  as  the  herring- 
bone or  double  helical  tooth.  The  obliquity  of  the 
twisted  tooth  if  twisted  in  one  direction  causes  an  end 
thrust  on  the  shaft,  but  if  the  herring-bone  twist  is  FIG.  185. 
used,  the  opposite  obliquities  neutralize  each  other.  This  form  of  tooth 
is  much  used  in  heavy  rolling-mill  practice,  where  great  strength  and 
resistance  to  shocks  are  necessary.  They  are  frequently  made  of  steel 
castings  (Fig.  185).  The  angle  of  the  tooth  with  a  line  parallel  to  the 
axis  of  the  gear  is  usually  30°. 

Spiral  or  Helical  Gears.  —  If  a  twisted  gear  has  a  uniform  twist  it 
becomes  what  is  commonly  called  a  spiral  gear  (properly  a  helical  gear). 
The  line  in  which  the  pitch-surface  intersects  the  face  of  the  tooth  is  part 
of  a  helix  drawn  on  the  pitch-surface.  A  spiral  wheel  may  be  made  with 
only  one  helical  tooth  wrapped  around  the  cylinder  several  times,  in 
which  it  becomes  a  screw  or  worm.  If  it  has  two  or  three  teeth  so 
wrapped,  it  is  a  double-  or  triple-threaded  screw  or  worm.  A  spiral-gear 
meshing  into  a  rack  is  used  to  drive  the  table  of  some  forms  of  planing- 
machine.  For  methods  of  laying  out  and  producing  spiral  gears  see 
Brown  and  Sharpe's  treatise  on  Gearing  and  Halsey's  Worm  and  Spiral 
Gearing,  also  Machy.,  May  1906  and  Machifs  Reference  Series  No.  20. 

Worm-gearine.  —  When  the  axes  of  two  spiral  gears  are  at  right 
angles,  and  a  wheel  of  one,  two,  or  three  threads  works  with  a  larger  wheel 
of  many  threads,  it  becomes  a  worm-gear,  or  endless  screw,  the  smaller 
wheel  or  driver  being  called  the  worm,  and  the  larger,  or  driven  wheel, 
the  worm-wheel.  With  this  arrangement  a  high  velocity  ratio  may  be 
obtained  with  a  single  pair  of  wheels.  For  a  one-threaded  wheel  the  veloc- 
ity ratio  is  the  number  of  teeth  in  the  worm-wheel.  The  worm  and  wheel 
are  commonly  so  constructed  that  the  worm  will  drive  the  wheel,  but  the 
wheel  wUl  not  drive  the  worm. 

To  find  the  diameter  of  a  worm-wheel  at  the  throat,  number  of  teeth  and 
pitch  of  the  worm  being  given:  Add  2  to  the  number  of  teeth,  multiply 

the  sum  by  0.3183,  and 
by  the  pitch  of  the  worm 
in  inches. 

To  find  the  number  of 
teeth,  diameter  at  throat 
and  pitch  of  worm  being 
given:  Divide  3.1416 
times  the  diameter  by  the 
pitch,  and  subtract  2 
from  the  quotient. 

In  Fig.  186  ab  is  the 
diam.  of  the  pitch-circle, 
cd  is  the  diam.  at  the 
throat. 

EXAMPLE.  —  Pitch  of 


FIG.  186. 


worm  1/4  in.,  number  of  teeth  70;  required  the  diam.  at  the  throat.    (70 
+  2)  X  0  .3183  X  0  .25  =  5  .73  in. 

For  design  of  worm  gearing  see  Kimball  and  Barr's  Machine  Design. 
For  efficiency  of  worm-gears  see  page  1171. 


FORMS  OF  THE  TEETH. 


1169 


The  Hindley  Worm.  —  In  the  Hindley  worm-gear  the  worm,  in- 
stead of  being  cylindrical  in  outline,  is  of  an  hour-glass  shape,  the  pitch 
line  of  the  worm  being  a  curved  line  corresponding  to  the  pitch  line  of  the 
gear.  It  is  claimed  that  there  is  surface  contact  between  the  faces  of 
the  teeth  of  the  worm  and  gear,  instead  of  only  line  contact  as  in  the  case 
of  the  ordinary  worm  gear,  but  this  is  denied  by  some  writers.  For 
discussion  of  the  Hindiey  worm  see  Am.  Mach.,  April  1,  1897  and 
Machy.,  Dec.  1908.  The  Hindley  gear  is  made  by  the  Albro-Clem 
Elevator  Co.,  Philadelphia. 

Teeth  of  Bevel-wheels.  (Rankine's  Machinery  and  Millwork.)  — 
The  teeth  of  a  bevel-wheel  have  acting  surfaces  of  the  conical  kind,  gen- 
erated by  the  motion  of  a  line  traversing  the  apex  of  the  conical  pitch- 
surface,  while  a  point  in  it  is  carried  round  the  traces  of  the  teeth  upon 
a  spherical  surface  described  about  that  apex. 

The  operations  of  drawing  the  traces  of  the  teeth  of  bevel-wheels  exactly, 
whether  by  involutes  or  by  rolling  curves,  are  in  every  respect  analogous 
to  those  for  drawing  the  traces  of  the  teeth  of  spur-wheels;  except  that  in 
the  case  of  bevel-wheels  all  those  operations  are  to  be  performed  on  the 
surface  of  a  sphere  described  about  the  apex,  instead  of  on  a  plane,  sub- 
stituting poles  for  centers  and  great  circles  for  straight  lines. 

In  consideration  of  the  practical  difficulty,  especially  in  the  case  of 
large  wheels,  of  obtaining  an  accurate  spherical  surface,  and  of  drawing 
upon  it  when  obtained,  the  follow- 
ing approximate  method,  proposed 
originally  by  Tredgold,  is  generally 
used: 

Let  O,  Fig.  187,  be  the  common 
apex  of  the  pitch-cones,  OBI,  OB'I, 
of  a  pair  of  bevel-wheels;  OC,  OC', 
the  axes  of  those  cones;  OI  their 
line  of  contact.  Perpendicular  to 
01  draw  AIA',  cutting  the  axes  in 
A,  A';  make  the  outer  rims  of  the 
patterns  and  of  the  wheels  portions 
of  the  cones  ABI,  A'B'I,  of  which 
the  narrow  zones  occupied  by  the 
teeth  will  be  sufficiently  near  for 
practical  purposes  to  a  spherical 
surface  described  about  O.  As  the 
cones  ABI,  A'B'I  cut  the  pitch- 
cones  at  right  angles  in  the  outer  pitch-circles  IB,  IB',  they  may  be  called 
the  normal  cones.  To  find  the  traces  of  the  teeth  upon  the  normal  cones, 
draw  on  a  flat  surface  circular  arcs,  ID,  ID',  with  the  radii  AI,  A' I;  those 
arcs  will  be  the  developments  of  arcs  of  the  pitch-circles  IB,  IB'  when  the 
conical  surfaces  ABI,  A'B'I  are  spread  out  flat.  Describe  the  traces  of 
teeth  for  the  developed  arcs  as  for  a  pair  of  spur-wheels,  then  wrap  the 
developed  arcs  on  the  normal  cones,  so  as  to  make  them  coincide  with 
the  pitch-circles,  and  trace  the  teeth  on  the  conical  surfaces. 

For  formulae  and  instructions  for  designing  bevel-gears,  and  for  much 
other  valuable  information  on  the  subject  of  gearing,  see  "Practical 
Treatise  on  Gearing,"  and  "Formulas  in  Gearing,"  published  by  Brown 
&  Sharpe  Mfg.  Co.;  and  "Teeth  of  Gears, "  by  George  B.  Grant,  Lexington, 
Mass.  The  student  may  also  consult  Rankine's  Machinery  and  Millwork, 
Reuleaux's  Constructor,  and  Unwin's  Elements  of  Machine  Design.  See 
also  article  on  Gearing,  by  C.  W.  MacCord  in  App.  Cyc.  Mech.,  vol.  ii. 

Annular  and  Differential  Gearing.  (S.  W.  Balch,  Am.  Mach., 
Aug.  24, 1893.)  —  In  internal  gears  the  sum  of  the  diameters  of  the  describ- 
ing circles  for  faces  and  flanks  should  not  exceed  the  difference  in  the 
pitch  diameters  of  the  pinion  and  its  internal  gear.  The  sum  may  be 
equal  to  this  difference  or  it  may  be  less;  if  it  is  equal,  the  faces  of  the 
teeth  of  each  wheel  will  drive  the  faces  as  well  as  the  flanks  of  the  teeth  of 
the  other  wheel.  The  teeth  will  therefore  make  contact  with  each  other 
at  two  points  at  the  same  time. 

Cycloidal  tooth-curves  for  interchangeable  gears  are  formed  with  de- 
scribing circles  of  about  5/8  the  pitch  diameter  of  the  smallest  gear  of  the 
series.  To  admit  two  such  circles  between  the  pitch-circles  of  the  pinion 
and  internal  gear  the  number  of  teeth  in  the  internal  gear  should  exceed 


1170 


GEAEING. 


the  number  in  the  pinion  by  12  or  more,  if  the  teeth  are  of  the  customary 
proportions  and  curvature  used  in  interchangeable  gearing. 

Very  often  a  less  difference  is  desirable,  and  the  teeth  may  be  modified 
in  several  ways  to  make  this  possible. 

First.  The  tooth  curves  resulting  from  smaller  describing  circles  may 
be  employed.  These  will  give  teeth  which  are  more  rounding  and  nar- 
rower at  their  tops,  and  therefore  not  as  desirable  as  the  regular  forms. 

Second.  The  tips  of  the  teeth  may  be  rounded  until  they  clear.  This 
is  a  cut-and-try  method  which  aims  at  modifying  the  teeth  to  such  out- 
lines as  smaller  describing  circles  would  give. 

Third.  One  of  the  describing  circles  may  be  omitted  and  one  only 
used,  which  may  be  equal  to  the  difference  between  the  pitch-circles. 
This  will  permit  the  meshing  of  gears  differing  by  six  teeth.  It  will  usu- 
ally prove  inexpedient  to  put  wheels  in  inside  gears  that  differ  by  much 
less  than  12  teeth. 

If  a  regular  diametral  pitch  and  standard  tooth  forms  are  determined 
on,  the  diameter  to  which  the  internal  gear-blank  is  to  be  bored  is  calcu- 
lated by  subtracting  2  from  the  number  of  teeth,  and  dividing  the  re- 
mainder by  the  diametral  pitch. 

The  tooth  outlines  are  the  match  of  a  spur-gear  of  the  same  number 
of  teeth  and  diametral  pitch,  so  that  the  spur-gear  will  fit  the  internal 
gear  as  a  punch  fits  its  die,  except  that  the  teeth  of  each  should  fail  to 
bottom  in  the  tooth  spaces  of  the  other  by  the  customary  clearance  of  one- 
tenth  the  thickness  of  the  tooth. 

Internal  gearing  is  particularly  valuable  when  employed  in  differential 
action.  This  is  a  mechanical  movement  in  which  one  of  the  wheels  is 
mounted  on  a  crank  so  that  its  center  can  move  in  a  circle  about  the  center 
of  the  other  wheel.  Means  are  added  which  restrain  the  wheel  on  the 
crank  from  turning  over  and  confine  it  to  the  revolution  of  the  crank. 

The  ratio  of  the  number  of  teeth  in  the  revolving  wheel  compared  with 
the  difference  between  the  two  will  represent  the  ratio  between  the  revolv- 
ing wheel  and  the  crank-shaft  by  which  the  other  is  carried.  The  advan- 
tage in  accomplishing  the  change  of  speed  with  such  an  arrangement,  as 
compared  with  ordinary  spur-gearing,  lies  in  the  almost  entire  absence  of 
friction  and  consequent  wear  of  the  teeth. 

But  for  the  limitation  that  the  difference  between  the  wheels  must  not 
be  too  small,  the  possible  ratio  of  speed  might  be  increased* almost  indefi- 
nitely, and  one  pair  of  differential  gears  made  to  do  the  service  of  a  whole 
fcrain  of  wheels.  If  the  problem  is  properly  worked  out  with  bevel-gears 
this  limitation  may  be  completely  set  aside,  and  external  and  internal 
bevel-gears,  differing  by  but  a  single  tooth  if  need  be,  made  to  mesh  per- 
fectly with  each  other. 

EFFICIENCY  OF  GEARING. 

An  extensive  series  of  experiments  on  the  efficiency  of  gearing,  chiefly 
worm  and  spiral  gearing,  is  described  by  Wilfred  Lewis  in  Trans.  A.  S. 
M.  E.,  vii,  273.  The  average  results  are  shown  in  a  diagram,  from 
which  the  following  approximate  average  figures  are  taken: 

EFFICIENCY  OF  SPUR,  SPIRAL,  AND  WORM-GEARING. 


Gearing. 

Pitch. 

Velocity  at  pitch-line  in  feet  per  min. 

3 

10 

40 

100 

200 

Spur  pinion  

0.90 
.81 
.75 
.67 
.61 
.51 
.43 
.34 

0.935 
.87 
.815 
.75 
.70 
.615 
.53 
.43 

0.97 
.93 
.89 
.845 
.805 
.74 
.72 
.60 

0.98 
.955 
.93 
.90 
.87 
.82 
.765 
.70 

0.985 
.965 
.945 
.92 
.90 
.86 
.815 
.765 

45° 
30 
20 
15 
'10 
7 
5 

Spiral  pinion  or  worm  

The  experiments  showed  the  advantage  of  spur-gearing  over  all  other 
kinds  in  both  durability  and  efficiency.  The  variation  from  the  mean 
results  rarely  exceeded  5%  in  either  direction,  so  long  as  no  cutting 
occurred,  but  the  variation  became  much  greater  and  very  irregular  as 
soon  as  cutting  began.  The  loss  of  power  varies  with  the  speed,  the 


EFFICIENCY   OF   GEARING. 


1171 


pressure,  the  temperature,  and  the  condition  of  the  surfaces.  The  high 
friction  of  worm-  and  spiral-gearing  is  largely  due  to  end  thrust  on  the 
collars  of  the  shaft,  and  may  be  considerably  reduced  by  roller-bearings 
for  the  collars. 

When  two  worms  with  opposite  spirals  run  in  two  spiral  worm-gears 
that  also  work  with  each  other,  and  the  pressure  on  one  gear  is  opposite 
that  on  the  other,  there  is  no  thrust  on  the  shaft.  Even  with  light  loads 
a  worm  will  begin  to  heat  and  cut  if  run  at  too  high  a  speed,  the  limit  for 
safe  working  being  a  velocity  of  the  rubbing  surfaces  of  200  to  300  ft. 
per  minute,  the  former  being  preferable  where  the  gearing  has  to  work 
continuously.  The  wheel  teeth  will  keep  cool,  as  they  form  part  of  a 
casting  having  a  large  radiating  surface;  but  the  worm  itself  is  so  small 
that  its  heat  is  dissipated  slowly.  Whenever  the  heat  generated  increases 
faster  than  it  can  be  conducted  and  radiated  away,  the  cutting  of  the 
worm  may  be  expected  to  begin.  A  low  efficiency  for  a  worm-gear  means 
more  than  the  loss  of  power,  since  the  power  which  is  lost  reappears  as 
heat  and  may  cause  the  rapid  destruction  of  the  worm. 

Unwin  (Elements  of  Machine  Design,  p.  294)  says:  The  efficiency  is 
greater  the  less  the  radius  of  the  worm.  Generally  the  radius  of  the 
worm  =  1 .5  to  3  times  the  pitch  of  the  thread  of  the  worm  or  the  circular 
pitch  of  the  worm-wheel.  For  a  one-threaded  worm  the  efficiency  is 
only  2/5  to  1/4:  for. a  two-threaded  worm,  4/7  10.2/5;  for  a  three-threaded 
worm,  2/3  to  1/2  .  As  so  much  work  is  wasted  hi  friction  it  is  natural  that 
the  wear  is  excessive.  The  table  below  gives  the  calculated  efficiencies 
of  worm-wheels  of  1,2,3,  and  4  threads  and  ratios  of  radius  of  worm  to 
pitch  of  teeth  of  from  1  to  6,  with  a  coefficient  of  friction  of  0.15. 


No.  of 
Threads. 

Radius  of  Worm  •£•  Pitch. 

1 

H/4 

H/2 

13/4 

2 

21/2 

3 

4 

6 

2 
3 
4 

0.50 
.67 
.75 
.80 

0.44 
.62 
.70 
.76 

0.40 
.57 
.67 
.73 

0.36 
.53 
.63 
.70 

0.33 
.50 
.60 
.67 

0.28 
.44 
.55 
.62 

0.25 
.40 
.50 
.57 

0.20 
.33 
.43 
.50 

0.14 
.25 
.33 
.40 

Efficiency  of  Worm  Gearing.  —  Worm  gearing  as  a  means  of  trans- 
mitting power  has  generally  been  looked  upon  with  suspicion,  its  efficiency 
being"  considered  necessarily  low  and  its  life  short.  When  properly  pro- 
portioned, however,  it  is  both  durable  and  reasonably  efficient.  Mr.  F. 
A.  Halsey  discusses  the  subject  in  Am.  Machinist,  Jan.  13  and  20,  1898. 
He  quotes  two  formulas  for  the  efficiency  of  worm  gearing: 


In  which  E  =  efficiency;  a  =  angle  of  thread,  being  angle  between  thread 
and  a  line  perpendicular  to  the  axis  of  the  worm:/  =  coefficient  of  friction. 

Eq.  (1)  applies  to  the  worm  thread  only,  while  (2)  applies  to  the  worm 
and  step  combined,  on  the  assumption  that  the  mean  friction  radius  of  the 
two  is  equal.  "Eq.  (1)  gives  a  maximum  for  E  when  tan  a  =  VI  +  /a  —  / 
.  .  .  (3)  and  eq.  (2)  a  maximum  when  tan  a:  =  V2+4/2  -  2f  ....  (4) 
Using  0.05  for/gives  a  in  (3)  =  43°  34'  and  in  (4)  =  52°  49'. 

On  plotting  equations  (1)  and  (2)  the  curves  show  the  striking  influence 
of  the  pitch-angle  upon  the  efficiency,  and  since  the  lost  work  is  expended 
in  friction  and  wear,  it  is  plain  why  worms  of  low  angle  should  be  short- 
lived and  those  of  high  angle  long-lived.  The  following  table  is  taken 
from  Mr.  Halsey  's  plotted  curves: 
RELATION  OF  THREAD-ANGLE,  SPEED  AND  EFFICIENCY  OF  WORM-GEARS. 


Velocity  of 
Pitch-line, 
Feet  per 
Minute. 

Angle  of  Thread. 

5 

-10 

20 

30 

40 

45 

Efficiency. 

3 

10 
20 
40 
100 
200 

35 
40 
47 
52 
60 
70 
76 

52 
56 
62 
67 
74 
82 
85 

66 
69 
74 
78 
83 
88 
91 

73 

76 
79 
83 
87 
91 
92 

76 
79 
82 
83 
88 
91 
92 

77 
80 
82 
86 
88 
91 
92 

1172 


GEARING. 


The  experiments  of  Mr.  Wilfred  Lewis  on  worms  show  a  very  satisfac- 
tory correspondence  with  the  theory.  Mr.  Halsey  gives  a  collection  of 
data  comprising  16  worms  doing  heavy  duty  and  having  pitch-angles 
ranging  between  4°  30'  and  45°,  which  show  that  every  worm  having  an 
angle  above  12°  30'  was  successful  in  regard  to  durability,  and  every  worm 
below  9°  was  unsuccessful,  the  overlapping  region  being  occupied  by 
worms  some  of  which  were  successful  and  some  unsuccessful.  In  several 
cases  worms  of  one  pitch-angle  had  been  replaced  by  worms  of  a  different 
angle,  an  increase  in  the  angle  leading  in  every  case  to  better  results  and  a 
decrease  to  poorer  results.  He  concludes  with  the  following  table  from 
experiments  by  Mr.  James  Christie,  of  the  Pencoyd  Iron  Works,  and  gives 
data  connecting  the  load  upon  the  teeth  with  the  pitch-line  velocity  of 
the  worm. 

LIMITING  SPEEDS  AND  PRESSURES  OF  WORM  GEARING. 


Double- 

Double- 

Single-thread 

thread 

thread 

Worm  \"  Pitch, 

Worm   2'- 

Worm  21/o' 

27/8  Pitch  Diam. 

Pitch.  27/8 

Pitch,  41/2 

Pitch  Diam. 

Pitch  Diam. 

Revolutions  per  minute  
Velocity  at  pitch-line,  feet  per 
minute  

128 
96 

201 
150 

272 
705 

425 
37,0 

128 
96 

201 
150 

272 
7.05 

201 
735 

272 
319 

425 
498 

Limiting  nressure.  oounds.  .  . 

1700 

1300 

1100 

700 

1100 

1100 

1100 

1100 

700 

400 

Efficiency  of  Automobile  Gears.    (G.  E.  Quick,  Horseless  Age,  Feb.  12, 
1908.) — A  set  of  slide  gears  was  tested  by  an  electric-driven  absorption  ' 
dynamometer.     The  following  approximate  results  are  taken  from  a  | 
series  of  plotted  curves: 


Horse-power  input  

2 

4 

6 

8    |    10 

14 

18 

r.p.m. 

Efficiency,  per  cent. 

Direct  driven,  third  speed..  .     . 

800 

89 

95 

97 

97,5 

97  5 

97  5 

96 

Direct  driven,  third  speed..  .     . 

1,500 

80 

89 

93 

95 

96  5 

97 

97 

Second  speed,  ratio  1  .76  to  1 

800 

87 

97  5 

94 

95 

94 

93 

Second  speed,  ratio  1.76  to  1 

1,500 

79 

88 

9?  5 

94 

95 

95 

94 

First  speed,  ratio  3.36  to  1  ..     . 

800 

75 

87,5 

93 

94 

94 

93  5 

97  *» 

First  speed,  ratio  3.36  to  1...     . 

1,500 

70 

84 

89 

97 

93 

92 

Reverse  speed,  ratio  4.32  to  1     . 

800 

75 

84 

87 

87 

86 

87  5 

Reverse  speed,  ratio  4.32  to  1... 

1,500 

70 

79 

83 

86 

87 

85 

Worm-gear  axle,  ratio  6.83  to  1.. 
Worm-gear  axle,  ratio  6.83  to  1  .. 

400 
800 

85 

87 
87 

86.5 
88  5 

85.5 
89 

84 
89 

80 

88 

75 

87 

Worm-gear  axle,  ratio  6.83  to  1.. 

1,500 

80 

85 

87.5 

88.5 

89 

89 

89 

Two  bevel- wheel  axles  were  tested,  one  a  floating  type,  ratio  15  to  32. 
141/2°  involute;  the  other  a  solid  wheel  and  axle  type,  ratio  13  to  54,  20° 
involute.  Both  gave  efficiencies  of  95  to  96  %  at  800  to  1500  r.p.m., 
and  10  to  26  H.P.,  with  lower  efficiencies  at  lower  power  and  at  lower 
speed.  The  friction  losses  include  those  of  the  journals  and  thrust  ball 
bearings. 

The  worm  was  6-threaded,  lead,  4.69  in.;  pitch  diam.,  2.08  in.;  the 
gear  had  41  teeth;  pitch  diam.,  10.2  in.  The  worm  was  of  hardened 
steel  and  the  gear  of  phosphor-bronze.  A  test  of  a  steel  gear  and  steel 
worm  gave  somewhat  lower  efficiencies.  In  both  tests  the  heating  was 
excessive  both  in  the  gears  and  in  the  thrust  bearings,  the  balls  in  which 
were7/lein.  diam. 

STRENGTH   OF   GEAR-TEETH. 

The  strength  of  gear-teeth  and  the  horse-power  that  may  be  transmitted 
by  them  depend  upon  so  many  variable  and  uncertain  factors  that  it  is 
not  surprising  that  the  formulas  and  rules  given  by  different  writers 
show  a  wide  variation.     In  1879  John  H.  Cooper  (Jour.  Frank.  Inst., 
July,  1879)  found  that  there  were  then  in  existence  about  48  well-estab-  j 
lished  rules  for  horse-power  and  working  strength,  differing  from  each 
other  in   extreme   cases   about   500%.     In   1886   Prof.   Wm.    Harkness 
(Proc.  A.  A.  A.  S.t  1886),  from  an  examination  of  the  bibliography  of  the  ' 
subject,  beginning  in  1796,  found  that  according  to  tne  constants  and 


STRENGTH  OF  GEAR-TEETH.  1173 

'formulae  used  by  various  authors  there  were  differences  of  15  to  1  in  the 

power  which  could  be  transmitted  by  a  given  pair  of  geared  wheels. 
The  various  elements  which  enter  into  the  constitution  of  a  formula  to 
represent  the  working  strength  of  a  toothed  wheel  are  the  following: 
1.  The  strength  of  the  metal,  usually  cast  iron,  which  is  an  extremely 
variable  quantity.  2.  The  shape  of  the  tooth,  and  especially  the  relation 
of  its  thickness  at  the  root  or  point  of  least  strength  to  the  pitch  and  to 
the  length.  3.  The  point  at  which  the  load  is  taken  to  be  applied, 
assumed  by  some  authors  to  be  at  the  pitch-line,  by  others  at  the  extreme 
end,  along  the  whole  face,  and  by  still  others  at  a  single  outer  corner. 
4.  The  consideration  of  whether  the  total  load  is  at  any  time  received 
by  a  single  tooth  or  whether  it  is  divided  between  two  teeth.  5.  The 
influence  of  velocity  in  causing  a  tendency  to  break  the  teeth  by  shock. 
6.  The  factor  of  safety  assumed  to  cover  all  the  uncertainties  of  the 
other  elements  of  the  problem. 

Prof.  Harkness,  as  a  result  of  his  investigation,  found  that  all  the 
formulae  on  the  subject  might  be  expressed  in  one  of  three  forms,  viz.; 
Horse-power  =  CVpf,    or    CFp2,    or    CVp*f; 

in  which  C  is  a  coefficient,  V  =  velocity  of  pitch-line  in  feet  per  second, 
p  =  pitch  in  inches,  and  /  =  face  of  tooth  in  inches. 

*'rom  an  examination  of  precedents  he  proposed  the  following  formula 
for  cast-iron  wheels: 

H.p.  =     °-910  Vpf 


0.65  V 

He  found  that  the  teeth  of  chronometer  and  watch  movements  were 
subject  to  stresses  four  times  as  great  as  those  which  any  engineer  would 
dare  to  use  in  like  proportion  upon  cast-iron  wheels  of  large  size. 

It  appears  that  all  of  the  earlier  rules  for  the  strength  of  teeth  neglected 
the  consideration  of  the  variations  in  their  form;  the  breaking  strength,  aa 
said  by  Mr.  Cooper,  being  based  upon  the  thickness  of  the  teeth  at  the 
pitch-line  or  circle,  as  if  the  thickness  at  the  root  of  the  tooth  were  the 
same  in  all  cases  as  it  is  at  the  pitch-line. 

Wilfred  Lewis  (Proc.  Eng'rs  Club,  Phila.,  Jan.,  1893;  Am.  Mach., 
June  22,  1893)  seems  to  have  been  the  first  to  use  the  form  of  the  tooth 
in  the  construction  of  a  working  formula  and  table.  He  assumes  that 
in  well-constructed  machinery  the  load  can  be  more  properly  taken  as 
well  distributed  across  the  tooth  than  as  concentrated  in  one  corner,  but 
that  it  cannot  be  safely  taken  as  concentrated  at  a  maximum  distance 
from  the  root  less  than  the  extreme  end  of  the  tooth.  He  assumes  that 
the  whole  load  is  taken  upon  one  tooth,  and  considers  the  tooth  as  a 
beam  loaded  at  one  end,  and  from  a  series  of  drawings  of  teeth  of  the 
involute,  cycloidal,  and  radial  flank  systems,  determines  the  point  of 
weakest  cross-section  of  each,  and  the  ratio  of  the  thickness  at  that  section 
to  the  pitch.  He  thereby  obtains  the  general  formula, 

W  =  spfy; 

In  which  W  is  the  load  transmitted  by  the  teeth,  in  pounds;  s  is  the  safe 
working  stress  of  the  material,  taken  at  8000  Ibs.  for  cast  iron,  when  the 
working  speed  is  100  ft.  or  less  per  minute;  p  =  pitch;  /  =  face,  in 
inches;  y  «=  a  factor  depending  on  the  form  of  the  tooth,  whose  value  for 
different  cases  is  given  in  the  table  on  page  1174. 

The  values  of  s  in  the  above  table  are  given  by  Mr.  Lewis  tentatively, 
in  the  absence  of  sufficient  data  upon  which  to  base  more  definite  values, 
but  they  have  been  found  to  give  satisfactory  results  in  practice. 

EXAMPLE.  Required  to  find  the  working  strength  of  a  12-toothed  pin- 
ion, 1-inch  pitch,  2  H-hich  face,  driving  a  wheel  of  60  teeth  at  100  feet  or 
less  per  minute,  and  let  the  teeth  be  of  the  20-degree  involute  form.  In 
the  formula  W  =  spfy  we  have  for  a  cast-iron  pinion  s  =  8000,  pf  =2.5, 
and  y  =  0.078;  and  multiplying  these  values  together,  we  have  W  = 
1560  pounds.  For  the  wheel  we  have  y  =  0.134  and  W  =  2680  pounds. 

The  cast-iron  pinion  is,  therefore,  the  measure  of  strength;  but  if  a 
steel  pinion  be  substituted  we  have  s  =  20,000  and  W  =  3900  pounds,  in 
which  combination  the  wheel  is  the  weaker,  and  it  therefore  becomes  the 
measure  of  strength. 

For  bevel-  wheels  Mr.  Lewis  gives  the  following,  referring  to  Fig.  188: 


1174 


GEAKING. 


D  =  large  diameter  of  bevel;  d  =  small  diameter  of  bevel;  p  =  pitch 
at  large  diameter;  n  =  actual  number  of  teeth;  /  =  face  of  bevel; 
N  —  formative,  number  of  teeth  =  n  X  secant  a,  or 
\  the  number  corresponding  to  radius  R;  y  =  factor  de- 

rv  T^fj  pending  upon  shape  of  teeth  and  formative  number  N; 

x    ^^  /^  \\W  =  working  load  on  teeth,  assumed  to  be  applied  at 
'  the  large  end  of  the  bevel  gear  on  the  pitch  line. 


W 


spfy  -—-  ;  or.  more  simply,  W 


spfy      ; 


FIG.  188. 


which  gives  almost  identical  results  when  d  is  not  less 
than  2/3  D,  as  is  the  case  in  good  practice. 

In  Am.  Mach.,  June  22,  1893,  Mr.  Lewis  gives  the 
following  formulae  for  the  working  strength  of  the  three 
systems  of  gearing,  which  agree  very  closely  with  those 
obtained  by  use  of  the  table: 


For  involute,  20°  obliquity,  W  =  spf  (  0.  154  -  ^?  )  ; 

For  involute  15°,  and  cycloidal,    W  =  spf  (o.!24  -  ^^)  : 

For  radial  flank  system,  W  =  spf  (o.075  -  ^p): 

in  which  the  factor  within  the  parenthesis  corresponds  to  y  in  the  general 
formula.     For  the  horse-power  transmitted,  Mr.  Lewis's  general  formula 

W  =  spfy  =   33'OOOH-P-,  may  take  the  form  H.P.  =  ^r£rz>  ™  which 

V  oo,UUU 

->  =  velocity   in    feet    per    minute;    or   since    v  =  dir  X  r.p.m.  •*•  12  » 
:)  .2618  d  X  r.p.m.,  in  which  d  =  diameter  in  inches, 


It  must  be  borne  in  mind,  however,  that  in  the  case  of  machines  which 
consume  power  intermittently,  such  as  punching  and  shearing  machines, 
the  gearing  should  be  designed  with  reference  to  the  maximum  load  W, 
which  can  be  brought  upon  the  teeth  at  any  time,  and  not  upon  the 
average  horse-power  transmitted. 

VALUES  OF  y  IN  LEWIS'S  FORMULA. 


Factor  for  Strength   y. 

Factor  for  Strength,  y. 

No.  of 
Teeth. 

Involute 
20°  Ob- 
liquity. 

Involute 
15°  and 
Cycloidal 

Radial 
Flanks. 

No.  of 
Teeth. 

Involute 
20°  Ob- 
liquity. 

Involute 
15°  and 
Cycloidal 

Radial 
Flanks. 

12 

0.078 

0.067 

0.052 

27 

0.111 

0.100 

0.064 

13 

.083 

.070 

.053 

30 

.114 

.102 

.065 

14 

.088 

.072 

.054 

34 

.118 

.104 

.066 

15 

.092 

.075 

.055 

38 

.122 

.107 

.067 

16 

.094 

.077 

.056 

43 

.126 

.110 

.068 

17 

.096 

.080 

.057 

50 

.130 

.112 

.069 

18 

.098 

.083 

.058 

60 

.134 

.114 

.070 

19 

.100 

.087 

.059 

75 

.138 

.116 

.071 

20 

.102 

.090 

.060 

100 

.142 

.118 

.072 

21 

.104 

.092 

.061 

150 

.146 

.120 

.073 

23 

.106 

.094 

.062 

300 

.150 

.122 

.074 

25 

.108 

.097 

.063 

Rack. 

.154 

.124 

.075 

SAFE  WORKING  STRESS,  s,  FOR  DIFFERENT  SPEEDS. 


Speed  of  Teeth  in 
Ft.  per  Minute. 

,<Kor|    20fl 

300 

600 

900 

1200 

1800 

2400 

Cast  iron  .  . 

8000     6000 

4800 

4000 

3000 

2400 

2000 

1700 

Steel  

20000  115000 

12000 

10000 

7500 

6000 

5000 

4300 

Comparison    of   the    Harkness  and   Lewis    Formulae.  —  Take   an 
average  case  in  which  the  safe  working  strength  of  the  material,  s  =  6000, 


STRENGTH  OF  GEAR-TEETH. 


1175 


D  *=  200  ft.  per  min.,  and  y  —  0.100,  the  value  in  Mr.  Lewis's  table  for  an 
involute  tooth  of  15°  obliquity,  or  a  cycloidal  tooth,  the  number  of  teetb 
in  the  wheel  being  27. 


TT  -P 

H'R 


"  33,000 
if  V  is  taken  in  feet  per  second. 

Prof.  Harkness  gives  H.P.  = 


6000  p/i?X  0.100  _  pfv  __  -  nQ1     fv 
33,000  -  55  -  1-091  P/V. 


0.910  Vpf 


If  the  V  in  the  denominator 


fl  +  0.65  V 

be  taken  at  200  •%•  60  =  31/3  ft.  per  sec.,  H.P.  =  0.571  p/V,  or  about 
52%  of  the  result  given  by  Mr.  Lewis's  formula.  This  is  probably  a? 
close  an  agreement  as  can  be  expected,  since  Prof.  Harkness  derived  his 
formula  from  an  investigation  of  ancient  precedents  and  rule-of-thumb 
practice,  largely  with  common  cast  gears,  while  Mr.  Lewis's  formula  was 
derived  from  considerations  of  modern  practice  witn  machine-molded 
and  cut  gears. 

Mr.  Lewis  takes  into  consideration  the  reduction  in  working  strength 
of  a  tooth  due  to  increase  in  velocity  by  the  figures  in  his  table  of  the 
values  of  the  safe  working  stress  s  for  different  speeds.  Prof.  Harkness 
gives  expression  to  the  same  reduction  by  means  of  the  denominator  of 
his  formula,  Vi  4-  0.65  V.  The  decrease  in  strength  as  computed  by 
this  formula  is  somewhat  less  than  that  given  in  Mr.  Lewis's  table,  and  as 
the  figures  given  in  the  table  are  not  based  on  accurate  data,  a  mean 
between  the  values  given  by  the  formula  and  the  table  is  probably  as 
near  to  the  true  value  as  may  be  obtained  from  our  present  knowledge. 
The  following  table  gives  the  values  for  different  speeds  according  to  Mr. 
Lewis's  table  and  Prof.  Harkness's  formula,  taking  for  a  basis  a  working 
stress  a,  for  cast-iron  8000,  and  for  steel  20,000  Ibs.  at  speeds  of  100  ft. 
per  minute  and  less: 


V  =  speed  of  teeth,  ft.  per  min.  . 
V  =  speed  of  teeth,  ft.  per  sec  .  . 

100 

1  2/3 

200  1  300 

31/sl    5 

600 
10 

900 
15 

1200 
20 

1800 
30 

2400 
40 

bafe  stress  s,  cast  iron,  Lewis  .  . 
Relative  do.,  s  *  8000  

8000 

.-6930 
1 

8000 
8000 
20000 
20000 

6000 
0.75 

.5621 
0.811 
6488 
6200 
15500 
15000 

4800 
0.6 
.4850 
0.700 
5600 
5200 
13000 
12000 

4000 
0.5 

.3650 
0.526 
4208 
4100 
10300 
10000 

3000 
0.375 
.3050 
0.439 
3512 
3300 
8100 
7500 

2400 
0.3 
.2672 
0.385 
3080 
2700 
6800 
6000 

2000 
0.25 
.2208 
0.318 
2544 
2300 
5700 
5000 

1700 
0.2125 
.1924 
0.277 
2216 
2000 
4900 
4300 

1  j.  \/l  +  0  65  V  .... 

Relative  val  c  •*•  0  693  

«,  -  8000  x  (c  -nO.  693)  
Mean  of  s  and  slt  cast-iron  =  s2. 
Mean  of  s  and  si,  for  steel  =  83.. 
Safe  stress  for  steel,  Lewis  

In  Am.  Mach.,  Jan.  30,  1902,  Mr.  Lewis  says  that  8,000  Ibs.  was  given 
as  safe  for  cast-iron  teeth,  either  cut  or  cast,  and  that  20,000  Ibs.  was 
intended  for  any  steel  suitable  f9r  gearing  whether  cast  or  forged. 
These  were  the  unit  stresses  for  static  loads. 

The  iron  should  be  of  good  quality  capable  of  sustaining  about  a  ton 
on  a  test  bar  1  in.  square  between  supports  12  in.  apart,  and  the  steel 
should  be  solid  and  of  good  quality.  The  value  given  for  steel  was  in- 
tended to  include  the  lower  grades,  but  when  the  quality  is  known  to  be 
high,  correspondingly  higher  values  may  be  assigned. 

Comparing  the  two  formulae  for  the  case  of  s  =  8000,  corresponding  to 
a  speed  of  100  ft.  per  min.,  we  have 


Harkness:  H.P.  = 
Lewis:    H.P. 


1 

spfyv 
~~  33,000 


o.65  V  X  0  .9107p/=  1  .053  pf, 
spfy  V       8000  X  1  2/3  pfy 
550  550 


24.24p/2/, 


in  which  y  varies  according  to  the  shape  and  number  of  the  teeth. 
For  radial-flank  gear  with  12  teeth  y  =  0.052;  24.24  pfy  =  1.260p/; 

For  20°inv.,  19  teeth,  or  15°inv.,  27  teeth  y  =  0.100;  24.24  pfy  =  2.424p/; 
For  20°  involute,  300  teeth  y  =  0.150;  24.24  pfy  =  3.636p/. 

Thus  the  weakest-shaped  tooth,  according  to  Mr.  Lewis,  will  transmit 
20  per  cent  more  horse-power  than  is  given  by  Prof.  Harkness's  formula, 
in  which  the  shape  of  the  tooth  is  not  considered,  and  the  average-shaped 


1176  GEABtNG. 

tooth,  according  to  Mr.  Lewis,  will  transmit  more  than  double  the 

horse-power  given  by  Prof.  Harkness's  formula. 

i    Comparison  of  Other  Formulae.— Mr,  Cooper,  in  summing  up  his 

examination,  selected  an  old  English  rule,  which  Mr.  Lewis  considers  as 
a  passably  correct  expression  of  good  general  averages,  viz.:  X  =  2000  rf, 
X  =  breaking  load  of  tooth  in  pounds,  p  =  pitch,  /  =  face.  If  a  factor 
of  safety  of  10  be  taken,  this  would  give  for  safe  working  load  W  =200  rf- 
George  B.  Grant,  in  his  Teeth  of  Gears,  page  33,  takes  the  breaking 
load  at  3500  pf,  and,  with  a  factor  of  safety  of  10,  gives  W  =  350  pf. 

Nystrom's  Pocket-Book,  20th  ed.,  1891,  says:  "The  strength  and  dura- 
bility of  cast-iron  teeth  require  that  they  shall  transmit  a  force  of  80  Ibs. 
per  inch  of  pitch  and  per  inch  breadth  of  face. "  This  is  equivalent  to 
W  =  80  pf,  or  only  40%  of  that  given  by  the  English  rule. 

F.  A.  Halsey  (Clark's  Pocket-Book)  gives  a  table  calculated  from  the 
formula  H.P.  =  pfd  X  r.p.m.  -i-  850. 

Jones  &  Laughlins  give  H.P.  =  pfd  X  r.p.m.  -*-  550. 
These  formulae  transformed  give  W  =  128  p/and  W  —  218  pf,  respec- 
tively. 

Unwin,  on  the  assumption  that_the  load  acts  on  the  corners  of  the 
teeth,  derives  a  formula  p  =  K  ^/W,  in  which  K  is  a  coefficient  derived 
from  existing  wheels,  its  values  being:  for  slowly  moving  gearing  not  sub- 
ject to  much  vibration  or  shock  K  =  0.04;  in  ordinary  mill-gearing, 
running  at  greater  speed  and  subject  to  considerable  vibration,  K  =  0  .05; 
and  in  wheels  subjected  to  excessive  vibration  and  shock,  and  in  mortise 
gearing,  K  =  0.06.  Reduced  to  the  form  W  =  Cpf,  assuming  that/  = 
2  p,  these  values  of  K  give  W  =  262  pf,  200  pf.  and  139  pf,  respectively. 
Unwin  also  give  the  following,  based  on  the  assumption_that  the  pres- 
sure is  distributed  along  the  edge  of  the  tooth:  p  =  Ki  ^p/f^W,  where 
KI  =  about  0  .0707  for  iron  wheels  and  0  .0848  for  mortise  wheels  when 
the  breadth  of  face  is  not  less  than  twice  the  pitch.  For  the  case  of  /= 
2  p  and  the  given  values  of  KI  this  reduces  to  W  —  200  p/and  W  =  139  pf, 
respectively. 

Box,  in  his  Treatise  on  Mill  Gearing,  gives  H.P.  =  12  pzf^dn  -s-  1000, 
in  which  n  =  number  of  revolutions  per  minute.  This  formula  differs 
/rom  the  more  modern  formulae  in  making  the  H.P.  vary  as  p2/,  instead 
of  as  pf,  and.  in  this  respect  it  is  no  doubt  incorrect. 

Making  the  H.P.  vary  as  ^dn  or  as  V-y,  instead  of  directly  as  v,  makes 
the  velocity  a  factor  of  the  working  strength  as  in  the  Harkness  and 
Lewis  formulas,  the  relative  strength  varying  as  1/^v,  which  for  different 
velocities  is  as  follows: 

Speed  of  teeth  in  H.  per  J  10Q  200  300  600  900  120Q  1800  2400 
Relative  strength  =  1  0.707  0.574  0.408  0.333  0.289  0.236  0.20 

showing  a  somewhat  more  rapid  reduction  than  is  given  by  Mr.  Lewis. 

For  the  purpose  of  comparing  different  formulas  they  may  in  general 
be  reduced  to  either  of  the  following  forms: 

H.P.  =  Cpfv,        H.P.  =  dpfdX  r.p.m.,         W  =  cpf, 

in  which  p  *=  pitch,  /  =  face,  d  =  diameter,  all  in  inches;  v  =  velocity 
in  feet  per  minute,  r.p.m.  revolutions  per  minute,  and  C,  Ci  and  c  coeffi- 
cients. The  formulae  for  transformation  are  as  follows: 

H.P.  =  Wv  +  33,000  =  WX  dX  r.p.m.  -5-  126,050; 
33,000  H.P.      126,050  H.P.  .          H.P.  H.P.       _  W 

T-       =   dX  r.p.m.    =33'OOOC7p/'p/=-ar==C1dXr.p.mrT 

Ci  «  0.2618  C;  c  =  33,000  C\  C  =  3.82  Ci,  =  00^;  c  =  126,050  Ct. 

oo,UUU 

In  the  Lewis  formula  C  varies  with  the  form  of  the  tooth  and  with  the 
speed,  and  is  equal  to  sy  •*•  33,000,  in  which  y  and  s  are  the  values  taken 
from  the  table,  and  c  =  sv. 

In  the  Harkness  formula  C  varies  with  the  speed  and  is  equal  to 


STRENGTH  OF  GEAR-TEETH.  117? 


Ql  f) 

-(V  being  in  feet  per  second),  =  0.01517 


.vi  +  0.65  V 

In  the  Box  formula  C  varies  with  the  pitch  and  also  with  the  velocity; 

and  equals  12P^Br'P'm'  -  0  .02345  JL  ,  c  =  33,000  C  =  774  JL. , 

Vv  Vv 

For  v  =  100  ft.  per  min.  C  =  77.4  p:  for  v  =  600  ft.  per  min.,  c  =  31.6  p. 

In  the  other  formulae  considered  C,  C\,  and  c  are  constants.  Reducing 
the  several  formulae  to  the  form  W  =  cpf,  we  have  the  following: 

COMPARK3ION  OF  DIFFERENT  FORMULAE  FOR  STRENGTH  OF  GEAR-TEETH. 

Safe  working  pressure  per  inch  pitch  and  per  inch  of  face,  or  value  ol 
c  in  formula  W  =  cpf: 

v  =  ft.  per  min.     100  600 

Lewis:  Weak  form  of  tooth,  radial  flank,  12  teeth  c  =    416  208 

Medium  tooth,  inv.  15°,  or  cycloid,  27  teeth,  c  =    800  400 

Strong  form  of  tooth,  inv.  20°,  300  teeth,  .c  =  1200  600 

Harkness:  Average  tooth .c  =     347  184 

Box:  Tooth  of  1  inch  pitch c  =      77.4  31.6 

Box:  Tooth  of  3  inches  pitch c  =     232  95 

The  Gleason  Works  gives  for  ft.  per  min.      500     1000  1500  2000  2500 

working  stress  in  pounds  =  p.f.  X  480       400     340     290     240 

These  are  for  cut  gears,  18  teeth  or  more,  rigidly  supported,  for  average 

steady  loads.     Hammering  loads,  as  in  rolling  mills  and  saw  mills,  require 

heavier  gears. 

C.  W.  Hunt,  Trans.  A.S.M.E.,  1908,  gives  a  table  of  working  loads  of 
cut  cast  gears  with  a  strong  short  form  of  tooth,  which  is  practically 
equivalent  to  W=  700  pf. 

Various,  in  which  c  is  independent  of  form  and  speed:  Old  English 
rule,  c  =  200;  Grant,  c  «  350;  Nystrom,  c  =  80;  Halsey,  c  =  128;  Jones 
&  Laughlins,  c  =  218;  Unwin,  c  =  262,  200,  or  139,  according  to  speed, 
shock,  and  vibration. 

The  value  given  by  Nystrom  and  those  given  by  Box  for  teeth  of  small 
pitch  are  so  much  smaller  than  those  given  by  the  other  authorities  that 
they  may  be  rejected  as  having  an  entirely  unnecessary  surplus  of  strength. 
The  values  given  by  Mr.  Lewis  seem  to  rest  on  the  most  logical  basis,  the 
form  of  the  teeth  as  well  as  the  velocity  being  considered;  and  since  they 
are  said  to  have  proven  satisfactory  in  an  extended  machine  practice, 
they  may  be  considered,  reliable  for  gears  that  are  so  well  made  that 
the  pressure  bears  along  the  face  of  the  teeth  instead  of  upon  the  corners. 
For  rough  ordinary  work  the  old  English  rule  W  =  200  pf  is  probably 
as  good  as  any,  except  that  the  figure  200  may  be  too  high  for  weak  forms 
of  tooth  and  for  high  speeds. 

The  formula  W=  200  pfis  equivalent  to  H.P.  =  p/d  X  r.p.m. -*-630»  pfv 
-s-165  or,  H.P.  =  0.0015873  pfd  X  r.p.m.  =  0  .006063  pfv. 

Raw-hide  Pinions.  —  Pinions  of  raw-hide  are  in  common  use  for 
gearing  shafts  driven  by  electric  motors  to  other  shafts  which  carry 
machine-cut  cast-iron  or  steel  gears,  in  order  to  reduce  vibration,  noise 
and  wear.  A  formula  for  the  maximum  horse-power  to  be  transmitted 
by  such  gears,  given  by  the  New  Process  Raw-Hide  Co.,  Syracuse,  N.  Y., 
is  H.P.  =  pitch  diam.  X  circ.  pitch  X  face  X  r.p.m.  -*-  850,  or  pfd  X 
r.p.m. -^  850.  This  is  about  3/4  of  the  H.P.  for  cast-iron  teeth  by  the  old 
English  rule.  The  formula  is  to  be  used  only  when  the  circular  pitch 
does  not  exceed  1.65  ins. 

Composite  gears  also  are  made,  consisting  of  alternate  sheets  of  raw- 
hide or  fibre  and  steel  or  bronze,  so  that  a  high  degree  of  strength  is 
combined  with  the  smooth-running  quality  of  the  fibre. 

Maximum  Speed  of  Gearing.  —  A.  Towler,  Eng'g,  April  19,  1880, 
p.  388,  gives  the  maximum  speeds  at  which  it  was  possible  under  favor- 
able conditions  to  run  toothed  gearing  safely  as  follows,  in  ft.  per  min.: 
Ordinary  cast-iron  wheels,  1800;  Helical,  2400;  Mortise,  2400;  Ordinary 
cast-steel  wheels,  2600;  Helical,  3000:  special  cast-iron  machine-cut 
wheels,  3000. 

Prof.  Coleman  Sellers  (Stevens  Indicator,  April,  1892)  recommends  that 
gearing  be  not  run  over  1200  ft.  per  minute,  to  avoid  great  noise,  Tke 


1178  GEARING. 

Walker  Company;  Cleveland,  Ohio,  say  that  2200  ft.  per  min.  for  iron 

gears  and  3000  ft.  for  wood  and  iron  (mortise  gears)  are  excessive,  and 
should  be  avoided  -if  possible.  The  Corliss  engine  at  the  Philadelphia 
Exhibition  (1876)  had  a  fly-wheel  30  ft.  in  diameter  running  35  r.p.m. 
geared  into  a  pinion  12  ft.  diam.  The  speed  of  the  pitch-line  was  3300  ft. 

A  Heavy  Machine-cut  Spur-gear  was  made  in  1891  by  the  Walker 

Company,  Cleveland,  Ohio,  for  a  diamond  mine  in  South  Africa,  with 
dimensions  as  follows:  Number  of  teeth,  192;  pitch  diameter,  30  ft. 
6.66  ins.;  face,  30  ins.;  pitch,  6  ins.;  bore,  27  ins.;  diameter  of  hub,  0  ft. 
2  Ins.:  weight  of  hub,  15  tons;  and  total  weight  of  gear,  663/4  tons.  The 
run  was  made  in  12  segments,  the  joints  of  the  segments  being  fastened 
with  two  bolts  each.  The  spokes  were  bolted  to  the  middle  of  the  seg- 
ments and  to  the  hub  with  four  bolts  in  each  end. 

Frictional  Gearing.  —  In  frictional  gearing  the  wheels  are  toothless, 
and  one  wheel  drives  the  other  by  means  of  the  friction  between  the  two 
surfaces  which  are  pressed  together.  They  may  be -used  where  the  power 
to  be  transmitted  is  not  very  great;  when  the  speed  is  so  high  that  toothed 
wheels  would  be  noisy;  when  the  shafts  require  to  be  frequently  put  into 
and  out  of  gear  or  to  have  their  relative  direction  of  motion  reversed; 
or  when  it  is  desired  to  change  the  velocity-ratio  while  the  machinery 
is  in  motion,  as  in  the  case  of  disk  friction-wheels  for  changing  the  feed 
In  machine  tools. 

Let  P  =  the  normal  pressure  in  pounds  at  the  line  of  contact  by  which 
two  wheels  are  pressed  together,  T  =  tangential  resistance  of  the  driven 
wheel  at  the  line  of  contact,  /  =  the  coefficient  of  friction,  V  the  veloc- 
ity of  the  pitch-surface  in  feet  per  second,  and  H.P.  =  horse-power;  then 
T  may  be  equal  to  or  less  than/P;  H.P.  =  TV  •*•  550.  The  value  of/ 
for  metal  on  metal  may  be  taken  at  0.15  to  0.20;  for  wood  on  metal, 
0.25  to  0.30;  and  for  wood  on  compressed  paper,  0.20.  The  tangential 
driving  force  T  may  be  as  high  as  80  Ibs.  per  inch  width  of  face  of  the 
driving  surface,  but  this  is  accompanied  by  great  pressure  and  friction  on 
the  journal-bearings. 

In  frictional  grooved  gearing  circumferential  wedge-shaped  grooves  are 
cut  in  the  faces  of  two  wheels  in  contact.  If  P  =  the  force  pressing  the 
wheels  together,  and  N  =  the  normal  pressure  on  all  the  grooves,  P  =  N 
(sin  a  +  /cos  a),  in  which  2  a  =  the  inclination  of  the  sides  of  the  grooves, 
and  the  maximum  tangential  available  force  T  =  fN.  The  inclination 
of  the  sides  of  the  grooves  to  a  plane  at  right  angles  to  the  axis  is  usually 

Frictional  Grooved  Gearing.  —  A  set  of  friction-gears  for  trans- 
mitting 150  H.P.  is  on  a  steam-dredge  described  in  Proc.  Inst.  M.  E.t 
July,  1888.  Two  grooved  pinions  of  54  in.  diam.,  with  9  grooves  of  13/4 in. 
pitch  and  angle  of  40°  cut  on  their  face,  are  geared  into  two  wheels  of 
1271/2  in.  diam.  similarly  grooved.  The  wheels  can  be  thrown  in  and  out 
of  gear  by  levers  operating  eccentric  bushes  on  the  large  wheel-shaft. 
The  circumferential  speed  of  the  wheels  is  about  500  ft.  per  min.  Allow- 
ing for  engine  friction,  if  half  the  power  is  transmitted  through  each  set 
of  gears  the  tangential  force  at  the  rims  is  about  3960  Ibs.,  requiring,  if 
the  angle  is  40°  and  the  coefficient  of  friction  0.18,  a  pressure  of  7524  Ibs. 
between  the  wheels  and  pinion  to  prevent  slipping. 

The  wear  of  the  wheels  proving  excessive,  the  gears  were  replaced  by 
spur-gear  wheels  and  brake-wheels  with  steel  brake-bands,  which  arrange- 
ment has  proven  more  durable  than  the  grooved  wheels.  Mr.  Daniel 
Adamson  states  that  if  the  frictional  wheels  had  been  run  at  a  higher 
speed  the  results  would  have  been  better,  and  says  they  should  run  at 
least  30  ft.  per  second. 

Power  Transmitted  by  Friction  Drives.  (W.  F.  M.  Goss,  Trans. 
A.  S.  M.  E.,  1907.) — A  friction  drive  consists  of  a  fibrous  or  somewhat 
yielding  driving  wheel  working  in  rolling  contact  with  a  metallic  driven 
wheel.  Such  a  drive  may  consist  of  a  pair  of  plain  cylinder  wheels 
mounted  upon  parallel  shafts,  or  a  pair  of  beveled  wheels,  or  of  any 
other  arrangement  which  will  serve  in  the  transmission  of  motion  by 
rolling  contact. 

Driving  wheels  of  each  of  the  materials  named  in  the  table  below  wer* 
tested  in  peripheral  contact  with  driving  wheels  of  iron,  aluminum  and1 
type  metal,  All  the  wheels  were  1§  in,  diam, ;  the  face  of 


FRICTION  CLUTCHES. 


1179 


Wheels  was  13/4  in.,  and  that  of  the  driven  wheels  1/2  in.  Records  were 
made  of  the  pressure  of  contact,  of  the  coefficient  of  friction  developed, 

and  of  the  percentage  of  slip  resulting  from  the  development  of  the  said 
coefficient  of  friction.  Curves  were  plotted  showing  the  relation  of  the 
coefficient  and  the  slip  for  pressures  of  150  and  400  Ibs.  per  inch  width 
of  face  in  contact.  Another  series  of  tests  was  made  in  which  the  slip 
was  maintained  constant  at  2%  and  the  pressures  were  varied.  In  most 
of  the  combinations  it  was  found  that  with  constant  slip  the  coefficient 
ot  friction  diminished  very  slightly  as  the  pressure  of  contact  was  in- 
creased, so  that  it  may  be  considered  practically  constant  for  all  pres- 
sures between  150  and  400  Ibs.  per  sq.  in. 

The  crushing  strength  of  each  material  under  the  conditions  of  the 
test  was  determined  by  running  each  combination  with  increasing  loads 
until  a  load  was  found  under  which  the  wheel  failed  before  15,000  revo- 
lutions had  been  made.  The  results  showed  the  failure  of  the  several 
fiber  wheels  under  loads  per  inch  of  width  as  follows:  Straw  fiber 
750  Ibs.;  leather  fiber,  1,200  Ibs.;  tarred  fiber,  1,200  Ibs.;  leather,  750  Ibs.; 
sulphite  fiber,  700  Ibs.  One-fifth  of  these  pressures  is  taken  as  a  safe 
working  load.  The  coefficient  of  friction  approaches  its  maximum 
value  when  the  slip  between  driver  and  driven  wheel  is  2%.  The  safe 
working  horse-power  of  the  drive  is  calculated  on  the  basis  of  60%  the 
coefficient  developed  at  a  pressure  of  150  Ibs.  per  inch  of  width,  a  re- 
duction of  40%  being  made  to  cover  possible  decrease  of  the  coefficient 
in  actual  service  and  to  cover  also  loss  due  to  friction  of  the  journals. 
From  these  data  the  following  table  is  constructed  showing  the  H.P. 
that  may  be  transmitted  by  driving  wheels  of  the  several  materials 
named  when  in  frictionai  contact  with  iron,  aluminum  and  type  metal. 


The  formula  for  horse-power  is  H.P.  =       X 


=  KdWN,  in 


ooUUU 

which  d  =  diam.  in  inches,  W  =  width  of  face  in  inches,  P  =  safe  work- 
ing pressure  in  Ibs.  per  in.  of  width,  N  =  revs,  per  min.,  /  =  coefficient 
of  friction,  0.6  a  factor  for  the  decrease  of  the  coefficient  in  service  and 
for  the  loss  in  journal  friction,  K  a  coefficient  including  P,  /  and  the 
numerical  constants. 
COEFFICIENTS  OF  FRICTION  AND  HORSE-POWER  OF  FRICTION  DRIVES. 


On  Iron. 

On  Aluminum. 

On  Type  Metal. 

/ 

k 

/ 

k 

/ 

k 

0.00022 
0.00035 
0.00031 
0.00034 
0.00029 

Straw  fiber  

0.255 
0.309 
0.150 
0.330 
0.135 

0.00030 
0.00059 
0.00029 
0.00037 
0.00016 

0.273 
0.297 
0.183 
0.318 
0.216 

0.00033 
0.00057 
0.00035 
0.00035 
0.00026 

0.186 
0.183 
0.165 
0.309 
0.246 

Leather  fiber 

Tarred  fiber  

Sulphite  fiber 

Leather  

Horse-power  =  K  X  d  WN. 

Friction  Clutches.  —  Much  valuable  information  on  different  forms  of 
friction  clutches  is  given  in  a  paper  by  Henry  Souther  in  Trans.  A.  S.  M. 
E.,  1908,  and  in  the  discussion  on  the  paper.  All  friction  clutches  contain 
two  surfaces  that  rub  on  each  other  when  the  clutch  is  thrown  into  gear, 
and  until  the  friction  between  them  is  increased,  by  the  pressure  with 
which  they  are  forced  together,  to  such  an  extent  that  the  surfaces  bind 
and  enable  one  surface  to  drive  the  other.  The  surfaces  may  be  metal 
on  metal,  metal  on  wood,  cork,  leather  or  other  substance,  leather  on 
leather  or  other  substance,  etc.  The  surfaces  may  be  disks,  at  right 
angles  to  the  shaft,  blocks  sliding  on  the  outer  or  inner  surface,  or  both, 
of  a  pulley  rim,  or  two  cones,  internal  and  external,  one  fitting  in  the 
other,  or  a  band  or  ribbon  around  a  pulley.  The  driving  force  which  is 
just  sufficient  to  cause  one  part  of  the  clutch  to  drive  the  other  is  the 
product  of  the  total  pressure,  exerted  at  right  angles  to  the  direction  of 
sliding,  and  the  coefficient  of  friction.  The  latter  is  an  axceedingly 
variable  quantity,  depending  on  the  nature  and  condition  of  the  sliding 
surfaces  and  on  their  lubrication.  The  surfaces  must  have  sufficient 
area  so  that  the  pressure  per  square  inch  on  that  area  will  not  be  suffi- 
cient to  cause  undue  heating  and  wear.  The  total  pressure  on  the  parts 
of  the  mechanism  that  forces  the  surfaces  together  also  must  not  cause 
undue  wear  of  these  parts. 


1180 


GEARING. 


For  cone  clutches,  Reuleaux  states  that  the  angle  of  the  cone  should 
not  be  less  than  10°,  hi  order  that  the  parts  may  not  become  wedged 
together.  He  gives  the  coefficient  of  cast  iron  on  cast  iron,  for  such 
clutches,  at  0.15. 

For  clutches  with  maple  blocks  on  cast  iron  Mr.  Souther  gives  a  coeffi- 
cient of  0.37,  and  for  a  speed  of  100  r.p.m.  he  gives  the  following  table  of 
capacity  of  such  clutches,  made  by  the  Dodge  Mfg.  Co. 


Horse- 
power. 

Block 

Area,  Ins. 

Diam.  at 
Block,  Ins. 

Circumferen- 
tial Pull  at 
Block  Center, 
Lbs. 

Total 
Pressure. 

Total  Pres- 
sure per 
Sq.  In. 

25 
32 
50 
98 

120 
141 
208 
280 

16 
18 
21.5 
27.5 

1,960 
2,240 
2,900 
4.500 

5,300 
6,000 
7,800 
12.000 

44 
44.5 
37.5 
43.5 

Prof.  I.  N.  Hollis  has  found  the  coefficient  of  cork  on  cast  iron  to  be 
from  0.33  to  0.37,  or  about  double  that  of  cast  iron  on  cast  iron  or  on 
bronze.  A  set  of  cork  blocks  outlasted  a  set  of  maple  blocks  in  the  ratio 
of  five  to  one.  Prof.  C.  M.  Allen  has  found  the  torque  for  cork  inserts 
to  be  nearly  double  that  of  a  leather-faced  clutch  for  a  given  dimension. 

Disk  clutches  for  automobiles  are  made  with  frictional  surfaces  of 
leather,  bronze,  or  copper  against  iron  or  steel.  The  Cadillac  Motor  Car 
Co.  give  the  following:  Mean  radius  of  leather  frictional  surface  45/ie  ins; 
area  of  do.,  361/2  sq.  ins.;  axial  pressure,  1000  to  1200  IDS.;  H. P.  capacity 
at  400  r.p.m..  51/2  H.P.:  at  1400  r.p.m.,  10  H.P. 

C.  H.  Schlesinger  (Horseless  Age,  Oct.  2,  1907)  gives  the  following 
formula  for  the  ordinary  cone  clutch: 

H.P.  =  PfrR  -3-  63,000  sin.  0, 

in  which  P  =  assumed  pressure  of  engaging  spring  in  Ibs.,  /  =•  coeff.  of 
friction,  which  in  ordinary  practice  is  aoout  0.25;  r  ~  mean  radius  of 
the  cone,  ins.;  #=r.p.m.  of  the  motor;  0  =  angle  of  the  cone  with  the 
axis.  Mr.  Souther  says  the  value  of  /  =  0.25  is  probably  near  enough 
for  a  properly  lubricated  leather-iron  clutch. 

The  Hele-Shaw  clutch,  with  V-shaped  rings  struck  up  in  the  surfaces 
of  disks,  is  described  in  Proc.  Inst.  M.  E.,  1903.  A  clutch  of  this  form 
18  ins.  diam.  between  the  V's  transmitted  1000  H.P.  at  700  or  800  r.p.m. 

Coil  Friction  Clutches.  (H.  L.  Nachman,  Am.  Mach.,  April  1,  1909.) 
—  Friction  clutches  are  now  in  use  which  will  transmit  1000,  and  even 
more,  horse-power.  A  type  of  clutch  which  is  satisfactory  for  the  trans- 
mission of  large  powers  is  the  coil  friction  clutch.  It  consists  of  a  steel 
coil  wound  on  a  chilled  cast-iron  drum.  At  each  end  of  the  coil  a  head 
is  formed.  The  head  at  one  end  is  attached  to  the  pulley  or  shaft  that  is 
to  be  set  in  motion,  while  that  at  the  other  end  of  the  coil  serves  as  a 
point  of  application  of  a  force  which  pulls  on  the  coil  to  wind  it  on  the 
drum,  thus  gripping  it  firmly. 

The  friction  of  the  coil  on  the  drum  is  the  same  as  that  of  a  rope  or 
belt  on  a  pulley.  That  is,  the  relation  of  the  tensions  at  the  two  ends  of 
the  coil  may  be  found  from  the  equation  PlQ=efia  where  P=pull  at  fixed 
end  of  coil;  Q=pull  at  free  end  of  coil;  e—  base  of  natural  logarithms  = 
2.718;  fi  =  coefficient  of  friction  between  coils  and  drum;  and  a=  Angle 
subtended  by  coil  in  radian  measure,  =  6. 283  for  each  turn  of  coil. 

Values  of  P/Q  for  different  numbers  of  turns  are  as  follows,  assuming 
N  =  0.05  for  steel  on  cast  iron,  lubricated: 
No.  of  turns    1234567          8 


P/Q 


1.37     1.87     2.57     3.51     4.81     6.58     8.60     12.33 


If  D  =  diam.  of  drum  in  ins.,  N  =  revs.,  per  min.,  then  H.P.  *=nDNP*- 
(12  X  33.000)  =  0.00000793  DNP. 


HOISTING  AND  CONVEYING. 


1181 


HOISTING  AND  CONVEYING. 

Strength  of  Ropes  and  Chains.— For  the  weight  and  strength  of  rope 
for  hoisting  see  notes  and  tables  on  pages  410  to  416.  For  strength  of 
chains  see  page  264. 

Working  Strength  of  Blocks. 

(Boston  and  Lockport  Block  Co.,  1908.) 

REGULAR  BLOCKS  WITH  LOOSE  HOOKS— LOADS  IN  POUNDS 


Size,  Inches. 

5 

6 

8 

10 

12 

14 

Rope  diameter,  inches  .... 
2  single  blocks 

9/16 
150 

3/4 
250 

V8 
700 

1 

2000 

11/8 
4000 

H/4 

7000 

2  double  blocks  

250 

400 

1200 

4000 

8000 

12000 

2  triple  blocks  

400 

650 

1900 

6000 

12000 

19000 

LOADS  IN  TONS. 


WIDE  MORTISE  WITH 
LOOSE  HOOKS. 

EXTRA  HEAVY  WITH 
SHACKLES. 

Size,  inches  

8 

1/2 

2 

10 

I  1/4 

3 

4 

12 

15/16 

6 
8 

14 

15/8 
6 
8 
10 

16 

13/4 
10 
12 
14 

18 
2 

20 
21/4 

22 

21/2 

24 
3 

Rope,  diam.,  in..  .  . 
2  single  blocks  
2  double  blocks.  .  .  . 
2  triple  blocks  
2  fourfold  blocks  .  .  . 

25 

30 
40 

30 
35 
45 

35 
40 
55 

40 
50 
70 

WORKING  LOADS  FOR  A  PAIR  OF  WIRE-ROPE  BLOCKS-TONS 


LOOSE  HOOKS. 

SHACKLES. 

Sheave 
Diam.,  In. 

Two 
Singles. 

Two 
Doubles. 

Two 
Triples. 

Two 

Singles. 

Two 
Doubles. 

Two 
Triples. 

s: 

10 

H 

16 
18 

3 

4 

6 
8 

4 

6 
7 

8 
10 

5 
6 

8 
10 
12 

4 
6 
8 
10 
12 
15 

5 
8 

to 

12 
15 

20 

6 
10 
12 
15 
20 
25 

Chain  Blocks. — Referring  to  the  table  on  the  next  page,  the  speed 
of  a  chain  block  is  governed  by  the  pull  required  on  the  hand  chain 
and  the  distance  the  hand  chain  must  travel  to  lift  the  load  the  re- 
quired distance.  The  speeds  are  given  for  short  lifts  with  men  ac- 
customed to  the  work;  for  continuous  easy  lifting  two-thirds  of  these 
speeds  are  attainable.  The  triplex  block  lifts  rapidly,  and  the  speed 
increases  for  light  loads  because  the  length  of  hand  chain  to  be  overhauled 
s  small.  This  fact  also  enables  the  operator  to  lower  the  load  very 
quickly  with  the  triplex  block.  The  12-  to  20-ton  triplex  blocks  are 
provided  with  two  separate  hand  wheels,  thus  permitting  two  men  to 
hoist  simultaneously,  thereby  securing  double  speed.  In  the  triplex 
block  the  power  is  transmitted  to  the  hoisting-chain  wheel  by  means  of  a 
train  of  spur  gearing  operated  by  the  hand  chain.  In  the  duplex  block 
the  power  is  transmitted  through  a  worm  wheel  and  screw.  In  the  dif- 
ferential block  the  power  is  applied  by  pulling  on  the  slack  part  of  the 
load  chain  and  the  force  is  multiplied  by  means  of  a  differential  sheave. 
(See  page  539.)  The  relative  efficiency  and  durability  of  the  three  types 
are  as  follows: 


Differen- 
tial. 

Duplex. 

Triplex. 

Relative  efficiency  

35 

50 

100 

Relative  durability  

20 

80 

100 

Relative  cost  

40 

80 

100 

1182 


HOISTING  AND   CONVEYING. 


Chain  Block  Hoisting  Speeds. 

(Yale  &  Towne  Mfg.  Co.,  1908.) 


.9 
fr* 

F 

Pull 
in  Pounds  re- 
quired on 
Hand-Chain 
to  Lift 
Full  Loads. 

Feet  of  Hand- 
Chain  to  be 
Pullea  by 
Operator  to 
Lift  Load 
One  Foot 
High. 

Hoisting  Speeds.      Feet  per  Minute 
Attainable  and  No.  of  Men  re- 
quired for  Hoisting  Full  Loads 
without  Pulling  over  80  Lb. 

Triplex. 

Duplex. 

Differ- 
ential. 

H 

9 

5 

H 

X 
5 

"ft 

Q 

I1 

1 

"a 

& 

X 

0> 

"ft 
Q 

L 
& 

Q 

"3 
£ 

t»-jT3 

&  3 

H.3 

<3-d 

S3 

a 

*8   . 
6  § 
£S 
•j— 

I 

•8  . 

d§ 
£S 

H— 

=3 
3 

&H 

IM 

°fl 

6£ 
&* 

V4 
,V3 

u/2 

3 
6 
8 
10 
12 
16 
20 

7? 

18 

6. 
6. 
3.70 
2.50 
2.30 
2.30 

1 
2 
3 
3 
4 
7 

62 
82 
110 
120 
114 
124 
110 
130 
135 
140 
130* 
135* 
140* 

68 
87 
94 
115 
132 
142 
145 
145 
160 
160 

122 
216 
246 
308 
557 

21 
31 
35 
42 
69 
84 
126 
126 
168 
210 
176* 

40 
59 
80 
93 
126 
155 
195 
252 
310 
390 

24 
30 
36 

42 
38 

8. 
4. 
4.8 
3.6 
2.3 
1.7 
1.3 
1.1 
0.8 
0.6 
1   1 

16. 
8. 
9.6 
7.2 
4.6 
3.5 
2.6 
2.2 
1.6 
1.2 
?  ? 

24. 
12. 
14.4 
10.8 
6.9 
5.2 
3.9 
3.3 
2.4 
1.8 
1  1 

1 
I 

2 
2 
2 
2 
2 
2 
2 
2 
4 

4. 
2. 
2.40 
1.80 
1.10 
0.80 
0.65 
0.50 
0.35 
0.30 

1 

1 

2 
2 
2 
2 
2 
2 
2 
2 

168* 

0  8 

1  6 

?  4 

4 

710* 

0.6 

1.2 

1.8 

4 

*  On  each  of  the  two  hand-chains. 

t  The  number  of  men  is  based  on  each  man  pulling  not  over  80  Ib 
One  man  pulling  160  Ib.  or  less,  as  given  in  the  first  two  columns,  can  lift 
the  full  capacity  of  any  Triplex  or  Duplex  Block. 

Efficiency  of  Hoisting  Tackle.  —  (S.  L.  Wonson,  Eng.  News,  June 
11,  1903. 


1  1/4  to  2-in.  Manila  rope. 

Parts  of  line. 

2 

3 

4 

5 

6 

7 

8 

9 

Ratio  of  load  to  pull 

1  91 

?  64 

'\  10 

1  84 

4  '-H 

4  7? 

5  OH 

5  M 

Efficiency,  per  cent  

96 

88 

,83 

77 

72 

67 

64 

60 

3/4-in.  Wire  rope. 

Parts  of  line. 

3 

4 

5 

6 

7 

8 

9 

10 

11  1   12 

13 

Ratio  load  to  pull  
Efficiency,  per  cent  

2.73 
91 

3.47 
87 

4.11 
82 

4.70 
78 

5.20 
74 

5.68 
71 

6.08 
68 

6.46 
65 

6.787.08 
62  1  59 

7.34 
56 

Proportions  of  Hooks. — The  following  formulae  are  given  by  Henry 
R.  Towne,  in  his  Treatise  on  Cranes,  as  a  result  of  an  extensive  experi- 
mental and  mathematical  investigation.  They  apply  to  hooks  of 
capacities  from  250  Ib.  to  20,000  Ib.  Each  size  of  hook  is  made  from 
some  commercial  size  of  round  iron.  The  basis  in  each  case  is.  there- 
fore, the  size  of  iron  of  which  the  hook  is  to  be  made,  indicated  by  A 
in  the  diagram.  The  dimension  D  is  arbitrarily  assumed.  The  other 
dimensions,  as  given  by  the  formulae,  are  those  which,  while  preserving 
a  proper  bearing-face  on  the  interior  of  the  hook  for  the  ropes  or  chains 
which  may  be  passed  through  it,  give  the  greatest  resistance  to  spread- 
ing and  to  ultimate  rupture,  which  the  amount  of  material  in  the  original 
bar  admits  of.  The  symbol  A  is  used  to  indicate  the  nominal  capacity 
of  the  hook  in  tons  of  2000  Ib.  The  formulae  which  determine  the  lines 


HOOKS.  1183 

of  the  other  parts  of  the  hooks  of  the  several  sizes  are  as  follows,  the 
measurements   being  all    expressed  in 
inches : 

D  =  0.5  A    +  1.25; 

E  =  0.64  A+  1.60; 

F  =  0.33  A +  0.85; 

G  =  0.75  D; 

H  =  1.08  A; 

/  =  1.33  A; 

J  =  1.20  A; 

K=  1.13  A; 

L  =  1.05  A; 
M=  0.50^4; 

AT  =0.85  £-0.16; 

O  =  0.363  A  +  0.66; 

Q  =  0.64  A  +  1.60; 

U=  0.866  A. 

The  dimensions  A  are  necessarily 
based  upon  the  ordinary  merchant  sizes 
of  round  iron.  The  sizes  which  it  has 
been  found  best  to  select  are  the  follow- 
ing: FIG.  189. 
Capacity  of  hook: 

1/8       1/41/2          111/22          345          6          8       10  tons 
Dimension  A: 

5/8      H/16       3/4        11/16        11/4      13/8         1  8/4      2      21/4        21/2        2  7/8    31/4    in. 

Experiment  has  shown  that  hooks  made  according  to  the  above  formulae 
will  give  way  first  by  opening  of  the  jaw,  which,  however,  will  not 
occur  except  with  a  load  much  in  excess  of  the  nominal  capacity  of  the 
hook.  This  yielding  of  the  hook  when  overloaded  becomes  a  source  of 
safety,  as  it  constitutes  a  signal  of  danger  which  cannot  easily  be  over- 
looked, and  which  must  proceed  to  a  considerable  length  before  rupture 
will  occur  and  the  load  be  dropped. 

Heavy  Crane  Hooks. — A.  E.  Holcomb,  vice-pres.  of  the  Earth  Mov- 
ing Machinery  Co.,  contributes  the  following  (1908).  Seven  years  ago, 
while  engaged  in  the  design  of  a  100- ton  crane,  I  made  a  study  of  the 
variations  in  strength  with  the  different  sectional  forms  for  hooks  in  most 

i    common  use.  As  a  result  certain  values  which  gave  the  best  results  were 

!  substituted  in  "Gordon's"  formula  and  a  formula  was  thereby  obtained 
which  was  good  for  hooks  of  any  size  desired,  provided  the  proper  allowable 
fiber  stress  per  square  inch  was  made  use  of  when  designing.  From  this 

*  formula  the  enclosed  table  was  made  up  and  was  published  in  the  American 
Machinist  of  Oct.  31,  1901.  Since  that  time  hundreds  of  hooks  of  cast 
or  hammered  steel  have  been  designed  and  made  according  to  my  formula, 

1    and  not  one  of  them,  so  far  as  I  know,  has  ever  failed. 

The  Industrial  Works,  Bay  City,  Michigan,  manufacturers  of  heavy 
cranes,  in  December,  1904,  made  the  following  test  under  actual  working 

i    conditions: 

A  hook  was  made  of  hammered  steel  having  an  elastic  limit  or  yield 
point  at  approximately  36,000  Ibs.  per  sq.  in.  fiber  stress  and  having  the 
following  important  dimensions:  d  =  75/8  in.;  r  =  41/2  in.;  D  =  207/i6in. 

When  the  applied  load  reached  150,000  Ibs.  the  hook  straightened  out 
until  the  opening  at  the  mouth  of  the  hook  was  21/2  in.  larger  than 
formerly,  and  the  distance  from  center  of  action  line  of  load  to  center  of 
gravity  of  section  was  found  to  have  decreased  1/2  in.,  at  which  point  the 
nook  held  the  load.  Upon  increasing  the  load  still  further,  the  hook 
opened  still  more.  From  the  dimensions  of  the  hook  as  originally  formed, 

i  we  find  from  the  formula  or  table  that  the  fiber  stress  with  a  load  of 
150,000  Ibs.  was  37,900  Ibs.  per  sq.  in.,  or  in  excess  of  the  yield  point, 

!  whereas  making  use  of  the  dimensions  obtained  from  the  hook  when  it 
held  we  find  that  the  fiber  stress  per  square  inch  was  reduced  to  35,940  Ibs., 
or  under  the  yield  point. 

The  designer  must  use  his  own  judgment  as  to  the  selection  of  a  proper 
allowable  fiker  stress ,  being  governed  therein  by  the  nature  of  the  material 


1184 


HOISTING  AND  CONVEYING. 


to  be  used  and  the  probability  of  the  hookibeing  overloaded  at  some  time. 
Under  average  conditions  I  have  made  use  of  the  following  values  for  (/): 


Values  of  (/)  in  pounds  for  a  load  of  — 

1,000  to 
5000 
Ibs. 

5,000  to 
15,000 
Ibs. 

15,000 

to 
30,000 
Ibs. 

30,000 
to 
60,000 

Ibs. 

60,000 
to 
100,000 

Ibs. 

100,000 
Ibs. 
and  up. 

Cftst  iron 

2,000 
6,000 
12,000 

2,500 
8,000 
16,000 

Steel  casting  

10,000 
20,000 

11,250 
22,500 

12,500 
25,000 

"27,566' 

Hammered  steel  

Mr.  Hplcomb's  formula  is  given  below,  and  his  table  in  condensed 
form  is  given  on  page  i!85. 

DIRECTIONS.  —  P  and  /being  known,  assume  r  to  suit  the  requirements 
for  which  the  hook  is  to  be  designed.  Divide  P  by /and  find  the  quotient 
in  the  column  headed  by  the  required  r.  At  the  side  of  the  Table,  in  the 
same  row,  will  be  found  the  necessary  depth  of  section,  d. 

Notation.  —P  =  load.  S  =  area  of  section.  R*  =  square  of  the  radius 
of  gyration.  /  =  allowable  fiber  stress  in  Ibs.  per  sq.  in.,  20,000  Ibs.  for 
hammered  steel.  For  other  letters  see  Fig.  190. 

?.  =  — ~__ .    General  formula. 


n—     S  =  - 


- 


<*2(&2+   4&C  +  C2). 


(1) 


Vr^X^ (3) 

b  +  c       3 

:^  +  r.          .    (4) 


••  0.66d;  c  =  0.22d, 


Assuming  b 
we  have: 


7.44  d+  12.393  r 


-  K.      (5) 


D  =  2r+  1.5  d. 


FIG.  190. 

For  values  of  K  and  r  intermediate  to  those  given  in  the  taoie  approx- 
imate values  of  d  may  be  found  by  interpolation.  Thus,  for  K  =  3.700, 
r  =»  2.75. 

r  =  2.5  3.0       Int.  for  2.75 

K  =  3.462  3.213  3.338 

K  =  4.128  3.842  3.985 

((3.700-3.338)) 


Tabular  values, 

d  =  6.50 
d  =  7.00 


Whence: 


=  6.5-t- 


X  (7.0  -  6.5)  =  6.78. 


1(3.985-3.338)) 

In  like  manner,  if  d  and  r  are  given  the  value  of  K  and  the  corresponding 
safe  load  may  be  found. 

Strength  of  Hooks  and  Shackles.  (Boston  and  Lockport  Block  Co., 
1908.) — Tests  made  at  the  Watertown  arsenal  on  the  strength  of  hooks 
and  shackles  showed  that  they  failed  at  the  loads  given  in  the  table  on 
page  1 185.  In  service  they  should  be  subjected  to  only  50  %  of  the  figures 
in  the  table.  Ordinarily  the  hook  of  a  block  gives  way  first,  and  where 
heavy  weights  are  to  be  handled  shackles  are  superior  to  hooks  and 
should  be  used  wherever  possible. 

Horse-power  Required  to  Raise  a  Load  at  a  Given  Speed.  —  H.P.  = 


Gross  weight  in  Ib. 


X  speed  in  ft.  per  min.    To  this  add  25  %  to  50  %  for 


33,000 
friction,  contingencies,  etc.     The  gross  weight  includes  the  weight  of 


HOOKS. 


1185 


Values  of  K. 


d. 


0.50  |  0.75  |  1.00  |   1.50  [  2.00  |  2.50  |  3.00  |  3.50  |  4.00  |  5.00  [  6.00 


2.00 
2.25 
2.50 
2.75 
3.00 
3.25 
3.50 
3.75 
4.00 
4.25 
4.50 
4.75 
5.00 
5.25 
5.50 
5  75 

0.379 
.496 
.629 
.778 
.944 
1.143 
1.342 
1.558 
1.790 
2.038 
2.304 
2.586 
2.884 
3.214 
3.532 

0.331 

.437 
.559 
.697 
.852 
.039 
.226 
.429 
.649 
.886 
2.138 
2.408 
2.694 
3.008 
3.315 
3.651 

0.292 
.391 
.504 
.632 
.776 
.953 
.129 
.321 
.530 
.754 
.995 
2.253 
2.527 
2.828 
3.124 
3.447 
3.787 
4.516 
5.311 
6.173 
7.102 
8.096 
9.158 

0.240 
.329 
.420 
.532 
.659 
.801 
.957 
.148 
.336 
.544 
.760 
.996 
2.248 
2.525 
2.801 
3.101 
3.418 
4.100 
4.848 
5.661 
6.540 
7.485 
8.496 
9.574 
10.788 
12.098 
13.374 
14.717 
16.126 
17.601 

0.203 
.275 
.360 
.460 
.572 
.700 
.841 
.998 
1.187 
1.373 
1.575 
1.793 
2.072 
2.281 
2.538 
2.818 
3.115 
3.754 
4.459 
5.227 
6.061 
6.960 
7.924 
8.954 
10.220 
11.381 
12.608 
13.901 
15.261 
16.686 
18.178 
19.735 
21.359 
23.050 
24.807 
26.630 
28.520 

0.176 
.239 
.316 
.404 
.506 
.621 
.750 
.893 
.067 
.239 
.426 
.627 
.843 
2.081 
2.321 
2.583 
2.861 
3.463 
4.128 
4.855 
5.648 
6.504 
7.424 
8.409 
9.460 
10.746 
11.922 
13.173 
14.485 
15.862 
17.305 
18.814 
20.389 
22.031 
23.738 
25.511 
27.351 

0.155 
.212 
.281 
.360 
.454 
.559 
.677 
.808 
.953 
.129 
.321 
.490 
.691 
.913 
2.140 
2.385 
2.646 
3.213 
3.842 
4.533 
5.287 
6.104 
6.984 
7  928 
8.932 
10.008 
11  316 
12.518 
13.785 
15.117 
16  514 
17.976 
19.504 
21.098 
22.758 
24.483 
26.274 

"0.411 

.508 
.617 
.738 
.873 
.038 
.214 
.374 
.563 
.770 
.983 
2.215 
2.461 
2.998 
3.594 
4.252 
4.970 
5.750 
6.593 
7.498 
8.467 
9.499 
10.766 
11.926 
13.150 
14.442 
15.792 
17.210 
18.694 
20.242 
2  .846 
23.535 
25.388 

• 

0.805 
0.943 
.124 
.275 
.453 
.647 
.849 
2.067 
2.300 
2.809 
3.377 
4.003 
4.689 
5.436 
6.243 
7.113 
8.044 
9.039 
10.267 
11.388 
12.572 
13.820 
15.132 
16.508 
17.948 
19.453 
2  .023 
22.658 
24.358 

1.628 
1.825 
2.035 
2.496 
3.012 
3.584 
4.213 
4.900 
5.645 
6.450 
7.316 
8.241 
9.228 
10.448 
11.558 
12.730 
13.965 
15.263 
16.624 
18.049 
19.536 
21.088 
22.704 



6.00 
6.50 
7.00 
7.50 
8.00 
8.50 
9.00 
9.50 
10.00 
10.50 
11.00 
11.50 
12.00 
12.50 
13.00 
13.50 
14.00 
14.50 
15.00 
15.50 
16.00 

4.003 
4.757 
5.578 

2.246 
2.719 
3.244 
3.825 
4.460 
5.152 
5.901 
6.708 
7.573 
8.498 
9.482 
10.697 
11.802 
12.967 
14.195 
15.484 
16.835 
18.248 
19.724 
21.262 

Strength  of  Hooks  and  Shackles. 


HOOKS.*                        |                       SHACKLES. 

4 

g 

4 

£ 

M 

c? 

I 

Inches. 

Z% 
1| 

l| 

Description   of 
Fracture. 

tnches. 

-£a  ^ 

|j 

Description     of 
Fracture. 

,1" 

H 

1 

i 

S 

1 

H 

1/2 

1  890 

isfo 

17310 

103  750 

Eye  of  shackle 

9/16 

2^560 

H/o 

20*940 

119800 

Eye  of  shackle. 

•fc 

3,020 
4,470 

15/8 
13/4 

23,670 
27,420 

125,900 
146,804 

Eye  of  shackle. 
Sheared    shackle 

20,700 

Eye  of  shackle. 

7/8 

6,280 

38,100 

Eye  of  shackle. 

pin. 

1 

12,600 
13,520 

51,900 
62,900 

Eye  of  shackle. 
Sheared    shackle 

17/8 

36,120 
38,100 

162,700 
196,600 

Eye  of  shackle. 
Shackle  at  neck 

pin. 

of  eye. 

H/4 

16,800 

75,200 

Eye  of  shackle. 

21/2 

55.380 

210,400 

Eye  of  shackle. 

*  AU  the  hooks  failed  by  straightening  the  hook, 


1186  HOISTING  AND  CONVEYING. 

cage,  rope,  etc.  In  a  shaft  with  two  cages  balancing  each  other  use  the 
net  load  +  weight  of  one  rope,  instead  of  the  gross  weight. 

To  find  the  load  which  a  given  pair  of  engines  will  start.  —  Let  A  =  area 
of  cylinder  in  square  inches,  or  total  area  of  both  cylinders,  if  there  are 
two;  P  =  mean  effective  pressure  in  cylinder  in  Ib.  per  sq.  in.;  S  =  stroke 
of  cylinder,  inches;  C  =  circumference  of  hoisting-drum,  inches;  L  — 
load  lifted  by  hoisting-rope,  Ib.;  F  =  friction,  expressed  as  a  diminution 

of  the  load.    Then  L  =  A  x^x2^  _  Ff 

An  example  in  ColVy  Engr.,  July,  1891,  is  a  pair  of  hoisting-engines 
24*  X  40",  drum  12  ft.  diam.,  average  steam-pressure  in  cylinder  = 
59.5  Ib.;  A  =  904.8;  P  =  59.5;  S  =  40;  C  =  452.4.  Theoretical  load, 
not  allowing  for  friction,  A  X  P  X  2  S  -*-  C  •*  9589  Ib.  The  actual  load 
that  could  just  be  lifted  on  trial  was  7988  Ib.,  making  friction  loss  F  = 
1601  Ib.,  or  20  +  per  cent  of  the  actual  load  lifted,  or  162/3%  of  the  theo- 
retical load. 

.  The  above  rule  takes  no  account  of  the  resistance  due  to  inertia  of 
the  load,  but  for  all  ordinary  cases  in  which  the  acceleration  of  speed  of 
the  cage  is  moderate,  it  is  covered  by  the  allowance  for  friction,  etc.  The 
resistance  due  to  inertia  is  equal  to  the  force  required  to  give  the  load  the 
velocity  acquired  in  a  given  time,  or,  as  shown  in  Mechanics,  equal  to  the 

wv 
product  of  the  mass  by  the  acceleration,  or  R  =  —^  •  in  which  R  ~ 

resistance  in  Ib.  due  to  inertia;  W  =  weight  of  load  in  Ib.;  V  =  maximum 
velocity  in  ft.  per  second;  T  =  time  in  seconds  taken  to  acquire  the 
velocity  V;  g  =  32.16.  ' 

Safe  Loads  for  Ropes  and  Chains. — The  table  on  p.  1187  was  pre- 
pared by  the  National  Founder's  Association  and  published  hi  Indust. 
Eng.,  Sept.,  1914.  It  shows  the  safe  loads  that  can  be  carried  by  wire 
rope,  crane  chain  and  manila  rope  of  the  sizes  given  when  used  hi  the 
positions  and  combinations  shown.  The  loads  in  the  table  are  lower 
than  those  usually  specified,  in  order  to  insure  absolute  safety.  When 
handling  molten  metal,  the  ropes  and  chains  should  be  25  per  cent 
stronger  than  the  figures  in  the  table. 

Effect  of  Slack  Rope  upon  Strain  in  Hoisting.  —  A  series  of  tests 
with  a  dynamometer  are  published  by  the  Trenton  Iron  Co.,  which  show 
that  a  dangerous  extra  strain  may  be  caused  by  a  few  inches  of  slack  rope. 
In  one  case  the  cage  and  full  tubs  weighed  11,300  Ib.;  the  strain  when  the 
load  was  lifted  gently  was  11,525  Ib.;  with  3  in.  of  slack  chain  it  was 
19,025  Ib.;  with  6  in.  slack  25,750  Ib.,  and  with  9  in.  slack  27,950  Ib. 

Limit  of  Depth  for  Hoisting.  —  Taking  the  weight  of  a  cast-steel 
hoisting-rope  of  IVsm.  diameter  at  2  Ib.  per  running  foot,  and  its  break- 
Ing  strength  at  84,000  Ib.,  it  should,  theoretically,  sustain  itself  until 
42  000  feet  long  before  breaking  from  its  own  weight.  But  taking  the 
usual  factor  of  safety  01  7,  then  the  safe  working  length  of  such  a  rope 
would  be  only  6000  ft.  If  a  weight  of  3  tons  is  now  hung  to  the  rope, 
which  is  equivalent  to  that  of  a  cage  of  moderate  capacity  with  its  loaded 
cars  the  maximum  length  at  which  such  a  rope  could  be  used,  with  the 
factor  of  safety  of  7,  is  3000  ft.,  or 

2  x  +  6000  —  84,000  ~  7;  /.  X  =  3000  feet. 

This  limit  may  be  greatly  increased  by  using  special  steel  rope  of  higher 
strength,  by  using  a  smaller  factor  of  safety,  and  by  using  taper  ropes. 
(See  paper  by  H.  A.  Wheeler,  Trans.  A.  I.  M.  E  xix.  107.) 

Large  Hoisting  Records.  —  At  a  colliery  in  North  Derbyshire  during 
the  first  week  in  June,  1890,  6309  tons  were  raised  from  a  depth  of  o09 
yards,  the  time  of  winding  being  from  7  a.m.  to  3.30  p.m. 

At  two  other  Derbyshire  pits,  170  and  140  yards  in  depth,  the  speed  of 
winding  and  changing  has  been  brought  to  such  perfection  that  tubs  are 
drawn  and  changed  three  times  in  one  minute.  (Proc.  Inst.  M.  E.,  1890.) 

At  the  Nottingham  Colliery  near  Wilkesbarre,  Pa.,  in  Oct.,  1891,  70,152 
tons  were  shipped  in  24.15  days,  the  average  hoist  per  day  being  1318  mine 
cars  The  depth  of  hoist  was  470  ft.,  and  all  coal  came  from  9ne opening. 
The'engines  were  first  motion,  22  X48  in.,  conical  drums  4ft.  1  in.  long,  7ft. 
diameter  at  small  end  and  9  ft.  at  large  end.  (Eng'g  News,  Nov.  1891 .) 
Large  Engines. — Two  34  X  60  in.  four-cylinder  engines  built  by 
Nordberg  Mfg.  Co.  for  the  Tamarack  copper  mine  at  Calumet,  Mich.,  ar« 


PNEUMATIC  HOISTING. 


1187 


Safe  Loads  for  Ropes  and  Chains. 


When  Used 

When  Used 

When  Used 

When  Used 

NOTE.     The  safe  loads  in 
table  are  for  each  SINGLE 

Straight. 

at  60° 
Angle. 

at  45° 
Angle. 

at  30° 
Angle. 

rope  or  chain. 

When  used 

double  or  in  other  multiples 

the  loads  may  b 

e  increased 

yv 

proportionately. 

/\ 

^X 

Dia. 

In. 

Lb. 

Lb. 

Lb. 

Lb. 

PLOW   STEEL   WIRE 

3/8 

.     1,500 

1,275 

1,050 

750 

KROPE. 

1/2 

2,400 

2,050 

1,700 

1,200 

5/8 

4,000 

3,400 

2,800 

2,000 

strands  of 

9  or 

3/4 

6,000 

5,100 

4,200 

3,000 

37  wires.] 

7/8 

8,000 

6,800 

5,600 

4,000 

1 

10,000 

8,500 

7,000 

5,000 

If  crucible  steel  rope 

1  1/8 

13,000 

11,000 

9,000 

6,500 

is  used  reduce  1 

oads 

H/4 

16,000 

13,500 

11,000 

8,000 

one-fifth. 

13/8 

19,000 

16,000 

13,000 

9,500 

1  1/2 

22,000 

19,000            16,000 

11,000 

3     V* 

600 

500 

425 

300 

CRANE  CH/ 

LlN. 

3    3/8 

1,200 

1,025 

850 

600 

2,400 

2,050 

1,700 

1,200 

[Best    grade    of 

O     5/g 

4,000 

3,400 

2,800 

2,000 

wrought  iron,  h 

and- 

*•*    3/4 

5,500 

4,700 

3,900 

2,750 

made,  tested,  short- 
link  chain.] 

6  H/8 

7,500 
9,500 
12,000 

6,400 
8,000 
10,200 

5,200 
6,600 
8,400 

3,700 
4,700 
6,000 

.2  1  1/4 

15,000 

12,750 

10,500 

7,500 

^  13/8 

22,000 

19,000 

.16,000 

11,000 

Dia. 

Cir. 

In. 

In. 

3/8 

1 

120 

100 

85 

60 

MANILA  ROPE. 

1/2 

U/2 

250 

210 

175 

125 

5/8 

2 

360 

300 

250 

180 

3/4 

21/4 

520 

440 

360 

260 

[Best  long  fibre 

7/8 

23/4 

620 

520 

420 

300 

grade.] 

1 

3 

750 

625 

525 

375 

H/8 

31/2 

.     1,000 

850 

700 

500 

H/4 

33/4 

1,200 

1,025 

850 

600 

H/2 

41/2 

1,600 

1,350 

1,100 

800 

13/4 

51/2 

2,100 

1,800 

1,500 

1,050 

2 

6 

2,800 

2,400 

2,000 

1,400 

21/2 

71/2 

4,000 

3,400 

2,800 

2,000 

3 

9 

6,000 

5,100 

4,200 

3,000 

designed  to  lift  a  load  from  a  depth  of  6,000  ft.  at  an  average  hoisting 
speed  of  5,000  ft.  per  min.  The  load  is  made  up  of  ore,  12,000  Ibs. ;  cage 
and  cars,  8,500  Ibs.;  6,500  ft.  9f  1^-in.  rope,  21,200  Ibs.;  total,  41,700 
Ibs.  The  center  lines  of  the  cylinders  are  placed  90°  apart  and  the  cranks 
135°  apart.  By  this  arrangement  three  of  the  four  cylinders  are  al- 
ways available  for  starting  the  hoist. 

Pneumatic  Hoisting.  (H.  A.  Wheeler,  Trans.  A.  I.  M.  E.  xix,  107.) — 
A  pneumatic  hoist  was  installed  in  1876  at  Epinac,  France,  consisting 
of  two  continuous  air-tight  iron  cylinders  extending  from  the  bottom  to 
the  top  of  the  shaft.  Within  the  cylinder  moved  a  piston  from  which 
was  hung  the  cage.  It  was  operated  by  exhausting  J/he  air  from,  above 
the  piston,  the  lower  side  being  open  to  the  atmosphere.  Its  use  was 
discontinued  on  account  of  the  failure  of  the  mine.  Mr.  Wheeler  gives 
a  description  of  the  system,  but  criticizes  it  as  not  being  equal  on  the 
whole  to  hoisting  by  steel  ropes. 

Pneumatic  hoisting-cylinders  using  compressed  air  have  been  used  at 
blast-furnaces,  the  weighted  piston  counterbalancing  the  weight  of  the 


1188  HOISTING  AND   CONVEYING. 

cage,  and  the  two  being  connected  by  a  wire  rope  passing  over  a  pulley- 
sheave  above  the  top  of  the  cylinder.  In  the  more  modern  furnaces 
steam-engine  or  electric  hoists  are  generally  used. 

Electric  Mine-Hoists. — An  important  paper  on  this  subject, 'by  D. 
B.  Rushfhore  and  K.  A.  Pauly,  will  be  found  ill  Trans.  A.  I.  M.  E.t 
1910.  See  also  Electrical  Hoisting,  page  1464. 

Counterbalancing  of  Winding-engines.  (H.  W.  Hughes,  Columbia 
JColl.  Qly.)  —  Engines  running  unbalanced  are  subject  to  enormous 
variations  in  the  load;  for  let  W  =  weight  of  cage  and  empty  tubs,  say 
6270  Ib.;  c  =  weight  of  coal,  say  4480  Ib.;  r  =  weight  of  hoisting  rope, 
eay  6000  Ib.;  r'  =  weight  of  counterbalance  rope  hanging  down  pit,  say 
6000  Ib.  The  weight  to  be  lifted  will  be: 

If  weight  of  rope  is  unbalanced.       II  weight  of  rope  is  balanced. 
At  beginning  of  lift:  •» 

W  +  c  +  r  -  W  or  10,480  Ib.  W  +  c  +  r  -  (W  +  r'), 

At  middle  of  lift: 


or 

f-4480 
Ib. 


2      2     \ 

At  end  of  lift: 

W  +  c  -  (W  +  r)  or  minus  1520  Ib.  W  +  c  +  r'  -  (W  +  r), , 
That  counterbalancing  materially  affects  the  size  of  winding-engines  is 
shown  by  a  formula  given  by  Mr.  Robert  Wilson,  which  is  based  on  the 
fact  that  the  greatest  work  a  winding-engine  has  to  do  is  to  get  a  given 
mass  into  a  certain  velocity  uniformly  accelerated  from  rest,  and  to  raise 
a  load  the  distance  passed  over  during  the  time  this  velocity  is  being 
obtained. 

Let  W  —  the  weight  to  be  set  in  motion:  one  cage,  coal,  number  of. empty 
tubs  on  cage,  one  winding  rope  from  pit  head-gear  to  bottom, 
and  one  rope  from  banking  level  to  bottom. 
v  =  greatest  velocity  attained,  uniformly  accelerated  from  rest; 
g  =  gravity  =  32.2; 

t  =  time  in  seconds  during  which  v  is  obtained; 
L  =  unbalanced  load  on  engine; 
R  =  ratio  of  diameter  of  drum  and  crank  circles; 
P  =  average  pressure  of  steam  in  cylinders; 
N  =  number  of  cylinders; 

S  =  space  passed  over  by  crank-pin  during  time  t : 

(7  =  2/3,  constant  to  reduce  angular  space  passed  through  by  crank  to 

the  distance  passed  through  by  the  piston  during  the  time  t; 

A  =  area  of  one  cylinder,  without  margin  f9r  friction.     To  this  an 

addition  for  friction,  etc.,  of  engine  is  to  be  made,  varying 

from  10  to  30%  of  A. 

1st.  Where  load  is  balanced. 


A 


PNSC 

2d.   Where  load  is  unbalanced: 

The  formula  is  the  same,  with  the  addition  of  another  term  to  allow  for 

the  variation  in  the  lengths  of  the  ascending  and  descending  ropes.     In 

[this  case 

/ii  =  reduced  length  of  rope  in  t  attached  to  ascending  cage; 
fe2  =  increased  length  of  rope  in  t  attached  to  descending  cage; 
w  «  weight  of  rope  per  foot  in  pounds.    Then 

\fWv\  ,   (  /,  vt\       hiw  4-  hzw  i  "1  p 
l(-2^)+{(L2)-          2         \\R 
~~ 


Applying  tne  above  formula  when  designing  new  engines,  Mr.  Wilson 

found  that  30  in.  diameter  of  cylinders  would  produce  equal  results,  when 

balanced,  to  those  of  the  36-in.  cylinder  in  use,  the  latter  being  unbalanced. 

Counterbalancing  may  be  employed  in  the  following  methods: 

(a)   Tapering  Rope.  —  At  the  initial  stage  the  tapering  rope  enables  us 

to  wind  from  greater  depths  than  is  possible  with  ropes  of  uniform  section. 


CRANES.  1189 

The  thickness  of  such  a  rope  at  any  point  should  only  be  such  as  to  safely 
bear  the  load  on  it  at  that  point. 

With  tapering  ropes  we  obtain  a  smaller  difference  between  the  initial 
and  final  load,  but  the  difference  is  still  considerable,  and  for. perfect 
equalization  of  the  load  we  must  rely  on  some  other  resource.  The  theory 
of  taper  ropes  is  to  obtain  a  rope  of  uniform  strength,  thinner  at  the  cage 
end  where  the  weight  is  least,  and  thicker  at  the  drum  end  where  it  is 
greatest. 

(6)  The  Counterpoise  System  C9nsists  of  a  heavy  chain  working  up  and 
down  a  staple  pit,  the  motion  being  obtained  by  means  of  a  special  small 
drum  placed  on  the  same  axis  as  the  winding  drum.  It  is  so  arranged 
that  the  chain  hangs  in  full  length  down  the  staple  pit  at  the  commence- 
ment of  the  winding;  in  the  center  of  the  run  the  whole  of  the  chain  rests 
on  the  bottom  of  the  pit,  and,  finally,  at  the  end  of  the  winding  the  counter- 
poise has  been  rewound  upon  the  small  drum,  and  is  in  the  same  con- 
dition as  it  was  at  the  commencement. 

(c)  Loaded-wagon  System.  —  A  plan,  formerly  much  employed,  was  to 
have  a  loaded  wagon  running  on  a  short  incline  in  place  of  this  heavy 
chain;  the  rope  actuating  this  wagon  being  connected  in  the  same  manner 
as  the  above  to  a  subsidiary  drum.     The  incline  was  constructed  steep 
at  the  commencement,  the  inclination  gradually  decreasing  to  nothing. 
At  the  beginning  of  a  wind  the  wagon  was  at  the  top  of  the  incline,  and 
during  a  portion  of  the  run  gradually  passed  down  it  till,  at  the  meet  of 
cages,  no  pull  was  exerted  on  the  engine  —  the  wagon  by  this  time  being 
at  the  bottom.     In  the  latter  part  of  the  wind  the  resistance  was  all 
against  the  engine,  owing  to  its  having  to  pull  the  wagon  up  the  incline, 
and  this  resistance  increased  from  nothing  at  the  meet  of  cages  to  its 
greatest  quantity  at  the  conclusion  of  the  lift. 

(d)  The  Endless-rope  System  is  preferable  to  all  others,  if  there  is  suffi- 
cient sump  room  and  the  shaft  is  free  from  tubes,  cross  timbers,  and  other 
impediments.     It  consists  in  placing  beneath  the  cages  a  tail  rope,  similar 
in  diameter  to  the  winding  rope,  And,  after  conveying  this  down  the  pit, 
it  is  attached  beneath  the  other  cage. 

(e)  Flat  Ropes  Coiling  on  Reels.  —  This  means  of  winding  allows  of  a 
certain  equalization,  for  the  radius  of  the  coil  of  ascending  rope  continues  to 
increase,  while  that  of  the  descending  one  continues  to  diminish.     Conse- 
quently, as  the  resistance  decreases  in  the  ascending  load  the  leverage 
increases,  and  as  the  power  increases  in  the  other,  the  leverage  diminishes. 
The  variation  in  the  leverage  is  a  constant  quantity,  and  is  equal  to  the 
thickness  of  the  rope  where  it  is  wound  on  the  drum. 

By  the  above  means  a  remarkable  uniformity  in  the  load  may  be  ob- 
tained, the  only  objection  being  the  use  of  flat  ropes,  which  weigh  heavier 
and  only  last  about  two-thirds  the  time  of  round  ones. 

'(/)  Conical  Drums.  —  Results  analogous  to  the  preceding  may  be 
obtained  by  using  round  ropes  coiling  on  conical  drums,  which  may  either 
be  smooth,  with  the  successive  coils  lying  side  by  side,  or  they  may  be 
provided  with  a  spiral  groove.  The  objection  to  these  forms  is,  that 
perfect  equalization  is  not  obtained  with  the  conical  drums  unless  the  sides 
are  very  steep,  and  consequently  there  is  great  risk  of  the  rope  slipping; 
to  obviate  this,  scroll  drums  were  proposed.  They  are,  however,  expen- 
sive, and  the  lateral  displacement  of  the  winding  rope  from  the  center 
line  of  pulley  becomes  very  great,  owing  to  their  necessary  large  width. 
(<7)  The  Koepe  System  of  Winding. — An  iron  pulley  with  a  single  cir- 
cular groove  takes  the  place  of  the  ordinary  drum.  The  winding  rope 
passes  from  one  cage,  over  its  head-gear  pulley,  round  the  drum,  and, 
after  passing  over  the  other  head-gear  pulley,  is  connected  with  the  second 
cage.  The  winding  rope  thus  encircles  about  half  the  periphery  of  the 
drum  in  the  same  manner  as  a  driving-belt  on  an  ordinary  pulley.  There 
is  a  balance  rope  beneath  the  cages,  passing  round  a  pulley  in  the  sump; 
the  arrangement  is  like  an  endless  rope,  with  the  cages  as  points  of 
attachment. 

CRANES. 

Classification  of  Cranes.  (Henry  R.  Towne,  Trans.  A.  S.  M.  E.  iv.; 
288.  Revised  in  Hoisting,  published  by  The  Yale  &  Towne  Mfg.  Co.) 

A  Hoist  is  a  machine  for  raising  and  lowering  weights.  A  Crane  is  a 
hoist  with  the  added  capacity  of  moving  the  load  in  a  horizontal  or 
lateral  direction. 


1190  HOISTING  AND   CONVEYING. 

Cranes  are  divided  into  two  classes,  as  to  their  motions,  viz.  Rotary  and 
Rectilinear,  and  into  four  groups,  as  to  their  source  of  motive  power,  viz. : 

Hand.  —  When  operated  by  manual  power. 

Power.  —  When  driven  by  power  derived  from  line  shafting. 

Steam,  Electric,  Hydraulic,  or  Pneumatic.  —  When  driven  by  an  engine 
or  motor  attached  to  the  crane,  and  operated  by  steam,  electricity,  water, 
or  air  transmitted  to  the  crane  from  a  fixed  source  of  supply. 

Locomotive.  —  When  the  crane  is  provided  with  its  own  boiler  or  other 
generator  of  power,  and  is  self-propelling;  usually  being  capable  of  both 
rotary  and  rectilinear  motions. 

Rotary  and  Rectilinear  Cranes  are  thus  subdivided. 

ROTAEY  CRANES. 

(1)  Swing-cranes.  —  Having  rotation,  but  no  trolley  motion. 

(2)  Jib-cranes.  —  Having  rotation,  and  a  trolley  traveling  on  the  jib. 

(3)  Column-cranes.  —  Identical  with  the  jib-cranes,  but  rotating  around 
a  fixed  column  (which  usually  supports  a  floor  above). 

(4)  Pillar-cranes.  —  Having  rotation  only;  the  pillar  or  column  being 
supported  entirely  from  the  foundation. 

(5)  Pillar  Jib-cranes.  —  Identical  with  the  last,  except  in  having  a  jib 
and  trolley  motion. 

(6)  Derrick-cranes.  —  Identical  with  jib-cranes,  except  that  the  head  of 
the  mast  is  held  in  position  by  guy-rods,  instead  of  by  attachment  to  a 
roof  or  ceiling. 

(7)  Walking-cranes. — Consisting  of  a  pillar  or  jib-crane  mounted  on 
wheels  and  arranged  to  travel  longitudinally  upon  one  or  more  rails. 

(8)  Locomotive-cranes. — Consisting  of  a  pillar-crane  mounted  on  a 
truck,  and  provided  with  a  steam-engine  capable  of  propelling  and  rotat- 
ing the  crane,  and  of  hoisting  and  lowering  the  load. 

RECTILINEAR  CRANES. 

(9)  Bridge-cranes.  —  Having  a  fixed  bridge  spanning  an  opening,  and  a 
trolley  moving  across  the  bridge. 

(10)  Tram-cranes.  —  Consisting  of  a  truck,  or  short  bridge,  traveling 
longitudinally  on  overhead  rails,  and  without  trolley  motion. 

(11)  Traveling-cranes.  —  Consisting  of  a  bridge  moving  longitudinally 
on  overhead  tracks,  and  a  trolley  moving  transversely  on  the  bridge. 

(12)  Gantries.  —  Consisting  of  an  overhead  bridge,  carried  at  each  end 
by  a  trestle  traveling  on  longitudinal  tracks  on  the  ground,  and  having 
a  trolley  moving  transversely  on  the  bridge. 

(13)  Rotary  Bridge-cranes.  —  Combining  rotary  and  rectilinear  move- 
ments and  consisting  of  a  bridge  pivoted  at  one  end  to  a  central  pier  or 
post,  and  supported  at  the  other  end  on  a  circular  track;  provided  with  a 
trolley  moving  transversely  on  the  bridge. 

For  descriptions  of  these  several  forms  of  cranes  see  Towne's  "  Treatise 
on  Cranes." 

Stresses  in  Cranes.  —  See  Stresses  in  Framed  Structures,  p.  541,  ante. 

Position  of  the  Inclined  Brace  in  a  Jib-crane.  —  The  most  econom- 
ical arrangement  is  that  in  which  the  inclined  brace  intersects  the  jib  at 
a  distance  from  the  mast  equal  to  four-fifths  the  effective  radius  of  the 
crane.  (Hoisting.) 

Electric  Overhead  Traveling  Cranes.  (From  data  supplied  by 
Alliance  Machine  Co.,  Alliance,  O.,  and  Pawling  &  Harnischfeger,  Mil- 
waukee.)—  Electric  overhead  traveling  cranes  usually  have  3  motors,  for 
hoisting,  traversing  the  hoist  trolley  on  the  bridge  and  for  moving  the 
bridge,  respectively.  The  usual  range  of  motor  sizes  is  as  follows:  Hoist, 
15-50  H.P.;  trolley,  3-15  H.P.;  bridge,  15-50  H.P.  The  speeds  at  which 
the  various  motions  are  made  range  as  follows,  the  figures  being  feet  per 
minute:  Hoist,  8-60;  trolley  traverse,  75-200;  bridge  travel,  200-600. 
These  speeds  are  varied  in  the  same  capacity  of  crane  to  suit  each  par- 
ticular installation.  In  general,  the  speed  of  the  bridge  in  feet  per  minute 
should  not  exceed  (length  of  runway  +  100).  If  the  runway  is  long  and 
covered  by  more  than  one  crane,  the  speed  may  be  made  equal  to  the 
average  distance  between  cranes  +  100.  Usually  300  ft.  per  min.  is  a 
good  speed.  ^For  small  cranes  in  special  cases,  the  speeds  may  be  increased, 
but  for  cranes  of  over  50  tons  capacity  the  speed  should  be  below  300  ft. 
per  min.  unless  the  building  is  made  especially  strong  to  stand  the  strains 
incident  to  starting  and  stopping  heavy  cranes  geared  for  high  speeds. 


CRANES. 


1191 


Cranes  of  over  15  tons  capacity  usually  have  an  auxiliary  hoist  of  1/5  the 
capacity  of  the  main  hoist,  and  usually  operated  by  a  separate  motor. 
Wire  rope  is  now  almost  exclusively  used  for  hoisting:  with  cranes.  The 
diameter  of  the  drums  and  sheaves  should  be  not  less  than  30  times 
the  diameter  of  the  hoisting  rope,  and  should  have  a  factor  of  safety  of  5. 
Cranes  are  equipped  with  automatic  load  brakes  to  sustain  the  load  when 
lifted  and  to  regulate  the  speed  when  lowering,  it  being  necessary  for  the 
hoist  to  drive  the  load  down. 

The  voltage  now  standard  for  crane  service  is  220  volts  at  the  crane 
motor,  although  110  volts  for  small  cranes  is  not  objectionable.  Voltages 
of  500-600  are  inadvisable,  especially  in  foundries  and  steel  works,  where 
dust  and  metallic  oxides  cover  many  parts  of  the  crane  and  necessitate 
frequent  cleaning  to  avoid  grounds.  On  account  of  the  danger  from  the 
higher  voltages,  the  operators  are  apt  to  neglect  this  part  of  their  work. 

Power  Required  to  Drive  Cranes.  (Morgan  Engineering  Co., 
Alliance,  O.,  1909.)  — The  power  required  to  drive  the  different  parts  of 
cranes  is  determined  by  allowing  a  certain  friction  percentage  over  the 
power  required  to  move  the  dead  load.  On  hoist  motions  331/3%  la 
allowed  for  friction  of  the  moving  parts,  thus  giving  a  motor  of  1/3  greater 
capacity  than  if  friction  were  neglected.  For  bridge  and  trolley  motions, 
a  journal  friction  of  the  track  wheel  axles  of  10%  of  the  total  weight  of 
the  crane  and  load  is  allowed.  There  is  then  added  an  allowance  of  33 1/3% 
of  the  horse-power  required  to  drive  the  crane  and  load  plus  the  track  wheel 
axle  friction,  to  cover  friction  of  the  gearing.  In  selecting  motors,  the 
most  important  consideration  is  the  maximum  starting  torque  which 
the  motor  can  exert.  With  alternating-current  motors,  this  is  less  than 
with  direct-current  motors,  requiring  a  larger  motor,  particularly  on  the 
bridge  and  trolley  motions  which  require  the  greatest  starting  torque. 

Walter  G.  Stephan  says  (Iron  Trade  Rev.,  Jan.  7,  1909)  that  the  bridge 
girders  should  be  made  of  two  plates  latticed,  or  box  girders,  their  depth 
varying  from  1/10  to  1/20  of  the  span.  Ihe  important  feature  of  crane 
girder  design  is  ample  strength  and  stiffness,  both  vertically  and  laterally. 
.  Especial  attention  should  be  given  to  the  transverse  strain  on  the  bridge 
due  to  sudden  stopping  or  starting  of  heavy  loads.  The  wheel  base  on 
the  end  trucks  should  have  a  ratio  to  the  crane  span  of  1  to  6,  although 
for  long  spans  this  ratio  must  necessarily  be  reduced  to  1  to  8.  Quick- 
traveling  cranes  should  have  as  long  a  wheel  base  as  possible,  since  the 
tendency  to  twist  increases  with  the  speed.  Where  several  wheels  are 
necessary  at  each  end  to  support  the  crane,  equalizing  means  should  be 
used. 

A  recent  development  in  cranes  is  the  four-  or  six-girder  crane  for  han- 
dling ladles  of  molten  metal  in  steel  works.  The  main  trolley  runs  on  the 
outer  girders,  with  the  hoist  ropes  depending  between  the  outer  and  inner 
girders.  The  auxiliary  trolley  runs  on  the  inner  girders,  thus  being  able 
to  pass  between  the  main  ropes,  and  tilt  the  ladle  in  either  direction. 

Dimensions  and  Wheel  Loads  of  Electric  Traveling  Cranes. 

Based  on  60-ft.  span  and  25-ft.  lift;  wire  rope  hoist. 
(Alliance  Machine  Co.,  1908.) 


Capacity, 
Tons  (2000 
Lb.). 

~T 

25 
40 
50 

Distance  Run- 
way Rail  to 
Highest  Point. 

Distance 
Center  of 
Rail  to  Ends 
of  Crane. 

Wheel  Base  of 
End  Truck. 

Maximum 
Load  per 
Wheel;  Trol- 
ley at  End  of 
Bridge. 

Ft.        In. 
6           0 
6           6 
7           4 
8           0 
8           9 

In. 
9 
10 
12 
12 
12 

Ft.     In. 
9         0 
10          0 
11          6 
12          3 
12          6 

Pounds. 
20,000 
27,000 
51,000 
82,000 
48,000* 

*  Has  8  track  wheels  on  bridge. 

Standard  cranes  are  built  in  intermediate  sizes,  varying  by  5  tons,  up 
(o  40  tons, 


1192 


HOISTING  AND   CONVEYING. 


Standard  Hoisting  and  Traveling  Speeds  of  Electric  Cranes. 

(Pawling  &  Harnischfeger,  1908.) 


Tons  (2000 
Lb.). 

Hoisting 
Speed,  Ft.  per 
Min. 

Bridge  Travel 
Speed,  Ft.  per 
Min. 

Capacity 
Aux.  Hoist, 
Tons. 

Speed  Aux. 
Hoist,  Ft.  per 
Min. 

10 

25-100 
20-75 

300-450 
300-450 

3 

30-75 

23 

10-40 

25Q-350 

d 

50-125) 
25-60   f 

40 

9-30 

250-350 

,2 

40-100  [ 
25-60   f 

50 

8-30 

200-300 

4 

40-100  \ 
25-6(1  } 

75 

6-25 

200-250 

15 

20-50 

»25 

5-15 

200-250 

25 

20-50 

150 

5-15 

200-250 

25 

20-50 

Trolley  travel  speed  from  100-150  ft.  per  min.  in  all  cases. 
Notable  Crane  Installations.     (1909.) 


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12 

*  Four-girder  ladle  crane,     t  On  each  trolley. 

4.  Divided  equally  between  2  motors  for  series-parallel  control. 

1.  Pawling  &  Harnischieger;  2.  Alliance  Mach.  Co.;  3.  Morgan  Ea- 
glneering  Co.;  4.  Midvale  Steel  Co.,  Phila.;  5.  Homestead  Steel  Works, 
Munhall,  Pa.;  6.  Indiana  Steel  Co.,  Gary,  Ind.;  7.  Oregon  Ry.  &  Nav. 
Co.,  Portland,  Ore.;  8.  El  Paso  &  S.  W.  Ry.,  El  Paso,  Tex.;  9.  C.  &  E.  I. 
Ry.,  Danville,  111.;  10.  3d  Ave.  Ry.,  N.  Y.  City;  11.  United  Rys.  Co., 
Baltimore;  12.  Carnegie  Steel  Co.,  Youngstown,  Ohio. 

A  150-ton  Pillar-crane  was  erected  in  1893  on  Finnieston  Quay, 
Glasgow.  The  jib  is  formed  of  two  steel  tubes,  each  39  in.  diam.  and  90 
ft.  long.  The  radius  of  sweep  for  heavy  lifts  is  65  ft.  The  jib  and  its  load 
are  counterbalanced  by  a  balance-box  weighted  with  100  tons  of  iron  and 
steel  punchings.  In  a  test  a  130-ton  load  was  lifted  at  the  rate  of  4  ft.  per 
minute,  and  a  complete  revolution  made  with  this  load  in  5  minutes. 
Eng'g  News,  July  20,  1893. 

Compressed-air  Traveling-cranes. —  Compressed-air  overhead  travel- 
ing-cranes have  been  built  by  the  Lane  &  Bodley  Co.,  of  Cincinnati. 
They  are  of  20  tons  nominal  capacity,  each  about  50  ft.  span  and  400  ft. 
length  of  travel,  and  are  of  the  triple-motor  type,  a  pair  of  simple  reversing- 
engines  being  used  for  each  of  the  necessary  operations,  the  pair  of  engines 
for  the  bridge  and  the  pair  for  the  trolley  travel  being  each  5-inch  bore  by 
7-inch  stroke,  while  the  pair  for  hoisting  is  7-inch  bore  by  9-inch  stroke. 


LIFTING  MAGNETS.  1193 

The  air-pressure  when  required  is  somewhat  over  100  pounds.  The  air- 
compressor  is  allowed  to  run  continuously  without  a  governor,  the  speed 
being  regulated  by  the  resistance  of  the  air  in  a  receiver.  An  auxiliary 
receiver  is  placed  on  each  traveler,  whose  object  is  to  provide  a  supply 
of  air  near  the  engines  for  immediate  demands  and  independent  of  the 
hose  connection.  Some  of  the  advantages  said  to  be  possessed  by  this 
type  of  crane  are:  simplicity;  absence  of  all  moving  parts,  excepting 
those  required  for  a  particular  motion  when  that  motion  is  in  use;  no 
danger  from  fire,  leakage,  electric  shocks,  or  freezing;  ease  of  repair: 
variable  speeds  and  reversal  without  gearing;  almost  entire  absence  of 
noise;  and  moderate  cost. 

Quay-cranes.  —  An  illustrated  description  of  several  varieties  of  sta- 
tionary and  traveling  cranes,  with  results  of  experiments,  is  given  in  a 
paper  on  Quay-cranes  in  the  Port  of  Hamburg  by  Chas.  Nehls,  Trans. 
A.  S.  C.  E.,  1893. 

Hydraulic  Cranes,  Accumulators,  etc.  —  See  Hydraulic  Pressure 
Transmission,  page  812,  ante. 

Electric  versus  Hydraulic  Cranes  for  Docks.  —  A  paper  by  V.  L. 
Raven,  in  Trans.  A.  S.  M.  E.,  1904,  describes  some  tests  of  capacity  and 
efficiency  of  electric  and  hydraulic  power  plants  for  dock  purposes  at  Mid- 
dlesbrough, Eng,  In  loading  two  cargoes  of  rails,  weighing  respectively 
1210  and  1225  tons,  the  first  was  done  with  a  hydraulic  crane,  in  7  hours, 
with  3584  Ibs.  of  coal  burned  in  the  power  station,  and  the  second  with 
an  electric  crane  in  5V4  hours,  with  2912  Ibs.  of  coal.  The  total  cost  in- 
cluding labor,  per  100  tons,  was  327  pence  with  the  hydraulic  and  245 
pence  for  the  electric  crane,  a  saving  by  the  latter  of  25  %. 

Loading  and  Unloading  and  Storage  Machinery  for  coal,  ore,  etc., 
is  described  by  G.  E.  Titcomb  in  Trans.  A.  S.  M.  E.,  1908.  The  paper 
illustrates  automatic  ore  unloaders  for  unloading  ore  from  the  hold  of  a 
vessel  and  loading  it  onto  cars,  and  car-dumping  machinery,  by  which 
a  50-ton  car  of  coal  is  lifted,  turned  over  and  its  contents  discharged 
through  a  chute  into  a  vessel.  Methods  of  storage  of  coal  and  of  re- 
loading it  on  cars  are  also  described. 

Power  Required  for  Traveling-Cranes  and  Hoists.  —  Ulrich  Peters, 
in  Machy,  Nov.  1907,  develops  a  series  of  formulse  for  the  power  re- 
quired to  hoist  and  to  move  trolleys  on  cranes.  The  following  is  a  brief 
abstract.  Resistance  to  be  overcome  in  moving  a  trolley  or  crane- 
bridge.  PI  =  rolling  friction  of  trolley  wheels,  Pz  =  journal  friction 
of  wheels  or  axles,  Ps  =  inertia  of  trolley  and  load.  P  =  sum  of  these 

resistances=P1+P24-P3  =  (r+L)  (&±&&  +  in  which  T=  weight 


of  trolley,  L  =  load,  ./i  =  coeff.  of  rolling,  friction,  about  0.002,  (0.001  to 
0.003  for  cast  iron  on  steel);  /2  =  coeff.  of  journal  friction,  =  0.1  for  start- 
ing and  0.01  for  running,  assuming  a  load  on  brasses  of  1000  to  3000  Ib. 
per  sq.  in.;  [fz  is  more  apt  to  be  0.05  unless  the  lubrication  is  perfect.  See 
Friction  and  Lubrication,  W.  K.]  d  =  diam.  of  journal;  D  =  diam.  of 
wheels;  v  =  trolley  speed  in  ft.  per  min.;  t  =  time  in  seconds  in  which 
the  trolley  under  full  load  is  required  to  come  to  the  maximum  ^speed. 
Horse-power  =  sum  of  the  resistances  X  speed,  ft.  per  min.  •*•  33,000. 

Force  required  for  hoisting  and  lowering:  Fh  =  actual  hoisting  force, 
F0  =  theoretical  force  or  pull,  L  =  load,  v  =  speed  in  ft.  per  min.  of 
the  rope  or  chain,  c  =  hoisting  speed  of  the  load  L,  c/v  =  transmission 
ratio  of  the  hoist,  e  =  efficiency  =  FQ/F^.  The  actual  work  to  raise 
the  load  per  minute  =  Fhv  =  Lc  =  F0v  -*-  e.  The  efficiency  e  is  the 
product  of  the  efficiencies  of  all  the  several  parts  of  the  hoisting  mech- 
anism, such  as  sheaves,  windlass,  gearing,  etc.  Methods  of  calculating 
these  efficiencies,  with  examples,  are  given  at  length  in  the  original  paper 
by  Mr.  Peters. 

Lifting  Magnets.  —  (From  data  furnished  by  the  Electric  Controller 
and  Mfg.  Co.,  Cleveland,  and  the  Cutler-Hammer  Clutch  Co.,  Milwaukee). 
Lifting  magnets  first  came  into  use  about  1898.  They  have  had  wide 
application  for  handling  pig  iron,  scrap,  castings,  etc.  A  lifting  magnet 
comprises  essentially  a  maynet  winding,  a  pole-piece,  a  shoe  and  a  pro- 
tecting case,  which  is  ribbed  to  afford  ample  radiating  surface  to  dissi- 
pate the  heat  generated  in  operation.  The  winding  usually  consists  of 
coils,  each  wound  with  copper  ribbon  and  insulated  with  asbestos.  The 
insulation  must  be  designed  to  withstand  a  higher  voltage  than  the  line 


1194 


HOISTING  AND   CONVEYING. 


voltage,  due  to  the  inductive  kick  when  the  circuit  is  opened.  The  weaf- 
ing  plate,  which  takes  the  shocks  incident  to  picking  up  the  load,  is  usually 
made  of  manganese  steel.  The  shape  of  the  pole  piece  or  lifting  surface  of 
the  magnet  must  be  varied,  as  the  same  shape  is  not  usually  applicable 
to  all  classes  of  materials.  For  handling  pig  iron,  scrap,  etc.,  a  concave 
pole  surface  is  usually  superior  to  a  flat  one,  which  is  adapted  to  hand- 
ling plates  or  flat  material  of  similar  character,  and  which  bear  equally 
on  the  piece  to  be  lifted  at  both  the  edge  and  center.  A  test  of  a  lift- 
ing magnet  made  at  the  works  of  the  Youngstown  Sheet  and  Tube  Co., 
in  1907,  showed  the  following  results: 

Total  pig  iron  unloaded,  109,350  pounds;  weight  of  average  lift,  785 
pounds;  time  required,  2  hours.  15  minutes;  current  on  magnet,  1  hour 
15  minutes;  current  required,  30  amperes. 

The  No.  3  and  No.  4  magnets  are  particularly  fitted  for  use  on  steam- 
driven  locomotive  cranes,  and  when  so  used  are  usually  supplied  with 
current  from  a  small  steam-driven  generator  set  mounted  on  the  crane, 
steam  being  drawn  from  the  boiler  of  the  crane.  Nos.  5  and  6  are  adapted 
for  use  with  overhead  electric  traveling  cranes  in  cases  where  large  lifts 
and  high  speed  of  handling  are  essential. 

SIZES  AND  CAPACITIES  OF  THE  ELECTEIC  CONTROLLER  &  MFG.  Co.'s 
TYPE  S-A  LIFTING  MAGNETS  (1909). 


Size. 

Diam. 

Weight. 

Average 
Current  at 
220  Volts. 

Lifts  in  Machine  Cast 
Pig  Iron. 

Maximum 
Lift. 

Average 
Lift. 

3 
4 
5 
6 

In. 
36 
43 
52 
61 

Lb. 
2,100 
3,200 
4,800 
6,600 

Amp. 

27 
35 
45 

Lb. 
1,405 

2,180 
3,087 
4,589 

Lb. 
750 
1,250 
1,800 
2,600 

SIZES  AND  CAPACITIES  OF  LIFTING  MAGNETS  (CUTLER-HAMMER),  1908. 


Size, 
In. 

Weight 
Lb. 

Maximum* 
Lifting 
Capacity, 
Lb. 

Average 
Lifting 
Capacity, 

Current 
Required 
at  220  Volts, 
Amperes. 

Head-room 
Required, 

10 

75 

800 

100-300 

1 

35 

50 

1,650 
5,000 

5,000 
20,000 

500-1,000 
1,000-2,000 

15-18 
30-35 

4 
6 

*This  capacity  can  be  obtained  only  under  the  most  favorable  con- 
ditions,  with  complete  magnetic  contact  between  the  magnet  and  the 
piece  to  be  lifted. 

The  capacity  of  a  lifting  magnet  in  service  depends  on  many  other 
factors  than  the  design  of  the  magnet.  Most  important  is  the  character 
of  the  material  handled.  Much  more  can  be  handled  at  a  single  lift 
with  material  like  billets,  ingots,  etc.,  than  with  scrap,  wire,  pig  iron, 
etc.  The  speed  of  the  crane,  from  which  the  magnet  is  suspended,  and 
the  distance  it  must  transport  the  material  are  also  important  factors  to 
be  considered  in  calculating  the  capacity  of  a  given  magnet  under  given 
conditions.  The  following  results  have  been  selected  from  a  great  num- 
ber of  tests  of  the  Electric  Controller  and  Mfg.  Co.'s  No.  2  Type  S  magnets 
in  commercial  service,  and  represent  what  is  probably  average  practice. 
It  should  be  borne  in  mind  that  the  average  lift  is  determined  from  a  large 
number  of  lifts,  including  lifts  made  from  a  full  car  of,  say,  pig  iron, 
where  the  magnetic  conditions  are  very  favorable,  and  also  the  "  lean  " 
lifts  where  the  car  is  nearly  empty,  and  magnetic  conditions  unfavorable; 
the  magnet  can  reach  only  a  few  pigs  at  one  time  on  the  lean  lifts,  with  a 
consequent  heavy  decrease  in  the  size  of  the  load.  The  average  lift  is 
therefore  less  than  the  maximum  lift  in  handling  a  given  lot  9f  material. 

When  operated  from  an  ordinary  electric  overhead  traveling  crane  a 
magnet  of  the  type  used  in  these  trials  will  handle  from  20  to  30  tons 
per  hour  of  the  scrap  used  by  open-hearth  furnaces.  If  operated  from 
a  special  fast  crane,  the  amount  may  be  somewhat  increased.  Average 
lifts  in  pounds  for  various  materials  are  as  follows: 


LIFTING  MAGNETS. 


1195 


Skull  cracker  balls  up  to  20,000;  ingot  (or  if  ground  man  places 

magnet,   two),  each,  6,000;  billet  slabs,  900-6,000. 

The  above  weights  depend  on  dimensions  and  whether  in  pile  or 
stacked  evenly. 

Machine  cast  pig  iron,  1,250;  sand  cast  pig  iron,  1,150. 

These  are  values  obtained  in  unloading  railway  cars,  including  lean 
lifts  in  cleaning  up. 

Machine  cast  pig  iron,  1,350;  sand  cast  pig  iron,  1,200. 

The  above  are  average  lifts  from  stockpile. 

Heavy  melting  stock  (billets,  crop  ends  of  billets,  rails  or  structural 
shapes,  1,250;  boiler  plate  scrap,  1,100;  farmers'  scrap  (harvesting 
machinery  parts,  plow  points,  etc.),  900;  small  risers  from  steel  castings, 
1,600;  fine  wire  scrap,  scrap  tubing  not  over  3  ft.  long,  loose  even  or 
lamination  scrap,  500;  bundled  scrap,  1,200;  miscellaneous  junk  deal- 
ers' scrap,  400-800. 


COMMERCIAL  RESULTS  WITH  A  52-iNCH,  5,000  POUND  MAGNET. 
(Electric  Controller  &  Mfg.  Co.,  1908.) 


Hoist 
speed, 
ft.  per 

min. 


Crane. 


Trolley 
speed, 
ft.  per 

min. 


80 
80 
80 
80 
200 
200 
200 
200 
171 
171 
171 
171 


Bridge 
speed, 
ft.  per 

min. 


315 
315 
315 
315 
550 
550 
550 
550 
160 
160 
160 
160 


Distance 
moved. 


— >  a 

03  O  o 


60 
35 
39.3 
33.9 
78. 
78 
26 
'   80 
25 
112 
7 
5 


•8 
& 


73 

55 

60 

55 

132 

168 

30 

300 

25 

56 

8 

4 


II 


1,650 

1,275 

1,328 

1,234 

1,182 

929 

173 

534 

2,000 

4,000 

1,740 

2,660 


oT  . 

II 


75 
60 
60 
55 

135 

190 
45 

300 
80 

120 
15 
10 


II 

¥ 


2 
3 

5 

6 
7 
8 
9 
10 
11 
12 


*  1.  Machine  cast  pig  handled  from  stock  pile  to  charging  boxes.  2. 
Bull  heads,  ditto.  3.  Sand  cast  pig  unloaded  from  car  to  stock  pile. 
4.  Baled  tin  and  wire  untoaded  from  car  to  stock  pile.  5.  Boiler  plate 
scrap  handled  from  stock  pile  to  charging  boxes.  6.  Farmers'  scrap,  com- 
prising knoiiers  and  butters  from  threshing  and  binding  machines,  sections 
of  cutter  bars  from  mowers,  broken  steel  teeth  from  hay  rakes,  plow  points, 
etc.f  from  stock  pile  to  charging  boxes.  7.  Small  risers  from  steel  castings, 
handled  from  stock  pile  to  charging  boxes.  8.  Laminated  plates  from 
armatures  and  transformers,  mixed  sizes,  from  stock  pile  to  charging 
boxes.  9.  Cast  iron  sewer  pipe,  3  feet  diameter,  weighing  2,000  pounds 
each,  lifted  from  cars  to  flat  boat.  Each  pipe  had  to  be  blocked  and 
lashed  to  prevent  washing  overboard.  10.  Pennsylvania  Railroad  East- 
River  tunnel  section  castings,  convex  on  one  side,  concave  on  other, 
weighing  4,000  pounds  each.  Handled  from  local  float  to  barge  for  ship- 
ment. 11.  Steel  plate  i/2-inch  X  10  inches  X6  feet  0  inches  handled 
from  car  to  float.  12.  Steel  rails,  40  pounds  per  yard,  25  feet  long. 
Handled  from  car  to  lighter,  about  8  rails  per  lift. 

The  above  results  of  tests  relate  to  the  Electric  Controller  &  Mfg. 
Co.'s  No.  2  Type  "  S  "  magnet,  52  in.  diameter  and  weighing  5200  Ibs. 
and  are  the  average  of  a  large  number  of  tests  made  at  various  plants 
between  the  years  1905  and  1908.  This  type  of  magnet  is  being  super- 
seded by  the  No.  4  Type  S-A  magnet  which  is  43  in.  diameter,  weighs 
3200  Ibs,  and  gives  substantially  the  same  average  lift. 


'1196  HOISTING  AND   CONVEYING. 

TELPHERAGE. 

Telpherage  Is  a  name  given  to  a  system  of  transporting  materials  !n 
which  the  load  is  suspended  from  a  trolley  or  small  truck  running  on  a 
cable  or  overhead  rail,  and  in  which  the  propelling  force  is  obtained 
from  an  electric  motor  carried  on  the  trolley.  The  trolley,  with  its 
motor,  is  called-  a  "  telpher."  A  historical  and  illustrated  description 
of  the  system  is  given  in  a  paper  by  O.  M.  Clark,  in  Trans.  A.  I.  E.  E., 
1902.  A  series  of  circulars  of  the  Link  Belt  Co.,  Philadelphia,  show 
numerous  illustrations  of  the  system  in  operation  for  handling  different 
classes  of  materials.  Telpherage  is  especially  applicable  for  moving 
packages  in  warehouses,  on  wharfs,  etc.  The  moving  machinery 
consists  of  the  telpher  or  the  conveying  power,  with  accompanying 
trailers;  the  portable  electric  hoist  or  the  vertical  elevating  power,  and 
the  carriers  containing  the  load.  Among  the  accessories  are  brakes, 
switches  and  controlling  devices  of  many  kinds. 

An  automatic  line  is  controlled  by  terminal  and  intermediate  switches 
which  are  operated  by  the  men  who  do  the  loading  and  unloading,  no 
additional  labor  being  required.  A  non-automatic  line  necessitates  a 
boy  to  accompany  the  telpher.  The  advisability  of  using  the  non- 
automatic  rather  than  the  automatic  line  is  usually  determined  by  the 
distance  between  stations. 

COAL-HANDLING  MACHINERY. 

The  following  notes  and  tables  are  supplied  by  the  Link-Belt  Co. 

In  large  boiler-houses  coal  is  usually  delivered  from  hopper-cars  into 
a  track-hopper,  about  10  feet  wide  and  12  to  16  feet  long.  A  feeder  set 
under  the  track-hopper  feeds  the  coal  at  a  regular  rate  to  a  crusher,  which 
reduces  it  to  a  size  suitable  for  stokers. 

After  crushing,  the  coal  is  elevated  or  conveyed  to  overhead  storage- 
bins.  Overhead  storage  is  preferred  for  several  reasons: 

1.  To  avoid  expensive  wheeling  of  coal  in  case  of  a  breakdown  of  the 
coal-handling  machinery. 

2.  To  avoid  running  the  coal-handling  machinery  continuously. 

3.  Coal  kept  under  cover  indoors  will  not  freeze  in  winter  and  clog  the 
supply-spouts  to  the  boilers. 

4.  It  is  often  cheaper  to  store  overhead  than  to  use  valuable  ground- 
space  adjacent  to  the  boiler-house. 

5.  As  distinguished  from  vault  or  outside  hopper  storage,  it  is  cheaper 
to  build  steel  bins  and  supports  than  masonry  pits. 

Weight  of  Overhead  Bins.  —  Steel  bins  of  approximately  rectangular 
cross-section,  say  10  X  10  feet,  will  weigh,  exclusive  of  supports,  about 
one-sixth  as  much  as  the  contained  coal.  Larger  bins,  with  sloping 
bottoms,  may  weigh  one-eighth  as  much  as  the  contained  coal.  Bag 
bottom  bins  of  the  Berquist  type  will  weigh  about  one-twelfth  as  much  as 
the  contained  coal,  not  including  posts,  and  about  one-ninth  as  much, 
including  posts. 

Supply-pipes  from  Bins.  —  The  supply-pipes  from  overhead  bins  to 
the  boiler-room  floor,  or  to  the  stoker-hoppers,  should  not  be  less  than  12 
inches  in  diameter.  They  should  be  fitted  at  the  top  with  a  flanged  cast- 
ing and  a  cut-off  gate,  to  permit  removal  of  the  pipe  when  the  boilers  are 
to  be  cleaned  or  repaired. 

Types  of  Coal  Elevators.  —  Coal  elevators  consist  of  buckets  of 
various  shapes  attached  to  one  or  more  strands  of  link-belting  or  chain,  or 
to  rubber  belting.  The  buckets  may  either  be  attached  continuously  or 
at  intervals.  The  various  types  are  as  follows: 

Continuous  bucket  elevators  consist  usually  of  one  strand  of  chain  and 
two  sprocket-wheels  with  buckets  attached  continuously  to  the  chain. 
Each  bucket  after  passing  the  head  wheel  acts  as  a  chute  to  direct  the 
flow  from  the  next  bucket.  This  type  of  elevator  will  handle  the  larger 
sizes  of  coal.  It  runs  at  slow  speeds,  usually  from  90  to  175  feet  per  min- 
ute, and  has  a  maximum  capacity  of  about  120  tons  per  hour. 

Centrifugal  discharge  elevators  consist  usually  of  a  single  strand  of  chain, 
Vvith  the  buckets  attached  thereto  at  intervals.  They  are  used  to  handle 
the  smaller  sizes  of  coal  in  small  quantities.  They  run  at  high  speeds, 
usuallv  34  to  40  revolutions  of  the  head  wheel  per  minute,  and  have  a 
capacity  up  to  40  tons  per  hour. 


COAL-HANDLING  MACHINERY.  1197 

Perfect  discharge  elevators  consist  of  two  strands  of  chain,  with  buckets 

at  intervals  between  them.  A  pair  of  idlers  set  under  the  head  wheels 
cause  the  buckets  to  be  completely  inverted,  and  to  make  a  clean  delivery 
into  the  chutes  at  the  elevator  head.  This  type  of  elevator  is  useful  in 
handling  material  which  tends  to  cling  to  the  buckets.  It  runs  at  slow 
speeds,  usually  less  than  150  feet  per  minute.  The  capacity  depends  on 
the  size  of  the  buckets. 

Combined  Elevators  and  Conveyors  are  of  the  following  types: 

Gravity  discharge  elevators,  consisting  of  two  strands  of  chain,  with 
spaced  V-shaped  buckets  fastened  between  them.  After  passing  the  head 
wheels  the  buckets  act  as  conveyor-flights  and  convey  the  coal  in  a  trough 
to  any  desired  point.  This  is  the  cheapest  type  of  combined  elevator  and 
.conveyor,  and  is  economical  of  power.  A  machine  carrying  100  tons  of 
coal  per  hour,  in  buckets  20  inches  wide,  10  inches  deep,  and  24  inches  long, 
spaced  3  feet  apart,  requires  5  H.P.  when  loaded  and  1 1/2  H.P.  when  empty 
for  each  100  feet  of  horizontal  run,  and  1/9  H.P.  for  each  foot  of  vertical  lift. 

Rigid  bucket-carriers  consist  of  two  strands  of  chain  with  a  special 
bucket  rigidly  fastened  between  them.  The  buckets  overlap  and  are  so 
shaped  that  they  will  carry  coal  around  three  sides  of  a  rectangle.  The 
coal  is  carried  to  any  desired  point  and  is  discharged  by  completely 
inverting  the  bucket  over  a  turn-wheel. 

Pivoted  bucket-carriers  consist  of  two  strands  of  long  pitch  steel  chain  to 
which  are  attached,  in  a  pivotal  manner,  large  malleable  iron  or  steel 
buckets  so  arranged  that  their  adjacent  lips  are  close  together'  or  overlap. 
Overlapping  buckets  require  special  devices  for  changing  the  lap  at  the 
corner  turns.  Carriers  in  which  the  buckets  do  not  overlap  should  be 
fitted  with  auxiliary  pans  or  buckets,  arranged  in  such  a  manner  as  to 
catch  the  spill  which  falls  between  the  lips  at  the  loading  point,  and  so 
shaped  as  t9  return  the  spill  to  the  buckets  at  the  corner  turns.  Pivoted 
bucket-carriers  will  carry  coal  around  four  sides  of  a  rectangle,  the  buckets 
being  dumped  on  the  horizontal  run  by  striking  a  cam  suitably  placed. 
Buckets  for  these  carriers  are  usually  of  2  ft.  pitch,  and  range  in  width 
from  18  in.  to  48  in.  They  run  at  low  speeds,  usually  not  over  50  ft.  per 
minute,  40  ft.  per  minute  being  most  usual.  At  the  latter  speed,  the 
capacities  when  handling  coal  vary  from  40  tons  per  hour  for  the  18  in. 
width  to  120  tons  for  the  48  in.  width.  On  account  of  the  superior  con- 
struction of  these  carriers  and  the  slow  speed  at  which  they  run,  they  are 
economical  of  power  and  durable.  The  rollers  mounted  on  the  chain 
joints  are  usually  6  in.  diameter,  but  for  severe  duty  8-in.  rollers  are  often 
used.  It  is  usual  to  make  these  hollow  to  carry  a  quantity  of  oil  for 
internal  lubrication. 

Coal  Conveyors.  —  Coal  conveyors  are  of  four  general  types,  viz., 
scraper  or  flight,  bucket,  screw,  and  belt  conveyors. 

The  flight  conveyor  consists  of  a  trough  of  any  desired  cross-section  and 
a  single  or  double  strand  of  chain  carrying  scrapers  or  flights  of  approxi- 
mately the  same  shape  as  the  trough.  The  flights  push  the  coal  ahead  of 
them  in  the  trough  to  any  desired  point,  where  it  is  discharged  through 
openings  in  the  bottom  of  the  trough. 

For  short,  low-capacity  conveyors,  malleable  link  hook-joint  chains 
are  used.  For  heavier  service,  malleable  pin-joint  chains,  steel  link  chains, 
or  monobar,  are  required.  For  the  heaviest  service,  two  strands  of  steel 
link  chain,  usually  with  rollers,  are  used. 

Flight  conveyors  are  of  three  types:  plain  scraper,  suspended  flight,  and 
roller  flight. 

In  the  plain  scraper  conveyor,  the  flight  is  suspended  from  the  chain 
and  drags  along  the  bottom  of  the  trough.  It  is  of  low  first  cost  and  is 
useful  where  noise  of  operation  is  not  objectionable.  It  has  a  maximum 
capacity  of  about  30  tons  per  hour,  and  requires  more  power  than  either 
of  the  other  two  types  of  flight  conveyors. 

Suspended  flight  conveyors  use  one  or  two  strands  of  chain.  The  flights 
are  attached  to  cross-bars  having  wearing-shoes  at  each  end.  These  wear- 
ing-shoes slide  on  angle-iron  tracks  on  each  side  of  the  conveyor  trough. 
The  flights  do  not  touch  the  trough  at  any  point.  This  type  of  conveyor 
is  used  where  quietness  of  operation  is  a  consideration.  It  is  of  higner 
first  cost  than  the  plain  scraper  conveyor,,  but  requires  one-fourth  less 
power  for  operation.  It  is  economical  up  to  a  capacity  of  about  80  tons 
per  hour. 


1198 


HOISTING  AND   CONVEYING. 


The  roller  flight  conveyor  is  similar  to  the  suspended  flight,  except 
that  the  wearing-shoes  are  replaced  by  rollers.  It  is  highest  in  first 
cost  of  all  the  flight  conveyors,  but  has  the  advantages  of  low  power 
consumption  (one-half  that  of  the  scraper),  low  stress  in  chain,  long 
life  of  chain,  trough,  and  flights,  and  noiseless  operation.  It  has  an 
economical  maximum  capacity  of  about  120  tons  per  hour. 

The  following  formula  gives  approximately  the  horse-power  at  the 
head  wheel  required  to  operate  flight  conveyors: 

H.P,  =  (ATL  +  BWS)  --  1000. 

T  =  tons  of  coal  per  hour;  L  =  length  of  conveyor  in  feet,  center  to 
center;  W  =  weight  of  chain,  flights,  and  shoes  (both  runs)  in  pounds; 
iS  =  speed  in  feet  per  minute ;  A  and  B  constants  depending  on  angle 
of  incline  from  horizontal.  See  example  below. 

EXAMPLE. — Required  the  H.P.  for  a  monobar  conveyor  200  ft. 
center  to  center  carrying  100  tons  of  coal  per  hour,  up  a  10°  incline  at 
a  speed  of  100  feet  per  minute.  Conveyor  has  No.  818  chain  and  8  X19 
suspended  flights,  spaced  18  inches  apart. 

H  P       0-5  X  100X200  +  0.008  (400  X  5.7  +  267  X  15.55)  X  100  _  15  15 

1000 

The  following  table  shows  the  conveying  capacities  of  various  sizes 
of  flights  at  100  feet  per  minute  in  tons,  of  2000  lb.,  per  hour.  The 
values  are  true  for  continuous  feed  only. 


Size  of 
Flight. 

Horizontal  Conveyors,  Tons. 

Inclined  Conveyors,  Tons. 

Flight 
Every 
16". 

Flight 
Every 
18". 

Flight 
Every 
24". 

Pounds 
Coal  per 
Flight. 

10° 
Flights 
Every 

20° 
Flights 
Every 

30° 
Flights 
Every 
24". 

6X14 
8X19 
10X24 
10X30 
10X36 
10X42 

69.75 

62 
130 

46.5 
97.5 
172.5 
220 
268 
315 

31 
65 
115 
147 
179 
210 

40.5 
78 
150 

184 
225 
264 

31.5 
62 
120 
146 
177 
210 

22.5 
52 
90 
116 
142 
167 

Bucket  Conveyors.  —  Rigid  bucket-carriers  are  used  to  convey  large 
quantities  of  coal  over  a  considerable  distance  when  there  is  no  inter- 
mediate point  of  discharge.  These  conveyors  are  made  with  two  strands 
of  steel  roller  chain.  They  are  built  to  carry  as  much  as  10  tons  of  coal 
per  minute. 

Screw  Conveyors.  —  Screw  conveyors  consist  of  a  helical  steel  flight, 
either  in  one  piece  or  in  sections,  mounted  on  a  pipe  or  shaft,  and  running 
in  a  steel  or  wooden  trough.  These  conveyors  are  made  from  4  to  18 
inches  in  diameter,  and  in  sections  8  to  12  feet  long.  The  speed  ranges 
from  20  to  60  revolutions  per  minute  and  the  capacity  from  10  to  30  tons 
of  coal  per  hour.  It  is  not  advisable  to  use  this  type  of  conveyor  for  coal, 
as  it  will  only  handle  the  smaller  sizes  and  the  nights  are  very  easily  dam- 
aged by  any  foreign  substance  of  unusual  size  or  shape. 

Belt  Conveyors.  —  Rubber  and  cotton  belt  conveyors  are  used  for 
handling  coal,  ore,  sand,  gravel  etc.,  in  all  sizes.  They  combine  a  high 
carrying  capacity  with  low  power  consumption. 

In  some  cases  the  belt  is  flat,  the  material  being  fed  to  the  belt  at  its 
center  in  a  narrow  stream.  In  the  majority  of  cases,  however,  the  belt 
is  troughed  by  means  of  idler  pulleys  set  at  an  angle  from  the  horizontal 
and  placed  at  intervals  along  the  length  of  the  belt.  Rubber  belts  are 
often  made  more  flexible  for  deep  troughing  by  removing  some  of  the 
layers  of  cotton  from  the  belt  and  substituting  therefor  an  extra  thickness 
of  rubber. 

Belt  conveyors  may  be  used  for  elevating  materials  up  to  about  23° 
incline.  On  greater  inclines  the  material  slides  back  on  the  belt  and  spills. 
With  many  substances  it  is  important  to  feed  the  belt  steadily  if  the  con- 
veyor stands  at  or  near  the  limiting  angle.  If  the  flow  is  interrupted 
the  material  may  slide  back  on  the  belt. 

Belt  conveyprs  are  run  at  any  speed  from  200  to  800  feet  per  minute, 
and  are  made  in  widths  varying  from  12  inches  to  60  inches. 


CONVERGES. 


1199 


Values  of  A  and  B. 


Angle, 
Deg. 

A 

B 

Angle, 
Deg. 

A 

B 

Angle, 
Deg. 

A 

B 

0 
2 

6 
8 

0.343 
0.378 
0.40 
0.44 
0.47 

0.01 
0.01 
0.01 
0.01 
0.01 

10 
14 
18 
22 
26 

0.50 
0.57 
0.63 
0.69 
0.74 

0.01 
0.01 
0.009 
0.009 
0.009 

30 
34 
38 
42 
46 

0.79 
0.84 
0.88 
0.92 
0.95 

0.009 
0.008 
0.008 
0.007 
0.007 

For  suspended  flight  conveyors  take  B  as  0.8  and  for  roller  flights  as 
0.6,  of  the  values  given  in  the  table. 

Weight  of  Chain  in  Pounds  per  Foot. 


LINK-BELTING. 

MONOBAR. 

Chain 
No. 

Pitch  of  Flights,  Inches. 

Chain 
No.* 

Pitch  of  Flights,  Inches. 

12 

18 

24 

36 

12 

18 

24 
3  6 

36 

48 

54 

72 

78 
88 
85 
103 
108 
110 
114 
122 
124 

2.4 
2.8 
3.1 
4.6 
4.9 
5.6 
6.3 
8.1 
8.9 

2.3 
2.7 

2.8  ' 
4.4 
4.7 
5.2 
6.0 
7.7 
8.4 

2.26 
2.6 
2.7 

4.3 
4.4 
4.9 
5.9 
7.4 
8.2 

2.2 
2.5 
2.6 
4.2 
4'.1 
4.7 
5.7 
7.2 
7.9 

612 
618 
818 
824 
1018 
1024 
1224 
1236 
1424 

3.9 

3  5 

3.0 
S  7 

2.8 
5  5 



2.7 
5.3 



4  9 

4.7 

4.6 

'  '8.8* 
13.8 
11.34 
19.4 

11.5 

'9!6 
14.7 

10.7 

ii*8 

'  9.07 
14.04 

10.4 

?0  5 

19.7 

*  In  monobar  the  first  one  or  two  figures  in  the  number  of  the  chain 
denote  the  diameter  of  the  chain  in  eighths  of  an  inch.  The  last  two 
figur.es  denote  the  pitch  in  inches. 


PIN  CHAINS. 

ROLLER  CHAINS. 

No. 

Pitch  of  Flights,  Inches. 

No. 

Pitch  of  Flights,  Inches. 

12 

18 

24 

36 

12 
7.7 
9.5 
10.5 

18 
6.9 
8.8 
9.5 

24 
"672 
8.0 
9.0 

36 
T7 
7.5 
7.8 

720 
730 
825 

5.9 
6.9 
9.6 

5.6 
6.6 
9.3 

5.4 
6.4 
9.1 

5.3 
6.3 
8.9 

1112 
1113 
1130 

Weight  of  Flights  with  Wearing-shoes  and  Bolts. 


Size,  Inches. 

Steel. 

Malleable  Iron. 

Suspended  Flights. 

Size. 

Weight,  Lb. 

4X10 

3.5 

4.3 

6X14 

12.37 

4X12 

3.9 

4.7 

8X19 

15.55 

5X10 

4.1 

5.2 

10X24 

25.57 

5X12 

4.6 

5.7 

10X30 

29.37 

5X15 

5.8 

5.9 

10X36 

33.17 

6X18 

8.1 

9.2 

10X42 

34.97 

8X18 

10.1 

12.7 

8X20 

11.0 

13.4 

8X24 

12.6 

14.4 

10X24 

15.2 

17.4 

Capacity  of  Belt  Conveyors  in  Tons  of  Coal  per  Hour. 


Width 
of 

S: 

•i 

18 

Velocity,  Feet  per 
Minute. 

Width 
of 
Belt, 
Ins. 

Velocity,  Feet  per  Minute. 

300 

34 
47 
62 
78 

350 

400 

300 

350 

400 

450 

500 

72 
91 

82 
104 

20 

24 
30 
36 

96 

139 
218 
315 

112 
162 
254 
368 

128 
186 
290 
420 

210 
326 
472 

520 

1200 


HOISTING  AND   CONVEYING. 


For  materials  other  than  coal,  the  figures  in  the  above  table  should  be 
multiplied  by  the  coefficients  given  in  the  table  below: 


Material. 

Coefficient. 

Material. 

Coefficient. 

Ashes  (damp)  

0  86 

Earth  

1.4 

Cement  

1.76 

Sand  

1.8 

Clay  

1.26 

Stone  (crushed)  

2.0 

Coke  

0.60 

Belt  Conveyor  Construction.  (C.  K.  Baldwin,  Trans.  A.  S.  M.  E.^ 
1908.) — The  troughing  idlers  should  be  spaced  as  follows,  depending 
on  the  weight  of  the  material  carried: 

Belt  width         12-16  in.         18-22  in.         24-30  in.         32-36  in. 
Spacing,  ft.          4>^-5  4-4  Y2  3^-4  3-3  Y2 

The  stress  in  the  belt  should  not  exceed  18  to  20  Ib.  per  inch  of  width 
per  ply  with  rubber  belts.  This  may  be  increased  about  20%  with 
belts  in  which  28  oz.  duck  is  used.  Where  the  power  required  is  small 
the  stiffness  of  the  belt  fixes  the  number  of  plies.  The  minimum  num- 
ber of  plies  is  as  follows: 

Belt  width,  in.  12-14  16-20  22-28  30-36 

Minimum  plies  3456 

Pulleys  of  small  diameter  should  be  avoided  on  heavy  belts,  or  the  con- 
stant bending  of  the  belt  under  heavy  stress  will  cause  the  friction  to 
lose  its  hold  and  destroy  the  belt.  In  many  cases  it  is  advisable  to 
cover  the  driving  pulley  with  a  rubber  lagging  to  increase  the  tractive 
power,  particularly  in  dusty  places.  The  minimum  size  of  driving 
pulleys  to  be  used  is  shown  in  the  table  below. 

Smallest  Diameter  of  Driving  Pulleys  for  Belt  Conveyors. 


Width  of 
Belt. 

Diameter 
of  Pulley. 

Width  of 
Belt. 

Diameter  of 
Pulley. 

Width  of 
Belt. 

Diameter  of 
Pulley. 

In. 
12 
14 
16 

16 

In. 
16-18 
16-18 
20-24 
20  24 

In. 
22 
24 
26 
28 

In. 
20-30 
24-30 
24-30 
24-30 

In. 
32 
34 
36 

In. 
30-36 
30-42 
30-48 

20 

20-24 

30 

30-36 

Horse-power  to  Drive  Belt  Conveyors.  (C.  K.  Baldwin,  Trans. 
A.  S.  M.  E.,  1908.)  —  The  power  required  to  drive  a  belt  conveyor  de- 
pends on  a  great  variety  of  conditions,  as  the  spacing  of  idlers,  type  of 
drive,  thickness  of  belt,  etc.  In  figuring  the  power  required,  the  belt 
should  run  no  faster  than  is  necessary  to  carry  the  desired  load.f  If  it 
should  be  necessary  to  increase  the  speed,  the  load  should  be  increased 
in  proportion  and  the  power  figured  accordingly. 

For  level  conveyors  H.P.  =  CX  TXL  +  1000.  , 

For  inclined  conveyors 

H.P.   =  (C  X  T  XL  -J-  1000)   +  (T  XH  -5-  1000). 

C  ~  power  constant  from  table  below;  T  =  load,  tons  per  hour;  L  = 
length  of  conveyor,  center  to  center,  ft. ;  H  =  vertical  height  material  is 
lifted,  ft.;  S  =  belt  speed,  ft,  per  minute;  B  =  width  of  belt,  in. 

For  each  movable  or  fixed  tripper  add  horse-power  in  column  3  of 
table.  Add  20%  to  horse-power  for  each  conveyor  under  50  ft.  long. 
Add  10%  to  horse-power  for  each  conveyor  between  50  ft.  and  100  ft. 
long.  The  formulae  above  do  not  include  gear  friction,  should  the 
conveyor  be  gear-driven. 

When  horse-power  ana  speed  are  known  the  stress  in  the  belt  in  pounds 
per  inch  of  width  is 

Stress  .H.P.XM.OOO. 

From  this  the  number  of  plies  can  be  found,  using  20  Ib.  per  ply  per 
inch  of  width  as  a  maximum  for  rubber  belts. 

Relative  Wearing  Power  of  Conveyor  Belts.  (T.  A.  Bennett, 
Trans.  A.  S.  M.  E.,  1908.) — Different  materials  used  in  the  construction 


PNEUMATIC    CONVEYING. 
Constants  for  Formulae  for  Belt  Conveyors. 


1201 


;  

1 

2 

3 

4 

5 

Width  of 
Belt, 
In. 

C  for  Mate- 
rial Weigh- 
ing from  25 
Lb.  to  75  Lb. 
per  Cu.  Ft. 

C  for  Mate- 
rial Weigh- 
ing from  75 
Lb.  to  125Lb. 
per  Cu.  Ft. 

H.P.  Re- 
quired for 
Each  Mov- 
able or 
Fixed 
Tripper. 

Minimum 
Plies  of 
Belt. 

Maximum 
Plies  of 
Belt. 

12 

0.234 

0.147 

1/2 

3 

4 

14 

0.226 

0.143 

1/2 

3 

4 

16 

0.220 

0.140 

3/4 

4 

5 

18 

0.209 

0.138 

1 

4 

5 

20 

0.205 

0.136 

1  1/4 

4 

6 

22 

0.199 

0.133 

1  1/2 

5 

6 

24 

0.195 

0.131 

13/4 

5 

7 

26 

0.187 

0.127 

2 

5 

7 

28 

0.175 

0.121 

21/4 

5 

8 

30 

0.167 

0.117 

21/2 

6 

8 

32 

0.163 

0.115 

23/4 

6 

9 

34 

0.161 

0.114 

3 

6 

10 

36 

0.157 

0.112 

31/4 

6 

10 

Of  conveyors  were  subjected  to  the  uniform  action  of  a  sand  blast  for  45 
minutes,  and  the  relative  abrasive  resisting  qualities  were  found  to  be  as 
follows,  taking  the  volume  of  rubber  belt  worn  away  as  1.0: 

Rubber  belt 1.0     Woven  cotton  belt,  high  grade  6 . 5 

Rolled  steel  bar 1.5     Stitched  duck,  high  grade 8.0 

Cast  iron 3.5     Woven  cotton  belt,  low  grade,  9.0  to 

Balata  belt,  including  gum  cover  5.0  15.0 

A  Symposium  on  Hoisting  and  Conveying  was  presented  at  the  Detroit 
meeting  of  the  A.  S.  M.  E,  1908  (Trans.,  vol.  xxx.),  in  papers  by  G.  E. 
Titcomb,  S.  B.  Peck,  C.  K.  Baldwin,  C.  J.  Tomlinson  and  E.  J.  Haddock. 
Among  the  subjects  discussed  are  the  loading  and  unloading  of  cargo 
steamers;  car  unloaders;  storing  of  ore  and  coal;  continuous  conveying  of 
merchandise;  conveying  in  a  Portland  cement  plant,  and  suspension 
cable  ways. 

PNEUMATIC  CONVEYING 

Pneumatic  Conveying. — A  pneumatic  conveying  system  consists  of 
a  pipe  line,  a  feeding  hopper,  a  blower  or  exhauster,  and  a  receiver.  It 
is  used  for  conveying  grain,  slack  coal,  sawdust,  shavings,  and  other 
light  material.  Grain  has  been  carried  over  2,000  ft.  Iwrizontally  and 
raised  to  any  desired  height.  The  pressure  system  is  simpler  and 
requires  less  pipe  than  the  vacuum  system,  but  the  latter  is  more  com- 
mon and  is  adapted  to  a  greater  variety  of  conditions.  The  principal 
advantages  of  the  pneumatic  system,  as  against  all  types  of  mechanical 
conveyors,  are  simplicity,  adaptability  to  peculiar  conditions,  the  little 
attention  required,  few  repairs,  and  shut-downs.  (For  details  of 
apparatus,  etc.,  see  bulletins  of  the  Connersville  Blower  Co.) 

Pneumatic  Postal  Transmission. — A  paper  by  A.  Falkenau  (Eng'rs 
Club  of  Philadelphia,  April,  1894),  entitled  the  "First  United  States 
Pneumatic  Postal  System,"  gives  a  description  of  the  system  used  in 
London  and  Paris,  and  that  recently  introduced  in  Philadelphia  between 
the  main  post-office  and  a  substation.  In  London  the  tubes  are  2  ]4  and 
3-inch  lead  pipes  laid  in  cast-iron  pipes  for  protection.  The  carriers 
used  in  2  J^-inch  tubes  are  but  1 H  inches  diameter,  the  remaining  space 
being  taken  up  by  packing.  Carriers  are  despatched  singly.  First, 
vacuum  alone  was  used ;  later,  vacuum  and  compressed  air.  The  tubes 
used  in  the  Continental  cities  in  Europe  are  wrought  iron,  the  Paris  tubes 
being  2  y2  inches  diameter.  There  the  carriers  are  despatched  in  trains 
of  six  to  ten,  propelled  by  a  piston.  In  Philadelphia  the  size  of  tube 
adopted  is  6  y%  inches,  the  tubes  being  of  cast  iron  bored  to  size.  The 
lengths  of  the  outgoing  and  return  tubes  are  2928  feet  each.  The  pressure 


1202  HOISTING  AND   CONVEYING. 

at  the  main  station  is  7  lb.,  at  the  substation  4  lb.,  and  at  the  end  of  the 
return  pipe  atmospheric  pressure.  The  compressor  has  two  air-cylinders 
18  X  24  in.  Each  carrier  holds  about  200  letters,  but  100  to  150  are 
taken  as  an  average.  Eight  carriers  may  be  despatched  in  a  minute, 
giving  a  delivery  of  48,000  to  72,000  letters  per  hour.*  The  time 
required  in  transmission  is  about  57  seconds. 

Pneumatic  postal  transmission  tubes  were  laid  in  1898  by  the  Batcheller 
Pneumatic  Tube  Co.  between  the  general  post-offices  in  New  York  and 
Brooklyn,  crossing  the  East  River  on  the  Brooklyn  bridge.  The  tubes 
are  cast  iron,  12-ft.  lengths,  bored  to  8 1/8  in.  diameter.  The  joints  are 
bells,  calked  with  lead  and  yarn.  There  are  two  tubes,  one  operating 
in  each  direction.  Both  lines  are  operated  by  air-pressure  above  the 
atmospheric  pressure.  One  tube  is  operated  by  an  air-compressor  in  the 
New  York  office  and  the  other  by  one  located  in  the  Brooklyn  office. 

The  carriers  are  24  in.  long,  in  the  form  of  a  cylinder  7  in.  diameter, 
and  are  made  of  steel,  with  fibrous  bearing-rings  which  fit  the  tube.  Each 
carrier  will  contain  about  600  ordinary  letters,  and  they  are  despatched 
at  intervals  of  10  seconds  in  each  direction,  the  time  of  transit  between 
the  two  offices  being  31/2  minutes,  the  carriers  travelling  at  a  speed  of 
from  30  to  35  miles  per  hour. 

One  of  the  air-compressors  is  of  the  duplex  type  and  has  two  steam- 
cylinders  10  X  20  in.  and  two  air-cylinders  24  X  20  in.,  delivering 
1570  cu.  ft.  of  free  air  per  minute,  at  75  r.p.m.  The  power  is  about  50  H.P. 

Two  other  duplex  air-compressors  have  steam-cylinders  14  X  18  in. 
and  air-cylinders  261/4X18  in.  They  are  designed  for  80  to  90  r.p.m. 
and  to  compress  to  20  lb.  per  sq.  in. 

Another  double  line  of  pneumatic  tubes  has  been  laid  between  the 
main  office  and  Postal  Station  H,  Lexington  Ave.  and  44th  St.,  in  New 
York  City.  This  line  is  about  31/2  miles  in  length.  There  are  three 
intermediate  stations.  The  carriers  can  be  so  adjusted  when  they  are 
put  into  the  tube  that  they  will  traverse  the  line  and  be  discharged  auto- 
matically from  the  tube  at  the  station  for  which  they  are  intended.  The 
tubes  are  of  the  same  size  as  those  of  the  Brooklyn  line  and  are  operated 
in  a  similar  manner.  The  initial  air-pressure  is  about  12  to  15  lb.  On 
the  Brooklyn  line  it  is  about  7  lb. 

There  is  also  a  tube  system  between  the  New  York  Post-office  and  the 
Produce  Exchange.  For  a  very  complete  description  of  the  system  and 
its  machinery  see  "The  Pneumatic  Despatch  Tube  System,"  by  B.  C. 
Batcheller,  J.  B.  Lippincott  Co.,  Philadelphia,  1897. 

WIRE-ROPE  HAULAGE. 

Methods  for  transporting  coal  and  other  products  by  means  of  wire  rope, 
though  varying  from  each  other  in  detail,  may  be  grouped  in  five  classes: 
I.  The  Self-acting  or  Gravity  Inclined  Plane. 
II.  The  Simple  Engine-plane. 

III.  The  Tail-rope  System. 

IV.  The  Endless-rope  System. 
V.   The  Cable  Tramway. 

The  following  brief  description  of  these  systems  is  abridged  from  a 
pamphlet  on  Wire-rope  Haulage,  by  Wm.  Hildenbrand,  C.E.,  published 
by  John  A.  Roebling's  Sons  Co.,  Trenton,  N.  J. 

I.  The  Self-acting  Inclined  Plane.  —  The  motive  power  for  the 
self-acting  inclined  plane  is  gravity;  consequently  this  mode  of  transport- 
ing coal  finds  application  only  in  places  where  the  coal  is  conveyed  from  a 
higher  to  a  lower  point  and  where  the  plane  has  sufficient  grade  for  the 
loaded  descending  cars  to  raise  the  empty  cars  to  an  upper  level. 

At  the  head  of  the  plane  there  is  a  drum,  which  is  generally  constructed 
of  wood,  having  a  diameter  of  seven  to  ten  feet.  It  is  placed  high  enough 
to  allow  men  and  cars  to  pass  under  it.  Loaded  cars  coming  from- the  pit 
are  either  singly  or  in  sets  of  two  or  three  switched  on  the  traclf  of  the 
plane,  and  their  speed  in  descending  is  regulated  by  a  brake  on  the  drum. 
Supporting  rollers,  to  prevent  the  rope  dragging  on  the  ground,  are 

*  A  report  of  a  U.  S.  Postal  Commission  states  that  up  to  the  present 
time  (1910),  the  sending  and  receiving  apparatus  does  not  permit  the 
successful  operation  of  carrier  service  with  an  interval  of  less  than 
13  to  15  seconds  between  carriers,  for  6-  and  8-in,  tubes. 


WIRE-ROPE  HAULAGE.  1203 

generally  of  wood,  5  to  6  in.  in  diameter  and  18  to  24  in.  long,  with 

3/4  to  7/8  in.  iron  axles.  The  distance  between  the  rollers  varies  from  15  to 
30  ft.,  steeper  planes  requiring  less  rollers  than  those  with  easy  grades. 
Considering  only  the  reduction  of  friction  and  what  is  best  for  the  preserva- 
tion of  rope,  a  general  rule  may  be  given  to  use  rollers  of  the  greatest 
possible  diameter,  and  to  place  them  as  close  as  economy  will  permit 

The  smallest  angle  of  inclination  at  which  a  plane  can  be  made  self- 
acting  will  be  when  the  motive  and  resisting  forces  balance  each  other. 
The  motive  forces  are  the  weights  of  the  loaded  car  and  of  the  descending 
rope.  The  resisting  forces  consist  of  the  weight  of  the  empty  car  and 
ascending  rope,  of  the  rolling  and  axle  friction  of  the  cars,  and  of  the  axle 
friction  of  the  supporting  rollers.  The  friction  of  the  drum,  stiffness  of 
rope,  and  resistance  of  air  may  be  neglected.  A  general  rule  cannot  be 
given,  because  a  change  in  the  length  of  the  plane  or  in  the  weight  of  the 
cars  changes  the  proportion  of  the  forces;  also,  because  the  coefficient  ot 
friction,  depending  on  the  condition  of  the  road,  construction  of  the  cars, 
etc.,  is  a  very  uncertain  factor. 

For  working  a  plane  with  a  5/8_in.  steel  rope  and  lowering  from  one  to 
four  pit  cars  weighing  empty  1400  Ib.  and  loaded  4000  lb.,  the  rise  in  100  ft. 
necessary  to  make  the  plane  self-acting  will  be  from  about  5  to  10  ft., 
decreasing  as  the  number  of  cars  increase,  and  increasing  as  the  length  or 
plane  increases. 

A  gravity  inclined  plane  should  be  slightly  concave,  steeper  at  the  top 
than  at  the  bottom.  The  maximum  deflection  of  the  curve  should  be  at 
an  inclination  of  45  degrees,  and  diminish  for  smaller  as  well  as  for  steeper 
inclinations. 

II.  The  Simple  Engine-plane.  —  The  name  "  Engine-plane"  is  given 
to  a  plane  on  which  a  load  is  raised  or  lowered  by  means  of  a  single  wire 
rope  and  stationary  steam-engine.     It  is  a  cheap  and  simple  method  of 
conveying  coal  underground,  and  therefore  is  applied  wherever  circum- 
stances permit  it.      Under  ordinary  conditions  such  as  prevail  in  the 
Pennsylvania  mine  region,  a  train  of  twenty-five  to  thirty  loaded  cars  will 
descend,  with  reasonable  velocity,  a  straight  plane  5000  ft.  long  on  a 
grade  of  1  s/4  ft.  in  100,  while  it  would  appear  that  21/4  ft.  in  100  is  neces- 
sary for  the  same  number  of  empty  cars.     For  roads  longer  than  5000  ft. 
or  containing  sharp  curves,  the  grade  should  be  correspondingly  larger. 

III.  The  Tail-rope  System.  —  Of  all  methods  for  conveying  coal 
underground  by  wire  rope,  the  tail-rope  system  has  found  the  most  appli- 
cation.    It  can  be  applied  under  almost  any  condition.     The  road  may  be 
straight  or  curved,  level  or  undulating,  in  one  continuous  line  or  with  side 
branches.     In  general  principle  a  tail-rope  plane  is  the  same  as  an  engine- 
plane  worked  in  both  directions  with  two  ropes.     One  rope,  called  the 
*'  main  rope,"  serves  for  drawing  the  set  of  full  cars  outward;  the  other, 
called  the  "  tail-rope,"  is  necessary  to  take  back  the  empty  set,  which  ou 
a  level  or  undulating  road  cannot  return  by  gravity.     The  two  drums  may 
be  located  at  the  opposite  ends  of  the  road,  and  driven  by  separate  engines, 
but  more  frequently  they  are  on  the  same  shaft  at  one  end  of  the  plane, 
In  the  first  case  each  rope  would  require  the  length  of  the  plane,  but  in  the 
second  case  the  tail  rope  must  be  twice  as  long,  being  led  from  the  drum 
around  a  sheave  at  the  other  end  of  the  plane  and  back  again  to  its  starting- 
point.  •   When  the  main  rope  draws  a  set  of  full  cars  out,  the  tail-rope  drum 
runs  loose  on  the  shaft,  and  the  rope,  being  attached  to  the  rear  car,  un- 
winds itself  steadily.     Going  in,  the  reverse  takes  place.     Each  drum  is 
provided  with  a  brake  to  check  the  speed  of  the  train  on  a  down  grade  and 
prevent  its  overrunning  the  forward  rope.     As  a  rule,  the  tail  rope  is 
strained  less  than  the  main  rope,  but  in  cases  of  heavy  grades  dipping  out- 
ward it  is  possible  that  the  strain  in  the  former  may  become  as  large,  or 
even  larger,  than  in  the  latter,  and  in  the  selection  of  the  sizes  reference 
should  be  had  to  this  circumstance. 

IV.  The  Endless-rope   System.  —  The  principal   features  of  this 
system  are  as  follows: 

1.  The  rope,  as  the  name  indicates,  is  endless.  2.  Motion  is  given  to 
the  rope  by  a  single  wheel  or  drum,  and  friction  is  obtained  either  by  a 
grip-wheel  or  by  passing  the  rope  several  times  around  the  wheel.  3.  The 
rope  must  be  kept  constantly  tight,  the  tension  to  be  produced  by  artificial 
means.  It  is  done  in  placing  either  the  return-wheel  or  an  extra  tension 
wheel  on  a  carriage  and  connecting  it  with  a  weight  hanging  over  a 
pulley,  or  attaching  it  to  a  fixed  post  by  a  screw  which  occasionally  can  be 


1204 


HOISTING  AND    CONVEYING. 


shortened.  4.  The  cars  are  attached  to  the  rope  by  a  grip  or  clutch, 
which  can  take  hold  at  any  place  and  let  go  again,  starting  and  stopping 
the  train  at  will,  without  stopping  the  engine  or  the  motion  of  the  rope 
5.  On  a  single-track  road  the  rope  works  forward  and  backward,  but  on  a 
double  track  it  is  possible  to  ran  it  always  in  the  same  direction,  the  full 
cars  going  on  one  track  and  the  empty  cars  on  the  other. 

This  method  of  conveying  coal,  as  a  rule,  has  not  found  as  general  an  in- 
troduction as  the  tail-rope  system,  probably  because  its  efficacy  is  not  so 
apparent  and  the  opposing  difficulties  require  greater  mechanical  skill  and 
more  complicated  appliances.  Its  advantages  are,  first,  that  it  requires 
one-third  less  rope  than  the  tail-rope  system.  This  advantage,  however, 
is  partially  counterbalanced  by  the  circumstance  that  the  extra  tension  in 
the  rope  requires  a  heavier  size  to  move  the  same  load  than  when  a  main 
and  tail  rope  are  used.  The  second  and  principal  advantage  is  that  it  is 
possible  to  start  and  stop  trains  at  will  without  signaling  to  the  engineer. 
On  the  other  hand,  it  is  more  difficult  to  work  curves  with  the  endless  sys- 
tem, and  still  more  so  to  work  different  branches,  and  the  constant  stretch 
of  the  rope  under  tension  or  its  elongation  under  changes  of  temperature 
frequently  causes  the. rope  to  slip  on  the  wheel,  in  spite  of  every  attention, 
causing  delay  in  the  transportation  and  injury  to  the  rope. 

Stress  in  Hoisting-ropes  on  Inclined  Planes. 

(Trenton  Iron  Co.,  1906.) 


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The  above  table  is  based  on  an  allowance  of  40  Ib.  per  ton  for  rolling 
friction,  but  an  additional  allowance  must  be  made  for  stress  due  to  the 
weight  of  the  rope  proportional  to  the  length  of  the  plane.  A  factor  of 
safety  of  5  to  7  should  be  taken. 

In  hoisting  the  slack-rope  should  be  taken  up  gently  before  beginning 
the  lift,  otherwise  a  severe  extra  strain  will  be  brought  on  the  rope. 

V.  Wire-rope  Tramways.  —  The  methods  of  conveying  products  on 
a  suspended  rope  tramway  find  especial  application  in  places  where  a  mine 
is  located  on  one  side  of  a  river  or  deep  ravine  and  the  loading  station  on 
the  other.  A  wire  rope  suspended  between  the  two  stations  forms  the 
track  on  which  material  in  properly  constructed  "  carriages  "  or  "  buggies" 
is  transported.  It  saves  the  construction  of  a  bridge  or  trestlework  and  is 
practical  for  a  distance  of  2000  feet  without  an  intermediate  support. 

There  are  two  distinct  classes  of  rope  tramways: 

1.  The  rope  is  stationary,  forming  the  track  on  which  a  bucket  holding 
the  material  moves  forward  and  backward,  pulled  by  a  smaller  endless 
wire  rope.  2.  The  rope  is  movable,  forming  itself  an  endless  line,  which 
serves  at  the  same  time  as  supporting  track  and  as  pulling  rope. 

Of  these  two  the  first  method  has  found  more  general  application,  and 
is  especially  adapted  for  long  spans,  steep  inclinations,  and  heavy  loads. 


WIRE-ROPE  HAULAGE.  1205 

The  second  method  is  used  for  long  distances,  divided  into  short  spans, 
and  is  only  applicable  for  light  loads  delivered  at  regular  intervals. 

For  detailed  descriptions  of  the  several  systems  of  wire-rope  transporta- 
tion, see  circulars  of  John  A.  Roebling's  Sons  Co.,  The  Trenton  Iron  Co., 
A.  Leschen  &  Sons  Rope  Co.  See  also  paper  on  Two-rope  Haulage  Sys- 
tems, by  R.  Van  A.  Norris,  Trans.  A.  S.  M.  E.,  xii.  626. 

In  the  Bleichert  System  of  wire-rope  tramways,  in  which  the  track  rope 
is  stationary,  loads  up  to  2000  Ib.  are  carried  at  a  speed  cf  3  to  4  miles  per 
hour.  While  the  average  spans  on  a  level  are  from  150  to  200  ft.,  in  cross- 
ing rivers,  ravines,  etc.,  spans  up  to  1500  ft.  are  frequently  adopted.  In  a 
tramway  on  this  system  at  Bingham,  Utah,  the  total  length  of  the  line  is 
12,700  ft.  with  a  fall  of  1120  ft.  The  line  operates  by  gravity  and  carries 
35  tons  per  hour.  The  cost  of  conveying  on  this  carrier  is  73/4  cents  per 
ton  of  2000  Ib.  for  labor  and  repairs,  without  any  apparent  deterioration 
in  the  condition  of  track  cables  and  traction  rope. 

The  Aerial  Wire-rope  Tramway  of  A.  Leschen  &  Sons  Co.  is  of  the 
double-rope  type,  in  which  the  buckets  travel  upon  stationary  track 
cables  and  are  propelled  by  an  endless  traction  rope.  The  buckets  are 
attached  to  the  traction  rope  by  means  of  clips  —  spaced  according  to 
the  desired  tonnage.  The  hold  on  the  rope  is  positive,  but  the  clip  is 
easily  removable.  The  bucket  is  held  in  its  normal  position  in  the  frame 
by  two  malleable,  iron  latches  —  one  on  each  side.  A  tripping  bar 
engages  these  latches  at  the  unloading  terminal  when  the  bucket  dis- 
charges its  material.  This  operation  is  automatic  and  takes  place  while 
the  carriers  are  moving.  At  the  loading  terminal,  the  bucket  is  auto- 
matically returned  to  its  normal  position  and  latched.  Special  carriers 
are  provided  for  the  accommodation  of  any  class  of  material.  At  each 
of  the  terminal  stations  is  a  10-ft.  sheave  wheel  around  which  the  trac- 
tion rope  passes,  these  wheels  being  provided  with  steel  grids  for  the 
control  of  the  traction  rope.  When  the  loaded  carriers  travel  down 
grade  and  the  difference  in  elevation  is  sufficient,  this  tramway  will 
operate  by  the  force  due  to  gravity,  otherwise  the  power  is  applied  to 
the  sheaves  through  bevel  gearing.  Numerous  modifications  of  the 
system  are  in  use  to  suit  different  conditions. 

An  Aerial  Tramway  21.5  miles  long,  with  an  elevation  of  the  loading 
end  above  the  discharging  end  of  11,500  ft.,  built  by  A.  Bleichert  &  Co. 
for  the  government  of  the  Argentine  Republic,  connecting  the  mines  9! 
La  Mejicana  with  the  town  of  Chilecito,  is  described  by  Wm.  Hewitt  in 
Indust.  Eng.,  Aug.  15,  1909.  Some  of  the  inclinations  are  as  much  as 
45  deg.,  there  are  some  spans  nearly  3000  ft.  long,  and  there  is  a  tunnel 
nearly  500  ft.  long.  The  line  is  divided  into  eight  sections,  each  with 
an  independent  traction  rope.  The  gravity  of  the  descending  loaded 
carriers  is  sufficient  to  make  the  line  self-operating  when  it  is  once  set 
in  motion,  but  in  order  to  ensure  full  control,  and  to  provide  for  carrying 
four  tons  upward  while  the  descending  carriers  are  empty,  four  steam 
engines  are  installed,  one  for  each  two  sections.  The  carriers  hold  10  cu. 
ft.,  or  about  1100  Ibs.  of  ore.  The  speed  is  500  ft.  per  minute,  and  the 
interval  between  carriers  45  seconds.  The  stress  in  the  traction  rope  is 
as  high  as  11,000  Ibs.  in  some  sections. 

Suspension  Cableways  or  Cable  Hoist-conveyors. 

(Trenton  Iron  Co.) 

In  quarrying,  rock-cutting,  stripping,  piling,  dam-building,  and  many 
other  operations  where  it  is  necessary  to  hoist  and  convey  large  individual 
loads  economically,  it  frequently  happens  that  the  application  of  a  system 
of  derricks  is  impracticable,  by  reason  of  the  limited  area  of  their  effi- 
ciency and  the  room  which  they  occupy.  To  meet  such  conditions  cable 
hoist-conveyors  are  adopted,  as  they  can  be  operated  in  clear  spans  up  to 
1500  ft.,  and  in  lifting  individual  loads  up  to  15  tons.  Two  types  are 
made  —  one  in  which  the  hoisting  and  conveying  are  done  by  separate 
running  ropes,  and  the  other  applicable  only  to  inclines  in  which  the 
carnage  descends  by  gravity,  and  but  one  running  rope  is  required.  The 
moving  of  the  carriage  in  the  former  is  effected  by  means  of  an  endless 
rope,  and  these  are  commonly  known  as  "  endless-rope  "  hoist-conveyors 
istinguish  them  from  the  latter,  which  are  termed  "inclined"  hoist- 
conveyors. 


1206  HOISTING  AND  CONVEYING. 

The  general  arrangement  of  the  endless-rope  hoist-conveyors  consists 
of  a  main  cable  passing  over  towers,  A-frames  or  masts,  as  may  be  most 
convenient,  and  anchored  firmly  to  the  ground  at  each  end,  the  requisite 
tension  in  the  cable  being  maintained  by  a  turnbuckle  at  one  anchorage. 

Upon  this  cable  travels  the  carriage,  which  is  moved  back  and  forth 
over  the  line  by  means  of  the  endless  rope.  The  hoisting  is  done  by  a 
separate  rope,  both  ropes  being  operated  by  an  engine  specially  designed 
for  the  purpose,  which  may  be  located  at  either  end  of  the  line,  and  is 
constructed  in  such  a  way  that  the  hoisting-rope  is  coiled  up  or  paid  out 
automatically  as  the  carriage  is  moved  in  and  out.  Loads  may  be  picked 
up  or  discharged  at  any  point  along  the  line.  Where  sufficient  inclination 
can  be  obtained  in  the  main  cable  for  the  carriage  to  descend  by  gravity, 
and  the  loading  and  unloading  are  done  at  fixed  points,  the  endless  rope  can 
be  dispensed  with.  The  carriage,  which  is  similar  in  construction  to  the 
carriage  used  in  the  endless-rope  cableways,  is  arrested  in  its  descent  by  a  | 
stop-block,  which  may  be  clamped  to  the  main  cable  at  any  desired  point, 
the  speed  of  the  descending  carriage  being  under  control  of  a  brake  on  the 
engine-drum. 

A  Double-suspension  Cableway,  carrying  loads  of  15  tons,  erected  near 
Williamsport,  Pa.,  by  the  Trenton  Iron  Co.,  is  described  by  E.  G.  Spilsbury 
in  Trans.  A.  I.  M.  E.,  xx.  766.  The  span  is  733  ft.,  crossing  the  Susque- 
hanna  River.  Two  steel  cables,  each  2  in.  diam.,  are  used.  On  these 
cables  runs  a  carriage  supported  on  four  wheels  and  moyed  by  an  endless 
cable  1  inch  in  diam.  The  load  consists  of  a  cage  carrying  a  railroad-car 
loaded  with  lumber,  the  latter  weighing  about  12  tons.  The  power  is 
furnished  by  a  50-H.P.  engine,  and  the  trip  across  the  river  is  made  in 
about  three  minutes. 

A  hoisting  cableway  on  the  endless-rope  system,  erected  by  the  Lidger- 
wood  Mfg.  Co.,  at  the  Austin  Dam,  Texas,  had  a  single  span  1350  ft.  in 
length,  with  main  cable  2 1/2  in.  diam.,  and  hoisting-rope  13/4  in.  diam. 
Loads  of  7  to  8  tons  were  handled  at  a  speed  of  600  to  800  ft.  per  minute. 

Another,  of  still  longer  span,  1650  ft.,  was  erected  by  the  same  company 
at  Holyoke,  Mass.,  for  use  in  the  construction  of  a  darn.  The  main  cable 
is  the  Elliott  or  locked-wire  cable,  having  a  smooth  exterior.  In  the  con- 
struction of  the  Chicago  Drainage  Canal  twenty  cableways,  of  700  ft.  span 
and  8  tons  capacity,  were  used,  the  towers  traveling  on  rails, 

Tension  required  to  Prevent  Slipping  of  Rope  on  Drum.  (Trenton 
Iron  Co.,  1906.)  —  The  amount  of  artificial  tension  to  be  applied  in  an 
endless  rope  to  prevent  slipping  on  the  driving-drum  depends  on  the  char- 
acter of  the  drum,  the  condition  of  the  rope  and  number  of  laps  which  it 
makes.  If  T  and  S  represent  respectively  the  tensions  in  the  taut  and 
slack  lines  of  the  rope;  W,  the  necessary  weight  to  be  applied  to  the  tail- 
sheave;  R,  the  resistance  of  the  cars  and  rope,  allowing  for  friction;  n,  the 
number  of  half-laps  of  the  rope  on  the  driving-drum;  and  /,  the  coefficient 
of  friction,  the  following  relations  must  exist  to  prevent  slipping: 

T  =  Sefnir,  W  =  T+  S,    and  R  =  T  -  S] 
ffnir  ,    i 

from  which  we  obtain    W  =  — ; R, 

efnir-  I 

In  which  e  —  2.71828,  the  base  of  the  Naperian  system  of  logarithms. 
The  following  are  some  of  the  values  of/: 

Dry.         Wet.       Greasy. 

Wire-rope  on  a  grooved  iron  drum 0.120       0.085       0.070 

Wire-rope  on  wood-filled  sheaves 0. 235       0. 170       0. 140 

Wire-rope  on  rubber  and  leather  filling     0 . 495       0 . 400       0 . 205 
The  importance  of  keeping  the  rope  dry  is  evident  from  these  figures. 

afmr   i    i 

The  values  of  the  coefficient  -j— •  corresponding  to  the  above  values 

of/,  for  one  UD  to  six  half-laps  of  the  rope  on  the  driving-drum  or  sheaves. 
are  given  in  the  table  at  the  top  of  p.  1207. 

When  the  rope  is  at  rest  the  tension  is  distributed  equally  on  the  two 
lines  of  the  rope,  but  when  running  there  will  be  a  difference  in  the 
tensions  of  the  taut  and  slack  lines  equal  to  the  resistance,  and  the 
values  of  T  and  S  may  be  readily  computed  from  the  foregoing  formulae. 


WIRE-ROPE  HAULAGE. 


1207 


VALUES  OF  COEFFICIENT  (efnir  -f  i)  4- 


—  l) 


/ 

n  =  Number  of  Half-laps  on  Driving-wheel. 

1        I        2        |        3        |          4          |          5 

6 

0.070 

9.130 

4.623 

3.  141 

2.418 

.999 

.729 

0.085 

7.536 

3.833 

2.629 

2.047 

.714 

.505 

0.120 

5.345 

2.777 

.953 

.570 

.358 

.232 

0.140 

4.623 

2.418 

.729 

.416 

.249 

.154 

0.170 

3.833 

2.047 

.505 

.268 

.149 

.085 

0.205 

3.212 

1.762 

.338 

.165 

.083 

.043 

0.235 

2.831 

1.592 

.245 

.110 

.051 

.024 

0.400 

1.795 

1.176 

.047 

.013 

.004 

.001 

0.495 

1.538 

1  093 

.019 

.004 

.001 

The  increase  in  tension  in  the  endless  rope,  compared  with  the  main 
rope. of  the  tail-rope  system,  where  the  stress  in  the  rope  is  equal  to 
the  resistance,  is  about  as  follows: 

n  =  123456 

Increase  in  tension  in  endless  rope, 

compared  with  direct  stress  %....     40         9         21/3    2/3     1/5     \/\Q 
These  figures  are  useful  in  determining  the  size  of  rope.   For  instance, 
if  the  rope  makes. two  half-laps  on  the  driving  drum,  the  strength  of  the 
rope  should  be  9  %  greater  than  a  main  rope  in  the  tail-rope  system. 

General  Formulae  for  Estimating   the  Deflection  of  a  Wire  Cable 
Corresponding  to  a  Given  Tension. 

(Trenton  Iron  Co.,  1906.) 

Let  s  =•  distance  between  supports  or  spanrAl?;  m  and  n  =  arms  into 
which  the  span  is  divided  by  a  vertical  through  the  required  point  of 
deflection  x,  m  representing  the  arm  corresponding  to  the  loaded  side; 
y  —  horizontal  distance  from  load  to  point  of  support  corresponding  with 
m;w  =  wt.  of  rope  per  ft.;  g  =  load;  t  —  tension;  h  =  required  deflection 
at  any  point  x\  all  measures  being  in  feet  and  pounds. 
A  B 


s- n — --=» 


FIG.  191. 

For  deflection  due  to  rope  alone, 

,       mnw    .  ws2    ^ 

h  =  -r-j-  at  x,  or  -—7  at  center  of  span. 

iL  t  o  t 

For  deflection  due  to  load  alone, 


h  =•  -T-  at  x,  or  ^  at  center  of  span. 
is  A  t 

If  y  =  1/2  $,  h  =  ^  at  #,  or  ^  at  center  of  span, 
at  x,  or  j-.  at  center  of  span. 


If  y  =  m,  h  = 
For  total  deflection, 

wmns  +  2  any 
h  =  -  — 

Z  IS 


A 
at  x,  or 


wsz  +  4  gu 
—   T\   yy 

o  t 


A 
at  center  of  span. 


rf  „  ,       wmn  -f  gn    .  ws*  +  2  gs    . 

If  2/  =  V2  s,  h  =  —  y    at  x,  or  -  —  —  —  at  center  of  span. 

2t  of 

wmns  +  2  gmn    A  wsz  +  2  gs    . 

If  y  =  m,  h  =  -  —  at  re,  or  -    .         at  center  of  span. 

^  tS  o  I 

If  the  tension  is  required  for  a  given  deflection,  transpose  t  and  h  in 
above  formulae. 


1208     TRANSMISSION  OF  POWER  BY  WIRE  ROPE. 

Taper  Ropes  of  Uniform  Tensile  Strength.  —  The  true  form  of  rope 
is  not  a  regular  taper  but  follows  a  logarithmic  curve,  the  girth  rapidly 
increasing  toward  the  upper  end.  Mr.  Chas.  D.  West  gives  the  following 
formula,  based  on  a  breaking  strain  of  80,000  Ib.  per  sq.  in.  of  the  rope, 
core  included,  and  a  factor  of  safety  of  10:  log  G  =  F  -7-36804-  log  g,  in 
which  F  =  length  in  fathoms,  and  G  and  g  the  girth  in  inches  at  any  two 
sections  F  fathoms  apart.  The  girth  g  is  first  calculated  for  a  safe  strain 
of  8000  Ib.  per  sq.  in.,  and  then  G  is  obtained  by  the  formula.  For  a 
mathematical  investigation  see  The  Engineer,  April,  1880,  p,  267. 


TRANSMISSION  OF  POWER  BY 
WIRE  ROPE. 


The  following  notes  have  been  furnished  to  the  author  by  Mr.  Wm. 
Hewitt,  Vice-President  of  the  Trenton  Iron  Co.  (See  also  circulars  of  the 
Trenton  Iron  Co.  and  of  the  J9hn  A.  Roebling's  Sons  Co.,  Trenton,  N.  J.; 
"  Transmission  of  Power  by  Wire  Ropes,"  by  A.  W.  Stahl,  Van  Nostrand's 
Science  Series,  No.  28;  and  Reuleaux's  Constructor.) 

The  load  stress  or  working  tension  should  not  exceed  the  difference 
between  the  safe  stress  and  the  bending  stress  as  determined  by  the  tablfe 
on  page  1209. 

The  approximate  strength  of  iron-wire  rope  composed  of  wires  hav- 
ing a  tensile  strength  of  75,000  to  90,000  Ibs.  per  sq.  in.  is  half  that  of 
cast-steel  rope  composed  of  wires  of  a  tensile  strength  of  150,000  to 
190,000  Ibs.  per  sq.  in.  Extra  strong  steel  wires  have  a  tensile  strength 
of  190,000  to  225,000  and  plow-steel  wires  225,000  to  275,000  Ibs.  per 
sq.  in. 

The  19-wire  rope  is  more  flexible  than  the  7-wire,  and  for  the  same 
load  stress  may  be  run  around  smaller  sheaves,  but  it  is  not  as  well 
adapted  to  withstand  abrasion  or  surface  wear. 

The  working  tension  may  be  greater,  therefore,  as  the  bending  stress 
is  less;  but  since  the  tension  in  the  slack  portion  of  the  rope  cannot  be 
less  than  a  certain  proportion  of  the  tension  in  the  taut  portion,  to  avoid 
slipping,  a  ratio  exists  between  the  diameter  of  sheave  and  the  wires 
composing  the  rope  corresponding  to  a  maximum  safe  working  tension. 
This  ratio  depends  upon  the  number  of  laps  that  the  rope  makes  about 

the  sheaves,  and  the  kind  of  filling  in 
the  rims  or  the  character  of  the  ma- 
terial upon  which  the  rope  tracks. 

For  ordinary  purposes  the  maximum 
safe  stress  should  be  about  one-third 
the  ultimate,  and  for  shafts  and  eleva- 
tors about  one-fourth  the  ultimate. 

*     l^H  ofT™    Hi         In  estimating  the  stress  due  to  the  load 

T    m  i\vm  W         for    shafts    and    elevators,    allowance 

!  should    be    made    for    the    additional 

stress  due  to  acceleration  in  starting. 
For  short  inclined  planes  not  used  for 
passengers  a  factor  of  safety  as  low  as 
21A  is  sometimes  used,  and  for  derricks, 
in  which  large  sheaves  cannot  be  used, 
and  long  life  of  the  rope  is  not  expected, 
the  factor  of  safety  may  be  as  low  as  2. 
The  Seale  wire  rope  is  made  of  six 
strands  of  19  wires,  laid  9  around  9 
around  1,  the  intermediate  layer  being  smaller  than  the  others.  It  is 
intermediate  in  flexibility  between  the  7-wire  and  the  ordinary  19-wire 
rope.  (In  the  Seale  cable  d  =  diam.  of  larger  wires.)  All  ropes  6 
strands  each.  Extra  flexible  rope  has  8  strands. 


Section 
of  Rim. 


FIG.  192. 


as 


The  sheaves  (Fig.  192),  are  usually  of  cast  iron,  and  are  made  as  light 
possible  consistent  with  the  requisite  strength.  Various  materials 
have  been  used  for  filling  the  bottom  of  the  groove,  such  as  tarred  oakum, 
jute  yarn,  hard  wood,  India-rubber,  and  leather.  The  filling  which 
gives  the  best  satisfaction,  however,  in  ordinary  transmissions  consists  of 


TRANSMISSION  OF  POWER  BY  WIRE  ROPE.        1209 
Approximate  Breaking  Strength  of  Steel-Wire  Ropes. 


6  Strands  of  19  Wires  Each. 

6  Strands  of  7  Wires  Each. 

m  fi 

Wt. 

Approximate  Breaking 
Stress,  Lbs. 

^  c 

wt. 

Approximate  Breaking 
Stress,  Lbs. 

If 

Lbs. 

Cast 
Steel. 

Extra 
Strong 
Steel. 

Plow 
Steel. 

I| 

Lbs. 

Cast 
Steel. 

Extra 
Strong 
Steel. 

Plow 
Steel. 

21/4 

8.00 

312,000 

364,000 

416,000 

U/2 

3.55 

136,000 

158,000 

182,000 

13/4 

6.30 
4.85 

248,000 
192,000 

288,000 
224,000 

330,000 
256,000 

13/8 
11/4 

3.00 
2.45 

116,000 
96,000 

136,000 
112,000 

156,000 
128,000 

>4  15 

168,000 

194,000 

222,000 

2.00 

80,000 

92,000 

106,000 

1  1/2 

3.55 

144,000 

168,000 

192,000 

] 

1.58 

64,000 

74,000 

84,000 

13/8 

3.00 

124,000 

144,000 

164,000 

7/8 

1.20 

48,000 

56,000 

64,000 

U/4 

2.45 

100,000 

116,000 

134,000 

3/4 

0.89 

37,200 

42,000 

48,000 

U/8 

2.00 

84,000 

98,000 

112,000 

0.75 

31,600 

36,800 

42,000 

1 

1  58 

68,000 

78,000 

88,000 

5/8 

0.62 

26,400 

30,200 

34,000 

7/8 

1.20 

52,000 

60,000 

68,000 

9/10 

0.50 

21,200 

24,600 

28,000 

0.89 

38,800 

44,000 

50,000 

V2 

0.39 

16,800 

19,400 

22,000 

5/8 

0,62 

27,200 

31,600 

36,000 

7/16 

0.30 

13,200 

15,000 

17,100 

0.50 

22,000 

25,400 

29,000 

3/8 

0.22 

9,600 

11,160 

12,700 

0  39 

17  600 

20  200 

22  800 

0  15 

6800 

7  760 

7/1A 

0  30 

13600 

15  600 

17  700 

9/QO 

0  125 

5*600 

6440 

3/Q 

0  22 

10*000 

if  500 

13  100 

5/1  fi 

0  15 

6  800 

8*100 

1/4 

0.10 

4'800 

5,400 

segments  of  leather  and  blocks  of  India-rubber  soaked  in  tar  and 
packed  alternately  in  the  groove.  Where  the  working  tension  is  very 
great,  however,  the  wood  filling  is  to  be  preferred,  as  in  the  case  of  long- 
distance transmissions  where  the  rope  makes  several  laps  about  the 
sheaves,  and  is  run  at  a  comparatively  slow  speed. 
The  Bending  Stress  is  determined  by  the  formula 

fc=  Ea 

2.06  (R  -T-  d)  +  C 

k  =  bending  stress  in  Ibs.;  E  =  modulus  of  elasticity  =  28,500,000; 
a  =  aggregate  area  of  wires,  sq.  ins.;  R  =  radius  of  bend;  d  =  diam.  of 
wires,  ins. 

For    7-wire  rope      d   =  1/9    diam.  of  rope;  C  =    9.27. 
'     19-wire     "         d   =  1/15      "  "      C   =  15.45. 

"  the  Scale  cable  d   =.  1/12  C  =  12.36. 

From  this  formula  the  tables  below  and  on  p.  1210  have  been  cal- 
culated. 

Bending  Stresses,  7-wire  Rope. 


Diam.  bend.     24        36       48 


60 


72 


84    [    96    j  108  |  120  |   132 


Diam.  Rope. 

V4 

826 

553 

412 

333 

277 

238 

208 

185 

166 

15! 

9/32 

1,120 

750 

563 

451 

376 

323 

282 

251 

226 

20ft 

5/16 

1,609 

1,078 

810 

649 

541 

464 

406 

361 

325 

29d 

3/8 

2,774 

1,859 

1,398 

1,120 

934 

801 

702 

624 

562 

511 

7/16 

4,385 

2,982 

2,217 

1,777 

1,482 

1,272 

1,113 

990 

892 

811 

Va 

6,200 

4,161 

3,131 

2,510 

2,095 

1,797 

1,574 

1,400 

1,260 

1,146 

9/16 

9,072 

6,095 

4,589 

3,679 

3,071 

2,635 

2,308 

2,053 

1,848 

1,681 

5/8 

8,547 

6,438 

5,164 

4,310 

3,699 

3,240 

2,882 

2,595 

2,360 

Jl/16 
3/4 



10,922 
14,202 

8,230 
10,706 

6,603 
8,591 

5,513 
7,174 

4,731 
6,158 

4,144 
5,394 

3,687 
4,799 

3,320 
4,322 

3,020 
3,931 

7/8 

...... 

22,592 

17,045 

13,685 

11,431 

9,815 

8,599 

7,651 

6,892 

6,269 

1 

25  476 

20  464 

17  100 

14686 

12869 

11  452 

10317 

9386 

U/8 

36289 

29*165 

24,416 

20,942 

18,355 

16,336 

14718 

13,391 

U/4 

40,020 

33,464 

28,754 

25,206 

22,437 

20,216 

18,396 

13/8 

44,551 

38.290 

33.571 

29.888 

26.933 

24.510 

n/2 

57,835|  49,718[43,599|38,821  134,987|  31,842 

1210       TRANSMISSION  OF  POWER  BY  WIRE  ROPE. 


Bending  Stresses,  19-wire  Rope. 


Diam.Bend. 

13 

34 

36 

48 

60 

73 

84 

96 

108 

130 

Diam.Rope. 

V4 

993 

502 

336 

252 

202 

168 

144 

126 

112 

101 

5/16 

1,863 

944 

632 

475 

380 

317 

272 

238 

212 

191 

3/8 

2,771 

1,406 

942 

708 

567 

473 

406 

355 

316 

285 

7/16 

4,859 

2,473 

1,658 

1,247 

1,000 

834 

716 

627 

557 

502 

V2 

7,125 

3,635 

2,440 

1,836 

1,472 

1,228 

1,054 

923 

821 

739 

o/ie 

5,319 

3,573 

2,690 

2,157 

1,800 

1,545 

1,353 

1,203 

1,084 

5/8 

7,452 

5,011 

3,774 

3,027 

2,526 

2,169 

1,900 

1,690 

1,522 

U/16 

9,767 

6,572 

4,953 

3,973 

3,317 

2,847 

2,494 

2,219 

1,998 

3/4 

12,512 

8,427 

6,352 

5,098 

4,257 

3,654 

3,201 

2,848 

2,565 

7/8 

19,436 

13,111 

9,891 

7,941 

6,633 

5,696 

4,990 

4,440 

3,999 

1 

29,799 

20,136 

15,205 

12,214 

10,206 

8,766 

7,681 

6,836 

6,158 

j;/8 

28,153 

21,276 

17,099 

14,293 

12,278 

10,761 

9,578 

8,689 

11/4 

38034 

28,766 

23,130 

19340 

16  618 

14  567 

12  967 

1  1  683 

13/8 

51*609 

39*,067 

31*430 

26*290 

22*594 

19*811 

17*637 

15*893 

H/2 

66065 

50*049 

40*284 

33*707 

28*976 

25*410 

22*625 

20*390 

15/8 
-    13/4 

62',  895 
79  749 

50*,647 
64,252 

42*,391 
53  798 

36*,450 
46  270 

31*,969 
40,590 

28*,  470 
36  152 

25*,661 
32  589 

17/8 

97018 

78,202 

65*,  500 

56*347 

49*438 

44*039 

39*701 

2 

94*016 

78*769 

67778 

59*478 

52*989 

47*777 

21/4 

134*319 

112*611 

96*943 

85*103 

75*840 

68  396 

2V2 

154*,  870 

133  ",386 

117*.  137 

104I.417 

94*189 

Horse-Power  Transmitted*  —  The  general  formula   for  the  amount 
of  power  capable  of  being  transmitted  is  as  follows: 

H.P.  =  [cd2 


In  which  d  =  diameter  of  the  rope  in  inches,  v  =  velocity  of  the  rope  In 
feet  per  second,  w  =  weight  of  the  rope,  QI  =  weight  of  the  terminal 
sheaves  and  shafts,  02  —  weight  of  the  intermediate  sheaves  and  shafts 
(all  in  Ibs.),  and  c  =  a  constant  depending  on  the  material  of  the  rope, 
the  filling  in  the  grooves  of  the  sheaves,  and  the  number  of  laps  about 
the  sheaves  or  drums,  a  single  lap  meaning  a  half-lap  at  each  end.  The 
values  of  c  for  one  up  to  six  laps  for  steel  rope  are  given  in  the  following 
table: 


Number  of  laps  about  sheaves  or  drums 


C  —  lor  steei  rope  on 

1 

2 

3 

4 

5 

6 

Iron                  

5.61 

8.81 

10.62 

11.65 

12.16 

12.56 

Wood  

6.70 

9.93 

11.51 

12.26 

12.66 

12.83 

Rubber  and  leather  

9.29 

11.95 

12.70 

12.91 

12.97 

13.00 

The  values  of  c  for  iron  rope  are  one  half  the  above. 

When  more  than  three  laps  are  made,  the  character  of  the  surface  in 
contact  is  immaterial  as  far  as  slippage  is  concerned. 

From  the  above  formula  we  have  the  general  rule,  that  the  actual 
horse-power  capable  of  being  transmitted  by  any  wire  rope  approximately 
equals  c  times  the  square  of  the  diameter  of  the  rope  in  inches,  less  six  mil' 
lionths  the  entire  weight  of  all  the  moving  parts,  multiplied  by  the  speed  of 
the  rope,  in  feet  per  second. 

Instead  of  grooved  drums  or  a  number  of  sheaves,  about  which  the 


rope  makes  two  or  more  laps,  it  is  sometimes'  found  more  desirable, 
especially  where  space  is  limited,  to  use  grip-pulleys.  The  rim  is  fitted 
with  a  continuous  se/ies  of  steel  jaws,  which  bite  the  rope  in  contact  by 


reason  of  the  pressure  of  the  same  against  them,  but  as  soon  as  relieved 
of  this  pressure  they  open  readily,  offering  no  resistance  to  the  egress  of 
the  rope. 

In  the  ordinary  or  "  flying  "  transmission  of  power,  where  the  rope 
makes  a  single  lap  about  sheaves  lined  with  rubber  and  leather  or  wood, 
the  ratio  between  the  diameter  of  the  sheaves  and  the  wires  of  the  rope, 
Corresponding  to  a  maximum  safe  working  tension,  is,:  For  7-wire  rope, 


TRANSMISSION  OF  POWER  BY  WIRE  ROPE.        1211 


steel,  79.6;  iron,  160.5.     For  12-wire  rope,  steel,  59.3;  iron,  120.     For 
19-wire  rope,  steel,  47.2;  iron,  95.8. 

Diameters  of  Minimum  Sheaves  in  Inches,  Corresponding  to  a  Maxi- 
mum Safe  Working  Tension. 


Diameter 
of  Rope, 
In. 

Steel. 

Iron. 

7-Wire. 

12-  Wire. 

19-  Wire. 

7-Wire. 

12-Wire. 

19-  Wire. 

1/4 

20 

15 

12 

40 

30 

24 

5/16 

25 

19 

15 

50 

38 

30 

3/8 

30 

22 

18 

60 

45 

36 

7/16 

35 

26 

21 

70 

53 

42 

1/2 

40 

30 

24 

80 

60 

48 

9/16 

45 

33 

27 

90 

68 

54 

5/8 

50 

37 

30 

100 

75 

60 

H/16 

55 

41 

32 

110 

83 

66 

8/4 

60 

44 

35 

120 

90 

72 

7/8 

70 

52 

41 

140 

105 

84 

1 

80 

59 

47 

160 

120 

96 

Assuming  the  sheaves  to  be  of  equal  diameter,  and  of  the  sizes  in  the 
above  table,  the  Horse-power  that  may  be  transmitted  by  a  steel  rope  making 
a  single  lap  on  wood-filled  sheaves  is  given  in  the  table  below. 

The  transmission  of  greater  horse-powers  than  250  is  impracticable 
with  filled  sheaves,  as  the  tension  would  be  so  great  that  the  filling  would 
quickly  cut  out,  and  the  adhesion  on  a  metallic  surface  would  be  insuffi- 
cient where  the  rope  makes  but  a  single  lap.  In  this  case  it  becomes 
necessary  to  use  the  Reuleaux  method,  in  which  the  rope  is  given  more 
than  one  lap,  as  referred  to  below,  under  the  caption  "  Long-distance 
Transmissions." 
Horse-power  Transmitted  by  a  Steel  Rope  on  Wood-filled  Sheaves. 


Diameter 
of  Rope, 
In. 

Velocity  of  Rope  in  Feet  per  Second. 

10 

20 

30 

40 

50 

60 

70 

80    I    90 

100 

& 

%» 
f 

» 

U/16 

%* 
7/8 

4 

10 
13 
17 

22 
27 
32 
38 
52 
68 

8 
13 
19 
26 
34 
43 
53 
63 
76 
104 
135 

13 

20 
28 
38 
51 
65 
79 
95 
103 
156 
202 

17 

26 
38 
51 
67 
86 
104 
126 
150 
206 

21 
33 
47 
63 
83 
106 
130 
157 
186 

25 
40 
56 
75 
99 
128 
155 
186 
223 

28 
44 
64 
88 
115 
147 
179 
217 

32 
51 
73 
99 
130 
167 
203 
245 

37 
57 
80 
109 
144 
184 
225 

40 
62 
89 
121 
159 
203 
24> 

The  horse-power  that  may  be  transmitted  by  iron  ropes  is  one-half  of  the 
above. 

This  table  gives  the  amount  of  horse-power  transmitted  by  wire  ropes 
under  maximum  safe  working  tensions.  In  using  wood-lined  sheaves, 
therefore,  it  is  well  to  make  some  allowance  for  the  stretching  of  the 
rope,  and  to  advocate  somewhat  heavier  equipments  than  the  above  table 
would  give;  that  is,  if  it  is  desired  to  transmit  20  horse-power,  for  in- 
stance, to  put  in  a  plant  that  would  transmit  25  to  30  horse-power,  avoid- 
ing the  necessity  of  having  to  take  up  a  comparatively  small  amount  of 
stretch.  On  rubber  and  leather  filling,  however,  the  amount  of  power 
capable  of  being  transmitted  is  40  per  cent  greater  than  for  wood,  so  that 
this  filling  is  generally  used,  and  in  this  case  no  allowance  need  be  made 
for  stretch,  as  such  sheaves  will  likely  transmit  the  power  given  by  the 
table,  under  all  possible  deflections  of  the  rope. 

Under  ordinary  conditions,  ropes  of  seven  wires  to  the  strand,  laid 
about  a  hemp  core,  are  best  adapted  to  the  transmission  of  power,  but 
conditions  often  occur  where  12-  or  19-wire  rope  is  to  be  preferred,  as 
stated  below,  under  "  Limits  of  Span." 

Deflections  of  the  Rope.  —  The  tension  of  the  rope  is  measured  by 
the  amount  of  sag  or  deflection  at  the  center  at  the  span,  and  the  deflec- 


1212 


TRANSMISSION  OF  POWER  BY  WIRE  ROPE. 


tion  corresponding  to  the  maximum  safe  working  tension  is  determined 
by  the  following  formulae,  in  which  S  represents  the  span  in  feet : 

Steel  Rope.        Iron  Rope. 

Def.  of  still  rope  at  center,  in  feet .  .h   =  .00004  Sz  h  =  .00008  Sz 

driving  "   ...hi    =  .000025 S*  7it  =  .00005  S2 

slack  "   ...fo    =  .0000875  £2  ^  =  .00017  5S2 

Limits  of  Span.  —  On  spans  of  less  than  sixty  feet,  it  is  impossible  to 
splice  the  rope  to  such  a  degree  of  nicety  as  to  give  exactly  the  required 
deflection,  and  as  the  rope  is  further  subject  to  a  certain  amount  of 
stretch,  it  becomes  necessary  in  such  cases  to  apply  mechanical  means 
for  producing  the  proper  tension  in  order  to  avoid  frequent  splicing, 
which  is  very  objectionable;  but  care  should  always  be  exercised  in  using 
such  tightening  devices  that  they  do  not  become  the  means,  in  unskilled 
hands,  of  overstraining  the  rope.  The  rope  also  is  more  sensitive  to 
every  irregularity  in  the  sheaves  and  the  fluctuations  in  the  amount  of 
power  transmitted,  and  is  apt  to  sway  to  such  an  extent  beyond  the 
narrow  limits  of  the  required  deflections  as  to  cause  a  jerking  motion, 
which  is  very  injurious.  For  this  reason  on  very  short  spans  it  is  found 
desirable  to  use  a  considerably  heavier  rope  than  that  actually  required 
to  transmit  the  power;  or  in  other  words,  instead  of  a  7-wire  rope  cor- 
responding to  the  conditions  of  maximum  tension,  it  is  better  to  use  a 
19-wire  rope  of  the  same  size  wires,  and  to  run  this  under  a  tension  con- 
siderably below  the  maximum.  In  this  way  are  obtained  the  advantages  of 
increased  weight  and  less  stretch,  without  having  to  use  larger  sheaves, 
while  the  wear  will  be  greater  in  proportion  to  the  increased  surface. 

In  determining  the  maximum  limit  of  span,  the  contour  of  the  ground 
and  the  available  height  of  the  terminal  sheaves  must  be  taken  into  con- 
sideration. It  is  customary  to  transmit  the  power  through  the  lower 
portion  of  the  rope,  as  in  this  case  the  greatest  deflection  in  this  portion 
occurs  when  the  rope  is  at  rest.  When  running,  the  lower  portion  rises 
and  the  upper  portion  sinks,  thus  enabling  obstructions  to  be  avoided 
which  otherwise  would  have  to  be  removed,  or  make  it  necessary  to  erect 
very  high  towers.  The  maximum  limit  of  span  in  this  case  is  determined 
by  the  maximum  deflection  that  may  be  given  to  the  upper  portion  of 
the  rope  when  running,  which  for  sheaves  of  10  ft.  diameter  is  about 
600  feet. 

Much  greater  spans  than  this,  however,  are  practicable  where  the  con- 
tour of  the  ground  is  such  that  the  upper  portion  of  the  rope  may  be  the 
driver,  and  there  is  nothing  to  interfere  with  the  proper  deflection  of  the 
under  portion.  Some  very  long  transmissions  of  power  have  been 
effected  in  this  way  without  an  intervening  support,  one  at  Lockport, 
N.Y.,  having  a  clear  span  of  1700  feet. 

Long-distance  Transmissions.  —  When  the  distance  exceeds  the 
limit  for  a  clear  span,  intermediate  supporting  sheaves  are  used,  with 
plain  grooves  (not  filled),  the  spacing  and  size  of  which  will  be  governed 
by  the  contour  of  the  ground  and  the  special  conditions  involved.  The 
size  of  these  sheaves  will  depend  on  the  angle  of  the  bend,  gauged  by  the 
tangents  to  the  curves  of  the  rope  at  the  points  of  inflection.  If  the  cur- 
vature due  to  this  angle  and  the  working  tension,  regardless  of  the  size  of 
the  sheaves,  as  determined  by  the  table  on  the  next  page,  is  less  than 
that  of  the  minimum  sheave  (see  table  p.  1211),  the  intermediate  sheaves 
should  not  be  smaller  than  such  minimum  sheave,  but  if  the  curvature  is 
greater,  smaller  intermediate  sheaves  may  be  used. 

In  very  long  transmissions  of  power,  requiring  numerous  intermediate 
supports,  it  is  found  impracticable  to  run  the  rope  at  the  high  speeds 
maintained  in  "  flying  transmissions."  The  rope  therefore  is  run  under 
a  higher  working  tension,  made  practicable  by  wrapping  it  several  times 
about  grooved  terminal  drums,  with  a  lap  about  a  sheave  on  a  take-up  or 
counter- weighted  carriage,  which  preserves  a  constant  tension  in  the  slack 
portion. 

Inclined  Transmissions.  —  When  the  terminal  sheaves  are  not  on 
the  same  elevation,  the  tension  at  the  upper  sheave  will  be  greater  than 
that  at  the  lower,  but  this  difference  is  so  slight,  in  most  cases,  that  it 
may  be  ignored.  The  span  to  be  considered  is  the  horizontal  distance 
between  the  sheaves,  and  the  principles  governing  the  limits  of  span  will 


TRANSMISSION  OF  POWER  BY  WIRE  ROPE.       1213 


hold  good  in  this  case,  so  that  for  every  steep  inclinations  it  becomes 
necessary  to  resort  to  tightening  devices  for  maintaining  the  requisite 
tension  in  the  rope.  The  limiting  case  of  inclined  transmissions  occurs 
when  one  wheel  is  directly  above  the  other.  The  rope  in  this  case  pro- 
duces no  tension  whatever  on  the  lower  wheel,  while  the  upper  is  sub- 
ject only  to  the  weight  of  the  rope,  which  is  usually  so  insignificant  that 
it  may  be  neglected  altogether,  and  on  vertical  transmissions,  therefore, 
mechanical  tension  is  an  absolute  necessity. 

Bending  Curvature  of  Wire  Ropes.  —  The  curvature  due  to  any 
bend  in  a  wire  rope  is  dependent  on  the  tension,  and  is  not  always  the 
same  as  the  sheave  in  contact,  but  may  be  greater,  which  explains  how 
it  is  that  large,  ropes  are  frequently  run  around  comparatively  small 
sheaves  without  detriment,  since  it  is  possible  to  place  these  so  close  that 
the  bending  angle  on  each  will  be  such  that  the  resulting  curvature  will 
not  overstrain  the  wires.  This  curvature  may  be  ascertained  from 
the  formula  and  table  below,  which  give  the  theoretical  radii  of 
curvature  in  inches  for  various  sizes  of  ropes  and  different  angles  for  one 
pound  tension  in  the  rope.  Dividing  these  figures  by  the  square  root 
of  the  actual  tension  in  pounds,  gives  the  radius  of  curvature  of  the  rope 
when  this  exceeds  the  curvature  of  the  sheave.  The  rigidity  of  the  rope 
or  internal  friction  of  the  wires  and  core  has  not  been  taken  into  account 
in  these  figures,  but  the  effect  of  this  is  insignificant,  and  it  is  on  the  safe 
side  to  ignore  it.  By  the  "angle  of  bend'T  is  meant  the  angle  between 
the  tangents  to  the  curves  of  the  rope  at  the  points  of  inflection.-  When 
the  rope  is  straight  the  angle  is  180°.  For  angles  less  than  160°  the 
radius  of  curvature  in  most  cases  will  be  less  than  that  corresponding  to 
the  safe  working  tension,  and  the  proper  size  of  sheave  to  use  in  such 
cases  will  be  governed  by  the  table  headed  "Diameters  of  Minimum 
Sheaves  Corresponding  to  a  Maximum  Safe  Working  Tension"  on  p.  1211. 

Radius  of  Curvature  of  Wire  Ropes  in  Inches  for  1-Ib.  Ten- 
sion. Formula:  R2  =  Ed*n+  20 £  (1  —  sin  ^  0);  in  which  R  =  radius  of 
curvature;  E  =  modulus  of  elasticity  =  28,500,000;  d  =  diameter  of  wires; 
n  =  no.  of  wires  in  the  rope;  6  =  angle  of  bend;  t  =  working  stress  (Ibs.  and 
ins.).  Divide  by  square  root  of  stress  in  pounds  to  obtain  radius  in  inches. 


Diam.  of  Rope. 

120° 

140° 

160° 

165° 

170° 

174° 

mc 

178C 

172  ~> 

i  7-  Wire  Rope.  19-  Wire  Rope,  j 

iA  

38 
61 
87 
116 
155 
195 
238 

66 
103 
145 
198 
259 
328 
406 

56 
91 
129 
174 
232 
290 
355 

98 
153 

216 
295 
386 
489 
605 

112 

181 
257 
346 
461 
578 
708 

196 
306 
430 
587 
769 
975 
1205 

149 
242 
342 
461 
615 
770 
943 

261 

407 
572 
782 
1024 
1298 
1606 

223 
362 
513 
690 
921 
1154 
1414 

391 
610 
858 
1172 
1535 
1946 
2407 

373 
604 
856 
1151 
1536 
1925 
2358 

651 

1018 
1431 
1954 
2559 
3246 
4013 

559 

1282 
1725 
2302 
2885 
3533 

976 
1525 
2145 
2929 
3835 
4864 
6015 

1126 
1824 
2586 
3479 
4643 
5818 
7125 

1969 
3076 
4325 
5907 
7735 
9809 
12129 

2181 
3533 
5007 
6737 
8991 
11266 
13797 

3812 
5957 
8375 
11438 
14978 
18994 
23487 

H  •  • 

?I:  ... 

</':: 

i  :::::::: 

IH  .  . 

\y±  

6/ 

a/ 

7X 

1  8  

\y*  . 

\y±  

The  7-wire  rope  has  6  strands  of  7  wires  each,  the  19-wlre  rope  has 
6  strands  of  19  wires  each. 


1214  ROPE-DRIVING. 

HOPE-DRIVING. 

The  transmission  of  power  by  cotton  or  manila  ropes  is  a  competitor 
with  gearing  and  leather  belting  when  the  amount  of  power  is  large,  or 
the  distance  between  the  power  and  the  work  is  comparatively  great. 
The  following  is  condensed  from  a  paper  by  C.  W.  Hunt,  Trans.  A.  S. 
M.  E.,  xii,  230: 

But  few  accurate  data  are  available,  on  account  of  the  long  period 
required  in  each  experiment,  a  rope  lasting  from  three  to  six  years. 
Installations  which  have  been  successful,  as  well  as  those  in  which  the 
wear  of  the  rope  was  destructive,  indicate  that  200  Ibs.  on  a  rope  one 
inch  in  diameter  is  a  safe  and  economical  working  strain.  When  the 
strain  is  materially  increased,  the  wear  is  rapid. 

In  the  following  equations 

C  =  circumference  of  rope,  inches;      g  =  gravity; 

D  =  sag  of  the  rope  in  feet ;  H  =  horse-power; 

F  =  centrifugal  force  in  pounds;         L  =  distance  between  pulleys,  ft.; 

P  =  pounds  per  foot  of  rope;  w  =  working  strain  in  pounds; 

R  =  force  in  pounds  doing  useful  work; 
S  =  strain  in  pounds  on  the  rppe  at  the  pulley; 
T  =  tension  in  pounds  of  driving  side  of  the  rope; 
t  =  tension  in  pounds  on  slack  side  of  the  rope; 
v  =  velocity  of  the  rope  in  feet  per  second; 
W  =  ultimate  breaking  strain  in  pounds. 
W  =  720  C2;         P  =  0.032  C2;         w  =  20  C2. 

This  makes  the  normal  working  strain  equal  to  1/36  of  the  breaking 
strength,  and  about  1/25  of  the  strength  at  the  splice.  The  actual  strains 
are  ordinarily  much  greater,  owing  to  the  vibrations  in  running,  as  well 
as  from  imperfectly  adjusted  tension  mechanism. 

For  this  investigation  we  assume  that  the  strain  on  the  driving  side 
of  a  rope  is  equal  to  200  Ibs.  on  a  rope  one  inch  in  diameter,  and  an 
equivalent  strain  for  other  sizes,  and  that  the  rope  is  in  motion  at  vari- 
ous velocities  of  from  10  to  140  ft.  per  second. 

The  centrifugal  force  of  the  rope  in  running  over  the  pulley  will  reduce 
the  amount  of  force  available  for  the  transmission  of  power.  The  cen- 
trifugal force  F  =  Pv2-  •*-  g. 

At  a  speed  of  about  80  ft.  per  second,  the  centrifugal  force  increases 
faster  than  the  power  from  increased  velocity  of  the  rope,  and  at  about 
140  ft.  per  second  equals  the  assumed  allowable  tension  of  the  rope. 
Computing  this  force  at  various  speeds  and  then  subtracting  it  from  the 
assumed  maximum  tension,  we  have  the  force  available  for  the  trans- 
mission of  power.  The  whole  of  this  force  cannot  be  used,  because  a 
certain  amount  of  tension  on  the  slack  side  of  the  rope  is  needed  to  give 
adhesion  to  the  pulley.  What  tension  should  be  given  to  the  rope  for 
this  purpose  is  uncertain,  as  there  are  no  experiments  which  give  accurate 
data.  It  is  known  from  considerable  experience  that  when  the  rope  runs  in 
a  groove  whose  sides  are  inclined  toward  each  other  at  an  angle  of  45° 
there  is  sufficient  adhesion  when  the  ratio  of  the  tensions  T  -*•  t  =  2. 

For  the  present  purpose  T  can  be  divided  into  three  parts:  1.  Tension 
doing  useful  work;  2.  Tension  from  centrifugal  force;  3.  Tension  to 
balance  the  strain  for  adhesion. 

The  tension  t  can  be  divided  into  two  parts:  1.  Tension  for  adhesion; 
2.  Tension  from  centrifugal  force. 

It  is  evident,  however,  that  the  tension  required  to  do  a  given  work 
should  not  be  materially  exceeded  during  the  life  of  the  rope. 

There  are  two  methods  of  putting  ropes  on  the  pulleys;  one  in  which 
the  ropes  are  single  and  spliced  on,  being  made  very  taut  at  first,  and 
less  so  as  the  rope  lengthens,  stretching  until  it  slips,  when  it  is  re- 
spliced.  The  other  method  is  to  wind  a  single  rope  over  the  pulleys 
as  many  turns  as  needed  to  obtain  the  necessary  horse-power  and  put  a 
tension  pulley  to  give  the  necessary  adhesion  and  also  take  up  the  wear. 
The  tension  t  on  one  of  the  ropes  required  to  transmit  the  normal  horse- 
power for  the  ordinary  speeds  and  sizes  of  rope  is  computed  by  formula 
(1),%  below.  The  total  tension  T  on  the  driving  side  of  the  rope  is 
assumed  to  be  the  same  at  all  speeds.  The  centrifugal  force,  as  well  as 
an  amount  equal  to  the  tension  for  adhesion  on  the  slack  side  of  the 


ROPE-DRIVING. 


1215 


rope,  must  be  taken  from  the  total  tension  T  to  ascertain  the  amount  of 
force  available  for  the  transmission  of  power. 

It  is  assumed  that  the  tension  on  the  slack  side  necessary  for  giving 
adhesion  is  equal  to  one  half  the  force  doing  useful  work  on  the  driving 


„   ..   80   90  100  110  120  130  14Q 

"  Velocity  of  Driving  Hope  in  feet  per  second    * 

FIG.  193. 

side  of  the  rope:  hence  the  force  for  useful  work  is  R  =  2/3  (T  -  F);  and 
the  tension  on  the  slack  side  to  give  the  required  adhesion  is  Vs  (T  —  F). 

t  =  (T  -  F)/3  +  F m 

The  sum  of  the  tensions  T  and  t  is  not  the  same  at  different  speeds,  as 
the  equation  (1)  indicates.     As  F  varies  as  the  square  of  the  velocity, 
there  is,  with  an  increasing  speed  of  the  rope,  a  decreasing  useful  force, 
and  an  increasing  total  tension,  t,  on  the  slack  side. 
With  these  assumptions  of  allowable  strains  the  horse-power  will  be 

H  =  2v  (!T-F)-K3X550) (2) 

Transmission  ropes  are  usually  from  1  to  2  inches  in  diameter.  A 
computatipn  of  the  horse-power  for  four  sizes  at  various  speeds  and 
under  ordinary  conditions,  based  on  a  maximum  strain  equivalent  to 
200  Ibs.  for  a  rope  one  inch  in  diameter,  is  given  in  Fig.  193.  The 
horse-power  of  other  sizes  is  readily  obtained  from  these.  The  maxi- 
mum power  is  transmitted,  under  the  assumed  conditions,  at  a  speed  of 
about  80  feet  per  second. 

The  wear  of  the  rope  is  both  internal  and  external;  the  internal  is 

caused  by  the  movement  of  the  fibers  on  each  other,  under  pressure  in 

bending  over  the  sheaves,  and  the  external  is  caused  by  the  slipping  and 

the  wedging  in  the  grooves  of  the  pulley.    Both  of  these  causes  of  wear 

Horse-power  of  Transmission  Rope  at  Various  Speeds. 

Computed  from  formula  (2)  given  above. 


it 

Speed  of  the  Rope  in  feet  per  minute. 

to*O    TO    ® 

IsSis 

1500 

2000 

2500 

3000 

3500 

4000 

4500 

5000 

6000 

7000 

8000 

V2 
5/8 
3/4 

|7/8 
1  1/4 
1  1/2 
,3/4 

1.45 
2.3 
3.3 
4.5 
5.8 
9.2 
13.1 
18 
23.2 

1.9 

3.2 
4.3 
5.9 
7.7 
12.1 
17.4 
23.7 
30.8 

2.3 
3.6 
5.2 
7.0 
9.2 
14.3 
20.7 
28.2 
36.8 

2.7 
4.2 
5.8 
8.2 
10.7 
16.8 
23.1 
32.8 
42.8 

3 

4.6 
6.7 
9.1 
11.9 
18.6 
26.8 
36.4 
47.6 

3.2 
5.0 
7.2 
9.8 
12.8 
20.0 
28.8 
39.2 
51.2 

3.4 
5.3 
7.7 
10.8 
13.6 
21.2 
30.6 
41.5 
54.4 

3.4 
5.3 
7.7 
10.8 
13.7 
21.4 
30.8 
41.8 
54.8 

3.1 
4.9 
7.1 
9.3 
12.5 
19.5 
28.2 
37.4 
50 

2.2 
3.4 
4.9 
6.9 
8.8 
13.8 
19.8 
27.6 
35.2 

0 
0 
0 
0 
0 
0 
0 
0 
0 

20 
24 
30 
36 
42 
54 
60 
72 
84 

1216 


ROPE-DRIVING. 


are,  within  the  limits  of  ordinary  practice,  assumed  to  be  directly  pro- 
portional to  the  speed. 

•  The  rope  is  supposed  to  have  the  strain  T  constant  at  all  speeds  on 
the  driving  side,  and  in  direct  proportion  to  the  area  of  the  cross-section; 
hence  the  catenary  of  the  driving  side  is  not  affected  by  the  speed  or  by 
the  diameter  of  the  rope. 

The  deflection  of  the  rope  between  the  pulleys  on  the  slack  side  varies 
with  each  change  of  the  load  or  change  of  the  speed,  as  the  tension  equa- 
tion (1)  indicates. 

The  deflection  of  the  rope  is  computed  for  the  assumed  value  of  T  and 
t  by  the  parabolic  formula  S  =  j^£  +  PD,  S  being  the  assumed  strain 

T  on  the  driving  side,  and  t,  calculated  by  equation  (1),  on  the  slack 
side.  The  tension  t  varies  with  the  speed. 

The  following  notes  are  from  the  circular  of  the  C.  W.  Hunt  Co. : 
For  a  temporary  installation,  it  might  be  advisable  to  increase  the  work 
to  double  that  given  in  the  table. 

For  convenience  in  estimating  the  necessary  clearance  on  the  driving 
and  on  the  slack  sides,  we  insert  a  table  showing  the  sag  of  the  rope  at 
different  speeds  when  transmitting  the  horse-power  given  in  the  pre- 
ceding table.  When  at  rest  the  sag  is  not  the  same  as  when  running, 
being  greater  on  the  driving  and  less  on  the  slack  sides  of  the  rope.  The 
sag  of  the  driving  side  when  transmitting  the  normal  horse-power  is  the 
same  no  matter  what  size  of  rope  is  used  or  what  the  speed  driven  at, 
because  the  assumption  is  that  the  strain  on  the  rope  shall  be  the  same 
at  all  speeds  when  transmitting  the  assumed  horse-power,  but  on  the 
slack  side  the  strains,  and  consequently  the  sag,  vary  with  the  speed  of 
the  rope  and  also  with  the  horse-power.  The  table  gives  the  sag  for 
three  speeds.  If  the  actual  sag  is  less  than  given  in  the  table,  the  rope 
is  strained  more  than  the  work  requires. 

;  This  table  is  only  approximate,  and  is  exact  only  when  the  rope  is 
running  at  its  normal  speed,  transmitting  its  full  load  and  strained  to  the 
assumed  amount.  All  of  these  conditions  are  varying  in  actual  work. 

SAG  OF  THE  ROPE  BETWEEN  PULLEYS. 


Distance 
between 
Pulleys 
in  feet. 

Driving  Side. 

Slack  Side  of  Rope. 

All  Speeds. 

80  ft.  per  sec. 

60ft.  per  sec. 

40ft.  per  sec. 

40 
60 
80 
100 
120 
140 
160 

Ofeet   4  inches 
0    "    10      " 
I    "     5      " 
2    "     0      " 
2    "    11       " 
3    "    10      •• 
5    "      1       " 

0  feet  7  inches 
1    ••    5      " 
2    "    4      " 
3    "    8      " 
5    "    3      " 
7    "    2      " 
9    "    3       " 

Ofeet   9  inches 
1    *'      8      " 
2    "    10      " 
4    "      5      " 
6    "      3       " 
8    "      9      " 
11    "     3      " 

0  feet  1  1  inches 
1    "    11       " 
3    "     3      " 
5    "     2      •• 
7    "     4      " 
9    "      9      " 
14    "      0       " 

The  size  of  the  pulleys  has  an  important  effect  on  the  wear  of  the  rope  — 
the  larger  the  sheaves,  the  less  the  fibers  of  the  rope  slide  on  each  other, 
and  consequently  there  is  less  internal  wear  of  the  rope.  The  pulleys 
should  not  be  less  than  forty  times  the  diameter  of  the  rope  for  economical 
wear,  and  as  much  larger  as  it  is  possible  to  make  them.  This  rule  apolies 
also  to  the  idle  and  tension  pulleys  as  well  as  to  the  main  driving-pulley. 

TENSION  ON  THE  SLACK  PART  OF  THE  ROPE. 


Speed  of 
Rope,  in  feet 
per  second 

Diameter  of  the  Rope  and  Pounds  Tension  on  the  Slack  Rope 

V2 

5/8 

3/4 

7/8 

1 

n/4 

H/2 

13/4 

2 

20 
30 
40 
50 
60 
70 
80 
90 

10 
14 
15 
16 
18 
19 
21 
24 

27 
29 
31 
33 
36 
39 
43 
48 

40 
42 
45 
49 
53 
59 
64 
70 

54 
56 
60 
65 
71 
78 
85 
93 

71 
74 
79 
85 
93 
101 
111 
122 

110 
115 
123 
132 
145 
158 
173 
190 

162 
170 
181 
195 
214 
236 
255 
279 

216 
226 
240 
259 
285 
310 
340 
372 

283 
296 
315 
339 
373 
406 
445 
487 

ROPE-DEIVING. 


1217 


The  angle  of  the  sides  of  the  grooves  in  which  the  rope  runs  varies, 
with  different  engineers,  from  45°  to  60U.  It  is  very  important  that  the 
sides  of  these  grooves  should  be  carefully  polished,  as  the  fibers  of  the 
rope  rubbing  on  the  metal  as  it  comes  from  the  lathe  tools  will  gradually 
break  fiber  by  fiber,  and  so  give  the  rope  a  short  life.  It  is  also  neces- 
sary to  carefully  avoid  all  sand  or  blow  holes,  as  they  will  cut  the  rope 
out  with  surprising  rapidity. 

Much  depends  also  upon  the  arrangement  of  the  rope  on  the  pulleys. 
especially  where  a  tension  weight  is  used.  Experience  shows  that  the 
increased  wear  on  the  rope  from  bending  the  rope  first  in  one  direction 
and  then  in  the  other  is  similar  to  that  of  wire  rope.  At  mines  where 
two  cages  are  used,  one  being  hoisted  and  one  lowered  by  the  same 
engine  doing  the  same  work,  the  wire  ropes,  cut  from  the  same  coil,  are 
usually  arranged  so  that  one  rope  is  bent  continuously  in  one  direction 
and  the  other  rope  is  bent  first  in  one  direction  and  then  in  the  other,  in 
winding  on  the  drum  of  the  engine.  The  rope  having  the  opposite  bends 
wears  much  more  rapidly  than  the  other,  lasting  about  three  quarters 
as  long  as  its  mate.  This  difference  in  wear  shows  in  manila  rope,  both 
in  transmission  of  power  and  in  coal-hoisting.  The  pulleys  should  be 
arranged,  as  far  as  possible,  to  bend  the  rope  in  one  direction. 
DIAMETER  OF  PULLEYS  AND  WEIGHT  OF  ROPE. 


Diameter  of 

i   ^ 
In  inches. 

Smallest  Diameter 
of  Pulleys,  in 
inches. 

Length  of  Rope  to 
allow  for  Splicing, 
in  feet. 

Approximate 
Weight,  in  Ibs.  per 
foot  of  rope. 

Va 

20 

6 

0.12 

5/8 

24 

6 

0.18 

3/4 

30 

7 

0.24 

7/8 

36 

8 

0.32 

1 

42 

9 

0.49 

H/4 

54 

10 

0.60 

n/2 

60 

12 

0.83 

13/4 

72 

13 

1.10 

2 

84 

14 

1.40 

For  large  amounts  of  power  it  is  common  to  use  a  number  of  ropes 
lying  side  by  side  in  grooves,  each  spliced  separately.  For  lighter  drives 
some  engineers  use  one  rope  wrapped  as  many  times  around  the  pulleys 
as  is  necessary  to  get  the  horse-power  required,  with  a  tension  pulley  to 
take  up  the  slack  as  the  rope  wears  when  first  put  in  use.  The  weight 
put  upon  this  tension  pulley  should  be  carefully  adjusted,  as  the  over- 
straining 9f  the  rope  from  this  cause  is  one  of  the  most  common  errors 
in  rope-driving.  We  therefore  give  a  table  showing  the  proper  strain  on 
the  rope  for  the  various  sizes,  from  which  the  tension  weight  to  transmit 
the  horse-power  in  the  tables  is  easily  deduced.  This  strain  can  be  still 
further  reduced  if  the  horse-power  transmitted  is  usually  less  than  the 
nominal  work  which  the  rope  was  proportioned  to  do,  or  if  the  angle  of 
groove  in  the  pulleys  is  acute. 

With  a  given  velocity  of  the  driving-rope,  the  weight  of  rope  required 
for  transmitting  a  given  horse-power  is  the  same,  no  matter  what  size 
rope  is  adopted.  The  smaller  rope  will  require  more  parts,  but  the 
weight  will  be  the  same. 

Miscellaneous  Notes  on  Rope-Driving.  —  Reuleaux  gives  formulae 
for  calculating  sources  of  loss  in  hemp-rope  transmission  due  to  (1)  journal 
friction,  (2)  stiffness  of  ropes,  and  (3)  creep  of  ropes.  The  constants  in 
these  formluse  are,  however,  uncertain  from  lack  of  experimental  data. 
He  calculates  an  average  case  giving  loss  of  power  due  to  journal  friction 
=  4%,  to  stiffness  7.8%,  and  to  creep  5%,  or  16.8%  in  all,  and  says  this 
is  not  to  be  considered  higher  than  the  actual  loss. 

Spencer  Miller,  in  a  paper  entitled  "A  Problem  in  Continuous  Rope- 
driving  "  (Trans.  A.  S.  C.  E.,  1897),  reviews  the  difficulties  which  occur  in 
rope-driving,  with  a  continuous  rope  from  a  large  to  a  small  pulley.  He 
adopts  the  angle  of  45°  as  a  minimum  angle  to  use  on  the  smaller  pulley, 
and  recommends  that  the  larger  pulley  be  grooved  with  a  wider  angle  to*  a 
degree  such  that  the  resistance  to  slipping  is  equal  in  both  wheels. 

Mr.  Miller  refers  to  a  250-H.P.  drive  which  has  been  running  ten  years,1 
large  pulley  being  grooved  60°  and  the  smaller  45°.  This  drive  was 

esigned  to  use  a  1  M-in.  manila  rope,  but  the  grooves  were  made  deep 


1218 


ROPE-DRIVING. 


Prom  the 


Data  of  Manila  Transmission  Rope. 

1  Blue  Book  "  of  The  American  Mfg.  Co.,  New  York. 


Length  of 

w 

i 

s 

£ 

JS 

Splice,  Ft. 

E1^ 

1 

Q 

Is 

H 

•%  m 

•8 

"o 

is 

Wrg 

III 

1 

• 

• 

^> 

|  . 

s 

2  •*•• 

'•§  S 

I 

a 

1 

|| 

12 

S 

1 

4* 

I* 

|^EH 

43 

w 

vO 

i"8 

|« 

3/4 

0.5625 

0.20 

3,950 

112 

6 

8 

28 

760 

7/8 

0  7656 

0.26 

5,400 

153 

6 

8 

4 

32 

650 

-I 

1. 

0.34 

7,000 

200 

7 

10 

14 

36 

570 

H/8 

1.2656 

0.43 

8,900 

253 

7 

10 

16 

40 

510 

I  V4 

1.5625 

0.53 

10,900 

312 

7 

10 

16 

46 

460 

13/8 

1.8906 

0.65 

13,200 

378 

8 

12 

16 

50 

415 

U/2 
15/8 
13/4 

2.25 
2.6406 
3.0625 

0.77 
0.90 
1.04 

15,700 
18,500 
21,400 

450 
528 
612 

8 
8 
8 

12 
12 
12 

18 
18 
18 

54 
60 
64 

380 
344 
330 

2 

4 

1.36 

28,000 

800 

9 

14 

20 

72 

290 

2V4 
21/2 

5.0625 
6.25 

1.73 
2.13 

35,400 
43,700 

1,012 
1,250 

9 
10 

14 
16 

20 
22 

82 
90 

255 
230 

Weight  of  transmission  rope 
Breaking  strength 
Maximum  allowable  tension 
Diam.    smallest    practicable 

sheave, 
Velocity  of  rope  (assumed) 


=-  0.34  X  diam.* 
=  7,000  X  diam.2 
=  200  X  diam.2 


36  X  diam. 
=  5.400  ft.  per  min. 
enough  so  that  a  7/8-in.  rope  would  not  bottom.    In  order  to  determine  the 
value  of  the  drive  a  common  7/8-in.  rope  was  put  in  at  first,  and  lasted  six 
years,  working  under  a  factor  of  safety  of  only  1'4.    He  recommends,  how- 
ever, for  continuous  rope-driving  a  factor  of  safety  .of  not  less  than  20. 

A  heavy  rope-drive  on  the  separate,  or  English,  rope  system  is  described 
and  illustrated  in  Power,  April,  1892,  It  is  in  use  at  the  India  Mill  at  Dar- 
wen,  England,  and  is  driven  by  a  2000-H.P.  engine  at  54  revs,  per  min. 
The  fly-wheel  is  30  ft.  diameter,  weighs  65  tons,  and  is  arranged  with  30 
grooves  for  1 3/4-in.  ropes.  These  ropes  lead  off  to  receiving-pulleys  upon 
the  several  floors,  so  that  each  floor  receives  its  power  direct  from  the  fly- 
wheel. The  speed  of  the  ropes  is  5089  ft.  per  min.,  and  five  7-ft.  receivers 
are  used.  Lambeth  cotton  ropes  are  used.  (For  much  other  information 
on  this  subject  see  "  Rope-Driving,"  by  J.  J.  Flather,  John  Wiley  &  Sons.) 

Cotton  Ropes  are  advantageously  used  as  bands  or  cords  on  the 
smaller  machine  appliances;  the  fiber,  being  softer  and  more  flexible 
than  manila  hemo,  gives  good  results  for  small  sheaves;  but  for  large 
drives,  where  power  transmitted  is  in  considerable  amounts,  cotton  rope, 
as  compared  with  manila,  is  hardly  to  be  considered,  on  account  of 
the  following  disadvantages:  It  is  less  durable;  it  is  injuriously  affected 
by  the  weather,  so  that  for  exposed  drives,  paper-mill  work,  or  use  in 
water-wheel  pits,  it  is  absolutely  unsatisfactory;  it  is  difficult,  if  not 
impossible,  to  splice  uniformly;  even  the  best  quality  cotton  rope  is 
much  inferior  to  manila  in  strength,  the  breaking  strain  of  the  highest 
grade  being  but  4000  X  diam.2  as  against  7000  X  diam.2  for  manila;  while, 
for  the  transmission  of  equal  powers,  the  cost  of  a  cotton  rope  varies 
from  one-third  to  one-half  more  than  manila.  —  ("  Blue  Book  "  of  the 
Amer.  Mfg.  Co.) 

A  different  opinion  is  found  in  a  paper  by  E.  Kenyon  in  Proc.  lust. 
Engrs.  and  Shipbuilders  of  Scotland,  1904.  He  says:  Evidences  of  the 
progress  of  cotton  in  the  manufacture  of  driving-ropes  are  so  far-reaching 
that  its  superiority  may  be  considered  as  much  an  accepted  principle  in 
rope  transmission  as  the  law  of  gravitation  is  in  science.  As  to  the  longevity 
of  cotton  ropes,  24  cotton  ropes  13/4-in.  diam.  are  transmitting  820  H.P.  at  a 
peripheral  speed  of  4396  ft.  per  min.,  from  a  driving  pulley  28  ft.  diam. 
All  the  card-room  ropes  in  this  drive  have  been  running  since  1878,  a 
period  of  26  years,  without  any  attention  whatever. 


FKICTION  AND   LUBRICATION, 


1219 


FRICTION  AND  LUBRICATION. 

,  Friction  is  defined  by  Rankine  as  that  force  which  acts  between  two 
bodies  at  their  surface  of  contact  so  as  to  resist  their  sliding  on  each 
other,  and  which  depends  on  the  force  with  which  the  bodies  are  pressed 
together. 

Coefficient  of  Friction. — The  ratio  of  the  force  required  to  slide  a 
body  along  a  horizontal  plane  surface  to  the  weight  of  the  body  is  called 
the  coefficient  of  friction.  It  is  equivalent  to  the  tangent  of  the  angle  of 
repose,  which  is  the  angle  of  inclination  to  the  horizontal  of  an  inclined 
plane  on  which  the  body  will  just  overcome  its  tendency  to  slide.  The 
angle  is  usually  denoted  by  0,  and  the  coefficient  by  /.  /  =  tan  6. 

Friction  of  Eest  and  of  Motion.  — •  The  force  required  to  start  a 
body  sliding  is  called  the  friction  of  rest,  and  the  force  required  to  con- 
tinue its  sliding  after  having  started  is  called  the  friction  of  motion. 

Rolling  Friction  is  the  force  required  to  roll  a  cylindrical  or  spheri- 
cal body  on  a  plane  or  on  a  curved  surface.  It  depends  on  the  nature  of 
the  surfaces  and  on  the  force  with  which  they  are  pressed  together,  but 
is  essentially  different  from  ordinary,  or  sliding,  friction. 

Friction  of  Solids. — Rennie's  experiments  (1829)  on  friction  of  solids, 
usually  unlubricated  and  dry*  led  to  the  following  conclusions: 

1.  The  laws  of  sliding  friction  differ  with  the  character  of  the  bodies 
rubbing  together. 

2.  The  friction  of  fibrous  material  is  increased  by  increased  extent  of 
surface  and  by  time  of  contact,  and  is  diminished  by  pressure  and  speed. 

3.  With  wood,  metal,  and  stones,  within  the  limit  of  abrasion,  friction 
varies  only  with  the  pressure,  and  is  independent  of  the  extent  of  surface, 
time  of  contact,  and  velocity. 

4.  The  limit  of  abrasion  is  determined  by  the  hardness  of  the  softer  of 
the  two  rubbing  parts. 

5.  Friction  is  greatest  with  soft  and  least  with  hard  materials. 

6.  The  friction  of  lubricated  surfaces  is  determined  by  the  nature  of 
the  lubricant  rather  than  by  that  of  the  solids  themselves. 

Friction  of  Rest.    (Rennie.) 


Pressure, 
Lbs. 
per  Square 
Inch. 

Values  of  /. 

Wrought  Iron  on 
Wrought  Iron. 

Wrought  on 
Cast  Iron. 

Steel  on 
Cast  Iron. 

Brass  on 
Cast  Iron. 

187 
224 
336 
448 
560 
672 
784 

0.25 
.27 
.31 
.38 
.41 
Abraded 

0.28 
.29 
.33 
.37 
.37 
.38 
Abraded 

0.30 
.33 
.35 
.35 
.36 
.40 
Abraded 

0.23 
.22 
.21 
.21 
.23 
.23 
.23 

Law  of  Unlubricated  Friction.  —  A.  M.  Wellington,  Eng'g  News, 
April  7,  1888,  states  that  the  most  important  and  the  best  determined  of 
all  the  laws  of  unlubricated  friction  may  be  thus  expressed: 

The  coefficient  of  unlubricated  friction  decreases  materially  with 
velocity,  is  very  much  greater  at  minute  velocities  of  0+,  falls  very 
rapidly  with  minute  increases  of  such  velocities,  and  continues  to  fall 
much  less  rapidly  with  higher  velocities  up  to  a  certain  varying  point, 
following  closely  the  laws  which  obtain  with  lubricated  friction. 

Friction  of  Steel  Tires  Sliding  on  Steel  Rails.  (Westinghouse  & 
Galton.) 

Speed,  miles  per  hour 10         15         25 .        38         45         50 

Coefficient  of  friction 0.110     .087     ,08O      .051      .047      .040 

Adhesion,  Ibs.  per  gross  ton        246       195       179       128       114         90 

Rolling  Friction  is  a  consequence  of  the  irregularities  of  form  and 
the  roughness  of  surface  of  bodies  rolling  one  over  the  other.  Its  laws 
are  not  yet  definitely  established  in  consequence  of  the  uncertainty 
which  exists  in  experiment  as  to  how  much  of  the  resistance  is  due  to 
roughness  of  surface,  how  much  to  original  and  permanent  irregularity 
of  form,  and  how  much  to  distortion  under  the  load.  (Thurston.) 


1220 


FRICTION  AND  LUBRICATION. 


Coefficients  of  Rolling  Friction. — If  R  =  resistance  applied  at  the 
circumference  of  the  wheel,  W  =  total  weight,  r  =  radius  of  the  wheel, 
and /  =  a  coefficient,  R  =  fW  -f-  r.  /is  very  variable.  Coulomb  gives 
0.06  for  wood,  0.005  for  metal,  where  W  is  in  pounds  and  r  in  feet.  Tred- 
gold  made  the  value  of  /  for  iron  on  iron  0.002.  For  wagons  on  soft  soil 
Morin  found  /  =  0.065,  and  on  hard  smooth  roads  0.002. 

A  Committee  of  the  Society  of  Arts  (Clark,  R.  T.  D.)  reported  a 
loaded  omnibus  to  exhibit  a  resistance  on  various  loads  as  below: 
Pavement.  Speed  per  hour.    Coefficient.      Resistance. 

Granite 2.87  miles.         0.007  17. 41  per  ton. 

Asphalt 3.56       "  0.0121  27.14 

Wood 3.34  0.0185  41.60 

Macadam,  graveled 3.45  0.0199  44.48 

Macadam,  granite,  new.. ..     3.51  0.0451         101.09 

Thurston  gives  the  value  of/  for  ordinary  railroads,  0.003;  welf-laiQ 
railroad  track,  0.002;  best  possible  railroad  track,  0.001. 

The  few  experiments  that  have  been  made  upon  the  coefficients  ol 
rolling  friction,  apart  from  axle  friction,  are  too  incomplete  to  serve  as  a 
basis  for  practical  rules.  (Trautwine.) 

Laws  of  Fluid  Friction.  —  For  all  fluids,  whether  liquid  or  gaseous, 
the  resistance  is  (1)  independent  of  the  pressure  between  the  masses  in 
contact;  (2)  directly  proportional  to  the  area  of  rubbing-surface;  (3)  pro- 
portional to  the  square  of  the  relative  velocity  at  moderate  and  high 
speeds,  and  to  the  velocity  nearly  at  low  speeds;  (4)  independent  of  the 
nature  of  the  surfaces  of  the  solid  against  which  the  stream  may  flow,  but 
dependent  to  some  extent  upon  their  degree  of  roughness;  (5)  proportional 
to  the  density  of  the  fluid,  and  related  in  some  way  to  its  viscosity. 
(Thurston.) 

The  Friction  of  Lubricated  Surfaces  approximates  that  of  solid  friction 
as  the  journal  is  run  dry,  and  that  of  fluid  friction  as  it  is  flooded  with  oil. 
Angles  of  Repose  and  Coefficients  of  Friction  of  Building  Materials. 
(From  Rankine's  Applied  Mechanics.) 


e. 

/  =  tan  9. 

1  -r-  tan  0 

Dry  masonry  and  brickwork.  .  . 
Masonry  and  brickwork    with 
damp  mortar.  

31°  to  35° 

361/2° 
22° 
35°  to  162/3° 
26  1/2°  to  11  1/3° 
31°  to  111/3° 
14°  to  81/2° 
27° 
181/4° 
14°  to  45° 

21°  to  37° 
45° 
17° 

39°  to  48° 

0.6  to  0.7 

0.74 
about  0.4 
0.7  to  0.3 
0.5  to  0.2 
0.6  to  0.2 
0.25  to  0.15 
0.51 
0.33 
0.25  to  1.0 

0.38  to  0.75 
1.0 
0.31 

0.81 

1.67  to  1.4 

1.35 
2.5 
1.43  to  3.  3 
2  to  5 
1.67  to  5 
4  to  6.67 
1.96 
3. 
4  to  1 

2.63  to  1.33 
3.23 
1.23  to  0.9 

Iron  on  stone 

Timber  on  timber  

Timber  on  metals  

Metals  on  metals 

Masonry  on  dry  clay            .   .   . 

Masonry  on  moist  clay  

Earth  on  earth 

Earth  on  earth,  dry  sand,  clay, 
and  mixed  earth  

Earth  pn  earth,  damp  clay  
Earth  on  earth    wet  clay  

Earth   on   earth,    shingle,  and 
gravel  

Coefficients  of  Friction  of  Journals.     (Morin.) 


Material. 

Unguent. 

Lubrication. 

Intermittent  . 

Continuous. 

Cast  iron  on  cast  iron  | 

Oil,  lard,  tallow. 
Unctuous  and  wet 
Oil,  lard,  tallow. 
Unctuous  and  wet 
Oil,  lard. 

Oil,  lard,  tallow. 

Oil,  lard. 
Unctuous. 
Olive  oil. 
Lard. 

0.07  to  0.08 
0.14 
0.07  to  0.08 
0.16 

0.03  to  0.054 
0.03  to  0.054 

0.09 
0.03  to  0.054 

Cast  iron  on  lignum  vitae  .  .  . 
Wrought  iron  on  cast  iron  .  ) 
Wrought  iron  on  bronze.  .  j 

Iron  on  lignum  vitas  | 
Bronze  on  bronze  | 

0.07  to  0.08 

0.11 
0.19 
0.10 
0  09 

FRICTION  AND  LTJBEICATION. 


1221 


Prof.  Thurston  says  concerning  the  foreg9ing  figures  that  much  better 
results  are  probably  obtained  in  good  practice  with  ordinary  machinery. 
Those  here  given  are  so  modified  by  variations  of  speed,  pressure,  and 
temperature,  that  they  cannot  be  taken  as  correct  for  general  purposes. 

Friction  of  Motion.- — The  following  is  a  table  of  the  angle  of  repose 
0,  the  coefficient  of  friction  /  =  tan  0,  and  its  reciprocal,  1  +  f,  for  the 
materials  of  mechanism — condensed  from  the  tables  of  General  Morin 
(1831)  and  other  sources,  as  given  by  Rankine: 


No. 


Surfaces. 


I 


I 


±f. 


1 

Wood  on  wood,  dry  

14°  to  26  1/2° 

0.25  to  0.5 

4  to  2 

7 

"      "        "    soaped 

1  1  1/2°  to  2° 

02  to  0  04 

5  to  25 

1 

Metals  on  oak  dry     

261/2°  to  31° 

05    to  0  6 

2  to  1  .67 

4 

"    wet  

131/2°  to  14° 

0.24  to  0.26 

4.17  to  3.  85 

*> 

**      "    soapy          .   .  . 

1  1  1/2° 

0  2 

ft 

"    elm  dry    

111/2°  to  14° 

0.2  to  0.25 

5  to  4 

28° 

0.53 

1.89 

8 

18l/20 

0.33 

3 

9 

Leather  on  oak              

15°  to  191/2° 

0.27  to  0.38 

3.  7  to  2.  86 

10 

29l/20 

0.56 

1.79 

11 

12 
13 
14 

**   metals,  wet  
greasy  .  . 
oily  
Metals  on  metals  dry  

20° 
13° 
81/2° 
81/2°  to  11° 

0.36 
0.23 
0.15 
0.15  to  0.2 

2.78 
4.35 
6.67 
6.67  to  5 

|5 

*'       "        "       wet 

161/2° 

0.3 

3.33 

16 

Smooth    surfaces,    occasion- 
ally greased  

4°  to  41/2° 

0.07  to  0.08 

14.3  to  12.5 

17 

Smooth     surfaces,     continu- 
ously greased             

3° 

0.05 

20 

18 

Smooth  surfaces,  best  results 

1  3/40  to  2° 

0.03  to  0.036 

19 

Bronze  on  lignum  vitse,    con- 
stantly wet  

3°? 

0.05? 

Average  Coefficients  of  Friction. — Journal  of  cast  iron  in  bronze 
bearing;  velocity  720  feet  per  minute;  temperature  70°  F.;  intermittent 
feed  through  an  oil-hole.  (Thurston  on  Friction  and  Lost  Work.) 


Pressures,  Pounds  per  Square  Inch. 


8 

16 

32 

48 

Sperm,  lard,  neatsfoot,  etc.  . 
Olive,  cotton-seed,  rape,  etc. 
Cod  and  menhaden 

.159 
.160 

?48 

to 
to 
to 

.250 
.283 
778 

.138  to 
.107  to 
124  to 

.192 
.245 
167 

.086 
.101 
097 

to 
to 
to 

.141 
.168 
10? 

.077 
.079 
081 

to 
to 

to 

.144 
.131 
1?? 

Mineral  lubricating-oils  .... 

.154 

to 

.261 

.145  to 

.233 

.086 

to 

.178 

.094 

to 

.222 

With  fine  steel  journals  running  in  bronze  bearings  and  continuous 
lubrication,  coefficients  far  below  those  above  given  are  obtained. 
Thus  with  sperm-oil  the  coefficient  with  50  Ibs.  per  square  inch  pres- 
sure was  0.0034;  with  200  Ibs.,  0.0051;  with  300  Ibs.,  0.0057. 

For  very  low  pressures,  as  in  spindles,  the  coefficients  are  much 
higher.  Thus  Mr.  Woodbury  found,  at  a  temperature  of  100°  and  a 
velocity  of  600  feet  per  minute, 

Pressures,  Ibs.  per  sq.  in. .  .         1  23  4  5 

Coefficient 0.38     0.27     0.22     0.18     0.17 

These  high  coefficients,  however,  and  the  great  decrease  in  the  co- 
efficient at  increased  pressures  are  limited  as  a  practical  matter  only  to 
the  smaller  pressures  which  exist  especially  in  spinning  machinery, 
where  the  pressure  is  so  light  and  the  film  of  oil  so  thick  that  the  viscos- 
ity of  the  oil  is  an  important  part  of  the  total  frictional  resistance. 

Experiments  on  Friction  of  a  Journal  Lubricated  by  an  Oil- 
bath  (reported  by  the  Committee  on  Friction,  Proc.  Inst.  M.  E., 
Nov.,  1883)  show  that  the  absolute  friction,  that  is,  the  absolute  tan- 
gential force  per  square  inch  of  bearing,  required  to  resist  the  tendency 
of  the  brass  to  go  round  with  the  journal,  is  nearly  a  constant  under  all 
loads,  within  ordinary  working  limits.  Most  certainly  it  does  not  in- 


1222  FBICTION  AND  LUBRICATION 

crease  in  direct  proportion  to  the  load,  as  it  should  do  according  to  thd 
ordinary  theory  of  solid  friction.  The  results  of  these  experiments 
seem  to  show  that  the  friction  of  a  perfectly  lubricated  journal  follows 
the  laws  of  liquid  friction  much  more  closely  than  those  of  solid  friction. 
They  show  that  under  these  circumstances  the  friction  is  nearly  inde- 
pendent of  the  pressure  per  square  inch,  and  that  it  increases  with  the 
velocity,  though  at  a  rate  not  nearly  so  rapid  as  the  square  of  the  velocity. 

The  experiments  on  friction  at  different  temperatures  indicate  a  great 
diminution  in  the  friction  as  the  temperature  rises.  Thus  in  the  case  of 
lard-oil,  taking  a  speed  of  450  r.p.m.,  the  coefficient  of  friction  at  a  tem- 
perature of  120°  is  only  one-third  of  what  it  was  at  a  temperature  of  60°. 

The  journal  was  of  steel,  4  ins.  diameter  and  6  ins.  long,  and  a  gun- 
metal  brass,  embracing  somewhat  less  than  half  the  circumference  of  the 
journal,  rested  on  its  upper  side,  on  which  the  load  was  applied.  When 
the  bottom  of  the  journal  was  immersed  in  oil,  and  the  oil  therefore  carried 
under  the  brass  by  rotation  of  the  journal,  the  greatest  load  carried  with 
rape-oil  was  573  Ibs.  per  sq.  in.,  and  with  mineral  oil  625  Ibs. 

In  experiments  with  ordinary  lubrication,  the  oil  being  fed  in  at  the 
center  of  the  top  of  the  brass,  and  a  distributing  groove  being  cut  in  the 
brass  parallel  to  the  axis  of  the  journal,  the  bearing  would  not  run  cool 
with  only  100  Ibs.  per  sq.  in.,  the  oil  being  pressed  out  from  the  bearing- 
surface  and  through  the  oil-hole,  instead  of  being  carried  in  by  it.  On 
introducing  the  oil  at  the  sides  through  two  parallel  grooves,  the  lubrica- 
tion appeared  to  be  satisfactory,  but  the  bearing  seized  with  380  Ibs. 
per  sq.  in. 

When  the  oil  was  introduced  through  two  oil-holes,  one  near  each  end 
of  the  brass,  and  each  connected  with  a  curved  groove,  the  brass  refused 
to  take  its  oil  or  run  cool,  and  seized  with  a  load  of  only  200  Ibs.  per  sq.  in. 

With  an  oil-pad  under  the  journal  feeding  rape-oil,  the  bearing  fairly 
carried  551  Ibs.  Mr.  Tower's  conclusion  from  these  experiments  is  that 
the  friction  depends  on  the  quantity  and  uniformity  of  distribution  of  the 
oil,  and  may  be  anything  between  the  oil-bath  results  and  seizing,  accord- 
ing to  the  perfection  or  imperfection  of  the  lubrication.  The  lubrication 
may  be  very  small,  giving  a  coefficient  of  Vioo;  but  it  appeared  as  though 
it  could  not  be  diminished  and  the  friction  increased  much  beyond  this 
point  without  imminent  risk  of  heating  and  seizing.  The  oil-bath  prob- 
ably represents  the  most  perfect  lubrication  possible,  and  the  limit 
beyond  which  friction  cannot  be  reduced  by  lubrication;  and  the  experi- 
ments show  that  with  speeds  of  from  100  to  200  feet  per  minute,  by 
properly  proportioning  the  bearing-surface  to  the  load,  it  is  possible  to 
reduce  the  coefficient  of  friction  to  as  low  as  Viooo.  A  coefficient  of  Visoo 
is  easily  attainable,  and  probably  is  frequently  attained,  in  ordinary 
engine-bearings  in  which  the  direction  of  the  force  is  rapidly  alternating 
and  the  oil  given  an  opportunity  to  get  between  the  surfaces,  while  the 
duration  of  the  force  in  one  direction  is  not  sufficient  to  allow  time  for 
the  oil  film  to  be  squeezed  out. 

Observations  on  the  behavior  of  the  apparatus  gave  reason  to  believe 
that  with  perfect  lubrication  the  speed  of  minimum  friction  was  from 
100  to  150  feet  per  minute,  and  that  this  speed  of  minimum  friction  tends 
to  be  higher  with  an  increase  of  load,  and  also  with  less  perfect  lubrica-  i 
tion.  By  the  speed  of  minimum  friction  is  meant  that  speed  in  approach- 
ing which  from  rest  the  friction  diminishes,  and  above  which  the  friction 
increases. 

Coefficients  of  Friction  of  Motion  and  of  Rest  of  a  Journal.  — 
A  cast-iron  journal  in  steel  boxes,  tested  by  Prof.  Thurston  at  a  sneed  of 
rubbing  of  150  feet  per  minute,  with  lard  "and  with  sperm  oil,  gave  the  | 
following : 

Press,  per  sq.  in.,  Ibs  .       50  100         250         500         750  1000 

Coeff.,  with  sperm.  ..    0.013     0.008     0.005       0.004     0.0043     0.009   ! 
Coeff.,  with  lard 0.02       0.01370.0085     0.00530.0066     0.125: 

The  coefficients  at  starting  were: 

Withsperm 0.07         0.135         0.14         0.15         0.185         0.18 

Withlard 0.07         0.11  0.11         0.10         0.12 

The  coefficient  at  a  speed  of  150  feet  per  minute  decreases  with  in-  i 
crease  of  pressure  until  500  Ibs.  per  sq.  in.  is  reached;  above  this  it 
creases.     The  coefficient  at  rest  or  at  starting  increases  with  the  pressure 
throughout  the  range  of  the  tests. 


FRICTION  AND   LUBRICATION. 


1223 


Coefficients  of  Friction  of  Journal  with  Oil-bath.  —  Abstract  of 
results  of  Tower's  experiments  on  friction  (Proc.  Inst.  M.  E.,  Nov., 
1883).  Journal,  4  in.  diam.,  6  in.  long;  temperature,  90°  F. 


Lubricant  in  Bath. 

Nominal  Load,  in  Lbs.  per  Sq.  In. 

625 

520 

415 

310 

205 

153 

100 

Coefficient  of  Friction. 

Lard,  oil'  157  ft  per  rnin 

.0009 
.0017 
.0014 
.0022 
seized 

.0012 
.0021 
.0016 
.0027 
.0015 
.0021 

.0009 
.0016 
.0012 
.002 

0014 
.0029 
.0022 
.004 
.0011 
.0019 

.0008 
.0016 
.0014 
.0024 

0056 

.0020 
.0042 
.0034 
.0066 
.0016 
.0027 

.0014 
.0024 
.0021 
.0035 

0098 

.0027 
.0052 
.0038 
.0083 
.0019 
.0037 

.002 
.004 

.0042 
.009 
.0076 
.0151 
.003 
.0064 

.004 
.007 
.004 
.007 

.0125 
.0152 

.0099 
.0133 

"      •«    471      "         "              

Mineral  grease:  157  ft.  per  min  — 
471      "         "    .... 

.001 
.002 

"471      "                 

Rape-oil*  157ft  per  min 

(573  lb. 
.001 

.001 
.0015 
.0012 
.0018 

"471      "         "     

Mineral-oil:  157  ft.  per  min  
"471      "         "      
Rape-oil  fed  by    ' 
siphon  lubricator:{]57ft,tper  min. 

Rape-oil,  pad 
under  journal:       j]^^.  per  min. 

.0013 



..... 

.0068 
0099 

.0077 
0105 



0099 

0078 

Comparative  friction  of  different  lubricants  under  same  circumstances, 
temperature  90°,  oil-bath:  sperm-oil,  100;  rape-oil,  106;  mineral  oil,  129; 
lard,  135;  olive  oil,  135;  mineral  grease,  217. 

Value  of  Anti-friction  Metals.  (Denton.)  —  The  various  white 
metals  available  for  lining  brasses  do  not  afford  coefficients  of  friction 
lower  than  can  be  obtained  with  bare  brass,  but  they  are  less  liable  to 
"overheating,"  because  of  the  superiority  of  such  material  over  bronze 
in  ability  to  permit  of  abrasion  or  crushing,  without  excessive  increase  of 
friction. 

Thurston  (Friction  and  Lost  Work)  says  that  gun-bronze,  Babbitt, 
and  other  soft  white  alloys  have  substantially  the  same  friction;  in  other 
words,  the  friction  is  determined  by  the  nature  of  the  unguent  and  not 
by  that  of  the  rubbing-surfaces,  when  the  latter  are  in  good  order.  The 
soft  metals  run  at  higher  temperatures  than  the  bronze.  This,  however, 
does  not  necessarily  indicate  a  serious  defect,  but  simply  deficient  con- 
ductivity. The  value  of  the  white  alloys  for  bearings  lies  mainly  in  their 
ready  reduction  to  a  smooth  surface  after  any  local  or  general  injury  by 
alteration  of  either  surface  or  form. 

Cast  Iron  for  Bearings.  (Joshua  Rose.)  —  Cast  iron  appears  to  be  an 
exception  to  the  general  rule,  that  the  harder  the  metal  the  greater  the 
resistance  to  'vear,  because  cast  iron  is  softer  in  its  texture  and  easier  to 
cut  with  steel  tools  than  steel  or  wrought  iron,  but  in  some  situations  it 
is  far  more  durable  than  hardened  steel;  thus  when  surrounded  by  steam 
it  will  wear  better  than  will  any  other  metal.  Thus,  for  instance,  ex- 
perience has  demonstrated  that  piston-rings  of  cast  iron  will  wear  smoother, 
better,  and  equally  as  long  as  those  of  steel,  and  longer  than  those  of 
either  wrought  iron  or  brass,  whether  the  cylinder  in  which  it  works  be 
composed  of  brass,  steel,  wrought  iron,  or  cast  iron;  the  latter  being  the 
more  noteworthy,  since  two  surfaces  of  the  same  metal  do  not,  as  a  rule, 
wear  or  work  well  together.  So  also  slide-valves  of  brass  are  not  found 
to  wear  so  long  or  so  smoothly  as  those  of  cast  iron,  let  the  metal  of  which 
the  seating  is  composed  be  whatever  it  may;  while,  on  the  other  hand,  a 
cast-iron  slide-valve  will  wear  longer  of  itself  and  cause  less  wear  tc 
its  seat,  if  the  latter  is  of  cast  iron,  than  if  of  steel,  wrought  iron,  or 
brass. 

Friction  of  Metals  under  Steam-pressure.  —  The  friction  of  brass 
upon  iron  under  steam-pressure  is  double  that  of  iron  upon  iron.  (G.  H. 
Babcock,  Trans.  A.  S.  M.  E.t  i,  151.) 

Morin's  "Laws  of  Friction."  —  1.  The  friction  between  two  bodies 
is  directly  proportioned  to  the  pressure-,  i.e.,  the  coefficient  is  constant 
*or  all  pressures. 


1224  FRICTION  AND   LUBRICATION. 


2.  The  coefficient  and  amount  of  friction,  pressure  being  the  same,  are 
independent  of  the  areas  in  contact. 

3.  The  coefficient  of  friction  is  independent  of  velocity,  although  static 
friction  (friction  of  rest)  is  greater  than  the  friction  of  motion. 

Eng'g  News,  April  7,  1888,  comments  on  these  "laws"  as  follows: 
From  1831  till  about  1876  there  was  no  attempt  worth  speaking  of  to 
enlarge  our  knowledge  of  the  laws  of  friction,  which  during  all  that  period 
was  assumed  to  be  complete,  although  it  was  really  worse  than  nothing, 
since  it  was  for  the  most  part  wholly  false.  In  the  year  first  mentioned 
Morin  began  a  series  of  experiments  which  extended  over  two  or  three 
years,  and  which  resulted  in  the  enunciation  of  these  three  "funda- 
mental laws  of  friction,"  no  one  of  which  is  even  approximately  true. 

For  fifty  years  these  laws  were  accepted  as  axiomatic,  and  were  quoted 
as  such  without  question  in  every  scientific  work  published  during  that 
whole  period.  Now  that  they  are  so  thoroughly  discredited  it  has  been 
attempted  to  explain  away  their  defects  on  the  ground  that  they  cover 
only  a  very  limited  range  of  pressures,  areas,  velocities,  etc.,  and  that 
Morin  himself  only  announced  them  as  true  within  the  range  of  his  con- 
ditions. It  is  now  clearly  established  that  there  are  no  limits  or  con- 
ditions within  which  any  one  of  them  even  approximates  to  exactitude, 
and  that  there  are  many  conditions  under  which  they  lead  to  the  wildest 
kind  of  error,  while  many  of  the  constants  were  as  inaccurate  as  the  laws. 
For  example,  in  Morin's  "Table  of  Coefficients  of  Moving  Friction  of 
Smooth  Plane  Surfaces,  perfectly  lubricated,"  which  may  be  found  in 
hundreds  of  text-books  now  in  use,  the  coefficient  of  wrought  iron  on 
brass  is  given  as  0.075  to  0.103,  which  would  make  the  rolling  friction  of 
railway  trains  15  to  20  Ibs.  per  ton  instead  of  the  3  to  6  Ibs.  which  it 
actually  is. 

General  Morin,  in  a  letter  to  the  Secretary  of  the  Institution  of  Mechan- 
ical Engineers,  dated  March  15,  1879,  writes  as  follows  concerning  his 
experiments  on  friction  made  more  than  forty  years  before:  "The  results 
furnished  by  my  experiments  as  to  the  relations  between  pressure,  surface, 
and  speed  on  the  one  hand,  and  sliding  friction  on  the  other,  have  always 
been  regarded  by  myself,  not  as  mathematical  laws,  but  as  close  approxi- 
mations to  the  truth,  within  the  limits  of  the  data  of  the  experiments 
themselves.  The  same  holds,  in  my  opinion,  for  many  other  laws  of 
practical  mechanics,  such  as  those  of  rolling  resistance,  fluid  resistance, 
etc. " 

Prof.  J.  E.  Denton  (Stevens  Indicator,  July,  1890)  says:  It  has  been 
generally  assumed  that  friction  between  lubricated  surfaces  follows  the 
simple  law  that  the  amount  of  the  friction  is  some  fixed  fraction  of 
the  pressure  between  the  surfaces,  such  fraction  being  independent  of  the 
intensity  of  the  pressure  per  square  inch  and  the  velocity  of  rubbing, 
between  certain  limits  of  practice,  and  that  the  fixed  fraction  referred  to 
is  represented  by  the  coefficients  of  friction  given  by  the  experiments  of 
Morin  or  obtained  from  experimental  data  which  represent  conditions  of 
practical  lubrication,  such  as  those  given  in  Webber's  Manual  of  Power. 

By  the  experiments  of  Thurston,  Woodbury,  Tower,  etc.,  however,  it 
appears  that  the  friction  between  lubricated  metallic  surfaces,  such  as 
machine  bearings,  is  not  directly  proportional  to  the  pressure,is  not 
independent  of  the  speed,  and  that  the  coefficients  of  Morin  and  Webber 
are  about  tenfold  too  great  for  modern  journals. 

Prof.  Denton  offers  an  explanation  of  this  apparent  contradiction  of 
authorities  by  showing,  with  laboratory  testing-machine  data,  that 
Morin's  laws  hold  for  bearings  lubricated  by  a  restricted  feed  of  lubricant, 
such  as  is  afforded  by  the  oil-cups  common  to  machinery;  whereas  the 
modern  experiments  have  been  made  with  a  surplus  feed  or  superabun- 
flance  or  lubricant,  sucn  as  is  provided  only  in  railroad-car  journals,  and 
a  few  special  cases  of  practice. 

That  the  low  coefficients  of  friction  obtained  under  the  latter  conditions 
are  realized  in  the  case  of  car-journals,  is  proved  by  the  fact  that  the 
temperature  of  car-boxes  remains  at  100°  at  high  velocities;  and  experi- 
ment shows  that  this  temperature  is  consistent  only  with  a  coefficient  of 
friction  of  a  fraction  of  one  per  cent.  Deductions  from  experiments  on 
train  resistance  also  indicate  the  same  low  degree  of  friction.  But  these 
low  coefficients  do  not  account  for  the  internal  friction  of  steam-engines 
as  well  as  do  the  coefficients  of  Morin  and  Webber, 


AND  LUfi&ICATlON.  1225 

In  American  Machinist,  Oct.  23,  1890,  Prof,  Benton  says:  Morin's 

measurements  of  friction  of  lubricated  journals  did  not  extend  to  light 
pressures.  They  apply  only  to  the  conditions  of  general  shafting  and 
engine  work. 

He  clearly  understood  that  there  was  a  frictional  resistance,  due  solely 
to  the  viscosity  of  the  oil,  and  that  therefore,  for  very  light  pressures, 
the  laws  which  he  enunciated  did  not  prevail. 

He  applied  his  dynamometers  to  ordinary  shaft-journals  without 
special  preparation  of  the  rubbing-surfaces,  and  without  resorting  to 
artificial  methods  of  supplying  the  oil. 

Later  experimenters  have  with  few  exceptions  devoted  themselves 
exclusively  to  the  measurement  of  resistance  practically  due  to  viscosity 
alone.  They  have  eliminated  the  resistance  to  which  Morin  confined  his 
measurements,  namely,  the  friction  due  to  such  contacts  of  the  rubbing- 
surfaces  as  prevail  with  a  very  thin  film  of  lubricant  between  compara- 
tively rough  surfaces. 

Prof.  Denton  also  says  (Trans.  A.  S.  M.  E.,  x,  518):  "I  do  not  believe 
there  is  a  particle  of  proof  in  any  investigation  of  friction  ever  made, 
that  Morin's  laws  do  not  hold  for  ordinary  practical  oil-cups  or  restricted 
rates  of  feed." 

Laws  of  Friction  of  Well-lubricated  Journals.  —  John  Goodman 
(Trans.  Inst.  C.  E.,  1886,  Eng'g  News,  April  7  and  14,  1888),  reviewing 
the  results  obtained  from  the  testing-machines  of  Thurston,  Tower,  and 
Stroudley,  arrives  at  the  following  laws: 

LAWS  OF  FRICTION:  WELL-LUBRICATED  SURFACES. 
(Oil-bath.) 

1.  The  coefficient  of  friction  with  the  surfaces  efficiently  lubricated  in 
from  Ve  to  Vio  that  for  dry  or  scantily  lubricated  surfaces. 

2.  The  coefficient  of  friction  for  moderate  pressures  and  speeds  varies 
approximately  inversely  as  the  normal  pressure;  the  frictional  resistance 
varies  as  the  area  in  contact,  the  normal  pressure  remaining  constant. 

3.  At  very  low  journal  speeds  the  coefficient  of  friction  is  abnormally 
high;  but  as  the  speed  of  sliding  increases  from  about  10  to  100  ft.  per 
min.,  the  friction  diminishes,  and  again  rises  when  that  speed  is  exceeded, 
varying  approximately  as  the  square  root  of  the  speed. 

4.  The  coefficient  of  friction  varies  approximately  inversely  as  the 
temperature,  within  certain  limits,  namely,  just  before  abrasion  takes 
place. 

The  evidence  upon  which  these  laws  are  based  is  taken  from  various 
modern  experiments.  That  relating  to  Law  1  is  derived  from  the  "  First 
Report  on  Friction  Experiments,"  by  Mr.  Beauchamp  Tower. 


Method  of  Lubrication. 

Coefficient  of 
Friction. 

Comparative 
Friction. 

Oil-bath  

0  00139 

1  00 

Siphon  lubricator  

0.0098 

7  06 

Pad  under  journal  

0.0090 

6.48 

With  a  load  of  293  Ibs.  per  sq.  in.  and  a  journal  speed  of  314  ft.  per 
min.  Mr.  Tower  found  the  coefficient  of  friction  to  be  0 .0016  with  an  oil- 
bath,  and  0.0097,  or  six  times  as  much,  with  a  pad.  The  very  low  co- 
efficients obtained  by  Mr.  Tower  will  be  accounted  for  by  Law  2,  as  he 
found  that  the  frictional  resistance  per  square  inch  under  varying  loads 
is  nearly  constant,  as  below: 

Load  in  Ibs.  per  sq.  in.    529     468     415     363     310     258   205     153    100 
Frictional  resist,  per  JQ  416  0>5U  Q  498  0.472  0.464  0.438  0.43  0.458  0.45 

The  frictional  resistance  per  square  inch  is  the  product  of  the  coefficient 
of  friction  into  the  load  per  square  inch  on  horizontal  sections  of  the  brass. 
Hence,  if  this  product  be  a  constant,  the  one  factor  must  vary  inversely 
as  the  other,  or  a  high  load  will  give  a  low  coefficient,  and  vice  versa. 

For  ordinary  lubrication,  the  coefficient  is  more  constant  under  varying 
loads-  the  frictionai  resistance  then  varies  directly  as  the  load,  as  shown 
by  Mr,  Tower  in  Table  VIII  of  bis  report  (Proc.  Inst.  M.  E.\  1883), 


1226 


FRICTION  AND  LUBRICATION* 


With  respect  to  Law  3,  A.  M.  Wellington  (Trans.  A.  S.  C.  E.,  1884), 
in  experiments  on  journals  revolving  at  very  low  velocities,  found  that 
the  friction  was  then  very  great,  and  nearly  constant  under  varying 
conditions  of  the  lubrication,  load,  and  temperature.  But  as  the  speed 
increased  the  friction  fell  slowly  and  regularly,  and  again  returned  to 
the  original  amount  when  the  velocity  was  reduced  to  the  same  rate. 
This  is  shown  in  the  following  table: 
Speed,  feet  per  minute: 

0+       2.16    '     3.33       4.86       8.82     21.42     35.37     53.01     89.28    106.02 
Coefficient  of  friction : 
0.118     0.094     0.070     0.069     0.055     0.047     0.040     0.035     0.030      0.026 

It  was  also  found  by  Prof.  Kimball  that  when  the  journal  velocity 
was  increased  from  6  to  110  ft.  per  min.,  the  friction  was  reduced 
70%;  in  another  case  the  friction  was  reduced  67%  when  the  velocity 
was  increased  from  1  to  100  ft.  per  min. ;  but  after  that  point  was  reached 
the  coefficient  varied  approximately  with  the  square  root  of  the  velocity. 

The  following  'results  were  obtained  by  Mr.  Tower: 


Feet  per  minute 

209 

262 

314 

366 

419 

471 

Nominal  Load 
per  Sq.  In. 

Coeff  .  of  friction  
»(           u 

0.0010 
.0013 
.0014 

0.0012 
.0014 
.0015 

0.0013 
.0015 
.0017 

0.0014 
.0017 
.0019 

0.0015 
.0018 
.0021 

0.0017 
.002 
.0024 

520  Ibs. 
468  Ibs. 
415  Ibs. 

The  variation  of  friction  with  temperature  is  approximately  in  the 
inverse  ratio,  Law  4.  Take,  for  example,  Mr.  Tower's  results,  at 
262  ft.  per  minute: 


Temp.  F. 

110° 

100° 

90° 

80° 

70° 

60° 

Observed. 

0  0044 

0.0051 

0.006 

0.0073 

0.0092 

0.0119 

Calculated  

0.00451 

0.00518 

0.00608 

0.00733 

0.00964 

0.01252 

This  law  does  not  hold  good  for  pad  or  siphon  lubrication,  as  then  the 
coefficient  of  friction  diminishes  more  rapidly  for  given  increments  of 
temperature,  but  on  a  gradually  decreasing  scale,  until  the  normal 
temperature  has  been  reached;  this  normal  temperature  increases 
directly  as  the  load  per  sq.  in.  This  is  shown  in  the  following  table 
taken  from  Mr.  Stroudley's  experiments  with  a  pad  of  rape-oil: 


Temp.  F  

105° 

110° 

115° 

120° 
0.0140 
0.0020 

125° 

130° 

135° 

140° 

145? 

Coefficient  
Decrease  of  coeff  .  . 

0.022 

0.0180 
0.0040 

0.0160 
0.0020 

0.0125 
0.0015 

0.0115 
0.0010 

0.0110 
0.0005 

0.0106 
0.0004 

0.0102 
0.0002 

In  the  Galton-Westinghouse  experiments  it  was  found  that  with 
velocities  below  100  ft.  per  min.,  and  with  low  pressures,  the  frictional 
resistance  varied  directly  as  the  normal  pressure ;  but  when  a  velocity  of 
100  ft.per  min.  was  exceeded,  the  coefficient  of  friction  greatly  diminished ; 
from  the  same  experiments  Prof.  Kennedy  found  that  the  coefficient  of 
friction  for  high  pressures  was  sensibly  less  than  for  low. 

Allowable  Pressures  on  Bearing-surfaces.  (Proc.  InsL  M.  E.t 
May,  1888.)  —  The  Committee  on  Friction  experimented  with  a  steel 
ring  of  rectangular  section,  pressed  between  two  cast-iron  disks,  the 
annular  bearing-surfaces  of  which  were  covered  with  gun-metal,  and  were 
12  in.  inside  diameter  and  14  in.  outside.  The  two  disks  were  rotated 
together,  and  the  steel  ring  was  prevented  from  rotating  by  means  of  a 
lever,  the  Iwlding  force  of  which  was  measured.  When  oiled  through 
grooves  cut  in  each  face  of  the  ring  and  tested  at  from  50  to  130  revs. 
per  min.,  it  was  found  that  a  pressure  of  75  Ibs.  per  sq.  in.  of  bearing- 
surface  was  as  much  as  it  would  bear  safely  at  the  highest  speed  without 
seizing,  although  it  carried  90  Ibs.  per  sq.  in.  at  the  lowest  speed.  The 
coefficient  of  friction  is  also  much  higher  than  for  a  cylindrical  bearing, 
and  the  friction  follows  the  law  of  the  friction  of  solids  much  more  nearly 
than  that  of  liquids.  This  is  doubtless  due  to  the  much  less  perfect 
lubrication  applicable  to  this  form  of  bearing  compared  with  a  cylindrical 
one.  The  coefficient  of  friction  appears  to  be  about  the  same  with  the 
same  load  at  all  speeds,  or,  in  other  words,  to  be  independent  of  the 
speed;  but  it  seems  to  diminish  somewhat  as  the  load  is  increased,  and 
may  be  stated  approximately  as  1/20  at  15  Ibs.  per  sq.  in.,  diminishing  to 
1/30  at  75  Ibs.  per  sq.  in. 

The  high  .coefficients  of  friction  are  explained  by  the  difficulty  of  lubri- 
cating a  collar-bearing.  It"  is  similar  to  the  slide-block  of  an  engine; 


FRICTION   AND   LUBRICATION.  1227 

which  can  carry  only  about  one-tenth  the  load  per  sq.  in.  that  can  be> 
carried  by  the  crank-pins. 

*  In  experiments  on  cylindrical  journals  it  has  been  shown  that  when  a 
cylindrical  journal  was  lubricated  from  the  side  on  which  the  pressure 
bore,  100  Ibs.  per  sq.  in.  was  the  limit  of  pressure  that  it  would  carry; 
but  when  it  came  to  be  lubricated  on  the  lower  side  and  was  allowed  to 
drag  the  oil  in  with  it,  600  Ibs.  per  sq.  in.  was  reached  with  impunity; 
and  if  the  600  Ibs.  per  sq.  in.,  which  was  reckoned  upon  the  full  diameter 
of  the  bearing,  came  to  be  reckoned  on  the  sixth  part  of  the  circle  that  was 
taking  the  greater  proportion  of  the  load,  it  followed  that  the  pressure 
upon  that  part  of  the  circle  amounted  to  about  1200  Ibs.  per  sq.  in. 

In  connection  with  these  experiments  Mr.  Wicksteed  states  that  in 
drilling-machines  the  pressure  on  the  collars  is  frequently  as  high  as  336 
Ibs.  per  sq.  in.,  but  the  speed  of  rubbing  in  this  case  is  lower  than  it  was 
in  any  of  the  experiments  of  the  Research  Committee.  In  machines 
working  very  slowly  and  intermittently,  as  in  testing-machines,  very 
much  higher  pressures  are  admissible.  Prof.  Thurston  (Friction  and 
Lost  Work,  p.  240)  says  7000  to  9000  Ibs.  pressure  per  square  inch 
is  reached  on  the  slow  working  and  rarely  moved  pivots  of  swing 
bridges. 

Mr.  Adamson  mentions  the  case  of  a  heavy  upright  shaft  carried  upon 
a  small  footstep-bearing,  where  a  weight  of  at  least  20  tons  was  carried 
on  a  shaft  of  5  in.  diameter,  or,  say,  20  sq.  in.  area,  giying  a  pressure  of 
1  ton  per  sq.  in.  The  speed  was  190  to  200  revs,  per  min.  It  was  neces- 
sary to  force  the  oil  under  the  bearing  by  means  of  a  pump.  For  heavy 
horizontal  shafts,  such  as  a  fly-wheel  shaft,  carrying  100  tons  on  two  jour- 
nals, his  practice  for  getting  oil  into  the  bearings  was  to  flatten  the  journal 
along  one  side  throughout  its  whole  length  to  the  extent  of  about  an 
eighth  of  an  inch  in  width  for  each  inch  in  diameter  up  to  8  in.  diameter; 
above  that  size  rather  less  flat  in  proportion  to  the  diameter.  At  first 
sight  it  appeared  alarming  to  get  a  continuous  flat  place  coming  round 
in  every  revolution  of  a  heavily  loaded  shaft;  yet  it  carried  tha  oil  effec- 
tually into  the  bearing,  which  ran  much  better  in  consequence  than  a 
truly  cylindrical  journal  without  a  flat  side. 

In  thrust-bearings  on  torpedo-boats  Mr.  Thornycroft  allows  a  pressure 
of  never  more  than  50  Ibs.  per  sq.  in. 

Mr.  Tower  says  (Proc.  Inst.  M.  E.,  Jan.,  1884) :  In  eccentric-pins  of  punch- 
ing and  shearing  machines  very  high  pressures  are  sometimes  used  with- 
out seizing.  In  addition  to  the  alternation  in  the  direction,  the  pressure 
is  applied  for  only  a  very  short  space  of  time  in  these  machines,  so  that 
the  oil  has  no  time  to  be  squeezed  out. 

In  the  discussion  on  Mr.  Tower's  paper  (Proc.  Inst.  M.  E..  1885)  it  was 
stated  that  it  is  well  known  from  practical  experience  that  with  a  con- 
stant load  on  an  ordinary  journal  it  is  difficult  and  almost  impossible 
to  have  more  than  200  Ibs.  per  square  inch,  otherwise  the  bearing  would 
get  hot  and  the  oil  go  out  of  it ;  but  when  the  motion  was  reciprocating, 
so  that  the  load  was  alternately  relieved  from  the  journal,  as  with  crank- 
pins  and  similar  journals,  much  higher  loads  might  be  applied  than  even 
700  or  800  Ibs.  per  square  inch. 

Mr.  Goodman  (Proc.  Inst.  C.  E.,  1886)  found  that  the  total  frictional 
resistance  is  materially  reduced  by  diminishing  the  width  of  the  brass. 

The  lubrication  is  most  efficient  in  reducing  the  friction  when  the  brass 
subtends  an  angle  of  from  120°  to  60°.  The  film  is  probably  at  its  best 
between  the  angles  80°  and  110°. 

In  the  case  of  a  brass  of  a  railway  axle-bearing  where  an  oil-groove  is 
cut  along  its  crown  and  an  oil-hole  is  drilled  through  the  top  of  the  brass 
into  it,  the  wear  is  invariably  on  the  off  side,  which  is  probably  due  to 
the  oil  escaping  as  soon  as  it  reaches  the  crown  of  the  brass,  and  so  leaving 
the  off  side  almost  dry,  where  the  wear  consequently  ensues. 

In  railway  axles  the  brass  wears  always  on  the  forward  side.  The 
same  observation  has  been  made  in  marine-engine  journals,  which  always 
wear  in  exactly  the  reverse  way  to  what  might  be  expected.  Mr.  Stroud- 
ley  thinks  this  peculiarity  is  due  to  a  film  of  lubricant  being  drawn  in 
from  the  under  side  of  the  journal  to  the  aft  part  of  the  brass,  which 
effectually  lubricates  and  prevents  wear  on  that  side;  and  that  when  the 
lubricant  reaches  the  forward  side  of  the  brass  it  is  so  attenuated  down 
to  a  wedge  shape  that  there  is  insufficient  lubrication,  and  greater  wear 
consequently  follows. 


1228  FRICTION  AND   LUBRICATION. 

C.  J.  Field  (Power,  Feb.,  1893)  says:  One  of  the  most  vital  points  of  an 
engine  for  electrical  service  is  that  of  main  bearings.  They  should  have 
a  surface  velocity  of  not  exceeding  350  feet  per  minute,  with  a  mean 
bearing-pressure  per  square  inch  of  projected  area  of  journal  of  not  more 
than  80  Ibs.  This  is  considerably  within  the  safe  limit  of  cool  perform- 
ance and  easy  operation.  If  the  bearings  are  designed  in  this  way,  it 
would  admit  the  use  of  grease  on  all  the  main  wearing-surface,  which  in 
a  large  type  of  engines  for  this  class  of  work  we  think  advisable. 

Oil-pressure  in  a  Bearing.  —  Mr.  Beauchamp  Tower  (Proc.  Inst. 
M.  E.,  Jan.,  1885)  made  experiments  with  a  brass  bearing  4  ins.  diameter 
by  6  ins.  long,  to  determine  the  pressure  of  the  oil  between  the  brass  and 
the  journal.  The  bearing  was  half  immersed  in  oil,  and  had  a  total 
load  of  8008  Ibs.  upon  it.  The  journal  rotated  150  r.p.m.  The  pressure 
of  the  oil  was  determined  by  drilling  small  holes  in  the  bearing  at  different 
points  and  connecting  them  by  tubes  to  a  Bourdon  gauge.  It  was  found 
that  the  pressure  varied  from  310  to  625  Ibs.  per  sq.  in.,  the  greatest 
pressure  being  a  little  to  the  "off"  side  of  the  center  line  of  the  top  of  the 
bearing,  in  the  direction  of  motion  of  the  journal.  The  sum  of  the  up- 
ward force  exerted  by  these  pressures  for  the  whole  lubricated  area  was 
nearly  equal  to  the  total  pressure  on  the  bearing.  The  speed  was  re- 
duced from  150  to  20  r.p.m.,  but  the  oil-pressure  remained  the  same, 
showing  that  the  brass  was  as  completely  oil-borne  at  the  lower  speed  as 
at  the  higher.  The  following  was  the  observed  friction  at  the  lower  speed: 

Nominal  load,  Ibs.  per  sq.  in.. ..       443          333          211  89 

Coefficient  of  friction 0 .00132  0 .00168  0 .00247    0 .0044    | 

The  nominal  load  per  square  inch  is  the  total  load  divided  by  the 
product  of  the  diameter  and  length  of  the  journal.  At  the  low  speed 
of  20  r.p.m.  it  was  increased  to  676  Ibs.  per  sq.  in.  without  any  signs  of 
heating  or  seizing. 

Friction  of  Car-lournal  Brasses.  (J.  E.  Denton,  Trans.  A.  5.  M.  E., 
xii,  405.)  —  A  new  brass  dressed  with  an  emery-wheel,  loaded  with  5000 
ibs.,  may  have  an  actual  bearing-surface  on  the  journal,  as  shown  by  the 
polish  or  a  portion  of  the  surface,  of  only  1  square  inch.  With  this  pressure 
of  5000  Ibs.  per  sq.  in.,  the  coefficient  of  friction  may  be  6%,  and  the 
brass  may  be  overheated,  scarred  and  cut,  but,  on  the  contrary,  it  may 
wear  down  evenly  to  a  smooth  bearing,  giving  a  highly  polished  area  of 
contact  of  3  sq.  ins.,  or  more,  inside  of  two  hours  of  running,  gradually 
decreasing  the  pressure  per  square  inch  of  contact,  and  a  coefficient  of 
friction  of  less  than  0.5%.  A  reciprocating  motion  in  the  direction  of  the 
axis  is  of  importance  in  reducing  the  friction.  With  such  polished  sur- 
faces any  oil  will  lubricate,  and  the  coefficient  of  friction  then  depends 
on  the  viscosity  of  the  oil.  With  a  pressure  of  1000  Ibs.  per  sq.  in.,  revo- 
lutions from  170  to  320  per  min.,  and  temperatures  of  75°  to  113°  F.,  with 
both  sperm  and  paramne  oils,  a  coefficient  of  as  low  as  0.11%  has  been 
obtained,  the  oil  being  fed  continuously  by  a  pad. 

Experiments  on  O  verheating  of  Bearings.  — Hot  Boxes.  (Denton.) 
—  Tests  with  car  brasses  loaded  from  1100  to  4500  Ibs.  per  sq.  in.  gave 
7  cases  of  overheating  out  of  32  trials.  The  tests  show  how  purely  a 
matter  of  chance  is  the  overheating,  as  a  brass  which  ran  hot  at  5000  Ibs. 
load  on  one  day  would  run  cool  on  a  later  date  at  the  same  or  higher 
pressure.  The  explanation  of  this  apparently  arbitrary  difference  of 
behavior  is  that  tne  accidental  variations  of  the  smoothness  of  the  sur- 
faces, almost  infinitesimal  in  their  magnitude,  cause  variations  of  friction 
which  are  always  tending  to  produce  overheating,  and  it  is  solely  a  matter 
of  chance  when  these  tendencies  preponderate  over  the  lubricating 
influence  of  the  oil.  There  is  no  appreciable  advantage  shown  by  sperm- 
oil,  when  there  is  no  tendency  to  overheat  —  that  is,  paraffine  can  lubri- 
cate under  the  highest  pressures  which  occur,  as  well  as  sperm,  when  the 
surfaces  are  within  the  conditions  affording  the  minimum  coefficients  of 

Sperm  and  other  oils  of  high  heat-resisting  qualities,  like  vegetable  oil 
and  petroleum  cylinder  stocks,  differ  from  the  more  volatile  lubricants, 
like  paraffine,  only  in  their  ability  to  reduce  the  chances  of  the  continual 
accidental  infinitesimal  abrasion  producing  overheating. 

The  effect  of  emery  or  other  gritty  substance  in  reducing  overheating 
of  a  bearing  is  thus  explained: 


FRICTION  AND   LUBRICATION*  1229 

The  effect  of  the  emery  upon  the  surfaces  of  the  bearings  is  to  cover  the 
latter  with  a  series  of  parallel  grooves,  and  apparently  after  such  grooves 
are  made  the  presence  of  the  emery  does  not  practically  increase  the 
friction  over  its  amount  when  pure  oil  only  is  between  the  surfaces. 

The  infinite  number  of  grooves  constitute  a  very  perfect  means  of  insuring 
a  uniform  oil  supply  at  every  point  of  the  bearings.  As  long  as  grooves 
in  the  journal  match  with  those  in  the  brasses  the  friction  appears  to 
amount  to  only  about  10%  to  15%  of  the  pressure.  But  if  a  smooth 
journal  is  placed  between  a  set  of  brasses  which  are  grooved,  and  pres- 
sure be  applied,  the  journal  crushes  the  grooves  and  becomes  brazed 
or  coated  with  brass,  and  then  the  coefficient  of  friction  becomes  upward 
of  40%.  If  then  emery  is  applied,  the  friction  is  made  very  much  less  by 
its  presence,  because  the  grooves  are  made  to  match  each  other,  and  a 
uniform  oil  supply  prevails  at  every  point  of  the  bearings,  whereas  before 
the  application  of  the  emery  many  spots  of  the  bearing  receive  no  oil 
between  them. 

Moment  of  Friction  and  Work  of  Friction  of  Sliding-surfaces,  etc. 

Moment  of  Friction,       Energy  lost  b'y  Fric- 
inch-lbs.  tion  in  ft.-lbs. 

per  min. 
Flat  surfaces  ............................  fWS 

Shafts  and  journals  .........     1/2  fWd  0.2QlSfWdn 

Flat  pivots  ----  '  ............     2/3/fPr  0.349  /PFm 

Collar-bearing  .............. 


Conical  pivot  ...............     2/sfWr  cosec  a  0.349/TFrn  cosec  a 

Conical  journal  .............     2/sfWr  sec  a  0.349  fWrn  sec  a 

Truncated-cone  pivot  ........     2/^r^f£  O'^^f^ 

Hemispherical  pivot  ........        fWr  0.5236  fWrn 

Tractiix,   or  Schiele's   "anti- 

friction" pivot  ...........        fWr  0.5236  fWrn 

In  the  above  /  =  coefficient  of  friction; 

W  =  weight  on  journal  or  pivot  in  pounds;  • 
r  =  radius,  d  =  diameter,  in  inches; 
S  =  space  in  feet  through  which  sliding  takes  place; 
TZ  =  outer  radius,  rt  =  inner  radius; 
n  =  number  of  revolutions  per  minute; 
a  *»  the  half-angle  of  the  cone,  i.e.,  the  angle  of  the  slope 

with  the  axis. 
To  obtain  the  horse-power,  divide  the  quantities  in  the  last  column 

by  33,000.     Horse-power  absorbed  by  friction  of  a  shaft  =  /og  r.^  • 


t 

The  formula  for  energy  lost  by  shafts  and  journals  is  approximately 
true  for  loosely  fitted  bearings.  Prof.  Thurston  shows  that  the  correct 
formula  varies  according  to  the  character  of  fit  of  the  bearing;  thus  for 
loosely  fitted  journals,  if  U  =  the  energy  lost, 


wn  inch-pounds  -  °-26/18/Wn  foot-lbs. 


For  perfectly  fitted  journals   U  =  2.54  fvrWn  inch-lbs.=  0.3325  fWdn 
ft.-lbs. 

For  a  bearing  in  which  the  journal  is  so  grasped  as  to  give  a  uniform 
pressure  throughout,  U  =  f^rWn  inch-lbs.  =  0.4112  fWdn  ft.-lbs. 

Resistance  of  railway  trains  and  wagons  due  to  friction  of  trains: 

Pull  on  draw-bar  =  /X  2240  •&•  R  pounds  per  gross  ton, 
in  which  R  is  the  ratio  of  the  radius  of  the  wheel  to  the  radius  .of  journal. 

A  cylindrical  journal,  perfectly  fitted  into  a  bearing,  and  carrying  a 
total  load,  distributes  the  pressure  due  to  this  load  unequally  on  the 
bearing,  the  maximum  pressure  being  at  the  extremity  of  the  vertical 
radius,  while  at  the  extremities  of  the  horizontal  diameter  the  pressure 
is  zero.  At  any  point  of  the  bearing-surface  at  the  extremity  of  a  radius 
which  makes  an  angle  6  with  the  vertical  radius  the  normal  pressure  is 
proportional  to  cos  0.  If  p  =  normal  pressure  on  a  unit  of  surface, 


1230  FRICTION  AND   LUBRICATION. 

w  =  total  load  on  a  unit  of  length  of  the  journal,  and  r  =  radius  of  journal, 

w  cos  0  =  1.57  rp,    p  =  w  cos  tt  •*-  1.57  r. 

Tests  of  Large  Shaft  Bearings  are  reported  by  Albert  Kingsbury 
in  Trans.  A.  S.  M.  E.,  1905.  A  horizontal  shaft  was  supported  in  two 
bearings  9  X  30  ins.,  and  a  third  bearing  15  X  40  ins.,  midway  between  the 
other  two,  was  pressed  upwards  against  the  shaft  by  a  weighed  lever,  so 
that  it  was  subjected  to  a  pressure  of  25  to  50  tons.  The  journals  were 
flooded  with  oil  from  a  supply  tank.  The  shaft  was  driven  by  an  electric 
motor,  and  the  friction  H.P.  was  determined  by  measuring  the  current 
supplied.  Following  are  the  principal  results: 

Load,  tons* 

25          25          25          25          25         33.6       42.3        47          47         50.5 
Load  per  sq.  in.* 

83          83          83          83          83          112        141        157        157        168 
Speed,  r.p.m. 

309  506  180  179  301  454  480  946  1243  1286 
Speed,  ft.  per  min.* 

1215      1990        708        704      1180      1785      1890      3720      4900      5050 
Friction  H.P.f 

12.6  21.7  6.43  5.12  10.1  16  17.9  41.9  47.8  52.3 
Coeff.  of  frictionf 

.0045     .0048     .0040     .0037     .0037     .0029     .0024     .0025     .0022     .0022 
*  On  the  large  bearing.  t  Three  bearings. 

The  last  three  tests  were  with  paraffin  oil;  the  others  with  heavy  machine 
oil. 

Clearance  between  Journal  and  Bearing.  —  John  W.  Upp,  in 
Trans.  A.  S.  M.  E.,  1905  gives  a  table  showing  the  diameter  of  bore 
of  horizontal  and  vertical  bearings  according  to  the  practice  of  one  of  the 
leading  builders  of  electrical  machinery.  The  maximum  diameter  of  the 
journal  is  the  same  as  its  nominal  diameter,  with  an  allowable  variation 
below  maximum  of  0.0005  in.  up  to  3  in.  diam.,  0.001  in.  from  31/2  to  9  in., 
and  0.0015  in.  from  10  to  24  in.  The  maximum  bore  of  a  horizontal  bear- 
ing is  larger  than  the  diam.  of  the  journal  by  from  0.002  in.  for  a  i/2-in. 
journal  to  0.009  'for  6  in.,  f9r  journals  7  to  15  in.  it  is  0.004  +  0.001  X 
diam.,  and  for  16  to  24  in.  it  is  uniformly  0.02  in.  For  vertical  journals  the 
clearance  is  less  by  from  0.001  to  0.004  in.  according  to  the  diameter.  The 
allowable  variation  above  the  minimum  bore  is  from  0.001  to  0.005. 

Allowable  Pressures  on  Bearings.  —  J.  T.  Nicholson,  in  a  pap._ 
read  before  the  Manchester  Assoc.  of  Engrs.  (Am.  Mach.,  Jan.  16,  1908, 
Eng.  Digest,  Feb.,  1908),  as  a  result  of  a  theoretical  study  of  the  lubrication 
of  bearings  and  of  their  emission  of  heat,  obtains  the  formula  p  =  P/ld  •• 
40  (dN)  /*,  in  which  p  =  allowable  pressure  per  sq.  in.  of  projected  area, 
P  =  total  pressure,  I  =  length  and  d  =  diam.  of  journal,  N  =  revs,  per 
min.  It  appears  from  this  formula  that  the  greater  the  speed  the  greater 
the  allowable  pressure  per  sq.  in.,  so  that  for  a  1-in.  journal  the  allowable 
pressure  per  sq.  in.  is  126  Ibs.  at  100  r.p.m.  and  189  Ibs.  at  500  r.p.m.,  and 
for  a  5-in.  journal  189  Ibs.  at  100  and  283  Ibs.  at  500  r.p.m.  W.  H.  Scott 
(Eng.  Digest,  Feb.,  1908)  says  this  is  contrary  to  the  teaching  of  practical 
experience,  and  therefore  the  formula  is  inaccurate.  Mr.  Scott,  from  a 
study  of  the  experiments  of  Tower,  Lasche,  and  Stribeck,  derives  the 
following  formulae  for  the  several  conditions  named: 


For  main  bearings  of  double-acting  vertical  engines,     p  =     750 
44     horizontal     4t     .   p  =     660 
44  single-acting  four-cycle  gas  en- 
gines .......................................   p  =  1350  D1/i2/Nl/4 

For  crank  pins  of  vert,  and  hor.  double-acting  engines  .  p  =  1560 
"     "         "     "  single-acting  four-cycle  gas  engines,  p  =  3000 
For  dead  loads  with  ordinary  lubrication  ..........  p  =    400  N 

11     forced  "  ........  p  =  1600  N' 

p  —  allowable  pressure  in  Ibs.  per  sq.  in.  of  projected  area;  D  =  diam,. 
in  ins.  ;  N  =  revs.  per.  min. 


FKICTION  AND  LUBRICATION.  1231 

F.  W.  Taylor  (Trans.  A.  S.  M.  E.,  1905),  as  the  result  of  an  investigation 
of  line  shaft  and  mill  "bearings  that  were  running  near  the  limit  of  dura- 
bility and  heating  yet  not  dangerously  heating,  gives  the  formula  PV  =* 
400.  P  =  pressure  in  Ibs.  per  sq.  in.  of  projected  area,  V  =  velocity  of 
circumference  of  bearing  in  ft.  per  sec. 

The  formula  is  applicable  to  bearings  in  ordinary  shop  or  mill  use  on 
shafting  which  is  intended  to  run  with  the  care  and  attention  which  such 
bearings  usually  receive,  and  gives  the  maximum  or  most  severe  duty  to 
which  it  is  safe  to  subject  ordinary  chain  or  oiled  ball  and  socket  bearings 
which  are  babbitted.  It  is  not  safe  for  ordinary  shafting  to  use  cast-iron 
boxes,  with  either  sight  feed,  wick  feed,  or  grease-cup  oiling,  under  as  severe 
conditions  as  P  X  V  =  200. 

Arcbbutt  and  Deeley's  "Lubrication  and  Lubricants  "  gives  the  follow- 
ing allowable  pressures  in  Ibs.  per  sq.  in.  of  projected  area  of  bearings. 
Crank-pin  of  shearing  and  punching  machine,  hard  steel,  inter- 
mittent load  bearing 300C 

Bronze  crosshead  neck  journals 1200 

Crank  pins,  large  slow  engine 80X  S° 

Crank  pins,  marine  engines 400-500 

Main  crankshaft  bearing,  fast  marine 40C 

Same,  slow  marine 600 

Railway  coach  journals 300-400 

Flywheel  shaft  journals 150-200 

Small  engine  crank  pin 150-200 

Small  slide  block,  marine  engine 100 

Stationary  engine  slide  blocks 25-125 

Same,  usual  case 30-  60 

Propeller  thrust  bearings 50-  70 

Shafts  in  cast-iron  steps,  high  speed 15  . 

Bearing  Pressures  for  Heavy  Intermittent  Loads.  (Oberlm  Smith, 
Trans.  A.  S.  M.  E.,  1905.)  —  In  a  punching  press  of  about  84  tons  capa- 
city, the  pressure  upon  the  front  journal  of  the  main  shaft  is  about 
2400  Ibs.  per  sq.  in.  of  projected  area.  Upon  the  eccentric  the  pressure 
against  the  pitman  driving  the  ram  is  some  7000  Ibs.  per  sq.  in.  —  both 
surfaces  being  of  cast  iron,  and  sometimes  running  at  a  surface  speed  of 
140  feet  per  minute.  Such  machines  run  year  in  and  year  out  with  but 
little  trouble  in  the  way  of  heating  or  "  cutting."  An  instance  of  excessive 
pressure  may  be  cited  in  the  case  of  a  Ferracute  toggle  press,  where  the 
whole  ram  pressure  of  400  tons  is  brought  to  bear  upon  hardened  steel 
toggle-pins,  running  in  cast  iron  or  bronze  bearings,  3  in.  in  diam.  by  nearly 
^4  in.  long.  These  run  habitually,  for  maximum  work,  under  a  load  of 
20,000  Ibs.  per  sq.  in. 

Bearings  for  Very  High  Rotative  Speeds.  (Proc.  Inst.  M.  E., 
Oct.,  1888,  p.  482.)  —  In  the  Parsons  steam-turbine,  which  has  a  speed  as 
high  as  18,000  rev.  per  min.,  as  it  is  impossible  to  secure  absolute  accuracy 
of  balance,  the  bearings  are  of  special  construction  so  as  to  allow  of  a 
certain  very  small  amount  of  lateral  freedom.  For  this  purpose  the 
bearing  is  surrounded  by  two  sets  of  steel  washers  Vi6  in.  thick  and  of 
different  diameters,  the  larger  fitting  close  in  the  casing  and  about  1/32  in. 
clear  of  the  bearing,  and  the  smaller  fitting  close  on  the  bearing  and  about 
V32  in.  clear  of  the  casing.  These  are  arranged  alternately,  and  are 
pressed  together  by  a  spiral  spring.  Consequently  any  lateral  movement 
of  the  bearing  causes  them  to  slide  mutually  against  one  another,  and  by 
their  friction  to  check  or  damp  any  vibrations  that  may  be  set  up  in  the 
spindle.  The  tendency  of  the  spindle  is  then  to  rotate  about  its  axis  of 
mass,  and  the  bearings  are  thereby  relieved  from  excessive  pressure,  and 
the  machine  from  undue  vibration.  The  allowing  of  the  turbine  itself 
to  find  its  own  center  of  gyration  is  a  well-known  device  in  other  branches 
of  mechanics:  as  in  the  instance  of  the  centrifugal  hydro-extractor,  where 
a  mass  very  much  out  of  balance  is  allowed  to  find  its  own  center  of 
gyration;  the  faster  it  runs  the  more  steadily  does  it  revolve  and  the  less 
is  the  vibration  Another  illustration  is  to  be  found  in  the  spindles  of 
spinning  machinery  which  run  at  about  10,000  or  11,000  revs,  per  min.: 
although  of  very  small  dimensions,  the  outside  diameter  of  Mie  largest 
portion  or  driving  whorl  being  perhaps  n9t  more  than  11/4  in.,  it  is  found 
impracticable  to  run  them  at  that  speed  in  what  might  be  called  a  hard- 
and-fast  bearing.  They  are  therefore  run  with  some  elastic  substance 


1232  FRICTION  AND  LUBRICATION. 

surrounding  the  bearing,  such  as  steel  springs,  hemp,  or  cork.  Any 
elastic  substance  is  sufficient  to  absorb  the  vibration,  and  permit  of 
absolutely  steady  running. 

Bearing  Pressures  in  Shafts  of  Parsons  Turbines. — The  product  of 
the  bearing  pressure  in  Ib.  per  sq.  in.  and  the  peripheral  velocity  in  ft. 
per  sec.  is  generally  about  2500  (Proc.,  Inst.  Elect.  Engrs.,  June,  1905). 

Thrust  Bearings  in  Marine  Practice.  (G.  W.  Dickie,  Trans.  A.  S. 
M.  E.,  1905.)  — The  approximate  pressure  on  a  thrust  bearing  of  a  propeller 
shaft  assuming  two  thirds  of  the  indicated  horse-power  to  be  effective 

on  the  propeller  is  P  =  I.H.P.  X  ^^  *  ^080°  =  ^nF'  X  2l7'1'  in 
which  S  =  speed  of  ship  in  knots  per  hour,  P  =  total  thrust  in  Ibs.  The 
following  are  data  of  water-cooled  bearings  which  have  given  satisfactory 
service: 

Speed  in  knots 22  221/2        28  21 

Thrust-ring  surface,  horse-shoe  type, 

sq.  ins 1188          891          581  2268 

Horse-power,  one  engine,  I.H.P 11,500       6,800       4,200      15,000 

Indicated  pressure  on  bearing,  Ibs,. ..   112,700     89,000     33,600     154,000 

Pressure  per  sq.  in.  of  surface,  Ibs 95          100  58  68. 1 

Mean  speed  of  bearing  surfaces,  ft.  per 

min , 642          610          827  504 

Bearings  for  Locomotives.  (G.  M.  Basford,  Trans.,  A.  S.  J\f.  E., 
1905.) — Bearing  areas  for  Ioc9motive  journals  are  determined  chiefly 
by  the  possibilities  of  lubrication.  On  driving  journals  the  following 
•  figures  of  pressure  in  Ibs.  per  sq.  in.  of  projected  area  give  good  service: 
passenger,  190;  freight,  200;  switching,  220  Ibs.  Crank  pins  may  be 
loaded  from  1500  to  1700  Ibs.;  wrist  pins  to  4000  Ibs.  per  sq.  in.  Car  and 
tender  bearings  are  usually  loaded  from  300  to  325  Ibs.  per  sq.  in. 

Bearings  of  Corliss  Engines.  (P.  H.  Been,  Trans,  A.  S.  M.  E., 
1905.)  —  In  the  practice  of  one  of  the  largest  builders  the  greatest  pressure 
allowed  per  sq.  m.  of  projected  area  for  all  shafts  is  140  Ibs.  On  most 
engines  the  pressure  per  sq.  in.  multiplied  by  the  velocity  of  the  bearing 
surface  in  ft.  per  sec.  lies  between  1000  and  1300. 

Edwin  Reynolds  says  that  a  main  engine  bearing  to  be  safe  against 
undue  heating  should  be  of  such  a  size  that  the  product  of  the  square  root 
of  the  speed  of  rubbing-surface  in  feet  per  second  multiplied  by  the  pounds 
per  square  inch  of  projected  area,  should  not  exceed  375  for  a  horizontal 
engine,  or  500  for  a  vertical  engine  when  the  shaft  is  lifted  at  every  revo- 
lution. Locomotive  driving  boxes  in  some  cases  give  the  product  as  high 
as  585,  but  this  is  accounted  for  by  the  cooling  action  of  the  air.  (Am. 
Mach.,  Sept.  17,  1903.) 

Temperature  of  Engine  Bearings.  (A.  M.  Mattice,  Trans.  A.  S.  M. 
E.,  1905.) — An  examination  of  the  temperature  of  bearings  of  a  large  num- 
ber of  engines  of  various  makes  showed  more  above  135°  F.  than  below 
that  figure.  Many  bearings  were  running  with  a  temperature  over  150°, 
and  in  one  case  at  180°,  and  in  all  of  these  cases  the  bearings  were  giving 
no  trouble. 

PIVOT-BEARINGS. 

The  Schiele  Curve.  —  W.  H.  Harrison  (Am.  Mack.,  1891)  says  the 
Schiele  curve  is  not  as  good  a  form  for  a  bearing  as  the  segment  of  a 
sphere.  He  says:  A  mill-stone  weighing  a  ton  frequently  bears  its  whole 
weight  upon  the  flat  end  of  a  hard-steel  pivot  1  Vs  in.  diam.,  or  1  sq.  in. 
area  of  bearing;  but  to  carry  a  weight  of  3000  Ibs.  he  advises  an  end 
bearing  about  4  ins.  diam.,  made  in  the  form  of  a  segment  of  a  sphere 
about  1/2  in.  in  height.  The  die  or  fixed  bearing  should  be  dished  to  fit 
the  pivot.  This  form  gives  a  chance  for  the  bearing  to  adjust  itself, 
which  it  does  not  have  when  made  flat,  or  when  made  with  the  Schiele 
curve.  If  a  side  bearing  is  necessary  it  can  be  arranged  farther  up  the 
shaft.  The  pivot  and  die  should  be  of  steel,  hardened;  cross-gutters 
should  be  in  the  die  to  allow  oil  to  flow,  and  a  central  oil-hole  should  be 
made  in  the  shaft. 

The  advantage  claimed  for  the  Schiele  bearing  is  that  the  pressure  is 
uniformly  distributed  over  its  surface,  and  that  it  therefore  wears  uni- 
formly. Wilfred  Lewis  (Am.  Mach.,  April  19,  1894)  says  that  its  merits 


BALL-BEARINGS,   BOLLER-BEAHINGS,   ETC.         1233 


as  a  thrust-bearing  have  been  vastly  overestimated;  that  the  term 
"anti-friction"  applied  to  it  is  a  misnomer,  since  its  friction  is  greater 
than  that  of  a  flat  step  or  collar  of  the  same  diameter.  He  advises  that 
flat  thrust-bearings  should  always  be  annular  in  form,  having  an  inside 
diameter  one-half  of  the  external  diameter. 

Friction  of  a  Flat  Pivot-bearing.  —  The  Research  Committee  on 
Friction  (Proc.  Inst.  M.  E.,  1891)  experimented  on  a  step-bearing,  flat- 
tended,  3  in.  diam.,  the  oil  being  forced  into  the  bearing  through  a  hole 
in  its  center  and  distributed  through  two  radial  grooves,  insuring  thorough 
lubrication.  The  step  was  of  steel  and  the  bearing  of  manganese-bronze. 
At  revolutions  per  min.  50  128  194  290  353 

The  coefficient  of  friction  \  0.0181     0.0053     0.0051     0.0044     0.0053 

varied  between  /  and      0.0221     0.0113     0.0102     0.0178     0.0167 

With  a  white-metal  bearing  at  128  revs,  the  coefficient  of  friction  was 
a  little  larger  than  with  the  manganese-bronze.  At  the  higher  speeds 
the  coefficient  of  friction  was  less,  owing  to  the  more  perfect  lubrication, 
as  shown  by  the  more  rapid  circulation  of  the  oil.  At  128  revs,  the 
bronze-bearing  heated  and  seized  on  one  occasion  with  a  load  of  260  Ibs., 
and  on  another  occasion  with  300  Ibs.  per  sq.  in.  The  white-metal  bear- 
ing under  similar  conditions  heated  and  seized  with  a  load  of  240  Ibs. 
per  sq.  in.  The  steel  footstep  on  manganese-bronze  was  afterwards 
tried,  lubricating,  with  three  and  with  four  radial  grooves;  but  the  friction 
was  from  one  and  a  half  times  to  twice  as  great  as  with  only  the  two 
grooves. 

Mercury-bath  Pivot.  —  A  nearly  frictionless  step-bearing  may  be 
obtained  by  floating  the  bearing  with  its  superincumbent  weight  upon 
mercury.  Such  an  apparatus  is  used  in  the  lighthouses  of  La  Heve, 
Havre.  It  is  thus  described  in  Eng'g,  July  14,  1893,  p.  41: 

The  optical  apparatus,  weighing  about  1  ton,  rests  on  a  circular  cast- 
iron  table,  which  is  supported  by  a  vertical  shaft  of  wrought  iron  2.36  in. 
diameter.  This  is  kept  in  position  at  the  top  by  a  bronze  ring  and  outer 
iron  support,  and  at  the  bottom  in  the  same  way,  while  it  rotates  on  a 
removable  steel  pivot  resting  in  a  steel  socket,  which  is  fitted  to  the  base 
of  the  support.  To  the  vertical  shaft  there  is  rigidly  fixed  a  floating  cast- 
iron  ring  17.1  in.  diameter  and  11.8  in.  in  depth,  which  is  plunged  into 
and  rotates  in  a  mercury  bath  contained  in  a  fixed  outer  drum  or  tank, 
the  clearance  between  the  vertical  surfaces  of  the  drum  and  ring  being 
only  0.2  in.,  so  as  to  reduce  as  much  as  possible  the  volume  of  mercury 
(about  220  Ibs.),  while  the  horizontal  clearance  at  the  bottom  is  0.4  in. 
BALL-BEARINGS,  BOIXEB-BEABINGS,  ETC. 

Friction-rollers.  —  If  a  journal  instead  of  revolving  on  ordinary 
bearings  be  supported  on  friction-rollers  the  force  required  to  make  the 
journal  revolve  will  be  reduced  in  nearly  the  same  proportion  that  the 
diameter  of  the  axles  of  the  rollers  is  less  than  the  diameter  of  the  rollers 
themselves.  In  experiments  by  A.  M.  Wellington  with  a  journal  31/2  in. 
diam.  supported  on  rollers  8  in.  diam.,  whose  axles  were  13/4  in.  diam.,  the 
friction  in  starting  from  rest  was  1/4  the  friction  of  an  ordinary  3V2-in 
bearing,  but  at  a  car  speed  of  10  miles  per  hour  it  was  V.2  that  of  the  ordi- 
nary bearing.  The  ratio  of  the  diam.  of  the  axle  to  diam.  of  roller  was 
13/4:  8,  or  as  1  to  4.6. 

Coefficients  of  Friction  of  Boiler  Bearings.  C.  H.  Benjamin,  Machy. 
Oct.,  1905.  —  Comparative  tests  of  plain  babbitted,  McKeel  plain  roller, 
and  Hyatt  roller  bearings  gave  the  following  values  of  the  coefficient  of 
friction  at  a  speed  of  560  r.p.m.: 


Diameter 
of  Journal. 

Hyatt  Bearing. 

McKeel  Bearing. 

Babbitt  Bearing. 

Max. 

Min. 

Ave. 

Max. 

Min. 

Ave. 
.022 

Max. 

Min. 

Ave. 

1  15/15 

23/16 
27/J6 

2  15/16 

.032 
.019 
.042 
.029 

.012 
.011 
.025 
.022 

.018 
.014 
.032 
.025 

.033 

.017 

.074 
.088 
.114 
.125 

.029 
.078 
.083 
.089 

.043 
.082 
.096 
.107 

.028 
.039 

.015 
.019 

.021 
.027 

The  friction  of  the  roller-bearing  is  from  one-fifth  to  one-third  that  ol 
a  plain  bearing  at  moderate  loads  and  speeds.  It  is  noticeable  that  as. 
the  load  on  a  roller-bearing  increases  the  coefficient  of  friction  decreases. 

A  slight  change  in  the  pressure  due  to  the  adjusting  nuts  was  sufficient 
to  increase  the  friction  considerably.  In  the  McKeel  bearing  the  rolls 


1234 


FRICTION  AND   LUBRICATION. 


t>ore  on  a  cast-iron  sleeve  and  in  the  Hyatt  on  a  soft-steel  one.  If  rollcH 
bearings  are  properly  adjusted  and  not  overloaded  a  saving  of  from  2-3 
to  3-4  of  the  friction  may  be  reasonably  expected. 

McKeel  bearings  contained  rolls  turned  from  solid  steel  and  guided  by 
spherical  ends  fitting  recesses  in  cage  rings  at  each  end.  The  cage  rings 
were  joined  to  each  other  by  steel  rods  parallel  to  the  rolls 

Lubrication  is  absolutely  necessary  with  ball  and  roller  bearings, 
although  the  contrary  claim  is  often  advanced.  Under  favorable  con- 
ditions an  almost  imperceptible,  film  is  sufficient;  a  sufficient  quantity 
to  immerse  half  the  lowest  ball  should  always  be  provided  as  a  rust 
preventive.  Rust  and  grit  must  be  kept  out  of  ball  and  roller  bearings. 
Acid  or  rancid  lubricants  are  as  destructive  as  rust.  (Henry  Hess.) 

Both  ball  and  roller  bearings,  to  give  the  best  satisfaction,  should  be 
made  of  steel,  hardened  and  ground;  accurately  fitted,  and  in  proper 
alignment  with  the  shaft  and  load;  cleaned  and  oiled  regularly,  and  fitted 
with  as  large-size  balls  or  rollers  as  possible,  depending  upon  the  revolutions 
per  minute  and  load  to  be  carried.  Oil  is  absolutely  necessary  on  both 
ball  and  roller  bearings,  to  prevent  rust.  (S.  S.  Eveland.) 

Roller  Bearings.  —  The  Mossberg  roller  bearings  for  journals  are  made 
in  the  sizes  given  in  the  table  below.  D  =  diam.  of  journal;  d  =  diam.  of 
roll;  N  =  number  of  rolls;  P  =  safe  load  on  journals,  in  Ibs.  The  rolls 
are  enclosed  in  a  bronze  supporting  cage.  (Trans.  A.  S.  M.  E.,  1905.) 


i  ^ 

d 

N 

P 

D 

d 

N 

P 

D 

d 

N 

P 

2 

V4 

20 

3,500 

6 

U/16 

24 

50,000 

15 

13/8 

28 

255,000 

21/2 

5/16 
3/8 

22 
22 

7,000 
13,000 

7 
8 

is/16 

7/8 

22 

22 

70.COO 
90,000 

18 
20 

13/8 
11/2 

32 
34 

325,000 
400,000 

4 

7/lfl 

24 

24,000 

9 

1 

24 

115,000 

24 

U/o 

38 

576,000 

5 

tt/te 

24 

37,000 

12 

H/4 

26 

175,000 

Surface  speed  of  journal  0  to  50  ft.  per  min.  Length  of  journal  li/2 
diameters.  The  rolls  are  made  of  tool  steel  not  too  high  in  carbon,  and  of 
spring  temper.  The  journal  or  shaft  should  be  made  not  above  a  medium 
spring  temper.  The  box  should  be  made  of  high  carbon  steel  and  tem- 
pered as  hard  as  possible. 

Conical  Roller  Thrust  Bearings.  —  The  Mossberg  thrust  bearing  is 
made  of  conical  rollers  contained  in  a  cage,  and  two  collars,  one  being 
stationary  and  the  other  fixed  to  the  shaft  and  revolving  with  it.  One 
side  of  each  collar  is  made  conical  to  correspond  with  the  rollers  which 
bear  on  it.  The  apex  of  the  cones  is  at  the  center  of  the  shaft.  The 
angle  of  the  cones  is  6  to  7  degrees.  Larger  angles  are  objectionable, 
giving  excessive  end  thrust.  The  following  sizes  are  made: 


Diameter 
of  Shaft. 
Ins. 

Outside 
Diameter 
of  Ring. 
Ins. 

No.  of 
Rolls. 

Safe  Pressure  on  Bearing. 

Area  of 
Pressure 
Plate. 
Sq.  ins. 

Speed 
75  Rev. 
Lbs. 

Speed 
150  Rev. 
Lbs. 

21/16-21/4 
31/16-31/4 
41/16-41/4 
51/16-51/4 
61/16-61/2 
81/16-81/2 
91/16-91/2 

59/16 
105/16 

$£ 

lo8^ 

30 
30 
30 
30 
30 
32 
32 

10 
20 
35 
54 
78 
132 
162 

19,000 
40,000 
70,000 
108,000 
125,000 
200,000 
300,000 

9500 
20,000 
35,000 
56,000 
62,000 
100,000 
150,000 

Plain  Roller  Thrust  Bearings.  —  S.  S.  Eveland,  of  the  Standard 
Roller  Bearing  Co.,  contributes  the  following  data  of  plain  roller  thrust 
bearings  in  use  in  1903.  The  bearing  consists  of  a  large  number  of  short 
cylindrical  rollers  enclosed  in  openings  in  a  disk  placed  between  two 
hardened  steel  plates.  He  says  "our  plain  roller  bearing  is  theoretically 
wrong,  but  in  practice  it  works  perfectly,  and  has  replaced  many  thou* 
sand  ball-bearings  which  have  proven  unsatisfactory." 


BALL-BEARINGS,    ROLLER-BEARINGS,    ETC.       1235 


Size  of 
Bearing, 
Ins. 

Number  and 
Size  of  Rollers, 
Ins. 

R.p.m. 

Wt.  on 
Bearings, 
Lbs. 

Lineal 
Inches. 

Weight 
per  lin. 
in.,  Lbs. 

Weight 
on  each 
Roll,Lb. 

43/4X   6H/16 
43/4X  71/4 

5  1/2  X  8  1/2 
7      Xl03/8 

71/2X11  5/16 
8       X151/2 

36       5/8  X5/16 
32       3/4  X5/8 
54       3/4X5/8 
48  1       XV2 
54  I       Xl/2 
70  1  1/4  X5/8 

500 
470 
.   420 
370 
325 
300 

6.000 
10,000 
15,000 
20,000 
25,000 
60,000 

11  V4 
12 
201/4 
24 
27 
45 

546 
833 
750 
833 
988 
1334 

167 
312 
279 
417 
463 
833 

The  Hyatt  Roller  Bearing.      (A.  L.  Williston,  Trans.  A.  S.  M.  E., 
1    1905.)  —  The  distinctive  feature  of  the  Hyatt  roller  bearing  is  a  flexible 
roller,  made  of  a  strip  of  steel  wound  into  a  coil  or  spring  of  uniform  diam- 
eter.    A  roller  of  this  construction  insures  a  uniform  distribution  of  the 
:    load  along  the  line  of  contact  of  the  roller  and  the  surfaces  on  which  it 
!    operates.     It  also  permits  any  slight  irregularities  in  either  journal  or  box 
without  causing  excessive  pressure.     The  roller  is  hollow  and  serves  as 
;    an  oil  reservoir.     For  a  heavy  load,  a  roller  of  heavy  stock  can  be  made- 
while  for  a  high-speed  bearing  under  light  pressure  a  roller  of  light  weight, 
;    made  from  thin  stock,  can  be  used.     Following  are  the  results  of  some  tests 
i   of  the  Hyatt  bearing  in  comparison  with  other  bearings: 

A  shaft  152  ft.  long,  215/16  in.  diam.  supported  by  20  bearings,  belt- 
:   driven  from  one  end,  gave  a  friction  load  of  2.28  H.P.  with  babbitted 
i   bearings,  and  0.80'  H.P.  with  Hyatt  bearings.     With  88  countershafts 
j  running  in  babbitted  bearings,  the  H.P.  required  was  8.85  when  the  main 
•  shaft  was  in  babbitted  bearings  and  6.36  H.P.  when  it  was  in  Hyatt  bearings. 
Comparative  tests  of  solid  rollers  and  of  Hyatt  rollers  were  made  in 
!   1898  at  the  Franklin  Institute  by  placing  two  sets  of  rollers  between  three 
fiat  plates,  putting  the  plates  under  load  in  a  testing  machine  and  measur- 
ing the  force  required  to  move  the  middle  plate.     All  the  rollers  were 
8/4  in.  diam.,  10  ins.  long.     The  Hyatt  rollers  were  made  of  1/2  X  Vs  in. 
.   Bteel  strip.     With  2000  Ibs.  load  and  plain  rollers  it  took  26  Ibs.  to  move 
:  the  plate,  and  with  the  Hyatt  rollers  9  Ibs.      With  3000  Ibs.  load  and 
plain  rollers  the  resistance  was  34  Ibs.,  with  Hyatt  rollers  17  Ibs. 

In  teats  with  a  pendulum  friction  testing  machine  at  the  Case  Scientific 
School,  with  a  bearing  115/16  in.  diam.  the  coefficient  of  friction  with  the 
Hyatt  bearing  was  from  0.0362  down  to  0.0196,  the  loads  increasing  from 
64  to  264  Ibs.;  with  cast-iron  bearings  and  the  same  loads  the  coefficient 
was  from  0.165  to  0.098. 

In  tests  at  Purdue  University  with  bearings  4  X  1V2  ins.  and  loads 
from  1900  to  8300  Ibs.,  the  average  coefficients  with  different  bearings  and 
:   different  speeds  were  as  follows: 

Hyatt  bearing  130  r.p.m.  0.0114  302  r.p.m.  0.0099  585  r.p.m.  0.0147 
Cast-iron  bearing  128  "  0.0548  302  "  0.0592  410  "  0.0683 
Bronze  bearing  130  "  0.0576  320  "  0.0661  582  "  0.140 

The  cast-iron  bearing  at  128  r.p.m.  seized  with  8300  Ibs.,  and  at  410 
r.p.m.  with  5900  Ibs.  The  bronze  bearing  seized  at  130  r.p.m.  with  3500  Ibs., 
at  320  r.p.m.  with  5100  Ibs.,  and  at  582  r.p.m.  with  2700  Ibs.  - 

The  makers  have  found  that  the  advantages  of  roller  bearings  of  the 
type  described  are  especially  great  with  either  high  speeds  or  heavy  loads. 
i  Generally,  the  best  results  are  obtained  for  line-shaft  work  up  to  speeds  of 
600  rev.  per  min.,  when  a  load  of  30  Ibs.  per  square  inch  of  projected  area 
is  allowed.  For  heavy  load  at  slow  speed,  such  as  in  crane  and  truck 
wheels,  a  load  of  500  Ibs.  gives  the  best  results. 

The  Friction  Coefficient  of  a  well-made  annular  ball-bearing  is  0.001 
and  0.002  of  the  load  referred  to  the  shaft  diameter  and  is  independent 
of  the  speed  and  load.  The  friction  coefficient  of  a  good  roller  bearing 
is  from  0.0035  to  0.014;  it  rises  very  much  if  the  load  is  light.  It  in- 
creases also  when  the  speeds  are  very  low,  though  not  so  much  as  with 
plain  bearings.  (Henry  Hess.) 

Notes  on  Ball  Bearings.  —  The  following  notes  are  contributed  by 
Mr.  Henry  Hess,  1910.  Ball  bearings  in  modern  use  date  from  the  bi- 
cycle. That  brought  in  the  adjustable  cup  and  cone  and  three-point 
contact  type.  Under  the  demands  for  greater  load  resistance  and  relia- 
bility the  two-point  contact  type,  without  adjustability,  was  evolved; 
that  is  now  used  under  loads  from  a  few  pounds  to  many  tons.  Such  a 


1236  FKICTION  AND  'LUBRICATION. 

bearing  consists  of  an  inner  race,  an  outer  race  and  the  series  of  balls 
that  roll  in  tracks  of  curved  cross  section.  Various  designs  are  used, 
differing  chiefly  in  the  devices  for  separating  the  balls  and  in  the  arrange- 
ment for  introducing  the  balls  between  the  races.  The  most  widely 
used  type  has  races  that  are  of  the  same  cross  section  throughout,  un- 
broken by  any  openings  for  the  introduction  of  balls.  To  introduce 
the  balls  the  two  races  are  first  eccentrically  placed;  the  balls  will  fill 
slightly  more  than  a  half  circumference;  elastic  separators  or  solid  cages 
are  used  to  space  the  balls. 

Another  type  has  a  filling  opening  of  sufficient  depth  cut  into  one  race; 
the  race  continuity  is  restored  by  a  small  piece  that  is  let  in.  This  type 
is  usually  filled  with  balls,  without  cages  or  separators.  The  filling 
opening  is  always  placed  at  the  unloaded  side  of  the  bearing,  where  the 
weakening  of  the  race  is  not  important.  This  type  has  been  almost  en- 
tirely discarded  in  favor  of  the  one  above  described. 

A  third  type  has  a  filling  opening  cut  into  each  race  not  quite  deep 
enough  to  tangent  the  bottom  of  the  ball  track.  As  this  weakened 
section  necessarily  comes  under  the  load  during  each  revolution,  the 
carrying  capacity  is  reduced.  After  slight  wear  there  develops  an  inter- 
ference of  the  balls  with  the  edges  of  these  openings,  which  seriously 
reduces  the  speeds  and  load  capacity.  This  interference  precludes  the 
use  of  this  type  to  take  end  thrust. 

The  carrying  capacity  of  a  ball-bearing  is  directly  proportional  to  the 
number  of  balls  and  to  the  square  of  the  ball  diameter. 

It  may  be  written  as: 

L  =  Knd2,  in  which  L  =  load  capacity  in  pounds;  n  =  number  of 
balls;  d^ball  diameter  in  eighths  of  an  inch.  K  varies  with  the  condition 
and  type  of  bearing,  as  also  with  the  material  and  speed. 

For  a  certain  special  steel  that  hardens  throughout  and  is  also  unusu- 
ally tough,  employed  by  "  DWF"  or  "  HB"  (the  originators  of  the  modern 
two-point  type),  the  following  values  apply.  For  other  steels  lesser  values 
must  be  used. 

I.  For  Radial  Bearings  : 

K  =*  9   for  uninterrupted   race   track,  cross-section  curvature  =  0.52 

and  9/16  in.  ball  diameter  respectively  for  inner  and  outer  races, 

separated  balls,  uniform  load,  and  steady  speed  up  to  3000 

revs,  per  min. 
K  =  5  for  full  ball  type,  filling  opening  in  one  race  at  the  unloaded 

side,  otherwise  as  above. 
K  =  2.5  for  both  ball  tracks  interrupted  by  filling  openings,  inelastic 

cage  separators  f9r  balls,  or  full   ball,  speeds  not  above  2000 

revs,  per  min.,  uniform  load. 
K  =  0.9  for  thrust  on  a  radial  bearing  of  the  first  type,  as  above.     The 

larger  the  balls  the  smaller  K.     The  type  with  filling  openings 

in  each  race  is  not  suitable  for  end  thrust. 

The  radial  load  bearing  is,  up  to  high  speeds,  practically  unaffected 
by  speed,  as  to  carrying  capacity. 

II.  Thrust  Bearings: 

With  the  thrust  type,  consisting  of  one  flat  plate  and  one  seat  plate 
with  grooved  ball  races,  the  load  capacity  decreases  with  speed  or 


KI=  constant  for  material  and  race  cross-section,  etc.,  R  =  revolu- 
tions per  minute.  R  ranges  from  about  3000  revs,  per  min.  down  to  1  rev. 
per  min.  as  for  crane  hooks  and  similar  elements. 

KI=  25  to  40  for  material  used  by  the  DWF  or  HB,  and  race  cross- 
section  radius  =  approx.  1.66  ball  radius. 

KI=  0.5  for  unhardened  steel,  occasionally  used  for  very  large  races; 
a  steel  that  is  fairly  hard  without  tempering  must  be  used,  and  then  only 
when  there  is  no  hammering  or  sharp  load  variation. 

Balls  must  be  carefully  selected  to  make  sure  that  all  that  are  used 
in  the  same  bearing  do  not  vary  among  one  another  by  more  than  O.OOOi 
inch.  A  ball  that  is  more  than  that  larger  than  its  fellows  will  sustain 
more  than  its  proportion  of  the  load,  and  may  therefore  be  overloaded 
and  will  in  turn  overload  the  races. 


BALL-BEARINGS,    ROLLER-BEARINGS,    ETC.       1237 


The  usual  test  of  ball  quality,  which  consists  in  compressing  a  ball 
between  flat  plates  and  noting  the  load  at  rupture,  gives  the  quality  of 
the  plates,  but  not  of  the  balls.  It  is  the  ability  of  the  ball  to  resist 
permanent  deformation  that  is  of  importance.  As  the  deformations 
involved  are  very  small  the  test  is  a  difficult  one  to  carry  out.  Of  even 
greater  importance  than  a  small  deformation  under  load  is  uniformity  of 
such  deformation  between  the  balls  employed;  a  hard  ball  will  deform 
less  than  its  softer  mate  and  so  will  carry  more  than  its  share  of  the 
load,  and  will  therefore  be  overloaded  and  in  turn  overload  the  races. 

Coned  bearings  for  balls  are  objectionable.  The  defect  in  all  these 
forms  of  bearings  is  their  adjustable  feature.  A  bearing  properly  propor- 
tioned with  reference  to  a  certain  load  may  be  enormously  overloaded  by 
a  little  extra  effort  applied  to  the  wrench,  or  on  the  other  hand  the  bear- 
ing may  be  adjusted  with  too  little  pressure,  so  that  the  balls  will  rattle, 
and  the  results  consequently  be  unsatisfactory.  The  prevalent  idea  that 
coned  ball-bearings  can  be  adjusted  to  compensate  for  wear  is  erroneous. 

Mr.  Hess's  paper,  in  Trans.  A.  S.  M.  E.,  1907,  contains  a  great  deal  of 
useful  information  on  the  practical  design  of  ball-bearings,  including 
different  forms  of  raceways.  He  prefers  a  two-point  bearing,  in  which 
the  ball  races  have  a  curved  section,  with  sustaining  surfaces  at  right 
angles  with  the  direction  of  the  load. 

Formulae  for  Number  of  Balls  in  a  Bearing.  (H.  Rolfe,  Am.  Mach., 
Dec.  3,  1896.) — Let  D  =  diam.  9f  ball  circle  (the  circle  passing  through 
the  centers  of  the  balls);  d  —  diam.  of  balls;  n  =  number  of  balls;  s  = 
average  clearance  space  between  the  balls.  Then  D  =  (d  +  s)  -r-  sin 
(180°/n);  d  =  D  sin  (180°/n)  -  s;  s  =  D  sin  (180° /n)  -  d;  n  =180°  4- 
angle  whose  sine  is  (d  +  s)  -=-£>.  The  clearance  s  should  be  about  0.003  in. 
VALUES  OF  180°/n  AND  OF  SIN  180°/n. 


£ 

8 
\ 

£ 

£ 

n. 

£ 

1 

n. 

s 

1 

». 

£ 

n. 

£ 

i 

1 

.S 

*w 

1 

a 
'53 

§ 

.& 
'53 

i 

a 

•z 

3 

60 

0.86603 

15 

12 

0.20791 

27 

'6.667 

0.11609 

39 

4.615 

0.08047 

A 

45 

.70711 

16 

11.250 

.19509 

28 

6.429 

.11197 

40 

4.500 

.07846 

5 

36 

.58799 

17 

10.588 

.18375 

29 

6.207 

.10812 

41 

4.390 

.07655 

6 

30 

.50000 

18 

10 

.17365 

30 

6 

.10453 

42 

4.286 

.07473 

7 

25.714 

.43388 

19 

9.474 

.16454 

31 

5.806 

.10117 

43 

4.186 

.07300 

8 

22.500 

.38268 

20 

9. 

.  15643 

32 

5.625 

.09801 

44 

4.091 

.07134 

9 

20 

.34202 

21 

8.571 

.14904 

33 

5.455 

.09506 

45 

4 

.06976 

10 

18 

.30902 

22 

8.182 

.14233 

34 

5.294 

.09227 

46 

3.913 

.06825 

11 

16.364 

.28173 

23 

7.826 

.13616 

35 

5.143 

.08963 

47 

3.830 

.06679 

12 

15 

.25882 

24 

7.500 

.  13053 

36 

5 

.08716 

48 

3.750 

.06540 

13 

13.846 

.23931 

25 

7.200 

.  12533 

37 

4.865 

.08510 

49 

3.673 

.06407 

14 

12.857 

.22252 

26 

6.923 

.12055 

38 

4.737 

.08258 

50 

3.600 

.06279 

Grades  of  Balls  for  Bearings.  (S.  S.  Eyeland,  Trans.  A.  S.  M.  E.t 
1905.)  — "A"  grade  balls  vary  about  0.0025  in.  in  diameter;  "B"  grade, 
0.001  to  0.002  in.;  while  "  high-duty"  or  special  balls  are  furnished  varying 
not  over  0.0001  in.  The  crushing  strength  of  balls  is  of  little  importance 
as  to  the  load  a  bearing  will  carry,  the  revolutions  per  minute  being  quite 
as  important  as  the  load. 

Saving  of  Power  by  Use  of  Bali-Bearings.  —  Henry  Hess  (Trans. 
A.  S.  M.  E.,  1909)  describes  a  series  of  tests  made  by  Dodge  and  Day  pn  a 
215/16  in.  line  shaft  72  ft.  long,  alternately  equipped  with  plain  ring-oiling 
babbitted  boxes  and  with  H  ess-Bright  ball-bearings.  Eight  countershafts 
were  driven  from  pulleys  on  the  line  shaft.  The  countershaft  pulleys  had 
plain  bearings.  The  conclusions  from  the  tests  made  under  normal  belt 
conditions  of  44  and  57  Ibs.  per  inch  width  of  angle  of  single  belt  are  as 
follows: 

a.  Savings  due  to  the  substitution  of  ball-bearings  for  plain  bearings  on 
line  shafts  may  be  safely  calculated  by  using  0.0015  as  the  coefficient  of 
ball-bearing  friction,  0.03  as  the  coefficient  of  line  shaft  friction,  and  0.08 
as  the  coefficient  of  countershaft  friction. 

b.  When  the  belts  from  line  shaft  to  countershaft  pull  all  in  one  direc- 
tion and  nearly  horizontally  the  saving  due  to  the  substitution  of  ball- 


1238  FRICTION  AND   LUBRICATION. 

bearings  for  plain  bearings  on  the  line  shaft  may  be  safely  taken  as  35% 
of  the  bearing  friction. 

c.  When  ball-bearings  are  used  also  on  the  countershafts  the  savings 
will  be  correspondingly  greater  and  may  amount  to  70%  or  more  of  the 
bearing  friction. 

d.  These  percentages  of  savings  are  percentages  of  the  friction  work 
lost  in  the  plain  bearings;  they  are  not  percentages  of  the  total  power 
transmitted.      The  latter  will  depend  upon  the  ratio  of  the  total  power 
transmitted  to  that  absorbed  in  the  line  and  countershafts. 

e.  The  power  consumed  in  the  plain  line  and  countershafts  varies,  as 
is  well  known,  from  10  to  60%  in  different  industries  and  shops.     The- 
substitution  of  ball-bearings  for  plain  bearings  on  the  line  shaft  only,  under 
conditions  of  paragraph  "a,"  will  thus  result  in  saving  of  total  power  of 
35  X  0.10  =  3.5%  to  35  X  0.60  =  21%.     By  using  ball-bearings  on  the 
countershafts  also,  the  saving  of  total  power  will  be  from  70  X  0.10  =  7% 
to  70  X  0.60  =  42%. 

KNIFE-EDGE  BEARINGS. 

Allowable  loads  on  knife-edges  vary  with  the  manner  in  which  the 
pivots  or  knife-edges  are  held  in  the  lever  and  the  pivot  supports  or 
seats  secured  to  the  base  of  weighing  machines.  The  extension  of  the 
pivot  beyond  the  solid  support  is  practically  worthless.  A  high-grade 
uniform  tool  steel  with  carbon  0.90%  to  1.00%  should  be  used.  The 
temper  of  the  seats  should  be  drawn  to  a  very  light  straw  color;  that  of 
the  pivots  should  be  slightly  darker.  The  angle  of  90°  for  the  knife-edge 
has  given  good  results  for  heavy  loads.  For  ordinary  weighing  ma- 
cliinery  and  most  testing  machinery  5000  Ib.  per  in.  of  length  is  ample. 
Loads  of  10,000  Ib.  per  inch  of  length  are  permissible,  but  the  pivot 
must  be  flat  at  its  upper  portion,  normal  to  the  load  and  supported  its 
whole  length,  with  a  minimum  deflection  of  parts  to  secure  reasonable 
accuracy.  The  edge  may  be  made  perfectly  sharp,  for  loads  up  to 
1000  Ib.  per  inch  of  length.  For  greater  loads  the  sharp  edge  is  rubbed 
with  an  oilstone,  so  that  a  smoothness  is  just  visible.  A  pronounced 
radius  of  knife-edge  will  decrease  the  sensibility  of  the  apparatus. 
(Jos.  W.  Bramwell,  Eng.  News,  June  14,  1906.) 

FRICTION  OF  STEAM-ENGINES. 

Distribution  of  the  Friction  of  Engines.  —  Prof.  Thurston,  in  his 
"Friction  and  Lost  Work,"  gives  the  following: 

3. 

35.0 
21.0 


Main  bearings  

1. 
.  .  .  .         47  0 

2. 
35  4 

Piston  and  rod  

.  ...          32.9 

25  0 

Crank-pin                       

6  8 

5  1 

54 

4  1 

Valve  and  rod                

25 

26  4 

Eccentric  strap       

53 

4  0 

Link  and  eccentric.  .  . 

13.0 

22.0 
9.0 
Total 100.0       100.0  100.0 

No.  1,  Straight-line,  6  x  12  in.,  balanced  valve;  No.  2,  Straight-line, 
6  x  12  in.,  unbalanced  valve;  No.  3,  7  x  10  in.,  Lansing  traction,  locomo- 
tive valve-gear. 

Prof.  Thurston's  tests  on  a  number  of  different  styles  of  engines  indicate 
that  the  friction  of  any  engine  is  practically  constant  under  all  loads. 
(Trans.  A.  S.  M.  E.,  viii,  86;  ix,  74.) 

In  a  straight-line  engine,  8  x  14  in.,  I.H.P.  from  7.41  to  57.54,  the 
friction  H.P.  varied  irregularly  between  1.97  and  4.02,  the  variation 
being  independent  of  the  load.  With  50  H.P.  on  the  brake  the  I.H.P. 
was  only  52.6,  the  friction  being  only  2.6  H.P.,  or  about  5%. 

A  compound  condensing-engine,  tested  from  0  to  102.6  brake  H.P.,  gave 
I.H.P.  from  14.92  to  117.8  H.P.,  the  friction  H.P.  varying  only  from 
14.92  to  17.42.  At  the  maximum  load  the  friction  was  15.2  H.P.,  or 
12.9%. 

The  friction  increases  with  increase  of  the  boiler-pressure  from  30  to  70 
IDS.,  and  then  becomes  constant.  The  friction  generally  increases  with 
Increase  of  speed,  but  there  are  exceptions  to  this  rule. 

Prof.  Den  ton  (Stevens  Indicator,  July,  1890),  comparing  the  calculated 
friction  on  a  number  of  engines  with  the  friction  as  determined  by  measure- 


FHICTION  BRAKES  AND  FHICTION  CLUTCHES.      1239 

ment,  finds  that  in  one  case,  a  75-ton  ammonia  ice-machine,  the  friction  of 
the  compressor,  171/2  H.P.,  is  accounted  for  by  a  coefficient  of  friction, 
of  71/2%  on  all  the  external  bearings,  allowing  6%  of  the  entire  friction 
of  the  machine  for  the  friction  of  pistons,  stuffing-boxes,  and  valves.  In 
the  case  of  the  Pawtucket  pumping-engine,  estimating  the  friction  of  the 
external  bearings  with  a  coefficient  of  friction  of  6%  and  that  of  the 
pistons,  valves,  and  stuffing-boxes  as  in  the  case  of  the  ice-machine,  we 
have  the  total  friction  distributed  as  follows: 

Horse-    Percent 

Crank-pins  and  effect  of  piston-thrust  on  main  shaft  0  .71*  ^11°  4* 

Weight  of  fly-wheel  and  main  shaft 1 .95  33  4 

Steam-valves 0  23  37 

Eccentric 0  '07  1  '2 

Pistons 0  .43  7  '2 

Stuffing-boxes,  six  altogether 0  72  113 

Air-pump 2.10  32  '.& 

Total  friction  of  engine  with  load 6 .21         100  0 

Total  friction  per  cent  of  indicated  power.     4.27 

The  friction  of  this  engine,  though  very  low  in  proportion  to  the  indi- 
cated power,  is  satisfactorily  accounted  for  by  Morin's  law  used  with  a 
coefficient  of  friction  of  5%.  In  both  cases  the  main  items  of  friction  are 
those  due  to  the  weight  of  the  fly-wheel  and  main  shaft  and  to  the  piston- 
thrust  on  crank-pins  and  main-shaft  bearings.  In  the  ice-machine  the 
latter  items  are  the  larger  owing  to  the  extra  crank-pin  to  work  the  pumps, 
while  in  the  Pawtucket  engine  the  former  preponderates,  as  the  crank- 
thrusts  are  partly  absorbed  by  the  piump-pistons,  and  only  the  surplus 
effect  acts  on  the  crank-shaft. 

Prof.  Denton  describes  in  Trans.  A.  S.  M.  E.,  x.  392,  an  apparatus  by 
which  he  measured  the  friction  of  the  piston  packing-ring.  When  the 
parts  of  the  piston  were  thoroughty  devoid  of  lubricant,  the  coefficient 
of  friction  was  found  to  be  about  7 1/2%;  with  an  oil-feed  of  one  drop  in 
two  minutes  the  coefficient  was  about  5%;  with  one  drop  per  minute  it 
was  about  3%.  These  rates  of  feed  gave  unsatisfactory  lubrication,  the 
piston  groaning  at  the  ends  of  the  stroke  when  run  slowly,  and  the  flow  of 
oil  left  upon  the  surfaces  was  found  by  analysis  to  contain  about  50%  of 
iron.  A  feed  of  two  drops  per  minute  reduced  the  coefficient  of  friction 
to  about  1%,  and  gave  practically  perfect  lubrication,  the  oil  retaining  its 
natural  color  and  purity. 

FRICTION  BRAKES  AND  FRICTION  CLUTCHES. 

Friction  Brakes  are  used  for  slowing  down  or  stopping  a  moving 
machine  by  converting  its  energy  of  motion  into  heat,  or  for  controlling 
the  speed  of  a  descending  load.  The  simplest  form  is  the  block  brake, 
commonly  used  for  railway  car  wheels,  which  resists  the  motion  of  the 
wheel  not  only  with  the  force  due  to  ordinary  sliding  friction,  but  with 
that  due  to  cutting  or  grinding  away  the  surface  of  the  metals  in  contact. 
If  P  =  total  pressure  acting  normal  to  the  sliding  surface,  /  =  coefficient 
of  friction,  and  v  —  velocity  in  feet  per  minute,  then  the  energy  absorbed, 
in  foot-pounds  per  minute,  is  Pfv.  If  the  surface  is  lubricated  and  the 
pressure  per  square  inch  not  great  enough  to  squeeze  out  the  lubricant, 
then  the  value  of  /  for  different  materials  may  be  taken  from  Morin's 
tables  for  friction  of  motion,  page  1221,  but  if  the  pressure  is  great  enough 
to  force  out  the  lubricant,  then  the  coefficient  becomes  much  greater 
and  the  surfaces  will  cut  and  wear,  with  a  rapid' rise  of  temperature. 

Other  forms  of  brakes  are  disk  brakes  and  cone  brakes,  in  which  a 
disk  or  cone  is  carried  by  the  rotating  shaft  and  a  mating  disk  or  cone 
is  pressed  against  it  by  a  lever  or  other  means;  and  band  brakes,  also 
called  strap  or  ribbon  brakes,  in  which  a  flexible  band  encircles  the 
cylindrical  surface  of  a  rotating  drum  or  wheel,  and  tension  applied 
to  one  end  of  the  band  brings  it  in  contact  with  that  surface.  For  band 
brakes  the  theory  of  friction  of  belts  applies.  See  page  1138.  For  much 
information  on  the  theory  and  practice  of  friction  brakes  see  articles  by 
C.  F.  Blake  in  Mach'y,  Jan.,  1901,  Mar.,  1905,  and  Aug.,  1906,  and  by 
3.  R.  Douglas,  Am.  Mach.,  Dec.  26,  1901,  and  R.  B.  Brown,  Mach'y. 
April,  1909.  For  friction  brake  dynamometers  see  Dynamometers. 


1240  FRICTION  AND  LUBRICATION. 

Friction  Clutches  are  used  for  putting  shafts  in  motion  gradually, 
without  shock.  If  two  shafts,  in  line  with  each  other,  one  in  motion  and 
the  other  at  rest,  each  having  a  disk  keyed  to  the  end,  and  the  disks 
almost  touching,  are  moved  toward  each  other  so  that  the  disks  are 
brought  in  contact  with  some  pressure,  the  shaft  at  rest  will  be  put  in 
motion  gradually,  while  the  disks  rub  on  each  other,  until  it  acquires  the 
velocity  of  the  driving  shaft,  when  the  friction  ceases  and  the  disks  may 
then  be  locked  together.  This  is  an  elementary  form  of  friction  clutch. 
A  great  variety  of  styles  are  made  in  which  the  sliding  surfaces  may  be 
disks,  cones,  and  gripping  btocks  of  various  forms.  The  work  done  by  a 
clutch  while  the  surfaces  are  in  sliding  contact,  and  before  they  are  locked 
together  is  the  overcoming  of  the  inertia  of  the  driven  shaft  and  of  all 
the  mechanism  driven  by  it,  and  giving  it  the  velocity  of  the  driving 
shaft.  The  principles  of  friction  brakes  apply  to  friction  clutches.  The 
sliding  surfaces  must  be  of  sufficient  area  to  keep  the  normal  pressure 
below  tha,t  at  which  they  will  overheat,  cut  and  wear,  and  to  dissipate 
the  heat  generated  by  friction.  The  following  values  of  the  coefficient 
of  friction  to  be  used  in  designing  clutches  are  given  by  C.  W.  Hunt: 
cork  on  iron,  0.35;  leather  on  iron,  0.3;  wood  on  iron,  0.2;  iron  on  iron, 
0.25  to  0.3.  Lower  values  than  these  should  be  assumed  for  velocities 
exceeding  400  ft.  per  minute.  The  pressure  per  square  inch  in  disk 
clutches  should  not  exceed  25  or  30  Ibs.,  and  wooden  surfaces  should 
not  be  loaded  beyond  20  to  25  Ibs.  per  sq.  in.  See  Kimball  and  Barr  on 
Machine  Design,  also  Trans.  A.  S.  M.  E.,  1903  and  1908. 

Electrically  Operated  Brakes  are  discussed  by  H.  A  Steen  in  a 
paper  read  before  the  Engrs.  Socy.  of  W.  Penna.,  reprinted  in  Iron  Trade 
Rev.,  Dec.  24,  1908.  Formulae  are  given  for  the  time  required  for  stop- 
ping, for  the  heat  generated  and  the  temperature  rise,  for  different  types 
of  brakes. 

Magnetic  and  Electric  Brakes. — For  braking  the  load  on  electric 
cranes  a  band  brake  is  used  which  is  held  off  the  drum  by  the  action  of 
a  magnet  or  solenoid,  and  is  put  on  by  the  action  of  a  spring  or  weight. 
The  solenoid  usually  consists  of  a  coil  of  wire  connected  in  series  with  the 
motor,  and  a  plunger  working  inside  of  the  coil.  It  should  be  so  pro- 
portioned that  its  action  is  not  delayed  by  residual  magnetism  when  the 
current  is  cut  off.  Too  rapid  action  is  prevented  by  making  the  end  of 
the  solenoid  an  air  dash-pot. 

For  electric-driven  machinery  an  electric  motor  makes  a  most  efficient 
brake  by  reversing  the  directi9n  of  the  electric  current,  causing  the  motor 
to  become  a  generator  supplying  current  to  a  rheostat  in  which  it  is  con- 
verted into  heat  and  dissipated.  In  some  cases  the  electric  current 
generated,  instead  of  being  absorbed  in  a  rheostat,  is  fed  into  the  main 
electric  circuit.  In  this  case  the  energy  of  the  rotating  mass,  instead  9f 
being  wasted  in  friction  or  in  electrical  heating,  is  converted  into  electric 
energy  and  thus  conserved  for  further  use. 

Design  of  Band  Brakes.  (R.  A.  Greene,  Am.  Mach.t  Oct.  8,  1908.)  — 
In  the  practice  of  the  Browning  Engineering  Co.,  Cleveland,  O.,  in 
regard  to  the  design  of  band  brakes  the  equations  are: 

2  T 

T=  PX,  t  =  T  -P,  S  =    * J  „ ,    #=  S  X  DX  0.262  X  revolutions  per 

L)  X  r 

minute,  in  which  T  =  the  greater  tension  on  the  band,  t  =  the  lesser 
tension  on  the  band,  P  =  equivalent  load  on  the  brake  drum,  X  =  factor 

from  the  accompanying  table,    X   =  \r  _ -,    in   which   N  =  1027288/C« 

where  /  =  the  coefficient  of  friction  and  c  the  length  of  arc  of  contact  in 
degrees  divided  by  360.  D  =  diam.  of  brake  drum,  F  =  width  of  face 
of  brake  drum,  S  =  a  checking  factor  which  has  a  maximum  limit  of  65, 
1?  =  a  checking  factor  which  has  a  limit  of  54,000  (Yale  &  Towne  practice) 
or  60,000  (Brown  hoist  practice). 

EXAMPLE. — A  band  brake  is  to  be  designed  having  an  arc  of  contact 
of  260°,  coefficient  of  friction  =  0.2,  drum  diameter  30  ins.,  face  4  ins  , 
speed  100  r.p.m.,  and  a  load  of  3000  Ibs.  acting  on  a  diameter  of  20  ins. 

Then 

P=  3000  X  20-4- 30=2000  pounds,  X  =  1.68  (from  table),  T  =  2000  X 
1.68  =  3360  pounds,  t  =  3360  -  2000  =  1360  pounds,  S  =  2  X3360-*- 
(30X4)=56  (within  the  limit),  *  =  56X30  X  0.262  X  100=44,000  (within 
the  limit). 


FRICTION   OF   HYDRAULIC   PLUNGER   PACKING.      1241 


Degrees. 

Values  of  X. 

Degrees. 

Values  of  X. 

f  =0.2. 

/  =0.3. 

/  =0.4. 

f  =0.2. 

/  =0.3. 

/  =0.4. 

180 
195 
210 
240 
250 

2.14 
2.03 
1.93 
1.76 
1.72 

.64 
'  .56 
.50 
.40 
.37 

.40 
.35 
.30 
.23 
.21 

260 
270 
280 
290 
300 

.68 
.64 
.60 
.57 
.54 

.35 

.32 
.30 
.28 
.26 

.19 
.18 
.17 
.15 
.14 

FRICTION  OF  HYDRAULIC  PLUNGER  PACKING. 

The  "Taschenbuch  der  Hutte"  (15th  edition,  vol.  1,  p.  202)  says:  "For 
stuffing-boxes  with  hemp,  cotton  or  leather  packing,  with  water  pressures 
between  1  and  50  atmospheres,  the  frictional  loss  is  dependent  upon  the 
water  pressure,  the  circumference  of  the  packed  surface,  and  a  coefficient 
n,  which  is  constant  lor  this  range  of  pressure.  The  loss  is  independent 
of  the  depth  of  stuffing-box  or  leather  ring,  and  is  given  by  the  formula 
F  =  Kpd,  in  which  F  =  total  frictional  loss  in  pounds,  p  —  pressure  in  pounds 
per  sq.  in.,  d  —  diameter  of  plunger  in  inches. 

K  is  a  coefficient,  which  depends  on  the  kind  and  condition  of  the  pack- 
ing, and  is  given  as  follows  for  various  cases. 

For  cotton  or  hemp,  loose  or  braided,  dipped  in  hot  tallow;  plungers 
smooth,  glands  not  pulled  down  too  tight,  packing  therefore  retaining 
its  elasticity;  dimensions  such  as  usually  occur,  K  =  0.072. 

Same  conditions,  after  packing  is  some  months  old,  K  =  0.132. 

Materials  the  same,  but  with  hard  packing,  unfavorable  conditions, 
etc.,  /C  =  as  much  as  0.299. 

Leather  packing;  soft  leather,  well  made,  etc.,  K  =  0.036  to  0.084. 

Hard,  stiffly  tanned  leather,  K  =  0.12  to  0.156. 

Unfavorable  conditions;  rough  plungers,  gritty  water,  etc.,  K=&s  much 
as  0.239. 

Weisbach-Hermann,  "  Mechanics  of  Hoisting  Machinery,"  gives  a 
formula  which  when  translated  into  the  same  notation  as  the  one  in 
"  Hutte  "  is 

F  =  0.0312  pd  to  0.0767  pd. 

Since  the  total  pressure  on  a  plunger  is  l/4nd?p,  the  ratio  of  the  loss  of 
pressure  to  the  total  pressure  is  Kpd-±-l/47td2p,  or,  using  the  extreme  values 
of  K,  0.0312  and  0.299.  the  ratio  ranges  from  0.04 -s-d  to  Q.38  +  d,  or  from 
4  to  38  per  cent  divided  by  the  diameter  in  inches. 

Walter  Ferris  (Am.  Mack.,  Feb.  3,  1898)  derives  from  the  formula 
given  above  the  following  formula  for  the  pressure  produced  by  a  hemp- 
packed  hydraulic  intensitier  made  with  two  plungers  of  different  diameters: 

A-KD 


in  which  ^2  =  pressure  per  sq.  in.  produced  by  the  intensifier,  pi=  initial 

Sressure,  A=area  and  D  =  diam.  of  the  larger  plunger,  o  =  area  and  d  = 
iam.  of  the  smaller  plunger,  and  K  an  experimental  coefficient.     He  gives 
the  following  results  of  tests  of  an  intensifier  with  a  small  plunger  8  ins. 
diam.  and  two  large  plungers,  14V4  and  173/4  ins.,  either  one  of  which  could 
be  used  as  desired. 

Diam.  of  large  plunger,  in.  141/4          141/4          173/4          173/4 

Initial  pressure,  Ibs.  per  sq.  in.  285  475  335  350 

Intensified  pressure,  ibs.  per  sq.  in.      750  1450  1450  1510 

Intensified  if  there  were  no  friction     905  1505  1650  1725 

Intensified  calculated  by  formula*     806  1433  1572  1643 

Efficiency  of  machine  0.83        0.965  0.88          0.875 

LUBRICATION. 

Measurement  of  the  Durability  of  Lubricants.  —  (J.  E.  Denton, 
Trans.  A.  S.  M.  E.,  xi,  1013.)  — Practical  differences  of  durability  of 
lubricants  depend  not  on  any  differences  of  inherent  ability  to  resist 
being  "worn  out"  by  rubbing,  but  upon  the  rate  at  which  they  flow 
through  and  away  from  the  bearing-surfaces.  The  conditions  which 


*  Assuming  K  =  0.2. 
each  case  was  0,953, 


The  efficiency  calculated  by  the  formula  in 


1242  FRICTION  AND   LUBRICATION. 

control  this  flow  are  so  delicate  in  their  influence  that  all  attempts  thus 
far  made  to  measure  durability  of  lubricants  may  be  said  to  have  failed 
to  make  distinctions  of  lubricating  value  having  any  practical  significance. 
In  some  kinds  of  service  the  limit  to  the  consumption  of  oil  depends  upon 
the  extent  to  which  dust  or  other  refuse  becomes  mixed  with  it,  as  in 
railroad-car  lubrication  and  in  the  case  of  agricultural  machinery.  The 
economy  of  one  oil  over  another,  so  far  as  the  quality  used  is  concerned  — 
that  is,  so  far  as  durability  is  concerned  — •  is  simply  proportional  to  the 
rate  at  which  it  can  insinuate  itself  into  and  flow  out  of  minute  orifices  or 
cracks.  Oils  will  differ  in  their  ability  to  do  this,  first,  in  proportion  to 
their  viscosity,  and,  second,  in  proportion  to  the  capillary  properties  which 
they  may  possess  by  virtue  of  the  particular  ingredients  used  in  their 
composition.  Where  the  thickness  of  film  between  rubbing-surfaces 
must  be  so  great  that  large  amounts  of  oil  pass  through  bearings  in  a  given 
time,  and  the  surroundings  are  such  as  to  permit  oil  to  be  fed  at  high 
temperatures  or  applied  by  a  method  not  requiring  a  perfect  fluidity,  it  is 
probable  that  the  least  amount  of  oil  will  be  used  when  the  viscosity  is  as 
great  as  in  the  petroleum  cylinder  stocks.  When,  however,  the  oil  must 
flow  freely  at  ordinary  temperatures  and  the  feed  of  oil  is  restricted,  as  in 
the  case  of  crank-pin  bearings,  it  is  not  practicable  to  feed  such  heavy 
oils  in  a  satisfactory  manner.  Oils  of  less  viscosity  or  of  a  fluidity 
approximating  to  lard-oil  must  then  be  used. 

Relatiw  Value  of  Lubricants.  (J.  E.  Denton,  Am.  Mach.,  Oct  30 
1890.)  —  The  three  elements  which  determine  the  value  of  a  lubricant 
are  the  cost  due  to  consumption  of  lubricants,  the  cost  spent  for  coal  to 
overcome  the  frictional  resistance  caused  by  use  of  the  lubricant,  and  the 
cost  due  to  the  metallic  wear  on  the  journal  and  the  brasses. 

The  Qualifications  of  a  Good  Lubricant,  as  laid  down  by  W.  H. 
Bailey,  in  Proc.  Inst.  C.  E.,  vol.  xlv,  p.  372,  are:  1.  Sufficient  body  to 
keep  the  surfaces  free  from  contact  under  maximum  pressure.  2.  The 
greatest  possible  fluidity  consistent  with  the  foregoing  condition.  3.  The 
lowest  possible  coefficient  of  friction,  which  in  bath  lubrication  would  be 
for  fluid  friction  approximately.  4.  The  greatest  capacity  for  storing 
and  carrying  away  heat.  5.  A  high  temperature  of  decomposition. 
6.  Power  to  resist  oxidation  or  the  action  of  the  atmosphere.  7.  Freedom 
from  corrosive  action  on  the  metals  upon  which  the  lubricant  is  used. 

The  Examination  of  Lubricating  Oils.  (Prof.  Thos.  B.  Stillman, 
Stevens  Indicator,  July,  1890.)  —  The  generally  accepted  conditions  of 
a  good  lubricant  are  as  follows: 

1.  "Body"  enough  to  prevent  the  surfaces  to  which  it  is  applied  from 
coming  in  contact  with  each  other.     (Viscosity.) 

2.  Freedom  from  corrosive  acid,  of  either  mineral  or  animal  origin. 

3.  As  fluid  as  possible  consistent  with  "body." 

4.  A  minimum  coefficient  of  friction. 

5.  High  "flash"  and  burning  points. 

6.  Freedom  from  materials  liable  to  produce  oxidation  or  "gumming." 
The  examinations  to  be  made  to  verify  the  above  are  both  chemical  and 

mechanical,  and  are  usually  arranged  in  the  following  order: 

1.  Identification  of  the  oil,  whether  a  simple  mineral  oil,  or  animal  oil, 
or  a  mixture.  2.  Density.  3.  Viscosity.  4.  Flash-point.  5.  Burning- 
point.  6.  Acidity.  7.  Coefficient  of  friction.  8.  Cold  test. 

Detailed  directions  for  making  all  of  the  above  tests  are  given  in  Prof, 
Stillman's  article.  See  also  Stillman's  Engineering  Chemistry,  p.  366. 

Notes  on  Specifications  for  Petroleum  Lubricants.  (C.  M.  Everest, 
Vice-Pres.  Vacuum  Oil  Co.,  Proc.  Engineering  Congress,  Chicago  World's 
Fair,  1893.)  —  The  specific  gravity  was  the  first  standard  established  for 
determining  quality  of  lubricating  oils,  but  it  has  long  since  been  dis- 
carded as  a  conclusive  test  of  lubricating  quality.  However,  as  the 
specific  gravity  of  a  particular  petroleum  oil  increases  the  viscosity  also 
increases. 

The  object  of  the  fire  test  of  a  lubricant,  as  well  as  its  flash  test,  is  the 
prevention  of  danger  from  fire  through  the  use  of  an  oil  that  will  evolve 
inflammable  vapors.  The  lowest  fire  test  permissible  is  300°,  which  gives 
a  liberal  factor  of  safety  under  ordinary  conditions. 

The  cold  test  of  an  oil,  i.e.,  the  temperature  at  which  the  oil  will  congeal, 
should  be  well  below  the  temperature  at  which  it  is  used;  otherwise  the 
coefficient  of  friction  would  be  correspondingly  increased," 


IMBRICATION.  1243 

Viscosity,  or  fluidity,  of  an  oil  is  usually  expressed  in  seconds  of  time  in 
which  a  given  quantity  of  oil  will  flow  through  a  certain  orifice  at  the  tem- 
perature stated,  comparison  sometimes  being  ma.de  with  water,  sometimes 
with  sperm-oil,  and  again  with  rape-seed  oil.  It  seems  evident  that 
within  limits  the  lower  the  viscosity  of  an  oil  (without  a  too  near  approach 
to  metallic  contact  of  the  rubbing  surfaces)  the  lower  will  be  the  coefficient 
of  friction.  But  we  consider  that  each  bearing  in  a  mill  or  factory  would 
probably  require  an  oil  of  different  viscosity  from  any  other  bearingin  the 
mill,  in  order  to  give  its  lowest  coefficient  of  friction,  and  that  slight 
variations  in  the  condition  of  a  particular  bearing  would  change  the  re- 
quirements of  that  bearing;  and  further,  that  when  nearing  the  "danger 
point"  the  question  of  viscosity  alone  probably  does  not  govern. 

The  requirement  of  the  New  England  Manufacturers'  Association,  that 
an  oil  shall  not  lose  over  5%  of  its  volume  when  heated  to  140°  Fahr.  for 
12  hours,  is  to  prevent  losses  by  evaporation,  with  the  resultant  effects. 

The  precipitation  test  gives  no  indication  of  the  quality  of  the  oil  itself, 
as  the  free  carbon  in  improperly  manufactured  oils  can  be  easily  removed. 

It  is  doubtful  whether  oil  buyers  who  require  certain  given  standards 
of  laboratory  tests  are  better  served  than  those  who  do  not.  Some  of 
the  standards  are  so  faulty  that  to  pass  them  an  oil  manufacturer  must 
supply  oil  he  knows  to  be  faulty;  and  the  requirements  of  the  best  stand- 
ards can  generally  be  met  by  products  that  will  give  inferior  results  in 
actual  serivce.  • 

Penna.  B.  B.  Specifications  for  Petroleum  Products,  1900.  — 
Five  different  grades  of  petroleum  products  will  be  used. 

The  materials  desired  under  this  specification  are  the  products  of  the 
distillation  and  refining  of  petroleum  unmixed  with  any  other  substances. 

150°  Fire-test  Oil.  —  This  grade  of  oil  will  not  be  accepted  if  sample 
(1)  is  not  "water-white"  in  color;  (2)  flashes  below  130°  Fahrenheit; 
(3)  burns  below  151°  Fahrenheit;  (4)  is  cloudy  or  shipment  has  cloudy 
barrels  when  received,  from  the  presence  of  glue  or  suspended  matter; 
(5)  becomes  opaque  or  shows  cloud  when  the  sample  has  been  10  minutes 
at  a  temperature  of  0°  Fahrenheit. 

300°  Fire-test  Oil.  —  This  grade  of  oil  will  not  be  accepted  if  sample 
(1)  is  not  "water-white"  in  color;  (2)  flashes  below  249°  Fahrenheit; 
(3)  burns  below  298°  Fahrenheit;  (4)  is  cloudy  or  shipment  has  cloudy 
barrels  when  received,  from  the  presence  of  glue  or  suspended  matter; 
(5)  becomes  opaque  or  shows  cloud  when  the  sample  has  been  10  minutes 
at  a  temperature  of  32°  Fahrenheit;  (6)  shows  precipitation  when  some 
of  the  sample  is  heated  to  450°  F.  The  precipitation  test  is  made  by 
having  about  two  fluid  ounces  of  the  oil  in  a  six-ounce  beaker,  with  a 
thermometer  suspended  in  the  oil,  and  then  heating  slowly  until  the 
thermometer  shows  the  required  temperature.  The  oil  changes  color, 
but  must  show  no  precipitation. 

Parafflne  and  Neutral  Oils.  —  These  grades  of  oil  will  not  be  accepted 
if  the  sample  from  shipment  (1)  is  so  dark  in  color  that  printing  with 
long-primer  type  cannot  be  read  with  ordinary  daylight  through  a  layer  of 
the  oil  1/2  inch  thick;  (2)  flashes  below  298°  F.:  (3)  has  a  gravity  at 
60°  F.,  below  24°  or  above  35°  Baume";  (4)  from  October  1st  to  May  1st 
has  a  cold  test  above  10°  F.,  and  from  May  1st  to  October  1st  has  a  cold- 
test  above  32°  F. 

The  color  test  is  made  by  having  a  layer  of  the  oil  of  the  prescribed 
thickness  in  a  proper  glass  vessel,  and  then  putting  the  printing  on  one 
side  of  the  vessel  and  reading  it  through  the  layer  of  oil  with  the  back 
of  the  observer  toward  the  source  of  light.  x 

Well  Oil.  —  This  grade  of  oil  will  not  be  accepted  if  the  sample  from 
shipment  (1)  flashes,  from  May  1st  to  October  1st,  below  298°  F.,  or 
from  October  1st  to  May  1st,  below  249°  F.;  (2)  has  a  gravity  at  60°  F., 
below  28°  or  above  31°  Baume;  (3)  from  October  1st  to  May  1st  has 
a  cold  test  above  10°  F.,  and  from  May  1st  to  October  1st  has  a  cold  test 
above  32°  F.;  (4)  shows  any  precipitation  when  5  cubic  centimeters  are 
mixed  with  95  c.c.  of  gasoline.  The  precipitation  test  is  to  exclude  tarry 
and  suspended  matter.  It  is  made  by  putting  95  c.c.  of  88°  B.  gasoline, 
which  must  not  be  above  80°  F.  in  temperature,  into  a  100  c.c.  graduate, 
then  adding  the  prescribed  amount  of  oil  and  shaking  thoroughly.  Allow 
to  stand  ten  minutes.  With  satisfactory  oil  no  separated  or  precipitated 
material  can  foe  seen. 


1244 


FRICTION  AND  LUBBICATION. 


500°  Fire-test  Oil  —  This  grade  of  oil  will  not  be  accepted  if  sample 
from  shipment  (1)  flashes  below  494°  F.;  (2)  shows  precipitation  with 
gasoline  when  tested  as  described  for  well  oil. 

Printed  directions  for  determining  flashing  and  burning  tests  and  for 
making  cold  tests  and  taking  gravity  are  furnished  by  the  railroad  company. 

Penna.  R.  K.  Specifications  for  Lubricating  Oils  (1894).  (In 
force  in  1902.) 


Constituent  Oils. 

Parts  by  volume. 

Extra  lard-oil           

1 

"4" 

Extra,  No   1  lard-oil 

1 

1 
4 

1 
2 

1 
2 

1 
"4 

1 
1 

"t 

1 
2 
.... 

£>3 

500°  fire-test  oil 

1 

Paraffine  oil                     

Well  oil          

1 

A 

Used  for  

B 

ct 

C2 

C3 

Di 

D2 

E 

A,  freight  dars;  engine  oil  on  shifting-engines;  miscellaneous  greasing 

in  foundries,  etc.  B,  cylinder  lubricant  on  marine  equipment  and  on 
stationary  engines.  C,  engine  oil;  all  engine  machinery;  engine  and 
tender  truck  boxes;  shafting  and  machine  tools;  bolt  cutting;  general 
lubrication  except  cars.  D,  passenger-car  lubrication.  E,  cylinder 
lubricant  for  locomotives.  Ci,  Di,  for  use  in  Dec.,  Jan.,  and  Feb.;  Ct, 
Dz,  in  March,  April,  May,  Sept.,  Oct.,  and  Nov.;  Cs,  Ds,  in  June,  July, 
and  August.  Weights  per  gallon,  A,  7.4  Ibs.;  B,  C,  D,  E,  7.5  Ibs. 

Grease  Lubricants.  — Tests  made  on  an  Olsen  lubricant  testing  machine 
at  Cornell  University  are  reported  in  Power,  Nov.  9,  1909.  It  was  found 
that  some  of  the  commercial  greases  stood  much  higher  pressures  than 
the  oils  tested,  and  that  the  coefficients  of  friction  at  moderate  loads  were 
often  as  low  as  those  of  the  oils.  The  journal  of  the  testing  machine 
was  33/4  in.  diam.,  3 1/2  in.  long,  and  the  babbitt  bearing  shoe  had  a  projected 
area  of  5.8  sq.  in.  The  speed  was  240  r.p.m.  and  each  test  lasted  one 
hour,  except  when  the  bearing  showed  overheating.  The  following  are 
the  coefficients  of  friction  obtained  in  the  tests: 


Lbs. 
per 
sq.in. 

Min- 
eral 
Grease, 

Ani- 
mal 
Grease. 

Graph- 
ite 
Grease. 

Min- 
eral 
Grease. 

Engine 
Oil. 

Engine 
Oil. 

Grease. 

Grease. 

86.2 
172.4 
258.6 
344.8 
431.0 

0.024 
0.021 
0.021 
0.025 
0.050 

0.023 
0.023 
0.023 
0.025 
0.035 

0.04 
0.05 

0.023 
0.018 
0.018 
0.019 
0.028 

0.019 
0.04 
0.06 

0.015 
0.022 
0.037 

0.020 
0.015 
0.014 
0.017 
0.026 

0.025 
0.022 
0.020 
0.020 
0.019 

Testing  Oil  for  Steam  Turbines.  (Robert  Job,  Trans.  Am.  Soc.  for 
Testing  Mails.,  1909.)  — 

In  some  types  of  steam-turbines,  the  bearings  are  very  closely  adjusted 
and,  if  the  oil  is  not  clear  and  free  from  waxy  substances,  clogging  and 
heating  quickly  results.  A  number  of  red  engine  and  turbine  oils  some 
of  which  had  given  good  service  and  others  bad  service  were  tested  and 
it  was  found  that  clearness  and  freedom  from  turbidity  were  of  importance, 
but  mere  color,  or  lack  of  color,  seemed  to  have  little  influence,  and  good 
service  results  were  obtained  with  oils  which  were  of  a  red  color,  as  well 
as  with  those  which  were  filtered  to  an  amber  color. 

Heating  Test. — It  was  found  that  on  heating  the  oils  to  450°  F.  all 
which  had  given  bad  service  showed  a  marked  darkening  of  color,  while 
those  which  had  proved  satisfactory  showed  little  change.  With  oils 
that  had  been  filtered  or  else  had  been  chemically  treated  in  such  manner 
that  the  so-called  "  amorphous  waxes  "  had  been  completely  removed, 
on  applying  the  heating  test  only  a  slight  darkening  of  color  resulted. 
It  is  of  advantage  in  addition  to  other  requirements  to  specify  that  an 
oil  for  steam  turbines  on  being  heated  to  450°  F.  for  five  minutes  shall 
show  not  more  than  a  slight  darkening  of  color.  The  test  is  that  com- 
monly used  in  test  of  300°  oil  for  burning  purposes. 

Separating  Test. — It  is  known  that  elimination  of  the  waxes  causes  an 
increase  in  the  ease  with  which  the  oil  separates  from  hot  water  when 
thoroughly  shaken  with  it.  This  condition  can  be  taken  advantage  9f 
py  prescribing  that  when  one  ounce  of  the  oil  is  place'd  in  a  4-oz.  bottle 


LUBRICATION. .'  1245 

"  with  twd  ounces  of  boiling  water,  the  bottle  corked  and  shaken  narcr  tor 
one  minute  and  let  stand,  the  oil  must  separate  from  the  water  within  a 
specified  time,  depending  upon  the  nature  of  the  oil,  and  that  there  must 
be  no  appearance  of  waxy  substances  at  the  line  of  demarcation  between 
the  oil  and  the  water. 

Quantity  of  Oil  needed  to  Run  an  Engine.— The  Vacuum  Oil  Co.  in 
1892,  in  response  to  an  inquiry  as  to  cost  of  oil  to  run  a  1000-H.P.  Corliss 
engine,  wrote:  The  cost  of  running  two  engines  of  equal  size  of  the  same 
make  is  not  always  the  same.  Therefore,  while  we  could  furnish  figures 
showing  what  it  is  costing  some  of  our  customers  having  Corliss  engines 
of  1000  H.P.,  we  could  only  give  a  general  idea,  which  in  itself  might  be 
considerably  out  of  the  way  as  to  the  probable  cost  of  cylinder-  and 
engine-oils  per  year  for  a  particular  engine.  Such  an  engine  ought  to 
run  readily  on  less  than  8  drops  of  600  W  oil  per  minute.  If  3000  drops 
are  figured  to  the  quart,  and  8  drops  used  per  minute,  it  would  take  about 
two  and  one  half  barrels  (52.5  gallons)  of  600  W  cylinder-oil,  at  65  cents 
per  gallon,  or  about  $85  for  cylinder-oil  per  year,  running  6  days  a  week 
and  10  hours  a  day.  Engine-oil  would  be  even  more  difficult  to  guess  at 
what  the  cost  would  be,  because  it  would  depend  upon  the  number  of 
cups  required  on  the  engine,  which  varies  somewhat  according  to  the 
style  of  the  engine.  It  would  doubtless  be  safe,  however,  to  calculate 
at  the  outside  that  not  more  than  twice  as  much  engine-oil  would  be 
required  as  of  cylinder-oil. 

The  Vacuum  Oil  Co.  in  1892  published  the  following  results  of  practice 
with  "600  W"  cylinder-oil: 
rnrii^  pnmnrmnri  Anmnp  I  2^  and  33  x  48;  83  revs,  per  min.;   1  drop  of 

ine'  1     oil  per  min.  to  1  drop  in  two  minutes, 
triple  exp.     '  20,  33,  and  46  x  48;  1  drop  every  2  minutes. 

(20  and  36  x  36;  143  revs,  per  min.;  2  dro^s 
Porter- Allen  of  oil  per  min.,  reduced  afterwards  to  .  drcp 

(     per  min. 

„       (15  and  25  x  16;  240  revs,  per  min.;  1  drop 
(     every  4  minutes. 

Results  of  tests  on  ocean-steamers  communicated  to  the  author  by 
Prof.  Denton  in  1892  gave:  for  1200-H.P.  marine  engine,  5  to  6  English 
gallons  (6  to  7.2  U.  S.  gals.)  of  engine-oil  per  24  hours  for  external  lubri- 
cation; and  for  a  1500-H.P.  marine  engine,  triple  expansion,  running 
75  revs,  per  min.,  6  to  7  English  gals,  per  24  hours.  The  cylinder-oil 
consumption  is  exceedingly  variable,  —  from  1  to  4  gals,  per  day  on 
different  engines,  including  cylinder-oil  used  to  swab  the  piston-rods. 

Cylinder  Lubrication.  —  J.  H.  Spoor,  in  Power,  Jan.  4, 1910,  has  made 
a  study  of  a  great  number  of  records  of  the  amount  of  oil  used  for  lubri- 
cating icylinders  of  different  engines,  and  has  reduced  them  to  a  sys- 
tematic basis  of  the  equivalent  number  of  pints  of  oil  used  in  a  10-hour 
day  for  different  areas  of  surface  lubricated.  The  surface  is  determined 
in  square  inches  by  multiplying  the  circumference  of  the  cylinder  by  the 
length  of  stroke.  The  results  are  plotted  in  a  series  of  curves  for  different 
types  of  engines,  and  approximate  average  figures  taken  from  these  curves 
are  given  below: 

Compound  Engines. 

Sq.  ins.  lubricated 2,000  4,000  6,000  8,000  10,000  12,000  18,000 

Pints  of  oil  used  in  10  hrs.      2        3.5       4.3        5        5.5  6         6.5 

Corliss  Engines. 

Sq.  ins.  lubricated 1,000     2,000     3,000     4,000 

Pints  of  oil  in  10  hrs.  Avge 0.9       1.65       2.25       3.75 

Max 1.2       2.25       

Min 1.00       

Automatic  high-speed  engines,  about  2  pints  per  1,000  sq.  in. 

Simple  slide-valve  engines,  about  0.5  pint  per  1,000  sq.  in. 

As  shown  in  the  figures  under  2,000  Corliss,  a  certain  engine  may  take 
21/4  times  as  much  oil  as  another  engine  of  the  same  size.  The  difference 
maybe  due  to  smoothness  of  cylinder  surf  ace,  kind  and  pressure  of  piston 
rings,  quality  of  oil,  method  of  introdiicing  the  lubricant,  etc.  Variations 
in  speed  of  a  given  type  of  engine  and  in  steam  pressure  do  not  appear  to 
make  much  difference,  but  the  small  automatic  high-speed  engine  takes 
more  oil  than  any  other  type.  Vertical  marine  engines  are  commonly  run 


1246  FKICTION  AND  LUBRICATION. 

without  any  cylinder  oil,  except  that  used  occasionally  to  swab  the  piston 
rods. 

Quantity  of  Oil  used  on  a  Locomotive  Crank-pin.  —  Prof.  Denton. 
Trans.  A.  S.  M.  E.%  xi,  1020,  says:  A  very  economical  case  of  practical 
oil-consumption  is  when  a  locomotive  main  crank-pin  consumes  about 
six  cubic  inches  of  oil  in  a  thousand  miles  of  service.  This  is  equivalent 
to  a  consumption  of  one  milligram  to  seventy  square  inches  of  surface 
rubbed  over. 

Soda  Mixture  for  Machine  Tools*  (Penna.  R.  R.  1894.)  —  Dissolve 
6  Ibs.  of  common  sal-soda  in  40  gallons  of  water  and  stir  thoroughly. 
When  needed  for  use  mix  a  gallon  of  this  solution  with  about  a  pint  of 
engine  oil.  Used  for  the  cutting  parts  of  machine  tools  instead  of  oil. 

Water  as  a  Lubricant.  (C.  W.  Naylor,  Trans.  A.  S.  M.  E.t  1905.)  — 
Two  steel  jack-shafts  18  ft.  long  with  bearings  5  X  14  ins.  each  receiving 
175  H.P.  from  engines  and  driving  5  electric  generators,  with  six  belts  all 
pulling  horizontally  on  the  same  side  of  the  shaft,  gave  trouble  by  heating 
when  lubricated  with  oil  or  grease.  Water  was  substituted,  and  the  shafts 
ran  for  11  years,  10  hours  a  day,  without  serious  interruption.  Oil  was  fed 
to  the  shaft  before  closing  down  for  the  night,  to  prevent  rusting.  The 
wear  of  the  babbitted  bearings  in  11  years  was  about  1/4  in.,  and  of  the  shaft 
nil. 

Acheson's  "  Deflocculated  "  Graphite.  (Trans.  A.I.E.E.,  1907; 
Eng.  News,  Aug.  1,  1907.)  — In  1906,  Mr.  E.  G.  Acheson  discovered  a 
process  of  producing  a  fine,  pure,  unctuous  graphite  in  the  electric  fur- 
nace. He  calls  it  deflocculated  graphite.  By  treating  this  graphite 
in  the  disintegrated  form  with  a  water  solution  of  tannin,  the  amount 
of  tannin  being  from  3%  to  6%  of  the  weight  of  the  graphite  treated, 
he  found  that  it  would  be  retained  in  suspension  in  water,  and  that  it 
was  in  such  a  fine  state  of  subdivision  that  a  large  part  of  it  would  run 
through  the  finest  filter  paper,  the  filtrate  being  an  intensely  black  liquid 
in  which  the  graphite  would  remain  suspended  for  months.  The  addition 
of  a  minute  quantity  of  hydrochloric  acid  causes  the  graphite  to  floccu- 
late and  group  together  so  that  it  will  no  longer  flow  through  filter  paper. 
The  same  effect  has  been  obtained  with  alumina,  clay,  lampblack  and 
siloxicon,  by  treatment  with  tannin.  The  graphite  thus  suspended  in 
water,  known  as  "aquedag"  has  been  successfully  used  as  a  lubricant 
for  journals  with  sight-feed  and  with  chain-feed  oilers.  It  also  prevents 
rust  in  iron  and  steel.  The  deflocculated  graphite  has  also  been  sus- 
pended in  oil,  in  a  dehydrated  condition,  making  an  excellent  lubricant 
known  as  "mtdag."  Tests  by  Prof.  C.  H.  Benjamin  of  oil  with  0.5% 
of  graphite  showed  that  it  had  a  lower  coefficient  of  friction  than  the  oil 
alone. 

SOLID   LUBRICANTS. 

Graphite  in  a  condition  of  powder  and  used  as  a  solid  lubricant,  so 
called,  to  distinguish  it  from  a  liquid  lubricant,  has  been  found  to  do  well 
where  the  latter  has  failed. 

Rennie,  in  1829,  says:  "Graphite  lessened  friction  in  all  cases  where  it 
was  used."  General  Morin,  at  a  later  date,  concluded  from  experiments 
that  it  could  be  used  with  advantage  under  heavy  pressures;  and  Prof. 
Thurston  found  it  well  adapted  for  use  under  both  light  and  heavy  pres- 
sures when  mixed  with  certain  oils.  It  is  especially  valuable  to  prevent 
abrasion  and  cutting  under  heavy  loads  and  at  low  velocities. 

For  comparative  tests  of  various  oils  with  and  without  graphite,  see 
paper  on  lubrication  and  lubricants,  by  C.  F.  Mabery,  Jour.  A.S.M.E., 
Feb.,  1910. 

Soapstone,  also  called  talc  and  steatite,  in  the  form  of  powder  and 
mixed  with  oil  or  fat,  is  sometimes  used  as  a  lubricant.  Graphite  or 
soapst9ne,  mixed  with  soap,  is  used  on  surfaces  of  wood  working  against 
either  iron  or  wood. 

Metaline  is  a  solid  compound,  usually  containing  graphite,  made  in  the 
form  of  small  cylinders  which  are  fitted  permanently  into  holes  drilled 
in  the  surface  of  the  bearing.  The  bearing  thus  fitted  runs  without  any 
other  lubrication. 

Bushings  fitted  with  graphite  packed  into  grooves  are  made  by  the 
Graphite  Lubricating  Co.,  Bound  Brook,  N.  J. 


THE  FOUNDRY. 


1247 


THE  FOUNDRY. 

(See  also  Cast-iron,  pp.  437  to  445,  and  Fans  and  Blowers,  pp.  653  to  673.) 

Cupola  Practice. 

The  following  table  and  the  notes  accompanying  it  are  condensed  from 
an  article  by  Simpson  Bolland  in  Am.  Mach.,  June  30,  1892: 


Diam.  of  lining  in 

36 

48 

54 

60 

66 

72 

84 

Height  to  char'g  door,  ft.  .. 
Fuel  used  in  bed,  Ibs  

12 
840 

13 
1380 

14 

1650 

15 

1920 

15 
2190 

16 

2460 

16 
3000 

First  charge  of  iron,  Ibs..  .  . 
Other  fuel  charges,  Ibs  

2520 
302 

4140 
554 

4950 
680 

5760 
806 

6570 
932 

7380 
1058 

9000 
1310 

Other  iron  charges,  Ibs  
Diam.  blast  pipe,  in  

2718 
14 

4986 
18 

6120 
20 

7254 
22 

8388 
22 

9522 
24 

11,790 
26 

No.  of  6-in.  round  tuyeres.  . 
Equiv.  No.  flat  tuyeres  
Width  of  flat  tuyeres,  in  — 
Height  of  flat  tuyeres,  in.  .  . 
Blast  pressure  oz 

3.7 
4 

2 
13.5 
8 

6.8 
6 
2.5 
13.5 
12 

10.7 
8 
2.5 
15.5 
14 

13.7 
8 

16.5 
14 

15.4 
8 

18.5 
14 

19 
10 
3 

18.5 
16 

31 
16 
3.5 
16 
16 

Size  of  Root  blower,  No  
Revs,  per  min  

2 
241 

4 
212 

4 
277 

5 

192 

240 

6 
163 

160 

Engine  for  blower,  H.P  
Sturtevant  blower,  No  
Engine  for  blower,  H.P  
Melting  cap.,  Ibs.  per  hr.  .  .  . 

2.5 
4 
3 
4820 

10 
6 

93/4 

10,760 

14 

7 
16 
13,850 

,8V, 

22 
16,940 

23 
8 
22 
21,200 

33 
9 
35 
26,070 

47 
10 
48 
37,530 

Mr.  Bolland  says  that  the  melting  capacities  in  the  table  are  not  sup-; 
posed  to  be  all  that  can  be  melted  in  the  hour  by  some  of  the  best  cupolas, 
but  are  simply  the  amounts  which  a  common  cupola  under  ordinary 
circumstances  may  be  expected  to  melt  in  the  time  specified. 

By  height  of  cupola  is  meant  the  distance  from  the  base  to  the  bottom 
side  of  the  charging  door.  The  distance  from  the  sand-bed,  after  it  has 
been  formed  at  the  bottom  of  the  cupola,  up  to  the  under  side  of  the 
tuyeres  is  taken  at  10  ins.  in  all  cases. 

All  the  amounts  for  fuel  are  based  upon  a  bottom  of  10  ins.  deep.  The 
quantity  of  fuel  used  on  the  bed  is  more  in  proportion  as  the  depth  is 
increased,  and  less  when  it  is  made  shallower. 

The  amount  of  fuel  required  on  the  bed  is  based  on  the  supposition  that 
the  cupola  is  a  straight  one  all  through,  and  that  the  bottom  is  10  ins. 
deep.  If  the  bottom  be  more,  as  in  those  of  the  Colliau  type,  then  addi- 
tional fuel  will  be  needed. 

First  Charge  of  Iron.  —  The  amounts  given  are  safe  figures  to  work  upon 
in  every  instance,  yet  it  will  always  be  in  order,  after  proving  the  ability 
of  the  bed  to  carry  the  load  quoted,  to  make  a  slow  and  gradual  increase 
of  the  load  until  it  is  fully  demonstrated  just  how  much  burden  the  bed 
will  carry. 

Succeeding  Charges  of  Fuel  and  Iron.  —  The  highest  proportions  are 
not  favored,  for  the  simple  reason  that  successful  melting  with  any  greater 
proportion  of  iron  to  fuel  is  not  the  rule,  but,  rather,  the  except^n. 

Diameter  of  Main  Blast-pipe.  —  The  sizes  given  are  of  sufficient  area 
for  all  lengths  up  to  100  feet. 

Tuyeres.  —  Any  arrangement  or  disposition  of  tuyeres  may  be  made, 
which  shall  answer  in  their  totality  to  the  areas  given  in  the  table.  On  no 
consideration  must  the  tuyere  area  be  reduced;  thus,  an  84-inch  cupola 
must  have  tuyere  area  equal  to  31  pipes  6  ins.  diam.,  or  16  flat  tuyeres 
16  X  31/2  ins.  The  tuyeres  should  be  arranged  in  such  a  manner  as  will 
concentrate  the  fire  at  the  melting-point  into  the  smallest  possible  com- 
pass, so  that  the  metal  in  fusion  will  have  less-  space  to  traverse  while 
exposed  to  the  oxidizing  influence  of  the  blast. 

To  accomplish  this,  recourse  has  been  had  to  the  placing  of  additional 
rows  of  tuyeres  in  some  instances — the  "Stewart  rapid  cupola"  having 
three  rows,  and  the  "Colliau  cupola,  furnace"  having  two  rows,  of  tuyeres* 


1248  THE   FOUNDRY. 

[Cupolas  as  large  as  84  inches  in  diameter  are  now  (1906)  built  without 
boshes.  The  most  recent  development  with  this  size"  cupola  is  to  place  a 
center  tuyere  in  the  bottom  discharging  air  vertically  upwards.] 

Blast-pressure.  —  About  30,000  cu.  ft.  of  air  are  consumed  in  melting  a 
ton  of  iron,  which  would  weigh  about  2400  pounds,  or  more  than  both 
iron  and  fuel.  When  the  proper  quantity  of  air  is  supplied,  the  com- 
bustion of  the  fuel  is  perfect,  and  carbonic-acid  gas  is  the  result.  When 
the  supply  of  air  is  insufficient,  the  combustion  is  imperfect,  and  car- 
bonic-oxide gas  is  the  result.  The  amount  of  heat  evolved  in  these  two 
cases  is  as  15  to  4V2,  showing  a  loss  of  over  two-thirds  of  the  heat  by 
imperfect  combustion.  fCombustion  is  never  perfect  in  the  cupola  except 
near  the  tuyeres.  The  CO2  formed  by  complete  combustion  is  largely 
reduced  to  CO  in  passing  through  the  hot  coke  above  the  fusion  zone.] 

It  is  not  always  true  that  we  obtain  the  most  rapid  melting  when  we  are 
forcing  into  the  cupola  the  largest  quantity  of  air.  Too  much  air  absorbs 
heat,  reduces  the  temperature,  and  retards  combustion,  and  the  fire  in  the 
cupola  may  be  extinguished  with  too  much  blast. 

Slag  in  Cupolas.  —  A  certain  amount  of  slag  is  necessary  to  protect  the 
molten  iron  which  has  fallen  to  the  bottom  from  the  action  of  the  blast ;  if 
it  was  not  there,  the  iron  would  suffer  from  decarbonization. 

When  slag  from  any  cause  forms  in  too  great  abundance,  it  should  be 
led  away  by  inserting  a  hole  a  little  below  the  tuyeres,  through  which  it 
will  find  its  way  as  the  iron  rises  in  the  bottom. 

With  clean  iron  and  fuel,  slag  seldom  forms  to  any  appreciable  extent 
in  small  heats;  but  when  the  cupola  is  to  be  taxed  to  its  utmost  capacity 
it  is  then  incumbent  on  the  melter  to  flux  the  charges  all  through  the  heat, 
carrying  it  away  in  the  manner  directed. 

The  best  flux  for  this  purp9se  is  the  chips  from  a  white-marble  yard. 
About  6  pounds  to  the  ton  of  iron  will  give  good  results  when  all  is  clean. 
[Fluor-spar  is  now  largely  used  as  a  flux.] 

When  fuel  is  bad,  or  iron  is  dirty,  or  both  together,  it  becomes  imperative 
that  the  slag  be  kept  running  all  the  time. 

Fuel  for  Cupolas.  —  The  best  fuel  for  melting  iron  is  coke,  because  it 
requires  less  blast,  makes  hotter  iron,  and  melts  faster  than  coal.  When 
coal  must  be  used,  care  should  be  exercised  in  its  selection.  All  anthra- 
cites which  are  bright,  black,  hard,  and  free  from  slate,  will  melt  iron 
admirably.  For  the  best  results,  small  cupolas  should  be  charged  with 
the  size  called  "egg,"  a  still  larger  grade  for  medium-sized  cupolas,  and 
what  is  called  "lump"  will  answer  for  all  large  cupolas,  when  care  is  taken 
to  pack  it  carefully  on  the  charges. 

Melting   Capacity   of   Different   Cupolas.  —  The  following    figures 
are  given  by  W.  B.  Snow,  in   The  Foundry,  Aug.,   1908,  showing  the 
records  of  capacity  and  the  blast  pressure  of  several  cupolas: 
Diam.  of  lining, 

ins 44      44      47      49      54      54      54      60      60      60      74 

Tons  per  hour ..    6.7     7.3     8.4     9.1     7.7     8.8    10.212.414.813.813.0 
Pressure,  oz.  per 

sq.  in 12.9  16.4  17.5  11.8  13.6  11.0  20.8  15.5  16.8  12.6     8.7 

From  plotted  diagrams  of  records  of  46  tests  of  different  cupolas  the 
following  figures  are  obtained: 

Diam.  of  lining,  ins 30     36      42      48      54        60        66         72 

Max.  tons  per  hour 3        5       7.3      9.512        15        18         21 

Avge.     "     "       "      2.5     4       5.5       7.5     9        11        13         16 

Max.  pressure,  oz 11      12     13.5     14     14.6     15.2     15.7      16 

For  a  given  cupola  and  blower  the  melting  rate  increases  as  the  square 
root  of  the  pressure.  A  cupola  melting  9  tons  per  hour  with  10  ounces 
pressure  will  melt  about  10  tons  with  12.5  ounces,  and  11  t9ns  with  15 
ounces.  The  power  required  varies  as  the  cube  of  the  melting  rate,  so 
that  it  would  require  (11/9)3  =  1.82  times  as  much  power  for  11  tons  as 
for  9  tons.  Hence  the  advantage  of  large  cupolas  and  blowers  with  light 
pressures. 

Charging  a  Cupola.  —  Chas.  A.  Smith  (Am.  Mach.,  Feb.  12,  1891) 
gives  the  following:  A  28-in.  cupola  should  have  from  300  to  400  Ibs.  of 
coke  on  bottom  bed;  a  36-in.  cupola,  700  to  800  Ibs.;  a  48-in.  cupola, 
1500  Ibs.;  and  a  60-in,  cupola  should  have  one  ton  of  fuel  ou  bottom  bed, 


THE   FOUNDRY. 


1249 


To  every  pound  of  fuel  on  the  bed,  three,  and  sometimes  four  pounds  of 
metal  can  be  added  with  safety,  if  the  cupola  has  proper  blast ;  in  after- 
charges,  to  every  pound  of  fuel  add  8  to  10  pounds  of  metal;  any  well- 
constructed  cupola  will  stand  ten. 

F.  P.  Wolcott  (Am.  Mach.,  Mar.  5,  1891)  gives  the  following  as  the 
practice  of  the  Colwell  Iron-works,  Carteret,  N.  J.:  "We  melt  daily  from 
twenty  to  forty  tons  of  iron,  with  an  average  of  11.2  pounds  of  iron  to 
one  of  fuel.  In  a  36-in.  cupola  seven  to  nine  pounds  is  good  melting, 
but  in  a  cupola  that  lines  up  48  to  60  inches,  anything  less  than  nine 
pounds  shows  a  defect  in  arrangement  of  tuyeres  or  strength  of  blast, 
or  in  charging  up." 

"The  Holder's  Text-book,"  by  Thos.  D.  West,  gives  forty-six  reports 
in  tabular  form  of  cupola  practice  in  thirty  States,  reaching  from  Maine 
to  Oregon. 

Improvement  of  Cupola  Practice.  —  The  following  records  are  given 
by  J.  R.  Fortune  and  H.  S.  Wells  (Proc.  A.  S.  M.  E.t  Mar.,  1908)  showing 
how  ordinary  cupola  practice  may  be  improved  by  making  a  few  changes. 
The  cupola  is  13  ft.  4  in.  in  height  from  the  top  of  the  sand  bottom  to 
the  charging  door,  and  of  three  diameters,  50  in.  for  the  first  3  ft.  6  in., 
then  54  in.  for  the  next  2  ft.  4  in.,  then  60  in.  to  the  top.  When  driven 
with  a  No.  8  Stuftevant  blower,  the  maximum  melting  rate,  from  iron 
down  to  blast  otf,  was  8.5  tons  per  hour.  A  No.  11  high-pressure  blower 
was  then  installed.  Test  No.  1  in  the  table  below  gives  the  result  with 
cupola  charges  as  follows  in  pounds:  Bed,  590  coke,  followed  by  826  coke, 
2000  iron;  400  co&e,  2000  iron;  300  coke,  2000  iron;  and  thereafter  all 
charges  were  200  eoke,  2000  iron.  The  time  between  starting  fire  and  start- 
ing blast  was  2  hr.  30  min.,  and  the  time  from  blast  on  to  iron  down, 
11  min.  The  melting  rate,  tons  per  hour,  is  figured  for  the  time  from 
iron  down  to  blast  off.  The  tuyeres  were  eight  rectangular  openings 
Hi/4  in.  high  and  of  a  total  area  of  1/9.02  of  the  area  of  the  54-in.  circle. 


No.  of  Test. 

1 

2 

8 

9 

10 

22.35 
11   17 

Total  tons... 
Tons  per  hr 

22.7 
9  45 

24. 
8  88 

22.15 
8  86 

24.25 
9  15 

24.25 
9  66 

22.65 
10  24 

24. 
10  43 

20.30 
10  91 

23.85 
11  35 

Lbs.  per  min* 
Iron  -T-  cokef 
Blast,  oz  

19.81 
7.54 
11.60 

18.61 
7.40 
10.63 

18.55 
7.28 
10.00 

19.17 
8.58 
9.47 

20.25 
8.94 
9.80 

21.44 
8.71 
9.86 

21.82 
9.02 
10.00 

22.95 
9.02 
10.13 

23.77 
10.02 
10.55 

23.39 
9.49 
10.55 

*  Per  sq.  ft.  cupola  area  at  54  in.  diam.  from  iron  down  to  blast  off. 
t  Including  bed.     • 

The  tuyeres  were  then  enlarged,  making  their  area  1/5.98  of  the  cupola 
(54  in.)  area,  and  the  results  are  shown  in  tests  No.  2  and  3  of  the  table. 
The  iron  was  too  hot,  and  the  coke  charge  was  decreased  to  a  ratio  of 
1/13.33  instead  of  1/10,  the  bed  of  coke  being  increased.  The  result, 
test  No.  4,  was  an  increased  rate  of  melting,  a  decrease  in  the  amount  of 
coke,  and  a  decrease  in  the  blast  pressure.  Tests  5,  6,  7,  8  and  9  were 
then  made,  the  coke  being  decreased,  while  the  blast  pressure  was  in- 
creased, resulting  in  a  decided  increase  in  the  melting  speed.  In  tests 
5,  6  and  7  the  iron  layer  was  13.33  times  the  weight  of  the  coke  layer; 
in  test  8,  14.28  times;  and  in  test  9,  15.38  times.  In  test  9  it  was  noticed 
that  the  iron  was  not  at  the  proper  temperature,  and  in  test  10  the  coke 
layer  was  increased  to  a  ratio  of  1  to  14.28  without  altering  the  blast 
pressure;  this  resulted  in  a  decreased  melt  per  hour.  It  has  been  found 
that  a  coke  charge  of  150  Ibs.  to  2000  Ibs.  of  iron,  with  a  blast  pressure 
of  10.5  ounces,  results  in  a  melt  of  11.5  tons  per  hour,  the  iron  coming 
down  at  the  proper  temperature. 

An  excess  of  coke  decreases  the  melting  rate.  Iron  in  the  cupola  is 
melted  in  a  fixed  zone,  the  first  charge  9f  iron  above  the  bed  being  melted 
by  burning  coke  in  the  bed.  As  this  iron  is  melted,  the  charge  of  coke 
above  it  descends  and  restores  to  the  bed  the  amount  which  has  been 
burned  away.  If  there  is  too  much  coke  in  the  charge,  the  iron  is  held 
above  the  melting  zone,  and  the  excess  coke  must  be  burned  away  before 
it  can  be  melted,  and  this  of  course  decreases  the  economy  and  the  melting 
speed. 


1250 


THE    FOUNDRY. 


Cupola  Charges  in  Stove-foundries.  (Iron  Age,  April  14,  1892.)  — 
No  two  cupolas  are  charged  exactly  the  same.  The  amount  of  fuel  on 
the  bed  or  between  the  charges  differs,  while  varying  amounts  of  iron  are 
used  in  the  charges.  Below  will  be  found  charging-lists  from  some  of  the 
prominent  stove-foundries  in  the  country: 


Ibs. 

A— Bed  of  f uel,  coke 1,500 

First  charge  of  iron 5,000 

All  other  charges  of  iron 1,000 

First  and  second  charges  of 
coke,  each 200 


Ibs. 
Four  next  charges  of  coke, 

each 150 

Six  next  charges  of  coke,  each  120 
Nineteen  next  charges  of  coke, 

each 100 


Thus  for  a  melt  of  18  tons  there  would  be  5120  Ibs.  of  coke  used,  giving 
a  ratio  of  7  to  1.  Increase  the  amount  of  iron  melted  to  24  tons,  and  a 
ratio  of  8  pounds  of  iron  to  1  of  coal  is  obtained. 


Ibs. 


Ibs 


Second  and  third  charges  of 
fuel 130 

All  other  charges  of  fuel, 
each 100 


B— Bed  of  fuel,  coke 1,600 

First  charge  of  iron 1 ,800 

First  charge  of  fuel .........       1 50 

All   other  charges  of   iron, 

each 1,000 

For  an  18-ton  melt  5060  Ibs.  of  coke  would  be  necessary,  giving  a  ratio 
of  7.1  Ibs.  of  iron  to  1  pound  of  coke. 
Ibs. 

C— Bed  of  fuel,  coke 1,600 

First  charge  of  iron 4,000 

First  and  second  charges  of 

coke 200 

In  a  melt  of  18  tons  4100  Ibs.  of  coke  would  be  used,  or  a  ratio  of  8.5  to  1. 


All  other  charges  of  iron . . . 
All  other  charges  of  coke. . . 


Ibs. 

2,000 

150 


Ibs. 

D— Bed  of  fuel,  coke 1 ,800 

First  charge  of  iron 5,600 


Ibs. 

All  charges  of  coke,  each 200 

All  other  charges  of  iron 2,900 


In  a  melt  of  18  tons,  3900  ibs.  of  fuel  would  be  used,  giving  a  ratio  of 
9.4  pounds  of  iron  to  1  of  coke.     Very  high,  indeed,  for  stove-plate. 

Ibs. 


All  other  charges  of  iron,  each  2,000 
All  other  charges  of  coal,  each      175 


Ibs. 

E-Bed  of  fuel,  coal 1,900 

First  charge  of  iron 5,000 

First  charge  of  coal 200 

In  a  melt  of  18  tons  4700  Ibs.  of  coal  would  be  used,  giving  a  ratio  of 
7.7  Ibs.  of  iron  to  1  Ib.  of  coal. 

These  are  sufficient  to  demonstrate  the  varying  practices  existing 
among  different  stove-foundries.  In  all  these  places  the  iron  was  proper 
for  stove-plate  purposes,  and  apparently  there  was  little  or  no  difference 
in  the  kind  of  work  in  the  sand  at  the  different  foundries. 

Foundry  Blower  Practice.  (W.  B.  Snow,  Trans.  A.  S.  M.  E.t 
1907.)  —  The  velocity  of  air  produced  by  a  blower  is  expressed  by  the 
formula  V  =  ^2  gp/d.  If  p,  the  pressure,  is  taken  in  ounces  per  sq.  in., 
and  d,  the  density,  in  pounds  per  cu.  ft.  of  dry  air  at  50°  and  atmospheric 
pressure  of  14.69  Ibs.  or  235  ounces.  =  0.77884  Ib.,  the  formula  reduces 
to'F  =  v^.746, 700  p/(235  4-  p),  no  allowance  being  made  for  change  of 
temperature  during  discharge.  From  this  formula  the  following  figures 
are  obtained.  Q  =  volume  discharged  per  min.  through  an  orifice  of 
1  sq.  ft.  effective  area,  H.P.  =  horse-power  required  to  move  the  given 
volume  under  the  given  conditions,  p  =  pressure  in  ounces  per  sq.  in. 


P 
I 

2 
3 

4 
5 

Q 

H.P. 

P 
6 
7 
8 
9 
10 

Q 

H.P. 

P 

Q 

H.P. 

P 

0 

H  .P. 

35.85 
50.59 
61.83 
71.24 
79.48 

0.00978 
0.02759 
0.05058 
0.07771 
0.1084 

86.89 
93.66 
99.92 
105.76 
111.25 

0.1422 
0.1788 
0.2180 
0.2596 
0.3034 

11 
12 
13 
14 
15 

116.45 
121.38 
126.06 
130.57 
134.89 

0.3493 
0.3972 
0.447C 
0.4986 
0.5518 

16 
17 
18 
19 
20 

139.03 
143.03 
146.88 
150.61 
154.22 

0.6067 
0.6631 
0.7211 
0.7804 
0.8412 

The  greatest  effective  area  over  which  a  fan  will  maintain  the  maximum 
velocity  of  discharge  is  known  as  the  "capacity  area"  or  "square  inches 
of  blast."  As  originally  established  by  Sturtevant  it  is  represented  by 
=  diam,  of  wheel  in  ins.,  W  =  width  of  wheel  at  circumference, 


THE    FOUNDRY. 


1251 


In  inches.  For  the  ordinary  type  of  fan  at  constant  speed  maximum 
efficiency  and  power  are  secured  at  or  near  the  capacity  area;  the  powei 
per  unit  of  volume  and  the  pressure  decrease  as  the  discharge  area  and 
volume  increase;  with  closed  outlet  the  power  is  approximately  one-third 
of  that  at  capacity  area. 

The  following  table  is  calculated  on  these  bases:  Capacity  area  per  inch 
of  width  at  periphery  of  wheel  =  1/3  of  diam.  Air,  50°  F.  Velocity 
of  discharge  =  circumferential  speed  of  the  wheel.  Power  =  double  the 
theoretical.  In  rotary  positive  blowers,  as  well  as  in  fans,  the  velocity 
and  the  volume  vary  as  the  number  of  revolutions,  the  pressure  varies 
as  the  square,  and  the  power  as  the  cube  of  the  number  of  revolutions. 
In  the  fan,  however,  increase  of  pressure  can  be  had  only  by  increasing 
the  revolutions,  while  in  the  rotary  blower  a  great  range  of  pressure  is 
obtainable  with  constant  speed  by  merely  varying  the  resistance.  With  a 
rotary  blower  at  constant  speed,  theoretically,  and  disregarding  the  effect 
of  changes  in  temperature  arid  density,  the  volume  is  constant:  the  velocity 
varies  inversely  as  the  effective  outlet  area;  the  pressure  varies  inversely 
as  the  square  of  the  outlet  area,  hence  as  the  square  of  the  velocity; 
and  the  power  varies  directly  as  the  pressure.  The  maximum  power  is 
required  when  a  fan  discharges  against  the  least,  and  when  a  rotary 
blower  discharges  against  the  greatest  resistance. 

PERFORMANCE  OF  CUPOLA  FAN  BLOWERS  AT  CAPACITY  AREA  PER  INCH 
OF  PERIPHERAL  WIDTH. 


B 

o'S 

P 

.2-3 

Q£ 

Item. 

Total  Pressure  in  Ounces  per  Square  Inch. 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

»! 

r.p.m. 
cu.  ft. 
h.p. 

2660.0 
520.0 
1.7 

2860.0 
560.0 
2.1 

3050.0 
600.0 
2.6 

3230.0 
640.0 
3.1 

3400.0 
670.0 
3.6 

3560.0 
700.0 
4.2 

3710.0 
730.0 
4.8 

3850.0 
760.0 
5.4 

3990.0 
780.0 
6.0 

4120.0 
810.0 
6.6 

4250.0 
830.0 
7.3 

-1 

r.p.m. 
cu.  ft. 
h.p. 

2000.0 
700.0 
2.3 

2150.0 
750.0 
2.9 

2290.0 
800.0 
3.5 

2420.0 
850.0 
4.2 

2550.0 
890.0 
4.9 

2670.0 
930.0 
5.6 

2780.0 
970.0 
6.4 

2890.0 
1010.0 
7.1 

2990.0 
1040.0 
8.0 

3090.0 
1080.0 
8.8 

3190.0 
1110.0 
9.7 

-1 

r.p.m. 
cu.  ft. 
h.p. 

1590.0 
870.0 
2.8 

1720.0 
940.0 
3.6 

1830.0 
1000.0 
4.4 

1940.0 
1060.0 
5.2 

2040.0 
1110.0 
6.1 

2140.0 
1160.0 
7.0 

2230.0 
1210.0 
7.9 

2310.0 
1260.0 
8.9 

2390.0 
1310.0 
10.0 

2470.0 
1350.0 
11.0 

2550.0 
1390.0 
12.1 

-1 

r.p.m. 
cu.  ft. 
h.p. 

1330.0 
1040.0 

1430.0 
1120.0 

1530.0 
1200.0 

1620.0 
1270.0 

1700.0 
1340.0 

1780.0 
1400.0 

1850.0 
1460.0 

1930.0 
15100 

2000.0 
1570  0 

2060.0 
16200 

2120.0 
16700 

3.4 

4.3 

5.2 

6.2 

7.3 

8.4 

9.5 

10.7 

11.9 

13.2 

14.5 

-! 

r.p.m. 
cu.  ft. 
h.p. 

1140.0 
1220.0 
3.9 

1230.0 
1310.0 
5.0 

1310.0 
1400.0 
6.1 

1380.0 
1480.0 
7.3 

1460.0 
1560.0 
8.5 

1530.0 
1630.0 
9.8 

1590.0 
1700.0 
11.1 

1650.0 
1770.0 
12.5 

1710.0 
1830.0 
13.9 

1770.0 
1890.0 
15.4 

1820.0 
1950.0 
17.0 

•1 

r.p.m. 
cu.  ft. 
h.p. 

1000.0 
1390.0 
4.5 

1070.0 
1500.0 
5.7 

1150.0 
1600.0 
7.0 

1210.0 
1690.0 
8.3 

1270.0 
1780.0 
9.7 

1330.0 
1860.0 
11.2 

1390.0 
1940.0 
12.7 

1450.0 
2020.0 
14.3 

1500.0 
2090.0 
15.9 

1550.0 
2160.0 
17.7 

1590.0 
2230.0 
21.0 

The  air  supply  required  by  a  cupola  varies  with  the  melting  ratio,  the 
density  of  the  charges,  and  the  incidental  leakage.  Average  practice  is 
represented  by  the  following: 

Lbs.  iron  per  Ib.  coke 6  7  8  9  10 

Cu.  ft.  air  per  ton  of  iron 33,000    31,00029,000    27,00025,000 

It  is  customary  to  provide  blower  capacity  on  a  basis  of  30,000  cu.  ft., 
which  corresp9nds  to  75  to  80%  of  the  chemical  requirements  for  complete 
combustion  with  average  coke,  and  a  melting  ratio  of  7.5  to  1. 

In  comparative  tests  with  a  54-inch  lining  cupola  under  identical  con- 
ditions as  to  contents,  alternately  run  with  a  No.  10  Sturtevant  fan  and 
a  33  cu.  ft.  Connersville  rotary,  with  the  fan  the  pressure  varied  between 
12V2  and  141/8  ounces  in  the  wind  box,  the  net  power  from  25  to  38.5  H.P., 
while  with  the  rotary  blower  the  pressure  varied  between  10 1/2  and  25 
ounces,  and  the  power  between  19  and  45  H,P.  With  the  fan  28.84  tons 


1252 


THE   FOUNDRY. 


were  melted  m  3.77  hours,  or  7.65  tons  per  hour,  while  with  the  rotary 
Dlower  2.82  hours  were  required  to  melt  31.5  tons,  an  hourly  rate  of  10  6 
tons,  an  increase  of  nearly  40  per  cent  in  output.  This  reduces  to  a  net 
input  of  4.09  H.P.  per  ton  melted  per  hour  with  the  fan,  and  2.98  H.P. 
with  the  rotary  blower;  an  apparent  advantage  of  27%  in  favor  of  the 
rotary.  Had  the  rotary  been  of  smaller  capacity  such  excessive  pressures 
would  not  have  been  necessary,  the  power  would  have  been  decreased, 
and  the  duration  of  the  heat  prolonged,  with  probable  decrease  in  the 
H.P.  hours  per  ton.  Had  the  fan  been  run  at  higher  speed  the  H.P. 
would  have  increased,  the  time  decreased  and  the  power  per  ton  per  hour 
would  have  more  closely  approached  that  required  by  the  rotary  blower. 
Theoretically,  for  otherwise  constant  conditions,  the  following  relations 
hold  for  cupolas  and  melting  rates  within  the  range  of  practical  operation: 

For  a  givenjcupolaj For  a  given  melting  rate:     For  a  given  volume; 

M  oc  F.v/P.or^/HJP.  V  oc  1  -r-  Z>*  M*D 

V^M  P  oc  d  For  a  given  cupola 

P  oo  F2  H.P.  oc  P  or  1  •*•  D«  E  OG  M2,  or  P 

H.P.  oc  Af3  or  VP*  E  oc  M,  P,  or  1  •*•  D4  Duration  of  heat 

oc  1  -f-  Vp 

M  =  melting  rate;  V  =  volume;  P  =  pressure;  H.P.  =  horse-power; 
D  =  diam.  of  lining;  E  =  operating  efficiency  =  power  per  ton  per  hour; 
d  =  depth  of  the  charge;  oc,  varies  as. 

These  relations  might  be  the  source  of  formulae  for  practical  use  were 
it  possible  to  establish  accurate  coefficients.  But  the  variety  in  cupolas, 
tuyere  proportions,  character  of  fuel  and  iron,  and  difference  in  charging 
practice  are  bewildering  and  discouraging.  Maximum  efficiency  in  a 
given  case  can  only  be  assured  after  direct  experiment.  Something  short 
of  the  maximum  is  usually  accepted  in  ignorance  of  the  ultimate  possi- 
bilities. 

The  actual  melting  range  of  a  cupola  is  ordinarily  between  0.6  and 
0.75  ton  per  hour  per  sq.  ft.  of  cross  section.  The  limits  of  air  supply 
per  minute  per  sq.  ft.  are  roughly  2500  and  4000  cu.  ft.  The  possible 
power  required  varies  even  more  widely,  ranging  from  1.5  to  3.75  H.P. 
per  sq.  ft.,  corresponding  to  2.5  and  5  H.P.  per  ton  per  hour  for  the  melting 
rates  specified.  The  power  may  be  roughly  calculated,  from  the  theoreti- 
cal requirement  of  0.27  H.P.  to  deliver  1000  cu.  ft.  per  minute  against 
1  oz.  pressure.  The  rjower  increases  directly  with  the  pressure,  and  de- 
pends also  on  the  efficiency  of.  the  blower.  Current  practice  can  only  be 
expressed  between  limits  as  in  the  following  table. 

RANGE  OF  PERFORMANCE  OF  CUPOLA  BLOWERS. 


Diameter  inside 
Lining,  in. 

Capacity  per 
Hour,  tons. 

Pressure 
per  sq. 
m.,  oz. 

Volume  of  Air 
permin.,  cu.  ft. 

Horse- 
power. 

18 

0  25-  0.5 

5-  7 

150^     300 

05-15 

24  .. 

1.00-  1.5 

7-  9 

600-     900 

20-60 

30 

2  00-  3  5 

8-11 

1  200-  2  000 

5  0-  15  0 

36     . 

4.00-  5.0 

8-12 

2  200-  2  800 

10  0-  23  0 

42... 

5.00-  7.0 

8-13 

2,700-  3,700 

12.0-  32.0 

48 

8  00-10  0 

8-13 

4  000-  5  000 

18  0-  45  0 

54... 

9.00-12.0 

9-14 

4,500-  6,000 

22.0-  60.0 

60 

12  00-15  0 

9-14 

6  000-  7  500 

30  0-  75  0 

66... 

14.00-18.0 

9-15 

7,000-  9  000 

35.0-  90  0 

72 

17  00-21  0 

10-15 

8  500-  10'  500 

45  0-110  0 

78  

19  00-24.0 

10-16 

9,500-12,000 

52.0-130  0 

84  

21.00-27.0 

10-16 

10,500-13,500 

60.0-150.0 

Results  of  Increased  Driving.  (Erie  City  Iron-works,  1891.)  — 
May-Dec.,  1890:  60-in.  cupola,  100  tons  clean  castings  a  week,  melting 
8  tons  per  hour;  iron  per  pound  of  fuel,  7V2  Iks.;  per  cent  weight  of  good 
castings  to  iron  charged,  753/4.  Jan.-May,  1891:  Increased  rate  of  melt- 
ing to  111/2  tons  per  hour:  iron  per  Ib.  fuel,  91/2;  per  cent  weight  of  good 
castings,  75;  one  week,  131/4  tons  per  hour,  10.3  Ibs.  iron  per  Ib.  fuel; 
per  cent  weight  of  good  castings,  75.3.  The  increase  was  made  by  putting 
m  an  additional  row  of  tuyeres  and  using  stronger  blast,  14  ounces.  Coke 
was  used  as  fuel.  (W.  O.  Webber,  Trans.  A.  S.  M .  E.,  xii,  1045.) 


THE  FOUNDRY.  1253 

Power  Required  for  a  Cupola  Fan.  (Thos.  D.  West,  The  Foundry, 
April,  1904.)  — The  power  required  when  a  fan  is  connected  with  a  cupola 
depends  on  the  length  and  diameter  of  the  piping,  the  number  of  bends, 
valves,  etc.,  and  on  the  resistance  to  the  passage  of  blast  through  the 
cupola.  The  approximate  power  required  in  everyday  practice  is  the 
difference  between  the  power  required  to  run  the  fan  with  the  outlet  open 
and  with  it  closed.  Another  rule  is  to  take  75%  of  the  maximum  power 
or  that  with  the  outlet  open.  A  fan  driving  a  cupola  66  ins.  diam., 
1800  r.p.m.,  driven  by  an  electric  motor  required  horse-power  and  gave 
pressures  as  follows  :  Outlet  open,  146.6;  outlet  closed,  37.2,  pressure 
15  oz.;  attached  to  cupola,  with  no  fuel  in  it,  120.5,  5  oz.;  after  kindling 
and  coke  had  been  fired,  101.0,  10  oz.;  during  the  run  70.8  to  76.7,  11  to 
13  oz.,  the  variations  being  due  to  changes  in  the  resistances  to  the  passage 
of  the  blast. 

Utilization  of  Cupola  Gases. — Jules  De  Clercy,  in  a  paper  read 
before  the  Amer.  Foundrymen's  Assn.,  advises  the  return  of  a  portion  of 
the  gases  from  the  upper  part  of  the  charge  to  the  tuyeres,  and  thus 
utilizing  the  carbon  monoxide  they  contain.  He  says  that  A.  Baillot 
has  thereby  succeeded  in  melting  15  Ibs.  of  iron  per  Ib.  of  coke,  and  at  the 
same  time  obtained  a  greater  melting  speed  and  a  superior  quality  of 
castings. 

Loss  in  Melting  Iron  in  Cupolas.  —  G.  O.  Vair,  Am.  Mack.,  March 
5,  1891,  gives  a  record  of  a  45-in.  Colliau  cupola  as  follows: 

Ratio  of  fuel  to  iron,  1  to  7.42. 
Good  castings 21,314  Ibs. 

K             New  scrap 3,005    " 
Millings 200    " 
Loss  of  metal 1,481    ' 
Amount  melted 26,000  Ibs. 
Loss  of  metal,  5.69%.    Ratio  of  loss,  1  to  17.55. 
se  of  Softeners    in  Foundry  Practice.       (W.  Graham,  Iron  Age, 
June  27,  1889.)  —  In  the  foundry  the  problem  is  to  have  the  right  pro- 
portions of  combined  and  graphitic  carbon  in  the  resulting  casting;  this 
is  done  by  getting  the  proper  proportion  of  silicon.     The  variations  in 
the  proportions  of  silicon  afford   a  reliable  and  inexpensive  means  of 
producing  a  cast  iron  of  any  required  mechanical  charae-ter  which  is 
possible  with  the  material  employed.     In  this  way,  by  mixing  suitable 
irons  in  the  right  proportions,  a  required  grade  of  casting  can  be  made 
more  cheaply  than  by  using  irons  in  which  the  necessary  proportions  are 
already  found. 

Hard  irons,  mottled  and  white  irons,  and  even  steel  scrap,  all  containing 
low  percentages  of  silicon  and  high  percentages  of  combined  carbon, 
could  be  employed  if  an  iron  having  a  large  amount  of  silicon  were  mixed 
with  them  in  sufficient  amount.  This  would  bring  the  silicon  to  the 
proper  proportion  and  would  cause  the  combined  carbon  to  be  forced  into 
the  graphitic  state,  and  the  resulting  casting  would  be  soft.  High-silicon 
irons  used  in  this  way  are  called  "softeners." 

Mr.  Keep  found  that  more  silicon  is  lost  during  the  remelting  of  pig  of 
over  10%  silicon  than  in  remelting  pig  iron  of  lower  percentages  of  silicon. 
He  also  points  out  the  possible  disadvantage  of  using  ferro-silicons  con- 
taining as  high  a  percentage  of  combined  carbon  as  0.70%  to  overcome 
the  bad  effects  of  combined  carbon  in  other  irons. 

The  Scotch  irons  generally  contain  much  more  phosphorus  than  is 
desired  in  irons  to  be  employed  in  making  the  strongest  castings.  It  is  a 
mistake  to  mix  with  strong  low-phosphorus  irons  an  iron  that  would 
increase  the  amount  of  phosphorus  for  the  sake  of  adding  softening 
qualities,  when  softness  can  be  produced  by  mixing  irons  of  the  same  low 
phosphorus. 

(For  further  discussion  of  the  influence  of  silicon,  see  pages  438  and  447.) 

Weakness  of  Large  Castings.  (W.  A.  Bole,  Trans.  A.  S.  M.  E., 
1907.)  —  Thin  castings,  by  virtue  of  their  more  rapid  cooling,  are  almost 
certain  to  be  stronger  per  unit  section  than  would  be  the  case  if  the  same 
metal  were  poured  into  larger  and  heavier  shapes.  Many  large  iron  castings 
are  of  questionable  strength,  because  of  internal  strains  and  lack  of  har- 
mony between  their  elements,  even  though  the  casting  is  poured  out  of  iron 
of  the  best  quality.  This  may  be  due  to  lack  of  experience  on  the  part  of 


1254:  THE   FOUNDRY. 


the  designer,  especially  in  the  cooling  and  shrinking  of  the  various  parts 
of  a  large  casting  after  being  poured. 

Castings  are  often  designed  with  a  .useless  multiplicity  9f  ribs,  walls, 
gussets,  brackets,  etc.,  which,  by  their  asynchronous  cooling  and  their 
inharmonious  shrinkage  and  contraction,  may  entirely  defeat  the  intention 
of  the  designer. 

There  are  some  castings  which,  by  virtue  of  their  shapes,  can  be  specially 
treated  by  the  foundryman,  and  artificial  cooling  of  certain  critical  parts 
may  be  effected  in  order  to  compel  such  parts  to  cool  more  rapidly  than 
they  would  naturally  do,  and  the  strength  of  the  casting  may  by  such 
means  be  beneficially  affected.  As  for  instance  in  the  case  of  a  fly-wheel 
with  heavy  rim  but  comparatively  light  arms  and  hub;  it  may  be  bene- 
ficial to  remove  the  flask  and  expose  the  rim  to  the  air  so  as  to  hasten  its 
natural  rate  of  cooling,  while  the  arms  and  hub  are  still  kept  muffled  up 
in  the  sand  of  the  mold  and  their  cooling  retarded  as  much  as  possible. 

Large  fillets  are  often  highly  detrimental  to  good  results.  Where  two 
walls  meet  and  intersect,  as  in  the  shape  of  a  T,  if  a  large  fillet  is  swept 
at  the  juncture,  there  will  be  a  pool  of  liquid  metal  at  this  point  which  will 
remain  liquid  for  a  longer  time  than  either  wall,  the  result  being  a  void, 
or  "draw,"  at  the  juncture  point. 

Risers  and  sink  heads  should  often  be  employed  on  iron  castings.  In 
large  iron-foundry  work  interior  cavities  may  exist  without  detection, 
and  some  of  these  may  be  avoided  by  the  use  of  suitable  feeding  devices, 
risers  and  sink  heads. 

Specimens  from  a  casting  having  at  one  point  a  tensile  strength  as  high 
as  30,250  Ibs.  per  sq.  in.  have  shown  as  low  as  20,500  in  another  and 
heavier  section.  Large  sections  cannot  be  cast  to  yield  the  high  strength 
of  specimen  test  pieces  cast  in  smaller  sections. 

The  paper  describes  a  successful  method  of  artificial  cooling,  by  means  of 
a  coil  of  pipe  with  flowing  water,  of  portions  of  molds  containing  cylinder 
heads  with  ports  cast  in  them.  Before  adopting  this  method  the  internal 
ribs  in  these  castings  always  cracked  by  contraction. 

Shrinkage  of  Castings.  —  The  allowance  necessary  for  shrinkage 
varies  for  different  kinds  of  metal,  and  the  different  conditions  under 
which  they  are  cast.  For  castings  where  the  thickness  runs  about  one 
inch,  cast  under  ordinary  conditions,  the  following  allowance  can  be  made: 

For  cast  iron,  Vs  inch  per  foot.  For  zinc,            5/16  inch  per  foot. 

'    brass,        3/16    '  •    tin,              1/12    ' 

"    steel,          V4  *    aluminum,  3/16    ' 

'    mal.  iron,  1/8  '    britannia,    V32    ' 

Thicker  castings,  under  the  same  conditions,  will  shrink  less,  and  thinner 
ones  more,  than  this  standard.  The  quality  of  the  material  and  the  man- 
ner of  molding  and  cooling  will  also  make  a  difference.  (See  also 
Shrinkage  of  Cast  Iron,  page  447.) 

Mr.  Keep  (Trans.  A.  S.  M.  E.,  vol.  xvi)  gives  the  following  "approxi- 
mate key  for  regulating  foundry  mixtures"  so  as  to  produce  a  shrinkage 
of  Vs  in.  per  ft.  in  castings  of  different  sections: 

Size  of  casting 1/2          1          2          3          4      in.  sq. 

Silicon  required,  per  cent 3.25     2.75     2.25     1.75      1.25  per  cent. 

Shrinkage  of  a  i/2-in.  test-bar..  0.125     .135     .145     .155      .165  in  per.  ft. 

Growth  of  Cast  Iron  by  Heating.  (Proc.  I.  and  S.  Inst.,  1909.)  — 
Investigations  by  Profs.  Rugan  and  Carpenter  confirm  Mr.  Outerbridge's 
experiments.  (See- page  449  )  They  found:  1.  Heating  white  iron  causes 
it  to  become  gray,  and  it  expands  more  than  sufficient  to  overcome  the 
original  shrinkage.  2.  Iron  when  heated  increases  in  weight,  probably 
due  to  absorption  of  oxygen.  3.  The  change  in  size  due  to  heating  is 
not  only  a  molecular  change,  but  also  a  chemical  one.  4.  The  growth  of 
one  bar  was  shown  to  be  due  to  penetration  of  gases.  When  heated  in 
vacuo  it  contracted. 

Hard  Iron  due  to  Excessive  Silicon.  —  W.  J.  Keep  in  Jour.  Am. 
Foundry  men's  Assn.,  Feb.,  1898,  reports  a  case  of  hard  iron  containing 
graphite,  3.04;  combined  C,  0.10;  Si,  3.97;  P,  0.61;  S,  0.05;  Mn,  0.56.  He 
says:  For  stove  plate  and  light  hardware  castings  it  is  an  advantage  to 
have  Si  as  high  as  3.50.  When  it  is  much  above  that  the  surface  of  the 
castings  often  become  very  hard,  though  the  center  will  be  very  soft. 


THE  FOUNDRY. 


1255 


The  surface  of  heavier  parts  of  a  casting  having  3.97  Si  will  be  harder  than 
the  surface  of  thinner  parts.  Ordinarily  if  a  casting  is  hard  an  increase 
of  silicon  softens  it,  but  after  reaching  3.00  or  3.50  per  cent,  silicon  hardens 

Ferro-Alloys  for  Foundry  Use.  E.  Houghton  (Iron  Tr.  Rev., 
Oct.  24,  1907.)  — The  objects  of  the  use  of  ferro-alloys  in  the  foundry  are: 
1,  to  act  as  deoxidizers  and  desulphurizers,  the  added  element  remaining 
only  in  small  quantities  in  the  finished  casting;  2,  to  alter  the  composition 
of  the  casting  and  so  to  control  its  mechanical  properties.  Some  of  these 
alloys  are  made  in  the  blast  furnace,  but  the  purest  grades  are  made  in 
the  electric  furnace.  The  following  table  shows  the  range  of  composition 
of  blast  furnace  alloys  made  by  the  Darwen  &  Mostyn  Iron  Co.  All  of 
these  alloys  may  be  made  of  purer  quality  in  the  electric  furnace. 


Ferro 
Mn. 

Spiegel- 
eisen. 

Silicon 
Spiegel. 

Ferro- 
sil. 

Ferro- 
phos. 

Ferro* 
Chrome. 

Mn... 

41.5-  87.9 
0.10-  0.63 
0.09-  0.20 
5.62-  7.00 
nil 

9.25-29.75 
0.42-  0.95 
0.06-  0.09 
3.94-  5.20 
nil-trace 

17.50-20.87 
9.45-14.23 
0.07-  0.10 
1.05-  1.89 
nil 

1.17-  2.20 
8.10-17.00 
0.06-  0.08 
0.90-  1.75 
0.02-  0.05 

3.00-  5.90 
0.50-  0.84 
15.71-20.50 
0.27-  0.30 
0.16-  0.33 

1.55-2.30 
0.13-0.36 
0.04-  0.07 
5.34-  7.12 
Cr,  13.50-41.39 

Si  
p 

C  ... 

s 

The  following  are  typical  analyses  of  other  alloys  made  in  the  electric 
furnace: 


Si 

Fe 

Mn 

Al 

Ca 

Mg 

C 

S 

P 

TI 

Ferro-tftanium                ... 

1.21 

0  30 

3.28 
0.55 
1.14 

0.03 
0.01 
0.01 

0.02 
0.03 
0.04 

53.0 

Ferro-aluminum-silicide  
Fei  ro-calcium-silicide  

45.65 
69.80 

44.15 
11.15 

tr. 
0.22 

9.45 
2.55 

nil 
15.05 

nil 

0.26 

Ferro-aluminum,  Al,  5,  10  and  20%.  Metallic  manganese.  Mn,  95  to 
98;  Fe,  2  to  4;  C,  under  5.  Do.  refined.  Mn,  99;  Fe,  1 ;  C,  0. 

Dangerous  Ferro-silicon.  —  Phosphoretted  and  arseniuretted  hydro- 
gen, highly  poisonous  gases,  are  said  to  be  disengaged  in  a  humid  atmos- 
phere from  ferro-silicon  containing  between  30  and  40%  and  between  47 
and  65%  of  Si,  and  there  is  therefore  danger  in  transporting  it  in  passenger 
steamships.  A  French  commission  has  recommended  the  abandonment 
of  the  manufacture  of  FeSi  of  these  critical  percentages.  (La  Lumiere 
Electrique,  Dec.  11, 1909.  Elep.  Rev.,  Feb.  26,  1910.) 

Quality  of  Foundry  Coke.  (R.  Moldenke,  Trans.  A.  S.  M.  E., 
1907.)  —  Usually  the  sulphur,  ash  and  fixed  carbon  are  sufficient  to  give 
a  fair  idea  of  the  value  of  coke,  apart  from  its  physical  structure,  specific 
gravity,  etc.  The  advent  of  by-product  coke  will  necessitate  closer 
attention  to  moisture  Beehive  coke,  when  shipped  in  open  cars,  may, 
through  inattention,  cause  the  purchase  of  from  6  to  10  per  cent  of  water 
at  coke  prices. 

Concerning  sulphur,  very  hot  running  of  the  cupola  results  in  less  sulphur 
in  the  iron.  In  good  coke,  the  amount  of  S  should  not  exceed  1.2  per 
cent;  but,  unfortunately,  the  percentage  often  runs  as  high  as  2.00.  If 
the  coke  has  a  good  structure,  an  average  specific  gravity,  not  over  11  per 
cent  of  ash  and  over  86  per  cent  of  fixed  carbon,  it  does  not  matter  much 
whether  it  be  of  the  "72  hour"  or  "24  hour"  variety.  Departure  from 
the  normal  composition  of  a  coke  of  any  particular  region  should  place  the 
foundryman  on  his  guard  at  once,  and  sometimes  the  plentiful  use  of 
limestone  at  the  right  moment  may  save  many  castings. 

Castings  made  in  Permanent  Cast-iron  Molds.  —  E.  A.  Custer,  in 
a  paper  before  the  Am.  Foundrymen's  Assn.  (Eng.  News,  May  27, 1909), 
describes  the  method  of  making  castings  in  iron  molds,  and  the  quality 
of  these  castings.  Very  heavy  m9lds  are  used,  no  provision  is  made 
against  shrinkage,  and  the  casting  is  removed  from  the  mold  as  soon  as 
1  it  has  set,  giving  it  no  time  to  chill  or  to  shrink  by  cooling.  Over  6000 
pieces  have  been  cast  in  a  single  mold  without  its  showing  any  signs  of 


1256 


THE   FOUNDRY. 


failure.  The  mold  should  be  so  heavy  that  it  will  not  become  highly 
heated  in  use.  Casting  a  4-in.  pipe  weighing  65  Ibs.  every  seven  min- 
utes in  a  mold  weighing  6500  Ibs.  did  not  raise  the  temperature  above 
300°  F.  In  using  permanent  molds  the  iron  as  it  comes  from  the  cupola 
should  be  very  hot.  The  best  results  in  casting  pipe  are  had  with  iron 
containing  over  3%  carbon  and  about  2%  silicon.  Iron  when  cast  in 
an  iron  mold  and  removed  as  soon  as  it  sets,  possesses  some  unusual  prop- 
erties. It  will  take  a  temper,  and  when  tempered  will  retain  magnetism. 
If  the  casting  be  taken  from  the  mold  at  a  bright  heat  and  suddenly 
quenched  in  cold  water,  it  has  the  cutting  power  of  a  good  high-carbon 
steel,  whether  the  iron  be  high  or  low  in  silicon,  phosphorus,  sulphur  or 
manganese.  There  is  no  evidence  of  "chill";  no  white  crystals  are  shown. 

Chilling  molten  iron  swiftly  to  the  point  of  setting,  and  then  allowing 
it  to  cool  gradually,  produces  a  metal  that  is  entirely  new  to  the  art.  It 
has  the  chemical  characteristics  of  cast  iron,  with  the  exception  of  com- 
bined carbon,  and  it  als9  possesses  some  of  the  properties  of  high-carbon 
steel.  A  piece  o-f  cast  iron  that  has  0.44%  combined,  and  over  2%  free 
carbon,  has  been  tempered  repeatedly  and  will  do  better  service  in  a  lathe 
than  a  good  non-alloy  steel.  Once  this  peculiar  property  is  imparted  to 
the  casting,  it  is  impossible  to  eliminate  it  except  by  remelting.  A  bar  of 
iron  so  treated  can  be  held  in  a  flame  until  the  metal  drips  from  the  end, 
and  yet  quenching  will  restore  it  to  its  original  hardness. 

The  character  of  the  iron  before  being  quenched  is  very  fine,  close- 
grained,  and  yet  it  is  easily  machined.  If  permanent  molds  can  be  used 
with  success  in  the  foundry,  and  a  system  of  continuous  pouring  be 
inaugurated  which  in  duplicate  work  would  obviate  the  necessity  of  having 
molders,  why  is  it  necessary  to  melt  pig  iron  in  the  cupola?  What  could 
be  more  ideal  than  a  series  of  permanent  molds  supplied  with  molten  iron 
practically  direct  from  the  blast  furnace?  The  interposition  of  a  reheating 
ladle  such  as  is  used  by  the  steel  makers  makes  possible  the  treatment  of 
the  molten  iron. 

The  molten  iron  from  the  blast  furnace  is  much  hotter  than  that  ob- 
tained from  the  cupola,  so  that  there  is  every  reason  to  believe  that  the 
castings  obtained  from  a  blast  fur'nace  would  be  of  a  better  quality  than 
when  the  pig  is  remelted  in  the  cupola. 

It  is  immaterial  whether  an  iron  contains  1.75  or  3%  silicon,  so  long  as 
the  molten  mass  is  at  the  proper  temperature,  so  that  the  high  tempera- 
tures obtained  from  .he  blast  furnace  would  go  far  toward  offsetting  the 
variations  in  the  impurities. 

R.  H.  Probert  (Castings,  July,  1909)  gives  the  following  analysis  of 
molds  which  gave  the  best  results:  Si,  2.02;  S,  0.07;  P,  0.89;  Mn,  0.29: 
C.C.,  0.84:  G.C.,  2.76.  Molds  made  from  iron  with  the  following  analysis 
were  worthless:  Si,  3.30;  S,  0.06;  P,  0.67;  Mn,  0.12;  C.C.,  0.19;  G.C.,  2.98. 

Weight  of  Castings  determined  from  Weight  of  Pattern. 

(Rose's  Pattern-makers'  Assistant.) 


A  Pattern  weighing  One 
Pound,  made  of  — 

Will  weigh  when  cast  in 

Cast 
Iron. 

Zinc. 

Copper. 

Yellow 
Brass. 

Gun 
metal. 

Mahogany  —  Nassau  

Ibs. 
10.7 
12.9 
8.5 
12.5 
16.7 
14.1 

Ibs. 
10.4 
12.7 
8.2 
12.1 
16.1 
13.6 

Ibs. 
12.8 
15.3 
10.1 
14.9 
19.8 
16.7 

Ibs. 
12.2 
14.6 
9.7 
14.2 
19.0 
16.0 

Ibs. 
12.5 
15. 
9.9 
14.6 
19.5 
16.5 

Honduras  

Spanish  

Pine  r^d 

1     white   

MoWing  Sand.  (Walter  Bagshaw,  Proc.  Tnst.  M.  E.,  1891.)— The 
chemical  composition  of  sand  will  affect  the  nature  of  the  casting,  no 
matter  what  treatment  it  undergoes.  Stated  generally,  good  sand  is 
composed  of  94  parts  silica,  5  parts  alumina,  and  traces  of  magnesia  and 
*xide  of  iron.  Sand  containing  much  of  the  metallic  oxides,  and  especially 


THE   FOUNDRY. 


1257 


lime,  is  to  be  avoided.  Geographical  position  is  the  chief  factor  governing 
the  selection  of  sand ;  and  whether  weak  or  strong,  its  deficiencies  are  made 
up  for  by  the  skill  of  the  inolder.  For  this  reason  the  same  sand  is  often 
used  f9r  both  heavy  and  light  castings,  the  proportion  of  coal  varying 
according  to  the  nature  of  the  casting.  A  common  mixture  of  facing- 
sand  consists  of  six  parts  by  weight  of  old  sand,  four  of  new  sand,  and  one 
of  coal-dust.  Floor-sand  requires  only  half  the  above  proportions  of  new 
sand  and  coal-dust  to  renew  it.  German  founders  adopt  one  part  by 
measure  of  new  sand  to  two  of  old  sand;  to  which  is  added  coal-dust  in 
the  proportion  of  one-tenth  of  the  bulk  for  large  castings,  and  one-twen- 
tieth for  small  castings.  A  few  founders  mix  street-sweepings  with  the 
coal  in  order  to  get  porosity  when  the  metal  in  the  mold  is  likely  to  be 
a  long  time  in  setting.  Plumbago  is  effective  in  preventing  destruction 
of  the  sand;  but  owing  to  its  refractory  nature,  it  must  not  be  dusted 
on  in  such  quantities  as  to  close  the  pores  and  prevent  free  exit  of  the 
gases.  Powdered  French  chalk,  soapstone,  and  other  substances  are 
sometimes  used  for  facing  the  mold;  but  next  to  plumbago,  oak  charcoal 
takes  the  best  place,  notwithstanding  its  liability  to  float  occasionally  and 
give  a  rough  casting. 

For  the  treatment  of  sand  in  the  molding-shop  the  most  primitive 
method  is  that  .of  hand-riddling  and  treading.  Here  the  materials  are 
roughly  proportioned  by  volume,  and  riddled  over  an  iron  plate  in  a  flat 
heap,  where  the  mixture  is  trodden  into  a  cake  by  stamping  with  the  feet; 
it  is  turned  over  with  the  shovel,  and  the  process  repeated.  Tough 
sand  can  be  obtained  in  this  manner,  its  toughness  being  usually  tested 
by  squeezing  a  handful  into  a  ball  and  then  breaking  it;  but  the  process 
is  slow  and  tedious.  Other  things  being  equal,  the  chief  characteristics 
of  a  good  molding-sand  are  toughness  and  porosity,  qualities  that  depend 
on  the  manner  of  mixing  as  well  as  on  uniform  ramming. 

Toughness  of  Sand.  —  In  order  to. test  the  relative  toughness,  sand 
mixed  in  various  ways  was  pressed  under  a  uniform  load  into  bars  1  in.  sq. 
and  about  12  in.  long,  and  each  bar  was  made  to  project  further  and 
further  over  the  edge  of  a  table  until  its  end  broke  off  by  its  own  weight. 
Old  sand  from  the  shop  floor  had  very  irregular  cohesion,  breaking  at  all 
lengths  of  projections  from  1/2  in.  to  1 1/2  in.  New  sand  in  its  natural  state 
held  together  until  an  overhang  of  23/4  in.  was  reached.  A  mixture  of  old 
sand,  new  sand,  and  coal-dust 

Mixed  under  rollers broke  at  2     to  2 1/4  in.  of  overhang. 

in  the  centrifugal  machine ...  '*  2      "  2Vi  " 

through  a  riddle "  1 3/4  "  2Vs  " 

showing  as  a  mean  of  the  tests  only  slight  differences  between  the  last 
three  methods,  but  in  favor  of  machine-work.  In  many  instances  the 
fractures  were  so  uneven  that  minute  measurements  were  not  taken. 

Heinrich  Ries  (Castings,  July,  19QS)  says  that  chemical  analysis  gives 
little  or  no  information  regarding  the  bonding  power,  texture,  permea- 
bility or  use  of  sand,  the  only  case  in  which  it  is  of  value  being  in  the 
selection  of  a  highly  silicious  sand  for  certain  work  such  as  steel  casting. 

Dimensions  of  Foundry  Ladles.  —  The  following  table  gives  the 
dimensions,  inside  the  lining,  of  ladles  from  25  Ibs.  to  16  tons  capacity. 
All  the  ladles  are  supposed  to  have  straight  sides.  (Am.  Mach.,  Aug.  4, 
1892.) 


Cap'y. 

Diam. 

Depth. 

Cap'y. 

Diam. 

Depth. 

Cap'y. 

Diam. 

Depth. 

16  tons 
14 
12 
10 
8 
6 
4 

m. 
54 
52 
49 
46 
43 
39 
34 

in. 
56 
53 
50 
48 
44 
40 
35 

3  tons 
2      " 

U/2" 
1  ton 

3/4" 
1/2" 
1/4" 

in. 
31 
27 

!f/2 

20 
17 
13V2 

in. 
32 
28 
25 
22 
20 
17 
131/2 

300  Ibs. 
250    " 
200    " 
150    "• 
100    " 
75    " 
50    " 

in. 

1U/2 
,03/4 

9 

8 
7 

61/2 

j|i/2 
'88 

81/2 
7V2 
61/2 

1258 


THE   MACHINE-SHOP. 


THE  MACHINE-SHOP. 

SPEED    OF   CUTTING-TOOLS   IN    LATHES,    MILLING 
MACHINES,    ETC. 

Relation  of  diameter  of  rotating  tool  or  piece,  number  of  revolution 
and  cutting-speed: 

Let  d  =  diam.  of  rotating  piece  in  inches,  n  =  No.  of  revs,  per  min.; 
=  speed  of  circumference  in  feet  per  minute; 
*dn      „«„„„,,_  S       '     3.82  £      J       3.825 


S  = 
S  -• 


T2~ 


d  = 


Approximate  rule:  Number  of  revolutions  per  minute  =  4  X  speed  Ln 
feet  per  minute  •*•  diameter  in  inches. 

Table  of  Cutting-speeds. 


Feet  per  minute. 


{J 

1J 

10 

20 

30 

40 

50 

75 

too 

150 

200 

250 

300 

Revolutions  per  minute. 

*/4 

152.8 

305.6 

458.4 

611.2 

764.0 

1145.9 

1527.9 

2291.83055.8)3819.74583.7 

3/8 

1/2 

101.9 
76.4 

203.7 
152.8 

305.6 
229.2 

407.4 
305.6 

509.3 
382.0 

763.7 
572.9 

1018.6 
763.9 

1  527.51  2036.  7i  2545.  8  3055.0 
1145.9  1527.9  1909.92291.8 

5/8 

61.1 

122.2 

183.4 

244.5 

305.6 

458.4 

611.2 

916.7 

1222.3  1527.9 

1833.5 

3/4 

50.9 

101.8 

152.8 

203.7 

254.6 

382,0 

509.3 

763.9 

1018.611273.2 

1527.9 

7/8 

43.7 

87.3 

130.9 

174.6 

218.3 

327.4 

436.6 

654.9 

873.  3!  1091.  5 

1309.8 

1 

38.2 

76.4 

114.6 

152.8 

191.0 

286.5 

382.0 

573.0 

763.9    954.9 

1145.9 

1  1/8 

34.0 

67.9 

101.8 

135.8 

169.7 

254.4 

339.5 

508.8 

678.4    848.0 

1017.6 

1  1/4 

30.6 

61.1 

91.7 

122.2 

152.8 

229.2 

305.6 

458.4 

611.2    763.9 

916.7 

1  3/8 

27.8 

55.6 

83.3 

111.1 

138.9 

208.3 

277.7 

416.5 

555.4    694.2 

833.1 

H/2 

25.5 

50.9 

76.4 

101.8 

127.2 

190.8 

254.4 

381.6 

508.8!  636.0 

763.2 

13/4 

21.8 

43.7 

65.5 

87.3 

109.2 

163.6 

218.1 

327.2 

436.2|  545.3 

654.3 

2 

19.1 

38.2 

57.3 

76.4 

95.5 

143.2 

191.0 

286.5 

382  0 

477.5 

573.0 

21/4 

17.0 

34.0 

50.9 

67.9 

84.9 

127.2 

169.6 

254.4 

339.2 

424.0 

508.8 

21/2 

15.3 

30.6 

45.3 

61.1 

76.4 

114.6 

152.8 

229.2 

305.6 

382  Oi  458.4 

23/4 

13.9 

27.8 

41.7 

55.6 

69.5 

104.0 

138.7 

208.3 

277.3 

346.6 

416.0 

12.7 

25.5 

38.2 

50.9 

63.7 

95.4 

127.2 

190.8 

254.4 

318.0 

381.6 

31/2 

109 

21  .8 

32.7 

43.7 

54.6 

81.6 

108.9 

163.3 

217.7 

272.2 

326.6 

4 

9.6 

19.1 

28.7 

38.2 

47.8 

71.6 

95.5 

143.2 

191.0 

238.7 

286.5 

41/2 

8.5 

17.0 

25.5 

34.0 

42.5 

63.6 

84.8 

127.2 

169.6 

212.0 

254.4 

7.6 

15.3 

22.9 

30.6 

33.1 

57.3 

76.4 

114.6 

152.8 

191.0 

229.2 

51/2 

6.9 

13.9 

20.8 

27.8 

34.7 

52.1 

69.4 

104.2 

138.9 

173.6 

208.3 

6 

6.4 

12.7 

19.1 

25.5 

31.8 

47.6 

63.4 

95.1 

126.8 

158  5 

190.2 

7 

5.5 

10.9 

16.4 

21.8 

27.3 

41.0 

54.6 

81.9 

109.2 

136.  6^   163.9 

8 

4.8 

9.6 

14.3 

19.1 

23.9 

35.8 

47.7 

71.6 

95.5 

119.4 

143.2 

9 

4.2 

8.5 

12.7 

17.0 

21.2 

31.8 

42.4 

63.6 

84.8 

106.0 

127.2 

10 

3.8 

7.6 

11.5 

15.3 

19.1 

28.6 

38.2 

57.3 

76.4 

95.5 

114.6 

11 

3.5 

6.9 

10.4 

13.9 

17.4 

26.0 

34.7 

52.1 

69.4 

86.8 

104.2 

12 

3.2 

6.4 

9.5 

12.7 

15.9 

23.8 

31.7 

47.6 

63.4 

79.3 

95.1 

13 

2.9 

5.9 

8.8 

11.8 

14.7 

22.1 

29.4 

44.1 

58  8 

73.5 

88.2 

14 

2.7 

5.5 

8.2 

10.9 

13.6 

20.5 

27.3 

40.9 

54.6 

68.3 

81.9 

15 

2.5 

5.1 

7.6 

10.2 

12.7 

19.1 

25.4 

38  2 

50.9 

63.  6|     763 

16 

2.4 

4.8 

7.2 

9.5 

11.9 

17.9 

23.9 

35.8 

47.8 

59  7 

71  6 

18 

2.1 

4.2 

6.4 

8.5 

10.6 

15.9 

21.2 

31.8 

42.4 

530 

63.6 

20 

.9 

3.8 

57 

7.6 

9.6 

14  3 

19.1 

28.6 

38.2 

47.8 

57  3 

22 

.7 

3.5 

5.2 

6.9 

8.7 

12.9 

17.2 

25.8 

34.4 

43.0 

51  6 

24 

.6 

3.2 

4.8 

6.4 

8.0 

11.9 

15.9 

23.8 

31.7 

40.1 

47.6 

26 

.5 

2.9 

4.4 

5.9 

7.3 

10.9 

14.5 

21.8 

29.0 

36.3 

43.5 

28 

.4 

2.7 

4.1 

5.5 

6.8 

10.3 

13.7 

20.5 

27.3 

34.2 

41.0 

30 

.3 

2.5' 

3.8 

5.1 

6.4 

9.5 

12.7 

19.1 

25.4 

31.8 

38.2 

36 

2.1 

3.2 

4.2 

5.3 

7.9 

10.6 

15.9 

21.2 

26.5 

31.8 

42 

0^9 

1.8 

2.7 

3.6 

4.5 

6.8 

9.1 

13.6 

18.2 

22.8 

27.3 

48 

0.8 

1.6 

2.4 

3.2 

4.0 

6.0 

7.9 

12.0 

15.9 

19.9 

23.9 

54 

0.7 

1.4 

2.1 

2.8 

3.5 

5.3 

7.0 

10.6 

14.1 

17.6 

21.1 

60 

0.6       1.3       1.9       2.5       3.2         4.8       6.3       9.5 

12.7      15.8 

19.0 

GEARING   OF  LATHES.  1259 

The  Speed  of  Counter-shaft  of  the  lathe  is  determined  by  an 
assumption  of  a  slow  speed  with  the  back  gear,  say  6  feet  per  minute, 
on  the  largest  diameter  that  the  lathe  will  swing. 

EXAMPLE.  —  A  30-inch  lathe  will  swing  30  inches  =,  say,  90  inches 
circumference  =  7  feet  6  inches;  the  lowest  triple  gear  should  give  a 
speed  of  5  or  6  feet  per  minute. 

Spindle  Speeds  of  Lathes.  —  The  spindle  speeds  of  lathes  are  usu- 
ally in  geometric  progression,  being  obtained  either  by  a  combination  of 
cone-pulley  and  back  gears,  or  by  a  single  pulley  in  connection  with  a 
gear  train.  Either  of  these  systems  may  be  used  with  a  variable  speed 
motor,  giving  a  wide  range  of  available  speeds. 

It  is  desirable  to  keep  work  rotating  at  a  rate  that  will  give  the  most 
economical  cutting  speed,  necessitating,  sometimes,  frequent  changes  in 
spindle  speed.  A  variable  speed  motor  arranged  for  20  speeds  in  geometric 
progression,  any  one  of  which  can  be  used  with  any  speed  due  to  the 
mechanical  combination  of  belts  and  back  gears,  gives  a  fine  gradation  of 
cutting  speeds.  The  spindle  speeds  obtained  with  the  higher  speeds  of 
the  motor  in  connection  with  a  certain  mechanical  arrangement  of  belt 
and  back  gears  may  overlap  those  obtained  with  the  lower  speeds  avail- 
able in  the  motor  in  connection  with  the  next  higher  speed  arrangement 
of  belt  and  gears,  -but  about  200  useful  speeds  are  possible.  E.  R.  Douglas 
(Elec.  Rev.,  Feb.  10,  1906)  presents  an  arrangement  of  variable  speed 
motor  and  geared  head  lathe,  with  22  speed  variations  in  the  motor  and  3  in 
the  head.  The  speed  range  of  the  spindle  is  from  4.1  to  500  r.p.m.  By 
the  use  of  this  arrangement,  and  taking  advantage  of  the  speed  changes 
possible  for  different  diameters  of  the  work,  a  saving  of  35.4  per  cent  was 
obtained  in  the  time  of  turning  a  piece  ordinarily  requiring  289  minutes. 

Rule  for  Gearing  Lathes  for  Screw-cutting.  (Garvin  Machine 
Co.)  —  Read  from  the  lathe  index  the  number  of  threads  per  inch  cut 
by  equal  gears,  and  multiply  it  by  any  number  that  will  give  for  a  pro- 
duct a  gear  on  the  index;  put  this  gear  upon  the  stud,  then  multiply  the 
number  of  threads  per  inch  to  be  cut  by  the  same  number,  and  put  the 
resulting  gear  upon  the  screw. 

EXAMPLE.  —  To  cut 


. 

.  threads  per  inch.     We  find  on  the  index 

that  48  into  48  cuts  6  threads  per  inch,  then  6  X  4  =  24,  gear  on  stud, 
and  \\1A  X  4  =  46,  gear  on  screw.  Any  multiplier  may  be  used  so  long 
as  the  products  include  gears  that  belong  with  the  lathe.  For  instance, 
instead  of  4  as  a  multiplier  we  may  use  6.  Thus,  6  X  6  =  36,  gear  upon 
stud,  and  11  ^  X  6  =  69,  gear  upon  screw. 

Rules  for  Calculating  Simple  and  Compound  Gearing  where 
there  is  no  Index.  (Am.  Mach.)  —  If  the  lathe  is  simple-geared, 
and  the  stud  runs  at  the  same  speed  as  the  spindle,  select  some 
gear  for  the  screw,  and  multiply  its  number  of  teeth  by  the  number 
of  threads  per  inch  in  the  lead-screw,  and  divide  this  result  by  the  num- 
ber of  threads  per  inch  to  be  cut.  This  will  give  the  number  of  teeth  in 
the  gear  for  the  stud.  If  this  result  is  a  fractional  number,  or  a  number 
which  is  not  among  the  gears  on  hand,  then  try  some  other  gear  for  the 
screw.  Or,  select  the  gear  for  the  stud  first,  then  multiply  its  number  of 
teeth  by  the  number  of  threads  per  inch  to  be  cut,  and  divide  by  the 
number  of  threads  per  inch  on  the  lead-screw.  This  will  give  the  num- 
ber of  teeth  for  the  gear  on  the  screw.  If  the  lathe  is  compound,  select 
at  random  all  the  driving-gears,  multiply  the  numbers  of  their  teeth 
together,  and  this  product  by  the  number  of  threads  to  be  cut.  Then 
select  at  random  all  the  driven  gears  except  'one;  multiply  the  numbers 
of  their  teeth  together,  and  this  product  by  the  number  of  threads  per 
inch  in  the  lead-screw.  Now  divide  the  first  result  by  the  second,  to 
obtain  the  number  of  teeth  in  the  remaining  driven  gear.  Or,  select 
at  random  all  the  driven  gears.  Multiply  the  numbers  of  their  teeth 
'  together,  and  this  product  by  the  number  of  threads  per  inch  in  the 
lead-screw.  Then  select  at  random  all  the  driving-gears  except  one. 
Multiply  the  numbers  of  their  teeth  together,  and  this  result  by  the  num- 
ber of  threads  per  inch  of  the  screw  to  be  cut.  Divide  the  first  result  by 
the  last,  to  obtain  the  number  of  teeth  in  the  remaining  driver.  When 
the  gears  on  the  compounding  stud  are  fast  together,  and  cannot  be 
changed,  then  the  driven  one  has  usually  twice  as  many  teeth  as  the 
other,  or  driver,  in  which  case  in  the  calculations  consider  the  lead-screw 
to  fcave  twice  as  many  threads  per  inch  as  it  actually  has,  and  then  ignore 


1260 


THE  MACHINE-SHOP. 


the  compounding  entirely.  Some  lathes  are  so  constructed  that  the  stud 
on  which  the  first  driver  is  placed  revolves  only  half  as  last  as  the  spindle. 
This  can  be  ignored  in  the  calculations  by  doubling  the  number  of  threads 
of  the  lead-screw.  If  both  the  last  conditions  are  present  ignore  them 
in  the  calculations  by  multiplying  the  number  of  threads  per  inch  in  the 
lead-screw  by  four.  If  the  thread  to  be  cut  is  a  fractional  one,  or  if  the 
pitch  of  the  lead-screw  is  fractional,  or  if  both  are  fractional,  then  reduce 
the  fractions  to  a  common  denominator,  and  use  the  numerators  of  these 
fractions  as  if  they  equaled  the  pitch  of  the  screw  to  be  cut,  and  of  the 
lead-screw,  respectively.  Then  use  that  part  of  the  rule  given  above 
which  applies  to  the  lathe  in  question.  For  instance,  suppose  it  is  desired 
to  cut  a  thread  of  25/32-inch  pitch,  and  the  lead-screw  has  4  threads  per 
inch.  Then  the  pitch  of  the  lead-screw  will  be  1/4  inch,  which  is  equal  to 
8/32  inch.  We  now  have  two  fractions,  25/32  and  8/32,  and  the  two  screws 
will  be  in  the  proportion  of  25  to  8,  and  the  gears  can  be  figured  by  the 
above  rule,  assuming  the  number  of  threads  to  be  cut  to  be  8  per  inch, 
and  those  on  the  lead-screw  to  be  25  per  inch.  But  this  latter  number 
may  be  further  modified  by  conditions  named  above,  such  as  a  reduced 
speed  of  the  stud,  or  fixed  compound  gears.  In  the  instance  given,  if 
the  lead-screw  had  been  2 1/2  threads  per  inch,  then  its  pitch  being  Vio 
inch,  we  have  the  fractions  4/io  and  25/32,  which,  reduced  to  a  common 
denominator,  are  64/160  and  125/160,  and  the  gears  will  be  the  same  as  if  the 
lead -screw  had  125  threads  per  inch,  and  the  screw  to  be  cut  64  threads 
per  inch. 

On  this  subject  consult  also  "Formulas  in  Gearing,"  published  by 
Brown  &  Sharpe  Mfg.  Co.,  and  Jamieson's  Applied  Mechanics. 

Change-gears  for  Screw-cutting  Lathes.  —  There  is  a  lack  of 
uniformity  among  lathe-builders  as  to  the  change-gears  provided  for 
screw-cutting.  W.  R.  Macdonald,  in  Am.  Mach.,  April  7,  1892,  pro- 
posed the  following  series,  by  which  33  whole  threads  (not  fractional) 
may  be  cut  by  changes  of  only  nine  gears: 


Spindle. 

fc 

Whole  Threads. 

I 

20 

30 

40 

50 

60 

70 

110 

120 

130 

20 

8 

6 

44/5 

4 

33/7 

22/n 

2 

1  H/13 

2 

11 

22 

44 

30 

18 

9 

7V* 

6 

51/7 

33/n 

3 

2  10/13 

3 

12 

24 

48 

40 

24 

16 

12 

93/5 

8 

66/7 

44/u 

4 

39/13 

4 

13 

26 

52 

50 

30 

20 

15 

10 

84/7 

55/u 

5 

48/13 

5 

14 

28 

66 

60 

36 

24 

18 

H2/5. 

102/7 

66/11 

6 

57/13 

6 

15 

30 

72 

70 

42 

28 

21 

164/5 

14 

77/n 

7 

68/13 

7 

16 

33 

78 

110 

66 

44 

33 

262/5 

22 

186/7 

11 

102/13 

8 

18 

36 

120 

72 

48 

36 

284/5 

24 

204/7 

131/n 

1  1  Vl3 

9 

20 

39 

130 

78 

52 

39 

31  Vs 

26 

223/7 

142/n 

13 

10 

21 

42 

Ten  gears  are  sufficient  to  cut  all  the  usual  threads,  with  the  exception 
of  perhaps  111/2,  the  standard  pipe-thread;  in  ordinary  practice  any 
fractional  thread  between  11  and  12  will  be  near  enough  for  the  custom- 
ary short  pipe-thread;  if  not,  the  addition  of  a  single  gear  will  give  it. 

In  this  table  the  pitch  of  the  lead-screw  is  12,  and  it  may  be  objected 
to  as  too  fine  for  the  purpose.  This  may  be  rectified  by  making  the  real 
pitch  6  or  any  other  desirable  pitch,  and  establishing  the  proper  ratio 
between  the  lathe  spindle  and  the  gear-stud. 

"Quick  Change  Gears."  —  About  1905,  lathe  manufacturers  began 
building  "quick  change"  lathes  in  which  gear  changing  for  screw- 
cutting  is  eliminated.  The  lead-screw  carries  a  cone  of  gears,  one  of  which 
is  in  mesh  with  a  movable  gear  in  a  nest  of  gears  driven  from  the  spindle. 
By  changing  the  position  of  this  movable  gear,  in  relation  to  the  cone  9f 
gears,  the  proper  ratio  of  speeds  between  the  spindle  and  lead-screws  is 
obtained  for  cutting  any  desired  thread  usual  in  the  range  of  the  machine. 
About  16  different  numbers  of  threads  per  inch  can  usually  be  cut  by 
means  of  the  "quick  change"  gear  train.  Different  threads  from  those 
usually  available  can  be  cut  by  means  of  change  gears  between  the  spindle 


TAYLOR'S  EXPERIMENTS. 


1261 


and  "  quick  change  "  gear  train.  The  threads  per  inch  usually  available 
range  from  2  to  46  in  a  12-in.  lathe  to  1  to  24  in  a  30-in.  lathe.  Catalogs 
of  lathe  manufacturers  should  be  consulted  for  constructional  details. 

Shapes  of  Tools.  For  illustrations  and  descriptions  of  various  forms 
of  cutting-  tools,  see  Taylor's  Experiments,  below;  also  see  Standard 
Planer  Tools,  p.  1271,  and  articles  on  Lathe  Tools  in  Appleton's  Cyc. 
Mech.,  vol.  ii,  and  in  Modern  Mechanism. 

Cold  Chisels.  —  Angle  of  cutting-faces  (Joshua  Rose):  For  cast  steel, 
about  65  degrees;  for  gun-metal  or  brass,  about  50  degrees;  for  copper 
and  soft  metals,  about  30  to  35  degrees. 

Metric  Screw-threads  may  be  cut  on  lathes  with  inch-divided  lead- 
ing-screws, by  the  use  of  change-  wheels  with  50  and  127  teeth;  since  127 
centimeters  =  50  inches  (127  X  0.3937  =  49.9999  in.). 

Rule  for  Setting  the  Taper  in  a  Lathe.  (Am.  Mach.)  —  IjTo  rule 
can  be  given  which  will  produce  exact  results,  owing  to  the  fapt  that 
the  centers  enter  the  work  an  indefinite  distance.  If  it  were  not  for 
this  circumstance  the  following  would  be  an  exact  rule,  and  it  is  an  approx- 
imation as  it  is.  To  find  the  distance  to  set  the  center  over:  Divide  the 
difference  in  the  diameters  of  the  large  and  small  ends  of  the  taper  by  2, 
and  multiply  this  quotient  by  the  ratio  which  the  total  length  of  the  shaft 
bears  to  the  length  of  the  tapered  portion.  EXAMPLE:  Suppose  a  shaft 
three  feet  long  is  -to  have  a  taper  turned  on  the  end  one  foot  long,  the  large 
end  of  the  taper  being  two  inches  and  the  small  end  one  inch  diameter, 


inches. 


F  Lubricants  for  Lathe  Centers.  —  Machinery  recommends  as  lubri- 
cants for  lathe  centers  to  prevent  cutting  or  abrasion:  1.  Dry  or 
powdered  red  lead  mixed  with  a  good  mineral  oil  to  the  consistency  of 
cream.  2.  White  lead  mixed  with  sperm  oil,  together  withi  enough 
graphite  to  give  the  mixture  a  dark  red  color.  3.  One  part  graphite, 
four  parts  tallow,  thoroughly  mixed. 

TAYLOR'S  EXPERIMENTS. 

Fred  W.  Taylor  directed  a  series  of  experiments,  extending  over  26 
years,  on  feeds,  speeds,  shape  of  tool,  composition  of  tool  steel,  and 
heat  treatment.  His  results  are  given  in  Trans.  A.  S.  M.  E.,  xxviii, 
"The  Art  of  Cutting  Metals."  The  notes  below  apply  mainly  to  tools 
rof  high  speed  steel  and  to  heavy  work  requiring  tools  not  less  than 
V2  by  3/4  inch  in  cross-section. 

Proper  Shape  of  Lathe  Tool.  —  Mr.  Taylor  discovered  the  best 
shape  for  lathe  tools  to  be  as  shown  in  Fig.  194  with  the  angles  given 
in  the  following  table,  when  used  on  materials  of  the  class  shown. 
The  exact  outline  of  the  nose  of  the  tool  is  shown  in  Fig.  195.  The 
actual  dimensions  of  a  1-inch  roughing  tool  are  shown  in  Fig.  196. 
Let  R  =  radius  of  point  of  tool,  A  =  width  of  tool,  L  —  length  of  shank, 
and  //  =  height  of  shank,  all  in  inches.  Then  L  =  I4A  -f  4;  H  =  1.5A; 
R  =  0.5  A  —  0.3125  for  cutting  hard  steel  and  cast  iron;  R  =?  0.5A  — 
0.1875  for  soft  steel.  The  meaning  of  the  terms  back  slope,  etc.,  is 
shown  in  Fig.  194. 

Angles  for  Tools. 


*  Material  cut. 

a  =  clearance. 

b  =  back  slope. 

c  =  side  slope. 

Cast  iron;  Hard  steel. 

6  degrees. 

8  degrees. 

14  degrees. 

Medium  or  Soft  steel. 

6  degrees. 

8  degrees. 

22  degrees. 

Tire  steel. 

6  degrees. 

5  degrees. 

9  degrees. 

*  As  far  as  the  shape  of  the  tool  is  concerned,  Taylor  divided  metals 
to  be  cut  into  general  classes:  (a)  cast  iron  and  hard  steel,  steel  of 
0.45-0.50  per  cent  carbon,  100,000  pounds  tensile  strength,  and  18  per 
cent  stretch,  being  a  low  limit  of  hardness;  (6)  soft  steel,  softer  than 
above;  (c)  chilled  iron;  (d)  tire  steel;  (e)  extremely  soft  steel  of  carbon, 
say,  0.10-0.15  per  cent. 

The  table  presupposes  the  use  of  an  automatic  tool  grinder.  If  tools 
are  ground  by  hand  the  clearance  angle  should  be  9  degrees.  The  lip 
angles  for  tools  cutting  hard  steel  and  cast  iron  should  be  68  degrees; 


Clearance- 
Flank- 

Section  Through  Line  A-B  Showing 
Greatest,  or  True  Slope  of  Lip  Surface. 

FIQ.  194. 


FIG.  195. 


TAYLOR  S   EXPERIMENTS. 


1263 


for  soft  steel,  61  degrees;  for  chilled  iron,  86  to  90  degrees;  for  tire  steel, 
74  degrees;  for  extremely  soft  steel,  keener  than  61  degrees.  A  tool 
should  be  given  more  side  than  back  slope;  it  can  then  be  ground  more 
times  without  weakening,  the  chip  does  not  strike  the  tool  post  or  clamps, 


r 


FIG.  196. 

and  it  is  also  easier  to  feed.  The  nose  of  the  tool  should  be  set  to  one 
side,  as  in  Fig.  196  above,  to  avoid  any  tendency  to  upset.  To  use 
a  tool  of  this  shape,  lathe  tool  posts  should  be  set  lower  below  the 
center  of  the  work  than  is  now  (1907)  customary. 

Forging  and  Grinding  Tools.  —  The  best  method  of  dressing  a  tool 
is  to  turn  one  end  up  nearly  at  right  angles  to  the  shank,  so  that  the 
nose  will  be  high  above  the  top  of  the  body  of  the  tool.  Dressing  can 
be  thus  done  in  two  heats.  Tools  should  leave  the  smith  shop  with 
a  clearance  angle  of  20  degrees.  Detailed  directions  for  dressing  a  tool 
are  given  in  Mr.  Taylor's  paper.  To  avoid  overheating  the  tool  in  grind 
ing,  a  stream  of  water,  of  at  least  five  gallons  a  minute,  should  be  thrown 
at  low  velocity  on  the  nose  of  the  tool  where  it  is  in  contact  with  the 
emery  wheel.  In  hand  grinding,  tools  should  not  be  held  firmly  against 
the  wheel,  but  should  be  moved  over  its  surface.  It  is  of  the  utmost 
importance  that  high  speed  steel  tools  should  not  be  heated  above  1200°  F. 
in  grinding.  Automatic  tool  grinders  are  economical,  even  in  a  small 
shop.  Grinding  machines  should  have  some  means  for  automatically 
adjusting  the  pressure  of  the  tool  against  the  grinding  wheel.  Each  size 
of  tool  should  have  adapted  to  it  a  pressure,  automatically  adjusted,  and 
which  is  just  sufficient  to  grind  rapidly  without  overheating  the  tool. 
Standard  shapes  should  be  adopted,  to  which  all  tools  should  be  ground, 
there  being  no  economy  in  automatic  grinding  without  standard  shapes, 

Best  Grinding  Wheel.  —  The  best  grinding  wheel  was  found  to  be 
a  corundum  wheel,  of  a  mixture  of  24  and  30  grit. 


1264  THE   MACHINE-SHOP. 

Pressure  of  Tool,  etc.  — Mr.  Taylor  found  that  there  is  no  definite 
relation  between  the  cutting  speed  of  tools  and  the  pressure  with  which 
the  chip  bears  on  the  lip  surface  of  the  tool.  He  found,  however,  that 
the  pressure  per  square  inch  of  sectional  area  of  the  chip  increases 
slightly  as  the  thickness  of  the  chip  decreases.  The  feeding  pressure  of 
the  tool  is  sometimes  equal  to  the  entire  driving  pressure  of  the  chip  against 
the  lip  surface  of  the  tool,  and  the  feed  gears  should  be  designed  to  deliver 
a  pressure  of  this  magnitude  at  the  nose  of  the  tool. 

Chatter.  —  Chatter  is  caused  by:  too  small  lathe  dogs;  imperfect 
bearing  at  the  points  where  the  face  plate  drives  the  dogs;  badly  made  or 
badly  fitted  gears;  shafts  in  the  machine  of  too  small  diameter,  or  of  too 
great  length;  loose  fits  in  bearings.  A  tool  which  chatters  must  be  run 
at  a  cutting  speed  about  15  per  cent  slower  than  can  be  used  if  the  tool 
does  not  chatter,  irrespective  of  the  use  or  non-use  of  water  on  the  tool. 
A  higher  cutting  speed  can  be  used  with  an  intermittent  cut,  as  occurs 
on  a  planer,  or  shaper,  or  in  turning,  say,  the  periphery  of  a  gear,  than 
with  a  steady  cut.  To  avoid  chatter,  tools  should  have  curved  cutting 
edges,  or  two  or  more  tools  should  be  used  at  the  same  time  in  the  same 
machine.  The  body  of  the  tool  should  be  greater  in  height  than  width, 
and  should  have  a  true,  solid  bearing  on  the  tool  support,  which  latter 
should  extend  to  almost  beneath  the  cutting  edge  of  the  tool.  Machines 
should  be  made  massive  beyond  the  metal  needed  for  strength  alone, 
and  steady  rests  should  be  used  on  long  work.  It  is  advisable  to  use  a 
steady  rest,  when  turning  any  cylindrical  piece  of  diameter  D,  when  the 
length  exceeds  12  Z), 

Use  of  Water  on  Tool.  —  With  the  best  high  speed  steel  tools,  a 
gain  of  14  per  cent  in  cutting  speed  can  be  made  in  cutting  cast-iron 
and  hard  steel  to  35  per  cent  on  very  soft  steel  by  throwing  a  heavy 
stream  of  water  directly  on  the  chip  at  the  point  where  it  is  being  re- 
moved from  the  forging  by  the  tool.  Not  less  than  three  gallons  a 
minute  should  be  used  for  a  2  X  2i/2-in.  tool.  The  gain  is  practically 
the  same  for  all  qualities  of  steel,  regardless  of  hardness  and  whether 
thick  or  thin  chips  are  being  cut. 

Interval  between  Grindings.  —  Mr.  Taylor  derived  a  table  showing 
how  long  various  sizes  of  tools  should  run  without  regrinding  to  give  the 
maximum  work  for  the  lowest  all-around  cost.  Time  a  tool  should  run 
continuously  without  regrinding  equals  7  X  (time  to  change  tool  + 
proper  portion  of  time  for  redressing  -f  time  for  grinding  +  time  equi- 
valent to  cost  of  the  tool  steel  ground  off). 

INTERVAL  BETWEEN  GRINDINGS,  AT  MAXIMUM  ECONOMICAL 
CUTTING  SPEEDS. 


Size  of  tool. 
Inches. 
Hours. 

1/2  X3/4       S/g 

&'    *&' 

78       7/8  X   1  3/8 

1X.V, 

Size  of  toot. 
Inches. 
Hours. 

1  V4X  1  7/8 

U/2X2  1/4 

13/4X2  3/4 

2  X  3 
2.75 

If  the  proper  cutting  speed  (A)  is  known  for  a  cut  of  given  duration, 
the  speed  for  a  cut  (B)  of  different  duration  can  be  obtained  by  multiply- 
ing (A)  by  the  factor  given  in  the  following  table: 

Duration  of  cut  in  minutes: 

At  known  speed  (A) 20         40         20         40         80         80 

At  derived  speed  (B) 40         80         80         20         40         20 

Factor 0.92     0.92     0.84     1.09     1.09     1.19 

For  cutting  speeds  of  high-speed  lathe  tools  to  last  11/2  hours,  see 
tables  on  pages  1266  and  1267. 

Effect  of  Feed  and  Depth  of  Cut  on  Cutting  Speed.— With  a  given 
depth  of  cut,  metal  can  be  removed  faster  with  a  coarse  feed  and  slow 
speed,  than  with  fine  feed  and  high  speed.  'With  a  given  depth  of  cut. 
a  cutting  speed  of  S,  and  a  feed  of  F,  5  varies  approximately  as  1[\/F. 
With  tools  of  the  best  high  speed  steel,  varying  the  feed  and  depth  of 
cut  varies  the  cutting  speed  in  the  same  ratio  when  cutting  hard  steel 
as  when  cutting  soft  steel. 


TAYLOR'S  EXPERIMENTS.  1265 

Best  High  Speed  Tool  Steel  —  Composition  —  Heat  Treatment. 

—  Mr.  Taylor  and  Maunsel  White  developed  a  number  of  high  speed 
steels,  the  one  showing  the  best  all-around  qualities  having  the  following 
chemical  composition:  Vanadium,  0.29;  tungsten,  18.19;  chromium, 
5.47;  carbon,  0.674;  manganese,  0.11;  silicon,  0.043.  The  use  of 
vanadium  materially  improves  high  speed  steel.  The  following  method 
of  treatment  is  described  as  the  best  for  this  or  any  other  composition  of 
high  speed  steel.  The  tool  should  be  forged  at  a  light  yellow  heat,  and, 
after  forging  slowly  and  uniformly  heated  to  a  bright  cherry  red,  allowing 
plenty  of  time  for  the  heat  to  penetrate  to  the  center  of  the  tool,  in  order 
to  avoid  danger  of  cracking  due  to  too  rapid  heating.  The  tool  should 
then  be  heated  from  a  bright  cherry  red  to  practically  its  melting-point  as 
rapidly  as  possible  in  an  intensely  hot  fire;  if  the  extreme  nose  of  the  tool 
is  slightly  fused  no  harm  is  done.  Time  should  be  allowed  for  the  tool 
to  become  uniformly  hot  from  the  heel  to  the  lip  surface. 

After  the  high  heat  has  been  given  the  tools,  as  above  described,  they 
should  be  cooled  rapidly  until  they  are  below  the  "breaking-down  point, 
or.  say,  down  to  or  below  1550°  F.  The  quality  of  the  tool  will  be  but 
little  affected  whether  it  is  cooled  rapidly  or  slowly  from  this  point  down 
to  the  temperature  of  the  air.  Therefore,  after  all  parts  of  a  tool  from 
the  outside  to  the  center  have  reached  a  uniform  temperature  below  the 
breaking-down  point,  it  is  the  practice  sometimes  to  lay  it  down  in  any 
part  of  the  room  or  shop  which  is  free  from  moisture,  and  let  it  cool  in 
the  air,  and  sometimes  to  cool  it  in  an  air  blast  to  the  temperature  of  the 
air. 

The  best  method  of  cooling  from  the  high  heat  to  below  the  breaking- 
down  point  is  to  plunge  the  tools  into  a  bath  of  red-hot  molten  lead  below 
the  temperature  of  1550°  F.  They  should  then  be  plunged  into  a  lead 
bath  maintained  at  a  uniform  temperature  of  1150°  F.,  because  the  same 
bath  is  afterward  used  for  reheating  the  tools  to  give  them  their  second 
treatment.  This  bath  should  contain  a  sufficiently  large  body  of  the  lead 
so  that  its  temperature  can  be  maintained  uniform;  and  for  this  purpose 
should  be  used  preferably  a  lead  bath  containing  about  3600  Ib.  of  lead. 

Too  much  stress  cannot  be  laid  upon  the  importance  of  never  allowing 
the  tool  to  have  its  temperature  even  slightly  raised  for  a  very  short 
time  during  the  process  of  cooling  down.  The  temperature  must  either 
remain  absolutely  stationary  or  continue  to  fall  after  the  operation  of 
cooling  has  once  started,  or  the  tool  will  be  injured.  Any  temporary  rise 
of  temperature  during  cooling,  however  small,  will  injure  the  tool.  This, 
however,  applies  only  to  cooling  the  tool  to  the  temperature  of  about 
1240°  F.  Between  the  limits  of  1240  degrees  and  the  temperature  of 
the  air,  the  tool  can  be  raised  or  lowered  in  temperature  time  after  time 
and  for  any  length  of  time  without  injury.  And  it  should  also  be  noted 
that  during  the  first  operation  of  heating  the  tool  from  its  cold  state  to 
the  melting-point,  no  injury  results  from  allowing  it  to  cool  slightly  and 
then  reheating.  It  is  from  reheating  during  the  operation  of  cooling 
from  the  high  heat  to  1240°  F.  that  the  tool  is  injured. 

The  above-described  operation  is  commonly  known  as  the  first  or  high- 
heat  treatment. 

To  briefly  recapitulate,  the  first  or  high-heat  treatment  consists  of 
heating  the  tool  — 

(a)  slowly  to  1500°  F.; 

(b)  rapidly  from  that  temperature  to  just  below  the  melting-point. 

(c)  coqiing  fast  to  below  the  breaking-down  point,  i.e.,  1550°F. 

(d)  cooling  either  fast  or  slowly  from  1550°  F.  to  temperature  of  the  air. 

Second  Treatment,  Reheating  the  Cooled  Tool.  —  After  air- 
temperature  has  been  reached  the  tool  should  be  reheated  to  a  temperature 
of  from  700  to  1240°  F.,  preferably  by  plunging  it  in  the  before-mentioned 
lead  bath  at  1150°  F.  and  kept  at  that  temperature  at  least  five  minutes. 
To  avoid  danger  of  fire  cracks,  the  tool  should  be  heated  slowly  before 
immersing  in  the  bath.  The  above  tool  heated  in  this  fashion  possesses 
a  high  degree  of  "red  hardness"  (ability  to  cut  steel  with  the  nose  of  the 
tool  at  red  heat),  while  it  is  not  extraordinarily  hard  at  ordinary  tem- 
peratures. It  is  difficult  to  injure  it  by  overheating  on  the  grindstone  or 
in  the  lathe.  It  will  operate  at  90  per  cent  of  its  maximum  cutting  speed, 
even  without  the  second  or  low-heat  treatment.  A  coke  fire  is  prefer- 
able for  giving  the  first  heat,  and  it  should  be  made  as  deep  as  possible. 


1266 


THE   MACHINE-SHOP. 


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1268  THE  MACHINE-SHOP. 

Cooling  the  tool  by  plunging  it  in  oil  or  water,  renders  it  liable  to  fire 
cracks  and  to  brittleness  in  the  body.  Next  to  the  lead  bath  an  air  blast 
is  preferable  for  cooling. 

Best  Method  of  Treating  Tools  in  Small  Shops.  —  For  small 
shops,  in  treating  high-speed  tools,  Mr.  Taylor  considers  the  best  method 
to  be  as  follows  for  the  blacksmith  who  is  equipped  only  with  the 
apparatus  ordinarily  found  in  a  smith-shop. 

After  the  tools  have  been  forged  and  before  starting  to  give  them  their 
heat,  fuel  should  be  added  to  the  smith's  fire  so  as  to  give  a  good  deep 
bed  either  of  coke  about  the  size  of  a  walnut  or  of  first-class  blacksmiths' 
soft  coal.  A  number  of  tools  should  then  be  laid  with  their  noses  at  a 
slight  distance  from  the  hotter  portion  of  the  fire,  so  that  they  may  all 
be  pre-heating  while  the  fire  is  being  blown  up  to  its  proper  intensity. 
After  reaching  its  proper  intensity,  the  tools  should  be  heated  one  at  a  time 
over  the  hottest  part  of  the  fire  as  rapidly  as  practicable  up  to  just  below 
their  melting-point.  During  this  operation  they  should  be  repeatedly 
turned  over  and  over  so  as  to  insure  a  uniform  high  heat  throughout  the 
whole  end  of  the  t9ol.  As  soon  as  each  tool  reaches  its  high  heat,  it 
should  be  placed  with  its  nose  under  a  heavy  air  blast  and  allowed  to 
cool  to  the  temperature  of  the  air  before  being  removed  from  the  blast. 

Unfortunately,  however,  the  blacksmith's  fire  is  so  shallow  that  it  is 
incapable  of  maintaining  its  most  intense  heat  for  more  than  a  com- 
paratively few  minutes,  and,  therefore,  it  is  only  through  these  few  min- 
utes that  first-class  high-speed  tools  can  be  properly  heated  in  the  smith's 
fire.  Great  numbers  of  high-speed  tools  are  daily  turned  out  from 
smiths'  fires  which  are  not  sufficiently  intense  in  their  heat,  and  they  are 
therefore  inferior  in  red  hardness  and  produce  irregular  cutting  tools. 

On  the  whole,  a  blacksmith's  fire  made  from  coke  may  be  regarded  as 
better  for  giving  the  high  heat  to  tools  than  a  soft-coal  fire,  merely 
because  a  coke  fire  can  be  more  easily  made  by  the  smith  which  will 
remain  capable  for  a  longer  period  of  heating  the  tools  quickly  to  their 
melting-points. 

Quality  of  Different  Tool  Steels.  —  Mr.  Taylor  in  a  letter  to  the 
author,  Dec.  30,  1907,  says  : 

First.  Any  of  a  half  dozen  makes  of  high  speed  tools  now  on  the  market 
are  amply  good,  and  but  little  attention  need  be  paid  to  the  special  direc- 
tions for  heating  and  cooling  high  speed  tools  given  by  the  makers  of  the 
tool  steel.  The  most  important  matter  is  that  an  intensely  hot  fire  should 
be  used  for  giving  the  tools  their  high  heat,  and  that  they  should  not  be 
allowed  to  soak  a  long  time  in  this  fire.  They  should  be  heated  as  fast 
as  possible  and  then  cooled  in  an  air  blast. 

Second.  The  greatest  number  of  tools  are  ruined  on  the  emery  wheel 
through  overheating,  either  because  a  wheel  whose  surface  is  glazed  is 
used,  or  because  too  small  a  stream  of  water  is  run  upon  the  nose  of  the 
tool.  The  emery  wheel  should  be  kept  sharp  through  frequent  dress- 
ings with  a  diamond  tool. 

Third.  Uniformity  is  the  most  important  quality  in  high  speed  tools. 
For  this  reason,  only  one  make  of  high  speed  tool  steel  should  be  used 
in  each  shop. 

Economical  Cutting  Speeds. — Tools  shaped  as  in  Fig.  196,  and 
of  the  chemical  composition  and  heat  treatment  given  in  the  preced- 
ing paragraphs,  should  be  run  at  the  cutting  speeds  given  in  the  tables 
on  pages  1266  and  1267  in  order  to  last  one  hour  and  30  minutes  with- 
out re-grinding. 

Cutting  Speed  of  Parting  and  Thread  Tools. — To  find  the  economical 
cutting  speed  of  a  parting  tool  of  the  best  high-speed  steel,  first  ascer- 
tain the  thickness  of  chip  which  is  to  be  cut  by  the  tool.  Then  from 
the  tables  on  pages  1266  and  1267,  under  the  standard  7/8-in.  tool  and 
3/16  in.  depth  of  cut,  and  opposite  the  feed  which  most  nearly  corre- 
sponds to  the  thickness  of  chip  to  be  taken  by  the  parting  tool,  find 
the  speed.  Divide  the  figure  so  found  by  2.7  to  ascertain  the  speed  for 
the  parting  tool.  For  thread  tools,  the  process  is  the  same,  except 
that  the  divisor  is  4.  The  thickness  of  chip  in  the  latter  case  is  the  ad- 
vance in  inches  per  revolution  of  the  tool  toward  the  center  of  the  work. 

Durability  of  Cutting  Tools.— E.  G.  Herbert  (Am.  Mach.,  June  24, 
1909)  shows  that  the  durability  of  a  tool  depends  mainly  on  the  tem- 
perature to  which  its  extreme  edge  is  raised,  and  that  the  rate  of  evolu- 
tion of  heat  and  consequently  the  durability  is  proportional  to  the  thick- 


STELLITE. 


1269 


ness  and  to  the  area  of  the  chip  and  to  the  cube  of  the  cutting  speed. 
Or  if  ti  =  thickness  or  feed,  Ci  =  depth  of  cut,  a\  =  area  of  the  cut  and 
s\  =  cutting  speed,  for  any  given  set  of  working  conditions,  and  fcc2a2  and 
s-2  values  for  another  set  of  conditions,  then  the  durability  of  the  tool 
will  be  the  same  when  fcaiSi3  =  22a2S23,  or  for  constant  durability  s2  = 

Sl^tfl'Ci)  -h(*22C2). 

Other  High-Speed  Steels.— Am.  Mach.  April  8,  May  20  and  27, 
1909,  describes  the  operations  of  some  new  varieties  of  high-speed  steel 
made  by  Sheffield  manufacturers,  which  show  results  superior  to  those 
of  the  earlier  high-speed  steels  in  endurance  of  tool,  ability  to  cut  very 
hard  metals,  and  higher  speeds.  The  following  are  the  results  of  some 
of  the  tests  in  lathe-work: 


Tool 
size, 
in. 

Material  Cut. 

Diam. 
in. 

Depth, 
cut  in. 

Feed 
in. 

Speed 
ft.  per 
min. 

Length  of 
Cut. 

1  I/  A 

Steel  2  00  0 

3/8 

Vl6 

36 

43/4  in.* 

\1/A 

Steel'  0  70  C 

l/4 

Vl6 

48 

13  in  t 

1  I/A 

Steel'  0  70  C     

3/16 

VlO 

65 

8  7/8  in. 

7/0 

Steel  0  40  C  

4 

1/8 

Vl6 

65 

28  ins.,  t 

7/g 

Steel,  0.40.C  

Vs 

V32 

120 

28  ins.,  § 

7/8 

5ft. 

1/8  to  3/ie 

VlO 

56 

4  1/2  ins. 

1/1 

5ft. 

5/16 

V32 

107 

6  ins. 

1/2 

Cast  iron        

5ft. 

Vs 

va 

55 

Sins. 

11/4 

Steel  0.40C  

5  3/8  in. 

Va 

Vio 

90 

54  ins. 

1x2 

Steel  

9  3/4  in. 

3/8 

Vs 

64 

72  ins. 

1x2 

Nickel  steel  

3  1/2  in. 

V2 

0072 

52 

124  ins. 

li/4 

U/4 

Steel  casting,  0.45C.. 
Steel,  0.60C  

20  in. 
7  1/2  in. 

3/8 
9/64 

Vs 

V26 

50 
115 

15  to  20  min.  U 
18  in. 

*  Then  1 3/4  in.  at  50  ft.  per  min.     t  Then  1  Vs  in.  at  65  ft.  per  min. 
±  Then  28  ins.  at  98  ft.     §  Then  22  ins.  at  160  ft.     ||  Required  28  H.P. 
Chilled  rolls,  too  hard  for  ordinary  high-speed  steel,  were  cut  at  a  speed 
of  80  ft.  per  min.,  with  5/16  in.  depth  of  cut  and  1/8  in.  feed. 
The  following  results  were  obtained  in  drilling: 


Drill 
size. 

Material. 

Rev. 

per 
min. 

Feed 
per 
rev. 

Speed 
per 
mm. 

Drilled  without  Re- 
grinding. 

3/4  in 

Close  cast  iron  

466 

0.018 

8  1/2  in. 

70  holes,  3  ins.  deep. 

3/4 

Steel  0  25  C 

247 

0.011 

60  holes,  23/4  ins.  deep. 

3/4 

is/ie 

Hard  steel  
Steel  

526 
400 

6  in. 

3V2 

12  holes,  21/2  ins.  deep. 
14  in.  at  one  operation. 

A  milling  cutter  5  in.  diam.,  with  54  teeth,  milling  teeth  in  saw-blanks, 
at  a  cutting  speed  of  56  ft.  per  min.  and  a  feed  of  1  in.  per  min.,  cuts 
80  blanks  (three  or  more  together),  each  32  in.  diam.,  3/8  in.  thick,  240 
teeth,  before  re-grinding. 

Stellite. — An  alloy  of  25%  chromium,  65%  cobalt  and  10%  molyb- 
denum, to  which  the  name  "stellite"  has  been  given,  is  described  in 
Ir.  Tr.  Review,  Mar.  5,  1914.  This  alloy  is  extremely  hard,  and  retains 
its  hardness  even  when  red  hot,  thus  making  it  useful  as  a  substitute 
for  tool  steel.  Tests  made  with  stellite  as  a  cutting  tool  on  various 
materials  showed  the  following  cutting  speeds,  the  speed  attained  by 
high-speed  steel  in  the  same  tests  being  given  for  comparison : 


Cutting  Speed, 
Ft.  per  Min. 

Cutting  Speed, 
Ft.  per  Min. 

Phosphor-bronze.  . 
Tool  steel.. 

Stellite.    Steel. 
.      900         125 
133           80 

Seamless  tubing. 
Cast  iron  .  . 

Stellite.    Steel. 
.  .      400         100 
200         100 

A  circular  issued  by  the  Midvale  Steel  Co.  gives  the  following  direc- 
tions for  the  use  of  stellite,  with  a  i/2-in.  square  lathe  tool:  For  cutting 
steel  of  0.30  carbon  or  under,  the  limits  will  be:  Depth  of  cut,  i/g  in.; 
feed,  Vie  in.  per  revolution;  speed,  100  to  300  ft.  per  min.,  depending 
on  the  other  conditions.  For  steel  of  0.35  to  1.00  carbon,  with  the 
same  depth  of  cut  and  feed  as  above  the  speed  should  be  from  50  to 


1270  THE  MACHINE-SHOP. 

150  ft.  per  min.  In  cutting  cast  iron  it  is  recommended  that  light 
cuts,  and  heavy  feeds,  say  up  to  1/4  in.,  be  used.  The  depth  of  cut 
can  run  to  1/4  or  3/g  in.  under  moderate  feeds.  Stellite  cannot  be 
forged,  but  is  cast  and  ground  to  shape.  It  is  extremely  brittle,  and 
its  use  is  restricted  to  such  tools  as  can  be  supported  close  to  the  cutting 
edge.  '  It  should  not  be  used  when  the  cut  is  one  that  will  subject  the 
tool  to  heavy  shocks.  The  fields  for  which  it  is  recommended  are: 
For  turning  steel,  where  turning  represents  a  large  proportion  of  the 
work  to  be  done,  and  where  the  capacity  of  the  lathe  has  not  been 
reached  with  the  steel  tool;  for  turning  cast  iron  that  is  not  so  hard 
that  a  slow  speed  with  a  steel  tool  is  necessary,  and  where  the  capacity 
of  the  machine  has  not  been  reached  with  a  steel  tool  ;  for  inserted  teeth 
in  milling  cutters  and  reamers  in.  a  limited  field  where  speed  is  important. 
For  other  data  on  the  heat  treatment,  forging,  etc.,  of  tool  steels,  see 
also  pages  491  to  497. 

PLANER  WORK. 

Work  that  Should  be  Planed.  —  The  planer  is  adapted  for  finishing 
flat  surfaces  where  great  accuracy  is  required.  The  Cincinnati  Planer 
Co.  gives  (1912)  in  "A*  Treatise  on  Planing"  the  following  list  of  work 
which  should  be  planed:  Locomotive  frames,  cylinders,  shoes,  wedges, 
and  driving-boxes;  printing-press  tables,  frames,  bearings,  bases; 
laundry  frames,  mangle  chests;  engine  steam  chests,  valves,  frames, 
pillow  blocks,  connecting-rods;  rolling-mill  guides,  frames,  bearings, 
key  ways,  tables;  woodworking  saw  tables,  frames,  knife  arbors,  knives, 
bases;  textile  machinery  frames,  guides,  bearing  stands,  legs;  electric 
motor  and  generator  bases  and  frame  segments;  forging  machinery 
dies,  guides,  arches,  header  frames,  bases;  machine  tool  beds,  tables, 
carriages,  rails,  slides,  knees,  columns. 


,         ,  ,  ,  . 

Cutting  and  Return  Speeds.  —  A  cutting  speed  of  about  55  ft. 
inute  is  about  as  high  as  it  is  practical  to  use  on  the  planer,  and 
should  be  decreased  for  most  materials.  The  table  below  shows  the 


per 
this 


. 

speeds  recommended  by  the  Cincinnati  Planer  Co.  The  lower  cutting 
speed  of  the  planer  tool,  as  compared  with  the  lathe,  is  probably  due  to 
the  absence  of  a  cooling  lubricant  on  long  cuts.  If  the  cut  is  inter- 
mittent, as  in  planing  a  series  of  castings  with  gaps  in  between,  the 
cutting  speed  can  be  higher  than  with  a  continuous  cut  of  equal  total 
length,  probably  due  to  the  partial  cooling  of  the  tool  during  the  inter- 
vals of  cutting.  Return  speeds  of  75  to  100  ft.  per  minute  are  as  high 
as  are  recommended,  although  the  author  has  seen  planers  operating 
at  a  return  speed  as  high  as  135  ft.  per  minute.  An  increase  in  the 
cutting  speed  is  much  more  effective  in  increasing  the  capacity  of  the 
machine  than  an  increase  in  the  return  speed,  and  it  is  better  to  increase 
the  cutting  speed  by  25  %  than  to  double  the  return  speed. 

PLANER  CUTTING  SPEEDS,  FEET  PER  MINUTE. 


Iron,  cast,  roughing 40  to  50 

Iron,  cast,  finishing 20  to  25 

Iron,  wrought,  roughing. .  30  to  45 
Iron  wrought,  finishing .  .          20 


Steel,  cast,  roughing ....  30  to  35 

Steel,  cast,  finishing 20 

Steel  machinery 30  to  35 

Bronze  and  Brass 50  to  60 


Planer  Feeds. — For  rough  -planing  cast-iron  feeds  range  from  i/s 
to  3/i6  in.;  for  steel  i/ie  to  i/g  in.  For  finishing  cast  iron  with  a  broad 
nose  tool  the  feed  may  range  from  1/2  to  3/4  in.  per  stroke.  The  feed 
should  be  as  heavy  as  possible,  in  order  to  decrease  the  time  required, 
although  when  planing  to  a  finished  edge,  a  feed  of  as  low  as  i/ie  in. 
•must  be  used  to  avoid  breaking  the  edge  at  the  end  of  the  stroke. 

Power  Requirements  for  Planing.— The  principal  power  requirement 
in  planing  is  that  required  for  reversing  at  the  end  of  the  stroke.  The 
largest  portion  is  used  in  reversing  the  planer  pulleys,  which,  running 
at  high  speeds,  store  up  considerable  energy.  The  substitution  of 
aluminum  alloy  pulleys  by  some  planer  builders  for  the  cast-iron  ones 
usually  employed  has  reduced  the  power  requirements  for  reversal  and 
has  increased  the  capacity  of  the  machine  by  increasing  the  number  of 
strokes  which  can  be  made  per  hour.  The  Cincinnati  Planer  Co.  (1912) 
reports  that  with  a  35-ft.  cutting  speed  and  an  85-ft.  return  speed,  on  a 
4-ft,  cut,  165  strokes  were  made  in  30  minutes  with  cast-iron  pulleys 


PLANER  WORK. 


1271 


and  189  in  the  same  time  with  aluminum  pulleys.  In  another  test, 
cast-iron  pulleys  required  39  horse-power  at  the  reverse  while  aluminum 
pulleys  required  30  horse-power.  For  other  data  on  power  required, 
see  pages  1296,  1302  and  1303. 

Time  Required  for  Planing. — The  Cincinnati  Planer  Co.  has  devised 
a  slide  rule,  shown  in  Fig.  197,  for  determining  the  time  required  to 
machine  work  in  a  variable  speed  planer.  It  is  adapted  for  use  with 
cutting  speeds  of  20  to  60  ft.  per  min.,  return  speeds  of  50  to  130  ft. 
per  min.  and  a  feed  range  of  from  i/ie  to  1  in.  per  stroke.  The  feed 
which  is  to  be  used  (scale  B)  is  set  opposite  the  intersection  of  the 


FIG.  197.    PLANER  TIME  SLIDE  .RULE. 

cutting-speed  curve  with  the  return  speed  line  (Scale  A).  The  time 
is  read  on  scale  D  underneath  the  figure  representing  the  area  in  square 
inches  to  be  planed  (width  X  length)  on  scale  C.  To  the  time  so  deter- 
mined must  be  added  the  time  required  for  setting  up  the  work  in  the 
machine. 

The  following  tables  have  also  been  prepared  by  the  Cincinnati 
Planer  Co.  for  determining  times  for  planer  operation. 

Planer  Table  Travel,  Feet  per  Hour. 

(Divide  by  length  of  stroke  in  feet  for  number  of  strokes  per  hour.) 


Speed 
of  Cut, 
Ft.  per 
Min. 

Return  Speed,  Feet  per  Minute. 

50 

60 

70 

80 

90 

100 

120  " 

150 

20 
25 
30 
35 
40 
45 
50 

857.1 
1000.0 
1125.0 
1235.3 
1333.3 
1421.0 
1500.0 

900.0 
1058.8 
1200.0 
1321.3 
1440.0 
1542.8 
1636.4 

933.3 
1105.3 
1260.0 
1400.0 
1527.3 
1643.5 
1750.0 

960.0 
1142.9 
1309.1 
1460.9 
1600.0 
1728.0 
1846.2 

981.8 
1173.9 
1350.0 
1512.0 
1661.5 
1800.0 
1928.6 

1000.0 
1200.0 
1384.6 
1555.6 
1714.3 
1862.1 
2000.0 

1028.6 
1241.4 
1440.0 
1625.8 
1800.0 
1863.6 
2117.6 

1058.8 
1285.7 
1500.0 
1702.7 
1894.7 
2076.9 
2250.0 

Time  of  Planer  Travel  per  Foot. 


* 

p* 

n 

'c     ** 

Jll 

1** 

Je§ 

m 

|  j| 

J&g 

*  0) 

•3  »c 

j£i 

'O       ^J 

1*1 

£  afe 

OQ 

h 

-  0) 

f  ad 

|£§ 

OT 

\A 

J&8 

f*d 

Jtfj 

•8    ^ 

III 

10 
15 
20 
25 
30 
35 
40 

6.0 
4.0 
3.0 
2.4 
2.0 
1.72 
1.5 

45 
50 
55 
60 
65 
70 
75 

1.33 
1.2 
1.09 
1.0 
0.923 
.    .857 
.80 

80 
85 
90 
95 
100 
105 
110 

0.75 
.705 
.666 
.631 
.60 
.571 
.545 

120 
130 
140 
150 
160 
170 
180 

0.5 
.461 
.428 
.40 
.375 
.353 
.333 

190 
200 
220 
240 
260 
280 
300 

0.316 
.30 
.273 
.25     - 
.23 
.214 
.20 

Standard  Planer  Tools. — Carl  G.  Earth  designed  for  the  use  of 
the  Watertown  Arsenal  a  full  line  of  planer  tools,  as  shown  in  the 
drawings,  Figs.  198  to  213,  and  in  the  tables  below.  These  tools  were 
developed  according  to  the  principles  discovered  by  Taylor  and  Barth 
in  the  investigation  into  the  "Art  of  Cutting  Metals"  (see  p.  1261), 


1272 


THE  MACHINE-SHOP. 


and  may  be  regarded  as  forming  a  standard  line  of  tools  of  the  best- 
shape  for  their  respective  purposes.  They  are  described  in  Am.  Mach.. 
Jan.  21  and  28,  1915. 

Round  Nose  Roughing  Tools  (Dimensions  in  Inches). 


FIG.  198.  FIG.  199. 

RIGHT  OR  LEFT  HAND  (Figs.  198  and  199). 

E  R  (rad.) 


C 

17/8 
23/8 
21/2 
27/8 
21/2 
31/4 
33/4 


Parting  Tools*  (Dimensions  in  Inches). 


FIG.  200. 
FLUSH  NOSE,  CENTRAL 


FIG.  201. 
HIGH  NOSE,  RIGHT  HAND, 


A 

5/8 

H/4 

(Fig.  200) 
B            C 

1                1  1/4 

1  1/8         1  1/2 
H/2        2 
1  7/8         2  1/2 

D 

13/4 
2 

21/4 
2 

E 

1/4 
3/8 
1/2 
5/8 

1 

l 

AL 
D 

1/4 
1/2 
1/2 

V2 
7/8 
1/4 

STRAIGHT  (Fig.  201). 
A            B            C           D 

1/2             3/4          11/8          H/2 
5/8          1                 13/8          15/8 
3/4          H/8          H/2          13A 
1  1/2          2                 2 

1/4         17/8         21/8         21/2 

STRAIGHT  (Fig.  202). 
E                 F 

1/4                  3 
5/16                  3  1/2 
1/4                    3 
3/8                  4  3/4 
1/2                 6 

A 

5/8 
8/4 

IJ/4 

H/4 

H/2 

SET  BACK  NOSE, 
B                   C 

1                        13/4 
H/8                2 
1                          1  3/4 
11/2                  23/4 

1  7/8                 3  1/2 
1  1/4                  2  1/8 
1  V2                  2  S/g 

CENTE 

1 
1 
1 
2 
2 
1 
2 

*  See  note  at  foot  of  page  1273. 


E 

1/4 
5/16 
5/16 
3/8 
1/2 

H 
H/8 

H/2 

17/8 
H/4 
H/3 


STANDARD   PLANER   TOOLS. 


1273 


FIG.  203. 


___  •     L 

<  I 

~a  f. 

1 

i  r 

FIG.  204.  FIG.  205. 

Finishing  Tools  (Dimensions  in  Inches). 

SHEARING  CUT  (Fig.  203). 
B  C  D  E 

3/4  3/4  3/4  7/8 

111  13/i6 

H/8  H/8  H/8  H/2 

H/2  H/2  H/2  2 

SQUARE,  HIGH  NOSE,  BENT  45  DEG.  (Fig.  204). 
A  B  C  D  E  F 

1  H/2  21/8  2  13/8  3/4 

H/4  17/8  27/8  21/2  13/8  7/8 


A 

1/2 
5/8 
3/4 


F 

7/16 
9/16 

5/8 
7/8 


External  Keyway  Tools  (Dimensions  in  In.)  C 
SET  BACK  NOSE  (Fig.  205).  *~ 

A  B        C       D 

1/2  3/4  1  1/4 

5/8  1  H/4  5/16 

3/4  H/8  H/2  3/8 


i   <3 


F  F  K 

1  1/2  i/2  Width 

13/4  5/8  of 

2  1/4  3/4  Keyway 


SET  BACK  NOSE*  (Fig.  206). 


A 

3/4 

H/4 
H/2 


B         C 

H/8  1 

H/2  H/4 

17/8  15/8 

2  1/4  2 


D 

1 

13/8 
13/4 
2 


E 

H/4 
H/2 
2 

21/2 


F 

25/8 
31/2 

41/2 
51/2 


Fig.  206. 


*  The  sides  of  the  nose  of  parting  tools  and  external  keyway  tools 
with  set  back  nose  (Fig.  206)  have  a  taper  back  from  the  ciitting  edge  of 
1  deg.  That  is,  in  the  plan  each  upper  edge  of  the  nose  tapers  inward 
1  deg.  from  a  plane  parallel  to  the  side  of  the  tool.  Each  side  also 
tapers  downwards  from  the  upper  edge  2  degs.  from  a  plane  parallel 
to  the  side  of  the  tool. 


1274 


THE   MACHINE-SHOP. 


i        !    ' 


1 


FIG.  207. 


FIG.  208. 


'  u 


s^  r 


^_j 


--JV 


FIG.  209. 


I  ill 


FIG.  211. 


3T 


FIG.  212. 


FIG.  213. 


MILLING  MACHINE   PRACTICE. 


1275 


Fillet  Forming  Tools  (Dimensions  in  Inches). 


ISO-DEGREE  (Fig. 

207). 

ISO-DEGREE  (Fig. 

208). 

A 

B 

C 

D 

E 

R 

A        B       C        D 

R 

5/8 

1 

1 

1/4 

0.04 

0.02 

5/8         1          1          0. 

2 

0.1 

5/8 

1 

1 

3/8 

0.10 

0.05 

5/8         110. 

4 

0.2 

3/i 

ll/o 

1  1/4 

1 

n  so 

n 

40 

u/4 

J.  Vo 

VARIOUS  RADII  (Fig 

209). 

Rad. 

A 

B 

C 

D 

E          F         G       H       J 

K 

L 

5/8 

.       3/4 

U/8 

U/4 

5/16 

3/16            7/8         5/8       1/4        1/4 

3/8 

V2 

0.8 

3/4 

U/8 

1.6 

3/8 

I/ 

t 

/8          5/8       1/4        1/4 

3/8 

1/2 

U/4 

U/2 

21/4 

21/2 

7/16 

5/16        1  1/8       1             1/4        S/g 

1/2 

5/8 

13/4 

^  U/2 

21/4 

31/2 

1/2 

3/8          U/8       1             V4        3/8 

1/2 

5/8 

Radius  Forming  Tools 

(Dimensions  in  Inches). 

ISO-DEGREE 

90-DEGREE,  RIGHT  AND 

LEFT 

(Fig. 

210). 

HAND  (Fig.  211). 

R(rad.)    A 

B 

C 

D 

K(rad.)    ABC 

D 

1/16 

5/8 

1 

3/ 

S 

1 

1/32 

5/8            1            1 

5/16 

1/8 

5/8 

1 

I/ 

2 

1 

1/16 

5/8            1            1 

3/8 

1/4 

5/8 

1 

1 

1/8 

5/8            1            1 

1/2 

i/a 

5/8 

1 

U/4 

1 

1/4 

5/8            1            1 

1 

1/2 

5/s            1            1 

1 

1/4 

90-DEGREE,  RIGHT  HAND  OR 

LEFT  HAND  (Figs.  212  and  213). 

R 

(rad.) 

A 

B 

C 

D             E             F 

3/4 

3/4 

1 

1/8 

5/16         1 

1/8         11/8         U/8 

1 

3/4 

1 

1/8 

3/ 

8            1 

1/4          1  3/8          1  1/4 

1 

1/2 

1 

1 

1/2 

5/ 

8          2 

21/4         2 

2 

1 

1/2 

21/4 

3/4          21/2         3               25/8 

MILLING   MACHINE  PRACTICE. 

Forms  of  Milling  Cutters. — Milling  cutters  are  made  from  either 
high  speed  or  carbon  steel.  The  former  can  be  subjected  to  the  more 
severe  service  and  are  especially  adapted  to  the  removal  of  large 
amounts  of  metal,  thus  dictating  their  use  as  roughing  cutters.  The 
varieties  of  cutters  in  common  use  and  the  work  to  which  they  are 
adapted  are  as  follows: 

The  Plain  Milling  Cutter  is  a  cylinder  with  teeth  on  the  periphery 
only,  and  is  used  for  producing  a  flat  surface  parallel  to  the  axis  of  the 
cutter.  Plain  milling  cutters  are  made  in  a  wide  variety  of  diameters 
and  widths  for  the  various  requirements  of  slab  milling,  key  way  cut- 
ting, sawing,  etc.  Cutters  less  than  3/4  in.  wide  are  usually  made  with 
straight  teeth,  while  wider  cutters  have  teeth  that  are  a  portion  of  a 
spiral.  The  spiral  form  enables  each  tooth  to  take  a  shearing  cut, 
reduces  the  stress  on  the  teeth,  and  prevents  shock  as  each  tooth 
engages  the  work,  thus  producing  smoother  surfaces  on  wide  work. 
The  spiral  cutter  requires  less  power  to  operate,  and  as  it  is  under 
less  strain,  the  tendency  to  chatter  is  reduced.  Cutters  for  milling 
wide  surfaces,  whether  of  the  spiral  or  straight  type  sometimes  have 
nicks  cut  in  the  teeth,  the  nicks  being  staggered  in  the  consecutive 
teeth.  It  is  claimed  that  such  cutters  can  be  run  with  coarser  feeds 
than  plain  cutters,  as  the  nicks  break  up  the  chips  and  prevent  jamming 
of  the  teeth.  Nicked  cutters  are  condemned  by  many  authorities, 
however,  for  the  reason  that  that  portion  of  a  following  tooth  opposite 
a  nick  is  required  to  do  double  the  usual  amount  of  work  With  a  re- 
sulting tendency  to  breakage. 

.  The  Side  Milling  Cutter  is  a  plain  milling  cutter  with  the  addition 
of  teeth  on  both  sides.  Side  milling  cutters  are  used  in  a  large  variety 
of  work.  Two  or  more  are  often  placed  on  the  same  arbor  with  a  space 
between  them,  in  which  case  they  are  known  as  straddle  mills.  Straddle 
mills  are  advantageously  used  where  the  work  has  to  be  milled  on 
two  parallel  sides,  *as  in  bolt  heads,  tongues,  etc.  Side  milling  cutters 
are  often  made  with  interlocking  side  teeth  for  milling  slots  to  a  stand- 
ard width,  the  width  of  the  slot  being  maintained  by  means  of  packing 
washers  between  the  two  parts  of  the  cutter. 


1276  THE   MACHINE-SHOP. 

Face  Milling  Cutters  have  teeth  cut  on  the  periphery  and  on  one  face 
of  a  disk.  The  face  mill  is  fastened  to  the  end  of  the  machine  spindle 
and  the  teeth  on  the  face  come  in  full  contact  with  the  work,  only  a 
small  portion  of  the  peripheral  teeth  being  in  action.  Some  face 
mills  have  no  teeth  at  all  on  the  periphery. 

The  End  Mill,  like  the  face  mill,  has  teeth  on  the  periphery  and 
on  one  end.  It  is  used  for  light  milling  operations,  such  as  the  milling 
of  slots,  facing  narrow  surfaces,  and  for  making  cuts  on  the  periphery 
of  pieces.  End  mills  are  of  four  general  types:  The  solid  end  mill,  the 
end  mill  with  center  cut,  the  slotting  end  mill  with  two  lips,  and  the 
shell  end  mill.  The  first  and  the  last  have  either  straight  or  spiral 
teeth.  In  the  solid  end  mill  the  teeth  are  cut  in  the  same  piece  that 
forms  the  shank.  The  shell  end  mill  has  a  hole  through  its  center  so 
that  it  can  be  mounted  on  an  arbor,  and  it  should  be  used  in  preference 
to  the  solid  mill  whenever  possible,  as  it  is  cheaper  to  replace  when 
worn  out  or  broken.  Tire  teeth  of  end  mills  with  center  cut  are  de- 
signed to  cut  at  the  inner  end,  whereas  the  teeth  of  solid  mills  have 
no  cutting  edge  at  this  point.  Center  cut  end  mills  are  used  for  mill- 
ing shallow  recesses  in  surfaces  where  there  has  been  no  hole  bored 
previously  for  starting  the  cut,  for  milling^squares  on  the  ends  of  shafts 
and  for  similar  work.  They  have  fewer  teeth  and  can  take  heavier 
cuts  than  solid .  end  mills  or  shell  end  mills.  Slotting  end  mills  are 
adapted  to  the  rapid  milling  of  deep  slots  from  the  solid  where  there 
has  been  no  hole  bored  for  starting  the  cut.  A  depth  of  cut  equal 
to  one-half  the  diameter  of  the  mill  can  usually  be  taken  from  solid 
stock. 

The  T-Slot  cutter  has  teeth  on  its  periphery  and  alternating  teeth 
on  its  sides,  the  teeth  being  cut  on  the  same  piece  that  forms  the  shank. 
In  making  a  T-slot,  a  groove  is  first  cut  with  an  ordinary  side  milling 
cutter  or  a  two-lipped  end  mill,  after  which  the  wide  groove  at  the 
bottom  is  cut  with  the  T-slot  cutter. 

Angular  Cutters  have  teeth  that  are  at  some  oblique  angle  to  the 
axis.  The  cutter  may  have  more  than  one  angle.  They  are  used  for 
milling  the  edge  of  a  piece  to  a  required  angle,  or  for  cutting  teeth  in 
cutters  or  reamers.  In  work  such  as  dovetailing  where  the  cutter 
cannot  be  fastened  to  the  arbor  with  a  nut,  it  is  made  with  a  threaded 
hole  or  with  the  cutter  in  one  piece  with  the  shank. 

Form  Cutters  are  of  irregular  outline  for  exactly  duplicating  pieces. 
In  one  style  of  form  cutter  the  teeth  are  sharpened  by  grinding  on  the 
tops  of  the  teeth,  which  necessarily  changes  the  contour  of  the  teeth 
and  therefore  the  outline  produced.  The  usual  style  is  so  made  that 
it  may  be  sharpened  by  grinding  the  face  of  the  tooth,  without  alter- 
ing the  contour.  This  permits  the  cutter  to  be  used  for  duplicate 
interchangeable  work  until  it  has  been  ground  to  a  point  where  the 
teeth  are  too  slender  to  stand  the  strain  of  the  work. 

Fly  Cutters  consist  of  a  single  cutter  similar  in  shape  to  a  planer 
tool,  held  in  and  rotated  by  an  arbor.  As  they  have  but  a  single 
cutting  edge,  they  are  used  but  rarely  outside  of  the  experiment  room 
or  tool-room.  The  fly  cutter  can  be  formed  exactly  to  any  desired 
shape  and  will  reproduce  this  shape  exactly.  Its  field  is  those  opera- 
tions that  would  not  bear  the  expense  of  special  shaped  commercial 
cutters,  as  where  but  one  or  two  teeth  are  to  be  made  of  a  special  form. 

Inserted  Tooth  Cutters. — When  it  is  required  to  use  plain  milling  cutters 
of  a  greater  diameter  than  about  8  in.,  or  side  milling  cutters  of  greater 
than  6  in.  diameter,  it  is  preferable  to  insert  the  teeth  in  a  disk  or  head, 
so  as  to  avoid  the  expense  of  making  solid  cutters  and  the  difficulty 
of  hardening  them,  not  merely  because  of  the  risk  of  breakage  in  hard- 
ening them,  but  also  on  account  of  the  difficulty  in  obtaining  a  uni- 
form degree  of  hardness  or  temper.  The  face  of  the  inserted  tooth 
should  be  undercut  a  few  degrees  from  the  radial  line,  thereby  giving 
a  smoother  cut  and  consuming  less  power  than  would  be  the  case  were 
the  face  of  the  tooth  flush  with  the  radial  line.  Drawings  of  inserted 
tooth  cutters  furnished  the  author  by  the  Cincinnati  Milling  Machine 
Co.,  show  a  rake  of  the  teeth  of  from  10  to  15  degrees. 

Number  of  Teeth. — There  is  no  standard  rule  for  the  number  of 
teeth  in  milling  cutters.  The  sizes  offered  commercially  by  cutter 
manufacturers  have  been  found  as  a  rule  satisfactory  for  most  purposes, 


MILLING  MACHINE   PRACTICE. 


1277 


but  in  roughing  out  work  where  as  much  metal  is  to  be  removed  as 
possible  in  a  given  time,  cutters  with  a  smaller  number  of  teeth  than 
the  standard  mills  are  advisable.  Furthermore,  a  short  lead  spiral 
on  coarse  tooth  cutters  adapts  them  to  a  large  range  of  work  that  is 
not  in  the  heavier  class.  Such  cutters  show  a  considerable  saving  of 
power  over  cutters  with  a  larger  number  of  teeth.  The  number  of  teeth 
in  cutters  of  various  types  is  given  in  Machinery,  April,  190£,  as  follows: 
Plain  milling  cutters  are  usually  manufactured  in  sizes  from  2  to  5 
in.  diameter,  and  up  to  6-in.  face.  The  use  of  solid  plain  milling 
cutters  of  over  5-in.  face  is  not  advised,  and  cutters  over  5-in.  face 
should  be  made  in  two  or  more  interlocking  sections. 

NUMBER  OF  TEETH  AND  AMOUNT  OF  SPIRAL  OF  PLAIN  MILLING  CUTTERS 
—  dia™-_I 


No.  of  teeth  = 


;  Length  of  Spiral  =  9  X  diam.  4-  4. 


Diameter  of  cutter, 

2     21/4     21/2     23/4     3      31/2     4     41/2     5     51/2     6     61/2     7      7  1/2     8 
Number  of  teeth, 

16   18        18        18        20   20       22   24        24   26        26   28        30   30        32 
Length  of  one  turn  of  spiral,  inches, 
22  241/4  261/2  283/4  31    35  1/2  40   441/2    49   531/2  58   621/2  67   71  1/2  76 

A  cutter  with  ah  included  angle  of  60°  (12°  on  one  side  and  48°  on  the 
other)  is  recommended  for  fluting  plain  milling  cutters,  although  cutters 
of  52°  (12°  and  40°)  are  commonly  furnished  by  manufacturers.  The 
angle  of  relief  of  milling  cutters  should  be  between  5°  and  7°. 

The  teeth  of  side  milling  cutters  should  have  the  same  general  form 
as  those  of  plain  milling  cutters,  excepting  that  the  cutter  used  to 
form  them  should  have  an  included  angle  of  about  75°. 

NUMBER  OF  TEETH  IN  SIDE  MILLING  CUTTERS. 

Number  of  teeth  =  3.1  diam.  +  11. 
Diameter  of  cutter, 

221/4     2  1/2     23/4       33  1/2     4     41/2     5     51/2     6      6  1/2     7     71/2     8     9 
Number  of  teeth, 

18  18        18        20        20    22      24    24      26  28      30     32      32     34      36  38 
Keyways  in  Milling  Cutters.  —  A   number   of  manufacturers   have 
adopted  the  keyways  shown  below,  as  standards.     The  dimensions  in 
inches  are  given  in  the  tables, 


FIG.  214. — SQUARE  KEYWAY.  r  FIG.  215. — HALF-RQUND  KEYWAY. 

SQUARE  KEYWAYS. 


Diam. 
Hole, 

3/8-8/16 

5/8-7/8 

15/16-H/8 

13/10-13/8 

17/16-13/4 

1  13/16-2 

21/16-21/2 

29/W-3 

Width 
W 

3/32 

VS 

5/32 

3/16 

V4 

5/16 

3/8 

7/16 

Depth. 
D 

3/64 

Vl6 

5/64 

3/32 

VS 

5/32 

3/16 

3/16 

Radius, 
R 

0.020 

0.030 

0.035 

0.040 

0.050 

0.060 

0.060 

0.060 

HALF-ROUND  KEYWAYS. 


Diam. 
Hole,  H 

8/8-5/8 

H/16-13/16 

7/8-1  3/16 

1  1/4-1  7/16 

H/2-2 

2  V16-2  7/16 

2  1/2-3 

Width 
W 

1/8 

3/16 

1/4 

5/10 

3/8 

7/16 

1/2 

Depth, 
D 

Vl6 

3/32 

1/8 

5/32 

3/16 

7/32 

1/4 

1278 


THE   MACHINE-SHOP. 


Diameter  of  Cutters. — It  is  advisable  to  use  cutters  of  as  small  a 
diameter  as  the  strength  will  admit.  The  smaller  the  cutter,  the 
shorter  the  distance  it  will  have  to  travel  in  milling  a  given  length. 
With  small  mills  also  there  is  less  liability  to  chatter  than  with  large 
ones.  In  addition  they  require  less  power  and  are  not  as  expensive 
as  large  ones.  The  Brown  &  Sharpe  Mfg.  Co.  states  that  a  difference 
of  1/2  in.  in  £he  diameter  of  the  mills  made  a  difference  of  10%  in  the 
cost  of  their  work.  In  surface  milling  the  cutter  should,  if  possible,  be 
wider  than  the  work. 

.Clearance  and  Rake  of  Cutters. — The  clearance  of  milling  cutters, 
or  the  amount  of  material  removed  from  the  top  of  the  teeth  back  of 
the  cutting  edge  to  permit  it  to  clear  the  surface  of  the  work  instead  of 
scraping  over  it,  depends  on  the  diameter  of  the  cutters.  It  must  be 
greater  for  small  cutters  than  for  large  ones.  For  plain  cutters  over 
3  in.  diameter,  the  clearance  angle  should  be  4  degrees,  and  for  cutters 
of  less  than  3  in.  it  should  be  6  degrees.  For  end  mills  it  should  be  about 
2  degrees.  It  is  considered  advisable  to  have  the  teeth  of  end  mills  from 
0.001  to  0.002  in.  lower  at  the  center  than  at  the  outside.  The  Cin- 
cinnati Milling  Machine  Co.  has  furnished  the  author  with  drawings 
of  cutters  of  various  types.  In  these  the  teeth  have  a  front  rake  of 
10  degrees.. 

Power  Required  for  Milling.  (Mech.  Engr.,  Oct.  26,  1907.)  — 
Mr.  S.  Strieff  made  a  series  of  experiments  to  determine  the  power 
required  to  drive  milling  cutters  of  high-speed  steel.  The  results  are 
shown  in  the  table  below.  A  proportionately  higher  amount  of  power 
is  required  for  light  than  heavy  milling,  as  the  power  to  drive  the  machine 
is  the  same  at  all  loads.  The  table  also  shows  that  the  depth  of  cut  does 
not  increase  the  power  required  in  the  same  proportion  as  the  width,  and 
that  work  with  a  quick  feed  and  a  deep  but  comparatively  narrow  cut 
requires  less  power  than  a  wide  cut  of  moderate  depth  with  slow  feed, 
the  amount  of  metal  removed  being  the  same  in  both  cases. 

Power  Required  for  Milling. 


"£ 

•  i'fc 

Feed. 

1^ 

fl 

n 

3 
O 

a; 

o 

S*- 

fclg 

Number  o 
Revoluti< 
of  Cuttei 
Minute. 

Per  Min- 
ute, In- 
ches. 

Per  Rev- 
olution, 
Inches. 

Cutting  S] 
of  Cuttei 
per  Mini 

Depth  of  < 
Inches. 

Width  of  i 
Inches. 

Horse-Po\ 
Required 

«3rf 

*!§! 

Horse-Po\ 
Required 
Pound-H 

24 

2.46 

0.10 

37 

0.26 

23.6 

25 

245 

0.102 

24 

3.50 

0.15 

37 

0.26 

10.2 

17 

150 

0.113 

24 

4.35 

0.18 

37 

0.14 

9.8 

17 

97 

0.175 

24 

3.50 

0.15 

37 

0.49 

9.8 

27 

490 

0.055 

19 

4.33. 

0.23 

29.5 

0.28 

9.3 

17 

331 

0.051 

23 

4.17 

0.18 

36 

0.28 

20.5 

27 

386 

0.070 

23 

4.17 

0.18 

36 

0.28 

9.8 

20 

183 

0.109 

40 

1.89 

0.05 

64 

0.24 

10.2 

17 

74 

0.230 

40 

3.94 

0.10 

64 

0.37 

13.8 

21 

331 

0.063 

40 

5.79 

0.14 

64 

0.16 

16.5 

17 

123 

0.138 

»•  P.  V.  Vernon  reports  (En'gr,  Mar.  9,  1909)  some  milling  machine 
tests  made  by  Alfred  Herbert,  Ltd.,  showing  the  horse-power  required 
to  slab  mild  steel  and  cast  iron.  The  tests  reported  include  44  on 
steel  and  38  on  cast  iron.  The  horse-power  was  determined  from  the 
current  readings  and  includes  the  motor  losses  and  also  a  constant 
loss  of  1.8  H.P.  in  the  jack  shaft  and  countershaft  of  the  machine. 

HORSE-POWER  PER  Cu.  IN.  PER  MINUTE  REQUIRED  FOR  SLABBING. 
Maximum.     Minimum.    Average. 

Steel 3.02  1.95  2.52 

Cast  iron 1.25  0.89  1.10 

Later  tests  reported  to  the  Manchester  Assoc.  of  Engrs.,  Nov.  23, 
1912,  by  Mr.  Vernon,  embodied  the  following  conclusions:  (1)  A  5-in. 
double  belt,  driving  a  16-in.  pulley  at  400  r.p.m.  (100,531  sq.  in.  of 


MILLING   MACHINE   PRACTICE. 


1279 


belt  per  min.)  geared  to  drive  4i/2-in.  high-speed  cutter  at  70  ft.  per 
min.  is  able  to  remove  as  much  as  48.1  cu.  in.  of  cast  iron  or  24.31  cu. 
in-  of  mild  steel  per  minute.  (2)  2090  sq.  in.  of  double  belt  passing 
over  a  pulley  per  minute  will  remove  1  cu.  in.  of  cast  iron  in  a  milling 
machine.  To  remove  1  cu.  in.  of  steel  the  belt  surface  passing  should 
be  4135  sq.  in.  (3)  A  4  i/2-in.  high-speed  cutter  on  a  2-in.  arbor,  run- 
ning at  70  ft.  per  min.  is  capable  of  removing  at  least  3.63  cu.  in.  of 
cast  iron,  and  possibly  as  much  as  6.01  cu.  in.,  and  at  least  2.125  cu. 
in.  of  mild  steel,  and  possibly  as  much  as  3.03  cu.  in.  per  min.  for  each 
inch  of  width  of  belt,  up  to  8  in.  From  the  earlier  tests  noted  above 
the  conclusion  was  reached  that  1  H.P.  would  remove  as  much  as  1.84 
cu.  in.  of  cast  iron  per  min.,  and  0.74  cu.  in.  of  mild  steel.  In  these 
tests  the  feed  in  cast  iron  ranged  between  1  27/32  and  109/ig  in.  per  min., 
the  depth  of  cut  from  0.14  to  1.10  in.,  while  in  steel  the  feeds  ranged 
from  5/8  to  103/8  in.  per  min.  and  the  depth  of  cut  from  0.10  to  1.10 
in.  per  min. 

A.  L.  De  Leeuw  gives  in  Am.  Mach.,  Aug.  8,  1912,  the  results  of  a 
large  number  of  tests  to  determine  the  horse-power  consumed  in  cutting 
machinery  steel  in  the  milling  machine.  From  the  tests  there  reported 
the  following  table  has  been  compiled,  the  figures  given  showing  the 
test  in  each  class  in  which  the  maximum  amount  of  metal  per  horse- 
power per  minute  was  removed.  The  figures  for  horse-power  are  net, 
the  motor  losses  having  been  deducted. 

Power  Required  for  Milling  Machinery  Steel  (A.  L.  De  Leeuw). 


£ 

3fc 

^ 

3fe 

^ 

*f 

3 

fe 

fe 

la 

9 

d 

8 

y 

s    • 

S 

U 

^ 

1 

oli 

o 
fc 

CJ 

O 

*0    • 

a  . 

^ 

o 

oli 

o 

.£J 

°fe 

AH 

.  o  i 

._§ 

£ 

.  o  »t 

"«.£ 

ex 

S!H 

1—1  S 

I 

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1 

ll 

•5  g 

g  +* 

^1 

1 

5l^ 

1 

|| 

0) 

Q 

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0 

w 

O 

5 

s~ 

1^ 

« 

t£ 

I 

0 

U 

S~ 

1/8 

20.5 

12.31 

10.96 

0.702 

B 

5/16 

20.0 

4.57 

11.959 

0.712 

A 

25.0 

15.4 

13.473 

0.714 

A 

20.0 

4.56 

7.34 

0.972 

A 

20.0 

11.81 

7.555 

0.977 

A 

21.5 

4.89 

7.14 

1.07 

C 

20.0 

11.83 

7.34 

1.007 

A 

16.0 

7.70 

11.0 

1.092 

2 

D 

22.0 

12.96 

6.85 

1.183 

C 

3/8 

20.0 

3.48 

10.96 

0.596 

B 

/16 

20.0 

7.34 

10.70 

0.643 

B 

20.0 

3.49 

7.07 

0.925 

A 

20.0 

7.29 

9.749 

0.701 

A 

40.5 

6.22 

12.35 

0.944 

3 

D 

20.0 

7.29 

7.07 

0.967 

A 

40. 

7.8 

14.55 

1.001 

3 

D 

21.5 

7.96 

6.85 

1.09 

C 

22. 

3.86 

6.85 

1.056 

1 

C 

/4 

20.0 

5.9 

12.62 

0.584 

B 

15.75 

7.66 

12.64 

1.137 

2 

D 

20.0 

5.84 

11.41 

0.64 

A 

1/2 

15.5 

4.61 

12.64 

0.912 

2 

D 

19.0 

5.58 

7.62 

0.915 

A 

40.0 

6.09 

15.93 

0.955 

3 

D 

21.5 

6.26 

7.14 

1.096 

C 

5/8 

40.0 

4.71 

17.07 

0.863 

3 

D 

5/16 

20.5 

4.68 

13.20 

0.554 

B 

3/4 

39.5 

3.63 

17.38 

0.782 

3 

D 

NOTE  1. — Cutter  No.  1  is  an  8-in.,  12-blade  face  mill;  No.  2  is  a 
10-in.,  16-blade  high-power  face  mill;  No.  3  is  a  41/2  in.,  10-tooth 
spiral  nicked  cutter. 

NOTE  2. — Material  A,  Elastic  Limit  36,400  Ib.  per  sq.  in.,  elongation 
36%,  reduction  of  area  66%;  material  B,  E.  L.  36,200  Ib.  per  sq.  in., 
elong.  36.5%,  red.  of  area  59. 6%;  material  C,  E.  L.  37,400  Ib.  per  sq.  in., 
elong.  36.5%,  red.  of  area  60%;  material  D,  E.  L.  55,000  Ib.  per  sq.  in., 
elong.  and  red.  of  area  not  given;  0.26  carbon,  0.5%  manganese. 

Modern  Milling  Practice  (1914).^ — The  limit  of  milling  operations  is 
determined  by  the  strength  and  durability  of  the  cutter.  A  rigid 
frame  on  the  machine  and  powerful  feed  mechanism  increase  these. 
The  chief  causes  of  low  output  are:  Improperly  constructed  cutters; 
insufficient  rigidity  in  the  machine;  and  timidity,  due  to  lack  of  ex- 
perience, of  both  builders  and  operators.  The  principal  cause  of 
cutter  failures  is  insufficient  space  for  chips  between  the  cutter  teeth. 
Fixed  rules  cannot  be  laid  down  for  proper  feeds  and  speeds  of  milling 
cutters,  these  depending  on  the  character  and  hardness  of  the  metal 


1280  THE  MACHINE-SHOP. 

being  cut.  On  roughing  cuts  it  is  desirable  to  run  the  cutter  at  a  speed 
well  within  its  limit,  and  use  as  heavy  a  feed  as  the  machine  can  pull. 
The  size  of  chip  taken  by  each  tooth  of  the  cutter  with  the  heaviest 
feeds  is  comparatively  light,  and  with  properly  sharpened  cutters 
there  is  little  danger  of  breaking  the  cutter  by  giving  too  great  a  feed. 
It  is  considered  better  practice,  however,  to  break  an  occasional  cutter 
than  to  run  machines  at  a  low  rate.  It  is  not  considered  desirable  to 
run  even  high  speed  steel  cutters  at  excessive  speeds.  The  great  value 
of  these  cutters  is  their  long  life  and  ability  to  hold  a  cutting  edge  as 
compared  with  carbon  steel  cutters.  It  is  important  to  keep  the 
cutters  sharp,  as  accurate  or  fast  work  is  impossible  with  dulled  teeth, 
and  a  dull  cutter  will  wear  away  faster  than  a  sharp  one.  Cutter 
grinders  should  always  be  used  for  sharpening  cutters. 

The  following  speeds  in  feet  per  minute  are  a  good  basis  for  roughing 
the  materials  indicated: 
Carbon  steel  cutters, 

Cast  Iron.     Machinery  Steel.     Tool  Steel.     Brass  and  Bronze. 

40  to  60  30  to  40  20  to  30  80  to  100 

High  speed  steel  cutters, 

80  to  100  80  to  100  60  to  80  150  to  200 

On  cast-iron  work  a  jet  of  air  delivered  to  the  cutter  with  sufficient 
force  to  blow  the  chips  away  as  fast  as  made  permits  faster  feeds  and 
prolongs  the  cutter's  life.  A  stream  of  oil  fed  under  heavy  pressure  to 
wash  the  chips  away  has  the  same  effect  when  cutting  steel.  On  finish- 
ing cuts  the  rate  of  feed  used  determines  the  grade  of  the  finish.  If  a 
spiral  mill  is  used  the  feed  should  range  from  0.036  in.  to  0.05  in.  per 
revolution  of  a  3-in.  diameter  cutter.  As  such  cuts  are  light  the  speed 
of  cutting  can  be  much  higher  than  that  used  for  roughing  cuts.  The 
nature  of  the  cut  is  a  factor  in  determining  speeds ;  a  saw  can  run  twice 
as  fast  as  a  surface  mill.  (Seepara?rar)h,p.  1282,  on  high-speed  milling:.) 
Keyseating  and  similar  work  can  be  best  done  with  a  plain  cutter 
rather  than  a  side  mill. 

Castings  should  be  pickled  in  a  solution  of  sulphuric  acid,  diluted 
with  water  to  a  specific  gravity  of  25  deg.  (Baume),  before  milling,  to 
rempve  the  hard  skin  and  sand  which  are  destructive  to  cutters.  If  the 
castings  are  later  to  be  painted,  they  should  not  be  immersed  in  the 
pickling  bath.  It  is  better  to  pour  the  solution  over  them,  allowing 
it  to  dry  before  making  another  application.  This  should  be  repeated 
4  or  5  times.  Forgings  should  be  pickled  in  a  solution  of  sulphuric  acid 
and  water  of  a  specific  gravity  of  30  deg.  (Baume),  for  from  3  to  12 
hours.  After  pickling,  forgings  and  castings  should  be  washed  with 
hot  water  to  remove  the  sand  and  acid. 

Milling  "with"  or  "against"  the  Feed.— Tests  made  with  the 
Brown  &  Sharpe  No.  5  milling-machine  (described  by  H.  L.  Arnold, 
in  Am.  Mack.,  Oct.  18,  1884)  to  determine  the  relative  advantage  of 
running  the  milling  cutter  with  or  against  the  feed  —  "with  the  feed" 
meaning  that  the  teeth  of  the  cutter  strike  on  the  top  surface  or 
"  scale "  of  cast-iron  work  in  process  of  being  milled,  and  "against  the 
feed  "  meaning  that  the  teeth  begin  to  cut  in  the  clean,  newly  cut  surface 
of  the  work  and  cut  upwards  toward  the  scale  —  showed  a  decided  advan- 
tage in  favor  of  running  the  cutter  against  the  feed.  The  result  is 
directly  opposite  to  that  obtained  in  tests  of  a  Pratt  &  Whitney  machine 
by  experts  of  the  Pratt  &  Whitney  Co. 

In  the  tests  with  the  Brown  &  Sharpe  machine  the  cutters  used  were  6 
inches  face  by  4 1/2  and  3  inches  diameter,  respectively,  15  teeth  in  each 
mill,  42  revolutions  per  minute  in  each  case,  or  nearly  50  feet  per  minute 
surface  speed  for  the  4l/2:inch  and  33  feet  per  minute  for  the  3-inch  mill. 
The  revolution  marks  were  6  to  the  inch,  giving:  a  feed  of  7  inches  per 
minute,  and  a  cut  per  tooth  of  0.011  inch.  When  the  machine  was 
forced  to  the  limit  of  its  driving  the  depth  of  cut  was  11/32  inch  when  the 
cutter  ran  in  the  "old"  way,  or  against  the  feed,  and  only  1/4  inch  when 
it  ran  in  the  "new"  way,  or  with  the  feed.  The  endurance  of  the  mill- 
ing cutters  was  much  greater  when  they  were  run  in  the  "old"  way. 
The  Brown  &  Sharpe  Mfg.  Co.  says  that  it  is  sometimes  advisable  to 
mill  with  the  feed,  as  in  surfacing  two  sides  of  a  piece  with  straddle 
mills,  the  cutters  will  then  tend  to  hold  the  work  down.  In  milling 
deep  slots  or  cutting  off  stock  with  thin  cutters  or  saws,  milling  with  the 
feed  is  less  likely  to  crowd  the  cutter  sidewfce  and  make  a  crooked  slot. 


MILLING  MACHINE  PRACTICE.  1281 

Lubricant  for  Milling  Cutters.  (Brown  &  Sharpe  Mfg.  Co.,  1907.) — 
An  excellent  lubricant,  to  use  with  a  pump,  for  milling  cutters  is  made 
by  mixing  together  and  boiling  for  one-half  hour,  1/4  Ib.  sal  soda,  tfz 
pint  lard  oil,  1/2  pint  soft  soap  and  water  enough  to  make  10  quarts. 
Oil  is  also  frequently  used  in  milling  steel,  wrought  iron,  malleable  iron 
or  tough  bronze. 

Typical  Milling  Jobs — Speeds — Feeds. — The  notes  below  compiled 
from  data  furnished  by  the  Brown  &  Sharpe  Mfg.  Co.  and  the  Cin- 
cinnati Milling  Machine  Co.  (1915)  show  examples  of  what  is  con- 
sidered good  commercial  milling  practice. 

Bars  of  0.60  Carbon  steel,  5/8  in.  thick,  21/2  in.  wide,  113/4  in.  long, 
had  22  rack  teeth,  7/16  in.  pitch  arid  Vs  in.  deep  milled  in  the  edge. 
The  bars  were  locked  four  at  a  time  in  a  vise.  A  gang  of  four  cutters 
was  used,  at  41  r.p.m.  and  a  feed  of  0.023  in.  per  revolution,  equivalent 
to  WIG  in.  per  minute.  Two  vises  were  used,  the  operator  loading  one 
while  the  bars  in  the  other  were  being  machined.  The  time  required 
per  piece  including  chucking  and  removing,  was  0.71  minute.  For 
milling  two  recesses  in  the  upper  edges  of  these  same  bars,  after  the  rack 
teeth  were  cut,  they  were  mounted  two  in  a  vise  with  distance  pieces 
between,  and  a  gang  of  foiir  3i/2-in.  side  mills  was  used,  milling  all  four 
recesses  at  once.  The  mills  rotated  at  50  r.p.m.,  and  the  feed  was 
0.068  per  revolution,  equivalent  to  3.4  in.  per  minute.  Two  vises  were 
used  as  before,  and  the  total  time  per  rack  was  2.2  minutes.  The  final 
operation  was  the  milling  of  a  slot  in  the  bar,  for  which  purpose  it  was 
held  at  the  ends  in  two  vises.  Two  holes  were  first  drilled  in  the  piece 
through  one  of  which  the  cutter  was  threaded.  The  slot  was  1-in. 
wide  and  9  in.  long.  A  is/ig-in.  helical  cutter  was  used  at  160  r.p.m. 
A  roughing  cut  was  first  taken  at  a  feed  of  0.015  per  revolution,  equiv- 
alent to  2.4  in.  per  min.,  after  which  the  piece  was  removed  and 
allowed  to  cool  before  the  finishing  cut  was  taken  at  a  feed  of  0.068  in. 
per  revolution,  or  10.8  in.  per  minute.  The  roughing  cut  removed 
11/2  cu.  in.  of  steel  per  minute.  The  total  time,  including  chucking, 
removing,  etc.,  was  7.5  minutes. 

Gray  iron  castings  8  1/4  in.  long,  8  1/2  in.  wide,  4 1/4  in.  thick,  with 
two  flanges  7/8  in.  high  and  7/g  in.  thick  projecting  above  the  upper 
face,  were  milled  on  the  entire  upper  surface  and  the  two  sides,  includ- 
ing top  and  sides  of  flanges  at  one  operation  by  a  gang  of  straddle  mills, 
the  largest  cutter  being  101/2  in.  diameter  and  running  at  21  r.p.m., 
with  6.3  in.  feed  per  minute.  Metal  was  removed  at  the  rate  of  19  cu.  in. 
per  minute,  the  maximum  depth  of  cut  being  3/16  in.  The  pieces  were 
held  in  a  string  jig,  removed  as  fast  as  they  were  traversed  by  the  gang 
of  cutters,  and  others  were  chucked  in  their  places.  They  were  milled 
in  lots  of  125  without  resharpening  of  the  cutters.  Time  per  piece, 
2  minutes. 

A  gray  iron  casting  22  in.  wide  and  9  in.  long  was  milled  on  its  upper 
surface  by  a  gang  of  three  6-in.  spiral  mills  with  a  total  face  width  of 
24  in.,  mounted  on  a  2-in.  arbor.  The  depth  of  cut  was  3/8  in.  and  the 
table  feed  was  73/4  in.  per  minute. 

A  surface  about  1  in.  wide  all  around  an  aluminum  transmission 
case  12  x  14  in.  was  milled  by  means  of  a  10i/2-in.  inserted  tooth  face 
mill  at  236  r.p.m.  Depth  of  cut,  i/g  in.,  table  feed,  0.068  in.  per  revolu- 
tion or  20  in.  per  minute.  A  double  fixture  was  used,  one  piece  being 
inserted  while  the  other  was  being,  milled.  Time,  including  chucking 
and  removal,  21/2  minutes  per  piec5. 

Gray  iron  castings,  10  1/4  in.  wide,  14  in.  long  X  1  3/4  in.  thick,  finished 
all  over,  and  a  slot  -Vs  X  1  in.  cut  from  the  solid.  A  gang  of  five  cutters 
was  used,  two  of  8  in.,  two  of  3  1/2  in.  and  one  of  53/4  in.  diameter,  re- 
spectively. These  took  a  cut  3/16  in.  deep  across  the  top,  and  two 
edges,  and  milled  the  slot  in  one  operation.  The  table  travel  was 
.2  in.  per  minute.  Tho  average  time,  including  chucking,  was  15.6 
minutes. 

Gray  iron  castings,  3  in.  and  61/2  in.  wide  X  251/4  in.  long,  1 1/4  in. 
thick,  were  surfaced  by  a  face  mill  8  in.  diameter  at  a  surface  speed  of 
80  feet  per  minute.  The  cut  was  3/16  in.,  and  the  table  travel  11.4  in. 
per  minute  in  the  3-in.  part  and  8  in.  per  minute  in  the  6  i/2-in.  part. 
The  total  time  for  finishing,  including  chucking,  was  seven  minutes. 
The  planer  required  23  minutes  for  the  same  operation.  In  finishing 


1282 


THE  MACHINE-SHOP. 


the  opposite  side  of  these  castings,  two  castings  were  milled  at  one  setting, 
3/i6  in.  of  stock  being  removed  all  over  and  two  slots  s/g  X  Vs  in. 
milled  from  the  solid.  A  gang  of  seven  cutters,  3  of  3  in.,  2  of  4  1/4  in., 
and  1  of  8  1/4  in.  diameter  was  used  at  38  r.p.m.  and  a  feed  of  0.1  in., 
giving  a  table  travel  of  3.8  in.  per  minute.  These  two  castings  were 
finished  in  18  minutes,  including  chucking,  the  actual  nulling  time  being 
eight  minutes  on  each  piece.  A  planer  working  at  55  ft.  cutting  speed 
finished  the  same  job  in  36  minutes. 

An  inserted- tooth  face  mill  12  in.  diameter  took  a  9-in.  cut,  i/g  in. 
deep  across  the  entire  face  of  a  gray  iron  casting  at  a  table  travel  of 
5  in.  per  minute.  The  length  of  cut  was  18  in.  and  the  time  required 
6 1/2  minutes. 

The  following  table  summarizes  a  number  of  typical  jobs  of  milling : 

Typical  Milling  Jobs. 


Cut,  In. 

Cutter. 

If 

i-s 

1 

o 

Nature  of 

Material 

M<^5 

jj 

2 

S  c   . 

Work. 

Cut. 

r 

J 

sfc 

I" 

H  a 

£S5 

d 

g 

rt 

°tf        . 

$ 

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eu  g 

PH 

"C-M 

o>  w 

3j9 

tb  <i5  3 

& 

P 

Q~ 

tf 

wfo 

£& 

HM 

S  a° 

Face  Milling 

Cast  Iron 

1/8 

6 

8 

26 

54 

0.168 

4.36 

3.27 

" 

8 

9.51 

26 

64 

0.58 

15.0 

15.0 

" 

0.150 

8 

9  51 

24 

60 

0.625 

15. 

18.0 

Mall.  Iron 

1/16-3/32 

62 

7.5 

56 

110 

0.223 

12.5 

SteeP 

5 

61 

32 

50 

0.148 

4.75 

'92  '  ' 

"      6 

1/86 

6 

9.5i 

24 

60 

0.52 

12.5 

9.375 

Surfacing 

Cast  Iron 

1/32 

3 

4 

68 

71 

0.18 

12.75 

1.75 

" 

0.1   . 

12 

4.54 

45 

52 

0.266 

12.0 

14.4 

«< 

0.1 

4 

3* 

104 

81 

0.144 

15.0 

6.0 

" 

i/a 

4 

35 

104 

81 

0.078 

8.125 

4.06 

" 

1/8 

8 

3.55 

90 

83 

0.167 

15.0 

15.00 

" 

1/8 

12 

3.5i 

53 

55 

0.226 

12.0 

14.4 

" 

0.225 

8 

3.55 

85 

77 

0.118 

10.0 

18.0 

" 

1/4 

8 

3.55 

81 

75 

0.154 

12.5 

25.0 

" 

1/4 

8 

3.55 

94 

86 

0.159 

15.0 

30.0 

Tool  Steel 

1/16 

21/2 

37 

37 

29 

0.05 

1.85 

0.289 

Steel 

0.1 

6 

35 

104 

81 

0.037 

3.875 

2.32 

" 

0.15 

6 

35 

104 

81 

0.037 

3.875 

3.48 

" 

0.166 

6 

3.55 

90 

83 

0.083 

7.5 

7.5 

" 

0.222 

6 

3.55 

105 

96 

0.071 

7.5 

10.0 

" 

0.240 

6 

3.55 

94 

86 

0.133 

12.5 

18.0 

" 

0.311 

6 

3.55 

100 

92 

0.075 

7.5 

14.0 

Brass 

0.01 

21/2 

37 

100 

78 

0.25 

25.0 

0.675 

Bronze 

1/64 

3 

33 

166 

130 

0.05 

8.3 

0.389 

T-Slotting 

Cast  Iron 

See  No 

te» 

1  1/16 

252 

75 

0.05 

12.6 

6.693 

Slotting!0 

Steel 

1  3/16 

1.5H 

163 

65 

0.007 

1.25 

2.2 

Sawing 

•  / 

3/64 

5 

70 

91 

0.05 

3.5 

1  Inserted  teeth,  high-speed  steel.  -  Maximum.  3  Chrome  nickel 
steel.  4  Carbon  steel,  nicked  spiral  cutter.  6  High-speed  steel,  spiral 
nicked  cutter.  •  Machinery  steel,  tensile  strength,  65,000  Ib.  7  End 
mill.  8End  mill  with  spiral  teeth;  work  done  by  peripheral  teeth. 
9  Both  sides  of  cutter  engaged,  making  slot  width  equal  to  cutter 
diameter;  slot  IVie  X  1/2  in.  10  Milling  slots  from  solid  plate  13/i6  in. 
thick.  11  Helical  end  mill,  front  of  which  is  formed  as  a  regular  twist 
drill.  Operator  first  drills  through  the^plate  with  it,  and  then  uses  it 
as  a  milling  cutter. 

High  Speed  Milling.— L.  P.  Alford  describes  (Am.  Mach.,  April  16, 
1914)  a  system  of  high-speed  milling  developed  by  the  Cincinnati 
Milling  Machine  Co.,  which  permits  of  cutter  speeds  and  feeds  from 
8  to  12  times  as  great  as  are  ordinarily  used.  The  fundamental  con- 
dition for  this  practice  is  the  provision  of  ample  lubrication  of  the 


MILLING  MACHINE  PBACTICE. 


1283 


cutter  and  work.  The  cutter  is  deluged  with  about  12  gal.  per  minute 
of  lubricant,  which  is  delivered  through  a  hood  which  complete!}'  sur- 
rounds the  cutter.  The  lubricant  is  delivered  under  pressure,  and 
in  addition  to  cooling  the  cutter  and  work,  washes  away  the  chips 
from  the  teeth  of  the  cutter,  preventing  them  from  being  carried  back 
into  the  cut,  clogging  it,  dulling  the  cutter  and  marring  the  finished 
surface.  -  Other  requisites  for  high-speed  milling  are  powerful,  heavy 
and  rigid  machines,  and  cutters  with  wide  spaced  teeth  which  will 
permit  the  use  of  heavy  feeds  and 'high  speeds.  The  following  tests 
were  cited  to  show  what  is  possible  with  this  system  of  milling.  The 
material  cut  was  machinery  steel,  0.2  carbon,  0.5  manganese,  with  a 
tensile  strength  of  55,000  to  65,000  Ib.  per  sq.  in.  The  cutters  were 
of  high  speed  steel. 

Data  and  Results  of  High  Speed  Milling  Tests. 


Cutter. 

d 

M 

Cut. 

Cutter 
Speed. 

1 

J 

. 

i 

> 

sf 

A 

fe 

£§ 

1 

jK 

J2  So 

rt  h-t 

5  ' 

p 

Jl 

M    . 

I* 

tx 

a 

•S 

i 

bo 

3 

I 

a.S 

T3  CB 

r 

1 

S 

25 

31/2 

9 

10 

6 

1  1/2 

1/8 

5 

18 

500 

458 

30  1/2 

2 

S 

25 

31/2 

9 

to 

6 

0.02 

5 

18 

500 

458 

7.23 

3 

H 

69 

31/2 

^ 

15 

6 

1  1/2 

(1/16  I 

510 

470 

301/2 

4 

L 

16 

15 

1 

U/2 

j  3/16  » 
M/4    f 

510 

835 

301/2 

1  7-Tooth  1 

5 

G 

7' 

M/2 

12 

10 

H/4 

-<30-PitchV.. 

181/4 

218 

200 

112 

(    Gear.    | 

62 

S 

25 

31/2 

9 

to 

6 

H/2 

.Vi 

5 

21/2 

87 

80 

20 

1  Diametral  Pitch.  2  Same  cutter  and  block  as  in  Test  No.  1,  but 
run  without  lubricant.  Test  stopped  when  cutter  showed  signs  of 
distress  after  cutting  2*/2  in.  Edges  of  teeth  blued. 

NOTE. — S,  spiral  mill;  H,  helical  mill;  L,  slotting  cutter;  G,  gear 
cutter. 

As  a  criterion  of  the  life  of  cutters  under  the  above  conditions,  a  cutter 
of  the  type  used  in  test  No.  5,  was  run  to  destruction.  It  milled  6700 
in.,  not  including  cutter  approach,  the  equivalent  of  cutting  223  gears 
of  1-in.  face,  7  pitch,  30  teeth. 

Limiting  Factors  of  Milling  Practice. — Discussing  the  above  tests 
Mr.  Alford  gives  the  following  as  the  limiting  factors  of  milling  ma- 
chine practice:  (1)  Power  of  the  machine.  Increased  speed  requires 
greater  power  per  cubic  inch  of  metal  removed;  according  to  the 
Cincinnati  Milling  Machine  Co.,  doubling  the  speed  necessitates  a  10% 
increase  of  power  per  cubic  inch  of  metal  removed.  (2)  Ability  of  the 
cutter  to  remove  metal.  Increased  speed,  with  the  same  feed  increases 
the  ability  of  the  cutter  to  cut,  due  to  the  smaller  chip  removed  by 
each  tooth.  This  means  a  decrease  of  strain,  wear  and  heating  effect. 
The  total  or  final  heating  effect  is  increased,  but  this  may  be  counter- 
acted by  copious  lubrication.  (3)  Size  and  spring  of  arbor.  The  size 
of  the  arbor  is  limited  by  the  size  of  commercial  cutters.  The  strain 
on  the  arbor  depends  on  the  feed  per  minute.  An  increase  of  speed, 
lessening  the  pressure  per  tooth,  reduces  the  arbor  strain,  and  tends 
to  do  away  with  the  limitation  imposed  by  the  arbor.  (4)  Heating  of 
the  cutter,  often  the  most  important  limitation.  This  can  be  over- 
come by  sufficient  lubricant  to  remove  all  heat  as  fast  as  it  is  generated. 
(5)  Wear  of  the  cutter.  This  is  dependent  on  the  number  of  lineal 
inches  milled,  depth  of  cut  and  feed  per  revolution  being  constant. 
Increased  speed  increases  the  wear  per  unit  of  time.  Wear  may  be 
somewhat  reduced  with  high  speed  by  copious  lubrication  which  washes 
away  the  chips,  thus  preventing  the  grinding  action  due  to  cutting 
up  chips.  (6)  Breakage  of  cutters.  Frail  cutters  limit  production, 
as  only  a  certain  maximum  feed  per  revolution,  dependent  on  their 


1284 


THE  MACHINE-SHOP. 


strength,  can  be  taken.  Increased  speed,  with  constant  feed,  will 
increase  production  without  increasing  the  cutter  strain  or  danger  of 
breakage.  (7)  Heating  of  work.  Uneven  local  heating  when  milling 
will  produce  uneven  surfaces,  for  the  swelled  portions  will  be  cut  away. 
This  action  is  progressive  as  the  total  heat  increases  as  the  cut  advances. 
The  absence  or  prevention  of  heating  by  copious  lubrication  does 
away  with  this  limitation.  (8)  Spring  of  work.  This  limitation  is 
minimized  for  the  same  reasons  given  in  (6).  (9)  Spring  of  fixture. 
The  same  analysis  applies  as  in  (6).  If  the  pressure  per  tooth  is  re- 
duced, the  pressure  for  holding  may  be  reduced,  and  clamping  fixtures 
may  be  made  to  operate  more  quickly.  An  increase  in  cutting  speed 
therefore  will  tend  to  increase  the  speed  of  operation  of  the  clamping 
devices  and  fixtures.  (10)  Spring  of  the  machine.  The  same  argu- 
ments apply  as  in  (9).  (11)  Distance  of  revolution  marks  on  the  work. 
This  is  the  limiting  feature  in  perhaps  90%  of  milling  work,  which  is 
governed  by  polishing  or  some  subsequent  operation.  If  the  marks 
are  far  apart,  polishing  cannot  be  satisfactorily  done.  Increased 
speed,  with  constant  feed  will  bring  these  marks  closer  together.  (12) 
Smoothness  of  cuC.  High  speed  milling,  both  by  the  action  of  centrif- 
ugal force  and  by  copious  flooding  removes  the  chips  completely  from 
the  cutter  and  eliminates  the  grinding  effect  on  the  finished  surface. 
With  a  given  distance  between  revolution  marks,  high  speed  will  give 
a  smoother  surface. 

Speeds  and  Feeds  for  Gear  Cutting. — The  speeds  and  feeds  which 
can  be  used  in  gear  cutting  are  affected  by  many  variables,  among 
which  may  be  noted:  The  material  and  shape  of  the  cutter,  the  latter 
condition  involving  both  the  strength  and  the  ability  of  the  teeth  to 
clear  themselves  of  chips;  the  material  and  shape  of  the  gear,  shape 
influencing  the  speed  and  feed  in  that  a  heavy  rugged  gear  will  permit 
,  higher  speeds  and  heavier  feeds,  even  in  hard  material  than  will  a  light 
springy  one;  accuracy  of  finish  required;  quality  of  lubricant  used; 
rigidity  of  machine.  The  following  table  shows  tentative  speeds 
recommended  by  Gould  and  Eberhardt,  which  may  serve  as  a  pre- 
liminary guide,  pending  the  determination  of  the  best  combination 
for  each  particular  case.  They  represent  average  practice  in  medium 
grades  of  cast  iron  and  steel. 


High-Speed  Steel  Cutters. 

Carbon  Steel  Cutters. 

Min. 

Average. 

Max. 

Min. 

Average  . 

Max. 

Cast  iron,  ft.  per  min.. 
Steel,  ft.  per  min  

60 
45 

70 
50 

80 
55 

35 

25 

60 
40 

45 
30 

The  feeds  in  inches  per  minute  recommended  by  the  same  company, 
depend  on  the  capacity  of  the  machine  and  on  the  size  of  the  teeth. 
Thus,  in  a  machine  whose  maximum  capacity  is  for  gears  with  teeth 
of  one  diametral  pitch  in  cast  iron  and  of  1 1/4  diametral  pitch  in  steel, 
the  feeds  range  from  2.3  ,in.  per  minute  in  cast  iron  for  gears  of  1 
diametral  pitch  to  6.9  in.  for  gears  of  6  diametral  pitch,  carbon  steel 
cutters  being  used.  For  high-speed  steel  cutters,  the  corresponding  fig- 
ures are  3.5  and  11.0  in.  In  steel,  the  feeds  under  the  same  conditions 
are  1.9  in.  and  4.5  in.  per  minute  with  carbon  steel  cutters  and  2.8  in. 
and  6.9  in.  per  minute  with  high-speed  steel  cutters.  Likewise  in  a 
machine  whose  maximum  capacity  is  teeth  of  4  diametral  pitch  for 
cast-iron  gears  and  5  diametral  pitch  for  steel  gears,  the  feed  given  for 
carbon  steel  cutters  for  gears  of  4  diametral  pitch  is  2.6  in.  per  minute 
in  cast  iron  and  1.5  in.  per  minute  in  steel.  For  gears  of  24  diametral 
pitch  the  figures  are  for  cast  iron  7.6  in.  per  minute,  and  for  steel  5.8  in. 
per  minute.  Using  high-speed  steel  cutters,  the  corresponding  figures 
are:  4  diametral  pitch,  cast  iron  4.5  in.  per  minute;  steel,  3.5  in.  per 
minute;  24  diametral  pitch,  cast  iron  10  in.  per  minute;  steel,  7.6  in.  per 
minute.  These  figures  merely  show  the  range  of  feeds  that  are  possible 
in  gear  cutting,  and  the  tables  furnished  by  the  manufacturers  of  gear- 
cutting  machines  should  be  consulted  for  the  proper  feeds  for  particular 
cases. 


DRILLS  AND   DRILLING. 


1285 


DRILLS  AND  DRILLING. 

r  Constant  for  Finding  Speeds  of  Drills. —  For  finding  the  speed  in 
feet  when  the  number  of  revolutions  is  given ;  or  the  number  of  revolu- 
tions, when  the  speed  in  feet  is  given. 

Constant  =  12  -=-  (size  of  drill  X  3.1416). 

Number  of  revolutions  =  Constant  X  speed  in  feet. 

Speed  in  feet  =  Number  of  revolutions  -r-  constant. 


Size 
Drill, 
In. 

Con- 
stant. 

Size 
Drill, 
In. 

Con- 
stant. 

Size 
Drill, 
In. 

Con- 
stant. 

Size 
Drill. 
In. 

Con- 
stant. 

Size 
Drill, 
In. 

Con- 
stant. 

1/8 

30.55 

3/4 

5.09 

3/8 

2.78 

2 

.91 

25/g 

.45 

3/16 

20.38 

13/16 

4.70 

7/16 

2.66 

21/16 

.85 

2  H/16 

.42 

1/4 

15.28 

7/8 

4.36 

1/2 

2.55 

21/8 

.80 

23/4 

.39 

5/16 

12.22 

15/16 

4.07 

9/16 

2.44 

23/i6 

.75 

2  13/16 

.36 

3/8 

10.19 

3.82 

5/8 

2.35 

21/4 

.70 

27/8 

.33 

7/16 

8.73 

1/16 

3.59 

H/16 

2.26 

25/16 

.65 

2  15/16 

.30 

1/2 

7.64 

1/8 

3.39 

3/4 

2.18 

23/8 

.61 

3 

.27 

9/16 

6.79 

3/16 

3.22 

13/16 

2.11 

27/16 

.57 

31/16 

.25 

i   5/8 

6.11 

3.06 

7/8 

2.04 

21/2 

.53 

31/8 

.22 

H/16 

5.56 

5/16 

2.91 

15/16 

1.97 

29/16 

.49 

31/4 

.18 

The  Cleveland  Twist  Drill  Co.,  Cleveland,  states  (1915)  that  it  is 

safe  to  start  carbon  steel  drills  with  a  peripheral  speed  of  30  ft.  per 
minute  in  soft  tool  and  machinery  steel,  35  ft.  per  min.  in  cast  iron,  and 

60  ft.  per  min.  in  brass.  In  all  cases  a  feed  of  from  0.004  to  0.007  in. 
per  revolution  should  be  used  for  drills  1/2  in.  diam.  and  smaller,  and  of 
from  0.005  to  0.015  in.  per  revolution  for  drills  larger  than  J^  in.  In 
the  case  of  high  speed  steel  drills  these  fee\Js  should  not  be  changed,  but 
the  peripheral  speed  may  be  increased  from  2  to  2  1/2  times.  The  table 
below  is  calculated  on  the  basis  of  the  speeds  given  above  for  carbon 
steel  drills,  and  on  the  basis  of  speeds  2  1/3  times  higher  for  high-speed 
drills.  The  running  speed  may  be  higher  or  lower  than  the  starting 
speed,  and  must  be  determined  by  good  individual  judgment  for  each 
case. 

Starting  Speeds  for  Carbon  and  High-Speed  Steel  Drills  in 
Steel,  Cast  Iron  and  Brass,     R.  P.  M. 


Steel. 

Cast 
Iron. 

Brass. 

Steel. 

Cast 
Iron. 

Brass. 

Drill 

Drill 

> 

Diam., 

T3 

d 

•d 

H 

Diam., 

J* 

'd 

J* 

"8 

c 

In. 

£ 

-si 

| 

.d! 

| 

In. 

A  0, 

.di, 

| 

8 

Jwo 

• 

tfS 

rt 

.MM 

8 

bcc/2 

Sf 

Sfw 

SPoa 

0 

W 

O 

w 

u 

a 

o 

W 

u 

w 

5 

a 

1/16 

1833 

4278 

2139 

4991 

3667 

H/8 

102 

238 

119 

278 

204 

475 

1/8 

917 

2139 

1070 

2496 

1833 

4278 

H/4 

92 

214 

107 

249 

183 

428 

3/16 

611 

1426 

713 

1664 

1222 

2852 

13/8 

83 

194 

97 

227 

167 

389 

1/4 

458 

1070 

535 

1248 

917 

2139 

H/2 

76 

178 

89 

208 

153 

357 

5/16 

367 

856 

428 

998 

733 

1711 

15/8 

70 

165 

82 

192 

141 

329 

3/8 

306 

713 

357 

832 

611 

1426 

13/4 

65 

153 

76 

178 

131 

306 

7/16 

262 

611 

306 

714 

524 

1222 

17/8 

61 

143 

71 

166 

122 

285 

1/2 

229 

535 

263 

614 

458 

1070 

2 

57 

134 

67 

156 

115 

267 

5/8 

183 

428 

215 

500 

367 

856 

2V4 

51 

119 

60 

139 

102 

238 

3/4 

153 

357 

178 

415 

306 

713 

21/2 

46 

107 

54 

125 

92 

214 

7/8 

131 

306 

153 

357 

262 

611 

23/4 

42 

97 

49 

114 

83 

194 

1 

115 

267 

134 

312 

229 

535 

3 

38 

89 

45 

104 

76 

178 

A  drill  with  a  tendency  to  wear  away  on  the  outside  is  running  too  fast; 
if  it  breaks  or  chips  on  the  cutting  edges  it  has  too  much  feed. 

Forms  of  Drills. — The  common  form  of  twist  drill  is  a  cylinder  with 
two  spiral  flutes  milled  in  it.  Another  type,  for  heavy  duty,  consists 
of  a  twisted  bar  of  flat  steel.  The  angle  that  the  cutting  edges  makes 
with  the  axis  of  the  drill  has  been  fixed  at  about  59°.  A  decrease 
in  this  angle  decreases  the  pressure  required  for  feeding  the  drill,  but 
increases  the  power  required  to  turn  it.  The  cutting  edge  of  a  spotting 


1286 


THE  MACHINE-SHOP. 


drill  should  make  an  angle  of  about  50°  with  the  axis  of  the  drill. 
The  clearance  angle,  that  is,  the  angle  between  the  surface  back  of  the 
cutting  edge  and  a  plane  perpendicular  to  the  axis  of  the  drill,  ranges 
from  12  to  15°,  the  angle  increasing  slightly  toward  the  center.  In 
general,  the  small  clearance  is  best  for  hard  metals  and  the  large 
clearance  for  soft  metals. 

Drilling  Compounds. —  The  following  drilling  compounds  or  lubri- 
cants are  recommended  when  drilling  the  materials  given  below : 


Steel  (hard) — kerosene,  turpentine, 

soda  water. 

Steel  (soft) — soda  water,  lard  oil. 
Iron  (wrought) — soda  water,  lard 

oil. 


Iron  (malleable) — soda  water. 
Iron  (cast) — none  or  air  blast. 
Brass — paraffine  oil. 
Aluminum — soda  water,  kerosene. 


Warming  the  lubricant  before  applying  it  to  high-speed  drills  is 
recommended,  and  precautions  should  be  taken  against  suddenly  chilling 
high-speed  drills  by  the  lubricant  after  they  have  become  heated. 

Twist  Drill  and  Steel  Wire  Gages. — Three  standards  of  gages  for 
twist  drills  and  steel  wire  are  in  use — the  Manufacturers'  Standard, 
used  by  the  Morse  Twist  Drill  Co.,  Brown  &  Sharpe,  and  other  manu- 
facturers, the  Stubs  gage,  and  that  of  the  Standard  Tool  Co.  The 
Stubs  and  Manufacturers'  gages  are  given  in  the  table  on  page  30. 
The  Standard  Tool  Co.  gage  agrees  with  the  Manufacturers'  gage  for 
sizes  from  Nos.  1  to  60,  inclusive,  and  with  the  Stubs  gage  for  sizes 
from  Nos.  61  to  80.  In  addition  it  has  additional  H  sizes  interpolated 
at  Nos.  601/2,  681/2,  69 1/2,  71 1/2.  731/2,  741/2,  781/2,  and  791/2. 

Power  Required  to  Drive  High-Speed  Drills. —  H.  M.  Norris,  me- 
chanical engineer  of  the  Cincinnnti-Bickford  Tool  Co.,  found  (1914) 
that  the  power  absorbed  by  a  6-foot,  high-speed,  high-power,  plain 
radial  drill  fitted  with  a  variable  speed  motor,  in  driving  drills  in 
machine  steel  under  a  stream  of  water,  varied  in  accordance  with  the 
formula: 

H.P.  =  0.152  (R  +  2.1)  di.s/o.74  [r  -  /—  +  6.8 

L        \    d 

R  =  ratio  between  speed  of  the  intake  shaft  and  speed  of  the  spindle; 
d  =  diameter  of  drill,  in.;  /=  feed  in  thousandths  of  an  inch  per  revolu- 
tion; r  =  rev.  per  min. 

The  values  deduced  from  this  formula  are  given  in  the  table,  p.  1287; 
the  figures  1,  2,  and  4  in  the  column  "Ratio  R" represent  the  ratios  of 
1  to  1,  1  to  2,  and  1  to  4  respectively.  The  table  also  gives  the  results 
obtained  in  drilling  medium  cast-iron,  but  these,  at  this  writing,  have 
not  been  reduced  to  a  formula. 

The  American  Tool  Works  Co.,  Cincinnati,  has  furnished  the 
author  with  the  tests  given  in  the  table  below,  made  in  1912,  showing 
the  power  required  to  drive  drills  in  a  6-foot  plain  triple-geared  radial 
drill  made  by  that  company.  This  table  shows  the  results  obtained 
with  speeds  and  feeds  higher  than  those  given  by  Mr.  Norris. 

Power  Required  to  Drive  Drills.     (Amer.  Tool  Works  Co.,  1912.) 


Size 
of 
Drill, 
In. 

Cast  Iron. 

Steel. 

Speed. 

Feed. 

Horse- 
power 

Speed. 

Feed. 

Horse- 
power. 

Rev. 
per 
Min. 

Ft. 
Min. 

Per 
Rev., 
In. 

In. 
per 
Min. 

Rev. 
per 
Min. 

Ft. 
per 
Min. 

Per 

Rev., 
In. 

In. 
per 
Min. 

U/4 

H/2 

yA 

f, 

430 
430 
430 
430 
297 
202 
178 
143 

111.25 
140 
157 
197 
156 
119 
116.5 
112 

0.049 
.049 
.049 
.049 
.049 
.036 
.036 
.036 

21.07 
21.07 
21.07 
21.07 
14.56 
7.27 
6.40 
5.14 

8.26 
11.65 
18.65 
19.75 
19.79 
14.82 
11.24 
14.31 

335 
258 
229 
178 
143 
143 
143 
47.5 

88 
84.5 
90 
81.5 
75 
84.2 
93.6 
37.2 

0.036 
.026 
.018 
.018 
.018 
.018 
.013 
.026 

12.06 
6.70 
4.12 
3.20 
2.57 
2.57 
1.86 
1.21 

13.50 
10.43 
14.86 
9.91 
12.32 
15.06 
13.51 
12.46 

DRILLS   AND   DRILLING. 


1287 


Power  Required  for  Drilling  Cast  Iron  and  Steel.     (H.  M.  N orris,  1915.) 


Cast  Iron. 

Machinery  Steel. 

c 

.S 

0.020  in. 

0.030  in. 

0.040  in. 

0.012  in. 

0.016  in. 

0.020  in. 

i9 

r 

Ifc 

c 

Feed. 

Feed. 

Feed. 

Feed. 

Feed. 

Feed. 

.2 

If 

'§ 
& 

&5 

M 

0) 
£ 

M. 

si 

M 

£ 

ft-S 

fc 

Jd 

ft-~ 

| 

**  . 

fe 

fc 

.5 

ft 

0 

•g  g 

w  ft 

"5  G 

<«  ft 

5  G 

w  p, 

"5  c 

03    ft 

3  c 

M    ft 

•5  c 

tl 

3 

-p 

i 

'-P 

ft'3 

g 

ft'3 

O 

8*1 

o 

£1 

i 

fa 

0 

8*1 

0 

Q 

O 

& 

tf 

Q 

w 

Q 

w 

Q 

W 

Q 

w 

Q 

W 

Q 

W 

3/4 

60 

306 

6.12 

2.76 

9.18 

3.52 

12.24 

4.20 

3.67 

2.84 

4.90 

3.53 

6.12 

4.15 

3/4 

70 

357 

7.14 

3.36 

10.71 

4.29 

14.28 

5.10 

4.28 

3.49 

5.72 

4.32 

7.14 

5.09 

3/4 

80 

408 

8.16 

3.98 

12.24 

5.08 

16.32 

6.04 

4.90 

4.12 

6.53 

5.10 

8.16 

6.02 

3/4 

90 

459 

9.18 

4.60 

13.77 

5.86 

18.35 

6.96 

5.51 

4.76 

7.34 

5.89 

9.18 

6.95 

3/4 

100 

509 

10.18 

5.21 

15.27 

6.64 

20.36 

7.89 

6.11 

5.40 

8.14 

6.68 

10.18 

7.88 

60 

229 

2 

4.58 

2.88 

6.87 

3.67 

9.16 

4.36 

2.75 

4.01 

3.66 

4.96 

4.58 

5.85 

70 

267 

5.34 

3.09 

8.00 

3.94 

10.67 

4.68 

3.21 

3.72 

4.27 

4.60 

5.34 

5.43 

80 

306 

6.12 

3.66 

9.18 

4.66  12.2-4 

5.54 

3.67 

4.394.89 

5.44 

6.12 

6.42 

90 

344 

6.88 

4.22 

10.32 

5.38  13.76 

6.39 

4.13 

5.165.50 

6.39 

6.88 

7.54 

100 

382' 

7.64 

4.79 

11.46 

6.11 

15.27 

7.26 

4.59 

5.79 

6.11 

7.17 

7.64 

8.46 

U/4 

60 

1831  2 

3.66 

3.10 

5.49 

3.95 

7.32 

4.70 

2.19 

4.21 

2.93 

5.21 

3.66 

6.15 

11/4 

70    214    2    4.28 

3.80 

6.42 

4.84 

8.56    5.75|2.57 

5.173.42 

6.40 

4.28 

7.55 

11/4 

80    245    2    4.90 

4.50 

7.36 

5.74 

9.80    6.822.94 

5.96j3.92 

7.57 

4.90 

8.93 

11/4 

90 

275 

5.48 

3.95 

8.22 

5.04  11.00    5.993.29 

5.3514.38 

6.62 

5.48 

7.81 

U/4 

100 

306 

6.12 

4.49 

9.18 

5.73 

12.24 

6.81 

3.67 

6.08 

4.89 

7.52 

6.12 

8.87 

U/2 

60 

153 

2 

3.12 

3.27 

4.59 

4.17 

6.12 

4.96 

1.84 

4.36 

2.45 

5.39 

3.12 

6.36 

U/2 

70    178 

2 

3.561  4.02 

5.34 

5.12    7.02 

6.0812.14 

5.352.85 

6.62 

3.56 

7.81 

U/2 

80    204    2    4.08    4.77    6.06 

6.08    8.16 

7.232.45 

6.35  3.  26|  7.86 

4.08 

9.27 

11/2 

90   230    2    4.60    5.51 

6.90 

7.03    9.20 

8.362.76 

7.353.68J  9.10 

4.60 

10.73 

U/2  100 

254 

2 

5.04    6.27 

7.62 

7.99 

10.16 

9.50 

3.05 

8.34 

4.07 

10.32 

5.04 

12.17 

13/4 

60 

131 

2 

2.62    3.42 

3.93 

4.36 

5.24 

5.18 

.57 

4.48 

2.10 

5.55 

2.62 

6.55 

13/4 

70 

153 

2 

3.06    4.2li  4.59 

5.37 

6.12 

6.38 

.84 

5.532.45 

6.84 

3.06 

8.07 

13/4    80    175    2 

3.50    5.00!  5.25 

6.38 

7.00 

7.58i2.10 

6.562.80 

8.12 

3.50 

9.58 

13/4  !  90    196    2    2.921  5.80    5.88 

7.39 

7.84    8.78:2.35 

7.602.14 

9.41 

3.92  11.10 

13/4 

100 

218 

2 

4.36 

6.59 

6.52 

8.40    9.12 

9.98 

2.62 

8.633.49 

10.68 

4.36 

12.60 

2 

60 

115 

4 

2.30 

4.87 

3.45 

6.22    4.60 

7.39 

.38 

6.82  1.84 

8.44 

2.30 

9.96 

2 

70 

134 

2.68 

4.38 

4.04 

5.59    5.36 

6.64    .61 

5.662.14 

7.00 

2.68 

8.26 

2 

80 

153 

2 

3.06 

5.21 

4.59 

6.65    6.12 

7.90 

.84 

6.73 

2.45 

8.33 

3.06 

9.83 

2 

90 

172 

2    3.44 

6.04 

5.16 

7.71    6.88 

9.16 

2.06 

7.81 

2.75 

9.66 

3.44 

11.40 

2 

100 

191 

2 

3.82 

6.87 

5.73 

8.77 

7.64 

10.32 

2.29 

8.87 

3.06 

10.98 

3.82 

12.95 

21/4 

60 

102 

4 

2.04 

5.18 

3.06 

6.60 

4.08 

7.84 

.22 

6.95 

1.63 

8.60 

2.04 

10.14 

21/4 

70 

119 

4 

2.38 

6.40 

3.57 

8.16    4.76 

9.70 

.43 

8.60 

1.90 

10.64 

2.38 

12.55 

21/4 

80 

136 

2 

2.68 

5.40 

4.08 

6.88    5.44 

8.18 

.63 

6.88 

2.18 

8.52 

2.68 

10.05 

21/4 

90 

153 

2 

3.06 

6.27 

4.59 

7.99    6.12 

9.50 

.84 

7.98 

2.45 

9.88 

3.06 

11.65 

21/4 

100 

170 

3.40 

7.13 

5.10 

9.09 

6.80 

10.80 

2.04 

90.9 

2.72 

11.25 

3.40 

13.27 

21/2 

60 

92 

4 

1.83 

5.46 

2.75 

6.96 

3.67 

8.27 

.10 

7.06 

1.47 

8.74 

1.83 

10.31 

21/2 

70 

107    4 

2.14    6.76 

3.21 

8.63    4.28 

10.26 

.28 

8.75 

1.71 

10.83 

2.14 

12.77 

2V  •>'  80 

122    4 

2.44    8.06 

3.66 

10.29 

4.88 

12.23 

.46 

10.43 

1.95 

12.91 

2.44 

15.23 

21/2    90 

138    2    2.76 

6.46 

4.14 

8.24 

5.52 

9.79    .66 

8.14 

2.21 

10.08 

2.76 

11.89 

21/2  100 

153 

2    3.06 

7.36 

4.59 

9.39 

6.12 

11.16 

.84 

9.28 

2.45 

11.49 

3.06 

13.55 

23/4    60 

83 

4    1.67 

5.73 

2.50 

7.30 

3.34 

8.68 

.00 

7.15 

1.33 

8.85 

1.67 

10.44 

23/4    70      97    4    1.94    7.11    2.92    9.06 

3.89 

10.77    .17 

8.87 

1.55 

10.98 

1.94 

12.95 

23/4 

80    111    4    2.22 

8.49    3.3310.83 

4.44 

12.87 

.33 

10.62 

1.78 

13.14 

2.22 

15.50 

23/4 

90    125    4    2.50    9.90    3.75 

12.62 

5.00 

15.00 

.50 

12.34 

2.00 

15.27 

2.50 

18.00 

23/4  100 

139 

2 

2.78 

7.59 

4.17 

9:68 

5.56 

11.50 

.67 

9.46 

2.23 

11.71 

2.78 

13.81 

3 

60 

76 

4 

1.53 

5.96 

2.29 

7.60 

3.06    9.03 

0.92 

7.22 

1.22 

8.94 

1.53 

10.55 

3 

70 

89 

4    1.78    7.42 

2.67 

9.46 

3.56 

11.25 

.07 

8.98)1.43 

11.12 

1.78 

13.12 

3 

80 

102 

4    2.04 

8.88 

3.06 

11.32 

4.08 

13.45 

.27 

10.75  1.63 

13.31 

2.04 

15.71 

3 

90 

115 

4 

2.30 

10.33 

3.45 

13.17 

4.60 

15.  6511.38 

12.52 

1.84 

15.48 

2.30 

18.26 

3 

100 

127 

4 

2.54il1.75 

3.81 

15.00 

5.08 

17.82'l.52 

14.26 

2.03 

17.65 

2.54 

20.82 

1288 


THE  MACHINE-SHOP. 


Feeds  for  Drills. —  According  to  Mr.  Norris,  the  rate  at  which  a  drill 
may  be  advanced  per  revolution  depends  upon  the  toughness  of  the 
material  to  be  drilled,  the  ability  of  the  machine  to  resist  thrust  without 
forfeiture  of  alignment  and  upon  the  knowledge  that  is  exercised  in  the 
grinding  of  the  drill — the  size  of  its  included  angle,  the  width  of  its 
chisel  point,  and  the  keenness  and  evenness  of  its  cutting  edges,  all  being 
deciding  factors.  Were  it  not  for  the  weakening  effect  on  the  drill  it 
could  be  said  that  the  stiff er  the  machine,  the  less  the  included  angle; 
the  narrower  the  chisel  point,  the  smaller  the  degree  of  the  spiral;  the 
greater  the  uniformity  of  the  cutting  lips  and  the  more  efficacious  the 
lubricant  in  minimizing  the  frictionai  resistance  of  the  chips,  the  coarser 
becomes  the  feed  it  is  permissible  to  use.  But,  inasmuch  as  the 
durability  of  the  drill  must  not  be  impaired,  the  advantage  obtainable 
through  the  application  of  these  axioms  has  its  limitations.  The 
keenness  of  edges  needed  to  attain  maximum  efficiency  in  cutting  cast- 
iron  disqualifies  for  work  in  steel  a  drill  suitable  for  use  in  cast-iron. 
The  highest  rate  of  feed  at  which  drills  of  from  3/8  to  3  in.  diam.  may 
be  operated  in  steel  appears  to  be  about  0.060  in.  per  revolution,  but 
the  employment  of  such  feeds  increases,  rather  than  decreases  the  cost  of 
work.  The  feeds  provided  in  the  product  of  the  Cincinnati-Bickford 
Tool  Co.  range  from  0.006  in.  to  0.040  in.  per  revolution,  which,  under 
favorable  conditions,  may  be  utilized  as  follows: 

CAST  IRON 


STEEL 

Hard 0 . 006  to  0 . 010  in. 

Medium 0.0X2  to  0.018  in. 

Soft 0. 020  to  0 . 028  in. 


Hard. 


0.015  to  0.020  in. 


Medium 0.020  to  0.030  in. 

Soft 0.030  to  0.040  in. 


Speed  of  Drills.  —  Mr.  Norris  says  further  that  while  an  occasional 
drill  is  found  that  will  withstand  for  days  a  cutting  speed  of  150  ft. 
per  minute,  in  either  cast-iron  or  steel  (the  latter  under  a  lubricant), 
it  is  rarely  expedient  to  drive  any  but  very  small  ones  faster  than  100 
ft.  per  mih.  Operating  drills  at  an  excessive  speed  is  an  expensive  fad. 
It  is  more  economical  to  err  in  the  other  direction.  The  most  satis- 
factory results  have  been  obtained  at  a  cutting  speed  of  80  ft.  per  min. 

in  cast-iron  and  ^  +  76  ft.  in  steel.      This   formula   will  decrease 

the  cutting  speed  from  100  ft.  per  min.  for  a  V^in.  drill  to  80  ft.  for  a 
3-in.  drill.  The  reason  for  this  reduction  is  that  a  stream  of  liquid 
sufficient  to  keep  a  small  drill  cool  is  insufficient  to  prevent  overheating 
in  a  large  one. 

In  order  to  facilitate  the  use  of  the  formulae  for  horse-power  there 

KO    O 

is  given  in  the  following  table  the  deduced  values  for  /°-74,  d1-25,  —£- 


+  6.8  and  ^  +  76. 

Values  of  f*-™, 


co  9  19 

1.25,  —2.  +  6.8  and  of  =£  +  76. 


* 

I. 

oo 

A 

L 

00 

J! 

3 

fl^C3 

* 

c  w 

I 

^ 

J| 

% 

«N  1 

2  Its 

I 

2 

•I" 

3 

"13 

*\. 

- 

0.008 

0.02807 

1/2 

0.421 

111.2 

100.0 

0.022 

0.05934 

17/8 

2.194 

34.6 

82 

.4 

.009 

.03063 

5/8 

.556 

90.3 

95.2 

.024 

.06329 

2 

2.378 

32.9 

82 

.0 

.010 

.03312 

3/4 

.698 

76.4 

92.0 

.026 

.06715 

21/8 

2.566 

31.4 

81 

.6 

.011 

.03553 

7/8 

.846 

66.6 

89.7 

.028 

.07094 

21/4 

2.756 

30.0 

81 

.3 

.012 

.03789 

1.000 

59.0 

88.0 

.030 

.07466 

23/8 

2.948 

28.8 

81 

.0 

.013 

.04021 

11/8 

.158 

53.2 

86.9 

.032 

.07831 

21/2 

3.144 

27.7 

80 

.0 

.014 

.04248 

H/4 

.322 

48.5 

85.6 

.034 

.08190 

25/8 

3.342 

26.7 

80 

.6 

.015 

.04470 

13/8 

.489 

44.8 

84.7 

.036 

.08544 

23/4 

3.541 

25.8 

80 

.4 

.016 

.04689 

11/2 

.660 

41.6 

84.0 

.038 

.08894 

27/8 

3.741 

25.0 

80 

.2 

.018 

.05115 

15/8 

.833 

38.9 

83.4 

.040 

.09237 

3 

3.948 

24.2 

80 

.0 

.020 

.05530 

13/4 

2.013 

36.6 

82.9 

^. 

DRILLS  AND  DRILLING. 


1289 


Extreme  Results  with  Drills. —  The  Cleveland  Twist  Drill  Co. 
furnishes  the  following  table  of  results  of  drilling  tests  made  at  the 
convention  of  Railway  Master  Mechanics'  Association  at  Atlantic  City, 
N.  J.,  June,  1911.  The  object  of  the  tests  was  to  demonstrate  good 
shop  practice,  drilling  being  done  at  speeds  and  feeds  considered 
economical  under  average  shop  conditions,  and  also  to  show  what  were 
the  ultimate  possibilities  of  drills  and  machines.  The  drills  used  were 
flat  twisted  drills,  and  the  ordinary  milled  drill.  The  record  per- 
formance for  high-speed  drilling  is  test  No.  4,  in  which  a  1 1/4  in.  drill  re- 
peatedly drilled  through  a  casting  at  57  1/2  in.  per  minute.  In  the  tests 
to  demonstrate  good  shop  conditions,  the  drill  in  test  No.  17  drilled  68 
holes,  removing  1418  cu.  in.  of  metal  without  being  reground,  and  was 
in  good  condition  at  the  close  of  the  test.  The  Cleveland  Twist  Drill 
Co.  does  not  recommend  the  high  speeds  and  heavy  feeds  attained  as 
economical  shop  practice,  but  points  out  that  the  results  can  be  duplicat- 
ed by  carefully  established  ideal  conditions  of  absolute  rigidity  in  the 
machine,  solid  clamping  of  the  work,  perfect  grinding  of  the  drill  and 
expert  handling. 

Record  Performances  of  High-Speed  Drills. 


No. 

Sizes  of 
Drill, 
In. 

Material 

R.P.M. 

Feed 
Rev. 

Inches 
Drilled 
per  Min. 

Rev., 
Speed  in 
Feet 
per  Min. 

Cu.  In. 
Metal 
Removed 
per  Min. 

j 

H/4 

500 

0.050 

25 

163.6 

30.68 

2 

HA 

o 

325 

0.100 

321/2 

106 

39.88 

3 

H/4 

jgj 

475 

0.100 

471/2 

155 

58.29 

4 

H/4 

H 

575 

0.100 

571/2 

188 

70.56 

5 

U/2 

^ 

300 

0.030 

9 

117 

15.90 

6 

U/2 

rt 

325 

0.100 

321/2 

127.6 

.    57.43 

7 

11/2 

335 

0.100 

331/2 

131.5 

59.19 

8 

U/2 

0 

355 

0.100 

351/2 

139.4 

62.73 

9 

13/4 

I—  I 

235 

0.100 

231/2 

107.6 

56.52 

10 

13/4 

M 

350 

0.100 

35 

160 

84.19 

11 

25/16 

a 

190 

0.050 

91/2 

115 

39.90 

12 

3 

o 

120 

0.100 

12 

94 

84.82 

13 

H/4 

350 

0.030 

101/2 

113.7 

12.88 

14 

15/8 

« 

225 

0.040 

9 

94.8 

18.66 

15 

25/16 

£41 

165 

0.020 

31/4 

100 

13.86 

16 

25/16 

C/2  O 

200 

0.020 

4 

121 

16.80 

17 

21/2* 

bl 

150 

0.015 

21/4 

98 

11.04 

18 

21/2* 

5^ 

150 

0.040 

6 

98 

29.45 

19 

21/2* 

175 

0.040 

7 

114.5 

34.36 

20 

13/4 

o^. 

275 

0.030 

81/4 

125 

19.84 

21 

3 

M| 

150 

0.030 

41/2 

117.8 

31.81 

22 

31/4 

150 

O.C30 

41/2 

127 

37.33 

*  Milled  drills;  all  other  drills  are  flat  twisted  drills. 

Experiments  on  Twist  Drills.— An  extensive  series  of  experiments 
on  the  forces  acting  on  twist  drills  of  high-speed  steel  when  operating 
on  cast-iron  and  steel  is  reported  by  Dempster  Smith  and  A.  Poliakoff, 
in  Proc.  Inst.  M.  &.,  1909.  Abstracted  in  Am.  Mach.,  May,  1909,  and 
Indust.  Eng.,  May,  1909.  Approximate  equations  derived  from  the 
first  set  of  experiments  are  as  follows: 

Torque  in  pounds-feet,  1=  (1800  t+  9) d\  for  medium  cast-iron; 
T  =  (3200  t  +  20)d2,  for  medium  steel.  End  thrust,  lb.,  P  =  115,000 
t  -  200,  for  medium  cast-iron;  P  =  160,000(d  -  0.5)£-  1000,  for 
medium  steel;  d  =  diam.,  t  =  feed  per  revolution  of  drill,  both  in  inches. 
The  steel  was  of  medium  hardness,  0.29  C,  0.625  Mn. 

The  end  thrust  in  enlarging  holes  in  medium  steel  from  one  size  to 
a  larger  was  as  follows:  3/4  in.  to  1  in.,  P  =  15,200  t  +  60;  1  in.  to  1 1/2  in., 
P  =  25,500  t  +  ;  3/4  in.  to  1 1/2  in.,  P  =  30,000  t  +  200. 

A  second  series  of  experiments  with  soft  cast-iron  of  C.C.,  0.2;  G.C., 
29;  Si,  1,41;  Mn,  0.68;  S,  0.035;  P,  1.48,  and  medium  steel  of  C,  0.31; 


1290 


THE  MACHINE-SHOPo 


Si,  0.07;  Mn,  0.50;  S,  0.018;  P,  0.033;  tensile  strength,  72,600  Ib.  per 
sq.  in.,  gave  results  from  which  were  derived  the  following  approximate 
equations : 
Torque,  lb.-ft.,   T  =  740  di.8#.7,  or  10  d2  +  100  £(14  d2  +  3)  for  cast  iron, 

T  =  1640  di-8^o.7,  or  28  d2(i  +  100  t)  for  medium  steel, 
End  thrust,  Ib.  P  =  35,500  do.?  #.75,  Or  200  d  +  10,000 1  for  cast  iron, 

P  =  35,500  do.7  £0.3,  or  750  d  +  1000  t  (75  d  +  50)  for 

medium  steel, 
and  for  different  sizes  of  drill  the  following  equations: 


Drill. 

3/4 

1 

IVa 

Cast  iron  T  =  

5  +  1.1001 

10  +  1,750  t 

25  +3,700  t 

Cast  iron  P  =   . 

1  25  +82,  000  t 

200  +89  000  t 

350  +  103  000  t 

Steel  T  =  

7  5  +3,350  £ 

17  5  -f  4,400  £ 

40  -f-9,000  t 

Steel  P  =  

550  +  109  ,000  t 

750  +  131,  000  t 

1.250  +  1  62,000  t 

Drill. 

2 

2V2 

3 

Cast  iron  T  =  
Cast  iron  P  =*  

40  +5,  900  t 
500  +  1  10,000  / 

60  +8,800  t 
600  +  1  26,000  t 

90  +  1  2,900  / 
850  +  140,000  t 

Steel  T  = 

75  +1  2,500  / 

112  5  +  19,050  t 

175  +26,250  t 

Steel  P  =  

1.  500  +  181,  250  t 

1,  725  +224.375* 

2,350  +280,000  t 

The  tests  above  referred  to  were  made'without  lubricants.  When 
lubricants  were  used  in  drilling  steel  the  average  torque  varied  from 
72%  with  1/400  in.  feed  to  92%  with  1/35  in.  feed  of  that  obtained  when 
operating  dry.  The  thrust  for  soft,  medium  and  hard  steel  is  26%, 
37%,  and  12%  respectively  less  than  when  operating  dry,  no  marked 
difference  being  found,  as  in  the  torque,  with  different  feeds.  The  horse- 
power varies  as  2-07  and  as  do.8  for  a  given  drill  and  speed.  The  torque 
and  horse-power  when  drilling  medium  steel  is  about  2.1  times  that 
required  for  cast  iron  with  the  same  drill  speed  and  feed.  The  horse- 
power per  cu.  in.  of  metal  removed  is  inversely  proportional  to  dO-2  jo.3, 
and  is  independent  of  the  revolutions. 

While  the  chisel  point  of  the  drill  scarcely  affects  the  torque  it  is  ac- 
countable for  about  20  %  of  the  thrust.  Tests  made  with  a  preliminary 
hole  drilled  before  the  main  drill  was  used  to  enlarge  the  hole  showed 
that  the  work  required  to  drill  a  hole  where  only  one  drill  is  used  is 
greater  than  that  required  to  drill  the  hole  in  two  operations,  with  drills 
of  different  diameter. 

For  economy  of  power  a  drill  with  a  larger  point  angle  than  120°  is  to 
be  preferred,  but  the  increased  end  thrust  strains  the  machine  in  propor- 
tion, and  there  is  more  danger  of  breaking  the  drill. 

Cutting  Speeds  for  Tapping  and  Threading.  (Am.  Mach.,  Aug.  3, 
1911.) — The  National  Machine  Co.,  for  tapping  and  threading,  uses 
speeds  of  233  r.p.m.  for  sizes  and  holes  up  to  1/4  in.  diameter,  and  140 
r.p.m.  for  sizes  from  1/4  in.  to  1/2  in.  diameter,  with  a  lubricant  of 
screw-cutting  oil.  Both  the  Bignall  &  Keeler  Co.  and  the  Standard 
Engineering  Co.  recommend  a  cutting  speed  of  15  ft.  per  minute. 
The  former  recommends  lard  oil  as  a  lubricant.  The  practice  of  the 
F.  E.  Wells  Co.  in  tapping  and  the  Landis  Machine  Co.  in  threading 
in  machines  of  the  bolt  cutter  type  is  as  follows: 

Speeds  for  Tapping  and  Threading— r.  p.  m. 


Mate- 
rial. 

F.  E.  Wells. 

Landis. 

Mate- 
rial. 

F.  E.  Wells. 

Landis. 

Steel. 

Cast 
Iron. 

Steel. 

Cast 
Iron. 

Steel. 

Cast 
Iron. 

Steel. 

Cast 
Iron. 

Lubri- 
cant. 

Oil. 

Oil  or 
Soda 
Comp. 

Oil. 

Petro- 
leum. 

Lubri- 
cant. 

Oil. 

Oil  or 
Soda 
Comp. 

Oil. 

Petro- 
leum. 

1/4  in. 

3/8   " 
1/2   " 
«/8  " 

299 
153 
115 
91 

382 
255 
191 
153 

280 
220 
175 

200 
150 
125 

3/4  in. 

!•/*;; 

76 

127 

140 
115 
75 
6 

100 
85 
55 
45 

CASE-HARDENING.  1291 

SAWING  METALS. 

Speeds  and  Feeds  for  Cold  Sawing  Metals.— (Mach'y,  Jan.,  1914). 
— For  sawing  0.30  carbon,  open-hearth  machine  steel  bars  in  a  cold 
sawing  machine,  a  feed  of  1  in.  per  minute  and  a  peripheral  speed  of 
approximately  45  ft.  per  minute  was  used.  The  bars  were  5  in.  diam- 
eter, and  an  average  of  145  were  sawed  with  one  sharpening  of  the 
saw.  For  some  classes  of  work  a  feed  of  2  in.  per  minute  can  be  used, 
but  3/4  in.  per  minute  is  advisable  for  0.30  carbon  steel  with  the  saw 
in  good  condition.  For  tool  steel  and  ajloy  steel  the  best  economy 
will  be  obtained  with  a  feed  of  1/2  in.  per  minute  and  a  surface  speed 
of  30  ft.  per  minute,  with  a  grinding  every  100  pieces. 

Hack  Sawing  Machines.— Charles  Wicksteed  (Proc.  Inst.  Mech. 
Engrs.,  1912)  says  that  the  important  considerations  to  be  observed  in 
using  hack  sawing  machines  are:  For  ordinary  work,  a  coarse  pitch 
tooth,  not  less  than  10  to  the  inch  is  best;  extra  strength  of  the  saw  is 
to  be  obtained  by  extra  depth,  not  extra  thickness,  of  blade;  the  greatest 
weight  that  a  blade  will  take  without  injury  is  7  Ib.  per  tooth  or  70  Ib. 
per  in. ;  a  6-in.  machine  thus  will  use  the  full  capacity  of  the  blade  on 
4-in.  bars  with  a  weight  of  210  Ib.  on  the  blade.  As  the  size  of  the 
machine  increases,  the  weight  increases  proportionately,  a  15-in.  ma- 
chine employing  700  Ib.  and  using  the  full  capacity  of  the  blade  when 
sawing  a  10-in.  surface.  A  hack  sawing  machine  will  cut  true  to  0.01 
in.  in  a  mild  steel  bar  at  a  speed  roughly  of  1  to  2  sq.  in.  per  minute. 

Saws  for  Copper. — A  special  saw  for  cutting  copper  has  teeth  with 
a  front  rake  of  10°.  The  metal  is  ground  away  at  the  sides  of  the 
teeth  to  provide  clearance.  The  number  of  teeth  should  be  com- 
paratively small.  A  pitch  of  about  1  in.  giving  10  teeth  in  3-in.  saw 
renders  good  service. 

CASE-HAEDENING,  ETC. 

Case-hardening  of  Iron  and  Steel,  Cementation,  Harveyizing. — 
When  iron  or  soft  steel  is  heated  to  redness  or  above  in  contact  with 
charcoal  or  other  carbonaceous  material,  the  carbon  gradually  penetrates 
the  metal,  converting  it  into  high  carbon  steel.  The  depth  of  penetra- 
tion and  the  percentage  of  carbon  absorbed  increase  with  the  tempera- 
ture and  with  the  length  of  time  allowed  for  the  process.  In  the(  old 
cementation  process  for  converting  wrought  iron  into  "blister  steel"  for 
re-melting  in  crucibles  flat  bars  were  packed  with  charcoal  in  an  oven 
which  was  kept  at  a  red  heat  for  several  days.  In  the  Harvey  process  of 
hardening  the  surface  of  armor  plate,  the  plate  is  covered  with  charcoal 
and  heated  in  a  furnace,  and  then  rapidly  cooled  by  a  spray  of  water. 

In  case-hardening,  a  very  hard  surface  is  given  to  articles  of  iron  or 
soft  steel  by  covering  them  or  packing  them  in  a  box  or  oven  with  a  ma- 
terial containing  carbon,  heating  them  to  redness  while  so  covered,  and 
then  chilling  them.  Many  different  substances  have  been  used  for  the 
purpose,  such  as  wood  or  bone  charcoal,  charred  leather,  sugar,  cyanide 
of  patassium,  bichromate  of  potash,  etc.  Hydrocarbons,  such  as  illu- 
minating gas,  gasolene  or  naphtha,  are  also  used.  Amer.  Machinist, 
Feb.  20,  1908,  describes  a  furnace  made  by  the  American  Gas  Furnace 
Company  of  Elizabeth,  N.  J.,  for  case-hardening  by  gas.  The  best  results 
are  obtained  with  soft  steel,  0.12  to  0.15  carbon,  and  not  over  0.35  man- 
ganese, but  steel  of  0.20  to  0.22  carbon  may  be  used.  The  carbon  begins 
to  penetrate  the  steel  at  about  1300°  F.,  and  1700°  F.  should  never  be 
exceeded  with  ordinary  steels.  A  depth  of  carbonizing  of  1/64  in.  is 
obtained  with  gas  in  one  hour,  and  1/4  in.  in  12  hours.  After  carbonizing 
the  steel  should  be  annealed  at  about  1625°  F.  and  cpoled  slowly,  then 
re-heated  to  about  1400°  F.  and  quenched  in  water.  Nickel-chrome  steels 
may  be  carbonized  at  2000°  F.  and  tungsten  steels  at  2200°  F. 

Change  of  Shape  due  to  Hardening  and  Tempering.  —  J.  E.  Storey. 
Am.  Mack.,  Feb.  20,  1908,  describes  some  experiments  on  the  change  of 
dimensions  of  steel  bars  4  in.  long,  7/s  in.  diam.  in  hardening  and  temper- 
ing. On  hardening  the  length  increased  in  different  pieces  .0001  to 
.0014  in.,  but  in  two  pieces  a  slight  shrinkage,  maximum  .00017,  was  found. 
The  diameters  increased  .0003  to  .0036  in.  On  tempering  the  length 
decreased  .0017  to  .0108  in.  as  compared  with  the  original  4  ins.  length, 
while  the  diameter  was  increased  .0003  to  .0029;  a  few  samples  showing 
a  decrease,  max.  0009  in.  The  general  effect  of  hardening  is  a  slight 
Increase  in  bulk,  which  increase  is  reduced  by  tempering. 


1292 


THE  MACHINE-SHOP. 


POWER  REQUIRED  FOR  MACHINE  TOOLS. 

Resistance  Overcome  in  Cutting  Metal.  (Trans.  S.  M.  E.t 
viii,  308.) — Some  experiments  made  at  the  works  of  William  Sellers 
&  Co.  showed  that  the  resistance  in  cutting  steel  in  a  lathe  would  vary 
from  180,000  to  700,000  pounds  per  square  inch  of  section  removed, 
while  for  cast  iron  the  resistance  is  about  one-third  as  much.  The 
power  required  to  remove  a  given  amount  of  metal  depends  on  the 
shape  of  the  cut  and  on  the  shape  and  sharpness  of  the  tool  used.  If 
the  cut  is  nearly  square  in  section,  the  power  required  is  a  minimum; 
if  wide  and  thin,  a  maximum.  The  dullness  of  a  tool  affects  but  little 
the  power  required  for  a  heavy  cut. 

F.  W.  Taylor,  in  the  Art  of  Cutting  Metals  (Trans.  A.  S.  M.  E., 
xviii)  gives  the  tangential  pressure  of  the  chip  on  the  tool  as  ranging 
from  70,000  Ib.  per  sq.  in.  when  cutting  soft  cast  iron  with  a  coarse 
feed,  to  198,000  Ib.  per  sq.  in.  when  cutting  hard  cast  iron  with  a  fine 
feed.  In  cutting  steel,  the  pressure  of  the  chip  on  the  tool  per  sq.  in. 
ranged  from  184,000  Ib.  to  376,000  Ib.  The  pressure,  he  found,  is 
independent  of  the  speed,  and  in  the  case  of  steel  is  independent  of 
the  hardness  of  the  steel.  It  increases  as  the  quality  of  the  steel  grows 
finer;  that  is,  high  grade  steel,  whether  hard  or  soft,  will  give  higher 
pressures  than  low  grade  steel.  He  also  found  that  an  increase  in 
the  tensile  strength  and  ductility  of  the  steel  increases  the  pressure, 
the  former  having  the  greater  effect. 

Horse-power  Required  to  Run  Lathes. — The  power  required  to 
do  useful  work  varies  with  the  depth  and  breadth  of  chip,  with  the 
shape  of  tool  and  with  the  nature  and  density  of  metal  operated  upon ; 
and  the  power  required  to  run  a  machine  empty  is  often  a  variable 
quantity.  For  instance,  when  the  machine  is  new,  and  the  working 
parts  have  not  become  worn  or  fitted  to  each  other  as  they  will  be  after 
running  a  few  months,  the  power  required  will  be  greater  than  will  be 
the  case  after  the  running  parts  have  become  better  fitted. 

Another  cause  of  variation  of  the  power  absorbed  is  the  driving-belt; 
A  tight  belt  will  increase  the  friction. 

A  third  cause  is  the  variation  of  journal-friction,  due  to  slacking  up 
or  tightening  the  cap-screws,  and  also  the  end-thrust  bearing  screw. 

Owing  to  the  demand  imposed  by  high  speed  tool  steels  stouter 
machines  are  more  necessary  than  formerly;  these  possess  more  rigid 
frames  and  powerful  driving  gears.  The  most  modern  (1915)  forms 
of  lathes  obtain  all  speed  changes  by  means  of  geared  head-stocks, 
power  being  delivered  at  a  single  speed  by  a  belt,  or  by  a  motor.  If  a 
motor  drive  is  used,  a  speed  variation  may  be  obtained  in  addition  to 
those  available  in  the  head,  by  using  a  variable  speed  motor,  whose 
range  usually  is  about  3:1.  The  tables  on  p.  1293  show  the  results  of 
tests  made  by  the  Lodge  &  Shipley  Co.  in  1906  to  determine  the  power 
required  to  remove  metal  in  a  20-in.  lathe  with  a  cone  pulley  drive,  and 
also  in  a  similar  lathe  with  a  geared  head. 

Power  Required  to  Drive  Machine  Tools. — The  power  required 
to  drive  a  machine  tool  varies  with  the  material  to  be  cut.  There  is 
considerable  lack  of  agreement  among  authorities  on  the  power  re- 
quired. Prof.  C.  H.  Benjamin  (Mach'y,  Sept.,  1902)  gives  a  formula 
H.P.  =  cW,  c  being  a  constant  and  W  the  pounds  of  metal  removed 
per  hour,  c  varies  both  with  the  quality  of  metal  and  the  type  of 
machine. 

Values  of  c. 


Lathe. 

Planer. 

Shaper. 

Milling 
Machine. 

Cast  iron  

0.035 

0.032 

0.030 

0.14 

0  067 

Tool  steel  

0.30 

Bronze  

0.10 

In  each  case  the  power  to  drive  the  machine  without  load  should  be 
added.  G.  M.  Campbell  (Proc.  Engr.  Soc.  W.,  Pa.,  1906)  gives,  ex- 
clusive of  friction  losses,  H.P.  =  Kw,  K  being  a  constant  and  w  the 
pounds  of  metal  removed  per  minute.  For  hard  steel  K  =  2.5;  for  soft 


POWER   REQUIRED   FOR  MACHINE   TOOLS.        1293 


Horse-power  Kequired  to  Remove  Metal  in  Lathes. 

(Lodge  &  Shipley  Mach.  Tool  Co.,  1906.) 
20-lNCH  CONE-HEAD  LATHE. 


Cutting 

Cut,  In. 

Diam. 

Cu.  in. 

Lb. 

H.P.  used 
by  Lathe. 

Cu.in. 

Material 

Speed, 

of 

remov- 

remov- 

remov- 

Cut. 

ft.  per 
min. 

Depth. 

Feed. 

work, 
in. 

ed  per 
min. 

ed  per 
hour. 

Idle. 

With 
Cut. 

ed  per 
HJP. 

Crucible 

f    35 

0.109 

1/8 

227/32 

5.74 

96 

0.48 

3.90 

1.471 

Steel 

S    65 

0.055 

V8 

35/8 

5.33 

90 

0.74 

4.60 

1.158 

0.60 

)    62.5 

0.109 

Vl6 

35/16 

5.125 

86 

0.49 

4.65 

1.102 

Carbon 

(    32.5 

0.094 

VlO 

3.656 

62 

0.49 

2.64 

1.384 

f    62.5 

0.273 

1/1? 

35/32 

17.09 

266 

0.66 

5.44 

3.141 

Cast 

)    60 

0.430 

Vl9 

221/64 

16.27 

253 

0.59 

4.77 

3.410 

Iron 

)    37.5 

0.334 

1/16 

221/32 

10.76 

167 

0.45 

3.91 

2.751 

(  115 

0.086 

Vl2 

155/64 

9.88 

153 

0.21 

2.54 

3.889 

Open- 
hearth 
Steel 
0.30 
Carbon 

%    50 

)    45 
)    45 
(    32.5 

0.109 
0.117 
0.217 
0.109 

1/8 
1/8 
Vl9 
1/8 

2V232 

217/64 
223/64 

8.2 
7.91 
6.439 
5.33 

138 
134 
109 
90 

0.69 
0.53 
0.69 
0.36 

5.34 
5.11 
4.10 
4.04 

1.535 
1.547 
1.570 
1.319 

Average  H.P.  running  idle  0.53;  average  H.P.  with  cut  4.25. 
20-lNCH  GEARED-HEAD  LATHE, 


H.P.  used 

Cutting 

Cut,  in. 

Diam. 

Cu.  in. 

Lb. 

by  Lathe. 

Cu.  in. 

Material. 

Speed, 

of 

remov- 

remov- 

remov- 

Cut. 

ft.  per 
min. 

Depth. 

Feed. 

work 
in. 

ed  per 

miii. 

ed  per 
hour. 

Idle. 

With 
Cut. 

ed  per 
H.P. 

0.50 

(  40 

0.266 

VlO 

227/32 

12.75 

215 

2.11 

11.1 

1.142 

Carbon 

)50 

0.281 

Vl5 

11.25 

190 

.58 

8.35 

1.347 

Crucible 

)75 

0.281 

1/15 

227/32 

16.87 

285 

.58 

12.69 

1.329 

Steel. 

(85 

0.109 

1/15 

2V4 

7.43 

126 

.28 

8.98 

0.827 

f  45 

0.609 

1/16 

721/32 

2057 

320 

.34 

694 

2.963 

Cast 

)62.5 

0.609 

Vl6 

721/32 

28.56 

445 

.35 

9.50 

3.006 

Iron 

)85 

0.641 

Vl6 

721/32 

40.82 

636 

.64 

12.69 

3.216 

(80 

0.281 

1/8 

3  3/32 

33.75 

526 

.18 

10.49 

3.217 

Open- 
hearth 

Qfool 

f  125 
)  105 

0.250 
0.188 

V28 

1/12 

4  21/32 
4  5/32 

13.4 
19.68 

226 
332 

1.62 
0.94 

10.60 
11.56 

1.265 
1.702 

oteei 
0  15 

)    40 

0.172 

1/6 

13.75 

232 

1.75 

12.49 

1.100 

Carbon 

(  180 

0.094 

1/16 

3  Vl6 

12.65 

213 

2.15 

11.20 

1.129 

Carbo 
TV! 


Average  H.P.  running  idle  1.543;  average  H.P.  with  cut  10.55. 


This 


steel  K  =  1.8;  for  wrought  iron,  K  =  2.0;  for  cast  iron,  K  =  1.4. 
formula  gives  results  aBout  50%  lower  than  Prof.  Benjamin's. 

L.  L.  Pomeroy  (Gen.  Elec.  Rev.,  1908)  gives:  H.P.  required  to  drive  = 
12  FDSNC,  in  which  F  =  feed  and  D  =  depth  of  cut,  in  inches,  S  = 
speed  in  ft.  per  min.,  N  =  number  of  tools  cutting,  C  =  a  constant, 
whose  values  with  ordinary  carbon  steel  tools  are:  for  cast  iron,  0.35  to 
0.5;  soft  steel  or  wrought  iron,  0.45  to  0.7;  locomotive  driving-wheel 
tires,  0.7  to  1.0;  very  hard  steel,  1.0  to  1.1.  This  formula  is  based  on 
Prof.  Flather's  dynamometer  tests.  An  analysis  of  experiments  by 
Dr.  Nicholson  of  Manchester,  which  confirm  the  formula,  showed  the 
average  H.P.  required  at  the  motor  per  pound  of  metal  removed  per 
minute  to  be  as  follows :  Medium  or  soft  steel,  or  wrought  iron,  2.4  H.P. ; 
hard  steel,  2.65  H.P.;  cast  iron,  soft  or  medium,  1.00  H.P.;  cast  iron, 
hard,  1.36  H.P. 


1294 


THE  MACHINE-SHOP. 


Actual  tests  (1906)  of  a  number  of  machine  tools  in  the  shops  of  the 
Pittsburg  and  Lake  Erie  R.R.  showed  the  horse-power  absorbed  hi 
driving  under  the  conditions  given  in  the  table  on  p.  1295.  The 
results  obtained  are  compared  with  those  computed  by  Campbell's 
formula  on  p.  1292.  It  will  be  observed  that  the  sizes  of  motors  actu- 
ally used  on  the  various  machines  in  the  table  agree  quite  closely  with 
the  sizes  recommend od  in  the  tables,  pp.  1294  to  1298. 

Sizes  of  Motors  for  Machine  Tools. — The  size  of  motor  applied  to 
machine  tools  which  are  driven  by  an  individual  motor  is  usually  deter- 
mined by  the  experience  of  the  manufacturer,  rather  than  by  any 
formula.  The  same  lathe,  for  instance,  will  be  fitted  with  a  larger 
motor  if  it  is  required  to  take  heavy  roughing  cuts  continuously  in 
tough  steel,  than  if  it  is  to  have  a  more  general  run  of  lighter  work  in 
cast  iron.  Even  if  it  does,  under  the  latter  conditions  of  service, 
occasionally  receive  a  job  up  to  the  limit  of  its  capacity,  the  motor  will 
be  able  to  stand  the  temporary  overload,  whereas  a  continuous  overload 
would  soon  ruin  it.  The  conditions  under  which  the  machine  will 
operate  should  therefore  be  stated  when  it  or  the  motor  to  drive  it 
is  purchased.  The  tables  given  on  pages  1294  to  1298  show  the 
sizes  of  motors  for  machine  tools  as  recommended  by  the  Westinghouse 
Elect.  &  Mfg.  Co.  The  sizes  given  embody  average  practice.  The 
type  of  motor  to  be  used  varies  with  the  conditions  of  servic*,  and  the 
type  suitable  for  the  different  classes  of  machinery  are  indicated  by 
the  following  symbols: 

A.  Adjustable  speed,  shunt  wound,  direct  current  motor;  used  where 
a  number  of  speeds  are  essential. 

B.  Constant  speed,  shunt  wound,  direct  current  motor;  used  when 
the  desired  speeds  are  obtainable  by.  a  cone  pulley  or  gear  box,  or  where 
only  a  single  speed  is  required. 

C.  Squirrel  cage  induction  motor;  used  where  direct  current  is  not 
available.     A  cone  pulley  or  gear  box  is  necessary  if  more  than  one 
speed  is  desired. 

D.  Constant  speed,  compound  wound,  direct-current  motor,  used 
when  different  speeds  are  obtainable  by  means  of  a  cone  pulley  or 
gear  box,  or  where  but  one  speed  is  necessary. 

E.  Wound  secondary  or  squirrel  cage  induction  motor  with  about 
10%  slip;  used  where  direct  current  is  not  available,  or  where  one 
speed  is  required. 

F.  Adjustable  speed,  compound  wound,  direct  current  motor;  used 
where  a  number  of  speeds  are  necessary. 

G.  Standard  bending  roll  motor. 

H.  Standard  machine  tool  traverse  motor. 


Turning  and  Boring  Machines* 

ENGINE  LATHES — Motor  A,  B  or  C. 


Swing,  in 12       14        16 


18 


Horse-power,  average 1/2     8/4-1     1-2     2-3 


20-22  24-27 

3  5 

7.5-10  7.5-10 

48-54  60-84 
15-20 
20-25 


20-25 
25-30 


Horse-power,  heavy 2  2-3      2-3     3-5 

Swing,  in 30  32-36       38-42 

Horse-power,  average 5-7.5  7.5-10       10-15 

Horse-power,  heavy 7.5-10  10-15       15-20 

WHEEL  LATHES — Motor  A,  B  or  C. 

Size,  in 48            51-60       79-84          90  100 

Horse-power 15-20         15-20       25-30  30-40  40-50 

H.P.  of  tail  stock  motor  (jff)     555  5-7.5  5-7.5 

AXLE  LATHES — Motor  A,  B  or  C. 

Single 5,     7.5,     10  Horse-power 

Double 10,       15,     20 

BUFFING  LATHES — Motor  B  or  C. 

Number  of  wheels 2  2  2  2 

Diameter  of  wheels,  in 6  10         12         14 

Horse-power 1/4-1/2       1-2       2-3       3-5 

For  brass  tubing  and  other  special  work  use  about  double  the 
above  H.P. 


POWER    REQUIRED    FOR   MACHINE    TOOLS.        1295 


Horse-power  to  Drive  Machine  Tools. 


J_ 

72-in.  wheel 
lathe    ' 

Material. 

Cut,  Inches. 

Speed, 
Ft.  per  Min. 

Wt.  Removed, 
Lb.  per  Min. 

H.P.Re 
quired. 

1 

3 

o 

§ 

I 

,d 
a 

& 

13 

3 

1 

J3 
~B 

K 

O 

fa 

Hard  steel 

Via 

1/8 
3/16 
3/16 

3/16  &  V4 
3/16&V4 
5/16&3/8 
3/8  &3/8 

13.7 
11.6 
13.2 
13.2 

1.69 
2.15 
5.55 
6.3 

4.5 
6.4 
8.4 
12.0 

4.2 
5.4 
13.9 
15.7 

25  H.P.  shunt 
wound  vari- 
able speed. 

90-in.  wheel 
lathe 

Hard  steel 

3/16 
3/16 

1/5 

3/16&3/16 
5/16&5/16 
1/4  &V4 

13.0 
8.8 
15.5 

3.1 
3.5 
5.3 

12.0 
8.1 
9.0 

7.7 
8.7 
13.2 

25  H.P.  shunt 
wound  vari- 
able speed. 

42-in.  lathe 

Soft  steel 
Cast  iron 

Vl6 
Vl6 
Vl6 
1/16 
Vl6 
Vl6 

1/4 
1/8 
>/8 
1/8 
3/16 
3/16 

44 
44 
44 
108 
46 
58 

2.33 
1.17 
1.17 
2.63 
1.74 
2.12 

3.8 
1.7 
2.6 
5.8 
2.9 
2.2 

4.2 
1.9 
1.9 
3.7 
2.5 
3.0 

15  H.P.  shunt 
wound  vari- 
able speed. 

30-in.  lathe 

Wro't  iron 
Cast  iron 

1/8 
1/8 
3/32 
3/32 
1/64     • 

3/16 
3/16 
5/32 
1/16 

V4 

54 
42 
42 
61 
47 

4.2 
3.2 
1.92 
1.12 
2.30 

6.6 
4.0 
3.0 
1.5 
2.0 

T9 
5.0 

T9 
2.6 
9.6 
7.2 
2.6 
2.7 

8.4 
6.4 
2.7 
1.6 
3.2 

10  H.P.  shunt 
wound  vari- 
able speed. 

Axle  lathe 

Soft  steel 

3/16 
Vl6 

1/4 
V4 

27 
51 

4.3 
2.7 

7.7 
4.9 

35H.P.sh.w'd 
var.  speed.^ 

72-in.  boring 
mill    .    . 

Soft  steel 
Cast  iron 

1/8 
3/16 
1/8 
1/8 
1/16 
Vl6 

1/16&V32 

1/32&V16 
1/8  &V8 
3/16 
3/8 
V4 

44 
40 
51 
47 
28 
39 

1.76 
2.38 
5.41 
3.75 
2.05 
1.90 

3.2 
4.3 
9.7 
6.8 
2.9 
2.7 

25  H.P.  shunt 
wound  vari- 
able speed. 

24-in.  drill 
press      . 

Wro't  iron 

1/64 
1/64 
1/64 

1/64 
1/64 

11/4to3* 
11/4to3* 
1l/4to3* 
1  1/4  drill 
11/4  drill 

25.1 
29.7 
25.9 
74.5 
20.9 

0.81 
0.96 
0.83 
0.52 
0.54 

2.3 
2.7 
1.3 
3.5 
1.2 

5.9 
6.5 
21.0 
2.7 
6.5 
9.3 
7.6 
23.2 

1.6 
1.9 
1.7 
1.0 
1.1 

60-in.  planer 

Soft  steel 
Wro't  iron 
Cast  iron 

1/6 
1/6 

* 

1/8 
1/8&V16 
1/7 
1/4 

% 
5/16&5/16 
1/32&V32 
1/8  &Vl6 
1/4  &5/16 
V4  &V4 
7/16&3/8 

25.5 
25.7 
23 
17.5 
22.2 
30 
22.6 
28.9 

3.62 
3.65 
8.95 
1.82 
1.72 
4.74 
5.03 
18.3 

6.5 
6.6 
17.9 
3.6 
3.4 
6.6 
7.1 
25.6 

20  H.P.   com- 
pound 
wound  vari- 
able speed. 

42-in.  planer 

Soft  steel 
Cast  iron 

5/32 

1/8 
3/16 
3/16 

3/8 
3/8 

» 

24.3 
36 
37 
37 

4.73 
3.7 
4.06 
2.71 

2.1 
7.8 
4.7 
4.1 

9.5 

1.4 
5.7 
3.8 

5   H.P.   com- 
pound 
wound  vari- 
able speed. 

19-in.slotter 

rlard  steel 
Soft  steel 

V32 
1/32 

1/4 
3/8 

30.0 
23.3 

0.8 
0.93 

2.0 
1.3 

2.0 
1.7 

3  H.P.  comp. 
w'd  var.  speed. 

Enlarging  hole  from  smaller  dimensions  to  larger. 


1296 


THE  MACHINE-SHOP. 


BOEING  AND  TURNING  MILLS — Motor  A,  B  or  C. 

In.           In.          In.         Ft.           Ft.          Ft.  Ft. 

37-42        50        60-84       7-9        10-12     14-16  16-25 

H. P.,  average..      5-7.5        7.5      7.5-10     10-15     10-15     15-20  20-25 

H.P.,  heavy...   7.5-10    7.5-10     10-15     30-40     .....  ..... 

CYLINDER  BORING  MACHINES — Motor  A,  B  or  C. 

Diameter  of  spindle,  in 4  6  8 

Maximum  boring  diameter,  in 10         30         40 

Horse-power 7.5         10         35 

HORIZONTAL  BORING,  DRILLING  AND  MILLING  MACHINES — 
Motors  A,  B  or  C. 

Size  of  spindle,  in 3.5-4.5        4.5-5.5       5.5-6.5 

Horse-power  per  spindle ...         5-7.5        7.5-10         10-15 

Drilling  Machines. 

Sensitive  Drills  up  to  1/2  in i/4-3/4  H.P.     Motor  A,  B  or  C. 

UPRIGHT  DRILLS — Motor  A,  B  or  C. 

Size,  in 12-20       24-28       30-32       36-40       50-60 

Horse-power 1235  5-7.5 

RADIAL  DRILLS — Motor  A,  B  or  C. 

Length  of  arm,  ft 3  4  5-7  8-10 

Horse-power,  average 1-2        2-3  3-5  5-7.5 

Horse-power,  heavy 3       5-7.5  5-7.5  7.5-30 

MULTIPLE  SPINDLE  DRILLS — Motor  A,  B  or  C. 

Size  of  drill,  in.      l/32-i/4     1/16-3/8      3/16-l/2      i/4-3/4       s/g-1       222 
No.  of  spindles, 

up  to 6-10          10  10  10  10          4      6        8 

Horse-power..          3  5  7.5  10        10-15    7.5    10      15 

Planing  Machinery. 

PLANERS — Motor  C,  D  or  F. 

Width,  in 22           24           27  30  36  42 

Distance  under  rail,  in.        22           24           27  30  36  42 

Horse-power 3          3-5         3-5  5-7.5  10-15  15-20 

Width,  in 48           54           60  72  84  100 

Distance  under  rail,  in..       48           54           60  72  84  100 

Horse-power 15-20     20-25     20-25  25-30  30  40 

SHAPERS — Motor  A,  B  or  C. 

Traverse  Head. 

Stroke,  in 12-16  18      20-24        30  20         ~24 

H. P.,  single  head 2  2-3       3-5        5-7.5          7.5  10 

SLOTTERS — KEYSEATERS — Motor  A,  B  or  C. 

Stroke,  in 6  8  10  12  14 

Horse-power 3         3-5  5  5  5-7 1/2 

Stroke,  in 16        18  20  24          30 

Horse-power 7.5    7.5-10     10-15     10-15  10-15 

Milling  Machinery. 

PLAIN  MILLING  MACHINES — Motor  A,  B  or  C. 

Table  feed,  in 34  42  50 

Cross  feed,  in 10  12  12 

Vertical  feed,  in 20  20  21 

Horse-power 7.5         10  15 

r  UNIVERSAL  MILLING  MACHINES — Motor  4^  B  or  C. 

Machine  number 1        H/2         2  3  4          "5 

Horse-power 1-2       1-2       3-5       5-7.5       7.5-10    •  10-15 


POWER  REQUIRED  FOR  MACHINE  TOOLS.          1297 

VERTICAL  MILLING  MACHINES — Motor  .4,  73  or  C. 

Height  under  Spindle,  in 12        14  18         20        24 

Horse-power 5          7.5         10         15         20 

VERTICAL  SLABBING  MACHINES — Motor  A,  B  or  C. 

Width  of  work,  in 24  32-36         42 

Horse-power 7.5  10  15 

HORIZONTAL  SLABBING  MACHINES — Motor  A,  B  or  C. 

Width  between  housings,  in .  .        24  30  36  60  72 

Horse-power,  average 7.5-10      7.5-10       10-15          25  25 

Horse-power,  heavy 10-15       10-15       20-25       50-60  75 

GEAR  CUTTERS — Motor  A,  B  or  C. 

Size,  in 36X9     48X10     30X12      60X12     72X14  64X20 

Horse-power..     2-3  3-5  5-7.5         5-7.5        7.5-10  10-15 

ROTARY  PLANERS — Motor  A,  B  or  C. 

Diam.  of  cutter,  in....    24     30     36-42     48-54     60     72     84  96-100 

Horse-power.    5       7.5      10  15       20     25     30          40 

SAWS,  COLD  AND  CUT-OFF — Motor  A,  B  or  C. 

Size  of  saw,  in 20         26        32  36  42         48 

Horse-power 3  5          7.5       10-15         20         25 

Bolt  and  Nut  Machinery. 

BOLT  CUTTERS — Motor  A,  B  or  C. 

Single.  Double.         Triple. 


Size,  in. .  .    1,  .1 1/4;  1 1/2 


H.P 1-2 


1  3/4,  212  1/4,  3  l/2  I   4,  6     II,  1 1/2  1  2,  2  1/2|  1,  1  1/2,  2 


2!  1, 

2-3    |       3-5    "  1 5-7.5  |  2-3"  |    3-5    I     3-7.5 

BOLT  POINTERS — Motor  B  or  C. 

Size,  in 1 1/2,  2  1/2         Horse-power 1-2 

NUT  TAPPERS — Motor  A,  B  or  C. 

4  Spindle.    6  Spindle.    10  Spindle. 

Size,  in 1,2  2  2 

Horse-power 3  3  5 

NUT  FACING  MACHINE — Motor  B  or  C. 

Size,  in 1,2         Horse-power 2-3 

BOLT  HEADING,  UPSETTING  AND  FORGING — Motor  D,  E  or  F. 

Size,  in 3/4-l  l/2        H/2-2         2 1/2-3          4-6 

Horse-power 5-7.5  10-15         20-25         30-40 

Bending  or  Forming  Machinery — Hammers. 

BULLDOZERS — Motor  D  or  E. 

Width,  in 29        34  39         45         63 

Head  movement,  in 14        16  16         18         20 

Horse-power 5          7.5         10         15         20 

BENDING  AND  STRAIGHTENING  ROLLS — Motor  E  or  G. 

Width,  ft 4       6          6           6         8        10       10  24 

Thickness,  in 3/8     s/16     7/16      3/4       7/8     ii/8     u/2  1 

Horse-power 5       5        7.5       15       25       35       50  50 

HAMMERS — Motor  D  or  E. 

Size,  Ib 15  to  75         100  to  200 

Horse-power 1/2  to    5  5  to  7 . 5 

Bliss  drop  hammers  require  approximately  1  H.P.  for  every  100  Ib. 
weight  of  hammer  head. 

Pipe  Threading  and  Cutting-off  Machinery. 

i  Motor  A,  B  or  C. 

Pipe  size,  in. .  1/4-2     1/2-3     1-4    H/4-6     2-8     3-10     4-12     8-18     24 
Horse-power.      2          3  33-5       3-5       5          5       7.5       10 


1298  THE  MACHINE-SHOP. 

Punching  and  Shearing  Machinery. 

Presses  for^notching  sheet-iron — Motor  AL  B  or  C — 1/2  to  3  H.P. 

PUNCHES — Motor  D  or  E. 

Diameter,  in..   3/8  i/2  5/8   s/4  7/8    i    i         n/4      is/4        2        2l/2 
Thickness,  in..   1/4   1/2  Vs   3/4  3/4  1/2  1.  1  1  1         H/2 

Horse-power.  .     1    2-3  2-3  3-5    5     5  7.5     7.5-10  10-15  10-15  15-25 

SHEARS — Motor  D  or  E. 

Width,  in 30-42       50-60       72-96 

Horse-power  to  cut  i/s-in.  iron.        345 
Horse-power  to  cut  l/4-in.  iron..         5  7.5  10 

Bolt  shears 71/2  H.P.         Double  angle  shears 10  H.P. 

LEVER  SHEARS — Motor  D  or  E. 

Size,  in 1X1      1 1/2  X  1 1/2     2X2      6X1     21/2X21/2 

Horse-power 5  7.5  15  15 

Size,  in 1X7     2,3/4  X  23/4     H/2  X  8     31/2  X  31/2    41/2  round 

Horse-power 15  20  25  30  30 

PLATE  SHEARS — Motor  D  or  E. 
Size  of  plate,  in., 

3/8  X  24  1  X  24  2  X  14  1  X  42  1 1/2  X  42  1 1/4  X  54  1  1/2  X  72  1 1/4  X  100 
Cuts  per  min., 

35  20  15          20  15  18  20  10-12 

Stroke,  in., 

•3  3         41/4  4  41/2  6  151/2  71/2 

Horse-power, 

10  15  30  20  60  75  10  75 

Hydrostatic  Wheel  Presses — Motor  B  or  C. 

Size,  tons .      100        200  300  400         600 

Horse-power 5         7.5  7.5  10 

Grinding  Machinery. 

GRINDING  MACHINES  (FOR  SHAFTS,  ETC.) — Motor  A,  B  or  C. 
Wheels  diameter,  in. ...    10        10        10          10        14       18       18       18 

Length  of  work,  in 50        72        96        120        72     120     144     168 

H.P.,  average  work....     555  5        10       10       10       10 

•'      heavy  work 7.5       7.5       7.5         7.5     15       15       15       15 

EMERY  WHEEL  GRINDERS,  ETC. — Motor  B  or  C. 

K  umber  of  wheels 2  2        2         2  2  2 

Size  of  wheels,  in 6  10       12         18  24  26 

Horse-power 1/2-1         2         3      5-7.5      7.5-10      7.5-10 

MISCELLANEOUS  GRINDERS — Motor  B  or  C. 

Wet  tool  grinder,  2  to  3  H.P.;  flexible  swinging  grinding  and  polish- 
ing machine,  3  H.P.;  angle  cock  grinder,  3  H. P.;  piston  rod  grinder, 
3  H.P.;  twist  drill  grinder,  2  H.P.;  automatic  tool  grinder,  3  to  5  H.P. 

In  selecting  a  motor  for  a  machine  tool,  advantage  should  be  taken 
of  the  fact  that  motors  will  stand  considerable  overloads  for  short 
periods.  This  will  lead  to  the  selection  of  smaller  nu>tors  than  are 
usual.  The  tendency  is  to  select  a  motor  to  fit  the  maximum  capacity 
of  the  machine,  rather  than  one  whose  capacity  is  more  nearly  that  of 
the  average  capacity  of  the  tool. 

A.  G.  Popcke  (Am.  Mach.,  Sept.  26  and  Oct.  3,  1912)  outlines  more 
accurate  methods  of  determining  the  sizes  of  motors  required  for 
driving  machine  tools,  based  upon  an  analysis  of  the  working  condi- 
tions, and  also  the  considerations  other  than  those  of  power  which 
govern  the  selection  of  the  motor.  To  determine  motor  capacity, 
the  following  data  are  necessary:  Horse-power,  speed  and  voltage;  and 
in  addition  for  alternating  current,  frequency  and  phase.  To  estimate 
the  horse-power  the  following  must  be  known:  Type  of  tool;  depth  of 
cut  (all  tools  being  considered),  inches;  feed,  in.  per  revolution;  speed, 
ft.  per  minute;  duration  of  both  average  and  maximum  cuts;  duration 
of  peak  of  maximum  load ;  number  of  peaks  per  hour.  From  the  area 
of  the  cut  (depth  X  feed)  and  the  cutting  speed,  the  cubic  inches  of 


POWER  REQUIRED  FOR  MACHINE  TOOLS.          1299 

metal  removed  per  minute  can  be  calculated  for  both  average  and 
maximum  cuts,  and  these  figures,  multiplied  by  the  constants  below 
give  the  horse-power  required,  to  which  the  friction  load  of  the  machine 
must  be  added. 

HORSE-POWER  CONSTANTS  FOR  CUTTING  METAL. 


H.P.  per  Cu. 

In.  per  Min. 

Steel,  50  carbon  or  more. .  1.0  to  1.25 
Brass  and  similar  alloys. .  0.2  to  0.25 


H.P.  per  Cu. 

In.  per  Min. 

Cast  iron 0.3  to  0.5 

Wrought  iron 0.6 

Machinery  steel 0.6 

These  constants  apply  to  round  nose  tools  used  in  accordance  with 
the  conditions  recommended  by  F.  W.  Taylor  (see  p.  1261).  For 
twist  drills  the  power  requirements  per  cubic  inch  are  about  double 
the  figures  given  above. 

The  size  of  the  motor  selected  will  depend  on  the  heating  of  the 
motor  while  under  load,  and  as  the  load  is  usually  intermittent,  the 
heating  will  depend  upon  the  square  root  of  the  mean  square  value  of 
the  power  required.  In  a  given  cycle  in  which  the  several  power  values 
are  Pi,  Pi,  Ps,  utilized  durmg  periods  of  ti,  h,  t3,  respectively,  the  square 
root  of  the  mean  square  will  be 


'Pi2  tl  +  P22  fe  +  P32  u  \ 

ti  +  h  +  t3 

The  heating  of  the  motor  will  be  the  same  as  if  it  were  run  constantly 
at  a  load  equal  to  the  square  root  of  the  mean  square  load.  In  making 
the  motor  selection,  however,  it  should  be  observed  whether  or  not  the 
duration  of  the  maximum  load  will  be  greater  than  the  motor  can  suc- 
cessfully withstand.  Thus  a  100%  overload  for  a  period  of  10  seconds 
can  easily  be  carried  by  a  properly  designed  motor,  while  if  prolonged 
such  a  load  may  burn  it  out.  When  selecting  motors  for  widely  fluctu- 
ating intermittent  loads,  the  limits  above  rated  load  which  must  be 
taken  into  consideration  are  for  alternating  current,  pull  at  starting 
torque,  and  speed  regulation;  and  for  direct  current  motors,  commuta- 
tion, speed  regulation  and  stability.  The  pull  at  the  starting  torque 
of  an  induction  motor  is  from  2.5  to  3.5  times  the  full-load  torque,  and 
the  speed  regulation,  or  percentage  drop  in  speed  between  no  load  and 
full  load,  known  as  the  slip,  is,  at  full  load,  from  5  to  7%.  At  other 
loads  it  is  approximately  proportional  to  the  load.  Commutating  pole, 
direct  current  motors  will  stand  100%  to  125%  overload  without 
sparking.  The  speed  regulation  at  full  load  is  10  to  15  %,  depending 
on  the  speed  of  the  motor.  With  non-commutating  pole  motors  the 
speed  decreases  with  overloads  in  proportion  to  the  loads,  while  on 
commutating  pole  motors  it  increases  up  to  100%  overload,  thus  giving 
approximately  the  same  speed  at  double  load  as  at  full  load.  A  com- 
mutating pole  motor  can  be  made  stable  at  overloads,  which  will  in- 
crease the  drop  in  speed.  The  better  the  speed  regulation,  however, 
the  less  certain  is  the  stability  and  the  motor  for  driving  machine  tools 
must  be  a  compromise  between  these  two  factors.  Motors,  however, 
are  available  which  can  be  safely  operated  on  intermittent  loads  where 
the  maximum  load  is  200%  of  the  rated  load.  In  machine  tool  work, 
a  large  speed  reduction,  giving  a  stable  motor  is  advisable  when  varia- 
tions occur  in  the  work  done  by  the  cutting  tool  on  long  jobs,  thus 
protecting  the  cutting  tools,  the  machines  and  the  work.  An  adjust- 
able speed  motor  with  a  speed  reduction  of  25  %  is  of  advantage  under 
such  circumstances. 

In  applying  the  principles  outlined  above  to  the  selection  of  a  machine 
tool  motor,  the  average  and  maximum  conditions  of  service  of  the 
machine  should  be  determined  by  laying  out  typical  jobs  in  which 
these  conditions  are  present.  The  power  cycles  are  determined  from 
the  amount  of  metal  removed  on  each  cut  as  previously  explained  and 
the  duration  of  each  cut  is  ascertained  from  the  length  of  the  cut,  the 
spindle  speed  and  the  feed  per  revolution.  The  square  root  of  the 
mean  square  value  of  the  power  required  is  next  determined,  the  time 
while  the  machine  is  idle  during  the  periods  of  adjustment  being  added 
in  the  denominator  of  the  formula  for  this  value,  A  motor  whose 


1300  THE  MACHINE-SHOP. 

capacity  is  in  the  neighborhood  of  the  value  ascertained  is  then  selected, 
and  the  relation  of  the  maximum  load  to  the  rated  motor  capacity  is 
observed  to  ascertain  whether  or  not  the  motor,  in  addition  to  carry- 
ing the  average  load,  is  capable  of  carrying  the  maximum  load  without 
injury.  For  instance,  if  the  square  root  of  the  mean  square  value  is 
5.5  II.  P.  a  5-H.P.  motor  would  be  under  an  overload  of  10%,  which 
is  well  within  the  capacity  of  a  well  designed  machine.  If  the  maxi- 
mum load  requires  8.3  H.P.  for  a  period  of  three  minutes  the  motor 
will  be  overloaded  66%  for  this  period  which  is  also  within  the  limits 
set  by  good  motor  design. 

According  to  Mr.  Popcke,  other  questions  than  horse-power  govern 
the  selection  of  a  motor  for  a  machine  tool.  The  speed  of  the^motor 
depends  upon  the  speed  of  the  machine  shaft,  which  ranges  from  50  to 
60  r.p.m.  on  forging  machines  to  200.  to  300  r.p.m.  on  machine  tools, 
and  as  high  as  1000  to  2000  r.p.m.  on  grinding  and  wood-working  ma- 
chinery. The  speeds  usually  obtainable  with  60-cycle  alternating 
current  motors  are  1700-1800,  1100-1200,  850-900,  650-720  and 
550-600  r.p.m.  The  speeds  available  on  standard  direct  current 
motors  are  approximately  the  same.  On  25-cycle  alternating  current 
motors  the  usual  speeds  are  700-750,  550^600,  and  350-375  r.p.m. 
The  following  factors  are  considered  in  selecting  motors  for  belt  drives: 
Speed  .reductions,  pulley  sizes,  belt  speeds,  motor  speeds,  distance 
between  pulley  centers,  arc  of  contact,  use  of  idler  pulleys,  mounting 
of  motor.  Involved  in  the  speed  reductions  are  the  sizes  of  the  motor 
and  machine  pulleys  and  the  belt  speed.  The  standard  sizes  of  motor 
pulleys  which  have  been  adopted  in  connection  with  standard  speed 
ratings  of  the  various  sizes  of  motors  have  standardized  the  belt  speeds. 
The  maximum  and  minimum  standard  speed  ratings  of  the  motors, 
together  with  the  maximum  and  minimum  pulley  diameters  are  given 
in  the  following  table: 
HORSE-POWER  OF  MOTOR. 

1          2         3          5       71/2     10       15       20       25       30       35       40       50 
R.P.M  ,  MAXIMUM. 

1700  1700  18CO  1800  1700  1700  1700  1700  1400  1700  1700  1700  1700 
Pulley  Diameter,  standard. 

31/231/24          4          5         6         7         8         9         9        10       11        11 
Pulley  Diameter,  minimum. 

3  3         33l/2441/25         6       6 1/2    61/2       7      7  1/2      8 

R.P.M.,  MINIMUM. 

850      850      850      650      600      600      650      600      600      675      600      565 

Pulley  Diameter,  standard. 

4          5          6         8         9        11        11        12        13        13        14        16 

Pulley  Diameter,  minimum. 

31/2      4       41/2       6       61/271/2      8         9        10        10        12    13  1/2 

The  minimum  size  of  pulley  is  specified  on  account  of  the  reduction 
of  pulley  size  increasing  the  strains  on  the  motor  bearings  and  shaft. 
The  arc  of  contact  has  great  effect  on  the  success  of  a  belt-driven  motor 
installation.  The  arc  of  contact  depends  on  the  distance  between  the 
pulley  centers  and  on  the  speed  reduction.  Where  it  is  necessary  to 
increase  the  arc  of  contact,  idler  pulleys  are  of  service.  In  machine 
work  the  size  of  the  motor  pulley  is  sometimes  fixed  by  the  necessity 
of  belting  the  motor  to  the  machine  flywheel,  in  which  case  care  must 
be  taken  that  the  diameter  of  the  motor  pulley  is  not  less  than  the 
minimum  size  specified.  The  arc  of  contact  must  also  be  considered, 
as  in  a  large  speed  reduction  this  will  be  decreased  and  will  seriously 
affect  the  amount  of  power  transmitted.  The  effect  of  decreasing  the 
arc  of  contact  is  shown  below,  the  power  transmitted  by  a  180  deg.  arc 
of  contact  being  taken  as  100. 

Arc  of  contact,  deg 180       170       160       150       140       130       120 

Power  transmitted,  % .  .  100  94  89  83  78  72  67 
The  cost  of  a  motor  per  horse-power  increases  as  the  speed  decreases. 
Therefore,  for  maximum  economy  in  first  cost  as  high  a  speed  as 
possible  should  be  selected  without,  however,  going  below  the  minimum 
pulley  diameter.  Back  geared  motors  are  useful  where  extremely  low 
speeds  are  required.  A  speed  ratio  of  6:1  between  the  armature  and 
the  motor  countershaft  is  usually  satisfactory,  any  further  speed 
reduction  to  the  machine  pulley  being  obtained  by  means  of  the  pulley 


POWER  REQUIRED   FOR  MACHINE   TOOLS.        1301 
Data  for  Standard  Geared  Connections  for  Constant  Speed  Motors. 


Maximum  Speed  Rating. 

Minimum  Speed  Rating. 

No.  of  Teeth. 

.s 

No.  of  Teeth. 

.S 

1 

1 

^  S 

_ 

xlj 

g 

1 

£S 

^ 

t* 

o 
PH 

i 

id 

lg 

*l 

Id 

£» 

5 

g 

S 

S" 

T3  o 

&'S 

OJ 

w  c 

PH" 

1 

i 

2 

i| 

•S-n 

.S'S 

.  o 

d 

PH 

o> 

5.2 

.s^ 

-S'S 

TiS 

jjj 

w 

« 

Q 

SS 

£3 

S 

£ 

b 

££ 

Ss 

S£ 

s 

j 

1700 

8 

17 

15 

13 

940 

1.63 

1200 

8 

17 

15 

13 

665 

1.63 

2 

1700 

8 

17 

15 

13 

940 

1.63 

850 

6 

18 

21 

19 

615 

2.38 

3 

1800 

8 

22 

20 

19 

1300 

2.38 

850 

6 

18 

18 

18 

670 

3.0 

5 

1800 

8 

22 

21 

19 

1300 

2.38 

850 

6 

21 

19 

18 

990 

3.0 

7.5 

1700 

6 

18 

18 

18 

1400 

3.0 

650 

5 

20 

18 

18 

685 

3.6 

10 

1700 

6 

21 

19 

18 

1420 

3.0 

600 

5 

21 

19 

19 

665 

3.8 

15 

1700 

5 

19 

18 

18 

1700 

3.6 

600 

41/9 

22 

19 

19 

770 

4.22 

20 

1700 

5 

20 

18 

18 

1780 

3.6 

650 

4 

21 

18 

18 

890 

4.5 

25 

1400 

5 

21 

19 

19 

1550 

3.8 

600 

4 

22 

19 

18 

864 

4.5 

30 

1700 

5 

21 

19 

19 

1880 

3.8 

600 

31/4 

20 

18 

970 

5.53 

35 

1700 

4V? 

22 

18 

18 

2180 

4.0 

675 

31/4 

20 

.... 

18 

1080 

5.53 

40 

1700 

4  1/9 

22 

19 

19 

2180 

4.22 

600 

3 

18 

15 

940 

5.0 

50 

1700 

4 

21 

18 

18 

2340 

4.5 

565 

3 

20 

18 

990 

6.0 

Data  for  Standard  Geared  Connections  for  Adjustable  Speed  Motors. 


Maximum  Speed  Rating. 

Horse- 

Min. 

Gear  Data. 

Pitch  Line 

Power  . 

Min. 
R.P.M. 
of 
Motor. 

Speed 
Ratio. 

Diam. 
of 
Pulley, 
in. 

Speed  at 
Min.  Diam. 

Min. 
No.  of 
Teeth. 

Min. 
Diam., 
in. 

Diam. 
Pitch. 

Min. 

Max. 

j 

740 

3 

3 

19 

2.38 

8 

460 

1380 

2 

1100 

2 

3 

19 

2.38 

8 

690 

1380 

3 

1000 

2 

3 

19 

2.38 

8 

625 

1250 

5 

1000 

2 

4 

18 

3.0 

6 

790 

1580 

7V2 

900 

2 

5 

18 

3.0 

6 

705 

1410 

10 

850 

2 

6 

18 

3.6 

5 

800 

1600 

15 

780 

2 

6l/2 

19 

3.8 

5 

780 

1560 

20 

650 

2 

71/2 

19 

4.22 

41/2 

720 

1440 

25 

550 

2 

9 

18 

4.5 

4 

645 

1290 

30 

550 

2 

10 

18 

5.53 

3l/4 

800 

1600 

40 

550 

2 

12 

15 

5.0 

31/2 

720 

1440 

50 

500 

2 

121/2 

18 

6.0 

3 

790 

1580 

Minimum  Speed  Rating. 

1 

450 

4 

3 

19 

2.38 

8 

280 

1120 

2 

450 

4 

4 

18 

3.0 

6 

355 

1420 

3 

375 

4 

5 

18 

3.0 

6 

294 

1176 

5 

375 

4 

6 

18 

3.6 

5 

355 

1420 

71/2 

350 

4 

61/2 

19 

3.8 

5 

350 

1400 

10 

375 

4 

7 

18 

4.0 

41/2 

390 

1560 

15 

375 

4 

9 

18 

4.5 

440 

1760 

20 

300 

4 

12 

15 

5.0 

3 

390 

1560 

25 

300 

4 

121/2 

18 

6.0 

3 

470 

1880 

30 

250 

4 

14 

18 

6.0 

3 

390 

1560 

40 

250 

4 

16 

19 

6.33 

3 

415 

1660 

50 

325 

3 

16 

19 

6.33 

3 

540 

1620 

1302 


THE  MACHINE-SHOP. 


on  the  motor  countershaft.  Back  geared  motors  are  used  where  che 
machine  speed  is  below  150  to  100  r.p.m.  The  initial  speed  of  the 
back  geared  motor  should  not  exceed  1200  r.p.m.  when  the  horse-power 
is  from  10  to  20  and  should  not  exceed  900  or  even  720  r.p.m.  when 
the  horse-power  is  greater  than  this  figure. 

For  equipment  where  the  motor  is  geared  to  the  machine,  the  follow- 
ing are  the  governing  considerations:  Speed  reduction,  pitch  line 
speed,  number  of  teeth  on  gears,  width  of  face  of  gears,  center  distances, 
use  of  idler  gears,  motor  mounting.  Noise  limits  the  pitch  line  speed 
to  about  1000  feet  per  minute  with  steel  gears.  For  speeds  of  1000 
to  2000  feet  per  minute,  cloth  or  rawhide  pinions  should  be  used  and 
speeds  in  excess  of  2000  feet  per  minute  should  be  avoided  if  possible. 
Stresses  in  bearings  and  motor  shafts  limit  the  minimum  size  of  motor 
pinions  just  as  they  limit  the  size  of  pulleys.  The  maximum  and 
minimum  speed  ratings  and  the  corresponding  standard  and  minimum 
sizes  of  pinions  for  constant  speed  and  adjustable  speed  motors  are 
given  in  the  tables  on  the  preceding  page.  The  second  table  also  gives 
the  minimum  pulley  diameters  for  adjustable  speed  motors. 

For  additional  data  on  machine  tool  motors  see  Electrical  Engineer- 
ing, p.  1466. 

Motor  Requirements  for  Milling  Machines. — See  p.  1278. 

Power  Required  for  Drilling. — See  p.  1286. 

Motor  Requirements  of  Planers.  (A.  G.  Popcke,  Am.  Mach.,  Sept. 
26,  1912.) — Manufacturers  usually  specify  motors  for  planers  that  are 
larger  than  necessary,  due  to  the  heavy  peak  load  imposed  at  the  instant 
of  reversal.  Before  the  advent  of  interpole,  commutating  motors,  this 
peak  load  caused  sparking  unless  a  large  motor  was  used.  The  com- 
mutating motor  eliminates  this  trouble  and  permits  the  use  of  a  smaller 
motor.  A  flywheel  on  the  countershaft,  from  which  the  forward  and 
reverse  belts  are  driven,  will  assist  in  the  carrying  of  the  peak  loads, 
and  will  allow  the  use  of  a  smaller  driving  motor  than  otherwise.  The 
table  below  shows  the  results  of  tests  of  planers  with  a  graphic  record- 
ing ammeter,  and  gives  the  power  required  at  different  portions  of  the 
planer  cycle.  It  also  shows  the  motors  recommended  and  installed, 
which  are  handling  the  work  satisfactorily,  and  also  the  size  of  motors 
specified  by  the  makers  of  the  tools. 

Power  Requirements  of  Planers. 


Observed  Power 

Motor 

Re  quirements. 

Motor 
In- 

Size of 

Used 

_ 

'cS 

stalled, 

Motor 

Planer. 

for 

•»& 

M 

<n  t* 

I     £ 

Remarks. 

Based 

Speci- 

Test. 

3  o 

o>o 

0>  o  3 

on 

fied. 

ra 

Is 

S5 

eftf 

Test. 

In.     Ft. 

H.P. 

K.W. 

K.W. 

K.W. 

K.W. 

H.P. 

H.P. 

56  X  15 

3 

1.3 

3.5 

4.0 

5.3 

Average  work 

) 

5 

1.8 

2.8 

3.5 

5.3 

5  Tons  on  table 

[    5 

15 

** 

5 

2.5 

6 

6 

Short  stroke 

f 

54  X  16 

30 

4 

"6  " 

8 

10.5 

Average  stroke 

30 

4 

7 

10 

12 

Short  stroke 

i     5 

15 

« 

5 

1.8 

2.3 

3.5 

5.5 

Average  stroke 

48  X  12 

5 

2 

7 

8 

9 

Average  work 

71/2 

15 

24  X  10 

71/2 

2 

4.5 

4.3 

5.5  { 

Motor  geared 
balance  wheel 

}     * 

71/2 

42  X  12* 

5 

1.5 

2.5 

5 

7 

Average  work 

71/2 

15 

48  X  12 

30 

5 

10 

14 

19 

No.  bal.  wheel 

71/2 

15 

37  X  8 
36  X  8 

5 

5 

1.8 
1.5 

3 

2 

4 
2.5 

6 
4 

Average  work 

5 
3 

10 
5 

36  X  8 

5 

1.8 

2 

3 

5 

" 

3 

5 

*  Open  side. 

The  Cincinnati  Planer  Co.  has  furnished  the  author  with  the  results 
of  a  test  of  72  in.  X  24  ft.  planer,  fitted  with  a  reversible  motor  drive, 
cutting  cast  iron,  To  run  the  table  in  the  direction^  the  cut  required 


POWER  REQUIRED  FOR  WOOD-WORKING  MACHINES.     1303 


2.06  H.P. ;  reversing  from  cutting  to  return  stroke,  13  H.P.;  reversing 
from  return  to  cutting  stroke,  14.4  H.P. 

Test  on  72  X  24-in.  Reversible  Motor-Driven  Planer. 


-Depth 
of  Cut, 
In. 

Feed, 
In. 

Number 
of  Tools 
Cutting. 

Cutting 
Speed, 
Ft.  per 
Min. 

H.P. 
Required, 
Including 
Friction. 

Pressure 
per  Sq.  In. 
in 
Cast  Iron. 

1/2 

3/16 

2 

30 

23 

123,200 

1/2 

3/16 

2 

40 

26.7 

108,680 

1/2 

3/16 

2 

60 

37.5 

104,133 

1/2 

3/32 

2 

30 

11.5 

111.419 

1/2 

3/32 

2 

60 

23 

123,200 

1/4 

3/16 

2 

30 

10.1 

95,090 

1/4 

3/16 

2 

60 

20.2 

106,830 

V4    . 

3/32 

2 

30 

7.3 

124,572 

1/4 

3/32 

2 

60 

14.4 

145.726 

Power  Required  for  Wood-Working  Machinery.  (E.  G.  Fox,  EL 
Rev.,  June  13,  1914.).  —  The  factors  influencing  the  power  required 
for  wood-  working  machines  are:  Design,  speed  of  working,  including 
feed  and  depth  of  cut,  condition  of  machine  and  cutters,  nature  of 
material.  Machines  handling  one  kind  of  material  may  be  motored 
for  their  ordinary  load,  while  those  having  diverse  work  must  be 
motored  for  their  heaviest  service.  The  data  below  are  based  upon 
tests  as  well  as  on  figures  furnished  by  manufacturers. 

Band  Saws.  —  The  motors  should  have  good  starting  torque,  and 
with  resaws  should  be  .capable  of  developing  1.5  full  load  torque 
at  starting,  and  should  have  good  overload  characteristics.  Belted 
motors  are  recommended  for  most  installations. 

BAND-SAWS. 

Wheel  diameter,  in  ............       42  38       36       36       34       30 

R.P.M  .......................    400-500  450     500     400     500     500 

Maximum  depth  of  timber,  in  ..        20  16       16       14       12       12 

H.P.  of  motor  .................          5  553 


3 


BAND-RESAWS. 


Wheel  diameter,  in  ..........        60  54  48  44  42  40  38 

R.P.M  ......................    550  600  650  650  650  700  450 

Width  saw  blade,  in  ..........        8  6  5  4  4  3  2 

Maximum  depth  of  timber,  in  ..      36  30  26  24  24  20  12 

H.P.  of  motor  ................      50  40  30  20  15  15  7.5 

R.P.M.  of  motor  .............    600  600  720  720  720  720  514 

Add  for  jointing  attachment  on  48-in.  saw,  7.5  H.P. 

BAND  RIP  SAWS  —  POWER  FEED. 

Wheel  Diam.,  Max.  Timber         Motor  Motor 

in.  R.P.M.  Depth,  in.  H.P.  R.P.M. 

42  650  12  15  720 

40  600  15  10  600 

Add  2  H.P.  for  return  rolls,  if  used.  Speeds  given  are  for  direct 
connection. 

Circular  Saws.  —  Circular  saws  are  not  as  widely  used  as  band-saws 
for  resawing,  as  they  require  more  power,  run  at  lower  speeds  and  waste 
more  stock.  Splitting  with  circular  saws  requires  from  15  to  20% 
more  power  than  cross-cutting.  Band-saws  require  about  the  same 
power  for  both. 

CIRCULAR  SAWS. 
Maximum  diameter  of  saw,  in  .......       42         36 

R.P.M.  of  saw  ....................      900     1000 

Maximum  capacity,  in.,  horizontal.  ..        17         14 
4    vertical  ............ 

Horse-power  ......................       25         25 


32  30  24 

1225  1200  1225 

11  10  8 

8  6  6 

20  20  20 


1304 


THE  MACHINE-SHOP. 


CIRCULAR  RIP-SAWS. 

Maximum  diameter  of  saw,  in 20  16  12 

Maximum  R.P.M.  of  saw 2100  2600  2400 

Maximum  thickness  of  stock,  in 6  5  2 

Feed,  ft.  per  min 60-180  64-194  50-100 

Horse-power 15  15  7.5 

HAND-FEED  CIRCULAR  RIP-SAWS. 
Maximum  diameter  of  saw,  in.        14         16         20         24         30         36 

R.P.M.  of  saw 2700     2400     2000     1600     1250     1000 

Horse-power 7.5         10         15         15         20         20 

POWER-FEED  GANG  RIPPING-MACHINE. 

Number  of  saws 2  3  4  8 

Maximum  R.P.M 3400         2300         2500         2500 

Diameter  of  saws,  in 10  15  14  14 

Feed,  ft.  per  min 180  200  100-180     90-200 

Horse-power 15  30  25  35 

CIRCULAR  CUT-OFF  SAWS. 

.  Maximum  saw  diameter,  in 14  16 

R.P.M.  of  saws 2700         2600 

Hcrse-power 5  7.5 

INSIDE  MOLDERS. 

Maximum  capacity,  in 8X4      10  X  4      12  X  6      14X6 

Horse-power 25  25  35  35 

OUTSIDE  MOLDERS. 
Maximum  capacity,  in.   4X4     6X4     8X4     10X4     12X5     14X6 

Horse-power 10  15          20          25  30  35 

STICKERS. 
Maximum  size  of  timber,  in...     16X4-     18X4      20  X  4 

Horse-power ". 5  7.5  10 

JOINTERS. 

Maximum  width  of.  timber,  in 8       12       16       20     24         36 

Horse-power 2         2         3         5       7.5       7.5 

The  recommendations  for  molders,  stickers  and  jointers  are  based 
on  a  maximum  depth  of  cut  of  3/32  in.  If  the  cut  is  greater,  the  size  of 
motor  should  be  correspondingly  increased. 

Surfacers. — The  motor  sizes  given  below  are  for  medium  work  with 
maximum  depths  of  cut  of  i/g  in.  For  planing  mill  work,  on  heavy 
stock  with,  deep  cuts  the  sizes  should  be  increased  about  5  H.P. 

SINGLE  SURFACERS. 
Maximum  width  of  timber,  in.  16       20       24       30       36 

Horse-power 7.5    10       10       15       15 

DOUBLE  SURFACERS. 

Maximum  width  of  timber,  in 26         30         36 

Horse-power,  heavy  work 35         35 

Horse-power,  medium  work 20         25         30 

Timber   Sizers. — The  following  figures  apply   to   heavy   service   in 
dressing  timber  to  size,  surfacing  four  sides  simultaneously. 
Max.  size  of  timber,  in.  .    20  X  16    20  X  18    20  X  20    30  X  18    30  X  20 

Horse-power 60          60-75       60-75          75  75 

DRUM  SANDERS. 

Number  of  drums 1          1         1         2          2         2         2 

Max.  Width  of  Stock,  in 30       36       42       30       36       42       48 

Horse-power 10       15       15       20       20       20       25 

Number  of  drums 3         3        3         3          3         3         3 

Maximum  width  of  stock,  in ...      30       36  42-48  54-66    72       78       84 

Horse-power 20       25       30       35       40       40       50 

When  material  is  sanded  to  size  and  full  width  of  sander  is  used  with 
panels  fed  continuously,  add  5  H.P.  to  above  motor  sizes. 
TENONERS — HAND-FEED. 

Length  of  tenon,  in 7  single      7  double 

Horse-power 7.5  10 


POWER  REQUIRED   FOR  MACHINES   IN   GROUPS.      1305 

Shapers.- — For  ordinary  service  on  reversible  single-  or  two-spindle 
machines,  use  a  5  H.P.  motor.  For  extra  heavy  work,  as  in  carriage 
factories,  railroad  shops,  etc.,  use  a  7.5  H.P.  motor. 

SCRAPING  MACHINES. 
Maximum  width  of  stock,  in.  .  .      12         26         30         42 

Horse-power 2  3  3  5 

AUTOMATIC  LATHES. 
Maximum  diameter  and  length  of  stock,  in.  2.75  X  72     3  X  50     5  X  50 

Horse-power 10  15-20         20 

BORERS. 

Number  of  bits 112          348 

Maximum  diameter  of  bits,  in 1       2       0.75     0.75     0.5     0.5 

Horse-power 3       5       3          5          5      10 

CHISEL  MORTISING-MACHINES. 

Maximum  number  of  chisels 1        1          1          1  2 

Maximum  size  of  chisel  square,  in 0.5     0.75     0.75     1.25       1 

Horse-power 2        2          3          5          3 

Maximum  number  of  chisels 3        4          5          6          7 

Maximum  size  of  chisel  square,  in 1         1  13/ie      is/ig      13/ig 

Horse-power 5        5          5          7.5       7.5 

PLANERS  AND  MATCHERS. 

For  planing  and  matching  timber  at  one  operation. 
Maximum  size  of  timber,  in. .    9X6     15  X  6     20  X  6     24  X  6     26  X  8 
Horse-power 35  40  45  45  45 

Box  board  matchers  are  similar  to  planers  and  matchers,  but  the 
work  is  much  lighter.  Hand-fed  machines  usually  require  a  7.5  H.P. 
motor,  while  power-fed  machines  require  10  H.P. 

Horse-power  Required  to  Drive  Shafting.  —  Samuel  Webber  in  his 
"Manual  of  Power"  gives,  among  numerous  tables  of  power  required 
to  drive  textile  machinery,  a  table  of  results  of  tests  of  shafting.  A  line 
of  21/8-in.  shafting,  342  ft.  long,  weighing  4098  lb.,  with  pulleys  weigh- 
ing 5331  lb.,  or  a  total  of  9429  lb.,  supported  on  47  bearings,  216  rev- 
olutions per  minute,  required  1.858  H.P.  to  drive  it.  This  gives  a 
coefficient  of  friction  of  5.52  %.  In  seventeen  tests  the  coefficient  ranged 
from  3.34%  to  11.4%,  averaging  5.73%.  J.  T.  Henthorn  states  (Trans. 
A.  S.  M.  E.,  vi,  462)  that  in  print-mills  which  he  examined  the  friction 
of  the  shafting  and  engine  was  in  7  cases  below  20%  and  in  35  cases 
between  20%  and  30%,  in  11  cases  from  30%  to  35%  and  in  2  cases 
above  35%,  the  average  being  25.9%.  Mr.  Barrus  in  eight  cotton- 
mills  found  the  range  to  be  between  18%  and  25.7%,  the  average  being 
22%.  Mr.  Flather  (Dynamometers)  believes  that  for  shops  using 
heavy  machinery  the  percentage  of  power  required  to  drive  the  shafting 
will  average  from  40%  to  50%  of  the  total  power  expended.  Under 
the  head  of  shafting  are  included  elevators,  fans  and  blowers. 

Power  Required  to  Drive  Machines  In  Groups.  —  L.  P.  Alford 
(Am.  Mac/2.,  Oct.  31,  1907)  gives  the  results  of  an  investigation  to 
determine  the  power  required  to  drive  machinery  in  groups.  The 
method  employed  comprised  disconnecting  parts  of  the  shafting  in  a 
belt-driven  plant,  and  driving  the  disconnected  porti9n  with  its  ma- 
chines by  an  electric  motor,  readings  of  the  power  required  being  taken 
every  5  minutes.  The  average  power  required  for  the  entire  factory 
was  considerably  less  than  the  sum  of  the  power  required  for  the  in- 
dividual machines,  due  to  tools  being  stopped  at  some  portion  of  the 
day  for  adjustment,  replacement  of  work,  etc.  The  conditions  of 
group  driving  are  such  that  fixed  rules  cannot  be  laid  down,  but  a  study 
must  be  made  of  each  individual  case.  The  results  of  the  several  thou- 
sand observations  made  in  the  investigation  are  given  in  the  accom- 
panying table.  The  observations  were  made  before  the  introduction 
of  high  speed  steel,  and  the  figures  probably  should  be  modified  some- 
what for  more  modern  practice.  The  sum  of  the  individual  horsepower 
values  as  given  in  the  table  is  about  20%  higher  than  the  power  actual jy 
used  in  the  factory,  due  to  a  lessening  of  the  average  horse-power  in 
each  department.  The  reason  for  this  is  the  working  conditions  exist- 
ing, in  that  all  tools  were  not  used  to  their  maximum  or  even  average 


1306 


THE  MACHINE-SHOP: 


capacity  at  the  same  time.  In  determining  the  size  of  motor  for  each 
department,  the  total  horse-power  required  by  the  tools  in  that  depart- 
ment, as  given  in  the  table,  was  diminished  by  20%,  and  the  friction 
load  of  line  and  countershafts  was  added. 

Power  Required  by  Machine  Tools  in  Groups. 


Size. 

Maxi- 
mum 
H.P. 

Aver- 
age 
H.P. 

Size. 

Maxi- 
mum 
H.P. 

Aver- 
age 
H.P. 

Size, 

Maxi- 
mum 
H.P. 

Aver- 
age 
H.P. 

Boring 
36  in.i 
42  «2 

Cam 
No.  2 
"    4 
"    5 
Note  3 
"     4 
Cutting- 
1  15/16  in. 
2  in. 
3  in. 
Drilling 
Note    5 
"       6 
"      7 
"       8 
"      9 
"     10 
"     11 
16  in. 
18  " 
20  " 
22  " 
24  " 
26  " 
28  " 
30  " 
34  " 
36  " 
46  " 
50  " 
Gear 
No.  4  1/2 
«    3 
«    3 

Gr 

No.  312 
"    4 

"    1113 

«    2" 

«      314 
«      115 
«      215 

Mach 
0.78 
1.72 

Cutte 

mes. 
0.52 
1.08 
rs. 
0.67 
0.32 
0.32 
0.32 
0.32 
chine. 
0.12 
0.14-0.18 
0.20-0.22 
ines. 
0.72 
1.12 
0.31 
0.32 
0.35 
0.48 
0.71 
0.25 
0.35 
0.42 
0.59 
0.47 
0.22 
0.25 
0.30 
0.45 
0.53 
0.63 
0.83 
rs. 
0.15-0.32 
0.20 
0.20 

0.32 
0.53 
0.80 
0.40 
0.50 
0.60 
0.76 

Grind 
Note  16 
"      17 
Drop 
40  Ib. 
250 
400' 
600 
800 
1000 
1500 
Power 
lOOlb. 
150  " 
Ke 
No.  4 
L 
20  in.i* 
30  "  is 
12  " 
14  " 
16  " 
16  " 
18  " 
20  " 
22  " 
24  " 
24  " 
28  " 
38  " 
10  "  19 

14    "  19 

15  «  20 

#21 

No.  I22 
2X24  in.  23 
14  in.24 

16   "  24 
36  "  25 

Milling 
No.  1 
"    3 
"    4 

"     41/2 

"    6 

ers  (C< 
3.29 

Hamm 

mi.} 
0.97 
0.41-0.82 
ers.  * 
0.10 
2.00 
2.50 
3.00 
3.50 
4.00 
5.00 
lers. 
1.50 
1.75 

0.28-0.32 

0.35 
0.41 
0.24 
0.26 
0.34 
0.36 
0.39 
0.44 
0.32 
0.25 
0.31 
0.31 
0.58 
0.10 
0.12 
0.25 
0.70 
0.33-0.63 
1.20-1.80 
0.31 
0.36 
1.30 
ines. 
0.30 
0.26 
0.19-0.29 
0.13-0.19 
0.26 

Milling  M 
No.    7 
14 
15 

326 

526 

3 
1 
2 
5 

7 

u/227 
PI 

17  in. 
22  X  60  in. 
22  X  60 
24  X  72 
26  X  60 
30  X  72 
30  X  96 
36X120 
50X108 
34  in.28 
24  «  29 

Polishi 
No.  3 

Fund- 
No.  3 
Profilin 
No.  T 

Ban 
36  in. 
Circ 
9  in. 
13  " 
13  " 
Ha 
12-14  in. 
Screw 
No.  1 
"    2 
"    2 

achine 

aners. 
2.01 
2.34 
1.44 

'l'.59' 
4.91 
5.46 
4.00 
2.94 
7.75 
3.40 
ngSta 

i  Press 
2.59 
y  ]Mac 

s  (Cow/.) 
0.83 
0.25 
0.25 
0.26 
0.55 
0.17-0.25 
0.15 
0.25 
0.30 
0.83 
0.20 

1.0  -0.43 
1.16-0.53 
0.70 
0.84 
0.81 
1.31 
1.56 
1.60 
1.14 
3.70 
2.00 
nds. 
1.00 
1.09 
es. 
1.26 
lines. 
0.50 
0.40 

30 

0.87 
iw. 
1.05 
1.04 
1.21 

7. 

0.06 
nes. 
0.60 
0.37 
0.72 

0.48 
0.48 

off  Ma 

0.28 
0.34 
r  Mach 

'3.*18' 

Hamn 

yseater 
0.64 
athes. 

0.48 
'6.48' 

0.37 

Cutte 

inders 
'1.42' 

'j.63' 
1.97 

'i.5b' 

Mach 
0.47 
0.64 

d-Saw 
3.00 
ular  82 
3.77 
3.75 
5.82 
ck  Sav 

Machi 

NOTES. — i  Single  head.  2  Double  head.  3  Lathe  type,  single  head.  4  Lathe 
type,  double  head.  5  No.  0  radial.  6  No.  1  radial.  7  Single  spindle, 
sensitive.  8  2-spindle.  » 3-spindle,  sensitive.  1°  4-spindle.  n  6-spindle. 
12  Cutter  and  reamer,  i3  Plain.  "Surface.  ^Universal.  ifi  Wet  tool, 
carrying  20-in.  wheel.  l7  Wet  grinder  with  two  24-in.  wheels.  18  Boring 
lathe,  is  Speed  lathe.  20  Squaring-up  lathe.  21  Gisholt  turret  lathe. 
22  Potter  &  Johnson  semi-automatic.  23  Jones  &  Lamson  flat  turret.  21  Wood 
turning.  25  putnam  gap  lathe,  used  for  wood  turning.  26  Vertical.  2?  Hand. 
88  Wood  panel  planer.  29  Wood  surfacer.  30  Used  for  pattern  work. 


MACHINE   TOOL  DRIVES,   SPEEDS   AND   FEEDS.      1307 

A  similar  investigation,  reported  by  H.  C.  Spillman  (Mach'y,  June, 
1913),  showed  that  but  20%  of  the  total  power  supplied  to  the  motor 
is  applied  in  useful  work  in  the  machines,  72%  being  absorbed  in  friction 
losses  in  machines  and  shafting,  and  8%  disappearing  as  electrical 
losses. 

MACHINE  TOOL  DRIVES,  SPEEDS  AND  FEEDS. 

Geometrical  Progression  of  Speeds  and  Feeds. — It  has  become 
generally  accepted  that  the  speeds  available  on  a  given  machine  tool 
should  be  in  a  geometric  progression.  There  is,  however,  by  no  means 
a  uniformity  in  the  ratio  of  the  various  geometric  series  adopted  by 
the  different  makers.  This  ratio  will  be  found  to  range  from  1.3  to  1.7 
on  the  usual  types  of  cone-driven  machines,  and  the  speeds  available 
under  different  conditions  of  open  belt  and  back  gear  operation  present 
many  duplications  and  are  often  far  from  a  true  geometric  progression 
when  considered  over  the  entire  range  of  speeds.  Carl  G.  Barth  (Am. 
Mach.,  Jan.  11,  1912)  suggests  a  ratio  of  ^2~"=  1.189.  With  this  ratio, 
the  revolutions  per  minute  of  the  spindle  are  doubled  every  fourth 
speed.  An  editorial  (Am.  Mach.,  Dec.  3,  1914)  discussing  the  advan- 
tage of  adopting  this  ratio  for  a  speed  series  shows  that  it  will  fulfill 
all  the  ordinary  requirements  of  machine  tool  work,  and  that  practically 
any  desired  speed  in  either  lathe  or  drill  press  can  be  obtained  when 
the  machine  is  speeded  according  to  a  geometric  progression  based 
on  the  ratio  1.189.  At  the  present  writing  (1915)  this  ratio  has  been 
adopted  by  several  machine  tool  builders. 

The  necessity  for  the  adoption  of  a  standard  ratio  for  speeds  and 
feeds  on  machine  tools  is  discussed  in  Am.  Mach.,  Dec.  3  and  10,  1914, 
in  describing  the  respeeding  of  machines  at  the  Watertown  arsenal  and 
elsewhere.  The  speeds  originally  available  on  many  of  the  machines 
presented  many  duplications  of  open  belt  speeds  when  back-geared,  and 
the  speeds  on  any  one  machine  considered  as  a  whole  were  not  in  any 
regular  series.  Thus  a  lathe  with  supposedly  20  speeds  had  practically, 
due  to  duplication  of  speeds  in  the  open  belt  and  back-gear  series,  only 
12  speeds.  The  rearrangement  of  the  gearing  and  the  pulleys  made 
all  20  speeds  available,  and  in  practical  accord  with  a  geometric  series 
with  a  ratio  of  1.189.  In  the  same  article  there  are  tabulated  the 
speeds  of  nine  16-in.  lathes  offered  in  response  to  a'  request  for  bids. 
In  no  case  did  the  speeds  available  on  one  lathe  correspond  with  those 
on  any  other,  nor  did  any  set  of  speeds  even  approximate  the  ideal 
speeds.  Even  three  machines  offered  by  one  maker  had  wide  variations 
in  their  speeds.  Such  a  condition  precludes  the  possibility  of  using 
machines  interchangeably  for  the  same  service,  and,  as  stated  by  Mr. 
Barth,  is  the  basis  of  much  of  the  trouble  regarding  piece  rates  in  machine 
shop  work.  See  also  article  by  Robert  T.  Kent,  Iron  Age,  July  3,  1913. 

A  geometrical  progression  of  the  fe^ds  available  on  machine  tools  is 
also  desirable,  and  Mr.  Barth  has  recommended  the  same  ratio  for 
the  feed  series  as  for  the  speed  series,  *\/2~=  1.189.  The  reasons  for 
adopting  this  ratio  are  given  in  the  article  above  cited,  Am.  Mach., 
Jan.  11,  1912. 

Methods  of  Driving  Machine  Tools. — P.  A.  Halsey  in  a  lecture  at 
Columbia  University  (Indust.  Eng.,  Sept.,  1914)  compares  the  relative 
advantages  of  the  ordinary  5-step  cone  pulley,  the  3-step  cone  pulley, 
the  constant  speed  pulley  and  the  individual  motor  as  a  drive  for 
machine  tools.  In  the  5-step  cone  pulley  drive  the  large  intervals 
between  the  speeds  available  on  the  different  cone  steps  decrease  the 
output  of  the  machine,  due  to  the  fact  that  except  in  those  few  cases 
where  the  cone  speed  is  nearly  equal  to  the  cutting  speed  the  next 
lower  cone  speed  must  be  used.  Also  on  account  of  the  proportions 
of  the  cone,  the  belt  speed  is  unnecessarily  low,  and  as  the  belt  is  moved 
to  the  largest  cone  step  its  speed  is  still  further  decreased.  On  the 
larger  steps  the  belt  is  frequently  incapable  of  delivering  the  power 
required  by  the  heavier  cuts  which  go  with  large  work.  This  defect 
is  remedied  in  the  3-step  cone  pulley,  in  which  the  difference  in  the 
diameters  of  the  steps  is  not  so  pronounced,  the  additional  number  of 
speed  changes  being  obtained  by  double  back  gears. 

Mr.  Halsey  compares  two  specific  cases:  (1)  A  5-step  cone  with 
single  back  gears,  the  cone  step  diameters  being  respectively  4,  6,  8,  30, 


1308  THE  MACHINE-SHOP. 

and  12  in.  (2)  A  3-step  cone  with  double  back  gears,  the  cone  step 
diameters  being  respectively  11  17/32,  129/32,  and  13  in.  In  case  1  a  2  1/2- 
in.  belt,  and  in  case  2  a  4-in.  belt,  is  used.  The  change  from  3  to  5  steps 
reduces  the  ratio  of  the  highest  to  the  lowest  speed  on  the  cone,  and  ife 
increases  the  'belt  speed  and  therefore  the  power  on  all  steps,  but 
particularly  on  the  large  ones  where  it  is  most  needed.  The  effect  of 
these  changes  can  be  shown  by  calculating  the  respective  powers  with 
the  belts  on  the  largest  steps  of  the  two  cones.  Assume  (case  1)  that 
the  speed  with  the  belt  on  the  4-in.  step  is  100.  Then  the  speed  with 
the  belt  on  the  largest  step  will  be  100  X  4/i2  =  331/3.  To  maintain 
the  same  cone  speed  in  case  2,  the  highest  belt  speed  will  be 
100  (11  17/32  -=-  4)  =  288  +;  the  lowest  will  be  288  (11  !7/32  +  13)  =  255  +. 
The  smallest  step  in  case  1  is  too  small  for  a  double  belt,  while  in  case  2 
a  double  belt  can  be  used  on  the  smallest  step.  In  order  to  compare 
the  power  capacities  of  the  two  machines  the  belt  speed  must  be 
multiplied  by  a  factor  reprasenting  the  greater  pulling  power  of  the 
double  belt,  say  1.43,  and  also  by  the  ratio  of  the  belt  widths,  1.6.  If 
LI  and  Z/2  represent  respectively  the  power  capacities  of  the  large  steps 
of  cases  1  and  2,  and  Si  and  82  the  power  capacities  of  the  small  steps, 
then 

fs-fljx  1.43x1.6-6.5 

- 


803  .       . 

That  is,  the  power  capacity  of  the  3-step  cone  is  6.5  times  as  great 
as  that  of  the  5-step  cone  with  the  belt  on  the  small  step,  and  17.5  times 
as  great  with  the  belt  on  the  large  step.  The  defect  of  the  arrange- 
ment given  in  case  2  is  that  it  provides  a  smaller  number  of  speeds 
and  a  smaller  range  of  speeds  than  does  case  1.  The  remedy  is  the 
provision  of  additional  back  gears  if  the  additional  speeds  or  greater 
range  is  necessary.  Mr.  Halsey  further  points  out  that  direct  connec- 
tion between  the  cone  pulley  and  the  work  spindle  has  been  retained 
in  many  cases  where  it  should  have  been  discarded,  since  with  large 
work  the  belt  speed  will  become  too  low  to  transmit  adequate  power, 
and  it  is  better  practice  to  interpose  gearing  between  the  pulley  and  the 
spindle,  and  thus  speed  up  the  belt  and  pulley.  In  changing  machines 
in  accordance  with  the  above  suggestions,  it  is  advisable  to  so  design 
the  gearing  as  to  obtain  speeds  which  will  be  in  geometric  progression 
as  explained  in  a  previous  paragraph.  For  methods  of  laying  out  cone 
pulleys,  see  p.  1  136.  For  methods  of  laying  out  the  driving  gears  of 
machine  tools  see  "Halsey's  Handbook  for  Machine  Designers  and 
Draftsmen,"  p.  77. 

In  the  Constant  Speed  Pulley  dwve,  the  belt  pulley  of  the  machine  is 
driven  at  a  constant  speed  and  the  power  is  transmitted  to  the  machine 
from  the  pulley  through  a  train  of  gears  arranged  in  a  gear  box.  By 
the  shifting  of  appropriate  levers  any  particular  set  of  gears  can  be  put 
in  engagement,  thus  making  instantly  available  any  speed  in  the  range 
of  the  machine.  This  arrangement  makes  the  obtaining  of  a  geometric 
series  of  speeds  a  particularly  easy  matter.  The  constant  speed  pulley 
drive  possesses  the  advantage  of  giving  a  self-contained  machine, 
particularly  adapted  to  the  individual  motor  drive.  It  has  found 
wide  application  in  the  milling  machine  and  in  certain  types  of  lathes. 

The  Individual  Motor  Drive  has,  according  to  Mr.  Halsey,  a  field  in 
the  driving  of  portable  floor  plate  tools,  for  machines  in  isolated  posi- 
tions, or  for  tools  so  located  that  line  shafts  cannot  be  conveniently 
laid  out  for  them,  and  for  large  machines  where  the  cost  of  the  motor 
Is  a  relatively  small  part  of  the  total  cost  of  the  tool.  The  disadvantage 
of  the  individual  motor  for  the  small  or  medium  size  tool  is  that  the 
power  capacity  of  the  motor  must  be  equal  to  the  maximum  power 
requirement  of  the  machine  and  that  no  advantage  can  be  taken  of 
the  average  power  requirements  of  several  machines  as  is  possible  in 
the  group  drive  where  one  motor  drives  several  machines.  This  in- 
creases the  first  cost  of  the  motors,  and  they  are  also  usually  worked 
at  low  efficiency,  due  to  the  fact  that  they  are  most  of  the  time 
underloaded. 


ABRASIVE  PROCESSES  1309 

ABRASIVE   PROCESSES. 

Abrasive  cutting  is  performed  by  means  of  stones,  sand,  emery,  glass, 
corundum,  carborundum,  crocus,  rouge,  chilled  globules  of  iron,  and  in 
some  cases  by  soft,  friable  iron  alone.  (See  paper  by  John  Richards, 
read  before  the  Technical  Society  of  the  Pacific  Coast,  Am.  Mach.t  Aug. 
20,  1891,  and  Eng.  &  M.  Jour.,  July  25  and  Aug.  15,  1891.) 

The  "  Cold  Saw."  —  For  sawing  any  section  of  iron  while  cold 
the  cold  saw  is  sometimes  used.  This  consists  simply  of  a  plain  soft 
steel  or  iron  disk  without  teeth,  about  42  inches  diameter  and  3/1(5  inch 
thick.  The  velocity  of  the  circumference  is  about  15,000  feet  per  minute. 
One  of  these  saws  will  saw  through  an  ordinary  steel  rail  cold  in  about 
one  minute.  In  this  saw  the  steel  or  iron  is  ground  off  by  the  friction 
of  the  disk,  and  is  not  cut  as  with  the  teeth  of  an  ordinary  saw.  It  has 
generally  been  found  more  profitable,  however,  to  saw  iron  with  disks  or 
band-saws  fitted  with  cutting-teeth,  which  run  at  moderate  speeds  and 
cut  the  metal  as  do  the  teeth  of  a  milling-cutter. 

Reese's  Fusing-disk.  —  Reese's  fusing-disk  is  an  application  of  the 
cold  saw  to  cutting  iron  or  steel  in  the  form  of  bars,  tubes,  cylinders, 
etc.,  in  which  the  piece  to  be  cut  is  made  to  revolve  at  a  slower  rate  or 
speed  than  the  saw.  By  this  means  only  a  small  surface  of  the  bar  to 
be  cut  is  presented  at  a  time  to  the  circumference  of  the  saw.  The 
saw  is  about  the  same  size  as  the  cold  saw  above  described,  and  is  rotated 
at  a  velocity  of  about  25,000  feet  per  minute.  The  heat  generated  by 
the  friction  of  this  saw  against  the  small  surface  of  the  bar  rotated  against 
it  is  so  great  that  the  particles  of  iron  or  steel  in  the  bar  are  actually  fused, 
and  the  "sawdust"  welds  as  it  falls  into  a  solid  mass.  This  disk  will  cut 
either  cast  iron,  wrought  iron,  or  steel.  It  will  cut  a  bar  of  steel  13/g 
inch  diameter  in  one  minute,  including  the  time  of  setting  it  in  the  machine, 
the  bar  being  rotated  about  200  turns  per  minute. 

Cutting  Stone  with  Wire.  —  A  plan  of  cutting  stone  by  means 
of  a  wire  cord  has  been  tried  in  Europe.  While  retaining  sand  as  the 
cutting  agent,  M.  Paulin  Gay,  of  Marseilles,  has  succeeded  in  applying 
it  by  mechanical  means,  and  as  continuously  as  formerly  the  sand-blast 
and  band-saw,  with  both  of  which  appliances  his  system  —  that  of  the 
"helicoidal  wire  cord"  —  has  considerable  analogy.  An  engine  puts  in 
motion  a  continuous  wire  cord  (varying  from  five  to  seven  thirty-seconds 
of  an  inch  in  diameter,  according  to  the  work),  composed  of  three  mild- 
steel  wires  twisted  at  a  certain  pitch,  that  is  found  to  give  the  best  results 
in  practice,  at  a  speed  of  from  15  to  17  feet  per  second. 

The  Sand-blast.  —  In  the  sand-blast,  invented  by  B.  F.  Tilghman, 
of  Philadelphia,  and  first  exhibited  at  the  American  Institute  Fair, 
New  York,  in  1871,  common  sand,  powdered  quartz,  emery,  or  any  sharp 
cutting  material  is  blown  by  a  jet  of  air  or  steam  on  glass,  metal,  or  other 
comparatively  brittle  substance,  by  which  means  the  latter  is  cut,  drilled, 
or  engraved.  To  protect  those  portions  of  the  surface  which  it  is  desired 
shall  not  be  abraded  it  is  only  necessary  to  cover  them  with  a  soft  or 
tough  material,  such  as  lead,  rubber,  leather,  paper,  wax,  or  rubber- 
paint.  (See  description  in  App.  Cyc.  Mech.;  also  U.  fc>.  report  of  Vienna 
Exhibition,  1873,  vol.  iii.  316.) 

A  "jet  of  sand"  impelled  by  steam  of  moderate  pressure,  or  even  by 
the  blast  of  an  ordinary  fan,  depolishes  glass  in  a  few  seconds;  wood  is 
cut  quite  rapidly;  and  metals  are  given  the  so-called  "frosted"  surface 
with,  great  rapidity.  With  a  jet  issuing  from  under  300  pounds  pressure, 
a  hole  was  cut  through  a  piece  of  corundum  1 1/2  inches  thick  in  25  minutes. 

The  sand-blast  has  been  a'pplied  to  the  cleaning  of  metal  castings  and 
sheet  metal,  the  graining  of  zinc  plates  for  lithographic  purposes,  the 
frosting  of  silverware,  the  cutting  of  figures  on  stone  and  glass,  and  the 
cutting  of  devices  on  monuments  or  tombstones,  the  recutting  of  files, 
etc.  The  time  required  to  sharpen  a  worn-out  14-inch  bastard  file  is 
about  four  minutes.  About  one  pint  of  sand,  passed  through  a  No. 
120  sieve,  and  4  H.P.  of  60-lb.  steam  are  required  for  the  operation. 
For  cleaning  castings,  compressed  air  at  from  8  to  10  pounds  pressure 
per  square  inch  is  employed.  Chilled-iron  globules  instead  of  quartz 
or  flint-sand  are  used  with  good  results,  both  as  to  speed  of  working  and 
cost  of  material,  when  the  operation  can  be  carried  on  under  proper 
conditions.  With  the  expenditure  of  2  H.P.  in  compressing  air,  2  square 
feet  of  ordinary  scale  on  the  surface  of  steel  and  iron  plates  can  be 


1310  THE  MACHINE-SHOP. 

removed  per  minute.  The  surface  thus  prepared  is  ready  for  tinning, 
galvanizing,  plating,  bronzing,  painting,  etc.  By  continuing  the  opera- 
tion the  hard  skin  on  the  surface  of  castings,  which  is  so  destructive  to 
the  cutting  edges  of  milling  and  other  tools,  can  be  removed.  Small 
castings  are  placed  in  a  sort  of  slowly  rotating  barrel,  open  at  one  or 
both  ends,  through  which  the  blast  is  directed  downward  against  them 
as  they  tumble  over  and  over.  No  portion  of  the  surface  escapes  the 
action  of  the  sand.  Plain  cored  work,  such  as  valve-bodies,  can  be 
cleaned  perfectly  both  inside  and  out.  One  hundred  Ibs.  of  castings 
can  be  cleaned  in  from  10  to  15  minutes  with  a  blast  created  by  2  H.P. 
The  same  weight  of  small  forgings  can  be  scaled  in  from  20  to  30  minutes. 
—  Iron  Age,  March  8,  1894. 

Polishing  and  Buffing. — The  type  of  polishing  wheel  to  be  used  de- 
pends on  the  class  of  work.  For  rough  polishing  on  flat  surfaces  or 
where  the  corners  are  to  be  square,  a  paper  or  a  wooden  wheel,  faced 
with  leather  to  which  emery  or  some  other  abrasive  is  glued  is  used. 
For  large  flat  work,  or  curved  surfaces,  bull  neck,  solid  canvas,  solid 
sheepskin,  paper  or  wooden  wheels  are  used.  These  wheels  are  also 
used  for  such  work  as  stove  trimmings,  agricultural  implements,  tools, 
cast  iron  and  brass  parts,  etc.  Loose  or  stitched  sheepskin,  loose  or 
stitched  canvas  and  solid  or  stitched  laminated  felt  wneels  are  used 
for  roughing  irregular  shapes  requiring  a  soft  faced  wheel  which  will 
come  in  contact  with  every  crevice  of  the  work.  Bull  neck  or  wooden 
wheels  are  used  whenever  coloring  or  finishing  is  to  be  done  on  cast 
or  sheet  metal.  For  work  requiring  a  high  polish,  as  guns,  cutlery, 
etc.,  sea  horse  is  often  employed.  The  hardness  of  the  wheel  depends 
on  the  service  in  which  it  is  to  be  used,  and  in  the  case  of  linen,  canvas, 
leather,  or  other  built-up  wheels  on  steel  centers,  is  governed  by  the 
depth  of  the  flanges  clamping  the  wheel  on  the  arbor;  the  larger  the 
flanges  the  harder  is  the  wheel.  For  most  polishing  operations,  a 
peripheral  speed  of  the  wheel  of  from  3000  to  6000  ft.  per  minute  is 
sufficient,  and  4000  ft.  will  serve  for  most  purposes.  These  are  the 
speeds  recommended  for  muslin,  felt  or  sea  horse  wheels,  although 
some  claims  are  advanced  for  speeds  as  high  as  7500  ft.,  it  being  stated 
that  lower  speeds  will  scratch  the  work. 

Buffing  is  the  process  of  obtaining  a  grainless  finish  of  high  luster 
on  plated  surfaces.  The  degree  of  luster  depends  on  the  finish  of  the 
surface  prior  to  plating.  The  work  is  done  on  a  soft  wheel  to  which 
a  polishing  composition  has  been  applied.  The  polishing  composition 
comprises  a  heavy  grease  containing  polishing  material,  as  flour-emery, 
rouge,  tripoli,  crocus,  etc.  According  to  the  Chicago  Wheel  and  Mfg. 
Co.  the  following  compositions  are  adapted  to  the  different  varieties 
of  work.  For  cutting  down  and  polishing  brass,  bronze  and  Britannia 
metal  preparatory  to  plating,  tripoli  composition;  for  smooth  surfaces 
on  nickel  and  brass,  crocus  composition;  for  coloring  brass,  copper, 
nickel,  bronze,  German  silver,  etc.,  either  in  solid  or  plated  metal, 
White  Diamond  XXX  composition;  for  chased  or  embossed  parts,  or 
for  cutting  down  silver-plated  pieces  which  are  afterward  to  be  colored 
with  rouge  and  alcohol,  White  Diamond  XXXX  composition  is  used; 
for  nickel-plated  pieces  with  a  high  luster,  White  Coloring  composition, 
made  of  Vienna  lime  is  used.  Where  rapid,  sharp,  even  cutting  is 
desired,  emery  cake  is  used.  Chandelier  rouge  is  used  to  produce  a 
deep  color  on  brass  and  bronze  parts. 

Laps  and  Lapping. — A  series  of  tests  was  made  by  W.  -A.  Knight 
and  A.  A.  Case  (Jour.  A.  S.  M.  E.,  Aug.,  1915)  to  determine  the  effect 
on  the  rate  of  cutting  with  different  combinations  of  abrasive  lubricant 
and  lap  material.  The  tests  were  made  with  hardened  steel  speci- 
mens, and  comparative  results  were  obtained  with  emery,  alunduin  and 
carborundum  used  in  connection  with  lard  oil,  machine  oil,  gasoline, 
kerosene,  turpentine,  alcohol  and  soda  water.  The  lap  materials  were 
cast  iron,  soft  steel  and  copper.  The  following  conclusions  were 
derived  from  the  invesigation :  The  initial  rate  of  cutting  is  not 
greatly  different  for  the  different  abrasives;  carborundum  maintains 
its  rate  better  than  either  of  the  others,  alundum  next,  and  emery  the 
least;  carborundum  wears  the  lap  about  twice  as  fast,  and  alundum 
11/4  times  as  fast  as  emery;  there  is  no  advantage  in  using  an  abrasive 
coarser  than  No.  150;  the  rate  of  cutting  is  practically  proportional  to 


EMERY  WHEELS   AND   GRINDSTONES.  1311 

the  pressure;  the  wear  of  the  laps  is  in  the  proportions  of  cast  iron 
1.00,  steel  1.27,  copper  2.62,  and  this  wear  is  inversely  proportional  to 
the  hardness  by  the  Brinell  test;  in  general,  copper  and  steel  cut  faster 
than  cast  iron,  but  where  permanence  of  form  is  a  consideration,  cast 
iron  is  the  superior  metal ;  gasoline  and  kerosene  are  the  best  lubricants 
to  use  with  cast-iron  lap,  kerosene,  on  account  of  its  non-evaporative 
qualities,  being  first  choice;  machine  and  lard  oil  are  the  best  lubri- 
cants to  use  with  copper  or  steel  lap,  but  they  are  least  effective  on  the 
cast  lap;  for  all  laps  and  all  abrasives  (of  those  tested)  the  cutting  is 
faster  with  lard  oil  than  with  machine  oil;  alcohol  shows  no  particular 
merit  for  the  work ;  turpentine  does  fairly  good  work  with  carborundum, 
but  in  general,  is  not  as  good  as  kerosene  or  gasoline;  soda  water  com- 
pares favorably  with  other  lubricants,  and  on  the  whole  it  is  slightly 
better  than  alcohol  or  turpentine;  wet  lapping  is  from  1.2  to  6  times 
as  fast  as  dry  lapping,  depending  on  the  material  of  the  lap  and  the 
method  of  charging. 

EMERY   WHEELS   AND   GRINDSTONES. 

References.  —  "American  Machinist  Grinding  Book";  "Grits  and 
Grinds,"  Norton  Company;  "Points  about  Grinding  Wheels  and  their 
Selection,"  Brown  &  Sharpe  Mfg.  Co.;  "Table  of  Causes  of  Grinding 
Wheel  Accidents,"  Independence  Inspection  Bureau;  "Safeguarding 
Grinding  Wheels,"  Report  of  Committee  of  National  Machine  Tool 
Builders'  Association;  Bulletin,  "Safeguarding  High  Speed  Grinding 
Wheels,  "National  Founders' Association;  "Operation  of  Grinding  Wheels 
in  Machine  Grinding,"  Geo.  I.  Alden,  Journal  A.S.M.E.,  Jan.,  1915. 

Selection  of  Abrasive  Wheels.  (Contributed  by  the  Norton  Com- 
pany, 1915.)  —  The  user  of  a  modern  grinding  wheel  should  thoroughly 
understand  these  essential  features;  the  definition  of  grain  and  grade, 
the  particular  conditions  of  grinding  which  cause  them  to  vary;  the 
methods  of  balancing  and  mounting;  truing  and  dressing;  the  effect  of 
machine  vibration  and  arc  of  contact  upon  grain  and  grade;  the  rela- 
tion of  work  speed  and  wheel  speed  for  production  and  finish;  safe- 
guards and  dust  removal  systems. 

Grain. —  Abrasive  grains  are  numbered  according  to  the  meshes  per 
lineal  inch  of  the  screen  through  which  they  have  been  graded.  The 
numbers  used  in  wheels  are  8,  10,  12,  14,  16,  20,  24,  30,  36,  46,  54,  60, 
70,  80,  90,  120,  150,  180,  200;  when  finer  than  200,  the  grains  are  termed 
flours,  being  designated  as  F,  2F,  3F,  4F,  XF,  65C,  65F,  F  being  the 
coarsest  and  65F,  the  finest.  Grits  from  12  to  30  are  generally  used 
on  all  heavy  work  such  as  snagging;  36  to  80  cover  nearly  all  tool  grind- 
ing, saw  gumming,  and  other  operations  where  precision  in  measurement 
is  sought;  90  and  finer  are  used  for  special  work  such  as  grinding  steel 
balls  and  fine  edge  work;  the  flour  sizes  are  used  mostly  for  sharpening 
and  rubbing  stones.  The  number  representing  the  grades  of  abrasive 
leave  a  degree  of  smoothness  of  surface  which  may  be  compared  to  that 
left  by  files  as  follows:  8  and  10  represent  the  cut  of  a  wood  rasp; 
16,  20,  coarse-rough  file;  24,  30,  ordinary  rough  file;  36,  40,  bastard  file; 
46,  60,  second-cut  file;  70,  80,  smooth  file;  90,  100,  superfine  file; 
120F,  2F,  dead-smooth  file. 

Grade.  —  When  the  retentive  properties  of  the  bond  are  great,  the 
wheel  is  called  hard ;  when  the  grains  are  easily  broken  out,  it  is  called 
soft.  A  wheel  is  of  the  proper  grade  when  its  cutting  grains  are  auto- 
matically replaced  when  dulled.  Wheels  that  are  too  hard  glaze.  Dress- 
ing re-sharpens  them,  the  points  of  the  dresser  breaking  out  and  break- 
ing off  the  cutting  grains  by  percussion. 

Soft  wheels  are  used  on  hard  materials,  like  hardened  steel.  Here  the 
cutting  particles  are  quickly  dulled  and  must  be  renewed.  On  softer 
materials,  like  mild  steel  and  wrought  iron,  harder  grades  can  be  used, 
the  grains  not  dulling  so  quickly. 

The  area  of  surface  to  be  ground  in  contact  with  the  wheel  is  of  the 
utmost  importance  in  determining  the  grade.  If  it  is  a  point  contact 
like  grinding  a  ball  or  if  an  extremely  narrow  fin  is  to  be  removed,  we 
must  use  a  very  strongly  bonded  wheel,  on  account  of  the  leverage  ex- 
erted oil  its  grain,  which  tends  to  tear  out  the  cutting  particles  before 


1312 


THE   MACHINE-SHOP. 


Revolutions  per  Minute  Required  for  Specified  Rates  of 

Periphery  Speed.    Also  Stress  per  Square  Inch  on 

Norton  Wheels  at  the  Specified  Rates. 


Surface  Speeds,  Feet  per  Minute. 

a* 

M 

1000 

2000 

3000 

4000 

5000 

6000 

7000 

8000 

9000 

1000C 

Stress  per  Square  Inch,  Pounds. 

1 

3 

12 

27 

48 

75 

108 

147 

192 

243 

300 

15 

Revolutions  per  Minute. 

i 

3820 

7639 

11459 

15279 

19099 

22918 

26738 

30558 

34377 

38197 

2 

1910 

3820 

5730 

7639 

9549 

11459 

13369 

15279 

17189 

19098 

3 

1273 

2546 

3820 

5093 

6366 

7639 

8913 

10186 

11459 

12732 

4 

955 

1910 

2865 

3820 

4775 

5729 

6684 

7639 

8594 

9549 

5 

764 

1528 

2292 

3056 

3820 

4584 

5347 

6111 

6875 

7639 

6 

637 

1273 

1910 

2546 

3183 

3820 

4456 

5093 

5729 

6366 

7 

546 

1091 

1637 

2183 

2728 

3274 

3820 

4365 

4911 

5457 

8 

477 

955 

1432 

1910 

2387 

2865 

3342 

3820 

4297 

4775 

10 

382 

764 

1146 

1528 

1910 

2292 

2674 

3056 

3438 

3820 

12 

318 

637 

955 

1273 

1591 

1910 

2228 

2546 

2865 

3183 

14 

273 

546 

818 

1091 

1364 

1637 

1910 

2183 

2455 

2728 

16 

239 

477 

716 

955 

1194 

1432 

1671 

1910 

2148 

2387 

18 

212 

424 

637 

849 

1061 

1273 

1485 

1698 

1910 

2122 

20 

191 

382 

573 

764 

955 

1146 

1337 

1528 

1719 

1910 

22 

174 

347 

521 

694 

868 

1042 

1215 

1389 

1563 

1736 

24 

159 

318 

477 

637 

796 

955 

1114 

1273 

1432 

1591 

30 

127 

255 

382 

509 

637 

764 

891 

1018 

1146 

1273 

36 

106 

212 

318 

424 

530 

637 

743 

849 

955 

1061 

Table  to  Figure  Surface  Speeds  of  Wheels. 
(Circumferences  in  Feet ,  Diameters  in  Inches. ) 


£ 

«£ 

IN 

£ 

-M 
P=4 

+a 

P4 

£ 

d 

d 

d 

d 

d 

d 

1 

1 

1 

1 

1 

1 

§ 

g 

§ 

B 

§ 

g 

0 

£ 

g 

1 

| 

5 

8 

q 

q 

Q 

6 

a 

0 

'& 

8 

8 

5 

i 

.262 

13 

3.403 

25 

6.546 

37 

9.687 

49 

12.828 

61 

15.970 

2 

.524 

14 

3.665 

26 

6.807 

38 

9.948 

50 

13.090 

62 

16.232 

3 

.785 

15 

3.927 

27 

7.069 

39 

10.210 

51 

13.352 

63 

16.493 

4 

1.047 

16 

4.189 

28 

7.330 

40 

10.472 

52 

13.613 

64 

16.755 

5 

1.309 

17 

4.451 

29 

7.592 

41 

10.734 

53 

13.875 

65 

17.017 

6 

1.571 

18 

4.712 

30 

7.854 

42 

10.996 

54 

14.137 

66 

17.279 

7 

1.833 

19 

4.974 

31 

8.116 

43 

11.257 

55 

14.499 

67 

17.541 

8 

2.094 

20 

5.236 

32 

8.377 

44 

11.519 

56 

14.661 

68 

17.802 

9 

2.356 

21 

5.498 

33 

8.639 

45 

11.781 

57 

14.923 

69 

18.064 

10 

2.618 

22 

5.760 

34 

8.901 

46 

12.043 

58 

15.184 

70 

18.326 

11 

2.880 

23 

6.021 

35 

9.163 

47 

12.305 

59 

15.446 

71 

18.588 

12 

3.142 

24 

6.283 

36 

9.425 

48 

12.566 

60 

15.708 

72 

18.850 

To  find  surface  speed,  in  feet,  per  minute,  of  a  wheel. 

RULE.- — Multiply  the  circumference  (see  above  table)  by  its  revolu- 
tions per  minute. 

Surface  speed  and  diam.  of  wheel  being  given,  to  find  number  of  revo- 
lutions of  wheel  spindle. 

RULE.  —  Multiply  surface  speed,  in  feet,  per  min.,  by  12  arid  divide  the 
product  by  3.14  times  the  diam,  of  the  wheel  in  inches. 


ABRASIVES.  1313 

they  have  done  their  work.  If  the  contact  is  a  broad  one,  as  in  grind- 
ing a  hole,  or  where  the  work  brings  a  large  part  pf  the  surface  of 
the  wheel  into  operation,  softer  grades  must  be  used,  because  the  depth 
of  cut.  is  so  infinitely  small  that  the  cutting  points  in  work  become 
dulled  quickly  and  must  be  renewed,  or  the  wheel  glazes  and  loses  its 
efficiency. 

Vibrations  in  grinding  machines  cause  percussion  on  the  cutting 
grains,  necessitating  harder  wheels.  Wheels  mounted  on  rigid  machines 
can  be  softer  in  grade  and  are  much  more  efficient. 

Speeds  of  Grinding  Wheels. —  The  factor  of  safety  in  vitrified  wheels 
is  proportional  to  the  grade  of  hardness.  Bursting  limits  are  from  12,000 
to  25,000  feet  per  minute,  surface  speed.  Wheels  are  tested  by  standard 
makers  at  speeds  in  excess  of  9000  feet  surface  speed  per  minute. 
Running  speeds  in  practice  are  from  4000  to  6000  feet,  depending  on 
work,  condition  of  machine,  and  mounting. 

Generally  speaking,  grinding  of  tools,  reamers,  cutters,  and  surface 
grinding  is  done  at  about  4000  feet,  snagging  and  rough  forms  of  hand 
grinding  at  5000  to  5500  feet,  cylindrical  grinding,  or  where  the  work  is 
rigidly  held  and  where  the  wheel  feed  is  under  control,  from  5500  to  6500 
feet,  and  in  some  instances  as  high  as  7500  feet. 

These  speeds  are  all  for  vitrified  wheels.  The  same  speeds  will  apply 
to  wheels  made  by  the  elastic  and  silicate  processes. 

Grain  Depth  of  Cut. — An  analysis  of  the  action  of  the  wheel  when 
in  operation  shows  how  theoretical  considerations  bear  out  the  truth  of 
the  empirical  rules  for  the  use  of  grinding  wheels  in  machine  grinding. 
A  paper  by  Geo.  I.  Alden  (Jour.  Am.  Soc.  M.  E.,  Jan.,  1915)  gives  the 
essential  distinction  between  the  radial  or  real  depth  at  which  the 
wheel  cuts  and  the  depth  which  the  abrasive  grain  in  the  wheel  cuts 
into  the  material  being  ground.  The  latter  depth  is  termed  the  "grain 
depth  of  cut."  This  grain  depth  of  cut  is  the  controlling  factor  in  se- 
curing the  correct  working  of  the  wheel.  A  formula  is  deduced  for  com- 
puting the  grain  depth  of  cut,  the  application  of  the  analysis  is  explained 
and  these  conclusions  reached  by  Prof.  Alden:  1 — Other  factors  remain- 
ing consta.nt,  increase  of  work  speed  increases  grain  depth  of  cut,  and 
makes  a  wheel  appear  softer.  2 — A  decrease  of  wheel  speed  increases 
grain  depth  of  cut.  3 — Diminishing  the  diameter  of  the  wheel  increases 
the  grain  depth  of  cut;  increasing  the  diameter  of  the  wheel  decreases 
the  grain  depth  of  cut.  4 — Decreasing  the  diameter  of  work  increases 
the  grain  depth  of  cut;  conversely,  increasing  the  diameter  of  work  de- 
creases the  grain  depth  of  cut. 

A  table  pf  arcs  of  contact  of  wheel  and  work  for  a  limited  range  of 
diameters  is  given,  also  a  table  of  values  of  one  of  the  factors  in  the 
formula  for  grain  depth  of  cut. 

Artificial  Abrasives. — Since  1900  artificial  abrasives,  made  in 
various  types  of  electric  furnaces,  have  been  displacing  natural  abra- 
sives, and  they  are  to-day  almost  exclusively  used.  This  has  been  due 
largely  to  the  ability  to  control  the  purity  of  the  raw  material  and  to 
insure  uniformity  of  cutting  action  of  the  finished  products.  Artificial 
abrasives  are  divided  into  the  aluminous  group  (examples,  Alundum, 
Aloxite  and  Boro-Carbone),  and  the  silicon  carbide  group  (examples, 
Crystolon,  Carborundum,  Carbolite).  The  abrasive  action  of  the 
aluminous  group  is  due  to  the  amount  of  oxide  of  aluminum,  which  in 
these  artificial  abrasives  is  in  excess  of  90%,  slightly  more  than  the  best 
corundum  and  considerably  in  excess  of  the  alumina  content  of  emery, 
which  rarely  exceeds  70%.  The  aluminous  abrasives  are  characterized 
by  a  high  degree  of  toughness  and  are  particularly  adapted  for  grinding 
materials  of  high  tensile  strength  such  as  steel  and  its  alloys.  The  sili- 
cate carbide  group  is  not  duplicated  by  Nature  and  is  somewhat  harder 
and  more  brittle  than  the  aluminous  group.  The  silicon  carbide  abra- 
sives are  now  recognized  as  standard  for  grinding  materials  of  low 
tensile  strength  such  as  cast  iron,  brass  pearl,  marble,  granite  and 
leather. 

Selection  of  Emery  Wheels. —  The  Norton  Co.  (1915)  publishes  the 
accompanying  table  showing  the  proper  grain  and  grade  of  wheel  for 
different  services.  The  column  headed  grain  indicates  the  coarseness  of 
the  material  composing  the  wheel,  being  designated  by  the  number  of 


1314 


THE  MACHINE-SHOP. 


meshes  per  inch  of  a  sieve  through  which  the  grains  pass.     A  No.  20 
grain  will  pass  through  a  20-mesh  sieve,  but  not  through  a  30-mesh,  etc. 

EXPLANATION    OF    GRADE    LETTERS. 


Extremely 
Soft. 
A 
B 
C 
D 

Soft. 

E 
F 
G 
H 

Medium 
Soft. 
I 
J 
K 
L 

Medium. 

M 
N 
0 
P 

Medium 
Hard. 
Q 
R 
S 
T 

Hard. 

U 
W 

Extremely 
Hard. 
Y 
Z 

FOP  Grinding  High-speed  Tool  Steel,  The  American  Emery  Wheel 
Co.  recommends  a  wheel  one  number  coarser  and  one  grade  softer  than 
a  wheel  for  grinding  carbon  steel  for  the  same  service. 

Balancing. —  The  standard  makers  of  grinding  wheels  send  out 
wheels  balanced  within  narrow  limits,  accomplished  by  inserting  lead 
near  the  hole.  As  the  wheels  wear  down  it  frequently  becomes  necessary 
for  the  user  to  balance  them  by  removing  some  of  the  lead. 

Mounting  Grinding  Wheels— Safety  Devices. —  A  code  for  the  mount- 
ing of  grinding  wheels  was  adopted  by  23  manufacturers  of  grinding 
wheels  in  the  U.  S.  and  Canada  in  1914,  and  approved  by  the  Na- 
tional Machine  Tool  Builders'  Association.  An  abstract  of  the  code  is 
given  in  Indust.  Eng.,  Jan.,  1915.  The  code  recognizes  as  safety  devices 
protection  flanges,  protection  hoods,  and  protection  chucks. 

Protection  flanges  of  the  double  or  single  concave  type,  used  in  con- 
junction with  wheels  having  double  or  single  convex  tapered  sides  or 
side  are  recommended.  For  double  tapered  wheels  they  shall  have  a 
oaper  of  not  less  than  3/4  in.  per  foot  for  each  flange.  For  single  tapered 
wheels  they  shall  have  a  taper  of  not  less  than  3/4  in.  per  foot.  Each 
flange,  whether  straight  or  tapered,  shall  be  recessed  at  the  center  at 
least  1/16  in.  on  the  side  next  to  the  wheel.  All  tapered  flanges  over  10  in. 
diameter  shall  be  of  steel  or  material  of  equal  strength.  Both  flanges  in 
contact  with  the  wheels  shall  be  of  the  same  diameter.  Wheels  should 
never  be  run  without  flanges. 

The  following  table  gives  the  dimensions  of  flanges  to  be  used  where 
no  hoods  are  provided:  A  =  Maximum  flat  spot  at  center  of  flange. 
B  =  Flat  spot  at  center  of  wheel.  C  =  Minimum  diameter  of  flange. 
D  =  thickness  of  flange  at  bore.  E  -  minimum  diameter  of  recess. 
F  =  Minimum  thickness  of  each  flange  at  bore;  all  dimensions  are 
in  inches. 

Dia.  of 
Wheel.  6     8 
AGO 


B 
C 
D 
E 


10  12  14  16  18  20  22 
044  4444 
11  2  41/2  41/2  6666 
35  6  6  8  10  12  14  16 


3/8  3/8      1/2     5/8 
2      31/2    4        4 


5/8       5/8 
51/2     7 


3/4      3/4     3/4 


24 
4 
6 

18 

3/4 


26 
4 
6 

20 

3/4 


28 
4 
6 

22 

7/8 


30 
4 
6 

24 


8       9    101/2  12       131/2  141/2  16 


F       3/8  3/8      l/2     5/8       8/4      7/8        1        1         1  l/8      1 1/8    1 1/8      1 1/4     1 1/4 

Where  protection  hoods  are  provided,  straight  flanges  and  straight 
wheels  may  be  used,  the  dimensions  being  as  follows,  and  the  reference 
letters  having  the  same  meaning  as  above: 

Dia.  of 

Wheel.  6      8  10      12      14        16       18  20      22      24      26        28     30 

C      2      3  31/24        41/251/26  7         71/28         8 1/2  10     10 

2  21/4    23/4  3           31/2    4  41/2!  5        51/26          77 


E 
F 


3/8  3/8  3/8   1/2 


1/2    5/8  V8   5/8   5/8   5/8   8/4  3/4 


Protection  hoods  shall  be  used  where  practical  with  wheels  not 
provided  with  protection  flanges,  and  shall  be  sufficiently  strong  to 
retain  all  pieces  of  a  broken  grinding  wheel.  They  shall  conform  as 
nearly  as  possible  to  the  periphery  of  the  wheel,  and  leave  exposed  the 


EMERV  WHEELS  AND   GRINDSTONES. 


1315 


Table  for  Selection  of  Grades. 


Class  of  Work. 

Alundum. 

Crystolon. 

Grain. 

Grade. 

Grain. 

Grade. 

Aluminum  castings 

36  to  46 

3  to  4  Elas 

20  to  24 
20  "  24 
24  "  36 
30  "  46 
16  "  30 
20  "  30 
16  "  24 
20  "  30 
20  "  30 

36  "60 

16  "  20 
20  "  30 

30   "36 
24  "  30 

24  "  46 
j  70  "  80 

1       80 
30  to  46 
30  "  50 

P    to    R 
Q    "     R 
P    "     R 
I     "     L 
I     "     L 
Q    "      S 
Q    "      S 
Q    "     R 
0    «     Q 

I     "     L 

R    "  S 
Q    "  S 

K    "  L 

R    "  S 

J     "  M 

\1A  to  2 
Elas 
J 
12   to  5 
)    Elas. 
KtoM 

Brass  or  bronze  castings  (large)    . 
Brass  or  bronze  castings  (small)  . 
Cast  iron,  cylindrical      

24  comb 
16  to  46 
24   "  30 
16  "  20 
20  "  30 

J  to    K 
H    "    K 
P    "    R 
Q    "    R 

P    "    U 

Cast  iron,  surfacing    . 

Cast  iron  (small)  castings.    .    .    . 
Cast  iron  (large)  castings  .... 
Chilled  iron  castings  

Dies  chilled  iron 

Dies,  steel     

36  to  60 
20  "  30 
30 

J    to     L 
P    "    R 

P    "    Q 

Hammers,  cast  steel  

Interior  of  Automobile  Cylinders, 
(cast  iron)     

Internal  grinding,  hardened  steel 
Knives  (paper),  automatic  grinding 
Knives  (planer)  ,  automatic  grinding 
Knives  (planing  mill),  hand  grind- 
ing      

46  to  60 
36  "  46 
30  "  46 

46  "  60 

30  "  60 
46  "120 
j  20    '24 
|  20    '36 
20    «  36 
14    '  20 
20    '30 

46  "  60 
46  "  60 
16  "  24 

J    to  M 
J     "   K 
J     "   K 

J    to  M 
J     "   M 
J     "   M 
PSil. 
0   toP 
0    "   Q 
P    "   U 
P    "   R 

I     "   M 
J     "   M 
Q    "  S 

Knives,  shear  and  shear  blades   . 
Lathe  centers  

Lathe  and  planer  tools  

Machine-shop  use,  general    .     .    . 
Malleable  iron  castings  (large) 
Malleable  iron  castings  (small) 
Milling  cutters,  automatic  or  semi- 
automatic grinding     

Milling  cutters,  hand  grinding  .    . 
Plows  (steel),  surfacing  

Pulleys  (C.I.),  surfacing  faces  of  . 
Radiators  (cast  iron),  edges  of  .    . 
Reamers,    taps,    milling    cutters, 
etc.,  hand  grinding     
Reamers,    taps,    milling    cutters, 

46  to  120 
46  "  60 

46  "  60 
24  "  36 

;o| 

K    "  0 

J     "   M 
J     "   M 

\y*  "  2 

Elas. 

Rolls,  (cast  iron)  wet      

Rolls  (chilled  iron),  finishing    .    . 

Rolls  (chilled  iron),  roughing.  .   . 
Rubber     .    .    . 

30  to  50 
36  "  50 
60 
(  24  comb. 
130  to  60 
16  "  36 
j  24  comb. 
1  46  to  60 
16  "  46 
10  "  20 
20  "  30 
16  "  46 

14  "  16 
16  "  24 
46  "  60 
36  "60 
12  "  30 
46  "  60 

J     to  K. 
M  "  N 
0    "  Q 
L    "  P 
L    "  0 
H    "  K 
K 
J     to  L 
H    "   K 
Q    "   W 
P    "    R 
L    "   P 

Q    "  U 
P    "   R 

M 
K  to  M 

P    "  U 
K   "  M 

Saws,  gumming  and  sharpening  . 
Saws,  cold  cutting-off     .    .    .    :    . 

Steel  (soft),  cylindrical  grinding  . 

Steel  (soft),  surface  grinding     .    . 
Steel  (hardened),  cylindrical  grind- 
ing 

Steel  (hardened)  ,  surface  grinding 
Steel,  large  castings 

Steel,  small  castings   

Steel  (manganese),  safe  work    .    . 
Steel      (manganese),     frogs    and 
switches    

Structural  steel 

Twist  drills,  hand  grinding    .    .    . 
Twist  drills,  special  machines  .    . 
Wrought  iron  

Woodworking  tools    

1316  THE  MACHINE-SHOP. 

least  portion  of  the  wheel  compatible  with  the  work.  A  sliding  tongue 
to  close  the  opening  in  the  hood  as  the  wheel  is  reduced  in  diameter 
should  be  provided.  Protruding  ends  of  the  wheel  arbors  and  their 
nuts  shall  be  guarded. 

Cups,  cylinders  and  sectional  ring  wheels  shall  be  either  protected  with 
hoods,  enclosed  in  protection  chucks,  or  surrounded  with  protection 
bands.  Not  more  than  one-quarter  of  the  height  of  such  grinding 
wheels  shall  protrude  beyond  the  provided  protection. 

Grinding  wheels  shall  fit  freely  on  the  spindles.  Wheel  arbor  holes 
shall  be  made  0.005  in.  larger  than  the  machine  arbor.  The  soft  metal 
bushing  shall  not  extend  beyond  the  sides  of  the  wheel  at  the  center. 
Ends  of  spindles  shall  be  threaded  left  and  right  so  that  the  nuts  on 
both  ends  will  tend  to  tighten  as  the  spindles  revolve.  Care  should 
be  taken  that  the  spindles  are  arranged  to  revolve  in  the  proper 
direction. 

Wheel  washers  of  compressible  material,  such  as  blotting  paper, 
rubber  or  leather,  not  thicker  than  0.025  in.,  shall  be  fitted  between  the 
wheel  and  its  flanges.  It  is  recommended  that  the  wheel  washers  be 
slightly  larger  than  the  diameter  of  the  flanges  used. 

When  tightening  clamping  nuts,  care  shall  be  taken  to  tighten  them 
only  enough  to  hold  the  wheel  flrmly.  Flanges  must  be  frequently  in- 
spected to  guard  against  the  use  of  those  which  have  become  bent  or 
out  of  balance.  If  a  tapered  wheel  has  broken,  the  flanges  must  be 
carefully  inspected  for  truth  before  using  with  a  new  wheel.  Clamping 
nuts  shall  also  be  inspected. 

Minimum  Sizes  of  Machine  Spindles  in  Inches  for  Various 
Diameters  and  Thickness  of  Grinding  Wheels. 


-  Thickness  of  Wheel  in  Inches  — 

2        2X  21A     3 


222 

2K    2M    2^ 

2X   3    2    3 


Safe  Speeds. — A  peripheral  speed  of  5,000  "ft.  per  min.  is  recom- 
mended as  the  standard  operating  spee.d  for  vitrified  and  silicate 
straight  wheels,  tapered  wheels  and  shapes  other  than  those  known  as 
cup  and  cylinder  wheels,  which  are  used  on  bench,  floor,  swing  frame 
and  other  machines  for  rough  grinding.  In  no  case  shall  a  peripheral 
speed  of  6500  ft.  be  exceeded. 

A  peripheral  speed  of  4500  ft.  per  min.  is  recommended  as  the 
standard  operating  speed  for  vitrified  and  silicate  wheels  of  the  cup  and 
cylinder  shape,  used  on  bench,  floor,  swing  frame,  and  other  machines 
for  rough  grinding.  In  no  case  shall  5500  ft.  be  exceeded. 

For  elastic,  vulcanite  and  wheels  of  other  organic  bonds,  the  recom- 
mendations of  individual  wheel  manufacturers  shall  be  followed. 

For  precision  grinding  an  operating  peripheral  speed  of  6500  ft.  per 
min.  may  be  recommended. 

If  a  wheel  spindle  is  driven  by  a  variable-speed  motor  some  device 
shall  be  used  which  will  prevent  the  motor  from  being  run  at  too  high 
speeds.  Cone  pulleys  determining  the  speed  of  a  wheel  should  never 
be  used  unless  belt-locking  devices  are  provided.  Machines  should 


EMERY  WHEELS  AND   GRINDSTONES.  1317 

V 

be  provided  with  a  stop  or  some  method  of  fixing  the  maximum  size 
of  wheel  which  may  be  used,  at  the  speed  at  which  the  wheel  spindle 
is  running. 

If  wheels  become  out  of  balance  through  wear  and  cannot  be  balanced 
by  truing  or  dressing,  they  should  be  removed  from  the  machine. 

A  wheel  used  in  wet  grinding  shall  not  be  allowed  to  stand  partly 
immersed  in  the  water.  The  water-soaked  portion  may  throw  the 
wheel  dangerously  out  of  balance. 

Wheel  dressers  shall  be  equipped  with  rigid  guards  over  the  tops  of 
the  cutters,  to  protect  operator  from  flying  pieces  of  broken  cutters. 

Goggles  shall  be  provided  for  use  of  grinding  wheel  operators  where 
there  is  danger  of  eye  injury. 

Work  shall  not  be  forced  against  a  cold  wheel,  but  applied  gradually, 
giving  the  wheel  an  opportunity  to  warm  and  thereby  eliminate  possible 
breakage.  This  applies  to  starting  work  in  the  morning  in  grinding 
rooms  which  are  not  heated  in  winter  and  new  wheels  which  have  been 
stored  in  a  cold  place. 

Grinding  as  a  Substitute  for  Finish  Turning  in  the  Lathe. — 
C.  H.  Norton  (Trans.  Am.  Soc.  M.  E.  1912)  recommends  the  use 
of  the  grinding  machine  as  a  substitute  for  the  lathe  for  many  forms 
of  cylindrical  work.  He  advocates  the  elimination  of  the  finishing 
cut  in  the  lathe,  claiming  it  is  more  economical  to  grind  to  size  immedi- 
ately after  the  roughing  cut  than  to  finish  turn  and  then  grind.  For 
this  practice,  work  should  not  be  turned  closer  than  1/32  in.  of  finish 
diameter,  and  coarse  feeds,  often  as  coarse  as  four  to  the  inch,  should 
be  used.  He  cites  instances  where  this  method  produced  pieces  in  18 
minutes,  where  the  former  method  of  rough  and  finish  turning  and  then 
grinding  to  size  required  28  %  minutes.  In  1913,  the  Norton  Grinding 
Co.  was  using  the  grinding  machine  to  the  exclusion  of  the  lathe  for 
automobile  crank-shafts  and  similar  pieces,  grinding  to  size  from  the 
rough  forging.  Instances  and  methods  are  shown  in  Indust.  Eng.t 
April,  1913. 

Truing  and  Dressing. — (Norton  Co.,  1915). — A  wheel  is  trued  to 
make  it  concentric  and  to  give  it  an  accurate  surface..  Dressing  is  to 
sharpen  or  renew  the  surface  of  the  wheel  when  glazed  or  loaded. 
Truing  on  precision  grinding  machines  is  performed  by  a  diamond  held 
rigidly  in  a  fixed  tool  post  —  never  in  the  hand.  There  should  always 
be  a  liberal  supply  of  lubricant  or  water  flowing  on  the  diamond  while 
the  truing  is  being  done.  In  modern  practice,  truing  is  for  two  other 
purposes,  as  well  as  to  make  the  wheel  perfectly  true:  one  for  sharpening 
the  wheel  to  obtain  production  and  the  other  for  dulling  the  wheel  to 
obtain  finish.  Truing  in  rough  grinding  operations  is  performed  by 
using  a  dresser,  usually  an  instrument  containing  steel-cutting  wheels, 
and  in  practice  the  rest  is  adjusted  to  form  a  rigid  support  for  the  lugs 
on  the  dresser,  care  being  taken  to  see  that  the  dresser  is  not  caught 
between  the  wheel  and  the  rest.  In  using  the  dresser  to  sharpen  up 
the  surface  of  the  wheel,  the  rest  is  left  in  its  usual  close  adjustment  to 
the  wheel.  Truing  and  dressing  are  two  of  the  most  neglected  and 
least  understood  features  in  the  proper  use  of  grinding  wheels. 

Special  Wheels. — Rim  wheels  and  iron-center  wheels  are  specialties 
that  require  the  maker's  guarantee  and  assignment  of  speed. 

Safe  Speeds  for  Grindstones  and  Emery  Wheels. — G.  D.  Hiscox 
(Iron  Age,  April  7,  1892),  by  an  application  of  the  formula  for  centri- 
fugal force  in  fly-wheels  (see  Fly-wheels),  obtains  the  figures  for  strains 
in  grindstones  and  emery  wheels  which  are  given  in  the  tables  below. 
His  formulae  are: 

Stress  per  sq.  in.  of  section  of  a  grindstone     =  (0.7071Z>xAr)2X0.0000795 
Stress  per  sq.in.  of  section  of  an  emery  wheel=  (0.7071Z>XA02X0.00010226 

D  =  diameter  in  feet,  N  =  revolutions  per  minute. 

He  takes  the  weight  of  sandstone  at  0.078  Ib.  per  cubic  inch,  and  that 
of  an  emery  wheel  at  0.1  Ib.  per  cubic  inch;  Ohio  stone  weighs  about 
0.081  Ib.  and  Huron  stone  about  0.089  Ib.  per  cubic  inch.  The  Ohio 
stone  will  bear  a  speed  at  the  periphery  of  2500  to  3000  ft.  per  min., 
which  latter  should  never  be  exceeded.  The  Huron  stone  can  be 
trusted  up  to  4000  ft.,  when  properly  clamped  between  flanges  and 
not  excessively  wedged  in  setting.  Apart  from  the  speed  of  grindstones 


1318 


THE  MACHINE-SHOP. 


as  a  cause  of  bursting,  probably  the  majority  of  accidents  have  really 
been  caused  by  wedging  them  on  the  shaft  and  over-wedging  to  true 
them.  The  holes  being  square,  the  excessive  driving  of  wedges  to  true 
the  stones  starts  cracks  in  the  corners  that  eventually  run  out  until 
the  centrifugal  strain  becomes  greater  than  the  tenacity  of  the  remain- 
ing solid  stone.  Hence  the  necessity  of  great  caution  in  the  use  of 
wedges,  as  well  as  the  holding  of  large  quick-running  stones  between 
large  flanges  and  leather  washers. 

The  Iron  Age  says  the  strength  of  grindstones  when  wet  is  reduced 
40  to  50%.  A  section  of  a  stone  soaked  all  night  in  water  broke  at  a 
stress  of  80  Ib.  per  sq.  in.  A  section  of  the  same  stone  dry  broke  at 
146  Ib.  per  sq.  in.  A  better  quality  stone  broke  at  stresses  of  186  and 
116  Ib.  per  sq.  in.  when  dry  and  wet  respectively. 

Strains  in  Grindstones. 

LIMIT  OF  VELOCITY  AND  APPROXIMATE  ACTUAL  STRAIN  PER  SQUARE 

•  INCH  OF  SECTIONAL  AREA  FOR  GRINDSTONES  OF 

MEDIUM  TENSILE  STRENGTH. 


Diam-  ' 
eter. 

Revolutions  per  Minute. 

100 

150 

200 

250 

300 

350 

400 

feet. 

fy, 

31/2 
4V2 

6 

7 

Ibs. 
1  .58 
2.47 
3.57 
4.86 
6.35 
8.04 
9.93 
14.30 
19.44 

Ibs. 
3.57 
5.57 
8.04 
10.93 
14.30 
18.08 
22.34 
32.17 

Ibs. 
6.35 
9.88 
14.28 
19.44 
27.37 
32.16 

Ibs. 
9.93 
15.49 
22.34 
30.38 

Ibs. 
14.30 
22.29 
32.16 

Ibs. 
18.36 
28.64 

Ibs. 
25.42 
39.75 

Approximate  breaking  strain   ten 
times  the  strain  for  size  opposite  the 
bottom  figure  in  each  column. 

The  figures  at  the  bottom  of  columns  designate  the  limit  of  velocity 
(in  revolutions  per  minute  at  the  head  of  the  columns)  for  stones  of  the 
diameter  in  the  first  column  opposite  the  designating  figure. 

A  general  rule  of  safety  for  any  size  grindstone  that  has  a  compact  and 
strong  grain  is  to  limit  the  peripheral  velocity  to  47  feet  per  second. 

Joshua  Rose  (Modern  Machine-shop  Practice)  says:  The  average  cir- 
cumferential speed  of  grindstones  in  workshops  may  be  given  as  follows: 

For  grinding  machinists'  tools,  about 900  feet  per  minute. 

carpenters'  600   " 

The  speeds  of  stones  for  file-grinding  and  other  similar  rapid  grinding 
is  thus  given  in  the  "Grinders'  List." 

Diam.  ft 8     71/2     7     61/2     6     51/2     5     41/2     4     31/2    3 

Revs,  per  min. .  : . . .    135  144  154  166  180  196  216  240  270  308  360 

TAPER  BOLTS,  PINS,  REAMERS,  ETC. 

Standard  Steel  Mandrels.  (The  Pratt  &  Whitney  Co.) — These 
mandrels  are  made  of  tool-steel,  hardened,  and  ground  true  on  their 
centers.  Centers  are  also  ground  to  true  60  degree  cones.  The  ends  are 
of  a  form  best  adapted  to  resist  injury  likely  to  be  caused  by  driving. 
They  are  slightly  taper.  Sizes,  -1/4  inch  diameter  by  33/4  inches  long  to 
4  inches  diameter  by  17  inches  long,  diameters  advancing  by  16ths. 

Taper  Bolts  for  Locomotives.  —  Bolt-threads,  U.  S.  Standard,  ex- 
cept stay-bolts  and  boiler-studs,  V- threads,  12  per  inch;  valves,  cocks, 
and  plugs,  V-threads,  14  per  inch,  and  i/g-inch  taper  per  1  inch. 
Standard  bolt  taper  1/15  inch  per  foot. 

Taper  Reamers.— The  Pratt  &  Whitney  Co.  makes  standard  taper 
reamers  for  locomotive  work  taper  i/ie  inch  per  foot  from  1/4  inch  diam- 
eter; 4-inch  length  of  flute  to  2-inch  diameter,  18-inch  length  of  flute, 
diameters  advancing  by  16ths  and  32ds.  P.  &  W.  Co.'s  standard  taper 
pin  reamers  taper  1/4  inch  per  foot,  are  made  in  15  sizes  of  diameters, 
0.135  to  1.250  inches;  length  of  flute,  1 7/16  inches  to  14  inches. 


TAPER   PINS,    BOLTS,    REAMERS,    ETC. 


1319 


Morse  Tapers. 


Number  of  J 
Taper. 

Diam  of  Plug 
at  Small  End. 

Diam.  at  End 
of  Socket. 

Standard  Plug 
Depth. 

Whole  Length 
of  Shank. 

Depth  of  Hole. 

End  of  Socket 
to  Key-  way. 

Length  of  Key- 
way,  ' 

Width  of  Key- 
way. 

4 

"5  o 

MH 
1 

Diameter  of 
Tongue. 

Thickness  of 
Tongue. 

Had.  of  Mill 
for  Tongue.  1 

Radius  of 
Tongue. 

Shank  Depth. 

Taper  per  Foot. 

D 

A 

P 

B 

// 

K 

L 

TF 

T 

d 

t 

R 

a 

S 

0 

252 

356 

2 

211/32 

21/32 

115/1G 

9/16 

.160 

1/4 

.235 

5/32 

5/32 

.04 

27/32 

.625 

1 

.369 

.475 

21/8 

29/16 

23/16 

21/16 

3/4 

.213 

3/8 

.343 

13/64 

3/16 

.05 

27/ie 

.600 

2 

.572 

.700 

29/16 

3l/8 

25/8 

21/2 

7/8 

26 

7/16 

l7/32 

1/4 

1/4 

.06 

215/16 

.602 

3 

.778 

.938 

33/16 

37/8 

31/4 

31/16 

1Vl6 

322 

Vl6 

23/32 

5/16 

9/32 

.08 

3U/16 

.602 

4 

1.020 

1.231 

41/16 

47/8 

41/8 

37/8 

U/4 

.478 

5/8 

31/32 

15/32 

5/16 

.10 

45/8 

.623 

5 

1.475 

1.748 

53/16 

61/8 

51/4 

415/ie 

U/2 

.635 

3/4 

U3/32 

5/8 

3/8 

.12 

57/8 

.630 

6 

2.116 

2.494 

7V4 

89/16 

73/8 

7 

13/4 

.76 

11/8 

2 

3/4 

V2 

.15 

81/4 

.626 

7 

2.75 

3.27 

10 

115/8 

101/8 

91/2 

25/8 

1.135 

l3/8 

25/8 

11/8 

3/4 

.18 

1U/4 

.625 

Brown  &  Sharpe  Mfg.  Co.  publishes  (Machy's  Data  Sheets)  a  list  of 
18  sizes  of  tapers  ranging  from  0.20  in.  to  3  in.  diam.  at  the  small  end; 
taper  0.5  in.  to  1  ft.,  except  No.  10,  which  is  0.5161  in.  per  ft. 


c 

J>~ 

i 

•*- 

FIG.  216. — Morse  Tapers.     See  table  above. 

The  Jar  no  Taper  is  0.05  inch  per  inch  =  0.6  inch  per  foot.  The 
number  of  the  taper  is  its  diameter  in  tenths  of  an  inch  at  the  small  end, 
in  eighths  of  an  inch  at  the  large  end,  and  the  length  in  halves  of  an  inch. 
Thus,  No.  3  Jarno  taper  is  11/2  inches  long,  0.3  inch  diameter  at  the  small 
end  ami  %  inch  diameter  at  the  large  end, 


1320 


THE    MACHINE-SHOP. 


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PUNCHES  AND   DIES,    PRESSES,   ETC 


1321 


Standard  Steel  Taper-pins.  —  The  following  sizes  are  made  by  The 

Pratt  &  Whitney  Co.:   Taper  1/4  inch  to  the  foot. 
Number: 

0123          456789          10 
Diameter  large  end: 

0.156  0.172  0.193  0.219  0.250  0.289  0.341  0.409  0.492  0.591  0.706 
Approximate  fractional  sizes: 

19/64        u/32     13/32        V2        1 


5/32        n/64 

Lengths  from 

3/4  3/4 

To* 

1  H/4 


3/l6 
3/4 


7/32 
3/4 


H/2      l3/4 


8/4         8/4          8/4 
2        21/4        31/4 


ll/4      1  1/2 
41/2     5V4 


23/32 

H/2 

6 


Diameter  small  end  of  standard  taper-pin  reamerrf 
0.135    0.146   0.162    0.183    0.208    0.240  0.279  0.331   0.398  0.482  0.581 

Dimensions  of  T-Slots,  T-Bolts  and  T-Nuts. 
(Pratt  &  Whitney  Standard — Dimensions  in  Inches). 


Slot. 

Bolt  and  Nut. 

Width 
8 

W 

BJ 

Min. 

c 

Diam. 
of 
Bolt. 

D 

Diam. 
of 
Head 
or 

Nut. 
H 

Thick- 
ness of 
Head 
or 
Nut. 
T 

Width 
of 
Stem. 

J 

Height 
of 
Stem. 

N 

Diam. 
of 
Hole. 

K 

5/16 
3/8 
7/16 

1/2 
5/8 
3/4 

7/8 

1/2 
5/8 
"/16 
13/16 
15/16 
13/16 
1  5/18 
15/8 
1  7/8 

3/16 

3/16 
1/4 
9/32 
5/16 
3/8 
1/2 
9/16 
5/8 

5/32 
5/32 
*/M 

7/32 
9/32 
13/32 
17/32 

H/15 
13/18 

3/16 
V4   ' 
5/16 

3/8 

»l« 

9/n 
«/il 

3/4 
7/8 

7/16 
9/16 
5/8 
3/4 
7/8 
11/8 
1  V4 
1  1/2 
13/4 

1/8 
1/8 
3/16 
'  3/16 
1/4 
H/32 
15/32 
9/16 
H/16 

3/16 
1/4 
5/16 
3/8 
7/16 
9/16 
H/16 
3/4 
7/8 

3/32 

1/8 
1/8 
5/32 
3/16 
3/16 
1/4 
5/16 
5/16 

1/8 
1/8     3/16 
3/16      V4 
1/4       5/iQ 
5/16     3/8 
7/16  '  V2 
9/16     5/8 
5/8       3/4 
3/4       7/8 

t  Maximum  thicknesses:  Up  to  5/g-in.  bolts,  5  +1/16  in.;  H/ie-in.  bolt, 
1  in.;  3/4-in.  bolt,  1  1/ie  in.;  7/8-in.  bolt,  1  3/16  in. 

PUNCHES   AND    DIES,   PRESSES,    ETC. 

Clearance  between  Punch  and  Die.  —  For  computing  the  amount 
of  clearance  that  a  die  should  have,  or,  in  other  words,  the  difference 
in  size  between  die  and  punch,  the  general  rule  is  to  make  the  diam- 
eter of  die-hole  equal  to  the  diameter  of  the  punch,  plus  2/10  the  thickness 
of  the  plate.  Or,  D  =  d  +  Q.2t,  in  which  D  =  diameter  of  die-hole, 
d  =  diameter  of  punch,  and  t  =  thickness  of  plate.  For  very  thick 
plates  some  mechanics  prefer  to  make  the  die-hole  a  little  smaller  than 
called  for  by  the  above  rule.  For  ordinary  boiler-work  the  die  is  made 
from  1/10  to  3/10  of  the  thickness  of  the  plate  larger  than  the  diameter 
of  the  punch;  and  some  boiler-makers  advocate  making  the  punch  fit 


*  Lengths  vary  by  1/4  inch  each  size, 
t  Taken  1/2  inch  from  extreme  end . 
about  1/2  inch. 


Each  size  overlaps  smaller  one 


1322 


THE   MACHINE-SHOP. 


the  die  accurately.      For  punching  nuts,  the  punch  fits  in  the  die. 
(Am.  Mach.) 

The  clearance  between  the  punch  and  die  when  blanking,  perforating 
and  forming  flat  thin  stock  of  different  materials  in  the  power  press 
for  light  machine  parts  such  as  typewriters,  adding  machines,  etc., 
are  shown  in  the  following  table  compiled  by  E.  Dean  (Am.  Mach., 
May  4,  1905).  In  using  the  table,  the  class  of  work  to  be  done  must 
be  considered.  For  perforating  work,  the  punch  is  made  to  the  de- 
sired size,  and  the  clearance  is  made  on  the  die.  For  blanking,  the 
die  is  of  the  desired  size  and  the  clearance  is  obtained  by  making  the 
punch  smaller. 

Punch  and  Die  Clearances  for  Different  Materials  and  Thicknesses. 


Thick- 
ness 
of 
Stock, 
In. 

Clearance 
for 
Brass 
and  Soft 
Steel,  In. 

Clearance 
for 
Medium 
Rolled 
Steel,  In. 

Clearance 
for 
Hard 
Rolled 
Steel,  In. 

Thick- 
ness 
of 
Stock, 
In: 

Clearance 
for 
Brass 
and  Soft 
Steel,  In. 

Clearance 
for 
Medium 
Rolled 
Steel,  In. 

Clear- 
ance for 
Hard 
Rolled 
Steel,  In. 

0.01 
.02 
.03 
.04 
.05 
.06 
.07 
.08 
.09 
.10 

0.0005 
.001 
.0015 
.002 
.0025 
.003 
.0035 
.004 
.0045 
.005 

0.0006 
.0012 
.0018 
.0024 
.003 
.0036 
.0042 
.0048 
.0054 
.006 

0.0007 
.0014 
.0021 
.0028 
.0035 
.0042 
.0049 
.0056 
.0063 
.007 

0.11 
.12 
.13 
.14 
.15 
.16 
.17 
.18 
.19 
.20 

0.0055 
.006 
.0065 
.007 
.0075 
.008 
.0085 
.009 
.0095 
.010 

0.0066 
.0072 
.0078 
.0084 
.009 
.0096 
.0102 
.0108 
.0114 
.0120 

0.0077 
.0084 
.0091 
.0098 
.0105 
.0112 
.0119 
.0126 
.0133 
.0140 

Kennedy's  Spiral  Punch.  (The  Pratt  &  Whitney  Co.)  —  B.  Mar- 
tell,  Chief  Surveyor  of  Lloyd's  Register,  reported  tests  of  Kennedy's 
spiral  punches  in  which  a  7/8-inch  spiral  punch  penetrated  a  5/g-inch 
plate  at  a  pressure  of  22  to  25  tons,  while  a  flat  punch  required  33  to  35 
tons.  Steel  boiler-plates  punched  with  a  flat  punch  gave  an  average 
tensile  strength  of  58,579  pounds  per  square  inch,  and  an  elongation  in 
two  inches  across  the  hole  of  5.2  per  cent,  while  plates  punched  with  a 
spiral  punch  gave  63,929  pounds,  and  10.6  per  cent  elongation. 

The  spiral  shear  form  is  not  recommended  for  punches  for  use  in  metal 
of  a  thickness  greater  than  the  diameter  of  the  punch.  This  form  is  of 
greatest  benefit  when  the  thickness  of  metal  v/orked  is  less  than  two 
thirds  the  diameter  of  punch. 

Size  of  Blanks  used  in  the  Drawing-press.  —  Oberlin  Smith 
(Jour.  Frank.  Inst.,  Nov.  1886)  gives  three  methods  of  finding  the 
size  of  blanks.  The  first  is  a  tentative  method,  and  consists  simply  in  a 
series  of  experiments  with  various  blanks,  until  the  proper  one  is  found. 
This  is  for  use  mainly  in  complicated  cases,  and  when  the  cutting  por- 
tions of  the  die  and  punch  can  be  finally  sized  after  the  other  work  is 
done.  The  second  method  is  by  weighing  the  sample  piece,  and  then, 
knowing  the  weight  of  the  sheet  metal  per  square  inch,  computing  the 
diameter  of  a  piece  having  the  required  area  to  equal  the  sample  in 
weight.  The  third  method  is  by  computation,  and  the  formula  is  x*= 
>/rf2  _j_  4^  for  a  sharp-cornered  cup,  where  x  =  diameter  of  blank, 
d  =  diameter  of  cup,  h  =  height  of  cup.  For  a  round-corner ed  cup 
where  the  corner  is  small,  say  radius  of  corner  less  than  1/4  height  of  cup, 
the  formula  is  x  =  (^(d*  +  4d/0—  r,  about  ;T  being  the  radius  of  the 
corner.  This  is  based  upon  the  assumption  that  the  thickness  of  the 
metal  is  not  to  be  altered  by  the  drawing  operation. 

Pressure  attainable  by  the  Use  of  the  Drop-press.  (R.  H. 
Thurston,  Trans.  A.  S.  M.  E.,  v,  53.)  —  A  set  of  copper  cylinders 
was  prepared,  of  pure  Lake  Superior  copper;  they  were  subjected  to  the 
action  of  presses  of  different  weights  and  of  different  heights  of  fall. 
Companion  specimens  of  copper  were  compressed  to  exactly  the  same 
amount,  and  measures  were  obtained  of  the  loads  producing  compression, 
and  of  the  amount  of  work  done  in  producing  the  compression  by  the 
drop.  Comparing  one  with  the  other  it  was  found  that  the  work  done 
with  the  hammer  was  90  per  cent,  of  the  work  which  should  have  been 


FLY-WHEELS   FOR   PUNCHES,    PRESSES,    ETC.         1323 

done  witJi  perfect  efficiency.  That  is  to  say,  the  work  done  in  the  test- 
ing-machine was  equal  to  90  per  cent  of  that  due  the  weight  of  the  drop 
falling  the  given  distance. 

Formula:  Mean  pressure  in  pounds 

For  pressures  per  square  inch,  divide  by  the  mean  area  opposed  to 
crushing  action  during  the  operation. 

Similar  experiments  on  Bessemer  steel  plugs  by  A.  W.  Moseley  and 
J.  L.  Bacon  (Trans.  A,  S.  M.  E.,  xxvii.  605)  indicated  an  efficiency  for  the 
drop  hammer  of  about  70  per  cent. 

An  extensive  series  of  experiments  is  reported  in  Am.  Mach.,  Mar. 
10,  1910.  These  were  made  by  W.  T.  Sears,  and  consisted  of  the 
compression  of  lead  plugs  under  a  falling  weight,  ranging  from  20  to 
200  lb.,  dropped  from  heights  ranging  up  to  360  in.  The  tests  showed 
that  after  a  certain  velocity  of  the  falling  weight  had  been  attained, 
the  speed  had  little  effect  on  the  compression  of  the  plug.  This  speed 
was  fixed  at  10  ft.  per  second,  but  its  exact  value  is  uncertain. 

Flow  of  Metals.  (David  Townsend,  Jour.  Frank.  Inst.,  March, 
1878.)  —  In  punching  holes  7/16-inch  diameter  through  iron  blocks  13/4 
inches  thick,  it  was  found  that  the  core  punched  out  was  only  !Vi6 
inches  thick,  and  its  volume  was  only  about  32  per  cent  of  the  volume 
of  the  hole.  Therefore,  68  per  cent  of  the  metal  displaced  by  punching 
the  hole  flowed  into  the  block  itself,  increasing  its  dimensions. 

Fly-wheels  for  Presses,  Punches,  Shears,  etc. — The  function  of  the 
fly-wheel  on  punching  and  other  machinery  in  which  action  is  inter- 
mittent is  to  store  up  energy  during  that  portion  of  the  stroke  when 
no  work  is  being  done  and  to  give  it  out  during  the  period  of  actual 
working.  The  giving  up  of  energy  is  accompanied  by  a  reduction  in 
the  velocity  of  the  fly-wheel. 
Notation: 

E  =  total  energy  in  the  wheel  at  maximum  velocity,  ft.-lb. 

E\  =  energy  given  out  by  the  wheel  during  speed  reduction, 

ft.-lb. 
vi  =  initial  velocity  of  the  center  of  gravity  of  fly-wheel  rim, 

ft.  per  sec. 
V2  =  velocity  of  center  of  gravijby  of  fly-wheel  rim  at  end  of  period 

in  which  energy  is  given  out. 
H.P.  =  horse-power  required. 

N  =  strokes  of  press  or  shear  per  min. 
.  T  =  time  required  per  stroke,  sees. 

t  =  time  required  for  actual  cutting  of  metal  per  stroke,  sees, 
w  =  weight  of  fly-wheel  rim,  lb. 
d  =  diameter  of  rim  at  center  of  gravity. 
R  =  r.p.m.  of  fly-wheel  at  initial  velocity. 
c  and  ci  =  constants. 

a  =  width  of  fly-wheel  rim,  in. 
b  =  depth  of  fly-wheel  rim,  in. 
y  =  ratio  of  depth  to  width  of  rim. 
g  =  acceleration  due  to  gravity  =  32.2 
Formulae: 

p  _  w  viz  _  wviz 
~    2  g    ~  64.4 


_  27r  RN 

60 

A  simplified  method  for  calculating  fly-wheels  for  punches  and  shears 
is  given  in  Machinery's  Handbook,  p.  289.     Using  the  notation  as  above, 

EN    =        E        .  „  _  „  /t__L\. 
'     33,000      TX550V 


1324 


THE  MACHINE-SHOP. 


For  cast-iron  fly-wheels  with  maximum  stresses  of  1000  Ib.  per  so; .  in.i 
=aEii  R=  1940 -i-D. 

VALUES  OF  c  AND  c\. 


Per  Cent 
Reduction. 

21/2 

5 

71/2 

10 

15 

20 

c       

0.00000213 
0.1250 

0.00000426 
0.0625 

0.00000617 
0.0432 

0.00000810 
0.0328 

0.00001180 
0.0225 

0.00001535 
0.0173 

Ci.  . 

For  belt-driven  machines,  the  limiting  low  velocity  vz  is  the  speed 
at  which  the  belt  will  run  off  the  pulley.  Wilfred  Lewis,  Trans.  A.  S. 
M.  E.,  vol.  vii,  shows  that  this  takes  place  when  the  slip  exceeds  20 
per  cent  of  the  belt  speed.  This  gives  a  limiting  condition  for  belt 

drives  of  punches  and  shears  of  W  =  180  (  —  j 

FORCING,  SHRINKING  AND  RUNNING  FITS. 

Forcing    Fits  of  Pins    and    Axles  by  Hydraulic    Pressure.  —  A 

4-inch  axle  is  turned  0.015  inch  diameter  larger  than  the  hole  into  which 
it  is  to  be  fitted.  They  are  pressed  on  by  a  pressure  of  30  to  35  tons. 
(Lecture  by  Coleman  Sellers,  1872.) 

For  forcing  the  crank-pin  into  a  locomotive  driving-wheel,  when  the 
pinhole  is  perfectly  true  and  smooth,  the  pin  should  be  pressed  in  with  a 
pressure  of  6  tons  for  every  inch  of  diameter  of  the  wheel  fit.  When  the 
hole  is  not  perfectly  true,  which  may  be  the  result  of  shrinking  the  tire  on 
the  wheel  center  after  the  hole  for  the  crank-pin  has  been  bored,  or  if  the 
hole  is  not  perfectly  smooth,  the  pressure  may  have  to  be  increased  to  9 
tons  for  every  inch  of  diameter  of  the  wheel-fit.  (Am.  Machinist.) 

Pressure  Table  for  Mounting  Wheels  and  Crank  Pins. 

(Santa  Fe  R.R.  System,  1915.) 


Driving  Axles. 

Eng.  Truck  Axles 

Crank  Pins. 

Car  Truck  Axles. 

Diam.  of  Wheel 
Fit,  In. 

Pressure,  Tons. 
Wheel 
Centers. 

Ic 
i—  i 

O  ±3 

ss 
5 

Pressure,  Tons 
Wheel 
Centers. 

I 

iSo 

Pressure,  Tons. 
Wheel 
Centers. 

Diam.  of  Wheel 
Fit,  In. 

Pressure, 
Tons. 
Wheels. 

Cast 
Iron. 

Steel 

Cast 
Iron. 

Steel 

Q  +£ 

g£ 

3 

3 
4 
5 
i 
7 

71/2 
8V2 
9V2 

Cast 
Iron. 

Steel 

Cast 
Iron. 

Steel 
or 
Steel 
Tired* 

4v, 

6 

8 
9 
10 
11 
12 

45-  50 
50-  55 
60-  65 
70-  75 
80-  85 
90-  95 
100-105 
110-115 
120-125 

72-  80 
80-  88 
96-104 
112-120 
128-136 
144-152 
160-168 
176-184 
192-200 

3V2 

[1/2 

fVi 

6Vi 

rl/2 

20-25 
25-30 
30-35 
35-40 
40-45 
45-50 
50-55 
55-60 
60-65 
65-70 

35-  42 
42-  50 
50-  57 
57-  65 
65-  72 
72-  80 
80-  87 
87-  95 
95-102 
102-110 

30 
40 
50 
60 
70 
75 
80 
85 
90 
95 

36-  45 
53-  60 
68-  75 
83-  90 
98-105 
105-113 

4 

h 

6V2 

25-35 
35-45 
40-50 
45-55 
50-60 
55-65 

30-40 
45-55 
50-60- 
50-65 
55-70 
60-75 

113-120 
120-128 
128-135 
135-143 

CRANK  AXLES. 
All  crank  discs, 
110-150  tons. 
All  center  webs 
150-200  tons. 

*  Tires  on. 

NOTE. — In  mounting  wheels  and  crank  pins,  care  should  be  taken  to 
see  that  for  at  least  two-thirds  of  the  wheel  fit  the  pressure  required 
shall  be  between  the  maximum  and  minimum  limits  given  in  the  table, 
or  if  only  one  pressure  is  shown  in  the  table,  the  actual  pressure  re- 
quired should  be  as  near  as  possible  to  that  pressure. 

In  mounting  driving  wheels  with  tires  on,  the  maximum  pressures 
given  in  the  tables  or  even  10  per  cent  higher  pressure  than  the  maxi- 
mum pressure  may  be  used. 

Shrinkage  of  Tires.— Allow  i/64  inch  for  each  12  in.  in  diameter. 


FORCE  AND   SHRINK   FITS. 


1325 


Ground  Fits  for  Machine  Parts. — The  practice  of  the  Brown  & 
•  Sharpe  Mfg.  Co.  in  tolerances  and  allowances  for  ground  fits  is  given  hi 
a  paper  by  W.  A.  Viall  (Trans.  A.  S.  M.  E.,  xxxii)  from  which  the 
table  below  has  been  prepared.  The  limfbs  given  can  be  recommended 
for  satisfactory  commercial  work  in  the  production  of  machine  parts 
and  may  be  followed  under  ordinary  conditions.  In  special  cases  it 
may  be  necessary  to  vary  slightly  from  the  tables. 

Allowances  and  Tolerances  for  Fits — Practice  of  the  Brown  & 
Sharpe  Mfg.  Co.       ^ 


Kind  of  Fit. 

Diameter,  Up  to  and  Including 

1/2  In. 

1  In. 

2  In. 

RUNNING  FITS 
Ordinary  speed  

-.00025  to  -.00075 

-.0005   to  -.001 
-.00025  to  -.0005 
Oto  -.00025 

Oto  +.00025 
+.0005    to  +.001 
+.00075  to  +.0015 

+.00025  to  +.0005 

+.0005    to  +.001 
0  to  +.0005 

-.00075  to  -.0015 

-.001      to  -.002 
-.0005    to  -.001 
Oto  -.0005 

+.00025  to      .0005 
+.001      to  +.002 
+.0015    to  +.0025 

+.0005    to  +.001 

+.001      to  +.0025 
Oto  +.00075 

-.0015  to  -.0025 

-.002    to  -.003 
-.001    to  -.002 
Oto  -.001 

+  0005  to  +.00075 
+.002    to  +.003 
+.0025  to  +.OC4 

+.001    to  +.0015 

+.0025  to  +.0035 
0  to  +.001 

High    speed,    heavy 
pressure,       rocker 
shafts  

SLIDING  FITS  

STANDARD  FITS.  . 

DRIVING  FITS 
For     pieces     to     be 
taken  apart  

Ordinary 

FORCING  FITS   .... 

SHRINKING  FITS 
For    pieces    to    take 
hardened  shells  3/g 
in.  thick  or  less.  .  .  . 
For    pieces    to    take 
shells    more    than 
3/8  in.  thick  
GRINDING  LIMITS  FOR 
HOLES  

Kind  of  Fit. 

Diameter  Up  to  and  Including 

3  1/2  In. 

6  In. 

12  In. 

RUNNING  FITS 
Ordinary  speed.' 

-  .0025    to  -  .0035 

-  .003     to  -  .0045 
-  .002     to  -  .0035 
Oto  -.0015 

+.00075  to  +.001 
+.003     to  +.004 
+.004     to  +.006 

+.0015    to  +.002 

+.0035    to  +.005 
Oto  +.0015 

-  .0035  to  -  .005 

-.0045  to  -.0065 
-  .003    to  -  .005 
0   to  -  .002 

+.001    to  +.0015 
+.004    to  +.005 
+.006   to  +.009 

+.002   to  +.003 

+.005   to  +.007 
0  to  +.002 

High    speed,    heavy 
pressure,       rocker 
shafts  

SLIDING  FITS  

STANDARD  FITS  

DRIVING  FITS 
For     pieces     to     be 
taken  apart  
Ordinary     

FORCING  FITS 

SHRINKING  FITS 
For    pieces    to    take 
hardened  shells  3/g 
in.  thick  or  less.  .  .  . 
For    pieces    to    take 
shells    more    than 
%   in.  thick  
GRINDING  LIMITS  FOR 
HOLES  

0  to  +.0025 

Running  Fits. — Wm.  Sangster  (Am.  Mach.,  July  8,  1909)  gives  the 
practice  of  different  manufacturers  as  follows : 

An  electric  manufacturing  Co.  allows  a  clearance  of  0.003  to  0.004  in.  for 
shafts  1 1/2  to  2 1/4  in.  diam, ;  0.003  to  0.006  for  21/2  in. ;  0.004  to  0.006  for 


1326 


THE  MACHINE-SHOP. 


23/4  to  31/2  ins.;  0.005  to  0.007  in.  for  4  and  41/2  ins.;  0.006  to  0  008  in 
for  5  ins.;  0.009  to  0.011  in.  for  6  ins.  Dodge  Mfg.  Co.  allows  from  I/R! 
for  1-in.  ordinary  bearings  to  a  little  over  1/32  in.  for  6-in.  Clutch  sleeves 
0.008  to  0.015  in.;  loose  pulleys  as  close  as  0.003  in.  in  the  smaller  sizes! 
and  about  1/64  in.  on  a  2i/2-in.  hole. 

Watt  Mining  Car  Wheel  Co.  allows  Vi6  in.  for  all  sizes  of  wheels,  and 
Vie  in.  end  play.  A  large  fan-blower  concern  allows  0.005  to  0.01  in. 
on  fan  journals  from  9/16  to  27/i6  ins. 

Limits  of  Diameters  for  Fits.  C.  W.  Hunt  Co.  (Am.  Mack  July  16 
1903.)  — For  parallel  shafts  and  bushings  (shafts  changing):  d  =  diam. 
in  ins. 

Shafts:  Press  fit,  +  0.001  d  +  (0  to  0.001  in.).     Drive  fit,  +  0.0005  d  + 

(0.  to  0.001  in.). 
Shafts:  Hand  fit,  +  0.001  to  0.002  in.  for  shafts  1  to  3  in.;  0.002  to  0  003 

in.  for  4  to  6  in.;  0.003  to  0.004  in.  for  7  to  10  in. 

Holes:  all  fits 0  to  —  0.002  in.  for  1  to  3  in.;  0  to  —  0.003  in.  for  4  to  6  in  • 
0  to  —  0.004  in.  for  7  to  10  in. 

Parallel  journals  and  bearings  (journals  changing): 

Close  fit  -  0.001  d  +  (0.002  to  0.004  in.);  Free  fit  -  0.001  d  +  (0  007 
to  0.01  in.);  Loose  fit,  -  0.003  d  +  (0.02  to  0.025).  Limits  of  diameters 
for  taper  shaft  and  bushings  (holes  changing).  Shaft  turned  to  standard 
taper  3/16  in.  per  ft.,  large  end  to  nominal  size  ±  0.001  in.  Holes  are 
reamed  until  the  large  end  is  small  by  from  0.001  d  +  0.004  to  0  005  in 
for  press  fit,  from  0.0005  d  +  0.001  in.  f9r  drive  fit,  and  from  0  to  0.001  in. 
for  hand  fit.  In  press  fits  the  shaft  is  pressed  into  the  hole  until  the 
true  sizes  match,  or  Vi6  in.  for  each  Viooo  in.  that  the  hole  is  small. 
The  above  formulae  apply  to  steel  shafts  and  cast-iron  wheels  or  other 
members. 

Shaft  Allowances  for  Electrical  Machinery. — The  General  Electric 
Co.  (1915)  gives  the  following  table  of  allowances  for  sliding  and  press 
fits. 


Press  Fit 

Press  Fit 

Nominal 
Diam., 
In. 

'  Sliding 
Fit. 

Com- 
mutator 
and  Split 
Hub. 

for 
Armature 
Spider 
Solid 

for 
Armature 
Spider 
Solid 

Press 
Fit  for 
Coupling. 

Shrink 
Fit. 

Steel. 

Cast  Iron. 

2 

-0.0015 

+0.0005 

4-0.00075 

4-0.0015 

4-0.00175 

+0.0025 

4 

-  .002 

-I-  .0005 

+  .0015 

4-  .0025 

4-  .003 

+  .004 

8 

-  .004 

+  .001 

4-  .002 

4-  .0035 

4-  .0045 

+  .006 

12 

-  .005 

+  .001 

4-  .0025 

4-  .0045 

4-  .0055 

+  .0075 

16 

-  .0055 

+  .001 

+  .003 

+  .005 

4-  .006 

+  .009 

20 

-  .006 

+  .0015 

+  .0035 

4-  .0055 

4-  .007 

+  .010 

24 

-  .007 

+  .0015 

4-  .0035 

4-  .006 

4-  .0075 

+  .011 

28 

-  .0075 

+  .0015 

4-  .004 

4-  -0065 

4-  .0085 

+  .012 

32 

-  .008 

+  .0015 

4-  .0045 

4-  .007 

4-  .009  . 

+  .0125 

36 

-  .0085 

+  .002 

4-  .0045 

4-  .0075 

4-  .0095 

+  .0135 

40 

-  .009 

+  .002 

4-  .005 

4-  .008 

4-  .010 

+  .014 

44 

-  .0095 

+  .002 

+  .005 

4-  .0085 

4-  .0105 

+  .0145 

48 

-  .010 

4-  .002 

4-  .0055 

4-  .009 

4-  .011 

+  .015 

Pressure  Required  for  Press  Fits.    (Am.  Mach.,  March  7,  1907.)  — 


Crank  fits  up  to  D  =10.  P  =  9.9  D  -  14. 

Crank  fits  D  =  12  to  24.  P  »  5  D  +  40. 

Straight  crank-pins.  P  =  13  D. 

Taper  crank-pins.  P  «=*  14  D  —  7. 

The  allowance  for  cranks  and  straight  pins  is  0.0025  inch  per  inch  of 
diameter  Taper  cranks,  taper  Vie  inch  per  inch,  are  fitted  on  the 
lathe  to  within  i/s  inch  of  shoulder  and  then  forced  home. 

Stresses  due  to  Force  and  Shrink  Fits. — S.  H.  .Moore,  Trans. 
A.  S.  M.  £?.,  vol.  xxiv,  gives  the  following  allowances  for  different  fits: 


FORCE  AND   SHRINK   FITS. 


1327 


For  shrinkage  fits,  d  =(17/16  u+  0.5)  •*•  1000.  For  forced  fits,  'd  = 
(2  D  +  0.5)  -s-  1000,  For  driven  fits,  d  =  (i/2  D  +  0.5)  •*•  1000.  d  = 
allowance  or  the  amount  the  diameter  of  the  shaft  exceeds  the  diameter 
of  the  hole  in  the  ring  and  D  =  nominal  diameter  of  the  shaft.  A.  L. 
Jenkins,  Eng.  News,  Mar.  17,  1910,  says  the  values  obtained  from  the 
formula  for  forced  fits  are  about  twice  as  large  as  those  frequently  used 
in  practice,  and  in  many,  cases  they  lead  to  excessive  stresses  in  the  ring. 
He  calculates  from  Lamp's  formula  for  hoop  stress  in  a  ring  subjected  to 
internal  pressure  the  relation  between  the  stress  and  the  allowance  for 
fit,  and  deduces  the  following  formulae. 

Sfo  =  15,000,000  d  *  (k  +  0.6);  Sh,  =  15,000,000  d  -s-  (1  +  0.6/fc) ;  for  a 

cast-iron  ring  on  a  steel  shaft. 
Shl  =  30,000,000  d  -4-  (1  +  fc);     Sh2  =  30,000,000,  d  •*•  (1  +  1/K);  for  a 

steel  ring  on  a  steel  shaft. 
8^=  radial  unit  pressure  between  the  surfaces;  8^=.  unit  tensile  or 

hoop  stress  in  the  ring; 

d  =  allowance  per  inch  of  diameter,  K  a  constant  whose  value  depends 
on  t,  the  thickness,  and  r,  the  radius  of  the  ring,  as  follows. 
Values  of  t  •*-  r, 

0.4      0.5      0.6      0.7      0.8      0.9       1.0       1.25     1.5      1.75   2.0      3.0 
Values  of  K, 
3.083  2.600  2.282  2.058  1.892  1.766  1.666  1.492  1.380  1.300  1.250  1.133. 

The  allowances  for  forced  and  shrinkage  fits  should  be  based  on  the 
stresses  they  produce,  as  determined  by  the  above  formula,  and  not  on 
the  diameter  of  the  shaft. 

Force  Required  to  Start  Force  and  Shrink  Fits.  (Am.  Mach., 
Mar.  7,  1907.)  —  A  series  of  experiments  was  made  at  the  Alabama  Poly- 
technic Institute  on  spindles  1  in.  diam.  pressed  or  shrunk  into  cast-iron 
disks  6  in.  diam.,  11/4. in.  thick.  The  disks  were  bored  and  finished  with 
a  reamer  to  1  in.  diam.  with  an  error  believed  not  to  exceed  0.00025  in. 
The  shafts  were  ground  to  sizes  0.001  to  0.003  in.  over  1  in.  Some  of  the 
spindles  were  forced  into  the  disks  by  a  testing  machine,  the  others  had 
the  disks  shrunk  on.  Some  of  each  sort  were  tested  by  pulling  the 
spindle  from  the  disk  in  the  testing  machine,  others  by  twisting  the  disk 
on  the  spindle,.  The  force  required  to  start  'the  spindle  in  the  twisting 
tests  was  reduced  to  equivalent  force  at  the  circumference  of  the  spindle, 
for  comparison  with  the  tension  tests.  The  results  were  as  follows: 
D  =  diam.  of  spindle;  F  =  force  in  Ibs.: 


Force  Fits, 
Tension. 

Force  Fits, 
Torsion. 

Shrink  Fits, 
Tension. 

Shrink  Fits, 
Torsion. 

D 

1.001 
1.0015 
1.002 
1  .0025 

F.lbs. 

Per 

sq.  in. 

D 

F.lbs. 

Per 

sq.in. 

D 

F.lbs. 

Per 
sq.in. 

D 

F.lbs. 

Per 

sq.in. 

700 
2290 
3118 
4395 
5410 

1000 
2150 
2570 
4000 

318 
685 
818 
1272 

1.0015 
1.0015 
1.002 
1.0025 

2200 
2800 
4200 
4600 

700 
892 
1335 
1465 

.001 
.001 
.002 
.002 
.0025 
.0025 

5320 
5820 
7500 
8100 
9340 
9710 

1695 
1853 
2385 
2580 
2974 
3090 

1.001 
1.0015 
1.0015 
1.0025 
1.003 

2200 
7200 
9800 
13800 
17000 

1328  THE  MACHINE-SHOP. 

KEYS. 

Formulae  for  Flat  and  Square  Keys. — Great  divergence  exists  in 
the  dimensions  of  square  and  flat  keys  as  given  by  various  authorities. 
The  following  are  the  formulae  in  common  use: 

Notation. — D  =  diameter  of  shaft;  w  =  width  of  key;  t=  thickness 
of  key ;  I  =  length  of  key,  all  dimensions  being  in  inches. 
E.  G.  Parkhurst's  rule:  w  =  i/s  D;  t  =  i/g£>;  taper  1 /sin.  per  ft. 

Michigan  saw-mill  practice:         w  =  1/4  D;  t  =  w. 
J.  T.  Hawkins's  rule:  w  =  1/3  Z>;  t  =  1/4  D. 

Machinery's  Handbook,  rule  1:  w  =  1/4  D;  t  =  i/e  D\  I  =  1.5  Z). 
Machinery's  Handbook,  rule  2:  w  =  3/16  D  +  i/ie;    t  =  i/s  D  -f-  l/s; 

I  =  0.3  Z>2  -=-  t. 

For  splines  or  feather  keys  interchange  w  and  t. 

F.  W.  Halsey  ("  Handbook  for  Machine  Designers  and  Draftsmen") 
says:  The  common  driven  key  for  securing  a  crank  or  gear  to  a  shaft 
is  commonly  made  with  a  width  of  1/4 -D  up  to  about  a  4-in.  shaft, 
about  13/8  in.  for  a  6-in.,  1  3/4  in.  for  an  8-in.,  and  21/4  in.  for  a  10-in. 
shaft.  The  depth  should  be  from  s/8  w  to  3/4  w.  If  the  work  is  at 
all  severe  the  length  should  be  at  least  1.5  D.  The  taper  is  commonly 
1/8  in.  per  ft. 

Unwin  ("Elements  of  Machine  Design  ")  gives:  Width  =  1/4  D+  i/s  in. 
Thickness  =  i/s  D  -f  i/s  in.  When  wheels  or  pulleys  transmitting  only 
a  small  amount  of  power  are  keyed  on  large  shafts,  he  says,  these 
dimensions  are  excessive.  In  that  case,  if  H.P.  =  horse-power  trans- 
mitted by  the  wheel  or  pulley,  JV  =  r.p.m.,  P  =  force  acting  at  the  cir- 
cumference, in  pounds,  and  R  =  radius  of  pulley  in  inches,  take 

8/100H.P.          \~PR '. 
D  =  y—N—  °rV^30 

John  Richards,  in  an  article  in  Gassier' s  Magazine,  writes  as  follows: 
There  are  two  kinds  or  systems  of  keys,  both  proper  and  necessary,  but 
widely  different  in  nature.  1.  The  C9mmon  fastening  key,  usually  made 
in  width  one  fourth  of  the  shaft's  diameter,  and  the  depth  five  eighths 
to  one-third  the  width.  These  keys  are  tapered  and  fit  on  all  sides,  or, 
as  it  is  commonly  described,  "bear  all  over."  They  perform  the  double 
function  in  most  cases  of  driving  or  transmitting  and  fastening  the 
keyed-on  member  against  movement  endwise  on  the  shaft.  Such  keys, 
when  properly  made,  drive  as  a  strut,  diagonally  from  corner  to  corner. 

2.  The  other  kind  or  class  of  keys  are  not  tapered  and  fit  on  their 
sides  only,  a  slight  clearance  being  left  on  the  back  to  insure  against 
wedge  action  or  radial  strain.  These  keys  drive  by  shearing  strain. 

For  fixed  work  where  there  is  no  sliding  movement  such  keys  are  com- 
monly made  of  square  section,  the  sides  only  being  planed,  so  the  depth 
is  more  than  the  width  by  so  much  as  is  cut  away  in  finishing  or  fitting. 

For  sliding  bearings,  as  in  the  case  of  drilling-machine  spindles,  the 
depth  should  be  increased,  and  in  cases  where  there  is  heavy  strain 
there  should  be  two  keys  or  feathers  instead  of  one. 

The  following  tables  are  from  proportions  adopted  in  practical  use. 

Flat  keys,  as  in  the  first  table,  are  employed  for  fixed  work  when  the 
parts  are  to  be  held  not  only  against  torsional  strain,  but  also  against 
movement  endwise;  and  in  case  of  heavy  strain  the  strut  principle  being 
the  strongest  and  most  secure  against  movement  when  there  is  strain 
each  way,  as  in  the  case  of  engine  cranks  and  first  movers  generally. 
The  objections  to  the  system  for  general  use  are,  straining  the  work  out 
of  truth,  the  care  and  expense  required  in  fitting,  and  destroying  the 
evidence  of  good  or  bad  fitting  of  the  keyed  joint.  When  a  wheel  or 
other  part  is  fastened  with  a  tapering  key  of  this  kind  there  is  no  means 
of  knowing  whether  the  work  is  well  fitted  or  not.  For  this  reason  such 
keys  are  not  employed  by  machine-tool-makers,  and  in  the  case  of 
accurate  work  of  any  kind,  indeed,  cannot  be,  because  of  the  wedging 
strain,  and  also  the  difficulty  of  inspecting  completed  work. 

I.  DIMENSIONS  OF  FLAT  KEYS,  IN  INCHES. 


Diam.  of  shaft  

1 

1  V4 

1  I/? 

13/4 

2 

2  if?, 

3 

31/2 

4 

5 

6 

7 

8 

Breadth  of  keys.  .  . 

1/4 

5/1fi 

3/8 

7/1R 

l/? 

5/8 

3/4 

7/8 

] 

H/8 

13/8 

M/2 

13/4 

Depth  of  keys..  .  . 

5/32 

3/16 

1/4 

9/32 

5/16 

3/8 

7/16 

1/2 

5/8 

H/16 

13/16 

7/8 

1 

KEYS. 


1329 


II.  DIMENSIONS  OF  SQUARE  KEYS,  IN  INCHES. 


Diameter  of  shaft  .  . 
Breadth  of  keys  .  .  . 
Depth  of  keys  

1 

5/32 
3/16 

1  V4 
7/32 

1/4 

1  V2 
9/32 
5/16 

1  3/4 
H/32 

3/8 

2 

13/32 

7/16 

21/2 
15/32 
1/2 

3 

17/32 
9/16 

31/2 
9/32 

5/8 

H/16 

3/4 

III.  DIMENSIONS  OF  SLIDING  FEATHER  KEYS,  IN  INCHES. 


Diameter  of  shaft  .  . 

1  V4 

1  1/7! 

1  3/4 

2 

21/4 

21/2 

3 

3V* 

4 

4  ^/?, 

Breadth  of  keys  .  .  . 

1/4 

1/4 

5/1fi 

5/16 

3/8 

3/8 

l/?, 

9/16 

9/16 

5/8 

Depth  of  keys  

3/8 

3/8 

7/16 

7/16 

1/2 

1/2 

5/8 

'  3/4 

3/4 

7/8 

Depth  of  Key  Seats. — The  depth  of-  a  flat  or  square  key  is  equally 
divided  between  the  shaft  and  the  hub.  The  depth  to  which  a  milling 
cutter  is  sunk  into  the  shaft  in  milling  a  key  way  is  equal  to  one-half 
the  depth  of  the  key  plus  the  height  of  the  arc  projecting  above  the 
intersection  of  the  side  of  the  key  way  with  the  circumference  of  the 
shaft.  This  height  can  be  calculated  from  the  formula 

h  =  r-  Vr2  -  (1/2  w)2 

in  which  r  is  the  radius  of  the  shaft,  h  the  height  of  the  arc,  and  w  the 
width  of  the  key. 

The  Lewis  Key. — The  disadvantage  of  the  ordinary  flat  key  is  that 
it  must  be  carefully  fitted.  A  key  fitting  tight  on  top  and  bottom  of 
the  keyway  drives  partly  by  friction.  If  fitted  only  on  the  sides  of 
the  keyway  it  exerts  a  prying  action  on  the  hub  and  shaft,  and  is  sub- 
jected to  severe  bending  and  shearing  stresses.  Square  or  flat  keys 
should  fit  tight  on  all  four  sides,  but  in  practice  this  is  prohibitive  on 
account  of  the  expense.  To  avoid  the  difficulty  inherent  in  ordinary 
flat  keys,  the  Lewis  key  shown  in  Fig.  217  was  devised  by  Wilfred 
Lewis.  It  is  subject  to  compression  only,  but  is  expensive  to  fit. 


FIG.  217. 


FIG.  218. 


The  Earth  Key.  (Fred.  Oyen,  Am.  Mach.,  Nov.  14,  1907,  and  Feb. 
20,  1908.) — The  key  shown  in  Fig.  218  was  devised  by  Carl  G.  Earth 
to  combine  the  advantages  of  the  Lewis  key  with  those  of  the  ordinary 
rectangular  key.  The  Barth  key  is  rectangular  with  one-half  of  both 
sides  bevelled  at  45°.  The  key  does  not  need  to  fit  tightly,  as  pressure 
tends  to  drive  it  into  its  seat.  There  is  no  tendency  to  turn  it,  and 
the  only  stress  to  which  it  is  subject  is  compression.  This  key  has 
been  used  in  many  cases  as  a  feather  to  replace  rectangular  feather 
keys  which  have  given  trouble.  It  has  found  wide  application  as  a 
feather  key  in  drill  sockets  and  drill  shanks,  reamers,  etc.,  which  are 
commonly  driven  with  a  tang. 

Reducing  sockets  for  drill  presses  are  fitted  with  a  Barth  key  dove- 
tailed inside  and  a  similar  keyway  on  the  outside.  No.  1  Morse  taper 
shank  has  a  keyway  for  No.  1  Barth  key  and  fits  into  a  No.  1  reducing 
socket.  No.  2  shank  has  No.  2  Morse  taper  and  a  keyway  for  No.  2 
Barth  key,  etc.  Dimensions  of  the  various  sizes  of  the  Barth  key  are 
shown  in  the  following  table: 


1330 


THE  MACHINE-SHOP. 


Dimensions  of  Dovetailed  Bar th  Keys. 


No.  of 
Earth  Key. 

No.  of  Morse 
Taper  in 
Which  Used. 

w, 
In. 

W, 
In. 

D, 
In. 

1 
2 
3 

4 

5 

2 
3 
4 
5 

1/8 
5/32 
3/16 

V4 
5/16 

0.132 
0.165 
0.199 
0.264 
0.329 

5/128 
3/64 
Vl6 
5/64 
3/23 

The  Earth  key  has  been  adapted  to  a  complete  line  of  standard  taper 
sockets,  shanks,  driving  keys,  holdback 
keys,  drifts,  adapters,  and  reducers  at  the 
Watertown  Arsenal.  The  standards,  which 
cover  both  Brown  &  Sharpe  and  Morse 
tapers  are  given  in  Am.  Mach.,  Dec.  24, 
1914. 

Do  trick  &  Harvey  Keys.  (Am.  Mach., 
Feb.  11,  1915.)— The  Detrick  &  Harvey 
Machine  Co.,  Baltimore,  uses  square  keys 
of  dimensions  shown  in  Pig.  219  and  the 
following  table.  Although  these  are  smaller 
than  the  square  key  generally  used,  there 
is  no  case  known  in  which  one  of  them  has 
sheared  off.  The  dimension  C  is  for  setting 
the  key,  and  the  dimension  B  gives  the 
diameter  across  the  corners  of  the  key.  All 
dimensions  are  in  inches. 


FIG.  219. 


Dimensions  of  Detrick  &  Harvey  Keys. 


D 

A 

B 

C 

D 

A 

B 

C 

D 

A 

B 

C 

1/2 

1/8 

0.623 

0.555 

3/8 

9/32 

1.652 

1.501 

31/2 

H/16 

4.177 

3.808 

9/16 

1/8 

.685 

.618 

1/2 

5/16 

1.806 

1.640 

33/4 

3/4 

4.487 

4.087 

5/8 

5/32 

.778 

.693 

5/8 

5/16 

1.931 

1.766 

4 

13/16 

4.797 

4.364 

H/16 

5/32 

.841 

.756 

3/4 

7/16 

2.176 

1.941 

41/4 

13/16 

5.049 

4.616 

3/4 

3/16 

.933 

.832 

7/8 

7/16 

2.302 

2.067 

41/2 

13/16 

5.303 

4.868 

13/16 

3/16 

.996 

.895 

2 

7/16 

2.428 

2.194 

43/4 

7/8 

5.619 

5.147 

7/8 

3/16 

.058 

.958 

2  1/4 

9/16 

2.796 

2.496 

5 

7/8 

5.864 

5.399 

15/16 

3/16 

.122 

1.022 

21/2 

9/16 

3.050 

2.749 

51/4 

7/8 

6.115 

5.650 

1/4 

.242 

1.109 

23/4 

5/8 

3.361 

3.027 

51/2 

15/16 

6.422 

5.928 

1  1/8 

1/4 

.368 

1.236 

5/8 

3.616 

3.280 

53/4 

15/16 

6.676 

6.180 

H/4 

9/32 

.524 

1.375 

31/4 

H/16 

3.925 

3.556 

6 

15/16 

6.927 

6.432 

FIG.  220. 


The  Kennedy  Key.  —  The  Kennedy 
key,  largely  used  in  rolling  mill  work,  is 
shown  in  Fig.  220.  In  these  keys  w  = 
I  =  1/4  D.  They  are  tapered  i/g  in.  per 
ft.  on  top,  while  the  sides  are  a  neat  fit. 
The  keys  are  so  set  in  the  shaft  that 
diagonals  through  them  intersect  at  the 
axis  of  the  shaft.  The  hub  is  bored  for 
a  press  fit  and  then  is  rebored  eccen- 
trically about  1/64  D  off  center.  The 
keyways  are  cut  in  the  eccentric  side. 
General  practice  is  to  use  single  keys 
for  diameters  up  to  and  including  6  in. 
where  the  torque  is  constant  and  the 
power  transmitted  always  in  one  direc- 
tion. For  shafts  above  6  in.  diameter 
double  keys  should  be  used,  and  if  the 
torque  is  intermittent  and  in  alternate 
directions,  double  keys  should  be  used 
down  to  shaft  diameters  of  4  in. 


KEYS. 


1331 


The  Nordberg  Key.  —  The  Nordberg 
Mfg.  Co.  has  adopted  for  the  ends  of 
shafts  round  keys  shown  in  Fig.  223. 
The  advantages  of  this  key  are:  No 
tendency  toward  deformation  ;  they  are 
a  driven  fit  in  the  direction  of  the 
shear;  they  are  always  in  true  shear  and 
are  cheaper  than  the  square  key.  In 
manufacturing  a  hole  A  is  drilled  in  the 
joint  and  next  a  hole  B  as  large  as  the 
size  of  the  keyway  will  admit  is  drilled 
in  the  shaft  in  order  to  avoid  the  ten- 
dency of  the  drill  used  for  drilling  the 
keyway  to  size  to  crowd  into  the  soft 
cast  iron.  In  the  table  the  reamer 
diameters  given  are  of  the  small  end. 
The  taper  is  i/ie  in.  per  ft.,  measured 
on  the  diameter. 


FIG.  221. 


Dimensions  of  Nordberg  Standard  Round  Keys. 


Diam. 
of 
Shaft, 
In. 

Diam. 
of 
Reamer 
In. 

Cutting 
Length 
of 
Reamer 
In. 

Diam. 
of 
Shaft, 
In. 

Diam. 
of 
Reamer 
In. 

Cutting 
Length 
of 
Reamer 
In. 

Diam. 
of 
Shaft, 
In. 

Diam. 
of 
Reamer 
In. 

Cutting 
Length 
of 
Reamer 
In. 

2  15/16-3 
3  7/16-3  1/2 
3  7/8  -4 

4  3/8  -4  1/2 
51/2 

6 

3/4 

7/8 

1/8 
1/4 
3/8 
1/2 

41/4 
4V2 
47/8 

45/8 
47/8 
61/8 

8> 

o  (• 

91 
10  J 
11  V 
12) 

13) 
14V 

15/8 
2 
29/16 

6  7/8  &  8 
101/4 
12 

16) 
17V 
18) 
19) 
20V 
21  f 
22) 
23V 

31/8 
3  H/16 
4  1/4 

12 
13 

14  1/4 

15\ 

24  f 

The  Woodruff  Key. — The  Woodruff  key  shown  in  Fig.  222  is  exten- 
sively used  in  machine  construction.  Dimensions  are  given  in  the 
following  table.  The  key  should  project  above  the  shaft  a  distance 
equal  to  one-half  the  thickness.  For  ordinary  practice  medium-sized 
keys  should  be  used: 

.&.          I 


STANDARD.  FIG.  222.  SPECIAL. 

Dimensions  of  Woodruff  Standard  Keys — Inches. 


o, 

a 

a 

0 

o 

0 

" 

««£-   • 

** 

H   • 

-H^ 

No. 

o   . 

.  s 

0   >> 

_,  rt 

0  0^ 

No. 

0     . 

.  ^ 

o  >> 

_,  cU 

yo^ 

*•«      >> 

No. 

°, 

i  ^ 

0   >> 

2s* 

Is 

QW 

.i*0 

o  K- 

2  g 

H  c 

is  £ 

a  >» 

OJ    0) 

QW 

ll* 

Of/2  O 

§£ 

5t2 

•M*0 

.2    OB 

•3  $ 
He 

i3  £ 

II 

m 

Otfi  o 

Is 

QW 

•« 

II 

in! 

Ssz 

Utt^ 

1 

1/2 

1/16 

1/3? 

3/64 

12 

7/8 

7/3? 

7/64 

1/16 

20 

1/4 

7/3? 

7/64 

5/64 

2 

1/2 

3/3? 

3/64 

3/64 

A 

7/8 

1/4 

1/8 

1/16 

21 

1/4 

1/4 

1/8 

5/64 

3 

I/? 

1/8 

Vlfi 

3/64 

13 

3/16 

3/3? 

1/16 

D 

1/4 

5/16 

5/3? 

5/64 

4 

5/8 

3/32 

3/64 

1/16 

14 

7/3? 

7/64 

1/16 

E 

1/4 

3/8 

3/16 

5/64 

5 

5/8 

1/8 

1/16 

Vl6 

15 

1/4 

1/8 

1/16 

22 

3/8 

1/4 

1/8 

3/32 

6 

5/8 

5/3? 

5/64 

1/16 

B 

5/16 

5/30 

1/16 

23 

3/8 

5/16 

5/3? 

3/32 

7 

3/4 

1/8 

1/16 

1/16 

16 

1/8 

3/16 

3/3? 

5/64 

F 

3/8 

3/8 

3/16 

3/32 

8 

3/4 

5/3? 

5/64 

1/16 

17 

1/8 

7/3? 

7/64 

5/64 

24 

1/2 

1/4 

1/8 

7/64 

9 

3/4 

3/1fi 

3/3? 

1/16 

18 

1/8 

1/4 

1/8 

5/64 

25 

I/? 

5/16 

5/3? 

7/64 

10 

7/8 

5/3? 

5/64 

1/16 

C 

1/8 

6/16 

5/3? 

5/64 

G 

1/2 

3/8 

3/16 

7/fi4 

11 

7/8 

3/16 

3/32 

1/16 

19 

1/4 

3/16 

3/32 

5/64 

1332  THE  MACHINE-SHOP. 

Dimensions  of  Woodruff  Special  Keys— Inches. 


No. 

26 

27 

28 

29 

30 

31 

32 

33 

34 

Dimension 
a 
6 

d 

e 

21/8 
3/16 
3/32 
17/32 
3/32 

21/8 
1/4 
1/8 
17/32 
3/32 

21/8 
5/16 
5/32 
17/32 
3/32 

21/8 
3/8 
3/16 
17/32 
3/32 

31/2 
3/8 
3/16 
13/16 
3/16 

31/2 
7/16 
7/32 
13/16 
3/16 

3l/2 

1/2 
1/4 
13/16  ^ 
3/16 

3l/2 

9/16 
9/32 
13/16 
3/16 

31/2 

5/8 
5/16 

^I6 
3/16 

Woodruff  Keys  Suitable  for  Different  Shaft  Diameters'. 


Shaft 
Diam. 

Key 
Nos. 

Shaft 
Diam. 

Key 
Nos. 

Shaft 
Diam. 

Key 

Nos. 

Shaft 
Diam. 

Key 
Nos. 

5/16-3/8 
7/16-1/2 
9/16-5/8 
H/16-3/4 

1 
2,4 
3,5 
3,  5.7 

13/16 
7/8-1-ViG 

I  1/16-1  1/8 

6,8 
6,  8,  10 
9,  11,  13 
9,11,13,16 

1  3/16 
1   1/4-1  5/i6 
1  3/8-1  7/i6 
1  1/2-1  5/8 

11,  13,  16 
12,14,17,20 
14,  17.20 
15,  18,21.24 

1  H/16-1  3/4 
1  13/16-2 
2    1/16-21/2 

18,21.24 
23.25 
25 

Cw3  K 


Gib  Keys. — ''Machinery's  Handbook "  gives  the  following  formulae  for 
dimensions  of  gib  keys.      (See  Pig.  223).     All  dimensions  are  in  inches. 

D  =  diameter  of  shaft;  w  =  width 
of  key;  T  =  thickness  of  key,  large 
end;  S  =  safe  shearing  strength  of 
material  in  key;  G  =  length  of  gib; 
h  =  projection  of  gib  above  top  oi' 
key. 

w  =  1/4  D  up  to  6  in.;  over  6  in. 
w  =  0.211  D. 

T  =  i/e  D  up  to  6  in. ;  over  6  in.  T  =   l/s  D. 

G  =  w. 

Length  =  length  of  hub  +  1/2  in.     Taper  1/s  in.  per  ft. 

Safe  twisting  moment  per  in.  of  length  of  key  =  1/2  D  X  W  X  S. 

Keyways    for   Milling    Cutters. — For   keyways   for   milling   cutters 
see  p.  1277. 


Length 

FIG.  223. 
Minimum  value  3/i6  in. 


HOLDING-POWER  OF  KEYS  AND  SET-SCREWS. 

Tests  of  the  Holding-power  of  Set-screws  in  Pulleys.  (G.  Lanza, 
Trans.  A.  S.  M.  E.,x,  230.) — These  tests  were  made  by  using  a  pulley 
fastened  -to  the  shaft  by  two  set-screws  with  the  shaft  keyed  to  the 
holders;  then  the  load  required  at  the  rim  of  the  pulley  to  cause  it  to 
slip  was  determined,  and  this  being  multiplied  by  the  number  6,037 
(obtained  by  adding  to  the  radius  of  the  pulley  one-half  the  diameter 
of  the  wire  rope,  and  dividing  the  sum  by  twice  the  radius  of  the  shaft, 
since  there  were  two  set-screws  in  action  at  a  time)  gives  the  holding- 
power  of  the  set-screws.  The  set-screws  used  were  of  wrought  iron, 
5/8  of  an  inch  in  diameter,  and  ten  threads  to  the  inch;  the  shaft  used 
was  of  steel  and  rather  hard,  the  set-screws  making  but  little  impression 
upon  it.  They  were  set  up  with  a  force  of  75  pounds  at  the  end  of  a 
ten-inch  monkey-wrench.  The  set-screws  used  were  of  four  kinds, 
marked  respectively  A,  B,  C,  and  D.  The  results  were  as  follows: 


A,  ends  perfectly  flat,  9/i6-in.  diam.        1412  to  2294  Ibs. 

B,  radius  of  rounded  ends  about  l/2-m.  2747  to  3079  Ibs. 

C,  radius  of  rounded  ends  about  l/4-in.   1902  to  3079  Ibs. 

D,  ends  cup-shaped  and  case-hardened  1962  to  2958  Ibs. 


average  2064. 

average  2912. 

average  2573. 

average  2470. 


REMARKS.  —  A.  The  set-screws  were  not  entirely  normal  to  the  shaft; 
hence  they  bore  less  in  the  earlier  trials,  before  they  had  become  flattened 
by  wear.  •— > 

B.  The  ends  of  these  set-screws,  after  the  first  two  trials,  were  found 
to  be  flattened,  the  flattened  area  having  a  diameter  of  about  1/4  inch. 


InB. 


DYNAMOMETERS.  1333 

The  ends  were  found,  after  the  first  two  trials,  to  be  flattened,  aa 


D.  The  first  test  held  well  because  the  edges  were  sharp,  then  the 
holding-power  fell  off  till  they  had  become  flattened  in  a  manner  similar 
to  B,  when  the  holding-power  increased  again. 

Tests  of  the  Holding-power  of  Keys.  (Lanza.)  —  The  load  was 
applied  as  in  the  tests  of  set-screws,  the  shaft  being  firmly  keyed  to  the 
holders.  The  load  required  at  the  rim  of  the  pulley  to  shear  the  keys 
was  determined,  and  this,  multiplied  by  a  suitable  constant,  determined 
in  a  similar  v/ay  to  that  used  in  the  case  of  set-screws,  gives  us  the  shear- 
ing strength  per  square  inch  of  the  keys. 

The  keys  tested  were  of  eight  kinds,  denoted,  respectively,  by  the 
letters  A,  B,  C,  D,  E,  F,  G  and  H,  arid  the  results  were  as  follows:  A,  B,  D, 
and  F,  each  4  tests;  E,  3  tests;  C,  G,  and  H,  each  2  tests. 

A,  Norway  iron,  2"  X  W  X  W32",  40,184  to  47,760  Ibs. ;  average,    42,726 

B,  refined  iron,  2"  X  1/4"  X  is/32",  36,482  to  39,254  Ibs. ;  average,    38,059 

C,  tool  steel,  1"  X  1/4"  X  15/32",  91,344  &  100,056  Ibs. ; 

D,  mach'y  steel,  2"  X  1/4"  X 15/32"  64,630  to  70,186  Ibs.;  average,     66,875 

E,  Norway  iron,  1 1/3"  X  W  X  7/io"  36,850  to  37,222  Ibs. ;  average,     37,036 

F,  cast-iron,  2"  X 1/4"  X 15/32",  30,278  to  36,944  Ibs.;  average,     33,034 

G,  cast-iron,  1 1/3"  X  3/8"  X  7/ie",  37,222  &  38,700. 
H,  cast-iron,  V  X 1/2"  X  7/i6",  29,814  &  38,978. 

The  first  dimension  is  the  length,  the  second  the  width  and  the  third 
the  height. 

In  A  ana  B  some  crushing  took  place  before  shearing.  In  E,  the 
keys,  being  only  7/iQ  inch  deep,  tipped  slightly  in  the  key-way.  In  H,  in 
the  first  test,  there  was  a  defect  in  the  key-way  of  the  pulley. 

DYNAMOMETERS. 

Dynamometers  are  instruments  used  for  measuring  power.  They  are 
of  several  classes,  as:  1.  Traction  dynamometers,  used  for  determining 
the  power  required  to  pull  a  car  or  other  vehicle,  or  a  plow  or  harrow. 
2.  Brake  or  absorption  dynamometers,  in  which  the  power  of  a  rotating 
shaft  or  wheel  is  absorbed  or  converted  into  heat  by  the  friction  of  a 
brake;  and  3.  Transmission  dynamometers,  in  which  the  power  in  a 
rotating  shaft  is  measured  during  its  transmission  through  a  belt  or  other 
connection  to  another  shaft,  without  being  absorbed. 

Traction  Dynamometers  generally  contain  two  principal  parts:  (1)  A 
spring  or  series  of  springs,  through  which  the  pull  is  exerted,  the  exten- 
sion of  the  spring  measuring  the 
amount  of  the  pulling  force;  and 
(2)  a  paper-covered  drum,  rota- 
ted either  at  a  uniform  speed  by 
clockwork,  or  at  a  speed  propor- 
tional to  the  speed  of  the  trac- 
tion, through  gearing,  on  which 
the  extension  of  the  spring  is  reg- 
istered by  a  pencil.  From  the 
average  height  of  the  diagram 
drawn  by  the  pencil  above  the 
FIG.  224.  zero-line  the  average  pulling 

force  in  pounds  is  obtained,  and 

this  multiplied  by  the  distance  traversed,  in  feet,  gives  the  work  done,  in 
foot-pounds.  The  product  divided  by  the  time  in  minutes  and  by  33,000 
gives  the  horse-power. 

The  Prony  brake  is  the  typical  form  of  absorption  dynamometer. 
(See  Fig.  224.  from  Flather  on  Dynamometers.) 

Primarily  this  consists  of  a  lever  connected  to  a  revolving  shaft  or  pul- 
ley in  such  a  manner  that  the  friction  induced  between  the  surfaces  in 
contact  will  tend  to  rotate  the  arm  in  the  direction  in  which  the  shaft 
revolves.  This  rotation  is  counterbalanced  by  weights  P,  hung  in  the 
scale-pan  at  the  end  of  the  lever.  In  order  to  measure  the  power  for  a 
given  number  of  revolutions  of  pulley,  we  add  weights  to  the  scale-pan 


1334  DYNAMOMETERS. 

and  screw  up  on  bolts  &,&,  until  the  friction  induced  balances  the  weights 
and  the  lever  is  maintained  in  its  horizontal  position  while  the  revolu- 
tions of  the  shaft  per  minute  remain  constant. 

For  small  powers  the  beam  is  generally  omitted  —  the  friction  being 
measured  by  weighting  a  band  or  strap  thrown  over  the  pulley.  Ropes 
or  cords  are  often  used  for  the  same  purpose. 

Instead  of  hanging  weights  in  a  scale-pan,  as  in  Fig.  224,  the  friction 
may  be  weighed  on  a  plat  form-scale;  in  this  case,  the  direction  of  rotation 
being  the  same,  the  lever-arm  will  be  on  the  opposite  side  of  the  shaft. 

In  a  modification  of  this  brake,  the  brake-wheel  is  keyed  to  the  shaft, 
and  its  rim  is  provided  with  inner  flanges  which  form  an  annular  trough 
for  the  retention  of  water  to  keep  the  pulley  from  heating.  A  small 
stream  of  water  constantly  discharges  into  the  trough  and  revolves  with 
the  pulley — the  centrifugal  force  of  the  particles  of  water  overcoming  the 
action  of  gravity ;  a  waste-pipe  with  its  end  flattened  is  so  placed  in  the 
trough  that  it  acts  as  a  scoop,  and  removes  all  surplus  water.  The  brake 
consists  of  a  flexible  strap  to  which  are  fitted  blocks  of  wood  forming  the 
rubbing-surface;  the  ends  of  the  strap  are  connected  by  an  adjustable 
bolt-clamp,  by  means  of  which  any  desired  tension  may  be  obtained. 

The  horse-power  or  work  of  the  shaft  is  determined  from  the  following : 

Let  W  =  work  of  shaft,  equals  power  absorbed,  per  minute; 

P    =  unbalanced  pressure  or  weight  in  pounds,  acting  on  lever- 
arm  at  distance  L ; 

L    «=  length  of  lever-arm  in  feet  from  center  of  shaft; 
V   a=  velocity  of  a  point  in  feet  per  minute  at  distance  L,  if  arm 

were  allowed  to  rotate  at  the  speed  of  the  shaft; 
N   =  number  of  revolutions  per  minute; 
H.P.  =  horse-power. 

Then  will  W  -  PV  =2  nLNP. 

Since  H.P.  =  PV  -*-  33,000,  we  have  H.P.  =  2  nLNP  •*•  33,000. 

If  L  =  33 -*•  2  it,  we  obtain  H.P.  =  NP  •*•  1000.  33 -J- 2  n  is  practically 
5  ft.  3  in.,  a  value  often  used  in  practice  for  the  length  of  arm. 

If  the  rubbing-surface  be  too  small,  the  resulting  friction  will  show 
great  irregularity  —  probably  on  account  of  insufficient  lubrication  — 
the  jaws  being  allowed  to  seize  the  pulley,  thus  producing  shocks  and 
sudden  vibrations  of  the  lever-arm. 

Soft  woods,  such  as  bass,  plane-tree,  beech,  poplar,  or  maple,  are  all 
to  be  preferred  to*  the  harder  woods  for  brake-blocks.  The  rubbing-sur- 
face should  be  well  lubricated  with  a  heavy  grease. 

The  Alden  Absorption-dynamometer.  (G.  I.  Alden,  Trans.  A.  S. 
M.  E.,  vol.  xi,  958;  also  xii,  700  and  xiii,  429.)  —  This  dynamometer  is  a 
friction-brake,  which  is  capable  in  quite  moderate  sizes  of  absorbing 
large  powers  with  unusual  steadiness  and  complete  regulation.  A 
smooth  cast-iron  disk  is  keyed  on  the  rotating  shaft.  This  is  inclosed 
in  a  cast-iron  shell,  formed  of  two  disks  and  a  ring  at  their  circumference, 
which  is  free  to  revolve  on  the  shaft.  To  the  interior  of  each  of  the  sides 
of  the  shell  is  fitted  a  copper  plate,  inclosing  between  itself  and  the  side  a 
water-tight  space.  Water  under  pressure  from  the  city  pipes  is  admitted 
into  each  of  these  spaces,  forcing  the  copper  plate  against'  the  central  disk. 
The  chamber  inclosing  the  disk  is  filled  with  oil.  To  the  outer  shell  is 
fixed  a  weighted  arm,  which  resists  the  tendency  of  the  shell  to  rotate 
with  the  shaft,  caused  by  the  friction  of  the  plates  against  the  central 
disk.  Four  brakes  of  this  type,  56  in.  diam.,  were  used  in  testing  the 
experimental  locomotive  at  Purdue  University  (Trans.  A.  S.  M.  E., 
xiii,  429).  Each  was  designed  for  a  maximum  moment  of  10,500  foot- 
pounds with  a  water-pressure  of  40  Ibs.  per  sq.  in.  The  area  in  effective 
contact  with  the  copper  plates  on  either  side  is  represented  by  an  annular 
surface  having  its  outer  radius  equal  to  28  ins.  and  its  inner  radius  equal 
to  10  ins.  The  apparent  coefficient  of  friction  between  the  plates  and  the 
disk  was  3V2%. 

Capacity  of  Friction-brakes.  —  W.  W.  Beaumont  (Proc.  Inst.  C.  E.. 
1889)  has  deduced  a  formula  by  means  of  which  the  relative  capacity  of 
brakes  can  be  compared,  judging  from  the  amount  of  horse-power  ascer- 
tained by  their  use. 

If  W  «  width  of  rubbing-surface  on  brake- wheel  in  inches;  V  •»  vel. 
of  point  on  Circqm,  of  wheel  in  feet  per  minute;  K  «  coefficient;  then 
K~  WV  -*-H.P. 


DYNAMOMETERS. 


1335 


Prof.  Flather  obtains  the  values  of  K  given  in  the  last  column  of  the 
subjoined  table: 


% 
Horse-power. 

R.P.M.  Brake- 
pulley. 

Brake- 
pulley. 

g 

*. 

££ 
o*S 
J.S 

Design  of  Brake. 

Value  of  K. 

•Sj 

®43 

8  o 

a  d 
b-t'~ 

Diameter, 
in  feet  . 

21 
19 

20 
40 
33 
130 
24 
180 
475 
125\ 
250| 
401 
125  f 

150 
148.5 
146 
180 
150 
150 
142 
100 
76.2 
290\ 
250  f 
322) 
290  f 

7 
7 
7 
10.5 
10.5 
10 
12 
24 
24 

24 
13 

5 

5 
5 
5 
5 
9 
6 
5 
7 

4 
4 

33 

33.38 
32.19 
32 
32 

'38.31 
126.1 
191 

63 
273/4 

Royal  Ag  Soc    compensating           

785 
858 
802 
741 
749 
282 
1385 
209 
847 

465 
847 

McLaren   compensating               

Garrett  water-cooled  and  comp  

Balk                                                        

Gatelv  &  Kletsch  water-cooled            

k           ' 

The  above  calculations  for  eleven  brakes  give  values  of  K  varying  from 
84.7  to  1385  for  actual  horse-powers  tested,  the  average  being  K  =  655. 

Instead  of  assuming  an  average  coefficient,  Prof.  Fiather  proposes  thq 
following: 

Water-cooled  brake,  non-compensating,  K  =  400;   W  =  400  H.P.  -*-  V. 

Water-cooled  brake,  compensating,  K  =  750;  F"  =  750  H.P.  -*•  V. 

Non-cooling  brake,  with  or  without  compensating  device,  /£  =  900:  W  = 
900  H.P.  +V. 

A  brake  described  in  Am.  Mach.,  July  27,  1905,  had  an  iron  water- 
cooled  drum,  30  in.  diam.,  20  in.  face,  with  brake  blocks  of  maple  attached 
to  an  iron  strap  nearly  surrounding  the  drum.  At  250  r.p.m.,  or  a  cir- 
cumferental  speed  of  1963  ft.  per  min.,  the  limit  of  its  capacity  was  about 
140  H.P.;  above  that  power  the  blocks  took  fire.  At  140  H.P.  the  total 
surface  passing  under  the  brake  blocks  per  minute  was  3272  sq.  ft.,  or 
23.37  per  H.P.  This  corresponds  to  a  value  of  K  =  285. 

Several  forms  of  Prony  brake,  including  rope  and  strap  brakes,  are 
described  by  G.  E.  Quick  in  Am.  Mach.,  Nov.  17,  1908.  Some  other 
forms  are  shown  in  Am.  Electrician,  Feb.,  1903. 

A  6000  H.P.  Hydraulic  Absorption  Dynamometer,  built  by  the  WTest- 
Inghouse  Machine  Co.,  is  described  by  E.  H.  Longwell  in  Eng.  News, 
Dec.  30,  1909.  It  was  designed  for  testing  the  efficiency  of  the  Melville 
and  Me  Alpine  turbine  reduction  gear  (see  page  1095).  This  dynamometer 
consists  of  a  rotor  mounted  on  a  shaft  coupled  to  the  reduction  gear  and 
rotating  within  a  closed  casing  which  is  prevented  from  turning  by  a 
6£  ft.  lever  arm,  the  end  of  which  transmits  pressure  through  an  I-beam 
lever  to  a  platform  scale.  The  rotor  carries  several  rows  of  steam  turbine 
vanes  and  the  casing  carries  corresponding  rows  of  stationary  vanes,  so 
arranged  as  to  baffle  and  agitate  the  water  passing  through  the  brake, 
which  is  heated  to  boiling  temperature  by  the  friction.  The  dynamom- 
eter was  run  for  40  hours  continuously,  and  proved  to  be  a  highly 
accurate  instrument. 

Transmission  Dynamometers  are  of  various  forms,  as  the  Batchelder 
dynamometer,  in  which  the  power  is  transmitted  through  a  "train-arm" 
of  bevel  gearing,  with  its  modifications,  as  the  one  described  by  the  author 
in  Trans.  A.  I.  M.  E.,  viii,  177,  and  the  one  described  by  Samuel  Webber 
in  Trans.  A.  S.  M.  E.,  x,  514;  belt  dynamometers,  as  the  Tatham;  the 
Van  Winkle  dynamometer,  in  which  the  power  is  transmitted  from  a 
revolving  shaft  to  another  in  line  with  it,  the  two  almost  touching, 
through  the  medium  of  coiled  springs  fastened  to  arms  or  disk  keyed  to 
the  shafts;  the  Brackett  and  the  Webb  cradle  dynamometers,  used  for 
measuring  the  power  required  to  run  dynamo-electric  machines.  De- 
scriptions of  the  four  last  named  are  given  in  Flather  on  Dynamometers, 

The  Kenerson  transmission  dynamometer  is  described  in  Trans.  A.  S. 
M.  E..  1909.  It  has  the  form  of  a  shaft  coupling,  one  part  of  which  con- 


1336     ICE-MAKING  OR  REFRIGERATING-MACHINES. 

tains  a  cavity  filled  with  oil  and  covered  by  a  flexible  copper  diaphragm. 

The  other  part,  by  means  of  bent  levers  and  a  thrust  ball-bearing,  brings 
an  axial  pressure  on  the  diaphragm  and  on  the  oil,  and  the  pressure  of  the 
oil  is  measured  by  a  gauge. 

Much  information  on  various  fprms  of  dynamometers  will  be  found  in 
Trans.  A.  S.  M.  E.,  vols.  vii  to  xv,  inclusive,  indexed  under  Dynamometers. 

ICE-MAKING-  OR  REFRIGERATING 
MACHINES. 

References. — An  elab9rate  discussion  of  the  thermodynamic  theory 
of  the  action  of  the  various  fluids  used  in  the  production  of  cold  was 
published  by  M.  Ledoiix  in  the  Annales  des  Mines,  and  translated  in  Van 
Nostrand's  Magazine  in  1879.  This  work,  revised  and  additions  made 
in  the  light  of  recent  experience  by  Professors  Den  ton,  Jacobus,  and 
Riesenberger,  was  reprinted  in  1892.  (Van  Nostrand's  Science  Series, 
No.  46.)  The  work  is  largely  mathematical,  but  it  also  contains  much 
information  of  immediate  practical  value,  from  which  some  of  the  mat- 
ter given  below  is  taken.  Other  references  are  Wood's  Thermody- 
namics, Chap.  V.  and  numerous  papers  by  Professors  Wood,  Denton, 
Jacobus,  and  Linde  in  Trans.  A.  S.  M.  E.,  vols.  x  to  xiv;  Johnson's 
Cyclopaedia,  article  on  Refrigerating-machines;  and  the  following  books: 
Siebel's  Compend  of  Mechanical  Refrigeration;  Modern  Refrigerating 
Machinery,  by  Lorenz,  translated  by  Pope;  Refrigerating  Machines,  by 
Gardner  T.  Voorhees;  Refrigeration,  by  J.  Wemyss  Anderson,  and  Re- 
frigeration, Cold  Storage  and  Ice-making,  by  A.  J.  Wallis-Taylor.  For 
properties  of  Ammonia  and  Sulphur  Dioxide,  see  papers  by  Professors 
Wood  and  Jacobus,  Trans.  A.  S.  M.  E.,  vols.  x  and  xii. 

For  illustrated  descriptions  of  refrigerating-machines,  see  catalogues  of 
builders,  as  Frick  &  Co.,  Waynesboro,  Pa.;  De  La  Vergne  Refrigerating- 
machine  Co.,  New  York;  Vilter  Mfg.  Co.,  Milwaukee;  York  Mfg.,  York,  Co., 
Pa.;  Henry  Vogt  Machine  Co.,  Louisville,  Ky.;  Carbondale  Machine  Co., 
Carbondale,  Pa.;  and  others.  See  also  articles  in  Ice  and  Refrigeration. 

Operations  of  a  Refrigerating-machine.  —  Apparatus  designed  for 
refrigerating  is  based  upon  the  following  series  of  operations: 

Compress  a  gas  or  vapor  by  means  of  some  external  force,  then  relieve 
it  of  its  heat  so  as  to  diminish  its  volume;  next,  cause  this  compressed  gas 
or  vapor  to  expand  so  as  to  produce  mechanical  work,  and  thus  lower 
its  temperature.  The  absorption  of  heat  at  this  stage  by  the  gas,  in 
resuming  its  original  condition,  constitutes  the  refrigerating  effect  of  the 
apparatus. 

A  refrigerating-machine  is  a  heat-engine  reversed. 

From  this  similarity  between  heat-motors  and  freezing-machines  it 
results  that  all  the  equations  deduced  from  the  mechanical  theory  of  heat 
to  determine  the  performance  of  the  first,  apply  equally  to  the  second. 

The  efficiency  depends  upon  the  difference  between  the  extremes  of 
temperature. 

The  useful  effect  of  a  refrigerating-machine  depends  upon  the  ratio 
between  the  heat-units  eliminated  and  the  work  expended  in  compressing 
and  expanding. 

This  result  is  independent  of  the  nature  of  the  body  employed. 

Unlike  the  heat-motors,  the  freezing-machine  possesses  the  greatest 
efficiency  when  the  range  of  temperature  is  small,  and  when  the  final 
temperature  is  elevated. 

If  the  temperatures  are  the  same,  there  is  no  theoretical  advantage  in 
employing  a  gas  rather  than  a  vapor  in  order  to  produce  cold. 

The  choice  of  the  intermediate  body  would  be  determined  by  practical 
considerations  based  on  the  physical  characteristics  of  the  body,  such  as 
the  greater  or  less  facility  for  manipulating  it,  the  extreme  pressures 
required  for  the  best  effects,  etc. 

Air  offers  the  double  advantage  that  it  is  everywhere  obtainable,  and 
that  we  can  vary  at  will  the  higher  pressures,  independent  of  the  tempera- 
ture of  the  refrigerant.  But  to  produce  a  given  useful  effect  the  apparatus 
must  be  of  larger  dimensions  than  that  required  by  liquefiable  vanors. 

The  maximum  pressure  is  determined  by  the  temperature  of  the  con- 
denser and  the  nature  of  the  volatile  liquid ;  this  pressure  is  often  high. 


BOILING  POINTS  OF  REFRIGERATING  LIQUIDS.      1337 


When  a  change  of  volume  of  a  saturated  vapor  is  made  under  constant 
pressure,  the  temperature  remains  constant.  The  addition  or  subtraction 
of  heat,  which  produces  the  change  of  volume,  is  represented  by  an 
increase  or  a  diminution  of  the  quantity  of  liquid  mixed  with  the  vapor. 

On  the  other  hand,  when  vapors,  even  if  saturated,  are  no  longer  in 
contact  with  their  liquids,  and  receive  an  addition  of  heat  either  through 
compression  by  a  mechanical  force,  or  from  some  external  source  of  heat, 
they  comport  themselves  nearly  in  the  same  way  as  permanent  gases, 
and  become  superheated. 

It  results  from  this  property,  that  refrigerating-machmes  using  a 
liquefiable  gas  will  afford  results  differing  according  to  the  method  of 
working,  and  depending  upon  the  state  of  the  gas,  whether  it  remains 
constantly  saturated,  or  is  supejrheated  during  a  part  of  the  cycle  of 
working. 

The  temperature  of  the  condenser  is  determined  by  local  conditions. 
The  interior  will  exceed  by  9°  to  18°  the  temperature  of  the  water  fur- 
nished to  the  exterior.  This  latter  will  vary  from  about  52°  F.,  the 
temperatiye  of  water  from  considerable  depth  below  the  surface,  to 
about  95°  F.,  the  temperature  of  surface-water  in  hot  climates.  The 
volatile  liquid  employed  in  the  machine  ought  not  at  this  temperature  to 
have  a  tension  above  that  which  can  be  readily  managed  by  the  apparatus. 

On  the  other  hand,  if  the  tension  of  the  gas  at  the  minimum  temperature 
is  too  low,  it  becomes  necessary  to  give  to  the  compression-cylinder 
large  dimensions,  in  order  that  the  weight  of  vapor  compressed  by  a 
single  stroke  of  the  piston  shall  be  sufficient  t<j  produce  a  notably  useful 
effect. 

These  two  conditions,  to  which  may  be  added  others,  such  as  those 
depending  upon  the  greater  or  less  facility  of  obtaining  the  liquid,  upon 
the  dangers  incurred  in  its  use,  either  from  its  inflammability  or  unhealth- 
fulness,  and  finally  upon  its  action  upon  the  metals,  limit  the  choice  to  a 
small  number  of  substances. 

The  gases  or  vapors  generally  available  are:  sulphuric  ether,  sulphurous 
oxide,  ammonia,  methylic  ether,  and  carbonic  acid. 

The  following  table,  derived,  from  Regnault,  shows  the  tensions  of  the 
vapors  of  these  substances  at  temperatures  between  —  22°  and  4- 104°. 

Pressures  and  Boiling-points  of  Liquids  available  for  Use 
in  Refrigerating-machines. 


Temp. 

of 
Ebulli- 

Tension of  Vapor,  in  Ibs.  per  sq.  in.,  above  Zero. 

tion. 

Deg. 

Fahr. 

Sul- 
phuric 
Ether. 

Sulphur 
Dioxide. 

Ammonia. 

ro•.)y  —  — 

Methylic 
Ether. 

Carbonic 
•Acid. 

Pictet 
Fluid. 

Ethyl 
Chlonde 

-31 

13.23 

-22 

5.56 

16.95 

11   15 

2  13 

—  13 

7  23 

21  51 

13  85 

251  6 

20ft 

-  4 

1.30 

9.27 

27.04 

17.06 

292.9 

""\3.5" 

3.63 

5 

1.70 

11.76 

33.67 

20.84 

340.1 

16.2 

4.63 

14 

2.19 

14.75 

41.58 

25.27 

393.4 

19.3 

5.84 

23 

2.79 

18.31 

50.91 

30.41 

453.4 

22.9 

7  28 

32 

3.55 

22.53 

61.85 

36.34 

520.4 

26.9 

9  00 

41 

4.45 

27.48 

74.55. 

43.13 

594.8 

31.2 

11  01 

50 

5.54 

33.26 

89.21 

50.84 

676.9 

36.2 

13  36 

59 

6.84 

39.93 

105.99 

59.56 

766.9 

41.7 

16  10 

68 

8.38 

47.62 

125.08 

69.35 

864.9 

48.1 

19  26 

77 

10.19 

56.39 

146.64 

80.28 

971.1 

55.6 

22  90 

86 

12.31 

66.37 

170.83 

92.41 

1085.6 

64.1 

27  05 

95 

14.76 

77.64 

197.83 

1207.9 

73  2 

31  78 

104 

17.59 

90.32 

227  76 

1338.2 

82  9 

37  12 

The  table  shows  that  the  use  of  ether  does  not  readily  lead  to  the 
production  of  low  temperatures,  because  its  pressure  becomes  then  very 
feeble.  Ammonia,  on  the  contrary,  is  well  adapted  to  the  production 
of  low  temperatures. 


1338      ICE-MAKING   OR  REFRIGERATING-MACHINES. 


i  Methylic  ether  yields  low  temperatures  without  attaining  too  great 
pressures  at  the  temperature  of  the  condenser.  Sulphur  dioxide  readily 
affords  temperatures  of  —  14  to  —  5,  while  its  pressure  is  only  3  to  4 
atmospheres  at  the  ordinary  temperature  of  the  condenser.  These  latter 
substances  then  lend  themselves  conveniently  for  the  production  of  cold 
by  means  of  mechanical  force. 

The  "  Pictet  fluid  "  is  a  mixture  of  97%  sulphur  dioxide  and  3%  carbonic 
acid.  At  atmospheric  pressure  it  affords  a  temperature  14°  low'er  than 
sulphur  dioxide.  (It  is  not  now  used  —  1910.) 

Carbonic  acid  is  in  use  to  a  limited  extent,  but  the  relatively  greater 
compactness  of  compressor  that  it  requires,  and  its  inoffensive  character, 
are  leading  to  its  recommendation  for  service  on  shipboard. 

Certain  ammonia  plants  are  operated  with  a  surplus  of  liquid  present 
during  compression,  so  that  superheating  is  prevented.  This  practice  is 
known  as  the  "cold  "  or  "  wet  "  system  of  compression. 

Ethyl  chloride,  CoHsCl,  is  a  colorless  gas  which  at  atmospheric  pressure 
condenses  to  a  liquid  at  54.5°  F.  The  latent  heat  at  23°  F.  is  given  at  174 
B.T.U.  Density  of  the  gas  (air  =  l)  =  2.227.  Specific  heat  at  constant 
pressure.  0.274;  at  constant  volume,  0.243. 

Nothing  definite  is  known  regarding  the  application  of  methylic  ether  or 
of  the  petroleum  product  chymogene  in  practical  refrigerating  service. 
The  inflammability  of  the  latter  and  the  cumbrousness  of  the  compressor 
required  are  objections  to  its  use. 

PROPERTIED  OF  SULPHUR  DIOXIDE  AND 
AMMONIA    GAS. 

Ledoux's  Table  for  Saturated  Sulphur-dioxide  Gas. 

Heat-units  expressed  in  B.T.U.  per  pound  of  sulphur  dioxide. 


£.1 

2--  • 

O»J3  bi)"*0 
|«.§ 

ffU 

Absolute  Pres- 
sure in  Ibs.  per 
sq.  in. 

P  •*-  144 

Total  Heat 
reckoned  from 
32°  F. 
A. 

Heat  of  Liquid 
reckoned  from 
32°  F. 
Q 

Latent  Heat  of 
Evaporation. 
r 

Heat  Equivalent 
of  External 
Work. 
APu 

Internal  La- 
tent Heat. 
P 

Increase  of 
Volume  dur- 
ing Evapo-  ; 
ration. 
U 

Density  of  Va- 
por or  Weight 
of  1  cu.  ft. 

1  -5-  V 

Des.  F. 

Lb. 

B.T.U, 

B.T.U. 

B.T.U. 

B.T.U. 

B.T.U. 

Cu.ft. 

Lb. 

-22 

5.56 

157.43 

-19.56 

176.99 

13.59 

163.39 

13.17 

0.076 

-13 

7.23 

158.64 

-  16.30 

174.95 

13.83 

161.12 

10.27 

.097 

-  4 

9.27 

159.84 

-  13.05 

172.89 

14.05 

158.84 

8.12 

.123 

5 

11.76 

161.03 

-    9,79 

170.82 

14.26 

156.56 

6.50 

.153 

14 

14.74 

162.20 

-   6.53 

168.73 

14.46 

154.27 

5.25 

.190 

23 

18.31 

163.36 

-   3.27 

166.63 

14.66 

151.97 

4.29 

.232 

32 

22.53 

164.51 

0.00 

164.51 

14.84 

149.68 

3.54 

.282 

41 

27.48 

165.65 

3.27 

162.38 

15.01 

147.37 

2.93 

.340 

50 

33.25 

166.78 

6.55 

160.23 

15.17 

145.06 

2.45 

.407 

59 

39.93 

167.90 

9.83 

158.07 

15.32 

142.75 

2.07 

.483 

68 

47.61 

168.99 

13.11 

155.89 

15.46 

140.43 

1.75 

.570 

77 

56.39 

170.09 

16.39 

153.70 

15.59 

138.11 

1.49 

.669 

86 

66.36 

171.17 

19.69 

151.49 

15.71 

135.78 

1.27 

.780 

95 

77.64 

172.24 

22.98 

149.26 

.  15.82 

133.45 

1.09 

.906 

104 

90.31 

173.30 

26.28 

147.02 

15.91 

131.11 

0.91 

1.046 

E.  F.  Miller  (Trans.  A.  S.  M.  E.,  1903)  reports  a  series  of  tests  on  the 
pressure  of  SO2  at  various  temperatures,  the  results  agreeing  closely  with 
those  of  Regnault  up  to  the  highest  figure  of  the  latter,  149°  F.,  178  Ibs. 
absolute.  He  gives  a  table  of  pressures  and  temperatures  for  every 
degree  between  —  40°  and  217°.  The  results  obtained  at  temperatures 
between  113°  and  212°  are  as  below: 
Temp.  °F. 

113      122      131      140      149      158      167      176      194      203      212 
Pres.  Ibs.  per  sq.  in. 

104,4  120,1  137,5  150.7  179.5  203.8  230.7  260.5  331.1  371.8  418, 


PROPERTIES   OP   AMMONIA. 


1339 


Properties  of  Ammonia. — For  a  discussion  of  the  properties  of  am- 
monia and  a  bibliography  of  investigations  of  ammonia,  see  Bulletin  66 
of  the  University  of  Illinois  Experiment  Station.  See  also  "Properties 
of  Steam  and  Ammonia,"  by  G.  A.  Goodenough  (John  Wiley  &  Sons, 
1915).  Prof.  Goodenough  says  that  experiments  on  the  properties  of 
ammonia  are  by  no  means  as  complete  or  as  concordant  as  the  experi- 
ments on  water  vapor;  hence  any  formulation  for  ammonia  must  be 
regarded  as  tentative  and  subject  to  revision  as  further  experimental 
evidence  becomes  available. 


Properties  of  Saturated  Ammonia. 

(From  Goodenough 's  Tables.) 


Absolute 
Pressure,  Lb. 
per  Sq.  In. 

Temperature, 
Deg.  F. 

3,a 
OH} 
»fe 

gft 
£^ 
>* 

& 

JJ  3 

£u 

M^ 

V  « 

£a 

Total  Heat 
B.T.tf. 

Latent  Heat 
B.T.U. 

Entropy. 

T3 

s;§ 

J 

*£ 

°l 

O  o/+3 
a  oj 
>.S 

Si 
£* 

-a 

8| 
a 

sti 

1 

-103.7 

225.0 

0.0044 

644.6 

603.0 

.8107 

5 

-  62.0 

49.3 

0.0203 

-98.1 

519.1 

617.2 

571.5 

-0.2207 

.5523 

10 

-  40.4 

25.75 

0.0388 

-75.7 

526.4 

602.2 

554.6 

-0.1661 

.4363 

15 

-26.4 

17.60 

0.0568 

-61.2 

530.9 

592.1 

543.3 

-0.1324 

.3669 

20 

-   15.9 

13.45 

0.0744 

-50.3 

534.0 

584.3 

534.7 

-0.1075 

.3168 

25 

-    7.2 

10.88 

0.0919 

-41.3 

536.5 

577.8 

527.4 

-0.0876 

.2771 

30 

+    0.1 

9.17 

0.1090 

-33.6 

538.5 

572.1 

521.3 

-0.0708 

.2447 

35 

6.5 

7.93 

0.  1  260 

-26.9 

540.3 

567.1 

515.8 

-0.0561 

.2167 

40 

12.2 

6.99 

0.1430 

-20.8 

541.8 

562.6 

511.0 

-0.0433 

.1924 

45 

17.4 

6.25 

0.1598 

-15.3 

543.! 

558.4 

506.4 

-0.0319 

.1707 

50 

22.1 

5.66 

0.1765 

-10.3 

544.3 

554.6 

502.3 

-0.0216 

.1512 

55 

26.4 

5.18 

0.1931 

-  5.7 

545.3 

551.1 

498.6 

-0.0122 

.1338 

60 

30.5 

4.77 

0.2096 

1  3 

546.3 

547.7 

495.0 

-0.0033 

.1175 

65 

34.3 

4.42 

0.2261 

+  2.7 

547.2 

544.5 

491.6 

+0.0051 

.1023 

70 

37.9 

4.12 

0.2425 

6.6 

548.1 

541.4 

488.4 

0.0128 

.0883 

75 

41.3 

3.86 

0.2589 

10.3 

548.8 

538.5 

485.3 

0.0201 

.0751 

80 

44.5 

3.63 

0.2753 

13.8 

549.5 

535.8 

482.3 

0.0271 

.0627 

85 

47.6 

3.43 

0.2917 

17.2 

550.2 

533.1 

479.5 

0.0336 

.0511 

90 

50.5 

3.25 

0.3081 

20.4 

550.9 

530.5 

476.8 

0.0398 

.0400 

95 

53.3 

3.08 

0.3246 

23.5 

551.5 

528.0 

474.3 

0.0458 

.0295 

100 

56.0 

2.93 

0.3409 

26.5 

552.1 

525.6 

471.8 

0.0516 

.0195 

110 

61.1 

2.678 

0.3735 

32.1 

553.1 

521.0 

467.0 

0.0625 

.0006 

120 

65.8 

2.466 

0.4056 

37.4 

554.1 

516.7 

462.5 

0.0725 

0.9834 

130 

70.4 

2.283 

0.4381 

42.5 

555.0 

512.5 

458.2 

0.0820 

0.9672 

140 

74.5 

2.124 

0.4707 

47.3 

555.9 

508.6 

454.2 

0.0910 

0.9521 

150 

78.5 

.989 

0.5028 

51.8 

556.7 

504.8 

450.3 

0.0993 

0.9382 

160 

82.3 

.868 

0.5353 

56.2 

557.4 

501.1 

446.6 

0.1074 

0.9249 

170 

85.9 

.763 

0.5673 

60.5 

558.1 

497.6 

443.0 

0.1152 

0.9121 

180 

89.4 

.666 

0.6000 

64.6 

558.8 

494.1 

439.5 

0.1226 

0.9001 

190 

92.7 

.580 

0.6330 

68.6 

559.4 

490.9 

436.2 

0.1296 

0.8887 

200 

95.9 

.504 

0.665 

72.3 

560.0 

487.6 

433.0 

0.1363 

0.8779 

220 

101.8 

.370 

0.730 

79.5 

561.0 

481.5 

426.8 

0.1488 

0.8578 

240 

107.4 

.258 

0.795 

86.4 

562.0 

475.6 

421.0 

0.1609 

0.8389 

260 

112.7 

.161 

0.861 

93.0 

562.9 

470.0 

415.4 

0.1722 

0.8213 

280 

117.6 

.079 

0.927 

99.2 

563.8 

464.6 

410.2 

0.1829 

0.8048 

300 

122.4 

.007 

0.993 

105.3 

564.6 

459.3 

405.0 

0.1932 

0.7893 

350 

133.2 

0.863 

.159 

119.6 

566.4 

446.8 

392.8 

0.2171 

0.7538 

400 

142.9 

0.752 

.330 

132.9 

567.9 

435.0 

381.5 

0.2390 

0.7220 

450 

151.8 

0.665 

.504 

145.6 

569.3 

423.8 

370.8 

0.2593 

0.6931 

500 

160.0 

0.597 

.675 

157.5 

570.5 

413.0 

360.5 

0.2786 

0.6664 

550 

167.6 

0.539 

.855 

169.2 

571.7 

402.5 

350.8 

0.2965 

0.6419 

600 

174.7 

0.491 

2.038 

180.4 

572.7 

392.3 

341.3 

0.3138 

0.6186 

650 

181.4 

0.449 

2.227 

191.4 

573.6 

382.2 

332.0 

0.3307 

0.5963 

700 

187.7 

0.414 

2.416 

202.1 

574.4 

372.2 

322.8 

0.3469 

0.5758 

761.4 

195.0 

0.376 

2.660 

215.2 

575.4 

360.2 

311.8 

0.3664 

0.5503 

1340        ICE-MAKING   OR  REFRIGERATING-MACHINES. 


f  =  volume, 
Pressure  in 


Properties  of  Superheated  Ammonia. 

(From  Goodenough's  Tables.) 

cu.  ft.  per  lb.,  n  =  entropy,  h  =  total  heat,  B.T.U.  per  Ib. 
lb.  per  sq.  in. ;  temperatures  in  deg.  F. 


Pressure,                15 
Temp.         (-26.4°  P.) 

20 
(-15.9°) 

25 

(-7.2°) 

30 

(+0.1°) 

Sat. 
25° 
50 
100 
150 
200 
240 

V 

17.6 
18.9 
21.1 
23.3 
25.5 
27.7 
29.3 

n 
.234 
.267 
.320 
.367 
.410 
.449 
.479 

h 
530.9 
545.2 
571.1 
596.4 
621.4 
646.5 
666.9 

V 

13.4 
14.0 
15.8 
17.5 
19.1 
21.4 
22.0 

n 
1.209 
1.229 
1.284 
1.332 
1.376 
1.431 
1.446 

h 
534.0 
542.9 
569.8 
595.5 
620.8 
656.2 
666.4 

V 

10.9 
11.1 
12.6 
13.9 
15.2 
16.5 
17.6 

n 
1.190 
1.199 
1.256 
1.305 
1.349 
1.389 
1.419 

h 

536.5 
540.8 
568.4 
594.5 
620.1 
645.6 
666.0 

V 

9.17 

id.4i 

11.55 
12.65 
13.74 
14.59 

n 
1.174 

Y.233 
1.283 
1.327 
1.367 
1.398 

h 
538.5 

56  7.  i 
593.7 
619.5 
645.2 
665.7 

Pressure,               40 
Temp.              (  2.2°) 

50' 

(22.1°) 

60 

(30.5°) 

70 

(37.9°) 

Sat. 
50 
100 
150 
200 
300 

6.99 
7.72 
8.59 
9.44 
10.26 

.149 
.195 
.247 
.292 
.333 

541.8 
564.3 
591.8 
618.2 
644.3 

5.67 
6.11 

6.83 
7.51 
8.17 
9.47 

1.130 
1.165 
1.218 
1.264 
1.306 
1.380 

544.3 
561.5 
590.0 
617.0 
643.3 
695.7 

4.77 
5.03 
5.65 
6.22 
6.79 
7.87 

1.114 
1.139 
1.194 
1.242 
1.283 
1.358 

546.3 
558.8 
588.2 
615.8 
642.4 
695.1 

4.12 
4.27 
4.81 
5.31 
5.80 
6.73 

1.101 
1.117 
1.174 
1.222 
1.265 
1.339 

548.1 
556.0 
586.5 
614.6 
641.5 
694.6 

Pressure,               80 
Temp.              (44.5°) 

90 

(50.5°) 

100 
(56.0°) 

120 

(65.8°) 

Sat. 
100 
150 
200 
300 
340 

3.63 
4.18 
4.62 
5.04 
5.87 

.090 
.156 
.205 
.248 
.323 

549.5 
584.7 
613.4 
640.6 
694.1 

3.25 
3.69 
4.09 
4.47 
5.21 
5.50 

1.080 
1.140 
1.190 
1.233 
.1.309 
1.337 

550.9 
582.9 
612.1 
639.8 
693.5 
714.9 

2.94 
3.29 
3.66 
4.01 
4.67 
4.93 

1.071 
1.125 
1.176 
1.220 
1.297 
1.324 

552.1 
581.1 
610.8 
638.9 
693.0 
714.6 

2.47 
2.71 
3.02 
3.31 
3.87 
4.09 

1.056 
1.099 
1.152 
1.197 
1.275 
1.302 

554.1 
577.5 
608.4 
637.1 
692.1 
713.9 

Pressure,              140 
Temp.               (74.5°) 

160 

(82.3°) 

200 
(95.9°) 

240 
(107.4°) 

Sat. 
100 
150 
200 
300 
360 

2.12 
2.29 
2.56 
2.82 
3.30 
3.58 

1.043 
.076 
.131 
.177 
.256 
.297 

555.9 
573.9 
605.9 
635.3 
691.1 
723.9 

1.87 
1.97 
2.22 
2.44 
2.66 
3.12 

1.032 
1.056 
1.112 
1.160 
1.202 
1.281 

557.4 
570.3 
603.5 
633.6 
662.1 
722.9 

1.50 
1.52 
1.73 
1.92 
2.27 
2.47 

1.014 
1.020 
1.080 
1.130 
1.212 
1.254 

560-0 
563.1 
598.4 
630.0 
687.7 
721.0 

1.26 

1.42 
1.57 
1.87 
2.04 

1.000 

Y.053 
1.105 
1.189 
1.232 

562.0 

593.5 
626.4 
685.6 
719.3 

Thermal  Properties  of  Liquid  Ammonia. 

(From  Goodenough's  Tables.) 


Satu- 

Satu- 

ration 

Vol. 

Weight 

ration 

Vol. 

Weight 

Temp. 

Pres- 

of 

of 

144  X 

Temp. 

Pres- 

of 

of 

144  X 

Deg.F. 

sure, 

1  Lb., 

1  Cu. 

Apv. 

°F. 

sure, 

1  Lb., 

1  Cu. 

Apv. 

Lb.per 

Cu.  Ft. 

Ft.,  Lb. 

Lb.per 

Cu.  Ft. 

Ft.,  Lb. 

Sq.  In. 

Sq.  In. 

-110 

0.758 

0.02202 

45.42 

0.003 

60 

107.7 

0.02609 

38.33 

0.520 

-100 

1.176 

.02220 

45.04 

.005 

70 

129.2 

.02643 

37.85 

.632 

-  80 

2.626 

.02258 

44.28 

.011 

80 

153.9 

.02678 

37.35 

.76 

-  60 

5.358 

.02299 

43.51 

.023 

90 

181.8 

.02714 

36.84 

.92 

-  40 

10.12 

.02342 

42.71 

.044 

100 

213.8 

.02754 

36.32 

1.09 

-  20 

17.91 

.02388 

41.88 

.079 

120 

289.9 

.02839 

35.23 

1.52 

0 

29.95 

.02437 

41.04 

.135 

140 

384.4 

.02936 

34.06 

2.09 

10 

38.02 

.02463 

40.61 

.173 

160 

500.1 

.0305 

32.80 

2.82 

20 

47.75 

.02490 

40.17 

.220 

180 

639.5 

.0318 

31.5 

3.77 

30 

59.35 

.02518 

39.72 

.247 

200 

805.6 

.0335 

29.9 

4.99 

40 

73.03 

.02547 

39.27 

.344 

250 

1357.4 

.0404 

24.8 

10.2 

50 

89.1 

.02577 

38.81 

.425 

273.2 

1690.0 

.0678 

14.75 

21.2 

A  =  reciprocal  of  Joule's  equivalent  = 
sq.  in.;  v  — •  vol.  of  1  lb.,  cu  ft. 


1/777.6;  p  =  pressure,  lb.  per 


PROPERTIES   OF  AMMONIA. 


1341 


Solubility  of  Ammonia.  (Siebel.) — One  pound  of  water  will  dis- 
solve the  following  weights  of  ammonia  at  the  pressures  and  tempera- 
tures F°  stated.  4 


Abs. 
Press, 
per 
sq.m. 

32° 

68° 

104° 

Abs. 
Press, 
per 
sq.m. 

32° 

68° 

104° 

Abs. 
Press, 
per 
sq.  in. 

32° 

68° 

104° 

0.486 
0.493 
0.511 
0.530 
0.547 
0.565 
0.579 

Ib. 
14.67 
15.44 
16.41 
17.37 
18.34 
19.30 
20.27 

Ib. 
0.899 
0.937 
0.980 
1.029 
1.077 
1.126 
1.177 

Ib. 
0.518 
0.535 
0.556 
0.574 
0.594 
0.613 
0.632 

Ib. 
0.338 
0.349 
0.363 
0.378 
0.391 
0.404 
0.414 

Ib. 
21.23 
22.19 
23.16 
24.13 
25.09 
26.06 
27.02 

Ib. 
.236 
.283 
.330 
.385 
.442 
.496 
.549 

Ib. 
0.651 
0.669 
0.685 
0.704 
0.722 
0.741 
0.761 

Ib. 
0.425 
0.434 
0.445 
0.454 
0.463 
0.472 
0.479 

Ib. 
27.99 
28.95 
30.88 
32.81 
34.74 
36.67 
38.60 

Ib. 
.603 
.656 
.758 
.861 
.966 
2.070 

Ib. 
0.780 
0.801 
0.842 
0.881 
0.919 
0.955 
0.992 

Strength  of  Aqua  Ammonia  at  60°  F. 

%NHabywt.      24          6          8           10        12        14        16        18 
Sp.  gr.                 0.986     .979     .972     .966     .960     .953     .945     .938     .931 
%  NHs                  20        22         24         26         28         30        32         34        36 
Sp.  gr.                 0.925     .919     .913     .907     .902     .897     .892     .888     .884 
Properties  of  Saturated  Vapors.  —  The  figures  in  the  following  table 
are  given  by  Lorenz,  on  the  authority  of  M  oilier  and  of  Zeuner. 

., 

Heat  of 
Vaporization, 
B.T.U.  per  Ib. 

Heat  of  Liquid, 
B.T.U.  per  Ib. 

Absolute 
Pressure, 
Ibs.  per  sq.  in. 

Volume  of 
lib., 
cubic  feet. 

NH3 

C02 

SO2 

NH3 

CO2 

S02 

NH3 

CO2    SO2 

NH3 

CO2 

S02 
8  06 

-  4° 
+  14° 
32° 
50° 
68° 
86° 
104° 

589  0 

117  6 

171.0 

-31.21 

-17.19 

-11.16 

27.1 

288.7    9.27 

10  33 

0  31? 

580  0 

110  7 

168  2 

-15  89 

-  9  00 

-  5.69 

41.5 

385  4  14  75 

6  92 

0  229 

5  ?7 

569.0 
555  5 

99.8 
86  0 

164.2 
158  9 

0 
16  51 

0 

10  28 

0 
5  90 

61.9 
89  1 

503.5  22.53 
650  1  33  26 

4.77 
3  38 

0.167 
0  120 

3.59 

?  44 

539.9 
521.4 
500.4 

66.5 
27.1 

152.5 
144.8 
135.9 

33.58 
51.28 
69.58 

23.08 
45.45 

12.03 
18.34 

24.88 

125.0 
170.8 
227.7 

826.447.61 
040.    66.36 
90.30 

2.47 
1.83 
1.39 

0.083 
0.048 

1.71 
1.22 
0  88 

The  figures  for  CO2  in  the  above  table  differ  widely  from  those  of 
Regnault,.and  are  no  doubt  more  reliable. 

Heat  Generated  by  Absorption  of  Ammonia.  (Berthelot,  from 
Siebel.)  —  Heat  developed  when  a  solution  of  1  Ib.  NH3  in  n  Ibs.  watei 
is  diluted  with  a  great  amount  of  water  =  Q  =  142/n  B.T.U.  Assuming 
925  B.T.U.  to  be  developed  when  1  Ib.  NH3  is  absorbed  by  a  great  deal 
(say  200  Ibs.)  of  water,  the  heat  developed  in  making  solutions  of  different 
strengths  (1  Ib.  NH3  to  n  Ibs.  water)  =  Qt=  925  —  142/n  B.T  U  Heat 
developed  when  b  Ibs.  NH3  is  added  to  a  solution  of  1  Ib.  NH3  +  n  Ibs 
water  =  Q3=  925&-  142  (26+  W)/n  B.T.U. 

Let  the  weak  liquor  enter  the  absorber  with  a  strength  of  10  %  =  1  Ib 
NH3  +  9  Ibs.  water,  and  the  strong  liquor  leave  the  absorber  with  a 
strength  of  25%,  =  3  Ibs.  NH3  +  9  Ibs.  water,  b  =  2,  n  =  9-  Q3  =  925  X 
2  -  142  (4  +  4)/9  =  1724  B.T.U.  Hence  by  dissolving  2  Ibs.  of  ammonia 
gas  or  vapor  in  a  solution  of  1  Ib.  ammonia  in  9  Ibs.  water  we  obtain 
12  Ibs.  of  a  25%  solution,  and  the  heat  generated  is  1724  B.T.U. 

Cooling  Effect,  Compressor  Volume,  and  Power  Required.  —  The 
following  table  gives  the  theoretical  results  computed  on  the  basis  of 
a  temperature  in  the  evaporator  of  14°  F.  and  in  the  condenser  of  68°  F  • 
in  the  first  three  columns  of  figures  the  cooling  agent  is  supposed  to  flow 
through  the  regulating  valve  with  this  latter  temperature;  in  the  last 
three  it  is  previously  cooled  to  50°  F. 

From  the  stroke-volume  per  100,000  B.T.U.  the  minimum  theoretical 
horse-power  is  obtained  as  follows:  Adiabatic  compression  is  assumed 
for  the  ratio  of  the  absolute  condenser  pressure  to  that  of  the  vaporizer 
and  the  mean  pressure  through  the  stroke  thus  found,  in  Ibs  per  sq  ft  • 
multiplying  this  by  the  stroke  volume  per  hour  and  dividing  by  1  980  000 
gives  the  net  horse-power.  The  ratio  of  the  mean  effective  pressure 
M.P.,  to  the  vaporizer  pressure,  V.P.,  for  different  ratios  of  condenser 
pressure,  C.P.,  to  vaporizer  pressure  is  given  on  the  next  page. 


1342       ICE-MAKING   OK  REFRIGERATING-MACHINES. 

Cooling  Effect,  Compressor  Volume,  and  Power  Required,  with 
_      Different  Cooling  Agents.     (Lorenz.) ___ 


Cooling  Agent. 

NH3 

CO2 

S02 

NH3 

C02 

SO2 

1.  Temp,  in  front  of  regulating 
valve  . 

68 

68 

68 

50 

50 

50 

2.  Vaporizer  pressure,  Ibs.  per 
sq.  in  

41  5 

385  4 

14  75 

41  5 

385  4 

14  75 

3.  Condenser  pressure,  Ibs.  per 
sq.  in  

125  0 

826  4 

47  61 

125  0 

826  4 

47  61 

4.  Heat  of  evaporation,  B.T.U. 
per  Ib  

580  2 

110  7 

168  2 

580  2 

110  7 

168  2 

5.  Heat  imparted  to  the  liquid 
6.  Cold  produced  per  Ib.  B.T.U 
7.  Cooling  agent  circulated  for 
yield  of  100,000  B.T.U.  per 
hour,  Ibs    .... 

49.47 
530.73 

188  4 

32.08 
78.62 

1272 

17.72 
150.48 

664  3 

32^4 
547.8- 

182  5 

19.28 
91.42 

1094 

11.59 
156.61 

638  5 

8.  Stroke  volume  for   100,666 
B.T.U.  per  hour,  cu.  ft  
9.  Minimum  H.P.  per  100,000 
B.T.U.  per  hour 

1,300 
4  98 

292 
4  98 

3,507 
4  98 

1,264 
4  98 

242 
4  98 

3,365 
4  98 

10.  Ratio  Heat  of  evap.  -*•  .cold 
produced  .  . 

1  093 

1  408 

1  118 

1  059 

1  211 

1  074 

1  1  .  Ratio  total  work  to  minimum 
12.  Total    I.H.P.    per    100,000 
B.T.U.  per  hour 

1.175 
5  85 

1.513 
7  53 

1.202 
5  99 

1.133 
5  67 

1.302 
6  48 

1.155 
5  75 

13.  Cooling  effect  per  I.H.P.  hr.. 

17,100 

13,300 

16.700 

17,600 

15,400 

17.400 

RATIOS  OP  CONDENSER  PRESSURE,  C.  P.,  AND  ME  AN  ^EFFECTIVE 
SURE,  M.  P.,  TO  VAPORIZER  PRESSURE,  V.  P. 


PRES- 


PH 

fc 

PH 

PH 

PH 

PH 

PH 

& 

PH 

PH 

PH 
>• 

PH 

•1- 

f 

•1- 

* 

•1- 

•!• 

* 

* 

•1- 

4 

•1- 

•1- 

6 

PH 

a 

g 

PH 

a 

| 

PH 

a 

PH 
O 

PH 
% 

PH 
O 

PH 
S 

S 

PH 
% 

1.0 

0. 

2.0 

0.752 

3.0 

.249 

4.0 

.684 

5.0 

1.947 

6.0 

2.216 

1.2 

0.186 

2.2 

0.865 

3.2 

.344 

4.2 

.711 

5.2 

2.006 

7.0 

2.454 

1.4 

0.350 

2,4 

0.970 

3,4 

.414 

4,4 

.766 

5.4 

2.062 

8.0 

2.666 

1  6 

0.487 

2  6 

1  070 

3  6 

491 

4  6 

829 

5  6 

2.116 

9  0 

2  858 

1.8 

0.630 

2.8 

1.163 

3.8 

.564 

4.8 

.891 

5.8 

2.168 

10  0 

3.036 

The  minimum  theoretical  horse-power  thus  obtained  is  increased  by 
the  ratio  of  the  heat  of  evaporation  to  the  available  cooling  action  (line 
4  -*-  line  6,  =  line  10  of  the  table)  and  by  an  allowance  for  the  resistance 
of  the  valves  taken  at  7.5%  to  obtain  the  total  H.P.  given  in  the  table. 

To  the  theoretical  horse-power  given  in  line  12  Lorenz  makes  numerous 
additions,  viz.:  friction  of  the  compression  and  driving  machine  0.90, 
1.10,  0.90,  0.85,  0.95,  0.85  respectively  for  the  six  columns  in  the  table; 
also  H.P.  for  stirring  0.3;  for  cooling- water  pumps,  0.45;  for  brine  pumps, 
2.2;  for  transmission  of  power,  0.6,  making  the  total  H.P.  for  the  six  cases 
10.30,  12.18,  10.44,  10.07, 10.98,  10.15.  He  also  makes  deductions  from 
the  theoretical  generation  of  cold  of  100,000  B.T.U.  per  hour,  for  a  brewery 
cooling  installation,  for  irregularities  of  valves,  etc.,  for  NHs  and  SO2 
machines  10%  and  for  CO*  machines  5%;  for  cooling  loss  through  stirring 
765  B.T.U.,  through  brine  pumps  5610  B.T.U.,  and  through  radiation 
4500  B.T.U.,  making  the  net  cooling  for  NH3  and  SOs  machines  79,125 
B.T.U.  and  for  COs  machines  84,125  B.T.U.,  and  the  cold  generated  per 
effective  H.P.  in  the  six  cases,  7682,  6908,  7578,  7848,  7662,  and  7796 
B.T.U. 

The  figures  given  in  the  tables  are  not  to  be  considered  as  holding 
generally  or  extended  t9  other  condenser  and  evaporator  temperatures. 
Each  change  of  condition  requires  a  separate  calculation.  The  final 
results  indicate  that  for  the  various  cooling  systems  no  appreciable 
difference  exists  in  the  work  required  for  the  same  amount  of  cold 
delivered  at  the  place  where  it  is  to  be  applied. 


PROPERTIES   OF   DIFFERENT   COOLING   AGENTS.       1343 


Properties  of  Brine  Used  to  Absorb  Refrigerating  Effect  of 
Ammonia.  (J.  E.  Den  ton,  Trans.  A.  S.  M.  E.,  x,  799). — A  solution  of 
Liverpool  salt  in  well-water  having  a  specific  gravity  of  1.17,  or  a  weight 
per  cubic  foot  of  73  Ibs.,  will  not  sensibly  thicken  or  congeal  at.0°  F. 

The  mean  specific  heat  between  39°  and  16°  Fahr.  was  found  by 
Denton  to  be  0.805.  Brine  of  the  same  specific  gravity  has  a  specific 
heat  of  0.805  at  65°  Fahr.,  according  to  Naumann. 

Naumann's  values  (Lehr-und  Handbuch  der  Thermochemie,  1882)  are: 

Specific  heat 0.791  0.805*0.863  0.895  0.941  0.962  0.978 

Specific  gravity 1.187  1.170  1.103  1.072  1.044  1.023  1.012 

Properties  of  Salt  Brine  (Carbondale  Calcium  Co.) 

Deg.  Baume"  60°  F 1  5          10          15          19 

Deg.  Salinometer  60°  F 4          20          40          60          80 

Sp.  gravity  60°  F 1.007     1.037     1.073     1.115     1.150 


Per  cent  of  salt,  by  wt.. ..        1            5  10  15  20 

Wt.  of  1  gallon,  Ibs 8.40       8,65       8.95       9.30  9.60 

Wt.  of  1  cu.  ft.,  Ibs 62.8  64.7  66.95  69.57  71.76 

Freezing  point  °  F 31.8  25.4  18.6  12.2  6.86 

Specific  heat 0.992  0.960     0.892  0.855  0.829 


23 

100 

1.191 
25 

9.94 
74.26 

1.00 

0.783 
brine. 


Chloride  of  Calcium  solution  is  commonly  used   instead  of   

According  to  Naumann,  a  solution  of  1.0255  sp.  gr.  has  a  specific  heat  of 
0.957.  A  solution  of  1.163  sp.  gr.  in  the  test  reported  in  Eng'g,  July  22, 
1887,  gave  a  specific  heat  of  0.827. 

H.  C.  Dickinson  (Science,  April  23, 1909)  gives  the  following  values  of  the 
specific  heat  of  solutions  of  chemically  pure  calcium  chloride. 

Density  Specific  Heat  Temperature,  C. 

1.07... 0.869  +  0.00057  t          (-     5°  to  +  15°) 

1.14 0.773  +  0.00064  t          (-  10°  to   +  20°) 

1.20 0.710  +  0.00064*          (-  20°  to  +  20°) 

1.26 0.662  +  0.00064  t          (-  25°  to  +  20°) 

The  advantages  of  chloride  of  calcium  solution  are  its  lower  freezing  point 
and  that  it  has  little  or  no  corrosive  action  on  iron  and  brass.  Calcium 
chloride  is  sold  in  the  fused  or  granulated  state,  in  steel  drums,  contain- 
ing about  75%  anhydrous  chloride  and  25%  water,  or  in  solution  contain- 
ing 40  to  50%  anhydrous  chloride,  in  tank  cars.  The  following  data 
are  taken  from  the  catalogue  of  the  Carbondale  Calcium  Co. 

PROPERTIES  OF  "  SOLVAY  "  CALCIUM  CHLORIDE  SOLUTION. 


&" 


m 


02 


I 

fflfa 


I. 

5.5 
11 
17 
20 


1.007 
1.041 
1.085 
1.131 
1.159 


+31.10 

27.68 
22.38 
12.20 
4.64 


1.169 
1.179 
1.189 
1.219 
1.250 


+  1.76 

-  1.48 

-  4.90 
-17.14 
-32.62 


32 

35 

35.5 

36.5 

37.5 


-54.40 
-25.24 
-  9.76 
+  2.84 
14.36 


Quantity  of  75%  calcium  chloride  required  to  make  solutions  of  different 

specific  gravities  and  freezing  points. 

Sp.  gravity] 1.250     1.225     1.200     1.175  1.150  1.125     1.100 

Lbs.  per  cu  ft.  solu- 
tion    28.06     25.06     22.05     19.15  16.26  13.47     10.70 

Lbs.  per  gallon 3.76       3.36       2.95.    2.56  2.18  1.80       1.43 

Freezing  point  °  F.    .-32.6   -19.5   -8.7      Zero  +7.5  +13.3   +18.5 

Boiling  points  of  calcium  chloride  solutions: 

Sp.  Gr.  at  59°  F..  .  .    1.104   1.185  1.238  1.341    1.383  solid  at  59°, 
Boiling  point  °  F...    215.6  221.0  230.0  240.8  248.0  266.0  282.2  306.5 
Sp.gr.atboilingpoint  1.085   1.119   1.209  1.308   1.365  1.452   1.526  1.619 

*  Interpolated. 


1344       ICE-MAKING   OR   REFRIGERATING-MACHINES 

"Ice-melting  Effect." — It  is  agreed  that  the  term  "ice-melting 
effect"  means  the  cold  produced  in  an  insulated  bath  of  brine,  on  the 
assumption  that  each  144  B.T.U.  represents  one  pound  of  ice,  this 
being  the  latent  heat  of  fusion  of  ice,  or  the  heat  required  to  melt  a  pound 
of  ice  at  32°  to  water  at  the  same  temperature.  The  performance  of  a 
machine,  expressed  in  pounds  or  tons  of  "ice-melting  capacity,"  does 
not  mean  that  the  refrigerating-machine  would  make  the  same  amount 
of  actual  ice,  but  that  the  cold  produced  is  equivalent  to  the  effect  of  the 
melting  of  ice  at  32°  to  water  of  that  temperature. 

in  maKing  artilicial  ice  tne  water  frozen  is  generally  about  70°  F.  when 
submitted  to  the  refrigerating  effect  of  a  machine;  second,  the  ice  is 
chilled  from  12°  to  20°  below  its  freezing-point;  third,  there  is  a  dissipa- 
tion of  cold,  from  the  exposure  of  the  brine  tank  and  the  manipulation  of 
the  ice-cans:  therefore  the  weight  of  actual  ice  made,  multiplied  by  its 
latent  heat  of  fusion,  144  thermal  units,  represents  only  about  three- 
fourths  of  the  cold  produced  in  the  brine  by  the  refrigerating  fluid  per 
I.H.P.  of  the  engine  driving  the  compressing-pumps.  Again,  there  is 
considerable  fuel  consumed  to  operate  the  brine-circulating  pump,  the 
condensing-water  and  feed-pumps,  and  to  reboil,  or  purify,  the  condensed 
steam  from  which  the  ice  fe  frozen.  This  fuel,  together  with  that  wasted 
in  leakage  and  drip  water,  amounts  to  about  one-half  that  required  to 
drive  the  main  steam-engine.  Hence  the  pounds  of  actual  ice  manu- 
factured from  distilled  water  is  just  about  half  the  equivalent  of  the 
refrigerating  effect  produced  in  the  brine  per  indicated  horse-power  of  the 
steam-cylinders. 

When  ice  is  made  directly  from  natural  water  by  means  of  the  "plate 
system,"  about  half  of  the  fuel,  used  with  distilled  water,  is  saved  by 
avoiding  the  rebelling,  and  using  steam  expansively  in  a  compound 
engine. 

Ether-machines,  used  in  India,  are  said  to  have  produced  about  6  Ibs. 
of  actual  ice  per  pound  of  fuel  consumed. 

The  ether  machine  is  obsolete,  because  the  density  of  the  vapor  of  ether, 
at  the  necessary  working-pressure,  requires  that  the  compressing-cylinder 
shall  be  about  6  times  larger  than  for  sulphur  dioxide,  and  17  times 
larger  than  for  ammonia. 

Air-machines  require  about  1.2  times  greater  capacity  of  compressing 
cylinder,  and  are,  as  a  whole,  more  cumbersome  than  ether  machines, 
but  they  remain  in  use  on  shipboard.  In  using  air  the  expansion  must 
take  place  in  a  cylinder  doing  work,  instead  of  through  a  simple  expansion- 
cock  which  is  used  with  vapor  machines.  The  work  done  in  the  expansion- 
cylinder  is  utilized  in  assisting  the  compressor. 

The  Allen  Dense  Air  Machine  takes  for  compression  air  of  considerable 
pressure  which  is  contained  in  the  machine  and  in  a  system  of  pipes.  The 
air  at  60  or  70  Ibs.  pressure  is  compressed  to  210  or  240  Ibs.  It  is  then 
passed  through  a  coil  immersed  in  circulating  water  and  cooled  to  nearly 
the  temperature  of  the  water.  It  then  passes  into  an  expander,  which  is, 
in  construction,  a  common  form  of  steam-engine  with  a  cut-off  valve. 
This  engine  takes  out  of  the  air  a  quantity  of  heat  equivalent  to  the 
work  done  by  the  air  while  expanding,  to  the  original  pressure  of  60  or 
70  Ibs.,  and  reduces  its  temperature  to  about  90°  to  120°  F.  below  the 
temperature  of  the  cooling  water  supply.  The  return  stroke  of  the  piston 
pushes  the  air  out  through  insulated  pipes  to  the  places  that  are  to  be 
refrigerated,  from  which  it  is  returned  to  the  compressor. 

The  air  pushed  out  by  the  expander  is  commonly  about  35  to  55  below 
zero  F.  In  arrangements  where  not  all  the  cold  is  taken  out  of  the  air 
by  the  refrigerating  apparatus,  the  highly  compressed  air  after  cooling 
in  the  coil  is  further  Cooled  by  being  brought  in  surface  contact  with  the 
returning  and  still  cold  air,  before  entering  the  expander.  By  this  means 
temperatures  of  70  to  90  below  zero  may  be  obtained. 

The  refrigerating:  effect  in  B.T.U.  per  minute  is:  Lbs.  of  air  handled  per 
min.  X  0.2375  X  difference  of  temperature  of  air  passing  out  of  ex- 
pander and  of  that  returning  to  the  machine. 

Carbon-dioxide  Machines  are  in  extensive  use  on  shipboard.  S.  H. 
Bunnell  (Eng.  News,  April  9,  1903)  says  there  are  over  1500  CO2  plants 
on  shipboard.  He  describes  a  large  duplex  CO2  compressor  built  by  the 
Brown-Oochrane  Co.,  Lorain,  O.  Tests  of  CO2  machines  by  a  committee 
of  the  Danish  Agricultural  Society  were  reported  in  1899,  in  "Ice  and 


MACHINES   USING  DIFFERENT   COOLING  AGENTS.    1345 

Cold  Storage,"  of  London.  Carbon-dioxide  machines  are  built  also  by 
Kroeschel  Bros.,  Chicago. 

Methyl-Chloride  machines  are  made  by  Railway  and  Stationary  Re- 
frigerating Co.,  New  York  City.  The  compressor  is  a  rotary  pump. 
When  driven  by  an  electric  motor  the  complete  apparatus  is  very  com- 
pact, and  is  therefore  suitable  for  refrigerator  cars  or  other  places  where 
space  is  restricted 

Sulphur-Dioxide  Machines. — Results  of  theoretical  calculations 
are  given  in  a  table  by  Ledoux  showing  an  ice-melting  capacity  per  hour 
per  horse-power  ranging  from  134  to  63  Ibs.,  and  per  pound  of  coal  rang- 
ing from  44.7  to  21.1  Ibs.,  as  the  temperature  corresponding  to  the  pres- 
sure of  the  vapor  in  the  condenser  rises  from  59°  to  104°  F.  The  theoret- 
ical results  do  not  represent  the  actual. 

Prof.  Denton  says  concerning  Ledoux's  theoretical  results:  The 
figures  given  are  higher  than  those  obtained  in  practice,  because  the 
effect  of  superheating  of  the  gas  during  admission  to  the  cylinder  is  not 
considered.  This  superheating  may  cause  an  increase  of  work  of  about 

25%.     -  

tank, 

that  i ^ -        ,  _  

conditions  of  an  absolute  pressure  in  the  condenser  9f  56  Ibs.  per  sq.  in. 
and  the  corresponding  temperature  of  77°  F.,  will  give  about  22  Ibs.  of 
ice-melting  capacity  per  pound  of  coal,  which  is  about  60%  of  the  theor* 
etir-al  amount  neglecting  friction,  or  70°^  including  friction. 

Sulphur-dioxide  machines  are  not  (1910)  used  in  the  United  States. 

Refrigera ting-Machines  using  Vapor  of  Water.  (Ledoux.) — In 
these  machines,  sometimes  called  vacuum  machines,  water,  at  ordinary 
temperatures,  is  injected  into,  or  placed  in  connection  with,  a  chamber 
in  which  a  strong  vacuum  is  maintained.  A  portion  of  the  water  vapor- 
izes, the  heat  to  cause  the  vaporization  being  supplied  from  the  water  not 
vaporized,  so  that  the  latter  is  chilled  or  frozen  to  ice.  If  brine  is  used 
instead  of  pure  water,  its  temperature  may  be  reduced  below  the  freez- 
ing-point of  water.  The  water  vapor  is  compressed  from,  say,  a  pressure 
of  0.1  Ib.  per  sq.  in.  to  1  Yi  Ibs.  and  discharged  into  a  condenser.  It  is 
then  condensed  and  removed  by  means  of  an  ordinary  air-pump.  The 
principle  of  action  of  such  a  machine  is  the  same  as  that  of  volatile- 
vapor  machines. 

A  theoretical  calculation  for  ice-making,  assuming  a  lower  temperature 
of  32°  F.,  a  pressure  in  the  condenser  of  1  Y^  Ibs.  per  sq.  in.  and  a  coal 
consumption  of  3  Ibs.  per  I.H.P.  per  hour,  gives  an  ice-melting  effect  of 
34.5  Ibs.  per  pound  of  coal,  neglecting  friction.  Ammonia  for  ice-making 
conditions  gives  40.9  Ibs.  The  volume  of  the  compressing  cylinder  is 
about  150  times  the  theoretical  volume  for  an  ammonia  machine  for 
these  conditions. 

[The  Patten  Vacuum  Ice  Co.,  Of  Baltimore,  has  a  large  plant  on  this 
system  in  operation  (1910).] 

Ammonia  Compression-machines. — "Cold"  vs.  "Dry"  Systems  of 
Compression. — In  the  "cold"  system  or  "humid"  system  some  of  the 
ammonia  entering  the  compression  cylinder  is  liquid,  so  that  the  heat 
developed  in  the  cylinder  is  absorbed  by  the  liquid  and  the  temperature 
of  the  ammonia  thereby  confined  to  the  boiling-point  due  to  the  con- 
denser-pressure. No  jacket  is  therefore  required  about  the  cylinder. 

In  the  "  dry  "  or  "  hot "  system  all  ammonia  entering  the  compressor  is 
gaseous,  and  the  temperature  becomes  by  compression  several  hundred 
degrees  greater  than  the  boiling-point  due  to  the  condenser-pressure.  A 
water-jacket  is  therefore  necessary  to  permit  the  cylinder  to  be  properly 
lubricated. 

Dry,  Wet  and  Flooded  Systems.  (York  Mfg.  Co.) — An  expansion 
system,  or  one  where  the  ammonia  leaves  the  coil  slightly  superheated, 
requires  about  33  jf  %  more  pipe  surface  than  a  wet  compression  system, 
in  which  the  ammonia  leaves  the  coils  containing  sufficient  entrained 
liquid  to  maintain  a  wet  compression  condition  in  the  compressor. 

The  flooded  system  is  ono  where  the  ammonia  is  allowed  to  flow  through 
the  coils  and  into  a  trap,  where  the  gas  is  separated  from  the  liquid,  the 
gas  passing  on  to  the  compressor,  while  the  liquid  goes  around  through 
the  coils  again,  together  with  the  fresh  liquid,  which  is  fed  into  the  trap. 
Such  a  system  requires  only  about  one-half  the  evaporating  surface  that 


1346      ICE-MAKING   OR  REFRIGERATING-MACHINES. 

an  expansion  system  does  to  do  the  same  work.  The  relative  proportions 
of  the  three  systems  may  be  expressed  as  follows: 

A  Dry  Compression  plant  will  need,  with  an  Expansion  Evaporating 
System,  a  medium  size  compressor,  a  large  size  evaporating  system,  a 
small  amount  of  ammonia. 

A  Dry  Compression  plant  will  need,  with  a  Flooded  Evaporating  Sys- 
tem, a  small  size  compressor,  a  small  size  evaporating  system,  a  large 
am;  unt  of  ammonia. 

A  Wet  Compression  plant  will  need,  with  a  Wet  Compression  Evapo- 
rating System,  a  large  size  compressor,  a  medium  size  evaporating  sys- 
tem, a  medium  amount  of  ammonia. 

The  Ammonia  Absorption-machine  comprises  a  generator  which 
contains  a  concentrated  solution  of  ammonia  in  water;  this  generator 
is  heated  either  directly  by  a  fire,  or  indirectly  by  pipes  leading  from  a 
steam-boiler.  The  vapor  passes  first  into  an  "  analyzer,"  a  chamber  con- 
nected with  the  upper  part  of  the  generator  which  separates  some  of  the 
water  from  the  vapor,  then  into  a  rectifier,  where  the  vapor  is  partly 
cooled,  precipitating  more  water,  which  returns  to  the  generator,  and 
then  to  the  condenser.  The  upper  part  of  the  cooler  or  brine-tank  is  in 
communication  with  the  lower  part  of  the  condenser. 

An  absorption-chamber  is  filled  with  a  weak  solution  of  ammonia ;  a 
tube  puts  this  chamber  in  communication  with  the  cooling-tank. 

The  absorption-chamber  communicates  witfi  the  boiler  by  two  tubes: 
one  leads  from  the  bottom  of  the  generator  to  the  top  of  the  chamber,  the 
other  leads  from  the  bottom  of  the  chamber  to  the  top  of  the  generator. 
Upon  the  latter  is  mounted  a  pump,  to  force  the  liquid  from  the  absorp- 
tion-chamber, where  the  pressure  is  maintained  at  about  one  atmosphere 
into  the  generator,  where  the  pressure  is  from  8  to  12  atmospheres. 

To  work  the  apparatus  the  ammonia  solution  in  the  generator  is  first 
heated.  This  releases  the  gas  from  the  solution,  and  the  pressure  rises. 
When  it  reaches  the  tension  of  the  saturated  gas  at  the  temperature  of 
the  condenser  there  is  a  liquefaction  of  the  gas,  and  also  of  a  small 
amount  of  steam.  By  means  of  a  cock  the  flow  of  the  liquefied  gas  into 
the  refrigerating  coils  contained  in  the  cooler  is  regulated.  It  is  here 
vaporized  by  absorbing  the  heat  from  the  substance  placed  there  to  be 
cooled.  As  fast  as  it  is  vaporized.it  is  absorbed  by  the  weak  solution  in 
the  absorbing-chamber. 

Under  the  influence  of  the  heat  in  the  boiler  the  solution  is  unequally 
saturated,  the  stronger  solution  being  uppermost.  The  weaker  portion 
is  conveyed  by  the  pipe  entering  the  "top  of  the  absorbing-chamber,  the 
flow  being  regulated  by  a  cock,  while  the  pump  sends  an  equal  quantity 
of  strong  solution  from  the  chamber  back  to  the  boiler. 

The  working  of  the  apparatus  depends  upon  the  adjustment  and  regu- 
lation of  the  flow  of  the  gas  and  liquid ;  by  these  means  the  pressure  is 
varied,  and  consequently  the  temperature  in  the  cooler  may  be  controlled. 

The  working  is  similar  to  that  of  compression-machines.  The  absorp- 
tion-chamber fills  the  office  of  aspirator,  and  the  generator  plays  the  part 
of  compressor.  The  mechanical  force  producing  exhaustion  is  here  re- 
placed by  the  affinity  of  water  for  ammonia  gas,  and  the  mechanical  force 
required  for  compression  is  replaced  by  the  heat  which  severs  this  affinity 
and  sets  the  gas  at  liberty. 

Reece's  absorption  apparatus  (1870)  is  thus  described  by  Wallis-Taylor. 
The  charge  of  liquid  ammonia  (26°  Baume)  is  vaporized  by  the  application 
of  heat,  and  the  mixed  vapor  passed  to  the  analyzer  and  rectifier,  wherein 
the  bulk  of  the  water  is  condensed  at  a  comparatively  elevated  temperature 
and  returned  to  the  generator.  The  ammoniacal  vapor  or  gas  is  then 
passed  to  the  condenser,  where  it  is  liquefied  under  the  combined  action 
of  the  cooling-water  and  of  the  pressure  maintained  in  the  generator.  The 
liquid  ammonia,  practically  anhydrous,  is  then  used  in  the  refrigerator, 
and  tb^  vapor  therefrom,  still  under  considerable  pressure,  is  admitted  to 
the  cylinder  of  an  engine  used  to  drive  a  pump  for  returning  the  strong 
solution  to  the  generator,  after  which  it  is  passed  to  the  absorber,  where 
it  meets  and  is  absorbed  by  the  weak  liquor  from  the  generator,  and  the 
strong  liquor  so  formed  is  forced  back  into  the  generator  by  means  of  the 
pump.  The  temperature  exchanger,  introduced  in  1875,  provides  for 
the  hot  liquor  on  its  way  from  the  generator  to  the  absorber  giving  up 
its  heat  to  the  cooler  liquid  from  the  absorber  on  its  way  to  the  generator. 

Wallis-Taylor  describes  also  marine  refrigerating,  ice-making  cold 


AMMONIA  MACHINES. 


1347 


storage,  the  application  of  refrigeration  in  breweries,  dairies,  etc.;  and  the 
management  and  testing  of  apparatus. 

For  the  best  results  the  following  conditions  are  necessary  (Voorhees): 
1.  The  generator  should  have  ample  liquid  evaporating  surface  to  make 
dry  gas.  2., The  temperature  of  the  gas  to  the  rectifier  should  be  as  low 
as  possible.  3.  The  drip  Iiqu9r  returned  to  the  generator  from  the  recti- 
fier should  be  as  hot  as  possible.  4.  The  gas  from  the  rectifier  to  the 
condenser  should  not  be  over  10°  to  50°  hotter  than  the  condensing  tem- 
perature of  the  gas.  5.  The  exchanger  should  exchange  upwards  of 
90%  of  the  heat  ot  the  hot  weak  liquor  to  the  cold  strong  liquor.  The 
weight  of  strong  liquor  pumped  should  be  from  7  to  8  times  that  of  the 
anhydrous  ammonia  circulated  in  the  refrigerator. 

To  produce  one  ton  of  refrigeration  at  8.5  Ibs.  suction  and  170  Ibs.  gauge 
condenser  pressure,  about  3.5  times  as  many  heat  units  are  actually  used 
by  an  absorption  machine  as  by  a  compression  machine  (compound  con- 
densing engine  driven),  but,  9wing  to  the  low  efficiency  of  the  steam 
engine,  due  to  the  heat  wasted  in  the  exhaust  and  in  cylinder  condensation, 
•  the  actual  weight  of  steam  used  per  hour  per  ton  of  refrigeration  is  the 
same  for  both  the  absorption  machine  and  the  compressor. 

Relative  Performance  of  Ammonia  Compression-  and  Absorp- 
tion- machines,  assuming  no  Water  to  be  Entrained  with  the 
Ammonia-gas  in  the  Condenser.  (Denton  and  Jacobus,  Trans.  A.  S. 
M.  E.,  xiii.)  —  It  is  assumed  in  the  calculation  for  both  machines  that 
1  Ib.  of  coal  imparts  10,000  B.T.U.  to  the  boiler.  The  condensed  steam 
from  the  generator  of  the  absorption-machine  is  assumed  to  be  returned 


Condenser. 


61.2 
59.0 
59.0 
59.0 
86.0 
86.0 
86.0 
85.0 
104.0 
104.0 


969 
967 
931 
1000 
988 
966 
1025 
1002 
1002 
1041 


*5%  of  water  entrained  in  the  ammonia  will  lower  the  economy  of 
the  absorption-machine  about  15  %  to  20  %  below  the  figures  given  in 
the  table. 

to  the  boiler  at  the  temperature  of  the  steam  entering1  the  generator. 
The  engine  of  the  compression-machine  is  assumed  to  exhaust  through  a 
feed- water  heater  that  heats  the  feed-water  to  212°  F.  The  engine  is 
assumed  to  consume  261/4  Ibs.  of  water  per  hour  per  horse-power.  The 
figures  for  the  compression-machine  include  the  effect  of  friction,  which 
is  taken  at  15%  of  the  net  work  of  compression. 

(For  discussion  of  the  efficiency  of  the  ab^rption  system,  see  Ledoux's 
work;  paper  by  Prof.  Linde,  and  discussion  on  the  same  by  Prof.  Jacobus, 
Trans.  A.  S.  M.  E.t  xiv.  1416,  1436;  and  papers  by  Denton  and  Jacobus. 
Trans.  A.  S.  M.  E.,  x,  792,  xiii,  507. 


1348      ICE-MAKING   OR  REFRIGERATING-MACHlNES. 


Relative  Efficiency  of  a  Refrigerating-Machine. —  The  efficiency 
of  a  refrigerating-machine  is  sometimes  expressed  as  the  quotient  of 
the  quantity  of  heat  received  by  the  ammonia  from  the  brine,  that  is,  the 
quantity  of  useful  work  done,  divided  by  the  heat  equivalent  of  the 
mechanical  work  done  in  the  compressor.  Thus  in  column  1  of  the  table 
of  performance  of  the  75-ton  machine  (page!363)  the  heat  given  by  the 
brine  to  the  ammonia  per  minute  is  14,776  B.T.U.  The  horse-power  of 
the  ammonia  cylinder  is  65.7,  and  its  heat  equivalent  =  65.7  x  33,000  •*• 
778  =  2786  B.T.U.  Then  14,776  •*•  2786  =  5.304,  efficiency.  The  ap- 
parent paradox  that  the  efficiency  is  greater  than  unity,  which  is  im- 
possible in  any  machine,  is  thus  explained.  The  working  fluid,  as 
ammonia,  receives  heat  from  the  brine  and  rejects  heat  into  the  condenser. 
(If  the  compressor  is  jacketed,  a  portion  is  rejected  into  the  jacket-water.) 
The  heat  rejected  into  the  condenser  is  greater  than  that  received  from  the 
brine;  the  difference  (plus  or  minus  a  small  difference  radiated  to  or  from 
the  atmosphere)  is  heat  received  by  the  ammonia  from  the  compressor. 
The  work  to  be  done  by  the  compressor  is  not  the  mechanical  equivalent 
of  the  refrigeration  of  the  brine,  but  only  that  necessary  to  supply  the  dif- 
ference between  the  heat  rejected  by  the  ammonia  into  the  condenser  and 
that  received  from  the  brine.  If  cooling  water  colder  than  the  brine  were 
available,  the  brine  might  transfer  its  heat  directly  into  the  cooling  water, 
and  there  would  be  no  need  of  ammonia  or  of  a  compressor;  but  since  such 
cold  water  is  not  available,  the  brine  rejects  its  heat  into  the  cplder 
ammonia,  and  then  the  compressor  is  required  to  heat  the  ammonia  to 
such  a  temperature  that  it  may  reject  heat  into  the  cooling  water. 

The  maximum  theoretical  efficiency  of  a  refrigerating  machine  is  ex- 
pressed by  the  quotient  T0  -*-  (Tt  —  T0),  in  which  Tt  is  the  highest  and  T0 
the  lowest  temperature  of  the  ammonia  or  other  refrigerating  agent. 

The  efficiency  of  a  refrigerating  plant  referred  to  the  amount  of  fuel 
consumed  is 

/-Pounds  circulated  per  hour^   ( 
1       x  specific  heat  x  range   >• 
Ice-melting  capacity )  =    I      of  temperature 

per  pound  of  fuel    j 

Cold  Watet 


144  X  pounds  of  fuel  used  per  hour 


1  I 


_____         Compressor  *          ^ 


Condenser 

309°            339°*            '10°                       3° 

82                             .  i    y                              61 

Brine  Tank 

Ammonia 
Coils 

|      {         85°                            *  Heat  received                                              U^~~ 
Warm  Water                                   from  compression.                          Heat  received 

9o  Brine  Outlet 


Cold  Rooa» 


Heat  rejected  from  brine 

DIAGRAM   OF  AMMONIA  COMPRESSION   MACHINE. 


II  «• 


Condenser 


Torce  Pump 
DIAGRAM  OF  AMMONIA  ABSORPTION   MACHINE. 


EFFICIENCY  OF  REFRIGERATING  SYSTEMS.   "    1349 

The  Ice-melting  capacity  is  expressed  as  follows: 

Tons  (of  2000  Ibs.)      ,      {  '"  *  MS  heat     }  of  brine  drculated  per 

Ice-melting  ca-         i  =  l       x  ra"ge  of  temp.  ) nour 

pacity  per  24  hours  J  144  x  2000 

The  analogy  between  a  heat-engine  and  a  refrigerating-machine  is  as 
follows:  A  steam-engine  receives  heat  from  the  boiler,  converts  a  part 
of  it  into  mechanical  work  in  the  cylinder,  and  throws  away  the  differ- 
ence into  the  condenser.  The  ammonia  in  a  compression  refrigerating- 
machine  receives  heat  from  the  brine- tank  or  cold  room,  receives  an 
additional  amount  of  heat  from  the  mechanical  work  done  in  the  com- 
pression-cylinder, and  throws  away  the  sum  into  the  condenser.  The 
efficiency  of  the  steam-engine  =  work  done  -i-  heat  received  from  boiler. 
The  efficiency  of  the  refrigerating-machine  =  heat  received  from  the 
brine-tank  or  cold-room  -j-  heat  required  to  produce  the  work  in  the 
compression-cylinder.  In  the  ammonia  absorption-apparatus,  the 
ammonia  receives  heat  from  the  brine-tank  and  additional  heat  from 
the  boiler  or  generator,  and  rejects  the  sum  into  the  condenser  and  into 
the  cooling  water  supplied  to  the  absorber.  The  efficiency  =  heat 
received  from  the  brine  -5-  heat  received  from  the  boiler. 

The  Efficiency  of  Refrigerating  Systems  depends  on  the  tempera- 
ture of  the  condenser  water,  whether  there  is  sufficient  condenser 
surface  for  the  compressor  and  whether  or  not  the  condenser  pipes  are 
free  from  uncondensable  foreign  gases.  With  these  things  right,  con- 
denser pressure  for  different  temperatures  of  cooling  water  should  be 
approximately  as  follows: 

1  gallon  per  minute  per  ton  per  24  hours 

— Cooling  water,  °  F 60     65  70     75     80     85  90 

Condenser  pressure,  gage,  Ib 183  200  220  235  255  280  300 

Condensed  liquid  ammonia,  °F 95  100  105  110  115  120  125 

2  gallons  per  minute  per  ton  per  24 

hours — Condenser  pressure,  gage,  Ib .    130  153  168  183  200  220  235 
Condensed  liquid  ammonia,  °  F 77     85     90     93  100  105  110 

3  gallons  per  minute  per  ton  per  24 

hours — Condenser  pressure,  gage,  Ib.  125  140  155  170  185  200  215 

Condensed  liquid  ammonia,  °  F 75     85     90     93     95  100  105 

The  evaporating  or  back  pressure  within  the  expansion  coils  of  a  re- 
frigerating system  depends  upon  the  temperatures  on  the  outside  of  such 
coils,  i.e.,  the  air  or  brine  to  be  copied.  For  average  practice  back  pres- 
sures for  the  production  of  required  temperatures  should  be  approxi- 
mately as  follows: 
Tempera  ture  of  room,  °P.  ...  10  15  20  28  32  36  40  50  60 

Back  pressure,  gage,  Ib 10     12     15     22     25     27     30     35     40 

Temperature  of  ammonia,  °  F. —10  —5  0  8  12  14  17  22  26 
The  condenser  pressure  should  be  kept  as  low  as  possible  and  the  back 
pressure  as  high  as  possible,  narrow  limits  between  such  pressures  being 
as  important  to  the  efficiency  of  a  refrigerating  system  as  wide  ones  are 
to  that  of  a  steam  engine  in  which  the  economy  increases  with  the  range 
between  boiler  pressure  and  condenser  pressure.  (F.  E.  Matthews, 
Power,  Jan.  26,  1909.) 

Cylinder-heating. — In  compression-machines  employing  volatile 
vapors  the  principal  cause  of  the  difference  between  the  theoretical  and 
the  practical  result  is  the  heating  of  the  ammonia,  by  the  warm  cylinder 
walls,  during  its  entrance  into  the  compressor,  thereby  expanding  it,  so 
that  to  compress  a  pound  of  ammonia  a  greater  number  of  revolutions 
must  be  made  by  the  compressing-pumps  than  corresponds  to  the  density 
of  the  ammonia-gas  as  it  issues  from  the  brine-tank.  t 

Volumetric  Efficiency. — The  volumetric  efficiency  of  a  compressor 
is  the  ratio  of  the  actual  weight  of  ammonia  pumped  to  the  amount 
calculated  from  the  piston  displacement.  Mr.  Voorhees  deduces  from 
Denton's  experiments  the  formula:  Volumetric  efficiency  =  E  —  1  — 
(ti—  fo)/1330,  in  which  t\  =  the  theoretical  temperature  of  gas  after 
compression  and  h  =  temperature  of  gas  delivered  to  the  compressor. 
The  temperature  ti,  =  Ti  —  460,  is  calculated  from  the  formula  for  adia- 
batic  compression,  Ti  =  To  (Pi/Po)  °'24.  in  which  T\  and  To  are  absolute 
temperatures  and  Pi  and  Po  absolute  pressures.  In  eight  tests  by  Prof. 
Denton  the  volumetric  efficiency  ranged  from  73.5%  to  84%,  and  they 


1350     ICE-MAKING  OB  REFRIGERATING-MACHINES. 


vary  less  than  1%  from  the  efficiencies  calculated  by  the  formula.  The 
temperature  of  the  gas  discharged  from  the  compressor  averaged  57°  less 
than  the  theoretical. 

The  volumetric  efficiency  of  a  dry  compressor  is  greatest  when  the  va- 
por comes  to  the  compressor  with  little  or  no  superheat;  30°  superheat  of 
the  suction  gas  reduces  the  capacity  of  the  compressor  4%,  and  100°  9%. 

The  following  table  (from  Voorhees)  gives  the  theoretical  discharge, 
temperatures  (h)  and  volumetric  efficiencies  (E)  by  the  formula,  and  the 
actual  cubic  feet  of  displacement  of  compressor  (F)  per  ton  of  refrigera- 
tion per  minute  for  the  given  gage. pressures  of  suction  and  condenser. 


Suction  Pressures. 

0 

15 

30 

Cond.  press.,  140.  . 
Cond.  press.,  1  70  .  . 
Cond.  press.,  200.  . 

ti 
323° 
221° 
167° 

E 
0.76 
0.83 
0.87 

F 
10.35 

4.57 
2.96 

ti 

358° 
254° 
192° 

E 
0.73 
0.81 
0.86 

F 
11.02 
4.78 
3.07 

ti 

388° 
280° 
216° 

E 
0.71 
0.79 
0.84 

F 
11.57 
5.03 
3.21 

Pounds  of  Ammonia  per  Minute  to  Produce  1  Ton  of  Refrigeration, 
and  Percentage  of  Liquid  Evaporated  at  the  Expansion  Valve. 


Condenser  Pressure  and 
Temperature. 

1401bs.,80°. 

1701bs.,90°. 

200  Ibs.,  100°. 

Refrigerator,  pressure  and 
temperature  0  lbs.,-29°... 
Refrigerator  pressure  and 
temperature  15  lbs.,-0°... 
Refrigerator  pressure  and 
temperature,  30  lbs.,-170.. 

0.431  lb.,  19% 
0.  420  lb.,  14.4% 
0.4151b.,11.6% 

0.441  lb.,  20.8% 
0.  430  lb.,  16.2% 
0.  425  lb.,  13.4% 

0.  451  lb.\  22.5% 
0.440  lb.,  18.0% 
0.  434  lb.,  15.2% 

Mean  Effective  Pressure,  and  Horse-power. — Voorhees  deduces 
the  following  (Ice  and  Refrig.,  1902) :  M.E.P.  =  4.333  p0  [(PI/PO)  o-231  — 1], 
po  =  suction  and  p\  condenser  pressure,  abs*.  Ibs.  per  sq.  in.  The  maxi- 
mum M.E.P.  occurs  when  po  =  pi  -r-  3.113.  The  percentage  of  stroke 
during  which  the  gas  is  discharged  from  the  compressor  is  Vi  =  (po/pi)0'769. 

The  compressor  horse-power,  C.H.P.,  is  0.00437  F  X  M.E.P. 

The  friction  of  the  compressor  and  its  engine  combined  is  given  by 
Voorhees  as  33Va%  of  the  compressor  H.P.  or  25%  of  the  engine  H.P. 
Values  of  the  mean  effective  pressure  per  ton  of  refrigeration  (M),  the 
compressor  horse-power  (C)  and  the  engine  horse-power  (E)  are  given 
below  for  the  conditions  named. 


Suction  Pressure. 

0 

15 

30 

Cond.  press.,  140... 
Cond.  press.,  1  70  ... 

(M) 
46.5 
50.5 

(C) 
2.10 
2.42 

(E) 
2.80 
3.23 

(M) 
59.5 
67.0 

(C) 
1.19 
1.40 

(E) 
1.59 
1.87 

(M) 
64.5 
75.0 

(C) 
0.83 
1.00 

ffl 

1.33 

Cond.  press.,  200... 

55.0 

2.78 

3.71 

74.5 

1.64 

2.19 

85.0 

1.19 

1.59 

By  cooling  the  liquid  between  the  condenser  and  the  expansion  valve 
the  capacity  will  be  increased  and  the  horse-power  per  ton  reduced.  With 
compression  from  15  to  170  Ibs.,  if  the  liquid  at  the  expansion  valve  is 
cooled  to  76°  instead  of  90°  the  H.P.  per  ton  will  be  reduced  3%. 

Prof.  Lucke  deduces  a  formula  for  the  I. H.P.  per  ton  of  refrigerating 
capacity,  as  follows: 

p  =  mean  effective  pressure,  Ibs.  per  sq.  in. ;  L  =  length  of  stroke  in 
ft.;  a  =  area  of  piston  in  sq.  ins. ;  n  =  no.  of  compressions  per  minute; 
EC  =  apparent  volumetric  efficiency,  the  ratio  of  the  volume  of  ammonia 
apparently  taken  in  per  stroke  to  the  full  displacement  of  the  piston; 
We  =  weight  of  1  cu.ft.  of  ammonia  vapor  at  the  back  pressure,  as  it- 
exists  in  the  cylinder  when  compression  begins;  Lc  =  latent  heat  of 
vaporization  available  for  refrigeration;  288,000  =  B.T.U.  equivalent 
to  1  ton  of  refrigeration ;  T  =  tons  refrigeration  per  24  hours. 
I.H.P.  =  pLan  +  33,000  0.87  x  j^ 

T          LaEc  nwc  X  Lc  X  60  X  24  ~    WCLC      EC 
144  X  288,000 

The  Voorhees  Multiple  Effect  Compressor  is  based  upon  the  fact 
that  both  the  economy  and  the  capacity  of  a  compression  machine  vary 
with  the  back  pressure.  In  the  past  it  has  always  been  necessary  to  run  a 
compressor  at  a  gas  suction  pressure  corresponding  to  the  lowest  required 


QUANTITY   OF   AMMONIA  KEQUIBED. 


1351 


temperature.  The  multiple  effect  compressor  takes  in  gas  from  two  or 
more  refrigerators  at  two  or  more  different  suction  pressures  and  tem- 
peratures on  the  same  suction  stroke  of  the  compressor.  The  suction  gas 
of  the  higher  pressure  helps  to  compress  the  lower  suction  pressure  gas. 
There  are  two  sets  of  suction  valves  in  the  compressor  cylinder ;  the  low 
temperature  and  corresponding  low  back  pressure  being  connected  to 
one  suction  port,  usually  in  the  cylinder  head,  and  the  high  back  pres- 
sure connected  to  the  other.  At  the  beginning  of  the  stroke  the  cylinder 
is  filled  with  the  low  pressure  gas  and  as  the  piston  reaches  the  end  of  its 
suction  stroke,  the  second  or  high  back  pressure  port  is  uncovered,  the 
low  pressure  suction  valve  closing  automatically,  and  the  cylinder  is 
completely  filled  with  gas  at  the  high  pressure.  By  this  means  the 
compressor  operates  with  an  economy  and  capacity  corresponding  to  the 
higher  back  pressure,  making  a  gain  in  capacity  of  often  50%  or  more. 
(Trans.  Am.  Soc.  Refrig.  Engrs.,  1906.) 

Quantity  of  Ammonia  Required  per  Ton  of  Refrigeration. — 
The  following  table  is  condensed  from  one  given  by  F.  E.  Matthews  in 
Trans.  A.  S.  M.  E.,  1905.  The  weight  in  Ibs.  per  minute  is  calculated 
from  the  formula  P  =  (144  X  2000)  -*•  [1440 1  -  (fti  -  ho)]  in  which 
I  is  the  latent  heat  of  evaporation  at  the  back  pressure  in  the  cooler,  and 
hi  and  /?<>  the  heat  of  the  liquid  at  the  temperatures  of  the  condenser  and 
the  cooler  respectively.  The  specific  heat  of  the  liquid  has  been  taken 
at  unity.  The  ton  of  refrigeration  is  2000  Ibs.  in  24  hours  =•  288,000 
B.T.U. 

B  =  Pounds  of  ammonia  evaporated  per  minute. 

C  =  Cubic  feet  of  gas  to  be  handled  per  minute  by  the  compressor.     | 


Head  or  Condenser  Gauge  Pressure  and  Corresponding 

I. 

Temperature. 

w. 
B.P. 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190 

200 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

63.5° 

68° 

72.6° 

77.4° 

80.3° 

83.8° 

87.4° 

90.8° 

93.8° 

96.9° 

100° 

572.78  ) 

B 

.4159 

.4199 

.4240 

.4284 

.4310 

.4343 

.4376 

.4408 

.4440 

.4470 

.4501 

.0556  > 
0      ) 

C 

7.482 

7.551 

7.626 

7.703 

7.761 

7.812 

7.870 

7.929 

7.986 

8.041 

8.095 

566.14) 

B 

.4122 

.4160 

.4202 

.4243 

.4271 

.4308 

.4335 

.4366 

.4397 

.4437 

.4458 

.0133  j 

C 

5.636 

5.675 

5.732 

5  .790 

5.826 

5.878 

5.914 

5.970 

5.999 

6.039 

6.081 

560.69  } 

B 

.4093 

.4130 

.4171 

.4204 

.4237 

.4271 

.4302 

.4332 

.4363 

.4392 

.4423 

.0910  > 
10 

C 

4.502 

4.543 

4.587 

4.625 

4.662 

4.698 

4.733 

4.766 

4.799 

4.833 

4.865 

556.11 

B 

.4068 

.4106 

.4145 

.4186 

.4211 

.4244 

.4276 

.4288 

.4336 

.4365 

.4394 

.1083  > 
15 

C 

3.756 

3.791 

3.827 

3.866 

3.889 

3.918 

3.948 

3.975 

4.003 

4.030 

4.058 

552,83 

B 

.4040 

.4077 

.4116 

.4158 

.4182 

.4214 

.4245 

.4275 

.4304 

.4333 

.4362 

'20 

C 

3.211 

3.241 

3.272 

3.305 

3,324 

3.350 

3.375 

3.398 

3.422 

3.444 

3.467 

548.40  J 

B 

.4025 

.4062 

.4102 

.4140 

.4167 

.4198 

.4229 

.4258 

.4287 

.4316 

.4345 

if 

C 

2.819 

2.843 

2.870 

2.898 

2.916 

2.938 

2.959 

2.980 

3.000 

3.020 

3.040 

545.13 

B 

.4013 

.4049 

.4088 

.4128 

.4152 

.4184 

.4213 

.4243 

.4273 

.4300 

.4329 

.1600  > 
30     ) 

C 

2.507 

2.530 

2.555 

2.580 

2.600 

2.615 

2.633 

2.653 

2.671 

2.687 

2.706 

542.80 

B 

.3991 

.4028 

.4066 

.4105 

.4130 

.4161 

.4188 

.4220 

.4249 

.4277 

.4305 

.1766 

C 

2.260 

2.280 

2.302 

2.925 

2.338 

2.356 

2.373 

2.390 

2.406 

2.422 

2.443 

539.35  ) 

1041   ( 

B 

.3984 

.4020 

.4058 

.4098 

.4122 

.4153 

.4183 

.4211 

.4240 

.4269 

.4296 

.  1  V4  1   > 

40     \ 

C 

2.052 

2.071 

2.090 

2.111 

2.123 

2.139 

2.155 

2.175 

2.185 

2.200 

2.214 

I,  Latent  heat  of  volatilization,     w,  weight  of  vapor  per  cubic  foot. 
B.P.  back  pressure  or  suction  gauge  pressure. 

Back  pressures       0  5  10        15      20      25        30        35       40 

Temperatures.  -28.5°  -17.5°  -8.5°  -1°5.66°  11.5°  16.8°  21.7°  26.1° 

Mr.  Matthews  defines  a  standard  ton  of  refrigeration  as  the  equiva- 
lent of  27  Ibs.  of  anhydrous  ammonia  evaporated  per  hour  from  liquid 


1352       ICE-MAKING   OR  REFRIGERATING-MACHINES. 


at  90°  F.  into  saturated  vapor  at  15.67  Ibs.  gauge  pressure  (0°  F.). 
which  requires  12,000  B.T.U.;  or  20,950  units  of  evaporation,  each  of 
which  is  equal  to  572.78  B.T.U.,  the  heat  required  to  evaporate  1  Ib. 
of  ammonia  from  a  temperature  of  —  28.5°  F.  into  saturated  vapor  at 
atmospheric  pressure. 

Size  and  Capacities  of  Ammonia  Refrigerating  -  Machines. — 
York  Mfg.  Co.  Based  on  15.67  Ibs.  back  pressure,  185  Ibs.  condensing 
pressure,  and  condensing  water  at  60°  F. 


SINGLE-ACTING  COMPRESSORS. 

DOUBLE-ACTING  COMPRESSOBS. 

Compressors  . 

Engine. 

Capacity 

Compressors. 

Engine. 

Capacity 

Tons 

Tons 

Bore. 

Stroke. 

Bore. 

Stroke. 

Refrig- 

Bore. 

Stroke. 

Bore. 

Stroke. 

Refrig- 

eration. 

eration. 

71/2 

10 

11  1/2 

10 

10 

9 

15 

13  I/? 

12 

20 

9 

12 

131/2 

12 

20 

11 

18 

16 

15 

30 

11 

15 

16 

15 

30 

121/0 

21 

18 

18 

40 

121/2 

18 

18 

18 

40 

14 

24 

20 

21 

65 

14 

21 

20 

21 

65 

16 

28 

24 

24 

90 

16 

24 

24 

24 

90 

18 

32 

26 

28 

125 

18 

28 

26 

28 

125 

21 

36 

28  l/o 

32 

175 

21 

32 

281/2 

32 

175 

24 

40 

34 

36 

250 

24 

36 

34 

36 

250 

26 

60 

38 

54 

350 

27  . 

42 

36 

42 

350 

30 

48 

44 

48 

500 

For  larger  capacities  the  machines  are  built  with  duplex  compressors, 
driven  by  simple,  tandem  or  cross  dbmpound  engines. 

DISPLACEMENT  AND  HORSE-POWER  PER  TON  OF  REFRIGERATION 
Dry  Compression.     S.A.,  Single-acting;  D.A.,  Double-acting. 


Condenser  Gauge 
Pressure  and 
Corresp.  Temp. 
of  Liquid  at 
Expansion  Valve. 

Suction  Gauge  Pressure  and  Corresponding  Temp. 

51b.= 
-  17.5°F. 

101b.= 
-  8.5°  F. 

15.671b. 
=  0°F. 

20  Ib.  = 
5.7°  F. 

25  Ib.  = 
1I.5°F. 

& 

v? 

55 

j 
^ 

dj 

5a 

g 

^ 

*& 

^ 

5s 

7829 
8901 
8092 
9224 
8362 
9555 
8630 
9890 

I.H.P. 
per  Ton. 

*| 

a5 

J 
$1. 

£& 
35 

I.H.P. 
per  Ton. 

1451b.  82°  F.,  S.A... 
145  Ib.  82°  F.,  D.A.. 
165  Ib.  89°  F.,  S.A.. 
165  Ib.  89°  F.,  D.A. 
1851b.  95.5°  F.,  S.A. 
185  Ib.  95.5°  F.,D.A. 
2051b.101.4°F.,S.A. 
2051b.l01.4°F.,D.A. 

12,608 
14,645 
13,045 
15,203 
13,491 
15,774 
13,947 
16,362 

1.654 
1.921 
1.834 
2.137 
2.013 
2.354 
2.192 
2.571 

9,811 
11,300 
10,148 
11,720 
10,487 
12,150 
10,834 
12,590 

.4 
.612 
.56 
.802 
.72 
.993 
.879 
2.184 

.195 
.358 
.341 
.529 
.4865 
.7 
.631 
.87 

6765 
7625 
6990 
7898 
7219 
8176 
7450 
8459 

.065 
.2 
.201 
.357 
.336 
.513 
.47 
.67 

5836 
6522 
6027 
6751 
6223 
6985 
6420 
7222 

0.943 
.054 
.071 
.2 
.197 
.344 
.323 
.488 

*  Cu.  in.  Displacement  per  Min.  per  Ton  of  Refrigeration. 

The  volumetric  efficiency  ranges  from  63.5  to  76.5%  for  double-acting 
and  from  74.5  to  85.5  %  for  single-acting  compressors,  increasing  with  the 
decrease  of  condenser  pressure  and  with  the  increase  of  suction  pressure. 

Where  the  liquid  is  cooled  lower  than  the  temperature  corresponding 
to  the  condensing  pressure,  there  will  be  a  reduction  in  horse-power  and 
displacement  proportional  to  the  increase  of  work  done  by  each  pound 
of  liquid  handled.  The  I.H.P.  is  that  of  the  compressor.  For  Engine 
Horse-power  add  17  %  up  to  20  tons  capacity  and  15  %  for  larger  machines. 

SMALL  SIZES  OF  REFRIGERATING-MACHINES. 


Single-acting, 
Vertical. 

Double-acting, 
Horizontal. 

Capacity,  tons  

1  1/4 

3 

6 

21/2 

6 

10 

Compressor,  diam.,  in  

4  1/2 
5 

6 
6 
6 
6 

2-6 
6 
8 
6 

4 
6 
6 
8 

51/2 
8 
8 
8 

7 
10 
10 
10 

Compressor,  stroke,  in    .    .      .        ... 

Engine  diam  ,  in 

Engine,  stroke,  in  

CONDENSERS   FOR  REFRIGERATING-MACHINES.       1353 


Rated  Capacity  of  Refrigerating -Machines.  —  It  is  customary  to 
rate  refrigerating  machines  in  tons  of  refrigerating  capacity  in  24  hours, 
on  the  basis  of  a  suction  pressure  of  15.67  Ibs.  gauge,  corresponding  to 
0°  F.  temperature  of  saturated  ammonia  vapor,  and  a  condensing  pressure 
of  185  Ibs.  gauge,  corresponding  to  95.5°  F.  The  actual  capacity  increases 
with  the  increase  of  the  suction  pressure,  and  decreases  with  the  increase 
of  the  condensing  pressure.  The  following  table  shows  the  calculated 
capacities  and  horse-power  of  a  machine  rated  at  40  H.P.,  when  run  at 
different  pressures.  (York  Mfg.  Co.)  The  horse-power  required  increases 
with  the  increase  of  both  the  suction  and  the  condensing  pressure. 


Condenser  Press. 
Temp. 

Suction  Gauge  Pressure  and  Corresponding  Temp. 

51b.= 
-17.5°F 

10  Ib.  = 
-8.5°  F. 

15.67  Ib. 

=  0°F. 

20  Ib.  = 
5.7°  F. 

25  Ib.  = 
11.5°  F. 

30  Ib.  = 
16.8°F. 

H 

OH 

w 

1 

Pk 
W 

• 

1 

Pu 
W 

• 

1 

Pk 
W 

1 

CM 

w 

1 

fC 

a 

63.4 
70.1 
76.5 
86.2 

145  Ib.  =    82°  F.. 
165  Ib.  =    89°  F  
185  Ib.  =    95.5°  F...... 
205  Ib.  =  101.4°  F  

26.6 
25.7 

24.8 
24 

50.6 
54.2 
57.4 
60.5 

34.2 
33.1 
32 
31 

55.1 
59.4 
63.3 
67 

42.8 
41.4 
40 
38.9 

58.8 
63.8 
68.6 
72.9 

49.6 
48 
46.5 
45 

60.7 
66.3 
71.4 
76.1 

57.5 
55.7 
53.9 
52.3 

62.3 
68.6 
74.2 
79.6 

65.3 
63.2 
61.3 
59.4 

Piston  Speeds  and  Revolutions  per  Minute. — There  is  a  great  diver- 
sity in  the  practice  of  different  builders  as  to  the  size  of  compressor,  the 
piston  speed  and  the  number  of  revolutions  per  minute  for  a  given 
rated  capacity.  F.  E.  Matthews,  Trans.  A.  S.  M.  E.,  1905,  has  plotted 
a  diagram  of  the  various  speeds  and  revolutions  adopted  by  four  promi- 
nent builders,  and  from  average  curves  the  following  figures  are  obtained: 


R.P.M  
Piston  speeds. 

90 
200 

78 
215 

73  68 
228|240 

64 
250 

60 
270 

581/2 
280 

57 
286 

56 
290 

55 

293 

54 
296 

53 
300 

52 
315 

51 
340 

481/2 
378 

46 
425 

Mr.  Matthews  recommends  a  standard  rating  of  machines  based  on 
these  revolutions  and  speeds  and  on  an  apparent  compressor  displace- 
ment of  4.4  cu.  ft.  per  minute  per  ton  rating. 

Condensers  for  Refrigerating^ Machines  are  of  two  kinds:  sub- 
merged, and  open-air  evaporative.  The  submerged  condenser  requires 
a  large  volume  of  cooling  water  for  maximum  efficiency.  According 
to  Siebel  the  amount  of  condensing  surface,  the  water  entering  at  70° 
and  leaving  at  80°,  is  40  sq  ft.  for  each  ton  of  refrigerating  capacity,  or 
64  lineal  feet  of  2-in.  pipe.  Frequently  only  20  sq.  ft.,  or  90  ft.  of  li/4-in. 
pipe,  is  used,  but  this  necessitates  higher  condenser  pressures.  If  F.  = 
sq.  ft.  of  cooling  surface,  h  =  heat  of  evaporation  of  1  Ib.  ammonia  at 
the  condenser  temperature,  K  .  =  Ibs.  of  ammonia  circulated  per  minute, 
m  =  B.T.IT,  transferred  per  minute  per  sq.  ft.  of  condenser  surface, 
t  =  temperature  of  the  ammonia  in  the  coils  and  t\  the  temperature  of 
the  water  outside,  F  =  hK  -*•  m(t  -  k).  For  t  =  80  and  t\  =  70,  m 
may  be  taken  at  0.5.  Practically  the  amount  of  water  required  will 
vary  from  3  to  7  gallons  per  minute  per  ton  of  refrigeration.  When 
cooling  water  is  scarce,  cooling  towers  are  commonly  used. 

E.  T.  Shinkle  gives  the  average  surface  of  several  submerged  con- 
densers as  equal  to  167  lineal  feet  of  1-in.  pipe  per  ton  of  refrigeration. 

Open  air  or  evaporation  surface  condensers  are  usually  made  of  a  stack 
of  parallel  tubes  with  return  bends,  and  means  for  distributing  the  water 
so  that  it  will  flow  uniformly  over  the  pipe  surface.  Shinkle  gives  as  the 
average  surface  of  open-air  coolers  142  ft.  of  1-in.  pipe,  or  99  ft.  of  1 1/4  in. 
pipe  per  ton  of  refrigerating  capacity. 

CAPACITY  OF  CONDENSERS.  (York  Mfg.  Co.) — The  following  table 
shows  the  capacities  and  horse-power  per  ton  refrigeration  of  one  section 
counter-current  double-pipe  condenser,  li/4-in.  and  2-in.  pipe,  12  pipes 
high,  19  feet  in  length  outside  of  water  bends,  for  water  velocities  100  ft. 
to  400  ft.  per  minute:  initial  temperature  of  condensing  water  70°. 

The  horse-power  per  ton  is  for  single-acting  compressor  with  15.67 
Ibs.  suction  pressure. 

The  friction  in  water  pump  and  connections  should  be  added  to 
water  horse-power  and  to  total  horse-power. 


1354      ICE-MAKING   OR   REFR1GERATING-MACHINES. 


Capacity  of  Condensers 


High  Pressure  Constant. 


Condensing  Water. 

Cap'y 
Tons 
Refrig. 
per  24 
hours. 

Con- 
densing 
Pressure 
Lbs.  per 
sq.  in. 

Horse-power  per  Ton 
Refrigeration. 

Veloc- 
ity 
thr'gh 
11/4-in. 
pipe. 
Ft.  per 
min. 

Total 
gallons 
used 
per 
mm. 

Gallons 
per  min 
per  ton 
Refrig. 

Fric- 
tion 
thr'gh 
Coil. 
Lbs. 
per 
sq.  in. 

Engine 
driving 
Com- 
pressor 

Circu- 
lating 
Water 
thr'gh 
Con- 
denser. 

Total 
Engine 
and 
Water 
Circu- 
lation. 

100 
150 
200 
250 
300 
400 

7.77 
11.65 
15.54 
19.42 
23.31 
31.08 

.16 
.165 
.165 
.18 
.24 
.30 

2.28 
5.75 
9.98 
15. 
21.6 
37.8 

6.7 
10. 
13.4 
16.4 
18.8 
24. 

185 
185 
185 
185 
185 
185 

.71 
.71 
.71 
.71 
.71 
.71 

0.0016 
0.004 
0.007 
0.011 
0.016 
0.030 

.7116 
.714 
.717 
.721 
.726 
.74 

Capacity  Constant. 

100 
150 
200 
250 
300 
400 

7.77 
11.65 
15.54 
19.42 
23.31 
31.08 

0.777 
1.165 
1.554 
1.942 
2.331- 
3.108 

2.28 
5.75 
9.98 
15. 
21.6 
37.8 

10. 
10. 
10. 
10. 
10. 
10. 

225 
185 
165 
155 
148 
140 

2.04 
.71 
.54 
.46 
.40 
.33 

0.001 
0.004 
0.009 
0.018 
0.030 
0.071 

2.041 
.714 
.549 
.478 
.43 
.401 

Cooling-Tower  Practice  in  Refrigerating  -  Plants.  (B.  F.  Hart, 
Jr.,  Southern  Engr.,  Mar.,  1909.) — The  efficiency  of  a  cooling-tower  de- 
pends on  exposing  the  greatest  quantity  of  water  surface  to  the  cooling 
air-currents.  In  a  tower  designed  to  handle  100  gallons  per  minute  the 
ranges  of  temperature  found  when  handling  different  quantities  of 
water  were  as  follows: 

Gallons  of  water  per  minute 148 

Temperature  of  the  atmosphere 78°- 

Relative  humidity,  % 47 

Initial  temperature 85.5° 

Final  temperature 78° 

Range 7.5° 


109 
78.5° 
49 
85° 
76° 
9° 


58 

78° 

47 

86° 

75° 

11° 


The  final  temperatures  which  may  be  obtained  when  the  initial 
temperature  does  not  exceed  100°  are  as  follows: 


Atmosphere  Temp. 

95° 

90° 

85° 

80° 

75° 

70° 

Final  temperature  of  water  leaving  tower. 

(90 
80 
60 
50 
40 

100 
98 
95 
92 
89 
85 

95 
92 
90 
88 
84 
80 

90 
88 
86 
83 
79 
76 

85 
83 
80 
78 
75 
71 

80 
78 
76 
74 
70 
67 

75 
73 
71 
69 
66 
63 

For  ammonia  condensers  we  figure  on  supplying  3  gallons  per  minute  of 
circulating  water  per  ton  of  refrigeration,  or  6  gallons  per  minute  per  ton  of 
ice  made  per  24  hours,  and  guarantee  a  reduction  range  from  150°  to  160° 
down  to  about  100°  when  the  temperature  of  the  atmosphere  does  not 
exceed  80°  nor  the  relative  humidity  60%.  When  the  temperature  of  the 
atmosphere  and  the  humidity  are  both  above  90°  the  speed  of  the  pumps 
and  the  ammonia  pressure  must  be  increased. 

The  Kefrigeratlng-Coils  of  a  Pictet  ice-machine  described  by  Ledoux 
had  79  sq.  ft.  of  surface  for  each  100,000  theoretic  negative  heat-units 
produced  per  hour.  The  temperature  corresponding  to  the  pressure  of 
the  dioxide  in  the  coils  is  10.4°  F.,  and  that  of  the  bath  (calcium  chloride 
solution)  in  which  they  were  immersed  is  19.4°. 


TEST-TRIALS  OF  REFRIGERATING-MACHINES.       1355 


Comparison    of  Actual   and    Theoretical   Ice-melting    Capacity. — 

The  following  is  a  comparison  of  the  theoretical  ice-melting  capacity  of 
an  ammonia  compression  machine  with  that  obtained  in  some  of  Prof. 
Schroter's  tests  on  a  Linde  machine  having  a  compression-cy Under 
9.9-in.  bore  and  16.5  in.  stroke,  and  also  in  tests  by  Prof.  Den  ton  on  a 
machine  having  two  single-acting  compression-cylinders,  12  in.  X  30  in.: 


No  of 

Temp,  in  Degrees  F. 
Corresponding  to 
Pressure  of  Vapor. 

Ice-melting  Capacity  per  Ib.  of  Coal, 
assuming  3  Ibs.  per  hour  per 
Horse-power. 

Test. 

Condenser. 

Suction. 

Theoretical 
Friction* 
Included. 

Actual. 

Per  cent  of 
Loss  Due  to 
Cylinder 
Superheating. 

&  f    1 

72.3 

26.6 

50.4 

40.6 

19.4 

SI    2 

70.5 

14.3 

37.6 

30.0 

20.2 

1      3 

69.2 

0.5 

29.4 

22.0 

25.2 

&(   4 

68.5 

-11.8 

22.8 

16.1 

29.4 

|  (24 

84.2 

15.0 

27.4 

24.2 

11.7 

c  i  26 

82.7 

-  3.2 

21.6 

17.5 

19.0 

§125 

84.6 

-10.8 

18.8 

14.5 

22.9 

*  Friction  taken  at  figures  observed  in  the  tests,  which  range  from 
14  %  to  20  %  of  the  work  of  the  steam-cylinder. 

TEST-TRIALS  OF  REFRIGERATING-MACHINES. 

(G.  Linde,  Trans.  A.  S.  M.  E.,  xiv,  1414.) 

The  purpose  of  the  test  is  to  determine  the  ratio  of  consumption  and 
production,  so  that  there  will  have  to  be  measured  both  the  refrigera- 
tive  effect  and  the  heat  (or  mechanical  work)  consumed,  also  the  cool- 
ing water.  The  refrigerative  effect  is  the  product  of  the  number  of 
heat-units  (Q)  abstracted  from  the  body  to  be  cooled,  and  the  quotient 
(Tc  -  T)  -5-  T:  in  which  Tc  =  absolute  temperature  at  which  heat  is 
transmitted  to  the  cooling  water,  and  T  =  absolute  temperature  at 
which  heat  is  taken  from  the  body  to  be  cooled. 

The  determination  of  the  quantity  of  cold  will  be  possible  with  the 
proper  exactness  only  when  the  machine  is  employed  during  the  test  to 
refrigerate  a  liquid ;  and  if  the  cold  be  found  from  the  quantity  of  liquid 
circulated  per  unit  of  time,  from  its  range  of  refrigeration,  and  from  its 
specific  heat.  Sufficient  exactness  cannot  be  obtained  by  the  refrigera- 
tion of  a  current  of  circulating  air,  nor  from  the  manufacture  of  a  certain 
quantity  of  ice,  nor  from  a  calculation  of  the  fluid  circulating  within  the 
machine  (for  instance,  the  quantity  of  ammonia  circulated  by  the  com- 
pressor). Thus  the  refrigeration  of  brine  will  generally  form  the  basis 
for  tests  making  any  pretension  to  accuracy.  The  degree  of  refrigeration 
should  not  be  greater  than  necessary  for  allowing  the  range  of  temperature 
to  be  measured  with  the  necessary  exactness;  a  range  of  temperature  of 
from  5°  to  6°  Fahr.  will  suffice. 

The  condenser  measurements  for  cooling  water  and  its  temperatures 
will  be  possible  with  sufficient  accuracy  only  with  submerged  condensers. 
The  measurement  of  the  quantity  of  brine  circulated,  and  of  the  cool- 
ing water,  is  usually  effected  by  water-meters  inserted  into  the  conduits. 
If  the  necessary  precautions  are  observed,  this  method  is  admissible. 
For  quite  precise  tests,  however,  the  use  of  two  accurately  gauged 
tanks  which  are  alternately  filled  and  emptied  must  be  advised. 

To  measure  the  temperatures  of  brine  and  cooling  water  at  the  entrance 
and  exit  of  refrigerator  and  condenser  respectively,  the  employment  of 
specially  constructed  and  frequently  standardized  thermometers  is  in- 
dispensable ;  no  less  important  is  the  precaution  of  using  at  each  spot  si- 
multaneously two  thermometers,  and  of  changing  the  position  of  one  such 
thermometer  series  from  inlet  to  outlet  (and  vice  versa)  after  the  expiration 
of  one-half  of  the  test,  in  order  that  possible  errors  may  be  compensated. 
It  is  important  to  determine  the  specific  heat  of  the  brine  used  in 
each  instance  for  its  corresponding  temperature  range,  as  small  differ- 
ences in  the  composition  and  the  concentration  may  cause  considerable 
variations.  (Continued  on  page  1358.) 


«f  £1P1?oni*  ^oppression-machines.—  •  Ammonia  gas  possesses  the  advantage  of  affording  about  three  times  the  useful  effect  ]rt 
of  sulphur  dioxide  for  the  same  volume  described  by  the  piston. 
Ihe  perfection  of  ammonia  apparatus  now  renders  it  so  convenient  and  reliable  that  no  practical  advantage  results  from  § 
tne  lower  pressures  afforded  by  sulphur  dioxide. 
The  results  of  the  calculations  for  ammonia  are  given  in  the  table  below:  '-' 

PERFORMANCE  OF  AMMONIA  COMPRESSION-MACHINES. 
ir?  44"bsrhersed  'n^"??,  ^ompression  as  in  ordinary  practice.  Temperature  of  condenser,  64.4°  Fahr.  Pressure  in  condenser,  g 

KING   OR   REFRIGERATING 

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TEST-TRIALS  OF  REFRIGERATING- MACHINES.      1357 


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1358      ICE-MAKING   OR   REFRIGERATING-MACHINES. 

As  regards  the  measurement  of  consumption,  the  programme  will  not 
have  any  special  rules  in  cases  where  only  the  measurement  of  steam  and 
cooling  water  is  undertaken,  as  will  be  mainly  the  case  for  trials  of  absorp- 
tion-machines. For  compression-machines  the  steam  consumption 
depends  both  on  the  quality  of  the  steam-engine  and  on  that  of  the 
remgerating-machine,  while  it  is  evidently  desirable  to  know  the  con- 
sumption of  the  former  separately  from  that  of  the  latter.  As  a  rule 
steam-engine  and  compressor  are  coupled  directly  together,  thus  render- 
ing a  direct  measurement  of  the  power  absorbed  by  the  refrigerating- 
machine  impossible,  and  it  will  have  to  suffice  to  ascertain  the  indicated 
work  both  of  steam-engine  and  compressor.  By  further  measuring 
the  work  for  the  engine  running  empty,  and  by  comparing  the  differences 
in  power  between  steam-engine  and  compressor  resulting  for  wide  varia- 
tions of  condenser-pressures,  the  effective  consumption  of  work  Le  for 
the  refrigerating-machine  can  be  found  very  closely.  In  general,  it  will 
suffice  to  use  the  indicated  work  found  in  the  steam-cylinder,  especially 
as  from  this  observation  the  expenditure  of  heat  can  be  directly  deter- 
mined. Ordinarily  the  use  of  the  indicated  work  in  the  compressor- 
cylinder,  for  purposes  of  comparison,  should  be  avoided;  firstly,  because 
there  are  usually  certain  accessory  apparatus  to  be  driven  (agitators,  etc.), 
belonging  to  the  refrigerating-machine  proper;  and  secondly,  because 
the  external  friction  would  be  excluded. 

Report  of  Test.  —  Reports  intended  to  be  used  for  comparison  with 
the  figures  found  for  other  machines  will  have  to  embrace  at  least  the 
following  observations: 
Refrigerator: 

Quantity  of  brine  circulated  per  hour  r  ........................  .... 

Brine  temperature  at  inlet  to  refrigerator  .......................... 

Brine  temperature  at  outlet  of  refrigerator  .......................  T 

Specific  gravity  of  brine  (at  64°  Fahr.)  ......  .  ...................... 

Specific  heat  of  brine  ............................................ 

Heat  abstracted  (cold  produced)  .  .  ..............................  Qe 

Absolute  pressure  in  the  refrigerator  .............................. 

Condenser: 

Quantity  of  cooling  water  per  hour  ................................. 

Temperature  at  inlet  to  condenser  ................................ 

Temperature  at  outlet  of  condenser  ............................  Tc 

Heat  abstracted  ..............................................  Qi 

Absolute  pressure  in  the  condenser  .....  ........................... 

Temperature  of  gases  entering  the  condenser  ............  ............ 


ABSORPTION-MACHINE  . 

Still: 

Steam  consumed  per  hour 

Abs.  pressure  of  heating  steam 

Temperature  of  condensed  steam  at 
outlet 

Heat  imparted  to  still Q'e 

Absorber: 

Quantity  of  cooling  water  per  hour . . 


Temperature  at  inlet 

Temperature  at  outlet 

Heat  removed Qz 

Pump  for  Ammonia  Liquor: 

Indicated  work  of  steam-engine  .... 


Steam-consumption  for  pump 

Thermal     equivalent    for    work    of 

pump ALp 

Total  sum  of  losses  by  radiation  and 

convection ±  Qz 

Heat  Balance: 

Qe  +  Q'e  =  QI  +  QZ  ^  Q3- 
For  the  calculation  of  efficiency  and  for  comparison  of  various  tests, 
the  actual  efficiencies  must  be  compared  with  the  theoretical  maximum 
of   efficiency    Q  -T-  GAL)    max.  =  T  +  (Tc  -  T}    corresponding    to    the 
temperature  range, 


COMPRESSION-MACHINE  . 
Compressor: 


Indicated  work  ..........  LI 

Temperature  of  gases  at  inlet 
Temperature  of  gases  at  exit 
Steam-engine: 

Feed-water  per  hour. 


Temperature  of  feed-water  . . 
Absolute  steam-pressure  be- 


fore steam-engine 


Indicated  work  of  steam-en- 
gine   Le 

Condensing  water  per  hour.. . 

Temperature  of  do 

Total  sum  of  losses  by  radia- 
tion and  convection.  .  ±  Q$ 
Heat  Balance: 

Qe  +  ALC  =  Qi  ±  Qs. 


PERFORMANCES   OF   ICE-MAKING  MACHINES.      1359 


Heat  Balance.  —  We  possess  an  important  aid  for  checking  the  cor- 
rectness of  the  results  found  in  each  trial  by  forming  the  balance  in  each 
case  for  the  heat  received  and  rejected.  Only  those  tests  should  be  re- 
garded as  correct  beyond  doubt  which  show  a  sufficient  conformity  in 
the  heat  balance.  It  is  true  that  in  certain  instances  it  may  not  be  easy 
to  account  fully  for  the  transmission  of  heat  between  the  several  parts  of 
the  machine  and  its  environment  by  radiation  and  convection,  but  gener- 
ally (particularly  for  compression-machines)  it  will  be  possible  to  obtain 
for  the  heat  received  and  rejected  a  balance  exhibiting  small  discrepancies 
only. 

Temperature  Range.  —  For  the  temperatures  (T  and  TC)  at  which  the 
heat  is  abstracted  in  the  refrigerator  and  imparted  to  the  condenser,  it  is 
correct  to  select  the  temperature  of  the  brine  leaving  the  refrigerator  and 
'that  of  the  cooling  water  leaving  the  condenser,  because  it  is  in  principle 
impossible  to  keep  the  refrigerator  pressure  higher  than  would  correspond 
to  the  lowest  brine  temperature,  or  to  reduce  the  condenser  pressure 
below  that  corresponding  to  the  outlet  temperature  of  the  cooling  water. 
Prof.  Linde  shows  that  the  maximum  theoretical  efficiency  of  a  com- 
pression-machine may  be  expressed  by  the  formula 
Q  -H  (AL)  =  T  +  (TC-  T7), 
in  which  Q  =  quantity  of  heat  abstracted  (cold  produced); 

AL  =  thermal  equivalent  of  the  mechanical  work  expended; 
L  =  the  mechanical  work,  and  A   =  I  -*-  778: 
T  =  absolute  temperature  of  heat  abstraction  (refrigerator); 
Tc  =  absolute  temperature  of  heat  rejection  (condenser). 
If  u  =  ratio  between  the  heat  equivalent  of  the  mechanical  work  AL 
and  the  quantity  of  heat  Q'  which  must  be  imparted  to  the  motor  to 
produce  the  work  L,  then 

AL  -J-  Q'  =  u,  and  Q'/Q  -  (Tc  -  70  *  (uT). 

It  follows  that  the  expenditure  of  heat  Q'  necessary  for  the  production 
of  the  quantity  of  cold  Q  in  a  compression-machine  will  be  the  smaller, 
the  smaller  the  difference  of  temperature  Tc  —  T. 

Metering  the  Ammonia.  —  For  a  complete  test  of  an  ammonia 
refrigerating-machine  it  is  advisable  to  measure  the  quantity  of  ammonia 
circulated,  as  was  done  in  the  test  of  the  75-ton  machine  described  by 
Prof.  Den  ton.  (Trans.  A.  S.  M.  E.,  xii,  326.) 

ACTUAL  PERFORMANCES  OF  ICE-MAKING  MACHINES. 

The  table  given  on  page  1360  is  abridged  from  Denton,  Jacobus,  and 
Riesenberger's  translation  of  Ledoux  on  Ice-making  Machines.  The 
following  shows  the  class  and  size  of  the  machines  tested,  referred  to  by 
letters  in  the  table,  with  the  names  of  the  authorities: 


Class  of  Machines. 

Authority. 

Dimensions  of  Com- 
pression-cylinder in 
inches. 

Bore. 

Stroke. 

A.  Ammonia  cold-compression  

Schroter. 

(  Renwick  & 
\  Jacobus. 
Denton. 

9.9 
11.3 
28.0 

10.0 
12.0 

16.5 

•    24.4 
23.8 

18.0 
30.0 

B.  Pictet  fluid  dry-compression  

C.  Bell-Coleman  air  

D.  Closed  cycle  air  

E.  Ammonia  dry-compression  

F.  Ammonia  absorption  

In  class  A,  a  German  double-acting  machine  with  compression  cylinder 
9.9  in.  bore,  16  in.  stroke,  tested  by  Prof.  Schroter,  the  ice-melting  capac- 
ity ranges  from  46.29  t9  16.14  Ibs.  of  ice  per  pound  of  coal,  according  as 
the  suction  pressure  varies  from  about  45  to  8  Ibs.  above  the  atmosphere, 
this  pressure  being  the  condition  which  mainly  controls  the  economy  of 
compression  machines.  These  results  are  equivalent  to  realizing  from 
72%  to  57%  of  theoretically  perfect  performances.  The  higher  per  cents 
appear  to  occur  with  the  higher  suction-pressures,  indicating  a  greater 
loss  from  cylinder-heating  (a  phenomenon  the  reverse  of  cylinder  conden- 


1360     ICE-MAKING   OK  REFKIGERATING-MACHINES. 


sation  in  steam-engines),  as  the  range  of  the  temperature  of  the  gas  in 
the  compression-cylinder  is  greater. 

In  E,  an  American  single-acting  compression-machine,  two  compression 
cylinders  each  12 X  30  in.,  operating  on  the  "dry  system,"  tested  by 
Prof.  Denton,  the  percentage  of  theoretical  effect  realized  ranges  from 
69.5 %  to  62.6 % .  The  friction  losses  are  higher  for  the  American  machine. 
The  latter's  higher  efficiency  may  be  attributed,  therefore,  to  more  perfect 
displacement. 

The  largest '  'ice-melting  capacity  "  in  the  American  machine  is  24.  IGlbs. 

Actual  .Performance  of  Ice-making  Machines. 


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33.23 

31.3 

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13.5 

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33.77 

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130 

60 

70 

31 

43 

37 

31.7 

12.0 

14.8 

19.5 

45.01 

35.2 

23.8 

52.0 

B 

11 

57 

21 

77 

28 

43 

37 

57.0 

21.5 

22.9 

25.6 

33.07 

39.9 

22.2 

24.1 

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15 

76 

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20.6 

22.9 

17.9 

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18.5 

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17.47 

42.2 

25.2 

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57.6 

15.7 

25.7 

5.7 

10.14 

54.5 

38.5 

16.8 

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15 

91 

15 

104 

14 

28 

23 

59.3 

27.2 

16.9 

15.7 

16.05 

36.2 

23.1 

31.5 

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16 

61 

22 

81 

31 

44 

37 

57.3 

21.6 

14.0 

28.1 

36.19 

33.4 

22.5 

26.8 

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17 

59 

16 

80 

16 

28 

23 

57.5 

20.5 

12.8 

19.3 

26.24 

34.6 

25.0 

25.6 

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79 

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57.8 

15.9 

21.1 

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11.93 

47.5 

33.4 

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54 

22 

75 

31 

43 

37 

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12.4 

22.3 

17.0 

38.04 

39.5 

22.6 

22.6 

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89 

16 

103 

16 

28 

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42.9 

19.9 

14.7 

11.9 

16.68 

37.7 

27.0 

32.7 

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22.7 

73.9 

24.16 

32.8 

11.7 

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72.6 

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28 

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19.7 

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152 

40 

79 

13 

21 

16 

4?  ?. 

70  1 

47.8 

*  Temperature  of  air  at  entrance  and  exit  of  expansion-cylinder. 

f  On  a  basis  of  3  Ibs.  of  coal  per  hour  per  H.P.  of  steam-cylinder  of 
compression-machine  and  an  evaporation  of  11.1  Ibs.  of  water  per  pound 
of  combustible  from  and  at  212°  F.  in  the  absorption-machine. 

J  Per  cent  of  theoretical  with  no  friction. 

§  Loss  due  to  heating  during  aspiration  of  gas  in  the  compression- 
cylinder  and  to  radiation  and  superheating  at  brine-tank. 

U  Actual,  including  resistance  due  to  inlet  and  exit  valves. 


PERFORMANCES   OF   ICE-MAKING   MACHINES.       1361 


This  corresponds  to  the  highest  suction-pressures  used  in  American 
practice  for  such  refrigeration  as  is  required  in  beer-storage  cellars  using 
the  direct-expansion  system.  The  conditions  most  nearly  corresponding 
to  American  brewery  practice  in  the  German  tests  are  those  in  line  5, 
which  give  an  "ice-melting  capacity"  of  19.07  Ibs. 

For  the  manufacture  of  artificial  ice,  the  conditions  of  practice  are  those 
of  lines  3  and  4,  and  lines  25  and  26.  In  the  former  the  condensing  pres- 
sure used  requires  more  expense  for  cooling  water  than  is  common  in 
American  practice.  The  ice-melting  capacity  is  therefore  greater  in  the 
German  machine,  being  22.03  and  16.14  Ibs.  against  17.55  and  14.52  for 
the  American  apparatus. 

CLASS  B.  Sulphur  Dioxide  or  Pictet  Machines.  —  No  records  are 
available  for  determination  of  the  "ice-melting  capacity"  of  machines 
using  pure  sulphur  dioxide.  In  the  "  Pictet  fluid, "  a  mixture  of  about  97  % 
of  sulphur  dioxide  and  3%  of  carbonic  acid,  the  presence  of  the  carbonic 
acid  affords  a  temperature  about  14  Fahr.  degrees  lower  than  is  obtained 
with  pure  sulphur  dioxide  at  atmospheric  pressure.  The  latent  heat  of 
this  mixture  has  never  been  determined,  but  is  assumed  to  be  equal  to 
that  of  pure  sulphur  dioxide. 

For  brewery  refrigerating  conditions,  line  17,  we  have  26.24  Ibs.  "ice- 
melting  capacity,"  and  for  ice-making  conditions,  line  13,  the  "ice- 
melting  capacity"  is  17.47  Ibs.  These  figures  are  practically  as  econom- 
ical as  those  for  ammonia,  the  per  cent  of  theoretical  effect  realized 
ranging  from  65.4  to  57.8.  At  extremely  low  temperatures,  —  15° 
Fahr.,  lines  14  and  18,  the  per  cent  realized  is  as  low  as  42.5. 

Performance  of  a  75-ton  Ammonia  Compression-machine.  (J.  E. 
Denton,  Trans.  A.  S.  M.  E.,  xii,  326.) — The  machine  had  two  single- 
acting  compression  cylinders  12  X  30  in.,  and  one  Corliss  steam- 
cylinder,  double-acting,  18  X  36  in.  It  was  rated  by  the  manufac- 
turers as  a  50-ton  machine,  but  it  showed  75  tons  of  ice-refrigerating 
effect  per  24  hours  during  the  test. 

The  most  probable  figures  of  performance  hi  eight  trials  are  as  follows: 


No.  of  Trials. 

Ammonia 
Pressures, 
Ibs.  above 
Atmosphere. 

Brine 
Tempera- 
tures, 
Degrees  F. 

w 

gg.3 

;p 

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tf£  V  3 

ft  <!>*£    O 

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CM  CM     •  U| 

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££oo  8. 
£qt-i<j>j  a 

Water-consump- 
tion, gals,  of 
Water  per  min. 
per  ton  of  Ca- 
pacity. 

Ratio  of  Actual 
Weights  of  Am- 
monia circu- 
lated. 

| 

1 

•3 

oS 

& 

Con- 
densing 

Suc- 
tion. 

Inlet. 

Outlet. 

8 
7 
4 
6 
2 

151 
161 
147 
152 
105 
135 

28 
27.5 
13.0 
8.2 
7.6 
15.7 

36.76 
36.36 
14.29 
6.27 

6.40 
4.62 

28.86 
28.45 
2.29 
2.03 
-2.22 
3.22 

70.3 
70.1 
42.0 
36.43 
37.20 
27.2 

22.60 
22.27 
16.27 
14.10 
17.00 
13.20 

0.80 
1.09 
0.83 
1.1 
2.00 
1.25 

.0 
.0 
.70 
.93 
.91- 
2.59 

.C 

.c 

.60 
.92 
.88 
2.57 

The  principal  results  in  four  tests  are  given  in  the  table  on  page 
1363.  The  fuel  economy  under  different  conditions  of  operation  is 
shown  in  the  following  table: 


Condensing  Pres- 
sure, Ibs. 

Suction-pressure, 
Ibs. 

Pounds  of  Ice-melting  Effect  with 
Engines  — 

B.T.U.  per  Ib.  of  Steam 
with  Engines  — 

Non-con- 
densing. 

Non-com- 
pound Con- 
densing. 

Compound 
Con- 
densing. 

Non-condens- 
ing. 

Condensing. 

ll 

65 

fi  * 

P-iU 

£S 
g  S 

fioQ 

£  . 

OJ  O 
PnO 

£S 

|! 

f^cc 

6j 

JSJQ 

Perlb. 
Steam. 

150 
150 
105 
105 

28 
7 
28 

24 
14 
34.5 
22 

2.90 
1.69 
4.16 
2.65" 

30 
17.5 
43 
27.5 

3.61 
2.11 
5.18 
3.31 

37.5 
21.5 
54 
34.5 

4.51 
2.58 
6.50 
4.16 

393 
240 
591 
376 

513 
300 
725 
470 

640 
366 
923 
591 

1362      ICE-MAKING   OK  KEFR1GERATING-MACHINES. 

The  non-condensing  engine  is  assumed  to  require  25  Ibs.  of  steam 
per  I.H.P.  per  hour,  the  non-compound  condensing  20  Ibs.,  and  the 
compound  condensing  16  Ibs.,  and  the  boiler  efficiency  is  assumed  at 
8.3  Ibs.  of  water  per  Ib.  coal  under  working  conditions.  The  following 
conclusions  were  derived  from  the  investigation: 

1.  The  capacity  of  the  machine  is  proportional,  almost  entirely,  to  the 
weight  of  ammonia  circulated.     This  weight  depends  on  the  suction- 
pressure  and  the  displacement  of  the  compressor-pumps.     The  practical 
suction-pressures  range  from  7  Ibs.  above  the  atmosphere,  with  which  a 
temperature  of  0°  F.  can  be  produced,  to  28  Ibs.  above  the  atmosphere, 
with  which  the  temperatures  of  refrigeration  are  confined  to  about  28°  F. 
At  the  lower  pressure  only  about  one-half  as  much  weight  of  ammonia 
can  be  circulated  as  at  the  upper  pressure,  the  proportion  being  about  in 
accordance  with  the  ratios  of  the  absolute  pressures,  22  and  42  Ibs. 
respectively.     For  each  cubic  foot  of  piston-displacement  per  minute  a 
capacity  of  about  one-sixth  of  a  ton  of  refrigerating  effect  per  24  hours 
can  be  produced  at  the  lower  pressure,  and  of  about  one-third  of  a  ton  at 
the  upper  pressure.     No  other  elements  practically  affect    the  capacity 
of  a  machine,  provided  the  cooling-surface  in  the  brine-tank  or  other  space 
to  be  cooled  is  equal  to  about  36  sq.  ft.  per  ton  of  capacity  at  28  Ibs.  back 
pressure.     For  example,  a  difference  of  100%  in  the  rate  of  circulation  of 
brine,  while  producing  a  proportional  difference  in  the  range  of  tempera- 
ture of  the  latter,  made  no  practical  difference  in  capacity. 

The  brine-tank  was  101/2  X  13  X  10 2/3  ft.,  and  contained  8000  lineal 
feet  of  1-in.  pipe  as  cooling-surface.  The  cqndensing-tank  was  12  X10 
X  10  ft.,  and  contained  5000  lineal  feet  of  1-in.  pipe  as  cooling-surface. 

2.  The  economy  in  coal-consumption  depends  mainly  upon  both  the 
suction-pressures  and  condensing-pressures.     Maximum  economy  with  a 
given  type  of  engine,  where  water  must  be  bought  at  average  city  prices, 
is  obtained  at  28  Ibs.  suction-pressure  and  about  150  Ibs.  condensiiig- 
pressure.     Under  these  conditions,  for  a  non-condensing  steam-engine 
consuming  coal  at  the  rate  of  3  Ibs.  per  hour  per  I.H.P.  of  steam-cylinders, 
24  Ibs.  of  ice-refrigerating  effect  are  obtained  per  Ib.  of  coal  consumed. 
For  the  same  condensing-pressure,  and  with  7  Ibs.  suction-pressure,  which 
affords  temperatures  of  0°  F.,  the  possible  economy  falls  to  about  14  Ibs.  of 
refrigerating  effect  per  Ib.  of  coal  consumed.     The  condensing-pressure  is 
determined  by  the  amount  of  condensing-water  supplied  to  liquefy  the 
ammonia  in  the  condenser.     If  the  latter  is  about  1  gallon  per  minute 
per  ton  of  refrigerating  effect  per  24  hours,  a  condensing-pressure  .of 
150  Ibs.  results,  if  the  initial  temperature  of  the  water  is  about  56°  F. 
Twenty-five  per  cent  less  water  causes  the  condensing-pressure  to  in- 
crease to  190  Ibs.     The  work  of  compression  is  thereby  increased  about 
20%,  and  the  resulting  "economy"  is  reduced  to  about  18  Ibs.  of  "ice 
effect"  per  Ib.  of  coal  at  28  Ibs.  suction-pressure  and  11.5  at  7  Ibs.     If,  on 
the  other  hand,  the  supply  of  water  is  made  3  gallons  per  minute,  the 
condensing-pressure  may  be  confined  to  about  105  Ibs.     The  work  of 
compression  is  thereby  reduced  about  25%,  and  a  proportional  increase 
of  economy  results.     Minor  alterations  of  economy  depend  on  the  initial 
temperature  of  the  condensing-water  and  variations  of  latent  heat,  but 
these  are  confined  within  about  5%  of  the  gross  result,  the  main  element 
of  control  being  the  work  of  compression,  as  affected  by  the  back  pressure 
and  condensing-pressure,  or  both.     If  the  steam-engine  supplying  the 
motive  power  may  use  a  condenser  to  secure  a  vacuum,  an  increase  of 
economy  of  25%  is  available  over  the  above  figures,  making  the  Ibs.  of 
"ice  effect"  per  Ib.  of  coal  for  150  Ibs.  condensing-pressure  and  28  Ibs. 
suction-pressure  30.0,  and  for  7  Ibs.  suction-pressure,  17.5.     It  is,  however, 
impracticable  to  use  a  condenser  in  cities  where  water  is  bought.     The 
latter  must  be  practically  free  of  cost  to  be  available  for  this  purpose. 
In  this  case  it  may  be  assumed  that  water  will  also  be  available  for  con- 
densing the  ammonia  to  obtain  as  low  a  condensing-pressure  as  about 
100  Ibs.,  and  the  economy  of  the  refrigerating-machine  becomes,  for 
28  Ibs.  back  pressure,  43.0  IDS.  of  "  ice-effect  "  per  Ib.  of  coal,  or  for  7  Ibs. 
back  pressure  27.5  Ibs.  of  ice  effect  per  Ib.  of  coal.     If  a  compound  con- 
densing-engine  can  be  used   with  a  steam-consumption  per  hour  per 
horse-power  of  16  Ibs.  of  water,  the  economy  of  the  refrigerating-machine 
may  be  25%  higher  than  the  figures  last  named,  making  for  28  Ibs.  back 
pressure  a  refrigerating-effect  of  54.0  Ibs.  per  Ib.  of  coal,  and  for  7  Ibs. 
back  pressure  a  refrigerating  effect  of  34.0  Ibs.  per  Ib.  of  coal. 


PERFORMANCES    OF   ICE-MAKING    MACHINES.       1363 


Performance  of  a  75-ton  Refrigerating-machine.     (Denton.) 


* 

Maximum  Capacity  and 
Economy  at  28  Ibs. 
Back  Pressure. 

Maximum  Capacity  and 
Economy  at  Zero, 
Brine,  and  8  Ibs.  Back 
Pressure. 

Maximum  Capacity  and 
Economy  for  Zero, 
Brine,  13  Ibs.  Back 
Pressure. 

Maximum  Capacity  and 
Economy  at  27.5  Ibs. 
Back  Pressure. 

Av  high  ammonia  press  above  atmos 

151  Ibs. 
28    " 
36.76° 
28.86° 
7.9° 
2281 
44.65° 
83.66° 
39.01° 
442 
25 
24.0° 
*28.17 

*71.3° 
+  14° 
34.2° 
*39° 
213° 
200° 
84.5° 

14776 
2786 
140 
17702 

17242 
6C3 
182 
18032 
330 
22% 
58.09 
32.5 
65.9 
85.0 
65.7 
23.0 

0.75 

74.8 

24.1 
$0.166 

$0.128 
$0.294 

152  Ibs. 
8.2    " 
6.27° 
2.03° 
4.24° 
2173 
56.65° 
85.4° 
28.75° 
315 
44 
16.2° 
14.68 

*68° 
-8° 
14.7° 
25° 
263° 
218° 
84.0° 

7186 
2320 
147 
9653 

9056 
712 
338 
10106 
453 
31% 
57.7 
27.17 
53.3 
71.7 
54.7 
24.0 

1.185 
36.43 

14.1 

$0.283 

$0.200 
$0.483 

147  Ibs. 
13    " 
14.29° 
2.29° 
12.00° 
943 
46.9° 
85.46° 
38.56° 
257 
40 
16.4° 
16.67 

*63.7° 
-5° 
3.0° 
10.13° 
239° 
209° 
82.5° 

8824 
2518 
167 
11409 

9910 
656 
250 
10816 
407 
26% 
57.88 
27.  S3 
59.86 
73.6 
59.37 
20.0 

0.797 

44  64 

17.27 

$0.231 

$0.136 
$0.467 

161   Ibs. 
27.5  " 

"28  '.45° 
7.91° 
2374 
54.00° 
82.86* 
28.80° 
601.5 
14 
29.1° 
28.32 

76.7° 
14° 
29.2° 
34° 
221° 
168° 
88.0° 

14647 
3020 
141 
17708 

17359 
406 
252 
18017 
309 
13% 
58.89 
32.97 
70.54 
88.63 
71.20 
19.67 

0.990 
74.56 

23.37 
$0.170 

$0.169 
$0.339 

Av.  back  ammonia  press,  above  atmos  
Av.  temperature  brine  inlet  
Av  temperature  brine  outlet              

Av  range  of  temperature     

Lbs.  of  brine.  circulated  per  minute  
AV  temp  condensing-water  at  inlet  

Av  temp  conderising-water  at  outlet  .... 

Av  range  of  temperature     .               

Lbs.  water  circulated  p.  min.  thro'  cond'ser 
ijbs  water  per  min  through  jackets 

Lbs  ammonia  circulated  per  min 

Probable  temperature  of  liquid  ammonia, 
entrance  to  brine-tank  

Temp,  of  amm.  corresp.  to  av.  back  press. 
Av.  temperature  of  gas  leaving  brine-  tanks 
Temperature  of  gas  entering  compressor  
Av.  temperature  of  gas  leaving  compressor 

Temperature  due  to  condensing  pressure.  .  . 
Heat  given  ammonia: 

By  compressor  B  T  U  per  minute       » 

By  atmosphere  B  T  U  per  minute    .... 

Total  heat  rec.  by  amm.,  B.T.U.  per  min.... 
Heat  taken  from  ammonia: 

By  jackets,  B.T.U.  per  min  

By  atmosphere  B.TU.  per  min  

Total  heat  rej.  by  amm.,  B.T.U.  per  min  
Dif  .  of  heat  rec'd  and  rej.,  B.T.U.  per  min..  . 
%  work  of  compression  removed  by  jackets 
Av.  revolutions  per  min.     ..        

Mean  eff.  press,  steam-cyl.,  Ibs.  per  sq.  in..  . 
Mean  eff.  press,  amm.-cyl.,  Ibs.  per  sq.  in.  .  . 
Av.  H.P.  steam-cylinder  

Av.  H.P.  ammonia-cylinder  

Friction  in  per  cent  of  steam  H.P  

Total  cooling  water,  gallons  per  min.  per 
ton  per  24  hours  

Tons  ice-melting  capacity  per  24  hours  
Lbs.  ice-refrigerating  eff.  per  Ib.  coal  at  3 
Ibs.  per  H.P.  per  hour.  .  .  . 

Cost  coal  per  ton  of  ice-refrigerating  effect 
at  $4  per  ton  

Cost  water  per  ton  of  ice-  refrigerating  effect 
atSlperlOOOcu.ft  

Total  cost  of  1  ton  of  ice-refrigerating  eff.  .  . 

Figures  marked  thus  (*)  are  obtained  by  calculation;  all  other  figures 
Obtained  from  experimental  data;  temperatures  in  Fahrenheit  are  degree* 


1364      ICE-MAKING    OR   REFRIGERATING-MACHINES. 


Ammonia  Compression-machine. 

ACTUAL  RESULTS  OBTAINED  AT  THE  MUNICH  TESTS. 
(Prof.  Linde,  Trans.  A.  S.  M.  E.,  xiv,  1419.) 


No.  of  Test  

1       1       2      |       3 

4 

5 

Temp,  of  refrig-  )  Inlet,  deg.  F  ...  . 
crated  brine       J  Outlet,  deg.  F... 
Specific  heat  of  brine  

43.194 
37.054 
0.861 
1,039.38 
.342,909 
*  338.  76 
15.80 
24,813 
21,703 
1,100.8 

28.344 
22.885 
0.851 
908.84 
263,950 
260.83 
16.47 
18,471 
16,026 
785.6 

13.952 

8.771 
0.843 
633.89 
172,776 
187.506 
15.28 
12,770 
11,307 
564.9 

-0.279 
-5.879 
0.837 
414.98 
121,474 
139.99 
14.24 
10,140 
8,530 
435.82 

28.251 
23.072 
0.851 
800.93 
220,284 
97.76 
21.61 
11,151 
10,194 
512.12 

Brine  circ  per  hour  cu  ft 

Cold  produced,  B.T.U.  per  hour.  .  ^ 
Cooling  water  per  hour,  cu.  ft  . 
I.H.P.  in  steam-engine  cylinder.  .  . 
Cold  pro-  )  Per  I.H.P.  in  comp.-cyl 
duced  per  >  Per  I.H.P.  in  steam-cyl 
h.,B.T.U.  )  Per  Ib.  of  steam.  .  . 

A  test  of  a  35-ton  absorption-machine  in  New  Haven,  Conn.,  by  Prof. 
Denton  (Trans.  A.  S.  M.  E.,  x,  792),  gave  an  ice-melting  effect  of  20.1 
Ibs.  per  Ib.  of  coal  on  a  basis  of  boiler  economy  equivalent  to  3  Ibs.  of 

steam  per  I.H.P.  in  a  good  non-condensing  steam-engine.  The  ammonia 
was  worked  between  138  and  23  Ibs.  pressure  above  the  atmosphere. 

Performance  of  a  Single-acting  Ammonia  Compressor.  —  Tests 
were  made  at  the  works  of  the  Eastman  Kodak  Co.,  Rochester,  N.Y.,  of 
a  machine  fitted  with  two  York  Mfg.  Co.'s  single-acting  compressors, 
15  in.  diam.,  22  in.  stroke,  to  determine  the  horse-power  per  ton  of 
refrigeration.  Following  are.  the  principal  average  results  (Bulletin 
of  York  Mfg.  Co.): 


Date  of  Test,  1908  

Mar.  CJMar.  7 

Mar.  8 

Mar.  9 

Mar. 
10. 

Mar. 
11. 

Mar. 
14. 

Temp,  dischg.  gas,  av  
Temp,  suction  gas,  av  .  .  .  . 
Temp,  suction  at  cooler.  . 
Temp,  liquid  at  exp.  valve 
Temp,  brine  inlet  

216.2 
15.2 
9.33 
74.85 
22.89 
13.58 
45.1 
20.76 
20.11 
183.96 
69.35 
49.08 
1.418 

217.8 
14.3 
9.36 
74.16 
23.19 
13.96 
45.0 
20.43 
19.90 
184.41 
69.80 
48.79 
1.427 

250.6 
16.8 
10.37 
71.98 
25.26 
14.44 
45.1 
21.04 
19.97 
186.99 
70.05 
50.38 
1.389 

245.8 
14.8 
9.29 
77.91 
22.73 
13.02 
34.3 
15.59 
20.04 
187.27 
52.57 
37.01 
1.422 

253.0 
13.5 
9.90 
76.61 
27.35 
15.53 
56.0 
25.99 
20.18 
187.90 
89.48 
61.39 
1.425 

242.9 
18.2 
13.20 
82.88 
28.41 
16.06 
67.8 

255.5 
17.9 
9.13 

76.98 
23.43 
12.87 
44.8 
20.40 
20.38 
183.81 
68.61 
49.31 
1.375 

Temp,  brine,  outlet  
Revs  per  min 

Lbs.  liquid  NHs  per  min.  . 
Sue.  press,  at  mach.  Ib.  .  . 
Condenser  pressure 

18.13 
186.8 
105.11 
66.65 
1,439 

Indicated  H.P  

Tons  Refrig.  Capy,  24  hrs. 
I.H.P.  per  ton  capacity  .  . 

Full  details  of  these  tests  were  reported  to  the  Am.  Socy.  of  Refrig. 
Engrs.  and  published  in  Ice  and  Refrigeration,  1908. 

Performance  of  Absorption  Machines.  —  From  an  elaborate  review 
by  Mr.  Voorhees  of  the  action  of  an  absorption  machine  under  certain 
stated  conditions,  showing  the  quantity  of  ammonia  circulated  per  hour 
per  ton  of  refrigeration,  its  temperature,  etc.,  at  the  several  stages  of 
the  operation,  and  its  course  through  the  several  parts  of  the  apparatus, 
the  following  condensed  statement  is  obtained: 

Generator.  —  30.9  Ibs.  dry  steam,  38  Ibs.  gauge  pressure  condensed, 
evaporates  32.2%  strong  liquor  to  22.3%  weak  liquor. 

Exchanger.  —  3.01  Ibs.  weak  liquor  at  264°  cools  to  111°. 

Absorber.  —  Adds  0.43  Ibs.  vapor  from  the  brine  cooler,  making  3.44 
Ibs.  strong  liquor  at  111°  to  go  to  the  r»nnn>. 

Exchanger.  —  3.44  Ibs.  heated  to  224°,  some  of  it  is  now  gas,  and  the 
rest  liquor  of  a  little  less  than  32%  NH3. 

Analyzer.  —  (A  series  of  shelves  in  a  tank  above  the  generator)  delivers 
strong  liquor  to  the  generator,  while  the  vapor,  91  %  NH3,  0.4982  Ib.,  goes 
to  the  rectifier. 

Rectifier.  —  Cools  the  gas  to  110°  separating  water  vapor  as  0.0682  Ib. 
drip  liquor  which  returns  through  a  trap  to  the. generator. 

Condenser.  — 0.43  Ib.  NHs  gas  at  110°  cooled  and  condensed  to  liquid 
at  90°  by  2  gals,  of  water  per  min.  heated  from  73°  to  86°. 


PERFORMANCES   OF  ICE-MAKING  MACHINES.        1365 


Expansion  Valve  and  Cooler.  —  Reduces  liquid  to  0°  and  boils  it  at  0°, 
cooling  3  gals,  of  brine  per  min.  from  12°  to  3°.  Gas  passes  to  absorber 
and  the  cycle  is  repeated. 

Of  the  2  gals,  per  min.  of  cooling  water  flowing  from  the  condenser, 
0.2  gal.  goes  to  the  rectifier,  where  it  is  heated  to  142°,  and  1.8  gal.  through 
the  absorber,  where  it  is  heated  to  110°. 

Heat  Balance.  —  Absorbed  in  the  generator  496;  in  the  brine  cooler, 
200,  Total  696  B.T.U.  Rejected;  condenser,  220;  absorber,  383;  rectifier, 
93;  Total  696  B.T.U. 

The  following  table  shows  the  strength  of  the  liquors  and  the  quantity 
of  steam  required  per  hour  per  ton  of  refrigeration  under  the  conditions 
stated:  v 

Condenser  Pressures. 


140 

170 

200 

Suction  Pressures. 

0 

15 

30 

0 

15 

30 

0 

15 

30 

SI  per  cent         .  .  . 

24 
13.13 
30.1 
1.7 

35 
25.75 
27.9 
1.6 

42 
33.70 
22.9 
1.4 

22 
10.85 
41.3 
2.1 

32 
22.3 
30.9 
1.9 

38 
29.15 
26.2 
1.8 

18 
6.28 
48.7 
2.4 

28 
17.7 
34.1 
2.3 

36 
26.9 
27.9 
2.2 

Wl  per  cent  
SG,  pounds  

SL,  pounds  

SI,  strong  liquor;  Wl,  weak  liquor;  SG,  Ibs.  of  steam  per  hour  per  ton 
of  refrigeration  for  the  generator,  SL,  do.  for  the  liquor  pump.  Pressures 
are  in  Ibs.  per  sq.  in.,  gauge. 

The  following  table  gives  the  steam  consumption  in  Ibs.  per  hour  per 
ton  of  refrigeration,  for  engine-driven  compressors  and  for  absorption 
machines  with  liquor  pump  not  exhausting  into  the  generator  at  the  suc- 
tion and  condenser  pressures  (gauge)  given:  SC,  simple  non-condensing 
engine,  CC.  compound  condensing  engine,  A,  absorption  machine. 

Condenser  Pressures. 


140 


170 


200 


Suction  Pressures. 

0 

15 

30 

0 

15 

30 

0 

15 

30 

sc 

78.3 
42.0 
31.8 

44.5 
23.8 
29.5 

31.1 
16.6 
24.3 

90.5 
48.4 
43.4 

52.5 

28.0 
32.8 

37.2 
19.0 
28.0 

104.0 
55.6 
51.1 

61.4 
32.7 
36.4 

44.5 
23.9 
30.1 

cc  

A  

The  economy  of  the  absorption  machine  is  much  better  for  all  condi- 
tions than  that  of  a  simple  non-condensing  engine-driven  compressor. 
At  suction  gauge  pressures  above  8  to  10  Ibs.  the  economy  of  the  com- 
pound condensing  engine-driven  compressor  exceeds  that  of  the  absorp- 
tion machine,  the  absorption  machine  giving  the  superior  economy  at 
suction  pressures  below  8  to  10  Ibs. 

Means  for  Applying  the  Cold.  (M.  C.  Bannister,  Liverpool  Eng'g 
Soc'y,  1890.)  —  The  most  useful  means  for  applying  the  cold  to  vari9us 
uses  is  a  saturated  solution  of  brine  or  chloride  of  magnesium,  which 
remains  liquid  at  5°  Fahr.  The  brine  is  first  cooled  by  being  circulated 
in  contact  with  the  refrigerator-tubes,  and  then  distributed  through 
coils  of  pipes,  arranged  either  in  the  substances  requiring  a  reduction  of 
temperature,  or  in  the  cold  stores  or  rooms  prepared  for  them;  the  air 
coming  in  contact  with  the  cold  tubes  is  immediately  chilled,  and  the 
moisture  in  the  air  deposited  on  the  pipes.  It  then  falls,  making  room 
for  warmer  air,  and  so  circulates  until  the  whole  room  is  at  the  tempera- 
ture of  the  brine  in  the  pipes. 

The  Direct  Expansion  Method  consists  in  cpnveying  the  compressed 
cooled  ammonia  (or  other  refrigerating  agent)  directly  to  the  room  to  be 
cooled,  and  then  expanding  it  through  an  expansion  cock  into  pipes  in  the 
room.  Advantages  of  this  system  are  its  simplicity  and  its  rapidity  of 


1366      ICE-MAKING  OR  REFBIGERATING-MACHINES. 

action  in  cooling  a  room;  disadvantages  are  the  danger  of  leakage  of  the 
gas  and  the  fact  that  the  machine  cannot  be  stopped  without  a  rapid  rise 
in  the  temperature  of  the  room.  With  the  brine  system,  with  a  large 
amount  of  cold  brine  in  the  tank,  the  machine  may  be  stopped  for  a  con- 
siderable time  without  serious  cooling  of  the. room. 

Air  has  also  been  used  as  the  circulating  medium.  The  ammonia-pipes 
refrigerate  the  air  in  a  cooling-chamber,  and  large  conduits  are  used  to 
convey  it  to  and  return  it  from  the  rooms  to  be  cooled.  An  advantage  of 
this  system  is  that  by  it  a  room  may  be  refrigerated  more  quickly  than  by 
brine-coils.  The  returning  air  deposits  its  moisture  on  the  ammonia- 
pipes,  in  the  form  of  snow,  which  is  removed  by  mechanical  brushes. 

'  ARTIFICIAL-ICE  MANUFACTURE. 

Under  summer  conditions,  with  condensing  water  at  70°,  artificial-ice 
machines  use  ammonia  at  a  condenser  pressure,  about  190  Ibs.  above  the 
atmosphere  and  15  Ibs.  suction-pressure. 

In  a  compression  type  of  machine  the  useful  circulation  of  ammonia, 
allowing  for  the  effect  of  cylinder-heating,  is  about  13  Ibs.  per  hour  per 
indicated  horse-power  of  the  steam-cylinder.  This  weight  of  ammonia 
produces  about  32  Ibs.  of  ice  at  15°  from  water  at  70°.  If  the  ice  is  made 
from  distilled  water,  as  in  the  "can  system,"  the  amount  of  the  latter 
supplied  by  the  boilers  is  about  33%  greater  than  the  weight  of  ice 
obtained.  This  excess  represents  steam  escaping  to  the  atmosphere 
from  the  re-boiler  and  steam-condenser,  to  purify  the  distilled  water,  or 
free  it  from  air;  also,  the  loss  through  leaks  and  drips,  and  loss  by  melting 
of  the  ice  in  extracting  it  from  the  cans.  The  total  steam  consumed  per 
horse-power  is,  therefore,  about  32  x  1.33  =  43.0  Ibs.  About  7.0  Ibs. 
of  this  covers  the  steam-consumption  of  the  steam-engines  driving  the 


the  required  amount  of  distilled  water.  There  is,  therefore,  nothing  to  be 
gained  by  using  steam  at  high  rates  of  expansion  in  the  steam-engines,  in 
making  artificial  ice  from  distilled  water.  If  the  cooling  water  for  the 
ammonia-coils  and  steam-condenser  is  not  too  hard  for  use  in  the  boilers, 
it  may  enter  the  latter  at  about  175°  F.,  by  restricting  the  quantity  to 
11/2  gallons  per  minute  per  ton  of  ice.  With  good  coal  8V2  Ibs.  of  feed- 
water  may  then  be  evaporated,  on  the  average,  per  Ib.  of  coal. 

The  ice  made  per  pound  of  coal  will  then  be  32  ~  (43.0  ~-  8.5)  «=  6.0 
Ibs.  This  corresponds  with  the  results  of  average  practice. 

If  ice  is  manufactured  by  the  "plate  system,"  no  distilled  water  is 
used  for  freezing.  Hence  the  water  evaporated  by  the  boiler  may  be 
reduced  to  the  amount  which  will  drive  the  steam-motors,  and  the  latter 
may  use  steam  expansively  to  any  extent  consistent  with  the  powei 
required  to  compress  the  ammonia,  operate  the  feed  and  filter  pumps, 
and  the  hoisting  machinery.  The  latter  may  require  about  15%  of  the 
power  needed  for  compressing  the  ammonia. 

If  a  compound  condensing  steam-engine  is  used  for  driving  the  com- 
pressors, the  steam  per  indicated  steam  horse-power,  or  per  32  Ibs.  of 
net  ice,  may  be  14  IDS.  per  hour.  The  other  motors  at  50  Ibs.  of  steam 
per  horse-power  will  use  7.5  Ibs.  per  hour,  marking  the  total  consumption 
per  steam  horse-power  of  the  compressor  21.5  Ibs.  Taking  the  evapora- 
tion at  8  Ibs.,  the  feed-water  temperature  being  limited  to  about  110°,  the 
coal  per  horse-power  is  2.7  Ibs.  per  hour.  The  net  ice  per  Ib.  of  coal  is 
then  about  32  -i-  2.7  =11.8  Ibs.  The  best  results  with  "plate-system" 
plants,  using  a  compound  steam-engine,  have  thus  far  afforded  about  10V2 
Ibs.  of  ice  per  Ib.  of  coal. 

In  the  "plate  system"  the  ice  gradually  forms,  in  from  8  to  10  days,  to 
a  thickness  of  about  14  inches,  on  the  hollow  plates,  10  x  14  feet  in  area,  in 
which  the  cooling  fluid  circulates. 

In  the  "can  system"  the  water  is  frozen  in  blocks  weighing  about 
300  Ibs.  each,  and  the  freezing  is  completed  in  from  40  to  48  hours.  The 
freezing-tank  area  occupied  by  the  "plate  system"  is,  therefore,  about 
twelve  times,  and  the  cubic  contents  about  four  times,  as  much  as  required 
in  the  "can  system." 

The  investment  for  the  "plate"  is  about  one-third  greater  than  for  the 
"can' !  system.  In  the  latter  system  ice  is  being  drawn  throughout  the 


ARTIFICIAL-ICE  MANUFACTURE.  1367 

24  hours,  and  the  hoisting  is  done  by  hand  tackle.  Some  "can"  plants 
are  equipped  with  pneumatic  hoists  and  on  large  hoists  electric  cranes  are 
used  to  advantage.  In  the  "plate  system"  the  entire  daily  product  is 
drawn,  cut,  and  stored  in  a  few  hours,  the  hoisting  being  performed 
by  power.  The  distribution  of  cost  is  as  follows  for  the  two  systems,  tak- 
ing the  cost  for  the  "can"  or  distilled-water  system  as  100,  which  repre- 
sents an  actual  cost  of  about  $1.25  per  net  ton: 

Can  System.   Plate  System. 

Hoisting  and  storing  ice 14.2  2.8 

Engineers,  firemen,  and  coal-passer 15.0  13.9 

Coal  at  $3.50  per  gross  ton 42 .2  20  .0 

Water  pumped  directly  from  a  natural  source 

at  5  cts.  per  1000  cubic  feet 1.3  2.6 

Interest  and  depreciation  at  10% 24 .6  32 .7 

Repairs 2.7  3.4 

100.00  75.4 

A  compound  condensing  engine  is  assumed  to  be  used  by  the  "plate 
system." 

Test  of  the  New  York  Hygeia  Ice-making  Plant.  —  (By  Messrs. 
Hupfel,  Griswold,  and  Mackenzie;  Stevens  Indicator,  Jan.,  1894.) 

The  final  results  of  the  tests  were  as  follows: 

Net  ice  made  per  pound  of  coal,  in  pounds 7.12 

Pounds  of  net  ice  per  hour  per  horse-power 37 .8 

Net  ice  manufactured  per  day  (12  hours)  in  tons 07 

Av.  pressure  of  ammonia-gas  at  condenser,  Ibs.  per  sq.  in.  above 

atmos 135 .2 

Average  back  pressure  of  amm.-gas,  Ibs.  per  sq.  in.  above  atmos.     15.8 

Average  temperature  of  brine  in  freezing-tanks,  degrees  F 19 .7 

Total  number  of  cans  filled  per  week 4389 

Ratio  of  cooling-surface  of  coils  in  brine-tank  to  can-surface 7  to  10 

An  Absorption  Evaporator  Ice-making  System,  built  by  the  Carbon- 
dale  Machine  Co.  is  in  operation  at  the  ice  plant  of  the  Richmond  Ice  Co., 
Clifton,  Staten  Island,  N.  Y.,  which  produces  the  extra  distilled  water  by 
an  evaporator  at  practically  no  fuel  cost,  and  thus  about  10  tons  of  dis- 
tilled water  ice  per  ton  of  coal  is  obtained.  Steam  from  the  boiler  at 
100  Ibs.  pressure  enters  an  evaporator,  distilling  off  steam  at  70  Ibs., 
which  operates  the  pumps  and  auxiliary  machinery.  These  exhaust 
into  the  ice  machine  generator  under  10  Ibs.  pressure,  where  the  exhaust 
is  condensed.  In  a  100-ton  plant  the  evaporator  will  condense  43  tons 
of  live  steam,  distilling  off  40  tons  of  steam  to  operate  the  auxiliaries, 
which  exhaust  into  the  generator;  20  tons  of  live  steam  has  to  be  added 
to  this  exhaust,  making  60  tons  in  all,  which  is  the  amount  required  to 
operate  the  generator.  The  60  tons  of  condensation  from  the  generator 
and  43  tons  from  the  evaporator  go  to  the  re-boiler,  making  103  tons  ol 
distilled  water  to  be  frozen  into  ice.  The  total  steam  consumption  is  the 
60  tons  condensed  in  the  generator  plus  3  tons  for  radiation,  or  63  tons 
in  all.  Hence  if  the  boiler  evaporates  6.6  Ibs.  water  per  pound  of  coal 
the  economy  of  the  plant  will  be  10 1/2  Ibs.  ice  per  pound  of  coal,  a  result 
which  cannot  be  obtained  even  with  compound  condensing  engines  and 
compression  machines. 

Heat-excnangmg  coils,  on  the  order  of  a  closed  feed-water  heater,  are 
used  to  heat  the  feed-water  going  to  the  boiler.  The  condensation  leav- 
ing the  generator  and  evaporator  at  a  high  temperature  is  utilized  for 
this  purpose;  by  this  means  securing  a  feed-water  temperature  con- 
siderably in  excess  of  212°. 

Ice-Making  with  Exhaust  Steam.  —  The  exhaust  steam  from  electric 
light  plants  is  oeing  utilized  to  manufacture  ice  on  the  absorption  system. 
A  10-ton  plant  at  the  Holdredge  Lighting  Co.,  Holdredge,  Neb.,  built  by 
the  Carbondale  Machine  Co.,  is  described  in  Elec.  World,  April  7,  1910. 
Here  11  tons  of  ice  were  made  per  day  with  exhaust  steam  from  the 
electric  engines  at  21/2  Ibs.  pressure,  using  6V3  K.W.,  or  8V2  H.P.,  for 
driving  the  circulating  pumps. 

Tons  of  Ice  per  Ton  of  Coal.  —  From  a  long  table  by  Mr.  Voorhees, 
showing  the  net  tons  of  plate  ice  that  may  be  made  in.  well-designed 
plants  under  a  variety  of  conditions  as  to  type  of  engine,  the  following 
figures  are  taken: 


1368 


MARINE  ENGINEERING. 


Compression,  Simple  Corliss  engine,  non-condensing 6.1  tons 

Absorption  liquor  pump  and  auxiliaries  not  exhausting  into 

generator,  simple,  non-condensing  engine 10.0 

Compression,  C9mpound  condensing  engine 11.2 

Compression  triple-expansion  condensing  engine 12.8 

Absorption,  pump  and  auxiliaries  exhausting  into  generator, 

Corliss  non-condensing  engine 13.3 

Compression  and  absorption,  compound  engine,  non-condensing  16.0 

Compression,  triple-expansion  condensing  engine,  multiple  effect  16.5 
Compression  and  absorption,  triple-expansion  non-condensing 

engine,  multiple  effect 19.5 

Standard  Ice  Cans  or  Moulds. 

(Buffalo  Refrigerating  Machine  Co.) 


Weight  of 
Block. 

Size  of  Can. 

Time  of 
Freezing. 

Weight  of 
Block. 

Size  of  Can. 

Time  of 
Freezing. 

pounds 

50 
100 
150 
150 
200 

4x10x24 
6x12x26 
8x15x32 
8x15x44 
10x15x36 
10x20x36 

hours 
12 
20 
36 
36 
48 
48 

pounds 
100 
200 
300 
400 
200 

11x11x32 
11x22x32 
11x22x44 
11x22x56 
14X14X40 

hours 
48 
54 
54 
54 
66 

The  above  given  time  of  freezing  is  with  a  brine  temperature  of  15°  F. 

Cubic  Feet  of  Well-insulated  Space  per  Ton  of  Refrigeration. 

(F.  W.  Niebling  Co.,  Cincinnati,  *O.) 


Room  Temperature. 


0°F. 


10° 


20° 


32° 


36° 


Size  of  Room. 

Cubic  Feet  per  Ton. 

Up  to  1,000  cu.  ft  

200 
600 
1000 

400 
1200 
2000 

800 
2500 
4000 

1400 
4500 
6000 

2000 
6000 
8000 

2500 
8000 
10.000 

1,000  to  10,000  cu.  ft  
Over  10,000  cu.  ft  

MARINE  ENGINEERING-. 

Rules  for  Measuring  Dimensions  and  Obtaining  Tonnage  t>f 
Vessels.  (Record  of  American  and  Foreign  Shipping.  American  Bureau 
of  Shipping,  N.  Y.,  1890.)  —  The  dimensions  to  be  measured  as  follows; 

I.  Length,   L.  —  From  the  fore-side  of  stem  to  the  after-side  of  stern- 
post  measured  at  middle  line,  on  the  upper  deck  of  all  vessels,  except 
those  having  a  continuous  hurricane-deck  extending  right  fore  and  aft, 
in  which  the  length  is  to  be  measured  on  the  range  of  deck  immediately 
below  the  hurricane-deck. 

Vessels  having  clipper  heads,  raking  forward,  or  receding  stems,  or 
raking  stern-posts,  the  length  to  be  the  distance  of  the  fore-side  of  stem 
from  aft-side  of  stern-post  at  the  deep-load  water-line  measured  at  middle 
line.  (The  inner  or  propeller-post  to  be  taken  as  stern-post  in  screw- 
steamers.) 

II.  Breadth,  B.  —  To  be  measured  over  the  widest  frame  at  its  widest 
part;  in  other  words,  the  molded  breadth. 

III.  Depth,  D.  —  To  be  measured  at  the  dead-flat  frame  and  at  middle 
line  of  yessel.     It  shall  be  the  distance  from  the  top  of  floor-plate  to  the 
upper  side  of  upper  deck-beam  in  all  vessels  except  those  having  a  con- 
tinuous hurricane-deck,  extending  right  fore  and  aft,  and  not  intended 
for  the  American  coasting  trade,  in  which  the  depth  is  to  be  the  distance 
from  top  of  floor-plate  to  ^midway  between  top  of  hurricane  deck-beam 
and  the  top  of  deck-beam  of  the  deck  immediately  below  hurricane-deck. 

In  vessels  fitted  with  a  continuous  hurricane-deck,  extending  right 
fore  and  aft,  and  intended  for  the  American  coasting  trade,  the  depth  is 


MAKINE   ENGINEERING.  1369 

to  be  the  distance  from  top  of  floor-plate  to  top  of  deck-beam  of  deck 
immediately  below  hurricane-deck. 

Rule  for  Obtaining  Tonnage.  —  Multiply  together  the  length,  breadth, 
and  depth,  and  their  product  by  0.75;  divide  the  last  product  by  100; 
the  quotient  will  be  the  tonnage.  L  X  B  X  D  X  0.75-7-100  =  tonnage. 

The  U.  S.  Custom-house  Tonnage  Law,  May  6,  1864,  provides  that 
"  the  register  tonnage  of  a  vessel  shall  be  her  entire  internal  cubic  capacity 
in  tons  of  100  cubic  feet  each."  This  measurement  includes  all  the  space 
between  upper  decks,  however  many  there  may  be.  Explicit  directions 
for  making  the  measurements  are  given  in  the  law. 

The  Displacement  of  a  Vessel  (measured  in  tons  of  2240  Ibs.)  is 
the  weight  of  the  volume  of  water  which  it  displaces.  For  sea-water  it  is 
equal  to  the  volume  of  the  vessel  beneath  the  water-line,  in  cubic  feet, 
divided  by  35,  which  figure  is  the  number  of  cubic  feet  of  sea-water  at 
60°  F.  in  a  ton  of  2240  Ibs.  For  fresh  water  the  divisor  is  35.93.  The 
U.  S.  register  tonnage  will  equal  the  displacement  when  the  entire  internal 
cubic  capacity  bears  to  the  displacement  the  ratio  of  100  to  35. 

The  displacement  or  gross  tonnage  is  sometimes  approximately  esti- 
mated as  follows:  Let  L  denote  the  length  in  feet  of  the  boat,  B  its  extreme 
breadth  in  feet,  and  D  the  mean  draught  in  feet;  the  product  of  these 
three  dimensions  will  give  the  volume  of  a  parallelopipedon  in  cubic  feet. 
Putting  V  for  this  volume,  we  have  V  =  L  X  B  X  D. 

The  volume  of  displacement  may  then  be  expressed  as  a  percentage 
of  the  volume  V,  known  as  the  "  block  coefficient. "  This  percentage  varies 
far  different  classes  of  ships.  In  racing  yachts  with  very  deep  keels  it 
varies  from  22  to  33:  in  modern  merchantmen  from  55  to  90;  for  ordinary 
small  boats  probably  50  will  give  a  fair  estimate.  The  volume  of  dis- 
placement in  cubic  feet  divided  by  35  gives  the  displacement  in  tons. 

Coefficient  of  Fineness.  —  A  term  used  to  express  the  relation  between 
the  displacement  of  a  Ship  and  the  volume  of  a  rectangular  prism  or  box. 
whose  lineal  dimensions  are  the  length,  breadth, 'and  draught. 

Coefficient  of  fineness  =  D  X  35-J-(L  X  B  X  T7);  D  being  the  displace- 
ment in  tons  of  35  cubic  feet  of  sea-water  to  the  ton,  L  the  length  between 
perpendiculars,  B  the  extreme  breadth  and  W  the  mean  draught,  all  in  feet. 

Coefficient  of  Water-lines.  —  An  expression  of  the  relation  of  the  dis- 
placement to  the  volume  of  the  prism  whose  section  equals  the  midship 
section  of  the  ship,  and  length  equal  to  the  length  of  the  ship. 

Coefficient  of  water-lines = D  X  35  •*•  (area  of  immersed  water  sectionX-L). 
Seaton  gives  the  following  values: 

Coefficient     Coefficient  of 
of  Fineness.       Water-lines 

Finely-shaped  ships 0 .55  0 .63 

Fairly-shaped  ships 0.61  0.67 

Ordinary  merchant  steamers  10  to  11  knots. . .         0  .65  0 . 72 

Cargo  steamers,  9  to  10  knots %    0  .70  0  .76 

Modern  cargo  steamers  of  large  size 0  .78  0 .83 

Resistance  of  Ships.  —  The  resistance  of  a  ship  passing  through  watei 
mav  vary  from  a  number  of  causes,  as  speed,  form  of  body,  displacement, 
midship  dimensions,  character  of  wetted  surface,  fineness  of  lines,  etc. 
The  resistance  of  the  water  is  twofold;  1st.  That  due  to  the  displacement 
of  the  water  at  the  bow  and  -its  replacement  at  the  stern,  with  the  con- 
sequent formation  of  waves.  2d.  The  friction  between  the  wetted  sur- 
face of  the  ship  and  the  water,  known  as  skin  resistance.  A  common 
approximate  formula  for  resistance  of  vessels  is 
Resistance  =  speech  x  x/displacementsxa  constant,  or  R  =  S*D2h  X  C. 

\f  Dl  =  displacement  in  pounds,  Si  =  speed  in  feet  per  minute,  R  re- 
sistance in  pounds,  R  =  cS^Di 2/3.  The  work  done  in  overcoming  the  re- 
sistance through  a  distance  equal  to  Si  is  R  X  Si  =  cS^Di2^;  and  if  E  is 
the  efficiency  of  the  propeller  and  machinery  combined,  the  indicated 
horse-power  I.H.P.  =  cS^D^h  ~  (E  X  33,000). 

If  S  =  speed  in  knots,  D  =  displacement  in  tons,  and  C  a  constant 
which  includes  all  the  constants  for  form  of  vessel,  efficiency  of  mechan- 
ism, etc.,  I.H.P.  =  SW 2/3  +  C. 

The  wetted  surface  varies  as  the  cube  root  of  the  square  of  the  displace- 
ment: thus,  let  L  be  the  length  of  edge  of  a  cube  just  immersed,  whose 


1370 


MARINE   ENGINEERING. 


displacement  is  D  and  wetted  surface  W.     Then  D  =  L3  or  L  =^Dt 
and  TF  =  5X  L*  =  5  X  (-\/D)2.     That  is,  TF  varies  as  Z)2'3. 

Another  approximate  formula  is 

I.H.P.  =  area  of  immersed  midship  section  X  £3  -~  K. 

The  usefulness  of  these  two  formulae  depends  upon  the  accuracy  of  the 
so-called  "constants"  C  and  K,  which  vary  with  the  size  and  form  of  the 
ship,  and  probably  also  with  the  speed.  Seaton  gives  the  following, 
which  may  be  taken  roughly  as  the  values  of  C  and  K  under  the  condi- 
tions expressed: 


General  Description  of  Ship. 

Speed, 
knots. 

Value 
of  C. 

Value 
of  K. 

Ship"}  over  400  feet  long  finely  shaped 

15  to 
15  " 
13  " 
11 
11 
9 
13 
11 
9 
11 
9 
11 
9 
9 
11 
10 
9 
9 

17 
17 
15 
13 
13 
11 
15 
13 
11 
13 
11 
12 
11 
11 
12 
11 
10 
10 

240 
190 
240 
260 
240 
260 
200 
240 
260 
220 
250 
220 
240 
220 
200 
210 
230 
200 

620 
500 
650 
700 
650 
700 
580 
660 
700 
620 
680 
600 
640 
620 
550 
580 
620 
600 

"         300         "                                 .... 

14                                                  4«                                          It 

Snips  over  300  feet  long  fairly  shaped 

Ships  over  250  feet  long  finely  shaped  

4<                                                   41                                          II 

Ships  over  250  feet  long  fairly  shaped 

Ships  over  200  feet  long,  finely  shaped  .  . 

Ships  over  200  feet  long,  fairly  shaped  

Ships  under  200  feet  long,  finely  shaped  

41                                                  ««        '                                  II 

Ships  under  200  feet  long,  fairly  shaped  

Coefficient  of  Performance  of  Vessels.  —  The  quotient 

^(displacement)2  X  (speed  in  knots)^-  tons  of  coal  in  24  hours 

gives  a  coefficient  of  performance  which  represents  the  comparative  cost 
of  propulsion  in  coal  expended.  Sixteen  vessels  with  three-stage  expan- 
sion-engines in  1890  gave  an  average  coefficient  of  14,810,  the  range  being 
from  12,150  to  16,700. 

In  1881  seventeen  vessels  with  two-stage  expansion-engines  gave  an 
average  coefficient  of  11,710.  In  1881  the  length  of  the  vessels  tested 
ranged  from  260  to  320,  and  in  1890  from  295  to  400.  The  speed  in  knots 
divided  by  the  square  root  of  the  length  in  feet  in  1881  averaged  0.539; 
and  in  1890,  0.579;  ranging  from  0.520  to  0.641.  (Proc.  Inst.  M.  E.t 
July,  1891,  p.  329.) 

Defects  of  the  Common  Formula  for  Resistance.  —  Modern 
experiments  throw  doubt  upon  the  truth  of  the  statement  that  the  resist- 
ance varies  as  the  square  of  the  speed.  (See  Robt.  Hansel's  letters  in 
Engineering,  1891;  also  his  paper  on  The  Mechanical  Theory  of  Steam- 
ship Propulsion,  read  before  Section  G  of  the  Engineering  Congress, 
Chicago,  1893.) 

Seaton  says:  In  small  steamers  the  chief  resistance  is  the  skin  resistance. 
In  very  fine  steamers  at  high  speeds  the  amount  of  power  required  seems 
excessive  when  compared  with  that  of  ordinary  steam&s  at  ordinary 
speeds. 

In  torpedo-launches  at  certain  high  speeds  the  resistance  increases  at  a 
lower  rate  than  the  square  of  the  speed. 

In  ordinary  sea-going  and  river  steamers  the  reverse  seems  to  be  the 
case. 

Rankine's  Formula  for  total  resistance  of  vessels  of  the  "wave-lino" 
type  is: 

R  =  ALBV*  (1  +  4  sin2  9  +  sin4  0), 

in  which  equation  9  is  the  mean  angle  of  greatest  obliquity  of  the  stream- 
lines, A  is  a  constant  multiplier,  B  the  mean  wetted  girth  of  the  surface 
exposed  to  friction,  L  the  length  in  feet,  and  V  the  speed  in  knots.  The 


MARINE  ENGINEERING.  1371 

power  demanded  to  impel  a  ship  is  thus  the  product  of  a  constant  to  be 
determined  by  experiment,  the  area  of  the  wetted  surface,  the  cube  ol 
the  speed,  and  the  quantity  in  the  parenthesis,  which  is  known  as  the 
"  coefficient  of  augmentation. "  In  calculating  the  resistance  of  ships  the 
last  term  of  the  coefficient  may  be  neglected  as  too  small  to  be  practically 
\mportant.  In  applying  the  formula,  the  mean  of  the  squares  of  the 
sines  of  the  angles  of  maximum  obliquity  of  the  water-lines  is  to  be  taken 
for  sin2  8,  and  the  rule  will  then  read  thus: 

To  obtain  the  resistance  of  a  ship  of  good  form,  in  pounds,  multiply  the 
length  in  feet  by  the  mean  immersed  girth  and  by  the  coefficient  of  aug- 
mentation, and  then  take  the  product  of  this  "augmented  surface,"  as 
Rankine  termed  it,  by  the  square  of  the  speed  in  knots,  and  by  the  proper 
constant  coefficient  selected  from  the  following: 

For  clean  painted  vessels,  iron  hulls A  =  0.01 

For  clean  coppered  vessels A  =  0.009  to  0.008 

For  moderately  rough  iron  vessels A  =  0.011  + 

The  net,  or  effective,  horse-power  demanded  will  be  quite  closely 
obtained  by  multiplying  the  resistance  calculated,  as  above,  by  the  speed 
in  knots  and  dividing  by  326.  The  gross,  or  indicated,  power  is  obtained 
by  multiplying  the  last  quantity  by  the  reciprocal  of  the  efficiency  of  the 
machinery  and  propeller,  which  usually  should  be  about  0.6.  Rankine 
uses  as  a  divisor  in  this  case  200  to  260. 

The  form  of  the  vessel,  even  when  designed  by  skillful  and  experienced 
naval  architects,  will  of  ten  vary  to  such  an  extent  as  to  cause  the  above 
constant  coefficients  to  vary  somewhat:  and  the  range  of  variation  with 
good  forms  is  found  to  be  from  0.8  to  1.5  the  figures  given. 

For  well-shaped  iron  vessels,  an  approximate  formula  for  the  horse- 
power required  is  H. P.  =  £F3~-  20,000,  in  which  S  is  the  "augmented 
surface."  The  expression  SV3  -f-  H.P.  has  been  called  by  Rankine  the 
coefficient  of  propulsion.  In  the  Hudson  River  steamer  "Mary  Powell," 
according  to  Thurston,  this  coefficient  was  as  high  as  23,500. 

The  expression  D»F*  •*-  H.P.  has  been  called  the  locomotive  performance. 
(See  Rankine's  Treatise  on  Shipbuilding,  1864;  Thurston's  Manual  of  the 
Steam-engine,  part  H,  p.  16;  also  paper  by  F.  T.  Bowles,  U.  S.  N.,  Proc. 
IT.  S.  Naval  Institute,  1883.) 

Rankine's  metnod  for  calculating  the  resistance  is  said  by  Seaton  to 
give  more  accurate  and  reliable  results  than  those  obtained  by  the  older 
rules,  but  it  is  criticised  as  being  difficult  and  inconvenient  of  application 

Empirical  Equations  for  Wetted  Surface.  (Peabody,  Naval  Archi- 
tecture, page  411). — L  =  length,  feet;  B  =  beam;  H  =  mean  draught; 
D  =  displacement  in  tons;  K=  block  coefficient. 

Taylor  Surface  =  C\/T>L.     Values  of  C  for  different  ratios  B  -i-  H  are: 

B   -f-  H   =     2  2.2        2.4        2.6        2.8        3.0        3.2        3.4 

C   =15.63   15.54   15.50   15.51   15.55   15.62   15.71   15.83 

Normand  Surface  =  1.52  LH  +  (3.74  +  0.85  K*)  LB. 
Mumford  Surface  =  L  (1.74  +  KB). 

Errors  of  these  approximate  equations  as  applied  to  several  types  of 
vessels  are  shown  by  Professors  Durand  and  McDermott  (Trans. 
Soc.  Nav.  Archts.  &  Mar.  Engrs.,  Vol.  2),  as  follows:  Taylor  -  2.69  to 
+  2.52%;  Normand,  -  1.55  to  +  2.57%;  Mumford,  0  to  -  0.95%, 
except  one  lake  freight  vessel,  L  =  299,  B  =  40.9,  D  =  15.9,  K  =  0.825, 
on  which  Mumford's  formula  was  —  12.55  %  in  error. 

•  E.  R.  Mumford's  Method  of  Calculating  Wetted  Surfaces  is  given 
in  a  paper  by  Archibald  Denny,  Eng'g,  Sept.  21,  1894.  The  following 
is  his  formula,  which  gives  closely  accurate  results  for  medium  draughts, 
beams,  and  finenesses; 

S  =  (L  X  D  X  1.7)  +  (L  X  B  X  C), 

in  which  S  =  wetted  surface  in  square  feet;  L  -=  length  between  perpen- 
diculars in  feet;  D  =  middle  draught  in  feet;  B  =  beam  in  feet;  C  — 
block  coefficient. 

The  formula  may  also  be  expressed  in  the  form  S  =  L(1.7  D  +  BC). 

In  the  case  of  twin-screw  ships  having  projecting  shaft-casings,  or  in 


1372 


MARINE  ENGINEERING. 


the  case  of  a  ship  having  a  deep  keel  or  bilge  keels,  an  addition  must  be 
made  for  such  projections.  The  formula  gives  results  which  are  in 
general  much  more  accurate  than  those  obtained  by  Kirk's  method.  It 
underestimates  the  surface  when  the  beam,  draught,  or  block  coefficients 
are  excessive;  but  the  error  is  small  except  in  the  case  of  abnormal  forms, 
such  as  stern-wheel  steamers  having  very  excessive  beams  (nearly  one- 
fourth  the  length),  and  also  very  full  block  coefficients.  The  formula 
gives  a  surface  about  6%  too  small  for  such  forms. 

The  wetted  surface  of  the  block  is  nearly  equal  to  that  of  the  ship  of 
the  same  length,  beam  and  draught;  usually  2%  to  5%  greater.  In 
exceedingly  fine  hollow-line  ships  it  may  be  8%  greater. 

Area  of  bottom  of  block  =  (F  +  M)  X  B; 

Area  of  sides  =  2  M  X  H. 


Area  of  sides  of  ends  =  4  X 


. 

X//; 


Tangent  of  half  angle  of  entrance  =  i/zB/F  =  B/(2  F). 
From  this,  by  a  table  of  natural  tangents,  the  angle  of  entrance  may  be 
obtained: 

Angle  of  Entrance     Fore-body  in 
of  the  Block  Model,  parts  of  length. 
Ocean-going  steamers,  14  knots  and  upw'd      18°  to  15°       0  .3    to  0  .36 

12  to  14  knots  .....     21°  to  18°       0  .26  to  0.3 
cargo  steamers,  10  to  12  knots..     30°  to  22°       0  .22  to  0  .26 
Dr.  Kirk's  Method.  —  This  method  is  generally  used  on  the  Clyde. 
The  general  idea  proposed  by  Dr.  Kirk  is  to  reduce  all  ships  to  so 
definite  and  simple  a  form  that  they  may  be  easily  compared;  and  the 
magnitude  of  certain  features  of  this  form  shall  determine  the  suitability 
of  the  ship  for  speed,  etc. 

The  form  consists  of  a  middle  body,  which  is  a  rectangular  parallele- 
piped, and  fore-body  and  after-body,  prisms  having  isosceles  triangles  for 
Inses,  as  shown  in  Fig.  225. 


FIG.  225. 

This  is  called  a  block  model,  and  is  such  that  its  length  is  equal  to  that 
of  the  ship,  the  depth  is  equal  to  the  mean  draught,  the  capacity  equal 
to  the  displacement  volume,  and  its  area  of  section  equal  to  the  area  of 
immersed  midship  section.  The  dimensions  of  the  block  model  may  be 
obtained  as  follows:  Let  AG  =  HB  =  length  of  fore-  or  after-body  =  F; 
GH  =  length  of  middle  body  =  M;  KL  =  mean  draught  =  H;  EK  = 
area  of  immersed  midship  section  •*•  KL  =B.  Volume  of  block =(F+M)  X 
BX  H;  midship  section  =  BX  H-,  displacement  in  tons  =  volume  in 
cubic  ft.  •*•  35. 

AH  =  AG  -h  GH  =  F  +  M  =  displacement  X  35  -»•  (B  X  #). 

To  find  the  Indicated  Horse-power  from  the  Wetted  Surface. 
(Seaton.)  —  In  ordinary  cases  the  horse-power  per  100  feet  of  wetted 
surface  may  be  found  by  assuming  that  the  rate  for  a  speed  of  1 
is  5,  and  that  the  quantity  varies  as  the  cube  of  the  speed.  For  example: 
To  find  the  number  of  I.'H.P.  necessary  to  drive  a  ship  at  a  speed  of  15 
knots,  having  a  wetted  skin  of  block  model  of  16,200  square  feet: 

The  rate  per  100  feet  =  (1 5/10)3  X  5  =  16.875. 
Then  I.H.P.  reauired  =  16.875  X  162  *=  2734. 
When  the  ship  is  exeptionally  well-proportioned,  the  bottom  quite 


TVTA.RINL  &NGINEEKING. 


1373 


clean,  and  the  etticiency  of  the  machinery  high,  as  low  a  rate  as  4  LH.P. 
per  100  feet  of  wetted  skin  of  block  model  may  be  allowed. 

The  gross  indicated  horse-power  includes  the  power  necessary  to  over- 
come the  friction  and  other  resistance  of  the  engine  itself  and  the  shafting, 
and  also  the  power  lost  in  the  propeller.  In  other  words,  I.H.P.  is  no 
meas'ire  of  the  resistance  of  the  ship,  and  can  only  be  relied  on  as  a  means 
of  deciding  the  size  of  engines  far  speed,  so  long  as  the  efficiency  of  the 
engine  and  propeller  is  known  definitely,  or  so  long  as  similar  engines  and 
propellers  are  employed  in  ships  to  be  compared.  The  former  is  difficult 
to  obtain,  and  it  is  nearly  impossible  in  practice  to  know  how  much  of 
the  power  shown  in  the  cylinders  is  employed  usefully  in  overcoming  the 
resistance  of  the  ship.  The  following  example  is  given  to  show  the  vari- 
ation in  the  efficiency  of  propellers: 

Knots.        I.H.P. 

H.M.S.  "Amazon,"  with  a  4-bladed  screw,  gave 12.064  with  1940 

H.M.S.  "Amazon,"  with  a  2-bladed  screw,  increased 

pitch,  and  fewer  revolutions  per  minute 12.396     '       1663 

H.M.S.  " Iris,"  with  a  4-bladerf  screw 16.577     "     7503 

H.M.S.  "Iris."  with  2-bladed  screw,  increased  pitch, 

fewer  revolutions  per  knot 18.587  7556 

Relative  Horse-power  Required  for  Different  Speeds  of  Vessels. 
(Horse-power  for  10  knots  =  1.)  — The  horsVpower  is  taken  usually  to 
vary  as  the  cube  of  the  speed,  but  in  different  vessels  and  at  different 
speeds  it  may  vary  from  the  2.8  power  to  the  3.5  power,  depending  upon 
the  lines  of  the  vessel  and  upon  the  efficiency  of  the  engines,  the  pro- 
peller, etc.  (The  power  may  vary  at  a  much  higher  rate  than  the  3.5 
power  of  the  speed  when  the  speed  is  much  less  than  normal,  and  the 
machinery  is  therefore  working  at  less  than  its  normal  efficiency  ) 


13    03 

Oj  0 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

HPoc 

g2-S 

.0769 

.239 

.535 

.666 

2.565 

3.729 

5.185 

6.964 

9.095 

11.60 

14.52 

17  87 

71  67 

g2-9 

.0701 

.227 

.524 

.697 

2,653 

3  908 

5  499 

7  464 

9  841 

12  67 

15  97 

19  80 

74  19 

S3 

.0640 

.216 

.512 

.728 

2.744 

4  096 

5.832 

8 

10,65 

13,82 

17,58 

71  95 

77 

g3-l 

.0584 

.205 

.501 

.760 

2.838 

4.293 

6.185 

8,574 

11.52 

15.09 

19.34 

74  33 

30  14 

g3-2 

.0533 

.195 

.490 

.792 

2.935 

4.500 

6.559 

9.189 

12.47 

16.47 

21.28 

26,97 

33  63 

g3-3 

.0486 

.185 

.479 

.825 

3,0^6 

4  716 

6  957 

9  849 

13  49 

17  98 

73  41 

79  90 

37  54 

g3-4 

.0444 

.176 

.468 

.859 

3.139 

4.943 

7,378 

10  56 

14.60 

19  62 

25  76 

33  14 

41  00 

gS-5 

0405 

167 

458 

893 

3  747 

5  181 

7  874 

11   31 

15  79 

71  47, 

28.34 

36.73 

46.77 

EXAMPLE  IN  USE  OF  THE  TABLE. — A  certain  vessel  makes  14  knots 
speed  with  587  I.H.P.  and  16  knots  with  900  I.H.P.  What  I.H.P.  will 
be  required  at  18  knots,  the  rate  of  increase  of  horse-power  wjth  increase 
of  speed  remaining  constant?  The  first  step  is  to  find  the  rate  of 
increase,  thus:  14*  :  16*  ::  587  :  9QO. 

x  log  16  -  x  log  14  =  log  900  -  log  587; 
X  (0.204120  -  0.146128)  =  2.954243  -  2.768638, 
whence  x  (the  exponent  of  S  in  formula  H.P.oc  S*)  =  3.2. 

From  the  table,  for  S3-2  and  16  knots,  the  I.H.P.  is  4.5  times  the 
I.H.P.  at  10  knots;  .-.  H.P.  at  10  knots  =  900  -=-  4.5  =  200. 

From  the  table  for  ,S3-2  and  18  knots,  the  I.H.P.  is  6.559  times  the 
I.H.P.  at  10  knots;  .-.  H.P.  at  18  knots  =  200  X  6.559  =  1312  H.P. 

Resistance  per  Horse-power  for  Different  Speeds.  (One  horse- 
power =  33.000  Ibs.  resistance  overcome  through  1  ft.  in  1  min.) — The 
resistances  per  horse-power  for  various  speeds  are  as  follows:  For  a 
speed  of  1  knot,  or  6080  feet  per  hour  =  10H/3  ft.  per  min.,  33,000  •*• 
1011/3  =  325.658  Ibs.  per  horse-power;  and  for  any  other  speed  325.658 
Ibs.  divided  by  the  speed  in  knots;  or  for 


1  knot    325.66  Ibs. 

2  knots  162.83 

108.55 
81.41 
65.13 
54.28 
46.52 


8  knots  40.71  Ibs. 


9 

10 
11 
12 
13 

14 


36.18 
32.57 
29.61 
27.14 
25.05 
23.26 


15  knots 

16 

17 

18 

19 

20 


21.71  IDS. 

20.35 

19.16 

18.09 

17.14 

16.28 


1374 


MARINE   ENGINEERING. 


More  accurate  methods  than  those  above  given  for  estimating  the  horse- 
power required  for  any  prop9sed  ship  are:  1.  Estimations  calculated 
from  the  results  of  trials  of  "similar"  vessels  driven  at  "corresponding" 
speeds;  "similar",  vessels  being  those  that  have  the  same  ratio  01  length 
to  breadth  and  to  draught,  and  the  same  coefficient  of  fineness,  and 
"corresponding"  speeds  ttwse  which  are  proportional  to  the  square  roots 
of  the  lengths  of  the  respective  vessels,  iroude  found  that  the  resistances 
of  such  vessels  varied  almost  exactly  as  wetted  surface  X  (speed)2 

2.  The  method  employed  by  the  British  Admiralty  and  by  some  Clyde 
shipbuilders,  viz.,  ascertaining  the  resistance  of  a  model  of  the  vessel, 
12  to  20  ft.  long,  in  a  tank,  and  calculating  the  power  from  the  results 
obtained. 

Estimated  Displacement,  Horse-power,  etc.  —  The  table  on  the 
next  page,  calculated  by  the  author,  will  be  found  convenient  for  making 
approximate  estimates. 

The  figures  in  7th  column  are  calculated  by  the  formula  H. P.  —  SZD$+  c 
in  which  c  =  200  for  vessels  under  200  ft.  long  when  C  =  0.65,  and  210 
when  C  =  0.55;  c  =  200  for  vessels  200  to  400  ft.  long  when  C  =0.75, 
220  when  C  =  0.65,  240  when  C  =  0.55;  c  =  230  for  vessels  over  400  ft. 
long  when  C  =  0.75,  250  when  C  =  0.65,  260  when  C  =  0.55. 

The  figures  in  the  8th  column -are  based  on  5  H.P.  per  100  sq.  ft.  of 
wetted  surface. 

The  diameters  of  screw  in  the  9th  column  are  from  formula  D  =  3.31 
-5/I.H.P.,  and  in  the  10th  column  from  formula  D  =  2.71  ^/I.H.P. 

To  find  the  diameter  of  screw  for  any  other  speed  than  10  knots,  revolu- 
tions being  100  per  minute,  multiply  the  diameter  given  in  the  table  by 
the  5th  root  of  the  cube  of  the  given  speed  •*•  10.  For  any  other  revolu- 
tions per  minute  than  100,  divide  by  the  revolutions  and  multiply  by  100. 

To  find  the  approximate  horse-power  for  any  other  speed  than  10  knots, 
multiply  the  horse-power  given  in  the  table  by  the  cube  of  the  ratio  of  the 
given  speed  to  10,  or  by  the  relative  figure  from  table  on  p.  1373. 

F.  E.  Cardullo,  Mach'y,  April,  1907,  gives  the  following  formula  as 
closely  approximating  the  speed  6fA  modern  types  of  hulls:  S  =  6.35 

/T  TT  "P 

',     ,  in  which  S  =  speed  in  knots,  D  =  displacement  in  tons. 
D '3 

we  take  S  =  10 knots,  then  I.H.P.  -~  D2/3  =  3.906.  Let  D  =  10,000,  and. 
S  =  10,  then  H.P.  =  1813.  The  table  on  page  1375  gives  for  a  displace- 
ment of  10,400  tons  and  a  coefficient  of  fineness  0.65,  1966  and  1760  H.P., 
averaging  1863  H.P. 

Internal  Combustion  Marine  Engines.  —  Linton  Hope  (Eng'g, 
April  8, 1910),  in  a  paper  on  the  application  of  internal  combustion  engines 
to  fishing  boats  and  fine-lined  commercial  vessels,  gives  a  table  showing 
the  brake  H.P.  required  to  propel  such  vessels  at  various  speeds.  The 
following  table  is  an  abridgment.  L=load  water  line;  D= displacement 
in  tons. 


Block  Coefficient. 


0.25 

0.3 

0.35 

0.4 

4 

5    1     6 

7 

8   |    9 

10 

L 

78 
71 
65 
59 
54 
50 
46 
41 
38 
35 
32 
30 
28 

D 

L  |    D 

L  |    D 

L 

D 

Brake  Horse-power. 

105 
81 

62 
47 
36 
28 
22 
17 
13 
9 
61/2 
41/2 
3V4 

75 
69 
63 
57 
52 
48 
44 
40 
37 
34 
31 
29 
27 

100 
77 
60 
45 
35 
27 
21 
16 
12 
81/2 
6 
41/4 

72 
66 
60 
54 
50 
46 
42 
38 
35 
32 
30 
28 
26 

95 
73 
58 
44 
34 
26 
20 
15 

,u/2 

58 

23/4 

69 
63 

57 
52 
48 
44 
40 
37 
34 
31 
29 
27 
25 

90 
70 
55 

42 
32 
25 
19 
14 
11 
71/2 

31/2 
21/2 

20 
17 
15 
13 
11 
9 
8 
7 
6 
5 
4 
3 
2V2 

30 
25 
22 
19 
16 
13 
12 
11 
9 

h 

41/2 

43 
37 
32 
27 
24 
20 
17 
15 
13 
11 
9 
7 
6V2 

60 
51 
44 
39 
34 
29 
25 
22 
19 
16 
14 
12 
11 

81 
69 
60 
53 
48 
44 
40 
37 
34 

110 
93 
82 
76 
71 

150 

Speed  in  Knots. 


MARINE    ENGINEERING. 


1375 


Estimated  Displacement,  Horse-power,  etc.,  of  Steam-vessels  of 
Various  Sizes. 


jl" 

S*J 

If 

m  <M 

1^ 

II 

Is0 

8BS  jf 
|-o  I 

Displacement. 
L£DX  C 

Wetted  Surface 
L  (1.7  D+  JiC) 

Sq.  ft. 

Estimated  Horse- 
power at  10  knots. 

Diam.  of  Sorew  for  10 
knots  speed  and  100  ' 
revs,  per  minute. 

85 

tons. 

Calc. 
from  Dis- 
placem't. 

\jaic.  irom 
Wetted 
Surface. 

If  Pitch  = 
Diam. 

If  Pitch  =1 
1.4  Diam. 

12 

3 

1.5 

0.55 

0.85 

48 

4.3 

2.4 

4.4 

3.6 

16  I 

3 

1.5 

.55 

1.13 

64 

*  5.2 

3.2 

4.6 

3.8 

16  1 

4 

2 

.65 

2.38 

96 

8.9 

4.8 

5.1 

4.2 

?nl 

3 

1.5 

.55 

1.41 

80 

6.0 

4.0 

4.7 

3.9 

20  i 

4 

2 

.65 

2.97 

120 

10.3 

6.0 

5.3 

4.3 

74] 

3.5 

1.5 

.55 

1.98 

104 

7.5 

5.2 

5 

4.1 

24  { 

4.5 

2 

.65 

4.01 

152 

12.6 

7.6 

5.5 

4.5 

30  i 

4 

2 

.55 

3.77 

168 

11.5 

8.4 

5.4 

4.4 

30  { 

5 

2.5 

.65 

6.96 

224 

18.2 

11.2 

5.9 

4.8 

40  J 

4.5 

2 

.55 

5.66 

235 

15.1 

11.8 

5.7 

4.7 

40{ 

6 

2.5 

.65 

11.1 

326 

24.9 

16.3 

6.3 

5.2 

50  1 

6 

3 

.55 

14.1 

420 

27.8 

21.0 

6.4 

5.4 

50  | 

8 

3.5 

.65 

26 

558 

43.9 

27.9 

7.1 

5.8 

60  1 

8 

3.5 

.55 

26.4 

621 

42.2 

31.1 

7.0 

5.7 

60  \ 

10 

4 

.65 

44.6 

798 

62.9 

39.9 

7.6 

6.2 

70 

10 

4 

.55 

44 

861 

59.4 

43.1 

7.5 

6.1 

70  i 

12 

4.5 

.65 

70.2 

1082 

85.1 

54.1 

8.1 

6.6 

8oi 

12 

4.5 

.55 

67.9 

1140 

79.2 

57.0 

7.9 

6.5 

WM 

14 

5 

.65 

104.0 

1408 

111 

70.4 

8.5 

7.0 

on  •{ 

13 

5 

.55 

91.9 

1408 

97 

70.4 

8.3 

6.8 

yj  I 

16 

6 

.65 

160 

1854 

147 

92.7 

9 

7.3 

( 

13 

5 

.55 

102   • 

1565 

104 

78.3 

8.4 

6.9 

100  { 

15 

5.5 

.65 

153 

1910 

143 

95.5 

8.9 

7.3 

( 

17 

6 

.75 

219 

2295 

202 

115 

9.6 

7.8 

14 

5.5 

.55 

145 

2046 

131 

102 

8.8 

7.2 

1205 

16 

6 

.65 

214 

2472 

179 

124 

9.4 

7.6 

( 

18 

6.5 

.75 

301 

2946 

250 

147 

10 

8.2 

16 

6 

;55 

211 

2660 

169 

133 

9.2 

7.4 

140 

18 

6.5 

.65 

306 

3185 

227 

159 

9.8 

8.0 

f 

20 

7 

.75 

420 

3766 

312 

188 

10.5 

8.5 

< 

17 

6.5 

.55 

278 

3264 

203 

163 

9.6 

7.8 

160  J 

19 

7 

.65 

395 

3880 

269 

194 

10.1 

8.3 

( 

21 

7.5 

.75 

540 

4560 

368 

228 

10.8 

8.8 

( 

20 

7 

.55 

396 

4122 

257 

206 

10.1 

8.2 

180) 

22 

7.5 

.65 

552 

4869 

337 

243 

10.6 

8.7 

( 

24 

8 

.75 

741 

5688 

455 

284 

11.3 

9.2 

22 

7 

.55 

484 

4800 

257 

240 

10.1 

8.2 

200  | 

25 

8 

.65 

743 

5970 

373 

299 

10.8 

8.8 

1 

28 

9 

.75 

1080 

7260 

526 

363 

11.6 

9.5 

( 

28 

8 

.55 

880 

7250 

383 

363 

10.9 

8.9 

250  { 

32 

10 

.65 

1486 

9450 

592 

473 

11.9 

9.7 

( 

36 

12 

.75 

2314 

11850 

875 

593 

12.8 

10.5 

32 

10 

.55 

1509 

10380 

548 

519 

11.7 

9.6 

300  J 

36 

12 

.65 

2407 

13140 

806 

657 

12.6 

10.4 

( 

40 

14 

.75 

3600 

17140 

1175 

857 

13.6 

11.1 

38 

12 

.55 

2508 

14455 

769 

723 

12.5 

10.2 

350] 

42 

14 

.65 

3822 

17885 

1111 

894 

13.5 

11.0 

I 

46 

16 

.75 

5520 

21595 

1562 

1080 

14.4 

11.8 

( 

44 

14 

.55 

3872 

19200 

1028 

960 

13.3 

10.8 

400  ] 

48 

16 

.65 

5705 

23360 

1451 

1168 

14.2 

11.6 

( 

52 

18 

.75 

8023 

27840 

2006 

1392 

15.2 

12.4 

( 

50 

16 

.55 

5657 

24515 

1221 

1226 

13.7 

11.2 

450  ] 

54 

18 

.65 

8123 

29565 

1616 

1478 

14.5 

11.9 

( 

58 

20 

.75 

11157 

34875 

2171 

1744 

15.4 

12.6 

CAA    ( 

52 

18 

.55 

7354 

29600 

1454 

1480 

14.2 

11.6 

500 

56 

20 

.65 

10400 

35200 

1966 

1760 

15.1 

12.4 

( 

60 

22 

.75 

14143 

41200 

2543 

2060 

15.9 

13.0 

( 

56 

20 

.55 

9680 

36245 

1747 

1812 

14.7 

12.0 

550 

60 

22 

.65 

13483 

42735 

2266 

2137 

15.5 

12.7 

( 

64 

24 

.75 

18103 

49665 

2998 

2483 

16.4 

13.4 

60 

22 

.55 

12446 

42900 

2065 

2145 

15.2 

12.5 

600  1 

64 

24 

.65 

17115 

50220 

2656 

2511 

15.4 

13.1 

( 

68 

26 

.75 

22731 

58020 

3489 

2901 

16.9 

13.8 

1376 


MARINE   ENGINEERING. 


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ft 


THE  SCREW-PROPELLER.  1377 

THE    SCREW-PROPELLER. 

The  "pitch"  of  a  propeller  is  the  distance  which  any  point  in  a  blade 
describing  a  helix  will  travel  in  the  direction  of  the  axis  during  one  revolu- 
tion, the  point  being  assumed  to  move  around  the  axis.  The  pitch  of  a 
propeller  with  a  uniform  pitch  is  equal  to  the  distance  a  propeller  will 
advance  during  one  revolution,  provided  there  is  no  slip.  In  a  case  of 
this  kind,  the  term  "  pitch"  is  analogous  to  the  term  "pitch  of  the  thread" 
of  an  ordinary  single-threaded  screw. 

Let  P  —  pitch  of  screw  in  feet,  R  =  number  of  revolutions  per  second, 
V  =  velocity  of  stream  from  the  propeller  =  P  X  R,  v  =  velocity  of  the 
ship  in  feet  per  second,  V  —  v  =  slip,  A  =  area  in  square  feet  of  section 
of  stream  from  the  screw,  approximately  the  area  of  a  circle  of  the  same 
diameter,  A  X  V  =  volume  of  water  projected  astern  from  the  ship  in 
cubic  feet  per  second.  Taking  the  weight  of  a  cubic  foot  of  sea-water 
at  64  Ibs.,  and  the  force  of  gravity  at  32,  we  have  from  the  common  for- 
mula for  force  of  acceleration,  viz.:  F=  M  j  =  —  ~,  or  F  «•  —  vi,  when 
t  =1  second. 

Thrust  of  screw  in  pounds  =  — ^—  (V  —  v)  «•  2  AV  (V  —  v). 

O4 

Rankine  (Rules,  Tables,  and  Data,  p.  275)  gives  the  following:  To 
calculate  the  thrust  of  a  propelling  instrument  (jet,  paddle,  or  screw)  in 
pounds,  multiply  together  the  transverse  sectional  area,  in  square  feet, 
of  the  stream  driven  astern  by  the  propeller;  the  speed  of  the  stream 
relatively  to  the  ship  in  knots?  the  real  slip,  or  part  of  that  speed  which  is 
impressed  on  the  stream  by  the  propeller,  also  in  knots;  and  the  constant 
5.66  for  sea-water,  or  5.5  for  fresh  water.  If  S  =  speed  of  the  screw  in 
knots,  s  =  speed  of  ship  in  knots,  A  —  area  of  the  stream  in  square  feet 
(of  sea-water), 

Thrust  in  pounds  =  A  X  S  (S  -  s)  X  5.66. 

The  real  slip  is  the  velocity  (relative  to  water  at  rest)  of  the  water  pro- 
jected sternward ;  the  apparent  slip  is  the  difference  between  the  speed  of 
the  ship  and  the  speed  of  the  screw;  i.e.,  the  product  of  the  pitch  of  the 
screw  by  the  number  of  revolutions. 

This  apparent  slip  is  sometimes  negative,  due  to  the  working  of  the 
screw  in  disturbed  water  which  has  a  forward  velocity,  following  the  ship. 
Negative  apparent  slip  is  an  indication  that  the  propeller  is  not  suited 
to  the  ship.  The  apparent  slip  should  generally  be  about  8%  to  10%  at 
full  speed  in  well-formed  vessels  with  moderately  fine  lines;  in  bluff  cargo 
boats  it  rarely  exceeds  5%. 

The  effective  area  of  a  screw  is  the  sectional  area  of  the  stream  of  water 
laid  hold  of  by  the  propeller,  and  is  generally,  if  not  always,  greater  than 
the  actual  area,  in  a  ratio  which  in  good  ordinary  examples  is  1.2  or  there- 
abouts, and  is  sometimes  as  high  as  1.4:  a  fact  probably  due  to  the  stiffness 
of  the  water,  which  communicates  motion  laterally  amongst  its  particles. 
(Rankine's  Shipbuilding,  p.  89.) 

Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  xi,  1028,  found  the  ratio  of  the 
effective  to  the  actual  disk  area  of  the  screws  of  different  vessels  to  be  as 
follows : 

Tug-boat,  with  ordinary  true-pitch  screw 1 .42 

Tug-boat,  with  screw  having  blades  projecting  backward  ...  0  57 

Ferryboat  "  Bergen, "  with  or-  (  at  speed  of  12.09  stat.  miles  per  hr  .'   1  '53 

dinary  true-pitch  screw         \  at  speed  of  13.4    stat.  miles  per  hr. .   1  !48 

Steamer  "Homer  Ramsdell,"  with  ordinary  true-pitch  screw 1 .20 

Size  of  Screw.  — Seaton  says:  The  size  of  a  screw  depends  on  so 
many  things  that  it  is  very  difficult  to  lay  down  any  rule  for  guidance, 
and  much  must  always  be  left  to  the  experience  of  the  designer,  to  allow 
for  all  the  circumstances  of  each  particular  case.  The  following  rules  are 
given  for  ordinary  cases  (Seaton  and  Rounthwaite's  Pocket-book): 

P  *=  pitch  of  propeller  in  feet  =  jgQoo^e) '  in  which  s  ~  sPeed  in 
knots,  R  =  revolutions  per  minute,  and  x  =  percentage  Of  apparent 
slip.  For  a  slip  of  10%,  pitcn  «=  U3,G  S  -r  #, 


1378 


MARINE   ENGINEERING. 


D  =diameter  of  propeller  = 


r~ ,  K  being  a  coefficient  given 


100  / 

in  the  table  below.     If  K  =  20,  D  =  20,000  "^I.H.P.  • 

Total  developed  area  of  blades  =  C  ^/I.H.P  +R 

cient  to  be  taken  from  the  table 


r-  (P  x  R)3. 
in  which  C  is  a  coeffi- 


Another formula  for  pitch,  given  in'Seaton's  Marine  Engineering,  is 
-,  in  which  C=  737  for  ordinary  vessels,  and  660  for  slow- 
speed  cargo  vessels  with  full  lines. 

Thickness  of  blade  at  root  =  \  ^  X  &,  in  which  d  •• 


=  diameter  of  tail 

shaft  in  inches,  n  =  number  of  "blades,  b  =  breadth  of  blade  in  inches 
where  it  joins  the  boss,  measured  parallel  to  the  shaft  axis;  k  =  4  for  cast 
iron,  1.5  for  cast  steel,  2  for  gun-metal,  1.5  for  high-class  bronze 

Thickness  of  blade  at  tip:  Cast  iron  0.04  D  +  0.4  in.;  cast  steel  0  03  D  4- 
0.4m.;  gun-metal  0.03  D  +  0.2  in.;  high-class  bronze  0.02  D  +03  in 
where  D  =  diameter  of  propeller  in  feet. 

Propeller  Coefficients. 


Description  of  Vessel. 

III 

<o| 
$ 

No.  of 
Blades 
per  Screw 

|&i 

£° 

SjO 

£° 

^  <a 

•ai^l 

2  05-73  d 
j«§-C« 

Bluff  cargo  boats      

8-10 
10-13 
13-17 
13-17 
17-22 
17-22 
16-22 
16-22 
20-26 

One 

Twin 
One 
Twin 

One 

4 
4 
4 
4 
4 
3 
4 
3 
3 

17    -17.5 
18    -19 
19.5-20.5 
20.5-21.5 
21     -22 
22    -23 
21     -22.5 
22    -23.5 
25 

19    -17.5 
17    -15.5 
15    -13 
14.5-12.5 
12.5-11 
10.5-  9 
11.5-10.5 
8.5-7 
7-6 

Cast  iron 
C.I.  or  S, 
G.M.orB 

B.orF.S. 

Cargo,  moderate  lines  
Pass,  and  mail,  fine  lines. 

"  ve*y  fr*?  • 

Naval  vessels,                ** 
Torpedo-boats,    "       " 

C.  I.,  cast  iron;  G.  M.,  gun-metal;  B.,  bronze;  S.,  steel;  F.S.,  forged  steel. 

From  the  formulae  D  =  20,000  k  '  **H'^' 
P  =  D  and  R  =  100,  we  obtain  D  =  ^400  X  I.H.P.  =  3.31  -y/I.H.P. 

If  P  =  1.4  D  and  R  =  100,  then  D  =  ^145.8  X  I.H.P.  =  2.71  ^/I.H.P. 

From  these  two  formulae  the  figures  for  diameter  of  screw  in  the  table 
on  page  1375  have  been  calculated.  They  may  be  used  as  rough  approx- 
imations to  the  correct  diameter  of  screw  for  any  given  horse-power,  for 
a  speed  of  10  knots  and  100  revolutions  per  minute. 

For  any  other  number  of  revolutions  per  minute  multiply  the  figures 
in  the  table  by  100  and  divide  by  the  given  number  of  revolutions.  For 
any  other  speed  than  10  knots,  since  the  I.H.P.  varies  appntximately  as 
the  cube  of  the  speed,  and  the  diameter  of  the  screw  as  the  5th  root  of  the 
I.H.P.,  multiply  the  diameter  given  for  10  knots  by  the  5th  root  of  the 
cube  of  one-tenth  of  the  given  speed.  Or,  multiply  by  the  following 
factors: 

For  speed  of  knots: 
45          6          7         8         9         11       12       13       14       15        16 

$(8  •*-  10)8 

=  0.577  0.660  0.736  0.807  0.875  0.939  1.059  1.116  1.170  1.224  1.275  1.327 

Speed: 

17        18        19        20        21        22       23        24       25        26        27         28 
^  (S  ~-  10)3 
=  1.375   1.423   1.470  1.515  1.561  1.605  1.648  1.691  1.733  1.774  1.815  1.855 

For  more  accurate  determinations  of  diameter  and  pitch  of  screw,  the 
formulae  and  coefficients  given  bv  Seaton,  quoted  above,  should  1 


THE  SCREW-PROPELLER. 


1379 


Efficiency  of  the  Propeller.  —  According  to  Rankine,  if  the  slip  of 
the  water  be  s,  its  weight  W,  the  resistance  R,  and  the  speed  of  the  ship  v. 
#  =  Ws  +  g-  Rv  =  Wsv  +  g. 

This  impelling  action  must,  to  secure  maximum  efnciencjr  of  propeller, 
be  effected  by  an  instrument  which  takes  hold  of  the  fluid  without  shock 
or  disturbance  of  the  surrounding  mass,  and,  by  a  steady  acceleration, 
gives  it  the  required  final  velocity  of  discharge.  The  velocity  of  the 
propeller  overcoming  the  resistance  R  would  then  be 

[v+  (v+s)]  +  2  =v  +  s/2; 
and  the  work  performed  would  be 

R(v+  s/2)  =  Wvs  -«-  g  +  Ws2  •*•  2  g, 

the  first  of  the  last  two  terms  being  useful,  the  second  the  minimum  lost 
work;  the  latter  being  the  wasted  energy  of  the  water  thrown  backward. 
The  efficiency  is  E  =  v  -*•  (v  +  s/2);  and  this  is  the  limit  attainable  with 
a  perfect  propelling  instrument,  which  limit  is  approached  the  more  nearly 
as  the  conditions  above  prescribed  are  the  more  nearly  fulfilled.  The 
efficiency  of  the  propelling  instrument  is  probably  rarely  much  above 
0.60,  and  never  above  0.80. 

In  designing  the  screw-propeller,  as  was  shown  by  Dr.  Froude,  the 
best  angle  for  the  surface  is  that  of  45°  with  the  plane  of  the  disk;  but  as 
all  parts  of  the  blade  cannot  be  given  the  same  angle,  it  should,  where 
practicable,  be  so  proportioned  that  the  "pitch-angle  at  the  center  of 
effort"  should  be  made  45°.  The  maximum  possible  efficiency  is  then, 
according  to  Froude,  77%.  In  order  that  the  water  should  be  taken  on 
without  shock  and  discharged  with  maximum  backward  velocity,  the 
screw  must  have  an  axially  increasing  pitch. 

The  true  screw  is  the  usual  form  of  propeller  in  all  steamers;  both  mer- 
chant andnaval.  (Thurston,  Manual  of  the  Steam-engine,  partii,  p.  176.) 

The  combined  efficiency  of  screw,  shaft,  engine,  etc.,  is  generally  taken 
at  50%.  In  some  cases  it  may  reach  60%  or  65%.  Rankine  takes  the 
effective  H.P.  to  equal  the  I.H.P.  -f-  1.63. 

.Results  of  Researches  on  the  efficiency  of  screw-propellers  are  sum- 
marized by  S.  W.  Barnaby,  in  a  paper  read  before  section  G  of  the  Engi* 
neering  Congress,  Chicago,  1893.  He  states  that  the  following  general 
principles  have  been  established: 

(a)  There  is  a  definite  amount  of  real  slip  at  which,  and  at  which  only, 
maximum  efficiency  can  be  obtained  with  a  screw  of  any  given  type, 
and  this  amount  varies  with  the  pitch-ratio.  The  slip-ratio  proper  to  a 
given  ratio  of  pitch  to  diameter  has  been  discovered  and  tabulated  for  a 
screw  of  a  standard  type,  as  below : 

Pitch-ratio  and  Slip  for  Screws  of  Standard  Form. 


Pitch-ratio. 

Real  Slip  of 
Screw. 

Pitch-ratio  . 

Real  Slip  of 
Screw. 

Pitch-ratio  . 

Real  Slip  of 
Screw. 

0.8 
0.9 
1.0 
I.I 
1.2 
1.3 

15.55 
16.22 
16.88 
17.55 
18.2 
18.8 

.4 
.5 
.6 

'.8 
.9 

19.5 
20.1 
20.7 
21.3 
21.8 
22.4 

2.0 

2!2 
2.3 
2.4 
25 

22.9 
23.5 
24.0 
24.5 
25.0 
25.4 

(5)  Screws  of  large  pitch-ratio,  besides  being  less  efficient  in  them- 
selves, add  to  the  resistance  of  the  hull  by  an  amount  bearing  some  pro- 
portion to  their  distance  from  it,  and  to  the  amount  of  rotation  left  in 
the  race. 

(c)  The  best  pitch-ratio  lies  probably  between  1.1  and  1.5. 

(d)  The  fuller  the  lines  of  the  vessel,  the  less  the  pitch-ratio  should  be. 

(e)  Coarse-pitched  screws  should  be  placed  further  from  the  stern 
than  fine-pitched  ones. 

(/)  Apparent  negative  slip  is  a  natural  result  of  abnormal  proportions 
of  propellers. 

.  (0)  Three  blades  are  to  be  preferred  for  high-speed  vessels,  but  when 
the  diameter  is  unduly  restricted,  four  or  even  more  may  be  advantageously 
employed. 

(fi)  An  efficient  form  of  blade  is  an  ellipse  having  a  minor  axis  equal 
to  four-tenths  the  major  axis. 

(i)  The  pitch  of  wide-bladed  screws  should  increase  from  forward  to 
aft,  but  a  uniform  pitch  gives  satisfactory  results  when  the  blades  are 


1380 


MAKINE  ENGINEERING. 


narrow,  and  the  amount  of  the  pitch  variation  should  be  a  function  of  the 
width  of  the  blade. 

0')  A  considerable  inclination  of  screw-shaft  produces  violation,  and 
with  right-handed  twin-screws  turning  outwards,  if  the  shafts  are  inclined 
at  all,  it  should  be  upwards  and  outwards  from  the  propellers. 

For  results  of  experiments  with  screw-propellers,  see  F.  C.  Marshall, 
Proc.  Inst.  M.  E.,  1881;  R.  E.  Froude,  Trans.  Inst.  Nav.  Archs.,  1886; 
G.  A.  Calvert,  Trans.  Inst.  Nav.  Archs.,  1887;  S.  W.  Barnaby,  Proc.  Inst. 


in  propellers* with  pitch  ratios  from  1.0  to  1.5  ratio  of  width  of  blade  to 
diameter  of  Vg  to  Vs.  and  ratio  of  developed  area  of  blade  to  disk  area  of 
0.201  to  0.322. 

One  of  the  most  important  results  deduced  from  experiments  on  model 
screws  is  that  they  appear  to  have  practically  equal  efficiencies  through- 
out a  wide  range  both  in  pitch-ratio  and  in  surface-ratio;  so  that  great 
latitude  is  left  to  the  designer  in  regard  to  the  form  of  the  propeller. 
Although  these  experiments  are  not  a  direct  guide  to  the  selection  of  the 
most  efficient  propeller  for  a  particular  ship,  they  supply  the  means  of 
analyzing  the  performances  of  screws  fitted  to  vessels,  and  of  thus  in- 
directly determining  what  are  likely  to  be  the  best  dimensions  of  screw 
for  a  vessel  of  a  class  whose  results  are  known.  (Proc.Jnst.  M.  E.,  July, 
1891.) 

Mr.  Barnaby  in  Proc.  Inst.  C.  E.,  1890,  gives  a  table  to  be  used  in  cal- 
culations for  determining  the  best  dimensions  of  screws  for  any  given 
speed  and  H.P.  from  which  the  following  table  is  abridged.  It  is  deduced 
from  Froude's  experiments  at  Torquay.  (Trans.  Inst.  Nav.  Archs.,  1886.) 

CA  =  disk  area  in  SQ-  ft.  X  FVH.P.  CR  =  revs,  per  min.  X  D/V. 
V  =  speed  in  knots,  D  =  diam.  of  screw  in  ft.  H.P.  =  effective  H.P. 
on  the  screw  shaft.  Disk  area  =  0.7854  Z)2=  CA  X  I. H.P./ F3.  Revs, 
per  min.  =  CR  X  V/D.  The  constants  CA  and  CR  assume  a  standard 
value  of  the  speed  of  the  wake,  equal  to  10%  of  the  speed  of  the  ship. 
In  a  very  full  ship  it  may  amount  to  30%,  therefore  V  should  be  reduced 
when  using  .the  constants  by  amounts  varying  from  20%  to  0  as  the 
form  varies  from  "very  full"  to  "fairly  fine." 


Effy.  of 
Screw,  %. 

6 

S 

6 

7 

6 

S 

6 

9 

6 

S 

6 

1 

6 

1 

Pitch  ratio. 

CA 

CB 

CA 

CR 

CA 

CR 

CA 

CR 

CA 

CR 

CA 

CR 

CA 

CR 

0.80 
.00 
.20 
.40 
.60 
.80 

468 
546 
625 
704 
780 

122 
99 
83 
72 
63 

304 
355 
405 
456 
507 
558 

128 
104 
87 
76 
67 
60 

215 
251 

288 
325 
360 
3Q6 

134 
109 
92 
80 
71 
64 

157 

184 
210 
236 
263 
?QO 

142 
115 
97 
85 
75 
68 

115 
135 
154 
173 
193 
71? 

150 

123 
104 
90 
80 
73 

86 
100 
115 
129 
144 
15Q 

160 
131 
111 
97 

87 
78 

65 
76 
87 
98 
109 
170 

171 

140 
119 
104 
93 
84 

200 

60Q 

55 

43? 

58 

315 

6? 

?3i 

67 

173 

7? 

131 

77 

2  20 

660 

50 

46Q 

•54 

34? 

57 

?50 

6? 

187 

67 

147 

7? 

2.40 

710 

47 

505 

50 

369 

53 

270 

57 

202 

62 

153 

67 

Comparison  of  Marine  Engines  for  the  Years  1872,  1881,  1891,  1901. 

(Jas.  McKechnie.  Proc.  Inst.  M.  E.  1901.) 

Average  Results. 


1872. 

1881. 

1891. 

1901. 

5274 

77.4 

158.5 

197 

Heating  surface  per  sq.  ft.  grate  

30  4 

31.0 

38  &  43* 

Heat'g  surf.,  per  I.H.P.,  sq.  ft  
Coal  per  sq  ft.  of  grate  Ibs  perhr.  ... 

4.41 

3.917 
13  8 

3.275 
15.0 

3.0 

18&28* 

55.67 

59.76 

63.75 

87 

376 

467 

529 

654 

Coal  per  I.H.P.  per  hr.,  Ibs  

2  11 

1.83 

1.52 

1.48 

Av.  consumption,  long  voyage  

2.0 

1.75 

1.55 

*  Natural  and  forced  draft  respectively. 
Summary  of  Results.     (1891  to  1901). — Steam  pressures  have  been 
increased  in  the  merchant  marine  from  158  Ibs.  to  197  Ibs.  per  sq.  in« 


MARINE  PRACTICE. 


1381 


the  maximum  attained  being  267  Ibs.  per  sq.  in.,  and  300  Ibs.  in  the 
naval  service.  The  piston  speed  of  mercantile  machinery  has  gone  up 
from  529  to  654  ft.  per  minute,  the  maximum  in  merchant  practice 
being  about  900  ft.,  and  in  naval  practice  960  ft.  for  large  engines,  and 
1300  ft.  in  torpedo-boat  destroyers.  Boilers  also  yield  a  greater  power 
for  a  given  surface,  and  thus  the  average  power  per  ton  of  machinery 
has  gone  up  from  an  average  of  6  to  about  7  I.H.P.,  while  ten  years  ago 
the  highest  sustained  ocean  speed  was  20.7  knots,  it  is  now  23.38  knots; 
the  highest  speed  for  large  warships  was  22  knots  and  is  now  23  knots 
on  a  trial  of  double  the  duration;  the  maximum  speed  attained  by  any 
craft  was  25  knots,  as  compared  with  36.581  knots  now,  while  tho 
number  of  ships  of  over  20  knots  was  8  in  1891,  and  is  58  now  (1901). 
Turbines  and  Boilers  of  the  "Lusitania."  (Thomas  Bell,  Proc. 
Inst.  Nav.  Archts.,  1908.) — Some  of  the  principal  dimensions  of  the 
turbines  and  boilers  of  the  "Lusitania"  are  as  follows: 


Turbines. 

Diameter 
of  Rotor, 
Ins. 

Length  of  Blades,  Ins. 

In  First 
Expansion. 

In  Last 
Expansion. 

H.P... 

96 
140 
104 

23/4 
81/4 
21/4 

V2V. 

-       8 

L.P            

Total  cooling  surface,  main  condensers,  82,800  sq.  ft;  area  of  exhaust 
jnlet,  158  sq.  ft;  bore  of  circulating  discharge  pipes,  32  ins. 

BOILERS.  —  Working  pressure,  195  Ibs.  per  sq.  in.;  23  double-ended 
boilers,  17  ft.  6  in.  mean  diameter  by  22  ft.  long;  2  single-ended  boilers, 
17  ft.  6  in.  mean  diameter  by  11  ft.  4  in.  long;  total  number  of  furnaces, 
192;  total  grate  surface,  4048  sq.  ft.;  total  heating  surface,  158,35.2  sq.  ft.; 
total  length  of  boiler-rooms,  336  ft.;  total  length  of  main  and  auxiliary 
engine  rooms,  149  ft.  8  in. 

The  following  are  the  weights  of  the  various  revolving  parts,  and  the 
size  of  bearings  and  the  pressure:  Weight  of  one  H.P.  turbine  rotor 
complete,  86  tons;  one  L.P.  rotor,  120  tons;  one  astern  rotor,  62  tons. 


Main  Bearing 
Journals. 

Pressure 
per  Sq.  In. 
of  Bearing 
Surface. 

At.  190  Revs. 
Surface  Speed 
of  Journal. 

Diameter. 

Effective 
Length. 

H  P.  rotor 

27  1/8  in. 
33  l/s  in. 
24  1/8  in. 

44  3/4  in. 
56  1/2  in. 
34  3/4  in. 

80  Ibs. 
72  Ibs. 
83  Ibs. 

1350  ft.  per  min. 
1  650  ft.  per  min. 
1200ft.  per  min. 

L.P.  rotor     

Astern  rotor  

Performance  of  the  "Lusitania."  (Thos.  Bell,  Proc.  Inst.  Nav. 
Archts.,  1908;  Power,  May  12,  1908.)  —  The  following  records  were  ob- 
tained in  the  official  trials: 


Speed  in  knots 15 .77 

Shaft  horse-power 13,400 

Steam  cons,  per  shaft,  H.P.  hr. 

of  turbines,  Ibs 21 . 23 

of  auxiliaries,  Ibs 5.3 

total  Ibs.. ***•••  26.53 

Temp,  of  feed- water,  *  F 200 

Coal    cons.    Ibs.    per    shaft 
H.P.  hr 


18 

20,500 

17.24 
3.72 

22°6096 


21 
33,000 

14.91 

2.6 

17.51 

199 


23 

48,000 

13.92 
2.01 


2.52       2.01        1.68       1.56 


25.4 
68,850 

12.77 

1.69 

14.46 

165 

1.43 


Estimated  steam  and  coal  consumption  under  service  conditions,  at 

same  speeds: 
Steam  cons,  of  auxiliaries, 

pershaft  H.P.  hr.,  Ibs..       6.97         4.92         3,41         2.65         2.17 
Steam    cons,    of   total   per 

shaft  H.P.  hr.,  Ibs 28.20       22.16       18.32       16.57       14.94 

Coal   cons.,   Ibs.   per  shaft 

H.P.hr.,lbs 2.76        2.17          1.8          1.62         1.46 

Est.  coal  cons.,  on  a  voyage 

of  3100  nautical  miles, 

gross  tons 3,270     3,440        3,930       4, 700       5,490 

The  following  figures  are  taken  from  the  records  of  a  voyage  from 


1382 


MARINE   ENGINEERING. 


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THE   PADDLE-WHEEL.  1383 

Queenstown  to  Sandy  Hook,  2781  nautical  miles,  Nov.  3-8, 1908,  4  days, 
18  hrs.,  40m.:  Averages:  Steam  pressure  at  bo>lers,  168  IDS.;  temperature 
hot-well,  74.5°;  feed-water,  197°;  vacuum,  28.1  in.;  speed,  24.25  knots; 
speed,  best  day,  24.8  knots;  revolutions,  181.1;  slip,  15.9%.  Total  coal, 
4976  tons.  Steam  consumption:  main  turbines,  851,500  Ibs.,  =  13.1  Ibs. 
per  shaft  H.P.  hr.  (on  a  basis  of  65,000  shaft  H.P.);  auxiliary  machinery, 
114,000  Ibs.,  =  1.75  per  H.P.  hr.;  evaporating  plant  and  heating,  32,500  Ibs., 
=  0.5.1b.  per  H.P.  hr.  Total,  998,000  Ibs.,  =  15.35  Ibs.  per  shaft  H.P. 
hour.  Average  coal  burned,  43 1/2  tons  per  hour.  Water  evaporated 
per  lb.,  coal  10.2  Ibs.  from  feed  at  196°,  =  10.9  Ibs.  from  and  at  212°. 
Coal  for  all  purposes  per  shaft  H.P.  hour,  1.5  Ibs.  Coal  per  sq.  ft.  of 
grate  per  hour,  24.1  Ibs.  The  coal  was  half  Yorkshire,  half  South  Wales. 

In  September,  1909,  the  "Lusitania"  made  the  westward  passage,  2784 
miles  from  Daunt's  Rock  near  Queenstown  to  Ambrose  Channel  Lightship, 
off  Sandy  Hook,  in  4  days  11  h.  42  m.,  averaging  25.85  knots  for  the  entire 
passage.  Four  successive  days  runs,  from  noon  to  noon,  were  650,  652. 
651  and  674  miles. 

Reciprocating  Engines  with  a  Low-Pressure  Turbine.  —  The 
"  Laurentic, "  built  for  the  Canadian  trade  of  the  White  Star  Line, 
14,000  tons  gross  register,  is  a  triple-screw  steamer,  with  the  two  outer 
screws  driven  by'  four-cylinder  triple-expansion  engines,  and  the  central 
screw  by  a  Parsons  turbine.  The  steam,  of  200  Ibs.  boiler  pressure,  first 
passes  to  the  reciprocating  engines,  where  it  expands  to  from  14  to  17  Ibs. 
absolute,  and  then  passes  to  the  turbine.  For  maneuvering  the  ship 
into  and  out  of  port  the  turbine  is  not  used,  and  the  steam  passes  directly 
from  the  engines  to  the  condensers.  During  the  trial  trip  the  combined 
engine-turbine  outfit  developed  12,000  H.P.,  with  a  speed  of  171/2  knots, 
and  showed  a  coal  consumption  of  1.1  Ibs.  and  a  water  consumption  of 
11  Ibs.  per  indicated  horse-power  hour.  (Power,  May  18,  1909.) 

The  "  Kronprinzessin  Cecilie"  of  the  North  German  Lloyd  Co.,  is 
probably  the  last  high-speed  transatlantic  steamer  of  very  great  power 
that  will  be  built  with  reciprocating  engines.  Its  dimensions  are:  length, 
706  ft.;  beam,  72  ft.;  depth,  44  ft.  2  in.;  displacement,  26,000  tons.  Four 
12,000  H.P.  engines,  two  on  each  shaft,  in  tandem.  Cylinders,  373/8, 
491/4,  74V8  and  1121/4  ins.,  by  6  ft.  stroke.  Steam,  230  Ibs.,  delivered 
from  19  cylindrical  boilers,  through  four  17-in.  steampipes.  Coal  used 
in  24  hours,  764  tons,  in  124  furnaces;  1.4  Ibs.  per  H.P.  hour,  including 
auxiliaries.  Speed  on  trial  trip  on  a  60-mile  course,  24.02  knots.  (Set. 
Am.,  Aug.  24,  1907.) 

THE   PADDLE-WHEEL. 

Paddle-wheels  with  Radial  Floats.  (Seaton's  Marine  Engineering.)  — 
The  effective  diameter  of  a  radial  wheel  is  usually  taken  from  the  centers 
of  opposite  floats;  but  it  is  difficult  to  say  what  is  absolutely  that  diameter, 
as  much  depends  on  the  form  of  float,  the  amount  of  dip,  and  the  waves 
set  in  motion  by  the  wheel.  The  slip  of  a  radial  wheel  is  from  15  to  30 
per  cent,  depending  on  the  size  of  float. 

Area  of  one  float  =  C  X  I.H.P.  •*-  D. 

D  {3  the  effective  diameter  in  feet,  and  C  is  a  multiplier,  varying  from  0.25 
in  tugs  to  0.175  in  fast-running  light  steamers. 

The  breadth  of  the  float  is  usually  about  1/4  its  length,  and  its  thickness 
about  i/g  its  breadth.  The  number  of  floats  varies  directly  with  the  diam- 
eter, and  there  should  be  one  float  for  every  foot  of  diameter. 

(For  a  discussion  of  the  action  of  the  radial  wheel,  see  Thurston, 
Manual  of  the  Steam-engine,  part  ii,  p.  182.) 

Feathering  Paddle-wheels.  (Seaton.)  —  The  diameter  of  a  feather- 
ing-wheel is  found  as  follows:  The  amount  of  slip  varies  from  12  to  20 
per  cent,  although  when  the  floats  are  small  or  the  resistance  great  it 
is  as  high  as  25  per  cent;  a  well-designed  wheel  on  a  well-formed  ship 
should  not  exceed  15  per  cent  under  ordinary  circumstances,  • 

If  K  is  the  speed  of  the  ship  in  knots,  S  the  percentage  of  slip,  and  R 
the  revolutions  per  minute, 

Diameter  of  wheel  at  centers  =  K  (100  +  S)  +  (3.14  X  R). 

The  diameter,  however,  must  be  such  as  will  suit  the  structure  of  the 
ship,  so  that  a  modification  may  be  necessary  on  this  account,  and  the 
revolutions  altered  to  suit  it.  The  diameter  will  also  depend  on  the 
amount  of  "dip"  or  immersion  of  float. 


1384-  MARINE  ENGINEERING. 

When  a  ship  is  working  always  in  smooth  water  the  immersion  of  the 
top  edge  should  not  exceed  1/8  the  breadth  of  the  float;  and  for  general 
service  at  sea  an  immersion  of  1/2  the  breadth  of  the  float  is  sufficient. 
If  the  ship  is  intended  to  carry  cargo,  the  immersion  when  light  need  not 
be  more  than  2  or  3  inches,  and  should  not  be  more  than  the  breadth  of 
float  when  at  the  deepest  draught;  indeed,  the  efficiency  of  the  wheel  falls 
off  rapidly  with  the  immersion  of  the  wheel. 

Area  of  one  float  =  C  X  I.H.P.  •*•  D. 

C  is  a  multiplier,  varying  from  0.3  to  0.35;  D  is  the  diameter  of  the 
wheel  to  the  float  centers,  in  feet. 

The  number  of  floats       =  1/2  (7)  +2). 
The  breadth  of  the  float  =  0.35  X  the  length. 
The  thickness  of  floats    =  1/12  the  breadth. 
Diameter  of  gudgeons     =  thickness  of  float. 
Seatonand  Rounthwaite's  Pocket-book  gives: 

Number  of  floats  =  60  -*•  V^5 
where  R  is  number  of  revolutions  per  minute. 

Area  of  one  float  (in  square  feet)  =  ^ 

where  N  —  number  of  floats  in  one  wheel. 

For  vessels  plying  always  in  smooth  water  K  =  1200.  For  sea-going 
steamers  K  =  1400.  For  tugs  and  such  craft  as  require  to  stop  and 
start  frequently  in  a  tide-way  K  =  1600. 

It  will  be  quite  accurate  enough  if  the  last  four  figures  of  the  cube 
(D  X  R)3  be  taken  as  ciphers. 

For  illustrated  description  of  the  feathering  paddle-wheel  see  Seaton's 
Marine  Engineering,  or  Seaton  and  Rounthwaite's  Pocket-book.  The 
diameter  of  a  feathering-wheel  is  about  one-half  that  of  a  radial  wheel 
for  equal  efficiency.  (Thurston.) 

Efficiency  of  Paddle-wheels.  —  Computations  by  Prof.  Thurston  of 
the  efficiency  of  propulsion  by  paddle-wheels  give  for  light  river  steamers 
with  ratio  of  velocity  of  the  vessel,  v,  to  velocity  of  the  paddle-float  at 
center  of  pressure,  V,  or  v/V,  =  3/4,  with  a  dip  =  3/2o  radius  of  the  wheel 
and  a  slip  of  25  per  cent,  an  efficiency  of  0.714;  and  for  ocean  steamers 
with  the  same  slip  and  ratio  of  v/V.  and  a  dip =1/3  radius,  an  efficiency  of 
0.685. 

JET-PROPULSION. 

Numerous  experiments  have  been  made  in  driving  a  vessel  by  the 
reaction  of  a  jet  of  water  pumped  through  an  orifice  in  the  stern,  but 
they  have  all  resulted  in  commercial  failure.  Two-jet  propulsion  steamers, 
the  " Waterwitch, "  1100  tons,  and  the  "Squirt,"  a  small  torpedo-boat, 
were  built  by  the  British  Government.  The  former  was  tried  in  1867, 
and  gave  an  efficiency  of  apparatus  of  only  18  per  cent.  The  latter  gave 
a  speed  of  12  knots,  as  against  17  knots  attained  by  a  sister-ship  having  a 
screw  and  equal  steam-power.  The  mathematical  theory  of  the  efficiency 
of  the  jet  was  discussed  by  Rankine  in  The  Engineer,  Jan.  11,  1867,  and 
he  showed  that  the  greater  the  quantity  of  water  operated  on  by  a  jet- 
propeller,  the  greater  is  the  efficiency.  In  defiance  both  of  the  theory 
and  of  the  results  of  earlier  experiments,  and  also  of  the  opinions  of  many 
naval  engineers,  more  than  $200,000  were  spent  in  1888-90  in  New  York 
upon  two  experimental  boats,  the  "Prima  Vista"  and  the  "Evolution," 
in  which  the  jet  was  made  of  very  small  size,  in  the  latter  case  only  5/g-inch 
diameter,  and  with  a  pressure  of  2500  Ibs.  per  square  inch.  As  had  been 
predicted,  the  vessel  was  a  total  failure.  (See  article  by  the  author  in 
Mechanics,  March,  1891.) 

The  theory  of  the  jet-propeller  is  similar  to  that  of  the  screw-propeller. 
If  A  =  the  area  of  the  jet  in  square  feet,  V  its  velocity  with  reference  to 
the  orifice,  in  feet  per  second,  v  =»  the  velocity  of  the  ship  in  reference  to 
the  <earth,  then  the  thrust  of  the  jet  (see  Screw-propeller,  ante)  is  2  A  V 
(V  —  v).  The  work  done  on  the  vessel  is  2  AV(V  -  v) v,  and  the  work 
wasted  on  the  rearward  projection  of  the  jet  is  1/2  X  2  AV(V  —  v)a. 

The  efficiency  is  2  ^  y  (/^/J^V  _,)2  -#;•  This  expression 
equals  unity  when  V  =  v,  that  is,  when  the  velocity  of  the  jet  with  refer- 
ence to  the  earth,  or  V  —  v,  =0;  but  then  the  thrust  of  the  propeller  is 
also  Q.  The  greater  the  value  of  V  as  compared  with  v,  the  J^  the 


CONSTRUCTION  OF  BUILDINGS. 


1385 


efficiency.  For  V  =  20  v,  as  was  proposed  in  the  "Evolution,"  the 
efficiency  of  the  jet  would  be  less  than  10  per  cent,  and  this  would  be 
further  reduced  by  the  friction  of  the  pumping  mechanism  and  of  the 
water  in  pipes. 


It  is  practically  impossible  to  devise  any  system  of  hydraulic  or  jet 
propulsion  which  can  compare  favorably,  under  these  conditions,  with 
the  screw  or  the  paddle-wheel. 

Reaction  of  a  Jet.  —  If  a  jet  of  water  issues  horizontally  from  a  vessel, 
the  reaction  on  the  side  of  the  vessel  opposite  the  orifice  is  equal  to  the 
weight  of  a  column  of  water  the  section  of  which  is  the  area  of  the  orifice, 
and  the  height  is  twice  the  head. 

The  propelling  force  in  jet-propulsion  is  the  reaction  of  the  stream 
issuing  from  the  orifice,  and  it  is  the  same  whether  the  jet  is  discharged 
under  water,  in  the  open  air,  or  against  a  solid  wall.  For  proof,  see 
account  of  trials  by  C.  J.  Everett,  Jr.,  given  by  Prof.  J.  Burkitt  Webb, 
Trans.  A.  S.  M.  E.,  xii,  904. 

CONSTRUCTION  OF  BUILDINGS.* 

FOUNDATIONS. 

Bearing  Power  of  Soils. —  Ira  O.  Baker,  •!  Treatise  on  Masonry 
Construction.'! 


Kind  of  Material. 

Bearing  Power  in 
Tons  per  Square  Foot. 

Minimum. 

Maximum. 

Rock  —  the  hardest  —  in  thick  layers,  in  native  bed. 

200 
25 
15 
5 
4 
2 

8 

4 

0.5       • 

30 
20 
10 
6 

10 
6 

1 

Rock  equal  to  best  brick  masonry  

Clay  on  thick  beds  always  dry..        

Clay  soft                         .   .          .                    

Sand  compact  and.  well  cemented  ..              

Sand   clean  drv                         

Quicksand,  alluvial  soils,  etc  

The  building  code  of  Greater  New  York  specifies  the  following  as  the 
maximum  permissible  loads  for  different  soUs: 

"  Soft  clay,  one  ton  per  square  foot; 

"  Ordinary  clay  and  sand  together,  in  layers,  wet  and  springy,  two 
tons  per  square  foot ; 

"Loam,  clay  or  fine  sand,  firm  and  dry,  three  tons  per  square  foot; 

"  Very  firm  coarse  sand,  stiff  gravel  or  hard  clay,  four  tons  per  square 
foot,  or  as  otherwise  determined  by  the  Commissioner  of  Build- 
ings having  jurisdiction." 


Pocket-book."  The  latter  in  its  preface  mentions  the  following  works  of 
reference:  "Notes  on  Building  Construction,"  3  vols.,  Rivingtons,  pub- 
lishers, London;  "Building  Superintendence,"  by  T.  M.  Clark  (J.  R. 
Osgood  &Co.,  Boston);  "  The  American  House  Carpenter,"  and  "  The  Theory 
of  Transverse  Strains,"  both  by  R.  G.  Hatfield;  "Graphical  Analysis  of 
Roof-trusses,"  by  Prof.  C.  E.  Greene;  "The  Fire  Protection  of  Mills,"  by 
C.  J.  H.  Woodbury;  "House  Drainage  and  Water  Service,"  by  James  C. 
Bayles;  "The  Builder's  Guide  and  Estimator's  Price-book,"  and  "Plaster- 
ing Mortars  and  Cements,  by  Fred.T.  Hodgson;  "Foundations  and  Con- 
crete Works,"  and  "Art  of  Building,"  by  E.  Dobson,  Weale's  Series, 
London. 


1386 


CONSTRUCTION  OF  BUILDINGS. 


Bearing:  rower  of  Piles.  —  Engineering  News  Formula:  Safe  load  in 
tons  =  2  Wh  -*•  (S  +  1).  W  =  weight  of  hammer  in  tons,  h  =  height  of  fall 
of  hammer  in  feet,  S  —  penetration  under  last  blow,  or  the  average  under 
last  five  blows,  in  inches. 

Safe  Strength  of  Brick  Piers,  exceeding  six  diameters  in  height. 
<  Kidder.) 

Piers  laid  with  rich  lime  mortar,  Ibs.  per  sq.  in.,  110  —  5  H/D. 
Piers  laid  with  1  to  2  natural  cement  mortar,  140  -  51/2  H/D. 
Piers  laid  with  1  to  3  Portland  cement  mortar,  200  —  6  H/D. 
H  =  height;  D  =  least  horizontal  dimension,  in  feet. 

Thickness  of  Foundation  Walls.     (Kidder.) 


Height  of  Building. 

Dwellings, 
Hotels,  etc. 

Warehouses. 

Brick. 

Stone. 

Brick. 

Stone. 

Two  stories      .       

Inches. 
12  or  16 
16 
20 

24 
28 

Inches. 
20 
20 
24 
28 
32 

Inches. 
16 
20 
24 
24 
28 

Inches. 
20 

24 
28 
28 

32 

Four  stories        .  «v   ... 

MASONRY. 

Allowable  Pressures  on  Masonry  in  Tons  per  Square  Foot.    (Kidder.) 


Different  Cities.* 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

Granite,  cut  

60 

72-172 

40 

40 

50-165 

Sandstone  hard   cut 

30 

28-115 

12 

Hard-burned  brick  in  Portland  cement.  .  . 

18 

121/2 

15 

Hard-burned  brick  in  natural  cement  
Hard-burned  brick  in  cement  and  lime  .  .  . 
Hard-burned  brick  in  lime  mortar 

15 
12 
8 

9 
6 

15 

m/, 

61/9 

iii/i 

15 

12 
8 

9 

*8* 

Pressed  brick  in  Portland  cement  

1? 

Pressed  brick  in  natural  cement  

9 

ii 

Rubble  stone  in  natural  cement  

8 

10 

12 

In  foundations: 
Dimension  stone  

6 

5-7 

V' 

Portland  cement  concrete!  

4 

15 

15 

10 

Natural  cement  concrete  

8 

4 

4 

*From  building  laws,  (1)  Boston,  1897;  (2)  Buffalo,  1897;  (3)  New 
York,  1899;  (4)  Chicago,  1893;  (5)  St.  Louis,  1897;  (6)  Philadelphia, 
1899;  (7)  Denver,  1898. 

Crushing  Strength  of  12-in.  Cubes  of  Concrete.  (Kidder.)  — 
Pounds  per  square  foot.  The  concrete  was  made  of  1  part  Portland 
cement,  2  parts  sand,  with  average  concrete  stone  and  gravel,  as  below. 


10  days. 

45  days. 

3  mos. 

6  mos. 

1  year. 

6  parts  stone  .  .  . 

130,750 

172,325 

324,875 

361,600 

440,040 

3  parts  stone,  3  gravel  
4  parts  stone,  2  gravel 

136,750 

266,962 

298,037 

396,200 
408,300 

6  parts  (3/4  stone,  1/4  grano- 
lithic)   

388,700 

6  parts  average  gravel  
6  parts  coarse  stone,  no  fine. 

99,900 

234,475 

385,612 
134,475 

265,550 
220,350 

406,700 
266,300 

Reinforced  Concrete. — The  building  laws  of  New  York,  St.  Louis, 
Cleveland  and  Buffalo,  and  the  National  Board  of  Fire  Underwriters  agree 
in  prescribing  the  following  as  the  maximum  allowable  working  stresses: 


BEAMS  AND   GIKDERS.  1387 


Extreme  fiber  stress  in  compression  in  con- 
crete          500  lbs.<4per  sq.  In. 

Shearing  stress  in  concrete 50 

Direct  compression  in  concrete 350 

Adhesion  of  steel  to  concrete 50 

Tensile  stress  in  steel 16,000 

Shearing  stress  in  steel 10,000 

BEAMS   AND    GIRDERS. 
Safe  Loads  on  Beams.  —  Uniformly  distributed  load: 

2  X  breadth  X  square  of  depth  X  A  § 
span  in  feet 

Breadth  in  inches  -       «Pan  in  feet  X  toad      . 
2  X  square  of  depth  X  A 


Safe  load  in  Ibs.  = 


The  depth  is  taken  in  inches.  The  coefficient  A,  is  1/18  the  maximum 
fiber  stress  for  safe  loads,  and  is  the  safe  Ipad  for  a  beam  1  in.  square,  1  ft. 
span.  The  foltowing  values  of  A  are  given  by  Kidder  as  one-third  of 
the  breaking  weight  of  timber  of  the  quality  used  in  first-class  buildings. 
The  values  for  stones  are  based  on  a  factor  of  safety  of  six. 
VALUES  FOR  A.  — -  COEFFICIENT  FOR  BEAMS. 


Cast  iron. .' 308 

Wrought  iron 666 

Steel. 888 

American  Woods: 

Chestnut 60 

Hemlock 55 

Oak,  white... 75 

Pine,  Georgia  yellow 100 

Pine,  Oregon 90 

Pine,  red  or  Norway 70 

Pine,  white,  Eastern 60 

Pine,  white.  Western 65 


Pine,  Texas  yellow 90 

Spruce 70 

Whitewood  (poplar) 65 

Redwood  (California) 60 

Bluestone     flagging     (Hudson 

River) 25 

Granite,  average 17 

Limestone 14 

Marble 17 

Sandstone 8  to  1 1 

Slate 50 


Safe  Loads  in  Tons,  Uniformly  Distributed,  for  White-oak  Beams. 

(In  accordance  with  the  Building  Laws  of  Boston.) 

W  —  safe  load  in  pounds;  P,  extreme  fiber- 
4  PBD2          stress  =  1000  Ibs.  per  square  inch,  for  white 
oak;  B,  breadth  in  inches;  D,  depth  in  inches; 
L,  distance  between  supports  in  inches. 


Formula:  W  = 


3L 


Distance  between  Supports  in  Feet. 


*! 

&•- 

6     |  8 

10 

11 

12 

14 

15 

16 

17 

18 

19 

21 

23 

25 

26 

•&• 

Safe  Load  in  Tons  of  2000  Pounds. 

2x6 

0  67 

0  50 

0  40 

0  36 

0  33 

0  29 

0  27 

0  25 

0  24 

0  22 

2x8 

1.19 

0!89 

OJI 

0!65 

0.59 

0.51 

0.47 

0.44 

0.42 

0.40 

0.37 

0.34 

0.31 

0.28 

2x10 

1.85 

1.39 

1.11 

1.01 

0.93 

0.79 

0.74 

0.69 

0.65 

0.62 

0.58 

0.53 

0.48 

0.43 

0.43 

2x12 

2.67 

2.00 

1.60 

1.45 

1.33 

1.14 

1.07 

1.00 

0.94 

0.89 

0.84 

0.76 

0.70 

0.64 

0.62 

3x6 

1.00 

0.75 

0.60 

0.55 

0.50 

0.43 

0.40 

0.37 

0.35 

0.33 

0.32 

0.29 

0.26 

3x8 

1.78 

1.33 

1.07 

0.97 

0.89 

0.76 

0.71 

0.67 

0.63 

0.59 

0.56 

0.51 

0.46 

6!43 

6.'4J 

3x10 

2.78 

2.08 

1.67 

1.52 

.39 

.19 

1.11 

1.04 

0.98 

0.93 

0.88 

0.79 

0.72 

0.67 

0.64 

3x12 

4.00 

3.00 

2.40 

2.18 

2.00 

1.71 

1.60 

1.50 

.41 

.33 

1.26 

1.14 

1.04 

0.96 

0.92 

3x14 

5.45 

4.08 

3.27 

2.97 

2  72 

2.37 

2.18 

2.04 

.92 

.82 

.72 

1.56 

1.42 

1.31 

1.25 

3x16 

7.11 

5.33 

4.27 

3.88 

3.56 

3.05 

2.84 

2.67 

2.51 

2.37 

2.25 

2.03 

1.86 

1.71 

1.64 

4x10 

3.70 

2.78 

2.22 

2.02 

1.85 

1.59 

1.48 

1.39 

1.31 

1.23 

1.17 

1.06 

0.97 

0.89 

0.85 

4x12 

5.33 

4.00 

3.20 

2.91 

2.67 

2.29 

2.13 

2.00 

1.88 

1.78 

1.68 

1.52 

1.39 

1.28 

1.23 

4x14 

7  76 

5  44 

4   36 

*  96 

3  63 

3  11 

7  90 

7,  7? 

?,  56 

7,  47, 

7.  29 

2.07 

1.90 

1.74 

1.68 

4X16 

9.48 

7.11 

5.69 

5.17 

4.74 

4.06 

3.79 

3.56 

3.35 

3.16 

3.00 

2.71 

2.47 

2.28 

2.19 

4x18 

12.00 

9.00 

7.20 

6.55 

6.00 

5.14 

4.80 

4.50 

4.24 

4.00 

3.79 

3.43 

3.13 

2.88 

2.77 

For  other  kinds  of  wood  than  white  oak  multiply  the  figures  in  the 
table  by  a  figure  selected  from  those  given  below  (which  represent  the 


1388 


CONSTRUCTION  OF  BUILDINGS- 


safe  stress  per  square  inch  on  beams  of  different  kinds  of  wood  accord- 
ing to  the  building  laws  of  the  cities  named)  and  divide  by  1000. 


Hem- 
lock. 

Spruce. 

White 
Pine. 

Oak. 

Yellow 
Pine. 

New  York  . 

800 

900 

900 

1100 

1  100* 

Boston  

750 

750 

lOOOf 

1250 

Chicago  

900 

1080 

1440 

*  Georgia  pine.  t  White  oak. 

Maximum  Permissible  Stresses  in  Structural  Materials  used  in 
Buildings.  (Building  Ordinances  of  the  City  of  Chicago,  1893.)  —  Cast 
iron,  crushing  stress:  For  plates,  15,000  Ibs.  per  square  inch;  for  lintels, 
brackets,  or  corbels,  compression  13,500  Ibs.  per  square  inch,  and  tension 
3000  Ibs.  per  square  inch.  For  girders,  beams,  corbels,  brackets,  and 
trusses,  16,000  Ibs.  per  square  inch  for  steel  and  12,000  Ibs.  for  iron. 

For  plate  girders: 

Flange  area  =  maximum  bending  moment  in  ft  .-Ibs.  •*-  (CD). 

D  =  distance  between  center  of  gravity  of  flanges  in  feet. 

C  =  13,500  for  steel,  10,000  for  iron. 

Web  area  =  maximum  shear  •*-  C. 

C  =  lOiOOQ  for  steel;  6,000  for  iron. 

For  rivets  in  single  shear  per  square  inch  of  rivet  area: 

If  shop-driven,  steel,  9000  Ibs.,  iron,  7500  Ibs.;  if  field-driven   steel 
7500  Ibs.,  iron,  6000  Ibs. 
For  timber  girders:  S  =  cbd~  -f-  I. 

b  =  breadth  of  beam  in  inches,  d  =  depth  of  beam  in  inches,  I  —  length 
of  beam  in  feet,  c  =  160  for  long-leaf  yellow  pine,  120  for  oak,  100  for 
white  or  Norway  pine. 

WALLS. 

Thickness  of  Walls  of  Buildings.  —  Kidder  gives  the  following  gen- 
eral rule  for  mercantile  buildings  over  four  stories  in  height : 

For  brick  equal  to  those  used  in  Boston  or  Chicago,  make  the  thickness 
of  the  three  upper  stories  16  ins.,  of  the  next  three  below  20  ins.,  the  next 
three  24  ins.,  and  the  next  three  28  ins.  For  a  poorer  quality  of  material 
make  only  the  two  upper  stories  16  ins.  thick,  the  next  three  20  ins.  and 
so  on  down. 

In  buildings  less  than  five  stories  in  height  the  top  story  may  be  12 
ins.  in  thickness. 

THICKNESS  OF  WALLS  IN  INCHES,  FOR  MERCANTILE  BUILDINGS  AND  FOR 
ALL  BUILDINGS  OVER  FIVE  STORIES  IN  HEIGHT  .  (The  figures  show  the 
range  of  the  thicknesses  required  by  the  ordinances  of  eight  different 
cities.  —  Condensed  from  Kidder.) 


Stories 


Stories. 


High. 

1st. 

2d. 

3d. 

4th. 

5th. 

6th. 

7th. 

8th. 

9th. 

10th 

llth 

12th 

2 

12-18 

12-13 

3 

13-20 

12-18 

12-16 

4 

16-22 

16-18 

12-18 

12-16 

5 

18-22 

16-22 

16-20 

12-20 

12-16 

6 

20-26 

18-22 

16-22 

16-20 

13-20 

12-16 

7 

20-28 

20-26 

18-24 

16-22 

16-20 

13-20 

12-17 

8 

22-32 

20-28 

20-26 

18-24 

16-22 

16-20 

13-20 

12-17 

9 

24-32 

24-32 

20-28 

20-26 

20-24 

16-22 

16-20 

16-20 

12-17 

10 

24-36 

24-32 

24-32 

20-28 

20-26 

20-24 

16-22 

16-20 

16-20 

12-17 

11 

28-36 

28-36 

24-32 

24-30 

24-28 

20-26 

20-24 

20-22 

16-20 

16-20 

13-17 

12 

28-40 

28-36 

28-36 

24-32 

24-32 

24-28 

20-26 

20-24 

20-22 

16-20 

16-20 

13-17 

(Extract  from  the  Building  Laws  of  the  City  of  New  York,  1893.) 
Walls   of  Warehouses,    Stores,   Factories,  and   Stables.  —  25    feet 
or  less  in  width  between  walls,  not  less  than  12  in.  to  height  of  40  ft. 
If  40  to  60  ft.  in  height,  not  less  than  16  in.  to  40  ft.,  and  12  in.  thence 
to  top; 


COLUMNS  AND   POSTS.  1389 

60  to  80  ft.  in  height,  not  less  than  20  in.  to  25  ft.,  and  16  in.  thence  to 

top; 
75  to  85  ft.  in  height,  not  less  than  24  in.  to  20  ft.;  20  in.  to  60  ft.,  and 

16  in.  to  top; 
85  to  100  ft.  in  height,  not  less  than  28  in.  to  25  ft.;  24  in;  to  50  ft.; 

20  in.  to  75  ft.,  and  16  in.  to  top; 

Over  100  ft.  in  height,  each  additional  25  ft.  in  height,  or  part  thereof, 
next  above  the  curb,  shall  be  increased  4  inches  in  thickness,  the 
upper  100  feet  remaining  the  same  as  specified  for  a  wall  of  that 
height. 

If  walls  are  over  25  feet  apart,  the  bearing- walls  shall,  be  4  inches 
thicker  than  above  specified  for  every  121/2  feet  or  fraction  thereof  that 
said  walls  are  more  than  25  feet  apart. 

Strength  of  Floors,  Roofs,  and  Supports. 

Floors  calculated  to 
bear  safely  per  sq.  ft.,  in 
addition  to  their  own  wt. 
Floors  of  dwelling,  tenement,  apartment-house  or  hotel,  not 

less  than 70  Ibs. 

Floors  of  office-building,  not  less  than 100  " 

Floors  of  public-assembly  building,  not  less  than 120  " 

Floors  of  store,  factory,  warehouse,  etc.,  not  less  than 150  " 

Roofs  of  all  buildings,  not  less  than 50  " 

Hivery  ttoor  shall  be  of  sufficient  strength  to  bear  safely  the  weight  to  be 
imposed  thereon,  in  addition  to  the  weight  of  the  materials  of  which  the 
floor  is  composed. 

Columns  and  Posts.  —  The  strength  of  all  columns  and  posts  shall 
be  computed  according  to  Gordon's  formulae,  and  the  crushing  weights  in 
pounds,  to  the  square  ~inch  of  section,  for  the  following-named  materials, 
shall  be  taken  as  the  coefficients  in  said  formulae,  namely:  Cast  iron,  80,000; 
wrought  or  rolled  iron,  40,000:  rolled  steel,  48,000:  white  pine  and  spruce, 
3500:  pitch  or  Georgia  piney  5000;  American  oak,  6000.  The  breaking 
strength  of  wooden  beams  and  girders  shall  be  computed  according  to 
the  formulae  in  which  the  constants  for  transverse  strains  for  central  load 
shall  be  as  follows,  namely:  Hemlock,  400;  white  pine,  450;  spruce,  450; 
pitch  or  Georgia  pine,  550 ;  American  oak,  550 ;  and  for  wooden  beams  and 
girders  carrying  a  uniformly  distributed  load  the  constants  will  be  doubled. 
The  factors  of  safety  shall  be  as. one  to  four  for  all  beams,  girders,  and 
other  pieces  subject  to  a  transverse  strain;  as  one  to  four  for  all  posts, 
columns,  and  other  vertical  supports  when  of  wrought  iron  or  rolled  steel; 
as  one  to  five  for  other  materials,  subject  to  a  compfessive  strain;  as  one 
to  six  for  tie-rods,  tie-beams,  and  other  pieces  subject  to  a  tensile  strain. 
Good,  solid,  natural  earth  shall  be  deemed  to  sustain  safely  a  load  of  four 
tons  to  the  superficial  foot,  or  as  otherwise  determined  by  the  super- 
intendent of  buildings,  and  the  width  of  footing-courses  shall  be  at  least 
sufficient  to  meet  this  requirement.  In  computing  the  width  of  walls, 
a  cubic  foot  of  brickwork  shall  be  deemed  to  weigh  115  Ibs.  Sandstone, 
white  marble,  granite,  and  other  kinds  of  building-stone  shall  be  deemed 
to  weigh  160  Ibs.  per  cubic  foot.  The  safe-bearing  load  to  apply  to 
good  brickwork  shall  be  taken  at  8  tons  per  superficial  foot  when  good 
lime  mortar  is  used,  111/2  tons  per  superficial  foot  when  good  lime  and 
cement  mortar  mixed  is  used,  and  15  tons  per  superficial  foot  when  good 
cement  mortar  is  used. 

Fire-proof  Buildings  —  Iron  and  Steel  Columns.  —  All  cast-iron, 
wrought-iron,  or  rolled-steel  columns  shall  be  made  true  and  snwoth  at 
both  ends,  and  shall  rest  on  iron  ofe  steel  bed-plates,  and  have  iron  or 
steel  cap-plates,  which  shall  also  be  made  true.  All  iron  or  steel  trimmer- 
beams,  headers,  and  tail-beams  shall  be  suitably  framed  and  connected 
together,  and  the  iron  girders,  columns,  beams,  trusses,  and  all  other  iron- 
work of  all  floors  and  roofs  shall  be  strapped,  bolted,  anchored,  and  con- 
nected together,  and  to  the  walls,  in  a  strong  and  substantial  manner. 
Where  beams  are  framed  into  headers,  the  angle-irons,  which  are  bolted 
to  the  tail-beams,  shall  have  at  least  two  bolts  for  all  beams  over  7  inches 
in  depth,  and  three  bolts  for  all  beams  12  inches  and  over  in  depth,  and 
these  bolts  shall  not  be  less  than  3/4  inch  in  diameter.  Each  one  of  such 


1390  CONSTRUCTION  OF  BUILDINGS. 

*  \ 

angles  or  knees,  when  bolted  to  girders,  shall  have  the  same  number~of 
bolts  as  stated  for  the  other  leg.  The  angle-iron  in  no  case  shall  be  less 
in  thickness  than  the  header  or  trimmer  to  which  it  is  bolted,  and  the 
width  of  angle  in  no  case  shall  be  less  than  one  third  the  depth  of  beam, 
excepting  that  no  angle-knee  shall  be  less  than  2 1/2  inches  wide,  nor 
required  to  be  more  than  6  inches  wide.  All  wrought-iron  or  rolled-steel 
beams  8  inches  deep  and  under  shall  have  bearings  equal  to  their  depth, 
if  resting  on  a  wall;  9  to  12  inch  beams  shall  have  a  bearing  of  10  inches, 
and  all  beams  more  than  12  inches  in  depth  shall  ha.ve  bearings  of  not 
less  than  12  inches  if  resting  on  a  wall.  Where  beams  rest  on  iron  sup- 
ports, and  are  properly  tied  to  the  same,  no  greater  bearings  shall  be 
required  than  one  third  of  the  depth  of  the  beams.  Iron  or  steel  floor- 
beams  shall  be  so  arranged  as  to  spacing  and  length  of  beams  that  the 
load  to  be  supported  by  them,  together  with  the  weights  of  the  materials 
used  in  the  construction  of  the  said  floors,  shall  n9t  cause  a  deflection  of 
the  said  beams  of  more  than  1/30  of  an  inch  per  linear  foot  of  span;  and 
they  shall  be  tied  together  at  intervals  of  not  more  than  eight  times  the 
depth  of  the  beam. 

Under  the  ends  of  all  iron  or  steel  beams,  where  they  rest  on  the  walls,  a 
stone  or  cast-iron  template  shall  be  built  into  the  walls.  Said  template 
shall  be  8  inches  wide  in  12-inch  walls,  and  in  all  walls  of  greater  thickness 
said  template  shall  be  12  inches  wide;  and  such  templates,  if  of  stone, 
shall  not  be  in  any  case  less  than  21/2  inches  in  thickness,  and  no  template 
shall  be  less  than  12  inches  long. 

No  cast-iron  post  or  columns  shall  be  used  in  any  building  of  a  less 
average  thickness  of  shaft  than  three  quarters  of  an  inch,  nor  shall  it 
have  an  unsupported  length  of  more  than  twenty  times  its  least  lateral 
dimensions  or  diameter.  No  wrought-iron  or  rolled-steel  column  shall 
have  an  unsupported  length  of  more  than  thirty  times  its  least  lateral 
dimensions  or  diameter,  nor  shall  its  metal  be  less  than  one  fourth  of  an 
inch  in  thickness. 

Lintels,  Bearings  and  Supports.  —  All  iron  or  steel  lintels  shall 
have  bearings  proportionate  to  the  weight  to  be  imposed  thereon,  but  no 
lintel  used  to  span  any  opening  more  than  10  feet  in  width  shall  have  a 
bearing  less  than  12  inches  at  each  end,  if  resting  on  a  wall;  but  if  resting 
on  an  iron  post,  such  lintel  shall  have  a  bearing  of  at  least  6  inches  at  each 
end,  by  the  thickness  of  the  wall  to  be  supported. 

Strains  on  Girders  and  Rivets.  —  Rolled  iron  or  steel  beam  girders, 
or  riveted  iron  or  steel  plate  girders  used  as  lintels  or  as  girders,  carrying 
a  wall  or  floor  or  both,  shall  be  so  prop9rtioned  that  the  loads  which  may 
come  upon  them  shall  not  produce  strains  in  tension  or  compression  upon 
the  flanges  of  more  than  12,000  Ibs.  for  iron,  nor  more  than  15,000  Ibs. 
for  steel  per  square  inch  of  the  gross  section  of  each  of  such  flanges,  nor 
a  shearing  strain  upon  the  web-plate  of  more  than  6000  Ibs.  per  square 
inch  of  section  of  such  web-plate,  if  of  iron,  nor  more  than  7000  pounds 
if  of  steel;  but  no  web-plate  shall  be  less  than  1/4  inch  in  thickness.  Rivets 
in  plate  girders  shall  not  be  less  than  5/s  inch  in  diameter,  and  shall  not  be 
spaced  more  than  6  inches  apart  in  any  case.  They  shall  be  so  spaced 
that  their  shearing  strains  shall  not  exceed  9000  Ibs.  per  square  inch,  on 
their  diameter,  multiplied  by  the  thickness  of  the  plates  through  which 
they  pass.  The  riveted  plate  girders  shall  be  proportioned  upon  the 
supposition  that  the  bending  or  chord  strains  are  resisted  entirely  by  the 
upper  and  lower  flanges,  and  that  tne  shearing  strains  are  resisted  en- 
tirely by  the  web-plate.  No  part  of  the  web  shall  be  estimated  as  flange 
area,  nor  more  than  one  half  of  that  portion  01  the  angle-iron  which  lies 
against  the  web.  The  distance  between  the  centers  of  gravity  of  the 
flange  areas  will  be  considered  as  the  effective  depth  of  the  girder. 

The  building  laws  of  the  city  of  New  York  contain  a  great  amount  of 
detail  in  addition  to  the  extracts  above,  and  penalties  are  provided  for 
violation.  See  An  Act  creating  a  Department  of  Buildings,  etc.,  Chapter 
275,  Laws  of  1892.  Pamphlet  copy  published  by  Baker,  Voorhies  &  Co., 
New  York. 

FLOORS. 

Maximum  Load  on  Floors.  (Eng'g,  Nov.  18,  1892,  p.  644.)  —  Maxi- 
mum load  per  square  foot  of  floor  surface  due  to  the  weight  of  a  dense 
crowd.  Considerable  variation  is  apparent  in  the  figures  given  by  many 
authorities,  as  the  following  table  shows: 


STRENGTH  OF  FLOCKS,          1391 

Authorities.  Weight  of  Crowd. 

Ibs.  per  sq.  ft. 

French  practice,  quoted  by  Trautwine  and  Stoney 41 

Hatfield  ("Transverse  Strains, "  p.  80) 70 

Mr.  Page,  London,  quoted  by  Trautwine 84 

Maximum  load  on  American  highway  bridges  according  to 

Waddell's  general  specifications ' 100 

Mr.  Nash,  architect  of  Buckingham  Palace 120 

Experiments  by  Prof.  W.  N.  Kernot,  at  Melbourne  j      j||j  2 

Experiments  by  Mr.  B.  B.  Stoney  ("On  Stresses,"  p.  617)  147^4 

Experiments  by  Prof.  L.  J.  Johnson,  Eng.  News,  April  14,  f       134.2 

1904 -. . (to  156.9 

The  highest  results  were  obtained  by  crowding  a  number  of  persons 
previously  weighed  into  a  small  room,  the  men  being  tightly  packed  so  as 
to  resemble  such  a  crowd  as  frequently  occurs  on  the  stairways  and  plat- 
forms of  a  theatre  or  other  public  building. 

Safe  Allowances  for  Floor  Loads.     (Kidder.)     Lbs.  per  square  foot 

For  dwellings,  sleeping  and  lodging  rooms 40  Ibs. 

For  schoolrooms 50 

For  offices,  Upper  stories 60 

For  offices,  first  story 80 

For  stables  and  carriage  houses 65. 

For  banking  rooms,  churches  and  theaters 80 

For  assembly  halls,  dancing  halls,  and  the  corridors  of  all 

public  buildings,  including  hotels 120     ' 

For  drill  rooms 150     ' 

For  ordinary  stores,  lighc  storage,  and  light  manufactur- 
ing          120*  M 

*  Also  to  sustain  a  concentrated  load  at  any  point  of  4000  Ibs. 

STRENGTH   OF   FLOORS. 

(From  circular  of  the  Boston  Manufacturers'  Mutual  Insurance  Co.)  * 

The  tables  on  p.  1393  were  prepared  by  C.  J.  H.  Woodbury,  for  deter- 
mining safe  loads  on  floors.  Care  should  be  observed  to  select  the 
figure  giving  the  greatest  possible  amount  and  concentration  of  load  as 
the  one  which  may  be  put  upon  any  beam  or  set  of  floor-beams;  and 
in  no  case  should  beams  be  subjected  to  greater  loads  than  those  speci- 
fied, unless  a  l9wer  factor  of  safety  is  warranted  under  the  advice  of  a 
competent  engineer.  These  tables  are  computed  for  beams  one  inch  in 
width,  because  the  strength  of  beams  increases  directly  as  the  width 
when  the  beams  are  broad  enough  not  to  cripple. 

Beams  or  heavy  timbers  used  in  the  construction  of  a  factory  or  ware- 
house should  not  be  painted,  varnished  or  oiled,  filled  or  encased  in 
impervious  concrete,  air-proof  plastering,  or  metal  for  at  least  three  years, 
lest  fermentation  should  destroy  them  by  what  is  called  "dry  rot." 

It  is,  on  the  whole,  safer  to  make  floor-beams  in  two  parts  with  a 
small  open  space  between,  so  that  proper  ventilation  may  be  secured. 

These  tables  apply  to  distributed  loads,  but  the  first  can  be  used  in 
respect  to  floors  which  may  carry  concentrated  loads  by  using  half  the 
figure  given  in  the  table,  since  a  beam  will  bear  twice  as  much  load 
when  evenly  distributed  over  its  length  as  it  would  if  the  load  was 
concentrated  in  the  centsr  of  the  span. 

The  weight  of  the  floor  should  be  deducted  from  the  figure  given  in 
the  table,  in  order  to  ascertain  the  net  load  which  may  be  placed  upon 
any  floor.  The  weight  of  spruce  may  be  taken  at  36  Ibs.  per  cubic 
foot,  and  that  of  Southern  pine  at  48  Ibs.  per  cubic  foot. 

Table  I  was  computed  upon  a  working  modulus  of  rupture  of  South- 
ern pine  of  2160  Ibs.,  using  a  factor  of  safety  of  six.  It  can  also  be 
applied  to  ascertaining  the  strength  of  spruce  beams  if  the  figures 
given  in  the  table  arc  multiplied  by  0.78;  or  in  designing  a  floor  to  be 
sustained  by  spruce  beams,  multiply  the  required  load  by  1.28,  and 
use  the  dimensions  as  given  by  the  table. 

EXAMPLE. — Required  the  safe  load  per  square  foot  of  floor,  which 
may  be  safely  sustained  by  a  floor  on  Southern  pine  10  X  14  in.  beams, 
8  ft,  on  centers,  and  20  ft.  span.  In  Table  I  a  1  X  14  in.  beam,  20  ft. 


1392  CONSTRUCTION  OF  BUILDINGS, 

span,  will  sustain  118  Ibs.  per  foot  of  span;  and  for  a  beam  10  ins.  wide 
the  load  would  be  1180  Ibs.  per  foot  of  span,  or  1471/2  Ibs.  per  sq.  ft.  of 
floor  for  Southern-pine  beams.  From  this  should  be  deducted  the 
weight  of  the  floor,  171/2  Ibs.  per  sq.  ft.,  leaving  130  Ibs.  per  sq.  ft.  as  a 
safe  load.  If  the  beams  are  of  spruce,  multiply  1471/2  by  0.78,  reduc- 
ing the  load  to  115  Ibs.  Deducting  the  weight  of  the  floor,  16  Ibs., 
leaves  the  safe  net  load  as  90  Ibs.  per  sq.  ft.  for  spruce  beams. 

Table  II  applies  to  floors  whose  strength  must  be  in  excess  of  that 
necessary  to  sustain  the  weight,  in  order  to  meet  the  conditions  of  deli- 
cate or  rapidly  moving  machinery,  to  the  end  that  the  vibration  or 
distortion  of  the  floor  may  be  reduced  to  the  least  practicable  limit. 

In  the  table  the  limit  is  that  of  a  load  which  would  cause  a  bending 
of  the  beams  to  a  curve,  of  which  the  average  radius  would  be  1250  ft. 

This  table  is  based  upon  a  modulus  of  elasticity  obtained  from  obser- 
vations upon  the  deflection  of  loaded  storehouse  floors,  and  is  taken  at 
2,000,000  Ibs.  for  Southern  pine;  the  same  table  can  be  applied  to  spruce, 
whose  modulus  ofxelasticity  is  taken  as  1,200,000  Ibs.,  if  six  tenths  91 
the  load  for  Southern  pine  is  taken  as  the  proper  load  for  spruce;  or,  in 
the  matter  of  designing,  the  load  should  be  increased  one  and  two  thirds 
times,  and  the  dimension  of  timbers  for  this  increased  load  as  found  in 
the  table  should  be  used  for  spruce. 

It  can  also  be  applied  to  beams  and  floor-timbers  supported  at  each 
end  and  in  the  middle,  remembering  that  the  deflection  of  a  beam  sup- 
ported in  that  manner  is  only  0.4  that  of  a  beam  of  equal  span  which 
rests  at  each  end ;  that  is  to  say,  the  floor-planks  are  2  V2  times  as  stiff, 
cut  two  bays  in  length,  as  they  would  be  if  cut  only  one  bay  in  length. 
When  a  floor-plank  two  bays  in  length  is  evenly  loaded,  3/16  of  the  load 
on  the  plank  is  sustained  by  the  beam  at  each  end  of  the  plank,  and  io/ifj 
by  the  beam  under  the  middle  of  the  plank;  so  that  for  a  completed  floor 
3/8  of  the  load  would  be  sustained  by  the  beams  under  the  joints  of  the 
plank,  and  5/g  of  the  load  by  the  beams  under  the  middle  of  the  plank: 
this  is  the  reason  of  the  importance  of  breaking  joints  in  a  floor-plank 
every  3  ft.  in  order  that  each  beam  shall  receive  an  identical  load.  If 
-  it  were  not  so,  3/g  of  the  whole  load  upon  the  floor  would  be  sustained 
by  every  other  beam,  and  5/8  of  the  load  by  the  alternate  beams. 

Repeating  the  former  example  for  the  load  on  a  mill  floor  on  Southern- 
pine  beams  10  X  14  ins.,  and  20  ft.  span,  8  ft.  centers:  In  Table  II  a 
1  X  14  in.  beam  should  receive  61  Ibs.  per  foot  of  span,  or  75  Ibs.  per 
sq.  ft.  of  floor,  for  Southern-pine  beams.  Deducting  the  weight  of  the 
floor,  171/2  Ibs.  per  sq.  ft.,  57  Ibs.  per  sq.  ft.  is  the  advisable  load. 

If  the  beams  are  of  spruce,  the  result  of  75  Ibs.  should  be  multiplied 
by  0.6,  reducing  the  load  to  45  Ibs.  The  weight  of  the  floor,  in  this 
instance  amounting  to  16  Ibs.,  would  leave  the  net  load  as  29  Ibs.  for 
spruce  beams. 

If  the  beams  were  two  spans  in  length,  they  could,  under  these  con- 
ditions, support  two  and  a  half  times  as  much  load  with  an  equal  amount 
of  deflection.,  unless  such  load  should  exceed  tlie  limit  of  safe  load  as  found 
by  Table  I,  as  would  be  the  case  under  the  conditions  of  this  problem. 

Maximum  Spans  for  1,  3  and  3  Inch  Plank.  (Am.  Macli.,  Feb.  11, 
1904.)  —  Let  w  =  load  per  sq.  ft.;  I  =  length  in  in*;  ;  W  =  wl/12;  S  = 
safe  fiber  stress,  using  a  factor  of  safety  of  10;  6  =  wic?*h  of  plank;  d  = 
thickness;  p  =  deflection,  E  =  coefficient  of  elasticity,  sT  =  moment  of 
inertia  =  Vl2  bd*. 

Then  Wl/S  =  Sbd*/Q;  s  =  5  Wl*  ^  384  EL  Taking  S  at  1200  Ibs.,  E 
at  850,000  and  s  =  L  -*•  360  for  long-leaf  yellow  pine,  the  following  figures 
for  maximum  span,  in  inches,  are  obtained: 

Uniform  load,  Ibs.  per  sq.ft..    40       60        80      100     150     200     250      300 

i  to  -niankJForstrengtn-  •   75       61       53       48       39       33      

1K  t  For  deflection  .37       33       30       28       24       22      

9  in    ninni,f  For  strength..  151     123     107       96       78       67       60       55 
lk  \  For  deflection .   75       66       60       55       48       44       41       38 

sir    T^ioni,  |  For  strength..  227     185     161      144     117     101       91       83 
1K1  For  deflection.  113       99       90       83       73       66       61       58 
For  white  oak  S  may  be  taken  at  1000  and  E  at  550,000;  for  Canadian 
spruce,  S  =  800,  E  =  600,000;  for  hemlock,  S  =  600,  E  =  450,000. 


BTREiSfGTll  OF  FL001W, 


1393 


I.  Safe  Distributed  Loads  upon  Southern-pine  Beams  One  Inch 
in  Width. 

(C.  J.  H,  Woodbury.) 

(If  the  load  is  concentrated  at  the  center  of  the  span,  the  beams 
will  sustain  half  the  amount  given  in  the  table.) 


1 

i 

a 
m 

Depth  of  Beam  in  inches. 

2 

3 

4  |  5 

6  |  7 

8 

9 

10  |  11 

12|l3 

14 

15 

16 

Load  in  pounds  per  foot  of  Span. 

5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

38 
27 
20 
15 

86 
60 

44 
34 
27 
22 

154 
107 

78 
60 
47 
33 
32 
27 

240 
167 
122 
94 
74 
60 
50 
42 
35 
31 
27 

346 
240 
176 
135 
107 
86 
71 
60 
51 
44 
38 
34 
30 

470 
327 
240 
184 
145 
118 
97 
82 
70 
60 
52 
46 
41 
36 

614 
427 
314 
240 
190 
154 
127 
107 
90 
78 
68 
60 
53 
47 
43 
38 

778 
540 
397 
304 
240 
194 
161 
135 
115 
9Q 
86 
76 
67 
60 
54 
49 
44 

960 
667 
490 
375 
296 
240 
198 
167 
142 
123 
107 
94 
83 
74 
66 
60 
54 
50 
45 

807 
593 
454 
359 
290 
240 
202 
172 
148 
129 
113 
101 
90 
80 
73 
66 
60 
55 
50 
46 

705 
540 
427 
346 
286 
240 
205 
176 
154 
135 
120 
107 
96 
86 
78 
71 
65 
60 
55 

828 
634 
501 
406 
335 
282 
240 
207 
180 
158 
140 
125 
112 
101 
92 
84 
77 
70 
65 

735 
581 
470 
389 
327 
278 
240 
209 
184 
163 
145 
130 
118 
107 
97 
89 
82 
75 

667 
540 
446 
375 
320 
276 
240 
211 
187 
167 
150 
135 
122 
112 
102 
94 
86 

759 
614 
508 
474 
364 
314 
273 
240 
217 
190 
170 
154 
139 
127 
116 
107 
98 

II.  Distributed  Loads  upon  Southern-pine  Beams  Sufficient  to 
Produce  Standard  Limit  of  Deflection. 


1 

ef 

a 

VI 

~T 

6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

Depth  of  Beam  in  inches. 

Deflection, 
inches.  I 

2 

3 

4 

5  |  6  |  7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

Load  in  pounds  per  foot  of  Span. 

3 

2 

10 

7 
5 
4 

23 
16 
12 
9 
7 
6 

44 
31 
23 
17 
14 
11 
9 

77 
53 
39 
30 
24 
19 
16 
13 
11 

122 
85 
62 
48 
38 
30 
25 
21 
18 
16 
14 

182 
126 
93 
71 
56 
46 
38 
32 
27 
23 
20 
18 
16 

259 
180 
132 
101 
80 
65 
54 
45 
38 
33 
29 
25 
22 
20 
18 

247 
181 
139 
110 
89 
73 
62 
53 
45 
40 
35 
31 
27 
25 
22 
20 

241 
185 
146 
118 
98 
82 
70 
60 
53 
46 
41 
37 
33 
30 
27 
24 
22 

240 
190 
154 
127 
107 
91 
78 
68 
60 
53 
47 
43 
38 
35 
32 
29 
27 
25 

305 
241 
195 
161 
136 
116 
100 
87 
76 
68 
60 
54 
49 
44 
40 
37 
34 
31 

301 
244 
202 
169 
144 
124 
108 
95 
84 
75 
68 
61 
55 
50 
46 
42 
39 

300 
248 
208 
178 
153 
133 
117 
104 
93 
83 
75 
68 
62 
57 
52 
48 

301 
253 
215 
186 
162 
147 
126 
112 
101 
91 
83 
75 
69 
63 
58 

.0300 
.0432 
.0588 
.0768 
.0972 
.1200 
.1452 
.1728 
.2028 
.2352 
.2700 
.3072 
.3468 
.3888 
.4332 
.4800 
.5292 
.5808 
.6348 
.6912 
.7500 

, 

Mill  Columns. — Timber  posts  offer  more  resistance  to  fire  than  iron 
pillars,  and  have  generally  displaced  them  in  millwork.    Experiments 


1394 


CONSTRUCTION   OF  BUlLblNGS. 


at  the  U.  S.  Arsenal  at  Watertown,  Mass.,  show  that  sound  timber  posts 
of  the  proportions  customarily  used  in  millwork  yield  by  direct  crush- 
ing, the  strength  being  directly  as  the  area  at  the  smallest  part.  The 
columns  yielded  at  about  4500  Ibs.  per  sq.  in.,  confirming  the  general 
practice  of  allowing  600  Ibs.  per  sq.  in.  as  a  safe  load.  Square  columns 
are  one  fourth  stronger  than  round  ones  of  the  same  diameter. 

COST  OF  BUILDINGS. 

Approximate  Cost  of  Mill. Buildings.  —  Chas.  T.  Main  (Eng.  News, 
Jan.  27,  1910)  gives  a  series  of  diagrams  of  the  cost  in  New  England 
Jan.,  1910,  per  sq.  ft.  of  floor  space  of  different  sizes  of  brick  mill  build- 
ings, one  to  six  stories  high,  of  the  type  known  as  "slow-burning,"  cal- 
culated for  total  floor  loads  of  about  75  Ibs.  per  sq.  ft.  Figures  taken 
from  the  diagrams  are  given  in  the  table  below.  The  costs  include 
ordinary  foundations  and  plumbing,  but  no  heating,  sprinklers  or  lighting. 
COST  OF  BRICK  MILL  BUILDINGS  PER  SQ.  FT.  OF  FLOOR  AREA. 


Length,  feet.         50       100     150      200      250      300      350      400      500 


One  Story. 


Width  25  ft. 
50 
75 
125 

$1.90 
1.52 
1.41 
1.32 

$1.66 
1.29 
1.21 
1.09 

$1.58 
1.21 
1.12 
1.02 

$1.54 
1.18 
1.08 
0.98 

$1.51 
1.16 
1.06 
0.96 

$1.49 
1.15 
1.04 
0.94 

$1.48 
1.14 
1.03 
0.94 

$1.47 
1.13 
1.02 
0.93 

$1.46 
1.13 
1.02 
0.92 

Two  Stories. 

25 
50 
75 
125 

2.00 
1.50 
1.34 
1.22 

1.62 
1.21 
1.08 
0.97 

1.52 
1.13 
1.01 
0.90 

1.47 
1.09 
0.97 
0.86 

1.44 
1.06 
0.94 
0.84 

1.41 
1.05 
0.92 
0.82 

1.39 
1.04 
0.92 
0.81 

1.38 
1.03 
0.91 
0.80 

1.36 
1.02 
0.90 
0.8J 

Three  Stories. 

25 
•      50 
75 
125 

1.$8 
1.47 
1.30 
1.18 

1.57 
1.17 
1.05 
0.93 

1  47 
1.07 
0.98 
0.86 

1.42 
1.03 
0.94 
0.82 

1.39 
1.01 
0.91 
0.80 

1.38 
1.00 
0.89 
0.78 

1.36 
0.98 
0.88 
0.77 

1.35 
0.98 
0.87 
0.76 

1.34 
0.98 
0.86 
0.76 

Four  Stories. 

25 
50 
75 
125 

2.00 
1.38 
1.32 
1.20 

1.61 
1.17 
1.08 
0.93 

1.50 
1.10 
0  97 
0.85 

1.45 
1.05 
0.93 
0.81 

1.42 
1.02 
0.90 
0.78 

1.40 
1.00 
0.88 
0.77 

1.38 
1.00 
0.88 
0.76 

1.37 
0.99 
0.87 
0.75 

1.36 
0.98 
0.87 
0.74 

Six  Stories. 

25 
50 
75 

125 

2.10 
1.53 
1.35 
1.22 

1.72 
1.21 
1.08 
0.96 

1.57 
1.12 
0.98 
0.86 

1.51 
1.08 
0.94 
0.82 

1.48 
1.05 
0.92 
0.79 

1.46 
1.04 
0.90 
0.78 

1.44 
1.03 
0.89 
0.77 

1.43 
1.02 
0.88 
0.76 

1.42 
1.02 
0.86 
0.76 

The  cost  per  sq.  ft.  of  a  building  100  ft.  wide  will  be  about  midway 
between  that  of  one  75  ft.  wide  and  one  125  ft.  wide,  and  the  cost  of  a 
five-story  building  about  midway  between  the  costs  of  a  four-  and  a  six- 
story.  The  data  for  estimating  the  above  costs  are  as  follows: 


Stories  High. 

1 

2 

3 

4 

5 

6 

Foundations,  includ-  )  Outside  walls 

$2.00 
1.75 

$2.90 
2.25 

$3.80 
2.80 

$4.70 
3.40 

$5.60 
3.90 

$6.50 
4.50 

Brick  walls,  cost  per  )  Outside  walls.  . 
sq.  ft.  of  surface.  .  .  )  Inside  walls  — 

0.40 
0.40 

0.44 
0.40 

0.47 
0.40 

0.50 
0.43 

0.53 
0.45 

0.57 
0.47 

Columns,  including  piers  and  castings,  cost  each  $15. 
Assumed  Height  of  Stories.  —  From  ground  to  first  floor,  3  ft.  Buildings 

COST  OF  BUILDINGS.  1395 

25  ft.  wide,  stories  13  ft.  high;  50  ft.  wide,  14  ft.  high;  75  ft.  wide,  15  ft 
high;  100  ft.  and  125  ft.  wide,  16  ft.  high. 

Floors,  32  cts.  per  sq.  ft.  of  gross  floor  space  not  including  columns. 
Columns  included,  38  cts. 

Roof,  25  cts.  per  sq.  ft.,  not  including  columns.  Columns  included, 
30  cts.  Roof  to  project  18  ins.  all  around  buildings. 

Stairways,  including  partitions,  $100"  each  flight.  Two  stairways  and 
one  elevator  tower  for  buildings  up  to  150  ft.  long;  two  stairways  and  two 
elevator  towers  for  buildings  up  to  300  ft.  long.  In  buildings  over  two 
stories,  three  stairways  and  three  elevator  towers  for  buildings  over  300  ft 
long. 

in  buildings  over  two  stories,  plumbing  $75  for  each  fixture  including 
piping  and  partitions.    Two  fixtures  on  each  floor  up  to  5000  sq.  ft.  oi 
floor  space  and  one  fixture  for  each  additional  5000  sq.  ft.  of  floor  or 
fraction  thereof. 
Modifications  of  the  above  Costs: 

1.  If  the  soil  is  poor  or  the  conditions  of  the  site  are  such  as  to  require 
more  than  ordinary  foundations,  the  cost  will  be  increased. 

2.  If  the  building  is  to  be  used  for  ordinary  storage  purposes  with  low 
stories  and  no  top  floors,  the  cost  will  be  decreased  from  about  10%  for 
large  low  buildings  to  25%  for  small  high  ones,  about  20%  usually  being 
a  fair  allowance. 

3.  If  the  building  is  to  be  used  for  manufacturing  and  is  substantially 
built  of  wood,  the  cost  will  be  decreased  from  about  6%  for  large  one- 
story  buildings  to  33%  for  high  small  buildings;  15%  would  usually  be  a 
lair  allowance. 

4.  If  the  building  is  to  be  used  for  storage  with  low  stories  and  built 
substantially  of  wood,  the  cost  will  be  decreased  from   13% -for  large 
one-story  buildings  to  50%  for  small  high  buildings;  30%  would  usually 
be  a  fair  allowance. 

5.  If  the  total  floor  loads  are  more  than  75  Ibs.  per  sq.  ft.  the  cost  is 
increased. 

6.  For  office  buildings,  the  cost  must  be  increased  to  cover  architectural 
features  on  the  outside  and  interior  finish. 

Reinforced-concrete  buildings  designed  to  carry  floor  loads  of  100  Ibs. 
per  so.  ft.  or  less  will  cost  about  25%  more  than  the  slow-burning  type 
of  mill  construction. 


1396  ELECTRICAL  ENGINEERING. 

ELECTRICAL  ENGINEERING.* 

STANDARDS  OF  MEASUREMENT. 

C.G.S.  (Centimeter,  Gramme,  Second)  or  "Absolute"  System 
of  Physical  Measurements: 

Unit  of  space  or  distance  ••  1  centimeter,  cm.; 

Unit  of  mass  =  1  gramme,  gm.; 

Unit  of  time  =  1  second,  sec.; 

Unit  of  velocity  =  space  -f-  time    =  1  centimeter  in  1  second; 
Unit  of  acceleration  =  change  of  1  unit  of  velocity  in  1  second ; 
Acceleration  due  to  gravity,  =  980.665  centimeters  per  sec.  per  sec. 

Unit  of  force  =  1  dyne=  ^  gm.  =  «f-2U>.=  0.000002248! Ib. 

A  dyne  is  that  force  which,  acting  on  a  mass  of  one  gramme  during  one 
second,  will  give  it  a  velocity  of  one  centimeter  per  second.  The  weight 
of  one  gramme  in  latitude  40°  to  45°  is  about  980  dynes,  at  the  equator 
973  dynes,  and  at  the  poles  nearly  984  dynes.  Taking  the  value  of  g, 
the  acceleration  due  to  gravity,  in  British  measures  at  32.1740  feet  per 
second  at  lat.  45°  at  the  sea  level,  and  the  meter  =  39.37  inches,  we  have 

1  gramme  =  32.174  X  12  -s-  0.3937  =  980.665  dynes. 
Unit  of  work    =  1  erg      =1  dyne-centimeter  =  0.000000073756  ft.-lb.; 
Unit  of  power  =  1  watt  =  10  million  ergs  per  second, 

=  0.73756  foot-pound  per  second. 

=  °55Q56  =  7^7  horse-power  =  0.0013410  H.P. 

C.G.S.  unit  magnetic  pole  is  one  which  reacts  on  an  equal  pole  at  a 
centimeter's  distance  with  the  force  of  1  dyne. 

C.G.S.  unit  of  magnetic  field  strength,  the  gauss,  is  the  intensity  of 
field  which  surrounding  unit  pole  acts  on  it  with  a  force  of  1  dyne. 

C.G.S.  unit  of  electro-motive  force  =  the  force  produced  by  the  cuttingr 
of  a  field  of  1  gauss  intensity  at  a  velocity  of  1  centimeter  per  second  (in 
a  direction  normal  to  the  field  and  to  the  cpnductor)  by  1  centimeter  ol 
conductor.  The  volt  is  100,000,000  times  this  unit. 

C.G.S.  unit  of  electrical  current  ==  the  current  in  a  conductor  (located 
in  a  plane  normal  to  the  field)  when  each  centimeter  is  urged  across  a 
magnetic  field  of  1  gauss  intensity  with  a  force  of  1  dyne.  One-tenth  of 
this  is  the  ampere. 

The  C.G.S.  unit  9f  quantity  of  electricity  is  that  represented  by  the 
flow  of  1  C.G.S.  unit  of  current  for  1  second.  One-tenth  of  this  is  the 
coulomb. 

The  Practical  Units  used  in  Electrical  Calculations  are: 

Ampere,  the  unit  of  current  strength,  or  rate  of  flow,  represented  by  /. 

Volt,  the  unit  of  electro-motive  force,  electrical  pressure,  or  difference 
of  potential,  represented  by  E. 

Ohm,  the  unit  of  resistance,  represented  by  R. 

Coulomb  (or  ampere-second),  the  unit  of  quantity,  Q. 

Ampere-hour  =  3600  coulombs,  Qf. 

Watt  (volt-ampere),  the  unit  of  power,  P. 

Joule  (or  watt-second),  the  unit  of  energy  or  work,  W. 

Farad,  the  unit  of  electrostatic  capacity,  represented  by  C. 

Henry,  the  unit  of  inductance,  represented  by  L. 

Using  letters  to  represent  the  units,  the  relations  between  them  may 
be  expressed  by  the  following  formulae,  in  which  t  represents  one  second 
and  T  one  hour: 

/=|,    Q  =  It,     Q'  =  IT,     C7  =  |,     W=QE,     P  =  IE. 

As  these  relations  contain  no  coefficient  other  than  unity,  the  letters 
may  represent  any  quantities  given  in  terms  of  those  units.  For  exam- 
ple, if  E  represents  the  number  of  volts  electro-motive  force,  and  R  the 
number  of  ohms  resistance  in  a  circuit,  then  their  ratio  E  -T-  R  will  give 
the  number  of  amperes  current  strength  in  that  circuit. 

The  above  six  formulae  can  be  combined  by  substitution  or  elimination, 

*  In  the  revision  of  this  chapter  the  author  has  had  the  assistance 
of  Mr.  David  B.  Rushmore. 


STANDARDS  OF  MEASUREMENTS,  1397 

so  as  to  give  the  relations  between  any  of  the  quantities.    The  most 
important  of  these  are  the  following: 


The  definitions  of  these  units  as  adopted  at  the  International  Electrical 
Congress  at  Chicago  in  1893.  and  as  established  by  Act  of  Congress  of 
the  United  States,  July  12,  1894,  are  as  follows: 

The  ohm  is  substantially  equal  to  109  (or  1,000,000,000)  units  of  resist- 
ance of  the  C.G.S.  system,  and  is  represented  by  the  resistance  offered 
to  an  unvarying  electric  current  by  a  column  of  mercury  at  32°  F.,  14.4521 
grammes  in  mass,  of  a  constant  cross-sectional  area,  and  of  the  length  of 
106.3  centimeters. 

The  ampere  is  Vio  of  the  unit  of  current  of  the  C.G.S.  system,  and  is 
the  practical  equivalent  of  the  unvarying  current  which  when  passed 
through  a  solution  of  nitrate  of  silver  in  water  in  accordance  with  standard 
specifications  deposits  silver  at  the  rate  of  0.001118  gramme  per  second. 

The  volt  is  the  electro-motive  force  that,  steadily  applied  to  a  con- 
ductor whose  resistance  is  one  ohm,  will  produce  a  current  of  one  ampere, 
and  is  practically  equivalent  to  1000/1434  (or  0.6974)  of  the  electro- 
motive force  between  the  Doles  or  electrodes  of  a  Clark's  cell  at  a  tem- 
perature of  15°C.,  and  prepared  in  the  manner  described  in  the  standard 
specifications.  [The  e.m.f.  of  a  Weston  normal  cell  is  1.0183  volts  at  20°  C.] 

The  coulomb  is  the  quantity  of  electricity  transferred  by  a  current  of  one 
ampere  in  one  second. 

The  farad  is  the  capacity  of  a  condenser  charged  to  a  potential  of  one 
volt  by  one  coulomb  of  electricity. 

The  joule  is  equal  to  10,000,000  units  of  work  in  the  C.G.S.  system,  and 
is  practically  equivalent  to  the  energy  expended  in  one  second  by  an 
ampere  in  an  ohm. 

The  watt  is  equal  to  10,000,000  units  of  power  in  the  C.G.S.  system,  and 
is  practically  equivalent  to  the  work  done  at  the  rate  of  one  joule  per 
second. 

The  henry  is  the  induction  jn  a  circuit  when  the  electro-motive  force 
induced  in  this  circuit  is  one  volt,  while  the  inducing  current  varies  at  the 
rate  of  one  ampere  per  second. 

The  ohm,  volt,  etc.,  as  above  defined,  are  called  the  "international" 
ohm,  volt,  etc.,  to  distinguish  them  from  the  "legal"  ohm,  B.A.  unit,  etc. 

The  value  of  the  ohm,  determined  by  a  committee  of  the  British  Asso- 
ciation in  1863,  called  the  B.A.  unit,  was  the  resistance  of  a  certain  piece 
of  copper  wire.  The  so-called  "legal"  ohm,  as  adopted  at  the  Inter- 
national Congress"  of  Electricians  in  Paris  in  1884,  was  a  correction  of  the 
B.A.  unit,  and  was  defined  as  the  resistance  of  a  column  of  mercury 
1  square  millimeter  in  section  and  106  centimeters  long,  at  a  temperature 
of  32°  F.  1  legal  ohm  =1.0112  B.A.  units;  1  international  ohm  =1.0023 
legal  ohm;  1  legal  ohm  =0.9977  int.  ohm. 

DERIVED  UNITS. 
1  megohm        =  1  million  ohms; 
1  microhm        =  1  millionth  of  an  ohm; 
1  milliampere  =  1/1000  of  an  ampere; 
1  micro-farad  =  1  millionth  of  a  farad. 

RELATIONS  OF  VARIOUS  UNITS. 
1  ampere  ..................      =1  coulomb  per  second; 

1  volt-ampere  (direct  current)      =  1  watt  =  1  volt-coulomb  per  sec.  ; 

(  =  0.73756  foot-pound  per  second, 
1  watt  ....................   •{   =  0.00094859  heat-unit  per  sec.  (Fahr.), 

=  1/745-7  of  one  horse-power; 
=  0.73756  foot-pound, 


1  joule  =  107  ergs . 


1  British  thermal  unit . 


:  work  done  by  one  watt  in  one  sec., 
=  0.00094859  heat-unit; 
=  0.23904  gram  calories; 
=  1054.2  joules; 
=  777.54  foot-pounds; 
=  25.200  gram  calories; 


1398  ELECTRICAL  ENGINEERING. 

1  mean  gram  calorie {  I  fc"***,1*  «*£ ; 

1  kilowatt,  or  1000  watts =  1000/745.7  or  1.3410  horse-powers; 


1  kilowatt-hour 

1000  volt-ampere  hours ..... 

1  British  Board  of  Trade  unit 

1  horse-power 


1.3410  horse-power  hours, 
=  2,655,220  foot-pounds, 
=  3415  heat-units; 
=  745.7  watts  =  745.7  volt-amperes, 


=  33,000  foot-pounds  per  minute. 
The  ohm,  ampere,  and  volt  are  denned  in  terms  of  one  another  as 
follows:  Ohm,  the  resistance  of  a  conductor  through  which  a  current  of 
one  ampere  will  pass  when  the  electro-motive  force  is  one  volt.  Ampere, 
the  quantity  of  current  which  will  flow  through  a  resistance  of  one  ohm 
when  the  electro-motive  force  is  one  volt.  Volt,  the  electro-motive  force 
required  to  cause  one  ampere  to  flow  through  a  resistance  of  one  ohm. 

For  Methods  of  Making  Electrical  Measurements,  Testing,  etc., 
see  "American  Handbook  for  Electrical  Engineers";  Karapetoff's 
"Experimental  Electrical  Engineering":  Bedell's  "Direct  and  Alter- 
nating Current  Manual";  1914  Standardization  Rules  of  A.  I.  E.  E. 

Equivalent  Electrical  and  Mechanical  Units. — H.   Ward   Leonard 
published  in  The  Electrical  Engineer,  Feb.  25,  1895,  a  table  of  useful 
equivalents  of  electrical  and  mechanical  units,  from  which  the  table  on 
page  1399  is  taken,  with  some  modifications. 
L  Units  of  the  Magnetic  Circuit. 

Unit  magnetic  pole  is  a  pole  of  such  strength  that  when  placed  at  a  dis- 
tance of  one  centimeter  from  a  similar  pole  of  equal  strength  it  repels  it 
with  a  force  of  one  dyne. 

Magnetic  Moment  is  the  product  of  the  strength  'of  either  pole  into  the 
distance  between  the  two  poles. 

Intensity  of  Magnetization  is  the  magnetic  moment  of  a  magnet  divided 
by  its  volume. 

Intensity  of  Magnetic  Field  is  the  force  exerted  by  the  field  upon  a  unit 
magnetic  pole.  The  unit  is  the  gauss. 

Gauss  =  unit  of  field  strength,  or  density,  symbol  H  is  that  intensity 
of  field  which  acts  on  a  unit  pole  with  a  force  of  one  dyne,  =  one  line  of 
force  per  square  centimeter.  One  gauss  produces  1  dyne  of  force  per 
centimeter  length  of  conductor  upon  a  'current  of  10  amperes,  or  an 
electro-motive  force  of  1/100,000,000  volt  in  a  centimeter  length  of  con- 
ductor when  its  velocity  across  the  field  is  1  centimeter  per  second.  A  field  of 
H  units  is  one  which  acts  with  H  dynes  on  unit  pole,  or  H  lines  per 
square  centimeter.  A  unit  magnetic  pole  has  4?r  lines  of.  force  proceeding 
from  it. 

Maxwell  =  unit  of  magnetic  flux,  is  the  amount  of  magnetism  passing 
through  a  square  centimeter  of  a  field  of  unit  density.  •  Symbol,  $. 

In  non-magnetic  materials  a  unit  of  intensity  of  flux  is  the  same  as 
unit  intensity  of  field.  The  name  maxwell  is  given  to  a  unit  quantity 
of  flux,  and  one  maxwell  per  square  centimeter  in  non-magnetic  materials 
is  the  same  as  the  gauss.  In  magnetic  materials  the  flux  produced  by 
the  molecular  magnets  is  added  to  the  field  (Norris). 

Magnetic  Flux,  <£,  is  equal  to  the  average  field  intensity  multiplied  by 
the  cross-sectional  area.  The  unit  is  the  maxwell.  Maxwells  per  square 
inch=  gausses  X  6.45. 

Magnetic  Induction,  symbol  B,  is  the  flux  or  the  number  of  magnetic 
lines  per  unit  of  area  of  cross-section  of  magnetized  material,  the  area 
being  at  every  point  perpendicular  to  the  direction  of  the  flux.  It  is 
equal  to  the  product  of  the  field  intensity,  H,  and  the  permeability, .«. 

Gilbert  =  unit  of  magnetomotive  force,  is  the  amount  of  M.M.F.  that 
would  be  produced  by  a  coil  of  10  -*•  4rc  or  0.7958  ampere-turns.  Symbol  F. 

The  M.M.F.  of  a  coil  is  equal  to  1.2566  times  the  ampere-turns. 

If  a  solenoid  is  wound  with  100  turns  of  insulated  wire  carrying  a  current 
of  5  amperes,  the  M.M.F.  exerted  will  be  500  ampere-turns  X  1.2566  = 
628.3  gilberts. 

Oersted  =  unit  of  magnetic  reluctance;  a  magnetic  circuit  has  a  re- 
luctance of  1  oersted  when  unit  m.m.f.  produces  unit  flux.  Symbol,  R. 

Reluctance  is  that  quantity  in  a  magnetic  circuit  which  limits  the  flux 

*Mean  of  the  values  of  Reynolds  and  Moorby  and  of  Barnes- 
Marks  &  Davis,  Steam  Tables,  1909* 


EQUIVALENT  ELECTRICAL  AND  MECHANICAL  UNITS.    1399 


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1400 


ELECTRICAL.  ENGINEERING. 


under  a  given  M.M.F.  It  corresponds  to  the  resistance  in  the  electric  cir- 
cuit. 

Permeance  is  the  reciprocal  of  reluctance. 

The  reluctivity  of  any  medium  is  its  specific  reluctance,  and  in  the  C.G.S. 
system  is  the  reluctance  offered  by  a  cubic  centimeter  of  the  body  between 
opposed  parallel  faces.  The  reluctivity  of  nearly  all  substances,  other 
than  the  magnetic  metals,  is  sensibly  that  of  vacuum,  is  equal  to  unity, 
and  is  independent  of  the  flux  density. 

Permeability  is  the  reciprocal  of  magnetic  reluctivity.  It  is  a  number 
and  the  symb9l  is  ft. 

Materials  differ  in  regard  to  the  resistance  they  offer  to  the  passage 
of  lines  of  force;  thus  iron  is  more  permeable  than  air.  The  permeability 
of  a  substance  is  expressed  by  a  coefficient,  //,  which  denotes  its  relation 
to  the  permeability  of  air,  which  is  taken  as  1.  If  H  =  number  of  mag- 
netic lines  per  square  centimeter  which  will  pass  through  an  air-space 
between  the  poles  of  a  magnet,  and  B  the  number  of  lines  which  will 
pass  through  a  certain  piece  of  iron  in  that  space,  then  n  —  B  -T-  H.  The 
permeability  varies  with  the  quality  of  the  iron,  and  the  degree  of  satura- 
tion, reaching  a  practical  limit  for  soft  wrought  iron  when  B=  about 
18,000  and  for  cast  iron  when  B  =  about  10,000  C.G.S.  lines  per  square 
centimeter. 

The  permeability  of  a  number  of  materials  may  be  determined  by  means 
of  the  table  on  page.  1431. 


ANALOGIES  BETWEEN  THE  FLOW  OF  WATER  AND 
ELECTRICITY. 


ELECTRICITY. 

Volts;  electro-motive  force;  differ- 
ence of  potential;  E.  or  E.M.P. 

Ohms,  resistance,  R.  Increases  di- 
rectly as  the  length  of  the  conduc- 
tor or  wire  and  inversely  as  its  sec- 
tional area,  R  «c  I  -f-  s.  It  varies 
with  the  nature  of  the  conductor. 

Amperes;  current;  current  strength; 
intensity  of  current;  rate  of  flow; 
1  ampere  =  1  coulomb  per  second-. 


WATER. 

Head,  difference  of  level,  in  feet. 

Difference  of  pressure,  Ibs.  per  sq.  in. 

Resistance  of  pipes,  apertures,  etc., 
increases  with  length  of  pipe,  with 
contractions,  roughness,  etc.;  de- 
creases with  increase  of  sectional 
area.  % 

Rate  of  flow,  as  cubic  ft.  per  second, 
gallons  per  min.,  etc.,  or  volume 
divided  by  the  time.  In  the  min- 
ing regions  sometimes  expressed 
in  "miners'  inches." 

Quantity,  usually  measured  in  cubic  •)  Coulomb,  unit  of  quantity,  Q,  — 
ft.  or  gallons,  but  is  also  equiva-  I  rate  of  flow  X  time,  as  ampere- 
lent  to  rate  of  flow  X  time,  as  cu.  f  seconds.  1  ampere-hour  =  3600 
ft.  per  second  for  so  many  hours.  J  coulombs. 

Joule,  volt-coulomb,  TF,  the  unit  of 

Work,  or  energy,  measured  in  foot- 
pounds; product  of  weight  of  fall- 
ing water  into  height  of  fall;  in 
pumping,  product  of  quantity  in 
cubic  feet  into  the  pressure  in  Ibs. 
per  square  foot  against  which  the 
water  is  pumped. 


Power,  rate  of  work.  Horse-power  = 
ft.-lbs.  of  work  in  1  min.  -7-  33,000. 
In  water  flowing  in  pipes,  rate  of 
flow  in  cu.  ft.  per  second  X  resist- 
ance to  the  flow  in  Ibs.  per  sq.  ft. 
^550. 


work,  =  product  of  quantity  by 
the  electro-motive  force  =  volt- 
ampere-second.  1  joule  =  0.7373 
foot-pound. 

If  /  (amperes)  =  rate  of  flow,  and 
E  (volts)  =  difference  of  pressure 
between  two  points  in  a  circuit, 
energy  expended  =  IEt,  =  I2Rt. 

Watt,  unit  of  power,  P,  =  volts  X 
amperes,  —  current  or  rate  of 
flow  X  difference  of  potential. 

1  watt  =  0.7373  foot-pound  per  sec. 
=  1/746  of  a  horse-power. 


ELECTRICAL  RESISTANCE. 

Laws  of  Electrical  Resistance.  —  The  resistance,  R,  of  any  con- 
ductor varies  directly  as  its  length,  I,  and  inversely  as  its  sectional  area,  s, 
or  R  QC  I  -T-  s. 

If  r  =  the  resistance  of  a  conductor  1  unit  in  length  and  1  square  unit 
in  sectional  area,  R  =  rl-i-  $.  The  common  unit  of  length  for  electrical 


ELECTRICAL  RESISTANCE. 


1401 


calculations  in  English  measure  is  the  foot,  and  the  unit  of  area  of  wires 
is  the  circular  mil  =  the  area  of  a  circle  0.001  in.  diameter.  1  mil-foot  = 
1  foot  long  1  circ.-mil  area. 

Resistance  of  1  mil-foot  of  soft  copper  wire  at  51°  F.  =  10  international 
ohms. 

EXAMPLE.  —  What  is  the  resistance  of  a  wire  1000  ft.  long,  0.1  in.  diam  ' 
0.1  in.  diam.  =  10,000  circ.  mils. 

R  =  rl  -f-  s  =  10  X  1000  -f-  10,000  =  1  ohm. 

Specific  resistance,  also  called  resistivity,  is  the  resistance  of  a  material 
of  unit  length  and  section  as  compared  with  the  resistance  of  soft  copper 

Conductivity  is  the  reciprocal  of  specific  resistance,  or  the  relative 
conducting  power  compared  with  copper  taken  at  100. 

Conductance  is  the  reciprocal  of  resistance. 

Relative  Conductivities  of  Different  Metals  at  0°  and  100°  C. 

(Matthiessen.) 


Metals. 

Conductivities. 

Metals. 

Conductivities. 

At    0°C. 
At  32°  F. 

At  100°C. 
At  21  2°  F. 

At    0°C. 
At  32°  F. 

At  100°C. 
At  212°  F. 

Silver,  .hard 

100 
99.95 
77.96 
29.02 
23.72 
18.00 
16.80 

71.56 
70.27 
55.90 
20.67 
16.77 

Tin 

12.36 
8.32 
4.76 
4.62 
1  60 

8.67 
5.86 
3.33 
3.26 

Copper,  hard.  .  .  . 
Gold,  hard  

Lead  

Arsenic  
Antimony  
Mercury,  pure 

Zinc,  pressed  .... 
Cadmium  
Platinum,  soft.  .  . 
Iron,  soft  

Bismuth  

1.245 

0.878 

Resistance   of  Various   Metals   and   Alloys.  —  Condensed    from    a 
table  compiled  by  H.  F.  Parshall  and  H.  M.  Hobart  from  different 

authorities.     R  =~resistance  in  ohms  per  mil  foot  =  resistance  per  centi- 
meter cube  X  6.015.     C  =  per  cent  increase  of  resistance  per  degree  C. 


R 

C 

R     |    C 

Aluminum,  99%  pure  
Aluminum,  94;  copper,  6.. 
Al.  bronze,  Al  10;  Cu,  90  .  . 
Antimony,  compressed.  .  . 
Bismuth,  compressed  
Cadmium  pure 

15.4 
17.4 
75.5 
211 
780 
60 
9.35 
9.54 
17.7 
37.8 
31.7 
53.0 
89  5 

0.423 
.381 
.105 
.389 
.354 
.419 
.428 
.388 

.158 

.090 
065 

White  cast  iron  

340 
684 
82.8 
63 
401 
177 
123 

287 
294 
393 
566 
73.7 
61.1 
539 
145 
33.6 
8.82 
78.5 
34.5 

.127 
.201 
.411 

.000 
.000 
.000 
.072 
.435 
.354 
.247 
.133 
.394 
.400 
.440 
.406 

Gray  cast  iron  

Wrought  iron  
Soft  steel,  C,  0.045  .  .  . 

Manganese  steel,  Mn,  12.  . 
Nickel  steel,  Ni,  4.35  
Lead  pure  ... 

Copper  annealed,  (D).  .  .  . 
Copper  annealed,  (M)  ... 
Copper  88;  silicon,  12  
Copper  65.8;  zinc,  34.2.  .  .  . 
Copper  90;  lead,  10  
Copper,  97;  aluminum,  3.  . 
Cu,  87;  Ni  6  5-  Al  65 

Manganin, 
Cu,  84;  Mn,  12;Ni,  4  
Cu,  80.5;  Mn,  3;Ni,  16.5 
Cu,  79.5;Mn,  19.7;  Fe,  0.8 
Mercury  

Nickel  

Copper,  65;  nickel,  25  
Cu,  70;  manganese,  30  
German  silver 
Cu,  60;  Zn,  25;  Ni,  15.... 
Gold,  99.9%  pure  
Gold  67-  silver  33 

205 
605 

180 
13.2 
61.8 
54.5 

.019 
.004 

.036 
.377 
.065 
.625 

Palladium  pure 

Platinum,  annealed  
Platinum,  67;  silver,  33  ... 
Phosphor  bronze  

Silver,  pure  
Tin  pure  

Iron,  very  pure  

Zinc,  pure  

(D)  Dewarand  Fleming;  (M)  Matthiessen. 

Conductivity  of  Aluminum. — J.  W.  Richards  (Jour.  Frank..  Inst.9 
Mar.,  1897)  gives  for  hard-drawn  aluminum  of  purity  98.5,  99.0,  99.5, 
and  99.75%  respectively  a  conductivity  of  55,  59,  61,  and  63  to  64%, 
copper  being  100%.  The  Pittsburg  Reduction  Co.  claims  that  its  purest 
aluminum  has  a  conductivity  of  over  64.5%.  (Eng'g  News,  Dec.  17, 
1896.) 

German  Silver.  — The  resistance  of  German  silver  depends  on  its 
composition.  Matthiessen  gives  it  as  nearly  13  times  that  of  copper, 
with  a  temperature  coefficient  of  0,0004433  per  degree  0,  Weston,  how- 


1402  ELECTRICAL  ENGINEERING. 

ever  (Proc.  Electrical  Congress,  1893,  p.  179),  has  found  copper-nickel- 
zinc  alloys  (German  silver)  which  had  a  resistance  of  nearly  28  times 


nearly 

M^__.  _,  temperature  coefficient  or  aho 
_            .       atthiessen. 

Conductors  and  Insulators  in  Order  of  Their  Value. 


that  of  copper,  and  a  temperature  coefficient  of  about  one-half  that 
Ma  " 


CONDUCTORS. 

All  metals 

Well-burned  charcoal 

Plumbago 

Acid  solutions 

Saline  solutions 

Metallic  ores 

Animal  fluids 

Living  vegetable  substances 

Moist  earth 

Water 


INSULATORS  (NON-CONDUCTORS). 

Dry  air  Ebonite 

Shellac  •    Gutta-percha 

Paraffin  India-rubber 

Amber  Silk 

Resins  Dry  paper 

Sulphur  Parchment 

Wax  Dry  leather 

Jet  Porcelain 

Glass  Oils 
Mica 


According  to  Culley,  the  resistance  of  distilled  water  is  6754  million 
times  as  great  as  that  of  copper.  Impurities  in  water  decrease  its 
resistance. 

Resistance  Varies  with  Temperature. —  For  every  degree  Centi- 
grade the  resistance  of  copper  increases  about  0.4%,  or  for  every  degree 
F.,  0.2222%.  Thus  a  piece  9f  copper  wire  having  a  resistance  of  10 
ohms  at  32°  would  have  a  resistance  of  11.11  ohms  at  82°  F. 

The  following  table  shows  the  amount  of  resistance  of  a  few  sub- 
stances used  for  various  electrical  purposes  by  which  1  ohm  is  increased 
by  a  rise  of  temperature  of  1°  C. 


Platinoid 0.00021 

Platinum  silver 0.00031 

German  silver  (see  above) . .  0.00044 


Gold,  silver 0 . 00065 

Cast  iron 0.00080 

Copper 0 . 00400 


Annealing. — Resistance  is  lessened  by  annealing.  Matthiessen  gives 
the  following  relative  conductivities  for  copper  and  silver,  the  comparison 
being  made  with  pure  silver  at  100°  C. : 

Metal.  Temp.  C.        Hard.      Annealed.          Ratio, 

Copper 11°  95.31  97.83  1  to  1.027 

Silver 14.6°  95.36          103.33  1  to  1.084 

Dr.  Siemens  compared  the  conductivities  of  copper,  silver,  and  brass 
with  the  following  results.  Ratio  of  hard  to  annealed: 

Copper 1  to  1.058       Silver 1  to  1.145      Brass 1  to  1.180 

STANDARD    VALUES    FOR    RESISTIVITY    AND    TEMPERATURE 
COEFFICIENT  OF   COPPER. 

Bureau  of  Standards,  1914. 

The  Bureau  of  Standards  made  measurements  of  a  large  number  of 
representative  samples  of  copper  and  established  standard  values  of 
resistivity  and  temperature  coefficients,  which  have  been  adopted  by 
the  International  Electrochemical  Commission. 

Conductivity  of  Copper. 

The  following  rules  of  the  International  Electrical  Commission  have 
been  adopted  by  the  American  Institute  of  Electrical  Engineers. 

The  following  shall  be  taken  as  normal  values  for  standard  annealed 
copper: 

(1)  At  a  temperature  of  20°  C.  the  resistance  of  a  wire  of  standard 
annealed  copper  one  meter  in  length  and  of  a  uniform  section  of  1  square 
millimeter  is  1/58  ohm   =  0.017241.  .  .  .ohm. 

(2)  At  a  temperature  of  20°  C.  the  density  of  standard  annealed 
copper  is  8.89  grams  per  cubic  centimeter. 

(3)  At  a  temperature  of  20°  C.  the  "constant  mass"  temperature 
coefficient  of  resistance  of  standard  annealed  copper,  measured  between 
two  potential  points  rigidly  fixed  to   the  wire,  is  0.00393  =  1/254.45 
, , , .  per  degree  centigrade, 


RESISTANCE  OF  COPPER.  1403  * 

(4)  As  a  consequence  it  follows  from  (1)  and  (2)  that,  at  a  temper- 
ature of  20°  C.  the  resistance  of  a  wire  of  standard  annealed  copper  of 
uniform  section,  one  meter  in  length  and  weighing  one  gram,  is  (1/58) 

X  8.89   =  0.15328 ohm. 

Paragraphs  (1)  and  (4)  define  what  are  sometimes  called  "volume 
resistivity"  and  "mass  resistivity"  respectively.  This  may  be  ex- 
pressed in  other  units  as  follows:  Volume  resistivity  =  1.7241 
microhm-cm,  (or  microhms  in  a  cm.  cube)  at  20°  C.  =  0.67879  microhm 
inch  at  20°  C.  and  mass  resistivity  =  875.20  ohms  (mile,  pound)  at 
20°  C. 

The  new  value  is  known  as  the  International  Annealed  Copper 
Standard,  and  is  equivalent  to 

0.'017241  ohm  (meter,  mm2)  at  20°  C. 

The  units  of  mass  resistivity  and  volume  resistivity  are  interrelated 
through  the  density;  this  was  taken  as  8.89  grams  per  cm3  at  20°  C.  by 
the  International  Electrochemical  Commission.  The  International 
Annealed  Copper  Standard,  in  various  units  of  mass  resistivity  and 
volume  resistivity,  is: 

0.15328    ohm  (meter,  gram)  at  20°  C. 
875.20  ohms  (mile,  pound)  at  20°  C. 

0.017241  ohm  (meter,  mm2)  at  20°  C. 
1.7241      microhm-cm,  at  20°  C. 
0.67879    microhm-inch  at  20°  C. 
10.371        ohms  (mil,  foot)  at  20°  C. 

The  Temperature  Coefficient  of  Resistance  of  Copper. — The  Bureau  of 
Standards'  investigation  of  the  temperature  coefficient  showed  that 
the  coefficient  varies  with  different  samples,  but  that  the  relation  of 
conductivity  to  temperature  coefficient  is  substantially  a  simple  pro- 
portionality. 

The  general  law  may  be  expressed  by  the  following  practical  rule: 
The  20°  C.  temperature  coefficient  of  a  sample  of  copper  is  the  product 
of  the  per  cent,  conductivity  by  0.00393.  There  are  sometimes  cases 
when  the  temperature  coefficient  is  more  easily  measured  than  the 
conductivity,  and  the  conductivity  can  be  computed  from  the  relation: 
per  cent,  conductivity  =  254.5  X  temperature  coefficient. 

When  a  temperature  coefficient  of  resistance  must  be  assumed  the 
best  value  to  assume  for  good  commercial  annealed  copper  wire  is  that 
corresponding  to  100  per  cent,  conductivity,  viz.: 

Co  =  0.00427,   ais  =  0.00401,   «2o  =  0.00393,   a2&  =  0.00385 
/  Rt  -  #20 


This  value  was  adopted  as  standard  by  the  International  Electro- 
chemical Commission  in  1913.  It  would  usually  apply  to  instruments 
and  machines,  since  they  are  generally  wound  with  annealed  wire. 
Experiment  has  shown  that  distortions  such  as  those  caused  by  winding 
and  ordinary  handling  do  not  affect  the  temperature  coefficient. 

Similarly,  when  assumption  is  unavoidable,  the  temperature  coeffi- 
cient of*  good  commercial  hard-drawn  copper  wire  may  be  taken  as 
that  corresponding  to  a  conductivity  of  97.3  per  cent.,  viz.: 

GO  =  0.00414,    aw  =  0.00390,    aw  =  0.00382,    an  =  0.00375 

Rule  for  reducing  resistivity  from  one  temperature  to  another: 
The  change  of  resistivity  of  copper  per  degree  C.  is  a  constant,  inde- 
pendent of  the  temperature  of  reference  and  of  the  sample  of  copper. 
This  "resistivity-temperature  constant"  may  be  taken,  for  general 
purposes,  as  0.00060  ohm  (meter,  gram),  or  0.0068  microhm-cm. 
More  exactly,  it  is: 

0.000.597     ohm  (meter,  gram) 
or,  0.000.0681  ohm  (meter,  mm2) 
or,  0.006.81       microhm-cm, 
or,  3.41  ohms  (mile,  pound) 

or,  0.002.68       microhm-inch, 
or,  0.040-9         ohm  (mil,  foot). 

Continued  on  p.  1406. 


1404 


ELECTRICAL  ENGINEERING. 


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1406  ELECTRICAL  ENGINEERING. 

Resistivity  of  Hard-Drawn  Copper  Wires.  —  In  general  the  resistivity 
ot  hard-drawn  wires  varies  with  the  size  of  the  wire,  while  the  resistivity 
of  annealed  wires  does  not.  The  difference  between  the  resistivity  of 
annealed  and  hard-drawn  wires  increases  as  the  diameter  of  the  wire 
decreases.  This  general  conclusion  is,  however,  complicated  in  any 
particular  case  by  the  number  of  drawings  between  annealings,  amount 
of  reduction  to  each  drawing,  etc.  For  No.  12  A.W.G.  (B.  &  S  ),  the 
conductivity  of  hard-drawn  wires  was  found  to  be  less  than  the  con- 
ductivity of  annealed  wires  by  2.7  per  cent, 


™  °f  CoPPer-—  The  international  standard  density  for  copper, 
at  20  C.,  is  8.89  grams  per  cubic  centimeter.  This  is  the  value  which 
has  been  used  by  the  A.I.E.E.,  and  most  other  authorities  in  the  past. 
Recent  measurements  have  indicated  this  value  as  a  mean.  This  den- 
sity, 8.89,  at  20°  C.,  corresponds  to  a  density  of  8.90  at  0°  C.  In 
English  units,  the  density  at  20°  C.  =  0.32117  pounds  per  cubic  inch. 
For  a  complete  treatise  on  this  subject,  see  Bulletin  No.  31,  Bureau 
of  Standards. 

Approximate  Rules  for  the  Resistance  of  Copper  Wire.  —  The  re- 

sistance of  any  copper  wire  at  20°  C.  or  68°  F.,  according  to  Matthies- 

sen's  standard,  is  R  =       '      -,   in  which  R  is  the  resistance  in  inter- 

national ohms,  I  the  length  of  the  wire  in  feet,  and  d  its  diameter  in 
mils,  (1  mil  =  Viooo  inch.) 

A  No.  10  wire,  A.W.G.  ,  0.1019  in.  diam  (practically  0.1  in.),  1000 
ft.  in  length,  has  a  resistance  of  1  ohm  at  68°  F.  and  weighs  31.4  Ibs. 

If  a  wire  of  a  given  length  and  size  by  the  American  or  Brown  & 
Sharpe  gauge  has  a  certain  resistance,  a  wire  of  the  same  length  and 
three  numbers  higher  has  twice  the  resistance,  six  numbers  higher 
four  times  the  resistance,  etc. 

Wire  gauge,  A.W.G.  No  .....   000       1       4       7     10     13     16     19     22 

Relative  resistance  ..........      16       8       4       2       1      1/2     1/4     Vs    Vie 

section  or  weight  ...     i/ie     Vs     1/4     V2       1       2       4      8     16 


DIRECT   ELECTRIC   CURRENTS. 

Ohm's    Law.  —  This    law  expresses    the    relation  between  the  three 
fundamental  units  of  resistance,  electrical  pressure,  and  current.    It  is: 

Current  =  ^Metrical  pressure          B  _  RmE 

resistance  R  I 

In  terms  of  the  units  of  the  three  quantities, 

volts  volts 

Amperes  =  ;  volts  =  amperes  X  ohms; 


EXAMPLES:  Simple  Circuits.  —  1.  If  the  source  has  an  effective  electrical 
pressure  of  100  volts,  and  the  resistance  is  two  onrns,  what  is  the  current? 

7=f  =  M  =  50  amperes. 

Li          Ji 

2.  What  pressure  will  give  a  current  of  50  amperes  through  a  resistance 
of  2  ohms?     E  =  IR  =  50  X  2  =  100  volts. 

3.  What  resistance  is  required  to  obtain  a  current  of  50  amperes  when 
the  pressure  is  100  volts?     R  =  E  -~  I  =  100  -=-  50  =  2  ohms. 

Ohm's  law  applies  equally  to  a  complete  electrical  circuit  and  to  any 
part  thereof. 

Series  Circuits.  —  If  conductors  are  arranged  one  after  the  other  they 
are  said  to  be  in  series,  and  the  total  resistance  of  the  circuit  is  the  sum  of 
the  resistances  of  its  several  parts.  Let  A,  Fig.  226,  be  a  source  of  current, 
such  as  a  battery  or  generator,  producing  a  aiflerence  of  potential  or 


DIRECT  ELECTRIC   CURRENTS.  1407 

E.M.F.  of  120  volts,  measured  across  ab,  and  let  the  circuit  contain  four 
conductors  whose  resistances,  n,  rz,  n,  r<t  are  1  ohm  each,  and  three 
other  resistances,  Ri,  Rz,  Rz,  each  2  ohms.  The 
total  resistance  is  10  ohms,  and  by  Ohm's  law 

^  „  „  .      the  current   /  =  E  +  R  =  120  •*•  10  =  12  am- 

•s-  A  rs  peres.    This  current  is  constant  throughout  the 

T_ <O_  circuit,  and  a  series  circuit  is  therefore  one  of 

constant  current.  The  drop  of  potential  in  the 
whole  circuit  from  a  around  to  b  is  120  volts, 
or  E  -  RI.  The  drop  in  any  portion  depends 
on  the  resistance  of  that  portion;  thus  from  a  to 
Ri  the  resistance  is  1  ohm,  the  constant  current  12  amperes,  and  the  drop 
1  X  12  =  12  volts.  The  drop  in  passing  through  each  of  the  resistance 
Ri,  Rz,  Rs  is  2  X  12  =  24  volts. 

Parallel,  Divided,  or  Multiple  Circuits.— Let  B,  Fig.  227,  be  a 
generator  producing  an  E.M.F.  of  220  volts  across  the  terminals  ab. 
The  current  is  divided,  so  that  part 
flows  through  the  main  wires  ac  and 
part  through  the  "shunt"  s,  having  a 
resistance  of  0.5  ohm.  Also  the  current 
has  three  paths  between  c  and  d,  viz., 
through  the  three  resistances  in  parallel 
Ri,  Rz,  Rs,  of  2  ohms  each.  Consider 

that  the  resistance  of  the  wires  is  so  small  , . 

that  it  may  be  neglected.     Let  Mie  con-  b  d  9          h 

ductances  of  the  four  paths  be  repre- 
sented by   Cs.     Ci,  Cz,   Ca.     The  total  FIG.  227. 
conductance  is  Cs  4-  Ci+  Cz  +  Cz  =  C  and   the  total  resistance  R  = 
1  -s-  C.     The  conductance  of  each  path  is  the  reciprocal  of  its  resistance, 
the  total  conductance  is  the  sum  of  the  separate  conductances,  and  the 
resistance  of  the  combined  or  "parallel"  paths  is  the  reciprocal  of  the 
total  conductance. 

K  =  l-  (o|5  +  |  +  l+|)=  1-3.5 -0.286  ohm. 

The  current  7  =  E  •*•  R  =  770  amperes. 

Conductors  in  Series  and  Parallel.  —  Let  the  resistances  in  parallel 
be  the  same  as  in  Fig.  227,  with  the  additional  resistance  of  0.1  ohm 
in  each  of  the  six  sections  of  the  main  wires,  ac,  bd,  etc.,  in  series.  The 
voltage  across  ab  being  220  volts,  determine  the  drop  in  voltage  at  the 
several  points,  the  total  current,  and  the  current  through  each  path. 
The  problem  is  somewhat  complicated.  It  may  be  solved  as  follows: 
Consider  first  the  points  eg:  here  there  are  two  paths  for  the  current, 
efqfi  and  eg.  Find  the  resistance  and  the  conductance  of  each  and  the 
total  resistance  (the  reciprocal  of  the  joint  conductance)  of  the  parallel 
paths.  Next  consider  the  points  cd;  here  there  are  two  paths  —  one 
through  e  and  the  other  through  cd.  Find  the  total  resistance  as  before. 
Finally  consider  the  points  ab;  here  there  are  two  paths  —  one  through 
c,  the  other  through  s.  Find  the  conductances  of  each  and  their  sum. 
The  product  of  this  sum  and  the  voltage  at  ab  will  be  the  total  amperes 
of  current,  and  the  current  through  any  path  will  be  proportional  to  the 
conductance  of  that  path.  The  resistances,  R,  and  conductances,  C, 
of  the  several  paths  are  as  follows: 

R  C 

Ra  of  efRzhg  =  0.1  4-  2  H-  0.1  =  2.2  0.4545 

Rb  of  eRzg  =  2  0.5 

Joint  Rc  =  1.048  0.9545 

Rd  of  ce  +  dg  +  Rc  =  1.248          0.8013 

Re  of  cRid  =  2  0.5 

Joint  Rf-  0.7687         1,3013  , 


1408  ELECTRICAL  ENGINEERING. 

Rg  of  ac  +  Id  +  Rf  =  0.9687         1.0332 

=  0.5  2 


Joint  Ra  +  Rfr  =  0.330  3.0332 

Total  current  =  220  X  3.0332  =  667.3  amperes. 
Current  through  s  =  220  X  2  =  440  amp.;  through  c  =  227.3  amp. 
"cRid  =  227.3     X  0.5         4-  1.3013  =    87.34  amp. 

e  =  227.3     X  0.8013  -f-  1.3013  =  139.96      " 
41  eRtg  =  139.96  X  0.5         -*-  0.9545  =    73.31      " 
44   /#3  =  139.96  X  0.4545  ~  0.9545  =    66.65      " 
The  drop  in  voltage  in  any  section  of  the  line  is  found  by  the  formula 
E  =  RI,  R  being  the  resistance  of  that  section  and  /  the  current  in  it. 
As  the  R  of  each  section  is  0.1  ohm  we  find  E  for  ac  and  bd  each  =  22.7 
volts,  for  ce  and  dg  each  14.0  volts,  and  for  ef  and  gh  each  6.67  volts. 
The  voltage  across  cd  is  220  -  2  X  22.7  =  174.6  volts;  across  eg,174.6-  2 
X  14.0  =  146.6,  and  across  fh  146.6  -  2X  667  =  133.3  volts.     Taking 
these  voltages  and  the  resistances  Ri,  Rz,  Rs,  each  2  ohms,  we  find  from 
/  =  E  -r  R  the  current  through  each  of  these  resistances  87.3,  73.3,  and 
66.65  amperes  as  before. 

Internal  Resistance.  —  In  a  simple  circuit  we  have  two  resistances, 
that  of  the  circuit  72  and  that  of  the  internal  parts  of  the  source  of  electro- 
motive force,  called  internal  resistance,  r.  The  formula  of  Ohm's  law 
when  the  internal  resistance  is  considered  is  7  =  E  •*•  (R  +  r). 

Power  of  the  Circuit.  —  The  power,  or  rate  of  work,  in  watts  = 
current  in  amperes  X  electro-motive  force  in  volts  =  /  X  E.  Since 
7  =  E  •*-  R,  watts  =  E2  -f-  R  =  electro-motive  force2  -~  resistance. 

EXAMPLE.  —  What  H.P.  is  required  to  supply  100  lamps  of  40  ohms 
resistance  each,  requiring  an  electro-motive  force  of  60  volts? 

The  number  of  volt-amperes  for  each  lamp  is  •=?-  =  j—  ,  1  volt-ampere 

Af)2 

=  0.00134  H.P.;  therefore  gp  X  100  X  0.00134  -  12  H.P.  (electrical) 
very  nearly. 

Electrical,  Brake,  and  Indicated  Horse-power.  —  The  power  given 
by  a  dynamo  =  volts  X  amperes  -f-  1000  =  kilowatts,  kw.  Volts  X  out 
amperes  -£•  746  —  electrical  horse-power,  E.H.P.  The  power  put  into  a 
dynamo  shaft  by  a  direct-connected  engine  or  other  prime  mover  is 
called  the  shaft  or  brake  horse-power,  B.H.P.  If  e\  is  the  efficiency  of  the 
dynamo,  B.H.P.  =  E.H.P.  -~  e\.  If  ei  is  the  mechanical  efficiency  of  the 
engine,  the  indicated  horse-power,  I.H.P.  =  brake  H.P.  -f-  62  =  E.H.P.  ~- 
(€1X62). 

If  ei  and  e2  each  =  91.5%,  I.H.P.  =  E.H.P.  X  1.194  «=  kw.  X  1.60.  In 
direct-connected  units  of  250  kw.  or  less  the  rated  H.P.  of  the  engine  is 
commonly  taken  as  1.6  X  the  rated  kw.  of  the  generator. 

Electric  motors  are  rated  at  the  H.P.  given  out  at  the  pulley  or  belt. 
H.P.  of  motor  =  E.H.P.  supplied  X  efficiency  of  motor. 

Heat  Generated  by  a  Current.  —  Joule's  law  shows  that  the  heat 
developed  in  a  conductor  is  directly  proportional,  1st,  to  its  resistance; 
2d,  to  the  square  of  the  current  strength;  and  3d,  to  the  time  during 
which  the  current  flows,  or  H  =  PRL  Since  /  =  E  •*•  R, 


Or,  heat  =  current2  X  resistance  X  time 

=  electro-motive  force  X  current  X  time. 
=  electro-motive  force2  X  time  •«•  resistance. 
Q  =  quantity  of  electricity  flowing  =  It  =  (Et  -£-  R). 
H  =  EQ\  or  heat  =  electro-motive  force  X  quantity. 

The  electro-motive  force  here  is  that  causing  the  flow,  or  the  differ- 
ence in  potential  between  the  ends  of  the  conductor. 

The  electrical  unit  of  heat,  or  "joule"  =  107  ergs  =  heat  generated  in 
?ne  second  by  a  current  of  1  ampere  flowing  through  a  resistance  of  one 


DIRECT   ELECTRIC    CURRENTS.  1409 

ohm  =  0.239" gramme  of  water  raised  1°  C.     H  =  PRt  X  0.239  gramme 
calories  =  I*Rt  X  0.0009478  British  thermal  units. 

In  electric  lighting  the  energy  of  the  current  is  converted  into  heat  in 
the  lamps.  The  resistance  of  the  lamp  is  made  great  so  that  the  required 
quantity  of  heat  may  be  developed,  wnile  in  the  wire  leading  to  and  from 
the  lamp  the  resistance  is  made  as  small  as  is  commercially  practicable, 
so  that  as  little  energy  as  possible  may  be  wasted  in  heating  the  wire. 

Heating  of  Conductors.  (From  Kapp's  Electrical  Transmission  of 
Energy.)  —  It  becomes  a  matter  of  great  importance  to  determine  before- 
hand what  rise  in  temperature'  is  to  be  expected  in  each  given  case,  and 
if  that  rise  should  be  found  o  be  greater  than  appears  safe,  provision  must 
be  made  to  increase  the  rate  at  which  heat  is  carried  off.  This  can  gen- 
erally be  done  by  increasing  the  superficial  area  of  the  conductor.  Say 
we  have  one  circular  conductor  of  1  square  inch  area,  and  find  that  with 
1000  amperes  flowing  it  would  become  too  hot.  Now  by  splitting  up  this 
conductor  into  10  separate  wires  each  one-tenth  of  a  square  inch  cross- 
sectional  area,  we  have  not  altered  the  total  amount  of  energy  trans- 
formed into  heat,  but  we  have  increased  the  surface  exposed  to  the  cooling 
action  of  the  surrounding  air  in  the  ratio  of  1 :  v^lO,  and  therefore  the  ten 
thin  wires  can  dissipate  more  than  three  times  the  heat,  as  compared  with 
the  single  thick  wire. 

Prof.  Forbes  states  that  an  insulated  wire  carries  a  greater  current  with- 
out overheating  than  a  bare  wire  if  the  diameter  be  not  too  great,  Assum- 
ing the  diameter  of  the  cable  to  be  twice  the  diam.  of  the  conductor,  a 
greater  current  can  be  carried  in  insulated  wires  than  in  bare  wires  up  to 
1.9  inch  diam.  of  conductor.  If  diam.  of  cable  =  4  times  diam.  of  con- 
ductor, this  is  the  case  up  to  1.1  inch  diam.  of  conductor. 

Heating  of  Bare  Wires.  —  The  following  formulae  are  given  by 
Keimelly: 

72  .  7    72 

x  90,000  +  t;  d=44.8     ' 


J.    •"•  -7j    /S    J7Ufuuw  T   «,,     u.  — l-*.o    ^     ~    .  ' 

T  =  temperature  of  the  wire  and  t  that  of  the  air,  in  Fahrenheit  degrees; 
7  -  current  in  amperes,  d  =  diameter  of  the  wire  in  mils. 

If  we  take  T  -  t  =  90°  F.,  ^/90  =  4.48,  then 

d  •=  10  $1*     and     7  =  V^3  .4.  1000. 

This  latter  formula  gives  for  the  carrying  capacity  in  amperes  of  bare 
wires  almost  exactly  the  figures  given  for  weather-proof  wires  in  the 
Fire  Underwriters'  table,  except  in  the  case  of  Nos.  18  and  16,  B.  &  S. 
gauge,  for  which  the  formula  gives  8  and  11  amperes,  respectively,  instead 
of  5  and  8  amperes,  given  in  the  table. 

Heating  of  Coils.  —  The  rise  of  temperature  in  magnet  coils  due  to 
the  passage  of  current  through  the  wire  is  approximately  proportional  to 
the  watts  lost  in  the  coil  per  unit  of  effective  radiating  surface,  thus: 
.      PR         .      PR 
toe—  or  «-•££• 

t  being  the  temperature  rise  in  degrees  Fahr.;  St  the  effective  radiating 
surface;  and  k  a  coefficient  which  varies  widely,  according  to  condition. 
In  electromagnet  coils  of  small  size  and  power,  k  may  be  as  large  as  0.015. 
Ordinarily  it  ranges  from  0.012  down  to  0.005;  a  fair  average  is  0.007. 
The  more  exposed  the  coil  is  to  air  circulation,  the  larger  is  the  value  of  k\ 
the  larger  the  proportion  of  iron  to  copper,  by  weight,  in  the  core  and 
winding,  the  thinner  the  winding  with  relation  to  its  dimension  parallel 
with  the  magnet  core,  and  the  larger  the  "space  factor"  of  the  winding, 
the  larger  will  be  the  value  of  k.-  The  space  factor  is  the  ratio  of  the 
actual  C9pper  cross-section  of  the  whole  coil  to  the  gross  cross-section  of 
copper,  insulation,  and  interstices. 

Fusion  of  Wires.  —  W.  H.  Preece  gives  a  formula  for  the  current 
required  to  fuse  wires  of  different  metals,  viz.,  I  =  ad*h  in  which  d  is  the 
diameter  in  inches  and  a  a  coefficient  whose  value  for  different  metals 
is  as  follows:  Copper,  10,244;  aluminum,  7585;  platinum,  5172;  German 
silver,  5230;  platinoid,  4750;  iron,  3148;  tin,  1462;  lead,  1379;  alloy  of  2 
lead  and  1  tin,  1318. 


1410 


ELECTRICAL   ENGINEERING. 


Allowable  Carrying  Capacity  of  Copper  Wires. 

(For  inside  wiring,  National  Board  of  Fire  Underwriters'  Rules.) 


B.&S. 

Gauge. 

Circular 
Mils. 

Amperes. 

Circular 
Mils. 

Amperes. 

Rubber 
Covered. 

Other  In- 
sulation. 

Rubber 
Covered. 

Other  In- 
sulation. 

18 

1,624 

3 

5 

200,000 

200 

300 

16 

2,583 

6 

8 

300,000 

270 

400 

14 

4,107 

12 

16 

400,000 

330 

500 

12 

6,530 

17 

23 

500,000 

390 

590 

10 

10,380 

24 

32 

600,000 

450 

680 

8 

16,510 

33 

46 

700,000 

500 

760 

6 

26,250 

46 

65 

800,000 

550 

840 

5 

33,100 

54 

77 

900,000 

600 

920 

4 

41,740 

65 

92 

,000,000 

650 

,000 

3 

52,630 

76 

110 

,100,000 

690 

,080 

2 

66,370 

90 

131 

,200,000 

730 

,150 

83,690 

107 

156 

,300,000 

770 

,220 

0 

105,500 

127 

185 

,400,000 

810 

,290 

00 

133,100 

150 

220 

,600,000 

890 

,430 

000 

167,800 

177 

262 

,800,000 

970 

,550 

0000 

211,600 

210 

312 

2,000,000 

1,050 

,670 

Wires  smaller  than  No.  14  B.  &  S.  gauge  must  not  be  used  except  in  fix- 
tures and  pendant  cords. 

The  lower  limit  is  specified  for  rubber-covered  wires  to  prevent  deteriora- 
tion of  the  insulation  by  the  heat  of  the  wires. 

For  insulated  aluminum  wire  the  safe-carrying  capacity  is  84  per  cent  of 
that  of  copper  wire  with  the  same  insulation. 

See  pamphlets  published  by  the  National  Board  of  Fire  Underwriters, 
New  York,  for  complete  specifications  and  rules  for  wiring. 

Underwriters'  Insulation.  —  The  thickness  of  insulation  required 
by  the  rules  of  the  National  Board  of  Fire  Underwriters  varies  with  the  size 
of  the  wire,  the  character  of  the  insulatipn,  and  the  voltage.  The  thick- 
ness of  insulation  on  rubber-covered  wires  carrying  voltages  up  to  600 
varies  from  1/32  inch  for  a  No.  18  B.  &  S.  gauge  wire  to  1/8  inch  for  a  wire  of 
1.000,000  circular  mils.  Weather-proof  insulation  is  required  to  be  slightly 
thicker.  For  voltages  of  over  600  the  insulation  varies  from  i/ie  inch 
for  No.  14  B.  &  S.  gage  to  9/64  inch  for  1,000,000  C.  JM.  and  over. 

ELECTRIC  TRANSMISSION,  DIRECT  CURRENTS. 

Cross-section  of  Wire  Required  fof  a  Given  Current. — 

Let  R  =  resistance  of  a  given  line  of  copper  wire,  in  ohms; 
r    =       "  "1  mil-foot  of  copper; 

L  =  length  of  wire,  in  feet; 
e    =  drop  in  voltage  between  the  two  ends; 
I    =  current,  in  amperes; 
A  =  sectional  area  of  wire,  in  circular  mils; 

then  I  =  — ;  R  =  y ;  R  =  r  ^;  whence  A  =  r-^. 

The  value  of  r  for  soft  copper  wire  at  68°  F.  is  10.371  international 
ohms.  For  ordinary  drawn  copper  wire  the  value  of  10.8  is  commonly 
taken,  corresponding  to  a  conductivity  of  97.2  per  cent. 

For  a  circuit,  going  and  return,  the  total  length  is  2  L,  and  the  formula 
becomes  A  =  21.67L  H-  e,  L  here  being  the  distance  from  the  point  of 
supply  to  the  point  of  deh'very. 

If  E  is  the  voltage  at  the  generator  and  a  the  per  cent  of  drop  in  the 
line,  then  e  =  Ea  -r-  100,  and  A  =  2160  IL  -=-  aE. 

jp  21  An  P7" 

If  P  =  the  power  in  watts,  =  El,  then  I  =  •=?,  and  A  = =^ — . 

Cj  CLEj* 

If  Pj.  =  the  power  in  kilowatts,  A  =  2,160,000  P^L  +  aE2. 

If  Lm  =  the  distance  in  miles  and  A^,  the  area  in  circular  inches,  then 


ELECTRIC   TRANSMISSION,   DIRECT  CURRENT.      1411 


Ac  =  6405  PkLm  +  aE2.  If  As  =  area  in  square  inches,  As  =  5030 
PkLm  H-  aE2.  When  the  area  in  circular  mils  has  been  determined  by 
either  of  these  formulae  reference  should  be  made  to  the  table  of  Allow- 
able Capacity  of  Wires,  to  see  if  the  calculated  size  is  sufficient  to  avoid 
overheating.  For  all  interior  wiring  the  rules  of  the  National  Board  of 
Fire  Underwriters  should  be  followed. 

Weight  o'f   Copper  for  a  Given  Power.  —  Taking  the  weight   of 
a  mil-foot  of  copper  at  0.000003027  lb.,  the  weight  of  copper  in  a  circuit  of 
length  2 Land  cross-section  A,  in  circ.  mils,  is  0.000006054 LA  Ibs.,  =  W. 
Substituting  for  A  its  value  2 160  PL  •*•  aE2  we  have 

W  =  0.0 130766  PL2 ' -*•  aE2;  P  in  watts,  L  in  ft. 

W  =  13.0766  PkL2  -*•  aE2;  P&  in  kilowatts,  L  in  ft. 

W  =  364,556,000  PkL2m  +  aE2;        Pk  in  kilowatts,  Lm  in  miles. 

The  weight  of  copper  required  varies  directly  as  the  power  transmitted ; 
inversely  as  the  percentage  of  drop  or  loss;  directly  as  the  square  of  the 
distance;  and  inversely  as  the  square  of  the  voltage. 

From  the  last  formula  the  following  table  has  been  calculated: 

WEIGHT  OF  COPPER  WIRE  TO  CARRY  1000  KILOWATTS  WITH  10%  Loss. 


Distance 
in  Miles. 

1 

5 

10 

20 

50 

100 

Volts. 

Weight  in  Lbs. 

500 
1,000 
2,000 
5,000 
10,000 
20,000 
40,000 
60.000 

145,822 
36,456 
9,114 
1,458 
365 
91 

3,645,560 
911,390 
227,848 
36,456 
9,114 
2,278 
570 

3,645,560 
911,390 
145,822 
36,456 
9,114 
2.278 
1,013 

3,645,560 
593,290 
145,822 
36,456 
9,114 
4,051 

3,645,560 
911,390 
227,848 
*    56,962 
25,316 

3,645.560 
911,390 
227,848 
101,266 

In  calculating  the  distance,  an  addition  of  about  5  per  cent  should 
be  made  for  sag  of  the  wires. 

Short-circuiting.  —  From  the  law  I  =  E/R  it  is  seen  that  with  any 
pressure  E,  the  current  I  will  become  very  great  if  R  is  made  very 
small.  In  short-circuiting  the  resistance  becomes  small  and  the  current 
therefore  great.  Hence  the  dangers  of  short-circuiting  a  current. 

ECONOMY  OF  ELECTRIC  TRANSMISSION. 

The  loss  of  power  in  a  transmission  line  is  ordinarily  given  in  per 
cent  of  the  total  power  consumed  in  the  conductors  at  maximum  load. 
Whatever  the  line  pressure  may  be,  the  size  of  the  conductors  varies 
inversely  with  the  percentage  of  loss.  Consequently  the  maximum  line 
loss  which  can  be  allowed  is  dependent  on  the  most  economical  size  of 
the  line  conductors. 

In  1881  Lord  Kelvin  gave  out  a  statement  in  regard  to  the  most 
economical  size  of  conductors.  This  statement,  which  is  known  as 
"Kelvin's  law,"  was  as  follows: 

"The  most  economical  area  of  conductor  will  be  that  for  which  the 
annual  interest  on  the  capital  outlay  equals  the  annual  cost  of  energy 
wasted." 

According  to  this  rule,  the  cheaper  the  cost  of  power,  the  less  should 
be  the  capital  outlay  for  the  conductors,  thus  allowing  a  smaller  size 
to  be  used.  George  Forbes  states  that  the  most  economical  section  of 
the  conductor  is  independent  of  the  voltage  and  the  distance,  and  is 
proportional  to  the  current. 

It  is  generally  assumed  that  the  cost  of  the  pole  line  and  the  insula- 
tors is  constant  and  not  affected  by  the  variation  in  the  size  of  the  line 
conductors. 

If  A  =  interest   cost   per  year   of  conductors   erected,    in   dollars, 
B  =  value  of  the  line  loss  per  year,  in  dollars;  then  for  the  most 
economical  cross-section  of  the  conductors 
A  =J3. 


1412        ELECTRICAL  ENGINEERING. 

If  K  =  Cost  per  kilowatt-year  of  lost  power,  in  dollars, 

KI  =  Cost  per  pound  of  wires  erected,  in  dollars, 

L  =  Length  of  line  in  1000  ft., 

£>a  s=  Cross-section  of  conductor  in  circular  mils, 

I  =  Line  current  in  amperes, 

p  =  per  cent  interest, 

then  A  =  ^  X  KI  x  0.003  XLXD*. 

L 
B  =  K  X  Iz  X  10.5  X  j=c2 

^  x  KI  x  0.003  XLXD*  =  KXI*X  lo.s'x  ^, 

Z>2  =  592  I 

D*  is  the  cross-section,  in  circular  mils,  that  will  give  the  most  eco- 
nomical line  loss. 

In  the  following,  the  above  equation  is  worked  out  for  three  different 
rates  of  interest: 

For  4%,  Z>2  =  296  I  \|— ;      For  5%,  DZ  =  265  I  \l— ; 
II  KI  i  KI  ' 


For  6%,  D*  =  242  I  \l— 
»  KI 

In  determining  the  value  of  I,  care  must  be  taken  that  the  annual 
mean  value  of  the  current  is  used.  The  value  of  K  must  also  be  the 
one  for  which  the  power,  representing  the  line  loss,  can  be  produced, 
and  not  that  for  which  it  can  be  sold. 

Wire  Tables.  —  The  tables  on  the  following  page  show  the  relation 
between  load,  distance,  and  "drop"  or  loss  by  voltage  in  a  two- wire 
direct-current  circuit  of  any  standard  size  of  wire.  The  tables  are  based 
on  the  formula 

(21.6  IL)  -7-  A  -  Drop  in  volts. 

I  =  current  in  amperes,  L  =  distance  in  feet  from  point  of  supply  to 
point  of  delivery,  A  =  sectional  area  of  wire  in  circular  mils.  The 
factors  I  and  L  are  combined  in  the  table,  in  the  compound  factor 
"ampere  feet." 

EXAMPLES  IN  THE  USE  OF  THE  WIRE  TABLES.  —  1.  Required  the  max- 
imum load  in  amperes  at  220  volts  that  can  be  carried  95  feet  by  No.  6 
wire  without  exceeding  11/2%  drop. 

Find  No.  6  in  the  220-volt  column  of  Table  I;  opposite  this  in  the 
1V2%  column  is  the  number  4005,  which  is  the  ampere-feet.  Dividing 
this  by  the  required  distance  (95  feet)  gives  the  load,  42.15  amperes. 

Example  2.  A  500- volt  line  is  to  carry  100  amperes  600  feet  with  a 
drop  not  exceeding  5  % ;  what  size  of  wire  will  be  required? 

The  ampere-feet  will  be  100  X  600  =  60,000.  Referring  to  the  5% 
column  of  Table  II,  the  nearest  number  of  ampere-feet  is  60,750,  which 
is  opposite  No.  3  wire  in  the  500- volt  column. 

These  tables  also  show  the  percentage  of  the  power  delivered  to  a  line 
that  is  lost  in  non-inductive  alternating-current  circuits.  Such  circuits 
are  obtained  when  the  load  consists  of  incandescent  lamps  and  the  cir- 
cuit wires  lie  only  an  inch  or  two  apart,  as  in  conduit  wiring. 

Efficiency  of  Electric  Systems. — The  efficiency  of  a  system  is  the 
ratio  of  the  power  delivered  by  the  electric  motors  at  the  distant  end  of 
the  line  to  the  power  delivered  to  the  dynamo-electric  machines  at  the 
other  end.  The  efficiency  of  a  generator  or  motor  varies  with  its  load 
and  with  the  size  of  the  machine,  ranging  about  as  follows: 

Average  Full-load  Efficiency  of  Generators: 

K.W 25       50       100       200       500       1000       2000       3000 

Eff.  % 88       90         91          92         93  94       94.5  95 

Average  Full-load  Efficiency  of  Motors: 

H.P 1         2         5          10         25         50         100         200         500 

Eff.  % ....    80       82       85         87         88          90    *       91  92  93 

The  efficiency  of  both  generators  and  motors  decreases,  at  first  very 


ELECTRIC  TRANSMISSION,   DIRECT  CURRENT.      1413 


WIRE  TABLE  —  RELATION  BETWEEN  LOAD,   DISTANCE,  Loss,  AND 

SIZE  OF  CONDUCTOR. 

NOTE.  —  The  numbers  in  the  body  of  the  tables  are  Ampere-Feet,  i.e., 
Amperes  X  Distance  (length  of  one  wire).    See  examples  below. 

Table  I.  —  110-volt  and  220-volt  Two-wire  Circuits. 


Wire  Sizes; 
B.  &  S.  Gauge. 

Line  Loss  in  Percentage  of  the  Rated  Voltage;  and  Power 
Loss  in  Percentage  of  the  Delivered  Power. 

110V. 

220V. 

1 

•H/2 

2 

3 

4 

5 

6 

8 

10 

0000 
000 

0000 
000 
00 
0 

1 

21,550 
17,080 
13,550 
10,750 
8,520 

32,325 
25,620 
20,325 
16,125 
12,780 

43,100 
34,160 
27,100 
21,500 
17,040 

64,650 
51,240 
40,650 
32,250 
25,560 

86,200 
68,320 
54,200 
43,000 
34,080 

107,750 
85,400 
67,750 
53,750 
42,600 

129,300 
102,480 
81,300 
64,500 
51,120 

172,400 
136,640 
108,400 
86,000 
68,160 

215,500 
170,800 
135,500 
107,500 
85,200 

00 
0 

1 
2 
3 

2 
3 
4 

6 

6,750 
5,360 
4,250 
3,370 
2,670 

10,140 
8,040 
6,375 
5,055 
4,005 

13,520 
10,720 
8,500 
6,740 
5,340 

20,280 
16,080 
12,750 
10,110 
8,010 

27,040 
21,4^0 
17,000 
13,480 
10,680 

33,800 
26,800 
21,250 
16,850 
13,350 

40,560 
32,160 
25,500 
20,220 
16,020 

54,080 
42,880 
34,000 
26,960 
21,360 

67,600 
53,600 
42,500 
33,700 
26,700 

4 

6 

7 
8 

7 
8 
9 
10 
11 

2,120 
1,680 
1,330 
1,055 
838 

3,180 
2,520 
1,995 
1,582 
1,257 

4,240 
3,360 
2,660 
2,110 
1,675 

6,360 
5,040 
3,990 
3,165 
2,514 

8,480 
6,720 
5,320 
4,220 
3,350 

10,600 
8,400 
6,650 
5,275 
4,190 

12,720 
10,800 
7,980 
6,330 
5,028 

16,960 
13,440 
10,640 
8,440 
6,700 

21,200 
16,800 
13,300 
10,550 
8,380 

9 

10 
11 
12 
14 

12 
13 
14 

665 
527 
418 
332 
209 

997 
790 
627 
498 
313 

1,330 
1,054 
836 
665 
418 

1,995 
1,580 
1,254 
997 
627 

2,660 
2,108 
1,672 
1,330 
836 

3,320 
2,635 
2,090 
1,660 
1.045 

3,990 
3,160 
2,508 
1,995 
1,354 

5,320 
4,215 
3,344 
2,660 
1,672 

.  6.650 
5J270 
4,180 
3,325 
2,090 

Table  II.  —  500,  1000,  and  2000  Volt  Circuits. 


Wire  Sizes; 
B.  &  S.  Gauge. 

Line  Loss  in  Percentage  of  the  Rated  Voltage  ;  and 
Power  Loss  in  Percentage  of  the  Delivered  Power. 

500V. 

1000V. 

2000V. 

1 

H/2 

2 

2V2 

3 

4 

5 

0000 
000 

00 
0 
1 
2 
3 

4 
5 
6 
7 

8 

9 

10 

n 

12 
14 

0000 
000 
00 
0 

1 

2 
3 

4 

6 

7 
8 
9 
10 
11 

12 
13 
14 

0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

97,960 
77,690 
61,620 
48,880 
38,750 

30,760 
24,370 
19,320 
15,320 
12,150 

9,640 
7,640 
6,060 
4,805 
3,810 

3,020 
2,395 
1,900 
1,510 
950 

146,940 
116,535 
92,430 
73,320 
58,125 

46,140 
36,555 
28,980 
22,980 
18,225 

14,460 
11,460 
9,090 
7,207 
5,715 

4,530 
3,592 
2,850 
2,265 
1,425 

195,920 
155,380 
123,240 
97,760 
77,500 

61,520 
48,740 
38,640 
30,640 
24,300 

19,280 
15,280 
12,120 
9,610 
7,620 

6,040 
4,790 
3,800 
3,020 
1,900 

244,900 
194,225 
154,050 
122,200 
96,875 

76,900 
60,925 
48,300 
38,300 
30,375 

24,100 
19,100 
15,150 
12,010 
9,525 

7,550 
5,985 
4,750 
3,775 
2.375 

293,880 
233,970 
184,860 
146,640 
116,250 

92,280 
73,110 
57,960 
45,960 
36,450 

28,920 
22,920 
18,180 
14,415 
11,430 

9,060 
7,185 
5,700 
4,530 
2,850 

391,840 
310,760 
246,480 
195,420 
155,000 

123,040 
97,480 
77,280 
61,280 
48,300 

38,560 
30,560 
24,240 
19,220 
15,220 

12,080 
9,580 
7,600 
6,040 
3,800 

489,800 
388,450 
308,100 
244,400 
193,750 

153,800 
121,850 
96,600 
76,600 
60,750 

48,200 
38,200 
30,300 
24,025 
19,050 

15,100 
11,975 
9,500 
7,550 
4,750 

1414 


ELECTRICAL  ENGINEERING. 


slowly  and  then  more  rapidly,  as  the  load  decreases.  Each  machine 
has  its  "characteristic"  curve  of  efficiency,  showing  the  ratio  of  output 
to  input  at  different  loads.  Roughly  the  decrease  in  efficiency  for  direct- 
current  machines  at  half-load  varies  from  3%  to  10%  for  the  smallest 
sizes.  The  loss  in  transmission,  due  to  fall  in  electrical  pressure  or 
"dop"  in  the  line,  is  governed  by  the  size  of  the  wires,  the  other 
conditions  remaining  the  same.  For  a  long-distance  transmission 
plant  this  will  vary  from  5  %  upwards. 

With  generator  efficiency  and  motor  efficiency  each  90%,  and  trans- 
mission loss  5  %,  the  combined  efficiency  is  0.90  X  0.90  X  0.95  =  76.95  %. 

Resistances  of  Pure  Aluminum  Wire.* 

Conductivity  62  in  the  Matthiesen  Standard  Scale.     Pure  aluminum 
weighs  167.111  pounds  per  cubic  foot. 


II 

OM 

gog 

<A 

Resistances  at  70°  F. 

oT  o 

a* 

Ow 

S* 

<ffi 

Resistances  at  70°  F. 

Ohms 
perlOOO 
Feet. 

Ohms 
Mile. 

Feet 
Ohm. 

Ohms  per 
Pound. 

Ohms 
perlOOO 
Feet. 

Ohms 
per 
Mile. 

Feet 
per 
Ohm. 

Ohms  per 
Pound. 

0000 

0.07904 

0.41730 

12652. 

0.00040985 

19 

12.985 

68.564 

77.05 

11.070 

000 

.09966 

.52623 

10034. 

.00065102 

20 

16.381 

86.500 

61.06 

17.595 

00 

.12569 

.66362 

7956. 

.0010364 

21 

20.649 

109.02 

48.43 

27.971 

0 

.15849 

.83684 

6310. 

.0016479 

22 

26.025 

137.42 

38.44 

44.450 

1 

.19982 

1.0552 

5005. 

.0026194 

23 

32.830 

173.35 

30.45 

70.700 

2 

.25200 

1.3305 

3968. 

.0041656 

24 

41.400 

218.60 

24.16 

112.43 

3 

.31778 

1.6779 

3147. 

.0066250 

25 

52.200 

275.61 

19.16 

178.78 

4 

.40067 

2.1156 

2496. 

.010531 

26 

65.856 

347.70 

15.19 

284.36 

5 

.50526 

2.6679 

1975. 

.016749 

27 

83.010 

438.32 

12.05 

452.62 

6 

.63720 

3.3687 

1569. 

.026628 

28 

104.67 

552.64 

9.55 

718.95 

7 

.80350 

4.2425 

1245. 

.042335 

29 

132.00 

697.01 

7.58 

1142.9 

8 

1.0131 

5.3498 

987.0 

.067318 

30 

166.43 

878.80 

6.01 

1817.2 

9 

1.2773 

6.7442 

783.0 

.10710 

31 

209.85 

1108.0 

4.77 

2888.0 

10 

1.6111 

8.5065 

620.8 

.17028 

32 

264.68 

1397.6 

3.78 

4595.5 

11 

2.0312 

10.723 

492.4 

.27061 

33 

333.68 

1760.2 

3.00 

7302.0 

12 

2.5615 

13.525 

390.5 

.43040 

34 

420.87 

2222.2 

2.38 

11627. 

13 

3.2300 

17.055 

309.6 

.68437 

35 

530.60 

2801.8 

1.88 

18440. 

14 

4.0724 

21.502 

245.6 

1.0877 

36 

669.00 

3532.5 

1.50 

29352. 

15 

5.1354 

27.114 

194.8 

1.7308 

37 

843.46 

4453.0 

1.19 

46600. 

16 

6.4755 

34.190 

154.4 

2.7505 

38 

1064.0 

5618.0 

0.95 

74240. 

17 

8.1670 

43.124 

122.5 

4.3746 

39 

1341.2 

7082.0 

0.75 

118070. 

18 

10.300 

54.388 

97.10 

6.9590 

40 

1691.1 

8930.0 

0.59 

187700. 

*  Calculated  on  the  basis  of  Dr.  Matthiessen's  standard,  viz.:    The 
resistance  of  a  pure  soft  copper  wire  1  meter  long,  having  a  weight  of 
1  gram  =  0.141729  International  Ohm  at  0°  C. 
(From  Aluminum  for  Electrical  Conductors;  Pittsburgh  Reduction  Co.) 

ELECTRIC   RAILWAYS. 

While  600  volts  is  still  maintained  as  a  standard  for  street  railway 
systems,  experience  has  shown  that  the  most  economical  operation  of 
high-speed  suburban  and  interurban  railroads  can  be  obtained  with 
1200  to  1500  volts  on  the  trolley.  Steam  railroad  electrifications  will, 
however,  be  accomplished  most  satisfactorily  with  2400  or  3000  volts 
direct  current. 

Schedule  Speeds,  Miles  per  Hour. 
CITY  SERVICE. 


Max. 


Stops  per  Mile. 


Speed. 

1 

2 

3 

4 

5 

6 

7 

8 

15... 

10.8 

9.9 

9.3 

8.7 

8.3 

7.9 

7.5 

7.2 

20... 

13.7 

12.1 

11  .1 

10.3 

9.6 

9.0 

8.6 

8.1 

25 

16  3 

14.2 

12.7 

11  .5 

10.6 

9.9 

9.3 

8.7 

30  

18.5 

15.6 

13.8 

12.4 

11.3 

10.5 

9.8 

9.2 

ELECTRIC   RAILWAYS. 


1415 


INTERURBAN  SERVICE. 


Max. 

Miles  I 

>etween 

Stops. 

Speed. 

1/1 

3/4 

1 

1.5 

2 

3 

4 

5 

10 

30. 

14  0 

15  5 

16  7 

18  5 

19.7 

21   0 

22  0 

22  5 

23  9 

40.  . 

15.4 

18.1 

20.0 

22.7 

24.5 

26.7 

28.0 

28.9 

30  8 

50 

16  2 

19  5 

21   9 

25  6 

27  9 

31   0 

32  9 

34  2 

37  2 

60  

17.0 

20.8 

23.6 

27.9 

30.9 

34.8 

37.5 

39.3 

43.6 

The  figures  in  the  above  tables  include  stops  of  5  seconds  each  for  the 
city  service  and  of  15  seconds  for  the  interurban  service,  besides  a  15  % 
margin  for  line  drop  and  traffic  delays.  The  ratio  of  acceleration  is 
approximately  1.5  miles  per  hour  per  second  for  the  city  service  and 
1.2  miles  per  hour  per  second  for  the  interurban  service,  the  braking 
being  1.5  miles  per  hour  per  second  and  the  coasting  approximately 
10%  of  the  running  time  exclusive  of  stop. 

Train  Resistance.  (General  Electric  Co.) — The  horse-power  output 
at  the  rim  of  the  wheels  is  equal  to, 

H  P  =      T  XF.X  Feet          T  X  F  X  V 

33,000  X  Minutes  375 

When  reduced  to  Kilowatts, 

_  TXFX  V  X  746  _  2  X  TXFX  V 


— 

375  X  1000 

The  kilowatt  input  to  train  is  equal  to, 


1000 


appro*. 


T ,          2XTXFXV 

KW.   =  — : 


1000  X  Eff. 
Where  T  =  Total  weight  of  train  in  tons. 

F  =  Train  resistance,  including  that  due  to  grades  and  curves, 

in  Ibs.  per  ton. 
V  =  Speed  in  miles  per  hour. 
Eff  =  Efficiency  of  motors  at  speed  V. 
The  train  resistance  may  be  found  from  the  following  formula: 


Where  F  =  Train  resistance  in  Ibs.,  per  ton. 
T  =  Total  weight  of  train  in  tons. 
V  =  Speed  in  miles  per  hour. 
A  =  End  cross-section  in  sq.  ft. 
N  =  Number  of  cars  in  train. 

— —  is  limited  to  a  value  of  3.5. 

VT 

Tractive  Resistance  of  a  28-ton  Electric    Car  (Harold   H.    Dunn, 
Bull.  74,  Univ'y  of  111.  Expt.  Station,  April,  1914). — Mean  of  all  tests: 
Miles  per  hr.  .5        10       15       -20         25         30         35         40         45 
Lb.  per  ton..  5.25    6.80    8.62    10.75    13.03    15.75    18.75    22.13    26.12 
Two  formulae  have  been  derived  from  the  results: 
R  =  4  +  0.222  S  +  0.00582  S*. 
R  =  4  +  0.222  3  +  0.00181  ~  S2. 

A  =  cross-sectional  area  of  the  car  in  sq.  ft.  W  =  weight  of  the  car 
in  tons. 

The  formulae  should  not  be  used  beyond  the  limit  of  45  miles  per  hour. 

Rates  of  Acceleration. — Electric  Locomotive  Passenger  Service,  0.3  to 
0.6  mile  per  hour  per  second. 

Electric  Motor  Cars,  Interurban  Service,  0.8  to  1.3  miles  per  hour 
per  second. 

Electric  Motor  Cars,  City  Service,  1.5  miles  per  hour  per  second. 

Electric  Motor  Cars,  Rapid  Transit  Service,  1.5  to  2.0  miles  per  hour 
per  second. 

Highest  Practical  Bate,  2.0  to  2,5  miles  per  Jiour  per  second, 


1416 


ELECTRICAL   ENGINEERING. 


Safe  Maximum  Speed  on  Curves. — 

Radius  of  Curve,  Ft.  10,000  5000  2000  1000  500  200  100  50 
Speed,  miles  per  hr.,  100  75  50  35  25  15  10  6 
The  above  values  apply  only  when  full  elevation  is  given  the  outer 
rail.  For  city  service  such  elevation  is  not  possible  and  the  maxi- 
mum speed  will,  therefore,  be  less  under  such  cpnditions.  The  same 
restriction  applies  with  steel  wheel  flanges  of  3/4  inch  or  less. 

Coefficient  of  Adhesion.  —  The  following  are  the  average  values  of 
the  coefficient  of  adhesion  between  wheels  and  rails,  based  on  a  uniform 
torque: 

Clean,  dry  rail,  30%. 

Wet  rail,  18%; 

Rail  covered  with  sleet,          15? 
Rail  covered  with  dry  snow,  10 £,  „  , 

Electrical  Resistance  of  Steel  Bails. — The  resistance  of  steel  rails 
varies  considerably,  due  to  the  difference  in  chemical  composition. 
Ordinary  traction  rails  have  a  specific  resistance  averaging  12  times 
that  of  copper,  while  for  contact  rails  (third  rails)  the  average  is  only 
8  times.  The  values  given  in  the  following  table  are  in  ohms  at  75°  F. 
and  with  no  joints. 


with  sand,  22%. 

with  sand,  20%. 

o',  with  sand,  15%. 


Weight  of  Rails, 
Lbs.  per  Yard. 

Actual 
Area, 
Sq.  In. 

Actual  Area 
in 
Circular  Mils. 

Resistance 
per  Mile, 
8  to  1  Ratio. 

Resistance 
per  Mile, 
1  2  to  1  Ratio. 

40. 

3  92 

4  918300 

0  09  1  1  8 

0  13395 

45.. 

4  42 

5,627  700 

0  07915 

0  1  1  905 

50... 

4.90 

6,238,800 

0  07135 

0   10710 

60. 

5  88 

7  486  600 

0  05955 

0  08920 

70... 

6  86 

8,734400 

0  05105 

0  07660 

75.. 

7.35 

9,230,900 

0  04780 

0  07185 

80. 

7  84 

9  982  1  00 

0  04465 

0  06695 

90.    . 

8  82 

1  1  ,229,900 

0  03975 

0  05955 

100  

9.80 

12,477,700 

0.03750 

0.05365 

Resistance  of  Rail  Bonds.  —  The  resistance  of  bonded  rails  will 
vary,  depending  on  the  amount  of  contact  made  by  the  splice  bars  and 
rail  ends,  but  in  selecting  bonds  this  element  of  the  return  circuit 
should  be  disregarded,  as  it  is  quite  unreliable  and  frequently  negligible. 


Size  of  Conductor. 

Diameter     of 
Terminal, 
in  Inches. 

Resistance  per  In. 
of  Conductor. 
75°  Fahr. 

Carrying 
Capacity, 
Amp. 

0.  .  , 

1/2 

00000829 

210 

00..  . 

5/8 

00000657 

265 

000.  . 

3/4 

00000521 

335 

0000.  . 

7/8 

000004  1  4 

425 

250,000  C.  M  .  . 

7/8 

00000350 

500 

300,000  C.  M.  . 

00000275 

600 

350,000  C.  M.  .  . 

00000250 

700 

400,000  C.  M.  .  . 

00000219 

800 

450,000  C.  M.  . 

00000196 

900 

500,000  C.  M  

.00000175 

1000 

Electric  Locomotives. — In  selecting  an  electric  locomotive  the  prin- 
cipal points  to  be  determined  are  the  weight  of  the  locomotive,  the 
type  and  capacity  of  the  equipment,  and  the  mechanical  features. 
The  weight  upon  the  drivers  must  be  enough  to  pull  the  heaviest 
trains  under  the  most  adverse  conditions.  Therefore  the  weight  of  the 
heaviest  train,  the  maximum  grade  and  curvature  must  be  ascertained. 
It  must  be  known  whether  the  locomotive  is  expected  to  start  the  train 
under  these  conditions,  or  whether  it  will  start  upon  the  level  and  only 
meet  maximum  grade  conditions  when  running. 

In  order  to  determine  the  motor  equipment  all  the  data  of  the  service 
conditions  are  required,  such  as  the  speed  required  under  various  condi- 
tions of  load  and  grade.  The  maximum  free-running  speed  will  be  ap- 
proximately 50  to  75  per  cent  greater  than  the  rated  full  load  speed. 
Mechanical  limitations  must  also  be  considered,  such  as  track  clear- 
ajices,  limiting  weight  on  drivers,  type  of  couplings,  etc, 


RAILWAYS. 


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ie  of  Road  and  Section  Electrified. 

altimore  &  Ohio,  Baltimore,  Md.  •• 
Baltimore  Tunnels 

ew  York  Central  R.R.,  New  York 
to  Harmon 

1 

ew  York,  New  Haven  &  Hartford  j 
R.R.,  New  York  to  New  Haven  ! 

rand  Trunk  Ry.  Co., 
St.  Clair  Tunnel  Co.,  Pt.  Huron, 
Mich.,  St.  Clair  Tunnel 

reat  Northern  R.R.,  Cascade  Tun- 
nel, Washington 

.ichigan  Central  R.R.,  Detroit 
River  Tunnel,  Detroit,  Mich. 

Dston  &  Maine  R.R.,  North  Adams, 
Mass.,  Hoosac  Tunnel 

snn.  Tunnel  &  Terminal  R.R.  — 
Pennsylvania  R.R.  into  New 
York  City 

utte,  Anaconda  &  Pacific  R.R.,  j 
Butte  to  Anaconda,  Montana 

orf  oik  &  Western  R.R.,  Bluefield  to 
Elkhorn,  W.  Va. 

anadian  Northern,  Montreal,  Can. 

Continuous  Rating,"  which  means 
Pounds  Tractive  Effort,"  in  which  1 

i 

m 

2; 

Z 

O 

O 

2 

W 

DH 

PP 

z 

0 

:  5 

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*  •»— 

ELECTRIC  WELDING. 


1419 


Relative  Efficiencies  of  Electric  Railway  Distributing  Systems.— The 

table  on  p.  1417  shows  the  approximate  all-day  combined  efficiencies 
from  prime  mover  to  train  wheels  for  various  methods  of  trunk  line 
electrifications.  The  trains  are  supposed  to  be  handled  by  electric 
locomotives,  and  in  each  instance  a  considerable  length  of  line  is  con- 
templated, making  it  necessary  to  have  a  100,000-volt  high-tension 
primary  distribution  or  a  multiplicity  of  power  sources. 

Space  will  not  permit  a  complete  treatment  9f  the  subject  of  Electric 
Railways  in  this  work.  For  further  information  consult:  "American 
Handbook  for  Electrical  Engineers";  Standard  Handbook  for  Electrical 
Engineers";  "Foster's  Electrical  Engineer's  Pocket  Book";  Burch, 
"Electric  Traction  for  Railway  Trains";  Harding,  "Electric  Railway 
Engineering." 

ELECTRIC  WELDING. 

Electric  welding  is  divided  into  two  general  classes,  arc  heating 
and  resistance  heating. 

Arc  Welding. — In  this  process  the  heat  of  the  arc  is  utilized  to 
bring  the  metals  to  be  welded  to  the  melting  temperature,  when  the- 
joint  is  filled  with  molten  metal,  usually  introduced  in  the  form  of  a 
rod.  This  system  is  usually  operated  by  direct  current,  and  as  the 
positive  side  of  a  direct  current  arc  generates  heat  at  a  rate  approxi- 
mately three  times  that  of  the  negative  side,  the  positive  side  is  used  for 
performing  the  welding  operation. 

Two  kinds  of  arcs  may  be  used  for  this  class  of  welding,  the  carbon 
arc  and  the  metallic  arc.  The  former  requires  an  e.  m.  f.  varying  from 
50  to  100  volts  and  the  value  of  the  current  is  varied  over  a  range  of 
100  to  750  amperes,  300  being  the  average.  The  metallic  arc,  how- 
ever, requires  an  e.  m.  f.  of  only  from  15  to  30  volts,  the  length  of  the 
arc  being  very  short  as  compared  with  the  carbon  arc. 

The  arc  should  be  as  stable  as  possible,  and  the  current  should, 
therefore,  be  of  a  constant  value.  The  regulation  may  be  accomplished 
by  inserting  resistance  in  series  in  the  circuit,  but  this  system  is  nat- 
urally very  wasteful  and  greater  economy  may  be  obtained  by  pro- 
viding motor-generator  sets,  with  the  generator  of  the  variable  voltage 

The  following  costs,  Table  I  (from  Electrical  World)  were  compiled 
from  the  records  of  an  electric  railway  repair  shop: 

TABLE  I. 

Data  on  Electric  Welding  Repairs  in  Railway  Shops. 


Time  in 
Minutes. 

Kw. 

Average 
Costs. 

Gear-case  lugs  ....            

10 

6 

$0.07 

Armature  shaft  (broken)  2-in  

60 

20-30 

0.80 

Dowel-pin  holes                                                 .' 

5-12 

4-8 

0.07 

Broken  motor  cases 

150-200 

75-90 

4.98 

Broken  lugs  on  a  compressor  cover,  doors 
and  grease-cup  hinges           .    .        .... 

2-5 

1-3 

0.03 

Broken  truck  frames  

30-60 

20-35 

0.63 

Worn  bolt  holes  in  motors  and  trucks  ..... 
Enlarged  and  elongated  holes  in  brake  levers 
Armature  shafts,  2-in.,  worn  in  journals  .  .  . 
Armature  shafts  worn  in  keyways      .    ... 

5-10 
2-4 
120-180 
10-15 

3-5 

1  V2-3 
60-90 
7-12 

0.05 
0.03 
3.75 
0.10 

Armature  shaft,  worn  thread  

20-30 

10-15 

0.24 

Air-brake  armature  shafts  (broken)  .            . 

20-30 

10-20 

0.27 

Leaking  axle  boxes  

5-15 

3-7 

0.08 

Resistance  Welding.  —  Resistance  welding  is  done  by  the  heat 
developed  by  a  large  amperage  carrying  through  the  joining  metals  by 
means  of  a  low  voltage.  Single-phase  alternating  current  is  generally 
used  for  the  operation,  which  may  be  broadly  divided  into  two  classes — 
butt-welding  and  spot-welding.  The  former  covers  all  work  on  which 
the  ends  or  the  sides  of  the  material  are  welded  together,  while  spot- 
welding  is  used  for  joining  metal  sheets  together  at  any  point  by  a 
spot  the  size  of  a  rivet,  without  punching  holes  or  using  rivets. 

For  resistance  welding  a  very  low  voltage  is  used,  varying  from  2 
to  8  volts,  the  line  voltage  being  stepped  down  by  special  transformers. 


1420 


ELECTRICAL   ENGINEERING. 


The  current  consumption,  in  amperes,  varies  with  the  work  and  the 
time  taken  to  make  the  weld. 

The  following  tables  (from  Iron  Trade  Review)  give  the  cost  of 
resistance  welding.  Table  II  gives  the  results  obtained  by  butt- 
welding  round  stock  ranging  from  1/4  to  1  inch  diameter,  in  the  short- 
est and  longest  time  possible.  The  difference  in  current  consumption 
is  very  great  and  in  most  cases  the  shorter  time  in  seconds  was  the  most 
economical  of  the  two,  although  neither  is  the  most  economical  rate 
at  which  the  material  can  be  welded. 

TABLE  II.— Shortest  and  Longest  Butt-welding  Periods. 


Size,  In. 

Time, 
Seconds. 

Current 
Amperes. 

Volts  per 
Square 
Inch. 

Size,  In. 

Time, 
Seconds. 

Current 
Amperes. 

Volts  per 
Square 
Inch. 

1/4 

i 

3/8 

$ 

9/16 

9/16 

2.7 
5 
4 
5.27 
4 
15.8 
3.6 
21.5 

1960 
1645 
4330 
2190 
6600 
1800 
8400 
3400 

39.5 
35.5 
45.5 
19.7 
36.6 
13 
8 
12.25 

5/8 
V8 
3/4 
3/4 
V8 

1V8 
1 

3.5 
10.85 
4 
22.2 

17 
33 
114 

9400 
5510 
10000 
9400 
11900 
10550 
7740 
4450 

33.7 
18.85 
16.26 
19.7 
27.7 
19.6 
10.35 
16.1 

Table  III  contains  the  results  of  tests  made  to  determine  the  cost  of 
power  for  making  electric  butt  welds  on  material  ranging  from  1/4  to 
2  inches  in  diameter. 

TABLE  HI.— Cost  of  Power. 


Area, 
Sq.  In. 

Kw. 

Welding 
Time, 
Seconds. 

Cost  per 
1000 
Welds* 

Area, 
Sq.  In. 

Kw. 

Welding 
Time, 
Seconds. 

Cost  per 
1000 
Welds* 

0.05 
0.11 
0.20 
0.31 
0.44 
0.60 

h 

10 
12 
15 

5 
6 
10 
12 
15 
20 

$0.07 
0.13 
0.22 
0.33 
0.50 
0.83 

0.79 
0.99 
1.23 
1.77 
2.41 
3.14 

18 
20 
26 
40 
45 
56 

30 
30 
40 
60 
70 
80 

$1.50 
1.66    , 
2.89 
6.67 
8.75     ' 
12.44 

Table  IV  gives  the  time,  power  and!  cost  per  100  spot-welds,  with 
current  at  1/4  cent  per  Kw.-hr.,  for  welding  Nos.  10  to  28  gage  sheets. 

TABLE  IV.— Cost  of  Welding. 


Gage. 

Kw. 

Time  in 
Seconds. 

Cost  per 
1000  Welds, 
Cents.* 

Gage. 

Kw. 

Time  in 
Seconds. 

Cost  per 
1000  Welds, 

Cents. 

10 
12 
14 
16 

18 

18 
16 
14 
12 
10 

1.5 

tlo 

0.9 
0.8 

3.5 

2.75 
2.5 
2.25 

20 
22 
24 
26 
28 

9 

8 

6 
5 

0.7 
0.6 
0.5 
0.4 
0.3 

1.75 
1.5 
1.25 

*  Current  at  1  cent  per  Kw.-hr. 

ELECTRIC  HEATERS. 

Wherever  a  comparatively  small  amount  of  heat  is  desired  to  be  auto- 
matically and  uniformly  maintained,  and  started  or  stopped  on  the 
instant  without  waste,  there  is  the  province  of  the  electric  heater. 

The  elementary  form  of  heater  is  some  form  of  resistance,  such  as 
coils  of  thin  wire  introduced  into  an  electric  circuit  and  surrounded  with 
a  substance  which  will  permit  the  conduction  and  radiafion  of  heat,  and 
at  the  same  time  serve  to  electrically  insulate  the  resistance. 

This  resistance  should  be  proportional  to  the  electro-motive  force  of 
the  current  used  and  to  the  equation  of  Joule's  law: 
H  =  imt  X  0.24, 


ELECTRIC  HEATING.  1421 

where  I  is  the  current  in  amperes!  R,  the  resistance  in  ohms;  t,  the  time 
in  seconds;  and  H,  the  heat  in  gram-centigrade  units. 

Since  the  resistance  of  metals  increases  as  their  temperature  increases, 
a  thin  wire  heated  by  current  passing  through  it  will  resist  more,  and 
grow  hotter  and  hotter  until  its  rate  of  loss  of  heat  by  conduction  and 
radiation  equals  the  rate  at  which  heat  is  supplied  by  the  current.  In  a 
short  wire,  before  heat  enough  can  be  dispelled  for  commercial  purposes, 
fusion  will  begin ;  and  in  electric  heaters  it  is  necessary  to  use  either  long 
lengths  of  thin  wire,  or  carbon,  which  alone  of  all  conductors  resists 
fusion.  In  the  majority  of  heaters,  coils  of  thin  wire  are  used,  separately 
embedded  in  some  substance  of  poor  electrical  but  good  thermal 
conductivity. 

Relative  Efficiency  of  Electric  and  of  Steam  Heating.  —  Suppose 
that  by  the  use  of  good  coal,  careful  firing,  well-designed  boilers  and 
triple-expansion  engines  we  are  able  in  daily  practice  to  generate  1  H.P. 
at  the  fly-wheel  with  an  expenditure  of  2  1/2  Ib.  of  coal  per  hour. 

We  have  then  to  convert  this  energy  into  electricity,  transmit  it  by 
wire  to  the  heater,  and  convert  it  into  heat  by  passing  it  through  a 
resistance-coil.  We  may  set  the  combined  efficiency  of  the  dynamo  and 
line  circuit  at  85.%,  and  will  suppose  that  all  the  electricity  is  converted 
into  heat  in  the  resistance-coils  of  the  radiator.  Then  1  brake  H.P.  at 
the  engine  =0.85  electrical  H.P.  at  the  resistance  coil  =  1,683,000 
ft.-lb.  energy  per  hour  =  2180  heat-units.  But  since  it  required  2  1/2 
Ibs.  of  coal  to  develop  1  brake  H.P.,  it  follows  that  the  heat  given  out 
at  the  radiator  per  pound  of  coal  burned  in  the  boiler  furnace  will  be 
2180-^21/2  =  872  H.U.  An  ordinary  steam-heating  system  utilizes 
9652  H.U.  per  Ib.  of  coal  for  heating;  hence  the  efficiency  of  the  electric 
system  is  to  the  efficiency  of  the  steam-heating  system  as  872  is  to  9652, 
or  about  1  to  11.  (Eng'g  News,  Aug.  9,  '90;  Mar.  30,  '92;  May  15,  '93.) 

Heat  Required  to  Warm  and  Ventilate  a  Room.  —  The  heat  re- 
quired to  raise  the  temperature  of  a  given  space  or  room  to  a  certain 
value  depends  upon  the  ventilation,  the  character  of  the  walls,  the  di- 
mensions, proportions  of  the  room,  etc.  One  watt-hour  of  electrical 
energy  will  raise  the  temperature  of  one  cubic  foot  of  air  (measured  at 
70°)  191°  F.,  or  1  watt  will  raise  the  temperature  of  a  cubic  foot  of  air 
at  the  rate  of  0.0531°  F.  per  second,  or  approximately  3.2°  per  minute. 
In  addition  to  raising  the  temperature  of  the  air  to  the  desired  value, 
the  loss  of  heat  through  conduction  and  ventilation  must  be  supplied. 
(See  Heating  and  Ventilation.) 

EXAMPLE.  Assume  a  room  of  a  capacity  of  3000  cu.  ft.,  in  which 
the  air  is  changed  every  20  minutes,  the  temperature  to  be  main- 
tained 30°  above  the  outside  air. 

3000  -T-  20   =  150  cu.  ft.  per  minute. 

(150  X  30)  -s-  3.2  =  1406  watts  necessary  to  supply  the  ventilation 
loss.  To  begin  with,  to  raise  the  air  in  the  room  30°  will  require 

(3000  X  30)  -T-  191   =471  watt-hours 

and  therefore  the  total  energy  used  during  the  first  hour  will  be 
1406  +  471   =  1877  watt-hours  or  1.88  Kw.-hours. 

Domestic  Heating. — Electric  heating  is  extensively  used  for  house- 
hold cooking  apparatus.  The  time  taken  to  heat  water  in  any  quantity 
to  any  definite  temperature  not  exceeding  boiling  point  can  be  deter- 
mined by  the  formula: 

V  (T*  -  Ti)  1831 
PX  Eff. 

Where  t  =  time  in  minutes,  V  =  number  of  pints,  T\  =  initial  tem- 
perature, °F.,  Tz  =  final  temperature,  °F.,  P  =  energy  consumption 
in  watts,  Eff.  =  Efficiency  of  cooking  utensil,  per  cent. 

EXAMPLE.  To  heat  1  pint  of  water  100°  F.  with  a  220- watt  heater 
with  50%  efficiency,  time  =  (1  X  100  X  1831)  -~  (220  X  50)  =  16.6  min. 

The  following  table  (compiled  by  the  National  Electric  Light  Asso- 
ciation) gives  the  watts  consumed  and  cost  of  operation  of  different 
domestic  heating  devices,  the  cost  of  current  being  at  the  rate  of  5  cents 
per  Kw.-hr. 


1422  ELECTRICAL  ENGINEERING. 

Cost  of  Operation  of  Domestic  Heating  Appliances. 

Apparatus.  Watts.       Cents  per  hr. 

Broilers,  3  heat* 300  to  1200  1.5    to  6 

Chafing  dishes,  3  heat 200  to    500  1       to  2.5 

Coffee  percolators  for  6-in.  stove 100  to    440  0.5   to  2.2 

Curling-iron  heaters 60  0.3 

Double  boilers  for  6-in.,  3-heat  stove 100  to    440  0.5    to  2.2 

Flatiron  (domestic  size) ,  3  Ib 275  1 

Flatiron  (domestic  size),  4  Ib 350  1.4 

Flatiron  (domestic  size) ,  5  Ib 400  2 

Flatiron  (domestic  size),  6  Ib 475  2.4 

Flatiron  (domestic  size),  7.5  Ib 540  2.7 

Flatiron  (domestic  size),  9  Ib 610  3.05 

Frying  kettles,  8  in.  diameter 825  4.125 

Griddle-cake  cookers,  9  in.  by  12  in.,  3-heat  330  to    880  1.7    to  4.4 

Griddle-cake  cookers,  12  in.  by  18  in.,  3-heat  500  to  1500  2.5    to  7.5 

Ornamental  stoves 250  to    500  1.25  to  2.5 

Ovens 1200  to  1500  6       to  7.5 

Plate  warmers 300  J .5 

Radiators . 700  to  6000  3.5  to  30 

Ranges:  3-heat,  4  to  6  people 1000  to  4515  5     to  22 

Ranges:  3-heat,  6  to  12  people 1100  to  5250  5.5  to  26 

Ranges:  3-heat,  12  to  20  people 2000  to  7200  10  to  36 

Toasters,  9  in.  by  12  in.,  3-heat 330  to    880  1.6  to  4.4 

Urns,  1-gal.,  3-heat 110  to  440  0.5  to  2.2 

Urns,  2-gal.,  3-heat 220  to    660  1.1  to  3.3 

Experience  has  shown  that  300  watt-hours  per  meal  per  person  is  a 

liberal  allowance  for  electric  cooking;  or  in  a  family  of  five,  four  kilo- 
watt hours  per  day  is  an  average. 

ELECTBIC   FURNACES. 

In  the  combustion  furnace,  no  matter  what  form  of  fuel  is  used,  the 
temperature  cannot  exceed  2000°  C.  (3632°  F.),  and  for  higher  temper- 
atures the  electric  furnace  must  be  used.  The  intensity  of  the  heat 
in  this  type  of  furnace  depends  .on  the  amount  of  current  that  passes, 
and  as  most  substances  are  conductors  when  hot,  the  degree  of  intensity 
possible  is  theoretically  unlimited.  In  practice,  however,  the  conduct- 
ing substance  begins  to  fuse  when  heated  to  its  melting  point,  and  one 
is  then  confronted  with  the  physical  difficulty  of  keeping  the  con- 
ducting medium  in  place,  or,  if  this  be  accomplished,  the  conducting 
medium  ultimately  vaporizes,,  the  gaseous  materials  escape,  and  heat 
is  thus  carried  away  from  the  furnace  as  rapidly  as  it  is  supplied.  The 
temperature  of  the  electric  arc,  which  is  somewhere  between  3600° 
and  4000°  C.  (6512°  -  7232°  F.),  is  perhaps  the  highest  temperature 
attainable  at  present. 

Electric  furnaces  may  be  divided  in  two  broad  classes,  arc  furnaces 
and  resistance  furnaces.  In  the  former  the  heat  is  generated  by  passing 
an  electric  current  through  the  space  between  the  ends  of  two  elec- 
trodes, forming  the  so-called  arc.  In  the  resistance  furnace  the  heat 
is  generated  in  the  interior  of  a  body  due  to  its  electrical  resistance. 

There  are  three  typical  forms  of  arc  furnaces,  their  common  feature 
being  that  most  and  sometimes  all  of  the  heat  is  transmitted  to  the 
material  by  radiation,  which  extends  in  all  directions.  In  all  the  fur- 
naces the  arc  must  be  started  by  a  quick  movement  of  the  electrodes  and 
afterwards  these  must  be  continuously  fed  together  as  they  are 
consumed. 

The  chief  characteristics  of  the  three  main  types  of  arc  furnaces  are: 

1.  The  direct-heating  type,  in  which  two  or  more  electrodes  are 
used  and  the  heating  is  accomplished  by  conduction  and  radiation. 
The  current  passes  from  one  electrode  down  through  the  slag,  across 
through  the  bath  and  up  through  the  slag  to  the  other  electrode.  The 
-  Heroult  furnace  belongs  to  this  type. 

The  Girod  furnace  is  also  T>f  the  direct-heating  type,  the  current 
arcing  from  the  electrodes,  which  are  connected  to  one  side  of  the  cir- 
cuit.  to  a  fixed  electrode  in  the  bottom. 

*  The  apparatus  can  be  set  at  three  different  heats  or  temperatures, 


ELECTRIC   FURNACES.  1423 

2.  The  indirect-heating  type.     To  this  type  belongs  the  Stassano 
furnace,  in  which  the  arc  extends  between  two  or  more  carbon  elec- 
trodes above  the  charge,  and  therefore  passes  over  but  does  not  come 
in  contact  with  the  charge,  the  heating  being  accomplished  by  radiation. 

3.  The  smothered  type,  in  which  the  arc  extends  from  the  end  of  the 
upper  electrode,  which  extends  beneath  the  surface  of  the  charge,  to 
the  lower  fixed  electrode  in  the  bottom  of  the  furnace. 

The  direct  and  indirect  heating  arc  furnaces  are  extensively  used 
for  melting  and  refining  metals,  while  examples  of  the  smothered  type 
are  the  ferro-silicon  and  calcium  carbide  furnaces. 

Resistance  furnaces  may  also  be  divided  in  two  distinct  types,  those 
of  direct  and  indirect  heating. 

1.  Direct  heating.    In  these  the  heat  is  produced  in  the  material  by 
its  own  resistance,  and  enters  the  material  at  the  highest  efficiency. 

The  material  may  be  placed  in  a  channel  between  two  electrodes  at 
the  ends  which  lead  the  current  to  and  from  it,  the  charge  being  sur- 
rounded with  insulating  material  to  reduce  the  loss  of  heat.  The 
Acheson  graphite  furnaces  are  of  this  type. 

Under  this  classification  also  come  the  induction  furnaces  in  which 
the  terminal  electrodes  are  eliminated  and  the  heat  generated  solely 
by  induction.  .The  furnace  consists  essentially  of  an  iron  core,  around 
one  leg  of  which  is  wound  a  primary  winding  enclosed  in  a  refractory 
case  and  usually  cooled  by  means  of  forced  draft.  The  annular  hearth 
surrounds  this  primary  coil  and  is  separated  from  it  by  means  of 
refractory  material.  This  hearth  contains  the  metal  and  acts  as  a 
secondary  winding  of  one  turn.  The  voltage  induced  in  this  turn  is 
quite  small  so  that  the  energy  transformed  from  the  primary  coil 
results  in  a  very  large  current  in  the  secondary,  which  heats  the  metal 
and  thus  nearly  all  the  electrical  energy  is  converted  into  heat  in  the 
metal  to  be  melted.  The  Kjellin  and  the  Rochling-Rodenhauser  fur- 
naces belong  to  this  type.  They  are  extensively  used  for  steel  refining. 

2.  Indirect  heating  furnaces  have  the  heat  generated  in  an  internal 
or  external  resistor  and  it  is  transferred  to  the  charge  by  conduction 
and  radiation.    Such  furnaces  are  used  for  small  moderate  temperature 
work. 

Uses  of  Electric  Furnaces. 

Pig  Iron.  —  When  the  electric  furnace  is  used  for  smelting  of  iron 
ore  it  is  only  necessary  to  supply  enough  carbon  for  the  reduction,  this 
amount  being  approximately  one-third  of  what  is  required  in  the 
ordinary  blast  furnace  for  both  the  heating  and  reduction.  From  re- 
peated trial  runs  with  electric  smelting  furnaces  in  Norway  and  Sweden 
it  has  been  found  that  coke  as  a  reducing  agent  does  not  give  "satisfac- 
tory results,  and  charcoal  is  therefore  used  exclusively. 

The  table  on  p.  1424  gives  a  summary  of  the  most  important  figures 
relating  to  the  economical  results  which  were  obtained  with  the  electric 
iron  ore  furnaces  in  Sweden. 

Steel  Refining.  —  Electric  furnaces  are  used  in  the  manufacture  of 
crucible  quality  steel,  and  the  number  is  constantly  increasing,  both 
arc  and  induction  furnaces  being  in  general  use. 

The  following  data  as  to  the  cost  of  electric  steel  refining  are  taken 
from  an  article  in  Stahl  und  Eisen,  April  10,  1913.  This  article  gives 
the  results  which  have  been  obtained  in  Germany  by  the  Heroult 
furnace  and  it  contains  a  discussion  of  electric  steel  production  from  a 
large-industry  point  of  view. 

The  total  refining  cost  must  include  many  items  as  well  as  the  cost 
of  current;  for  example,  the  cost  of  fluxes  (ore,  lime,  sand,  etc.),  the 
additions  of  ferro-alloys,  relining,  maintenance,  and  repairs,  electrode 
consumption,  wages,  and,  finally,  interest  and  depreciation.  The  totals 
of  these  items  and  the  cost  of  current,  which  is  the  largest  item,  are 
given  below: 

Total  Refining  Costs  (Per  Ton). 

5- ton  10- ton  15-ton  20- ton 

Basic.    Acid.  Basic.    Acid.  Basic.    Acid.  Basic.    Acid. 
Total  costs ....    $2.79    $1.79    $2.45    $1.45    $2.28    $1.34    $2.15    $1.25 
Cost  of  current       1.19      0.77      1.07      0.59      1.01      0.54      0.95      0.48 
The  figures  are  based  on  prevailing  market  prices.    Current  is  taken 


1424 


ELECTRICAL  ENGINEERING. 


Data  on  Electric  Smelting  of  Pig  Iron  in  Sweden. 


Nov.  15,  1910, 
May  29,  1911. 

Aug.  4,  1911, 
to 
June21,1912. 

Aug.  12,  1912, 
Sept.  30,  191  2. 

October  to 
December, 
1912. 

Ore,    concentrates 
and  briquettes,  kg. 
Limestone  kg. 

4,336,338 
345,405 

7,917,214 
647,479 

1,406,530 
1  08,  1  50 

2,914,830 
169,944 

Charcoal  hi.* 

65,474 

107,282 

21,859 

44,934 

Coke                     kg. 

70854 

Elec.  energy,  kw.  hrs. 
Iron  in  ore,  per  cent. 
Iron  produced  .  .  kg. 
Slag    per    ton    of 
iron  ....            kg. 

6,339,131 
60.79 
2,636,098 

350 

10,845,180 
60.75 
4,809,670 

324 

1,939,073 
68.67 
965,915 

192 

3,957,565 
65.38 
1,905,865 

Electrodes  per  ton 
of  iron,  gross  .kg. 
Electrodes  per  ton 
of  iron,  net.  .kg. 
Charcoal  per  ton 
of  iron.              hi 

10.00 
4.95 
24  84 

6.08 
5.17 
22  31 

3.02 
3.02 
22  63 

2.78 
2.78 
23  58 

Working  time  

Hr.       Min. 
4,441          20 

Hr.       Min. 
7,218        23 

Hr.       Min. 
1  ,  1  73        08 

Hr.       Min. 
2,158        30 

Repairs 

236          53 

506        07 

13        47 

49        30 

Repairs  in  per  cent, 
of  total  time  .... 
Average  load,  kw  .  . 
Kw.-hrs.  per  ton  of 
iron  

5.05 
1,427 

2,405 

6.55 
1,502 

2,255 

1  .16 
1,653 

2,007 

2.24 
1,833 

2,076 

Iron  per  kw.  year, 
tons    .... 

3.64 

3.88 

4.36 

4.22 

Iron  per  h.p.  year, 
tons  .  . 

2.68 

2.86 

3.20 

3.10 

*  1  hectoliter  =  3.53  cu.  ft.   =  2.84  U.  S.  bushels. 

at  0.595c.  per  Kw.-hr.,  which  is  a  figure  that  should  be  easy  of  attain- 
ment for  most  steel  plants.  The  time  per  heat  is  taken  as  2 1/4  to  2  1/2 
hours.  Three-phase  furnaces  are  considered,  and  in  the  installation 
cost  of  the  plant  must  be  included  transformers,  cables,  and  switch- 
boards. The  amount  of  current  required  is  as  follows: 
Size  of  Furnace,  Tons  1  2  5  10  25 

Kilowatts 300-350  400-450  750-800  1000-1200  3000-3500 

Ferro- Alloys.  —  The  electric  furnace  has  clearly  demonstrated  its 
advantages  in  the  manufacture  of  ferro-alloys.  The  production  of  a 
ferro-alloy  low  in  carbon  or  with  a  high  percentage  of  the  alloying 
element  is  limited  in  the  blast  furnace  by  three  difficulties  —  first,  the 
temperature  is  too  low  for  the  reduction  of  some  of  the  oxides  of  the 
alloying  metals;  second,  it  is  difficult  to  obtain  an  alloy  containing 
a  high  percentage  of  the  special  metal;  and  third,  it  is  impossible  to 
produce  a  ferro-alloy  low  in  carbon,  because  of  the  great  excess  of 
carbon  in  the  charge.  With  the  crucible,  owing  to  the  small  scale  of 
operation  necessary,  the  process  is  expensive.  Owing  to  the  temper- 
ature limitation,  certain  oxides  can  not  be  reduced  and  metals  of  high 
melting  point  can  not  be  melted ;  it  is  difficult  to  obtain  an  alloy  with  a 
high  percentage  of  the  special  metal ;  and  if  a  graphite  crucible  is  used, 
the  percentage  of  carbon  tends  to  be  high  in  the  ferro-alloy. 

Non-ferrous  Metals.  —  In  the  metallurgy  of  non-ferrous  metals  the 
electric  furnace  has  had  a  greater  application  for  the  treatment  of  zinc 
ores  than  in  the  metallurgy  of  any  of  the  other  non-ferrous  metals 
except  aluminum.  Since  1885,  when  an  electric  furnace  for  the  treat- 
ment of  zinc  ores  was  patented  by  the  Cowles  brothers,  experimental 
work  has  been  done  on  a  very  large  scale.  However,  the  process  has 
not  been  applied  to  any  great  extent  because  of  the  difficulty  of  con- 
densing the  zinc  vapor  produced  in  smelting  in  the  electric  furnace,  and 


ELECTRIC  ACCUMULATORS. 


1425 


eo  it  may  be  said  that  the  electric  smelting  of  zinc  ores  is  yet  in  the 
experimental  stage. 

Silundum,  or  silicified  carbon,  is  a  product  obtained  when  carbon  is 
heated  in  the  vapor  of  silicon  in  an  electric  furnace.  It  is  a  form  of  car- 
borundum, and  has  similar  properties;  it  is  very  hard,  resists  high 
temperatures,  and  is  acid-proof.  It  is  a  conductor  of  electricity,  its 
resistance  being  about  three  times  that  of  carbon.  It  can  be  heated  in 
the  air  up  to  1600°  C.  without  showing  any  sign  of  oxidation.  At  about 
3700°,  however,  the  silicon  leaves  the  carbon  and  combines  with  the 
oxygen  of  the  air.  Silundum  can  not  be  melted.  The  first  use  to  which 
the  material  was  applied  was  for  electric  cooking  and  heating.  For 
heating  purposes  the  silundum  rods  can  be  used  single,  in  lengths  up  to 
32  in.,  depending  on  the  diameter,  as  solid,  round,  flat,  or  square  rods  or 
tubes,  or  in  the  form  of  a  grid  mounted  in  a  frame  and  provided  with 
contact  wires. — (EL  Review,  London.  Eng.  Digest,  Feb.,  1909.) 

PRIMARY  BATTERIES. 

Following  is  a  partial  list  of  some  of  the  best  known  primary  cells  or 
batteries. 


Name. 

Elem< 

mts. 

+  . 

Electrolyte. 

Depolarizer. 

E.M.F. 
volts. 

Daniell  
Gravity 

Cu 
Cu 
Pt 
C 
Cu 
C 
Pt 
Pt 
C 

Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Cd 
Zn 

Dilute  H2SO4 
ZnSO4 
Dilute  H2SO4 
Dilute  H2SO4 
Cone.  NaOH 
NH4C1 
ZnS04 
CdS04 
Various  electro 

Concent.  CuSO4 
Concent.  CaSO4 
HN03 
K?Cr2O7 
CuO 
MnO2 
Hg2S04 
Hg2S04 
yte  pastes. 

1.07 

i!f 

2.1 
0.7-0.9 
1.4 
1.44 
1.02 
1-1.8 

Grove  

Fuller 

Edison-  Lalande  
Leclanche 

Clark  

\Veston 

Dry  battery  

The  gravity  cell  is  used  for  telegraph  work.  It  is  suitable  for  closed 
circuits,  and  should  not  be  used  where  it  is  to  stand  for  a  long  time  on 
open  circuit. 

The  Fuller  cell  is  adapted  to  telephones  or  any  intermittent  work.  It 
can  stand  on  open  circuit  for  months  without  deterioration. 

The  Edison-Lalande  cell  is  suitable  for  either  closed  or  open  circuits. 

The  Leclanche  cell  is  adapted  for  open  circuit  intermittent  work,  such 
as  bells,  telephones,  etc. 

The  Clark  and  Weston  cells  are  used  for  electrical  standards.  The 
Weston  cell  has  largely  superseded  the  Clark. 

Dry  cells  are  in  common  use  for  house  service,  igniters  for  gas  engines, 
etc. 

Batteries  are  coupled  in  series  of  two  or  more  to  obtain  an  e.m.f. 
.greater  than  that  of  one  cell,  and  in  multiple  to  obtain  more  amperes 
without  change  of  e.m.f. 

Spark  coils,  or  induction  coils,  with  interrupters,  are  used  to  obtain 
ignition  sparks  for  gas  engines,  etc. 

ELECTRIC   ACCUMULATORS   OR   STORAGE  BATTERIES. 

Secondary  or  storage  batteries  may  be  divided  in  two  general 
classes:  viz.,  the  lead  battery  and  the  Edison  alkaline  battery.  They 
are  composed  of  a  number  of  cells  connected  in  series  or  multiple.  The 
voltage  is  independent  of  the  size  of  the  cell  and  is  a  function  of  the 
electro -chemical  properties  used  for  the  electrodes  and  electrolytes, 
being  approximately  two  volts  per  cell.  The  current,  however,  is  ap- 
proximately proportional  to  the  surface  of  the  electrodes  that  are  sub- 
merged in  the  electrolyte. 

Lead  Batteries.  —  The  lead  battery  consists  of  two  electrodes,  the 
positive  and  negative,  immersed  in  the  electrolyte.  The  two  electrodes 
are  sponge  lead  (Pb)  for  the  negative,  and  peroxide  of  lead  (Pbp2)  for 
the  positive,  these  forming  the  active  couple,  the  electrolyte  being  di- 
lute sulphuric  acid.  The  two  sets  of  electrodes  are  called  an  element 
and  they  can  be  readily  distinguished  by  their  colors,  the  positive  pe 


1426  ELECTRICAL  ENGINEERING. 

oxide  plate  being  of  a  velvety  brown  chocolate  color  and  the  negative 
lead  sponge  plate  of  a  light  gray. 

Inside  of  the  cell  the  current  starts  from  the  negative  electrode  to- 
ward the  positive,  and  the  positive  electrode,  therefore,  is  that  por- 
tion of  the  battery  from  which  the  electric  current  passes  out  into  the 
load  circuit,  this  being  termed  "discharge,"  as  compared  to  the  storing 
of  energy,  which  is  termed  "charge."  When  the  cell  gives  out  current, 
the  elements  gradually  change  in  composition,  becoming  mixtures  or 
compounds  of  lead  and  lead  sulphate  at  the  negative  electrode,  and  lead 
peroxide  and  lead  sulphate  at  the  positive  electrode,  the  chemical 
change  caused  by  the  giving  out  of  electrical  energy  being  a  gradual 
formation  of  lead  sulphate. 

Lead  batteries  are  made  with  two  different  types  of  plates,  the 
"formed"  or  Plante  plate,  and  the  "pasted"  or  Faure  plate.  In  the 
former,  the  active  material  is  formed  electro-chemically  on  the  surface  of 
the  plate  body,  while  in  the  latter  it  is  first  applied  mechanically  in  the 
form  of  lead  oxide  and  afterward!  subjected  to  the  forming  process.  As 
a  rule  the  negative  plates  are  always  of  the  Faure  type.  Positive  Plante 
plates  have  a  long  life,  while  the  life  of  positive  Faure  plates  is  limited 
to  a  considerable  extent  by  the  number  of  charges.  The  latter,  how- 
ever, give  a  greater  capacity  for  the  same  weight  than  the  formed  plate, 
and  are,  therefore,  used  where  light  weight  is  required,  such  as  for  elec- 
tric vehicles.  Positive  plates  have  ordinarily  a  shorter  life  than 
negative. 

The  capacity  of  a  storage  battery  is  measured  in  ampere-hours,  and 
varies  with  the  discharge  rate.  An  arbitrary  standard  of  the  8-hour 
rate  is  now  universally  adopted,  but  if  the  rate  is  increased,  the  capacity 
is  diminished.  So,  for  example,  at  a  one-hour  discharge  rate  only  about 
half  the  number  of  ampere-hours  can  be  obtained  from  a  cell  that  it  can 
supply  at  the  8-hour  rate.  An  80-ampere-hour  battery  thus  means  one 
which  will  discharge  10  amperes  continuously  for  eight  hours  without 
falling  below  the  minimum  allowable  voltage. 

When  a  battery  is  being  discharged,  the  voltage  sinks  gradually  and 
it  should  never  be  discharged  below  some  fixed  limit,  because  an  ex- 
cessive quantity  cf  sulphate  will  then  form,  which  may  injure  the  plates 
both  electrically  and  mechanically,  tending  to  crack  and  loosen  the 
active  material.  This  condition  is  indicated  by  the  deposit  of  white 
sulphate  on  the  surfaces  of  the  plates.  The  voltage  at  which  a  lead 
battery  is  assumed  to  be  completely  discharged  depends  on  the  dis- 
charge rate  and  may  be  computed  from  the  formula 

E  =  1.66+  0.0175* 
where  t  =  time  of  discharge  in  hours. 

Thus  for  an  8-hour  rate  the  discharge  should  be  stopped  when  the 
voltage  has  dropped  to  180,  while  for  an  1-hour  rate,  it  should  be 
stopped  when  it  has  dropped  to  168. 

The  voltage  rises  gradually  during  the  charging  from  about  2.15  per 
cell  at  the  beginning  to  about  2.55  at  the  end.  The  rate  of  charging  is 
usually  specified  by  the  manufacturer.  In  certain  instances  it  is  equal 
to  the  8-hour  discharge  rate,  while  in  others  the  instructions  may  be  to 
start  the  charge  between  the  3-  and  5-hour  rate,  reducing  the  current 
to  the  8-hour  rate  as  soon  as  the  plates  gas  freely.  The  time  required 
for  a  charge  will,  of  course,  depend  upon  the  amount  of  the  previous 
discharge.  If  this  has  been  two-thirds  of  the  rated  capacity  of  the  bat- 
tery, about  three  hours  at  the  starting  rate  and  an  hour  and  a  half  or  two 
hours  afc  the  finishing  rate  will  be  necessary;  i.e.,  from  10  to  15  per  cent 
more  charge  than  the  amount  taken  out  on  the  discharge  is  ordinarily 
required. 

At  regularly  weekly  or  bi-weekly  intervals  the  battery  should  be 
given  an  overcharge  f9r  the  purpose  of  equalizing  all  cells,  reducing 
all  sulphate,  and  keeping  the  plates  in  good  general  condition.  Such 
overcharge  is  a  regular  charge  continued  until  the  voltage  does  not 
show  any  rise  for  four  or  five  consecutive  readings  15  minutes  apart, 
all  cells  then  gasing  freely.  A  charging  voltage  of  2.7  volts  should  be 
provided  for  such  overcharges. 

The  specific  gravity  of  the   electrolyte,  will  reach  a  maximum  in 

e  same  manner  as  the  voltage,  and  readings  of  this  in  the  various 

Is  of  the  battery  should  be  taken  toward  the  end  of  the  charge 

\ 


ELECTRIC  ACCUMULATORS.  1427 

with  a  hydrometer.  These  readings  will  act  as  a  check  on  those  taken 
on  the  voltage,  and  while  it  may  not  be  found  practicable  to  do  this 
every  time  the  battery  is  charged,  it  is  very  important  and  should  be 
done  at  least  once  a  week.  If  batteries  are  used  intermittently  and 
allowed  to  stand  some  time  without  charge  or  discharge,  the  electrolyte 
should  be  of  low  density,  not  over  1.210. 

Several  different  methods  may  be  adopted  for  controlling  the  dis- 
charge voltage  and  maintaining  a  uniform  pressure  at  the  lights,  viz.: 
(1)  by  connecting  in  additional  or  "end"  cells  one  at  a  time,  as  the 
voltage  drops,  by  means  of  an  end  cell  switch;  (2)  by  a  rheostat,  whose 
resistance  is  cut  out  step  by  step;  (3)  by  counter  electro-motive  force 
cells,  which,  like  a  rheostat,  cut  down  the  battery  voltage  at  the  be- 
ginning of  discharge,  and  are  cut  out  of  circuit  one  by  one  by  means 
of  an  end  cell  switch. 

Also,  several  methods  may  be  employed  for  obtaining  the  necessary 
increase  of  voltage  for  charging,  viz.;  (1)  by  dividing  the  battery  into 
two  equal  parts  and  charging  these  in  parallel  through  a  suitable  re- 
sistance, the  generator  running  at  normal  (lamp)  voltage;  (2)  by 
raising  the  voltage  of  the  generator  sufficiently  to  charge  all  the  cells  in 
one  series;  (3)  by  means  of  a  booster,  whose  voltage  is  added  to  that 
of  the  generator,  and  is  varied  to  give  the  total  required. 

In  a  lead  storage-cell,  if  the  surface  and  quantity  of  active  material 
be  accurately  proportioned,  and  if  the  discharge  be  commenced  imme- 
diately after  the  termination  of  the  charge,  then  a  current  efficiency  of 
as  much  as  98  %  may  be  obtained,  provided  the  rate  of  discharge  is  low 
and  well  regulated.  Since  the  current  efficiency  decreases  as  the  dis- 
charge rate  increases,  and  since  very  low  discharge  rates  are  seldom  used 
in  practice,  efficiencies  as  high  as  this  are  never  obtained  practically,  the 
average  being  about  90%. 

After  a  battery  has  been  erected  and  all  connections  made  and  the 
current  ready,  the  electrolyte  may  be  poured  into  the  jars,  and  as  soon 
thereafter  as  possible  the  initial  charging  should  commence.  Never 
allow  a  battery  to  stand  longer  than  two  hours  after  the  acid  is  put  in, 
before  starting  the  charge.  This  should  be  as  continuous  as  possible, 
until  all  cells  gas  freely  and  the  specific  gravity  and  voltage  show  no 
rise  over  a  period  of  10  hours.  The  duration  of  such  a  charge  may  vary 
from  30  to  100  hours,  and  is  always  given  by  the  manufacturer.  The 
temperature  in  any  one  cell  should  not  be  permitted  to  go  above  100°  F. ; 
if  this  occurs,  the  charging  rate  must  be  reduced  or  the  charge  tem- 
porarily stopped. 

The  level  of  the  electrolyte  should  be  kept  above  the  top  of  the  plates 
by  adding  pure  fresh  water.  Addition  of  new  electrolyte  is  seldom 
necessary  and  should  be  done  only  on  advice  from  the  manufacturer. 

The  sediment  which  collects  in  the  bottom  of  the  cells  should  always 
be  removed  before  it  touches  the  plates. 

The  battery  room  should  be  well  ventilated,  especially  when  charging, 
and  great  care  taken  not  to  bring  an  exposed  flame  near  the  cells  when 
charging  or  shortly  after. 

Metals  or  impurities  of  any  kind  must  not  be  allowed  to  get  into 
the  cells.  If  this  should  happen,  the  impurity  should  be  removed  at  once, 
and  if  badly  contaminated,  the  electrolyte  replaced  with  new.  If  in 
doubt  as  to  the  purity  of  electrolyte  or  water,  the  manufacturers  should 
be  consulted. 

To  take  cells  out  of  commission,  the  electrolyte  should  be  drawn  off; 
the  cells  filled  with  water  and  allowed  to  stand  for  12  or  15  hours.  The 
water  can  then  be  drawn  off  and  the  plates  allowed  to  dry.  When 
putting  into  service  again,  the  same  procedure  should  be  followed  as 
with  the  initial  charge. 

Lead  storage  batteries  are  extensively  used  for  the  following  appli- 
cations: 

Stand-by  service  in  central  stations. 

Voltage  regulation  on  D.  C.  distribution  lines. 

To  carry  peak  loads  of  central  stations. 

Voltage  regulation  in  isolated  building  plants. 

To  carry  load  of  isolated  plant,  when  the  plant  is  shut  down  for 
the  night. 

To  furnish  country  places  with  power  where  such  places  are  off  the 
line  of  central  stations, 


1428  ELECTRICAL  ENGINEERING. 

To  furnish  current  for  talking  circuits  in  telephone  service. 

To  furnish  current  for  signal  work. 

To  light  trains  in  connection  with  a  generator  system. 

To  operate  submarine  torpedo  boats. 

For  ignition,  starting  and  lighting  on  gas  cars. 

To  propel  electric  pleasure  and  commercial  vehicles. 

To  regulate  long  distance  transmission  lines. 

For  a  complete  treatise  on  lead  storage  batteries  see  Lyndon,  "  Storage 
Battery  Engineering." 

Edison  Alkaline  Battery. — The  Edison  storage  battery  is  considerably 
lighter,  although  not  as  efficient  as  the  lead  battery,  and  for  that 
reason  it  is  extensively  used  for  vehicle  service.  Its  weight  varies  from 
14  to  18  watt-hours  per  pound. 

The  active  materials  of  this  battery  are  oxides  of  nickel  and  iron  in 
the  positive  and  negative  grids  respectively,  the  electrolyte  being  a 
solution  of  caustic  potash  in  water  with  a  small  amount  of  lithium 
hydrate.  The  first  charging  of  a  cell  reduces  the  iron  oxide  to  metallic 
iron  while  converting  the  nickel  hydrate  to  a  very  high  oxide  of  nickel, 
black  in  color.  On  discharge,  the  metallic  iron  goes  back  to  iron 
oxide  and  the  high  nickel  oxide  goes  to  a  lower  oxide,  but  not  to  its  orig- 
inal form  of  green  nickel  hydrate,  and  every  cycle  thereafter  during 
charging  the  positive  changes  to  a  high  nickel  oxide.  Current  passing 
in  either  direction  (charge  or  discharge)  decomposes  the  potassium 
hydrate  of  the  electrolyte  and  the  oxidation  and  the  reduction  at  the 
electrodes  are  brought  about  by  the  action  of  its  elements.  An  amount 
of  potassium  hydrate  equal  to  that  decomposed  is  always  reformed  at 
one  of  the  electrodes  by  a  secondary  chemical  reaction,  and  con- 
sequently there  is  none  of  it  lost  and  its  density  remains  constant.  The 
eventual  results  of  charging,  therefore,  are  a  transference  of  oxygen  from 
the  iron  to  the  nickel  electrode  and  that  of  discharging  is  a  transference 
back  again. 

The  density  of  the  electrolyte  does  not  change  during  charge  or  dis- 
charge and  consequently  hydrometer  readings  are  unnecessary. 

To  give  the  best  output  and  efficiency,  the  manufacturer  gives  the 
normal  rate  of  charge  as  7  hours  and  discharge  as  5  hours.  The  rates 
are,  however,  optional,  and  may  with  certain  restrictions  be  based  on 
the  operating  conditions.  The  discharge  starts  at  1.44  volts  per  cell, 
falls  rapidly  for  the  first  hour,  and  slowly  for  4  l/2  hours.  The  voltage  at 
the  end  of  5  hours,  the  normal  discharge  period,  is  1.11  per  cell. 

The  charge  starts  at  1.54  volts  per  cell,  rises  rapidly  for  three- 
quarters  of  an  hour,  and  then  slowly  until  it  becomes  practically  con- 
Btant  at  the  end  of  7  hours.  The  voltage  is  then  1.81  per  cell. 

ELECTROLYSIS. 

Electrolysis  is  the  separation  of  a  chemical  compound  into  its  con- 
stituents by  an  electric  current.  Faraday  gave  the  nomenclature  of 
electrolysis.  The  compound  to  be  decomposed  is  the  electrolyte,  and 
the  process  electrolysis.  The  plates  or  poles  of  the  battery  are  elec- 
trodes. The  plate  where  the  greatest  pressure  exists  is  the  anode,  and 
the  other  pole  is  the  cathode.  The  products  of  decomposition  are  ions. 

Lord  Rayleigh  found  that  a  current  of  one  ampere  will  deposit 
0.017253  grain,  or  0.001118  gram  of  silver  per  second  on  one  of  the 
plates  of  a  silver  voltameter,  the  liquid  employed  being  a  solution  of 
silver  nitrate  containing  from  ]  5  %  to  20  %  of  the  salt.  The  weight  of 
hydrogen  similarly  set  free  by  a  current  of  one  ampere  is  0.00001038 
gram  per  second. 

Knowing  the  amount  of  hydrogen  thus  set  free,  and  the  chemical 
equivalents  of  the  constituents  of  other  substances,  we  can  calculate 
what  weight  of  their  elements  will  be  set  free  or  deposited  in  a  given 
time  by  a  given  current.  Thus,  the  current  that  liberates  1  gram  of 
hydrogen  will  liberate  8  grams  of  oxygen,  or  107.7  grams  of  silver,  the 
numbers  8  and  107.7  being  the  chemical  equivalents  for  oxygen  and 
silver  respectively. 

To  find  the  weight  of  metal  deposited  by  a  given  current  in  a  given 
time,  find  the  weight  of  hydrogen  liberated  by  the  given  current  in  the 
given  time,  and  multiply  by  the  chemical  equivalent  of  the  metal. 


ELECTROLYSIS. 


1429 


The  table  below  (from  "Practical  Electrical  Engineering")  is  calcu- 
lated upon  Lord  Rayleigh's  determination  of  the  electro-chemical 
equivalents  and  Roscoe's  atomic  weights. 

ELECTRO-CHEMICAL  EQUIVALENTS. 


Clements. 

Valency.* 

Atomic  Weight.f 

Chemical  Equiv- 
alent. 

Electro-chemical 
Equivalent  (mil- 
ligrams per 
coulomb). 

Coulombs  per 
gram. 

Grams  per 
ampere  hour. 

ELECTRO-POSITIVE. 

Hi 

1  00 

1  00 

0  010384 

96293.00 

0.03738 

Potassium  

K{ 

39  04 

39  04 

0  40539 

2467  50 

1.45950 

Nai 

22  99 

22  99 

0  23873 

4188.90 

0.85942 

Aluminum  

A13 

27  1 

9  1 

0  09449 

1058  30 

0.34018 

Mo-2 

23  94 

11  97 

0  12430 

804.03 

0.44747 

Gold  

196  2 

65  4 

0  67911 

1473  50 

2.44480 

Silver  

A  0-1 

107  66 

107  66 

1   11800 

894  41 

4.02500 

Copper  (cupric)       
(cuprous)    .  .  . 

Cu2 
Cut 

63.00 
63  00 

31.5 
63  00 

0.32709 
0  65419 

3058.60 
1525  30 

1.17700 
2.35500 

Mercury  (mercuric)  .... 
(mercurous).  . 
Tin   (stannic) 

Hg2 
Hgl 

Sn4 

199.8 
199.8 
117  8 

99.9 
199.8 
29  45 

1  .03740 
2.07470 
0  30581 

963.99 
481.99 
3270  00 

3.73450 
7.46900 
1   10090 

'     (stannous)  

Sn2 

117  8 

58  9 

0  61162 

1635.00 

2.20180 

Fe4 

55  9 

18  641 

0  19356 

5166.4 

0.69681 

"     (ferrous)  .  . 

Fe2 

55  9 

27  95 

0  29035 

3445.50 

1  .04480 

Nickel  .. 

Ni2 

58  6 

29  3 

0  30425 

3286  80 

1  .09530 

Zinc  

Zn<> 

64*9 

32  45 

0  33696 

2967.10 

1.21330 

Lead  

Pb2 

206.4 

103.2 

1.07160 

933.26 

3.85780 

ELECTRO-NEGATIVE. 
Oxygen 

On 

15  96 

7  98 

0  08286 

Chlorine    •  

cii 

35  37 

35  37 

0  36728 

Iodine 

I, 

126  53 

126  53 

1  31300 

Bromine 

Br, 

79  75 

79  7*> 

0  82812 

Nitrogen  

N3J 

14]01 

4.67 

0.04849 

*  Valency  is  the  atom-fixing  or  atom-replacing  power  of  an  element  com- 
pared with  hydrogen,  whose  valency  is  unity. 

fAtomic  weight  is  the  weight  of  one  atom  of  each  element  compared 
with  hydrogen,  whose  atomic  weight  is  unity. 

tBecquerel's  extension  of  Faraday's  law  showed  that  the  electro-chemical 
equivalent  of  an  element  is  proportional  to  its  chemical  equivalent.  The 
latter  is  equal  to  its  combining  weight,  and  not  to  atomic  weight  •*-  valency, 
as  denned  by  Thompson,  Hospitalier,  and  others  who  have  copied  their 
tables.  For  example,  the  ferric  salt  is  an  exception  to  Thompson's  rule, 
as  are  sesqui-salts  in  general. 

Thus:  Weight  of  silver  deposited  in  10  seconds  by  a  current  of  10  amperes 
=  weight  of  hvdrogen  liberated  per  second  X  number  of  seconds  X  current 
strength  X  107.7  =  0.00001038X10X10X107.7  =  0.1 1178  gram. 

Weight  of  copper  deposited  in  1  hour  by  a  current  of  10  amperes  = 

0.00001038  X  3600  X10X  31.5  =  11.77  grams. 

Since  1  ampere  per  second  liberates  0.00001038  gram  of  hydrogen, 
strength  of  current  in  amperes 

=  weight  In  grams  of  H  liberated  per  second  •*•  0.00001038 

weight  of  element  liberated  per  second 
~~  0.00001038  Xchemical  equivalent  of  element 


1430  ELECTRICAL   ENGINEERING. 

THE  MAGNETIC  CIRCUIT. 

For  units  of  the  magnetic  circuit,  see  page  1398. 

Lines  and  Loops  of  Force.  —  It  is  conventionally  assumed  that  the 
attractions  and  repulsions  shown  by  the  action  of  a  magnet  or  a  con- 
ductor upon  iron  filings  are  due  to  "  lines  of  force  "  surrounding  the 
magnet  or  conductor.  The  "  number  of  lines  "  indicates  the  magnitude 
of  the  forces  acting.  As  the  iron  filings  arrange  themselves  in  concentric. 
circles,  we  may  assume  that  the  forces  may  be  represented  by  closed 
curves  or  *'  loops  of  force."  The  following  assumptions  are  made  con- 
cerning the  loops  of  force  in  a  conductive  circuit: 

1.  That  the  lines  or  loops  of  force  in  the  conductor  are  parallel  to  the 
axis  of  the  conductor. 

2.  That  the  loops  of  force  external  to  the  conductor  are  proportonal  in 
number  to  the  current  in  the  conductor,  that  is,  a  definite  current  gener- 
ates a  definite  number  of  loops  of  force.     These  may  be  stated  as  the 
strength  of  field  in  proportion  to  the  current. 

3.  That  the  radii  of  the  loops  of  force  are  at  right  angles  to  the  axis  oi 
the  conductor. 

The  magnetic  force  proceeding  from  a  point  is  equal  at  all  points  on  the 
surface  of  an  imaginary  sphere  described  by  a  given  radius  about  that 
point.  A  sphere  of  radius  1  cm.  has  a  surface  of  4  it  square  centimeters 
If  <£=  total  flux,  expressed  as  the  number  of  lines  of  force  emanating  from 
a  magnetic  pole  having  a  strength  M, 


. 

Magnetic  moment  of  a  magnet  =  product  of  strength  of  pole  M  and  its 
length,  or  distance  between  its  poles  L.  Magnetic  moment  =<£L-*-  4?r. 

If  B  =  number  of  lines  flowing  through  each  square  centimeter  of  cross- 
section  of  a  bar-magnet,  or  the  "  specific  induction,"  and  A  =  cross-section 
Magnetic  Moment  =  LAB-^47t. 

If  the  bar-magnet  be  suspended  in  a  magnetic  field  of  density  H  and  so 
placed  that  the  lines  of  the  field  are  all  horizontal  and  at  right  angles  to  the 
axis  of  the  bar,  the  north  pole  will  be  pulled  forward,  that  is,  in  the  direc- 
tion in  which  the  lines  flow,  and  the  south  pole  will  be  pulled  in  the 
opposite  direction,-  the  two  forces  producing  a  torsional  moment  or  torque, 
Torque  =  JfLH  =Z/ABH  -5-  4rc,  in  dyne-centimeters. 

Magnetic  attraction  or  repulsion  emanating  from  a  point  varies  inversely 
as  the  square  of  the  distance  from  that  point.  The  law  of  inverse  squares, 
however,  is  not  true  when  the  magnetism  proceeds  from  a  surface  of  appre- 
ciable extent,  and  the  distances  are  small,  as  in  dynamo-electric  machines 
and  ordinary  electromagnets. 

The  Magnetic  Circuit.  —  In  the  electric  circuit 

Current  =PK]V;-F-    .  or  7-f  ;  Amperes  =  ^ 
Resistance  '  R  '  ohms 

Similarly,  in  the  magnetic  circuit 

™  Magnetomotive  Force  F  Gilberts 

Flux=  -       Reluctance  --  •  OT  *~  R  '      Maxwells-  ^^^- 
Reluctance  is  the  reciprocal  of  permeance,  and  permeance  is  equal  to 
permeability  X  path  area  -5-  path  length  (metric  measure);  hence 

<b=  Ffj.a-r-  I. 

One  ampere-turn  produces  1.257  gilberts  of  magnetomotive  force  and 
one  inch  equals  2.54  centimeters;  hence,  in  inch  measure, 

<£=  (1.257^)  /»  6.45  a  -f-  2.541=  3.192tiaAt+  I. 

The  ampere-turns  required  to  produce  a  given  magnetic  flux  in  a  given 
path  will  be 

At=*  #-5-  3.192  /to  =  0.3133  #-5-/ta. 

Since  magnetic  flux-?-  area  of  path  =  magnetic  density,  the  ampere-turn 
required  to  produce  a  density  B,  in  lines  of  force  per  square  inch  of  area 
of  path,  will  be 

At=  0.3133  Bl  -i-  v. 

This  formular  is  used  in  practical  work,  as  the  magnetic  density  must 
be  predetermined  in  order  to  ascertain  the  permeability  of  the  material 
under  its  working  conditions.  When  a  magnetic  circuit  includes  several 
qualities  of  material,  such  as  wrought  iron,  cast  iron,  and  air,  it  is  most 
direct  to  work  in  terms  of  ampere-turns  per  unit  length  of  path.  The 


THE  MAGNETIC  CIRCUIT. 


1431 


ampere-turns  for  each  material  are  determined  separately,  and  the  wind- 
ing is  designed  to  produce  the  sum  of  all  the  ampere-turns.  The  following 
table  gives  the  average  results  from  a  number  of  tests  made  by  Dr.  Samuel 
Sheldon: 

VALUES  OP  B  AND  H 


05  Q 

e 

Cast  Iron. 

Cast  Steel. 

Wrought  Iron. 

Sheet  Metal. 

H 

!Ai 

l-Sj 

§ 

S&. 

03 

0) 

g.lc. 

i 

x  o,  . 

| 

IN 

1    0> 

x  a  . 

||| 

00  6  1 

jtJ 

mll 

it 

"4* 

&  a;  g 

10 
20 

7.95 
15.90 

20.2 
40.4 

4.3 

5.7 

27.7 
36.8 

11.5 
13.8 

74.2 
89.0 

13.0 
14.7 

83.8 
94.8 

14.3 
15.6 

92.2 
100.7 

30 

23.85 

60.6 

6.5 

41.9 

14.9 

96.1 

15.3 

98.6 

16.2 

104.5 

40 

31.80 

80.8 

7.1 

45.8 

15.5 

100.0 

15.7 

101.2 

16.6 

107.1 

50 

39.75 

101.0 

7.6 

49.0 

16.0 

103.2 

16.0 

103.2 

16.9 

109.0 

60 

47.70 

121.2 

8.0 

51.6 

16.5 

106.5 

16.3 

105.2 

17.3 

111.6 

70 

55,65 

141.4 

8.4 

59.2 

16.9 

109.0 

16.5 

106.5 

17.5 

112.9 

80 

63.65 

161.6 

8.7 

56.1 

17.2 

111.0 

16.7 

107.8 

17.7 

114.1 

90 

71.60 

181.8 

9.0 

58.0 

17.4 

112.2 

16.9 

109.0 

18.0 

116.1 

100 

79.50 

202.0 

9.4 

60.6 

17.7 

114.1 

17.2 

110.9 

18.2 

117.3 

150 

119.25 

303.0 

10.6 

68.3 

18.5 

119.2 

18.0 

116.1 

19.0 

122.7 

200 

159.0 

404.0 

11.7 

75.5 

19.2 

123.9 

18.7 

120.8 

1.96 

126.5 

250 

198.8 

505.0 

12.4 

80.0 

19.7 

127.1 

19.2 

123.9 

20.2 

130.2 

300 

238.5 

606.0 

13.2 

85.1 

20.1 

129.6 

19.7 

127.1 

20.7 

133.5 

H  =  1.257  ampere-turns  per  cm.  =  0.495  ampere-turns  per  inch. 

EXAMPLE. —  A  magnetic  circuit  consists  of  12  ins.  of  cast  steel  of  8sq. 
ins.  cross-section;  4  ins.  of  cast  iron  of  22  sq.  ins.  cross-section;  3  ins.  of 
sheet  iron  of  8  sq.  ins.  cross-section;  and  two  air-g?pseach  Vie  in.  long  and 
of  12  sq.  ins.  area.  Required,  the  ampere-turns  to  produce  a  flux  of 
768,000  maxwells,  which  is  to  be  uniform  throughout  the  magnetic  circuit.  - 

The  flux  density  in  the  steel  is  768,000-^8  =  96,000  maxwells;  the  am- 
pere-turns per  inch  of  length,  according  to  Sheldon's  table,  are  60.6,  so 
that  the  12  in.  of  steel  will  require  727.2  ampere-turns. 

The  density  in  the  cast  iron  is  768,000-^-22  =  34,900;  the  ampere-turn, 
=  4X  40=160. 

The  density  in  the  sheet  iron  =  768,000  •*-  8  =  96,000;  ampere-turns  per 
inch  =  30;  total  ampere-turns  for  sheet  iron  =  90. 

The  air-gap  density  is  768,000  -*•  12  =  64,000;  ampere-turns  per  in.  = 
0.3133B;  ampere-turns  required  for  air-gap  =  0.3133  X  64,000-^-8=2506.4. 

The  entire  circuit  will  require  727.2+  160+  90  +  2506.4  =  3483.6  am- 
pere-turns, assuming  uniform  flux  throughout. 

In  practice  there  is  considerable  "leakage"  of  magnetic  lines  of  force; 
that  is,  many  of  the  lines  stray  away  from  the  useful  path,  there  being  no 
material  opaque  to  magnetism  and  therefore  no  means  of  restricting  it  to 
a  given  path.  The  amount  of  leakage  is  proportional  to  the  permeance 
of  the  leakage  paths  available  between  two  points  in  a  magnetic  circuit 
which  are  at  different  magnetic  potentials,  such  as  opposite  ends  of  a 
magnet  coil.  It  is  seldom  practicable  to  predetermine  with  any  approach 
to  accuracy  the  magnetic  leakage  that  will  occur  under  given  conditions 
unless  one  has  profuse  data  obtained  experimentally  under  similar  con- 
ditions. In  dynamo-electric  machines  the  leakage  coefficient  varies  from 
1 .3  to  2. 

Tractive  or  Lifting  Force  of  a  Magnet.  —  The  lifting  power  or 
"  pull  "  exerted  by  an  electro-magnet  upon  an  armature  in  actual  contact 
with  its  pole-faces  is  given  by  the  formula 

Lbs.=  B2<z-r-  72, 134,000, 

a  being  the  area  of  contact  in  square  inches  and  B  the  magnetic  density 
over  this  area.  If  the  armature  is  very  close  to  the  pole-faces  this  for- 
mula also  applies  with  sufficient  accuracy  for  all  practical  puposes,  but 
a  considerable  air-gap  renders  it  inapplicable. 

The  design  of  solenoids  for  the  coif-and-plunger  type  of  electro-magnets 


1432 


ELECTRICAL  ENGINEERING. 


is  described  by  C.  R.  Underbill  in  his  book,  "  Solenoids,  Electro-Magnets; 
and  Electro-Magnetic  Windings." 

Various  forms  of  magnetic  chucks  are  illustrated  and  described  by 
O.  S.  Walker,  hi  Am.  Mach.,  Feb.  11,  1909. 

For  magnets  used  in  hoisting,  see  page  1193. 

Determining  the  Polarity  of  Electro  -  Magnets. — If  a  wire  ifi 
wound  around  a  magnet  in  a  right-handed  helix,  the  end  at  which  the 
current  flows  into  the  helix  is  the  south  pole.  If  a  wire  is  wound  around 
an  ordinary  wood-screw,  and  the  current  flows  around  the  helix  in  the 
direction  from  the  head  of  the  screw  to  the  point,  the  head  of  the  screw 
is  the  south  pole.  If  a  magnet  is  held  so  that  the  south  pole  is  opposite 
the  eye  of  the  observer,  the  wire  being  wound  a  a  right-handed  helix 
around  it,  the  current  flows  in  a  right-handed  direction,  with  the  hands 
of  a  clock. 

Determining  the  Direction  of  a  Current. — Place  a  wire  carrying 
a  current  above  and  parallel  to  a  pivoted  magnetic  needle.  If  the  cur- 
rent be  flowing  along  the  wire  from  N.  to  S.,  it  will  cause  the  N.-seeking 
pole  to  turn  to  the  eastward;  if  it  be  flowing  from  S.  to  N.,  the  pole  will 
turn  to  the  westward.  If  the  wire  be  below  the  needle,  these  motions 
will  be  reversed. 

Maxwell's  rule.  The  direction  of  the  current  and  that  of  the  resisting 
magnetic  force  are  related  to  each  other  as  are  the  rotation  and  the  for- 
ward travel  of  an  ordinary  (right-handed)  corkscrew. 

DYNAMO-ELECTRIC   MACHINES. 

A  dynamo-electric  machine  is  a  machine  for  converting  mechanical 
energy  into  electrical  energy,  or  vice  versa.  It  may  be  either  a  direct 
current  or  an  alternating  current  machine. 

Rating.  —  The  A.  I.E.  E.  Standardization  Rules  (1914)  recommend 
that  in  the  case  of  Direct  Current  Generators,  the  rating  shall  be  ex- 
pressed in  Kilowatts  (Kw.)  available  at  the  terminals. 

In  the  case  of  Alternators  and  Transformers,  the  rating  shall  be 
expressed  in  kilovolt-amperes  (Kv.-a.)  available  at  the  terminals,  at  a 
specified  power  factor.  The  corresponding  kilowatts  should  also 
preferably  be  stated. 

In  the  case  of  Motors,  it  is  recommended  that  the  rating  shall  be 
expressed  in  kilowatts  (Kw.)  available  at  the  shaft.  Since  the  input  of 
machinery  of  this  class  is  measured  in  electrical  units  and  since  the  out- 
put has  a  definite  relation  to  the  input,  it  is  logical  to  measure  the 
delivered  power  in  the  same  units  as  are  employed  for  the  receiving 
power.  However,  on  account  of  the  prevailing  practice  of  expressing 
mechanical  output  in  horse-power,  it  is  recommended  that  for  machin- 
ery of  this  class  the  rating  should,  for  the  present,  be  expressed  both  in 
kilowatts  and  in  horse-power;  as  follows: 


approx.  equiv.  h.p.- 


The  horse-power  rating  of  a  motor  may,  for  practical  purposes,  be 
taken  as  4/3  of  the  kilowatt  rating. 

There  are  various  kinds  of  ratings,  such  as: 

Continuous  Rating. — A  machine  rated  for  continuous  service  shall  be 
able  to  operate  continuously  at  its  rated  output,  without  exceeding  any 
of  the  limitations  specified. 

Short-Time  Rating. — A  machine  rated  for  short-time  service  (i.e., 
service  including  runs  alternating  with  stoppages  of  sufficient  duration 
to  ensure  substantial  cooling)  shall  be  able  to  operate  at  its  rated  out- 
put during  a  limited  period,  to  be  specified  in  each  case,  without  exceed- 
ing any  of  the  limitations  specified. 

Nominal  Ratings. — For  railway  motors  and  railway  sub-station 
machinery,  certain  nominal  ratings  are  employed. 

Duty-Cycle  Operation. — Many  machines  are  operated  on  a  cycle  of 
duty  which  repeats  itself  with  more  or  less  regularity.  For  purposes  of 
rating,  either  a  continuous  or  a  "short-time"  " equivalent  load "  may  be 
selected  which  shall  simulate  as  nearly  as  possible  the  thermal  condi- 
tions of  the  actual  duty  cycle. 

Standard  durations  of  equivalent  tests  shall  be  for  machines  oper- 
ating under  specified  duty-cycles:  5  min.,  10  min.,  30  min.,  60  min.. 


DYNAMO-ELECTRIC  MACHINES.  1433 

120  min.,  and  continuous.  Of  these  the  first  5  are  short-time  ratings 
selected  as  being  thermally  equivalent  to  the  specified  duty  cycle. 
When,  for  example,  a  short-time  rating  of  10  minutes'  duration  is 
adopted,  and  the  thermally  equivalent  load  is  25  kw.  for  that  period, 
then  such  a  machine  shall  be  stated  to  have  a  10-minute  rating  of 
25  kw.  In  every  case  the  equivalent  short-time  test  shall  commence 
only  when  the  windings  and  other  parts  of  the  machine  are  within  5°  C. 
of  the  ambient  temperature  at  the  time  of  starting  the  test.  In  the 
absence  of  any  specification  as  to  the  kind  of  rating,  the  continu- 
ous rating  shall  be  understood. 

Temperature  Limitations  of  the  Capacity  of  Electrical  Machinery. — 
The  capacity,  so  far  as  relates  to  temperature,  is  usually  hmi ted  by  the 
maximum  temperature  at  which  the  materials  in  the  machine,  espe- 
cially those  employed  for  insulation,  may  be  operated  for  long  periods 
without  deterioration.  When  the  safe  limits  are  exceeded,  deterioration 
is  rapid.  The  insulating  material  becomes  permanently  damaged  by 
excessive  temperature,  the  damage  increasing  with  the  length  of  time 
that  the  excessive  temperature  is  maintained,  and  with  the  amount  of 
excess  temperature,  until  finally  the  insulation  breaks  down. 

Ambient  Temperature  of  Reference  for  Air. — The  standard  ambient 
temperature  of  reference,  when  the  cooling  medium  is  air,  shall  be  40°  C. 
(104°  P.). 

The  permissible  rises  in  temperature  given  in  column  2  of  the  table 
on  p.  1434  have  been  calculated  on  the  basis  of  the  standard  ambient 
temperature  of  reference,  by  substracting  40°  C.  from  the  highest  tem- 
peratures permissible,  which  are  given  in  column  1  of  the  same  table. 

Altitude. — Increased  altitude  has  the  effect  of  increasing  the  temper- 
ature rise  of  some  types  of  machinery.  In  the  absence  of  information  in 
regard  to  the  height  above  sea  level  at  winch  the  machine  is  intended  to 
work  in  ordinary  service,  this  height  is  assumed  not  to  exceed  1000 
meters  (3300  feet).  For  machinery  operating  at  an  altitude  of  1000 
meters  or  less,  a  test  at  any  altitude  less  than  1000  meters  is  satisfactory, 
and  no  correction  shall  be  apDlied  to  the  observed  temperatures. 
Machines  intended  for  operation  at  higher  altitudes  shall  be  regarded  as 
special.  When  a  machine  is  intended  for  service  at  altitudes  above 
1000  meters  (3300  feet)  the  permissible  temperature  rise  at  sea  level, 
until  more  nearly  accurate  information  is  available,  shall  be  reduced  by 
1  per  cent  for  each  100  meters  (130  ft.)  by  which  the  altitude  exceeds 
1000  meters.  Water-cooled  oil  transformers  are  exempt  from  this 
reduction. 

Ambient  Temperature  of  Reference  for  Water-Cooled  Machinery. — For 
water-cooled  machinery,  the  standard  temperature  of  reference  for  in- 
coming cooling  water  shall  be  25°  C.  (77°  F.),  measured  at  the  intake  of 
the  machine. 

Corrections  for  the  Deviation  of  the  Ambient  Temperature,  at  the  time 
of  test,  from  the  reference  value  of  40°  C.  —  The  effect  on  the  temperature 
rise  of  the  precise  value  of  the  ambient  temperature  at  the  time  of  test 
is  small,  obscure,  and  of  doubtful  direction.  No  correction  shall  be 
made  for  ambient  temperature  deviations  from  the  standard  value  of 
40°  C.  It  is  desirable,  however,  that  tests  should  be  conducted  at 
ambient  temperatures  not  lower  than  25°  C.  Exception  to  this  rule  is 
made  in  the  case  of  air-blast  transformers,  in  which,  if  the  ingoing  air 
temperature  during  the  test  differs  from  40°  C.,  a  correction  on  account 
of  difference  in  resistance  and  difference  in  convection  shall  be  made  by 
changing  the  "observable"  temperature  rise  of  the  windings  by  0.5  per 
cent  for  each  degree  centigrade.  Thus  with  a  room  temperature  of 
30°  C.  the  "observable"  rise  of  temperature  shall  be  increased  by  5 
per  cent,  and  with  a  room  temperature  of  15°  C.  the  "observable"  rise 
of  temperature  shall  be  increased  by  12.5  per  cent. 

The  actual  temperatures  attained  in  the  different  parts  of  a  machine, 
and  not  the  rises  in  temperature,  affect  the  life  of  the  insulation  of  the 
machine.  The  temperatures  in  the  different  parts  of  a  machine  which  it 
is  desired  to  ascertain,  are  the  maximum  temperatures  reached  in  those 
parts. 

As  it  is  usually  impossible  to.  determine  the  maximum  temperature 
attained  in  insulated  windings,  it  is  convenient  to  apply  a  correction  to 
the  observable  temperature,  to  approximate  the  difference  between 
the  actual  maximum  temperature  and  the  observable  temperature  by 


1434  ELECTRICAL  ENGINEERING. 

the  method  used.  This  correction  or  margin  of  security  is  provided  to 
cover  the  errors  due  to  fallibility  in  the  location  of  the  measuring 
devices,  as  well  as  inherent  inaccuracies  in  measurement  and  methods. 

Methods  of  Determining  the  Temperature  of  Different  Parts  of  a 
Machine. — Three  methods  will  be  considered.  One  or  other  of  these 
methods  will  usually  be  appropriate  for  commercial  measurements  on 
any  particular  type  of  machine. 

No.  1.  Thermometer  Method. — This  method  consists  in  the  deter- 
mination of  the  temperature  by  mercury  or  alcohol  thermometers,  by 
resistance  thermometers,  or  by  thermo-couples,  applied  to  the  hottest 
accessible  part  of  the  completed  machine,  as  distinguished  from  the 
thermo-couples  or  resistance  coils  imbedded  in  the  machine  as  described 
under  Method  No.  3.  When  Method  No.  1  is  used,  the  hottest-spot 
temperature  for  windings  shall  be  estimated  by  adding  a  hottest-spot 
correction  of  15°  C.  to  the  highest  temperature  observed,  in  order  to 
allow  for  the  impossibility  of  locating  any  of  the  thermometers  at  the 
hottest  spot. 

Exception.  In  cases  where  the  thermometer  is  applied  directly  to 
the  surfaces  of  a  bare  winding,  such  as  an  edgewise  strip  conductor,  or  a 
cast  copper  winding,  a  hottest-spot  correction  of  5°  C.  instead  of  15°  C. 
shall  be  made.  For  bare  metallic  surfaces  not  forming  part  of  a  winding, 
no  correction  is  to  be  applied. 

No.  2.  Resistance  Method.  This  method  consists  in  the  measurement 
of  the  temperature  of  windings  by  their  increase  in  resistance,  corrected 
to  the  instant  of  shut-down  when  necessary.  In  the  application  of 
this  method  thermometer  measurements  must  also  be  made  whenever 
practicable  without  disassembling  the  machine,  in  order  to  increase 
the  probability  of  revealing  the  highest  observable  temperature. 
Whichever  method  yields  the  higher  temperature,  that  temperature 
shall  be  taken  as  the  "highest  observable"  temperature  and  a  hottest- 
spot  correction  of  10°  C.  added  thereto. 

In  the  case  of  resistance  measurements,  the  temperature  coefficient 
of  copper  shall  be  deduced  from  the  formula  I/ (234. 5  -f  t).  Thus,  at 
an  initial  temperature  t  =  40°  C.,  the  temperature  coefficient  or  in- 
crease in  resistance  per  degree  centigrade  rise  is  I/ (274. 5)  =  0.00364. 

No,  3.  Imbedded  Temperature-Detector  Method.  Thermo-couples  or 
resistance  coils,  located  as  nearly  as  possible  at  the  estimated  hottest 
spot.  This  method  is  only  to  be  used  with  coils  placed  in  slots. 

Temperature  Limits. — In  the  following  table  column  1  gives  the  per- 
missible limits  for  the  hottest-spot  temperatures  of  insulations,  and 
column  2  the  highest  permissible  temperature  rise  of  the  hottest  spot 
above  40°  0.  permitted  under  rated-load  conditions,  for  the  purpose  of 
fixing  the  Institute  rating.  The  rise  of  temperature  observed  must  never 
exceed  the  limits  in  column  2  of  the  table.  The  highest  temperatures 
attained  in  any  machine  corresponding  to  the  output  for  which  it  is 
rated  must  not  exceed  the  values  indicated  in  column  1  of  the  table 
and  the  clauses  following: 

Hottest-Spot  Temperatures    and   Corresponding   Permissible   Tem- 
perature Rises. 


Class. 

Insulation. 

Col.  1. 

Col.  2. 

A  1 
A2 
B 

C 

Cotton,  silk,  paper,  and  other  fibrous  materials,  not  so 
treated  as  to  increase  the  thermal  limit 

95°  C. 
105°  C. 

125°  C. 
Nolim 
fie 

55°  C. 
65°  C. 

85°  C. 
t  speci- 
d. 

Similar  to  A  1,  but  treated  or  impregnated  and  in- 
cluding enameled  wire  . 

Mica,  asbestos,  or  other  material  capable  ryf  resisting 
high  temperatures,  in  which  any  Class  A  material 
or  binder,  if  used,  is  for  structural  purposes  only, 
and  may  be  destroyed  without  impairing  the  insu- 
lating or  mechanical  qualities  • 

Fireproof  and  refractory  materials  

DYNAMO-ELECTRIC  MACHINES. 


1435 


Summary  of  (he  Temperature  Conditions  under  the  Three  Methods 
of  Measurement  for  Insulations  of  Classes  A19  A2,  and  B. 


& 

5 

AI 

Hottest 
Spot 
Temp. 

Thermometer 
only. 

Resistance.* 

Imbedded  Thermo-couples  or  Resistance  Coils. 

Double-layer 
Windings. 
All  voltages. 

Single-layer 
Windings. 
5000  volts  or 
less. 

Single-layer    Windings    above    5000 
volts. 

a     b 

a      6 

a    b 

a    b 

Hottest 
Spot 
Correction. 

Limiting 
Observable 
Temperat'r 

Limiting 
Observable 
Temp.  Rise 
above  40°. 

95° 

15    80 

10    85 

5     90 

10  85 

10+(E-5)f 

85  -  (E-5) 

45  -  (E-5) 

A2 

105° 

15    90 

10    95 

5   100 

10  95 

10-KE-5) 

95  -  (E-5) 

55  -  (E-5) 

B 

125° 

15  110 

10  115 

5   120 

10  115 

10+(E-5) 

115-  (E-5) 

75  -  (E-5) 

*  With  thermometer  check  when  practicable. 

a  Hottest-spot  correction.         b  Limiting  observable  temperature. 
The  limit  of  the  observable  temperature  rise  above  40°  always  =  (b  —40°). 

t  In  this  formula  E  represents  the  rated  pressure  between  terminals 
in  kilo  volts.  Thus  for  a  three-phase  machine  with  single-layer  winding 
of  11  kilo  volts  between  terminals,  the  hottest  spot  correction  to  be  added 
to  the  maximum  observable  temperature  will  be  16°  C. 

Special  Cases  of  Temperature  Limits.  —  Tem.perature  of  Oil. 
The  oil  in  which  apparatus  is  immersed  shall  in  no  part  have  an  observ- 
able temperature  in  excess  of  90°  C. 

Water-cooled  Transformers.  The  hottest-spot  temperature  shall  not 
exceed  85°  C. 

Commutators.  The  observable  temperature  shall  in  no  case  be  per- 
mitted to  exceed  the  values  given  in  the  table  for  the  insulation  em- 
ployed, either  in  the  commutator  or  in  any  insulation  whose  temper- 
ature would  be  affected  by  the  heat  of  the  commutator. 

For  commutators  so  constructed  that  no  difficulties  from  expansion 
can  occur,  the  following  temperature  limits  are  suggested: 

Current  per  Brush  Arm.  Maximum  Permissible  Temp. 

200  amperes  or  less.  130°  C. 

200  to  900  amperes.  130°  C.  less  5  deg.   for  each  100 

amperes  increase  above  200. 
900  amperes  and  over.  95°  C. 

Moving  Force  of  a  Dynamo-electric  Machine.  —  A  wire  through 
which  a  current  passes  has,  when  placed  in  a  magnetic  field,  a  tendency 
to  move  perpendicular  t9  itself  and  at  right  angles  to  the  lines  of  the 
field.  The  force  producing  this  tendency  is  P  =  IBI  dynes,  in  which 
1= length  of  the  wire,  /  =  the  current  in  C.G.S.  units,  and  £  =  the  induc- 
tion, or  flux  density,  in  the  field  in  gausses  or  lines  per  square  centimeter. 

If  the  current  /  is  taken  in  amperes,  P  =  lBI-irlQ  =  lBfX  10~*. 

If  Pfr  is  taken  in  kilograms, 

Pk  =  ZB/ -5-9,810,000  =  10.1937  IBI X  1CT8  kilograms. 

EXAMPLE. — The  mean  strength  of  field,  B,  of  a  dynamo  is  5000  C.G.S. 
lines-  a  current  of  100  amperes  flows  through  a  wire;  the  force  acts  upon 
lOcentimetersof  the  wire  =  10.1937  X 10  X 100  X5000  X  10~8  =  0.5097  kilo- 
grams. 

Torque  of  an  Armature.  —  The  torque  of  an  armature  is  the  moment 
tending  to  turn  it.  In  a  generator  it  is  the  moment  which  must  be 
applied  to  the  armature  to  turn  it  in  order  to  produce  current.  In  a  motor 
it  is  the  turning  moment;  which  the  armature  gives  to  the  pulley. 


1436  ELECTRICAL  ENGINEERING. 

Let  /  ==  current  in  the  armature  in  amperes,  E—  the  electromotive  fores 
in  volts,  T  =  the  torque  in  pound-feet,  <£=  the  flux  through  the  armature 
in  maxwells,  N  =  the  number  of  conductors  around  the  armature,  and  n  = 
the  number  of  revolutions  per  second.  Then 

Watts  «  IE  =  2nnTX  1.356.* 

In  any  machine  if  the  flux  be  constant,  E  is  directly  proportional  to  the 
speed  and  =  <j>Nn  •*•  108;  whence 

^/-MO8  = 
AN1 
=  = 


108X2*X1.356      8.52  X  10* 

Let  I  —  length  of  armature  in  inches,  d  =  diameter  of  armature  in  inches, 
B  =  flux  density  in  maxwells  per  square  inch,  and  let  m  =  the  ratio  of  the 
conductors  under  the  influence  of  the  pole-pieces  to  the  whole  number  of 
conductors  on  the  armature.  Then 

<£  •=  iwe/X  IX  BXm. 

These  formulae  apply  to  both  generators  and  motors.  They  show  that 
torque  is  independent  of  the  speed  and  varies  directly  with  the  current  and 
the  flux.  The  total  peripheral  force  is  obtained  by  dividing  the  torque  by 
the  radius  (in  feet)  of  the  armature,  and  the  drag  on  each  conductor  is 
obtained  by  dividing  the  total  peripheral  force  by  the  number  of  conductors 
under  the  influence  of  the  pole-pieces  at  one  time. 

EXAMPLE.  —  Given  an  armature  of  length  I  =  20  inches,  diameter  d  =  12 
inches,  number  of  conductors  N  =  120,  of  which  80  are  under  the  influence 
of  the  pole-pieces  at  one  time;  let  the  flux  density  B  =  30,000  maxwells 
per  sq.  in.  and  the  current  /  =  400  amperes. 

0  =  i|£  X  20  X  30,000  X  ~~  =  7,540,000. 

7,540,000  X  120  X  400 
T=      8.52X100,000,000      =  42 
Total  peripheral  force  =  424.8  -J-  0.5  =  849.6  Ibs. 
Drag  per  conductor  =  849.6  •*-  120  =  7.08  Ibs. 

The  work  done  in  one  revolution  =  torque  X  circumference  of  a  circle 
of  1  foot  radius  =  424.8  X  6.28  =  2670  foot-pounds. 

Let  the  revolutions  per  minute  equal  500,  then  the  horse-power 
_2670X500 

33000 

Torque,  Horse-pow0*  and  Revolutions.  —  T—  torque  in  pound-feet, 
H.P.  =  T  X  Rpm.  >fe72832  t  33,000  =  IE  -=-  745.7.  Whence  Torque 
=  7.  0432  El  -r-  Rpm.xmJ?.  times  the  watts  4-  the  revs,  per  min.  nearly. 

Electromotive  Force  of  the  Armature  Circuit.  —  From  the  horse- 
power, calculated  as  above,  together  with  the  amperes,  we  can  obtain 
theE.M.F.,  IE=  H.P.  X  745.7,  whence  E  M  F.or£=  H.P.  X  745.  7^-  7. 

If  H.P.,  as  above,  =  40.5,  and  1=  400,  E  =40'5^45'7  =  75.5  volts. 

The  E.M.F.  may  also  be  calculated  by  the  following  formulae: 
/=  Total  current  through  armature; 
ea=  E.M.F.  in  armature  in  volts; 

Af=  Number  of  active  conductors  counted  all  around  armature; 
p  =  Number  of  pairs  of  poles  (p  =  1  in  a  two-pole  machine); 
n=  Speed  in  revolutions  per  minute; 
tf»=  Total  flux  in  maxwells. 

\  ef,=4>N  ~  10~8  for  two-pole  machines. 
Electromotive       1 

force:  |       _  p$N  n^  for   multipolar   machines  with  series- 

[ea~    108  60       wound  armature 

Strength  of  the  Magnetic  Field.  —  Let  /  =  current  in  amperes.  N  =* 
number  of  turns  in  the  coil.  A  —  area  of  the  cross-section  of  the  core  in 

*  1  ft.-lb.  per  second  =  1.356  watts. 


DIRECT-CURRENT  GENERATORS.  1437 

square  centimeters,  1=  length  of  core  In  centimeters,  p  the  permeability  of 
the  core,  and  #=  flux  in  maxwells.    Then 

Magnetomotive  Force  ^  1.257  N  1  t 
*)a*  Reluctance  *  ' 


In  a  dynamo-electric  machine  the  reluctance  will  be  made  up  of  three 
separate  quantities,  viz.:  that  of  the  field  magnet  cores,  that  of  the  air 
spaces  between  the  field  magnet  pole-pieces  and  the  armature,  and  that 
of  the  armature.  The  total  reluctance  is  the  sum  of  the  three.  Let  Li, 
L2,  L2  be  the  length  of  the  path  of  magnetic  lines  in  the  field  magnet 
cores,*  in  the  air-gaps,  and  in  the  armature  respectively;  and  let  AI, 
A2,  Az  be  the  areas  of  the  cross-sections  perpendicular  to  the  path  of  the 
magnetic  lines  in  the  field  magnet  cores,  the  air-gaps,  and  the  armature 
respectively.  Let  the  permeability  of  the  field  magnet  cores  be  /n,  and  of 
the  armature  jus.  The  permeability  of  the  air-gaps  is  taken  as  unity.  Then 
the  total  reluctance  of  the  machine  will  be 

.Li     t  L2  +   Lz  9 
AIHI      AZ     ASUS 

1.257  NT 
UX'^~ 


The  ampere-turns  necessary  to  create  a  given  flux  in  a  machine  may  be 
found  by  the  formula, 


[(Li  -?•  Atf*i)  +  (L2-^2)  +  (£3  -s-  Aw*)] 
1.257 

But  the  total  flux  generated  by  the  field  coils  is  not  available  to  produce 
current  in  the  armature.  There  is  a  leakage  between  the  field  magnets, 
and  this  must  be  allowed  for  in  calculations.  The  leakage  coefficient 
varies  from  1.3  to  2  in  different  machines.  The  meaning  of  the  coefficient 
is  that  if  a  flux  of  say  100  maxwells  per  square  cm.  are  desired  in  the  field 
coils,  it  will  be  necessary  to  provide  ampere  turns  for  1.3  X  100  =  130 
maxwells,  if  the  leakage  coefficient  be  1.3. 

Another  method  of  calculating  the  ampere-turns  necessary  to  produce  a 
given  flux  is  to  calculate  the  magnetomotive  force  required  in  each  portion 
of  the  machine,  separately,  introducing  the  leakage  coefficient  in  the  calcu- 
lation for  the  field  magnets,  and  dividing  the  sum  of  the  magnetomotive 
forces  by  1.257. 

In  the  ordinary  type  of  multipolar  machine  there  are  as  many  magnetic 
circuits  as  there  are  poles.  Each  winding  energizes  part  of  two  circuits. 
The  calculation  is  made  in  the  same  manner  as  for  a  single  magnetic  circuit. 

DIRECT-CURRENT   GENERATORS. 

Direct-current  generators  may  be  separately  excited,  in  which  case 
the  field  magnets  are  excited  or  magnetized  from  some  external  source, 
as,  for  instance,  a  storage  battery  or  another  continuous-current  dynamo. 
Such  generators  are  used  to  some  extent  in  connection  with  regulating 
sets,  but  as  a  rule  almost  all  direct-current  generators  are  self-excited,  » 
in  which  case  the  magnetizing  current  for  the  field-coils  is  furnished  by 
the  dynamo  Itself. 

Direct-current  generators  (as  well  as  motors)  may  be  classified  accord- 
ing to  the  manner  of  the  field-  winding  into  : 

1.  Series-wound  Dynamo.  —  The  field-  winding  and  the  external  circuit 
are  connected  in  series  with  the  armature-  winding,  so  that  the  entire 
armature  current  must  pass  through  the  field-coils. 

Since  in  a  series-wound  dynamo  the  armature-coils,  the  field,  and  the 
external  circuit  are  in  series,  any  increase  in  the  resistance  of  the  exter- 
nal circuit  will  decrease  the  electro-motive  force  from  the  decrease  in  the 
magnetizing  currents.  A  decrease  in  the  resistance  of  the  external  cir- 

*  The  length  of  the  path  in  the  field-magnet  cores  LI  includes  that 
portion  of  the  path  which  lies  in  the  piece  joining  the  cores  of  the 
various  field-magnets. 


1438  ELECTRICAL  ENGINEERING. 

cuit  will,  in  a  like  manner,  increase  the  electro-motive  force  from  the 
increase  in  the  magnetizing  current.  The  use  of  a  regulator  avoids 
these  changes  in  the  electro-motive  force. 

2.  Shunt-wound  Dynamo. — The  field-magnet   coils  are  placed  in  a 
shunt  to  the  armature  circuit,  so  that  only  a  portion  of  the  current 
generated  passes  through  the  field-magnet  coils,  but  all  the  difference 
of  potential  of  the  armature  acts  at  the  terminals  of  the  field-circuit. 

In  a  shunt- wound  dynamo  an  increase  in  the  resistance  of  the  external 
circuit  increases  the  electro-motive  force,  and  a  decrease  in  the  resistance 
of  the  external  circuit  decreases  the  electro- motive  force.  This  is  just 
the  reverse  of  the  series-wound  dynamo. 

In  a  shunt-wound  dynamo  a  continuous  balancing  of  the  current 
occurs,  the  current  dividing  at  the  brushes  between  the  field  and  the 
external  circuit  in  the  inverse  proportion  to  the  resistance  of  these 
circuits.  If  the  resistance  of  the  external  circuit  becomes  greater,  a 
proportionately  greater  current  passes  through  the  field  magnets,  and 
so  causes  the  electro-motive  force  to  become  greater.  If,  on  the  con- 
trary, the  resistance  of  the  external  circuit  decreases,  less  current  passes 
through  the  field,  and  the  electro-motive  force  is  proportionately 
decreased. 

3.  Compound-wound  Dynamo.  —  The  field  magnets  are  wound  with 
two  separate  sets  of  C9ils,  one  of  which  is  in  series  with  the  armature 
and  the  external  circuit,  and  the  other  in  shunt  with  the  armature  or 
the  external  circuit. 

A  compound  generator  is  made  for  the  purpose  of  delivering  current 
at  constant  potential  either  at  the  terminals  of  the  machine  or  at  some 
distant  receiving  point  on  the  line.  In  the  former  case  the  machine  is 
flat-compounded,  the  ideal  being  the  same  terminal  voltage  at  full  load 
as  at  no  load,  giving  a  practically  horizontal  voltage  characteristic. 
In  the  latter  case  the  machine  is  over-compounded,  giving  a  terminal 
voltage  which  rises  from  no  load  to  full  load  to  compensate  for  line 
drop,  so  that  at  the  receiving  end  of  the  line  the  voltage  will  be  constant 
at  all  loads. 

The  standard  voltages  for  ordinary  light  and  power  service  are  125 
and  250  volts,  while  for  railway  service  they  have  been  built  for  voltages 
as  high  as  1200,  and  in  one  particular  installation  two  such  machines 
are  connected  in  series  furnishing  a  supply  voltage  of  2400  volts. 

Many  direct-current  generators  are  provided  with  commutatinp? 
poles,  and  such  machines  may  be  operated  over  an  extremely  wide  range 
of  load  and  voltage  with  fixed  brush  positions  and  sparkless  commu- 
tation. The  commutating  winding  produces  a  magnetic  field  which  is 
in  a  direction  to  assist  the  reversal  of  current  in  the  coil  undergoing 
commutation  and  also  directly  opposed  to  the  field  generated  by  arma- 
ture reaction  which  tends  to  retard  the  reversal  of  current  in  this  coil. 
The  commutating  field  thus  completely  nullifies  the  distortive  effect  of 
armature  reaction  on  the  main  field  flux  in  the  commutating  zone,  and 
generates  an  e.m.f.  which  helps  the  brush  to  commutate  the  current 
without  sparking,  and  with  a  consequent  increased  life  of  the  commu- 
tator and  brushes. 

Commutating  poles  are  placed  between  the  main  poles  of  direct- 
current  generators  and  motors.  They  are  used  for  the  purpose  of 
nullifying  the  effect  of  the  armature  reaction  upon  the  magnetic  field 
adjacent  to  the  neutral  point.  The  armature  reaction  tends  to  move  the 
neutral  point  from  its  proper  mechanical  position,  and  it  is  obvious  that 
a  number  of  ampere  turns  setting  up  magnetic  lines  of  force  equal  to 
and  opposing  the  directions  of  those  set  up  by  the  armature  ampere 
turns  will  nullify  that  effect  on  the  neutral  occasioned  by  the  armature 
reaction. 

The  commutating  pole  winding  is  connected  in  series  with  the  arma- 
ture and  has  a  number  of  turns  per  pole  sufficient  to  give  a  magnetic 
strength  that  will  not  only  counteract  the  armature  reaction  above 
referred  to,  but  will  actually  reverse  the  current  in  the  coil  when  it  is 
in  the  commutating  zone. 

The  commutating  zone  is  the  region  over  which  the  brushes  may  have 
to  be  moved  in  order  to  obtain  good  commutation  between  no  load  and 
full  load.  With  commutating  pole  machines  no  such  movement  is 
necessary  and  the  reversal  takes  place  in  the  coils  short  circuited  under 
the  brushes. 


ALTERNATING  CURRENTS.          1439 

Inasmuch  as  the  commutating  windings  are  directly  in  series  with 
the  armature,  their  strength  varies  directly  with  the  armature  current 
and  provides  the  correct  rectifying  effect  for  proper  reversal  of  current 
in  the  coils  at  all  loads.  Hence  it  is  unnecessary  to  shift  the  brushes  as 
the  load  changes. 

Parallel  Operation. — The  first  requisite  for  satisfactory  parallel 
operation  of  direct  current  generators  is  that  they  have  the  same  char- 
acteristics. They  must  have  the  same  degree  of  compounding  for  any 
percentage  of  their  rated  load.  The  resistance  of  series  fields  with  their 
shunt  resistances  and  cable  connections  to  the  bus-bar  should  further- 
more be  inversely  proportional  to  the  capacities  of  the  machines;  i.e.,  no 
matter  what  size  cables  are  used,  the  resistances  of  the  two  connections 
must  be  so  proportioned  that  the  drop  will  be  the  same  for  both  ma- 
chines between  the  equalizer  junction  and  the  main  bus-bar  when  each 
machine  is  delivering  its  full-load  current. 

Three-Wire  System. — The  chief  advantage  of  the  Edison  three- 
wire  system  over  the  ordinary  two-wire  installation  is  that  of  econ- 
omy in  distribution.  In  a  two-wire  system  with  a  given  load  and  a 
given  percentage  of  voltage  drop,  the  distribution  at  250  volts  requires 
only  one-quarter  the  weight  of  copper  required  for  a  distribution  at  125 
volts.  A  neutral,  wire  in  the  three-wire  system  will,  however,  modify 
this  proportion  of  copper,  the  final  saving  depending  on  the  size  of  the 
neutral.  In  well-designed  systems,  the  maximum  unbalanced  current 
carried  by  the  neutral  will  be  about  25  per  cent  of  the  full  load.  There- 
fore the  size  of  the  neutral  need  not  be  larger  than  25  per  cent  of  the 
capacity  of  the  outside  mains,  and  the  weight  of  the  copper  in  this  case 
would  be  9/32  of  that  used  in  distributing  the  same  power  by  a  two- 
wire  system. 

The  practical  methods  available  for  operating  direct-current  three- 
wire  systems  are:  1.  Two  generators.  2.  One  generator  with  balancer 
set.  3.  One  generator  with  storage  battery.  4.  One  generator  with 
balancing  coil.  5.  Three-wire  generator. 

ALTERNATING   CURRENTS.* 

The  advantages  of  alternating  over  direct  currents  are:  1.  Greater 
simplicity  of  dynamos  and  motors,  no  commutators  being  required;  2. 
The  feasibility  of  obtaining  high  voltages,  by  means  of  static  trans- 
formers, for  cheapening  the  cost  of  transmission;  3.  The  facility  of 
transforming  from  one  voltage  to  another,  either  higher  or  lower,  for 
different  purposes. 

A  direct  current  is  uniform  in  strength  and  direction,  while  an  alter- 
nating current  rapidly  rises  from  zero  to  a  maximum,  falls  to  zero,  re- 
verses its  direction,  attains  a  maximum  in  the  new  direction,  and  again 
returns  to  zero.  This  series  of  changes  can  best  be  represented  by  a 
curve  the  abscissas  of  which  represent  time  and  the  ordinates  either 
current  or  electro-motive  force  (e.m.f.).  The  curve  usually  chosen  for 
this  purpose  is  the  sine  curve,  Fig.  228 ;  the  best  forms  of  alternators  give  a 
curve  that  is  a  very  close  approximation  to  the  sine  curve,  and  all  calcu- 
lations and  deductions  of  formulae  are  based  on  it.  The  equation  of  the 
sine  curve  is  y  =  sin  x,  in  which  y  is  any  ordinate,  and  x  is  the  angle 
passed  over  by  a  moving  radius  vector. 

After  the  flow  of  a  direct  current  has  been  once  established,  the  only 
opposition  to  the  flow  is  the  resistance  offered  by  the  conductor  to  the 
passage  of  current  through  it.  This  resistance  of  the  conductor,  in 
treating  of  alternating  currents,  is  sometimes  spoken  of  as  ohmic  resist- 
ance. The  word  resistance,  used  alone,  always  means  the  ohmic 
resistance.  In  alternating  currents,  in  addition  to  the  resistance,  sev- 

*  Only  a  very  brief  treatment  of  the  subject  of  alternating  currents  can 
be  given  in  this  book.  The  following  works  are  recommended  as  val- 
uable for  reference:  Steinmetz,  "Theoretical  Elements  of  Electrical 
Engineering.  Alternating  Current  Phenomena";  Cohen,  "Formulae 
and  Tables  for  the  Calculation  of  Alternating  Current  Problems ' ' ;  Jack- 
son, "Alternating  Currents  and  Alternating  Current  Machinery"; 
Bedell,  "Direct  and  Alternating  Current  Manual";  Timbie,  "Alter- 
nating Currents," 


1440  ELECTRICAL  ENGINEERING. 

eral  other  quantities,  which  affect  the  flow  of  current,  must  be  taken 
into  consideratioa  These  quantities  are  inductance,  capacity,  and  skin 
effect.  They  are  discussed  under  separate  headings. 
•  The  current  and  the  e.m.f.  may  be  in  phase  with  each  other,  that  is 
they  may  attain  their  maximum  strength  at  the  same  instant,  or  they 
may  not,  depending  on  the  character  of  the  circuit.  In  a  circuit  .con- 
taining only  resistance,  the  current  and  e.m.f.  are  in  phase;  in  a  current 
containing  inductance  the  e.m.f.  attains  its  maximum  value  before  the 
current,  or  leads  the  current.  In  a  circuit  containing  capacity  the  cur- 
rent leads  the  e.m.f.  If  both  capacity  and  inductance  are  present  in  a 
circuit,  they  will  tend  to  neutralize  each  other. 

Maximum,  Average,  and  Effective  Values. — The  strength  and  the 
e.m.f.  of  an  alternating  current  being  constantly  varied,  the  maximum 
value  of  either  is  attained  only  for  an  instant  in  each  period.  The  maxi- 
mum values  are  little  used  in  calculations,  except  in  deducing  formulae 
and  for  proportioning  insulation,  which  must  stand  the  maximum 
pressure.  The  average  value  is  obtained  by  averaging  the  ordinates  of 
the  sine  curve  representing  the  current,  and  is  2  -j-  IT  or  0.637  of  the 
maximum  value. 

The  value  of  greatest  imp9rtance  is  the  effective,  or  "square  root  of 
the  mean  square,"  value.  It  is  obtained  by  taking  the  square  root  of  the 
mean  of  the  squares  of  the  ordinates  of  the  sine  curve.  The  effective 
value  is  the  value  shown  on  alternating-current  measuring  instruments. 
The  product  of  the  square  of  the  effective  value  of  the  current  and  the 
resistance  of  the  circuit  is  the  heat  lost  in  the  circuit. 

The  relation  of  the  maximum,  average,  and  effective  values  is: } 
^Effec.  =  %ax.  X  0.707  ;     #Aver.  =  £Max.  X  0.637  ;     %ax.  =  1.41  X  %fec. 

Frequency.  —  The  time  required  for  an  alternating  current  to  pass 
through  one  complete  cycle,  as  from  one  maximum  point  to  the  next  (a 
and  b,  Fig.  228) ,  is  termed  the  period.  The  number  of  periods  in  a  second 
is  termed  the  frequency  of  the  current.  Since  the  current  changes  its 
direction  twice  in  each  period,  the  number  of  reversals  or  alternations  is 
doable  the  frequency.  A  current  of  120  alternations  per  second  has  a 
period  of  1/60  and  a  frequency  of  60.  The  frequency  of  a  current  is  equal 
to  one-half  the  number  of  poles  on  the  generator,  multiplied  by  the  number 
of  revolutions  per  second.  Frequency  is  denoted  by  the  letter/. 

The  frequencies  most  generally  used  in  the  United  States  are  25,  40,  60, 
125,  and  133  cycles  per  second.  The  Standardization  Report  of  the 
A  I.E.E.  recommends  the  adpptionof  three  frequencies,  viz.  25, 60  and  120. 

With  the  higher  frequencies  both  transformers  and  conductors  will  be 
less  costly  in  a  circuit  of  a  given  resistance  but  the  capacity  and  inductance 
effects  in  each  will  be  increased,  and  these  tend  to  increase  the  cost.  With 
high  frequencies  it  also  becomes  difficult  to  operate  alternators  in  parallel. 

A  l9w  frequency  current  cannot  be  used  on  lighting  circuits,  as  the  lights 
will  nicker  when  the  frequency  drops  below  a  certain  figure.  For  arc  lights 
the  frequency  should  not  be  less  than  40.  For  incandescent  lamps  it  should 
not  be  less  than  25.  If  the  circuit  is  to  supply  both  power  and  light  a 
frequency  of  60  is  usually  desirable.  For  power  transmission  to  long  dis- 
tances a  l9w  frequency,  say  25,  is  considered  desirable,  in  order  to  lessen 
the  capacity  effects.  If  the  alternating  current  is  to  be  converted  into 
direct  current  for  lighting  purposes  a  low  frequency  may  be  used,  as  the 
frequency  will  then  have  no  effect  on  the  lights. 

Inductance. — Inductance  is  that  property  of  an  electrical  circuit  by 
which  it  resists  a  change  in  the  current.  A  current  flowing  through  a 
conductor  produces  a  magnetic  flux 
around  tne  conductor,  n  tne  current 
be  changed  in  strength  or  directipn, 
the  flux  is  also  changed,  producing 
in  the  conductor  an  e.m.f.  whose  direc- 
tion is  opposed  to  that  of  the  current 
in  the  conductor.  This  counter  e.m.f. 
is  the  counter  e.m.f.  of  inductance. 
It  is  proportional  to  the  rate  of  change 
of  current,  provided  that  the  perme- 
ability of  the  medium  around  the  con- 
duet  or  remains  constant,  The  unit  of  FJG.  228, 


ALTERNATING   CURRENTS.  1441 

Inductance  is  the  henry,  symbol  L.  A  circuit  has  an  inductance  of  one 
henry  if  a  uniform  variation  of  current  at  the  rate  of  one  ampere  per 
second  produces  a  counter  e.m.f.  of  one  volt. 

The  effect  of  inductance  on  the  circuit  is  to  cause  the  current  to  lag 
behind  the  e.m.f.  as  shown  in  Fig.  228,  in  which  abscissas  represents  time, 
and  ordinates  represent  e.m.f.  and  current  strengths  respectively. 

Capacity.  —  Any  insulated  conductor  "has  the  power  of  holding  a  quan- 
tity of  static  electricity.  This  power  is  termed  the  capacity  of  the  body. 
The  capacity  of  a  circuit  'is  measured  by  the  quantity  of  electricity  in  it 
when  at  unit  potential.  It  may  be  increased  by  means  of  a  condenser. 
A  condenser  consists  of  two  parallel  conductors,  insulated  from  each  other 
by  a  non-conductor.  The  conductors  are  usually  in  sheet  form. 

The  unit  of  capacity  is  a  farad,  symbol  C.  A  condenser  has  a  capacity 
of  one  farad  when  one  coulomb  of  electricity  contained  in  it  produces  a  dif- 
ference of  potential  of  one  volt,  or  when  a  rate  of  change  of  pressure  of 
one  volt  per  second  produces  a  current  of  one  ampere.  The  farad  is  too 
large  a  unit  to  be  conveniently  used  in  practice,  and  the  micro-farad  or 
one-millionth  of  a  farad  is  used  instead.  The  effect  of  capacity  on  a 
circuit  is  to  cause  the  e.m.f.  to  lag  behind  the  current.  Both  inductance 
and  capacity  may  be  measured  with  a  Wheatstone  bridge  by  sub- 
stituting for  a  standard  resistance  a  standard  of  inductance  or  a  stand- 
ard of  capacity. 

Power  Factor.  —  In  direct-current  work  the  power,  measured  in  watts, 
is  the  product  of  the  volts  and  amperes  in  the  circuit.  In  alternating-cur- 
rent work  this  is  only  true  when  the  current  and  e.m.f.  are  in  phase.  If 
the  current  either  lags  or  leads,  the  values  shown  on  the  vole  and  ammeters 
will  not  be  true  simultaneous  values.  Referring  to  Fig.  228,  it  will  be 
seen  that  the  product  of  the  ordinates  of  current  and  e.m.f.  at  any  partic- 
ular instant  will  not  be  equal  to  the  product  of  the  effective  values  which 
are  shown  on  the  instruments.  The  power  in  the  circuit  at  any  instant  is 
the  product  of  the  simultaneous  values  of  current  and  e.m.f..  and  the  volts 
and  amperes  shown  on  the  recording  instruments  must  be  multiplied 
together  and  their  product  multiplied  by  a  power  factor  before  the  true 
watts  are  obtained.  This  power  factor,  which  is  the  ratio  of  the  volt- 
amperes  to  the  watts,  is  also  the  cosine  of  the  angle  of  lag  or  lead  of 
the  current.  Thus 

P  =  I  X  E  X  power  factor  =  I  X  E  X  cos  0, 
where  0  is  the  angle  of  lag  or  lead  of  the  current. 

A  watt-meter,  however,  gives  the  true  power  in  a  circuit  directly. 
The  method  of  obtaining  the  angle  of  lag  is  shown  on  p.  1442. 

Reactance,  Impedance,  Admittance.  —  In  addition  to  the  ohmic  re- 
sistance of  a  circuit  there  are  also  resistances  due  to  inductance,  capacity, 
and  skin  effect.  The  virtual  resistance  due  to  inductance  and  capacity 
is  termed  the  reactance  of  the  circuit.  If  inductance  only  be  present  in 
circuit,  the  reactance  will  vary  directly  as  the  inductance.  If  capacity 
only  be  present,  the  reactance  will  vary  inversely  as  the  capacity. 

Inductive  reactance  =2  TT/L;  Condensive  reactance  =     *     . 

2  7T  J  O 

The  total  apparent  resistance  of  the  circuit,  due  to  both  the  ohmic  resist- 
ance and  the  total  reactance,  is  termed  the  impedance,  and  is  equal  to  the 
square  root  of  the  sum  of  the  squares  of  the  resistance  and  the  reactance. 
Impedance  =Z  =  ^/II2  +  (2  Tr/D2  when  inductance  is  present  in  the  circuit. 

Impedance  =Z=-y  #2  +  (^fc]  when  caPacity  is  present  in  the  circuit. 

Admittance  is  the  reciprocal  of  impedance,  =  1  •*•  Z. 
.  If  both  inductance  and  capacity  are  present  in  the  circuit,  the  reactance 
of  one  tends  to  balance  that  of  the  other;  the  total  reactance  is  the  alge- 
braic sum  of  the  two  reactances;  thus,  _ 

Total  reactance  =  X  =  2  TT/L  -  -^Jc  ;    Z  =  \  R*  +  (2  **L  ~  J^fC  )*' 


In  all  cases  the  tangent  of  the  angle  of  lag  or  lead  is  the  reactance  divided 
by  the  resistance,    In  the  last  case 


1442 


ELECTRICAL   ENGINEERING. 


Skin  Effect. — Alternating  currents  tend  to  have  a  greater  density  at 
the  surface  than  at  the  axis  of  a  conductor.  The  effect  of  this  is  to  make 
the  virtual  resistance  of  a  wire  greater  than  its  true  ohmic  resistance. 
"With  low  frequencies  and  small  wires  the  skin  effect  is  small,  but  it  be- 
comes quite  important  with  high  frequencies  and  large  wires.  With 
magnetic  material  it  is  much  higher  than  with  non-magnetic. 

The  skin  effect  factor,  by  which  the  ohmic  resistance  is  to  be  multi- 
plied to  obtain  the  virtual  resistance  is  given  by  Berg  in  the  following 
approximate  formula: 

1+X|777W 


2 
For  Copper  Cable:  lj  \  =0.0105  dzf;  for  Aluminum  Cable:  ( ^\  =0.0063 

d2  /,  where  d  =  diameter  of  cable,  and  /  =  frequency. 

For  the  same  per  cent  increase,  due  to  skin  effect,  a  cable  can  have 
13%  larger  diameter  than  a  solid  wire;  in  other  words,  the  skin  effect  is 
the  same  as  long  as  the  ohmic  resistance  is  the  same,  whether  a  solid 
wire  or  a  cable  is  used. 

Ohm's  Law  applied  to  Alternating- Current  Circuits. — To  apply 
Ohm's  law  to  alternating-current  circuits  a  slight  change  is  necessary 
in  the  expression  of  the  law.  Impedance  is  substituted  for  resistance. 
The  law  should  read 

E  E 


1  = 


Impedance  Polygons. — 1 .  Series  Circuits. — The  impedance  of  a  circuit 
can  be  determined  graphically  as  follows :  Suppose  a  circuit  to  contain 
a  resistance  R  and  an  inductance  L,  and  to  carry  a  current  I  of  frequency 
/.  In  Fig.  229  draw  the  line  ab  proportional  to  R,  and  representing  the 
direction  of  current.  At  b  erect  be  perpendicular  to  ab  and  propor- 
tional to  2  irfL.  Join  a  and  c.  The  line,  ac  represents  the  impedance  of 
the  circuit.  The  angle  9  between  ab  and  ac  is  the  angle  of  lag  of  the  cur- 
rent behind  the  e.m.f.,  and  the  power  factor  of  the  circuit  is  cosine  0. 
The  e.m.f.  of  the  circuit  is  E  =  IZ. 


FIG.  229. 


27T/L 

R 61 


FIG.  230. 


1 

27T/K 


FIG.  231. 


FlG.  232. 


If  the  above  circuit  contained,  instead  of  the  inductance  I/,  a  capacity 
C,  then  would  the  polygon  be  drawn  as  in  Fig.  230.  The  line  be  would 

be  proportional  to  ^— ^  and  would  be  drawn  in  a  direction  opposite  to 

"  7TJ  O 

that  of  be  in  Fig.  229.     The  impedance  would  again  be  Z,  the  e.m.f. 
would  be  Z  X  /,  but  the  current  would  lead  the  e.m.f.  by  the  angle  0. 

Suppose  the  circuit  to  contain  resistance,  inductance,  and  capacity, 
the  lines  of  the  impedance  polygon  would  then  be  laid  off  as  in  Fig.  231. 
The  impedance  of  ttye  circuit  would  be  represented  by  afl,  ami  the  angle 


ALTERNATING  CURRENTS. 


1443 


of  lag  by  0.    If  the  capacity  of  the  circuit  had  been  such  that  cd  was 
less  than  be,  then  would  the  e.m.f.  have  led  the  current. 

If  between  the  inductance  and  capacity  In  the  circuit  in  the  previous  ex- 
amples there  be  interposed  another  resistance,  the  impedance  polygon  will 
take  the  form  of  Fig.  232.  The  lines  representing  either  resistances,  in-  \ 
ductances,  or  capacities  in  the  circuit  follow  each  other  in  all  cases  as  do 
the  resistances,  inductances,  and  capacities  in  the  circuit,  each  line  having 
its  appropriate  direction  and  magnitude. 

EXAMPLE. — A  circuit  (Fig.  233)  contains  a  resistance,  Rit  of  15  ohms,  a 
capacity.  C^t  of  100  microfarads  (0.000100  farad),  a  resistance,  R&  of  12 


FIG.  233. 


ohms,  and  inductance  of  Z/i,  of  0.05  henry,  and  a  resistance  72a,  of  20  ohms. 
Find  the  impedance  and  electromotive  force  when  a  current  of  2  amperes 
is  sent  through  the  circuit,  and  the  current  when  e.m.f.  of  120  volts  is 
impressed  on  the  circuit,  frequency  being  taken  as  60.  Also  find  the  angle 
of  lag,  the  power  factor,  and  the  power  in  the  circuit  when  120  volts  are 
impressed. 

The  resistance  is  represented  in  Fig.  234  by  the  horizontal  line  06,  15 
units  long.  The  capacity  is  represented  by  the  line  be,  drawn  downwards 
from  b  and  whose  length  is 


a  -".55 

S       1 
ii       -j 

S       * 

t?    C          CM 

e     R3=20   . 

d 
4. 

CJ  R2=12 
FIG.  23 

2X3.1416X60X0.0001 
From  the  point  c  a  horizontal  line  cd,  12  units  long,  is  drawn  to  represent 
R2.     From  the  point  d  the  line  de  is  drawn  vertically  upwards  to  represent 
the  inductance  LI.     Its  length  is 

27T/Z,!  =2X3.1416X60X0.05  =  18.85. 
From  the  point  e  a  horizontal  line  ef,  20 
units  long,  is  drawn  to  represent  Rs.  The 
line  adjoining  a  and  /  will  represent  the 
impedance  of  the  circuit  in  ohms.  The 
angle  d,  between  ab  and  a/,  is  the  angle  of 
lag  of  the  e.m.f.  behind  the  current.  The 
impedance  in  this  case  is  47.5  ohms,  and 
the  angle  of  lag  is  9°  15'. 

The  e.m.f.  when  a  current  of  2  amperes 
is  sent  through  is 

IZ  =  E  =  2  X  47.5  =  95  volts. 
If  an  e.m.f.  of  120  volts  be  impressed  on  the  circuit,  the  current  flowing 
through  will  be 

,     120       120 

/=  -5T-  =  T^T  —  2.53  amperes. 

46          47. o 

The  power  factor  ==  cos  6  =  cos  9°  15'  =  0.987. 

The  power  in  the  circuit  at  120  volts  is 

I  X  E  X  cos  e  =  2.53  X  120  X  0.987  =  299.6  watts. 

2.  Parallel  Circuits. — If  two  circuits  be  ar- 
ranged in  parallel,  the  current  flowing  in  each 
circuit  will  be  inversely  proportional  to  the 
impedance  of  that  circuit.  The  e.m.f.  of  each 
circuit  is  the  e.m.f.  across  the  terminals  at 
either  end  of  the  main  circuit,  where  the  vari- 
ous branches  separate.  Consider  a  circuit, 
Fig.  235,  consisting  of  two  branches.  The 
first  branch  contains  a  resistance  R,  and  an 
inductance  Lj.  hi  series  with  it.  The  second  FIG.  235. 


1444 


ELECTRICAL  ENGINEERING. 


branch  contains  a  resistance  #2  in  series  with,  an  inductance  L2.  The 
impedance  of  the  circuit  may  be  determined  by  treating  each  of  the 
two  branches  as  a  separate  series  circuit,  and  drawing  the  impedance 
polygon  for  each  branch  on  that  assumption.  Having  found  the  im- 
pedance the  current  flowing  in  either  branch  will  be  the  reciprocal  of 
the  impedance  multiplied  by  the  e.m.f.  across  the  terminals.  The 
current  in  the  entire  circuit  is  the  geometrical  sum  of  the  current  in 
the  two  branches. 

The  admittance  of  the  equivalent  simple  circuit  may  be  obtained  by 
drawing  a  parallelogram,  two  of  whose  adjoining  sides  are  made  parallel  to 
the  impedance  lines  of  each  branch  and  equal  to  the  two  admittances 
respectively. 

The  diagonal  of  the  parallelogram  will  represent  the  admittance  of  the 
equivalent  simple  circuit.  The  admittance  multiplied  by  the  e.m.f.  gives 
the  total  current  in  the  circuit. 

EXAMPLE.  —  Given  the  circuit  in  Fig.  236,  consisting  of  two  branches. 
Branch  1  consists  of  a  resistance  RI  =  12  ohms,  an  inductance  LI  =  0.05 
henry,  a  resistance  R2  =  4  ohms,  and  a  capacity  Ci  =  120  microfarads 
(0.00012  farad).  Branch  2  consists  of  an  inductance  L2  =  0.015  henry,  a 
resistance  Rz  =10  ohms,  and  an  inductance  La  =  0.03  henry.  An  e.m.f. 
of  100  volts  is  impressed  on  the  circuit  at  a  frequency  of  60.  Find  the  ad- 
mittance of  the  entire  circuit,  the  current,  the  power  factor,  and  the  power 


R1=12      U=.05 


=.0619 
FlG.  237. 


AWERNAT1NG  CURRENTS. 


1445 


In  the  circuit.  Construct  the  impedance  polygons  for  the  two  branches 
separately  as  shown  in  Fig.  237,  a  and  &.  The  impedance  in  branch 
1  is  16.4  ohms,  and  the  current  is  (1/16.4)  X  100  =  6.19  amperes.  The 
angle  of  lead  of  the  current  is  1°  45'.  The  impedance  in  branch  2  is 
19.5  ohms  and  the  current  is  (1/19.5)  X  100  =  5.13  amperes.  The 
angle  of  lag  of  the  current  is  61°. 

The  current  in  the  entire  circuit  is  found  by  taking  the  admittances  of 
the  two  branches,  and  drawing  them  from  the  point  o,  in  Fig.  237  c,  parallel 
to  the  impedance  lines  in  their  respective  polygons.  The  diagonal  from  o 
is  the  admittance  of  the  entire  circuit, and  in  this  case  is  equal  to  0.092. 
The  current  in  the  circuit  is  0.092  X  100  =  9.2  amperes.  The  power  factor 
is  0.944  and  the  power  in  the  circuit  is  100  X  0.944  X  9.2  =  868.48  watts. 

Self-Inductance  of  Lines  and  Circuits.  —  The  following  formulae 
and  table,  taken  from  Crocker's  "  Electric  Lighting,"  give  a  method  of  cal- 
culating the  self-inductance  of  two  parallel  aerial  wires  forming  part  of  the 
same  circuit  and  composed  of  copper,  or  other  non-magnetic  material: 

L  per  foot  =  (l5.24  +  140.3  log  ~\  lO"9. 

(2  A\ 
80.5  -f  740  log  ~j-\  10-«. 

in  which  L  is  the  inductance  in  henrys  of  each  wire,  A  is  the  Interaxial  dis- 
tance between  the  two  wires,  and  d  is  the  diameter  of  each,  both  in  inches. 
If  the  circuit  is  of  iron  wire,  the  formulae  become 

L  per  foot  =  (2286  +  140.3  log  ^)  10-*. 
L  per  mile  =  (l2070  +  740  log  ^-£\  lO"6. 

INDUCTANCE,  IN  MILLIHENRYS  PER  MILE,  FOR  EACH  OF  Two 
PARALLEL  COPPER  WIRES. 


Interaxial 
Distance, 

Ins. 

American  Wire  Gauge  Number. 

0000 

000 

00 

0 

1 

2 

3 

4 

6 

8 

10 

1.615 
1.838 
2.061 
2.192 
2.356 
2.507 

12 

6 
12 
24 
36 
60 
% 

.130 
.353 
.576 
.707 
.871 
2.023 

1.168 
1.391 
1.614 
1.745 
1.909 
2.059 

1.205 
1.428 
1.651 
1.784 
1.946 
2.097 

1.242 
1.465 
1.688 
1.818 
1.982 
2J34 

1.280 
1.502 
1.725 
1.856 
2.023 
2.172 

1.317 
1.540 
1.764 
1.893 
2.058 
2.210 

!:$ 

1.800 
1.931 
2.095 
2.246 

1.392 
1.614 
1.838 
1.968 
2.132 
2.283 

1.466 
1.689 
1.912 
2.043 
2.208 
2.358 

1.540 
1.764 
1.986 
2.117 
2.282 
2.433 

1.690 
1.913 
2.135 
2.266 
2.432 
2.582 

Capacity  of  Conductors.  —  AH  conductors  are  included  in  three 
classes,  viz.:  1.  Insulated  conductors  with  metallic  protecti9n;  2.  Single 
aerial  conductor  with  earth  return;  3.  Metallic  circuit  consisting  of  two 
parallel  aerial  wires.  The  capacity  of  the  lines  may  be  calculated  by 
means  of  the  following  formulae  taken  from  Crocker's  "  Electric  Lighting. 

Class  1.     C  per  foot  =  ^^^,'  C  per  mile-  38'83  "  ^ 


'  log(D  +  dy 
Class  2.     C  per  foot  =  fj3,1  *  ™  " ,   C  per  mile  - 


log  (D  H-  d) ' 
38.83  X  10-9 
=  log  (4/1  -T-  d) 


feperfootofeachwire^jfl^. 

OlaSS    O.     "^  i  Q     .  n  \f    -I  r\     t) 

C  per  mile  of  each  wire  -  iy'4J 


~log(2A+d) 

In  which  C  is  the  capacity  in  farads,  D  the  internal  diameter  of  the  metallic 
covering,  d  the  diameter  of  the  conductor,  h  the  height  of  the  conductor 
above  the  ground,  and  A  the  interaxial  distance  between  two  parallel  wires 
all  in  inches;  A:  is  a  dielectric  constant  which  for  air  is  equal  to  1  and  for 
pure  rubber  is  equal  to  2.5.  The  formulae  in  classes  2  and  3  assume  the  wires 
to  be  bare.  If  they  are  insulated,  k  must  be  introduced  in  the  numerator 
and  given  a  value  slightly  greater  than  1. 

Single-phase  and  Polyphase  Currents.  —  A  single-phase   current 
is  a  simple  alternating  current  carried  on  a  single  pair  of  wires  and  is 


1446 


ELECTRICAL   ENGINEERING. 


generated  on  a  machine  having  a  single  armature  winding.     It  is  repre- 
sented by  a  single  sine  curve. 

Polyphase  currents  are  known  as  two-phase,  three-phase,  six-phase,  or 
any  other  number,  and  are  represented  by  a  corresponding  number  of  sine 
curves.  The  most  commonly  used  systems  are  the  two-phase  and  three- 
phase. 

1.  Two-phase  Currents. — In  a  two-phase  system  there  are  two  single- 
phase  alternating  currents  bearing  a  definite  time  relation  to  each  other 
and  represented  by  two  sine  curves  (Fig.  238). 
The  two  separate  currents  may  be  generated  by 
the  same  or  by  separate  machines.  If  by  sepa- 
rate machines,  the  armatures  of  the  two  should 
be  positively  coupled  together.  Two-phase  cur- 
rents are  usually  generated  by  a  machine  with 
two  armature  windings,  each  winding  termi- 
nating in  two  collector  rings.  The  two  windings 
are  so  related  that  the  two  currents  will  be  90° 


vxy 


FIG.  238. 


apart.  For  this  reason  two  phase-currents  are  also  called  "  quarter- 
phase  "  currents. 

Two-phase  currents  may  be  distributed  on  either  three  or  four  wires. 
The  three-wire  system  of  distribution  is  shovyn  in  Fig.  239-  One  of  the 
return  wires  is  dispensed  with,  connection  being  made  across  to  the  other 
as  shown.  The  common  return  wire  should  be  made  1.41  times  the  area 
of  either  of  the  other  two  wires,  these  two  being  equal  in  size. 

The  four-wire  system  of  distribution  is  shown  in  Fig.  240.  The  two 
phases  are  entirely  independent,  and  for  lighting  purposes  may  be  operated 
as  two  single-phase  circuits. 


FIG.  239. 


FIG.  240. 


2.  Three-phase  Currents. — Three-phase  currents  consist  of  three  alter- 
nating currents,  differing  in  phase  by  120°,  and  represented  by  three  sine 
curves,  as  in  Fig.  241.  They  may  be  distributed  by  three  or  six  wires.  If 
distributed  by  the  six-wire  system,  it  is  analogous  to  the  four-wire,  two- 
phase  system,  and  is  equivalent  to  three  single-phase  circuits.  In  the 
three-wire  system  of  distribution  the  circuits  may  be  connected  in  two 
different  ways,  known  respectively  as  the  Y  or  star  connection,  and  the  A 
(delta)  or  mesh  connection. 


XXX 


FIG.  241. 


FIG.  242. 


The  Y  connection  is  shown  in  Fig.  242.  The  three  circuits  are  joined 
at  the  point  o,  known  as  the  neutral  point,  and  the  three  wires  carrying  the 
current  are  connected  at  the  points  a,  b,  and  c,  respectively.  If  the  three 
circuits  ao,  bo,  and  co  are  compo3ed  of  lights,  they  must  be  equally  loaded 
or  the  lights  will  fluctuate.  If  the  three  circuits  are  perfectly  balanced, 
fche  lights  will  remain  steady.  In  this  form  of  connection  each  wire  may 


ALTERNATING   CURRENTS. 


1M7 


be  considered  as  the  return  wire  for  the  other 
two.  If  the  three  circuits  are  unbalanced,  a 
return  wire  may  be  run  from  the  neutral  ppint 
o  to  the  neutral  point  of  the  armature  wind- 
ing on  the  generator.  The  system  will  then 
be  four-wire,  and  will  work  properly  with  un- 
balanced circuits. 

The  A  connection  is  shown  in  Fig.  243. 
Each  of  the  three  circuits  ab,  ac,  be,  receives 
the  current  due  to  a  separate  coil  in  the  arma- 
ture winding.  This  form  of  connection  will 
work  properly  even  if  the  circuits  are  unbal- 
anced; and  if  the  circuit  contains  lamps,  they 
will  not  fluctuate  when  the  circuit  changes 
from  a  balanced  to  an  unbalanced  condition, 
or  vice  versa. 

Measurement  of  Power  in  Polyphase  Circuits. —  1.  Two-phase 
Circuits. — The  power  of  two-phase  currents  distributed  by  four  wires 
may  be  measured  by  two  wattmeters  introduced  into  the  circuit  as  shown 
in  Fig.  240.  The  sum  of  the  readings  of  the  two  instruments  is  the  total 
power.  If  but  one  wattmeter  is  available,  it  should  be  introduced  first  in 
one  circuit,  and  then  in  the  other.  If  the  current  or  e.m.f.  does  not  vary 
during  the  operati9n,  the  result  will  be  correct.  If  the  circuits  are  per- 
fectly balanced,  twice  the  reading  of  one  wattmeter  will  be  the  total  power,, 
Wi 


FIG.  243. 


FIG.  244. 


FIG.  245. 


The  power  of  two-phase  currents  distributed  by  three  wires  may  be 
measured  by  two  wattmeters  as  shown  in  Fig.  239.  The  sum  of  the  two 
readings  is  the  total  power.  If  but  one  wattmeter  is  available,  the  coarse- 
wire  coil  should  be  connected  in  series  with  the  wire  ef  and  one  extremity 
of  the  pressure-coil  should  be  connected  to  some  point  on  ef.  The  other 
end  should  be  connected  first  to  the  wire  a  and  then  to  the  wire  d,  a  read- 
ing being  taken  in  each  position  of  the  wire.  The  sum  of  the  readings 
gives  the  power  in  the  circuits. 

2.  Three-phase  Circuits. — The  power  in  a  three-phase  circuit  may  be 
measured  by  three  wattmeters,  connected  as  in  Fig.  244  if  the  system  is 
Y-connected,  and  as  in  Fig.  245  if  the  system  is  A-connected.  The  sum 
of  the  wattmeter  readings  gives  the  power  in  the  system.  If  the  circuits 
are  perfectly  balanced,  three  times  the  reading  of  one  wattmeter  is  the 
total  power. 

The  power  in  a  A-connected  system 
may  be  measured  by  two  watt-meters,  as 
shown  in  Fig.  246.  If  the  power  factor  of 
the  system  is  greater  than  0.50,  the  arith- 
metical sum  of  the  readings  is  the  power 
in  the  circuit.  If  the  power  factor  is  less 
than  0.50,  the  arithmetical  difference  of 
the  readings  is  the  power.  Whether  the 
power  factor  is  greater  or  less  than  0.50 
may  be  discovered  by  interchanging  the 
wattmeters  without  disturbing  the  rela- 
tive connection  of  their  coarse-  and  fine- 
wire  coils.  If  the  deflections  of  the  needles 
are  reversed,  the  difference  of  the  readings 


FIG.  246. 


is  the  power.     If  the  needles  are  deflected  in  the  same  direction  as  at 
first,  the  sum  of  the  readings  is  the  power. 


1448  ELECTRICAL   ENGINEERING. 

ALTERNATING-CURRENT  GENERATORS. 

Synchronous  Generators. — The  function  of  the  alternating-current 
synchronous  generator  is  to  transform  mechanical  energy  into  electrical 
energy,  either  single-phase  or  polyphase.  It  comprises  a  comparatively 
constant  magnetic  field  and  an  armature  generating  electro-motive  forces 
and  delivering  currents  in  synchronism  with  the  motion  of  the  machine. 

Alternating-current  generators  are  generally  designed  to  operate  at 
normal  load  and  80%  power  factor  without  exceeding  a  specified  tem- 
perature rise,  and  should  such  a  machine  have  to  be  operated  with  a  load 
of  lower  power  factor,  its  rating  will  be  reduced,  when  based  on  the  same 
temperature  guarantee. 

Synchronous  generators  are  almost  always  of  the  revolving  field  type, 
and  may  be  either  of  a  horizontal  or  vertical  design. 

Rating.  —  The  normal  full-load  rating  is  usually  based  on  continu- 
ous operation  with  a  certain  rated  voltage,  current,  power  factor,  fre- 
quency and  speed.  The  overload  guarantees  should  refer  to  the  normal 
conditions  of  operation,  and  an  overload  capacity  of  25%  for  two  hours 
has  generally  been  accepted  as  standard,  although  in  several  instances 
a  50%  two-hour  overload  is  required.  Of  late  (1915),  however,  gen- 
erators are  often  given  a  maximum  continuous  rating  with  a  temper- 
ature rise  not  exceeding  50°  C.  (122°  P.). 

The  rated  full-load  current  is  that  current  which,  with  rated  terminal 
voltage,  gives  the  rated  kilowatts  or  rated  kilovolt-amperes.  In  ma- 
chines in  which  the  rated  voltage  differs  from  the  no-load  voltage,  the 
rated  current  should  refer  to  the  former.  The  rated  output  may  be 
determined  as  follows: 

If  E  =  full-load  terminal  voltage  and  I  =  rated  current,  then  for  a 

El 

single-phase  generator,  K.V.A.  =  77^-. 

lOUO 

For  a  two-phase  generator  the  total  output  is  equal  to  the  output  of 
the  two  single-phase  circuits,  and  if  I,  in  this  case,  is  the  rated  current 

O     771     7° 

per  circuit,  the  output  for  a  two-phase  generator  is,  K.V.A.  =  —  ^-. 

100O 

For  a  three-phase  generator  there  are  three  circuits  to  be  considered, 
whether  the  machine  is  star  or  delta  connected.  If  E  is  the  terminal 
voltage  and  I  the  line  current,  then  for  a  three-phase  generator, 

KVA    -  V3X  EI 
1000 

The  capacity  of  a  polyphase  generator,  whether  operating  two-  or 
three-phase,  is  always  the  same,  while,  if  operating  under  the  same 
conditions  single-phase,  in  which  case  one  phase  is  ineffective,  the 
rating  is  only  about  71%  of  what  it  would  be  if  operated  as  a  poly- 
phase generator.  This  relation,  however,  does  not  hold  true  for  a  ma- 
chine which  is  initially  built  for  single-phase  service,  and  in  such  a  case 
the  distribution  of  the  winding  can  be  made  such  as  to  increase  the 
capacity  somewhat.  The  inherent  regulation  is  generally  made  poorer 
thereby,  but  by  the  use  of  massive  damping  devices  it  can  be  materially 
improved. 

Efficiency. — The  efficiency  of  a  generator  is  the  ratio  of  the  power 
output  to  the  power  input,  the  difference  between  these  two  quantities 
being  equal  to  the  losses.  The  method  commonly  and  most  readily 
used  for  obtaining  the  efficiency  is  to  determine  these  losses  and  then 
compute  the  efficiency  by  dividing  the  power  output  by  the  sum  of  the 
power  output  plus  the  losses. 

The  guaranteed  efficiency  should  always  refer  to  the  energy  load 
(the  energy  load  is  the  load  doing  useful  work,  and  is  equal  to  the  total 
K.V.A.  X  the  power  factor  of  the  load),  and  if  is  most  important  that 
the  power  factor  of  the  load  is  also  given.  In  certain  cases  the  guaran- 
teed efficiency  is  based  on  a  K.V.A.  output,  but  the  inconsistency  of 
such  a  method  is  apparent,  as  the  following  example  will  illustrate: 

Assume  a  generator  rated  100  K.V.A.  (ICO  Kw.  at  unity  power- 
factor)  or  100  K.V.A.  (80  Kw.  0.8  P.F.),  and  that  the  losses  at  unity  and 
80%  power  factors  are  10  and  11  Kw.  respectively,  the  efficiency  is  then; 


ALTERNATING-CURRENT  GENERATORS.         1449 
> 

Based  on  100  Kw.  1.0  P.F., 
inn 


Based  on  80  Kw.  0.8  P.F., 


Based  on  100  K.V.A.  0.8  P.F., 


From  the  last  two  values  it  is  seen  that  for  80%  power-factor  if  based 
on  ths  K.V.A.,  a  2  %  greater  efficiency  guarantee  can  be  made,  although 
this  value  has  no  meaning,  as  it  is  based  on  apparent  power. 

The  losses  in  the  generator  consist  of:  The  copper  losses  in  the 
armature  and  field,  proportional  to  the  square  of  the  armature  and  field 
currents  respectively;  the  core  loss,  slightly  increasing  from  no-load  to 
full-load;  the  load  loss,  having  a  value  approximately  one-third  of  the 
short-circuiting  core  loss;  and  finally,  the  friction  and  windage  losses, 
which  are  practically  constant. 

Regulation.  —  Such  a  close  inherent  voltage-  regulation  as  was  for- 
merly required  is  not  any  longer  desirable,  since  a  good  voltage  regula- 
tion may  readily  be  accomplished  by  means  of  automatic  voltage  regu- 
lators, which  perform  their  function  whether  the  fluctuations  are  due  to 
a  change  of  load,  speed,  or  power  factor. 

A  close  inherent  regulation  would  require  a  low  reactance  generator, 
which  means  an  expensive  machine.  A  low  reactance  machine  also,  in 
case  of  short  circuits,  would  allow  a  very  large  current  to  flow  through 
the  machine  and  through  any  other  apparatus  that  may  be  within  the 
circuit  enclosed  by  the  short-circuit.  These  short-circuit  currents  reach 
enormous  values  in  large  central  stations,  and  in  order  to  reduce  the 
currents  to  safe  values  large  reactances  are  necessary.  It  is,  however, 
not  possible  to  design  high-speed  turbo-generators  for  the  necessary 
reactance,  and  external  reactances  must  usually  be  inserted  in  the  gen- 
erator leads  or  between  the  bus-sections.  By  so  limiting  the  abnormal 
flow  of  current  the  generating  system  is  relieved  from  the  disastrous 
effects  of  such  short  circuits. 

Rating  of  a  Generating  Unit.  —  In  determining  the  proper  rating 
and  capacity  of  the  generators  for  a  power  station,  the  generator  and  the 
prime  mover  must  of  necessity  be  treated  together  as  a  combination  so 
as  to  secure  the  highest  operating  efficiency.  With  steam-engines  the 
ratings  are  usually  such  that  the  engine  is  working  under  its  most  eco- 
nomical load  at  the  rating  of  the  electrical  generator.  With  gas  engines, 
however,  the  efficiency  increases  with  the  load  beyond  the  capacity  of 
the  engine,  and  for  this  reason  the  rating  of  such  an  engine  is  generally 
made  as  nearly  as  possible  to  its  maximum  capacity  with  only  a  small 
margin  for  regulating  purposes.  With  steam  turbines  the  efficiency 
curve  is  very  flat  so  that  it  is  the  desirable  overload  capacity  which 
limits  the  rating  of  the  turbine.  In  the  water-wheel  unit,  the  efficiency 
usually  falls  off  rapidly  above  and  below  the  maximum  point,  so  that 
the  rating  of  the  generator  should  correspond  to  the  point  of  maximum 
efficiency  of  the  wheel. 

The  effect  of  the  power  factor  should  also  be  considered  when  deter- 
mining the  prime  mover  as  well  as  the  generator  capacity,  and  many 
mistakes  have  been  made  in  this  respect.  The  generator  may,  for  ex- 
ample, have  been  designed  and  rated  on  the  basis  of  unity  power  factor 
operation  with  a,  prime  mover  having  a  corresponding  capacity.  After 
installation  it  is,  however,  found  that  the  actual  operating  power  factor 
is  0.80,  with  the  result  that  only  80  per  cent  of  the  prime  mover  capacity 
can  be  utilized  without  overloading  the  generator. 

Windings.  —  The  greatest  number  of  all  alternating-current  gener- 
ators are  wound  three-phase  with  the  armature  windings  connected  in 
star.  This  is  preferable  to  delta  connection,  as  a  smaller  number  of 
conductors  is  required  for  a  given  voltage,  while  on  the  other  hand  the 
danger  of  the  circulation  of  triple-frequency  currents  in  the  closed 
armature  winding  is  avoided. 


1450  ELECTRICAL  ENGINEERING. 

Voltages. — Standard  generator  voltages  for  all  frequencies  are  240, 
480,  600,  1150,  2300,  4000,  6600,  with  the  corresponding  motor  voltages 
220,  440,  550, 1040,  2090,  6000.  There  is  no  nwtor  voltage  corresponding 
to  4000  volts,  since  this  is  only  used  on  lighting  three-phase,  four-wire 
distributing  systems.  In  addition  11,000  volts  is  also  standard  for  60 
cycles,  and  13,200  volts  for  25  cycles. 

Parallel  Operation.  —  In  order  that  an  alternating-current  generator 
shall  be  able  to  carry  a  load,  a  current  must  flow  corresponding  to  this 
load.  The  e.m.f.  required  to  generate  this  current  is  the  resultant  of  the 
terminal  and  the  induced  e.m.f. 's  of  the  generator,  the  displacement  be- 
tween these  e.m.f. 's  being  due  to  the  impulse  of  the  prime  mover.  In 
the  same  manner  when  two  or  more  generators  are  operating  in  parallel 
the  division  in  load  between  the  different  units  is  entirely  dependent  on 
the  turning  efforts  of  the  prime  movers,  and  a  change  in  the  field  excita- 
tion, as  with  direct-current  generators,  will  have  no  effect  whatsoever. 

For  a  satisfactory  parallel  operation  it  is  important  that  the  e.m.f. 's 
and  frequencies  of  the  generators  be  the  same,  as.  if  this  is  not  the 
case,  cross  currents  will  flow  between  the  units.  These  cross  currents 
may  be  either  wattless  or  they  may  represent  a  transfer  of  energy,  de- 
pending on  whether  they  are  caused  by  a  difference  in  the  e.m.f.  or  in 
the  frequency  of  the  machines. 

Exciters  (E.  A.  Lof,  in  Coal  Age). — Synchronous  generators  as  well  as 
synchronous  motors  are  dependent  on  a  direct-current  excitation  for 
their  operation,  and  the  energy  for  the  excitation  is  generally  obtained 
from  direct-current  generators,  termed  "exciters."  These  should  have 
a  capacity  sufficient  to  excite  all  of  the  synchronous  apparatus  in  the 
station  when  these  machines  are  operating  at  their  maximum  load  and 
true  operating  power  factor.  It  is  not  enough  to  provide  for  the 
excitation  when  operating  at  unity  power  factor,  because  the  exci- 
tation which  is  required  at  lower  power  factors  is  considerably  higher 
than  at  unity  power  factor. 

For  small  and  medium  size  plants  a  125- volt  exciter  pressure  is  gen- 
erally chosen,  while  for  larger  installations  a  250- volt  excitation  will 
prove  more  economical. 

There  are  many  different  ways  of  driving  exciters.  They  may  be 
direct-connected  to  the  main  units  if  these  are  of  moderate  speed.  Such 
an  arrangement  may  prove  satisfactory  for  two  or  three  units,  but 
when  the  number  of  units  is  higher  the  system  becomes  rather  compli- 
cated. Another  objection  is  that  in  case  of  trouble  with  an  exciter,  the 
whole  generating  unit  will  have  to  be  shut  down.  When  two  direct- 
connected  units  are  used,  they  should  each  have  a  capacity  sufficiently 
large  to  excite  both  the  generators,  and  with  three  units  the  capacity  of 
either  exciter  should  preferably  be  such  that  it  can  excite  two  of  the 
generators.  For  four  or  more  units  it  should  only  be  necessary  to  give 
each  exciter  a  capacity  sufficient  for  one  generator,  and  if  necessary  a 
motor-driven  exciter  unit  can  be  installed  as  a  reserve. 

The  system,  however,  which  seems  to  be  the  most  widely  used  and 
which  offers  the  greatest  reliability,  is  that  in  which  the  excitation  is 
obtained  from  a  common  source,  consisting  of  as  few  exciters  as  possible. 
One  or  two  units  are  then  generally  provided  for  normal  excitation,  de- 
pending on  the  size  of  the  station,  a  third  unit  being  installed  as  a  re- 
serve. It  is  also  common  practice  to  have  the  regular  units  driven  by 
prime  movers,  such  as  steam-engines  or  water-wheels,  while  the  reserve 
unit  is  motor-driven. 

Still  another  system  which  is  becoming  common  is  to  install  low- 
voltage  generators,  driven  either  by  a  non-condensing  steam  turbine  in 
case  of  a  steam-plant  or  a  water-wheel  in  a  hydro-electric  plant.  The 
exciters  are  then  motor-driven,  current  for  driving  them  being  obtained 
from  the  low  voltage  generator.  The  steam  from  the  turbines  would 
then,  of  course,  be  taken  to  the  feed-water  heaters,  and  in  addition  to 
the  exciters,  all  the  other  auxiliaries,  such  as  the  circulating  pumps, 
etc.,  would  also  be  motor-driven. 

In  order  to  insure  a  close  voltage  regulation  of  the  system,  automatic 
regulators  are  commonly  installed  in  connection  with  the  exciters,  their 
principle  being  to  automatically  increase  or  decrease  the  excitation  by 
rapidly  opening  or  closing  a  shunt  circuit  across  the  exciter-field  rheo- 
stat, and  thus  keep  a  constant  bus-bar  voltage  regardless  of  the  load. 


TRANSFORMERS.  1451 

TRANSFORMERS. 

A  transformer  consists  essentially  of  two  coils  of  wire,  one  coarse  and 
one  fine,  wound  upon  an  iron  core.  Its  function  is  to  transform  elec- 
trical energy  from  one  potential  to  another,  although  it  may  also  be 
used  for  phase  transformation.  If  the  transformer  causes  a  change  from 
high  to  low  voltage,  it  is  known  as  a  "step-down"  transformer;  if  from 
low  to  high  voltage,  it  is  known  as  a  "step-up"  transformer. 

Primary  and  Secondary. — In  regard  to  the  use  of  the  terms  high-  • 
voltage,  low- voltage,  primary  and  secondary,  the  A.I.E.E.  Standardiza- 
tion Rules  read  as  follows: 

"The  terms  ' high- voltage '  and  ' low- voltage '  are  used  to  distinguish 
the  winding  having  the  greater  from  that  having  the  lesser  number  of 
turns.  The  terms  'primary'  and  'secondary'  serve  to  distinguish  the 
windings  in  regard  to  energy  flow,  the  primary  being  that  which  receives 
the  energy  from  the  supply  circuit,  and  the  secondary  that  which  re- 
ceives the  energy  by  induction  from  the  primary." 

The  terms  primary  and  secondary  are,  however,  often  confused,  and 
in  order  to  avoid  any  misunderstanding,  it  is  preferable  that  the  terms 
high- voltage  and  low- voltage  be  used  instead  of  primary  and  secondary. 

Voltage  Ratio. — The  A.I.E.E.  Standardization  Rules  also  state  that 
"  The  voltage  ratio  of  a  transformer  is  the  ratio  of  the  r.m.s.  (square  root 
of  mean  square)  primary  terminal  voltage  to  the  r.m.s.  secondary  ter- 
minal voltage  under  specified  conditions  of  load."  It  also  defines 
"The  ratio  of  a  transformer,  unless  otherwise  specified,  as  the  ratio  of 
the  number  of  turns  in  the  high-voltage  winding  to  that  in  the  low- 
voltage  winding:  i.e.,  the  turn-ratio.'11 

The  two  ratios  are  equal  when  one  of  the  windings  is  open  and  the 
transformer  does  not  carry  any  load.  When  loaded,  the  resistance 
and  inductance  of  the  windings  cause  a  drop  in  the  voltage,  thus  modi- 
fying the  ratio  of  transformation  slightly. 

Rating. — A  transformer  should  be  rated  by  its  kilovolt  -  ampere 
(K.V.A.)  output.  It  is  equal  to  the  product  of  the  voltage  and  current, 
and  is,  therefore,  the  same  whether  the  different  coils  are  connected  in 
series  or  parallel.  If  the  load  is  of  unity  power  factor,  the  kilowatt  out- 
put is  the  same  as  the  kilo  volt-ampere  output,  but  if  the  power  factor 
is  less,  the  kilowatt  output  will  be  correspondingly  less.  For  example,  a 
100  K.V.A.  transformer  will  have  a  full-load  rating  of  100  K.W.  at  100% 
power  factor,  90  K.W.  at  90%  power  factor,  etc. 

Efficiency.— There  are  two  sources  of  loss  in  the  transformer,  viz., 
the  copper  loss  and  the  iron  loss.  The  copper  loss  is  proportional  to  the 
square  of  the  current,  being  the  12  R  loss  due  to  heat.  If  Ii,  Ri,  be  the 
current  and  resistance  respectively  of  the  primary,  and  Ii,  Ri,  the  cur- 
rent and  resistance  respectively  of  the  secondary,  then  the  total  copper 
loss  is  Wc  =  /i2  .R!  -f  722#2  and  the  percentage  of  copper  loss  is 

— *       2'  — ,  where  Wp  is  the  energy  delivered  to  the  primary.   The  iron 

loss  is  constant  at  all  loads,  and  is  due  to  hysteresis  and  eddy  currents. 

The  efficiency  of  a  transformer  is  the  ratio  of  the  output  in  watts  at 
the  secondary  terminals  to  the  input  at  the  primary  terminals.  At  full 
load  the  output  is  equal  to  the  input  less  the  iron  and  copper  losses. 
The  full-load  efficiency  of  a  transformer  is  usually  very  high,  being  from 
92  per  cent  to  98  per  cent.  As  the  copper  loss  varies  as  the  square  of 
the  load,  the  efficiency  of  a  transformer  varies  considerably  at  different 
loads.  Transformers  on  lighting  circuits  usually  operate  at  full  load 
but  a  very  small  part  of  the  day,  though  they  use  some  current  all  the 
time  to  supply  the  iron  losses.  For  transformers  operated  only  a  part  of 
the  time,  the  "all-day"  efficiency  is  more  important  than  the  full-load 
efficiency.  It  is  computed  by  comparing  the  watt-hours  output  to  the 
watt-hours  input. 

The  all-day  efficiency  of  a  10-Kw.  transformer,  whose  copper  and 
iron  losses  at  full  load  are  each  1.5  per  cent,  and  which  operates  3  hours 
at  full  load,  2  hours  at  half  load,  and  19  hours  at  no  load,  is  computed  as 
follows: 

Iron  loss,  all  loads  =  10  X  0.015  =  0.15  K.W. 
Copper  loss,  full  load  =  10  X  0.015  =  0.15  K.W. 


1452 


ELECTRICAL  ENGINEERING. 


Copper  less,  1/2  load  =  0.15  X  (1/2) 2  =  0.0375  K.W. 
Iron  loss,  K.W.  hours  =  0.15  X  24  =  3.6. 
Copper  loss,  full  load,  K.W.  hours  =  0.15  X  3  =  0.45. 
Copper  loss,  1/2  load,  K.W.  hours  =  0.0375  X  2  =  0.075. 

Output,  K.W.  hours  =   j  (10  X  3)  +  (5  X  2)  }  =40. 

Input,  K.W.  hours  =  40  +  3.6  +  0.45  +  0.075  =  44.125. 
All-day  efficiency  =  40  -r  44.125  =  0.907. 

Connections. — Among  the  great  variety  of  transformer  manipula- 
tions in  power  and  general  distribution  work,  either  for  straight  voltage 
transformation  or  for  phase  transformation,  the  following  are  the  most 
generally  used: 

Voltage  Transformation: 
Single-phase. 
Two-phase. 

Three-phase,  delta-delta. 
Three-phase,  delta-star,  and  vice  versa. 
Three-phase,  star-star. 
Three-phase,  open-delta. 
Three-phase,  Tee. 
Phase  Transformation: 

Two-  or  three-phase  to  single-phase. 
Two-phase  to  six-phase. 
Three-phase  to  two-phase. 
Three-phase  to  six-phase. 

The  transformer  connections  mostly  used  are  delta-delta  or  delta-star 
with  neutral  grounded. 

For  moderate  voltage  systems,  the  isolated  delta  connection  is  to 
be  preferred,  although  for  high-tension  systems  with  very  high  voltages 


FIG.  247. 


FIG.  249. 


practice  has  proved  that  the  high-tension  winding  star  connected  and 
the  neutral  grounded  will  give  a  more  satisfactory  operation. 

Tee -Connection. — (Fig.  247.) — T- connection  requires  only  two  single 
transformers  of  which  one  is  provided  with  a  50  per  cent  tap  to  which 
the  other  is  connected.  The  latter  may  be  designed  for  only  86.6%  of 
the  line  or  main  transformer  voltage,  but  generally  it  is  made  identical 
with  the  main  transformer  and  operated  at  reduced  flux  density. 

Delta-Connection. —  (Fig.  248.) — The  e.m.f.  between  the  mains  is  the 
same  as  that  in  any  one  transformer  measured  between  terminals,  and 
each  transformer  must,  therefore,  be  wound  for  the  full  line  voltage,  but 

only  for or  57.7  per  cent  of  the  line  current. 

\/~3 

Star-Connection. — (Fig.  249.) — In  the  star-connection  each  trans- 
former has  one  terminal  connected  to  a  common  junction,  or  neutral 
point.  Each  transformer  is  wound  for  only  57.7  per  cent  of  the  line 
voltage,  but  for  the  full  line  current. 

Reactance. — In  order  to  obtain  a  good  voltage  regulation,  it  has  been 
the  custom  to  design  the  transformers  with  a  reactance  as  low  as  H/2  to 
2  per  cent.  Recent  experience  has,  however,  shown  that  in  high  power 
systems  such  transformers  are  unsafe,  owing  to  the  enormous  mechan- 
ical strain  produced  on  the  transformer  and  system  by  the  excessive 
short-circuit  currents  permitted  by  such  low  impedance  transformers. 


SYNCHRONOUS   CONVERTERS.  1453 

A  2  per  cent  reactance  means  that  at  full  load  current,  2  per  cent  or  1/50 
of  the  supply  voltage  is  consumed  by  the  reactance.  At  short  circuit 
the  total  voltage  would  have  to  be  consumed  by  the  transformer  re- 
actance, and  the  short-circuit  current  at  full  voltage  is  then  fifty  times 
full  load  current.  Safety  thus  requires  that  in  high  power  systems  the 
transformers  should  be  designed  for  a  much  higher  reactance  and  the 
present  practice  (1915)  is,  therefore,  to  design  such  transformers  for 
6  to  8  per  cent  reactance,  and  sometimes  even  for  as  high  as  10  per  cent. 

Cooling. — According  to  the  method  used  in  diss.'pating  the  heat 
generated  by  the  losses,  transformers  may  be  classified  as:  1.  Oil 
cooled.  2.  Water  cooled.  3.  Air  blast. 

Parallel  Operation. — In  order  that  two  or  more  transformers  or  groups 
of  transformers  shall  operate  successfully  in  parallel,  it  is  necessary  that 
their  polarity  be  the  same,  that  their  voltages  and  voltage  ratios  be 
identical,  and  that  their  impedances  be  inversely  proportional  to  the 
ratings. 

Auto  Transformers. — -Auto  transformers  may  be  used  where  the 
required  voltage  change  is  small.  Their  action  is  similar  to  that  of 
ordinary  transformers,  the  essential  difference  between  the  two  being 
that  in  the  transformer  the  high- voltage  and  low-voltage  windings  are 
separate  and  insulated  from  each  other  while  in  the  auto-transformer  a 
portion  of  the  winding  is  common  to  both  the  high  and  low  voltage 
circuits. 

The  high-  and  low- voltage  currents  in  both  types  of  transformers 
are  in  opposite  direction  to  each  other,  and  thus  in  an  auto-transformer 
a  portion  of  the  winding  carries  only  the  difference  between  the  two 
currents. 

Auto  transformers  are  extensively  used  for  alternating  current  motor 
starters,  and  also  to  some  extent  in  moderate  voltage  generating  stations. 

Constant-Current  Transformers. — The  transformers  heretofore  dis- 
cussed are  constant-potential  transformers  and  operate  at  a  constant 
voltage  with  a  variable  current.  For  the  operation  of  lamps  in  series  a 
constant-current  transformer  is  required.  There  are  a  number  of  types 
of  this  transformer.  That  manufactured  by  the  General  Electric  Co. 
operates  by  causing  the  primary  and  secondary  coils  to  approach  or  to 
separate  on  any  change  in  the  current. 

SYNCHRONOUS  CONVERTERS. 

A  synchronous  converter  is  essentially  a  continuous-current  gener- 
ator, which,  in  addition  to  its  commutator,  is  supplied  with  two  or  more 
collector  rings  connected  to  suitable  points  in  the  armature  winding.  If 
such  a  machine  be  driven  by  mechanical  power,  it  will  evidently  deliver 
either  alternating  or  direct  current,  and,  conversely,  if  supplied  with 
electric  power,  it  will  operate  either  as  a  synchronous  motor,  as  a  direct- 
current  motor,  or  as  a  synchronous  converter.  When  operated  as  a 
converter,  the  alternating  current  enters  the  armature  winding  through 
the  collector  rings,  and  aftei*  being  rectified  by  the  commutator,  is  de- 
livered as  direct  current,  or  vice  versa. 

The  alternating  and  direct  current  e.m.f.  stand  hi  a  certain  relation 
or  ratio  to  each  other,  and  this  depends  upon  the  number  of  phases  and 
frequency  of  the  system  used,  and  also  upon  the  ratio  of  maximum  to 
the  square  root  of  the  mean  square  value  of  the  impressed  e.m.f.  (that 
is,  the  e.m.f.  of  the  supply  circuit).  It  also  depends  upon  the  load  of 
the  machine,  the  ohmic  armature  losses,  the  position  of  the  direct- 
current  brushes  on  the  commutator,  the  excitation,  the  ratio  of  pole  arc 
to  pole  pitch,  and  upon  the  operating  conditions,  that  is,  whether  the 
machine  is  used  to  convert  from  alternating  to  direct  current  or  vice 
versa.  Synchronous  converters  for  60  cycles,  which  usually  have  a 
lower  ratio  of  pole  arc  to  pole  pitch  than  25  cycle  converters,  have,  as  a 
rule,  a  higher  voltage  ratio  and,  when  used  as  inverted  converters,  a 
lower  voltage  ratio  than  corresponding  25  cycle  machines. 

In  the  two-ring  or  single-phase  converter,  the  two  collector  rings  are 
connected  to  armature  conductors  with  the  same  angular  distance  apart 
as  commutator  bars  under  adjacent  sets  of  brushes.  At  this  instant 
the  e.m.f.  between  the  collector  rings  is  at  its  maximum  value  and 
equal  to  the  e.m.f.  between  the  direct-current  brushes.  Therefore, 
tne  direct-current  e.m.f.  (JS)  of  a  two-ring  single-phase  synchronous 


1454  ELECTRICAL  ENGINEERING. 

converter  is  equal  to  the  maximum  value  (\/2~X  E2)  of  the  sine  wave 
e.m.f.  between  the  two  collector  rings.     Therefore, 

„         E 

E2  =  —  — 
V^2 

in  which  E%  is  the  effective  value  of  the  single-phase  alternating  e.m.f. 

The  effective  e.m.f.  between  the  two  collector  rings,  which  are  con- 
nected to  the  armature  winding  at  points  120  electrical  degrees  apart, 
that  is,  between  any  two  rings  of  a  three-ring  three-phase  converter,  is 
represented  by  that  chord  of  a  polygon  which  subtends  an  angle  of 
120  degrees.  Likewise,  the  e.m.f.  between  two  rings  which  are  con- 
nected to  the  armature  winding  at  points  90  electrical  degrees  apart,  as 
between  two  adjacent  rings  in  a  four-ring  quarter-phase  converter,  is 
represented  by  the  chord  which  subtends  an  'angle  of  90  electrical  de- 
grees; and  the  chord  which  subtends  an  angle  of  60  electrical  degrees 
represents  the  e.m.f.  between  two  adjacent  rings  of  a  six-ring  six- 
phase  synchronous  converter. 

In  general,  the  effective  e.m.f.,  E\,  between  adjacent  rings  of  an 
n-ring  converter,  is  represented  by  that  chord  of  a  polygon  which  sub- 


n 

tends  an  angle  of  —  ^—  or  —  .     Therefore, 


This  gives  the  following  theoretical  values  of  the  effective  alternating 
e.m.f.  between  adjacent  collector  rings  of  a  two-ring,  three-ring,  four- 
ring  and  six-ring  synchronous  converter,  expressed  in  terms  of  the 
e.m.f.,  E,  between  the  direct-current  brushes: 

7^ 

For  single-phase       Ei  =  —-=  =  0.707  E, 


For  three-phase        Ei  =  =  0.612  E, 

2  \^2 

77" 

For  quarter-phase    Ei  =  —  =  0.500  E, 

For  six-phase  Ei  =      Ef__  =  0.354  E. 

2  V2 

The  above  ratios  represent,  as  before  stated,  the  effective  alternating 
e.m.f.  between  two  adjacent  collector  rings.  For  quarter-  and  six-phase 
converters  the  different  phases  of  the  supply  circuit,  however,  are  not 
connected  as  a  rule  to  adjacent  rings  and  the  ratios  given  above  are  not 
the  ones  to  be  used  for  determining  the  alternating  supply  voltage  for 
these  types  of  synchronous  converters. 

For  the  four-ring  quarter-phase  converter,  each  phase  of  the  supply 
circuit  is  generally  connected  to  diametrically  opposite  points  of  the 
armature  winding  and  the  ratio  will,  under  such  conditions,  be  equal 
to  the  ratio  for  the  two-ring  single-phase  converters,  that  is,  for  quarter- 

phase  Ei  =  -^L  =  0.707  E. 

V/2 

For  six-phase  synchronous  converters  two  different  arrangements  of 
the  connections  are  generally  used.  One  is  called  the  "double  delta" 
connection  and  the  other  the  "diametrical"  connection.  In  the  first 
case,  the  voltage  ratio  is  the  same  as  for  the  three-phase  synchronous 
converter  and  simpfy  consists  of  two  "delta"  systems.  The  trans- 
formers can  also  be  connected  in  "double-star,"  and  in  such  a  case  the 
ratio  between  the  three-phase  voltage  between  the  terminals  of  each 
star  and  the  direct  voltage  will  be  the  same  as  for  "double-delta," 

while  the  voltage  of  each  transformer  coil,  or  voltage  to  neutral,  is  —  —  = 

V^ 
times  as  much.    With  the  diametrical  connection  the  ratio  is  the  same 


SYNCHRONOUS    CONVEHTEKb.  1455 

as  for  the  two-ring  single-phase  converter,  it  being  analogous  to  three 
such  systems.     Therefore 

Six-phase  double-delta,  JEj.  =  — ?^  =  0.612  E. 
2\/2 

Six-phase  diametrical,     EI  =  -^L  =  0.707  E. 

Vz 

The  ratio  of  the  effective  e.m.f.,  E0,  between  any  collector  ring  and 
the  neutral  point  is  always 

EQ  =  —-=  =  0.354  E. 
2  \/2 

The  given  voltage  ratios  are,  as  stated,  only  theoretical ,  as  the  losses 
in  the  winding  have  been  neglected  and  the  assumption  has  been  made 
that  both  the  impressed  and  the  counter  generated  converter  e.m.f. 
has  a  sine  wave  shape.  The  ratio  between  the  alternating  and  direct 
terminal  voltages  is  somewhat  different  from  the  theoretical  ratio  due 
to  the  voltage  drop  in  the  armature  and  to  the  wave  shapes  of  the 
e.m.f. 's.  The  exact  ratios  are  always  furnished  by  the  manufacturer. 

Synchronous  converters  may  be  either  of  the  shunt-  or  compound- 
wound  type,  the  choice  depending  on  the  character  of  the  service  for 
which  they  are  to  be  used.  In  the  majority  of  installations,  especially 
for  power  purposes,  compound- wound  converters  are  generally  used 
because  they  automatically  regulate  for  a  comparatively  constant 
direct-current  voltage. 

In  order  to  change  the  direct  voltage  in  the  ordinary  type  of  syn- 
chronous converter  with  constant  voltage  ratio,  it  is  necessary  to 
provide  means  for  changing  the  applied  alternating  voltage  correspond- 
ingly. This  can  be  done  in  several  ways,  one  of  which  is  to  provide  taps 
on  the  step-down  transformers  and  adjust  the  ratio  of  transformation 
by  means  of  a  dial  switch.  A  much  better  method,  however,  is  the  use 
of  an  induction  regulator  between  the  transformer  secondary  terminals 
and  the  synchronous  converter.  This  regulator  consists  of  a  stationary 
series  winding  and  a  movable  potential  winding,  which  can  be  turned 
through  a  certain  angle,  and  at  each  angular  position  will  raise  or  lower 
the  voltage  at  the  collector  rings  a  certain  amount,  through  the  mutual 
action  of  the  current  and  potential  windings.  This  method  of  control 
is  generally  used  with  shunt- wound  synchronous  converters  in  order  to 
keep  the  voltage  constant,  when  the  line  drop  is  excessive.  The  induc- 
tion regulator  is  either  hand-operated  by  means  of  chain  or  motor 
drive,  or  the  control  can  be  made  automatic  by  using  a  contact-making 
voltmeter  and  relay,  which  will  automatically  control  the  regulator 
motor. 

The  voltage  regulation  can  also  be  accomplished  by  taking  ad  van  tag/" 
of  the  fact  that  an  alternating  current  passing  over  an  inductive  circuit 
will  decrease  in  potential  if  lagging,  and  increase  if  leading.  By  pro- 
viding the  synchronous  converter  with  a  series  field  winding  in  addition 
to  the  shunt  field,  the  excitation  can  be  automatically  regulated  as  the 
load  comes  on.  The  inductance  of  the  supply  circuit  and  step-down 
transformers  is,  however,  frequently  not  sufficient  to  cause  the  required 
boost  in  the  voltage,  and  in  such  a  case  it  becomes  necessary  to  insert 
extra  reactance  coils  in  the  line  or  provide  the  step-down  transformers 
with  extra  high  reactance. 

There  are  three  feasible  methods  of  starting  synchronous  converters: 
First,  the  application  of  alternating  current  at  reduced  voltage  to  the 
collection  rings;  second,  the  application  of  direct  current  to  the  commu- 
tator and  starting  the  machine  as  a  direct-current  motor;  third,  the  use 
of  an  auxiliary  starting  motor  mechanically  connected. 

The  alternating  current  starting  method  has  many  advantages  over 
the  other  methods.  It  is  self-synchronizing,  and,  therefore,  entirely 
eliminates  the  difficulty  of  accurately  adjusting  the  speed.  When  the 
speed  of  the  prime  movers  is  liable  to  be  variable,  the  ability  to  start  a 
machine  quickly  and  get  it  on  the  line  in  the  shortest  possible  time  is  a 
great  advantage  inherent  to  .this  method  of  starting.  It  is  possible  for 
the  Converter  to  drop  into  step  with  its  direct-current  voltage  reversed 
from  that  of  the  bus  to  which  the  machine  is  to  be  connected,  but  the 


1456  ELECTRICAL  ENGINEERING. 

machine  can  easily  be  made  to  drop  back  a  pole  by  a  self-exciting  field 
reversing  switch  on  the  machine  frame.  This  method  of  starting  makes 
the  operation  of  the  machine  so  simple  that  the  liability  of  confusion 
and  mistakes  by  operators  Is  greatly  reduced. 

If  several  synchronous  converters  are  to  supply  the  same  direct- 
current  system,  they  can  be  connected  in  parallel  in  the  same  manner 
as  shunt-  or  compound -wound  generators,  and  they  are  even  frequently 
operated  in  parallel  with  such  generators  and  storage  batteries.  The 
different  converters  will  divide  the  load  according  to  their  direct-current 


r s  voltage  regulation  from  no-load  to  1 

load,  and  if  a  battery  is  also  operated  in  parallel  the  voltage  drop  should 
be  sufficiently  large  so  as  to  cause  the  battery  to  take  the  excessive 
loads.  Synchronous  converters  operated  in  parallel  should  not  be  con- 
nected to  the  same  transformer  secondaries.  Such  a  connection  would 
form  a  closed  local  circuit  in  which  heavy  cross-currents  would  flow 
when  any  difference  in  the  operating  conditions  of  the  machine  occurs, 
as,  for  example,  if  the  brushes  of  one  of  the  machines  were  slightly 
displaced  relative  to  the  other. 

Compound-wound  converters  for  parallel  operation  should  be  pro- 
vided with  equalizer  switches.  For  connecting  a  compound- wound  con- 
verter in  parallel  with  one  already  running,  the  equalizer  switch  is 
closed  first,  so  as  to  energize  the  series  field  from  the  running  machine. 
Next,  the  shunt  field  circuit  is  closed  and  the  field  adjusted  so  that  the 
voltage  will  correspond  to  that  of  the  first  machine,  and  finally  the 
main  switch  is  closed.  The  load  can  then  be  transferred  from  the  first 
to  the  second  converter  by  weakening  the  shunt  field  of  the  former  and 
strengthening  that  of  the  latter. 

MOTOR-GENERATORS. 

Motor-generator  sets  may  be  divided  into  three  general  classes: 

1.  Direct  current  to  direct  current  sets,  including  balancing  sets  for 
three-wire  lighting  systems,  and  for  variable  speed  motor  work,  boosters 
for  storage  battery  charging  and  railway  or  lighting  feeders. 

2.  Alternating  current  to  direct  current  sets  or  vice  versa.    These  are 
used  for  excitation  purposes  and  for  supply  of  lighting,  railway  or 
power  systems.     The  sets  may  be  driven  either  with  synchronous  or 
induction  motors,  the  former  being  equipped  with  an  auxiliary  squirrel 
cage  winding  on  the  fields  so  as  to  be  self-starting  at  reduced  voltage. 

3.  Alternating  current  to  alternating  current  sets  between  the  two 
periodicities;  commonly  called  "frequency  changers." 

Balancers. — The  balancer  set,  a  form  of  direct-current  compensator, 
is  a  variation  of  the  regular  motor-generator  set,  in  that  the  units  of 
which  it  is  composed  may  be,  alternately,  motor  or  generator,  and  the 
secondary  circuit  is  interconnected  with  the  primary.  On  account  of 
the  latter  feature,  the  efficiency  of  transformation  is  higher  and  a 
larger  output  is  obtainable  from  a  given  amount  of  material  than  in  the 
straight  motor-generator  set. 

Balancer  sets  are  widely  used  to  provide  the  neutral  of  Edison 
three-wire  lighting  systems.  They  are  also  installed  for  power  service 
in  connection  with  the  use  of  250-volt  motors  on  a  500-volt  service 
or  125- volt  motors  on  a  250-volt  service. 

The  potential  of  the  system  being  given,  the  capacity  of  a  three- wire 
balancer  set  is  fixed  by  the  maximum  current  the  neutral  wire  is  required 
to  carry.  This  figure  is  a  more  definite  specification  of  capacity  than  a 
statement  in  per  cent  of  unbalanced  load. 

As  designed  for  power  work  and  generally  for  lighting  service,  the 
brushes  of  each  machine  are  set  at  the  neutral  point  in  order  to  get  the 
best  results  for  operating  alternately  either  as  a  generator  or  motor. 
Where  the  changes  of  balance  are  so  gradual  as  to  permit  of  hand  ad- 
justment, if  desired,  a  considerable  increase  in  output  is  obtainable. 

Boosters. — Boosters  are  extensively  used  in  railway  stations  to  raise 
the  potential  of  the  feeders  extending  to  distant  points  of  the  system; 
for  storage-battery  charging  and  regulation;  and  in  connection  with  the 
Edison  three-wire  lighting  system.  The  design  of  the  various  sets  is 
closely  dependent  upon  their  application. 


ALTERNATING-CURRENT  CIRCUITS.  1457 

Booster  sets  are  constructed  in  either  "series-  or  shunt-wound  types, 
and  they  may  be  arranged  for  either  automatic  or  hand  regulation, 
depending  on  the  nature  of  the  service  required. 

Where  there  are  a  number  of  lighting  feeders  connected  and  run  at 
full  load  for  only  a  short  time  each  day  it  will  generally  be  economical 
to  install  boosters  rather  than  to  invest  in  additional  feeder  copper. 
It  is  important,  however,  to  consider  each  case  where  the  question  of 
installing  a  booster  arises,  as  a  separate  problem,  and  to  determine  if 
the  value  of  the  power  lost  represents  an  amount  lower  than  the  interest 
charge  on  the  extra  copper  necessary  to  deliver  the  same  potential 
without  the  use  of  a  booster. 

Dynamotors.  —  A  dynamotor  is  a  machine  for  reducing  a  direct- 
current  voltage,  and  it  is  extensively  used  in  connection  with  high  voltage 
railway  equipments  for  obtaining  a  moderate  voltage  for  the  control.  It 
has  two  armature  windings  and  commutators  on  one  drum,  with  the  field 
between  them.  The  control  current  is  taken  midway  between  the  arma- 
tures and  is  returned  to  the  ground  side  of  the  dynamotor.  This  insures 
that  the  maximum  potential  on  the  control  circuit,  under  normal  condi- 
tions, will  be  approximately  one-half  of  the  line  voltage,  and  the  potential 
to  grounded  parts  no  greater  than  when  operated  directly  on  a  line  voltage 
of  one-half  the  amount. 

Frequency  Changers. — A  periodicity  of  25  cycles  has  been  quite  gen- 
erally selected  for  railway  service.  Also  in  certain  large  cities,  current  of 
the  same  frequency  is  generated  in  central  stations  and  distributed:  to 
substations  in  which  are  installed  rotary  converters  supplying  an  Edison 
three-wire  network. 

Inasmuch  as  the  periodicity  of  60  cycles  is  more  favorable  than  25 
cycles  for  alternating  current  lighting,  frequency  changers,  similar  to  that 
shown  above,  are  installed  to  furnish  high  tension  60-cycle  current  for 
distribution  to  outlying  districts  beyond  the  reach  of  the  three-wire 
system. 

In  the  design  of  frequency  changers  speeds  must  be  selected  that  are 
common  to  the  two  periodicities  of  the  system  upon  which  they  are  tc  . 
be  used;  since  300  r.p.m.  is  the  highest  speed  common  to  25  and  60  cycles, 
at  which  speed  small  sets  are  expensive  per  kilowatt,  a  line  of  sets  with ' 
4  or  8  pole  motors  and  10  or  20  pole  generators  has  been  developed,  giving 
62 1/2  cycles  from  25  cycles  or  60  cycles  from  24  cycles. 

Where  parallel  operation  is  required  between  synchronous  motor- 
driven  frequency  changers,  a  mechanical  adjustment  is  necessary  between 
the  fields  or  armatures  of  the  generator  and  motor  to  obtain  equal  division 
of  the  load.  The  adjustment  is  best  obtained  by  the  cradle  construction. 
The  stator  of  one  machine  is  bolted  to  a  cradle  fastened  to  the  base,  and 
by  taking  out  the  bolts  the  frame  can  be  turned  around  through  a  small 
angle  relatively  to  the  cradle,  and  therefore  to  the  stator  field  of  the  other 
machine,  where  the  bolts  can  be  replaced. 

The  Mercury  Arc  Rectifier  consists  of  a  mercury  vapor  arc  enclosed 
In  an  exhausted  glass  vessel  into  which  are  sealed  two  terminal  anodes 
connected  to  the  two  wires  of  an  alternating-current  circuit.  A  third 
terminal,  at  the  bottom  of  the  vessel,  is  a  mercury  cathode.  When  an 
arc  is  operating,  it  is  a  good  conductor  from  either  anode  to  the  cathode, 
but  practically  an  insulator  in  the  other  direction.  The  two  anodes 
connected  across  the  terminals  of  the  alternating-current  line  become 
alternately  positive  and  negative.  While  either  anode  is  positive,  there 
is  an  arc  carrying  the  current  between  it  and  the  cathode.  When  the 
polarity  of  the  alternating-current  reverses,  the  arc  passes  from  the  other 
anode  to  the  mercury  cathode,  which  is  always  negative.  The  current 
leading  out  from  the  mercury  cathode  is  uni-directional.  By  means  of 
reactances,  the  pulsations  are  smoothed  out  and  the  current  at  the  cathode 
becomes  a  true  direct  current  with  pulsations  of  small  amplitude. 

ALTERNATING-CURRENT    CIRCUITS. 

Calculation  of  Alternating-current  Circuits. — The  following  formulae 
and  tables  are  issued  by  the  General  Electric  Co.  They  afford  a  con- 
venient method  of  calculating  the  sizes  of  conductors  for,  and  determining 
the  losses  in,  alternating-current  circuits.  They  apply  only  to  circuits 
in  which  the  conductors  are  spaced  18  inches  apart,  but  a  slight  increase 
or  decrease  in  this  distance  does  not  alter  the  figures  appreciably.  If 


1458 


KLECTH1CAL  ENGINEERING. 


the  conductors  arc  less  than  18  inches  apart,  the  loss  of  voltage  is  de- 

creased, and  vice  versa. 

Let  W  ==  total  power  delivered  In  watts: 

D  =  distance  of  transmission  (one  way)  in  feet; 

P*  —  per  cent  loss  of  delivered  power  (  W)  ; 

E  =  voltage  between  main  conductors  at  consumers  end  of  circuit-, 

K  —  a  constant;  for  continuous  current  =  2160; 

T  =  a  variable  depending  on  the  system  and  nature  of  the  load;  for 
continuous  current  =  1; 

M  =  a  variable,  depending  on  the  size  of  wire  and  frequency;  for  con- 
tinuous current  =  1  ; 

A  =  a  factor;  for  continuous  current  =  6.04. 

D  X  W  X  K 
Area  of  conductor,  circular  mills  =  — 


p  x  E* 

Current  in  main  conductors  =  Wx  T  +  E; 
Volts  lost  in  lines  =  P  X  E  X  M  -r  100; 

^  z>2  x  WXKXA 

Pounds  copper  =  - 


The  value  of  M  is  found  from  the  formula:    M  -- 

X  =  0.000882  /  flogio  (£}  +  0.109J 

X  =  Reactance. 

R  =  Resistance,  ohms  per  1000  ft.,  at  60°  F. 
sen's  standard.) 

d  =  inches  between  wires. 

r  =  radius  of  wire,  inches. 

/  =  cycles  per  second. 


(Wire  100%  Matthics- 


VALUES  OF  M  —  WIRES  18  IN.  APART,  f 

WIRES  36  IN.  APART.  $ 

25  Cycles. 

60  Cycles. 

25  Cycles. 

Power 

Factors. 

0.95    0.90    0.85    0.80 

0.95    0.90    0.85    0.80 

0.95    0.90    0.85    0.80 

Wire  Sizes. 
0000 
000 
00 
0 
1 
2 

4 

6 
7 

8 
9 
10 

.17    1.16    1.12    1.06 
.12    1.09    1.05    0.99 
.08    1.04    0.99      .92 
.05    1.00      .94      .87 
.02    0.96      .90      .83 
.00      .93      .86      .79 
0.98      .91      .84      .76 
.96     .89      .81      .74 
.95      .88      .80      .72 
.94     .86     .78     .70 
.94     .85     .77     .69 
.93     .85     .76     .68 
.92     .84     .76     .67 
.92      .83      .75      .67 

( 

.53 
.41 
.32 
.24 
.18 
.12 
.08 
.05 
.02    ( 
.00 
).98 
.97 
.95 
.94 

.64      .67      .66 
.49      .50      .47 
.36      .35      .31 
.26      .24      .19 
.17      .14      .08 
.10      .06      .00 
.05    0.99    0.93 
.00      .94      .87 
).97      .90      .83 
.94      .87      .79 
.91      .84      .76 
.89      .82      .74 
.88      .80      .72 
.86      .79      .71 

.22    1.23    1.20    1.15 
.16    1.15    1.11     1.05 
.11     1.08    1.04    0.97 
.07    1.03    0.98      .91 
.04    0.99      .93      .86 
.02      .95      .89     .82 

JFor   higher   volt- 
ages,   10,000  to  200,- 
000. 

Per  cent  of 
Power  Factor. 

Value  of  K. 

Value  of  T. 

sL 

•a4** 
>*o 

100 

95 

85 

J0_ 

3380 
1690 
1690 

100    95 

85 

80 

System: 
Single-phase 

2160 
1080 
1080 

2400,3000 
1200  1500 
1200  1500 

1.00  1.05  1.17 
0.500.530.59 
0.58  0.61  0.68 

1.25 
0.62 
0.72 

•  6.04 
12.08 
9.06 

Two-phase,  4-  wire     

Three-phase,  3-wire  

*  P  should  be  expressed  as  a  whole  number,  not  as  a  decimal;  thus 
a  5  per  cent  loss  should  be  written  5,  not  .05. 

t  As  corrected  by  Harold  Pender,  see  Elect.  World,  July  1,  1905.  The 
formula  for  M  is  approximate,  and  gives  values  correct  within  2  %  for 
any  case  likely  to  arise  in  practice. 


ALTERNATING-CURRENT   CIRCUITS. 


1459 


.  Relative  Weight  of  Copper  Required  in  Different  Systems  for 
Equal  Effective  Voltages. 

Direct  current,  ordinary   two- wire  system 1 . 000 

three-wire  system,  all  wires  same  size 0. 375 

neutral  one-half  size 0.313 

Alternating  current,  single-phase  two-wire,  and  two-phase  four- wirel. 000 
Two-phase  three-wire,  voltage  between  outer  and  middle  wire 

same  as  in  single-phase  two-wire 0 . 729 

voltage  between  two  outer  wires  same ...   1 . 457 

Three-phase  three- wire 0 . 750 

"      four-wire 0.333 

The  weight  of  copper  is  inversely  proportional  to  the  squares  of  the 
voltages,  other  things  being  equal.  The  maximum  value  of  an  alter- 
nating e.m.f.  is  1.41  times  its  effective  rating.  For  derivation  of  the 
above  figures  see  Crocker's  "Electric  Lighting,"  vol.  ii. 

Approximate  Rule  for  Size  of  Wires  for  Three-Phase  Transmission 
Lines.    (General  Electric  Co.) 

The  table  given  below  is  for  use  in  making  rough  estimates  for  the 
sizes  of  wires  for  three-phase  transmission,  as  in  the  following  example. 

Required. — The  size  of  wires  to  deliver  500  Kw.  at  6000  volts,  at  the 
end  of  a  three-phase  line  12  miles  long,  allowing  an  energy  loss  of  10% 
and  a  power  factor  of  85%.  If  the  example  called  for  the  transmission 
of  100  Kw.  (on  which  the  table  is  based),  we  should  look  in  the  6000- 
volt  column  for  the  nearest  figure  to  the  given  distance,  and  take  the 
size  of  wire  corresponding.  But  the  example  calls  for  the  transmission 
of  five  times  this  amount  of  power,  and  the  size  of  wire  varies  directly 
as  the  distance,  which  in  this  case  is  12  miles.  Therefore  we  look  for 
the  product  5  X  12  =  60  in  the  6000- volt  column  of  the  table.  The 
nearest  value  is  60.44  and  the  size  of  wire  corresponding  is  No.  00,  which 
is,  therefore,  the  size  capable  of  transmitting  100  Kw.  over  a  line  60.44 
miles  long,  or  500  Kw.  over  a  line  12  miles  long,  as  required  by  the  example. 

If  it  is  desired  to  ascertain  the  size  of  wire  which  will  given  an  energy 
loss  of  5%,  or  one-half  the  loss  for  which  the  table  is  computed,  it  is 
only  necessary  to  multiply  the  value,  obtained  by  2,  since  the  area 
varies  inversely  as  the  per  cent  energy  loss. 

DISTANCES  TO  WHICH  100  Kw.  THREE-PHASE  CURRENT  CAN  BE  TRANS- 
MITTED OVER  DIFFERENT  SIZES  OF  WIRES  AT  DIFFERENT  POTEN- 
TIALS, ASSUMING  AN  ENERGY  Loss  OF  10%  AND  A  POWER  FACTOR 
OF  85%. 


Num- 

Area  in 

Distance  of  Transmission  for  Various  Potentials  at 

ber 

Circular 

Receiving  End,  in  Miles. 

B.  &  S. 

Mils. 

2,000 

4,000 

6.000 

8,000 

10,000 

15,000 

20.000 

25,000 

30,000 

6 

26,250 

1.32 

5.28 

11.92 

21.12 

33.1 

74.50 

132.4 

206.75 

298 

5 

33,100 

1.66 

6.64 

15.00 

26.56 

41.6 

93.75 

166.4 

260.00 

375 

4 

41,740 

2.10 

8.40 

18.96 

33.60 

52.6 

118.50 

210.4 

328.75 

474 

3 

52,630 

2.54 

10.16 

23.84 

40.64 

66.2 

149.00 

254.8 

413.75 

596 

2 

66.370 

3.33 

13.32 

30.04 

53.28 

83.4 

187.75 

333.6 

521.25 

751 

83,690 

4.21 

16.84 

37.92 

67.36 

105.3 

212.00 

421.2 

658.00 

948 

0 

105,500 

5.29 

21.16 

47.68 

84.64 

132.4 

298.00 

529.6 

827.50 

1192 

00 

133,100 

6.71 

26.84 

60.44 

107.36 

167.9 

377.75 

671.6 

1049.25 

1511 

000 

167,800 

8.45 

33.80 

76.16 

135.20 

211.4 

476.00 

845.6 

1321.25 

1904 

0000 

211,600 

10.62 

42.48 

95.68 

169.92 

265.7 

598.00 

1062.8 

1660.50 

2392 

250,000 

12.58 

50.32 

113.32 

201.28 

3147 

708.25 

1258.8 

1966.75 

2833 

500,000 

25.17 

100.68 

226.64 

402.72 

629.4 

1416.50 

2517.6 

3933.75 

5666 

Notes  on  High-tension  Transmission. — The  cross-sectional  area  and, 
consequently,  weight  of  conductors  vary  inversely  as  the  square  of  the 
voltage  for  a  given  power  transmission.  The  cost  of  conductors  is  there- 
fore reduced  75%  every  time  the  voltage  is  doubled.  The  cost  of  other 
apparatus  and  appliances  increases  with  increasing  voltage.  For  long- 
distance lines  the  saving  in  copper  with  the  'highest  practicable  voltages 
is  so  great  that  the  other  expenses  are  rendered  practically  negligible.  In 
the  shorter  lines,  however,  the" most  suitable  voltage  must  be  determined 


1460 


ELECTRICAL  ENGINEERING. 


in  each  individual  case.    The  voltages  in  the  following  table  will  serve  ad 
a  guide. 

VOLTAGES  ADVISABLE  FOR  VARIOUS  LINE  LENGTHS. 


Miles. 

Volts. 

Miles. 

Volts. 

Miles. 

Volts. 

1-2 
2-3 

500-1000 
1000-2300 
2300-6600 

3-10 
10-15 
15-20 

6600-13,200 
13,200-22,000 
22,000-44,000 

20-40 
40-60 
60-100 

44,000-  66,000 
66,000-  88,000 
88,000-110,000 

Standard  machinery  is  made  for  2300,  6600,  13,200,  22,000,  33,000, 
44,000,  66,000,  88,000  and  110,000  volts,  and  standard  generators  are 
made  for  the  above  voltages  up  to  and  including  13,200  volts.  When 
the  line  voltage  is  higjier  than  13,200,  step-up  transformers  must  be 
employed.  In  a  given  case  the  saving  in  cost  of  conductor  by  using  the 
higher  voltage  may  be  more  than  offset  by  the  cost  of  transformers,  and 
the  question  of  voltage  must  be  determined  for  each  case. 

Line  Spacing. — Line  conductors  should  be  so  spaced  as  to  lessen  the 
tendency  to  leakage  and  to  prevent  the  wires  from  swinging  together 
or  against  the  towers.  With  suspended  disk  insulators  the  radius  of  free 
movement  is  increased,  and  special  account  should  be  taken  of  spacing 
when  these  insulators  are  used.  The  spacing  should  be  only  sufficient 
for  safety,  since  increased  spacing  increases  the  self-induction  of  the  line, 
and  while  it  lessens  the  capacity,  it  does  so  only  in  a  slight  degree.  The 
following  spacing  is  in  accordance  with  average  practice. 

CONDUCTOR  SPACING  ADVISABLE  FOR  VARIOUS  VOLTAGES. 
Volts.                                      Spacing.        Volts.  Spacing. 

33,000 3  feet.        88,000 8  feet. 


44,000 4  feet.  110,000 10  feet. 

66,000 6  feet.  140,000 12  feet. 

Aluminum  Conductors. — The  conductivity  of  aluminum  is  generally 
taken  at  63.3%,  that  of  hard-drawn  copper  of  the  same  cross-sectional 
area.  The  weight  of  Al  is  30.2  %  that  of  C9pper,  and  therefore  an  Al 
conductor  of  the  same  length  and  conductivity  as  a  given  copper  con- 
ductor weighs  47.7%  as  much.  The  cost  of  Al  must  therefore  be  2.097 
times  that  of  hard-drawn  copper  to  give  equal  cost  for  the  same  length 
and  conductivity.  Owing  to  the  mechanical  unreliability  of  solid  Al 
conductors,  stranded  conductors  are  used  in  all  sizes,  including  even  the 
smallest. 

The  Size  of  the  Line  Conductors  depends  on  both  economical  and 
electrical  considerations,  except  where  the  length  of  the  span  is  the  gov- 
erning feature.  With  expensive  steel  towers  it  becomes  necessary  to 
string  the  conductors  for  higher  stresses  so  as  to  reduce  the  sags  and 
consequently  the  height  of  the  towers  as  much  as  possible.  It  has,  there- 
fore, become  a  general  practice  to  erect  the  conductors  so  that  the  stress 
at  the  worst  load  conditions  equals  one-half  the  ultimate  strength  of  the 
conductor  material,  which  gives  a  factor  of  safety  of  two.  The  load  to 
which  a  line  conductor  is  subjected,  besides  its  own  weight  and  ice,  is 
acting  in  a  vertical  direction,  the  pressure  imposed  by  the  wind  acting  in 
a  horizontal  direction.  It  is  also  evident  that  the  stress  will  be  greater 
in  extremely  cold  weather  because  of  the  contraction  of  the  wires,  and 
it  is  generally  agreed  that  the  worst  load  condition  would  occur  at  0°  F. 
with  an  actual  wind  velocity  of  56  miles  per  hour  (8  pounds  pressure 
per  square  foot  projected  area)  and  with  an  ice  covering  one-half  inch 
thick.  The  maximum  temperature  is  considered  to  be  130°  F.,  and  the 
cables  should  be  so  supported  that  at  this  temperature  the  sag  does  not 
become  excessive,  but  allows  a  clearance  between  the  lowest  conductor 
and  ground  of  from  25  to  30  feet. 

Line  conductors  may  be  either  of  copper  or  aluminum.  It  is  advisable  for 
mechanical  reasons  in  spans  of  200  to  300  feet  never  to  use  smaller  cable 
than  No.  5  B.  &  S.  copper,  or  No.  1.  B.  &  S.  aluminum  (equivalent  of 
No.  3  copper).  For  spans  greater  than  300  feet,  the  minimum  sizes  of 
cable  allowable  are  those  which  will  give  a  reasonable  sag  at  the  most 
severe^  climatic  conditions  assumed.  Frequently  the  size  of  conductors, 


ELECTRIC   MOTORS.  1461 

determined  by  electrical  considerations,  limits  the  length  of  spans  to  a 
smaller  value  than  is  economical.  This  may  occur  even  with  moderately 
long  spans  —  500  to  600  feet  —  when  the  character  of  the  country  is  such  as 
to  make  transportation  costly  or  when  expensive  foundations  must  be 
used.  In  such  cases  it  will  often  be  found  that  a  saving  can  be  made  by 
increasing  the  size  of  conductor,  thereby  allowing  an  increase  in  the  length 
of  span  and  the  use  of  fewer  towers  of  approximately  the  same  height  and 
not  greatly  increased  weight. 

The  sag  or  deflection  at  the  center  of  a  span  can  be  figured  by  the 
formula: 


~    8T 

where  D  =  deflection  in  feet;  S  =  length  of  span  in  feet;   W  =  resultant  of 
weight  and  wind  in  Ibs.  per  foot  of  cable;  T  =  tension  on  cable  in  Ibs. 

A  135,000-  Volt  Three-phase  Transmission  System  from  Cook  Falls, 
Mich.,  to  Flint,  Mich.,  125  miles  distant,  is  described  in  Power,  Aug. 
9,  1910.  The  generating  equipment  comprises  three  3000-K.W. 
GCFcycle  alternators,  mounted  on  horizontal  shafts  driven  by  water- 
wheels.  The  available  head  of  water  is  40  ft.,  and  the  flow  averages 
1  100  cu.  ft.  per  second.  The  transmission  line  consists  of  three  No.  0 
copper  wires  carried  on  suspension-type  insulators  hung  from  the  cross- 
arms  of  55-ft.  tripod  steel  towers.  The  wires  are  at  the  angles  of  an 
isosceles  triangle  with  a  12-ft.  base  and  17-ft.  sides,  the  lowest  wire 
40  ft.  above  the  ground.  The  insulators  have  eight  disks  linked  in 
series,  each  disk  having  been  tested  to  withstand  continuously  75,000 
volts,  and  subjected  to  100,000  volts  for  a  brief  period. 

ELECTRIC   MOTORS. 

Classification.  —  Motors  maybe  classified  according  to  type,  speed,  and 
mechanical  features.  The  first  cover: 

Direct  Current  —  1.  Series.    2.  Shunt.     3.  Compound. 

Alternating  Current   (single-phase  and  polyphase)  —  1.  Synchronous. 
2.  Synchronous  Induction.  3.  Induction.    3a.  Phase-  wound.   3  b.  Squirrel- 
Cage.     4.  Commutator. 
According  to  their  speed,  they  are  classified  as  — 

Constant  Speed:  covering  cases  where  the  speed  is  constant  or  varies 
slightly. 

Adjustable  Speed:  covering  cases  where  the  speed  may  be  varied  over  a 
considerable  range,  but  when  once  fixed  remains  at  this  value  independent 
of  the  load  changes. 

Varying  Speed:  covering  cases  where  the  speed  changes  with  the 
load,  usually  decreasing  as  the  load  increases. 

Multi-Speed:  covering  cases  where  several  -distinct  speeds  may  be 
obtained  by  changing  the  connections  of  the  windings  or  by  other  means. 

According  to  their  mechanical  features  motors  may  be  classified  as: 
(1)  Open.  (2)  Mechanically  Protected.  (3)  Semi-Enclosed.  (4)  Totally 
Enclosed.  (5)  Enclosed,  Externally  Ventilated.  (6)  Enclosed,  Self-  Venti- 
lated. (7)  Moisture  Proof.  (8)  Splash  and  Water  Proof.  (9)  Submergible. 
(10)  Acid  Proof.  (11)  Explosion  Proof. 

Limitations.  —  The  principal  limitations  in  the  ratings  of  motors  are: 
(1)  Mechanical  Strength.  (2)  Heating.  (3)  Commutation.  (4)  Reg- 
ulation. (5)  Efficiency. 

CHARACTERISTICS    OF    MOTORS    AFFECTING    THEIR 
APPLICATIONS. 

(D.  B.  Rushmore,  "American  Handbook  for  Electrical  Engineers.") 

Series  Motor.  —  This  motor  is  used  when  a  powerful  starting  torque  and 
rapid  acceleration  are  required,  without  an  excessive  instantaneous  de- 
mand of  energy.  The  torque  is  practically  independent  of  the  voltage  and 
at  low-flux  densities  varies  directly  as  the  square  of  the  current,  but  as 
the  magnetization  approaches  saturation  it  becomes  more  nearly  p:*opor- 
tional  to  the  first  power  of  the  current.  The  maximum  torque  exists  at 


1462  ELECTRICAL  ENGINEERING. 

low  speed,  this  being  the  most  valuable  feature  of  the  series  motor. 
Dangerously  high  speeds  may  be  attained  by  the  armature  with  very 
light  loads,  and  series  motors  should  for  this  reason  be  either  geared  or 
direct  connected  to  the  load. 

Speed  Control  of  Series  Motor. — The  speed  of  a  series  motor  on 
constant  potential  varies  automatically  with  the  load,  increasing  as  the 
load  decreases.  The  speed  may,  however,  be  adjusted  if  some  means  of 
varying  the  impressed  voltage  is  provided.  As  the  work  required  of  a 
series  motor  is  very  often  intermittent  in  character,  the  insertion  of  re- 
sistance in  the  armature  circuit  to  reduce  the  speed  is  permissible  from  an 
economic  standpoint  in  such  cases.  In  others,  such  as  railway  work,  where 
two  or  four  motors  are  used,  reduced  voltage  is  most  readily  and  economi- 
cally obtained  by  connecting  the  motors  in  series  or  in  series  parallel. 

Shunt  Motor. — This  motor  has  good  starting  characteristics  and  a  prac- 
tically constant  speed,  varying  only  slightly  with  load  changes.  The  speed 
can,  however,  be  adjusted,  either  by  changing  the  e.m.f.  impressed  on  the 
armature  or  by  changing  the  field  flux. 

Speed  Adjustment  by  Armature-voltage  Control,  i.e.,  by  changing 
the  e.m.f.  impressed  on  the  armature,  does  not  change  the  full-load  torque 
which  the  motor  is  capable  of  exerting,  since  the  rated  torque  depends  only 
upon  field  flux  and  rated  armature  current.  These  methods  are  therefore 
constant-torque  methods  and  are  properly  adapted  to  loads  in  which  the 
torque  remains  constant  regardless  of  speed.  The  method  most  generally 
used  for  varying  the  impressed  e.m.f.  with  a  single-voltage  system  is  by 
means  of  inserting  resistance  in  series  with  the  armature.  The  efficiency 
with  this  method  is,  of  course,  very  low  at  slow  speeds.  The  speed  regu- 
lation with  varying  loads  may  also  be  very  poor. 

There  are  several  systems  of  controlling  the  motor  speeds  by  applying 
different  voltages,  such  as  by  the  use  of  three-wire  generators  or  two-wire 
generators  with  balancer  sets  or  by  the  Ward  Leonard  system.  This  latter 
system,  which  is  the  most  practical,  consists  of  a  constant-speed  motor 
driving  a  generator  which  supplies  current  to  the  motor  whose  speed  is  to 
be  adjusted.  This  arrangement  is  very  satisfactory,  but  on  account  of  the 
expense  of  providing  three  full-sized  machines  instead  of  one  to  perform 
the  work,  the  cost  may  be  prohibitive  except  with  very  large  motors,  such 
iis  for  hoists,  etc. 

Speed  Adjustment  by  Shunt-field  Control,  i.e.,  by  inserting  resistance 
in  the  shunt-field  circuit,  is  the  simplest  of  all  methods  of  speed  variation, 
but  with  ordinary  shunt  motors  the  range  of  speed  variation  by  this  means 
is  small.  Where  a  variation  of  more  than  from  20  to  30  per  cent  is  desired, 
a  motor  of  modified  design  and  of  a  certain  increased  size  is  generally  re- 
quired, because  the  field  must  be  more  powerful  with  respect  to  the  arma- 
ture than  in  the  case  of  standard  single-speed  motors.  Variable-speed 
motors  of  the  field-weakening  type  are  not  constant  torque,  but  constant- 
output  motors,  i.e.,  the  torque  falls  proportionally  as  the  speed  increases. 

A  speed  variation  up  to  3  to  1  meets,  as  a  rule,  afl  requirements,  and  such 
motors  can  readily  be  obtained  in  commercial  sizes.  Should  a  greater 
speed  variation  be  desired,  say  4  to  1  or  5  to  1,  it  is  possible  to  accomplish 
this  by  the  commutating-pole  shunt  motor  with  field  control  only.  A 
combined  field  and  armature  control  would,  however,  be  a  better  method. 

Compound  Motor. — This  motor  is  provided  with  both  a  series  and  a 
shunt  field.  The  two  fields  are  usually  connected  so  that  they  act  in  the 
same  direction,  in  which  case  the  motor  is  called  a  "cumulative"  com- 
pound motor.  "Differential"  compound  motors,  with  the  two  fields 
opposing,  are  sometimes  employed  for  special  services.  The  cumulative, 
or  ordinary,  compound  motor  combines  the  characteristics  of  the  shunt 
and  series  motors,  having  a  speed  not  extremely  variable  under  load 
changes,  but  developing  a  powerful  starting  torque  and  an  increasing 
torque  with  increasing  load.  Motors  having  a  comparatively  weak  series 
field  are  employed  extensively  in  shop  practice  where  the  motor  may  be 
required  to  start  under  heavy  load,  but  must  maintain  an  approximately 
constant  speed  after  starting,  or  when  the  load  is  removed.  The  heavily 
compounded  motor  is  used  where  powerful  starting  torque  and  rapid  accel- 
eration are  necessary,  with  a  speed  not  varying  too  widely  under  load 
changes,  such  as  for  rolling  mills,  etc. 

The  speed  control  employed  with  compound  motors  may  be  any  of  the 
various  methods  explained  in  connection  witn  the  shunt  motor.  For 


CHAHACTEtttSTtCS   OF  MOTORS.  1463 

certain  service  the  control  may  be  entirely  rheostatic,  the  series  winding 
being  cut  out  after  the  motor  has  come  up  to  speed. 

Induction  Mo  toy. — The  induction  motor  is  essentially  a  constant-speed 
machine,  although  the  speed  may  be  varied  either  by  varying  the  applied 
stator  frequency  or  by  introducing  resistance  in  the  rotor  circuit.  It  is 
built  in  two  distinct  types,  namely,  the  squirrel-cage  and  the  phase-wound. 

Squirrel-cage  Motor. — The  squirrel-cage  type  is  used  for  constant- 
speed  service  with  infrequent  starting.  It  has  a  relatively  small  starting 
torque  per  ampere  and  draws  a  large  starting  current  from  the  line.  By 
increasing  the  resistance  of  the  rotor,  it  may,  however,  also  be  built  in  the 
smaller  sizes  for  a  high  starting  torque,  rapid  acceleration  and  frequent 
starting,  for  such  applications  as  sugar  and  laundry  centrifugals,  etc., 
where  simplicity  of  control  is  desirable.  They  are  also  used  for  operat- 
ing punches,  shears,  etc.,  where  a  fly-wheel  is  provided  for  storing  the 
'  energy. 

Induction  Motor  with  Wound  Rotor. — For  service  requiring  high 
starting  torque  combined  with  moderate  starting  current  a  motor  with 
the  wound  type  of  rotor  is  best  adapted.  A  motor  with  the  resistance 
mounted  inside  the  rotor  should  not  be  used  to  operate  machinery  having 
large  inertia  or  excessive  static  friction,  since  full  starting  current  may  be 
required  for  a  long  period  before  the  apparatus  attains  full  speed,  and,  as 
the  capacity  of  the  internal  resistance  is  small,  excessive  temperatures  may 
result.  This  type  of  motor  is,  as  a  rule,  not  built  above  200  horse-power, 
due  to  mechanical  difficulties  involved  in  connection  with  the  internal 
resistance. 

A  motor  with  external  resistance  should  be  used  for  moderate  and  large 
sizes.  The  rotor  must  then  be  provided  with  collector  rings  and  brushes. 
The  contact  resistance  of  these  as  well  as  the  leads  and  the  controller 
fingers,  which  are  in  the  circuit  all  the  time,  may  impair  the  efficiency  and 
regulation  of  the  motor,  especially  if  the  controller  and  the  resistance  are 
located  some  distance  from  the  motor.  The  phase-wound  induction  motor 
with  an  external  variable-rotor  resistance  is  best  adapted  for  a  variable- 
speed  service,  as  the  losses  necessary  to  obtain  reduced  speeds  are  external 
to  the  motor  itself. 

Multi-speed  Induction  Motors. — It  often  happens  that  the  service 
is  such  that  two  or  three  speeds  will  be  satisfactory  for  the  operation  of 
the  machinery  and  that  these  speeds  must  be  independent  of  the  load. 
Under  such  conditions  multi-speed  motors  can  frequently  be  used.  In 
these  motors  the  different  synchronous  speeds  are  produced  by  changing 
the  number  of  poles  in  the  magnetic  circuit.  Each  of  these  speeds  is  fixed, 
if  no  resistance  is  used  in  the  secondary  circuit.  With  multi-speed  motors, 
as  with  single-speed  motors,  however,  resistance  may  be  used  in  the  sec- 
ondary circuit  for  varying  the  speed. 

A  change  of  the  number  of  poles  jnay  be  made  hi  any  of  the  following 
ways: 

1.  By  the  use  of  single  magnetic  and  electric  circuits,  changing  the 
number  of  poles  by  re-grouping  the  coils.  2.  By  the  use  of  single  mag- 
netic circuits  and  independent  electric  circuits.  3.  By  means  of  separate 
magnetic  and  electric  circuits,  the  so-called  Cascade  connection. 

Synchronous  Motor. — The  speed  of  a  synchronous  motor  is  constant, 
being  fixed  by  the  number  of  poles  and  the  frequency  of  the  applied  volt- 
age. The  single-phase  type  is  not  self-starting  and  the  polyphase  type  has 
in  itself  a  very  poor  starting  torque.  They  may,  however,  be  made  self- 
starting  in  the  same  manner  as  squirrel-cage  induction  motors,  by  the  use- 
of  an  amortisseur  or  cage- winding,  similar^in  construction  to  that  used 
for  induction  motors. 

The  speed-torque  curve  of  a  synchronous  motor  is  similar  to  that  of  an 
induction  motor  except  that  the  torque  values  are  lower  for  a  given  resis- 
tance of  rotor  winding  on  account  of  the  construction  of  the  machine.  The 
starting  winding  must  be  designed  with  both  the  load  at  start  and  the  load 
at  synchronous  speed  in  mind,  because  too  great  a  slip  may  cause  the 
'  motor  to  shut  down  when  the  field  is  put  on.  It  is,  however,  seldom  that 
the  same  motor  will  be  called  upon  to  start  a  heavy  load  and  at  the  same 
time  synchronize  a  heavy  load,  as  the  load  usually  consists  principally  of 
either  static  friction,  as  in  the  use  of  motor-generator  sets,  line  shafting, 
etc.,  or  it  comes  up  with  the  speed  as  in  the  case  of  a  fan  blower  or  centrif- 
ugal pump.  The  former  case  would  be  met  by  a  high-resistance  squint 
cage  winding  and  the  latter  would  require  a  low  resistance. 


1464  ELECTRICAL  ENGINEERING. 

Single-phase  Series  Motor. — This  type  of  commutator1  motor  has  a  very 
powerful  starting  torque,  high  power  factor,  and  relatively  high  efficiency. 
It  is  most  generally  used  for  traction  work,  the  speed  being  controlled  by 
varying  the  applied  voltage  which  can  most  readily  be  done  by  means  of 
an  auto-transformer  with  a  number  of  taps. 

Repulsion  Induction  Motor. — This  type  of  commutator  motor  has  a 
limited  speed  and  an  increase  of  torque  with  decrease  in  speed.  The  action 
of  the  compensating  field  insures  a  power  factor  approximately  unity  at 
full  load  and  closely  approaching  unity  over  a  wide  range  in  load.  In  ad- 
dition, it  serves  to  restrict  the  maximum  no-load  speed  and  also  permits, 
where  varying  speed  service  is  involved,  an  increase  over  the  synchronous 
speed. 

Starting  of  Repulsion  Motors. — A  repulsion  motor,  if  started  by 
directly  closing  the  line  switch,  will  develop  about  21/2  times  full-load 
torque.  The  starting  current  corresponding  to  full-load  starting  torque  is 
from  2  to  21/4  times  full-load  running  current.  'As  a  general  rule,  starting 
boxes  are  not  required  up  to  and  including  2-horse-power  rating.  From 
2  to  5  horse-power  the  use  of  a  rheostat  is  optional,  dependent  upon  the 
degree  and  care  to  be  exercised  in  maintaining  voltage  regulation.  Start- 
ing boxes  should,  however,  preferably  be  used  on  sizes  above  5  horse- 
power, especially  where  light  and  power  circuits  are  combined. 

Reversible  Repulsion  Motors. —  The  repulsion  motor  may  be  designed 
for  reversible  service.  This  is  accomplished  by  adding  an  auxiliary  revers- 
ing winding  spaced  90°  from  the  main  field  winding  and  connected  in 
series  with  it.  By  reversing  the  relative  polarity  of  the  two  wincttngs, 
the  direction  of  rotation  is  changed  in  a  simpler  manner  than  by  mechani- 
cal shifting  of  the  brush  holder  yoke.  Instant  reversal  may  be  effected 
from  full  speed  in  one  direction  to  full  speed  in  the  other,  about  200  per 
cent  of  normal  running  torque  being  developed  at  the  moment  of  speed 
reversal  in  either  direction. 

Variable-speed  Repulsion  Motors. — In  addition  to  the  constant-speed 
lepulsion  motor,  two  other  types  are  also  available,  one  for  constant- 
torque  and  variable-speed  service,  the  other  for  adjustable  speed  inde- 
pendent of  torque.  In  general,  variable^speed  repulsion  motors  are  not 
applicable  to  lathes,  boring  mills,  or  similar  machines  where  the  service 
requires  adjustable  speed  and  constant  horse-power  at  all  speeds  below 
and  above  normal.  When  a  certain  amount  of  variable  speed  is  required 
lit  approximately  constant  torque,  such  as  in  driving  fans,  blowers,  print- 
ing presses,  etc.,  the  repulsion  motor  successfully  meets  a  wide  field  of 
application. 

MOTOR  APPLICATIONS. 

Pumps  (E.  A.  Lof,  in  Coal  Age), — Pumps  are  either  of  the  reciprocating 
or  centrifugal  type.  In  the  former  the  volume  of  water  can  be  varied 
either  by  changing  the  speed  or  by  the  use  of  a  by-pass  valve.  The  latter 
method  is,  of  course,  less  economical,  and  speed  variation  is,  therefore, 
preferable.  In  starting  large  pumps  the  water  may,  however,  be  delivered 
through  a  by-pass  until  the  motor  is  up  to  speed,  when  this  passage  is 
gradually  closed  and  the  water  delivered  into  the  pipe  system.  The  load 
at  starting,  therefore,  only  consists  of  the  friction  losses,  and  usually  does 
not  exceed  25  per  cent  of  the  full-load  torque. 

Either  direct-  or  alternating-current  motors  may  be  used  for  driving 
reciprocating  pumps.  When  of  the  former  class,  the  compound-wound 
type  is  generally  selected  for  single-acting  pumps  on  account  of  their 
rather  pulsating  load,  while  for  duplex  and  triplex  pumps,  having  steadier 
characteristics  of  power  demand,  the  shunt- wound  motor  is  used  to  ad- 
vantage. Both  squirrel-cage  and  phase-wound  induction  motors  are 
suitable,  the  latter  as  a  rule  being  selected  where  it  is  desirable  to  reduce 
the  starting  current  to  a  minimum  or  where  a  somewhat  variable  speed 
is  required. 

Synchronous  motors  may  also  be  used  for  driving  large  pumps  of  mod- 
erate speed,  and  are  admirably  adapted  for  such  service,  while  their 
characteristics  are  such  that  by  over-exciting  their  fields  they  may  be 
made  to  considerably  improve  the  power  factor  of  the  system.  By-pass 
valves  should  preferably  be  provided  on  the  pumps,  when  this  type  of 
motor  is  employed,  so  as  to  reduce  the  starting  current  as  much  as  possible. 

In  selecting  the  motor  equipment  for  a  centrifugal  pump,  its  character- 
istics as  affected  by  the  service  conditions  must  be  carefully  predetermined, 


MOTOR  APPLICATIONS.  1465 

and  in  some  respects  the  operating  features  of  this  type  of  water  lift  are 
entirely  opposite  to  those  of  reciprocating  pumps. 

With  constant  speed  an  increase  of  the  resistance  against  which  the 
reciprocating  pump  operates  increases  the  water  pressure  and,  therefore, 
the  load  on  the  motor,  while  with  the  centrifugal  pump  an  increase  of  the 
resistance  reduces  the  load.  The  volume  of  water  delivered  by  a  recip- 
rocating pump  is  not  affected  by  the  reduction  of  the  head,  but  the 
required  power  is  lessened.  A  reduction  of  the  head  with  a  centrifugal 
pump,  however,  increases  the  volume  of  water,  and  as  the  efficiency  at  the 
same  time  goes  down  rapidly,  the  load  increases.  It  is,  therefore,  of  im- 
portance to  know  what  this  overload,  caused  by  a  reduction  of  the  head, 
amounts  to,  and  the  duration  of  the  overload;  and  the  capacity  of  the 
motor  should,  as  a  rule,  be  governed  by  the  low-  and  not  the  high-head 
conditions. 

The  starting  condition  must  be  given  careful  consideration  in  selecting 
the  motors.  In  starting  a  centrifugal  pump  the  discharge  valve  may  be 
entirely  closed  until  the  motor  comes  up  to  speed,  so  that  the  latter  may 
start  as  nearly  light  as  possible.  As  'the  machine  accelerates,  the  water  is 
churned  around  in  the  casing,  causing  the  motor  to  load  up  as  it  ap- 
proaches full  speed,  when,  with  pumps  of  the  usual  design,  it  takes  from 
40  to  50  per  cent  of  full-load  torque  to  drive  it  even  though  pumping 
no  water. 

Shunt-wound,  direct-current  motors  and  either  squirrel-cage  or  phase- 
wound  induction  motors  are  well  adapted  for  this  type  of  pump  and  will 
readily  meet  the  above  conditions.  A  synchronous  motor  may  lead  to 
difficulties  unless  precautions  are  taken  in  designing  the  squirrel-cage 
starting  winding  with  a  sufficiently  low  resistance  so  that  it  will  develop 
enough  torque  to  pull  the  motor  into  synchronism.  When  this  is  done, 
however,  the  starting  current  is  increased  and  a  compromise  must  usually 
be  made. 

Fans.  — Either  direct-  or  alternating-current  motors  can  be  used  for 
driving  fans.  Where  the  air-supply  must  be  regulated,  such  as  in  mines, 
the  motors  must  be  of  the  adjustable-speed  type.  Direct-current  motors 
may  be  either  of  the  shunt-  or  compound- wound  type,  the  speed  regulation 
being  accompanied  by  field  control.  Shunt-wound  motors  are  generally 
used,  but  compound-wound  motors  are  preferable  for  very  large  fans 
requiring  a  great  starting  torque. 

With  an  alternating-current  system,  the  phase-wound  induction  motor 
should  be  used,  the  speed  regulation  being  accomplished  by  inserting 
resistance  in  the  secondary  rotor  circuit. 

Air  Compressors. — Air  compressors  may  be  divided  in  two  classes, 
centrifugal  and  reciprocating.  The  former  require  a  high  speed  for  their 
operation,  while  the  speed  of  the  latter  is  comparatively  low. 

Shunt-wound,  direct-current  motors  and  both  squirrel-cage  and  phase- 
wound  induction  motors  are  used  for  driving  them,  the  phase-wound  type 
being  preferable  for  larger  units,  where  a  low  starting  current  is  desirable. 

With  direct-current  systems,  shunt-wound  motors  are  usually  used  for 
centrifugal  compressors  and  compound-wound  for  the  reciprocating  type. 

Hoists  (E.  A.  Lof,  in  Coal  Age}. — The  two  principal  classes  of  electric 
mine-hoist  equipments  are:  The  direct-current  motor  operated  from  its 
own  motor-generator  set  by  generator  field  control,  and  the  induction 
motor.  The  direct-current  motor  lends  itself  well  to  direct  connection,  as 
the  characteristics  of  slow-speed  motors  of  this  type  are  excellent.  The 
cost  of  a  direct-connected  motor  will,  in  practically  all  cases,  be  higher 
than  that  of  a  geared  motor,  but  in.  some  instances  this  is  largely  offset  by 
the  saving  in  gearing,  etc.  Where,  however,  a  considerable  saving  can  be 
made  by  using  a  geared  motor,  and  where  the  mechanical  advantages  of  a 
direct-connected  hoist  are  not  an  important  consideration,  a  geared  direct- 
current  motor  should  be  employed.  Such  a  motor  should  be  separately 
excited  and  shunt-wound,  and  the  current  should  be  obtained  from  a 
separately  excited  generator  of  similar  type,  both  machines  being  driven 
by  a  direct-coupled  induction  motor  where  the  source  of  supply  is  alter- 
nating current,  as  is  almost  invariably  the  case. 

The  control  of  the  hoist  motor  is  effected  by  regulating  and  reversing 
the  exciting  current  of  the  direct-current  generator,  thus  varying  the 
voltage  impressed  upon  the  motor  terminals.  The  current  for  the  motor 
and  dynamo  fields  is  supplied  from  the  direct-connected  exciter,  and  in, 


1466  ELECTRICAL   ENGINEERING. 

the  case  of  the  motor  it  is  maintained  constant.  As  the  rapidity  of  hoist- 
ing is  practically  proportional  to  the  voltage  impressed  upon  the  motor 
armature,  the  controlling  gear  is  arranged  so  that  the  speed  will  be  directly 
proportional  to  the  distance  by  which  the  controlling  lever  is  moved  away 
from  the  neutral  position.  This  system  of  hoisting  has  the  great  advan- 
tage that  the  rheostatic  losses  are  reduced  to  a  minimum  and  that  the 
operator  has  perfect  control  over  the  motor. 

In  many  cases  it  is  highly  desirable  to  reduce  the  instantaneous  peak 
loads  and  equalize  the  current  input  to  the  hoist.  This  is  especially  true 
where  the  power  charge  is  based  wholly  or  partly  on  the  maximum  de- 
mand, and  any  practicable  method,  therefore,  by  which  energy  may  be 
taken  from  the  line  and  stored  during  periods  of  light  load  and  discharged 
when  the  hoist  load  is  heavy,  makes  it  possible  to  greatly  reduce  the 
maximum  input  and  consequently  the  charge  for  power. 

The  simplest  method  of  effecting  this  is  by  adding  a  fly-wheel  to  the 
motor-generator  set,  previously  described.  In  order  to  permit  the  fly- 
wheel to  take  care  of  the  peaks,  and  equalize  the  load,  the  speed  of  the 
set  must  be  varied  according  to  the  demand  for  power.  This  is  accom- 
plished by  an  automatic  slip  regulator  connected  in  i,he  secondary  circuit 
of  the  induction  motor,  which,  in  this  case,  must  be  of  the  phase-wound 

The  second  important  class  of  electric  hoisting  systems  is,  as  previously 
stated,  driven  by  induction  motors.  Excessive  low-speed  motors  of  this 
type  and  of  moderate  capacities  do  not  show  particularly  good  electrical 
characteristics.  For  large-capacity  hoists  at  high-rope  speeds,  using  as 
small  a  drum  diameter  as  is  consistent  with  good  practice,  a  direct- 
connected  induction  motor  is,  in  some  instances,  entirely  feasible,  and  a 
number  of  such  equipments  are  in  actual  operation  abroad.  However, 
the  great  majority  of  induction- motor-driven  hoists  now  in  use  and  which 
will  be  installed  in  the  future  are  and  will  continue  to  be  of  the  geared  type. 

The  induction  motor  must  be  of  the  phase-wound  type,  and  the  speed 
control  is  accomplished  by  cutting  in  or  out  resistance  in  the  secondary 
circuit.  Drum  controllers  with  grid  rasistances  are  used  up  to  about  200 
lorse-power,  while  between  this  and  400  horse-power  it  is  customary  to 
provide  a  complete  magnetic-contactor  control.  Above  400  horse-power 
the  liquid  rheostat  is  usually  employed  as  a  secondary  resistance  and 
control. 

For  equalizing  the  load  taken  by  an  induction-motor-driven  hoist,  a 
fly-wheel  motor  balancer  may  be  used.  This  consists  of  a  shunt-wound  or 
compound-wound  direct-current  motor,  connected  to  a  heavy  fly-wheel 
and  carrying  a  direct^connected  exciter.  The  motor  balancer  is  floated 
indirectly  across  the  incoming  line  circuit,  being  tied  in  by  means  of  a 
rotary  converter  or  motor-generator  set.  A  regulator  actuated  by  the 
line  current  controls  the  direct-current  motor  field,  so  that  when  the 
power  taken  by  the  hoist  drops  below  the  average,  the  field  is  automati- 
cally reduced,  causing  the  fly-wheel  set  to  speed  up  and  absorb  power 
from  the  supply  system  and  store  it  in  the  fly-wheel.  When  the  load  on 
the  hoist  motor  exceeds  the  average,  the  operation  is  reversed,  the  fly- 
wheel set  slows  down,  and  power  is  returned  to  the  system  through  the 
rotary  converter. 

Machine  Tools  (Abstracted  from  C.  Fair,  General  Electric  Review,  1914). 
— In  general,  the  most  satisfactory  electrical  equipment  for  machine  shops, 
using  a  large  number  of  motors,  would  be  one  having  available  both  A.C. 
and  D.C.  distribution;  A.C.  for  all  constant  speed  machines  and  D.C.  for 
adjustable  speed  machines. 

In  the  smaller  shops,  with  rare  exceptions,  the  cilice  of  motors  would 
depend  upon  the  current  available,  which  in  the  majority  of  cases  would 
be  alternating  current.  The  size  and  product  of  the  small  factory  make 
a  proper  layout  a  comparatively  simple  matter,  while  in  larger  factories 
skill  and  ingenuity  are  essential  to  obtain  the  most  advantageous  equip- 
ment. The  standard  motor  of  to-day  will  answer  for  the  majority  of  the 
machine  tools,  although  special  motors  are  in  some  cases  necessary. 

When  equipping  tools  with  individual  drives,  the  controlling  apparatus 
as  well  as  the  motor  should  be  attached  directly  to  the  tool  whenever 
possible.  In  the  case  of  portable  tools  this,  of  course,  is  a  necessity. 

A  graphic  recording  wattmeter  in  circuit  with  a  tool  is  of  value  in 
efficient  management,  as  it  not  only  tells  the  actual  power  consumed  t 


MOTOR  APPLICATIONS. 


1467 


the  machine,  showing  whether  or  not  the  tool  is  properly  motored,  but  it 
also  shows  whether  the  tool  is  operating  at  its  maximum  rate,  by  register- 
ing the  time  of  unproductive  cycles  or  the  length  of  time  the  tool  is  idle. 
By  analysis,  the  cause  of  the  lost  time  may  be  discovered  and  a  change  of 
operating  conditions  can  be  made  with  a  corresponding  increase  in 
production. 

Motors  for  Machine  Tools. 


Tool 

] 

D.  C. 

A. 

C. 

Shunt. 

Comp. 

* 

t 

Bolt  cutter 

y 

* 

Bolt  and  rivet  header  . 

120% 

# 

t 

Bulldozers  

/  40% 
{20% 

T 

Boring  machines     .... 

y 

(40% 

'  *  ' 

Boring  mills  

v 

* 

Raising  and  lowering  cross  rails  on  bor- 
ing mills  and  planers 

** 

20% 

f 

v 

* 

Bending  machines 

{20% 

* 

t 

*# 

140% 
{20% 

I  50% 
J  20% 

'  # 

jj 

Centering  machines   

v 

I  50% 

'  * 

Chucking  machines 

v 

* 

Boring,  milling  and  drilling  machines.  . 
Drill,  radial  

V 

* 
* 

Drill  press  . 

V 

* 

Grinder  —  tool,  etc  

v 

* 

Grinder  —  castings    ... 

v 

20% 

* 

Gear  cutters  

v  . 

20% 

* 

{20% 

t 

Keyseater  —  milling  —  broach 

v 

(40% 

'  *  ' 

Keyseater  —  reciprocating  . 

20% 

*     - 

Lathes  

v 

* 

Lathe  carriages 

** 

50% 

t 

Milling  machines  

v 

* 

Heavy  slab  milling         .                           . 

V 

20% 

* 

Pipe  cutters  

v 

* 

Punch  presses  

\m 

* 

t 

Planers 

I  40% 
§20% 

'  * 

t 

Planers  —  rotary  . 

v 

io%? 

* 

Saw  —  small  circular  

v 

* 

Saw  —  cold  bar  and  I-beam    

20% 

* 

Saw  —  hot 

20% 

* 

Screw  machine    ...        ....                 .    . 

v 

* 

Shapers 

v 

10% 

* 

Shears      .                                *- 

{20% 

* 

t 

Blotters 

v 

(  40% 
20% 

'  *  ' 

Swaging 

*20% 

* 

t 

Tappers 

v 

*40% 

'  *  ' 

Tumbling  barrels  or  mills  

20% 

* 

*  Squirrel  cage  rotor. 

t  Squirrel  cage  rotor — high  starting  torque. 

j  Slip  ring  induction  motor  with  external  rotor  resistance. 

§  Does  not  apply  to  reversing  motors. 

**  D.  C.  series  mo  tor. 


1468 


ELECTRICAL  ENGINEERING. 


The  table  on  p.  1467  will,  in  a  general  way,  aid  in  the  choice  of  motors. 
The  great  variety  and  size  of  tools  of  the  same  name  make  it  necessary 
in  a  general  list,  such  as  this,  to  double-check  a  number  of  tools.  It 
must  be  kept  in  mind,  however,  that  various  circumstances,  such  as  size 
and  roughness  of  work,  and  fly-wheel  capacity,  etc.,  may  call  for  radical 
departures  in  the  choice  of  motors,  this  list  being  compiled  to  meet  average 
conditions. 

Shunt  motors,  for  instance,  are  used  in  the  following  cases:  When  work 
is  of  a  fairly  steady  nature,  when  considerable  range  of  adjustment  of 
speed  is  required,  as  on  lathes  and  boring  mills,  and  on  group  and  line- 
shaft  drives,  etc. 

Compound-wound  motors  are  used  where  there  are  sudden  calls  for 
excessive  power  of  short  duration,  as  on  planers  without  reversing 
motor  drives,  punch  presses,  bending  rolls,  etc. 

Series  motors  should  be  used  where  speed  regulation  is  not  essential, 
and  where  excessive  starting  torque  is  required,  as,  for  instance,  in  moving 
carriages  of  large  lathes,  in  raising  and  lowering  the  cross  rails  of  planers 
and  boring  mills,  and  for  operating  cranes,  etc.,  but  not  where  the  motor 
can  be  run  without  load,  through  the  opening  of  a  clutch,  or  by  a  belt 
leaving  ics  pulley,  as  the  motor  would  run  away  if  the  operator  failed  to 
shut  off  the  power. 

When  in  doubt  as  to  the  choice  of  compound  or  series  motors  of  small 
horse-power,  the  choice  might  be  determined  by  the  simplicity  of  control 
in  favor  of  the  series  motor. 

The  alternating-current  motor  of  the  squirrel-cage  rotor  type  corre- 
sponds to  the  constant-speed,  shunt,  direct-current  motor;  but  with  a 
high-resistance  rotor  it  approaches  more  closely  the  characteristics  of  a 
compound,  direct-current  motor.  It  is  understood  that  the  variable- 
speed  machines  checked  in  the  table  above  under  the  alternating-current 
squirrel-cage  rotor  column  have  the  necessary  mechanical  speed  changes. 

The  slip-ring  induction  motor  with  external  rotor  resistance  would  be 
used  for  variable  speed,  but  this  must  not  be  construed  to  mean  that  it 
corresponds  to  a  direct-current,  adjustable-speed  motor,  as  it  has  the 
characteristics  of  a  direct- current  shunt  motor  with  armature  control. 

The  self-contained,  rotor  resistance  type  could  be  used  for  lineshaft 
drives,  and  for  groups  when  of  sufficient  size. 

Multi-speed,  alternating-current  motors  are  those  giving  a  number  of 
definite  speeds,  usually  600  and  1200,  or  600,  900,  1200,  and  1800  r.p.m., 
and  are  made  for  both  constant  power  and  constant  torque.  These  motors 
would  be  used  where  alternating  current  only  was  available,  and  where 
the  speed  ranges  of  the  motor,  together  with  one  or  two  change  gears, 
would  give  the  required  speeds.  These  motors  should,  however,  be  used 
with  discretion,  especially  on  sizes  above  six  horse-power. 

The  adjustable  speed,  A.C.,  commutator  brush-shifting  type  of  motor 
wifch  shunt  characteristics  would,  on  account  of  high  cost,  be  used  mostly 
where  an  adjustable  speed  motor  w^as  highly  desirable  and  where  A.C. 
only  was  available  and  where  there  were  not  enough  machines  calling  for 
adjustable  speed  drive  to  warrant  putting  in  a  motor-generator  set. 

ILLUMINATION— ELECTRIC  AND  GAS  LIGHTING.* 

Illumination. — Some  writers  distinguish  "lighting"  and  "illumina- 
tion." Lighting  refers  to  the  character  of  the  lights  themselves,  as 
dazzling,  brilliant,  or  soft  and  pleasing,  and  illumination  to  the  quantity 
of  light  reflected  from  objects,  by  which  they  are  rendered  visible.  If 
the  objects  in  a  room  are  clearly  seen,  then  the  room  is  well  illuminated. 

The  quantity  of  light  is  estimated  in  candle-power  per  square  foot  of 
area  or  per  cubic  foot  of  space.  The  amount  of  illumination  given  by 
one  candle  at  a  distance  of  1  ft.  is  known  as  a  foot-candle.  Since  the 
illumination  varies  inversely  as  the  square  of  the  distance,  one  foot- 
candle  is  given  by  a  16-candle-power  lamp  at  a  distance  of  4  ft.,  or  by  a 
25-c.-p.  lamp  at  a  distance  of  5  ft. 

Terms,  Units,  Definitions. — Quantity  of  light  proceeding  from  a 
source  of  light,  measured  in  units  of  luminous  flux,  or  lumens. 

Intensity  with  which  the  flux  is  emitted  from  a  radiant  in  a  single 
direction,  called  candle-power. 

Illumination,  density  of  the  light  flux  incident  upon  an  area. 

*  Contributed  by  Prof.  W.  H.  Timbie. 


ILLUMINATION.  1469 

Luminosity,  brightness  of  surface;  flux  emitted  per  unit  area  of 
surface. 

Candle-power,  the  unit  of  luminous  intensity.  A  spermaceti  candlo- 
burning  at  the  rate  of  120  grains  per  hour  is  the  old  standard  used  in 
the  gas  industry.  It  is  very  unsatisfactory  as  a  standard  and  is  being 
displaced  by  others. 

The  hefner  lamp,  burning  amyl  acetate,  is  the  legal  standard  in  Ger- 
many. The  unit  of  luminous  intensity  produced  by  this  lamp  when 
constructed  and  operated  as  prescribed  is  called  a  hefner.  The  standard 
laboratories  of  Great  Britain,  France,  and  America  have  agreed  upon 
the  following  relative  values  of  the  units  used  in  the  several  countries: 
1  International  Candle  =  1  Pentane  Candle  =  1  Bougie  Decimale  =  J 
American  Candle  =1.11  Hefners  =  0.104  Carcel  unit.  1  Hefner  = 
0.90  International  Candle. 

Intrinsic  Brilliancy  of  a  source  of  light  =  candle-power  per  square 
inch  of  surface  exposed  in  a  given  direction. 

Lumen,  the  unit  of  luminous  flux,  is  the  quantity  of  light  included  in 
a  unit  solid  angle  and  radiated  from  a  source  of  unit  intensity.  A  unit 
solid  angle  is  the  angular  space  subtended  at  the  surface  of  a  sphere  by 
an  area  equal  to  the  square  of  the  radius,  or  by  1  -r-4n,  or  1/12.5664  of 
the  surface  of  the  sphere.  The  light  of  a  source  whose  average  intensity 
in  all  directions  is  1  candle-power,  or  one  mean  spherical  candle-power, 
has  a  total  flux  of  12.5664  lumens. 

Foot-candle,  the  unit  of  illumination,  =  1  lumen  per  square  foot;  the 
illumination  received  by  a  surface  every  point  of  which  is  distant  one 
foot  from  a  source  of  one  candle-power. 

Lux,  or  meter-candle,  1  lumen  per  square  meter;  1  foot-candle  =  10.76 
meter-candles. 

Law  of  Inverse  Squares. — The  illumination  of  any  surface  is  inversely 
proportional  to  the  square  of  its  distance  from  the  source  of  light.  This 
is  strictly  true  when  the  source  of  light  is  a  point,  and  is  very  nearly 
true  in  all  cases  when  the  distance  is  more  than  ten  times  the  greatest 
dimension  of  the  light-giving  surface. 

Law  of  Cosines. — When  a  surface  is  illuminated  by  a  beam  of  light 
striking  it  at  an  angle  other  than  a  right  angle,  the  illumination  is  pro- 
portional to  the  cosine  of  the  angle  the  beam  makes  with  a  normal  to 
the  surface. 

If  E  =  the  illumination  at  any  point  in  a  surface,  I  the  intensity  of 
light  coming  from  a  source,  Q  the  angle  of  deviation  of  the  direction  of 
the  beam  from  a  normal  to  the  surface,  and  I  the  distance  from  the 
source,  then  E  =  I  cos  6  ~  I*. 

Relative  Color  Values  of  Various  Illuminants. — The  light  pro- 
ceeding from  any  source  may  be  analyzed  in  terms  of  the  elementary 
color  elements,  red,  green  and  blue,  by  means  of  the  spectroscope,  or  by 
a  colorimeter.  The  following  relative  values  have  been  obtained  by 
the  Ives  colorimeter  (Trans.  III.,  Eng.  Soc.,  iii,  631).  In  all  cases  the 
red  rays  in  the  light  are  taken  as  100,  and  the  two  figures  given  are 
respectively  the  proportions  of  green  and  blue  relative  to  100  red. 

Average  daylight,  100,100.  Blue  sky,  106,120.  Overcast  sky,  92,  85. 
Afternoon  sunlight,  91,  56.  Direct-current  carbon  arc,  64,  39.  Mercury 
arc  (red  100),  130,  190.  Moore  carbon  dioxide  tube,  120,  520.  Wels- 
bach  mantle,  3/4%  cerium,  81,  28.  Do.,  11/4%  cerium,  69,  14.5.  Do., 
13/4%  cerium,  63,  12.3.  Tungsten  lamp,  1.25  watts  per  mean  horizon- 
tal candle-power,  55,  12.1.  Nernst  glower,  bare,  51.5,  11.3.  Tantalum 
lamp,  2  watts  per  m.  h.  c.-p.,  49,  8.3.  Gem  lamp,  2.5  watts  per  m.  h. 
c.-p.,  48,  8.3.  Carbon  incandescent  lamp,  3.1  watts  per  m.  h.  c.-p.,  45, 
7.4.  Flaming  arc,  36.5,  9.  Gas  flame,  open  fish-tail  burner,  40,  5.8. 
Moore  nitrogen  tube,  28,  6.6.  Hefner  lamp,  35,  3.8. 

Relation  of  Illumination  to  Vision.— Wickenden  gives  the  following 
summary  of  the  principles  of  effective  vision: 

1.  The  eye  works  with  approximately  normal  efficiency,  upon  sur- 
faces possessing  an  effective  luminosity  of  one  foot-candle  or  more. 

2.  Excessive  illumination  and  inadequate  illumination  strain  and 
fatigue  the  eye  in  an  effort* to  secure  sharp  perception. 

3.  Intrinsic  brilliancy  of  more  than  5  c.-p.  per  sq.  in.  should  be  re- 
duced by  a  diffusing  medium  when  the  rays  enter  the  eye  at  an  angle 
below  60°  with  the  horizontal. 


1470  ELECTRICAL  ENGINEERING. 

4.  Flickering,  unsteady,  and  streaky  illumination  strains  the  retina 
in  the  effort  to  maintain  uniform  vision. 

5.  True  color  values  are  obtained  only  from  light  possessing  all  the 
elements  of  diffused  daylight  in  approximately  equivalent  proportions. 

6.  An  excess  of  ultra-violet  rays  is  to  be  avoided  for  hygienic  reasons. 

7.  Esthetic  considerations  commend  light  of  a  faint  reddish  tint-  as 
warm  and  cheerful  in  comparison  with  the  cold  effects  of  the  green  tints, 
although  the  latter  are  more  effective  in  revealing  fine  detail. 

Types  of  Electric  Lamps. — The  carbon  arc  lamp  is  now  rapidly  dis- 
appearing on  account  of  the  cost  of  maintenance  of  the  open  type  and 
the  low  efficiency  of  the  enclosed  type.  Gas-filled  tungsten  lamps  now 
operate  at  less  cost  on  the  same  circuits  on  which  these  arcs  formerly 
burned. 

The  Flaming  Arc. — The  carbons  are  impregnated  with  calcium  fluor- 
ide or  other  luminescent  salts.  The  current  is  usually  8  to  12  amperes 
and  the  voltage  per  lamp  35  to  60.  The  regenerative  flame  arc  is  a 
highly  efficient  variety  of  the  flame  arc. 

The  Magnetite  Arc  has  for  a  cathode  a  thin  iron  tube  packed  with- a 
mixture  of  magnetite,  FesCU,  and  titanium  and  chromium  oxides.  The 
anode  consists  of  copper  or  brass.  It  is  well  adapted  to  series  opera- 
tion with  low  currents.  The  4-ampere  lamp,  using  80  volts  per  lamp, 
is  highly  successful  for  street  illumination. 

The  Tungsten  Incandescent  (vacuum)  depends  upon  the  heating  of 
a  drawn  tungsten  filament  to  incandescence  in  a  vacuum.  They  are 
made  in  sizes  for  25,  40,  60,  100,  150,  250,  400,  500,  750,  and  1000  watts 
and  average  about  1  candle-power  for  each  watt,  with  a  life  of  1000 
hours,  before  the  candle-power  falls  below  80%  at  rated  voltage. 

The  Tungsten  Incandescent  (gas-filled)  has  the  advantage  of  having 
longer  life  and  being  smaller  than  the  vacuum  lamp  of  the  same  watt- 
age. They  are  filled  with  an  inert  gas,  generally  nitrogen  or  argon, 
and  have  an  efficiency  of  2  candle-power  per  watt  in  the  larger 'sizes 
(the  average  being  about  1.7  candle-power  per  watt),  with  a  life  of 
1300  hours. 

The  Mercury  Vapor  Lamp  is  an  arc  of  luminous  mercury  vapor  con- 
tained in  a  glass  tube  from  which  the  air  has  been  exhausted.  A  small 
quantity  of  mercury  is  contained  in  the  tube,  and  platinum  wires  are 
inserted  in  each  end.  When  the  tube  is  placed  in  a  horizontal  position 
so  that  a  thin  thread  of  mercury  lies  along  it,  making  electrical  con- 
nection with  the  wires,  and  a  current  is  passed  through  it,  part  of  the 
mercury  is  vaporized,  and  on  the  tube  being  inclined  so  that  the  liquid 
mercury  remains  at  one  end,  an  electric  arc  is  formed  in  the  vapor 
throughout  the  tube.  The  tubes  are  made  about  one  inch  in  diameter 
and  of  different  lengths,  as  below.  The  mercury  vapor  lamp  is  very 
efficient,  ranging  from  1.9  c.-p.  per  watt  for  the  900  c.-p.  size  to  1.55 
c.-p.  per  watt  for  the  300  c.-p.  size.  The  color  of  the  light  is  unsatis- 
factory, being  deficient  in  red  rays,  but  it  possesses  a  very  penetrating 
quality  which  makes  it  valuable  in  drafting  rooms  and  wherever  a 
light  is  needed  to  bring  small  details  out  sharply.  The  spectrum  con- 
sists of  three  bands,  of  yellow,  green,  and  violet,  respectively.  The 
intrinsic  brilliancy  of  the  lamp  is  very  moderate,  about  17  c.-p.  per  sq. 
in.  Commercial  lamps  are  made  of  the  sizes  given  below.  The  lamp 
is  essentially  a  direct-current  lamp,  but  it  may  be  adapted  to  alternat- 
ing-current by  use  of  the  principle  of  the  mercury-arc  rectifier.  The 
tubes  have  a  life  ordinarily  of  about  1000  hours. 

The  Quartz-Tube  Mercury-Arc  Lamp  operates  at  a  higher  voyage 
and  gives  much  nearer  a  white  light.  Owing  to  the  injurious  ultra- 
violet rays  given  out  by  this  form,  it  must  always  be  enclosed  in  a 
globe  of  clear  glass.  The  efficiency  ranges  from  2.4  to  3.3  c.-p.  per 
watt  and  the  life  averages  3000  hours.  It  is  made  in  sizes  from  1000 
to  3500  c.-p. 

Street  Lighting. — Street  lighting  may  be  divided  into  three  classes: 

(a)  "White-Way"  or  display  illumination. 

(b)  Main  road  illumination. 

(c)  Residence  district  lighting. 

The  object  of  "  White- Way"  illumination  is  generally  advertising  and 
many  more  lights  are  used  than  are  necessary  for  proper  road  illumina- 
tion. The  lamps  generally  used  are  the  titanium  arc,  the  magnetite 


ILLUMINATION. 


1471 


arc,  the  yellow  flaming  arc,  and  the  white  flaming  arc  of  over  1000  c.-p. 
See  last  column  of  Table  VI. 

In  "Main-road"  illumination  the  purpose  is  to  illuminate  the  road 
appreciably  for  night  automobile  travel.  The  lamps  generally  used 
are  some  type  of  the  300-watt  flaming  arc,  the  magnetite  arc,  or  the 
titanium  arc  of  Table  IV.  These  are  usually  placed  from  200  to  300 
ft.  apart  at  heights  varying  from  15  to  18  ft. 

For  Residential-district  Lighting,  where  vehicle  travel  is  infrequent 
and  slow,  the  smaller  sizes  (40  to  100  c.-p.)  of  tungsten  lamps  are  used 
spaced  from  100  to  200  ft.  at  height  varying  from  15  to  18  ft.  according 
to  shading  of  the  road  by  the  foliage.  Tungsten  lamps  of  the  higher 
candle-powers  of  200  to  450  are  also  used  with  spacings  of  200  ft.  and 
over,  with  reflectors  designed  to  give  the  best  distribution  of  the  light. 

I  Hum  illation  by  Arc  Lamps  at  Different  Distances.  —  Several  dia- 
grams and  curves  showing  the  light  distribution  in  a  vertical  plane 
and  the  illumination  at  different  distances  of  different  types  of  lamps 
are  given  by  Wickenden.  From  the  latter  are  taken  the  approximate 
figures  in  the  table  below.  The  carbon  and  the  magnetite  lamps  were 
25  ft.  high,  the  flame  arcs  21  ft. 

TABLE  I. — Illumination  by  Arc  Lamps. 


Horizontal  Distance  from  Lamp,  Feet. 

20 

30 

40 

50 

100 

150 

200 

250 

Kind  of  Lamp. 

Foot-candles,  normal  illumination. 

A.  Open  carbon  arc,  D.C.,        6.6  amp. 
B.  Enclosed  carbon  arc,  A.C.  6.6 
C.  Flame  arc,                             10 
D.  Regenerative  arc,                  7 
E.  Magnetite  arc,                       6.6 
F.  Magnetite  arc,                       4 

6!io 

0.40 
0.19 

0.29 
.135 

0.20 
0.10 
1.10 
0.65 
0.51 
0.21 

.032 
.027 
.31 
.15 
.15 
.07 

.OH 
.013 
.14 
.055 
.075 
.035 

.006 
.006 
.08 
.03 
.045 
.022 

.002 
.002 
.05 
.02 
.025 
.018 

0.85 
0.69 
0.30 

6'.47 

1.00 
0.40 

A.  6.6  amp.,  D.C.,  open  arc,  clear  globe. 

B.  6.6  amp.,  A.C.,  enclosed  arc,  opal  inner  and  clear  outer  globe, 
small  reflector. 

C.  10  amp.,  flame  arc,  vertical  electrodes;  50  volts,  1520 M.H. C.-P.*; 
0.33  watt  per  M.L.H.C.-P.*;   10  hours  per  trim. 

D.  7  amp.,  regenerative  flame  arc,  70  volts,  2440  M.L.H.C.-P.,  0.2 
watt  per  M.L.H.C.-P.,  70  hours  per  trim. 

E.  6.6  amp.,  B.C.  series  magnetite  arc,  79  volts,  510  watts,  1450 
M.L.H.C.-P.  75  to  100  hours  per  trim. 

F.  4  amp.,  B.C.  series  magnetite  arc,  80  volts,  320  watts,  575  M.L.H. 
C.-P.,  150  to  200  hours  per  trim. 

TABLE  II. — Data  of  Some  Arc  Lamps. 


Type  of  Lamp. 

Hours 
Trim. 

Am- 
peres. 

Ter- 
minal 
Volts. 

Ter- 
minal 
Watts. 

Watts 
per 
M.L.H. 
C.-P. 

D.C.  series  carbon,  open 

9  to  12 

9  6 

50 

480 

0  6 

D.C.  series  carbon,  enclosed  
A.C.  series  carbon,  enclosed  
D.C.  multiple  carbon,  enclosed.  . 
A.C.  multiple  carbon,  enclosed.  .  . 
D.C.  flame  arcs,  open  

100  to  150 
70  to  1  00 
100  to  150 
70  to  100 
10  to  16 

6.6 
7.5 
5.0 
6.0 
10 

72 
75 
110 
110 
55 

475 
480 
550 
430 
440 

0.9 
1.25 
2.25 
2.40 
0.45 

Regenerative,  semi-enclosed  
A.C.  flame  arcs,  open 

70 
10  to  16 

5 
10 

70 
55 

350 
467 

0.26 
0.55 

Magnetite,  open  

70  to  100 

6.6 

80 

528 

0.45 

Values  of  watts  per  M.L.H.  C.-  P.  approximate  for  open  carbon  arcs  and 
magnetite  arcs  with  clear  globes,  enclosed  arcs  with  opalescent  inner  and 
clear  outer  globes,  and  for  flame  and  regenerative  arcs  with  opal  globes. 

*  M.H. C.-P.  =mean  horizontal  candle-power; 

,-P,  =mean  lower  hemispherical  candle-power, 


1472 


ELECTRICAL   ENGINEERING. 


Relative  Efficiency  of  Dluminants. — The  advent  of  the  gas-filled 
tungsten  incandescent  lamp  of  high  efficiency  and  high  candle-power 
has  driven  the  less  efficient  arc  lamps  from  the  field.  At  present  (1915) 
the  incandescent  lamp  of  the  200-  or  300-watt  size  is  more  efficient  than 
the  arc  lamp  of  the  same  candle-power.  On  the  other  hand,  the  1000- 
c.-p.  arcs  are  more  efficient  than  the  incandescent  lamps  of  the  same 
size.  The  field  for  the  arc  lamp  seems  to  be  in  the  higher  candle-power 
sizes.  Dr.  Steinmetz  in  The  General  Electric  Review  for  March,  1914, 
gives  the  following  tables. 

r  TABLE  III.— Relative  Efficiency  of  Dluminants. 

(Irrespective  of  Size,  in  Available  Mean  Spherical  C.-P.  per  Watt). 


Available 
Mean 
Spherical 
C.-P.  per 
Watt. 

(Street 
Lighting) 
10°  C.-P.* 
per  Watt 

Available 
Mean 
Spherical 
C.-P. 

3.1  watt  per  h.  c.-p.  carbon  filament.  .  .  . 
2.5  watt  per  h.  c.-p.  gem  filament  
450  watt   6.6  amp.   series   enclosed   a.c. 
carbon  arc     .                            

0.21 
0.26 

0.39 

0.4 
0.5 

0.5 

Any 
Any 

175 

Nitrogen  M^oore  tube 

0  45 

480  watt  6.6  amp.   series  enclosed  d.c. 
carbon  arc                                         

(D.62 

1.0 

300 

1  watt  per  h.  c.-p.  mazda  lamp  
500  watt  d.c.  "intensified"  carbon  arc  . 

0.64 
0.78 

1.25 

Any 

4  amp.  300  watt  d.c.  special  magnetite  arc 
Neon  M^oore  tube 

.0 

2.2      ' 

300 

0.5  watt  per  h.  c.-p.  gas-filled  mazda  lamp 
4  amp.  300  watt  d.c.  special  magnetite  arc 
6.6  amp.  500  watt  d.c.  standard  magnetite 
arc 

.28 
.4 

.5 

2.5 
3.0 

3.2 

Above  350 

(420) 

750 

Mercury  lamp  in  glass  tube,  best  values 

55 

6.6  amp.  500  watt  d.c.  special  magnetite 
arc                                          .      .  . 

.7 

3.6 

850 

220  watt  a.c.  titanium  arc  
300  watt  yellow  flame  arc,  best  value.  .  .  . 
500  watt  white  flame  arc,  best  values.  .  .  . 
Mercury  lamp  in  quartz  tube,  best  values 

.9 
.95 
.95 
2  0 

4.0 
4.0 
4.0 

420 

(585) 
(975) 

Exper.  350  watt  a.c.  titanium  arc  
Melting  tungsten  in  vacuum 

2.7 
2  88 

5.4 

(950) 

500  watt  yellow  flame  arc,  best  value.  .  .  . 
Exper.  500  watt  a.c.  titanium  arc  ....... 
Titanium  arc,  best  values  (high  power)  .  . 

3.1 

3.6 
5.2 

6.2 
7.0 

(1550) 
(1800) 

*The  expression  10°  c.-p.  per  watt  means  the  candle-power  per  watt 
on  a  circle  10°  below  the  horizontal  plane  of  the  filament. 

TABLE  IV. — Efficiency  of  300-Watt  llluminants. 


Available 
Mean 
Spherical 
C.-P.  per 
Watt. 

Available 
Mean 
Spherical 
C.-P. 

Mazda  lamp  (1  watt  per  h.  c.-p)..          .            .        ... 

0.64 

190 

Standard  4  amp.  d.c.  magnetite  arc  

.0 

300 

White  flame  carbon  arc,  best 

.2 

360 

Gas-filled  mazda  lamp  (0.5  watt  per  h.  c.-p.)  

.28 

384 

Special  4  amp.  d.c.  magnetite  arc 

4 

420 

Yellow  flame  carbon  arc,  best  

.95 

585 

A.C.  titanium  arc  

2.4 

720 

ILLUMINATION. 


1473 


TABLE  V.— Efficiency  of  500-Watt  Illuminants. 


Available 
Mean 
Spherical 
C.-P.  per 
Watt. 

Available 
Mean 
Spherical 
C.-P. 

A.C.  series  enclosed  carbon  arc  

0.42 

210 

Mazda  lamp  (1  watt  per  h.  c.-p.) 

0  64 

320 

D.C.  series  enclosed  carbon  arc  

0.65 

325 

Gas-filled  mazda  lamp  (0.5  watt  per  h.  c.-p.)     

1.28 

640 

Standard  6.6  amp.  d.c.  magnetite  arc  

1.5 

750 

Special  6.6  amp.  d.c.  magnetite  arc 

1  7 

850 

White  flame  carbon  arc,  best  

1  95 

975 

Quartz  mercury  lamp 

2  0 

1000 

Yellow  flame  carbon  arc,  best  

3  ] 

1550 

A.C.  titanium  arc  

3.6 

1800 

Characteristics  of  Tungsten  Lamps.  Vacuum  Type. — The  accom- 
panying Table  VII  refers  to  tungsten  lamps  of  the  25,  60,  and  100  watt 
size.  They  show  the  changes  which  take  place  in  the  candle-power, 
watts,  watts  per  candle-power  and  life  when  used  at  the  various  voltages. 
It  is  to  be  noted  that  a  4%  increase  in  voltage  above  the  normal  (100%) 
increases  the  candle-power  15%,  the  efficiency  6%,  but  decreases  the 
life  38%. 

TABLE  VI.— Relative  Efficiency  of  Various  C-P.  of  Illiiminaiits. 


200  Mean 
Spherical 
C.-P. 

300  Mean 
Spherical 
C.-P. 

400  Mean 
Spherical 
C.-P. 

500  Mean 
Spherical 
C.-P. 

1000  Mean 
Spherical 
C.-P. 

Type. 

S 

£ 

Type. 

1 

Type. 

4^ 

1 

Type. 

« 

£ 

Type. 

1 

A.C. 

carbon  
D.C. 
carbon  
Mazda  

490 

380 
310 

A.C. 

carbon  
D.C. 
carbon  
Mazda  

Standard 
magnetite 
Special 
magnetite.  . 

620 

480 
470 

300 
250 

Mazda  .  .  . 

6?n 

Standard 
magnetite 

400 

Gas-filled 
mazda 

780 
700 
55C 
520 

400 
360 

Standard 
magnetite. 
Gas-filled 
mazda  
Special 
magnetite.  . 

Titanium.  . 

350 
310 
290 
210 

Gas-filled 
mazda  
Special 
magnetite  .  . 
White 
Flame  
Yellow 
Flame  
Titanium.  . 

390 
350 
350 

280 
250 

Standard 
magnetite.  . 
Special 
magnetite.  . 
White 
Flame  
Yellow 
Flame  
Titanium  .  . 

Interior  Illumination. — There  are  three  systems  for  artificially  light- 
ing interiors.  All  three  are  easily  adapted  for  the  use  of  either  gas  or 
electricity  or  both:  (1)  Direct  lighting;  (2)  indirect  lighting;  (3)  semi- 
indirect  lighting. 

(1)  Direct  Lighting. — When  the  room  is  illuminated  almost  entirely 
by  the  light  which  comes  directly  from  the  lamps  without  reflection 
from  walls  and  ceilings,  it  is  said  to  be  illuminated  by  direct  lighting. 
This  is  the  usual  form  of  lighting. 

(2)  Indirect  Lighting. — When  a  room  is  illuminated  by  the  light  of 
concealed  lamps  which  is  reflected  from  the  walls  and  ceiling,  ,the 
system  of  illumination  is  said  to  be  indirect.     The  ceiling  and  walls 
must  be  light-colored.     There  is  an  entire  lack  of  shadows  in  a  room 
thus  lighted. 

(3)  Semi-indirect  Lighting. — When  a  room  is  illuminated  mostly  by 
light  reflected  from  the  walls  and  ceiling  but  still  receives  15  or  20% 
directly  from  the  lamps,  the  system  of  illumination  is  said  to  be  semi- 
indirect.     This  system  produces  particularly  pleasing  effects. 

The  Quantity  of  Electricity  and  Gas  Necessary  to  Illuminate  Various 
Rooms. — Practically  all  modern  illumination  is  done  either  by  tungsten 
incandescent  electric  lamps  or  gas  lamps  with  incandescent  mantles. 


1474 


ELECTRICAL   ENGINEERING. 


TABLE  VII.— Characteristics  of  Mazda  (Vacuum)  Lamps. 


Per  Cent  of 
Rated  Voltage. 

o  '. 

jjj 

s^ 

Per  Cent  of 
Rated  Watts. 

Efficiency  in 
C.-P.  per  Watt. 

Life  in  Per  Cent 
of  Rated  Life. 

Per  Cent  of 
Rated  Amperes. 

Per  Cent  of 
Rated  Ohms. 

Per  Cent  of 
Rated  Voltage. 

Per  Cent  of 
Rated  C.-P. 

Per  Cent  of 
Rated  Watts. 

Efficiency  in 
C.-P.  per  Watt. 

Life  in  Per  Cent 
of  Rated  Life. 

Per  Cent  of 
Rated  Amperes  . 

Per  Cent  of 
Rated  Ohms. 

50 

8 

33 

67 

77 

10? 

108 

103 

0  934 

80 

60 
70 
75 

15 

27 
36 

44 
57 
63 

0.231 
0.429 
0.500 

72 
82 
84 

80 

87 
88 

104 
106 
108 

115 
123 
130 

106 
110 
113 

0.971 
.01 
.03 

62 
48 
35 

"103" 

"l6i' 

80 

45 

71 

0  578 

88 

92 

110 

139 

117 

08 

25 

106 

104 

85 

57 

77 

0.658 

91 

94 

115 

161 

.16 

108 

106 

90 
92 
94 
96 
Q8 

69 
75 
81 
87 
93 

85 
88 
91 
94 
97 

0.736 
0.769 
0.799 
0.833 
0  880 

230 
180 
135 

94 
96  ' 

96 
'  '98  ' 

120 
125 
130 
140 
150 

187 
213 
242 

133 
142 

.27 
.35 
.47 
.67 
85 

112 
114 
117 
122 
127 

108 
110 
112 
115 
118 

100 

100 

100 

0.909 

100 

100 

100 

The  following  table  of  electricity  and  gas  necessary  to  light  rooms 
used  for  given  purposes  is  based  on  the  fact  that  in  the  modern  mazda 
lamps  1.1  watt  produces  1  c.-p.,  and  in  the  best  gas  lamps  with  incan- 
descent mantles,  0.04  cu.  ft.  per  hour  of  gas  produces  1  c.-p.  Inasmuch 
as  there  are  no  bright  spots  in  the  room  to  fatigue  the  eye,  when  in- 
direct and  semi-indirect  systems  are  used,  a  lower  degree  of  illumina- 
tion is  sufficient  to  enable  objects  to  be  clearly  seen.  Hence,  although 
the  indirect  and  semi-indirect  systems  are  less  efficient,  the  following 
table  applies  to.  all  these  methods : 


TABLE  VIII. — Electricity  or  Gas  Necessary  to  Sufficiently 
Illuminate  Booms. 


Use  of  Rooms. 

Watts 

S?2?- 

Work- 
ing 
Plane. 

Cu.  Ft. 
per  Hour 
per  Sq. 
Ft.  of 
Working 
Plane. 

Use  of  Rooms. 

Watts 
per  Sq. 
Ft.  of 
Work- 
ing 
Plane. 

Cu.  Ft. 
per  Hour 
per  Sq. 
Ft.  of 
Working 
Plane. 

Assembly  hall  .... 
Ball  room  . 

0.8-0.1 
1.2-1.3 

0.032-0.04 
0.05  -0.052 

Library  (book 
stacks)  

0.3-0.6 

0.012-0.24 

Barber  shop  
Bed   room    (resi- 
dence)   
Church  
Class  room 
(school)  
Corridor  
Dining  room 
(residence)  
Drafting  room  .  .  . 
Drill  hall  .  . 

1.5-1.7 

0.3-0.35 
1.0-1.3 

1.2-1.3 
0.4-0.5 

0.9-1.0 
2.5-2.8 
0.5-0.6 

0.06  -0.07 

0.012-0.014 
0.04  -0.05 

0.048-0.052 
0.016-0.02 

0.036-0.04 
0.10  -0.112 
0.02  -0.025 

Library  (resi- 
dence)   
Lobby  (hotel)  
Machine  shop.  .  .  . 
Music  room  (resi- 
dence)   
Office      (banking 
and  accounting)  . 
Office  (general)..  . 
Operating     room 
(hospital)  

1.0-1.1 
1.5-1.6 
2.0-2.2 

0.5-0.6 

1.5-1.6 
1.3-1.5 

3.5-3.9 

0.04  -0.044 
0.06  -0.065 
0.08  -O.OCC 

0.02-  0.025 

0.06  -0.065 
0.052-0.06 

0.14  -0.15 

Foundry  
Kitchen  
Library      (public 
reading  room)..  . 

3.0-4.0 
1.2-1.3 

1.4-1.5 

0.12  -0.16 
0.05  -0.052 

0.055-0.06 

Restaurant  
Store  
Warerooms  
Wood-working 
shop  

1.5-1.7 
1.4-1.7 
0.3-0.9 

1.5-1.8 

0.06  -0.07 
0.055-0.07 
0.012-0.030 

0.06  -0.072 

For  gas-filled  tungsten  and  Welsbach  "Kinetic"  use  0.6  of  above 
values.     Data  on  gas  furnished  by  F.  R.  Pierce,  Welsbach  Co. 


ILLUMINATION. 


1473 


Example  of  Use  of  Table  Tin. 

Specify  the  proper  lighting  arrangements  for  a  banking  office  25  ft.  X 
40  ft.  with  a  13-ft.  ceiling. 

The  four-lamp  fixture  is  an  efficient  and  pleasing  arrangement  of 
lamps.     It  does  not  give  quite  as  uniform  distribution  of  light  as 
individual  lamps  uniformly  spaced,  but  the  effect  is  much  more  pleasing 
and  the  distribution  is  very  satisfactory. 
Using  Electricity. — 

Watts  per  sq.  ft.  needed  =1.5-1.6  (Table  VIII). 
Total  watts  needed          =  1.5  X  40  X  25. 

=  1500  watts. 

Using  four-lamp  fixtures,  we  shall  need  six  fixtures,  as  in  Fig.  250,  in 
two  rows  of  3  each. 


Watts  per  fixture  =  ^p  =  250. 
250 


Watts  per  lamp 


4 


=  62.5. 


On  consulting  Table  IX  we  find  we  can  use  60-watt  lamps  as  the 
standard  lamp  nearest  the  size  computed.     If  at  any  place  more  light 

is  needed,  100-watt  lamps  may  be 
substituted  in  the  nearest  fixture. 

Using  Gas.  —  To  use  gas  with  the 
same  number  of  similar  fixtures,  we 
would  have  to  use  lamps  which 
correspond  to  the  60-watt  mazda. 
Allowing  25  watts  to  the  cu.  ft.  per 
hour  of  gas,  we  would  need  a  lamp 

which  would  burn  —  or  2  1/2  cu.  ft. 


c: 

\ 

/"     ?         % 

/^              V 

* 

/ 

E'  <-o  ttT> 
jj 

V|         ^ 

<  [14  ft—  > 

^           / 

«=  14-  ft:  > 

u*. 

1      V 

/       f           \ 

/»             V 

^ 

'• 

^ 

S         7 

^ 

FIG.  250. 


per  hour  of  gas.     By  Table  IX,  we 
see  that  this  is  a  standard  size. 

The  foregoing  rules  are  merely 
intended  to  serve  as  a  guide  for 
planning  correct  illumination.  They 
are  not  intended  to  take  the  place  of  judgment  and  intelligence.  The 
details  of  each  lighting  project  differ  slightly  from  the  details  of  every 
other  lighting  project  and  due  weight  should  be  given  to  ways  in  which 
these  details  affect  the  application  of  general  rules. 

TABLE  IX.  —  Standard  Units;  Mazda  and  Welsbach. 


Watts 
(105- 
125 
Volts). 

C.-P. 
per 
Watt. 

Welsbach 
Inverted. 

Watts 
(105- 
125 
Volts). 

C.-P. 

per 

Watt. 

Welsbach 
Inverted. 

Wei 
Up 

sbach 
right. 

Cu. 
Ft. 

Equiv. 
Watts 
per 
Hour. 

Cu. 
Ft. 

Equiv. 
Watts 
per 
Hour. 

Cu. 
Ft. 

Equiv. 

Watts 

H^r. 

10 
15 
20 
25 
40 
60 
100 

0.77 
0.80 
0.855 
0.88 
0.91 
0.935 
0.98 

150 
250 
400 
500 
750 
1000 

.11 
.11 
.33 
.43 
.67 
.82 

10 

250 

1.6 
2.5 
4.0 
4.5 

40 
62.5 
100 
112.5 

5.5 

135.5 

Cost  of  Electric  Lighting.  (A.  A.  Wohlauer,  El  World,  May  16, 
1908,  corrected,  July,  1915.) — The  following  table  shows  the  relative 
cost  of  1000  candle-hours  of  illumination  by  lamps  of  different  kinds, 
based  on  costs  of  2,  4  and  10  cents  per  Kw.-hour  for  electric  energy. 
The  life,  K,  is  that  of  the  lamp  for  incandescent  lamps,  of  the  electrode 
"  :  arc  lamps,  and  of  the  vapor  tube  for  vapor  lamps. 


1476  ELECTRICAL  ENGINEERING. 

Ls  —  mean  spherical  candle-power. 
Ss  =  watts  per  mean  spherical  candle. 
P  =  renewal  cost  per  trim  or  life,  cents. 
K  =  life  in  hours. 
Cr  =  1000P/(KLS). 

GI  =  (Ss  X  R)  +  Cr  =  cost'per  1000  candle-hours. 
R  =  rate  in  cts.  per  K.W.  hour. 

Illuminant.    I  Amp.  I  Volts.  |  Ls  \  Ss    I  P  I  K  I    C  r\  Rating. 


Incandescent  Lamps. 


R=2       4      10 


Carbon  ...    . 

0.31 

110 

13  2 

3  8 

16 

450 

2  7 

16  c.-p. 

10  3 

17  9 

40  7 

Gem  

0.45 

110 

16  5 

3  OS 

?0 

450 

2.7 

20  c.-p. 

8  8 

14  9 

33  ? 

Tungsten  

0.91 

110 

72 

1.4 

70 

1000 

0.97 

100  Watt 

3.8 

6.6 

15.0 

Direct-Current  Arc  Lamps. 


TT 

8.6 

9 

9.2 

7.11 

5.4 

3.6 
1.76 


Open  arc 

Enclosed 

Carbon 

Miniature 

Magnetite.  .  .  . 

Flaming 

Inclined  flam- 
ing  

Inclined  en- 
closed flaming 


10 
5.0 

10 
2.5 
3.5 

10 

10 
5.5 


55 
110 
HO 
110 
110 

55 

55 
100 


400 


1.3 


260  2.1 

5502.0 

150 

225 

600 

1100 


1.8 
1.7 
0.75 

0.5 


1500  0.365 


2 
0.2 

2 

0.31 

2.4 

1.6 
0.1 


10  amp. 

10 
2.5 
3.5 
10 

10 
5.5 


4.6 
4.4 

5.6 
3.71 
3.9 

2.6 

1.03 


21.2 
21 
20 
17.3 
9.9 

6.6 


Mercury-Vapor  Lamps. 


Cooper  Hewittl  3.5 
Quartz |  3.5 


110  I  7701  0.5 
220  113001  0.6 


1200140000.4    I 
70030000.135 


3.5amp.| 


.4  12.4  15.4 
.3412.5416.14 


Recent  Street  Lighting  Installations. 

(Preston  S.  Millar,  Proc.  A.  I.  E.  E.,  July,  1915). 


& 

o 

Width, 
Roadway, 
Ft. 

No.  of 
Lighting 
Units. 

Linear 
Spacing, 
Ft.4 

Height  in 
Feet. 

Kind  of 
Buildings.5 

Location  of 
Lamps.6 

Kind  of 
Mount.9 

Lamps.10 

Globesll. 

1 

2 
3 

4 

5 

6 
7 
8 

36 
47 
42 
80 

901  j 

109 
60 

50 
90 
102 
222 
82 
(twin) 
123 
2003 

80 
69 
94 
100 

}i« 

100 
100 
100 

18 
24 
25 
14.5 

14 

15 
19 
13.5 

B 

"B' 

B 
B 

A 
B 
B 

0 

S 

s 

0 

s 

s 
s 
o 

K 
P 
P 
P 

P 
P 
P 
P 

D.C.,  6.6  amp.  LA. 
A.C.,  SF. 
A.C.,  SF. 
6.6  amp.  Mag. 

600  c.-p.  Mazda  C. 

6.6  amp.  Mag. 
120v.,  400w  M.C. 
400  c.-p.,  15  amp.  M.C. 

A 
B 
B 
A 

N 

A 
C 
K 

9 
10 

50 
92 

56 

400 
92 

17.5 
19.8 

R 
B 

s 
o 

P 

K 

1000  c.-p.  M.C. 
4.0  amp.  D.C.  LA. 

A 

A 

11 

1? 

80 
36 

79 

105 
220 

22 
22 

Ap. 

note7 
note8 

P 
p 

120v.,  400w.,  M.C. 
600  c.-p.  M.C. 

C 

B 

13 

502 

246 

120 

10.25 

R 

S 

P 

5.5  amp.  series  M.C. 

B 

(NOTES.) — *  Between  building  lines.  2 160  ft.  between  building  lines. 
8  Two  per  post.  4  Along  one  curb.  5  Kind  of  buildings:  B,  business 
structures;  A,  all  kinds;  Ap.,  apartments;  R,  residences.  6O,  both 
curbs,  opposite;  S,  staggered.  7  In  center  of  block  (on  center  isle) .  On 
curb  of  intersecting  streets  at  house  line  of  cross-street  intersection, 
s  East  curb  only.  »K,  brackets  on  trolley  poles;  P,  ornamental  posts. 


ELECTRICAL  SYMBOLS. 


1477 


10  LA,  luminous  arc;  SF,  series  flame  arc;  Mag.,  inverted  magnetite; 
M.C.,  Mazda  C.  "A,  alabaster;  B,  alba;  N,  novulux;  C,  Carrara; 
R,  C.R.I.,  globe  and  translucent  glass  reflectors. 

Cities.  —  1.  5th  Ave.,  Pittsburgh;  2.  Federal  St.,  Pittsburgh;  3. 
Dearborn  St.,  Chicago;  4.  Main  St.,  Rochester,  N.  Y.;  5.  Main  St., 
Hartford,  Conn.;  6.  Penna.  Ave.,  Washington,  D.  C.;  7.  5th  Ave., 
New  York;  8.  Market  St.,  Corning,  N.  Y.;  9.  Lake  Ave.,  Rochester; 
10.  Grand  Ave.,  Milwaukee;  11.  7th  Ave.,  New  York;  12.  Troy  St., 
Chicago;  13.  16th  St.,  Washington. 

SYMBOLS  USED  IN  ELECTRICAL  DIAGRAMS. 


a-  SPST 
cb  ED-  SPOT 

a  H~     DPST 
- 


Galvanometer.  Ammeter.         Voltmeter.         Wattmeter* 


Switches;  5,  single;         wvyv\A_ 
D,  double;  P,  pole;    Non-inductive 
1  ,  throw.  Resistance. 


<>  <>    <>$ 
Lamps. 


Inductive 
Resistance. 


Capacity 
or  Condense*. 


Motor         Shunt-wound  Motor        Series-wound 
or  Generator.        or  Generator.         Motor  or  Generator. 


luuJ 

n 


Two-phase      Three-phase  Battery.  Trans-     Compound-         Separately 
Generator.       Generator.  former,  wound  Motor     excited  Motor 

or  Generator,     or  Generator. 


INDEX. 


A  BBREVIATIONS,  1 

/A    Abrasion,   resistance    to,   of 
*•  *•       manganese  steel,  495 
Abrasive  processes,  1309-1318 
Abrasives,  artificial,  1313 
Abscissas,  70 
Absolute  temperature,  567 

zero,  567 

Absorption  of  gases,  605 
of  water  by  brick,  370 
refrigerating  machines,  1346, 

1364 

Accelerated  motion,  526 
Acceleration,    definition   of,    521, 

526 

force  of,  526 

ratesof ,  on  electric  railways,  1415 
work  of,  529 

Accumulators,  electric,  1425 
Acetylene   and    calcium   carbide, 

855 

blowpipe,  857 
flame  welding,  488 
generators  and  burners,  857 
heating  value  of,  856 
Acheson's  deflocculated  graphite, 

1246 

Acme  screw  thread,  234 
Adhesion    between    wheels    and 

rails,  1416 

Adiabatic  compression  of  air,  633 
curve,  959 
expansion,  601 

expansion    in    compressed    air- 
engines,  638 

expansion  of  air,  635,  638 
expansion  of  steam,  959 
Admiralty  metal,  composition  of, 

390 

Admittance    of    alternating    cur- 
rents, 1441 
Aerial  tramways,  track  cable  for, 

260 

Air  (see  also  Atmosphere),  606-681 
and  vapor  mixture,  weight  of, 

610-613 

-bound  pipas,  748 
carbonic  acid  allowable  in,  681, 

685 

compressed,  623,  632-653 
(see  Compressed  air) 
Air  Compressors,  centrifugal,  648 
effect   of  intake   temperatures, 

647 
electric  motors  for,  1465 


Air    compressors,    high    altitude, 

table  of,  639 
hydraulic,  650 
intercoolers  for,  648 
steam  consumption  of,  644 
tables  of,  641-643 
tests  of,  643 

Air,  contamination  of,  687 
cooling  of,  594,  710 
density  and  pressure,  607,  613 
Air,  flow  of,  in  pipes,  617-624 
in  long  pipes,  618-624 
in  ventilating  ducts,  683 
through  orifices,  615-617,  670 
Air,  friction   of,    in  underground 

passages,  714 
head   of,    due   to   temperature 

differences,  716 
heating  of  (see  also  Heating) 
heating,  heat-units  absorbed  in, 

691 

heating  of,  by  compression,  632 
horse-power   required   to   com- 
press, 637 

in  feed-pump  discharges,  1074 
inhaled  by  a  man,  687 
leaks  in  steam  boilers,  891 
-lift  pump,  808 
-lift  pump  for  oil  wells,  809 
liquid,  605 
loss   of  pressure   of,    in   pipes, 

617-624 

manometer,  607 
pipes  in  house  heating,  capacity 

of,  691 
pressures,  conversion  table  for, 

607 

properties  of,  606 
-pump,  1071-1073 
-pump  for  condenser,  1071, 

-pump,  maximum  work  of,  1074 

pyrometer,  555 

saturated,  temperatures,  pres- 
sures and  volume,  table,  1072 

saturated,  volume  at  different 
vacuums,  1072 

specific  heat  of,  564 

thermometer,  557 

velocity  of,  in  pipes,  by  ane- 
mometer, 624 

volume  at  different  tempera- 
tures, 692 

volume  transmitted  in  pipes, 
table,  623,  624 


1479 


1480 


air-alt 


INDEX. 


alt-ana 


Air,  volumes,  densities,  and  pres- 
sures, 607,  613 

washing,  687 

water  vapor  in  1  pound  of,  1081 

weight  and  volume  of,  27 

weight  of,  176 

weight  of  (table),  609,  613 
Alcohol  as  fuel,  843 

denatured,  843 

engines,  1102 

vapor  tension  of,  844 
Alden   absorption   dynamometer, 

1334 

Algebra,  33-37 
Algebraic  symbols,  1 
Alligation,  9 

Alloy  steels,  470-480  (see  Steel) 
Alloys,  384-410 

aluminum,  396-399 

aluminum-antimony,  399 

aluminum-copper,  396 

aluminum-silicon-iron,  398 

aluminum,  tests  of,  398 

aluminum- tungsten,  399 

aluminum-zinc,  399 

antimony,  405,  407 

bearing  metal,  405 

bismuth,  404 

caution  as  to  strength  of,  398 

composition  by  mixture  and  by 
analysis,  388 

composition  of,  in  brass  foun- 
dries, 390 

copper-manganese,  401 

copper-tin,  384 

copper-tin-lead,  394 

copper-tin-zinc,  387-390 

copper-zinc,  386 

copper-zinc-iron,  393 

ferro-,  1255 

ferro-,  manufacture  of,  1424 

for  casting  under  pressure,  395 

fusible,  404 

Japanese,  393 

liquation  of  metals  in,  388 

magnetic,       of      non-magnetic 
metals,  402 

miscellaneous,      analyses     and 
properties,  392 

nickel,  402 

the  strongest  bronze,  389 

vanadium  and  copper,  395 

white  metal,  407 
Alternating  currents,  1440-1460 

admittance,  1441 

average,   maximum,   and  effec- 
tive values,  1440 

calculation  of  circuits,  1457 

capacity,  1440 

capacity  of  conductors,  1446 

converters,  1453 

delta  connection,  1446 

frequency,  1440 

generators,  for,  1448 

impedance,  1441 

impedance  polygons,  1442 

inductance,  1440 

induction  motor,  1463 


Alternating  currents,  measure- 
ment of  power  in  polyphase 
circuits,  1447 

motors,  variable  speed,  1463 

Ohm's  law  applied  to,  1442 

power  factor,  1440 

reactance,  1441 

single  and  polyphase,  1445 

skin  effect,  1442 

standard  voltages  of,  1460 

synchronous  motors,  1463 

transformers,  1451 

Y-connection,  1446 
Altitude  by  barometer,  608 
Aluminum,  177,  380 

alloys  (see  a Iso  Alloys),  396-399 

alloys,  tests  of,  398 

alloys  used  in  automobile  con- 
struction, 400 

brass,  397 

bronze,  396 

bronze  wire,  248 

coating  on  iron,  473 

conductors,  cost  compared  with 
copper,  1459 

effect  of,  on  cast  iron,  439 

electrical  conductivity  of,  1401 

plates,  sheets,  and  bars,  weight 
of,  tables,  230 

properties  and  uses,  380 

sheets  and  bars,  table,  230 

solder,  382-383 

steel,  496 

strength  of,  381,  383 

thermit  process,  400 

tubing,  226 

wire,  248,  381,  383 

wire,    electrical    resistance    of, 

table,  1414 
Ammonia,  aqua,  strength  of,  1341 

-absorption  refrigerating  ma- 
chine, 1346,  1364 

-absorption  refrigerating  ma- 
chine, test  of,  1364 

carbon  dioxide  and  sulphur 
dioxide,  cooling  effect,  and 
compressor  volume,  1341 

-compression  machines,  tests  of, 
1359-1364 

-compression  refrigerating  ma- 
chines, 1345,  1356 

gas,  properties  of,  1338 

heat  generated  by  absorption 
of,  1341 

liquid,  properties  of,  1340 

solubility  of,  1341 

superheated,  properties  of,  1340 
Ampere,  definition  of,  1397 
Analyses,  asbestos,  270 

boiler  scale,  722 

boiler  water,  722 

cast  iron,  439-450 

coals,  821-830 

crucible  steel,  490,  494 

fire-clay,  269 

gas,  854 

gases  of  combustion.  817 

magnesite,  270 


ana-arm 


INDEX. 


art-baz 


1481 


Analyses  of  rubber  goods,  378 
Analytical  geometry,  7O-73 
Anchor  bolts  for  chimneys,  957 

forgings,  strength  of,  353 
Anemometer,  624 
Angle,     economical,     of    framed 

structures,  548 
of  repose  of  building  material, 

1220 
Angles,  Carnegie  steel,  properties 

of,  table,  317-321 
plotting,  without  protractor,  53 
problems  in,  38 
steel,  gage  lines  for,  321 
steel,  tests  of,  362 
steel,  used  as  beams,  table  of 

safe  loads,  321 
trigonometrical    properties    of, 

66 

Angular  velocity,  522 
Animal  power,  532-534 
Annealing,  effect  on  conductivity, 

1402 

effect  of,  on  steel,  479 
influence  of,  on  magnetic  capac- 
ity of  steel,  483 
.  malleable  castings,  455 
of  steel,  484,  492  (see  Steel) 
of  steel  forgings,  482 
of  structural  steel,  484 
Annuities,  15-17 
Annular  gearing,  1169 
Anthracite,  classification  of,  819, 

828 

composition  of,  819,  820,  828 
gas,  845 
sizes  of,  823 
space  occupied  by,  823 
Anti-friction  curve,  50,  1232 

metals,  1223 
Anti-logarithm,  136 
Antimony,  in  alloys,  405,  407 

properties  of,  177 
Apothecaries'  measure  and  weight, 

18,  19 
Arbitration    bar,    for    cast    iron, 

441 

Arc,  circular,  length  of,  58 
circular,  relations  of,  58 
lamps  (see  Electric  lighting) 
lights,  electric,  1469 
Arcs,  circular,  table,  122-124 
Arches,  corrugated,  195 
Area  of  circles,   square  feet,   di- 
ameters   in  feet  and  inches, 
131.  132 

of  circles,  table,  111-119 
of    geometric    .alplane    figures, 

54-61 

of  irregular  figures,  56,  57 
of  sphere,  62 
Arithmetic,  2-32 
Arithmetical  progression,  10 
Armature  circuit,  e.m.f.  of,  1436 

torque  of,  1435 
"Armco  ingot  iron,"  477 
Armor-plates,  heat  treatment  of, 
482 


Artesian  well  pumping  by  com- 
pressed air,  810 
Asbestos,  270 

Asphaltum  coating  for  iron,  471 
Asses,  work  of,  534 
Asymptotes  of  hyperbola,  73 
Atmosphere  (see  also  Air) 

equivalent  pressures  of,  27 

moisture  in,  609-613 

pressure  of,  607,  608 
Atomic  weights  (table),  173 
Austenite,  480 
Autogenous  welding,  488 
Automatic  cut-off  engines,  water 

consumption  of,  967 
Automobile  engines,  rated  capac- 
ity of,  1101 

gears,  efficiency  of,  1172 

screws  and  nuts,  table,  232 
Automobiles,  steel  used  in,  510 
Avogadro's  law  of  gases,  604 
Avoirdupois  weight,  19 
Axles,  forcing  fits  of,  by  hydraulic 
pressure,  1324 

railroad,  effect  of  cold  on,  465 

steel,  specifications  for,  507,  509 

steel,  strength  of,  354 

BABBITT  metal,  407,  408 
Bagasse  as  fuel,  839 
Balances,   to    weigh   on    in- 
correct, 20 

Balls  and  rollers,  carrying  capac- 
ity of,  340 

for  bearings,  grades  of,  1237 
hollow    copper,    resistance    to 

collapse,  345 
Ball-bearings,  1233,  1235 

saving  of  power  by,  1237 
Band  brakes,  design  of,  1240 
Bands  and  belts  for  carrying  coal, 

etc.,  1198 

and  belts,  theory  of,  1138 
Bank  discount,  13 
Bar  iron  (see  Wrought  iron) 
Bars,  eye,  tests  of,  360 

iron  and  steel,  commercial  sizes 

of,  182 

Lowmoor  iron,  strength  of,  352 
of  various  materials,  weights  of, 

181 

steel  (see  Steel) 

twisted,  tensile  strength  of,  280 
wrought-iron,  compression  tests 

of,  359 
Barometer,  leveling  with,  607 

to  find  altitude  by,  608 
Barometric  readings  for  various 

altitudes,  608 
Barrels,  to  find  volume  of,  65 

number  of,  in  tanks,  134 
Barth  key,  1329 
Basic  Bessemer  steel,  strength  of, 

476 
Batteries,  primary  electric,  1425 

storage,  1425-1428 
Baume's  hydrometer,  175 
Bazin's  experiments  on  weirs,  763 


1482 


bea-bel 


INDEX. 


bcl-hlo 


Beams  and  girders,  safe  loads  on, 
1387 

formula  for  flexure  of,  299 

formulae  for  transverse  strength 
of,  299 

of  uniform  strength,  301 

special,  coefficients  for  loads  on, 
300 

steel,  formulae  for  safe  loads  on, 
298 

wooden,  safe  loads,  by  building 
laws,  1387 

yellow  pine,  safe  loads  on,  1387, 

1393 
Beardslee's  tests  on  elevation  of 

elastic  limit,  275 
Bearing-metal  alloys,  405 

practice,  407 
Bearing-metals,  anti-friction,  1223 

composition  of,  390 
Bearing  pressure  on  rivets,  426 

pressure       with       intermittent 

loads,  1231 

Bearings,   allowable  pressure  on, 
1226,  1230 

and  journals  clearance  in,  1230 

ball,  1233,  1235 

cast-iron,  1223 

conical  roller,  1234 

engine,   calculating  dimensions 
of,  1042-1044 

engine,  temperature  of,  1232 

for  high  rotative  speeds,  1231 

for  steam  turbines,  1232 

knife-edge,  1238 

mercury  pivot,  1233 

of  Corliss  engines,  1232 

of  locomotives,  1232 

oil  pivot,  in  Curtis  steam  tur- 
bine, 1083 

oil  pressure  in,  1228 

overheating  of,  1228 

pivot,  1229,  1232 

roller,  1233 

shaft,  length  of,  1034 

steam-engine,  1232,  1238 

thrust,  1232 

Bed-plates  of  steam-engine,  1044 
Bell-metal,  composition  of,  390 
Belt  conveyors,  1198-1201 

dressings,  1151 

factors,  1142 

Belts   and   pulleys,    arrangement 
of,  1149 

care  of,  1150 

cement  for  leather  or  cloth,  1 152 

centrifugal  tension  of,  1139 

effect  of  humidityon,  1150 

endless,  1151 

evil  of  tight,  1149 

lacing  of,  1147 

length  of,  1148 

open  and  crossed,  1136 

quarter  twist,  1147 

sag  of,  1149 

steel,  1152 
Belting,  1138-1152 

Earth's  studies  on,  1146 


Belting,  formulae,  1139 

friction  of,  1138 

horse-power  of,  1139-1142 

notes  on,  1146 

practice,  1139 

rubber,  1152 

strength  of,  357,  1150 

Taylor's  rules  for,  1143 

theory  of,  1138 

vs,  chain  drives,  1155 

width    for    given    horse-power, 

1140 

Bends,  effects  of,  on  flow  of  water 
in  pipes,  747,  748 

in  pipes,  624 

in  pipes,  table,  221,  222 

pipe,  flexibility  of,  221 

valves,  etc.,  resistance  to  flow 

in,  879 
Bending  curvature  of  wire  rope, 

1213 

Bent  lever,  514,  536 
Bernouilli's  theorem,  617,  765 
Bessemer  converter,  temperature 
in,  555 

steel,  475  (see  Steel,  Bessemer) 
Bessemerized  cast  iron,  453 
Bethlehem  girder  beams,  proper- 
ties of,  table,  331 

I-beams,  table,  332 

steel  H-columns,  333 
Bevel  wheels,  1169 
Billets,  steel,  specifications  for,  507 
Binomial,  any  power  of,  33 

theorem,  37 

Bins,  coal-storage,  1196 
Birmingham  gage,  28 
Bismuth  alloys,  404 

properties  of,  178 
Bituminous  coal  (see  Coal) 

coating  for  pipe,  206 
Black  body  radiation,  579 
Blast  area  of  fans,  655 

pipes  (see  Pipes) 

Blast  -  furnace,     consumption    of 
charcoal  in,  837 

gas,  855 

steam-boilers  for,  899 

temperatures  in,  555 
Blechynden's  tests  of  heat  trans- 
mission, 593 
Blocks  or  pulleys,  538,  539,  1181 

or  pulleys,  strength  of,  1181 
Blooms,  steel  weight  of,  table,  190 
Blow,  force  of,  529 
Blowers  (see  also  Fans),  663-681 

and  fans,  comparative  efficiency, 
656 

blast-pipe  diameters  for,  671 

in  foundries,  1250 

rotary,  677 

rotary,  for  cupolas,  678 

steam-jet,  679 

Blowing-engines,    dimensions    of, 
680 

horse-power  of,  680 
Blowing-machines,  centrifugal, 
648,  649 


bio-bra 


INDEX. 


bra-bul 


1483 


Blowpipe,  acetylene,  857 

Blue  heat,  effect  on  steel,  482 

Board  measure,  20 

Boats  (see  Ships) 

Boats,  motor,  power  required  for, 

1101 

Bodies,  falling,  laws- of,  521 
Boiler  compounds,  930 

explosions,  932 

feed-pumps,  792 

feeders,  gravity,  938 

furnaces,  height  of,  889 

furnaces,  use  of  steam  in,  854 

heads,  914 

heads,  strength  of,  337,  338 

heating-surface  for  steam  heat- 
ing, 693-697 

plate,     strength    of,     at    high 
temperatures,  463 

scale,  analyses  of,  722 

tube    joints,     rolled,     slipping 
point  of,  364 

tubes,  dimensions  of,  table,  204 

tubes,  expanded,  holding  power 

of,  364 
Boilers  for  house  heating,  693 

for  steam-heating,  694-697 

horse-power  of,  885 

incrustation  of,  721,  927-932 

locomotive,  1113 

natural  gas  as  fuel  for,  847 

of  the  "Lusitania,"  1381 

steam,     885-944     (see    Steam- 
boilers) 
Boiling-point  of  water,  719 

of  substances,  559 
Boiling,  resistance  to,  570 
Bolts  and  nuts,  231-238 

and  pins,  taper,  1318 

effect  of  initial  strain  in,  347 

hanger,  243 

holding  power  of  in  white  pine, 
346 

square-head,    table   of  weights 
of,  242 

strength  of,  tables,  348 

stud,  237 

track,  weight  of,  244,  245 
Bonds,  rail,  electric  resistance  of, 

1416 

Boosters,  1456 
Boyle's   or   Mariotte's   law,    600, 

603 
Braces,  diagonal,  stresses  in,  542, 

545 

Brackets,  cast-iron, strength  of,  292 
Brake  horse-power,  970 

horse-power,  definition  of,  1017 

Prony,  1333 
Brakes,  band,  design  of,  1240 

electric,  1240 

friction,  1239 

magnetic,  1240 
Brass  alloys,  390 

and  copper-lined  iron  pipe,  227 

and    copper    tubes,    coils    and 
bends,  222 

influence  of  lead  on,  394 


Brass  plates,  bars,  and  wire,  tables, 
228,  229 

rolled,  composition  of,  391 

sheets  and  bars,  table,  228,  229 

tube,  seamless,  table,  224,  225 

wire,  weight  of,  table,  229 
Brazing  metal,  composition  of,  390 

of  aluminum  bronze,  397 

solder,  composition  of,  390 
Brick,  absorption  of  water  by,  370 

fire,  number  required  for  vari- 
ous circles,  table,  267 

fire,  sizes  and  shapes  of,  266 

kiln,  temperature  in,  555 

magnesia,  269 

piers,  safe  strength  of,  1386 

sand-lime,  tests  of,  371 

specific  gravity  of,  177 

strength  of,  358,  370-372 

weight  of,  180,  370 

zirconia,  270 

Bricks  and  blocks,  slag,  268 
Brickwork,     allowable    pressures 
on,  1386 

measure  of,  180 

weight  of,  180 
Bridge  iron,  durability  of,  466 

links,  steel,  strength  of,  353 

members,    strains    allowed    in, 
287 

trusses,  543-547 
Brine,  boiling  of,  570 

properties  of,  570,  571,  1343 
Brinell's  tests  of  hardness,  364 
Briquettes,  coal,  831 
Britannia  metal,  composition  of, 

407 
British    thermal    unit    (B.T.U.), 

560,  867 

Brittleness  of  steel  (see  Steel) 
Bronze,  aluminum,    strength,   ot, 
396 

ancient,  composition  of,  388 

deoxidized,  composition  of,  395 

Gurley's,  composition  of,  390 

manganese,  401 

navy-yard,  strength  of,  398 

phosphor,  394 

strength  of,  356 

Tobin,  391,  392 

variation  in  strength  of,  386 
Buffing  and  polishing,  1310 
Building-laws,  New    York    City, 
1388-1390 

-laws  on   columns,  New  York, 
Boston,  and  Chicago,  292 

-materials,  coefficients    of   fric- 
tion of,  1220 

-materials,  sizes    and    weights, 

177,  180,  191 

Buildings,  construction  of,  1385- 
1395 

fire-proof,  1389 

heating  and  ventilation  of,  684 

mill,  approximate  cost  of,  1394 

transmission   of  heat   through 
walls  of,  688 

walls  of,  1388 


1484 


hill-car 


INDEX. 


rar-oas 


Bulkheads,   plating  and  framing 

for,  table,  339 

stresses  in  due  to  water-pres- 
sure, 338 
Buoyancy,  719 
Burners,  acetylene,  857 

fuel  oil,  842 
Burning  of  steel,  481 
Burr  truss,  stresses  in,  544 
Bush-metal,  composition  of,  390 
Bushel  of  coal  and  of  coke,  weight 

of,  834 
Butt-joints,  riveted,  428 

CG.   S.  system  of  measure- 
ments, 1396 
•    COa,  (see  also  carbon  dioxide, 

carbonic  acid) 

COa  recorders,  autographic,  891 
CO2,     temperature    required    for 

production  of,  852 
Cable,  formula  for  deflection  of, 

1207 

traction  ropes,  256 
Cables  (see  Wire  rope) 

chain,  proving  tests  of,  264 
chain,  wrought-iron,  264,  265 
galvanized  steel,  255 
suspension-bridge,  255 
Cable-ways,  suspension,  1205 
Cadmium,  properties  of,  178 
Calcium   carbide   and   acetylene, 

855 
chloride     in     refrigerating-ma- 

chines,  1343 
Calculus,  73-82 
Caloric  engines,  1095 
Calorie,  definition  of,  560 
Calorimeter     for     coal,     Mahler 

bomb,  826 
steam,  942-944 
steam,  coil,  943 
steam,  separating,  943 
steam,  throttling,  943 
Calorimetric  tests  of  coal,  826,  827 
Cam,  537 
Campbell's  formulae  for  strength 

of  steel,  477 
Canals,  irrigation,  755 
Candle-power,  definition  of,  1469 
of  electric  lights,  1468-1476 
of  gas  lights,  860 
per  watt  of  lamps,  1475 
Canvas,  strength  of,  357 
Cap  screws,  dimensions  of,  238 

table  of  standard,  238 
Capacity,  electrical,  1440 

electrical,  of  conductors,  1445 
Car  heating  by  steam,  702 
journals,  friction  of,  1228 
wheel,  irons  used  for.  453 
Cars,  steel  plate  for,  507 
Carbon,  burning  out  of  steel,  485 
dioxide  (see  also  CO 2) 
dioxide  exhaled  by  a  man,  687 
dioxide  in  air,  687 
dioxide,  pressure,  volume,  etc., 
1341 


Carbon,  effect  of,  on  strength  of 
steel,  476 

gas,  845 
Carbonic  acid,   allowable  in  air, 

681,  685 

Carbonizing  (see  Case-hardening) 
Carborundum*  made  in  the  elec- 
tric furnace,  1425 
Cargo  hoisting  by  rope,  414 
Carnegie    steel    sections,    proper- 
ties of,  305-321 
Carnot  cycle,  598,  600 

cycle,  efficiency  of  steam  in,  881 
Carriages,  resistance  of,  on  roads, 

534 

Carriers,  bucket,  1197 
Case-hardening  of  iron  and  steel, 

510,  1291 

Casks,  volume  of,  65 
Cast  copper,  strength  of,  356,  384 
Cast-iron,  437-454 

addition  to,  of  ferro-silicon, 
titanium,  vanadium,  and 
manganese,  450 

analyses  of,  439-450 

bad,  453 

bars,  tests  of,  444 

beams,  strength  of,  451 

Bessemeri zed,  453 

chemistry  of,  438-443 

columns,  eccentric  loading  of, 
296 

columns,  strength  of,  289-292 

columns,  tests  of,  290 

columns,  weight  of,  table,  200 

combined  carbon  changed  to 
graphite  by  heating,  448 

compressive  strength  of,  283 

corrosion  of,  466 

cylinders,  bursting  strength  of, 
452 

durability  of,  466 

effect  of  cupola  melting,  450 

expansion  in  cooling,  448 

growth  of  by  heating,  1254 

hard,  due  to  excessive  silicon, 
1254 

influence  of  length  of  bar  on 
strength,  446 

influence  of  phosphorus,  sul- 
phur, etc.,  438 

journal  bearings,  1223 

malleable,  454 

manufacture  of,  437 

mixture  of,  with  steel,  453 

mobility  of  molecules  of,  449 

permanent  expansion  of,  by 
heating,  453 

pipe,  196-200  (see  Pipe,  cast- 
iron) 

pipe-fittings,  sizes  and  weights, 
206-216 

relation  of  chemical  composi- 
tion to  fracture,  446 

shrinkage  of,  438,  447,  1254 

specific  gravity  and  strength, 
452 

specifications  for,  441 


cas-cha 


INDEX. 


cha-chl 


1485 


Cast-iron  strength  in  relation  to 
silicon  and  cross-section,  447 

strength  in  relation  to  size  of 
bar  and  to  chemical  consti- 
tution, 446 

strength  of,  445-447 

tests  of,  352,  444-447 

theory  of  relation  of  strength 
to  composition,  446 

variation  of  density  and  te- 
nacity, 452 

water  pipe,  transverse  strength 
of,  452 

white,  converted  into  gray  by 

heating,  448 

Castings,     deformation    of,     by 
shrinkage,  448 

from  blast-furnace  metal,  450 

hard,  from  soft  pig,  450 

hard  to  drill,  due  to  low  Mn, 
450 

iron,  analysis  of,  439 

iron,  chemical  standards  for, 
441 

iron,  strength  of,  352 

made  in  permanent  cast-iron 
molds,  1255 

shrinkage  of,  1254 

specifications  for,  441 

steel,  489,  510 

steel,  specifications  for,  489,  510 

steel,  strength  of,  355 

weakness  of  large,  1253 

weight  of,  from  pattern,  1256 
Catenary,  to  plot,  52 
Cement  as  a  preservative  coating, 
471 

for  leather  belts,  1152 

Portland,  strength  of.  358 

Portland,  tests  of,  373 

weight  and  specific  gravity  of, 

Cements,  mortar,  strength  of,  372 
Cementation    or    case-hardening, 

510,  1291 

Cementite,  439,  480 
Center  of  gravity,  516 

of  gravity,   of  regular  figures, 

516 

of  gyration,  518 
of  oscillation,  518 
of  percussion,  518 
Centigrade-Fahrenheit    conver- 
sion table,  550,  551 
Centigrade,    thermometer    scale, 

550,  551 
Centrifugal  air  compressors,  648, 

649 

fans  (see  Fans,  centrifugal) 
fans,  high-pressure,  648,  649 
force,  521 

force  in  fly-wheels,  1047 
pumps  (see  Pumps,  centrifugal), 

796-802 

tension  of  belts,  1139 
Chain-blocks,  efficiency  of,  1181 
Chain-cables,  proving  tests  of,  264 
weight  and  strength  of,  264 


Chain-drives,  1153 

silent,  1156 

vs.  belting,  1155 
Cham-hoists,  1181 
Chains,  formulae  for  safe  load  on, 
348 

link-belt,  1196 

monobar,  1199 

pin,  1199 

pitch,    breaking    and    working 
strains  of,  265 

roller,  1199 

sizes,    weights   and   properties, 
264,  265 

specifications  for,  264 

strength  of,  tables,  264,  265 

tests  of,  264,  265 
Chalk,  strength  of,  371 
Change  gears  for  lathes,  1260 
Channels,  Carnegie  steel,  proper- 
ties of,  table,  312-313 

open,  velocity  of  water  in,  755 

safe  loads,  table,  313 

strength  of,  352 
Charcoal,  836-837 

absorption  of  gases  and  water 


by,  837 
mshe' 


bushel  of,  180 

composition  of,  836 

pig  iron,  440,  452 

results  from  different  methods 
of  making,  837 

weights  per  cubic  foot,  180 
Charles's  law,  600,  604 
Chatter  in  tools,  1264 
Chemical  elements,  table,  173 

symbols,  173 

Chemistry  of  cast  iron,  438-443 
Chezy's  formula  for  flow  of  water, 

728 

Chilling  cast  iron,  441 
Chimneys,  944-958 

anchor  bolts  for,  957 

draught  intensity  in,  945 

draught,  power  of,  946 

draught,  theory,  944 

draught  with  oil  fuel,  952 

effect  of  flues  on  draught,  947 

for  ventilating,  712 

height  of,  948 

height  of  water  column  due  to 
unbalanced  pressure  in,  946 

interior,  of  Equitable  building, 
954 

largest  in  the  world,  952,  954 

lightning  protection  of,  949 

radial  brick,  954 

rate    of    combustion    due    to 
height  of,  947 

reinforced  concrete,  958 

sheet  iron,  958 

size  of,  table,  950 

size  of,  for  oil  fuel,  951 

stability  of,  954 

steel,  956 

steel,  design  of,  956 

steel,  foundation  for,  957-,  958 

tall  brick,  953 


1486 


chi-cla 


INDEX. 


cla-coe 


Chimneys,  velocity  of  air  in,  946 
velocity  of  gas  in,  951 
with  forced  draught,  952 
Chisels,    cold,    cutting   angle   of, 

1261 

Chord  of  circle,  58 
Chords  of  trusses,  strains  in,  545 
Chrome  paints,  anti-corrosive,  469 
Chrome  steel,  496 
Chromium- vanadium  steels,  500- 

502 

Cippoleti  weir,  764 
Circle,  57-60 
area  of,  57 

circumferences    in   feet,    diam- 
eters in  inches,  table,  1310 
circumferences  of,  1  inch  to  32 

feet,  120 

diameter  of  to  enclose  a  num- 
ber of  rings,  51 
equation  of,  71 

large,  to  describe  an  arc  of,  51 
length  of  arc  of,  58 
length    of   arc    of,    Huyghen's 

approximation,  58 
length  of  chord  of,  58 
problems,  37-44 
properties  of,  57,  58 
relation  of  arc,  chord,  etc.,  of, 

58 

relations  of,  to  equal,  inscribed 
and  circumscribed  square,  59 
sectors  and  segments  of,  60 
Circles,  area  in  square  feet,  diam- 
eter in  inches  (table  of  cyl- 
inders), 131,  132 
circumference     and     area     of, 

table,  111-119 

diameter  of  and  sides  of  equiva- 
lent square,  125 
number   inscribed   in   a   larger 

circle,  125 
^Circuits,  alternating  current  (see 

Alternating  Current) 
electric  (see  Electric  circuits) 
electric,  e.m.f.  in,  1406 
electric,    polyphase,    1445    (see 

Alternating  currents) 
electric,  power  of,  1408 
magnetic,  1430 
Circular  arcs,  lengths  of,  58 
arcs,  lengths  of,  tables,  122-124 
curve,  formulae  for,  59 
functions,  Calculus,  81 
inch,  18 
measure,  20 
mil,  18,  29,  30 
mil  wire  gage,  29,  30 
pitch  of  gears,  1158 
ring,  60 

segments,  areas  of,  121,  122 
Circumference  of  circles,    1   inch 

to  32  feet,  table,  120 
of  circles,  table,  111-119 
Cisterns   and   tanks,    number  of 

barrels  in,  134 
capacity  of,  132-134 
Classification  of  iron  and  steel,  436 


Clay,  cubic  feet  per  ton,  181 

fire,  analysis,  269 

melting  point  of,  556 
Clearance    between   journal    and 
bearing,  1230 

in  steam-engines,  966,  1021 

of  rivet  heads,  322 
Clutches,  friction,  1179,  1239 
Coal,  analysis  of,  821-830 

analyses  and  heating  values  of 
various,  tables,  828-830 

and  coke,  Connellsville,  824 

anthracite,  sizes  of,  823 

approximate  heating  value  of, 
822 

bituminous,     classification    of, 
819 

briquets,  831 

burning,  Illinois  without  smoke, 
921 

caking  and  non-caking,  820 

calorimeter,  826 

calorimetric  tests  of,  826,  827 

cannel,  821 

classification  of,  819-821 

conveyors,  1197 

cost  of  for  steam  power,  1010 

cubic  feet  per  ton,  180 

Dulong's   formula   for   heating 
value  of,  827 

efficiencies    of,    in    gas-engine 
tests,  853 

foreign,  analysis  of,  825 

-gas,  composition  of,  860 

-gas,  manufacture,  858 

heating  value  of,  821-824,  828- 
830 

products  of  distillation  of,  834 

purchase  of,  by  specification,  830 

Rhode  Island  graphitic,  821 

sampling,  for  analysis,  825,  900 

semi-anthracite,  824 

semi-bituminous,     composition 
of,  819-823,  828 

space  occupied  by  anthracite,- 
823 

spontaneous  combustion  of,  832 

steam,  relative  value  of,  826 

storage  bins,  1196 

tests  of,  822,  823 

vs.  oil  as  fuel,  842,  843 

washing,  833 

weathering  of,  830 

weight  of  bushel  of,  834 

Welsh,  analysis  of,  825 
Coals,  furnaces  for  different,  827 
Coatings,  preservative,  471-474 
Coatings,  protective,  for  pipe,  206 
Coefficient  of  elasticity,  274,  374 

expansion,  566   (see  Expansion 
by  heat) 

fineness,  1369 

friction,  definition,  1219 

friction  of  journals,  1220 

friction,  rolling,  1220 

friction,  tables,  1220-1223 

performance  of  ships,  1370 

propellers,  1378 


INDEX. 


corn-corn 


1487 


Coefficient  of  transverse  strength, 

297 

water  lines,  1369 
Coils  and.  bends  of  brass  tubes, 

222 

electric,  heating  of,  1409 
heat  radiated  from,  in  blower 

system,  708 
Coiled  pipes,  221 
Coke,  analyses  of,  833 

by-products  of  manufacture  of, 

833,  834 

foundry,  quality  of,  1255 
ovens,     generation     of     steam 

from  waste  heat  of,  834 
weight  of,  180,  834 
Coking,  experiments  in,  833 
Cold-chisels,  form  of,  1261 

-drawing,  effect  of,  on  steel,  361 
-drawn  steel,  tests  of,  361 
effect  of,  on  railroad  axles,  465 
effect  of,  on  strength  of  iron  and 

steel,  464 

-rolled  steel,  tests  of,  361 
-rolling,  effect  of,  on  steel,  479 
-saw,  1309 
Collapse  of  corrugated  furnaces, 

342 

of  tubes,  tests  of,  341-344 
resistance   of  hollow   cylinders 

to,  341-345 

Collars  for  shafting,  1133 
Cologarithm,  137 
Color  determination  of  tempera- 
ture, 558 
Color  scale  for  steel  tempering, 

493 
Color    values    of   various    illumi- 

nants,  1469 

Columns,  built  steel,  tests  of,  287 
Carnegie    channel,    dimensions 

and  safe  loads,  323-327 
Carnegie  plate  and  angle,  323, 

328-330 

cast-iron,  strength  of,  289-292 
cast-iron,  tests  of,  290 
cast-iron,  weight  of,  table,  200 
comparison  of  formulae  for,  286 
eccentric,  loading  of,  296 
Gordon's  formula  for,  284 
Hodgkinson's  formula  for,  283 
made  of  old  boiler  tubes,  tests 

of,  363 
mill,  1393 

permissible  stresses  in,  286 
strength     of,     by    New    York 

building  laws,  1389 
wrought-iron,  tests  of,  360 
wrought-iron,  ultimate  strength 

of,  table,  285 
Combination,  10 
Combined  stresses,  335 
Combustion,  analyses  of  gases  of, 

817 

heat  of,  560 
of  fuels,  816 

of  gases,  rise  of  temperature  in, 
818 


Combustion,  rate  of,  due  to  chim- 
neys, 947 

spontaneous,  of  coal,  832 
theory  of,  816 

Commutating-pole  motors,  1437 
Composition  of  forces,  513 
Compound    engines    (sec    Steam- 
engines,  compound),  976-983 
interest,  13,  14 
locomotives,  1122,  1124 
proportion,  7 
numbers,  5 
units  of  weights  and  measures, 

27 

Compressed-air,  623,  632-653 
adiabatic  and  isothermal  com- 
pression, 633 
cranes,  1192 
diagrams,  curve  of,  636 
drills  driven  by,  645 
engines,  adiabatic  expansion  in, 

638 

engines,  efficiency,  641 
flow  of,  in  pipes,  618-624 
for   motors,    effect   of  heating, 

639-641 
formulae,  633 
for  street  railways,  652 
gain  due  to  reheating,  647 
hoisting  engines,  646 
horse-power   required   to   com- 
press air,  637 
locomotives,  1128 
loss  of  energy  in,  632 
losses  due  to  heating,  633 
machines,  air  required  to  run, 

645,  647 
mean  effective  pressures,  tables, 

636,  637 

mine  pumps,  652 
moisture  in,  611 
motors,  639-641 
motors  with  return-air  circuit, 

648 

Popp  system,  639-641 
practical  applications  of,  647 
pumping  with  (see  also  Air-lift), 

645 

reheating  of,  641 
table  for  pumping  plants,  645 
tramways,  652 

transmission,  efficiencies  of,  641 
two-stage  compression,  635 
volumes,     pressures,     tempera- 
tures, table,  636 
work  of  adiabatic  compression, 

634 

Compressed  steel,  488 
Compressibility  of  liquids,  175 

of  water,  721 
Compression,  adiabatic,  formulae 

for,  633 

and  flexure  combined,  335 
and  shear  combined,  335 
and  torsion  combined,  335 
in  steam-engines,  965 
of  air,  tables,  635-638 
Compressive  strength,  281-283 


1488 


coin-con 


INDEX. 


con-cop 


Compressive  strength  of  iron  bars, 

359  • 

strength  of  woods,  366 
tests,  specimens  for,  282 
Compressor  volume  in  refrigerat- 
ing, 1341 
Compressors,  air,  effect  of  intake 

temperature,  647 
air,  tables  of,  641-643 
Concrete,    crushing    strength    of 

12-in.  cubes,  1386 
durability  of  iron  in,  466 
reinforced,    allowable    working 

stresses,  1386 

Condenser,  barometric,  1069 
the  Leblanc,  1056 
tubes,    heat    transmission    in, 

589 

Condensers,  1069-1079 
air-pump  for,  1071,  1073 
calculation  of  surface  of,  939 
choice  of,  1078 
circulating  pump  for,  1075 
continuous  use  of  cooling  water 

in,  1076 

contraflow,  1071 
cooling- towers  for,  1079 
cooling  water  required,  1068 
ejector,  1069 

evaporative  surface,  1076 
for  refrigerating  machines,  1353 
heat  transference  in,  1070 
increase  of  power  due  to,  1077 
jet,  1068 
surface,  1069 
tubes  and  tube  plates  of,  1072, 

1073 
Condensing      apparatus,      power 

used  by,  1071 

Conductance,  electrical,  1401 
Conduction  of  heat,  580 

of  heat,  external  and  internal, 

580 
Conductivity,  electrical,  of  metal, 

1401 

electric,  of  steel,  477 
Conductors,  electrical,  heating  of, 

1408 
electrical,  in  series  or  parallel, 

resistance  of,  1407 
Conduit,  water,  efficiency  of,  766 
Cone,  measures  of,  62 

pulleys,  1136 
Conic  sections,  73 
Connecting  -  rods ,    steam  -  engine, 

1025 

tapered,  1026 

Connections,  transformer,  1452 
Conoid,  parabolic,  65 
Conoidal  fans,  666 
Conservation  of  energy,  531 
Constantan,    copper-nickel   alloy, 

403 

Constants,  steam-engine,  971-974 
Construction  of  buildings,   1385- 

1395 

Controllers,    for   electric   motors, 
1462 


Convection,     Dulong's     law     of, 

table  of  factors,  for,  597 
loss  of  heat  due  to,  596 
of  heat,  580 

Conversion  tables,  metric,  23-26 
Converter,     Bessemer,     tempera- 
ture in,  555 
Converters,  electric,  1453 

synchronous,  1453 
Conveying  of  coal  in  mines,  1203 
Conveyors,  belt,  1198-1201 
cable-hoist,  1205 
coal,  1197 
horse-power  required  for,  1198, 

1200 

screw,  1198 
Cooling    agents    in    refrigeration, 

1342 

air  for  ventilation,  710 
effect,  in  refrigerating,  1341 
of  air,  594 

of  air  by  washing,  687 
Cooling-tower,  air  per  pound  of 
circulating  water,  table,  1081 
air  supply  required  for,  1080 
for  condensers,  1079 
practice  in  refrigerating  plants, 

1354 

water  evaporated  per  pound  of 
.     air,  1080 
water   vapor   mixed   with   air, 

table,  1081 
Co-ordinate  axes,  70 
Copper,  178 

and  brass-lined  iron  pipe,  227 

ball  pyrometer,  553 

balls,  hollow,  345 

cast,  strength  of,  356,  384 

castings  of  high  conductivity, 

368 

density  of,  1406 
drawn,  strength  of,  356 
effect  of  on  cast-iron,  438 
electric  conductivity  of,  1402 
-manganese  alloys,  401 
-nickel  alloys,  402 
plates,  strength  of,  356 
resistivity  of,  1403 
temperature  coefficient  of,  1403 
tubing,  bends  and  coils,  222 
rods,  weight  of,  table,  230 
steels,  499 

strength   of  at   high   tempera- 
tures, 368 
-tin  alloys,  384 

-tin  alloys,  properties  and  com- 
position of,  384 
-tin-zinc  alloys,  law  of  variation 

of  strength  of,  388 
-tin-zinc  alloys,  properties  and 

composition,  387 
-vanadium  alloys,  395 
weight  required  in  different  sys- 
tems of  transmission,  1459 
Copper-wire  and  plates,  weight  of, 

table,  229 

carrying    capacity    of,    Under- 
writer's table,  1410 


cop-era 


INDEX. 


cra-eur 


1489 


Copper-wire,  cross-section  required 

for  a  given  current,  1410 
electrical  resistance,  table,  1404 
stranded,  253 
table    of    electrical    resistance, 

1404 
weight  of  for  electric  circuits, 

1410 
Copper-zinc   alloys,    strength   of, 

386 
-zinc  alloys,  table  of  composition 

and  properties,  386 
-zinc-iron  alloys,  393 
Cord  of  wood,  weight  of,  181 
yield  of  charcoal  from,  836 
Cordage,  technical  terms  relating 

to,  411 

weight  of,  411,  415, 
Cork,  properties  of,  377 
Corrosion   by  stray  electric  cur- 
rents, 470 

due  to  overstrain,  470 
electrolytic  theory  of,  468 
of  iron,  467 
of  pipe  in   hot-water  heating, 

708 

of  steam-boilers,  467,  927-932 
prevention  of,  468 
resistance   of  aluminum  alloys 

to,  401 

resistance  to  of  nickel  steel,  498 
Corrosive  agents  in  atmosphere, 

466 

Corrugated  arches,  195 
furnaces,  342,  917 
plates,    properties   of  Carnegie 

steel,  table,  310 
sheets,  sizes  and  weights,  194 
Cosecant  of  an  angle,  table,  170- 

172 
Cosine  of  an  angle,  66 

of  an  angle,  table,  170-172 
Cost  of  coal  for  steam-power,  1010 

of  steam-power,  1009-1011 
Cotangent  of  an  angle,  66 
Cotangents  of  angles,  table,  170- 

172 

Cotton  ropes,  strength  of,  357 
Coulomb,  definition  of,  1397 
Counterbalancing      of     hoisting- 
engines,  1188 
of  locomotives,  1126 
of  steam-engines,  1008 
Counterpoise  system  of  hoisting, 

1189 

Couples,  515 
Couplings,  flange,  1133 

hose,  standard  sizes,  218 
Coverings  for  steam-pipe,  tests  of, 

584-587 
Coversed  sine  of  angles,  table,  170- 

172 
Cox's  formula  for  loss   of  head, 

.     734 
Crane  chains,  264,  265 

installations,  notable,  1192 
pillar,  150-ton,  1192 
Cranes,  1189-1193 


Cranes  and  hoists,  power  required 

for,  1193 

classification  of,  1189 
compressed  air,  1192 
electric,  1190-1192 
electric,    loads   and   speeds   of, 

1191 

guyed,  stresses  in,  542 
jib,  1190 

power  required  for,  1191 
quay,  1193 

simple,  stresses  in,  541 
traveling,  1190-1193 
Crank  angles,  steam-engine,  table, 

1058 

arm,  dimensions  of,  1029 
pins,  steam-engine,  1027-1029 
pins,    steel,    specifications    for, 

507 
shaft,  steam-engine,  torsion  and 

flexure  of,  1038 
shafts,     steam-engines,     1030- 

1038 

Cranks,  steam-engines,  1029 
Critical  point  in  heat  treatment 

of  steel,  480 
temperature    and    pressure    of 

gases  and  liquids,  606 
Cross-head  guides,  1025 

pin,  1029 
Cross-sections    of    materials,    for 

draftsmen,  271 
Crucible  steel,  475,  490-494   (see 

Steel,  crucible) 
Crushing    strength    of    masonry 

materials,  371 
Crystallization  of  iron  by  fatigue, 

466 

Cubature  of  volumes,  77 
Cube  root,  9 

roots,  table  of,  93-108 
Cubes  of  decimals,  table,  108 

of  numbers,  table,  93-108 
Cubic  feet  and  gallons,  table,  130 

measure,  18 
Cupola  fan,   power  required  for, 

1253 

gases,  utilization  of,  1253 
loss  in  melting  iron  in,  1253 
practice,  1247-1257 
practice,  improvement  of,  1249 
results    of    increased    driving, 

1252 

Cupolas,  blast-pipes  for,  671 
blast-pressure  in,  1247-1251 
blowers  for,  661,  662 
charges  for,  1247-1250 
charges  in  stove  foundries,  1250 
dimensions  of,  1247 
rotary  blowers  for,  678 
slag  in,  1248 
Current  motors,  765 
Currents,    electric     (see    Electric 

currents) 

Curve,  railway  degree  of,  54 
Curve  of  P  Vn,  construction  of ,  602 
Curves  in  pipe-lines,  resistance  of, 
747 


1490 


cut-dif 


INDEX. 


dif-dyn 


Cut-off  for  various  laps  and  travel 

9f  slide  valves,  1060 
Cutting  metal  by  oxy-acetylene 

flame,  488 
metal,  resistance  overcome  in, 

1292 
speeds  of  machine  tools,  (see  also 

Tools,  cutting),  1258 
speeds  of  tools,  1268 
stone  with  wire,  1309 
Cycloid,  construction  of,  50 
differential  equations  of,  81 
integration  of,  81 
measures  of,  61 
Cycloidal  gear-teeth,  1162 
Cylinder  condensation  in  steam- 
engines,  966-968 
lubrication,  1245 
measures  of,  62 

Cylinders,  cast-iron,  weight  of,  200 
hollow,  resistance  of  to  collapse, 

341-345 

hollow,  under  tension,  339 
hooped,  340 
hydraulic   press,    thickness   of, 

340,  813 

locomotive,  1112 
steam-engine  (see  Steam-engines) 
tables  of  capacities  of,  131 
thick  hollow,  under  tension,  339 
thin  hollow,  under  tension,  340 
Cylindrical  ring,  64 

tanks,  capacities  of,  table,  132 

D ALTON'S    law    of    gaseous 
pressures,  604 
Dam,  stability  of,  515 
Darcy's  formula,  flow  of  water,  732 
formula,  table,  of  flow  of  water 

in  pipes,  740,  741 
Decimal  equivalents  of  feet  and 

inches,  5 

equivalents  of  fractions,  3 
gage,  32, 
Decimals,  3 

square  and  cubes  of,  108 
Delta  connection  for  alternating 

currents,  1447 
Delta    connection    transformers, 

1452 

metal  wire,  248,  393 
Denominate  numbers,  5 
Deoxidized  bronze,  395 
Derrick,  stresses  in,  542 
Detrick  and  Harvey  key,  1330 
Diagonals,  formulae  for  strains  in, 

545 

Diametral  pitch,  1158 
Diesel  oil  engine,  1102 
Differential  calculus,  73-82 
coefficient,  75 
coefficient,  sign  of,  78 
gearing,  1169 

of  exponential  function,  79,  80 
partial,  75 
pulley,  539 
screw,  540,  541 
second,  third,  etc.,  77 


Differential  windlass,  540 
Differentials    of    algebraic    func- 
tions, 74 

Differentiation,  formulae  for,  74 
Discount,  12 

Disk  fans  (see  Fans,  disk) 
Displacement  of  ships,  1369,  1374 
Distillation  of  coal,  834 
Distiller  for  marine  engines,  1082 
Distilling      apparatus,      multiple 

system,  570 
Doble  motor,  tests  of,  782 

nozzle,  efficiency  of,  782 
Domed  heads  of  boilers,  339 
Domes  on  steam  boilers,  918 
Draught,  chimney  .intensity  of,  945 

chimney,  with  oil  fuel,  952 

forced,  chimneys  with,  952 

forced  for  steam  boilers,  923 

power  of  chimneys,  945,  946 

theory  of  chimneys,  944 
Drawing-press,  blanks  for,  1322 
Dressings,  belt,  1151 
Driers  and  drying,  574 

performance  of,  575 
Drift  bolts,  resistance  of  in  timber, 

346 

Drill  gage,  table,  30 
Drills,  feeds  and  speeds  for,  1288 

for  pipe  taps,  201 

high-speed  steel,  1285 

performance  of,  1289 

rock,  air  required  for,  645 

speed  of,  1285 

tap,  sizes  of,  236,  1320 

twist,  experiments  with,  1289 
Drilling  compounds,  1286 

high-speed,  data  on,  1289 

holes,  speed  of,  1287 

steel  and  cast  iron,  power  re- 
quired for,  1286,  1287 
Drop  hi  electric  circuits,  1407 

press,  pressures  obtainable  by, 

1322 

Drums,  steam-boiler,  913 
Dry  measure,  19 
Drying  and  evaporation,  569-577 

apparatus,  design  of,  576 

in  a  vacuum,  573 

of  different  materials,  574 
Ductility  of  metals,  table,  180 
Dulong's     formula     for     heating 
value  of  coal,  827 

law  of  convection,  table  of  fac- 
tors for,  597 

law  of  radiation,  table  of  factors 

for,  596 
Durability  of  cutting  tools,  1268 

of  iron,  465-467 
Durand's  rule  for  areas,  56 
Dust  explosions,  837 

fuel,  837 
Duty,  measure  of,  27 

of  pumping-engines,  802 

trials  of  pumping-engines,  802- 

806 

Dynamics,  fundamental  equations 
of,  525 


dyn-ele 


INDEX. 


ele-ele 


1491 


Dynamo-electric  machines,  classi- 
fication of,  1437 

e.m.f.  of  armature  circuit,  1436 

moving  force  of,  1435 

torque  of  armature,  1435 

strength  of  field,  1436 
Dynamometers,  1333 

Alden  absorption,  1334 

hydraulic  absorption,  6000  H.P., 
1335 

Prony  brake,  1333 

traction,  1333 

transmission,  1335 
Dynamotors,  1457 
Dyne,  definition  of,  512 

EARTH,  cubic  feet  per  ton,  181 
Eccentric  loading  of  columns, 
296 

Eccentric,  steam-engine,  1039 
Economical     angle     of     framed 

structures,  548 

Economics  of  power-plants,  1011 
Economizers,  fuel  (see  Fuel  econ- 
omizers), 924 
Edison  wire  gage,  29,  30 
Efficiency,  definition  of,  12 

of  a  machine,  532 

of  compressed-air  engines,  641 

of  compressed-air  transmission, 
641 

of  differential  screw,  541 

of  electric  systems,  1412 

of  fans,  656,  657 

of  hydraulic  turbines,  7715 

of  injector,  937 

of  pumps,  790 

of  riveted  joints,  428-434 

of  screw,  538 

of  screw  bolts,  538 

of  steam-boilers,  891 

of  steam-engines,  964 
Ejector  condensers,  1069 
Elastic  Limit,  273-278 

apparent,  273 

Bauschinger's  definition  of,  275 

elevation  of,  275 

relation  of,  to  endurance,  275 

Wohler's  experiments  on,  275 
Elastic  resilience,  274 

resistance  to  torsion,  334 
Elasticity,  coefficient  of,  274 

moduli  of,  of  materials,  374 

modulus  of,  274 
Electric  brakes,  1240 

circuits  (see  Circuits,  electric) 

conductivity  of  steel,  477 

current,  alternating,  1440-1461 
(see  Alternating  currents) 

current,  cost  of  fuel  for,  796 

current  determining  the  direc- 
tion of,  1432 

current  required  to  fuse  wires, 
1409 

currents,  direct,  1406 

currents,  heating  due  to,  1408 

currents,     short-circuiting     of, 
1411 


Electric  furnaces,  1422 

heaters,  713,  1420 

heating,  713 

lighting,  1468-1477 

lighting,  cost  of,  1475 

lighting,  terms  used  in,  1468 

locomotive,  1416 

Electric  Motors  (see  also  Motors) , 
1461 

alternating     current,     variable 
speed,  1463 

changing  the  number  of  poles, 
1463 

for    the    machine-shop,    1294- 
1303,  1466 

for  machine  tools,  1294-1303, 
1467 

for  wood-working  tools,  1303- 
1305 

selection  of,   for  different  ser- 
vice, 1464 

speed  control  of,  1462 

types  used  for  various  purposes, 

1464 
Electric  power,  cost  of,  1012 

process    of   treating    iron   sur- 
faces, 473 
Electric  Railways,  1414 

adhesion    between    wheel    and 
rail,  1416 

cars,  resistance  of,  1110 

efficiency    of   distributing    sys- 
tems, 1417 

safe  speed  on  curves,  1416 

steam  railroads  electrified,  1418 
Eectric  resistanceof  steel  rails.  1416 

smelting  of  pig  iron,  1424 

stations,    economy    of   engines 
in,  992 

storage  batteries,  1425-1428 

transmission,     direct    current, 
1410-1413 

transmission,      high      tension, 
notes  on,  1459 

transmission,  lines,  spacing  for 
high  voltages,  1460 

transmission,  sag  of  wires,  1461 

vs.  steam  heating,  1421 

welding,  1419 

wires    (see   Wires   and   Copper 

wires) 
Electrical  and  mechanical  units, 

equivalent  values  of,  1399 
Electrical  engineering,  1396-1477 

horse-power,  970,  1408 

machinery,     shaft    fits,    allow- 
ances for,  1326 

resistance,  1400 

resistance    of   different    metals 

and  alloys,  1401 
.  resistance  of  rail  bonds,  1416 

symbols,  1477 

units,  relations  of,  1397,  1399 
Electricity,   analogies  to  flow  of 
water,  1400 

standardsof  measurements,  1396 

units  used  in,  1396 
Electro-chemical  equivalents,  1429 


1492 


ele-ent 


INDEX. 


ent-eye 


Electro  -  magnetic  measurements, 

1398 

-magnets,  1430^1437 
-magnets,  polarity  of,  1432 
-magnets,  strength  of,  1431 
-motive  force  of  armature  cir- 
cuit, 1436 
Electrolysis,  1428 
Electrolytic  theory  of  corrosion, 

468 
Elements,  chemical,  table,  173 

of  machines,  535-541 
Elevators,  coal,  1196 
gravity  discharge,  1197 
perfect  discharge,  1197 
Ellipse,  construction  of,  45-48 
equations  of,  71 
measures  of,  60 
Ellipsoid,  64 

Elongation,  measurement  of,  279 
Emery,  grades  of,  1311 

wheels,  safe  speeds,  1316,  1317 
wheels,  speed  and  selection  of, 

1310-1315 

wheels,  stress  in,  1310 
wheels,    truing    and    dressing, 

1317 

E.M.P.  of  electric  circuits,  1407 
Endless  screw,  540 
Endurance  of  materials,  relation 

of,  to  elastic  limit,  275 
Energy,   available,   of  expanding 

steam,  870 
conservation  of,  531 
definition  of,  528 
intrinsic  or  internal,  600 
measure  of,  528 
mechanical,  of  steam  expanded 

to  various  pressures,  963 
of  recoil  of  guns,  531 
of  water  flowing  in  a  tube,  746, 

765 

sources  of,  531 
Engines,  alcohol,  1102 

alcohol  consumption  in,  844 
automobile,  capacity  of,  1101 
blowing,  680 
compressed    air,    efficiency    of, 

639-641 

fire,  capacities  of,  752 
gas,  1095-1108  (see  G  as-engines) 
hoisting  (see  Hoisting  engines), 

1186 

hot-air  or  caloric,  1095 
hydraulic,  815 

internal  combustion,  1095-1108 
marine,  steam-pipes  for,  880 
oil  and  gasoline,  1101 
petroleum,  1102 
pumping,   802-806   (see  Pump- 
ing-engines) 

steam,    959-1095    (see    Steam- 
engines) 
solar,  1015 
winding  (see  Hoisting  engines), 

1186 

Entropy,  definition  of,  599 
of  water  and  steam,  602 


Entropy    of    water    and    steam, 
tables,  869,  871-873 

-temperature  diagram,  599 
Epicycloid,  50 

Equalization  of  pipes,  625,  884 
Equation  of  payments,  14 
Equation  of  pipes,  884 
Equations,  algebraic,  34-36 

of  circle,  71 

of  ellipse,  71 

of  hyberbola,  72 

of  parabola,  72 

quadratic,  35 

referred  to  co-ordinate  axes,  70 
Equilibrium  of  forces,  516 
Equivalent  orifice,  mine  ventila- 
tion, 715 

E  qui  valen  ts ,  electro-chemical  ,1429 
Erosion  of  soils  by  water,  755 
Ether,  petroleum,  as  fuel,  841 
Euler's  formula  for  long  columns, 

284 
Evaporation,  569-577 

by  exhaust  steam,  572 

by  multiple  system,  570 

factors  of,  908-912 

in  a  vacuum,  573 

in  salt  manufacture,  570 

latent  heat  of,  569 

of  sugar  solutions,  572 

of  water   from   reservoirs   and 
channels,  569 

total  heat  of,  569- 

unit  of,  886 
Evaporator,  for    marine    engines, 

1082 

Evolution,  8 
Exciters,  1449 
Exhauster,  steam-jet,  679 
Exhaust-steam,    evaporation    by, 
572 

for  heating,  1009 

Expansion,  adiabatic,  formulae  for, 
638 

by  heat,  565 

coefficients  of,  566 
Expansion  of  air,  adiabatic,  638 

cast  iron,  permanent  by  heat- 
ing, 453 

gases,  construction  of  curve  of, 
602 

gases,  curve  of,  73 

iron  and  steel  by  heat,  465 

liquids,  567 

nickel  steel,  499 

solids  by  heat,  566 

steam,  959 

steam,  actual  ratios  of,  965 

timber,  367 

water,  716 
Explosions,  dust,  837 

of  fuel  economizers.  927 
Explosive  energy  of  steam-boilers, 

932 
Exponential  function,  differential 

of,  79,  80 

Exponents,  theory  of,  36 
Eye-bars,  tests  of,  360 


fac-fec 


INDEX. 


fee-fla 


1493 


FACTOR  of  evaporation,  908 
of  safety,  374-377 
of  safety,  formulae  for,  376 
of  safety  in  steam-boilers,  918 
Factory  heating  by   fan  system, 

708,  710 
Fahrenheit-Centigrade  conversion 

table,  550,  551 
Failures  of  stand-pipes,  350 

of  steel,  486 

Fairbairn's    experiments  on   riv- 
eted joints,  424 
Fall  increaser  for  turbines,  780 
Falling  bodies,  graphic  represen- 
tation, 522 
height  and  velocity  of  tables, 

523,  524 
laws  of,  521 
Fan  blowers,  types  of,  654 

tables,  caution  in  regard  to,  662 
Fans  (see  also  Blowers) 
and  blowers,  653-681 
and   chimneys  for  ventilation, 

712 

and  rotary  blowers,   compara- 
tive efficiencies,  657 
best  proportions  of,  653 
blast-area  of,  655 
centrifugal,  648,  649,  653 
centrifugal,  high-pressure,  648 
conoidal,  666 

cupola,  power  required  for,  1253 
design  of,  653 
disk,  675-677 

disk,  influence  of  speed  on  effi- 
ciency, 675,  677 
effect  of  resistance  on  capacity 

of,  664 

efficiency  of,  656,  657,  668 
electric  motors  for,  1464 
experiments  on,  657 
for  cupolas,  661 
high-pressure,  capacity  of,  663 
horse-power  of,  668 
influence  of  spiral  casings,  674 
methods  of  testing,  667 
multiblade,  655,  658 
multiblade,    characteristics    of, 

656 

pipe  lines  for,  670 
pressure  characteristics  of,  655 
pressure  due  to  velocity  of,  653 
quantity   of  air   delivered   by, 

655 

relation  of  speed  volume,  pres- 
sure and  power,  656 
Farad,    definition   and   value   of, 

1397 
Fatigue,  crystallization  of  iron  by, 

465 

effect  of,  on  iron,  465 
Feed  and  depth  of  cut,  effect  of, 

on  speed  of  tools,  1264 
-pump  (see  Pumps) 
Feeds  and  speeds  of  drills,  1288 
Feed-water,  cold,  strains  caused 

by,  939 
heaters,  938-940 


Feed-water  heaters,  capacity  of, 

939 

heaters:  closed  vs.  open,  940 
heaters,  proportions  of,  940 
heaters,  transmission  of  heat 

in,  590 

heating,  Nordberg  system,  1003 
heating,  saving  due  to,  938 
purification  of,  723-726 
to  boilers  by  gravity,  938 
Feet  and  inches,  decimal  equiva- 
lents of,  table,  5 
Fellows  stub  tooth  gear,  1167 
Fence  wires,  corrosion  of,  468 
Ferrite,  439.  480 

Ferro-alloys  for  foundry  use,  1255 
manufacture  of,  1424 
silicon,  addition  of,  to  cast-iron, 

450 

silicon,  dangerous,  1255 
Field,  magnetic,  1398 
Fifth   roots   and   fifth  powers   of 

numbers,  109 

powers,  square  roots  of,  110 
Fineness,  coefficient  of,  1369 
Finishing   temperature,    effect   of 

in  steel  rolling,  478 
Fink  roof  truss,  547 
Fire,  temperature  of,  817,  818 
Fire-brick  arches  in  locomotives, 

1115 
number    required    for    various 

circles,  table,  267 
refractoriness  of,  268 
sizes  and  shapes  of,  266 
weight  of,  266 
Fire-clay,  analysis  of,  269 

pyrometer,  553,  556 
Fire-engines,  capacities  of,  752 
Fire-proof  buildings,  1389 
Fire-streams.  749-752 

discharge  from  nozzles  at  differ- 
ent pressures,  750,  753 
effect  of  increased  hose  length, 

750 

friction  loss  in  hose,  752 
hydrant  pressure  required  for, 

table,  750 

Fireless  locomotive,  1127 
Fits,  force  and  shrink,  1324-1327 
force  and  shrink,   pressure  re- 
quired to  start,  1327 
limits  of  diameter  for,  1325 
press,     pressure    required    for, 

1324-1326 
running,  1325 
stresses  due  to,  1326 
Fittings    (see  Pipe-fittings),   206- 

216 

Flagging,  strength  of,  373 
Flanges,  brass,  214,  215 

cast-iron,  forms  of,    210,    214- 

216 

forged  and  rolled  steel,  211 
forged  steel,  for  riveted  pipe,  211 
for  riveted  pipe,  211 
pipe,  extra  heavy,  tables,  210, 
212 


1494 


fla-flo 


INDEX. 


flo-fou 


,  is,  pipe,  tables,  209-213 

__  during,  dimensions  of,  214 
Flanged   fittings,    cast-iron,   208- 

210 
Flat  plates  in  steam-boilers,  916 

plates,  strength  of,  336 

steel  ropes,  258,  261 

surfaces  in  steam-boilers,  916 
.Flattened  strand  rope,  258,  261 
Flexure    and    compression    com- 
bined, 335 

and  tension  combined,  335 

and  torsion  combined,  335 

of  beams,  formula  for,  297,  299 
Flight  conveyors,  1197 
Flights,  sizes  and  weights  of,  1 199 
Floors,  maximum  load  on,  1390- 
1393 

strength  of,  1390-1393 
Flow  of  air  in  long  pipes,  618-624 

air  in  pipes,  617-624 

air    through    orifices,    615-617, 
670 

compressed  air,  618-624 

gas  in  pipes,  864-866 

gas  in  pipes,  tables,  865,  866 

gases,  605 

metals,  1323 

Flow  of  steam  at  low  pressure, 
699 

capacities  of  pipes,  877-878 

in  long  pipes,  877 

in  pipes,  877-879 

into  atmosphere,  876 

loss  of  pressure  due  to  friction, 
877 

loss  of  pressure  due  to  radiation, 
880 

Napier's  rule,  876 

resistance  of  bends,  valves,  etc., 

.     879 

tables  of,  699,  877-879 

through  a  nozzle,  876,  1085 

through  safety  valves,  934 
Flow  of  water,  726-746 

approximate  formulae,  734,  737, 
746 

Chezy's  formula,  728 

D'Arcy's  formula,  732 

experiments    and    tables,    737- 
753 

exponential  formula,  736 

fall  per  mile  and  slope,  table, 

formulae  for,  726-746 

in  cast-iron  pipe,  737 

in  house  service  pipes,  table,  744 

in   pipes   at   uniform   velocity, 

table,  739 
in  pipes,   table  from   D'Arcy's 

formula,  740,  741 
table  from  Hazen  &  Williams' 

formula,  742,  743 
table  from  Kutter's  formula, 

738,  739 

in  riveted  steel  pipes,  734-736 
in  20-in.  pipe,  737 
Kutter's  formula,  730 


Flow  of  water  over  weirs,  726,  762 
through  nozzles,  table,  753 
through  orifices,  726 
through     rectangular     orifices, 

760 

values  of  c,  732,  736 
values  of  coefficient  of  friction, 

734 

Flowing  water,  horse-power  of,  765 
water,  measurement  of,  757-764 
Flues,  collapsing  pressure  of,  341 
corrugated,   341,   917    (see  also 

Tubes  and  Boilers) 
Flux,  magnetic,  1398 
Fly-wheels,  arms  of,  1050 
centrifugal  force  in,  1047 
diameters    for   various   speeds, 

1048 
for  presses,  punches,  shears,  etc., 

1323 
for  steam-engines,  1040,  1044- 

1052 

speed,  variation  in,  1044-1049 
strains  in,  1049 
thickness  of  rim  of,  1052 
weight  of,  1045-1048 
weight  of,  for  alternating  cur- 
rent units,  1047 
wire  wound,  for  extreme  speeds, 

1052 

wooden  rim,  1051 
Foaming    or    priming    of   steam- 
boilers,  721,  930 
Foot-pound,  unit  of  work,  528 
Force,  centrifugal,  521 
definitions  of,  512 
graphic  representation  of,  513 
moment  of,  514 
of  a  blow,  529,  1322 
of  acceleration,  526 
units  of,  512 
work,  power,  etc.,  528 
Forces,  composition  of,  513 
equilibrium  of,  516 
parallel,  515 
parallelogram  of,  513 
parallelopipedon  of,  514 
polygon  of,  513 
resolution  of,  513 
Forced  draught,   chimneys  with, 

952 

draught  in  steam-boilers,  923 
Forcing  and  shrinking  fits,  1323- 

1327  (see  Fits) 
Forging    and    grinding    of   tools, 

1263 

heating  of  steel  for,  492 
hydraulic,  814,  815 
of  tool  steel,  488,  492,  1263 
Forgings,  steel,  annealing  of,  482 

strength  of,  353 
Forging-press,  hydraulic,  814 
Fottinger     transformer     or     hy- 
draulic pinion,  1095 
Foundation    walls,    thickness   of, 

13S6 

Foundations,  masonry,  allowable 
pressures  on,  1386 


fou-fru 


INDEX. 


fru-fur 


1495 


Foundations  of  buildings,  1386 
Foundry  coke,  quality  of,  1255 

irons    (see   Pig   iron   and    Cast 
iron) 

ladles,  dimensions  of,  1257 

molding-sand,  1256 

practice,  1247-1257 

practice,  shrinkage  of  castings, 

practice,  use  of  softeners,  1253 
use  of  ferro  alloys  in,  1255 
Fractions,  2 

product  of,  in  decimals,  4 
Framed    structures,    stresses    in, 

541-548 

Frames,  steam-engine,  1043 
Framing,  for  tanks  with  flat  sides, 

339 

Francis's  formulae  for  weirs,  762 
Freezing  point  of  brine,  1343 

point  of  water,  719 
French  measures  and  weights,  21— 

26 

thermal,  unit,  560 
Frequency  changers,  1457 
of  alternating  currents,  1440 
standard,   in   electric   currents, 

1440 
Friction    and    lubrication,    1219- 

1246 
brakes    and    friction    clutches, 

1239 

brakes,  capacity  of,  1334 
clutches,  1179 

coefficient  of,  definition,  1219 
coefficient    of,    in    water-pipes, 

734 

coefficients  of,  tables,  1219-1221 
drives,   power  transmitted  by, 

1178 

fluid,  laws  of,  1220 
laws  of,  of  lubricated  journals, 

1225 
loss  of  head  by,  in  water-pipes, 

728,  735,  745 
moment  of,  1229 
Morin's  laws  of,  1223 
of  air  in  mine  passages,  714 
of  car  journals,  1228 
of  hydraulic  packing,  813,  1241 
of    lubricated    journals,    1220- 

1232 
of  metals,  under  steam  pressure, 

1223 

of  motion,  1219-1222 
of  pivot  bearings,  1229,  1232 
of  rest,  1219 
of  solids,  1219 
of  steam-engines,  1238 
of  steel  tires  on  rails,  1219 
rollers,  1233 
rolling,  1219 

unlubricated,  law  of,  1219 
work  of,  1229 
Frictional  gearing,  1 178 

resistance  of  surfaces  moved  in 

water,  756 
Frustum  of  cone,  62 


Frustum  of  parabolic  conoid,  65 

of  pyramid,  62 

of  spheroid,  64 

of  spindle,  65 
Fuel,  816-858 

bagasse,  839 

charcoal,    836-837    (sec    Char- 
coal) 

coke,  824,  832-834  (see  Coke) 

combustion  of,  816 

dust,  837 
Fuel,  economizers,  924-927 

equation  of,  925 

explosions  of,  927 

heating  surface  of,  925 

heat  transmission  in,  925 

saving  due  to,  925 

tests  of,  926 
Fuel  for  cupolas,  1248,  1255 

gas,  845  (see  Gas) 

gas,  for  small  furnaces,  854 
eat  of  combustion  of,  560,  817 
liquid,  840-844 
peat,  838 
pressed,  831 
sawdust,  838 

solid,  classification  of,  818 
straw,  839 

theory  of  combustion  of,  816 
turf,  838 

value  of  illuminating  gas,  863 
weight  of,  180 
wet  tan  bark,  838 
wood,  835,  836 
Fuel-oil,  burners  for,  842 

California,    heating    values   of, 

842 

chimney  draught  with,  952 
chimney  table  for,  951 
specifications  for  purchaseof ,  843 
Functions,    trigonometric,    tables 

of,  170-172 
trigonometric,  of  half  an  angle, 

69 
of  sum  and  difference  of  angles, 

68 

of  twice  an  angle,  69 
Furnace    for    melting     iron     for 

malleable  castings,  454 
flues,  steam-boiler,  formulae  for, 

917 

heating  (see  Heating) 
Furnaces,  blast,  gases  of,  855 
blast,  temperature  in,  555 
corrugated,  342   917 
down  draught,  919 
electric,  1422 
for  different  coals,  827 
for  house  heating,  690 
gas,  fuel  for,  854 
hot-air,  heating  by,  690 
industrial,  temperatures  in,  554 
open    hearth,    temperature    in, 

554,  555 

steam-boiler      (see     Boiler-fur- 
naces) 
steam-boiler,  combustion  space 

in,  889 


1496 


ffns-gas 


INDEX. 


gas-gca 


Fusible  alloys,  404 

plugs  in  boilers,  404,  918 
Fusibility  of  metals,  180 
Fusing-disk,  1309 

temperatures  of  substances,  554, 

559 
Fusion,  latent  heat  of,  568 

of  electrical  wires,  1409 

g,  value  of,  522,  525 

GAGE,  decimal,  32 
lines  for  steel  angles,  321 
sheet  metal,  28,  29,  31,  32 

Stub's  wire,  28, 

Gages,   limit,   for  iron  for  screw 
threads,  232  '     . 

wire,  28-30 

Gallon,  British  and  American,  27 
Gallons  and  cubic  feet,  table,  130 

per     minute,     cubic    feet     per 

second, 130 

Galvanic  action,  corrosion  by,  467 
Galvanized  sheets,  weights  of,  192 

wire,  test  for,  474 

wire  rope,  255,  262 
Galvanizing  by  cementation,  474 

iron  surfaces,  473.  474 

of  welded  pipe  206 
Gas  (see  also  Fuel-gas,  Water-gas, 
Producer    gas,    Illuminating- 
gas) 

ammonia,    properties    of,    1339 

analyses  by  volume  and  weight, 
854 

and  electric  lighting,  1468 

and  oil  engines,  rules  for  testing, 
1105 

and   vapor  mixtures,   laws  of, 
604 

anthracite,  845 

bituminous,  846 

carbon,  845 

coal,  858 

exhausters,  rotary,  679 

fuel  (see  also  Water-gas) 

fuel,  cost  of,  863 

fuel  for  small  furnaces,  854 

flow  of,  in  pipes,  864-866  (see 
Flow  of  gas) 

illuminating,    858-866    (see    Il- 
luminating-gas ) 

lamps,  pipe  services  for,  864 

lights,  candle-power  of,  860 

lights,  Welsbach,  standard  sizes, 
1474 

meter,    Thomas    electric,    667, 
669 

natural,  847-848 

perfect,  equations  of  a,  600 

pipe,     cast-iron,     weights    and 
dimensions,  198,  199 

produced  from  ton  of  coal,  848 

producer,  848-855  (see  also  Gas- 
Producers) 

sulphur-dioxide,  properties    of, 
1338,  1341 

table  of  factors  for  equivalent 
volumes  of,  865 


Gas,    water,    846,    859-864     (see 

Water-gas) 
Gases,  absorption  of,  605 

Avogadrp's  law  of,  604 

combustion  of,  rise  of  tempera- 
ture in,  818 

cupola,  utilization  of,  1253 

densities  of,  604 
_  expansion  of,  601,  603 

expansion  of  by  heat,  table,  565 

flow  of,  605 

heat  of  combustion  of,  560 

ignition  temperature  of,  858 

law  of  Charles,  600,  604 

liquefaction  of,  605 

Mariotte's  law  of,  603 

of  combustion,  analyses  of,  817 

physical  properties  of,  603-606 

specific  heats  of,  563,  564 

waste,    use    of,    under    boilers, 
898,  899 

weight  and  specific  gravity  of, 

table,  176 
Gas-engine,  1095-1108 

calculation  of  the  power  of,  1097 

conditions    of    maximum    effi- 
ciency, 1103 

economical  performance  of,  1104 

efficiency  of,  1103 

four-cycle  and  two-cycle,  1096 

governing,  1103 

heat  losses  in,  1104 

horse-power,  estimate  of,  1101 

ignition  in,  1102 

mean  effective  pressure  in,  1098 

pressures  developed  in,  1097 

pumps,  808 

sizes  of,  1100 

temperatures  and  pressures  in, 
1096,  1099 

tests  of,  1105-1108 

tests  with  different  coals,  853 
Gas-producers,  capacity  of.  851 

and  scrubbers,   proportions  of, 
849 

combustion  in,  849 

practice,  851 

use  of  steam  in,  854 
Gasoline  engines,  1101 

fuel  value  of,  841 

vapor  pressures  of,  844 
Gauss,    definition   and   value   of, 

1398 

Gear,   reduction,  for  steam   tur- 
bines, 1095 

reversing,  1039 

stub- tooth,  1167, 

wheels,  calculation  of  speed  of, 
1162 

wheels,  formulae  for  dimensions 
of,  1160 

wheels,  milling  cutters  for,  1162 

wheels,  proportions  of,  1161 

worm,  540 

Gears,   automobile,   efficiency   of, 
1172 

lathe,  for  screw  cutting,  1259 

of  lathes,  quick  change,  1260 


gea-gor 


INDEX. 


goY-har 


1497 


Gears,  spur,  machine-cut,  1178 

with  short  teeth,  1160 
Gear-box  drive  for  machine  tools, 

1308 
-cutting,  speeds  and  feeds  for, 

1284 

Gearing,  annular,  1169 
bevel,  1169 
chordal,  pitch,  1159 
comparison  of  formulae,   1174- 

1177 

cycloidal  teeth,  1162 
diameters    for    1-inch    circular 

pitch,  1159 
differential,  1169 
efficiency  of ,  1170-1172 
forms  of  teeth,  1162-1167 
f Fictional.  1178 
involute  teeth,  1165 
pitch,  pitch-circle,  etc.,  1157 
proportions  of  teeth,  1159,  1161 
racks,  1165 
raw-hide,  1177 

relation  of  diametral  and  cir- 
cular pitch,  1158 
speed  of,  1177 
spiral,  1168 
stepped,  1168 
strength  of,  1172-1177 
stub- tooth,  1167 
toothed-wheel,   539,   1157-1180 
twisted,  1168 
worm,  1168 

worm,  efficiency  of,  1171 
Generator  sets,   standard  dimen- 
sions of,  1007 
Generators,  acetylene,  857 

alternating-current,     1448    (see 

Dynamo  electric  machines) 
electric,  1437,  1448 
Geometrical  problems,  37-53 
progression,  11 
propositions,  53 
Geometry,  analytical,  70-73 
German  silver,  356,  402 
conductivity  of,  1401 
Gesner  process,  treating  iron  sur- 
faces, 473 
Gib  keys,  1332 
Gilbert,  unit  of  magneto-motive 

force,  1398 

Girder  beams,  Bethlehem  steel/331 
Girders,  allowed  stresses  in  plate 

and  lattice,  289 
and  beams,  safe  load  on,  1387 
and  beams,  New  York  building 

laws,  1390 

plate,  strength  of,  353 
Warren,  stresses  in,  546 
Glass,  skylight,  sizes  and  weights, 

196 

strength  of,  365 
weight  of,  177 
Gold,     melting    temperature    of, 

554,  559 

properties  of,  178 
Gordon's    formula    for    columns, 
284 


Governor,  inertia,  1066 
Governors,  steam-engine,  1065 

impulse  wheel,  782 
Governing  of  gas-engines,  1103 
Grade  line,  hydraulic,  748 
Grain,  weight  of,  180 
Granite,  strength  of,  357,  370 
Graphite,      Acheson's      defloccu- 
lated,  1246 

lubricant,  1246 

paint,  471 

Grate-surface,  for  house  heating, 
boilers  and  furnaces,  693 

in  locomotives,  1115 

of  a  steam-boiler,  888 
Gravel,  cubic  feet  per  ton,  181 
Gravity,  acceleration  due  to,  521, 
525 

boiler-feeders,  938 

center  of,  516 

specific    (see   Specific   gravity), 

Grease  lubricants,  1244 
Greatest    common    measure    or 

divisor,  2 
Greek  letters,  1 
Greenhouses,    hot-water,    heating 

of,  703 

steam-heating  of,  702 
Grinding  as  a  substitute  for  finish 

turning,  1317 
of  tools,  1263 
wheel     (see     Grindstones    and 

Emery  wheels) 
wheel  for  high-speed  tools,  1263, 

1314 
Grindstones,  speed  of,  1317 

strains  in,  1318 
Guest's    formula    for    combined 

stresses,  335 
Gun-bronze,  variation  in  strength 

of,  386 
Gun-iron,    variation    in    strength 

of,  452 
Gun-metal  (bronze),  composition 

of,  390 

Guns,  energy  of  recoil  of,  531 
Gurley's  bronze,  composition  of, 

390 
Guy  ropes  for  stand-pipes,  349 

ropes,  wire,  255 
Gyration,  center  of,  518 
radius  of,  293 
table  of  radii  of,  519 

H-  COLUMNS,         Bethlehem 
steel,  333 
Halpin  heat  storage  system, 
927,  1014 
Hammering,    effect   of,    on   steel, 

488 

Hanger  bolts,  243 
Hardening  and  tempering,  change 

of  shape  due  to,  1291 
of  soft  steel,  479 
Hardness,   electro-magnetic  tests 

of,  365 
of  copper-tin  alloys,  385 


1498 


har-hea 


INDEX. 


hea-hea 


Hardness  of  metals,  Brinell's  tests, 
364 

of  water,  723 

scleroscope  tests  of,  365 
Harvey  process  of  hardening  steel, 

1291 
Harveyizing     steel     armor-plate, 

1291 
Haulage,  wire-rope,  1202-1205 

wire-rope,  endless  rope  system, 
1203 

wire-rope,  engine-plane,  1203 

wire-rope,  inclined-plane,  1202 

wire-rope,  tail-rope  system,  1203 

wire-rope  tramway,  1204 
Hauling  capacity  of  locomotives, 

1111 
Hawley    down-draught    furnace, 

919 

Hawsers,  steel  wire,  262 
Hazen  &  Williams'  formula,  table 

of  flow  of  water,  742,  743 
Head,  loss  of,  728,  735,  745  (see 
Loss  of  head) 

of  air,  due  to  temperature  differ- 
ences, 716 

of  water,  728 

of  water,  comparison  of,  with 

various  units,  718 
Heads  of  boilers,  914 

of  boilers,    unbraced,   wrought 

iron,  strength  of,  337 
Heat,  549-597 

conducting    power    of    metals, 
580 

conduction    by    various     sub- 
stances, 580-587 

conduction  of,  579 

convection  of,  579 

effect  of  on  gram  of  steel,  479 

expansion  due  to,  565 

generated   by   electric   current, 
1408 

-insulating  materials,   tests  of, 
581 

latent,  568  (see  Latent  heat) 

loss  by  convection,  596 

losses    in    steam-power   plants, 
1012 

mechanical  equivalent  of,  560, 
868 

of  combustion,  560 

of  combustion  of  fuels,  560,  817 

produced  by  human  beings,  686 

quantitative    measurement    of, 
560 

radiating  power  of  substances, 
578 

radiation  of,  578  (see  also  Ra- 
diation) 

reflecting  power  of  substances, 
578 

resistance,  coefficients  of,  583 

resistance,    reciprocal    of    con- 
ductivity, 582 

specific,    562-565    (see    Specific 
heat) 

steam,  storing  of,  927,  1014 


Heat  storage,  Halpin  system,  927, 

1014 
Heat  transmission,  Blechynden's 

tests  of,  593 

from  flame  to  water,  592 
from  gases  to  water,  592 
from  steam  to  water,  587 
in  condenser  tubes,  589 
in  feed-water  heater,  590 
in  radiators,  698 
resistance  of  metals  to,  580 
through  building  walls,  etc.,  582, 

688 

through  plates,  580,  591 
through  plates  from  steam  or 

hot  water  to  air,  595 
Heat  treatment  of  a  motor-truck 

axle,  479 
treatment   of  high   speed   tool 

steel,  1265 

treatment  of  steel  (see  Steel) 
unit  of,  560,  867 
units  per  pound  of  water,  717 
Heaters  and  condensers,  calcula- 
tion of  surface  of,  939 
cast  iron,  for  hot-blast  heating, 

709 

cast  iron,  tests  of,  709 
electric,  1420 
feed-water,  938-940 
feed- water,  open-type,  940 
feed-water,  transmission  of  heat 

in,  590 

Heating  and  Ventilation,  681-716 
allowance    for     exposure     and 

leakage,  688 
blower  system,  708—710 
boiler  heating  surface,  694 
computation  of  radiating   sur- 
face, 698 

heating  surface,  indirect,  698 
heating  value  of  radiators,  684, 

697 

quantity  of  heat  required,  690 
steam-heating,      694-703      (see 

Steam-heating) 
transmission    of   heat    through 

building  walls,  688 
Heating  a  building  to  70°  in  zero 

weather,  711 

air,  heat  absorbed  in,  691 
and  ventilating  by  electric  cur- 
rent, 1421 
by  blower   system,  capacity  of 

fans  for,  711 
by  electricity,  713 
by  exhaust  steam,  1009 
by  hot-air  furnaces,  690 
by  hot  water,  703-  708  (see  Hot- 
water  heating) 

by  overhead  steam  pipes,  702 
by  steam  (see  Steam-heating) 
domestic,  by  electricity,  1421 
furnace,  size  of  air  pipes  for,  692 
furnace,  with  forced  air  supply, 

690 

guarantees,  performance  of,  712 
of  electrical  conductors,  1408 


bca-liol 


INDEX. 


hoi-how 


1499 


Heating  of  factories  by  blower  sys- 
tem, 708,  710 
of  greenhouses,  702 
of  large  buildings,  684 
of  steel  for  forging,  492 
of  tool  steel,  492 
problems,   standard  values  in, 

687 

steam  and  electric,  1421 
value  of  coals,  826-830 
value  of  wood,  835 
water  by  steam  coils,  591 
Seating-surface    of   steam-boiler, 

887,  888 
Height,  table  of,  corresponding  to 

a  given  velocity,  523 
Helical  steel  springs,  418 
Helix,  61 

Hemp  rope,  strength  of,  357 
rope,    table    of    strength    and 

Weight  of,  410,  415 
Henry,   definition  and  value  of, 

1397 
High-speed  tool  steel   (see  Steel, 

and  Tools) 

Hindley  worm  gear,  1169 
Hobson's     hot-blast     pyrometer, 

555 

Hodgkinson's  column  formula,  283 
Hoist,  hydraulic,  783 
Hoists,  electric  motors  for,  1464 
Hoisting   by   hydraulic   pressure, 

813 

counterpoise  system,  1189 
cranes,  1189-1193  (see  Cranes) 
effect  of  slack  rope,  1186 
endless  rope  system,  1189 
engines,  1186 

engines,  compressed-air,  646 
engines,     counterbalancing    of, 

1188 

horse-power  required  for,  1184 
Koepe  system,  1189 
loaded  wagon  system,  1189 
limit  of  depth  for,  1186 
of  cargoes,  414 
pneumatic,  1187 
suspension  cable  ways,  1205 
with  tapering  ropes,  1188 
Hoisting-rope,  410-415 
flexible  steel  wire,  258,  259 
iron  or  steel,  tables,  255-261 
ion-spinning,  258,  261 
tresses  in,  on  inclined  planes, 

1204 
tension     required    to    prevent 

slipping,  1206 

wire,  sizes  and  strength  of,  410 
Holding  power  of  bolts  in  white 

pine,  346 

of  expanded  boiler  tubes,  364 
of  lag-screws,  347 
of  nails  in  wood,  347 
f  nails,  spikes  and  screws,  346, 

347 
of  tubes  expanded  into  sheets, 

364 
of  wood  screws,  346 


Holes,  tube,  in  steam-boilers,  916 
Hollow  cylinders,  resistance  of  to 

collapse,  341-345 
shafts,  torsional  strength  of,  334 
Homogeneity    test    for    fire-box 

steel,  508 
Hooks  and  shackles,  strength  of, 

1184 

heavy  crane,  1183 
proportions  of,  1182 
Horse  gin,  534 
work  of,  533 

Horse-power  (see  also  Power) 
brake,  970 

brake,  definition  of,  1017 
computed  from  torque,  1436 
constants,     of     steam-engines, 

971-974 

definition  of,  27,  528 
electrical,  970,  1408 
electrical,  brake  and  indicated, 

1408 

hours,  definition  of,  528 
nominal,  definition  of,  974 
of  compound  engine,   estimat- 
ing, 971 

of  flowing  water,  765 
of  marine  and  locomotive  boil- 
ers, 888 

of  steam-boilers,  885 
of  steam-boilers,  builders'  rat- 
ing, 888 

of  steam-engines,  970-976 
water  and  steam,  cost  of,  767 
Hose  couplings,  national  standard, 

218 

fire,  friction  losses  in,  752 
hydrant  pressures  required  with 

different  lengths  of,  750 
rubber-lined,    friction    loss    in, 

752 

specifications  for,  379 
Hot-air  engines,  1095 

heating  (see  Heating) 
Hot-blast    pyrometer,    Hobson's, 

555 
Hot-blast  system  of  heating,  708 

(see  Heating) 
Hot  boxes,  1228 
Hot-water  Heating  (see  Heating), 

703-708 

arrangement  of  mains,  703 
computing     radiating     surface, 

704-706 

corrosion  of  pipe  in,  708 
indirect,  705 
of  greenhouses,  703 
rules  for,  703 
size  of  pipes  for,  704 
sizes  of  flow  and  return  pipes, 

707 

velocity  of  flow,  703 
with  forced  circulation,  707 
House-heating  (see  Heating) 
House-service  pipes,  flow  of  water 

in,  table,  744 

Howden  system  of  forced  draught, 
923 


1500 


How-Ill 


INDEX. 


ill-Int 


Howe  truss,  stresses  in,  546 
.tumidity  and  temperature,  com- 
fortable, 685 
relative,  table  of,  610 
Humphrey  gas  pump,  808 
Hyatt  roller  bearings,  1235 
Hydraesfer  process,  treating  iron 

surfaces,  473 

Hydrant  pressures  required  with 
different  lengths  of  hose,  750 
Hydraulic  air  compressor,  650 
apparatus,  efficiency  of,  812 
cylinders,  thickness  of,  813 
engine,  815 
forging,  814,  815 
formulae,  726-746 
formulae,  approximate,  734,  737, 

746 

grade-line,  748 
packing,  friction  of,  813 
pipe,  riveted,  table,  219 
power  in  London,  814 
press,    thickness    of    cylinders 

for,  340 

presses  hi  iron  works,  813 
ram,  810-812 
riveting  machines,  814 
turbines     (see     Turbines,     hy- 
draulic) 

Hydraulics  (see  Flow  of  water) 
Hydraulic  pressure,  hoisting  by, 

813 

transmission,  812-816 
transmission,  energy  of,  812 
transmission,    speed    of    water 
through  pipes  and  valves,  813 
transmission,  references,  816 
Hydrometer,  175 
Hygrometer,   dry  and  wet  bulb, 

610 

Hyperbola,  asymptotes  of,  73 
construction  of,  49 
equations  of,  72 
Hyperbolic    curve    on    indicator 

diagrams,  974 

logarithms,  tables  of,  164-166 
Hypocycloid,  50 

I-BEAMS  (see  also  Beams) 
Bethlehem  steel,  332 
Carnegie,  table  of,  307-310 
safe  loads  on,  309 
spacing,  for  uniform  load,  311 
Ice-making,   absorption  evapora- 
tor system,  1367 
machines,    1336-1367    (see   Re- 
frigerating machines) 
plant,  test  of,  1367 
tons  of  ice  per  ton  of  coal,  1367 
with  exhaust  steam,  1367 
Ice,  manufacture,  1366 
-melting  effect,  1343 
properties  of,  720 
strength  of,  368 
Ignition  in  gas  engines,  1102 
temperature  of  gases,  858 
Illuminants,  relative  color  values 
of,  1469 


Illuminants,  relative  efficiency  of, 

1472 

Illuminating  coal-gas,  858 
Illuminating-gas,  858-866 

calorific  equivalents  of  constit- 
uents, 860 
fuel  value  of,  863 
space  required  for  plants,  862 
Illuminating  water-gas,  859 
Illumination    by    arc    lamps    at 

different  distances,  1471 
definition  of,  1468 
electric  and  gas  lighting,  1468 
interior,  1473 
of  buildings,  watts  per  square 

foot,  required  for,  1369 
relation  of,  to  vision,  1469 
Impact,  530 
Impedance,  1441 
polygons,  1442 
Impulse   water   wheels,    780    (see 

Water  wheel,  tangential) 
Impurities  of  water,  720 
Incandescent  lamps  (see  Lamps), 

1470 
Inches  and  fractions  as  decimals 

of  a  foot,  table,  5 
Inclined  plane,  527,  537 
motion  on,  527 
stresses   in   hoisting   ropes   on, 

1204 

wire-rope  haulage,  1202 
Incrustation  and  scale,  721,  927— 

932 

India  rubber,   action  under  ten- 
sion, 378 

vulcanized,  tests  of,  378 
Indicated  horse-power,  970-976 
Indicator   diagrams,   analysis   of, 

1017 
diagrams,    to    draw    clearance 

line  on,  974 
diagrams,    to    draw   expansion 

curve,  974 
diagrams,  tests  of  locomotives, 

1122 
rig,  969 
Indicators,  steam-engine,  968-976 

(see  Steam-engines) 
steam-engine,  errors  of,  969 
Indirect  heating  radiators,  698 
Inductance,  1440 

of  lines  and  circuits,  1445 
Induction,  magnetic,  1398 

motors,  1463 
Inertia,  definition  of,  513 

moment,  of,  293,  517 
Ingot  iron,  "Armco,"  477 
Injector,  807 

efficiency  of,  937 
equation  of,  936 
performance  of,  937 
Inspection  of  steam-boilers,  932 
Insulation,  underwriters',  1410 
Insulators,  electrical  value  of,  1402 

heat,  581 
Integrals,  75 
table  of,  80,  81 


Int-iro 


INDEX. 


irr-Iam 


1501 


Integration,  76 

Intensity  of  magnetization,  1398 

Interest,  12 

compound,  13,  14 
Intercoolers  for  air  compressors, 

648 

Interpolation,  formula  for,  86 
Invar,  iron-nickel  alloy,  499,  567 
Involute,  52 

gear-teeth,  1165 

gear-teeth,    approximation    of, 

1166 

Involution,  7 

Iridium,  properties  of,  178 
Iron  and  steel,  178,  436-511 
classification  of,  436 
effect  of  cold   on   strength  of, 

464 

electric  furnaces,  1423 
inoxidizable  surface  for,  472 
preservative  coatings  for,  471- 

474 

relative  corrosion  of,  468 
rustless  coatings  for,  471-474 
sheets,  weight  of,  183 
tensile   strength  at   high   tem- 
peratures, 463 
Iron  bars  (see  Bars) 

bars,    weight    of    square    and 

round,  181,  184 
bridges,  durability  of,  466 
cast,  437-454  (see  Cast-iron) 
castings,  chemical  standards  for, 

441 

coated  with  aluminum,  473 
coated  with  lead,  474 
coefficients  of  expansion  of,  465 
color    of   at    various    tempera- 
tures, 558 

-copper-zinc  alloys,  393 
corrosion  of,  467 
corrugated,   sizes  and  weights, 

194 

durability  of,  465-467 
electrolytic,  properties  of,  460 
flat-rolled,  weight  of,  188,  189 
for  stay-bolts,  462 
inoxidizable    surfaces,    produc- 
tion of,  472 

latent  heat  of  fusion  of,  568 
malleable,    454    (see   Malleable 

iron) 

pig  (see  Pig-iron  and  Cast-iron) 
plates,  approximating  weight'of , 

486 

plates,  weight  of,  table,  187 
properties  of,  178 
rivets,    shearing    resistance    of, 

430 

rope,  table  of  strength  of,  410 
shearing  strength  of.  362 
sheets,  weights,  31,  32,  183 
-silicon-aluminum  alloys,  398 
specific  heat  of,  562,  563 
tubes,    collapsing    pressure    of, 

341 

wrought,  459-463  (see  Wrought 
iron)  ^ 


Irregular  figure,  area  of,  56,  57 

solid,  volume  of,  65 
Irrigation  canals,  755 
Isothermal  compression  of  air,  633 

expansion,  601 

expansion  of  steam,  959 

JAPANESE  alloys,  composition 
of,  393 
Jarno  tapers,  1319 
Jet  condensers,  1068 

propulsion  of  ships,  1384 
reaction  of  a,  1385 
water  wheels,  781 
Jets,  steam  (see  Steam  jets) 

vertical  water,  749 
Joints,  pipe  (see  Pipe  joints) 
riveted,    424-435    (see   Riveted 

joints) 

Joists,  contents  of,  21 
Joule,    definition    and    value    of, 

1396,  1397 

Joule's  equivalent,  560 
Journals     (see    also    Shafts    and 

Bearings) 

coefficients  of  friction  of,  1220 
Journal-bearings,  cast-iron,  1223 
friction  of,  1220-1232 
of  engines,  1034 

KAOLIN,  melting  point  of,  556 
Kelvin's    rule    for    electric 
transmission,  1411 
Kennedy  key,  1330 
Kerosene  as  fuel,  841 

for  scale  in  boilers,  929 
Keys,  dimensions  of,  1328 
gib,  1332 

holding  power  of,  1332 
various  forms  of,  1328 
Key-seats,  depth  of,  1329 
Keyways  for  milling  cutters,  1277 
Kinetic  energy,  528 
King-post  truss,  stresses  in,  543 
Kirkaldy's    tests    of   strength    of 

materials,  352-358 
Knife-edge  bearings,  1238 
Koepe's  system  of  hoisting,  1189 
Knot,  on  nautical  mile,  17 
Knots,  varieties  of,  415,  416 
Krupp  steel  tires  and  axles,  354 
Kutter's  formula,  flow  of  water,  730 
formula,  tables  of  flow  of  water, 
738,  739 

LACING  of  belts,  1147 
Ladles,     foundry,    sizes    of, 
1257 
Lag  screws,  holding  power  of,  347 

screws,  sizes  and  weights,  241 
Lamps,  arc,  1470 
arc,  data  of,  1471 
arc,  illumination  by,  at  differ- 
ent distances,  1471 
arrangement  of,  in  rooms,  1475 
electric,  life  of,  1476 
incandescent,  characteristics  of, 

1474 
incandescent  electric,  1470 


1502 


lam-Jin 


INDEX. 


lin-Ioc 


Lamps,  mercury  vapor,  1470 

tungsten,  1473 
Land  measure,  17 
Lang-lay  wire-rope,  254 
Lap  and  lead  in  slide  valves,  1052- 

1054 

Lap  joints,  riveted,  426,  427 
Laps  and  lapping,  1310 
Latent  heat  of  evaporation,  569 

of  fusion  of  iron,  568 

of  fusion  of  various  substances, 

568 
Lathe,  change-gears  for,  1260 

cutting  speed  of,  1259 

horse-power  to  run,  1292,  1293 

power  required  for,  1293 

rules  for  screw-cutting  gears, 
1259 

setting  taper  in,  1261 

topis,  forms  of,  1261 
Lattice   girders,   allowed   stresses 

in,  289 
Laws  of  falling  bodies,  521 

of  motion,  513 
Lead  and  tin  tubing,  226,  227 

coatings  on  iron  surfaces,  474 

effect  of,  on  copper  alloys,  394 

-lined  iron  pipes,  227 

paint  as  a  preservative,  471 

pipe,  tin-lined,  sizes  and  weights, 
table,  226 

pipe,  weights  and  sizes  of, 
table,  226,  227 

properties  of,  178 

sheet,  weight  of,  228 

waste-pipe,    weights   and   sizes 

of,  227 

Leakage  of  steam  in  engines,  976 
Least  common  multiple,  2 
Leather,  strength  of,  357 
Lea-Deagan  two-stage  pump,  test 

of,  801 

Le  Chatelier's  pyrometer,  554 
Lentz  compound,  engine,  997 
Leveling  by  barometer,  607 

by  boiling  water,  607 
Lever,  535 

bent,  514,  536 
Lewis's  key,  1329 
Lighting,  electric  and  gas,  1468 

electric,  cost  of,  1475 

of  streets,  1471 

quantity  of  gas  and  electricity 
required  for  different  rooms, 
1473 

street,  recent  installations,  1476 
Lightning  protection  of  chimneys, 

949 

Lights  (see  Lamps) 
Lignites,  analysis  of,  829 
Lime  and  cement  mortar,  strength 
of,  372 

and  cement,  weight  of,  180 
Limestone,  strength  of,  371 
Limit,  elastic,  273-278 

gages  for  screw-thread  iron,  232 
Lines  of  force,  1430 
Links,  steel  bridge,  strength  of,  353 


Link-belting,    sizes   and   weights, 

1199 
Link-motion,  locomotive,  1119 

steam-engine,  1062-1065 
Lintels  in  buildings,  1390 
Liquation  of  metals  in  alloys,  388 
Liquefaction  of  gases,  605 
Liquid  air  and  other  gases,  605,  606 

measure,  18 

Liquids,  absorption  of  gases  by, 
605 

Compressibility  of,  175 

expansion  of,  567 

specific  gravity  of,  175 

specific  heats  of,  563 
Loading  and  storage  machinery, 

1193 

Lock- joints  for  pipes,  212 
Locomotive  boilers,  1113 

boiler  tubes,  seamless,  222 

boilers,  size  of,  1113 

crank-pin,  quantity  of  oil  used 
on,  1246 

engine  performance,  1122 

forgings,  strength  of,  353 
Locomotives,  1108-1129 

boiler  pressure,  1117 

classification  of,  1116 

compounding  of,  1125 

compressed-air,  1128 

compressed-air,  with  compound 
cylinders,  1129 

counterbalancing  of,  1126 

dimensions  of,  1120-1122 

drivers,  sizes  of,  1118 

economy   of  high   pressure   in, 
1116 

effect  of  speed  on  cylinder  pres- 
sure, 1117 

efficiency  of,  1111 

exhaust-nozzles,  1115 

fire-brick  arches  in,  1115 

fireless,  1127 

fuel  efficiency  of,  1119 

fuel  waste  of,  1125 

grate-surface  of,  1115 

hauling  capacity  of,  1111 

horse-power  of,  1113 

indicator  tests  of,  1122 

leading  types  of,  1116 

light,  1127 

link-motion,  1119 

Mallet  compound,  1120 

narrow  gage,  1127 

performance  of  high  speed,  1118 

petroleum  burning,  1127 

safety  valves  for,  935 

smoke-stacks,  1115 

speed  of,  1118 

steam  distribution  of,  1117 

steam-ports,  size  of,  1118 

superheating  in,  1126 

testing,  1123 

tractive  force  of,  1112.  1125 

types  of,  1116 

valve  travel,  1118 

water  consumption  of,  1122 

weight  of,  1124 


loc-mac 


INDEX. 


mac-man 


1503 


Locomotives,  Wootten,  1114 
Logarithmic  curve,  73 

ruled  paper,  84 

sines,  etc.,  table,  167 
Logarithms,  79 

four-place,  table,  168 

hyperbolic,  tables  of,  164-166 

six-place,  table,  137-164 

use  of,  135-137 

Logs,  area  of  water  required  to 
store,  181 

lumber,  etc.,  weight  Of,  181 

weight  of,  181 
Long  measure,  17 
Loop,  steam,  883 
Loops  of  force,  1430 
Lord   and   Haas's   tests   of  coal, 

822,  823 
Loss  and  profit,  12 

of  head,  Cox's  formula,  734 

of  head  in  cast-iron  pipe,  tables, 
745 

of  head  in  flow  of  water,  728, 
735,  745 

of  head  in  riveted  steel  pipes,  735 
Lowmoor  iron  bars,  strength  of, 

352 

Lubricant,  water  as  a,  1246 
Lubricants,  examination  of,  1242 

grease,  1244 

measurement  of  durability,  1241 

oil,  specifications  for,  1242 

qualifications  of  good,  1242 

relative  value  of,  1242 

soda  mixture,  1246 

solid,  1246 

specifications     for     petroleum, 

1242 
Lubrication,  1241-1246 

of    engines,     quantity     of    oil 
needed  for,  1245 

of  steam-engine  cylinders,  1245 
Lumber,  weight  of,  181 
Lumen,  definition  of,  1469 
"Lusitania, "      performance      of, 
1376,  1381 

turbines  and  boilers  of,  1381 
Lux,  definition  of,  1469 

MACHINE  screws,  A.  S.  M. 
E.  standard,  table,  234- 
237 

screws,  taps  for,  1320 
shop,  1258-1333 
shops,  electric  motors  for,  1294- 

1308,  1466 
Machine  tools,  drives,  feeds  and 

speeds,  1307 
electric  motors  for,  1294-1308, 

1466 
gear  connections  of,  to  motors, 

1301 
individual  motors  for  driving, 

1308 

methods  of  driving,  1307 
power  required  for,  1270,  1278, 

1286,  1293 
sizes  of  motors  for,  1294 


Machine  tools,  soda  mixture  for, 
1246 

speed  of,  1258 

Machines,     dynamo-electric     (see 
Dynamo-electric-machines) 

efficiency  of,  532 

elements  of,  535-541 

in   groups,  power  required  for 

driving,  1305 

Machinery,   coal-handling,    1196- 
1199 

horse-power    required    to    run, 

1292-1308 

Maclaurin's  theorem,  78 
Magnalium,       magnesium-alumi- 
num alloy,  399 
Magnesia  bricks,  269 
Magnesite,  analysis  of,  270 
Magnesium,  properties  of,  179 
Magnet,  electro,  1430 
Magnets,  lifting,  1193 
Magnetic  alloys,  402 

balance,  for  testing  steel,  483 

brakes,  1240 

capacity  of  iron  and  steel,  ef- 
fect of  annealing  on,  483 

circuit,  1430 

circuit,  units  of,  1398 

field,  1398 

field,  strength  of,  1436 

flux,  magnetic  induction,  1398 

moment,  1398 

pole,  unit  of,  definition,  1398 
Magnetization,  intensity  of,  1398 
Magneto-motive  force,  1398 
Magnolia  metal,  composition  of, 

405 

Mahler's  calorimeter,  826 
Malleability  of  metals,  table,  180 
Malleable  cast  iron,  454 

castings,  annealing,  455 

castings,  design  of,  457 

castings,  tests  of,  458 

iron,  pig  iron  for,  454 

iron,  composition  and  strength 
of,  454,  458 

iron,   improvement  in  quality, 
458 

iron,  physical  characteristics, 45 6 

iron,  shrinkage  of,  455 

iron,  specifications,  457 

iron,  strength  of,  454,  458 

iron  test  bars,  457 
Mandrels,  standard  steel,  1318 
Manganese  bronze,  401 

-copper  alloys,  401 

effect  of,  on  cast  iron,  438,  450 

effect  of,  on  steel,  476 

properties  of,  179 

steel,  494 

sulphide,  dangerous  in  steel,  486 
Manganin,  high  resistance  alloy, 

404,  1402 

Manhole     openings     in     steam- 
boilers,  914 
Manila  rope,  411 

rope,   weight  and  strength  of, 
410-415 


1504 


man-mer 


INDEX. 


mer-mod 


Manograph,  a  high-speed  engine- 
indicator,  969 
Manometer,  air,  607 

work  of,  tables,  532,  533 
Man-wheel,  533 
Marble,  strength  of,  357 
Marine     engineering,     1368-1385 
(see  Ships  and  Steam-engines) 
engine,     internal     combustion, 

1374 

engine  practice,  advance  in,  1380 
Mariotte's  law  of  gases,  603 
Martensite,  439,  480 
Masonry,  allowable  pressures  on, 

1386 

crushing  strength  of,  371 
materials,,  weight  and  specific 

gravity  of,  177 
Mass,  definition  of,  511 
Materials,  173-273 

standard      cross-sections,      for 

draftsmen,  271 
strength  of,  272-379 
strength    of,    Kirkaldy's    tests, 

352-358 

various,  weights  of,  table,  181 
Maxima  and  minima,  78,  79 
Maxwell,  definition  and  value  of, 

1398 
Measures  and  weights,  compound 

units,  27 
and  weights,  metric  system,  21- 

26 

apothecaries,  19 
board  and  timber,  20 
circular,  20 
dry,  19 
liquid,  18 
long,  17 
nautical,  17 

of  work,  power  and  duty,  27 
old  land,  17 
shipping,  19,  1316 
solid  or  cubic,  18 
square,  18 
surface,  18 
time,  20 

Measurement  of  air  velocity,  624 
of  elongation,  279 
of  flowing  water,  757-764 
of  vessels,  1368 

Measurements,  miner's  inch,  761 
Mechanics,  511-548 
Mechanical    equivalent    of   heat, 

560,  868 
and  electrical  units,  equivalent 

values  of,  1399 
powers,  535 
stokers,  918 

Mekarski     compressed-air    tram- 
way, 652 

Melting-points  of  substances,  tem- 
peratures, 554,  559 
Mensuration,  54-66 
Mercurial  thermometer,  549 
Mercury-arc  rectifier,  1456 
Mercury-bath  pivot,  1233 
properties  of,  179 


Mercury  vapor  lamp,  1460 
Mesure  and   Nonet's   pyrometric 

telescope,  556 

Metacenter,  definition  of,  719 
Metals,  anti-friction,  1223 

coefficients  of  expansion  of,  566 
coefficients  of  friction  of,  1220 
electrical  conductivity  of,  1401 
flow  of,  1323 

heat-conducting  power  of,  580 
life  of,  under  shocks,  276 
properties  of,  177-180 
resistance  overcome  in  cutting 

of,  1292 

specific  gravity  of,  174 
specific  heats  of,  562,  563 
table  of  ductility,   infusibility, 
malleability  and  tenacity,  180 
tenacity  of,  at  various  tempera- 
tures, 463 
weight  of,  174 
Metaline  lubricant,  1246 
Metallography,  480 
Meter,  Thomas  electric,  for  meas- 
uring gas,  667,  669 
Venturi,  758 

water,  V-notch  recording,  759 
Meters,  water  delivered  through, 

749 

Methane  gas,  physical  laws  of,  604 
Metric  conversion   tables,   meas- 
ures and  weights,  21-26 
screw-threads,  cutting  of,  1261 
Microscopic  constituents  of  cast 

iron  and  steel,  439,  480 
Mil,  circular,  18,  29, 
Mill  buildings,  columns,  1393 
buildings,  approximate  cost  of, 

1394 

power,  766 

Milling  cutters,   diameter,   clear- 
ance and  rake  of,  1278 
for  gear-wheels,  1162 
inserted  teeth,  1276 
keyways  in,  1277 
lubricant  for,  1281 
number  of  teeth  in,  1276 
side,  1275 
spiral,  1275 

Milling,  high-speed,  1282 
jobs,  typical,  1281 
machines,     cutting     speed     of, 

1280,  1284 
machines,    high    results    with, 

1282 

machines,  typical  jobs  on,  1281 
power  required  for,  1278 
practice,  modern,  1279,  1283 
with  or  against  the  feed,  128O 
Mine  fans,  experiments  on,  673 
ventilating  fans,  673 
ventilation,  714 

Mines,  centrifugal  fans  for,  672 
Miner's  inch,  18 

inch  measurements,  761 
Modulus  of  elasticity,  274 

of  elasticity  of  various  materials 
374 


moci-nal 


INDEX. 


nap-orl 


1505 


Modulus  of  resistance,  or  section 
modulus,  294 

of  rupture,  297 
Moisture  in  atmosphere,  609-613 

in  steam,  determination  of,  942- 
944 

in  steam  escaping  from  boilers, 

944 

Molding-sand,  1256 
Molds,  cast-iron,  for  iron  castings, 

analysis  of,  1256 
Moment  of  a  couple,  515 

of  a  force,  514 

of  friction,  1229 

of  inertia,  293,  295,  517 

statical,  514 

Moments,   method  of,  for  deter- 
mining stresses,  545 

of  inertia  of  regular  solids,  517 

of  inertia  of  structural  shapes, 

295 

Momentum,  527 
Mond  gas  producer,  852 
Monel  metal,  copper-nickel  alloy, 

403 

Monobar  chain  conveyor,  1197 
Morin's  laws  of  friction,  1223 
Morse  tapers,  1319 
Mortar,  strength  of,  372 
Motion,  accelerated,  formulae  for. 
527 

friction  of,  1219,  1221 

Newton's  laws  of,  513 

on  inclined  planes,  527 

perpetual,  532 

retarded,  521 
Motor  applications,  1464-1468 

boats,  power  of  engines  for,  1374 

-driven  machine  tools,  1308 

generators,  1456 

repulsion,  induction,  1464 

squirrel-cage,  1463 

temperatures,  limits  of,  1432 
Motors,  alternating-current,  1463 

commutating  pole,  1437 

compressed-air,  639-641 

electric  (see  Electric  motors) 

electric,  classification  of,  1461 

gear  connections  of,  for  machine 
tools,  1301 

sizes  of,  for  machine  tools,  1294 

water  current,  765 
Moving  strut,  536 
Mule,  work  of,  534 
Multiphase  electric  currents,  1445 
Multiple  system  of  evaporation, 

570 

Multivane  fans,  658 
Muntz  metal,  composition  of,  390 
Mushet  steel,  496 

NAILS,  cut,  table  of  sizes  and 
weights,  244 
cut  vs.  wire,  347 
holding  power  of,  346 
wire,  table  of  sizes  and  weights, 

246,  247 
Nail-holding  power  of  wood,  347 


Naphtha  as  fuel,  841 

Napier's  rule  for  flow  of  steam, 

876 

Natural  gas,  847,  848 
Nautical  measure,  17 

mile,  17 

Newton's  laws  of  motion,  513 
Nickel,  effect  .of  on  properties  of 

steel,  498 

Nickel,  properties  of,  179,  379 
steel,  497 
steel,  tests  of,  497 
steel,  uses  of,  498 
Nickel-copper  alloys,  402 

-vanadium  steels,  499 
Niter  process,  treating  iron  sur- 
faces, 473 

Nordberg  feed-water  heating  sys- 
tem, 1003 
key,  1331 

pumping-engine,  805 
Nozzle,  efficiency  of  Doble,  782 
Nozzles,  flow  of  steam  through; 

876,  1085 

flow  of  water  in,  753 
for     measuring     discharge     of 

pumping-engines,  759 
water,  efficiency  of,  784 
Nut  and  bolt  heads,  231 

OATS,  weight  of,  180 
Ocean  waves,  power  of,  784 
Oersted,    unit   of  magnetic 

reluctance,  1398 

Ohm,  definition  and  value  of,  1397 
Ohm's  law,  1406 

law  applied  to  alternating  cur- 
rents, 1442 
law  applied  to  parallel  circuits, 

1407 
law  applied  to  series  circuits, 

1407 

Oil  as  fuel  (see  Fuel  oil),  842,  843 
engines,  1102 
fire-test  of,  1243 
for  scale  removal  in  boilers,  930 
for  steam  turbines,  1244 
fuel,  chimney  draught  with,  952 
fuel,  chimney  table  for,  951 
lubricating,  1242-1245  (see  Lub- 
ricants) 
paraffine,  1243 
pressure  in  a  bearing,  1228 
quantity    needed    for    engines, 

1245 

tempering  of  steel  forgings  482 
vs.  coal  as  fuel,  842,  843 
well,  1243 

we.ls,  air-lift  pump  for,  809 
Open-hearth     steel      (see     Steel, 

open-hearth),  475 
furnace,  temperatures  in,  554 
Ordinates  and  abscissas,  70 
Ores,  cubic  feet  per  ton,  181 
Orifice,  equivalent,  in  mine  ven- 
tilation, 715 

flow  of  air  through,  615-617, 
670 


1506 


ori-pew 


INDEX 


pho-pip 


Orifice,  flow  of  water  through,  726 
rectangular,      flow     of     water 

through,  table,  760 
Oscillation,  center  of,  518 

radius  of,  518 
Overhead    steam-pipe    radiators, 

702 

Ox,  work  of,  534 
Oxy-acetylene  welding,  488 
Oxygen,  effect  of  on  strength  of 

steel,  477 

7T  value  and  relations  of,  57 » 

PACKING,  hydraulic,  friction 
of,  1241 
-rings  of  engines,  1023 
Paddle-wheels,  1383 
Paint,  471 

chrome,    preventing   corrosion, 
469 

for  roofs,'  192 

qualities  of,  472 

quantity  of,  for  surface,  472 
Paper,  logarithmic  ruled,  84 
Parabola,  area  of  by  calculus,  76 

construction  of,  48,  49 

equations  of,  72 

path  of  a  projectile,  525 
Parabolic  conoid,  65 

spindle,  65 
Parallel  forces,  515    , 

operation  of  motors,  1439,  1450 
Parallelogram  area  of,  54 

of  forces,  513 

of  velocities,  523 
Parallelopipedon  of  forces,  514 
Parentheses  in  algebra,  34 
Partial  payments,  14 
Part-ing  and  threading  tools,  speed 

of,  1268 
Patterns,  weight  of,  for  castings, 

1256 

Payments,  equation  of,  14 
Pearlite,  439,  480 
Peat,  838 

Pelton  water-wheel,  780 
Pendulum,  520 

conical,  520 
Percentage,  12 
Percussion,  center  of,  518 
Perforated  plates,  strength  of,  425 
Permeability,      magnetic,      1400, 

1430 

Permeance,  magnetic,  1400 
Permutation,  10 
Perpetual  motion,  532 
Petroleum  as  a  metallurgical  fuel, 
843 

-burning  locomotives,  1127 

cost  of  as  fuel,  842 

engines,  1102 

for  scale  removal  in  boilers,  930 

Lima,  841 

products  of  distillation  of,  840 

products,  specifications  for,  1242 

value  of  as  fuel,  841 
Pewter,  composition  of,  407 


Phosphor-bronze,  composition  of, 

390 

specifications  for,  395 
springs,  424 
strength  of,  395 
Phosphorus,  influence  on  steel, 476 

influence  of,  on  cast  iron,  438 
Piano-wire,  strength  of,  250 
Pictet  fluid,  for  refrigerating,  1337 
Piezometer,  757 
Pig  Iron  (see  also  Cast  iron) 
analysis  of,  439 
charcoal,  strength  of,  452 
distribution  of  silicon  in,  448 
electric  smelting  of,  1424 
for  malleable  castings,  454 
grading  of,  437 

influence  of  silicon,  etc.,  on,  438 
sampling,  443 
specifications  for,  443 
Piles,  bearing  power  of,  1386 
Pillars,  strength  of,  283 
Pine,  strength  of,  366 
Pinions,  raw-hide,  1177 
Pins,  forcing  fits  of  by  hydraulic 

pressure,  1324 
Pins,  taper,  1321 
Pipe  bends,  flexibility  of,  221 
branches,  compound  pipes,  for- 
mula for,  746 
cast-iron,  friction  loss  in,  table, 

747,  748 
cast-iron ,      specifications      for 

metal  for,  441 
cast-iron,  threaded,  199 
corrosion  of  in  hot- water  heat- 
ing, 708 

coverings,  tests  of,  584-587 
dimensions,     Briggs    standard, 

221,  222 

fittings,  flanged,  208-214 
fittings,  screwed,  207,  216 
fittings,  strength  of,  216 
fittings,  valves,  etc.,  resistance 

of,  701 
flanges,    extra    heavy,    tables, 

210,  212 

flanges,  tables,  209-213 
iron  and  steel,  strength  of,  363 
iron,  lead-,  brass-  and  copper- 
lined,  227 

iron,  lead-covered,  228 
iron,  tin-  and  lead-lined,  227 
joints,  bell  and  spigot,  lead  re- 
quired for,  199 

lines  for  fans  and  blowers,  670 
lines,  long,  743 
specialties,  205 
threading  of,  force  required  for, 

363 
welded,    weight    and    bursting 

strength  of,  205 
wooden  stave,  218,  735 
Pipes,  see  also  Tubes 
air-bound,  748 

air,  loss  of  pressure  in,  617-624 
and    valves    for    superheated 
steam,  882 


pip-pip 


INDEX. 


pis-pla 


1507 


Pipes,  bent  and  coiled,  221,  222 
block-tin,  weights  and  sizes  of, 

2^7 

coiled,  table  of,  221 
Pipes,  cast-iron,  bell  and  spigot 

for  gas,  198 
flanged,  for  gas,  199 
for  high-pressure  service,  198 
formulae  for  thickness  of,  196 
safe  pressures  for,  tables,  196-198 
thickness  of,  for  various  heads, 

196-200 

transverse  strength  of,  452 
underground,  weight  of,  197 
weight  and  dimensions,  196-200 
Pipes,  effects  of  bends  in,  624,  747 
equalization  of,  table  625 
equation  of,  884 
flow  of  air  in,  617-624 
flow  of  gas  in,  864-866 
flow  of  steam  in,  877-879 
flow  of  water  in,  728-746 
for  steam  heating,  698 
house-service,  flow  of  water  in, 

table,  744 
iron  and  steel,  corrosion  of,  466, 

467 

lead,  safe  heads  for,  226 
lead, (tin-lined,  sizes  and  weights, 

table,  227 
lead,     weights    and    sizes    of, 

table,  226 
maximum  and  mean  velocities 

in,  758 

proportioning  to  radiating  sur- 
face, 699,  700      ' 
rectangular,  flow  of  air  in,  622 
resistance  of  the  inlet,  735 
rifled,  for  conveying  heavy  oils, 

746 

riveted,  flanges  for,  table,  211 
riveted  hydraulic,  weights  and 

safe  heads,  table,  219 
riveted    iron,    dimensions     of, 

table,  220 
riveted  steel,  loss  of  head  in, 

734 

riveted  steel,  water,  351 
sizes  of  threads  on,  201,  217 
spiral  riveted,  table  of,  220 
steam  (see  Steam-pipes) 
steam,  sizes  of  in  steam  heat- 
ing, 699-701 

table  of  capacities  of,  131 
used  as  columns,  363 
volume  of  air  transmitted  in, 

table,  623,  624 
water,  loss  of  head  in,  728,  735, 

745  (see  Loss  of  head) 
welded,  extra  strong,  203,  204 
welded,  standard,  table  of  di- 
mensions, 202 
Pipe-joint,    Converse    lock-joint, 

212 

Matheson,  212 
Rockwood,  212 

Piping,    power-house,    identifica- 
tion of  by  different  colors,  885 


Piston  rings,  steam-engine,  1023 
rods,  steam-engine,  1024 
valves,  steam-engine,  1061 
Pistons,  steam-engine,  1023 
Pitch,  diametral,  1158 
of  gearing,  1157 
of  rivets,  427 
of  screw-propeller,  1377 
Pitot  tube,  best  form  of,  667 
gage,  757 

measurements,  accuracy  of*  669. 
use  in  testing  fans,  667 
Pivot-bearings,  1229,  1232 

mercury  bath,  1233 
Plane,  inclined,  527,  537  (see  In- 
clined plane) 

surfaces,  mensuration  of,  54 
Planer,   horse-power  required   to 

run,  1302 

tools,  standard,  1271-1274 
work,  1270-1274 
Planers,  feeds  and  speeds  of,  1270 

power  requirements  of,  1302 
Planing,  time  required  for,  1271 

work  requiring,  1270 
Planished  and  Russia  iron,  473 
Plank,  wooden,  maximum  spans 

for,  1392 
Plants,  high  pressure  water-power, 

782 
Plate-girder,  strength  of,  353 

-girders,  allowed  stresses  in,  289 
Plates  (see  also  Sheets) 

acid  pickled,  heat  transmission 

through,  591 
areas  of,  in  square  feet,  table, 

128,  129 

brass,  weight  of,  tables,  228,  229 
Carnegie  trough,  properties  of, 

table,  308 

circular,  strength  of,  336 
copper,  strength  of,  356 
copper,  weight  of,  table.  229 
corrugated  steel,  properties  of, 

table,  310 

flat,  cast-iron,  strength  of,  336 
flat,  for  steam-boilers,  916 
flat,  unstayed,  strength  of,  337 
for  stand-pipes,  349 
iron  and  steel,   approximating 

weight  of,  486 

iron,  weight  of,  table,  187,  188 
of  different  materials,  table  for 

calculating  weights  of,  181 
perforated,  strength  of,  425  < 
punched,  loss  of  strength  in, 

424 

stayed,  strength  of,  338 
steel   boiler,   specifications  for, 

507 
steel,  for  cars,  specifications  for, 

507 

steel,  specifications  for,  507 
steel,  tests  of,  353,  355 
transmission  of  heat  through, 

587 

transmission  of  heat  through, 
from  air  to  water,  592 


1508 


pla-prc 


INDEX. 


pre-pum 


Plates,  transmission  of  heat 
through,  from  steam  to  wair, 
595 

Plating  for  bulkheads,  table,  339 
steel,  stresses  in,  due  to  water 

pressure,  338 
for  tanks,  table,  338 
Platinite,  499,  567 
Platinum,  properties  of,  179 
pyrometer,  553 
wire,  248 

Plenum  system  of  heating,  708 
Plow-steel  wire,  250 

-steel  wire-rope,  257,  259 
Plugs,   fusible,   in  steam  boilers, 

918 

Plunger  packing,  hydraulic,  fric- 
tion of,  1239 

Pneumatic  conveying,  1201 
hoisting,  1187 
postal  transmission,  1201 
Polarity  of  electro-magnets,  1432 
Poles,  tubular,  206 
Polishing  and  buffing,  1310 

wheels,  speed  of,  1310 
Polyedron,  63 
Polygon,  area  of,  55 
construction  of,  42-45 
of  forces,  513 
Polygons,  impedance,  1442 

table  of,  45,  55 
Polyphase  circuits,  1445 
Popp   system  of  compressed-air, 

639-641 
Population  of  the  United  States, 

11 
Port    opening    in    steam-engines, 

1057 

Portland  cement,  strength  of,  358 
Postal    transmission,    pneumatic, 

1201 

Potential  energy,  528 
Pound,  British  avoirdupois,  26 

-calorie,  definition  of,  560 
Pounds  per  square  inch,  equiva- 
lents of,  27 
Power,  animal,  532 

and  work,  definition  of,  528 

electrical,  cost  of,  1012 

factor  of  alternating  currents, 

1440 

hydraulic,  in  London,  814 
measures  of,  27 
of  a  waterfall,  765 
of  electric  circuits,  1408 
of  ocean  waves,  784 
required     for     machine     tools, 

1292-1302 
required  to  drive  machines  in 

groups,  1305 
tidal,  787 
unit  of,  528 

Powers  of  numbers,  algebraic,  33 
of  numbers,   tables,  7,    8,    93- 

110 

Power-plant  economics,  1011 
Pratt  truss,  stresses  in,  544 
Preservative  coatings,  471-474 


Press  fits,  pressure  required  for, 
1324-1326 

forging,  high-speed,  steani  hy- 
draulic, 815 

hydraulic  forging,  814 

hydraulic,  thickness  of  cylinders 

for,  340 

Presses,  hydraulic,  in  iron  works, 
813 

punches  and  shears,  fly-wheels 
for,  1323 

punches,  etc.,  1321 
Pressed  fuel,  831 
Pressure,  collapsing  of  flues,  342 

collapsing  of  hollow  cylinders, 

341 
Pressures    of    fluids,    conversion 

table  for,  607 
Priming,    or    foaming,    of   steam 

boilers,  721,  930 
Prism,  62 
Prismoid,  63 

rectangular,  62 
Prismoidal  formula,  63 
Problems,  geometrical,  37-53 

in  circles,  39-44 

in  lines  and  angles,  37-39 

in  polygons,  42-45 

in  triangles,  41 
Process,  the  Thermit,  400 
Producer-gas,  848-855  (see  Gas) 
Producers,  gas  (see  Gas-producers) 

gas,  use  of  steam  in,  854 
Profit  and  loss,  12 
Progression,  arithmetical  and  geo- 
metrical, 10,  11 

Projectile,  parabola  path  of,  525 
Prony  brake,  1333 
Propeller,   screw    (see   Screw-pro- 
peirer)  1377 

shafts,  strength  of,  354 
Proportion,  6 

compound,  7 
Protective     coatings     for     pipes, 

206 
Pulleys,  1135-1138 

arms  of,  1050 

cone,  1136 

cone,  on  machine  tools,  1307 

convexity  of,  1136 

differential,  539 

for  rope-driving,  1217 

or  blocks,  538 

proportions  of,  1111 

speed  of,  1148,  1162 
Pulsometer,  806 

tests  of,  807 

Pumps,  air-,  for  condensers,  1071, 
1073 

air-lift,  808 

and  pumping-engines,  788-812' 

boiler-feed,  792 

boiler-feed,  efficiency  of,  937 

centrifugal,  796-802 

centrifugal,  combination  single 
stage  and  two  stage,  798 

centrifugal,  design  of,  797 

centrifugal,  multi-stage,  797 


pum-pyr 


INDEX. 


qua-rca 


1509 


Pumps,    centrifugal,    relation    of 

height  of  lift  to  velocity,  797 
centrifugal,   tests  of,   798,  800, 

802 

circulating,  for  condensers,  1075 
depth  of  suction  of,  788 
direct-acting,  efficiency  of,  790 
direct-acting,      proportion      of 

steam  cylinder,  790 
electric  motors  for,  1463 
feed,  for  marine  engines,  1076 
gas-engine,  808 
high-duty,  793 
horse-power  of,  788 
jet,  807 

leakage,  test  of,  803 
lift,  water  raised  by,  790 
mine,  operated  by  compressed 

air,  652 

piston  speed  of,  791,  792 
rotary,  801 
rotary,  tests  of,  802 
speed  of  water  in  passages  of, 

790 

steam,  sizes  of,  tables,  789,  791 
suction  of,  with  hot  water,  788 
theoretical  capacity  of,  788 
underwriters',  sizes  of,  792 
vacuum,  806 
valves  of,  792,  793 
Pump-inspection  table,  751 
Pumping  by  compressed  air,  645, 

808  (see  also  Air-lift) 
by  gas-engines,  cost  of,  795 
by  steam  pumps,  cost  of  fuel 

for,  795 

cost  of  electric  current  for,  794 
Pumping-engine,  72,000,000  gal., 

screw,  794 

the  d'Auria,  793 

Pumping-engines,  duty  trials  of, 
802-806 

economy  of,  794 

high-duty  records,  806 

table  of  data  for  duty  trials  of, 
803-805 

use  of  nozzles  to  measure  dis- 
charge of,  759 
Punches  and  dies,  clearance  of,  1321 

spiral,  1322 

Punched  plates,  strength  of,  425 
Punching  and  drilling  of  steel,  483, 

485 

Purification  of  water,  723-726 
Pyramid,  62 

frustum  of,  62 
Pyrometer,  air,  Wiborgh's,  555 

copper-ball,  553 

fire-clay,  Seger's,  555 

Hobson's  hot-blast,  555 

Le  Chatelier's,  554 

principles  of,  549 

thermo-electric,  553 

Uehling-Steinbart,  557 
Pyrometers,  graduation  of,  554 
Pyrometric  telescope,  556 
Pyrometry,  549 


Q 


UARTER-TWIST  belt,  1147 
Queen-post  truss,  inverted, 

stresses  in,  544 
truss,  stresses  in,  543 
Quenching  test  for  soft  steel,  507 

RACK,  gearing.  1165 
Radian,  definition  of,  523 
Radiating    power    of    sub- 
stances, 578 
surface,    computation    of,    for 

hot-water  heating,  704 
surface,    computation    of,    for 

steam  heating,  698 
surface,  proportioning  pipes  for, 

700 

Radiation,  black  body,  579 
of  heat,  578 

of  various  substances,  578,  595 
Stefan  and  Boltzman's  law,  579 
table  of  factors  for  Dulong's 

laws  of,  596 
Radiators,  experiments  with,  697, 

708 

indirect,  698 

overhead  steam-pipe,  702 
steam  and  hot-water,  697 
steam,  removal  of  air  from, 

702 

transmission  of  heat  in,  697 
Radius  of  gyration,  293,  518 
of  gyration,  graphical   method 

for  finding,  294 
of  gyration  of  structural  shapes, 

293,  294 

of  oscillation,  518 
Rails,  steel,  electric  resistance  of, 

1416 

steel,  specifications  for,  508        ! 
steel,  strength  of,  353 
Railroad  axles,  effect  of  cold  on, 

465 
steam,  electrifications  of,  table, 

1418 
track,  material  required  for  one 

mile  of,  244,  245 
trains,  resistance  of,  1108-1111 
trains,  speed  of,  1118 
Railway  curve,  degree  of  a,  54 
street,  compressed-air,  652 
track  bolts  and  nuts,  244,  245 
Railways,    electric    (sec    Electric 

railways),  1414 
narrow-gage,  1127 
Ram,  hydraulic,  810 
Rankine  cycle  efficiency  for  differ- 
ent conditions,  1091 
cycle,  efficiency  of,  996,  1089 
Rankine's   formula  for  columns, 

284 

Ratio,  6 

Raw-hide  pinions,  1177 
Reactance  of  alternating  currents, 

1441 

in  transformers,  1452 
Reaction  of  a  jet,  1385 
Reamers,  taper,  1318 
Reaumur  thermometer-scale,  549  „ 


1510 


INDEX. 


ref-riv 


Recalescence  of  steel,  480 
Receiver-space  in  engines,  980 
Receivers  on  steam  pipe  lines,  884 
Reciprocals  of  numbers,  tables  of, 

87-92 
use  of,  92 
Recorder,  carbon  dioxide,  or  CO*. 

890 
continuous,  of  water  pr  steam 

consumption,  970 
Rectangle,  definition  of,  54 

value  of  diagonal  of,  54 
Rectangular  prismoid,  62 
Rectifier,  in  absorption  refrigerat- 
ing machine,  1346 
mercury  arc,  1456 
Reduction,     ascending    and    de- 
scending, 5 

Reese's  fusing  disk,  1309 
Reflecting   power   of  substances, 

578 

Refrigerating    (see   also  Ice-mak- 
ing), 1336-1367 
air-machines,  1343 
direct-expansion  method,   1365 
Refrigerating  -  machines,     actual 
and  theoretical  capacity,  1355 
ammonia  absorption,  1346,  1364 
ammonia     compression,     1345, 

1356 

condensers  for,  1353 
cylinder-heating,  1349 
diagrams  of,  1348 
dry,  wet,  and  flooded  systems, 

1345 

ether-machines,  1343 
heat-balance,  1359 
ice-melting  effect,  1343 
liquids  for,  pressure  and  boiling 

points  of,  1337 
mean    effective    pressure    and 

horse-power,  1350 
operations  of,  1336 
performance  of,  1364 
pipe-coils  for,  1354 
pounds  of  ammonia  per  minute, 

1350 

properties  of  brine,  1343 
properties  of  vapor,  1337 
quantity  of  ammonia  required 

for,  1351 

rated  capacity  of,  1353 
relative  efficiency  of,  1348 
relative    performance    of    am- 
monia-compression   and    ab- 
sorption machines,  1347 
sizes  and  capacities,  1352 
speed  of,  1353 
sulphur-dioxide,  1345 
temperature  range,  1360 
test  reports  of,  1358 
tests  of,  1355 
using  water  vapor,  1345 
volumetric  efficiency,  1349 
Vqorhees  multiple-effect,  1351 
Refrigerating  plants,  cooling-tower 

practice  in,  1354 
systems,  efficiency  of,  1349 


Refrigeration,  1336-1367 
a  reversed  heat  cycle,  600 
cooling  effect,  compressor  vol- 
ume,   and    power    required, 
1341 

cubic  feet  space  per  ton  of,  1308 
means    of    applying    the    cold, 

1365 

Regenerator,  heat,  1014 
Regnault's  experiments  on  steam, 

870 
Reinforced      concrete,      working 

stresses  of,  1387 

Reluctance,  magnetic,  1398,  1430 
Reluctivity,  magnetic,  1400 
Reservoirs,  evaporation  of  water 

in,  569 
Resilience,  elastic,  274 

of  materials,  274 

Resistance,  elastic  to  torsion,  334 
Resistance,     electrical     (see    also 

Electrical  resistance),  1400 
effect  of  annealing  on,  1402 
effect  of  temperature  on,  1402 
in  circuits,  1406 
internal,  1408 
of  copper  wire,  1402,  1404 
.of  copper  wire,  rule  for,  1406 
of  steel,  477 
of  steel  rails,  1416 
standard  of,  1402 
Resistance,  elevation  of  ultimate, 

275 
frictional,  of  surfaces  moved  in 

water,  756 

moment  of,  and  section  mod- 
ulus, 294,  295 

of  metals  to  repeated  shocks,  276. 
of  ships,  1369 
of  trains,  1108-1111 
tractive,  of  an  electric  car,  1415 
work  of,  of  a  material,  274 
Resistivity,  definition  of,  1403 

of  copper,  1403,  1406 
Resolution  of  forces,  513 
Retarded  motion,  521 
Reversing-gear  for  steam-engines, 

dimensions  of,  1039 
Rhomboid,  definition  and  area  of, 

54 
Rhombus,  definition  and  area  of, 

54 

Rivet-iron  and  steel,  shearing  re- 
sistance of,  430 
spacing  for  structural  work,  321, 

322 

Rivets,  bearing  pressure  on,  426 
center  distances,  of  staggered, 

322 

cone-head,  239 
diameters  of,  for  riveted  joints, 

table,  429 
in  steam-boilers,  rules  for,  913, 

914 
length     required     for     various 

grips,  241 

minimum    spacing    and    clear- 
ance, 322 


rlv-rop 


IN&EX. 


rop-sca 


1511 


Rivets,    oval    head,     sizes    and 

weights,  238 
pitch  of,  426 

pressure  required  to  drive,  435 
round  head,  weight  of,  243 
shearing  value,  area  of  rivets, 

and  bearing  value,  240 
steel,    chemical    and    physical 

tests  of,  435 

steel,  specifications  for,  505 
tinners',  table,  239 
Riveted  iron  pipe,  dimensions  of, 

table,  220 

Riveted  joints,  355,  424-435 
British  rules  for,  433 
drilled,  vs.  punch  holes,  424 
efficiencies  of,  428-434,  914 
notes  on,  425 

of  maximum  efficiency,  431 
proportions  of,  427-434 
single  riveted  lap,  427 
table  of  proportions,  434 
tests  of  double-riveted  lap  and 

butt,  429 

tests  of,  table,  359 
triple  and  quadruple,  431 
triple,     working    pressures    on 

steam-boilers  with,  917 
Riveted  pipe,  flow  of  water  in, 

734-736 

pipe,  weight  of  steel  for,  221 
Riveting,  cold,  pressure  required 

for,  435 
efficiency  of  different  methods, 

425 
hand  and  hydraulic,  strength  of, 

425 

machines,  hydraulic,  814 
of  structural  steel,  484 
pressure  required  for,  435 
Roads,  resistance  of  wagons  on,  534 
Rock-drills,  air  required  for,  645 
requirements  of  air-driven,  645 
Rods  of  different  materials,  tables 
for  calculating  weights  of,  181 
Roller  bearings,  1233 

chain  and  sprocket  drives,  1153 
Rollers  and  balls,  steel,  carrying 

capacity  of,  340 
Rolling  of  steel,  effect  of  finishing 

temperature,  478 
Roof  construction,  191-195 
paints,  192 

-truss,  stresses  in,  547 
snow  and  wind  loads  on,  191 
strength  jof,  1389 
Roofing  materials  and  roof  con- 
struction, 191-195 
materials,  weight  of  various,  191 
Rope-driving,  1214-1218 
English  practice,  1218 
horse-power  of,  1215 
pulleys  for,  1217 
sag  of  rope,  1216 
tension  of  rope,  1214 
weight  of  rope,  1218 
Ropes  and  cables,  410-415 
cotton  and  hemp,  strength  of  ,357 


Ropes,  cotton,  -for  transmission, 

1218 
for    hoisting    or    transmission, 

410-415 
hemp,  iron  and  steel,  table  of 

strength  and  weight  of,  410 
hoisting  (see  Hoisting-rope) 
locked-wire,  262 
manila,  411 

manila,  data  of,  1214-1218 
manila,     hoisting    and    trans- 
mission, life  of,  415 
manila,  weight  and  strength  of, 

410-415 
splicing  of,  412 
table  of  strength  of  iron,  steel 

and  hemp,  410 

taper,  of  uniform  strength,  1208 
technical  terms  relating  to,  411 
wire,  "Lang  Lay,"  254 
wire  (see  also  Wire-rope) 
wire,  track  cable  for  aerial  tram- 
ways, 260 
Rotary  blowers,  677 

steam-engines,  1082 
Rotation,  accelerated,  work  of,  529 
Rubber  belting,  1152 
goods,  analysis  of,  378 
vulcanized,  tests  of,  378 
Rule  of  three,  6,  7 
Runnel's,   hydraulic  turbine,   de- 
termination   of    dimensions, 
769a 

Running  fits,  1325 
Rupture,  modulus  of,  297 
Russia  and  planished  iron,  473 

SAFETY,  factor  of,  374-377 
valves  for  locomotives,  935 
valves  for  boilers, 932-935 
valves,  spring-loaded,  933 

Sag  of  rope  between  pulleys,  1216 
of  wires  between  poles,  1461 

Salt,  solubility  of,  571 
weight  of,  180 

Salt-brine  manufacture,  evapora- 
tion in,  570 

properties  of,  570,  571,  1343 
solution,  specific  heat  of,  564 
solution  test  of  hydraulic  tur- 
bine discharge,  774 

Sampling  coal  for  analysis,  825 

Sand,  cubic  feet  per  ton,  181 
molding,  1256' 

Sand-blast,  1309 

Sand-lime  brick,  tests  of,  371 

Sandstone,  strength  of,  371 

Saturation  point  of  vapors,  604 

Sawdust  as  fuel,  838 

Sawing  metal,  1309 

-machines  for  metals,  1291 
metals,  speeds  and  feeds  for,1291 

Scale,  boiler,  721,  927-932 
boiler,  analyses  of,  722 
effect  of,  on  boiler  efficiency,  928 
removal  of,  from  boilers,  930 

Scales,  thermometer    comparison 
of,_550,  551 


1512 


sca-sha 


JNDEX. 


sha-she 


Scantling,  table  of  contents  of,  21 
Schiele  pivot  bearing,  1233 
Schiele's  anti-friction  curve,  50 
Scleroscope,  for  testing  hardness, 

365 
Screw,  61 

-bolts*  efficiency  of,  538 

conveyors,  1198 

differential,  540 

efficiency  of  a,  538 

(element  of  machine) ,  537 

heads,  machine,  dimensions  of, 
237 

-propeller,  1377 

-propeller,  coefficients  of,  1378 

-propeller,  efficiency  of,  1379 

-propeller,  slip  of,  1379 
Screws  and  nuts  for  automobiles, 
table,  233 

cap,  table  of  standard,  238 

lag,  holding  power  of,  347 

lag,  table  of,  241 

machine,  A.  S.  M.  E.  standard, 
234 

machine,  dimensions  of,  234-238 

set,  table  of  standard,  238 

wood,  236 

wood,  holding  power  of,  346 
Screw-threads,  231-238 

Acme,  234 

A.  S.  M.  E.  standard,  table,  237 

British    Association    standard, 
232 

English  or  Whit  worth  standard, 
table,  232 

International  (metric)  standard, 
232 

limit  gages  for,  232 

metric,  cutting  of,  1261 

standard    sizes    for    bolts    and 
taps,  235,  236 

U.S.  or  Sellers  standard,  table 

of,  231 

Scrubbers  for  gas  producers,  849 
Sea-water,  freezing-point  of,  719 
Secant  of  an  angle,  66 

of  an  arc,  67 
Secants  of  angles,  table  of,  170- 

172 
Section    modulus    of    structural 

shapes,  294,  295 
Sector  of  circle,  60 
Sediment  in  steam-boilers,  928 
Seger  pyrometer  cones,  555 
Segment  of  circle,  60 
Segments,  circular,  areas  of,  121, 

122 

Segregation  in  steel  ingots,  487 
Self-inductance  of  lines  and  cir- 
cuits, 1445 
"Semi-steel,"  453 
Separators,  steam  941 

steam,  efficiency  of,  941 
Set-screws,  dimensions  of,  238 

holding  power  of,  1332 

standard  table  of,  238 
Sewers,  grade  of,  757 
Shackles,  strength  of,  1184 


Shaft  bearings,  1034 

bearings,  large,  tests  of,  1230 
couplings,  flange,  1133 
fit,  allowances  for  electrical  ma- 
chinery, 1326 
-governors,  1066 
speeds  in  geometrical  progres- 
sion, 1138 
Shafts   and   bearings  of  engines, 

1042-1044 
bearings  for,  1034 
bending  resistance  of,  1032 
dimensions  of,  1030-1033 
equivalent  twisting  moment  of, 

1032 

fly-wheel,  1033 
hollow,  1133 
hollow,    torsi onal   strength   of, 

334 

steam-engine,  1030-1038 
steel  propeller,  strength  of,  354 
twisting  resistance  of,  1030 
Shafting,  1130-1134 
collars  for,  1133 
deflection  of,  1131 
formulae  for,  1130 
horse-power     transmitted     by, 

1130 

keys  for,  1328 
laying  out,  1134 
power  required  to  drive,  1305 
torsion  tests  of,  361 
Shaku-do,  Japanese  alloy,  393 
Shapers,  motors  required  to  run, 

1296 

Shapes  of  test  specimens,  280 
structural  steel,  dimensions  and 

weights,  302-305 
Shear  and  compression  combined, 

335 

and  tension  combined,  335 
poles,  stresses  in,  542 
Shearing,   effect  of  on  structural 

steel,  483 

resistance  of  rivets,  430 
strength  of  iron  and  steel,  362 
strength  of  rivets,  240 
strength  of  woods,  table,  367 
strength,     relation     to     tensile 

strength,  362 

Sheaves,    diameter   of,    for   wire- 
rope,  1211 
for  wire-rope  transmission,  1208, 

1211 

size  of  for  manila  rope,  414 
Sheet  aluminum,  weight  of,  230 
brass,  weight  of,  table,  228 
copper,  weight  of,  229 
iron  and  steel,  weight  of,  183 
metal  gage,  28,  29,  31,  32 
metal,   weight   of,    by   decimal 

gage,  32 

metals,  strength  of  various,  356 
Sheets  (see  Plates) 
Shelby  cold-drawn  tubing,  223 
Shells  for  steam-boilers,  material 

for,  908 
spherical,  strength,  of,  339 


she-sin 


INDEX. 


sin-spe 


1513 


tiherardizing,  474 

Shibu-ichi,  Japanese  alloy,  393 

Shingles,   weights   and   areas   of, 

196 
Ship  "  Lusitania,"  performance  of, 

1376,  1381 

Ships,   Atlantic   steam,  perform- 
ance of,  1376,  1383 
coefficient  of  fineness  of,  1369 
coefficient  of  performance,  1370 
C9efficient  of  water-lines,  1369 
displacement  of,  1369,  1374 
horse-power  for  given  speeds, 

horse-power    of,    from    wetted 

surface,  1372 

horse-power   of   internal   com- 
bustion engines  for,  1374 
horse-power  required  for,  1373- 

1375 

jet  propulsion  of,  1384 
relation  of  horse-power  to  speed, 

1373/1376 
resistance  of,  1369 
resistance  of,  per  horse-power, 

1373 

resistance    of,    Rankine's    for- 
mula, 137O 

rules  for  measuring,  1368 
rules  for  tonnage,  1369 
small   sizes,   engine  power  re- 
quired for,  1374 
wetted  surface  of,  1371' 
wetted  surface,  empirical  equa- 
tions for,  1371 
with  reciprocating  engine,  and 

turbine  combined,  1383 
Shipbuilding,  steel  for,  507 
Shipping  measure,  19,  1368 
Shocks,    resistance   of  metals   to 

repeated,  276 
stresses  produced  by,  276 
Short  circuits,  electric,  1411 
Shrinkage  fits  (see  Fits,  1324) 
of  alloys,  409 
of  castings,  1254 
of  cast  iron,  438,  447 
of  malleable  iron  castings,  455 
strains    relieved     by    uniform 

cooling,  448 

Sign  of  differential  coefficients,  78 
of  trigonometrical  functions,  67 
Signs,  arithmetical,  1 
Silicon-aluminum-iron  alloys,  398 
-bronze,  395 
-bronze  wire,  248,  395 
distribution  of,  in  pig  iron,  448 
excessive,     making     cast    iron 

hard,  1254 
influence  of,  on  cast  iron,  438, 

447 

influence  of,  on  steel,  476 
Silundum,  1425 
Silver,  melting  temperature,  554, 

559 

properties  of,  179 

Simpson's  rule  for  areas,  56  * 

Sine  of  an  angle,  66  4 


Sines  of  angles,  table,  170-172 

Single-phase  circuits,  1445 

Sinking  fund,  17 

Siphon,  754 

Sirocco  fans,  653,  664-666 

Skin  effect  in  alternating  currents, 

1442 
Skylight  glass,  sizes  and  weights, 

196 

Slag  bricks  and  slag  blocks,  268 
in  cupolas,  1248 
in  wrought  iroh,  460 
Slate   roofing,    sizes,    areas,    and 

weights,  195 
Slide  rule,  82 

Slide-valve,  cut-off  for  various'  laps 
and  travels,  table,  1060,  1061 
definitions,  1052 
diagrams,  1053-1055 
effect  of  lap  and  lead,   1052- 

1057 

lead,  1057 
port  opening,  1057 
ratio  of  lap  to  travel,  1058 
relative    motion   of   cross-head 

and  crank,  1060 
steam-engine,  .^1052-1062 
Slope,  table  of,  and  fall  in  feet  per 

mile,  729 

Slotters,  power  required  for,  1295 
Smoke-prevention,  92O-922 
Smoke-stacks,  locomotive,  1115 

sheet-iron,  958 
Snow  load  on  roofs,  191 

weight  of,  720 
Soapstone  lubricant,  1246 

strength  of,  371 
Soda  mixture  for  machine  tools, 

1246 

Softeners  in  foundry  work,  1253 
Softening  of  water,  724 
Soils,  bearing  power  of,  1385 

resistance  of,  to  erosion,  755 
Solar  engines,  1015 
Solder,   brazing,   composition   of, 

390 

for  aluminum,  382,  383 
Solders,   composition  of  various, 

383,  409 

Soldering  aluminum-bronze,  397- 
Solid  bodies,  mensuration  of,  61- 

66 

measure,  18 
of  revolution,  64 
I   Solubility  of  common  salt,  571 
|       of  sulphate  of  lime,  571 
Soot,  effect  of  on  boiler  tubes,  931 
Sorbite,  480 

i    Sources  of  energy,  531 
i   Specific    discharge    of   hydraulic 
<        turbine,  7706 

Specific  gravity,  173-175 
£i      and  Baume's  hydrometer  com- 
pared, table,  175 
and  strength  of  cast  iron,  452 
of  brine,  571 
of  cast  iron,  452 
of  copper-tin  alloys,  384 


1514 


spe-sph 


INDEX. 


sph-sta 


Specific  gravity  of  coppor-zilic  al- 
loys, 388 

of  gases,   170 

of  ice,  7 HO 

of  li(|iiids,  table,  175 

of  metals,  table,   1  /  I 

of  steel,    ISC) 

of  stones,  brick,  etc.,  177 
Specific  heal,  502  505.  720 

determination  of,  502 

of  air,  502,  614. 
of  gases,  503,  504 
of  k-e,  720 

of  iron  and  steel,  502,  563 
of  liquids,  503 
of  superheated  strain  809 
Of  metals,  502.  503 
of  solids,  502.  503 
of  saturated  steam,  807 
of  water.  50-1.  720 
of  woods.  503 

Specifications  for  boiler-plate,  507 
castings.   I  II 
cast  iron,  441 
chains.  20-1 

elliptical  steel  springs, 423 
foundry  pig  iron,  443 
fuel  oil.  8-13 
gal\ani/,ed  \\ire,  250 
helical  steel  springs,  423 
liose.  379 

malleable  iron,    157 
metal  for  cast-iron  pipe,  441 
oils.   12-12 
petroleum  lubricants.  1212 

phosphor-bronze,  395 

purchase  of  coal.  830 

spring  steel.  507 

steel  axles.  5O7.  5O9 

steel  billets.  5O7 

steel  castings.  -189.  510 

steel  crank-pins,  507 

steel  for  automobiles,  510 

steel  forgings,  500 

steel  for  ships,  507 

steel  rails.  5OS 

steel  ri\  ets,  505 

steel  splice-bars,  509 

steel  tires.  5O9 

structural  steel.  501 

tin  and  (erne-plate,   191 

\\  rought  iron.   101 .   102 
Sjieed  of  cut  ting.  elVect  of  feed  and 
dept  li  of  cut  on.    120-1 

of  cutting  tools,  1258 

vessels.   1373 
Speeds  in  geometrical  progression, 

L807 

Spelter,  (.svc  /inc) 
Sphere,  measures  of.  02 

Spheres  of  different  materials,  table 

for  calculating  weight  of.  IS  I 
(able  of   volumes  and   surfaces, 

120.   127 

Spherical  pol>gon.  area,  of,  03 
segment ,  volume  of.  (VI 
shells  and  domed  boiler  heads, 

339 


Spherical  polvgon  shells,  strength 
of.  339 

shells,    thickness  of,    to   resist    a 
giren  pressure,  339 

t  riangle,  area  of.  03 

/one,  area,  and  volume  of,  0-1 
Spheroid,  <>  1 
Spikes,  holding  power  of,  3-10 

railroad  and  boat,  215,  2  IS 

wrought-,  215 
Spindle,    surface   and    volume   of, 

0-1.  05 
Spiral.  51.  01 

conical,  01 

construction  of,  51 

gears,   1  108 

plane,  01 

-rivet (vl  pipe-fittings,  table,  220 

-riveted  pipe,  table  of,  220 
Splice-bars,      steel,      specifications 

for,  509 

Splices,  railroad  track,  tables,  245 
Splicing  of  ropes.  -112 

Of  wire  i-o pe.  203 
Spontaneous  combustion  of  coal, 

832 
Springs,   117   -121 

elliptical,  si/es  of.    123 

elliptical,  specifications  for.  -123 

for  engine-governors,  1000  loos 

helical,   118   -122 

helical,    formula'    for    deflection 

and  strength,   1 18 
helical,  specification  for.  123 
helical,  steel,  tables  of  capacity 

and  dellection.    1  IS    122 
laminated  steel.   1 17 

phosphor-bronze,  -12 1 

semi-ellipt  ical,    1 17 

steel,  chromium-vanadium,    121 

steel,  strength  of.  355 

to  resist   torsion,    123 
Sprocket   wheels.    1  15-1.    1  150 
Spruce,  strength  of,  307 
Square,  definition  of,  5-1 

measure,   18 

root.  8 

roots  of  lift  h  powers.  1  1O 

roots,  tables  of,  93    108 

side  of.   equivalent,   to   circle   of 
same  area.   125 

\alue  of  diagonal  of.  5  1 

Squares  of  decimals,  table,  HIS 

of  numbers,  table.  93    I  OS 
Squirrel-cage  motor,   1-103 
Stability 

of  chimneys.  9;">  1 

of  dam,  515 
.Stand-pipes.  3-19   351 

at  Yonkers.   N.  V..  350 

failures  of.  35O 

guy-ropes  for.  3-19 

heights    of.     for    various    diam- 
eters and  plates,  table.  351 

thickness     of     plates    of.    table. 
35 1 

thickness  of  side  plates.  3-19 

wind-strain  on,  319 


sta-ste 


INDEX. 


>tc->te 


.      transformers, 

1  \^-2 

;tl  moment.  ")l") 
-holt  iron.  462 
May-bolts  in  steam-boilers,  916 

steam-boiler,  loads  on.  91 1> 

steam-boiler,   material  for 
Stayed  surfaces,  strength  of,  338 
.Steam,  867-885 

boilers  (see  Steam-boilers  beloic) 

calorimeters,  942-944 

consumption,     continuous     re- 
corder for,  970 

consumption    in    engines,    Wil- 
lan's  law,  991 

determining   moisture  in,   942- 
945 

-domes  on  boilers,  918 

-drums,  913 

dry,  definition,  867 

dry.  identification  of.  944 

energy  of,  expanded  to  various 
pressures,  963 

engines  (see  Steam-engines,  be- 
lou:) 

entropy  of.  tables.  -S7 1-874 

expanding,  available  energy  of, 
870 

expansion  of,  959 

fire-engines,  capacity  and  econ- 
omy of.  993,  994  ' 

flow   of.   876-882    (see  Flow  of 
steam) 
ous,  870 

generation  of.  from  waste  heat 
of  coke-ovens.  834 

heat    required    to    generate    1 
pound  of,  867 

heating,  694-703 

heating,     diameter     of    supply- 
mains,  699.  701 

heating,  indiree' 

heating  of  greenhouses,  7o2 

heating,  pipes  for,  699-701 

heating,    vacuum    systems    of, 
. 

jackets  on  engines,  1004 

-jet  bio  we; 

-jet  exhauster.  679 

-jet  ventilator,  679 

latent  heat  of.  867 

loop.  883 

loss  of  pressure  in  pipes,  880 

maximum  efficiency  of,  in  Car- 
not  cyel. 

mean  pressure  of  expanded,  960 

-metal (bronze  alloy;.  39O. 

moisture     in,     escaping     from 
boilers.  945 

pipe   coverings,   tests   of,    584- 
587 

pipes  (sec  Steam -Pipes  below) 

ports,  area  of.  880 

power,  cost  of.  1009-1011 

receivers  on  pipelines,  884 

Regnault's  experiments  on,  870 

sampling  for  moisture.  942 

saturated,  definition,  867 


strain,  satu  i  olume 

and  latent  heat  of.  M;<.I.  s,  i 

saturated,  properties  of  at  high 
temperatures. 

saturated,   properties  of.   table, 
869,  871-874 

saturated,  specific  heat  of,  867 

saturated.      temperature      and 
pressure  of,  868 

saturated,  total  heat  of,  867 

separators.  941 

separators,  efficiency  of,  941 

-ships.    Atlantic,    performances 
of.  1376.   ! 

superheated     (see    also    Super- 
heated steam) 

superheated,  definition,  867 

superheated,  economy  of  steam- 
engines  with,  998 

superheated,   pipes  and  valves 
for,  882 

superheated,  properties  of,  870, 
875 

superheated,  specific  heat  of,  869 

superheated,  volume  of ,  869 

temperature  of,  867 

vessels  (see  Ships) 

weight  of,  per  cubic  foot,  table, 
871 

wet.  definition,  867 
Steam-boilers,    885-944   (see  also 
Boilers) 

air-leakage  in,  891 

braces  in  916 

bumped  heads,  rules  for,  914 

combustion   space   in   furnaces 
of,  889 

compounds,  929 

conditions  to  secure  fuel  econ- 
omy in,  890,  893 

construction  of,  908-918 

corrosion  of,  4G7,  927-932 

curves  of  performance  of,  894, 
895 

dangerous,  932 

domes  on,  918 

down-draught  furnace  for.  919 

effect  of  rate  of  driving,  893 

effect  of  soot  on,  931 
Steam-boiler  efficiency,  at  differ- 
ent rates  of  driving,  898 

computation  of,  687,  891 

effect  of  excess  air  supply,  896' 

effect  of  imperfect  combustion, 
896 

effect  of  quality  of  coal,  895 

maximum,  898 

obtained  in  practice.  897 

relation  of,  to  rate  of  driving, 
air-supply,  etc.,  893 

straight  line  formula  for.  896 
Steam-boilers,    evaporative    tests 
of.  898,  899-908 

excess  air  supply  to,  896 

explosive  energy  of.  932 

factors  of  evaporation,  908-912 

factors  of  safety  of.  918 

feed-pumps  for,  efficiency  of,  937 


1516 


ste-ste 


INDEX. 


ste-ste 


Steam-boilers,  feed- water  heaters 
for,  938-940  (see  Feed-water 
heaters) 

feed-water,  saving  due  to  heat- 
ing of,  938 

flat  plates  in,  rules  for,  916 
flues  and  gas  passages,  propor- 
tions of,  889 

foaming  or  priming  of,  721,  930 
for  blast-furnaces,  899 
forced  combustion  in,  923 
fuel  economizers,  924 
furnace  formulae,  917 
furnaces,  height  of,  889 
fusible  plugs  in,  918 
grate-surface,  887,  888 
grate-surface,  relation  to  heat- 
ing surface,  887 
gravity  feeders,  938 
heating-surface  in,  887,  888 
heating-surface,  relation  of,  to 

grate-surface,  887 
heat  losses  in,  892 
height  of  chimney  for,  948,  950 
high  rates  of  evaporation,  898 
horse-power  of,  885 
hydrostatic  test  of,  918 
imperfect  combustion  in,  896 
incrustation  of,  927-932 
injectors  on,   936-938   (see  In- 
jectors) 

man-hole  openings  in,  914 
marine,  corrosion  of,  930 
measure  of  duty  of,  886 
t     mechanical  stokers  for,  918 
moisture     in     steam     escaping 

from,  944 

performance  of,  889 
'  plates,  ductility  of,  913 
plates,  tensile  strength  of,  908, 

913 

pressure  allowable  in,  917,  918 
proportions  of,  887-889 
proportions  of  grate-  and  heat- 
ing-surface for  given   horse- 
power, 887,  888 
proportions    of    grate-spacing, 

889 
quench-bend  tests  of  steel 'for, 

913 

riveting  rules  for,  914 
safety-valves,  932-935 
safety-valves,  discharge  of  steam 

through,  934 

safety-valves,  formulae  for,  932 
safety-valves,  spring-loaded,  933 
safe  working-pressure,  918 
scale  compounds,  929 
scale  in,  927-932 
sediment  in,  928 
shells,  material  for,  908> 
smoke  prevention,  920-923 
stay-bolts  in,  916 
stays,  loads  on,  916 
stays,  material  for,  908 
steel  for,  913 

strain    caused    by    cold    feed- 
water,  939 


Steam-boilers,   strength  of,  9C8- 

918 
strength      of      circumferential 

seams,  913 

strength  of  rivets,  914 
tests,  heat-balance  in,  907 
tests,  rules  for,  899-9O8 
thickness  of  plates,  913 
tube  holes,  916 
tube-plates,  rules  for,  914 
tube  spacing  in,  916 
tubes,  holding  power  of,  916 
tubes,     iron     and    steel,     916, 

917 

tubes,  material  for,  913 
tubes,  size  of,  917 
use  of  kerosene  in,  929 
use  of  zinc  in,  931 
using  waste  gases,  898,  899 
working  pressures  on  with  triple 

riveted  joints,  917 
Steam-engines,  959-1095 

advantages     of     compounding, 

976 
advantages  of  high  initial  and 

low  back  pressure,  996 
and  turbine,  best  economy  of, 

in  1904,  1005 
bearings,  size  of,  1034 
bed-plates,  dimensions  of,  1044 
clearance  in,  966 
Steam-engines,  compound,  976- 

983 

best  cylinder  ratios,  982 
calculation  of  cylinders  of,  982 
combined     indicator     diagram, 

979 

cylinder  proportions,  980 
economy  of,  997 
estimating  horse-power  of,  971 
formulae     for     expansion     and 

work  in,  031 
high-speed,      performance      of, 

989,  990 

high-speed,  sizes  of,  989,  990 
non-condensing,    efficiency    of, 

1000 

receiver,  ideal  diagram,  977 
receiver  space  in,  980 
receiver  type,  977 
steam- jacketed,      performances 

of,  989 

steam-jacketed,  tost  of,  1005 
Sulzer,  water-consumption    of, 

998 
test  of  with  and  without  jackets, 

1005 
two-cylinder  vs.  three-cylinder, 

997 
velocity  of  steam  in  passages  of, 

986 

water  consumption  of,  988 
Woolf,  ideal  diagram,  977 
Steam-engines,    compression,    ef- 
fect of,  965 

condensers,  1069-1079  (see  Con- 
densers) 
connecting-rod  ends,  1026 


ste-ste 


INDEX. 


ste-ste 


1517 


dteam- engines,   connecting-rods, 
dimensions  of,  1025, 1040, 1041 
cost  of  power  from,  1009-1011 
counterbalancing  of,  1008 
crank-angles,  table,  1058 
crank-piiis,£dimensions  of,  1027, 

1040,  1041 

crank-pins,  pressure  on,  1028 
crank-pins,  strength  of,  1027 
cranks,  dimensions  of,  1027 
crank-shafts,      dimensions      of, 

1030-1038,  1040,  1041 
crank-shaft^,  formulae  for  torsion 

and  flexure,  1038 
crank-shafts    for    triple-expan- 
sion, 1038 

crank-shafts,  three-throw,  1038 
cross-head   and  crank,  relative 

motion  of,  1060 
cross-head,  dimensions  of,  1040, 

1041 
cross-head  pin,   dimensions  of, 

1029,  1040,  1041 
cut-off,  most  economical  point 

of,  1009 

cylinder   condensation,    experi- 
ments on,  967 
cylinder  condensation,  loss  by, 

966 

cylinder,  finding  size  of,  970 
cylinders,  dimensions  of,   1021, 

1022,  1039,  1041 
cylinders,  ratios  of,  980,  982,  986 
cylinder-head     bolts,     size     of, 

1022,  1039,  1041 
cylinder-heads,    dimensions   of, 

1022,  1039 
design,  current  practice,  1039- 

1041 
dimensions   of  parts   of,    1007, 

1021-1042 
eccentric-rods,    dimensions    of, 

1039 

eccentrics,  dimensions  of,  1039 
economic  performance  of,  987— 

1007 

Steam-engines,  economy  at  vari- 
ous loads  and  speeds,  992,  993 
effect  on  of  wet  steam,  1001 
of  in  central  stations,  992 
of  simple  and  compound  com- 
pared, 997 
tests  of  high  speed,  994 
under  variable  loads,  992 
with  superheated  steam,  998 
Steam-engines,    effect  of  leakage 

on  indicator  diagram,  976 
effect  on,  of  moisture  in  steam, 

1001 
efficiency  in  thermal  units  per 

minute,  964 

estimating     I.H.P.     of     single 

cylinder  and  compound,  970 

exhaust  sjteam  used  for  heating, 

1009 

expansions  in,  table,  965 
fly-wheels    (see     Fly-wheels), 
1040,  1041,  1044-X052 


Steam-engines,    foundations   em- 
bedded in  air,  1009 
frames,  dimensions  of,  1044 
friction  of,  1238 
governors,  fly-ball,  1066 
governors,  fly-wheel,  1066 
governors,  shaft,  1066 
governors,    springs    for,    1066-" 

1068 

guides,  sizes  of,  1024 
highest  economy  of,  1003 
high  piston  speed  in,  995 
high-speed,  British,  995 
high-speed  Corliss,  995 
high-speed,  economy  of,  994 
high-speed,      performance     of, 

988,  989,  992 

high-speed,  sizes  of,  988-992 
high-speed  throttling,  996 
horse-power  constants,  971-974 
indicated  horse-power,  970-976 
indicator   diagrams,    (see   Indi- 
cator), 968-976 
indicator  rigs,  969 
indicators,  errors  of,  969 
influence  of  vacuum  and  super- 
heat on  economy,  1001 
Lentz  compound,  997 
limitations  of  speed  of,  995 
link  motions,  1062-1065 
mean  and  terminal  pressures,  960 
mean  effective  pressure,  calcula- 
tions of,  961 
measures  of  duty  of,  963 
non-condensing,  998—990 
oil  required  for,  1245 
pipes  for,  879,  1039,  1040 
piston-rings,  size  of,  1023 
piston-rod  guides,  size  of,  1024 
piston-rods,  fit  of,  1024 
piston-rods,  size  of,  1024,   1040, 

1041 

pistons,  clearance  of,  1021 
pistons,    dimensions    of,    1022, 

1040,  1041 
piston-valves,  1061 
prevention  of  vibration  in,  1008 
proportions,    current    practice, 

1039-1041 

proportions  of,  1021 — 1042 
quadruple-expansion,  986 
quadruple,  performance  of,  1003 
Rankine  cycle  efficiencies,  996 
ratio    of   cylinder    capacity    in 

compound  marine,  980 
ratio  of  expansion  in,  962 
reciprocating  parts,  weight  of, 

1040,  1041 

relative  cost  of,  1011 
reversing  gear,   dimensions  of, 

1039 

rolling-mill,  sizes  of,  1008 
rotary,  1082 
rules  for  tests  of,  1015 
setting  the  valves  of,  1061 
shafts  and  bearings  (see  Snafts) , 

1030-1033,  1040,  1041 
single-cylinder,  economy  of,  987 


1518 


ste-ste 


INDEX. 


ste-ste 


Steam  -  engines ,  single  -  cylinder, 
high-speed,  sizes  and  perform- 
ance of,  989 

single-cylinder,  water  consump- 
tion of,  987-1007 
slide  valves  (see  Slide  Valves), 

1053-1055 

small,  coal  consumption  of,  993 
small,  water  consumption  of,  992 
Sulzer    compound    and    triple- 
expansion,  998 
superheated  steam  in,  998 
steam    consumption    of   differ- 
ent types,  999 

steam-jackets,  influence  of,  1004 
steam-turbines  and  gas-engines 

compared,  1013 
Stumpf  uniflow,  997 
test  of  with  superheated  steam. 

998 

three-cylinder,  1038 
to  change  speed  of,  1066 
to  put  on  center,  1061 
Steam-engines,  triple-expansion, 

983-986 

crank-shafts  for,  1038 
cylinder  proportions,  983-985 
cylinder  ratios,  986 
high-speed,  sizes  and  perform- 
ances of,  990,  991 
non-condensing,  990 
sequence  of  cranks  in,  986 
steam-jacketed,  performance  of, 

990,  991 

theoretical  mean  effective  pres- 
sures, 984 
types  of,  986 

water  consumption  of,  998 
Steam-engines,  using  superheated 

steam,  998-1002 
use  of  reheaters  in,  1004 
valve-rods,  dimensions  of,  1038 
Walschaerts  valve-gear,  1064 
water  consumption  of,  967,  975, 

987-1006 

water  consumption  from  indi- 
cator-cards, 975 

with  variable  loads,  wasteful,  964 
with     sulphur-dioxide     adden- 
dum, 1007 

wrist-pin,  dimensions  of,  1029 
Steam-pipes,  882-885 
copper,  strength  of,  882 
copper,  tests  of,  882 
failures  of,  882 
for  engines,  879 
for  marine  engines,  880 
proportioning  for  minimum  loss 
by  radiation  and  friction,  880 
riveted-steel,  883 
uncovered,  loss  from,  884 
underground,   condensation  in, 

884 

valves  in,  883 
wire-wound,  882 
Steam  turbines,  1083-1095 
and  gas-engine,  combined  plant 
of,  10 14 


Steam  turbines  and  steam-engines 

compared,  1005,  1092 
effect  of  pressure,  vacuum  and 

superheat,  1090 
effect  of  vacuum  on,  1088 
efficiency  of,  1087 
heat     consumption     of     ideal 

engine,  1091 

impulse  and  reaction,  1082,  1087 
low-pressure,  1069 
low  -  pressure,    combined    with 

high  -  pressure    reciprocating 

engine,  1383      • 
most  economical  vacuum,  1075 
Rankine  cycle  ratio  of,  1089 
reduction  gear  for,  1095 
speed  of  the  blades,  1086 
steam    consumption    of,    1088, 

1092 

testing  oil  for,  1244 
tests  of,  1088 
theory  of,  1084 

using  exhaust,  from  reciprocat- 
ing engines,  1093,  1383 
30,000  K.W.,  1092 
Steel,  475-511 

analyses  and  properties  of,  476 
and  iron,  classification  of,  436 
alloy,  heat  treatment  of,  502- 

504 

aluminum,  496 
annealing  of,  484,  492 
axle,   effect  of  heat  treatment 

on,  479 
axles,    specifications    for,    507, 

509 

axles,  strength  of,  354 
bars,  effect  of  nicking,  485 
beams,  safe  load  on,  298 
bending  tests  of,  478 
Bessemer        basic,        ultimate 

strength  of,  476 
Bessemer,  range  of  strength  of, 

478 

blooms,  weight  of,  table,  190 
bridge-links,  strength  of,  353 
brittleness  due  to  heating.  483 
burning  carbon  out  of,  485 
burning,    overheating,    and   re- 
storing, 481 
Campbell's  formulae  for  strength 

of,  477 

castings,  489,  510 
castings,  specifications  for,  489, 

510 

castings,  strength  of,  355 
cementation  or  case-hardening 

of,  1291 
chrome,  496 
chromium  nickel,  501 
chromium-vanadium,  500-502 
chromium -vanadium    spring, 

424 

cold-drawn,  tests  of,  361 
cold-rolled,  tests  of,  361 
color-scale  for  tempering,  493 
comparative  tests  of  large  and 

small  pieces,  480 


ste-ste 


INDEX. 


ste-stc 


1519 


Steel,  copper-,  499 
corrosion  of,  467,  468 
crank-pins,    specifications    for, 

507 
critical  point  in  heat  treatment 

of,  480 

crucible,  475,  490-494 
crucible,  analyses  of,  490,  494 
crucible,    effect   of  heat   treat- 
ment, 481,  491 
crucible,  selection  of  grades  of, 

490 
crucible,    specific    gravities    of, 

490 

dangerous,  containing  mangan- 
ese sulphide,  486 
effect  of  annealing,  47.9 
effect  of  annealing  on  grain  of, 

479 
effect  of  annealing  on  magnetic 

capacity,  483 

effect  of  cold  on  strength  of,  464 
effect  of  finishing  temperature 

in  rolling,  478 
effect  of  heating,  481 
effect  of  heat  on  grain,  479,  491 
effect  of  oxygen  on  strength  of, 

477 
effect  of  vibration  and  load  on, 

278 

electric  conductivity  of,  477 
endurance   of,    under   repeated 

stresses,  487 

expansion  of,  by  heat,  566 
eye-bars,  test  of,  360 
failures  of,  486 
fatigue  resistance  of,  500 
fire-box,  homogeneity  test   for, 

508 

fluid-compressed,  488 
for    bridges,    specifications    of, 

504,  505 
for  car-axles,  specifications,  507, 

509 
for  different  uses,  analyses  of, 

505-510 

forgings,  annealing  of,  482 
forgings,  oil-tempering  of,  482 
forgings,  specifications  for,  506 
for  rails,  specifications,  508 
for  ships,  specifications  of,  507 
for  steam  boilers,  913 
hardening  of  soft,  479 
Harvey  i/ing,  1291 
heating  in  a  lead  bath,  492 
heating  in  melted  salts  by  an 

electric  current,  492 
heating  of,  for  forging,  492 
heat  treatment  of  Cr-Va  steel, 

.502 
high  carbon,   resistance  of,   to 

shock,  277 
high-speed  tool,  494 
high-speed    tool,    emery    wheel 

for  grinding,  1263,  1314 
high-speed  tool,  Taylor's  experi- 
ments, 1261 
high-speed  tool,  tests  of,  1369 


Steel,  high-strength,  for  shipbuild- 
ing, 507 

ingots,  segregation  in,  487 

life  of,  under  shock,  276 

low  strength  of,  477 

low  strength  of,  due  to  insuffi- 
cient work,  478 

manganese,  494 

manganese,  resistance  to  abra- 
sion of,  495 

manufacture  of,  475 

melting  temperature  of,  555 

mixture  of,  with  cast  iron, 
453 

Mushet,  490 

nickel,  497 

nickel,  tests  of,  497 

nickel-vanadium,  499 

of  different  carbons,  uses  of,  494 

open-hearth,  range  of  strength 
of,  478 

plates  (see  Plates,  steel) 

quench-bend  tests  of,  for  boilers, 
913 

rails,  electric  resistance  of,  1416 
.    rails,  specifications  for,  508 

rails,  strength  of,  353 

range  of  strength  in,  478 

recalescence  of,  480 

relation  between  chemical  com- 
position and  physical  char- 
acter of,  476 

rivet,  shearing  resistance  of,  430 

rivets,  specifications  for,  505 

shearing  strength  of,  362 

sheets,  weight  of,  183 

soft,  quenching  test  for,  507 

specific  gravity  of,  486 

specifications  for,  504-511 

splice-bars,  specifications  for, 
509 

spring,  strength  of,  355 

springs  (see  Springs,  steel) 

static  and  dynamic  properties 
of,  500 

strength  of,  Campbell's  formulae 
for,  477 

strength  of,  Kirkaldy's  tests, 
353 

strength  of,  variation  in,  478 
Steel,  structural,  annealing  of,  484 

effect  of  punching  and  shearing, 

483 

'  punching  of,  483 
•  punching  and  drilling  of,  485 

riveting  of,  484 

shapes,  properties  of,  305-321 

specifications  for,  504 

treatment  of,  483-485 

upsetting  of,  484 

welding  of,  forbidden,  484 
Steel  struts,  formulae  for,  285 

tempering  of,  493 

tensile  strength  of,  at  high 
temperatures,  463 

tensile  strength  of,  pure,  477 

tires, .specifications  for,  509 

tires,  strength  of,  354 


1520 


ste-str 


INDEX. 


str-str 


Steel  tool,  composition  and  heat 

treatment  of,  1265 
tool,  heating  of,  492 
tool,  high-speed,  1265 
tungsten,  496 

used    in    automobile    construc- 
tion, 510 

very  pure,  low  strength  of,  477 
water-pipe,  351 
welding  of,  484,  498 
wire  gage,  tables,  30 
working  of,  at  blue  heat,  482 
working      stresses      in      bridge 

members,  287 
Stefan    and     Boltzman    law    of 

radiation,  579 
Stellite,    alloy   for   cutting   tools, 

1269 

Sterro  metal,  393 
St.  Gothard  tunnel,  loss  of  pres- 
sure in  air-pipes  in,  620 
Stoker,  Riley,  919 

Taylor  gravity  underfeed,  919 
Stokers,    mechanical,    for   steam- 
boilers,  918 
underfeed,  919 

Stone-cutting  with  wire,  1309 
strength  of,  357,  370 
weight  and  specific  gravity  of, 

table,  177 

Storage  batteries,  1425-1428 
batteries,  Edison  alkaline,  1428 
batteries,  rules  for  care  of,  1427 
of  steam  heat,  927,  1014 
Storms,  pressure  of  wind  in,  627 
Stove    foundries,   cupola   charges 

in,  1250 

Stoves,   for   heating   compressed- 
air,  efficiency  of,  641 
Straight-line  formula  for  columns, 

285 

formula  for  boiler  efficiency,  896 
Strain  and  stress,  272 
Strand,  steel  wire,  for  guys,  255 
Straw  as  fuel,  839 
Stream,    open,    measurement    of 

flow,  760 
Streams,   fire,   749-752    (see   Fire 

streams) 

running,  horse-power  of,  765 
Street-lighting  installations,  1476 

kinds  of,  1472 
Strength  and  specific  gravity  of 

cast  iron,  452 
compressive,  281-283 
compressive,  of  woods,  368 
loss  of,  in  punched  plates,  424 
Strength  of  aluminum,  381 
aluminum-copper  alloys,  396 
anchor  forgings,  353 
basic  Bessemer  steel,  476 
belting,  357 

blocks  for  hoisting,  1 181 
boiler-heads,  337,  338 
boiler-plate    at    high    tempera- 
tures, 463 
bolts,  348 
brick,  358 


Strength  of  brick  and  stone,  370- 

372 

bridge-links,  353 
bronze,  356,  384 
canvas,  357 
castings,  352 
cast  iron,  444-447 
cast-iron  beams,  451 
cast-iron  columns,  289 
cast-iron  cylinders,  452 
cast-iron  flanged  fittings,  452 
cast  iron,  relation  to  size  of  bar, 

444 

cast-iron  water-pipes,  196,  452 
cement  mortar,  372 
chain  cables,  tables,  264,  265 
chains,  table,  264,  265 
chalk,  371 

columns,  283-293,  1389 
copper   at    high    temperatures, 

368 

copper  plates,  356 
copper- tin  alloys,  385 
copper-tin-zinc   alloys,   graphic 

representation,  388 
copper-zinc  alloys,  388 
cordage,  table,  410,  415,  1218 
crank-pins,  1027 
electro-magnet,  1431 
flagging,  373 
flat  plates,  336 
floors,  1390-1393 
German  silver,  356 
glass,  365 
granite,  357 
gun-bronze,  386 
hand    and     hydraulic    riveted 

joints,  425 
ice,  368 
iron  and  steel,  effect  of  cold  on, 

464 

iron  and  steel  pipe,  363 
lime-cement  mortar,  372 
limestone,  371 
locomotive  forcings,  353 
Lowmoor  iron  bars,  352 
malleable  iron,  454,  45S 
marble,  357 
masonry  materials,  371 
materials,  272-379 
materials,  Kirkaldy's  tests,  352- 

358 

perforated  plates,  425 
phosphor-bronze,  395 
Portland  cement,  358 
riveted  joints,  359,  424-435 
roof  trusses,  547 
rope,  357,  411,  1218 
sandstone,  371 
silicon-bronze  wire,  395 
soapstone,  371 
spring  steel,  355 
spruce  timber,  367 
stayed  surfaces,  338 
steam-boilers,  908-918 
steel  axles,  354 
steel  castings,  355 
steel,  formulae  for,  476,  477 


str-sul 


INDEX. 


sul-tay 


1521 


Strength  of  steel  propeller-shafts, 

354 

steel  rails,  353 
steel  tires,  354 
structural  shapes,  305-321 
timber,  368 
twisted  iron,  280 
unstayed  surfaces,  337 
various  sheet  metals,  356 
welds,  264,  355 
wire,  357,  358 

wire  and  hemp  rope,  356,  357 
wrought-iron  columns,  285 
yellow  pine,  368 
zinc  plates,  370 

Strength,  range  of,  in  steel,  478 
shearing,     of    iron    and    steel, 

362 

shearing,  of  woods,  table,  367 
tensile,  278 
tensile,  of  iron  -and  steel  at  high 

temperatures,  463 
tensile,  of  pure  steel,  477 
torsional,  334 
transverse,  297-300 
Stress  and  strain,  272 

due  to  temperature,  335 
Stresses  allowed  in  bridge  mem- 
bers, 287 
combined,  335 
effect  of,  272 

in  framed  structures,  541-548 
in   plating   of   bulkheads,    etc., 

due  to  water-pressure,  338 
in   steel   plating   due   to   water 

pressure,  338 
produced  by  shocks,  276 
Structural   materials,  permissible 

stresses  in,  1387,  1388 
shapes,  elements  of,  294 
shapes,  moment  of  inertia  of, 

295 
shapes,   radius  of  gyration  of, 

295 

shapes,  steel    (sec  Steel,  struc- 
tural,    also    Beams,    angles, 
etc.) 
steel    shapes,    dimensions    and 

weights,  302-305 
steel  shapes,  properties  of,  305- 

321 

work,  rivet  spacing  for,  321,  322 
Structures,    framed,    stresses    in.   ' 

541-548 

Strut,  moving,  536 
Struts,  steel,  formulae  for,  285 
strength  of,  283 
wrought-iron,  formulae  for,  285 
Stub  gear  teeth,  1167 
Stud  bolts,  237 
Stumpf  uniflow  engine,  997 
Suction  lift  of  pumps,  788 
Sugar  manufacture,  839 
Sugar  solutions,  concentration  of, 

572 

Sulphate  of  lime,  solubility  of,  571 
S ulpliur-dioxide  refrigerating-ma- 
chine,  1345 


Sulphur  -  dioxide  -  addendum     to 

steam-engine,  1007 
dioxide,  properties  of,  1338 
influence  of,  on  cast  iron,  438 
influence  of,  on  steel,  476 
Sum    and    difference    of    angles, 

functions  of,  68 
Sun,  heat  of,  as  a  source  of  power, 

1015 
Superheated   steam,    economy   of 

steam-engines  with,  998  * 
steam,  effect  of  on  steam  con- 
sumption, 998 
steam,  practical  application  of, 

1002 
Superheating,    economy    duo    to, 

1006 

in  locomotives,  1126 
Surface  condensers,  1069 

of  sphere,  table,  126,  127 
Surfaces  of  geometrical  solids,  61- 

66 
of   revolution,    quadrature    of, 

unstayed  flat,  337 
Suspension  cableways,  1205 
Sweet's  slide-valve  diagram,  1054 
Symbols,  chemical,  173 

electrical,  1477 
Synchronous  converters,  1453 

generators,  1448,  1453 

-motor,  1463 

T -CONNECTIONS,         trans- 
formers, 1452 
T-shapes,  properties  of  Car- 
negie steel,  table,  313-315 
T-slots,  T-bolts  and  T-nuts,  1321 
Tackle,  hoisting,  1182 
Tackles,  rope,  efficiency  of,  415 
Taggers,  tin,  192 

Tail-rope,  system  of  haulage,  1203 
Tanbark  as  fuel,  838 
Tangent  of  an  angle,  66 
Tangents  of  angles,  table  of,  170- 

172 
Tangential     or*   impulse     water 

wheels,  tables  of,  785 
Tanks    and    cisterns,    number   of 

barrels  in,  134 

capacities  of,  tables,  132-134 
with    flat    sides,     plating    and 

framing  for,  339 
Tap-drills,  sizes  of,  235,  23«,  i:*2O 

for  pipe  taps,  201 
Taper  pins,  1321 

to  set  in  a  lathe,  1261 
Tapers,  Jarno,  1319 

Morse,  1319 
Tapered  wire  rope,  1208 
Taps,  A.  S.  M.  E.  standard,  235, 

236 
Tapping    and    threading,    speeds 

for,  1290 

Taylor's  experiments  on  cutting 
tools  of  high-speed  steel,  1261 
Taylor's  rules  for  belting,  1143 
Taylor's  theorem,  78 


1522 


tay-thr 


INDEX. 


thr-too 


Taylor -White    high-speed   tools, 

cutting  speeds  of,  1266 
Teeth  of  gears,  forms  of,  1 162-1 167 
of    gears,     proportions,     1159, 

1161 
Telegraph  poles,  tubular,  206 

-wire,  tests  of,  table,  250 
Telpherage,  1196 
Temperature,  absolute,  567 

and  humidity,  comfortable,  685 
coefficient     of     resistance     of 

copper,  1403 
conversion  table,  552 
determination  of  by  color,  558 
determinations       of      melting- 
points,  554,  559 
effect  of  on  strength,  368,  463- 

465 

-entropy  diagram,  600 
-entropy  diagram  of  water  and 

steam,  602 
of  fire,  817,  818 
rise  of,  in  combustion  of  gases, 

818 

stress  due  to,  335 
Temper  carbon,  in  cast-iron,  439 
Tempering,  effect  of,  on  steel,  493 
oil,  of  steel  forgings,  482 
steel,  change  of  shape  due  to, 

1291 

Tenacity  of  different  metals,  180 
of  metals  at  various  tempera- 
tures, 368,  463-465 
Tensile  strength  (see  Strength) 
strength,  increase  of,  by  twist- 
ing, 280 
tests,    precautions    in   making, 

279 

tests,  specimens  for,  280 
Tension  and  flexure,  combined,  335 

and  shear,  combined,  335 
Terne-plate,  or  roofing  tin,  193 
Terra  cotta,  weight  of,  196 
Tests,  compressive  (see  Compres- 

sive  strength) 
of  steam-boilers,  rules  for,  899- 

908  »• 

of  steam-engines,  rules  for,  1015 
of   strength    of   materials    (see 

Strength) 

quench-bend,  of  steel   913 
tensile  (see  Strength  and  Ten- 
sile strength) 
Thermal  capacity,  562 
storage,  927,  1014 
units,  560 
Thermit  process,  401 

welding  process,  488 
Thermodynamics,  597-603 

laws  of,  598 
Thermometer,  air,  557 

centigrade  and  Fahrenheit  com- 
pared, tables,  550 
Threads,  pipe,  standard,  201,  217 
Threading     and     parting     tools, 

speed  of,  1268 

and  tapping,  speeds  for,  1290 
pipe,  force  required  for,  3(»a 


Three-phase  circuits,  1445 

transmission,   rule  for  sizes  of 

wires,  1459 

Throttle  valves,  size  of,  880 
Thrust  bearings,  1232 
Tides,  utilization  of  power  of,  787 
Ties,  railroad,  required  per  mile 

of  track,  245 
Tiles,  weight  of,  196 
Timber  (see  also  Wood) 

beams,  safe  loads,  1387,  1393 
beams,  strength  of,  368- 
expansion  of,  367 
measure,  20 
preservation  of,  368 
strength  of,  368-369 
table  of  contents  in  feet,  21 
to  compute  volume  of  square, 

21 

Time,  measures  of,  20 
Tin,  alloys  of  (see  Alloys) 
lined  iron  pipe,  227 
plates,  192-194 
properties  of,  179 
Tires,  locomotive,  shrinkage  fits, 

1324 

steel,  friction  of  on  rails,  1219 
steel,  specifications  for,  509 
steel,  strength  of,  354 
Titanium,  additions  to  cast-iron, 

439,  451 

-aluminum  alloy,  401 
Tobin  bronze,  392 
Toggle-joint,  536 
Tonnage  of  vessels,  1369 
Tons  per  mile,  equivalent  of,  in 

Ibs.  per  yard,  27 

Tools,  cutting,  durability  of,  1268 
cutting,  effect  of  feed  and  depth 

of  cut  on  speed  of,  1264 
cutting,    in    small    shops,    best 

method  of  treatment,  1268 
cutting,  interval  between  grind- 
ings  of,  1264 

cutting,  pressure  on,  1264 
cutting,  use  of  water  on,  1264 
economical    cutting    speed    of, 

1268 

forging  and  grinding  of,  1263 
high   speed,    table    of    cutting 

speeds,  1266 

machine  (see  Machine  tools) 
parting     and     thread  -  cutting , 

speed  of,  1268 
standard  planing,  1271 
Tool-steel  (see  also  Steel) 
best  quality,  1265 
high-speed,     composition     and 

heat-treatment  of,  1265 
high-speed,  new  (1909),  tests  of, 

1269 

high-speed,     Taylor's      experi- 
ments, 1265 
in  small  shops,  best  treatment 

of,  1268 

of  different  qualities,  1268 
Toothed-wheel  gearing,  539, 11 57-. 
1180 


tor-tri 


INDEX. 


tro-iur 


1523 


Torque  computed  from  watts  and 

revolutions,  1436 
horse -power   and    revolutions, 

1436 

of  an  armature,  1435 
Torsion    and    compression    com- 
bined, 335 

and  flexure  combined,  335 
elastic  resistance  to,  334 
of  shafts,  1030,  1130 
tests  of  shafting,  361 
Torsional  strength,  334 
Track  bolts,  244,  245 

spikes,  245 

Tractive  force  of  locomotive,  1112 
Tractrix,     Schiele's     anti-friction 

curve,  50 
Train  resistance,  electric  cars,  1415 

loads,  average,  1125 
Trains,     railroad,    resistance    of, 

1108 

railroad,  speed  of,  1187 
Trammels,  to  describe  an  ellipse 

with,  45 
Tramways,  compressed-air,  652 

wire-rope,  1204 
Transformers,    constant    current, 

1453 

efficiency  of,  1451 
electrical,  1451 

primary  and  secondary  of,  1451 
Transmission,  compressed-air  (see 

Compressed-air) 
electric,  1410,  1457 
electric,  area  of  wires,  1410, 1457 
electric,  economy  of,  1411 
electric,  efficiency  of,  1411 
electric,  weight  of  copper  for, 

1411,  1457 

electric,  wire  table  for,  1413, 1457 
hydraulic-pressure  (see  Hydrau- 
lic-pressure transmission) 
of  heat  (see  Heat) 
of    power    by    wire-rope     (see 

Wire-rope),  1208-1213 
pneumatic  postal,  1201 
rope  (see  Rope-driving) 
rope,  iron  and  steel,  256,  257 

>      wire-rope  (see  Wire-rope) 
Transporting  power  of  water,  755 
Transverse  strength,  297-300 
Trapezium  and  Trapezoid,  54 
Trapezoidal  rule,  56 
Triangles,  mensuration  of,  54 
problems  in,  41 
solution  of,  69 
spherical,  63 
Trigonometrical  computations  by 

slide  rule,  83 
formulae,  68 

functions,  logarithmic,  167 
functions,  table,  170-172 
Trigonometry,  66-70 
Triple  effect  evaporators,  570 
Triple-expansion       engine        (see 

Steam-engines) 

Triple-riveted      joints,      working 
pressures  on  boilers  with,  917 


Troostite,  480 

Trough  plates,  properties  of,  308 

Troy  weight,  19 

Trusses,  bridge,  stresses  in,  543- 

547 

roof,  stresses  in,  547 
Tubes  (see  also  Pipe) 
aluminum   226 
aluminum  bronze,  397 
boiler  (see  Steam-boiler  tubes) 
boiler,  table,  204 
boiler,  used  as  columns,  336 
brass,  seamless,  224,  225 
collapse  of,  formulae  for,  341-344 
collapse  of,  tests  of,  341-344 
collapsing    pressure    of,    table, 

334 

copper,  225 
expanded,  holding  power  of,  364, 

916 

lead  and  tin,  227 
of  different   materials,    weight 

of,  181 

seamless,  222-225 
steel,  cold-drawn,  Shelby,  223 
surface  per  foot  of  length,  224 
Tube-plates,    steam-boiler,    rules 

for,  914 
Tube-spacing     in     steam-boilers, 

916 
Tungsten    and    aluminum    alloy, 

399 

electric  lamps,  1473 
steel.  496 

Turbines,  hydraulic,  768-780 
American    high-speed   runners, 

comparison  of,  770 
capacity  criterion,  770 
capacity  of,  769B 
determination  of  dimensions  of 

runners,  7 69 A 
determination    of    sizes,     770, 

770B,  771A 

discharge  loss  of,  769B 
draft  tubes  for,  778 
efficiency  of  77  IB 
estimating  weights  of,  771 A 
fall  increaser  for,  780 
gate    opening,    relation    of    to 

efficiency,  772 
10,000   H.P.    machine   at   Sno- 

qualmie  Falls,  779 
13,500    H.P.    machine  at   Du- 

luth,  779 
limiting     profiles     of    runners, 

769B 

power  table  for,  776,  777 
recent  practice,  778 
selection  of,  771,  771  A 
some  large,  779 
specific  discharge,  770,  770B 
specific  speed,  770 
speed  criterion,  770 
tests  of  discharge  by  salt  solu- 
tion, 774 

type  characteristics,  770 
Turbines,      steam      (see     Steam- 
turbines) 


1524 


tur-vaii 


INDEX, 


van-wat 


Turf  or  peat,  as  fuel,  838 
Turnbuckles,  243 
Tuyeres  for  cupolas,  1247 
Twist-drill  (see  Drills) 

and  steel  wire  gages,  1286 

gage,  table,  30 

sizes  and  speeds,  1285 
Twisted  steel  bars,  strength  of,  280 
Two-phase  currents,  1445 
Type   characteristic   of  turbines, 
770 

-metal,  408 

UEHLING      and      Steinbart 
pyrometer,  557 
Underwriters'  rules  for  elec- 
trical wiring,  1410 
Unequal  arms  on  balances,  20 
U inflow    steam-engines,    Stumpf, 

997 

Unions,  pipe  fittings,  207 
Unit  of  evaporation,  886 
.  of  force,  512 
of  heat,  560 
of  power,  528 
of  work,  528 
Units,  electrical  and  mechanical, 

equivalent  values  of,  1399 
electrical,  relations  of,  1397 
of  the  magnetic  circuit,  1399 
united  States,  population  of,   11 

standard  sheet  metal  gage,  29, 
Unstayed    surfaces,    strength    of, 

337 
Upsetting  of  structural  steel,  484 

V -NOTCH      recording     water 
meter,  759 
Vacuum    at    different    tem- 
peratures, 788 
drying  in,  573 
for  turbines,  most  economical, 

1075 

high,  advantage  of,  1078 
high,  influence  of  on  steam-en- 
gine economy,  1001 
inches  of  mercury  and  absolute 

pressure,  1071 
pumps,  806 

systems  of  steam  heating,  702 
Valves  and  elbows,  friction  of  air 

in,  624 
and  fittings,  loss  of  pressure  due 

to,  747,  748 
and    pipe    fittings,    description 

and  sizes,  206-208 
for  superheated  steam,  882 
in  steam  pipes,  883 
pump,  792,  793 
straight-way  gate,  217,  218 
Valve-gear,  Stephenson,  1062 

Walschaerts,  1064 
Valve-stem  or  rod,  design  of  (see 

Steam-engines) ,  1038 
Vanadium-chrome  steel,  500-502 
-copper  alloys,  395 
effect  of  on  cast  iron,  439,  450 
-nickel  steels,  499 


Vanadium  steel  spring,  424. 

Vapor  and  gases,  mixtures  of,  604 
pressures  of  various  liquids,  844 
saturation  point  of,  604 
water,  and  air  mixture,  weight 
of,  610-613 

Vapors     used     in     refrigerating, 
properties  of,  1341 

Varnishes,  471 

Velocity,  angular,  522 

due   to   falling  a  given  height, 

of  gas  in  chimneys,  951 

parallelogram  of,  523 

table   of   height   corresponding 

to  a  given,  523 
Ventilating  ducts,  quantity  of  air 

carried  by,  683 
fans,  653-660,  672 
Ventilation  (see  also  Heating  and 

Ventilation) 
by  chimneys,  712 
by  steam-jet,  679 
cooling  air  for,  710 
of  mines  (see  Mine- ventilation) 
of  mines,  equivalent  orifice.  715 
problems,   standard    values  in, 

687 

standards  of,  686 
Ventilators,  centrifugal  for  mines, 

672 

Venturi  meter,  758 
Versed  sine  of  an  arc,  67 

sines,  table,  170-172 
Verticals,  formulae  for  strains  in, 

545 
Vessels  (see  also  Ships) 

framing  of,  table,  339 
Vibrations  in  engines,  preventing, 

1008 

Vis-viva,  528 
Volt,  definition  of,  1397 
Voltages    used    in    long-distance 

transmission,  1459 
Volumes  of  revolution,   cubature 

of,  77 
Vulcanized  India  rubber,  378 

WALLS   of  buildings,   thick- 
ness of,  1388 
of  warehouses,  factories, 
etc.,  1388 
windows,  etc.,  heat  loss  through, 

688 

Walschaerts  valve-gear,  1064  j 
Warren  girder,  stresses  in,  546 
Washers,  cast  and  wrought,  tables 

of,  242,  243 
Washing  of  coal,  833 
Water,  716-726 

abrading  power  of,  755 
amount  of  to  develop  a  given 

horse-power,  783 
analysis  9f ,  722 
as  a  lubricant,  1246 
boiling-point   at  various   baro- 
metric pressures,  608 
boiling-point  of,  719 


wat-wat 


INDEX. 


wat-wlr 


1525 


Water,  comparison  of  head  in  feet 

with  various  units,  718 
compressibility  of,  720 
conduits,  long,  efficiency  of,  766 
consumption     of     locomotives 

1122 
consumption   of   steam-engines 

(sec  Steam-engines) 
current  motors,  765 
drums  for  boilers,  913 
erosion  and  abrading  by,  755 
flow  of  (sec  Flow  of  water) 
flowing   in    a    tube,    power  of, 

765 
flowing,  measurement  of,  757- 

764 

freezing-point  of,  719 
frictional  resistance  of  surfaces 

moved  in,  756 
-gas,  846,  859-864 
-gas  analyses  of,  860 
-gas,  manufacture  of,  859 
-gas  plant,  efficiency  of,  861 
-gas  plant,  space  required  for, 

862 

hammer,  749 
hardness  of,  723 
head  of,  718 

heating  of,  by  steam  coils,  591 
heat-units  per  pound  of,  717 
horse-power  required  to  raise, 

788 

impurities  of,  720 
in  pipes,  loss  of  energy  in,  812 
jets,  vertical,  749 
meter,  V-notch  recording,  759 
meters,  capacity  of,  749 
pipe,       cast-iron,       transverse 

strength  of,  452 
pipes,  compound  with  branches, 

746 

-power,  765 

-power  plants,  high  pressure,  782 
-power,  value  of,  766 
pressure    on    vertical    surfaces, 

719 

pressure  per  square  inch,  equiv- 
alents of,  27,  718 
pressures  and  heads,  table,  718 
prices  charged  for  in  cities,  749 
pumping  by  compressed  air,  808 
purification  of,  723-726 
-softening  apparatus,  724 
specific  heat  of,  564,  720 
total  heat  and  entropy  of,  869, 

87 1-873 

tower  (see  Stand-pipe) 
lower  at  Yonkers,  N.  Y.,  350 
transporting  power  of,  755 
under  pressure,  energy  of,  765 
units  of  pressure  and  head,  718 
vapor  and  air  mixture,  weight  of, 

610-613 
velocity  of,   in  open  channels, 

755 

weight    at    different    tempera- 
tures, 716,  717 
weight  of  one  cubic  foot,  27 


Waterfall,  power  of  a,  765 
Water-wheels,  768 

impulse,  780 

jet,  power  of,  784 

Pelt-on,  780 

tangential,  choice  of,  781 

tangential,  governing,  782 

tangential,  power  of,  784,  785 

tangential,  reversible,  781 
Waves,  ocean,  power  of,  784 
Weathering  of  coal,  830 
Wedge,  537 
Wedge,  volume  of,  62 
Weighing  on  incorrect  balance,  20 
Weight    and    specific    gravity    of 
materials,    174-177    (see  also 
Material  in  question) 
.     definition  of,  511 

measures  of,  19 
Weights  and  measures,  17-27 
Weir  dam  measurement,  762 

flow  of  water  over,  762 

trapezoidal,  764 

triangular  or  V-notch,  759 
Welds,  strength  of,  355 

electric,  1419 

electric  arc,  1419 

of  steel,  484,  487 
Welding,  oxy-acetylene,  488 

process,  the  thermit,  488 
Well,  artesian,  pumping  by  com- 
pressed air,  810 
Welsbach    gas    lights,     standard 

sizes,  1474 

Wheat,  weight  of,  180 
Wheel  and  axle,  539 
Wheels,     turbine     (see     Turbine 

wheel) 

Whipple  truss,  544 
White-metal  alloys,  407 
Whitworth  process  of  compressing 

steel,  488 

Wiborgh  air-pyrometer,  555 
Wild  wood   pumping-engine,    high 

economy  of,  805 

Willans  law  of  steam  consump- 
tion. 991 
Wind,  626,  627 

force  of,  627 

loads  on  roofs,  191 

pressure  of,  in  storms,  627 

strain  on  stand-pipes,  349 
Winding    engines     (see    Hoisting 

engines)  1186 
Windlass,  539 

differential,  540 

Windows,  heat-loss  through,  688 
Windmills,  627-632 

capacity  and  economy,  627-632 
Wire,    aluminum,    properties    of, 
248,  1414 

aluminum-bronze,  248 

brass,  properties  of,  248 

brass,  weight  of,  table,  229 

copper,    hard-drawn    specifica- 
tion for,  251,  252 

copper,   rule  for  resistance  of, 
140G 


1526 


wir-wlr 


INDEX. 


Woh-zon 


Wire,  copper,  stranded,  253 

copper,     telegraph     and     tele- 
phone, 251,  252 

copper,  weight  of  bare  and  in- 
sulated, 252 

gages,  tables,  28 

galvanized,    for   telegraph   and 
telephone  lines,  250 

galvanized    iron,    specifications 
for,  250 

galvanized  steel  strand,  255 

insulated  copper,  252 

nails,  246,  247 

of  different  metals,  248 

phosphor-bronze,  248 

piano,  strength  of,  250 

platinum,  properties  of,  248 

plow  steel,  250 

silicon-bronze,  248,  395 

steel,  properties  of,  249 

stranded  feed,  table,  253 

telegraph,  tests  of,  250 

weight  per  mile-ohm,  250 

-wound  fly-wheels,  1052 
Wires  of  various  metals,  strength 
of,  358 

sag  of  between  poles,  1461 
Wire-rope,  253-263 

bending  curvature  of,  1213 

bending  of,  254 

breaking  strength  of,  254,  1209 

exposure  to  heat,  256 

extra  flexible,  258,  259 

flat,  260,  261 

flattened  strand,  258,  261 

flexible  hoisting,  258,  259 

galvanized,  255,  262 

galvanized  steel  hawser,  262 

haulage  (see  Haulage) 

horse-power     transmitted     by, 
1210 

iron  and  steel,  table  of  strength 
of,  261,  410 

locked,  262 

notes  on  use  of,  254,  256 

plow  steel,  257-259 

protection  of,  256 

radius  of  curvature  of,  1213 

sag  or  deflection  of,  1211 

sheaves  for,  1208,  1211 

splicing  of,  263 

steel-clad  hoisting,  260 

strength  of,  356 

table  of  strength  of,  410 

tapered,  1208 

tramways,  1204 

varieties  and  uses,  254,  256 
Wire-rope    transmission,    deflec- 
tion of  rope,  1207,  1211 

inclined,  1212 

limits  of  span,  1212 

long  distance,  1212 

of  power  by,  1208 

sheaves  for,  1211 
Wiring  rules,  Underwriters',  1410 

table  for  direct  currents,   1413 

table  for  three-phase  transmis- 
sion lines,  1459 


Wohlor's  experiments  on  strength 

of  materials,  275 
Wood  (sec  also  Timber) 

as  fuel,  835,  836 

composition  of,  835 

drying  of,  368 

expansion  of,  by  heat,  368 

expansion  of,  by  water,  368 

heating  value  of,  835 

holding  power  of  bolts  in,  346 

nail-holding  power  of,  346,  347 

screws,  236 

screws,  holding  power  of,  346 

strength  of,  368,  369 

strength  of,  Kirkaldy 's  tests,  358 

weight  of,  181 

weight  and  specific  gravity  of, 
table,  176 

weight  and  heating  values  of, 
835 

weight  per  cord,  181 
Woods,         American         shearing 
strength  of,  367 

tests  of,  366 
Wood-working  machinery,  power 

required  for,  1303 
Wooden  fly-wheels,  1051 

stave  pipe,  218,  735 
Woodruff  key,  1331,  1332 
Woolf  compound  engines,  977 
Wootten  locomotive,  1114 
Work,  definition  of,  27,  528 

energy,  power,  528 

of  accelerated  rotation,  529 

of  acceleration,  529 

of  a  man,  horse,  etc.,  532-534 

of  friction,  1229 
Worm  gearing,  540,  1168 
Wrist-pins,  dimensions  of,  1029 
Wrought-iron,  chemical  composi- 
tion of,  460 

effect  of  rolling  on  strength  of, 
460 

manufacture  of,  459 

slag  in,  460 

specifications,  461,  462 

strength  of,  352,  359,  459-463 

strength  of,   at  high  tempera- 
tures, 463 

strength  of,  Kirkaldy 's  tests,  352 


ACHT     rigging,'    galvanized 

steel  rope,  255 
Yield  point,  273 


Z-BARS,   Carnegie,  properties 
of,  316 
Zero,  absolute,  567,  868 
Zeuner's  slide-valve  diagram,  1055 
Zinc  alloys  (see  Alloys) 
plates,  strength  of,  370 
properties  of,  179 
sheet,  weight  of,  table,  228 
use  of  in  steam-boilers,  931 
Zirconia,  270 
Zone  of  spheroid,  64 
of  spindle,  65 
spherical,  64 


Y 


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